LMFDB - Embedded newform 7.18.c.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,18,Mod(2,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.8255461141$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 231900 x^{18} + 2573595 x^{17} + 36222331443 x^{16} + 522056283042 x^{15} + \cdots + 54\!\cdots\!25 $ x^20 - 5x^19 + 231900x^18 + 2573595x^17 + 36222331443x^16 + 522056283042x^15 + 3095689791534860x^14 + 63517964980290950x^13 + 191169147185579182773x^12 + 4661871029431062841865x^11 + 6728981840934861993437384x^10 + 251477264592720071695768485x^9 + 169785400547236219777139622573x^8 + 7884822396560931315753101896470x^7 + 2084722393634413874384133666310116x^6 + 170299785457406646702831504431152090x^5 + 19136307004107023234373216890155693651x^4 + 919913048844099315146584754515161210807x^3 + 39214983331357496369283116903046958144404x^2 + 515992296986415442815810669806567791765095*x + 5495215718943433371703477919782244002731225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{50}\cdot 3^{18}\cdot 7^{19} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2.6
Root			$-7.21985 + 12.5051i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.18.c.a.4.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43970 + 2.49364i) q^{2} +(3646.82 + 6316.47i) q^{3} +(65531.9 + 113505. i) q^{4} +(804501. - 1.39344e6i) q^{5} -21001.3 q^{6} +(-6.26914e6 + 1.39043e7i) q^{7} -754795. q^{8} +(3.79715e7 - 6.57686e7i) q^{9} +O(q^{10})$	\(q+(-1.43970 + 2.49364i) q^{2} +(3646.82 + 6316.47i) q^{3} +(65531.9 + 113505. i) q^{4} +(804501. - 1.39344e6i) q^{5} -21001.3 q^{6} +(-6.26914e6 + 1.39043e7i) q^{7} -754795. q^{8} +(3.79715e7 - 6.57686e7i) q^{9} +(2.31648e6 + 4.01227e6i) q^{10} +(2.17631e8 + 3.76948e8i) q^{11} +(-4.77965e8 + 8.27860e8i) q^{12} +3.39665e9 q^{13} +(-2.56465e7 - 3.56510e7i) q^{14} +1.17355e10 q^{15} +(-8.58830e9 + 1.48754e10i) q^{16} +(1.99795e10 + 3.46056e10i) q^{17} +(1.09335e8 + 1.89375e8i) q^{18} +(1.46561e10 - 2.53851e10i) q^{19} +2.10882e11 q^{20} +(-1.10688e11 + 1.11074e10i) q^{21} -1.25330e9 q^{22} +(-2.44628e11 + 4.23709e11i) q^{23} +(-2.75260e9 - 4.76764e9i) q^{24} +(-9.12973e11 - 1.58132e12i) q^{25} +(-4.89016e9 + 8.47001e9i) q^{26} +1.49580e12 q^{27} +(-1.98902e12 + 1.99596e11i) q^{28} -3.11829e11 q^{29} +(-1.68956e10 + 2.92640e10i) q^{30} +(-2.10217e12 - 3.64106e12i) q^{31} +(-7.41955e10 - 1.28510e11i) q^{32} +(-1.58732e12 + 2.74932e12i) q^{33} -1.15058e11 q^{34} +(1.43312e13 + 1.99216e13i) q^{35} +9.95338e12 q^{36} +(8.99033e12 - 1.55717e13i) q^{37} +(4.22009e10 + 7.30941e10i) q^{38} +(1.23869e13 + 2.14548e13i) q^{39} +(-6.07233e11 + 1.05176e12i) q^{40} -4.81124e13 q^{41} +(1.31660e11 - 2.92008e11i) q^{42} +4.11144e13 q^{43} +(-2.85236e13 + 4.94043e13i) q^{44} +(-6.10963e13 - 1.05822e14i) q^{45} +(-7.04384e11 - 1.22003e12i) q^{46} +(7.90090e13 - 1.36848e14i) q^{47} -1.25280e14 q^{48} +(-1.54026e14 - 1.74336e14i) q^{49} +5.25764e12 q^{50} +(-1.45723e14 + 2.52400e14i) q^{51} +(2.22589e14 + 3.85535e14i) q^{52} +(-2.04299e14 - 3.53855e14i) q^{53} +(-2.15351e12 + 3.72999e12i) q^{54} +7.00338e14 q^{55} +(4.73192e12 - 1.04949e13i) q^{56} +2.13793e14 q^{57} +(4.48941e11 - 7.77588e11i) q^{58} +(1.53799e14 + 2.66388e14i) q^{59} +(7.69047e14 + 1.33203e15i) q^{60} +(-2.03427e14 + 3.52345e14i) q^{61} +1.21060e13 q^{62} +(6.76415e14 + 9.40279e14i) q^{63} -2.25095e15 q^{64} +(2.73260e15 - 4.73301e15i) q^{65} +(-4.57055e12 - 7.91642e12i) q^{66} +(-1.54429e15 - 2.67479e15i) q^{67} +(-2.61859e15 + 4.53554e15i) q^{68} -3.56846e15 q^{69} +(-7.03100e13 + 7.05550e12i) q^{70} -8.29735e13 q^{71} +(-2.86607e13 + 4.96418e13i) q^{72} +(-1.78519e15 - 3.09205e15i) q^{73} +(2.58868e13 + 4.48373e13i) q^{74} +(6.65889e15 - 1.15335e16i) q^{75} +3.84177e15 q^{76} +(-6.60555e15 + 6.62857e14i) q^{77} -7.13341e13 q^{78} +(-6.55653e15 + 1.13562e16i) q^{79} +(1.38186e16 + 2.39345e16i) q^{80} +(5.51265e14 + 9.54819e14i) q^{81} +(6.92676e13 - 1.19975e14i) q^{82} -1.40495e16 q^{83} +(-8.51435e15 - 1.18357e16i) q^{84} +6.42942e16 q^{85} +(-5.91925e13 + 1.02524e14i) q^{86} +(-1.13718e15 - 1.96966e15i) q^{87} +(-1.64267e14 - 2.84519e14i) q^{88} +(7.44848e15 - 1.29011e16i) q^{89} +3.51842e14 q^{90} +(-2.12941e16 + 4.72279e16i) q^{91} -6.41238e16 q^{92} +(1.53324e16 - 2.65565e16i) q^{93} +(2.27499e14 + 3.94040e14i) q^{94} +(-2.35817e16 - 4.08447e16i) q^{95} +(5.41154e14 - 9.37307e14i) q^{96} -1.27713e17 q^{97} +(6.56482e14 - 1.33094e14i) q^{98} +3.30552e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9}+O(q^{10}) $ 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9} + 222553738 q^{10} - 148256184 q^{11} + 2808533140 q^{12} + 3578734040 q^{13} + 25683984606 q^{14} - 26900793736 q^{15} - 50209759472 q^{16} + 15259176570 q^{17} + 81764237020 q^{18} - 71656970872 q^{19} - 180641544216 q^{20} - 669146889614 q^{21} + 1499692748380 q^{22} - 316306503180 q^{23} + 694489934496 q^{24} + 591325905568 q^{25} + 4488505674324 q^{26} - 11473086373360 q^{27} + 2858273469380 q^{28} + 284876854680 q^{29} - 9357829097258 q^{30} - 1607821082076 q^{31} + 18893460602400 q^{32} + 9589772011550 q^{33} - 32628298247940 q^{34} - 103506510744 q^{35} + 76724663114416 q^{36} + 5528585266950 q^{37} - 15690283928010 q^{38} + 28451541414128 q^{39} - 91022360866896 q^{40} - 66727631114424 q^{41} - 74393390286880 q^{42} - 93028396916240 q^{43} + 162849953080692 q^{44} + 8592264491540 q^{45} - 563088234018354 q^{46} + 162460135616460 q^{47} + 16\!\cdots\!20 q^{48}+ \cdots + 92\!\cdots\!80 q^{99}+O(q^{100}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9 + 222553738 * q^10 - 148256184 * q^11 + 2808533140 * q^12 + 3578734040 * q^13 + 25683984606 * q^14 - 26900793736 * q^15 - 50209759472 * q^16 + 15259176570 * q^17 + 81764237020 * q^18 - 71656970872 * q^19 - 180641544216 * q^20 - 669146889614 * q^21 + 1499692748380 * q^22 - 316306503180 * q^23 + 694489934496 * q^24 + 591325905568 * q^25 + 4488505674324 * q^26 - 11473086373360 * q^27 + 2858273469380 * q^28 + 284876854680 * q^29 - 9357829097258 * q^30 - 1607821082076 * q^31 + 18893460602400 * q^32 + 9589772011550 * q^33 - 32628298247940 * q^34 - 103506510744 * q^35 + 76724663114416 * q^36 + 5528585266950 * q^37 - 15690283928010 * q^38 + 28451541414128 * q^39 - 91022360866896 * q^40 - 66727631114424 * q^41 - 74393390286880 * q^42 - 93028396916240 * q^43 + 162849953080692 * q^44 + 8592264491540 * q^45 - 563088234018354 * q^46 + 162460135616460 * q^47 + 1626223055746720 * q^48 + 37188390461684 * q^49 - 156105592028976 * q^50 - 41571323179104 * q^51 - 664578572037800 * q^52 + 349838159677350 * q^53 - 2197621449925058 * q^54 - 630210277345912 * q^55 - 3391192609585536 * q^56 + 3387478208982380 * q^57 + 1117009291618900 * q^58 + 2898325666051656 * q^59 + 1851302466771436 * q^60 + 4829263771794542 * q^61 - 12440234322280740 * q^62 + 1252577979478000 * q^63 + 2254847316158720 * q^64 + 2323606775562324 * q^65 + 7963993945620406 * q^66 + 1327703510619200 * q^67 + 570001815036780 * q^68 - 19909363410939516 * q^69 - 17777971289904490 * q^70 + 15480661755189216 * q^71 + 16233423509033760 * q^72 - 3163858704730590 * q^73 - 4018632851551110 * q^74 - 8119026314209112 * q^75 - 14641245177256376 * q^76 - 46825571816043510 * q^77 + 48702643123708840 * q^78 + 40826108816616316 * q^79 + 90814104963906864 * q^80 - 69159481630723930 * q^81 + 21247223257167740 * q^82 + 10623055038659280 * q^83 - 178832833754555092 * q^84 + 51769432859611308 * q^85 + 113956439761484328 * q^86 + 171557044814594000 * q^87 - 117726124940340000 * q^88 + 31115179936936434 * q^89 - 503037784464315176 * q^90 - 219799610507722112 * q^91 + 208501803198310920 * q^92 + 257332309943680890 * q^93 + 405400048855155726 * q^94 - 22431094320108540 * q^95 + 232620528206160416 * q^96 - 702800336503765080 * q^97 - 760473415304075970 * q^98 + 928280307128172080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.43970	+	2.49364i	−0.00397665	+	0.00688777i	−0.868007	−	0.496552i	$-0.834599\pi$
$2$	−1.43970	+	2.49364i	−0.00397665	+	0.00688777i	0.864030	+	0.503440i	$0.167932\pi$
$3$	3646.82	+	6316.47i	0.320910	+	0.555832i	0.980676	−	0.195639i	$-0.0626780\pi$
$3$	3646.82	+	6316.47i	0.320910	+	0.555832i	−0.659766	+	0.751471i	$0.729345\pi$
$4$	65531.9	+	113505.i	0.499968	+	0.865971i
$5$	804501.	−	1.39344e6i	0.921046	−	1.59530i	0.123246	−	0.992376i	$-0.460669\pi$
$5$	804501.	−	1.39344e6i	0.921046	−	1.59530i	0.797800	−	0.602922i	$-0.205997\pi$
$6$	−21001.3			−0.00510459
$7$	−6.26914e6	+	1.39043e7i	−0.411031	+	0.911621i
$7$	−6.26914e6	+	1.39043e7i	−0.411031	+	0.911621i
$8$	−754795.			−0.0159061
$9$	3.79715e7	−	6.57686e7i	0.294034	−	0.509281i
$10$	2.31648e6	+	4.01227e6i	0.00732536	+	0.0126879i
$11$	2.17631e8	+	3.76948e8i	0.306114	+	0.530205i	0.977509	−	0.210895i	$-0.0676377\pi$
$11$	2.17631e8	+	3.76948e8i	0.306114	+	0.530205i	−0.671395	+	0.741100i	$0.734304\pi$
$12$	−4.77965e8	+	8.27860e8i	−0.320890	+	0.555797i
$13$	3.39665e9			1.15487			0.577433	−	0.816438i	$-0.304054\pi$
$13$	3.39665e9			1.15487			0.577433	+	0.816438i	$0.304054\pi$
$14$	−2.56465e7	−	3.56510e7i	−0.00464451	−	0.00645629i
$15$	1.17355e10			1.18229
$16$	−8.58830e9	+	1.48754e10i	−0.499905	+	0.865861i
$17$	1.99795e10	+	3.46056e10i	0.694656	+	1.20318i	0.970297	+	0.241918i	$0.0777766\pi$
$17$	1.99795e10	+	3.46056e10i	0.694656	+	1.20318i	−0.275641	+	0.961261i	$0.588890\pi$
$18$	1.09335e8	+	1.89375e8i	0.00233854	+	0.00405047i
$19$	1.46561e10	−	2.53851e10i	0.197976	−	0.342905i	−0.749896	−	0.661556i	$-0.769896\pi$
$19$	1.46561e10	−	2.53851e10i	0.197976	−	0.342905i	0.947872	+	0.318651i	$0.103230\pi$
$20$	2.10882e11			1.84198
$21$	−1.10688e11	+	1.11074e10i	−0.638613	+	0.0640838i
$22$	−1.25330e9			−0.00486924
$23$	−2.44628e11	+	4.23709e11i	−0.651359	+	1.12819i	0.331435	+	0.943478i	$0.392467\pi$
$23$	−2.44628e11	+	4.23709e11i	−0.651359	+	1.12819i	−0.982793	+	0.184708i	$0.940866\pi$
$24$	−2.75260e9	−	4.76764e9i	−0.00510443	−	0.00884114i
$25$	−9.12973e11	−	1.58132e12i	−1.19665	−	2.07266i
$26$	−4.89016e9	+	8.47001e9i	−0.00459251	+	0.00795446i
$27$	1.49580e12			1.01925
$28$	−1.98902e12	+	1.99596e11i	−0.994940	+	0.0998407i
$29$	−3.11829e11			−0.115753			−0.0578766	−	0.998324i	$-0.518433\pi$
$29$	−3.11829e11			−0.115753			−0.0578766	+	0.998324i	$0.518433\pi$
$30$	−1.68956e10	+	2.92640e10i	−0.00470157	+	0.00814335i
$31$	−2.10217e12	−	3.64106e12i	−0.442683	−	0.766749i	0.555205	−	0.831714i	$-0.312640\pi$
$31$	−2.10217e12	−	3.64106e12i	−0.442683	−	0.766749i	−0.997888	+	0.0649646i	$0.979307\pi$
$32$	−7.41955e10	−	1.28510e11i	−0.0119290	−	0.0206616i
$33$	−1.58732e12	+	2.74932e12i	−0.196470	+	0.340296i
$34$	−1.15058e11			−0.0110496
$35$	1.43312e13	+	1.99216e13i	1.07573	+	1.49536i
$36$	9.95338e12			0.588030
$37$	8.99033e12	−	1.55717e13i	0.420786	−	0.728822i	−0.575231	−	0.817991i	$-0.695088\pi$
$37$	8.99033e12	−	1.55717e13i	0.420786	−	0.728822i	0.996017	+	0.0891690i	$0.0284211\pi$
$38$	4.22009e10	+	7.30941e10i	0.00157457	+	0.00272723i
$39$	1.23869e13	+	2.14548e13i	0.370608	+	0.641913i
$40$	−6.07233e11	+	1.05176e12i	−0.0146503	+	0.0253750i
$41$	−4.81124e13			−0.941011			−0.470505	−	0.882397i	$-0.655928\pi$
$41$	−4.81124e13			−0.941011			−0.470505	+	0.882397i	$0.655928\pi$
$42$	1.31660e11	−	2.92008e11i	0.00209815	−	0.00465346i
$43$	4.11144e13			0.536429			0.268214	−	0.963359i	$-0.413566\pi$
$43$	4.11144e13			0.536429			0.268214	+	0.963359i	$0.413566\pi$
$44$	−2.85236e13	+	4.94043e13i	−0.306095	+	0.530172i
$45$	−6.10963e13	−	1.05822e14i	−0.541637	−	0.938143i
$46$	−7.04384e11	−	1.22003e12i	−0.00518046	−	0.00897281i
$47$	7.90090e13	−	1.36848e14i	0.483999	−	0.838311i	−0.515832	−	0.856690i	$-0.672517\pi$
$47$	7.90090e13	−	1.36848e14i	0.483999	−	0.838311i	0.999831	+	0.0183786i	$0.00585042\pi$
$48$	−1.25280e14			−0.641698
$49$	−1.54026e14	−	1.74336e14i	−0.662106	−	0.749410i
$50$	5.25764e12			0.0190347
$51$	−1.45723e14	+	2.52400e14i	−0.445844	+	0.772224i
$52$	2.22589e14	+	3.85535e14i	0.577397	+	1.00008i
$53$	−2.04299e14	−	3.53855e14i	−0.450734	−	0.780694i	0.547698	−	0.836676i	$-0.315504\pi$
$53$	−2.04299e14	−	3.53855e14i	−0.450734	−	0.780694i	−0.998432	+	0.0559819i	$0.982171\pi$
$54$	−2.15351e12	+	3.72999e12i	−0.00405322	+	0.00702038i
$55$	7.00338e14			1.12778
$56$	4.73192e12	−	1.04949e13i	0.00653791	−	0.0145004i
$57$	2.13793e14			0.254130
$58$	4.48941e11	−	7.77588e11i	0.000460311	−	0.000797282i
$59$	1.53799e14	+	2.66388e14i	0.136368	+	0.236196i	0.926119	−	0.377231i	$-0.123124\pi$
$59$	1.53799e14	+	2.66388e14i	0.136368	+	0.236196i	−0.789751	+	0.613427i	$0.789790\pi$
$60$	7.69047e14	+	1.33203e15i	0.591108	+	1.02383i
$61$	−2.03427e14	+	3.52345e14i	−0.135864	+	0.235323i	−0.925927	−	0.377702i	$-0.876714\pi$
$61$	−2.03427e14	+	3.52345e14i	−0.135864	+	0.235323i	0.790063	+	0.613025i	$0.210048\pi$
$62$	1.21060e13			0.00704159
$63$	6.76415e14	+	9.40279e14i	0.343414	+	0.477378i
$64$	−2.25095e15			−0.999620
$65$	2.73260e15	−	4.73301e15i	1.06369	−	1.84236i
$66$	−4.57055e12	−	7.91642e12i	−0.00156259	−	0.00270648i
$67$	−1.54429e15	−	2.67479e15i	−0.464614	−	0.804736i	0.534570	−	0.845124i	$-0.320474\pi$
$67$	−1.54429e15	−	2.67479e15i	−0.464614	−	0.804736i	−0.999184	+	0.0403888i	$0.987140\pi$
$68$	−2.61859e15	+	4.53554e15i	−0.694612	+	1.20310i
$69$	−3.56846e15			−0.836110
$70$	−7.03100e13	+	7.05550e12i	−0.0145775	+	0.00146283i
$71$	−8.29735e13			−0.0152491			−0.00762454	−	0.999971i	$-0.502427\pi$
$71$	−8.29735e13			−0.0152491			−0.00762454	+	0.999971i	$0.502427\pi$
$72$	−2.86607e13	+	4.96418e13i	−0.00467693	+	0.00810068i
$73$	−1.78519e15	−	3.09205e15i	−0.259084	−	0.448747i	0.706912	−	0.707301i	$-0.250087\pi$
$73$	−1.78519e15	−	3.09205e15i	−0.259084	−	0.448747i	−0.965997	+	0.258554i	$0.916754\pi$
$74$	2.58868e13	+	4.48373e13i	0.00334664	+	0.00579655i
$75$	6.65889e15	−	1.15335e16i	0.768035	−	1.33028i
$76$	3.84177e15			0.395928
$77$	−6.60555e15	+	6.62857e14i	−0.609169	+	0.0611292i
$78$	−7.13341e13			−0.00589513
$79$	−6.55653e15	+	1.13562e16i	−0.486232	+	0.842179i	−0.999875	−	0.0158255i	$-0.994962\pi$
$79$	−6.55653e15	+	1.13562e16i	−0.486232	+	0.842179i	0.513643	+	0.858004i	$0.328296\pi$
$80$	1.38186e16	+	2.39345e16i	0.920871	+	1.59500i
$81$	5.51265e14	+	9.54819e14i	0.0330551	+	0.0572530i
$82$	6.92676e13	−	1.19975e14i	0.00374207	−	0.00648146i
$83$	−1.40495e16			−0.684696			−0.342348	−	0.939573i	$-0.611222\pi$
$83$	−1.40495e16			−0.684696			−0.342348	+	0.939573i	$0.611222\pi$
$84$	−8.51435e15	−	1.18357e16i	−0.374781	−	0.520980i
$85$	6.42942e16			2.55924
$86$	−5.91925e13	+	1.02524e14i	−0.00213319	+	0.00369480i
$87$	−1.13718e15	−	1.96966e15i	−0.0371464	−	0.0643394i
$88$	−1.64267e14	−	2.84519e14i	−0.00486909	−	0.00843351i
$89$	7.44848e15	−	1.29011e16i	0.200564	−	0.347387i	−0.748146	−	0.663534i	$-0.769056\pi$
$89$	7.44848e15	−	1.29011e16i	0.200564	−	0.347387i	0.948710	+	0.316147i	$0.102389\pi$
$90$	3.51842e14			0.00861561
$91$	−2.12941e16	+	4.72279e16i	−0.474686	+	1.05280i
$92$	−6.41238e16			−1.30263
$93$	1.53324e16	−	2.65565e16i	0.284123	−	0.492115i
$94$	2.27499e14	+	3.94040e14i	0.00384940	+	0.00666735i
$95$	−2.35817e16	−	4.08447e16i	−0.364691	−	0.631663i
$96$	5.41154e14	−	9.37307e14i	0.00765624	−	0.0132610i
$97$	−1.27713e17			−1.65454			−0.827268	−	0.561808i	$-0.810106\pi$
$97$	−1.27713e17			−1.65454			−0.827268	+	0.561808i	$0.810106\pi$
$98$	6.56482e14	−	1.33094e14i	0.00779473	−	0.00158029i
$99$	3.30552e16			0.360031
$100$	1.19658e17	−	2.07253e17i	1.19658	−	2.07253i
$101$	4.01807e16	+	6.95950e16i	0.369221	+	0.639509i	0.989444	−	0.144916i	$-0.0462913\pi$
$101$	4.01807e16	+	6.95950e16i	0.369221	+	0.639509i	−0.620223	+	0.784425i	$0.712958\pi$
$102$	−4.19597e14	−	7.26763e14i	−0.00354593	−	0.00614174i
$103$	−3.69435e16	+	6.39881e16i	−0.287357	+	0.497717i	−0.973178	−	0.230053i	$-0.926110\pi$
$103$	−3.69435e16	+	6.39881e16i	−0.287357	+	0.497717i	0.685821	+	0.727770i	$0.259443\pi$
$104$	−2.56377e15			−0.0183694
$105$	−7.35713e16	+	1.63173e17i	−0.485959	+	1.07780i
$106$	1.17652e15			0.00716966
$107$	1.76154e16	−	3.05107e16i	0.0991128	−	0.171668i	−0.812205	−	0.583372i	$-0.801733\pi$
$107$	1.76154e16	−	3.05107e16i	0.0991128	−	0.171668i	0.911318	+	0.411704i	$0.135066\pi$
$108$	9.80227e16	+	1.69780e17i	0.509594	+	0.882643i
$109$	−4.97085e16	−	8.60977e16i	−0.238949	−	0.413872i	0.721464	−	0.692452i	$-0.243470\pi$
$109$	−4.97085e16	−	8.60977e16i	−0.238949	−	0.413872i	−0.960413	+	0.278580i	$0.910136\pi$
$110$	−1.00828e15	+	1.74639e15i	−0.00448480	+	0.00776789i
$111$	1.31144e17			0.540137
$112$	−1.52990e17	−	2.12670e17i	−0.583861	−	0.811620i
$113$	2.34134e17			0.828509			0.414255	−	0.910161i	$-0.364042\pi$
$113$	2.34134e17			0.828509			0.414255	+	0.910161i	$0.364042\pi$
$114$	−3.07798e14	+	5.33122e14i	−0.00101059	+	0.00175039i
$115$	3.93607e17	+	6.81748e17i	1.19986	+	2.07822i
$116$	−2.04347e16	−	3.53940e16i	−0.0578730	−	0.100239i
$117$	1.28976e17	−	2.23393e17i	0.339570	−	0.588152i
$118$	−8.85702e14			−0.00216915
$119$	−6.06419e17	+	6.08533e16i	−1.38237	+	0.138719i
$120$	−8.85787e15			−0.0188057
$121$	1.57997e17	−	2.73658e17i	0.312588	−	0.541419i
$122$	−5.85748e14	−	1.01454e15i	−0.00108057	−	0.00187160i
$123$	−1.75457e17	−	3.03901e17i	−0.301980	−	0.523044i
$124$	2.75518e17	−	4.77211e17i	0.442655	−	0.766701i
$125$	−1.71038e18			−2.56659
$126$	−3.31855e15	+	3.33012e14i	−0.00465371	+	0.000466992i
$127$	5.56730e17			0.729983			0.364992	−	0.931011i	$-0.381072\pi$
$127$	5.56730e17			0.729983			0.364992	+	0.931011i	$0.381072\pi$
$128$	1.29656e16	−	2.24571e16i	0.0159041	−	0.0275467i
$129$	1.49937e17	+	2.59698e17i	0.172145	+	0.298165i
$130$	7.86828e15	+	1.36283e16i	0.00845982	+	0.0146528i
$131$	−2.08884e17	+	3.61797e17i	−0.210426	+	0.364468i	−0.951848	−	0.306571i	$-0.900818\pi$
$131$	−2.08884e17	+	3.61797e17i	−0.210426	+	0.364468i	0.741422	+	0.671039i	$0.234152\pi$
$132$	−4.16081e17			−0.392916
$133$	2.61080e17	+	3.62925e17i	0.231225	+	0.321424i
$134$	8.89326e15			0.00739044
$135$	1.20337e18	−	2.08430e18i	0.938779	−	1.62601i
$136$	−1.50805e16	−	2.61201e16i	−0.0110493	−	0.0191379i
$137$	1.54814e16	+	2.68146e16i	0.0106583	+	0.0184606i	0.871305	−	0.490741i	$-0.163274\pi$
$137$	1.54814e16	+	2.68146e16i	0.0106583	+	0.0184606i	−0.860647	+	0.509202i	$0.829941\pi$
$138$	5.13752e15	−	8.89844e15i	0.00332492	−	0.00575893i
$139$	3.87049e17			0.235581			0.117791	−	0.993038i	$-0.462419\pi$
$139$	3.87049e17			0.235581			0.117791	+	0.993038i	$0.462419\pi$
$140$	−1.32205e18	+	2.93215e18i	−0.757110	+	1.67918i
$141$	1.15253e18			0.621281
$142$	1.19457e14	−	2.06906e14i	6.06403e−5	−	0.000105032i
$143$	7.39217e17	+	1.28036e18i	0.353521	+	0.612317i
$144$	6.52222e17	+	1.12968e18i	0.293978	+	0.509184i
$145$	−2.50867e17	+	4.34514e17i	−0.106614	+	0.184661i
$146$	1.02806e16			0.00412116
$147$	5.39481e17	−	1.60867e18i	0.204070	−	0.608513i
$148$	2.35661e18			0.841518
$149$	−3.39282e17	+	5.87654e17i	−0.114414	+	0.198170i	−0.917545	−	0.397632i	$-0.869832\pi$
$149$	−3.39282e17	+	5.87654e17i	−0.114414	+	0.198170i	0.803132	+	0.595802i	$0.203166\pi$
$150$	1.91736e16	+	3.32097e16i	0.00610842	+	0.0105801i
$151$	−2.85468e18	−	4.94445e18i	−0.859514	−	1.48872i	−0.872393	−	0.488805i	$-0.837433\pi$
$151$	−2.85468e18	−	4.94445e18i	−0.859514	−	1.48872i	0.0128793	−	0.999917i	$-0.495900\pi$
$152$	−1.10624e16	+	1.91606e16i	−0.00314903	+	0.00545429i
$153$	3.03462e18			0.817008
$154$	7.85710e15	−	1.74262e16i	0.00200141	−	0.00443890i
$155$	−6.76478e18			−1.63092
$156$	−1.62348e18	+	2.81195e18i	−0.370585	+	0.641872i
$157$	1.33769e18	+	2.31695e18i	0.289207	+	0.500920i	0.973621	−	0.228173i	$-0.0732752\pi$
$157$	1.33769e18	+	2.31695e18i	0.289207	+	0.500920i	−0.684414	+	0.729094i	$0.739942\pi$
$158$	−1.88789e16	−	3.26992e16i	−0.00386715	−	0.00669811i
$159$	1.49008e18	−	2.58089e18i	0.289290	−	0.501065i
$160$	−2.38761e17			−0.0439485
$161$	−4.35774e18	−	6.05767e18i	−0.760750	−	1.05751i
$162$	−3.17463e15			−0.000525794
$163$	4.79346e16	−	8.30251e16i	0.00753450	−	0.0130501i	−0.862234	−	0.506511i	$-0.830935\pi$
$163$	4.79346e16	−	8.30251e16i	0.00753450	−	0.0130501i	0.869768	+	0.493461i	$0.164268\pi$
$164$	−3.15290e18	−	5.46098e18i	−0.470476	−	0.814887i
$165$	2.55400e18	+	4.42366e18i	0.361916	+	0.626857i
$166$	2.02271e16	−	3.50345e16i	0.00272280	−	0.00471603i
$167$	−1.49260e18			−0.190921			−0.0954606	−	0.995433i	$-0.530432\pi$
$167$	−1.49260e18			−0.190921			−0.0954606	+	0.995433i	$0.530432\pi$
$168$	8.35469e16	−	8.38381e15i	0.0101578	−	0.00101932i
$169$	2.88680e18			0.333718
$170$	−9.25645e16	+	1.60326e17i	−0.0101772	+	0.0176274i
$171$	−1.11303e18	−	1.92783e18i	−0.116423	−	0.201651i
$172$	2.69430e18	+	4.66667e18i	0.268197	+	0.464532i
$173$	−6.93030e18	+	1.20036e19i	−0.656690	+	1.13742i	0.324777	+	0.945790i	$0.394711\pi$
$173$	−6.93030e18	+	1.20036e19i	−0.656690	+	1.13742i	−0.981467	+	0.191630i	$0.938623\pi$
$174$	6.54882e15			0.000590873
$175$	2.77106e19	−	2.78071e18i	2.38134	−	0.238964i
$176$	−7.47633e18			−0.612112
$177$	−1.12176e18	+	1.94294e18i	−0.0875237	+	0.151596i
$178$	2.14472e16	+	3.71476e16i	0.00159515	+	0.00276287i
$179$	1.06745e19	+	1.84888e19i	0.757002	+	1.31117i	0.944373	+	0.328877i	$0.106670\pi$
$179$	1.06745e19	+	1.84888e19i	0.757002	+	1.31117i	−0.187370	+	0.982289i	$0.559996\pi$
$180$	8.00750e18	−	1.38694e19i	0.541603	−	0.938083i
$181$	−2.61639e18			−0.168824			−0.0844122	−	0.996431i	$-0.526901\pi$
$181$	−2.61639e18			−0.168824			−0.0844122	+	0.996431i	$0.526901\pi$
$182$	−8.71120e16	−	1.21094e17i	−0.00536379	−	0.00745616i
$183$	−2.96744e18			−0.174400
$184$	1.84644e17	−	3.19813e17i	0.0103606	−	0.0179451i
$185$	−1.44654e19	−	2.50549e19i	−0.775126	−	1.34256i
$186$	4.41483e16	+	7.64671e16i	0.00225972	+	0.00391394i
$187$	−8.69634e18	+	1.50625e19i	−0.425288	+	0.736620i
$188$	2.07104e19			0.967937
$189$	−9.37740e18	+	2.07980e19i	−0.418945	+	0.929173i
$190$	1.35803e17			0.00580100
$191$	−2.02554e19	+	3.50834e19i	−0.827479	+	1.43324i	0.0725306	+	0.997366i	$0.476893\pi$
$191$	−2.02554e19	+	3.50834e19i	−0.827479	+	1.43324i	−0.900010	+	0.435870i	$0.856441\pi$
$192$	−8.20878e18	−	1.42180e19i	−0.320788	−	0.555622i
$193$	−2.60575e19	−	4.51330e19i	−0.974308	−	1.68755i	−0.682201	−	0.731165i	$-0.738977\pi$
$193$	−2.60575e19	−	4.51330e19i	−0.974308	−	1.68755i	−0.292107	−	0.956386i	$-0.594356\pi$
$194$	1.83869e17	−	3.18471e17i	0.00657952	−	0.0113961i
$195$	3.98612e19			1.36539
$196$	9.69425e18	−	2.89072e19i	0.317935	−	0.948046i
$197$	−6.07020e18			−0.190651			−0.0953257	−	0.995446i	$-0.530389\pi$
$197$	−6.07020e18			−0.190651			−0.0953257	+	0.995446i	$0.530389\pi$
$198$	−4.75896e16	+	8.24276e16i	−0.00143172	+	0.00247981i
$199$	−1.66793e19	−	2.88894e19i	−0.480759	−	0.832699i	0.518998	−	0.854776i	$-0.326305\pi$
$199$	−1.66793e19	−	2.88894e19i	−0.480759	−	0.832699i	−0.999756	+	0.0220772i	$0.992972\pi$
$200$	6.89107e17	+	1.19357e18i	0.0190341	+	0.0329680i
$201$	1.12635e19	−	1.95089e19i	0.298199	−	0.516495i
$202$	−2.31393e17			−0.00587305
$203$	1.95490e18	−	4.33575e18i	0.0475782	−	0.105523i
$204$	−3.81981e19			−0.891632
$205$	−3.87065e19	+	6.70416e19i	−0.866714	+	1.50119i
$206$	−1.06375e17	−	1.84248e17i	−0.00228544	−	0.00395850i
$207$	1.85778e19	+	3.21777e19i	0.383042	+	0.663449i
$208$	−2.91714e19	+	5.05264e19i	−0.577324	+	0.999954i
$209$	1.27585e19			0.242413
$210$	−3.00973e17	−	4.18381e17i	−0.00549116	−	0.00763322i
$211$	6.77087e19			1.18643			0.593217	−	0.805043i	$-0.297858\pi$
$211$	6.77087e19			1.18643			0.593217	+	0.805043i	$0.297858\pi$
$212$	2.67761e19	−	4.63776e19i	0.450706	−	0.780645i
$213$	−3.02589e17	−	5.24100e17i	−0.00489358	−	0.00847593i
$214$	5.07218e16	+	8.78527e16i	0.000788275	+	0.00136533i
$215$	3.30766e19	−	5.72903e19i	0.494076	−	0.855764i
$216$	−1.12902e18			−0.0162124
$217$	6.38050e19	−	6.40274e18i	0.880941	−	0.0884011i
$218$	2.86262e17			0.00380087
$219$	1.30206e19	−	2.25523e19i	0.166286	−	0.288015i
$220$	4.58944e19	+	7.94915e19i	0.563855	+	0.976625i
$221$	6.78634e19	+	1.17543e20i	0.802235	+	1.38951i
$222$	−1.88809e17	+	3.27026e17i	−0.00214794	+	0.00372034i
$223$	−9.93093e19			−1.08742			−0.543712	−	0.839272i	$-0.682981\pi$
$223$	−9.93093e19			−1.08742			−0.543712	+	0.839272i	$0.682981\pi$
$224$	2.25198e18	−	2.25983e17i	0.0237387	−	0.00238214i
$225$	−1.38668e20			−1.40742
$226$	−3.37083e17	+	5.83845e17i	−0.00329470	+	0.00570658i
$227$	−3.95732e19	−	6.85427e19i	−0.372547	−	0.645270i	0.617410	−	0.786642i	$-0.288182\pi$
$227$	−3.95732e19	−	6.85427e19i	−0.372547	−	0.645270i	−0.989957	+	0.141371i	$0.954849\pi$
$228$	1.40102e19	+	2.42664e19i	0.127057	+	0.220069i
$229$	−3.80251e19	+	6.58614e19i	−0.332253	+	0.575479i	−0.982953	−	0.183856i	$-0.941142\pi$
$229$	−3.80251e19	+	6.58614e19i	−0.332253	+	0.575479i	0.650700	+	0.759335i	$0.274475\pi$
$230$	−2.26671e18			−0.0190858
$231$	−2.82761e19	−	3.93064e19i	−0.229466	−	0.318979i
$232$	2.35367e17			0.00184119
$233$	1.23562e20	−	2.14015e20i	0.931877	−	1.61406i	0.151767	−	0.988416i	$-0.451504\pi$
$233$	1.23562e20	−	2.14015e20i	0.931877	−	1.61406i	0.780110	−	0.625643i	$-0.215163\pi$
$234$	3.71374e17	+	6.43239e17i	0.00270070	+	0.00467775i
$235$	−1.27126e20	−	2.20188e20i	−0.891571	−	1.54425i
$236$	−2.01575e19	+	3.49139e19i	−0.136359	+	0.236181i
$237$	−9.56418e19			−0.624147
$238$	7.21318e17	−	1.59980e18i	0.00454174	−	0.0100731i
$239$	2.03463e20			1.23624			0.618121	−	0.786083i	$-0.287894\pi$
$239$	2.03463e20			1.23624			0.618121	+	0.786083i	$0.287894\pi$
$240$	−1.00788e20	+	1.74570e20i	−0.591034	+	1.02370i
$241$	9.35409e19	+	1.62018e20i	0.529489	+	0.917101i	0.999408	+	0.0343922i	$0.0109495\pi$
$241$	9.35409e19	+	1.62018e20i	0.529489	+	0.917101i	−0.469920	+	0.882709i	$0.655717\pi$
$242$	4.54937e17	+	7.87974e17i	0.00248611	+	0.00430607i
$243$	9.25633e19	−	1.60324e20i	0.488411	−	0.845953i
$244$	−5.33237e19			−0.271711
$245$	−3.66840e20	+	7.43725e19i	−1.80536	+	0.366017i
$246$	1.01042e18			0.00480348
$247$	4.97817e19	−	8.62244e19i	0.228636	−	0.396010i
$248$	1.58670e18	+	2.74825e18i	0.00704136	+	0.0121960i
$249$	−5.12361e19	−	8.87435e19i	−0.219726	−	0.380577i
$250$	2.46244e18	−	4.26506e18i	0.0102065	−	0.0176781i
$251$	4.51518e20			1.80904			0.904521	−	0.426429i	$-0.140229\pi$
$251$	4.51518e20			1.80904			0.904521	+	0.426429i	$0.140229\pi$
$252$	−6.23992e19	+	1.38394e20i	−0.241699	+	0.536060i
$253$	−2.12955e20			−0.797560
$254$	−8.01525e17	+	1.38828e18i	−0.00290289	+	0.00502795i
$255$	2.34469e20	+	4.06113e20i	0.821286	+	1.42251i
$256$	−1.47481e20	−	2.55444e20i	−0.499684	−	0.865478i
$257$	−4.47930e17	+	7.75838e17i	−0.00146818	+	0.00254296i	−0.866759	−	0.498728i	$-0.833801\pi$
$257$	−4.47930e17	+	7.75838e17i	−0.00146818	+	0.00254296i	0.865290	+	0.501271i	$0.167134\pi$
$258$	−8.63457e17			−0.00273825
$259$	1.60151e20	+	2.22625e20i	0.491454	+	0.683166i
$260$	7.16291e20			2.12724
$261$	−1.18406e19	+	2.05086e19i	−0.0340353	+	0.0589510i
$262$	−6.01461e17	−	1.04176e18i	−0.00167358	−	0.00289873i
$263$	1.01939e20	+	1.76564e20i	0.274610	+	0.475639i	0.970037	−	0.242959i	$-0.0781179\pi$
$263$	1.01939e20	+	1.76564e20i	0.274610	+	0.475639i	−0.695427	+	0.718597i	$0.744785\pi$
$264$	1.19810e18	−	2.07518e18i	0.00312508	−	0.00541279i
$265$	−6.57433e20			−1.66059
$266$	−1.28088e18	+	1.28535e17i	−0.00313340	+	0.000314432i
$267$	1.08653e20			0.257452
$268$	2.02400e20	−	3.50567e20i	0.464585	−	0.804685i
$269$	4.62083e19	+	8.00351e19i	0.102760	+	0.177986i	0.912821	−	0.408360i	$-0.133899\pi$
$269$	4.62083e19	+	8.00351e19i	0.102760	+	0.177986i	−0.810061	+	0.586346i	$0.800566\pi$
$270$	3.46500e18	+	6.00156e18i	0.00746640	+	0.0129322i
$271$	1.13746e19	−	1.97013e19i	0.0237518	−	0.0411393i	−0.853905	−	0.520429i	$-0.825772\pi$
$271$	1.13746e19	−	1.97013e19i	0.0237518	−	0.0411393i	0.877657	+	0.479289i	$0.159106\pi$
$272$	−6.86361e20			−1.38905
$273$	−3.75969e20	+	3.77279e19i	−0.737513	+	0.0740083i
$274$	−8.91546e16			−0.000169537
$275$	3.97383e20	−	6.88287e20i	0.732624	−	1.26894i
$276$	−2.33848e20	−	4.05036e20i	−0.418029	−	0.724047i
$277$	2.83737e20	+	4.91447e20i	0.491856	+	0.851920i	0.999956	−	0.00937835i	$-0.00298527\pi$
$277$	2.83737e20	+	4.91447e20i	0.491856	+	0.851920i	−0.508100	+	0.861298i	$0.669652\pi$
$278$	−5.57236e17	+	9.65161e17i	−0.000936825	+	0.00162263i
$279$	−3.19290e20			−0.520654
$280$	−1.08171e19	−	1.50367e19i	−0.0171107	−	0.0237854i
$281$	−7.62281e20			−1.16980			−0.584900	−	0.811106i	$-0.698866\pi$
$281$	−7.62281e20			−1.16980			−0.584900	+	0.811106i	$0.698866\pi$
$282$	−1.65929e18	+	2.87398e18i	−0.00247062	+	0.00427924i
$283$	2.67093e20	+	4.62619e20i	0.385903	+	0.668403i	0.991894	−	0.127068i	$-0.0405566\pi$
$283$	2.67093e20	+	4.62619e20i	0.385903	+	0.668403i	−0.605991	+	0.795471i	$0.707223\pi$
$284$	−5.43741e18	−	9.41787e18i	−0.00762405	−	0.0132052i
$285$	1.71996e20	−	2.97906e20i	0.234066	−	0.405414i
$286$	−4.25701e18			−0.00562333
$287$	3.01624e20	−	6.68968e20i	0.386785	−	0.857845i
$288$	−1.12693e19			−0.0140301
$289$	−3.84744e20	+	6.66396e20i	−0.465093	+	0.805565i
$290$	−7.22346e17	−	1.25114e18i	−0.000847935	−	0.00146867i
$291$	−4.65747e20	−	8.06697e20i	−0.530957	−	0.919645i
$292$	2.33974e20	−	4.05255e20i	0.259068	−	0.448719i
$293$	2.92233e20			0.314307			0.157154	−	0.987574i	$-0.449768\pi$
$293$	2.92233e20			0.314307			0.157154	+	0.987574i	$0.449768\pi$
$294$	3.23475e18	+	3.66128e18i	0.00337978	+	0.00382543i
$295$	4.94927e20			0.502405
$296$	−6.78585e18	+	1.17534e19i	−0.00669306	+	0.0115927i
$297$	3.25533e20	+	5.63840e20i	0.312008	+	0.540413i
$298$	−9.76930e17	−	1.69209e18i	−0.000909966	−	0.00157611i
$299$	−8.30916e20	+	1.43919e21i	−0.752232	+	1.30290i
$300$	1.74548e21			1.53597
$301$	−2.57752e20	+	5.71665e20i	−0.220489	+	0.489020i
$302$	1.64395e19			0.0136720
$303$	−2.93063e20	+	5.07601e20i	−0.236973	+	0.410450i
$304$	2.51742e20	+	4.36031e20i	0.197939	+	0.342840i
$305$	3.27314e20	+	5.66924e20i	0.250274	+	0.433487i
$306$	−4.36894e18	+	7.56723e18i	−0.00324896	+	0.00562736i
$307$	1.46371e21			1.05872			0.529359	−	0.848398i	$-0.322433\pi$
$307$	1.46371e21			1.05872			0.529359	+	0.848398i	$0.322433\pi$
$308$	−5.08111e20	−	7.06321e20i	−0.357501	−	0.496960i
$309$	−5.38905e20			−0.368863
$310$	9.73927e18	−	1.68689e19i	0.00648562	−	0.0112334i
$311$	−7.20601e20	−	1.24812e21i	−0.466908	−	0.808708i	0.532377	−	0.846507i	$-0.321299\pi$
$311$	−7.20601e20	−	1.24812e21i	−0.466908	−	0.808708i	−0.999285	+	0.0377988i	$0.987965\pi$
$312$	−9.34961e18	−	1.61940e19i	−0.00589494	−	0.0102103i
$313$	1.13648e21	−	1.96843e21i	0.697322	−	1.20780i	−0.272069	−	0.962278i	$-0.587708\pi$
$313$	1.13648e21	−	1.96843e21i	0.697322	−	1.20780i	0.969392	−	0.245520i	$-0.0789587\pi$
$314$	−7.70350e18			−0.00460030
$315$	1.85439e21	−	1.86086e20i	1.07786	−	0.108162i
$316$	−1.71865e21			−0.972403
$317$	−8.87441e20	+	1.53709e21i	−0.488805	+	0.846635i	−0.999917	−	0.0128791i	$-0.995900\pi$
$317$	−8.87441e20	+	1.53709e21i	−0.488805	+	0.846635i	0.511112	+	0.859514i	$0.329234\pi$
$318$	4.29054e18	+	7.43144e18i	0.00230081	+	0.00398513i
$319$	−6.78637e19	−	1.17543e20i	−0.0354337	−	0.0613730i
$320$	−1.81089e21	+	3.13655e21i	−0.920697	+	1.59469i
$321$	2.56960e20			0.127225
$322$	2.13795e19	−	2.14540e18i	0.0103091	−	0.00103451i
$323$	1.17129e21			0.550102
$324$	−7.22509e19	+	1.25142e20i	−0.0330530	+	0.0572494i
$325$	−3.10105e21	−	5.37117e21i	−1.38197	−	2.39365i
$326$	1.38023e17	+	2.39063e17i	5.99242e−5	+	0.000103792i
$327$	3.62556e20	−	6.27965e20i	0.153362	−	0.265632i
$328$	3.63150e19			0.0149678
$329$	1.40744e21	+	1.95648e21i	0.565283	+	0.785796i
$330$	−1.47080e19			−0.00575686
$331$	6.56317e20	−	1.13677e21i	0.250366	−	0.433647i	−0.713260	−	0.700899i	$-0.752782\pi$
$331$	6.56317e20	−	1.13677e21i	0.250366	−	0.433647i	0.963627	+	0.267252i	$0.0861156\pi$
$332$	−9.20692e20	−	1.59469e21i	−0.342327	−	0.592927i
$333$	−6.82753e20	−	1.18256e21i	−0.247450	−	0.428596i
$334$	2.14890e18	−	3.72201e18i	0.000759227	−	0.00131502i
$335$	−4.96952e21			−1.71172
$336$	7.85398e20	−	1.74192e21i	0.263758	−	0.584986i
$337$	−2.51502e21			−0.823543			−0.411772	−	0.911287i	$-0.635090\pi$
$337$	−2.51502e21			−0.823543			−0.411772	+	0.911287i	$0.635090\pi$
$338$	−4.15613e18	+	7.19863e18i	−0.00132708	+	0.00229857i
$339$	8.53843e20	+	1.47890e21i	0.265877	+	0.460512i
$340$	4.21332e21	+	7.29768e21i	1.27954	+	2.21623i
$341$	9.14994e20	−	1.58482e21i	0.271023	−	0.469425i
$342$	6.40973e18			0.00185190
$343$	3.38962e21	−	1.04868e21i	0.955324	−	0.295559i
$344$	−3.10329e19			−0.00853250
$345$	−2.87083e21	+	4.97242e21i	−0.770096	+	1.33384i
$346$	−1.99552e19	−	3.45633e19i	−0.00522286	−	0.00904625i
$347$	−1.45138e21	−	2.51387e21i	−0.370665	−	0.642011i	0.619003	−	0.785389i	$-0.287537\pi$
$347$	−1.45138e21	−	2.51387e21i	−0.370665	−	0.642011i	−0.989668	+	0.143378i	$0.954204\pi$
$348$	1.49043e20	−	2.58151e20i	0.0371440	−	0.0643354i
$349$	6.83543e21			1.66245			0.831227	−	0.555933i	$-0.187639\pi$
$349$	6.83543e21			1.66245			0.831227	+	0.555933i	$0.187639\pi$
$350$	−3.29609e19	+	7.31035e19i	−0.00782385	+	0.0173524i
$351$	5.08071e21			1.17710
$352$	3.22945e19	−	5.59357e19i	0.00730325	−	0.0126496i
$353$	−5.87985e20	−	1.01842e21i	−0.129802	−	0.224824i	0.793798	−	0.608182i	$-0.208101\pi$
$353$	−5.87985e20	−	1.01842e21i	−0.129802	−	0.224824i	−0.923600	+	0.383358i	$0.874768\pi$
$354$	−3.22999e18	−	5.59451e18i	−0.000696103	−	0.00120569i
$355$	−6.67522e19	+	1.15618e20i	−0.0140451	+	0.0243268i
$356$	1.95245e21			0.401102
$357$	−2.59588e21	−	3.60851e21i	−0.520720	−	0.723849i
$358$	−6.14725e19			−0.0120413
$359$	−3.36141e21	+	5.82214e21i	−0.643012	+	1.11373i	0.341745	+	0.939793i	$0.388982\pi$
$359$	−3.36141e21	+	5.82214e21i	−0.643012	+	1.11373i	−0.984757	+	0.173936i	$0.944351\pi$
$360$	4.61151e19	+	7.98738e19i	0.00861534	+	0.0149222i
$361$	2.31059e21	+	4.00206e21i	0.421611	+	0.730251i
$362$	3.76683e18	−	6.52434e18i	0.000671356	−	0.00116282i
$363$	2.30474e21			0.401251
$364$	−6.75601e21	+	6.77956e20i	−1.14902	+	0.115303i
$365$	−5.74476e21			−0.954515
$366$	4.27223e18	−	7.39972e18i	0.000693530	−	0.00120123i
$367$	3.07708e21	+	5.32966e21i	0.488064	+	0.845352i	0.999906	−	0.0137276i	$-0.00436976\pi$
$367$	3.07708e21	+	5.32966e21i	0.488064	+	0.845352i	−0.511841	+	0.859080i	$0.671036\pi$
$368$	−4.20188e21	−	7.27788e21i	−0.651235	−	1.12797i
$369$	−1.82690e21	+	3.16429e21i	−0.276689	+	0.479239i
$370$	8.33038e19			0.0123296
$371$	6.20087e21	−	6.22248e20i	0.896963	−	0.0900089i
$372$	4.01905e21			0.568209
$373$	5.80373e21	−	1.00524e22i	0.802015	−	1.38913i	−0.116274	−	0.993217i	$-0.537095\pi$
$373$	5.80373e21	−	1.00524e22i	0.802015	−	1.38913i	0.918288	−	0.395913i	$-0.129572\pi$
$374$	−2.50403e19	−	4.33711e19i	−0.00338245	−	0.00585857i
$375$	−6.23744e21	−	1.08036e22i	−0.823645	−	1.42660i
$376$	−5.96356e19	+	1.03292e20i	−0.00769855	+	0.0133343i
$377$	−1.05917e21			−0.133680
$378$	−3.83621e19	−	5.33268e19i	−0.00473393	−	0.00658060i
$379$	−1.22497e22			−1.47806			−0.739031	−	0.673672i	$-0.764716\pi$
$379$	−1.22497e22			−1.47806			−0.739031	+	0.673672i	$0.764716\pi$
$380$	3.09071e21	−	5.35326e21i	0.364668	−	0.631623i
$381$	2.03029e21	+	3.51657e21i	0.234259	+	0.405748i
$382$	−5.83235e19	−	1.01019e20i	−0.00658120	−	0.0113990i
$383$	−6.06659e20	+	1.05076e21i	−0.0669507	+	0.115962i	−0.897558	−	0.440897i	$-0.854660\pi$
$383$	−6.06659e20	+	1.05076e21i	−0.0669507	+	0.115962i	0.830607	+	0.556859i	$0.187994\pi$
$384$	1.89133e20			0.0204151
$385$	−4.39052e21	+	9.73768e21i	−0.463553	+	1.02811i
$386$	1.50060e20			0.0154979
$387$	1.56118e21	−	2.70404e21i	0.157728	−	0.273193i
$388$	−8.36929e21	−	1.44960e22i	−0.827216	−	1.43278i
$389$	9.38472e21	+	1.62548e22i	0.907507	+	1.57185i	0.817517	+	0.575905i	$0.195350\pi$
$389$	9.38472e21	+	1.62548e22i	0.907507	+	1.57185i	0.0899897	+	0.995943i	$0.471317\pi$
$390$	−5.73883e19	+	9.93995e19i	−0.00542968	+	0.00940449i
$391$	−1.95502e22			−1.80988
$392$	1.16258e20	+	1.31588e20i	0.0105315	+	0.0119202i
$393$	−3.04704e21			−0.270111
$394$	8.73928e18	−	1.51369e19i	0.000758155	−	0.00131316i
$395$	1.05495e22	+	1.82722e22i	0.895684	+	1.55137i
$396$	2.16617e21	+	3.75191e21i	0.180004	+	0.311777i
$397$	5.06527e21	−	8.77331e21i	0.411987	−	0.713582i	−0.583120	−	0.812386i	$-0.698168\pi$
$397$	5.06527e21	−	8.77331e21i	0.411987	−	0.713582i	0.995107	+	0.0988036i	$0.0315016\pi$
$398$	9.60530e19			0.00764725
$399$	−1.34030e21	+	2.97263e21i	−0.104456	+	0.231671i
$400$	3.13636e22			2.39285
$401$	1.02547e22	−	1.77617e22i	0.765943	−	1.32665i	−0.173803	−	0.984780i	$-0.555606\pi$
$401$	1.02547e22	−	1.77617e22i	0.765943	−	1.32665i	0.939746	−	0.341872i	$-0.111061\pi$
$402$	3.24321e19	+	5.61741e19i	0.00237167	+	0.00410785i
$403$	−7.14032e21	−	1.23674e22i	−0.511240	−	0.885493i
$404$	−5.26623e21	+	9.12138e21i	−0.369197	+	0.639468i
$405$	1.77397e21			0.121781
$406$	7.99731e18	+	1.11170e19i	0.000537617	+	0.000747337i
$407$	7.82631e21			0.515234
$408$	1.09991e20	−	1.90511e20i	0.00709165	−	0.0122831i
$409$	1.45048e22	+	2.51231e22i	0.915934	+	1.58644i	0.805528	+	0.592558i	$0.201882\pi$
$409$	1.45048e22	+	2.51231e22i	0.915934	+	1.58644i	0.110407	+	0.993887i	$0.464785\pi$
$410$	−1.11452e20	−	1.93040e20i	−0.00689324	−	0.0119395i
$411$	−1.12916e20	+	1.95576e20i	−0.00684068	+	0.0118484i
$412$	−9.68391e21			−0.574678
$413$	−4.66812e21	+	4.68439e20i	−0.271373	+	0.0272319i
$414$	−1.06986e20			−0.00609291
$415$	−1.13029e22	+	1.95771e22i	−0.630637	+	1.09230i
$416$	−2.52016e20	−	4.36504e20i	−0.0137764	−	0.0238614i
$417$	1.41150e21	+	2.44479e21i	0.0756004	+	0.130944i
$418$	−1.83685e19	+	3.18151e19i	−0.000963995	+	0.00166969i
$419$	−1.10441e22			−0.567951			−0.283976	−	0.958832i	$-0.591653\pi$
$419$	−1.10441e22			−0.567951			−0.283976	+	0.958832i	$0.591653\pi$
$420$	−2.33421e22	+	2.34235e21i	−1.17631	+	0.118041i
$421$	−1.30581e21			−0.0644885			−0.0322443	−	0.999480i	$-0.510265\pi$
$421$	−1.30581e21			−0.0644885			−0.0322443	+	0.999480i	$0.510265\pi$
$422$	−9.74804e19	+	1.68841e20i	−0.00471804	+	0.00817188i
$423$	−6.00018e21	−	1.03926e22i	−0.284624	−	0.492983i
$424$	1.54204e20	+	2.67088e20i	0.00716943	+	0.0124178i
$425$	3.64816e22	−	6.31879e22i	1.66252	−	2.87957i
$426$	1.74255e18			7.78403e−5
$427$	−3.62379e21	−	5.03740e21i	−0.158681	−	0.220582i
$428$	4.61747e21			0.198213
$429$	−5.39157e21	+	9.33848e21i	−0.226897	+	0.392997i
$430$	9.52408e19	+	1.64962e20i	0.00392954	+	0.00680616i
$431$	−1.63404e22	−	2.83025e22i	−0.661009	−	1.14490i	−0.980351	−	0.197261i	$-0.936795\pi$
$431$	−1.63404e22	−	2.83025e22i	−0.661009	−	1.14490i	0.319342	−	0.947639i	$-0.396538\pi$
$432$	−1.28464e22	+	2.22506e22i	−0.509530	+	0.882532i
$433$	8.77900e21			0.341427			0.170714	−	0.985321i	$-0.445393\pi$
$433$	8.77900e21			0.341427			0.170714	+	0.985321i	$0.445393\pi$
$434$	−7.58941e19	+	1.68325e20i	−0.00289431	+	0.00641926i
$435$	−3.65946e21			−0.136854
$436$	6.51498e21	−	1.12843e22i	0.238934	−	0.413846i
$437$	7.17060e21	+	1.24198e22i	0.257907	+	0.446708i
$438$	3.74915e19	+	6.49371e19i	0.00132252	+	0.00229067i
$439$	−2.64747e22	+	4.58555e22i	−0.915973	+	1.58651i	−0.110502	+	0.993876i	$0.535246\pi$
$439$	−2.64747e22	+	4.58555e22i	−0.915973	+	1.58651i	−0.805471	+	0.592636i	$0.798087\pi$
$440$	−5.28612e20			−0.0179386
$441$	−1.73144e22	+	3.51030e21i	−0.576342	+	0.116847i
$442$	−3.90813e20			−0.0127608
$443$	1.29885e22	−	2.24968e22i	0.416033	−	0.720591i	−0.579503	−	0.814970i	$-0.696753\pi$
$443$	1.29885e22	−	2.24968e22i	0.416033	−	0.720591i	0.995536	+	0.0943792i	$0.0300866\pi$
$444$	8.59413e21	+	1.48855e22i	0.270052	+	0.467743i
$445$	−1.19846e22	−	2.07580e22i	−0.369457	−	0.639918i
$446$	1.42976e20	−	2.47642e20i	0.00432431	−	0.00748992i
$447$	−4.94920e21			−0.146866
$448$	1.41115e22	−	3.12977e22i	0.410875	−	0.911275i
$449$	−2.25773e22			−0.645027			−0.322513	−	0.946565i	$-0.604528\pi$
$449$	−2.25773e22			−0.645027			−0.322513	+	0.946565i	$0.604528\pi$
$450$	1.99641e20	−	3.45788e20i	0.00559683	−	0.00969400i
$451$	−1.04708e22	−	1.81359e22i	−0.288057	−	0.498929i
$452$	1.53432e22	+	2.65752e22i	0.414228	+	0.717465i
$453$	2.08210e22	−	3.60630e22i	0.551653	−	0.955491i
$454$	2.27894e20			0.00592596
$455$	4.86779e22	+	6.76668e22i	1.24232	+	1.72695i
$456$	−1.61370e20			−0.00404223
$457$	1.66283e22	−	2.88011e22i	0.408847	−	0.708144i	−0.585914	−	0.810374i	$-0.699264\pi$
$457$	1.66283e22	−	2.88011e22i	0.408847	−	0.708144i	0.994761	+	0.102229i	$0.0325975\pi$
$458$	−1.09490e20	−	1.89642e20i	−0.00264251	−	0.00457696i
$459$	2.98854e22	+	5.17631e22i	0.708030	+	1.22634i
$460$	−5.15876e22	+	8.93524e22i	−1.19979	+	2.07809i
$461$	4.91417e22			1.12200			0.560999	−	0.827816i	$-0.310417\pi$
$461$	4.91417e22			1.12200			0.560999	+	0.827816i	$0.310417\pi$
$462$	1.38725e20	−	1.39209e19i	0.00310956	−	0.000312040i
$463$	−2.03123e22			−0.447015			−0.223507	−	0.974702i	$-0.571751\pi$
$463$	−2.03123e22			−0.447015			−0.223507	+	0.974702i	$0.571751\pi$
$464$	2.67808e21	−	4.63857e21i	0.0578657	−	0.100226i
$465$	−2.46699e22	−	4.27295e22i	−0.523380	−	0.906521i
$466$	3.55784e20	+	6.16237e20i	0.00741151	+	0.0128371i
$467$	1.24296e22	−	2.15287e22i	0.254252	−	0.440377i	−0.710440	−	0.703758i	$-0.751504\pi$
$467$	1.24296e22	−	2.15287e22i	0.254252	−	0.440377i	0.964692	+	0.263381i	$0.0848375\pi$
$468$	3.38081e22			0.679096
$469$	4.68723e22	−	4.70356e21i	0.924585	−	0.0927807i
$470$	7.32092e20			0.0141819
$471$	−9.75661e21	+	1.68989e22i	−0.185619	+	0.321501i
$472$	−1.16087e20	−	2.01069e20i	−0.00216909	−	0.00375697i
$473$	8.94778e21	+	1.54980e22i	0.164208	+	0.284417i
$474$	1.37696e20	−	2.38496e20i	0.00248202	−	0.00429898i
$475$	−5.35225e22			−0.947635
$476$	−4.66469e22	−	6.48435e22i	−0.811267	−	1.12774i
$477$	−3.10301e22			−0.530124
$478$	−2.92926e20	+	5.07363e20i	−0.00491611	+	0.00851495i
$479$	−1.53690e21	−	2.66198e21i	−0.0253392	−	0.0438888i	0.853078	−	0.521784i	$-0.174733\pi$
$479$	−1.53690e21	−	2.66198e21i	−0.0253392	−	0.0438888i	−0.878417	+	0.477895i	$0.841400\pi$
$480$	−8.70718e20	−	1.50813e21i	−0.0141035	−	0.0244280i
$481$	3.05370e22	−	5.28916e22i	0.485951	−	0.841693i
$482$	−5.38684e20			−0.00842237
$483$	2.23712e22	−	4.96168e22i	0.343667	−	0.762216i
$484$	4.14153e22			0.625137
$485$	−1.02745e23	+	1.77960e23i	−1.52390	+	2.63948i
$486$	2.66527e20	+	4.61639e20i	0.00388449	+	0.00672813i
$487$	−3.46943e22	−	6.00923e22i	−0.496892	−	0.860642i	0.503102	−	0.864227i	$-0.332192\pi$
$487$	−3.46943e22	−	6.00923e22i	−0.496892	−	0.860642i	−0.999994	+	0.00358524i	$0.998859\pi$
$488$	1.53545e20	−	2.65948e20i	0.00216107	−	0.00374308i
$489$	6.99235e20			0.00967158
$490$	3.42682e20	−	1.02184e21i	0.00465827	−	0.0138904i
$491$	−7.44341e22			−0.994442			−0.497221	−	0.867624i	$-0.665646\pi$
$491$	−7.44341e22			−0.994442			−0.497221	+	0.867624i	$0.665646\pi$
$492$	2.29961e22	−	3.98304e22i	0.301961	−	0.523011i
$493$	−6.23020e21	−	1.07910e22i	−0.0804087	−	0.139272i
$494$	1.43342e20	+	2.48275e20i	0.00181842	+	0.00314959i
$495$	2.65929e22	−	4.60603e22i	0.331605	−	0.574357i
$496$	7.22162e22			0.885198
$497$	5.20173e20	−	1.15368e21i	0.00626785	−	0.0139014i
$498$	2.95059e20			0.00349510
$499$	−6.86055e22	+	1.18828e23i	−0.798922	+	1.38377i	0.121397	+	0.992604i	$0.461263\pi$
$499$	−6.86055e22	+	1.18828e23i	−0.798922	+	1.38377i	−0.920319	+	0.391169i	$0.872071\pi$
$500$	−1.12084e23	−	1.94136e23i	−1.28322	−	2.22259i
$501$	−5.44325e21	−	9.42798e21i	−0.0612685	−	0.106120i
$502$	−6.50052e20	+	1.12592e21i	−0.00719394	+	0.0124603i
$503$	2.46368e22			0.268075			0.134037	−	0.990976i	$-0.457206\pi$
$503$	2.46368e22			0.268075			0.134037	+	0.990976i	$0.457206\pi$
$504$	−5.10555e20	−	7.09718e20i	−0.00546239	−	0.00759322i
$505$	1.29302e23			1.36028
$506$	3.06592e20	−	5.31033e20i	0.00317162	−	0.00549341i
$507$	1.05276e22	+	1.82344e22i	0.107093	+	0.185491i
$508$	3.64835e22	+	6.31913e22i	0.364968	+	0.632144i
$509$	−5.24416e22	+	9.08315e22i	−0.515911	+	0.893583i	0.483919	+	0.875113i	$0.339213\pi$
$509$	−5.24416e22	+	9.08315e22i	−0.515911	+	0.893583i	−0.999829	+	0.0184705i	$0.994120\pi$
$510$	−1.35026e21			−0.0130639
$511$	5.41843e22	−	5.43731e21i	0.515579	−	0.0517376i
$512$	4.24818e21			0.0397565
$513$	2.19226e22	−	3.79711e22i	0.201788	−	0.349507i
$514$	−1.28977e18	−	2.23395e18i	−1.16769e−5	−	2.02250e-5i
$515$	5.94422e22	+	1.02957e23i	0.529338	+	0.916841i
$516$	−1.96513e22	+	3.40370e22i	−0.172134	+	0.298146i
$517$	6.87793e22			0.592636
$518$	−7.85717e20	+	7.88455e19i	−0.00665983	+	0.000668304i
$519$	−1.01094e23			−0.842953
$520$	−2.06256e21	+	3.57245e21i	−0.0169191	+	0.0293048i
$521$	6.12242e22	+	1.06043e23i	0.494086	+	0.855782i	0.999977	−	0.00681526i	$-0.00216938\pi$
$521$	6.12242e22	+	1.06043e23i	0.494086	+	0.855782i	−0.505891	+	0.862598i	$0.668836\pi$
$522$	−3.40940e19	−	5.90525e19i	−0.000270694	−	0.000468855i
$523$	3.83861e22	−	6.64866e22i	0.299854	−	0.519361i	−0.676249	−	0.736673i	$-0.736396\pi$
$523$	3.83861e22	−	6.64866e22i	0.299854	−	0.519361i	0.976102	+	0.217312i	$0.0697289\pi$
$524$	−5.47542e22			−0.420825
$525$	1.18620e23	+	1.64892e23i	0.897021	+	1.24694i
$526$	−5.87047e20			−0.00436812
$527$	8.40006e22	−	1.45493e23i	0.615024	−	1.06525i
$528$	−2.72648e22	−	4.72241e22i	−0.196433	−	0.340232i
$529$	−4.91610e22	−	8.51493e22i	−0.348536	−	0.603682i
$530$	9.46509e20	−	1.63940e21i	0.00660358	−	0.0114377i
$531$	2.33600e22			0.160387
$532$	−2.40846e22	+	5.34170e22i	−0.162739	+	0.360936i
$533$	−1.63421e23			−1.08674
$534$	−1.56428e20	+	2.70941e20i	−0.00102380	+	0.00177327i
$535$	−2.83432e22	−	4.90918e22i	−0.182575	−	0.316229i
$536$	1.16562e21	+	2.01891e21i	0.00739021	+	0.0128002i
$537$	−7.78560e22	+	1.34851e23i	−0.485859	+	0.841533i
$538$	−2.66105e20			−0.00163457
$539$	3.21946e22	−	9.60008e22i	0.194661	−	0.580457i
$540$	3.15437e23			1.87744
$541$	1.99415e22	−	3.45398e22i	0.116837	−	0.202368i	−0.801675	−	0.597760i	$-0.796058\pi$
$541$	1.99415e22	−	3.45398e22i	0.116837	−	0.202368i	0.918513	+	0.395391i	$0.129391\pi$
$542$	3.27520e19	+	5.67281e19i	0.000188905	+	0.000327193i
$543$	−9.54151e21	−	1.65264e22i	−0.0541775	−	0.0938381i
$544$	2.96478e21	−	5.13515e21i	0.0165730	−	0.0287053i
$545$	−1.59962e23			−0.880333
$546$	4.47204e20	−	9.91848e20i	0.00242308	−	0.00537412i
$547$	−2.85773e23			−1.52450			−0.762252	−	0.647281i	$-0.775906\pi$
$547$	−2.85773e23			−1.52450			−0.762252	+	0.647281i	$0.775906\pi$
$548$	−2.02905e21	+	3.51442e21i	−0.0106576	+	0.0184595i
$549$	1.54488e22	+	2.67582e22i	0.0798971	+	0.138386i
$550$	1.14423e21	+	1.98186e21i	0.00582679	+	0.0100923i
$551$	−4.57020e21	+	7.91582e21i	−0.0229164	+	0.0396924i
$552$	2.69345e21			0.0132993
$553$	−1.16796e23	−	1.62358e23i	−0.567891	−	0.789421i
$554$	−1.63399e21			−0.00782377
$555$	1.05506e23	−	1.82741e23i	0.497491	−	0.861680i
$556$	2.53641e22	+	4.39319e22i	0.117783	+	0.204006i
$557$	−1.58008e23	−	2.73677e23i	−0.722618	−	1.25161i	−0.959947	−	0.280182i	$-0.909605\pi$
$557$	−1.58008e23	−	2.73677e23i	−0.722618	−	1.25161i	0.237329	−	0.971429i	$-0.423728\pi$
$558$	4.59683e20	−	7.96194e20i	0.00207046	−	0.00358615i
$559$	1.39651e23			0.619504
$560$	−4.19422e23	+	4.20884e22i	−1.83254	+	0.183893i
$561$	−1.26856e23			−0.545917
$562$	1.09746e21	−	1.90085e21i	0.00465189	−	0.00805730i
$563$	1.92209e23	+	3.32916e23i	0.802514	+	1.39000i	0.917956	+	0.396681i	$0.129838\pi$
$563$	1.92209e23	+	3.32916e23i	0.802514	+	1.39000i	−0.115442	+	0.993314i	$0.536829\pi$
$564$	7.55271e22	+	1.30817e23i	0.310621	+	0.538011i
$565$	1.88361e23	−	3.26251e23i	0.763095	−	1.32172i
$566$	−1.53814e21			−0.00613841
$567$	−1.67320e22	+	1.67903e21i	−0.0657797	+	0.00660090i
$568$	6.26280e19			0.000242553
$569$	−9.47086e22	+	1.64040e23i	−0.361356	+	0.625886i	−0.988184	−	0.153271i	$-0.951019\pi$
$569$	−9.47086e22	+	1.64040e23i	−0.361356	+	0.625886i	0.626828	+	0.779157i	$0.284353\pi$
$570$	4.95247e20	+	8.57793e20i	0.00186160	+	0.00322438i
$571$	6.80767e22	+	1.17912e23i	0.252111	+	0.436669i	0.964107	−	0.265515i	$-0.0855420\pi$
$571$	6.80767e22	+	1.17912e23i	0.252111	+	0.436669i	−0.711996	+	0.702183i	$0.752209\pi$
$572$	−9.68845e22	+	1.67809e23i	−0.353499	+	0.612278i
$573$	−2.95471e23			−1.06219
$574$	1.23391e21	+	1.71525e21i	0.00437053	+	0.00607544i
$575$	8.93356e23			3.11780
$576$	−8.54719e22	+	1.48042e23i	−0.293922	+	0.509088i
$577$	2.75948e23	+	4.77955e23i	0.935044	+	1.61954i	0.774555	+	0.632507i	$0.217974\pi$
$577$	2.75948e23	+	4.77955e23i	0.935044	+	1.61954i	0.160490	+	0.987038i	$0.448693\pi$
$578$	−1.10783e21	−	1.91882e21i	−0.00369903	−	0.00640691i
$579$	1.90054e23	−	3.29183e23i	0.625330	−	1.08310i
$580$	−6.57590e22			−0.213215
$581$	8.80785e22	−	1.95348e23i	0.281432	−	0.624184i
$582$	2.68215e21			0.00844573
$583$	8.89235e22	−	1.54020e23i	0.275952	−	0.477963i
$584$	1.34746e21	+	2.33386e21i	0.00412103	+	0.00713783i
$585$	−2.07522e23	−	3.59439e23i	−0.625518	−	1.08343i
$586$	−4.20728e20	+	7.28723e20i	−0.00124989	+	0.00216487i
$587$	−1.10067e23			−0.322279			−0.161139	−	0.986932i	$-0.551517\pi$
$587$	−1.10067e23			−0.322279			−0.161139	+	0.986932i	$0.551517\pi$
$588$	2.17945e23	−	4.41858e22i	0.628983	−	0.127519i
$589$	−1.23238e23			−0.350563
$590$	−7.12548e20	+	1.23417e21i	−0.00199789	+	0.00346045i
$591$	−2.21369e22	−	3.83422e22i	−0.0611820	−	0.105970i
$592$	1.54423e23	+	2.67469e23i	0.420706	+	0.728684i
$593$	−2.19994e23	+	3.81040e23i	−0.590807	+	1.02331i	0.403317	+	0.915060i	$0.367857\pi$
$593$	−2.19994e23	+	3.81040e23i	−0.590807	+	1.02331i	−0.994124	+	0.108247i	$0.965476\pi$
$594$	−1.87468e21			−0.00496299
$595$	−4.03070e23	+	8.93963e23i	−1.05193	+	2.33306i
$596$	−8.89351e22			−0.228813
$597$	1.21653e23	−	2.10709e23i	0.308561	−	0.534443i
$598$	−2.39254e21	−	4.14401e21i	−0.00598274	−	0.0103624i
$599$	1.46767e23	+	2.54208e23i	0.361827	+	0.626702i	0.988262	−	0.152772i	$-0.0488199\pi$
$599$	1.46767e23	+	2.54208e23i	0.361827	+	0.626702i	−0.626435	+	0.779474i	$0.715487\pi$
$600$	−5.02610e21	+	8.70545e21i	−0.0122165	+	0.0211595i
$601$	−2.28006e23			−0.546403			−0.273202	−	0.961957i	$-0.588083\pi$
$601$	−2.28006e23			−0.546403			−0.273202	+	0.961957i	$0.588083\pi$
$602$	−1.05444e21	−	1.46577e21i	−0.00249145	−	0.00346334i
$603$	−2.34556e23			−0.546449
$604$	3.74145e23	−	6.48037e23i	0.859460	−	1.48863i
$605$	−2.54217e23	−	4.40317e23i	−0.575816	−	0.997343i
$606$	−8.43848e20	−	1.46159e21i	−0.00188472	−	0.00326443i
$607$	2.25332e23	−	3.90286e23i	0.496271	−	0.859566i	−0.503720	−	0.863867i	$-0.668036\pi$
$607$	2.25332e23	−	3.90286e23i	0.496271	−	0.859566i	0.999991	+	0.00430065i	$0.00136895\pi$
$608$	−4.34967e21			−0.00944661
$609$	3.45158e22	−	3.46361e21i	0.0739215	−	0.00741791i
$610$	−1.88494e21			−0.00398101
$611$	2.68366e23	−	4.64823e23i	0.558955	−	0.968138i
$612$	1.98864e23	+	3.44442e23i	0.408478	+	0.707505i
$613$	−1.63663e23	−	2.83473e23i	−0.331541	−	0.574246i	0.651273	−	0.758843i	$-0.274235\pi$
$613$	−1.63663e23	−	2.83473e23i	−0.331541	−	0.574246i	−0.982814	+	0.184597i	$0.940902\pi$
$614$	−2.10731e21	+	3.64997e21i	−0.00421015	+	0.00729220i
$615$	−5.64622e23			−1.11255
$616$	4.98583e21	−	5.00321e20i	0.00968951	−	0.000972328i
$617$	7.52601e23			1.44258			0.721291	−	0.692632i	$-0.243549\pi$
$617$	7.52601e23			1.44258			0.721291	+	0.692632i	$0.243549\pi$
$618$	7.75863e20	−	1.34383e21i	0.00146684	−	0.00254064i
$619$	−3.60168e23	−	6.23830e23i	−0.671637	−	1.16331i	−0.977440	−	0.211215i	$-0.932258\pi$
$619$	−3.60168e23	−	6.23830e23i	−0.671637	−	1.16331i	0.305802	−	0.952095i	$-0.401075\pi$
$620$	−4.43308e23	−	7.67832e23i	−0.815411	−	1.41233i
$621$	−3.65915e23	+	6.33784e23i	−0.663899	+	1.14991i
$622$	4.14980e21			0.00742693
$623$	1.32685e23	+	1.84445e23i	0.234247	+	0.325625i
$624$	−4.25532e23			−0.741076
$625$	−6.79457e23	+	1.17685e24i	−1.16730	+	2.02182i
$626$	3.27238e21	+	5.66792e21i	0.00554602	+	0.00960599i
$627$	4.65280e22	+	8.05888e22i	0.0777929	+	0.134741i
$628$	−1.75322e23	+	3.03667e23i	−0.289188	+	0.500889i
$629$	7.18490e23			1.16920
$630$	−2.20575e21	+	4.89210e21i	−0.00354129	+	0.00785417i
$631$	−5.91014e23			−0.936156			−0.468078	−	0.883687i	$-0.655053\pi$
$631$	−5.91014e23			−0.936156			−0.468078	+	0.883687i	$0.655053\pi$
$632$	4.94883e21	−	8.57163e21i	0.00773406	−	0.0133958i
$633$	2.46921e23	+	4.27680e23i	0.380738	+	0.659458i
$634$	−2.55530e21	−	4.42591e21i	−0.00388762	−	0.00673355i
$635$	4.47889e23	−	7.75767e23i	0.672348	−	1.16454i
$636$	3.90591e23			0.578544
$637$	−5.23173e23	−	5.92156e23i	−0.764645	−	0.865469i
$638$	3.90814e20			0.000563631
$639$	−3.15063e21	+	5.45705e21i	−0.00448374	+	0.00776606i
$640$	−2.08617e22	−	3.61336e22i	−0.0292968	−	0.0507436i
$641$	4.41620e23	+	7.64908e23i	0.612006	+	1.06003i	0.990902	+	0.134586i	$0.0429704\pi$
$641$	4.41620e23	+	7.64908e23i	0.612006	+	1.06003i	−0.378896	+	0.925439i	$0.623696\pi$
$642$	−3.69946e20	+	6.40766e20i	−0.000505931	+	0.000876297i
$643$	9.81778e23			1.32501			0.662506	−	0.749056i	$-0.269493\pi$
$643$	9.81778e23			1.32501			0.662506	+	0.749056i	$0.269493\pi$
$644$	4.02001e23	−	8.91594e23i	0.535424	−	1.18751i
$645$	4.82497e23			0.634215
$646$	−1.68631e21	+	2.92077e21i	−0.00218756	+	0.00378897i
$647$	3.12964e23	+	5.42070e23i	0.400690	+	0.694015i	0.993809	−	0.111099i	$-0.0354372\pi$
$647$	3.12964e23	+	5.42070e23i	0.400690	+	0.694015i	−0.593120	+	0.805114i	$0.702104\pi$
$648$	−4.16092e20	−	7.20693e20i	−0.000525777	−	0.000910673i
$649$	−6.69431e22	+	1.15949e23i	−0.0834884	+	0.144606i
$650$	1.78583e22			0.0219825
$651$	2.73128e23	+	3.79673e23i	0.331839	+	0.461287i
$652$	1.25650e22			0.0150680
$653$	−4.30551e23	+	7.45736e23i	−0.509639	+	0.882720i	0.490299	+	0.871554i	$0.336888\pi$
$653$	−4.30551e23	+	7.45736e23i	−0.509639	+	0.882720i	−0.999938	+	0.0111657i	$0.996446\pi$
$654$	1.04395e21	+	1.80817e21i	0.00121974	+	0.00211265i
$655$	3.36094e23	+	5.82132e23i	0.387623	+	0.671383i
$656$	4.13204e23	−	7.15691e23i	0.470416	−	0.814784i
$657$	−2.71146e23			−0.304718
$658$	−6.90505e21	+	6.92912e20i	−0.00766032	+	0.000768701i
$659$	−8.03072e23			−0.879485			−0.439743	−	0.898124i	$-0.644930\pi$
$659$	−8.03072e23			−0.879485			−0.439743	+	0.898124i	$0.644930\pi$
$660$	−3.34737e23	+	5.79782e23i	−0.361893	+	0.626818i
$661$	−1.12511e23	−	1.94874e23i	−0.120083	−	0.207990i	0.799717	−	0.600377i	$-0.204983\pi$
$661$	−1.12511e23	−	1.94874e23i	−0.120083	−	0.207990i	−0.919800	+	0.392387i	$0.871649\pi$
$662$	1.88980e21	+	3.27323e21i	0.00199124	+	0.00344893i
$663$	−4.94971e23	+	8.57315e23i	−0.514890	+	0.891816i
$664$	1.06045e22			0.0108909
$665$	7.15753e23	−	7.18247e22i	0.725736	−	0.0728266i
$666$	3.93185e21			0.00393610
$667$	7.62822e22	−	1.32125e23i	0.0753969	−	0.130591i
$668$	−9.78130e22	−	1.69417e23i	−0.0954545	−	0.165332i
$669$	−3.62163e23	−	6.27285e23i	−0.348965	−	0.604425i
$670$	7.15464e21	−	1.23922e22i	0.00680694	−	0.0117900i
$671$	−1.77088e23			−0.166359
$672$	9.63998e21	+	1.34005e22i	0.00894206	+	0.0124303i
$673$	−3.52834e23			−0.323179			−0.161589	−	0.986858i	$-0.551662\pi$
$673$	−3.52834e23			−0.323179			−0.161589	+	0.986858i	$0.551662\pi$
$674$	3.62087e21	−	6.27154e21i	0.00327495	−	0.00567238i
$675$	−1.36563e24	−	2.36533e24i	−1.21969	−	2.11257i
$676$	1.89177e23	+	3.27664e23i	0.166848	+	0.288990i
$677$	−1.99705e23	+	3.45899e23i	−0.173934	+	0.301263i	−0.939792	−	0.341747i	$-0.888981\pi$
$677$	−1.99705e23	+	3.45899e23i	−0.173934	+	0.301263i	0.765858	+	0.643010i	$0.222315\pi$
$678$	−4.91712e21			−0.00422920
$679$	8.00653e23	−	1.77576e24i	0.680066	−	1.50831i
$680$	−4.85289e22			−0.0407076
$681$	2.88632e23	−	4.99926e23i	0.239108	−	0.414147i
$682$	2.63464e21	+	4.56333e21i	0.00215553	+	0.00373349i
$683$	1.11087e24	+	1.92409e24i	0.897610	+	1.55471i	0.830541	+	0.556958i	$0.188032\pi$
$683$	1.11087e24	+	1.92409e24i	0.897610	+	1.55471i	0.0670693	+	0.997748i	$0.478635\pi$
$684$	1.45878e23	−	2.52668e23i	0.116416	−	0.201638i
$685$	4.98193e22			0.0392670
$686$	−2.26500e21	+	9.96228e21i	−0.00176325	+	0.00775539i
$687$	−5.54682e23			−0.426493
$688$	−3.53103e23	+	6.11592e23i	−0.268163	+	0.464473i
$689$	−6.93930e23	−	1.20192e24i	−0.520538	−	0.901598i
$690$	−8.26628e21	−	1.43176e22i	−0.00612481	−	0.0106085i
$691$	−7.01162e23	+	1.21445e24i	−0.513162	+	0.888823i	0.486721	+	0.873557i	$0.338193\pi$
$691$	−7.01162e23	+	1.21445e24i	−0.513162	+	0.888823i	−0.999883	+	0.0152658i	$0.995141\pi$
$692$	−1.81662e24			−1.31330
$693$	−2.07228e23	+	4.59608e23i	−0.147984	+	0.328212i
$694$	8.35824e21			0.00589603
$695$	3.11381e23	−	5.39329e23i	0.216981	−	0.375822i
$696$	8.58340e20	+	1.48669e21i	0.000590855	+	0.00102339i
$697$	−9.61264e23	−	1.66496e24i	−0.653678	−	1.13220i
$698$	−9.84099e21	+	1.70451e22i	−0.00661101	+	0.0114506i
$699$	1.80243e24			1.19620
$700$	2.13155e24	+	2.96305e24i	1.39753	+	1.94270i
$701$	−7.91531e23			−0.512702			−0.256351	−	0.966584i	$-0.582520\pi$
$701$	−7.91531e23			−0.512702			−0.256351	+	0.966584i	$0.582520\pi$
$702$	−7.31471e21	+	1.26695e22i	−0.00468093	+	0.00810760i
$703$	−2.63527e23	−	4.56441e23i	−0.166611	−	0.288579i
$704$	−4.89876e23	−	8.48490e23i	−0.305998	−	0.530004i
$705$	9.27207e23	−	1.60597e24i	0.572228	−	0.991128i
$706$	3.38610e21			0.00206471
$707$	−1.21957e24	+	1.22382e23i	−0.734751	+	0.0737312i
$708$	−2.94043e23			−0.175036
$709$	2.19606e23	−	3.80369e23i	0.129167	−	0.223724i	−0.794187	−	0.607673i	$-0.792103\pi$
$709$	2.19606e23	−	3.80369e23i	0.129167	−	0.223724i	0.923354	+	0.383950i	$0.125436\pi$
$710$	−1.92207e20	−	3.32912e20i	−0.000111705	−	0.000193479i
$711$	4.97923e23	+	8.62428e23i	0.285937	+	0.495258i
$712$	−5.62207e21	+	9.73772e21i	−0.00319019	+	0.00552557i
$713$	2.05700e24			1.15338
$714$	1.27356e22	−	1.27800e21i	0.00705643	−	0.000708102i
$715$	2.37880e24			1.30244
$716$	−1.39904e24	+	2.42321e24i	−0.756955	+	1.31108i
$717$	7.41993e23	+	1.28517e24i	0.396722	+	0.687144i
$718$	−9.67887e21	−	1.67643e22i	−0.00511407	−	0.00885783i
$719$	−5.46164e23	+	9.45984e23i	−0.285185	+	0.493956i	−0.972654	−	0.232258i	$-0.925389\pi$
$719$	−5.46164e23	+	9.45984e23i	−0.285185	+	0.493956i	0.687469	+	0.726214i	$0.258722\pi$
$720$	2.09885e24			1.08307
$721$	−6.58102e23	−	9.14823e23i	−0.335617	−	0.466538i
$722$	−1.33063e22			−0.00670640
$723$	−6.82253e23	+	1.18170e24i	−0.339836	+	0.588614i
$724$	−1.71457e23	−	2.96973e23i	−0.0844069	−	0.146197i
$725$	2.84691e23	+	4.93100e23i	0.138516	+	0.239917i
$726$	−3.31814e21	+	5.74719e21i	−0.00159564	+	0.00276372i
$727$	−5.46273e23			−0.259637			−0.129819	−	0.991538i	$-0.541440\pi$
$727$	−5.46273e23			−0.259637			−0.129819	+	0.991538i	$0.541440\pi$
$728$	1.60727e22	−	3.56473e22i	0.00755042	−	0.0167460i
$729$	1.49263e24			0.693054
$730$	8.27075e21	−	1.43254e22i	0.00379578	−	0.00657448i
$731$	8.21447e23	+	1.42279e24i	0.372633	+	0.645420i
$732$	−1.94462e23	−	3.36818e23i	−0.0871947	−	0.151026i
$733$	−7.82533e23	+	1.35539e24i	−0.346832	+	0.600730i	−0.985685	−	0.168598i	$-0.946076\pi$
$733$	−7.82533e23	+	1.35539e24i	−0.346832	+	0.600730i	0.638853	+	0.769329i	$0.279409\pi$
$734$	−1.77203e22			−0.00776346
$735$	−1.80757e24	−	2.04591e24i	−0.782803	−	0.886021i
$736$	7.26012e22			0.0310801
$737$	6.72171e23	−	1.16423e24i	0.284450	−	0.492682i
$738$	−5.26039e21	−	9.11127e21i	−0.00220059	−	0.00381153i
$739$	−1.77055e24	−	3.06668e24i	−0.732202	−	1.26821i	−0.955940	−	0.293561i	$-0.905160\pi$
$739$	−1.77055e24	−	3.06668e24i	−0.732202	−	1.26821i	0.223739	−	0.974649i	$-0.428174\pi$
$740$	1.89590e24	−	3.28379e24i	0.775077	−	1.34247i
$741$	7.26178e23			0.293487
$742$	−7.37575e21	+	1.63586e22i	−0.00294695	+	0.00653601i
$743$	−1.72986e24			−0.683291			−0.341645	−	0.939829i	$-0.610984\pi$
$743$	−1.72986e24			−0.683291			−0.341645	+	0.939829i	$0.610984\pi$
$744$	−1.15728e22	+	2.00447e22i	−0.00451929	+	0.00782764i
$745$	5.45905e23	+	9.45535e23i	0.210760	+	0.365048i
$746$	1.67113e22	+	2.89448e22i	0.00637867	+	0.0110482i
$747$	−5.33482e23	+	9.24018e23i	−0.201324	+	0.348703i
$748$	−2.27955e24			−0.850522
$749$	3.13796e23	+	4.36205e23i	0.115758	+	0.160914i
$750$	3.59202e22			0.0131014
$751$	7.61214e23	−	1.31846e24i	0.274516	−	0.475475i	−0.695497	−	0.718529i	$-0.744816\pi$
$751$	7.61214e23	−	1.31846e24i	0.274516	−	0.475475i	0.970013	+	0.243054i	$0.0781491\pi$
$752$	1.35711e24	+	2.35058e24i	0.483907	+	0.838152i
$753$	1.64660e24	+	2.85200e24i	0.580540	+	1.00552i
$754$	1.52489e21	−	2.64119e21i	0.000531598	−	0.000920754i
$755$	−9.18636e24			−3.16661
$756$	−2.97519e24	+	2.98555e23i	−1.01410	+	0.101763i
$757$	2.95541e24			0.996099			0.498050	−	0.867149i	$-0.334050\pi$
$757$	2.95541e24			0.996099			0.498050	+	0.867149i	$0.334050\pi$
$758$	1.76359e22	−	3.05463e22i	0.00587774	−	0.0101805i
$759$	−7.76608e23	−	1.34512e24i	−0.255945	−	0.443310i
$760$	1.77994e22	+	3.08294e22i	0.00580081	+	0.0100473i
$761$	1.48378e24	−	2.56999e24i	0.478191	−	0.828250i	−0.521497	−	0.853253i	$-0.674626\pi$
$761$	1.48378e24	−	2.56999e24i	0.478191	−	0.828250i	0.999687	+	0.0250028i	$0.00795947\pi$
$762$	−1.16921e22			−0.00372627
$763$	1.50875e24	−	1.51401e23i	0.475510	−	0.0477168i
$764$	−5.30949e24			−1.65485
$765$	2.44135e24	−	4.22854e24i	0.752502	−	1.30337i
$766$	−1.74682e21	−	3.02558e21i	−0.000532480	−	0.000922282i
$767$	5.22402e23	+	9.04827e23i	0.157487	+	0.272775i
$768$	1.07567e24	−	1.86311e24i	0.320707	−	0.555481i
$769$	1.57381e24			0.464063			0.232032	−	0.972708i	$-0.425463\pi$
$769$	1.57381e24			0.464063			0.232032	+	0.972708i	$0.425463\pi$
$770$	−1.79612e22	−	2.49677e22i	−0.00523799	−	0.00728128i
$771$	−6.53408e21			−0.00188461
$772$	3.41520e24	−	5.91529e24i	0.974246	−	1.68744i
$773$	−4.12722e23	−	7.14855e23i	−0.116448	−	0.201694i	0.801910	−	0.597445i	$-0.203817\pi$
$773$	−4.12722e23	−	7.14855e23i	−0.116448	−	0.201694i	−0.918358	+	0.395752i	$0.870484\pi$
$774$	4.49526e21	+	7.78602e21i	0.00125446	+	0.00217279i
$775$	−3.83844e24	+	6.64837e24i	−1.05947	+	1.83506i
$776$	9.63973e22			0.0263172
$777$	−8.22163e23	+	1.82346e24i	−0.222013	+	0.492401i
$778$	−5.40448e22			−0.0144354
$779$	−7.05141e23	+	1.22134e24i	−0.186298	+	0.322677i
$780$	2.61218e24	+	4.52443e24i	0.682652	+	1.18239i
$781$	−1.80576e22	−	3.12767e22i	−0.00466796	−	0.00808514i
$782$	2.81465e22	−	4.87512e22i	0.00719727	−	0.0124660i
$783$	−4.66434e23			−0.117982
$784$	3.91613e24	−	7.93951e23i	0.979875	−	0.198658i
$785$	4.30469e24			1.06549
$786$	4.38684e21	−	7.59822e21i	0.00107414	−	0.00186046i
$787$	3.00849e24	+	5.21086e24i	0.728725	+	1.26219i	0.957422	+	0.288691i	$0.0932201\pi$
$787$	3.00849e24	+	5.21086e24i	0.728725	+	1.26219i	−0.228697	+	0.973498i	$0.573447\pi$
$788$	−3.97791e23	−	6.88995e23i	−0.0953197	−	0.165099i
$789$	−7.43506e23	+	1.28779e24i	−0.176250	+	0.305274i
$790$	−6.07524e22			−0.0142473
$791$	−1.46782e24	+	3.25546e24i	−0.340543	+	0.755287i
$792$	−2.49499e22			−0.00572670
$793$	−6.90968e23	+	1.19679e24i	−0.156905	+	0.271767i
$794$	1.45850e22	+	2.52619e22i	0.00327666	+	0.00567534i
$795$	−2.39754e24	−	4.15266e24i	−0.532899	−	0.923008i
$796$	2.18605e24	−	3.78636e24i	0.480728	−	0.832646i
$797$	−2.58868e24			−0.563227			−0.281613	−	0.959528i	$-0.590870\pi$
$797$	−2.58868e24			−0.563227			−0.281613	+	0.959528i	$0.590870\pi$
$798$	−5.48303e21	−	7.62192e21i	−0.00118031	−	0.00164074i
$799$	6.31425e24			1.34485
$800$	−1.35477e23	+	2.34653e23i	−0.0285496	+	0.0494494i
$801$	−5.65660e23	−	9.79752e23i	−0.117945	−	0.204287i
$802$	2.95275e22	+	5.11431e22i	0.00609178	+	0.0105513i
$803$	7.77028e23	−	1.34585e24i	0.158619	−	0.274736i
$804$	2.95247e24			0.596360
$805$	−1.19468e25	+	1.19884e24i	−2.38773	+	0.239605i
$806$	4.11197e22			0.00813209
$807$	−3.37026e23	+	5.83747e23i	−0.0659536	+	0.114235i
$808$	−3.03282e22	−	5.25300e22i	−0.00587287	−	0.0101721i
$809$	2.89414e24	+	5.01281e24i	0.554572	+	0.960547i	0.997937	+	0.0642054i	$0.0204513\pi$
$809$	2.89414e24	+	5.01281e24i	0.554572	+	0.960547i	−0.443365	+	0.896341i	$0.646215\pi$
$810$	−2.55399e21	+	4.42365e21i	−0.000484281	+	0.000838799i
$811$	6.87263e24			1.28957			0.644786	−	0.764363i	$-0.276946\pi$
$811$	6.87263e24			1.28957			0.644786	+	0.764363i	$0.276946\pi$
$812$	6.20235e23	−	6.22397e22i	0.115168	−	0.0115569i
$813$	1.65924e23			0.0304887
$814$	−1.12676e22	+	1.95160e22i	−0.00204891	+	0.00354881i
$815$	−7.71268e22	−	1.33588e23i	−0.0138792	−	0.0240395i
$816$	−2.50303e24	−	4.33538e24i	−0.445759	−	0.772078i
$817$	6.02577e23	−	1.04369e24i	0.106200	−	0.183944i
$818$	−8.35305e22			−0.0145694
$819$	2.29754e24	+	3.19380e24i	0.396598	+	0.551308i
$820$	−1.01460e25			−1.73332
$821$	1.82460e22	−	3.16030e22i	0.00308497	−	0.00534332i	−0.864479	−	0.502669i	$-0.832351\pi$
$821$	1.82460e22	−	3.16030e22i	0.00308497	−	0.00534332i	0.867564	+	0.497326i	$0.165685\pi$
$822$	−3.25131e20	−	5.63143e20i	−5.44061e−5	−	9.42341e-5i
$823$	−4.42456e24	−	7.66356e24i	−0.732776	−	1.26921i	−0.955692	−	0.294368i	$-0.904891\pi$
$823$	−4.42456e24	−	7.66356e24i	−0.732776	−	1.26921i	0.222916	−	0.974838i	$-0.428442\pi$
$824$	2.78848e22	−	4.82979e22i	0.00457074	−	0.00791675i
$825$	5.79673e24			0.940426
$826$	5.55259e21	−	1.23150e22i	0.000891590	−	0.00197745i
$827$	8.52013e24			1.35410			0.677048	−	0.735939i	$-0.263259\pi$
$827$	8.52013e24			1.35410			0.677048	+	0.735939i	$0.263259\pi$
$828$	−2.43488e24	+	4.21733e24i	−0.383018	+	0.663407i
$829$	−3.68791e24	−	6.38764e24i	−0.574204	−	0.994551i	−0.996128	−	0.0879196i	$-0.971978\pi$
$829$	−3.68791e24	−	6.38764e24i	−0.574204	−	0.994551i	0.421923	−	0.906632i	$-0.361355\pi$
$830$	−3.25455e22	−	5.63705e22i	−0.00501565	−	0.00868736i
$831$	−2.06947e24	+	3.58443e24i	−0.315683	+	0.546779i
$832$	−7.64567e24			−1.15443
$833$	2.95561e24	−	8.81331e24i	0.441738	−	1.31721i
$834$	−8.12855e21			−0.00120255
$835$	−1.20080e24	+	2.07985e24i	−0.175847	+	0.304576i
$836$	8.36089e23	+	1.44815e24i	0.121199	+	0.209923i
$837$	−3.14442e24	−	5.44630e24i	−0.451206	−	0.781511i
$838$	1.59002e22	−	2.75400e22i	0.00225855	−	0.00391191i
$839$	−1.04645e25			−1.47144			−0.735719	−	0.677287i	$-0.763156\pi$
$839$	−1.04645e25			−1.47144			−0.735719	+	0.677287i	$0.763156\pi$
$840$	5.55313e22	−	1.23162e23i	0.00772972	−	0.0171436i
$841$	−7.15991e24			−0.986601
$842$	1.87998e21	−	3.25622e21i	0.000256449	−	0.000444182i
$843$	−2.77990e24	−	4.81493e24i	−0.375400	−	0.650212i
$844$	4.43707e24	+	7.68524e24i	0.593179	+	1.02742i
$845$	2.32243e24	−	4.02257e24i	0.307369	−	0.532379i
$846$	3.45539e22			0.00452741
$847$	2.81451e24	+	3.91243e24i	0.365085	+	0.507502i
$848$	7.01831e24			0.901297
$849$	−1.94808e24	+	3.37417e24i	−0.247680	+	0.428995i
$850$	1.05045e23	+	1.81944e23i	0.0132226	+	0.0229021i
$851$	4.39858e24	+	7.61856e24i	0.548165	+	0.949449i
$852$	3.96585e22	−	6.86905e22i	0.00489327	−	0.00847539i
$853$	2.11838e24			0.258784			0.129392	−	0.991594i	$-0.458697\pi$
$853$	2.11838e24			0.258784			0.129392	+	0.991594i	$0.458697\pi$
$854$	1.77786e22	−	1.78406e21i	0.00215034	−	0.000215783i
$855$	−3.58173e24			−0.428925
$856$	−1.32960e22	+	2.30293e22i	−0.00157650	+	0.00273058i
$857$	9.17231e23	+	1.58869e24i	0.107682	+	0.186510i	0.914831	−	0.403838i	$-0.132324\pi$
$857$	9.17231e23	+	1.58869e24i	0.107682	+	0.186510i	−0.807149	+	0.590348i	$0.798991\pi$
$858$	−1.55245e22	−	2.68893e22i	−0.00180458	−	0.00312563i
$859$	2.13690e24	−	3.70122e24i	0.245948	−	0.425994i	−0.716450	−	0.697638i	$-0.754234\pi$
$859$	2.13690e24	−	3.70122e24i	0.245948	−	0.425994i	0.962398	+	0.271645i	$0.0875676\pi$
$860$	8.67027e24			0.988089
$861$	5.32548e24	−	5.34404e23i	0.600941	−	0.0603036i
$862$	9.41015e22			0.0105144
$863$	5.67624e24	−	9.83153e24i	0.628013	−	1.08775i	−0.359937	−	0.932977i	$-0.617202\pi$
$863$	5.67624e24	−	9.83153e24i	0.628013	−	1.08775i	0.987950	−	0.154774i	$-0.0494650\pi$
$864$	−1.10982e23	−	1.92226e23i	−0.0121586	−	0.0210594i
$865$	1.11509e25	+	1.93139e25i	1.20968	+	2.09523i
$866$	−1.26392e22	+	2.18917e22i	−0.00135774	+	0.00235167i
$867$	−5.61236e24			−0.597012
$868$	4.90800e24	+	6.82257e24i	0.516996	+	0.718671i
$869$	−5.70762e24			−0.595370
$870$	5.26853e21	−	9.12536e21i	0.000544222	−	0.000942620i
$871$	−5.24540e24	−	9.08530e24i	−0.536568	−	0.929362i
$872$	3.75197e22	+	6.49861e22i	0.00380075	+	0.00658310i
$873$	−4.84947e24	+	8.39953e24i	−0.486489	+	0.842624i
$874$	−4.12941e22			−0.00410243
$875$	1.07226e25	−	2.37815e25i	1.05495	−	2.33976i
$876$	3.41305e24			0.332550
$877$	−2.23677e23	+	3.87420e23i	−0.0215837	+	0.0373840i	−0.876615	−	0.481192i	$-0.840204\pi$
$877$	−2.23677e23	+	3.87420e23i	−0.0215837	+	0.0373840i	0.855032	+	0.518576i	$0.173537\pi$
$878$	−7.62314e22	−	1.32037e23i	−0.00728502	−	0.0126180i
$879$	1.06572e24	+	1.84588e24i	0.100864	+	0.174702i
$880$	−6.01472e24	+	1.04178e25i	−0.563783	+	0.976502i
$881$	1.20945e24			0.112277			0.0561387	−	0.998423i	$-0.482121\pi$
$881$	1.20945e24			0.112277			0.0561387	+	0.998423i	$0.482121\pi$
$882$	1.61742e22	−	4.82297e22i	0.00148710	−	0.00443437i
$883$	−8.54424e24			−0.778050			−0.389025	−	0.921227i	$-0.627188\pi$
$883$	−8.54424e24			−0.778050			−0.389025	+	0.921227i	$0.627188\pi$
$884$	−8.89443e24	+	1.54056e25i	−0.802184	+	1.38942i
$885$	1.80491e24	+	3.12619e24i	0.161227	+	0.279253i
$886$	3.73992e22	+	6.47774e22i	0.00330884	+	0.00573108i
$887$	−2.56176e24	+	4.43709e24i	−0.224485	+	0.388819i	−0.956165	−	0.292829i	$-0.905403\pi$
$887$	−2.56176e24	+	4.43709e24i	−0.224485	+	0.388819i	0.731680	+	0.681648i	$0.238737\pi$
$888$	−9.89871e22			−0.00859149
$889$	−3.49022e24	+	7.74091e24i	−0.300046	+	0.665468i
$890$	6.90171e22			0.00587681
$891$	−2.39945e23	+	4.15597e23i	−0.0202372	+	0.0350519i
$892$	−6.50792e24	−	1.12721e25i	−0.543677	−	0.941677i
$893$	−2.31593e24	−	4.01131e24i	−0.191641	−	0.331932i
$894$	7.12537e21	−	1.23415e22i	0.000584035	−	0.00101158i
$895$	3.43506e25			2.78894
$896$	2.30966e23	+	3.21065e23i	0.0185751	+	0.0258211i
$897$	−1.21208e25			−0.965596
$898$	3.25046e22	−	5.62996e22i	0.00256505	−	0.00444279i
$899$	6.55516e23	+	1.13539e24i	0.0512420	+	0.0887537i
$900$	−9.08717e24	−	1.57394e25i	−0.703667	−	1.21879i
$901$	8.16358e24	−	1.41397e25i	0.626210	−	1.08463i
$902$	6.02992e22			0.00458201
$903$	−4.55088e24	+	4.56674e23i	−0.342570	+	0.0343764i
$904$	−1.76723e23			−0.0131784
$905$	−2.10489e24	+	3.64578e24i	−0.155495	+	0.269325i
$906$	5.99520e22	+	1.03840e23i	0.00438747	+	0.00759932i
$907$	−1.20304e25	−	2.08372e25i	−0.872202	−	1.51070i	−0.859714	−	0.510776i	$-0.829358\pi$
$907$	−1.20304e25	−	2.08372e25i	−0.872202	−	1.51070i	−0.0124878	−	0.999922i	$-0.503975\pi$
$908$	5.18661e24	−	8.98347e24i	0.372523	−	0.645230i
$909$	6.10289e24			0.434253
$910$	−2.38818e23	+	2.39650e22i	−0.0168351	+	0.00168938i
$911$	4.66378e24			0.325711			0.162855	−	0.986650i	$-0.447930\pi$
$911$	4.66378e24			0.325711			0.162855	+	0.986650i	$0.447930\pi$
$912$	−1.83612e24	+	3.18025e24i	−0.127041	+	0.220042i
$913$	−3.05762e24	−	5.29595e24i	−0.209595	−	0.363030i
$914$	4.78797e22	+	8.29301e22i	0.00325169	+	0.00563209i
$915$	−2.38731e24	+	4.13493e24i	−0.160631	+	0.278221i
$916$	−9.96742e24			−0.664464
$917$	−3.72100e24	−	5.17253e24i	−0.245765	−	0.341636i
$918$	−1.72105e23			−0.0112624
$919$	−1.21514e25	+	2.10469e25i	−0.787853	+	1.36460i	0.139427	+	0.990232i	$0.455474\pi$
$919$	−1.21514e25	+	2.10469e25i	−0.787853	+	1.36460i	−0.927280	+	0.374369i	$0.877859\pi$
$920$	−2.97093e23	−	5.14580e23i	−0.0190851	−	0.0330564i
$921$	5.33790e24	+	9.24551e24i	0.339753	+	0.588470i
$922$	−7.07494e22	+	1.22542e23i	−0.00446180	+	0.00772806i
$923$	−2.81832e23			−0.0176106
$924$	2.60847e24	−	5.78529e24i	0.161501	−	0.358190i
$925$	−3.28317e25			−2.01414
$926$	2.92437e22	−	5.06516e22i	0.00177762	−	0.00307893i
$927$	2.80561e24	+	4.85945e24i	0.168985	+	0.292691i
$928$	2.31363e22	+	4.00732e22i	0.00138082	+	0.00239164i
$929$	−1.23279e25	+	2.13525e25i	−0.729044	+	1.26274i	0.228243	+	0.973604i	$0.426702\pi$
$929$	−1.23279e25	+	2.13525e25i	−0.729044	+	1.26274i	−0.957288	+	0.289138i	$0.906631\pi$
$930$	1.42069e23			0.00832521
$931$	−6.68296e24	+	1.35489e24i	−0.388058	+	0.0786743i
$932$	3.23889e25			1.86364
$933$	5.25580e24	−	9.10331e24i	0.299671	−	0.519045i
$934$	3.57899e22	+	6.19899e22i	0.00202214	+	0.00350245i
$935$	1.39924e25	+	2.42356e25i	0.783420	+	1.35692i
$936$	−9.73504e22	+	1.68616e23i	−0.00540123	+	0.00935521i
$937$	8.44191e24			0.464146			0.232073	−	0.972698i	$-0.425449\pi$
$937$	8.44191e24			0.464146			0.232073	+	0.972698i	$0.425449\pi$
$938$	−5.57532e22	+	1.23654e23i	−0.00303770	+	0.00673728i
$939$	1.65781e25			0.895111
$940$	1.66615e25	−	2.88586e25i	0.891515	−	1.54415i
$941$	−1.63087e25	−	2.82474e25i	−0.864782	−	1.49785i	−0.867264	−	0.497849i	$-0.834123\pi$
$941$	−1.63087e25	−	2.82474e25i	−0.864782	−	1.49785i	0.00248160	−	0.999997i	$-0.499210\pi$
$942$	−2.80932e22	−	4.86589e22i	−0.00147628	−	0.00255699i
$943$	1.17697e25	−	2.03857e25i	0.612935	−	1.06163i
$944$	−5.28351e24			−0.272684
$945$	2.14366e25	+	2.97988e25i	1.09644	+	1.52415i
$946$	−5.15286e22			−0.00261200
$947$	−7.39992e24	+	1.28170e25i	−0.371751	+	0.643891i	−0.989835	−	0.142221i	$-0.954576\pi$
$947$	−7.39992e24	+	1.28170e25i	−0.371751	+	0.643891i	0.618084	+	0.786112i	$0.287909\pi$
$948$	−6.26759e24	−	1.08558e25i	−0.312054	−	0.540493i
$949$	−6.06368e24	−	1.05026e25i	−0.299208	−	0.518244i
$950$	7.70565e22	−	1.33466e23i	0.00376842	−	0.00652709i
$951$	−1.29453e25			−0.627450
$952$	4.57722e23	−	4.59317e22i	0.0219881	−	0.00220647i
$953$	3.07423e25			1.46368			0.731840	−	0.681476i	$-0.238662\pi$
$953$	3.07423e25			1.46368			0.731840	+	0.681476i	$0.238662\pi$
$954$	4.46742e22	−	7.73779e22i	0.00210812	−	0.00365137i
$955$	3.25910e25	+	5.64492e25i	1.52429	+	2.64015i
$956$	1.33333e25	+	2.30940e25i	0.618082	+	1.07055i
$957$	4.94973e23	−	8.57318e23i	0.0227421	−	0.0393904i
$958$	8.85070e21			0.000403061
$959$	−4.69893e23	+	4.71530e22i	−0.0212100	+	0.00212839i
$960$	−2.64159e25			−1.18184
$961$	2.43685e24	−	4.22076e24i	0.108064	−	0.187172i
$962$	8.79283e22	+	1.52296e23i	0.00386492	+	0.00669424i
$963$	−1.33777e24	−	2.31708e24i	−0.0582850	−	0.100953i
$964$	−1.22598e25	+	2.12346e25i	−0.529455	+	0.917043i
$965$	−8.38532e25			−3.58953
$966$	9.15184e22	+	1.27219e23i	0.00388332	+	0.00539817i
$967$	1.62622e25			0.683995			0.341998	−	0.939701i	$-0.388897\pi$
$967$	1.62622e25			0.683995			0.341998	+	0.939701i	$0.388897\pi$
$968$	−1.19255e23	+	2.06556e23i	−0.00497206	+	0.00861187i
$969$	4.27148e24	+	7.39842e24i	0.176533	+	0.305764i
$970$	−2.95846e23	−	5.12420e23i	−0.0121201	−	0.0209926i
$971$	1.84471e25	−	3.19513e25i	0.749143	−	1.29755i	−0.199092	−	0.979981i	$-0.563799\pi$
$971$	1.84471e25	−	3.19513e25i	0.749143	−	1.29755i	0.948234	−	0.317572i	$-0.102868\pi$
$972$	2.42634e25			0.976761
$973$	−2.42647e24	+	5.38163e24i	−0.0968312	+	0.214761i
$974$	1.99798e23			0.00790387
$975$	2.26179e25	−	3.91753e25i	0.886978	−	1.53629i
$976$	−3.49418e24	−	6.05210e24i	−0.135838	−	0.235279i
$977$	−9.08695e24	−	1.57391e25i	−0.350199	−	0.606562i	0.636085	−	0.771619i	$-0.280553\pi$
$977$	−9.08695e24	−	1.57391e25i	−0.350199	−	0.606562i	−0.986284	+	0.165057i	$0.947219\pi$
$978$	−1.00669e21	+	1.74364e21i	−3.84605e−5	+	6.66156e-5i
$979$	6.48409e24			0.245582
$980$	−3.24813e25	−	3.67642e25i	−1.21958	−	1.38039i
$981$	−7.55004e24			−0.281036
$982$	1.07163e23	−	1.85612e23i	0.00395455	−	0.00684948i
$983$	5.26385e23	+	9.11725e23i	0.0192574	+	0.0333548i	0.875494	−	0.483230i	$-0.160536\pi$
$983$	5.26385e23	+	9.11725e23i	0.0192574	+	0.0333548i	−0.856236	+	0.516585i	$0.827203\pi$
$984$	1.32434e23	+	2.29383e23i	0.00480332	+	0.00831960i
$985$	−4.88348e24	+	8.45843e24i	−0.175599	+	0.304146i
$986$	3.58785e22			0.00127903
$987$	−7.22535e24	+	1.60250e25i	−0.255366	+	0.566373i
$988$	1.30491e25			0.457244
$989$	−1.00577e25	+	1.74205e25i	−0.349407	+	0.605191i
$990$	7.65718e22	+	1.32626e23i	0.00263736	+	0.00456804i
$991$	−4.27416e24	−	7.40307e24i	−0.145957	−	0.252805i	0.783773	−	0.621048i	$-0.213293\pi$
$991$	−4.27416e24	−	7.40307e24i	−0.145957	−	0.252805i	−0.929730	+	0.368243i	$0.879959\pi$
$992$	−3.11942e23	+	5.40300e23i	−0.0105615	+	0.0182930i
$993$	9.57387e24			0.321380
$994$	2.12798e21	+	2.95809e21i	7.08244e−5	+	9.84524e-5i
$995$	−5.36741e25			−1.77120
$996$	6.71519e24	−	1.16310e25i	0.219712	−	0.380552i
$997$	6.20290e24	+	1.07437e25i	0.201227	+	0.348535i	0.948924	−	0.315505i	$-0.102174\pi$
$997$	6.20290e24	+	1.07437e25i	0.201227	+	0.348535i	−0.747697	+	0.664040i	$0.768840\pi$
$998$	−1.97543e23	−	3.42155e23i	−0.00635407	−	0.0110056i
$999$	1.34478e25	−	2.32922e25i	0.428887	−	0.742854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.c.a.2.6	✓	20
7.2	even	3		49.18.a.f.1.5		10
7.4	even	3	inner	7.18.c.a.4.6	yes	20
7.5	odd	6		49.18.a.g.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.c.a.2.6	✓	20	1.1	even	1	trivial
7.18.c.a.4.6	yes	20	7.4	even	3	inner
49.18.a.f.1.5		10	7.2	even	3
49.18.a.g.1.5		10	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43970 + 2.49364i) q^{2} +(3646.82 + 6316.47i) q^{3} +(65531.9 + 113505. i) q^{4} +(804501. - 1.39344e6i) q^{5} -21001.3 q^{6} +(-6.26914e6 + 1.39043e7i) q^{7} -754795. q^{8} +(3.79715e7 - 6.57686e7i) q^{9} +O(q^{10})\)	\(q+(-1.43970 + 2.49364i) q^{2} +(3646.82 + 6316.47i) q^{3} +(65531.9 + 113505. i) q^{4} +(804501. - 1.39344e6i) q^{5} -21001.3 q^{6} +(-6.26914e6 + 1.39043e7i) q^{7} -754795. q^{8} +(3.79715e7 - 6.57686e7i) q^{9} +(2.31648e6 + 4.01227e6i) q^{10} +(2.17631e8 + 3.76948e8i) q^{11} +(-4.77965e8 + 8.27860e8i) q^{12} +3.39665e9 q^{13} +(-2.56465e7 - 3.56510e7i) q^{14} +1.17355e10 q^{15} +(-8.58830e9 + 1.48754e10i) q^{16} +(1.99795e10 + 3.46056e10i) q^{17} +(1.09335e8 + 1.89375e8i) q^{18} +(1.46561e10 - 2.53851e10i) q^{19} +2.10882e11 q^{20} +(-1.10688e11 + 1.11074e10i) q^{21} -1.25330e9 q^{22} +(-2.44628e11 + 4.23709e11i) q^{23} +(-2.75260e9 - 4.76764e9i) q^{24} +(-9.12973e11 - 1.58132e12i) q^{25} +(-4.89016e9 + 8.47001e9i) q^{26} +1.49580e12 q^{27} +(-1.98902e12 + 1.99596e11i) q^{28} -3.11829e11 q^{29} +(-1.68956e10 + 2.92640e10i) q^{30} +(-2.10217e12 - 3.64106e12i) q^{31} +(-7.41955e10 - 1.28510e11i) q^{32} +(-1.58732e12 + 2.74932e12i) q^{33} -1.15058e11 q^{34} +(1.43312e13 + 1.99216e13i) q^{35} +9.95338e12 q^{36} +(8.99033e12 - 1.55717e13i) q^{37} +(4.22009e10 + 7.30941e10i) q^{38} +(1.23869e13 + 2.14548e13i) q^{39} +(-6.07233e11 + 1.05176e12i) q^{40} -4.81124e13 q^{41} +(1.31660e11 - 2.92008e11i) q^{42} +4.11144e13 q^{43} +(-2.85236e13 + 4.94043e13i) q^{44} +(-6.10963e13 - 1.05822e14i) q^{45} +(-7.04384e11 - 1.22003e12i) q^{46} +(7.90090e13 - 1.36848e14i) q^{47} -1.25280e14 q^{48} +(-1.54026e14 - 1.74336e14i) q^{49} +5.25764e12 q^{50} +(-1.45723e14 + 2.52400e14i) q^{51} +(2.22589e14 + 3.85535e14i) q^{52} +(-2.04299e14 - 3.53855e14i) q^{53} +(-2.15351e12 + 3.72999e12i) q^{54} +7.00338e14 q^{55} +(4.73192e12 - 1.04949e13i) q^{56} +2.13793e14 q^{57} +(4.48941e11 - 7.77588e11i) q^{58} +(1.53799e14 + 2.66388e14i) q^{59} +(7.69047e14 + 1.33203e15i) q^{60} +(-2.03427e14 + 3.52345e14i) q^{61} +1.21060e13 q^{62} +(6.76415e14 + 9.40279e14i) q^{63} -2.25095e15 q^{64} +(2.73260e15 - 4.73301e15i) q^{65} +(-4.57055e12 - 7.91642e12i) q^{66} +(-1.54429e15 - 2.67479e15i) q^{67} +(-2.61859e15 + 4.53554e15i) q^{68} -3.56846e15 q^{69} +(-7.03100e13 + 7.05550e12i) q^{70} -8.29735e13 q^{71} +(-2.86607e13 + 4.96418e13i) q^{72} +(-1.78519e15 - 3.09205e15i) q^{73} +(2.58868e13 + 4.48373e13i) q^{74} +(6.65889e15 - 1.15335e16i) q^{75} +3.84177e15 q^{76} +(-6.60555e15 + 6.62857e14i) q^{77} -7.13341e13 q^{78} +(-6.55653e15 + 1.13562e16i) q^{79} +(1.38186e16 + 2.39345e16i) q^{80} +(5.51265e14 + 9.54819e14i) q^{81} +(6.92676e13 - 1.19975e14i) q^{82} -1.40495e16 q^{83} +(-8.51435e15 - 1.18357e16i) q^{84} +6.42942e16 q^{85} +(-5.91925e13 + 1.02524e14i) q^{86} +(-1.13718e15 - 1.96966e15i) q^{87} +(-1.64267e14 - 2.84519e14i) q^{88} +(7.44848e15 - 1.29011e16i) q^{89} +3.51842e14 q^{90} +(-2.12941e16 + 4.72279e16i) q^{91} -6.41238e16 q^{92} +(1.53324e16 - 2.65565e16i) q^{93} +(2.27499e14 + 3.94040e14i) q^{94} +(-2.35817e16 - 4.08447e16i) q^{95} +(5.41154e14 - 9.37307e14i) q^{96} -1.27713e17 q^{97} +(6.56482e14 - 1.33094e14i) q^{98} +3.30552e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9}+O(q^{10}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9} + 222553738 q^{10} - 148256184 q^{11} + 2808533140 q^{12} + 3578734040 q^{13} + 25683984606 q^{14} - 26900793736 q^{15} - 50209759472 q^{16} + 15259176570 q^{17} + 81764237020 q^{18} - 71656970872 q^{19} - 180641544216 q^{20} - 669146889614 q^{21} + 1499692748380 q^{22} - 316306503180 q^{23} + 694489934496 q^{24} + 591325905568 q^{25} + 4488505674324 q^{26} - 11473086373360 q^{27} + 2858273469380 q^{28} + 284876854680 q^{29} - 9357829097258 q^{30} - 1607821082076 q^{31} + 18893460602400 q^{32} + 9589772011550 q^{33} - 32628298247940 q^{34} - 103506510744 q^{35} + 76724663114416 q^{36} + 5528585266950 q^{37} - 15690283928010 q^{38} + 28451541414128 q^{39} - 91022360866896 q^{40} - 66727631114424 q^{41} - 74393390286880 q^{42} - 93028396916240 q^{43} + 162849953080692 q^{44} + 8592264491540 q^{45} - 563088234018354 q^{46} + 162460135616460 q^{47} + 16\!\cdots\!20 q^{48}+ \cdots + 92\!\cdots\!80 q^{99}+O(q^{100}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9 + 222553738 * q^10 - 148256184 * q^11 + 2808533140 * q^12 + 3578734040 * q^13 + 25683984606 * q^14 - 26900793736 * q^15 - 50209759472 * q^16 + 15259176570 * q^17 + 81764237020 * q^18 - 71656970872 * q^19 - 180641544216 * q^20 - 669146889614 * q^21 + 1499692748380 * q^22 - 316306503180 * q^23 + 694489934496 * q^24 + 591325905568 * q^25 + 4488505674324 * q^26 - 11473086373360 * q^27 + 2858273469380 * q^28 + 284876854680 * q^29 - 9357829097258 * q^30 - 1607821082076 * q^31 + 18893460602400 * q^32 + 9589772011550 * q^33 - 32628298247940 * q^34 - 103506510744 * q^35 + 76724663114416 * q^36 + 5528585266950 * q^37 - 15690283928010 * q^38 + 28451541414128 * q^39 - 91022360866896 * q^40 - 66727631114424 * q^41 - 74393390286880 * q^42 - 93028396916240 * q^43 + 162849953080692 * q^44 + 8592264491540 * q^45 - 563088234018354 * q^46 + 162460135616460 * q^47 + 1626223055746720 * q^48 + 37188390461684 * q^49 - 156105592028976 * q^50 - 41571323179104 * q^51 - 664578572037800 * q^52 + 349838159677350 * q^53 - 2197621449925058 * q^54 - 630210277345912 * q^55 - 3391192609585536 * q^56 + 3387478208982380 * q^57 + 1117009291618900 * q^58 + 2898325666051656 * q^59 + 1851302466771436 * q^60 + 4829263771794542 * q^61 - 12440234322280740 * q^62 + 1252577979478000 * q^63 + 2254847316158720 * q^64 + 2323606775562324 * q^65 + 7963993945620406 * q^66 + 1327703510619200 * q^67 + 570001815036780 * q^68 - 19909363410939516 * q^69 - 17777971289904490 * q^70 + 15480661755189216 * q^71 + 16233423509033760 * q^72 - 3163858704730590 * q^73 - 4018632851551110 * q^74 - 8119026314209112 * q^75 - 14641245177256376 * q^76 - 46825571816043510 * q^77 + 48702643123708840 * q^78 + 40826108816616316 * q^79 + 90814104963906864 * q^80 - 69159481630723930 * q^81 + 21247223257167740 * q^82 + 10623055038659280 * q^83 - 178832833754555092 * q^84 + 51769432859611308 * q^85 + 113956439761484328 * q^86 + 171557044814594000 * q^87 - 117726124940340000 * q^88 + 31115179936936434 * q^89 - 503037784464315176 * q^90 - 219799610507722112 * q^91 + 208501803198310920 * q^92 + 257332309943680890 * q^93 + 405400048855155726 * q^94 - 22431094320108540 * q^95 + 232620528206160416 * q^96 - 702800336503765080 * q^97 - 760473415304075970 * q^98 + 928280307128172080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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