LMFDB - Embedded newform 7.18.c.a.2.9

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			2.9
Root			$134.761 - 233.413i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.18.c.a.4.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(282.522 - 489.343i) q^{2} +(11021.2 + 19089.3i) q^{3} +(-94101.8 - 162989. i) q^{4} +(-274540. + 475518. i) q^{5} +1.24550e7 q^{6} +(-6.98844e6 + 1.35570e7i) q^{7} -3.22819e7 q^{8} +(-1.78365e8 + 3.08938e8i) q^{9} +O(q^{10})$	\(q+(282.522 - 489.343i) q^{2} +(11021.2 + 19089.3i) q^{3} +(-94101.8 - 162989. i) q^{4} +(-274540. + 475518. i) q^{5} +1.24550e7 q^{6} +(-6.98844e6 + 1.35570e7i) q^{7} -3.22819e7 q^{8} +(-1.78365e8 + 3.08938e8i) q^{9} +(1.55128e8 + 2.68689e8i) q^{10} +(6.19681e7 + 1.07332e8i) q^{11} +(2.07424e9 - 3.59268e9i) q^{12} +2.37982e9 q^{13} +(4.65963e9 + 7.24990e9i) q^{14} -1.21031e10 q^{15} +(3.21375e9 - 5.56638e9i) q^{16} +(-3.28597e9 - 5.69147e9i) q^{17} +(1.00784e11 + 1.74564e11i) q^{18} +(4.41305e10 - 7.64363e10i) q^{19} +1.03339e11 q^{20} +(-3.35815e11 + 1.60102e10i) q^{21} +7.00295e10 q^{22} +(9.89224e10 - 1.71339e11i) q^{23} +(-3.55786e11 - 6.16240e11i) q^{24} +(2.30725e11 + 3.99627e11i) q^{25} +(6.72354e11 - 1.16455e12i) q^{26} -5.01665e12 q^{27} +(2.86727e12 - 1.36699e11i) q^{28} +3.09897e12 q^{29} +(-3.41940e12 + 5.92257e12i) q^{30} +(2.89538e10 + 5.01494e10i) q^{31} +(-3.93154e12 - 6.80963e12i) q^{32} +(-1.36593e12 + 2.36586e12i) q^{33} -3.71344e12 q^{34} +(-4.52799e12 - 7.04507e12i) q^{35} +6.71380e13 q^{36} +(-1.21854e13 + 2.11057e13i) q^{37} +(-2.49357e13 - 4.31899e13i) q^{38} +(2.62286e13 + 4.54293e13i) q^{39} +(8.86268e12 - 1.53506e13i) q^{40} +1.39808e13 q^{41} +(-8.70409e13 + 1.68852e14i) q^{42} -1.30947e13 q^{43} +(1.16626e13 - 2.02003e13i) q^{44} +(-9.79369e13 - 1.69632e14i) q^{45} +(-5.58956e13 - 9.68140e13i) q^{46} +(5.50751e13 - 9.53928e13i) q^{47} +1.41678e14 q^{48} +(-1.34954e14 - 1.89485e14i) q^{49} +2.60740e14 q^{50} +(7.24309e13 - 1.25454e14i) q^{51} +(-2.23946e14 - 3.87885e14i) q^{52} +(-3.94894e13 - 6.83977e13i) q^{53} +(-1.41732e15 + 2.45487e15i) q^{54} -6.80510e13 q^{55} +(2.25600e14 - 4.37646e14i) q^{56} +1.94549e15 q^{57} +(8.75528e14 - 1.51646e15i) q^{58} +(6.64148e14 + 1.15034e15i) q^{59} +(1.13892e15 + 1.97267e15i) q^{60} +(6.98772e14 - 1.21031e15i) q^{61} +3.27204e13 q^{62} +(-2.94177e15 - 4.57709e15i) q^{63} -3.60053e15 q^{64} +(-6.53358e14 + 1.13165e15i) q^{65} +(7.71812e14 + 1.33682e15i) q^{66} +(7.25266e14 + 1.25620e15i) q^{67} +(-6.18431e14 + 1.07115e15i) q^{68} +4.36099e15 q^{69} +(-4.72671e15 + 2.25349e14i) q^{70} -2.96069e15 q^{71} +(5.75797e15 - 9.97309e15i) q^{72} +(-4.39057e15 - 7.60469e15i) q^{73} +(6.88529e15 + 1.19257e16i) q^{74} +(-5.08575e15 + 8.80878e15i) q^{75} -1.66110e16 q^{76} +(-1.88816e15 + 9.00193e13i) q^{77} +2.96407e16 q^{78} +(-5.31440e15 + 9.20482e15i) q^{79} +(1.76461e15 + 3.05639e15i) q^{80} +(-3.22556e16 - 5.58684e16i) q^{81} +(3.94989e15 - 6.84141e15i) q^{82} +3.04847e16 q^{83} +(3.42103e16 + 5.32277e16i) q^{84} +3.60852e15 q^{85} +(-3.69955e15 + 6.40780e15i) q^{86} +(3.41545e16 + 5.91573e16i) q^{87} +(-2.00045e15 - 3.46488e15i) q^{88} +(2.49305e16 - 4.31808e16i) q^{89} -1.10677e17 q^{90} +(-1.66313e16 + 3.22633e16i) q^{91} -3.72351e16 q^{92} +(-6.38213e14 + 1.10542e15i) q^{93} +(-3.11199e16 - 5.39012e16i) q^{94} +(2.42312e16 + 4.19697e16i) q^{95} +(8.66609e16 - 1.50101e17i) q^{96} +4.40038e16 q^{97} +(-1.30850e17 + 1.25052e16i) q^{98} -4.42118e16 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 $

$2$	282.522	−	489.343i	0.780365	−	1.35163i	−0.151364	−	0.988478i	$-0.548367\pi$
$2$	282.522	−	489.343i	0.780365	−	1.35163i	0.931729	−	0.363154i	$-0.118300\pi$
$3$	11021.2	+	19089.3i	0.969839	+	1.67981i	0.696010	+	0.718032i	$0.254957\pi$
$3$	11021.2	+	19089.3i	0.969839	+	1.67981i	0.273829	+	0.961778i	$0.411710\pi$
$4$	−94101.8	−	162989.i	−0.717940	−	1.24351i
$5$	−274540.	+	475518.i	−0.314312	+	0.544404i	−0.979291	−	0.202458i	$-0.935107\pi$
$5$	−274540.	+	475518.i	−0.314312	+	0.544404i	0.664979	+	0.746862i	$0.268440\pi$
$6$	1.24550e7			3.02731
$7$	−6.98844e6	+	1.35570e7i	−0.458191	+	0.888854i
$7$	−6.98844e6	+	1.35570e7i	−0.458191	+	0.888854i
$8$	−3.22819e7			−0.680290
$9$	−1.78365e8	+	3.08938e8i	−1.38118	+	2.39227i
$10$	1.55128e8	+	2.68689e8i	0.490556	+	0.849669i
$11$	6.19681e7	+	1.07332e8i	0.0871627	+	0.150970i	0.906311	−	0.422612i	$-0.138887\pi$
$11$	6.19681e7	+	1.07332e8i	0.0871627	+	0.150970i	−0.819148	+	0.573582i	$0.805553\pi$
$12$	2.07424e9	−	3.59268e9i	1.39257	−	2.41201i
$13$	2.37982e9			0.809145			0.404573	−	0.914506i	$-0.367420\pi$
$13$	2.37982e9			0.809145			0.404573	+	0.914506i	$0.367420\pi$
$14$	4.65963e9	+	7.24990e9i	0.843847	+	1.31294i
$15$	−1.21031e10			−1.21933
$16$	3.21375e9	−	5.56638e9i	0.187065	−	0.324006i
$17$	−3.28597e9	−	5.69147e9i	−0.114248	−	0.197883i	0.803231	−	0.595668i	$-0.203112\pi$
$17$	−3.28597e9	−	5.69147e9i	−0.114248	−	0.197883i	−0.917479	+	0.397785i	$0.869779\pi$
$18$	1.00784e11	+	1.74564e11i	2.15564	+	3.73368i
$19$	4.41305e10	−	7.64363e10i	0.596120	−	1.03251i	−0.397268	−	0.917703i	$-0.630042\pi$
$19$	4.41305e10	−	7.64363e10i	0.596120	−	1.03251i	0.993388	−	0.114807i	$-0.0366249\pi$
$20$	1.03339e11			0.902628
$21$	−3.35815e11	+	1.60102e10i	−1.93748	+	0.0923706i
$22$	7.00295e10			0.272075
$23$	9.89224e10	−	1.71339e11i	0.263395	−	0.456214i	−0.703747	−	0.710451i	$-0.748491\pi$
$23$	9.89224e10	−	1.71339e11i	0.263395	−	0.456214i	0.967142	+	0.254237i	$0.0818243\pi$
$24$	−3.55786e11	−	6.16240e11i	−0.659772	−	1.14276i
$25$	2.30725e11	+	3.99627e11i	0.302416	+	0.523800i
$26$	6.72354e11	−	1.16455e12i	0.631429	−	1.09367i
$27$	−5.01665e12			−3.41839
$28$	2.86727e12	−	1.36699e11i	1.43425	−	0.0683789i
$29$	3.09897e12			1.15036			0.575181	−	0.818026i	$-0.304932\pi$
$29$	3.09897e12			1.15036			0.575181	+	0.818026i	$0.304932\pi$
$30$	−3.41940e12	+	5.92257e12i	−0.951522	+	1.64808i
$31$	2.89538e10	+	5.01494e10i	0.00609720	+	0.0105607i	0.869058	−	0.494710i	$-0.164726\pi$
$31$	2.89538e10	+	5.01494e10i	0.00609720	+	0.0105607i	−0.862961	+	0.505271i	$0.831393\pi$
$32$	−3.93154e12	−	6.80963e12i	−0.632103	−	1.09483i
$33$	−1.36593e12	+	2.36586e12i	−0.169068	+	0.292834i
$34$	−3.71344e12			−0.356620
$35$	−4.52799e12	−	7.04507e12i	−0.339881	−	0.528819i
$36$	6.71380e13			3.96640
$37$	−1.21854e13	+	2.11057e13i	−0.570328	+	0.987837i	0.426204	+	0.904627i	$0.359850\pi$
$37$	−1.21854e13	+	2.11057e13i	−0.570328	+	0.987837i	−0.996532	+	0.0832098i	$0.973483\pi$
$38$	−2.49357e13	−	4.31899e13i	−0.930382	−	1.61147i
$39$	2.62286e13	+	4.54293e13i	0.784741	+	1.35921i
$40$	8.86268e12	−	1.53506e13i	0.213823	−	0.370353i
$41$	1.39808e13			0.273445			0.136722	−	0.990609i	$-0.456343\pi$
$41$	1.39808e13			0.273445			0.136722	+	0.990609i	$0.456343\pi$
$42$	−8.70409e13	+	1.68852e14i	−1.38709	+	2.69084i
$43$	−1.30947e13			−0.170849			−0.0854247	−	0.996345i	$-0.527225\pi$
$43$	−1.30947e13			−0.170849			−0.0854247	+	0.996345i	$0.527225\pi$
$44$	1.16626e13	−	2.02003e13i	0.125155	−	0.216775i
$45$	−9.79369e13	−	1.69632e14i	−0.868240	−	1.50384i
$46$	−5.58956e13	−	9.68140e13i	−0.411089	−	0.712027i
$47$	5.50751e13	−	9.53928e13i	0.337383	−	0.584365i	−0.646557	−	0.762866i	$-0.723792\pi$
$47$	5.50751e13	−	9.53928e13i	0.337383	−	0.584365i	0.983940	+	0.178501i	$0.0571249\pi$
$48$	1.41678e14			0.725692
$49$	−1.34954e14	−	1.89485e14i	−0.580122	−	0.814530i
$50$	2.60740e14			0.943979
$51$	7.24309e13	−	1.25454e14i	0.221604	−	0.383829i
$52$	−2.23946e14	−	3.87885e14i	−0.580917	−	1.00618i
$53$	−3.94894e13	−	6.83977e13i	−0.0871236	−	0.150903i	0.819171	−	0.573550i	$-0.194434\pi$
$53$	−3.94894e13	−	6.83977e13i	−0.0871236	−	0.150903i	−0.906294	+	0.422647i	$0.861101\pi$
$54$	−1.41732e15	+	2.45487e15i	−2.66760	+	4.62041i
$55$	−6.80510e13			−0.109585
$56$	2.25600e14	−	4.37646e14i	0.311703	−	0.604678i
$57$	1.94549e15			2.31256
$58$	8.75528e14	−	1.51646e15i	0.897702	−	1.55487i
$59$	6.64148e14	+	1.15034e15i	0.588875	+	1.01996i	0.994380	+	0.105868i	$0.0337622\pi$
$59$	6.64148e14	+	1.15034e15i	0.588875	+	1.01996i	−0.405506	+	0.914093i	$0.632905\pi$
$60$	1.13892e15	+	1.97267e15i	0.875404	+	1.51624i
$61$	6.98772e14	−	1.21031e15i	0.466694	−	0.808337i	−0.532582	−	0.846378i	$-0.678778\pi$
$61$	6.98772e14	−	1.21031e15i	0.466694	−	0.808337i	0.999276	+	0.0380409i	$0.0121117\pi$
$62$	3.27204e13			0.0190322
$63$	−2.94177e15	−	4.57709e15i	−1.49353	−	2.32378i
$64$	−3.60053e15			−1.59895
$65$	−6.53358e14	+	1.13165e15i	−0.254324	+	0.440502i
$66$	7.71812e14	+	1.33682e15i	0.263869	+	0.457034i
$67$	7.25266e14	+	1.25620e15i	0.218203	+	0.377939i	0.954259	−	0.298982i	$-0.0966470\pi$
$67$	7.25266e14	+	1.25620e15i	0.218203	+	0.377939i	−0.736055	+	0.676921i	$0.763314\pi$
$68$	−6.18431e14	+	1.07115e15i	−0.164046	+	0.284136i
$69$	4.36099e15			1.02180
$70$	−4.72671e15	+	2.25349e14i	−0.980000	+	0.0467222i
$71$	−2.96069e15			−0.544124			−0.272062	−	0.962280i	$-0.587706\pi$
$71$	−2.96069e15			−0.544124			−0.272062	+	0.962280i	$0.587706\pi$
$72$	5.75797e15	−	9.97309e15i	0.939600	−	1.62744i
$73$	−4.39057e15	−	7.60469e15i	−0.637201	−	1.10367i	−0.986044	−	0.166484i	$-0.946759\pi$
$73$	−4.39057e15	−	7.60469e15i	−0.637201	−	1.10367i	0.348843	−	0.937181i	$-0.386575\pi$
$74$	6.88529e15	+	1.19257e16i	0.890128	+	1.54175i
$75$	−5.08575e15	+	8.80878e15i	−0.586589	+	1.01600i
$76$	−1.66110e16			−1.71191
$77$	−1.88816e15	+	9.00193e13i	−0.174128	+	0.00830165i
$78$	2.96407e16			2.44954
$79$	−5.31440e15	+	9.20482e15i	−0.394116	+	0.682629i	−0.992988	−	0.118216i	$-0.962283\pi$
$79$	−5.31440e15	+	9.20482e15i	−0.394116	+	0.682629i	0.598872	+	0.800845i	$0.295616\pi$
$80$	1.76461e15	+	3.05639e15i	0.117594	+	0.203678i
$81$	−3.22556e16	−	5.58684e16i	−1.93412	−	3.34999i
$82$	3.94989e15	−	6.84141e15i	0.213387	−	0.369597i
$83$	3.04847e16			1.48566			0.742828	−	0.669483i	$-0.233484\pi$
$83$	3.04847e16			1.48566			0.742828	+	0.669483i	$0.233484\pi$
$84$	3.42103e16	+	5.32277e16i	1.50586	+	2.34295i
$85$	3.60852e15			0.143638
$86$	−3.69955e15	+	6.40780e15i	−0.133325	+	0.230926i
$87$	3.41545e16	+	5.91573e16i	1.11567	+	1.93239i
$88$	−2.00045e15	−	3.46488e15i	−0.0592959	−	0.102704i
$89$	2.49305e16	−	4.31808e16i	0.671298	−	1.16272i	−0.306238	−	0.951955i	$-0.599070\pi$
$89$	2.49305e16	−	4.31808e16i	0.671298	−	1.16272i	0.977536	−	0.210768i	$-0.0675963\pi$
$90$	−1.10677e17			−2.71018
$91$	−1.66313e16	+	3.22633e16i	−0.370743	+	0.719212i
$92$	−3.72351e16			−0.756408
$93$	−6.38213e14	+	1.10542e15i	−0.0118266	+	0.0204843i
$94$	−3.11199e16	−	5.39012e16i	−0.526564	−	0.912036i
$95$	2.42312e16	+	4.19697e16i	0.374735	+	0.649060i
$96$	8.66609e16	−	1.50101e17i	1.22608	−	2.12363i
$97$	4.40038e16			0.570073			0.285036	−	0.958517i	$-0.407994\pi$
$97$	4.40038e16			0.570073			0.285036	+	0.958517i	$0.407994\pi$
$98$	−1.30850e17	+	1.25052e16i	−1.55365	+	0.148480i
$99$	−4.42118e16			−0.481548
$100$	4.34233e16	−	7.52113e16i	0.434233	−	0.752113i
$101$	4.01129e16	+	6.94775e16i	0.368597	+	0.638429i	0.989346	−	0.145580i	$-0.0465048\pi$
$101$	4.01129e16	+	6.94775e16i	0.368597	+	0.638429i	−0.620749	+	0.784009i	$0.713171\pi$
$102$	−4.09267e16	−	7.08871e16i	−0.345864	−	0.599054i
$103$	2.05829e16	−	3.56507e16i	0.160100	−	0.277301i	−0.774805	−	0.632201i	$-0.782152\pi$
$103$	2.05829e16	−	3.56507e16i	0.160100	−	0.277301i	0.934904	+	0.354900i	$0.115485\pi$
$104$	−7.68252e16			−0.550453
$105$	8.45817e16	−	1.64082e17i	0.558686	−	1.08380i
$106$	−4.46266e16			−0.271953
$107$	−7.48897e16	+	1.29713e17i	−0.421366	+	0.729828i	−0.996073	−	0.0885313i	$-0.971783\pi$
$107$	−7.48897e16	+	1.29713e17i	−0.421366	+	0.729828i	0.574707	+	0.818359i	$0.305116\pi$
$108$	4.72076e17	+	8.17660e17i	2.45420	+	4.25080i
$109$	2.95588e16	+	5.11973e16i	0.142089	+	0.246106i	0.928283	−	0.371874i	$-0.121285\pi$
$109$	2.95588e16	+	5.11973e16i	0.142089	+	0.246106i	−0.786194	+	0.617980i	$0.787951\pi$
$110$	−1.92259e16	+	3.33003e16i	−0.0855164	+	0.148119i
$111$	−5.37192e17			−2.21250
$112$	5.30043e16	+	8.24691e16i	0.202282	+	0.314730i
$113$	−2.25989e16			−0.0799687			−0.0399843	−	0.999200i	$-0.512731\pi$
$113$	−2.25989e16			−0.0799687			−0.0399843	+	0.999200i	$0.512731\pi$
$114$	5.49645e17	−	9.52013e17i	1.80464	−	3.12573i
$115$	5.43164e16	+	9.40787e16i	0.165577	+	0.286787i
$116$	−2.91619e17	−	5.05098e17i	−0.825890	−	1.43048i
$117$	−4.24478e17	+	7.35217e17i	−1.11757	+	1.93569i
$118$	7.50547e17			1.83815
$119$	1.00123e17	−	4.77343e15i	0.228236	−	0.0108813i
$120$	3.90711e17			0.829497
$121$	2.45043e17	−	4.24428e17i	0.484805	−	0.839707i
$122$	−3.94837e17	−	6.83879e17i	−0.728383	−	1.26160i
$123$	1.54086e17	+	2.66884e17i	0.265197	+	0.459335i
$124$	5.44920e15	−	9.43830e15i	0.00875485	−	0.0151638i
$125$	−6.72288e17			−1.00884
$126$	−3.07088e18	+	1.46407e17i	−4.30639	+	0.205310i
$127$	1.05269e18			1.38028			0.690140	−	0.723676i	$-0.257549\pi$
$127$	1.05269e18			1.38028			0.690140	+	0.723676i	$0.257549\pi$
$128$	−5.01914e17	+	8.69341e17i	−0.615666	+	1.06636i
$129$	−1.44320e17	−	2.49969e17i	−0.165696	−	0.286995i
$130$	3.69176e17	+	6.39432e17i	0.396931	+	0.687505i
$131$	−1.12897e17	+	1.95543e17i	−0.113730	+	0.196986i	−0.917271	−	0.398263i	$-0.869613\pi$
$131$	−1.12897e17	+	1.95543e17i	−0.113730	+	0.196986i	0.803541	+	0.595249i	$0.202947\pi$
$132$	5.14146e17			0.485521
$133$	7.27843e17	+	1.13245e18i	0.644613	+	1.00295i
$134$	8.19616e17			0.681113
$135$	1.37727e18	−	2.38551e18i	1.07444	−	1.86099i
$136$	1.06077e17	+	1.83731e17i	0.0777216	+	0.134618i
$137$	−6.50636e17	−	1.12694e18i	−0.447933	−	0.775843i	0.550318	−	0.834955i	$-0.314507\pi$
$137$	−6.50636e17	−	1.12694e18i	−0.447933	−	0.775843i	−0.998251	+	0.0591117i	$0.981173\pi$
$138$	1.23208e18	−	2.13402e18i	0.797381	−	1.38110i
$139$	−1.42563e18			−0.867722			−0.433861	−	0.900980i	$-0.642849\pi$
$139$	−1.42563e18			−0.867722			−0.433861	+	0.900980i	$0.642849\pi$
$140$	−7.22178e17	+	1.40097e18i	−0.413576	+	0.802305i
$141$	2.42798e18			1.30883
$142$	−8.36462e17	+	1.44880e18i	−0.424615	+	0.735455i
$143$	1.47473e17	+	2.55431e17i	0.0705273	+	0.122157i
$144$	1.14644e18	+	1.98570e18i	0.516739	+	0.895018i
$145$	−8.50792e17	+	1.47361e18i	−0.361572	+	0.626262i
$146$	−4.96174e18			−1.98900
$147$	2.12977e18	−	4.66454e18i	0.805631	−	1.76446i
$148$	4.58667e18			1.63784
$149$	−2.91086e18	+	5.04175e18i	−0.981606	+	1.70019i	−0.325465	+	0.945554i	$0.605521\pi$
$149$	−2.91086e18	+	5.04175e18i	−0.981606	+	1.70019i	−0.656141	+	0.754638i	$0.727812\pi$
$150$	2.87368e18	+	4.97735e18i	0.915508	+	1.58571i
$151$	−3.24111e18	−	5.61377e18i	−0.975865	−	1.69025i	−0.677051	−	0.735936i	$-0.736742\pi$
$151$	−3.24111e18	−	5.61377e18i	−0.975865	−	1.69025i	−0.298814	−	0.954311i	$-0.596591\pi$
$152$	−1.42462e18	+	2.46751e18i	−0.405534	+	0.702406i
$153$	2.34441e18			0.631185
$154$	−4.89397e17	+	9.49390e17i	−0.124662	+	0.241835i
$155$	−3.17959e16			−0.00766570
$156$	4.93632e18	−	8.54995e18i	1.12679	−	1.95166i
$157$	−2.52027e18	−	4.36523e18i	−0.544879	−	0.943758i	−0.998615	−	0.0526213i	$-0.983242\pi$
$157$	−2.52027e18	−	4.36523e18i	−0.544879	−	0.943758i	0.453736	−	0.891136i	$-0.350091\pi$
$158$	3.00288e18	+	5.20113e18i	0.615109	+	1.06540i
$159$	8.70444e17	−	1.50765e18i	0.168992	−	0.292702i
$160$	4.31746e18			0.794710
$161$	1.63152e18	+	2.53848e18i	0.284822	+	0.443153i
$162$	−3.64517e19			−6.03727
$163$	3.11450e17	−	5.39447e17i	0.0489546	−	0.0847919i	−0.840510	−	0.541796i	$-0.817744\pi$
$163$	3.11450e17	−	5.39447e17i	0.0489546	−	0.0847919i	0.889464	+	0.457005i	$0.151078\pi$
$164$	−1.31562e18	−	2.27872e18i	−0.196317	−	0.340031i
$165$	−7.50006e17	−	1.29905e18i	−0.106280	−	0.184082i
$166$	8.61261e18	−	1.49175e19i	1.15935	−	2.00806i
$167$	−4.48174e18			−0.573267			−0.286633	−	0.958040i	$-0.592536\pi$
$167$	−4.48174e18			−0.573267			−0.286633	+	0.958040i	$0.592536\pi$
$168$	1.08408e19	−	5.16841e17i	1.31805	−	0.0628388i
$169$	−2.98685e18			−0.345284
$170$	1.01949e18	−	1.76581e18i	0.112090	−	0.194145i
$171$	1.57427e19	+	2.72672e19i	1.64669	+	2.85215i
$172$	1.23223e18	+	2.13429e18i	0.122660	+	0.212453i
$173$	2.68486e18	−	4.65031e18i	0.254407	−	0.440646i	−0.710327	−	0.703872i	$-0.751453\pi$
$173$	2.68486e18	−	4.65031e18i	0.254407	−	0.440646i	0.964734	+	0.263226i	$0.0847863\pi$
$174$	3.85976e19			3.48251
$175$	−7.03016e18	+	3.35167e17i	−0.604145	+	0.0288030i
$176$	7.96601e17			0.0652203
$177$	−1.46395e19	+	2.53563e19i	−1.14223	+	1.97840i
$178$	−1.40868e19	−	2.43991e19i	−1.04772	−	1.81470i
$179$	−6.80687e18	−	1.17898e19i	−0.482721	−	0.836098i	0.517082	−	0.855936i	$-0.327018\pi$
$179$	−6.80687e18	−	1.17898e19i	−0.482721	−	0.836098i	−0.999803	+	0.0198381i	$0.993685\pi$
$180$	−1.84321e19	+	3.19253e19i	−1.24669	+	2.15933i
$181$	−1.38576e19			−0.894169			−0.447085	−	0.894492i	$-0.647538\pi$
$181$	−1.38576e19			−0.894169			−0.447085	+	0.894492i	$0.647538\pi$
$182$	1.10891e19	+	1.72535e19i	0.682794	+	1.06236i
$183$	3.08053e19			1.81047
$184$	−3.19340e18	+	5.53114e18i	−0.179185	+	0.310358i
$185$	−6.69076e18	−	1.15887e19i	−0.358522	−	0.620978i
$186$	3.60619e17	+	6.24610e17i	0.0184582	+	0.0319705i
$187$	4.07251e17	−	7.05379e17i	0.0199163	−	0.0344960i
$188$	−2.07307e19			−0.968883
$189$	3.50586e19	−	6.80108e19i	1.56628	−	3.03845i
$190$	2.73834e19			1.16972
$191$	−6.88481e18	+	1.19248e19i	−0.281260	+	0.487157i	−0.971695	−	0.236237i	$-0.924086\pi$
$191$	−6.88481e18	+	1.19248e19i	−0.281260	+	0.487157i	0.690435	+	0.723394i	$0.257419\pi$
$192$	−3.96823e19	−	6.87317e19i	−1.55073	−	2.68594i
$193$	1.90171e19	+	3.29386e19i	0.711061	+	1.23159i	0.964459	+	0.264232i	$0.0851185\pi$
$193$	1.90171e19	+	3.29386e19i	0.711061	+	1.23159i	−0.253398	+	0.967362i	$0.581548\pi$
$194$	1.24320e19	−	2.15329e19i	0.444865	−	0.770528i
$195$	−2.88032e19			−0.986614
$196$	−1.81845e19	+	3.98269e19i	−0.596382	+	1.30617i
$197$	−7.86457e18			−0.247008			−0.123504	−	0.992344i	$-0.539413\pi$
$197$	−7.86457e18			−0.247008			−0.123504	+	0.992344i	$0.539413\pi$
$198$	−1.24908e19	+	2.16348e19i	−0.375783	+	0.650876i
$199$	−1.74920e18	−	3.02970e18i	−0.0504183	−	0.0873270i	0.839715	−	0.543028i	$-0.182722\pi$
$199$	−1.74920e18	−	3.02970e18i	−0.0504183	−	0.0873270i	−0.890133	+	0.455701i	$0.849389\pi$
$200$	−7.44824e18	−	1.29007e19i	−0.205731	−	0.356336i
$201$	−1.59867e19	+	2.76897e19i	−0.423244	+	0.733081i
$202$	4.53311e19			1.15056
$203$	−2.16570e19	+	4.20127e19i	−0.527085	+	1.02250i
$204$	−2.72635e19			−0.636393
$205$	−3.83829e18	+	6.64812e18i	−0.0859469	+	0.148864i
$206$	−1.16303e19	−	2.01442e19i	−0.249873	−	0.432792i
$207$	3.52886e19	+	6.11217e19i	0.727590	+	1.26022i
$208$	7.64816e18	−	1.32470e19i	0.151363	−	0.262168i
$209$	1.09387e19			0.207838
$210$	−5.63960e19	−	8.77462e19i	−1.02893	−	1.60090i
$211$	5.56672e19			0.975435			0.487718	−	0.873001i	$-0.337830\pi$
$211$	5.56672e19			0.975435			0.487718	+	0.873001i	$0.337830\pi$
$212$	−7.43205e18	+	1.28727e19i	−0.125099	+	0.216678i
$213$	−3.26305e19	−	5.65177e19i	−0.527712	−	0.914024i
$214$	4.23160e19	+	7.32935e19i	0.657639	+	1.13906i
$215$	3.59502e18	−	6.22676e18i	0.0537000	−	0.0930112i
$216$	1.61947e20			2.32550
$217$	−8.82217e17	+	4.20603e16i	−0.0121806	+	0.000580717i
$218$	3.34041e19			0.443526
$219$	9.67791e19	−	1.67626e20i	1.23597	−	2.14076i
$220$	6.40372e18	+	1.10916e19i	0.0786755	+	0.136270i
$221$	−7.82003e18	−	1.35447e19i	−0.0924430	−	0.160116i
$222$	−1.51769e20	+	2.62871e20i	−1.72656	+	2.99049i
$223$	−5.27407e19			−0.577503			−0.288752	−	0.957404i	$-0.593240\pi$
$223$	−5.27407e19			−0.577503			−0.288752	+	0.957404i	$0.593240\pi$
$224$	1.19793e20	−	5.71123e18i	1.26277	−	0.0602035i
$225$	−1.64613e20			−1.67076
$226$	−6.38468e18	+	1.10586e19i	−0.0624048	+	0.108088i
$227$	6.97874e19	+	1.20875e20i	0.656988	+	1.13794i	0.981391	+	0.192018i	$0.0615031\pi$
$227$	6.97874e19	+	1.20875e20i	0.656988	+	1.13794i	−0.324404	+	0.945919i	$0.605164\pi$
$228$	−1.83074e20	−	3.17094e20i	−1.66028	−	2.87569i
$229$	−2.26724e19	+	3.92698e19i	−0.198106	+	0.343129i	−0.947914	−	0.318526i	$-0.896812\pi$
$229$	−2.26724e19	+	3.92698e19i	−0.198106	+	0.343129i	0.749809	+	0.661655i	$0.230146\pi$
$230$	6.13824e19			0.516841
$231$	−2.25283e19	−	3.50516e19i	−0.182821	−	0.284450i
$232$	−1.00041e20			−0.782579
$233$	−5.91676e19	+	1.02481e20i	−0.446230	+	0.772893i	−0.998137	−	0.0610127i	$-0.980567\pi$
$233$	−5.91676e19	+	1.02481e20i	−0.446230	+	0.772893i	0.551907	+	0.833906i	$0.313900\pi$
$234$	2.39849e20	+	4.15431e20i	1.74423	+	3.02109i
$235$	3.02407e19	+	5.23784e19i	0.212087	+	0.367346i
$236$	1.24995e20	−	2.16498e20i	0.845553	−	1.46454i
$237$	−2.34285e20			−1.52892
$238$	2.59511e19	−	5.03431e19i	0.163400	−	0.316983i
$239$	−1.10473e20			−0.671233			−0.335616	−	0.941999i	$-0.608945\pi$
$239$	−1.10473e20			−0.671233			−0.335616	+	0.941999i	$0.608945\pi$
$240$	−3.88963e19	+	6.73704e19i	−0.228094	+	0.395070i
$241$	−1.20424e20	−	2.08581e20i	−0.681661	−	1.18067i	−0.974474	−	0.224502i	$-0.927924\pi$
$241$	−1.20424e20	−	2.08581e20i	−0.681661	−	1.18067i	0.292812	−	0.956170i	$-0.405409\pi$
$242$	−1.38460e20	−	2.39821e20i	−0.756650	−	1.31056i
$243$	3.87068e20	−	6.70421e20i	2.04237	−	3.53748i
$244$	−2.63023e20			−1.34023
$245$	1.27154e20	−	1.21519e19i	0.625773	−	0.0598042i
$246$	1.74131e20			0.827803
$247$	1.05023e20	−	1.81905e20i	0.482347	−	0.835450i
$248$	−9.34683e17	−	1.61892e18i	−0.00414787	−	0.00718432i
$249$	3.35979e20	+	5.81933e20i	1.44085	+	2.49562i
$250$	−1.89937e20	+	3.28980e20i	−0.787260	+	1.36358i
$251$	−1.00057e20			−0.400886			−0.200443	−	0.979705i	$-0.564238\pi$
$251$	−1.00057e20			−0.400886			−0.200443	+	0.979705i	$0.564238\pi$
$252$	−4.69189e20	+	9.10189e20i	−1.81737	+	3.52555i
$253$	2.45201e19			0.0918330
$254$	2.97407e20	−	5.15125e20i	1.07712	−	1.86563i
$255$	3.97704e19	+	6.88844e19i	0.139306	+	0.241284i
$256$	4.76400e19	+	8.25150e19i	0.161411	+	0.279572i
$257$	2.21013e20	−	3.82805e20i	0.724412	−	1.25472i	−0.234803	−	0.972043i	$-0.575445\pi$
$257$	2.21013e20	−	3.82805e20i	0.724412	−	1.25472i	0.959216	−	0.282676i	$-0.0912220\pi$
$258$	−1.63094e20			−0.517215
$259$	−2.00973e20	−	3.12693e20i	−0.616723	−	0.959556i
$260$	2.45928e20			0.730357
$261$	−5.52748e20	+	9.57388e20i	−1.58885	+	2.75197i
$262$	6.37916e19	+	1.10490e20i	0.177502	+	0.307442i
$263$	7.15608e19	+	1.23947e20i	0.192775	+	0.333896i	0.946169	−	0.323673i	$-0.104918\pi$
$263$	7.15608e19	+	1.23947e20i	0.192775	+	0.333896i	−0.753394	+	0.657570i	$0.771585\pi$
$264$	4.40948e19	−	7.63745e19i	0.115015	−	0.199212i
$265$	4.33657e19			0.109536
$266$	7.59787e20	−	3.62234e19i	1.85865	−	0.0886125i
$267$	1.09906e21			2.60420
$268$	1.36498e20	−	2.36421e20i	0.313314	−	0.542675i
$269$	4.23890e20	+	7.34200e20i	0.942669	+	1.63275i	0.760353	+	0.649510i	$0.225026\pi$
$269$	4.23890e20	+	7.34200e20i	0.942669	+	1.63275i	0.182316	+	0.983240i	$0.441641\pi$
$270$	−7.78221e20	−	1.34792e21i	−1.67692	−	2.90450i
$271$	1.21728e19	−	2.10839e19i	0.0254186	−	0.0440263i	−0.853036	−	0.521852i	$-0.825241\pi$
$271$	1.21728e19	−	2.10839e19i	0.0254186	−	0.0440263i	0.878455	+	0.477825i	$0.158575\pi$
$272$	−4.22412e19			−0.0854870
$273$	−7.99182e20	+	3.81015e19i	−1.56770	+	0.0747412i
$274$	−7.35277e20			−1.39821
$275$	−2.85952e19	+	4.95283e19i	−0.0527188	+	0.0913116i
$276$	−4.10377e20	−	7.10794e20i	−0.733594	−	1.27062i
$277$	−4.77597e20	−	8.27223e20i	−0.827912	−	1.43398i	−0.899674	−	0.436563i	$-0.856196\pi$
$277$	−4.77597e20	−	8.27223e20i	−0.827912	−	1.43398i	0.0717621	−	0.997422i	$-0.477138\pi$
$278$	−4.02772e20	+	6.97621e20i	−0.677140	+	1.17284i
$279$	−2.06574e19			−0.0336852
$280$	1.46172e20	+	2.27428e20i	0.231218	+	0.359750i
$281$	−1.10004e21			−1.68812			−0.844062	−	0.536246i	$-0.819842\pi$
$281$	−1.10004e21			−1.68812			−0.844062	+	0.536246i	$0.819842\pi$
$282$	6.85959e20	−	1.18812e21i	1.02136	−	1.76906i
$283$	−1.39980e20	−	2.42453e20i	−0.202247	−	0.350302i	0.747005	−	0.664818i	$-0.231491\pi$
$283$	−1.39980e20	−	2.42453e20i	−0.202247	−	0.350302i	−0.949252	+	0.314516i	$0.898158\pi$
$284$	2.78607e20	+	4.82561e20i	0.390648	+	0.676622i
$285$	−5.34116e20	+	9.25116e20i	−0.726866	+	1.25897i
$286$	1.66658e20			0.220148
$287$	−9.77040e19	+	1.89538e20i	−0.125290	+	0.243052i
$288$	2.80500e21			3.49218
$289$	3.92025e20	−	6.79007e20i	0.473895	−	0.820810i
$290$	4.80735e20	+	8.32658e20i	0.564317	+	0.977426i
$291$	4.84976e20	+	8.40003e20i	0.552879	+	0.957614i
$292$	−8.26321e20	+	1.43123e21i	−0.914944	+	1.58473i
$293$	−2.08080e20			−0.223798			−0.111899	−	0.993720i	$-0.535693\pi$
$293$	−2.08080e20			−0.223798			−0.111899	+	0.993720i	$0.535693\pi$
$294$	−1.68085e21	−	2.36003e21i	−1.75621	−	2.46584i
$295$	−7.29342e20			−0.740362
$296$	3.93367e20	−	6.81332e20i	0.387988	−	0.672016i
$297$	−3.10873e20	−	5.38447e20i	−0.297956	−	0.516076i
$298$	1.64476e21	+	2.84881e21i	1.53202	+	2.65354i
$299$	2.35418e20	−	4.07756e20i	0.213125	−	0.369143i
$300$	1.91431e21			1.68454
$301$	9.15115e19	−	1.77525e20i	0.0782817	−	0.151860i
$302$	−3.66274e21			−3.04612
$303$	−8.84187e20	+	1.53146e21i	−0.714960	+	1.23835i
$304$	−2.83649e20	−	4.91294e20i	−0.223026	−	0.386293i
$305$	3.83682e20	+	6.64557e20i	0.293375	+	0.508140i
$306$	6.62349e20	−	1.14722e21i	0.492555	−	0.853130i
$307$	2.16038e21			1.56262			0.781309	−	0.624144i	$-0.214552\pi$
$307$	2.16038e21			1.56262			0.781309	+	0.624144i	$0.214552\pi$
$308$	1.92351e20	+	2.99278e20i	0.135336	+	0.210569i
$309$	9.07397e20			0.621084
$310$	−8.98305e18	+	1.55591e19i	−0.00598204	+	0.0103612i
$311$	−1.32034e20	−	2.28690e20i	−0.0855507	−	0.148178i	0.820075	−	0.572256i	$-0.193932\pi$
$311$	−1.32034e20	−	2.28690e20i	−0.0855507	−	0.148178i	−0.905626	+	0.424078i	$0.860598\pi$
$312$	−8.46709e20	−	1.46654e21i	−0.533851	−	0.924657i
$313$	3.04013e20	−	5.26567e20i	0.186537	−	0.323092i	−0.757556	−	0.652770i	$-0.773607\pi$
$313$	3.04013e20	−	5.26567e20i	0.186537	−	0.323092i	0.944094	+	0.329678i	$0.106940\pi$
$314$	−2.84813e21			−1.70082
$315$	2.98412e21	−	1.42270e20i	1.73451	−	0.0826940i
$316$	2.00038e21			1.13181
$317$	1.26251e21	−	2.18673e21i	0.695393	−	1.20446i	−0.274655	−	0.961543i	$-0.588564\pi$
$317$	1.26251e21	−	2.18673e21i	0.695393	−	1.20446i	0.970048	−	0.242913i	$-0.0781030\pi$
$318$	−4.91840e20	−	8.51892e20i	−0.263751	−	0.456829i
$319$	1.92037e20	+	3.32618e20i	0.100269	+	0.173670i
$320$	9.88489e20	−	1.71211e21i	0.502571	−	0.870478i
$321$	−3.30151e21			−1.63463
$322$	1.70313e21	−	8.11979e19i	0.821245	−	0.0391534i
$323$	−5.80046e20			−0.272421
$324$	−6.07062e21	+	1.05146e22i	−2.77716	+	4.81018i
$325$	5.49085e20	+	9.51043e20i	0.244698	+	0.423830i
$326$	−1.75983e20	−	3.04812e20i	−0.0764050	−	0.132337i
$327$	−6.51549e20	+	1.12852e21i	−0.275607	+	0.477366i
$328$	−4.51327e20			−0.186022
$329$	9.08352e20	+	1.41330e21i	0.364829	+	0.567635i
$330$	−8.47574e20			−0.331749
$331$	1.91361e21	−	3.31447e21i	0.729988	−	1.26438i	−0.226899	−	0.973918i	$-0.572859\pi$
$331$	1.91361e21	−	3.31447e21i	0.729988	−	1.26438i	0.956888	−	0.290459i	$-0.0938079\pi$
$332$	−2.86866e21	−	4.96867e21i	−1.06661	−	1.84742i
$333$	−4.34690e21	−	7.52905e21i	−1.57545	−	2.72875i
$334$	−1.26619e21	+	2.19311e21i	−0.447357	+	0.774846i
$335$	−7.96459e20			−0.274336
$336$	−9.90108e20	+	1.92073e21i	−0.332505	+	0.645034i
$337$	2.84638e21			0.932048			0.466024	−	0.884772i	$-0.345686\pi$
$337$	2.84638e21			0.932048			0.466024	+	0.884772i	$0.345686\pi$
$338$	−8.43853e20	+	1.46160e21i	−0.269448	+	0.466697i
$339$	−2.49067e20	−	4.31397e20i	−0.0775567	−	0.134332i
$340$	−3.39569e20	−	5.88150e20i	−0.103123	−	0.178615i
$341$	−3.58842e18	+	6.21533e18i	−0.00106290	+	0.00184099i
$342$	1.77907e22			5.14008
$343$	3.51196e21	−	5.05371e20i	0.989804	−	0.142433i
$344$	4.22722e20			0.116227
$345$	−1.19727e21	+	2.07373e21i	−0.321165	+	0.556275i
$346$	−1.51706e21	−	2.62763e21i	−0.397061	−	0.687730i
$347$	9.89682e20	+	1.71418e21i	0.252752	+	0.437780i	0.964283	−	0.264876i	$-0.0853309\pi$
$347$	9.89682e20	+	1.71418e21i	0.252752	+	0.437780i	−0.711530	+	0.702655i	$0.751998\pi$
$348$	6.42799e21	−	1.11336e22i	1.60196	−	2.77468i
$349$	−5.53596e21			−1.34641			−0.673205	−	0.739456i	$-0.735083\pi$
$349$	−5.53596e21			−1.34641			−0.673205	+	0.739456i	$0.735083\pi$
$350$	−1.82216e21	+	3.53485e21i	−0.432523	+	0.839059i
$351$	−1.19388e22			−2.76598
$352$	4.87260e20	−	8.43960e20i	0.110192	−	0.190857i
$353$	2.74242e21	+	4.75001e21i	0.605408	+	1.04860i	0.991987	+	0.126342i	$0.0403236\pi$
$353$	2.74242e21	+	4.75001e21i	0.605408	+	1.04860i	−0.386578	+	0.922257i	$0.626343\pi$
$354$	8.27195e21	+	1.43274e22i	1.78271	+	3.08774i
$355$	8.12830e20	−	1.40786e21i	0.171025	−	0.296223i
$356$	−9.38401e21			−1.92781
$357$	1.19460e21	+	1.85867e21i	0.239631	+	0.372841i
$358$	−7.69237e21			−1.50680
$359$	−2.13757e21	+	3.70238e21i	−0.408900	+	0.708236i	−0.994767	−	0.102172i	$-0.967421\pi$
$359$	−2.13757e21	+	3.70238e21i	−0.408900	+	0.708236i	0.585867	+	0.810407i	$0.300754\pi$
$360$	3.16159e21	+	5.47603e21i	0.590655	+	1.02305i
$361$	−1.15481e21	−	2.00019e21i	−0.210717	−	0.364972i
$362$	−3.91508e21	+	6.78112e21i	−0.697779	+	1.20859i
$363$	1.08027e22			1.88073
$364$	6.82359e21	−	3.25319e20i	1.16052	−	0.0553284i
$365$	4.82155e21			0.801120
$366$	8.70320e21	−	1.50744e22i	1.41283	−	2.44709i
$367$	−5.13010e21	−	8.88560e21i	−0.813700	−	1.40937i	−0.910257	−	0.414043i	$-0.864116\pi$
$367$	−5.13010e21	−	8.88560e21i	−0.813700	−	1.40937i	0.0965570	−	0.995327i	$-0.469217\pi$
$368$	−6.35824e20	−	1.10128e21i	−0.0985441	−	0.170683i
$369$	−2.49369e21	+	4.31920e21i	−0.377675	+	0.654152i
$370$	−7.56115e21			−1.11911
$371$	1.20324e21	−	5.73651e19i	0.174050	−	0.00829793i
$372$	2.40228e20			0.0339632
$373$	−4.47124e21	+	7.74442e21i	−0.617879	+	1.07020i	0.371993	+	0.928235i	$0.378674\pi$
$373$	−4.47124e21	+	7.74442e21i	−0.617879	+	1.07020i	−0.989872	+	0.141962i	$0.954659\pi$
$374$	−2.30115e20	−	3.98571e20i	−0.0310840	−	0.0538390i
$375$	−7.40945e21	−	1.28335e22i	−0.978409	−	1.69465i
$376$	−1.77793e21	+	3.07946e21i	−0.229518	+	0.397538i
$377$	7.37500e21			0.930809
$378$	−2.33758e22	−	3.63702e22i	−2.88460	−	4.48813i
$379$	7.62274e21			0.919767			0.459883	−	0.887979i	$-0.347891\pi$
$379$	7.62274e21			0.919767			0.459883	+	0.887979i	$0.347891\pi$
$380$	4.56040e21	−	7.89884e21i	0.538074	−	0.931972i
$381$	1.16019e22	+	2.00951e22i	1.33865	+	2.31861i
$382$	3.89022e21	+	6.73807e21i	0.438971	+	0.760321i
$383$	−4.91076e21	+	8.50568e21i	−0.541949	+	0.938684i	0.456843	+	0.889547i	$0.348980\pi$
$383$	−4.91076e21	+	8.50568e21i	−0.541949	+	0.938684i	−0.998792	+	0.0491364i	$0.984353\pi$
$384$	−2.21269e22			−2.38839
$385$	4.75570e20	−	9.22567e20i	0.0502109	−	0.0974051i
$386$	2.14910e22			2.21955
$387$	2.33564e21	−	4.04545e21i	0.235973	−	0.408717i
$388$	−4.14083e21	−	7.17213e21i	−0.409278	−	0.708890i
$389$	−5.24282e19	−	9.08083e19i	−0.00506983	−	0.00878121i	0.863479	−	0.504384i	$-0.168280\pi$
$389$	−5.24282e19	−	9.08083e19i	−0.00506983	−	0.00878121i	−0.868549	+	0.495603i	$0.834947\pi$
$390$	−8.13756e21	+	1.40947e22i	−0.769919	+	1.33354i
$391$	−1.30022e21			−0.120369
$392$	4.35657e21	+	6.11692e21i	0.394651	+	0.554117i
$393$	−4.97704e21			−0.441199
$394$	−2.22192e21	+	3.84847e21i	−0.192757	+	0.333865i
$395$	−2.91804e21	−	5.05419e21i	−0.247751	−	0.429117i
$396$	4.16041e21	+	7.20605e21i	0.345722	+	0.598809i
$397$	1.57596e21	−	2.72964e21i	0.128182	−	0.222017i	−0.794790	−	0.606884i	$-0.792419\pi$
$397$	1.57596e21	−	2.72964e21i	0.128182	−	0.222017i	0.922972	+	0.384867i	$0.125753\pi$
$398$	−1.97675e21			−0.157379
$399$	−1.35959e22	+	2.63750e22i	−1.05959	+	2.05553i
$400$	2.96597e21			0.226286
$401$	8.29141e21	−	1.43611e22i	0.619300	−	1.07266i	−0.370313	−	0.928907i	$-0.620750\pi$
$401$	8.29141e21	−	1.43611e22i	0.619300	−	1.07266i	0.989614	−	0.143753i	$-0.0459171\pi$
$402$	9.03318e21	+	1.56459e22i	0.660570	+	1.14414i
$403$	6.89049e19	+	1.19347e20i	0.00493352	+	0.00854511i
$404$	7.54939e21	−	1.30759e22i	0.529261	−	0.916707i
$405$	3.54219e22			2.43166
$406$	1.44401e22	+	2.24672e22i	0.970729	+	1.51035i
$407$	−3.02042e21			−0.198845
$408$	−2.33821e21	+	4.04989e21i	−0.150755	+	0.261115i
$409$	−1.09787e22	−	1.90156e22i	−0.693269	−	1.20078i	−0.970761	−	0.240049i	$-0.922837\pi$
$409$	−1.09787e22	−	1.90156e22i	−0.693269	−	1.20078i	0.277492	−	0.960728i	$-0.410497\pi$
$410$	2.16881e21	+	3.75649e21i	0.134140	+	0.232337i
$411$	1.43416e22	−	2.48404e22i	0.868847	−	1.50489i
$412$	−7.74756e21			−0.459768
$413$	−2.02365e22	+	9.64789e20i	−1.17641	+	0.0560863i
$414$	3.98793e22			2.27115
$415$	−8.36928e21	+	1.44960e22i	−0.466959	+	0.808798i
$416$	−9.35637e21	−	1.62057e22i	−0.511463	−	0.885880i
$417$	−1.57122e22	−	2.72143e22i	−0.841550	−	1.45761i
$418$	3.09044e21	−	5.35280e21i	0.162189	−	0.280920i
$419$	−1.63949e22			−0.843123			−0.421561	−	0.906800i	$-0.638518\pi$
$419$	−1.63949e22			−0.843123			−0.421561	+	0.906800i	$0.638518\pi$
$420$	−3.47028e22	+	1.65448e21i	−1.74882	+	0.0833763i
$421$	−2.86214e22			−1.41349			−0.706746	−	0.707467i	$-0.749838\pi$
$421$	−2.86214e22			−1.41349			−0.706746	+	0.707467i	$0.749838\pi$
$422$	1.57272e22	−	2.72404e22i	0.761196	−	1.31843i
$423$	1.96470e22	+	3.40295e22i	0.931971	+	1.61422i
$424$	1.27479e21	+	2.20801e21i	0.0592693	+	0.102657i
$425$	1.51631e21	−	2.62633e21i	0.0691007	−	0.119686i
$426$	−3.68754e22			−1.64723
$427$	1.15248e22	+	1.79314e22i	0.504659	+	0.785195i
$428$	2.81890e22			1.21006
$429$	−3.25068e21	+	5.63034e21i	−0.136800	+	0.236945i
$430$	−2.03135e21	−	3.51840e21i	−0.0838113	−	0.145165i
$431$	1.72786e22	+	2.99275e22i	0.698961	+	1.21064i	0.968827	+	0.247738i	$0.0796872\pi$
$431$	1.72786e22	+	2.99275e22i	0.698961	+	1.21064i	−0.269866	+	0.962898i	$0.586979\pi$
$432$	−1.61223e22	+	2.79246e22i	−0.639462	+	1.10758i
$433$	2.05188e22			0.798003			0.399001	−	0.916950i	$-0.369357\pi$
$433$	2.05188e22			0.798003			0.399001	+	0.916950i	$0.369357\pi$
$434$	−2.28664e20	+	4.43590e20i	−0.00872038	+	0.0169168i
$435$	−3.75071e22			−1.40267
$436$	5.56307e21	−	9.63552e21i	0.204023	−	0.353378i
$437$	−8.73099e21	−	1.51225e22i	−0.314030	−	0.543916i
$438$	−5.46845e22	−	9.47163e22i	−1.92901	−	3.34114i
$439$	2.04369e21	−	3.53977e21i	0.0707076	−	0.122469i	−0.828504	−	0.559983i	$-0.810808\pi$
$439$	2.04369e21	−	3.53977e21i	0.0707076	−	0.122469i	0.899212	+	0.437514i	$0.144141\pi$
$440$	2.19682e21			0.0745497
$441$	8.26100e22	−	7.89492e21i	2.74982	−	0.262797i
$442$	−8.83733e21			−0.288557
$443$	1.49095e22	−	2.58240e22i	0.477564	−	0.827164i	−0.522106	−	0.852881i	$-0.674853\pi$
$443$	1.49095e22	−	2.58240e22i	0.477564	−	0.827164i	0.999669	+	0.0257164i	$0.00818668\pi$
$444$	5.05507e22	+	8.75564e22i	1.58844	+	2.75127i
$445$	1.36888e22	+	2.37098e22i	0.421994	+	0.730915i
$446$	−1.49004e22	+	2.58083e22i	−0.450663	+	0.780572i
$447$	−1.28325e23			−3.80800
$448$	2.51621e22	−	4.88123e22i	0.732627	−	1.42124i
$449$	7.90153e21			0.225744			0.112872	−	0.993610i	$-0.463995\pi$
$449$	7.90153e21			0.225744			0.112872	+	0.993610i	$0.463995\pi$
$450$	−4.65069e22	+	8.05524e22i	−1.30380	+	2.25825i
$451$	8.66364e20	+	1.50059e21i	0.0238342	+	0.0412820i
$452$	2.12659e21	+	3.68337e21i	0.0574127	+	0.0994417i
$453$	7.14421e22	−	1.23741e23i	1.89286	−	3.27854i
$454$	7.88660e22			2.05076
$455$	−1.07758e22	−	1.67660e22i	−0.275013	−	0.427891i
$456$	−6.28041e22			−1.57321
$457$	−1.78677e22	+	3.09478e22i	−0.439320	+	0.760925i	−0.997637	−	0.0687027i	$-0.978114\pi$
$457$	−1.78677e22	+	3.09478e22i	−0.439320	+	0.760925i	0.558317	+	0.829628i	$0.311447\pi$
$458$	1.28109e22	+	2.21892e22i	0.309189	+	0.535532i
$459$	1.64846e22	+	2.85521e22i	0.390544	+	0.676442i
$460$	1.02225e22	−	1.77060e22i	0.237748	−	0.411792i
$461$	2.17879e22			0.497460			0.248730	−	0.968573i	$-0.419987\pi$
$461$	2.17879e22			0.497460			0.248730	+	0.968573i	$0.419987\pi$
$462$	−2.35170e22	+	1.12119e21i	−0.527139	+	0.0251317i
$463$	−7.86148e22			−1.73008			−0.865040	−	0.501703i	$-0.832707\pi$
$463$	−7.86148e22			−1.73008			−0.865040	+	0.501703i	$0.832707\pi$
$464$	9.95932e21	−	1.72500e22i	0.215192	−	0.372724i
$465$	−3.50430e20	−	6.06963e20i	−0.00743449	−	0.0128769i
$466$	3.34324e22	+	5.79065e22i	0.696445	+	1.20628i
$467$	−2.58936e21	+	4.48491e21i	−0.0529663	+	0.0917403i	−0.891293	−	0.453428i	$-0.850201\pi$
$467$	−2.58936e21	+	4.48491e21i	−0.0529663	+	0.0917403i	0.838327	+	0.545168i	$0.183534\pi$
$468$	1.59777e23			3.20940
$469$	−2.20987e22	+	1.05357e21i	−0.435912	+	0.0207824i
$470$	3.41746e22			0.662022
$471$	5.55530e22	−	9.62205e22i	1.05689	−	1.83059i
$472$	−2.14400e22	−	3.71351e22i	−0.400606	−	0.693869i
$473$	−8.11454e20	−	1.40548e21i	−0.0148917	−	0.0257932i
$474$	−6.61908e22	+	1.14646e23i	−1.19311	+	2.06653i
$475$	4.07280e22			0.721104
$476$	−1.01998e22	−	1.58698e22i	−0.177391	−	0.276002i
$477$	2.81742e22			0.481332
$478$	−3.12110e22	+	5.40591e22i	−0.523807	+	0.907260i
$479$	3.39593e22	+	5.88193e22i	0.559896	+	0.969769i	0.997505	+	0.0706029i	$0.0224923\pi$
$479$	3.39593e22	+	5.88193e22i	0.559896	+	0.969769i	−0.437608	+	0.899166i	$0.644174\pi$
$480$	4.75838e22	+	8.24176e22i	0.770741	+	1.33496i
$481$	−2.89991e22	+	5.02279e22i	−0.461478	+	0.799303i
$482$	−1.36090e23			−2.12778
$483$	−3.04765e22	+	5.91219e22i	−0.468182	+	0.908235i
$484$	−9.22361e22			−1.39224
$485$	−1.20808e22	+	2.09246e22i	−0.179181	+	0.310350i
$486$	−2.18711e23	−	3.78818e23i	−3.18758	−	5.52106i
$487$	8.13959e21	+	1.40982e22i	0.116575	+	0.201914i	0.918408	−	0.395634i	$-0.129475\pi$
$487$	8.13959e21	+	1.40982e22i	0.116575	+	0.201914i	−0.801833	+	0.597548i	$0.796142\pi$
$488$	−2.25577e22	+	3.90711e22i	−0.317487	+	0.549904i
$489$	1.37303e22			0.189912
$490$	2.99773e22	−	6.56549e22i	0.407498	−	0.892484i
$491$	−8.50034e20			−0.0113565			−0.00567824	−	0.999984i	$-0.501807\pi$
$491$	−8.50034e20			−0.0113565			−0.00567824	+	0.999984i	$0.501807\pi$
$492$	2.89995e22	−	5.02286e22i	0.380791	−	0.659550i
$493$	−1.01831e22	−	1.76377e22i	−0.131426	−	0.227637i
$494$	−5.93426e22	−	1.02784e23i	−0.752814	−	1.30391i
$495$	1.21379e22	−	2.10235e22i	0.151356	−	0.262157i
$496$	3.72201e20			0.00456229
$497$	2.06906e22	−	4.01381e22i	0.249313	−	0.483646i
$498$	3.79686e23			4.49755
$499$	−2.81219e22	+	4.87086e22i	−0.327484	+	0.567219i	−0.982012	−	0.188819i	$-0.939534\pi$
$499$	−2.81219e22	+	4.87086e22i	−0.327484	+	0.567219i	0.654528	+	0.756038i	$0.272867\pi$
$500$	6.32635e22	+	1.09576e23i	0.724283	+	1.25450i
$501$	−4.93943e22	−	8.55535e22i	−0.555976	−	0.962979i
$502$	−2.82683e22	+	4.89622e22i	−0.312837	+	0.541850i
$503$	7.67080e22			0.834666			0.417333	−	0.908754i	$-0.362965\pi$
$503$	7.67080e22			0.834666			0.417333	+	0.908754i	$0.362965\pi$
$504$	9.49660e22	+	1.47757e23i	1.01604	+	1.58084i
$505$	−4.40504e22			−0.463418
$506$	6.92749e21	−	1.19988e22i	0.0716633	−	0.124124i
$507$	−3.29188e22	−	5.70171e22i	−0.334870	−	0.580012i
$508$	−9.90597e22	−	1.71576e23i	−0.990958	−	1.71639i
$509$	−2.00647e22	+	3.47531e22i	−0.197393	+	0.341895i	−0.947682	−	0.319215i	$-0.896581\pi$
$509$	−2.00647e22	+	3.47531e22i	−0.197393	+	0.341895i	0.750289	+	0.661110i	$0.229914\pi$
$510$	4.49441e22			0.434837
$511$	1.33780e23	−	6.37806e21i	1.27296	−	0.0606891i
$512$	−7.77363e22			−0.727494
$513$	−2.21388e23	+	3.83454e23i	−2.03777	+	3.52952i
$514$	−1.24882e23	−	2.16302e23i	−1.13061	−	1.95828i
$515$	1.13017e22	+	1.95751e22i	0.100643	+	0.174318i
$516$	−2.71615e22	+	4.70451e22i	−0.237920	+	0.412090i
$517$	1.36516e22			0.117629
$518$	−2.09794e23	+	1.00021e22i	−1.77824	+	0.0847786i
$519$	1.18362e23			0.986936
$520$	2.10916e22	−	3.65318e22i	0.173014	−	0.299669i
$521$	1.11344e23	+	1.92853e23i	0.898556	+	1.55635i	0.829341	+	0.558743i	$0.188716\pi$
$521$	1.11344e23	+	1.92853e23i	0.898556	+	1.55635i	0.0692155	+	0.997602i	$0.477950\pi$
$522$	3.12328e23	+	5.40967e23i	2.47977	+	4.29508i
$523$	1.93229e22	−	3.34683e22i	0.150941	−	0.261438i	−0.780632	−	0.624990i	$-0.785103\pi$
$523$	1.93229e22	−	3.34683e22i	0.150941	−	0.261438i	0.931574	+	0.363552i	$0.118436\pi$
$524$	4.24951e22			0.326605
$525$	−8.38791e22	−	1.30507e23i	−0.634308	−	0.986916i
$526$	8.08701e22			0.601740
$527$	1.90282e20	−	3.29579e20i	0.00139318	−	0.00241307i
$528$	8.77952e21	+	1.52066e22i	0.0632532	+	0.109558i
$529$	5.09537e22	+	8.82545e22i	0.361246	+	0.625696i
$530$	1.22518e22	−	2.12207e22i	0.0854781	−	0.148052i
$531$	−4.73844e23			−3.25336
$532$	1.16085e23	−	2.25196e23i	0.784383	−	1.52164i
$533$	3.32719e22			0.221256
$534$	3.10509e23	−	5.37817e23i	2.03223	−	3.51993i
$535$	−4.11205e22	−	7.12227e22i	−0.264881	−	0.458787i
$536$	−2.34130e22	−	4.05524e22i	−0.148442	−	0.257108i
$537$	1.50040e23	−	2.59877e23i	0.936324	−	1.62176i
$538$	4.79034e23			2.94250
$539$	1.19749e22	−	2.62269e22i	0.0724048	−	0.158578i
$540$	−5.18416e23			−3.08554
$541$	−4.22303e22	+	7.31450e22i	−0.247427	+	0.428557i	−0.962811	−	0.270175i	$-0.912918\pi$
$541$	−4.22303e22	+	7.31450e22i	−0.247427	+	0.428557i	0.715384	+	0.698731i	$0.246252\pi$
$542$	−6.87818e21	−	1.19134e22i	−0.0396716	−	0.0687132i
$543$	−1.52728e23	−	2.64532e23i	−0.867200	−	1.50204i
$544$	−2.58378e22	+	4.47525e22i	−0.144433	+	0.250165i
$545$	−3.24603e22			−0.178641
$546$	−2.07142e23	+	4.01839e23i	−1.12236	+	2.17728i
$547$	−1.55632e22			−0.0830245			−0.0415123	−	0.999138i	$-0.513218\pi$
$547$	−1.55632e22			−0.0830245			−0.0415123	+	0.999138i	$0.513218\pi$
$548$	−1.22452e23	+	2.12093e23i	−0.643178	+	1.11402i
$549$	2.49273e23	+	4.31754e23i	1.28917	+	2.23291i
$550$	1.61576e22	+	2.79857e22i	0.0822798	+	0.142513i
$551$	1.36759e23	−	2.36874e23i	0.685753	−	1.18776i
$552$	−1.40781e23			−0.695123
$553$	−8.76503e22	−	1.36375e23i	−0.426177	−	0.663086i
$554$	−5.39728e23			−2.58429
$555$	1.47481e23	−	2.55444e23i	0.695417	−	1.20450i
$556$	1.34154e23	+	2.32362e23i	0.622972	+	1.07902i
$557$	−1.32388e23	−	2.29303e23i	−0.605453	−	1.04868i	−0.991980	−	0.126397i	$-0.959659\pi$
$557$	−1.32388e23	−	2.29303e23i	−0.605453	−	1.04868i	0.386526	−	0.922278i	$-0.373675\pi$
$558$	−5.83617e21	+	1.01085e22i	−0.0262868	+	0.0455301i
$559$	−3.11631e22			−0.138242
$560$	−5.37674e22	+	2.56340e21i	−0.234920	+	0.0112000i
$561$	1.79536e22			0.0772624
$562$	−3.10786e23	+	5.38296e23i	−1.31735	+	2.28172i
$563$	3.34134e22	+	5.78738e22i	0.139508	+	0.241635i	0.927311	−	0.374293i	$-0.122114\pi$
$563$	3.34134e22	+	5.78738e22i	0.139508	+	0.241635i	−0.787802	+	0.615928i	$0.788781\pi$
$564$	−2.28477e23	−	3.95735e23i	−0.939660	−	1.62754i
$565$	6.20430e21	−	1.07462e22i	0.0251351	−	0.0435353i
$566$	−1.58190e23			−0.631306
$567$	9.82824e23	−	4.68568e22i	3.86384	−	0.184211i
$568$	9.55768e22			0.370162
$569$	6.40221e22	−	1.10890e23i	0.244273	−	0.423093i	−0.717654	−	0.696400i	$-0.754784\pi$
$569$	6.40221e22	−	1.10890e23i	0.244273	−	0.423093i	0.961927	+	0.273307i	$0.0881173\pi$
$570$	3.01799e23	+	5.22732e23i	1.13444	+	1.96491i
$571$	2.26063e23	+	3.91553e23i	0.837187	+	1.45005i	0.892237	+	0.451567i	$0.149135\pi$
$571$	2.26063e23	+	3.91553e23i	0.837187	+	1.45005i	−0.0550503	+	0.998484i	$0.517532\pi$
$572$	2.77550e22	−	4.80731e22i	0.101269	−	0.175402i
$573$	−3.03516e23			−1.09111
$574$	6.51454e22	+	1.01359e23i	0.230745	+	0.359015i
$575$	9.12955e22			0.318620
$576$	6.42209e23	−	1.11234e24i	2.20844	−	3.82513i
$577$	−2.38933e23	−	4.13844e23i	−0.809620	−	1.40230i	−0.913127	−	0.407675i	$-0.866340\pi$
$577$	−2.38933e23	−	4.13844e23i	−0.809620	−	1.40230i	0.103507	−	0.994629i	$-0.466994\pi$
$578$	−2.21512e23	−	3.83669e23i	−0.739622	−	1.28106i
$579$	−4.19184e23	+	7.26048e23i	−1.37923	+	2.38890i
$580$	3.20244e23			1.03835
$581$	−2.13040e23	+	4.13281e23i	−0.680714	+	1.32053i
$582$	5.48066e23			1.72579
$583$	4.89417e21	−	8.47695e21i	0.0151879	−	0.0263061i
$584$	1.41736e23	+	2.45494e23i	0.433482	+	0.750812i
$585$	−2.33073e23	−	4.03694e23i	−0.702532	−	1.21682i
$586$	−5.87873e22	+	1.01823e23i	−0.174644	+	0.302493i
$587$	1.24210e23			0.363691			0.181846	−	0.983327i	$-0.441793\pi$
$587$	1.24210e23			0.363691			0.181846	+	0.983327i	$0.441793\pi$
$588$	−9.60684e23	+	9.18112e22i	−2.77251	+	0.264965i
$589$	5.11098e21			0.0145386
$590$	−2.06055e23	+	3.56898e23i	−0.577752	+	1.00070i
$591$	−8.66773e22	−	1.50129e23i	−0.239558	−	0.414927i
$592$	7.83216e22	+	1.35657e23i	0.213377	+	0.369579i
$593$	3.21328e23	−	5.56557e23i	0.862947	−	1.49467i	−0.00612405	−	0.999981i	$-0.501949\pi$
$593$	3.21328e23	−	5.56557e23i	0.862947	−	1.49467i	0.869071	−	0.494687i	$-0.164717\pi$
$594$	−3.51314e23			−0.930059
$595$	−2.52179e22	+	4.89208e22i	−0.0658136	+	0.127673i
$596$	1.09567e24			2.81894
$597$	3.85567e22	−	6.67821e22i	0.0977953	−	0.169386i
$598$	−1.33022e23	−	2.30400e23i	−0.332631	−	0.576133i
$599$	2.81840e23	+	4.88161e23i	0.694823	+	1.20347i	0.970240	+	0.242145i	$0.0778508\pi$
$599$	2.81840e23	+	4.88161e23i	0.694823	+	1.20347i	−0.275417	+	0.961325i	$0.588816\pi$
$600$	1.64178e23	−	2.84364e23i	0.399051	−	0.691177i
$601$	3.57571e23			0.856898			0.428449	−	0.903566i	$-0.359060\pi$
$601$	3.57571e23			0.856898			0.428449	+	0.903566i	$0.359060\pi$
$602$	−6.10165e22	−	9.49352e22i	−0.144171	−	0.224314i
$603$	−5.17449e23			−1.20551
$604$	−6.09988e23	+	1.05653e24i	−1.40122	+	2.42699i
$605$	1.34549e23	+	2.33045e23i	0.304760	+	0.527860i
$606$	4.99605e23	+	8.65342e23i	1.11586	+	1.93273i
$607$	1.49468e23	−	2.58886e23i	0.329189	−	0.570171i	−0.653163	−	0.757218i	$-0.726558\pi$
$607$	1.49468e23	−	2.58886e23i	0.329189	−	0.570171i	0.982351	+	0.187046i	$0.0598915\pi$
$608$	−6.94003e23			−1.50724
$609$	−1.04068e24	+	4.96152e22i	−2.22880	+	0.106260i
$610$	4.33595e23			0.915758
$611$	1.31069e23	−	2.27018e23i	0.272992	−	0.472836i
$612$	−2.20613e23	−	3.82113e23i	−0.453153	−	0.784884i
$613$	−2.31709e23	−	4.01333e23i	−0.469386	−	0.813000i	0.530002	−	0.847997i	$-0.322191\pi$
$613$	−2.31709e23	−	4.01333e23i	−0.469386	−	0.813000i	−0.999387	+	0.0349968i	$0.988858\pi$
$614$	6.10354e23	−	1.05716e24i	1.21941	−	2.11209i
$615$	−1.69211e23			−0.333419
$616$	6.09534e22	−	2.90599e21i	0.118457	−	0.00564753i
$617$	−2.57831e23			−0.494209			−0.247105	−	0.968989i	$-0.579479\pi$
$617$	−2.57831e23			−0.494209			−0.247105	+	0.968989i	$0.579479\pi$
$618$	2.56360e23	−	4.44029e23i	0.484672	−	0.839477i
$619$	−4.79440e23	−	8.30414e23i	−0.894054	−	1.54855i	−0.834971	−	0.550293i	$-0.814516\pi$
$619$	−4.79440e23	−	8.30414e23i	−0.894054	−	1.54855i	−0.0590822	−	0.998253i	$-0.518817\pi$
$620$	2.99205e21	+	5.18239e21i	0.00550351	+	0.00953236i
$621$	−4.96260e23	+	8.59547e23i	−0.900389	+	1.55952i
$622$	−1.49211e23			−0.267043
$623$	4.11178e23	+	6.39749e23i	0.725907	+	1.12944i
$624$	3.37169e23			0.587190
$625$	8.54107e21	−	1.47936e22i	0.0146734	−	0.0254152i
$626$	−1.71781e23	−	2.97534e23i	−0.291135	−	0.504260i
$627$	1.20558e23	+	2.08813e23i	0.201569	+	0.349128i
$628$	−4.74324e23	+	8.21553e23i	−0.782380	+	1.35512i
$629$	1.60163e23			0.260635
$630$	7.73463e23	−	1.50045e24i	1.24178	−	2.40895i
$631$	−1.07382e23			−0.170091			−0.0850456	−	0.996377i	$-0.527104\pi$
$631$	−1.07382e23			−0.170091			−0.0850456	+	0.996377i	$0.527104\pi$
$632$	1.71559e23	−	2.97149e23i	0.268113	−	0.464386i
$633$	6.13521e23	+	1.06265e24i	0.946015	+	1.63855i
$634$	−7.13373e23	−	1.23560e24i	−1.08532	−	1.87983i
$635$	−2.89005e23	+	5.00571e23i	−0.433839	+	0.751431i
$636$	−3.27642e23			−0.485304
$637$	−3.21167e23	−	4.50940e23i	−0.469403	−	0.659073i
$638$	2.17019e23			0.312984
$639$	5.28085e23	−	9.14670e23i	0.751530	−	1.30169i
$640$	−2.75591e23	−	4.77338e23i	−0.387022	−	0.670342i
$641$	3.38697e23	+	5.86640e23i	0.469373	+	0.812977i	0.999387	−	0.0350115i	$-0.0111468\pi$
$641$	3.38697e23	+	5.86640e23i	0.469373	+	0.812977i	−0.530014	+	0.847989i	$0.677813\pi$
$642$	−9.32750e23	+	1.61557e24i	−1.27561	+	2.20942i
$643$	2.51900e23			0.339965			0.169982	−	0.985447i	$-0.445629\pi$
$643$	2.51900e23			0.339965			0.169982	+	0.985447i	$0.445629\pi$
$644$	2.60215e23	−	5.04796e23i	0.346579	−	0.672336i
$645$	1.58486e23			0.208322
$646$	−1.63876e23	+	2.83842e23i	−0.212588	+	0.368213i
$647$	1.46073e23	+	2.53006e23i	0.187018	+	0.323925i	0.944255	−	0.329215i	$-0.106784\pi$
$647$	1.46073e23	+	2.53006e23i	0.187018	+	0.323925i	−0.757236	+	0.653141i	$0.773451\pi$
$648$	1.04127e24	+	1.80354e24i	1.31576	+	2.27896i
$649$	−8.23120e22	+	1.42569e23i	−0.102656	+	0.177805i
$650$	6.20515e23			0.763816
$651$	−1.05260e22	−	1.63774e22i	−0.0127887	−	0.0198979i
$652$	−1.17232e23			−0.140586
$653$	−6.39050e23	+	1.10687e24i	−0.756437	+	1.31019i	0.188220	+	0.982127i	$0.439728\pi$
$653$	−6.39050e23	+	1.10687e24i	−0.756437	+	1.31019i	−0.944657	+	0.328060i	$0.893605\pi$
$654$	3.68154e23	+	6.37662e23i	0.430149	+	0.745040i
$655$	−6.19893e22	−	1.07369e23i	−0.0714934	−	0.123830i
$656$	4.49308e22	−	7.78225e22i	0.0511519	−	0.0885977i
$657$	3.13250e24			3.52035
$658$	9.48218e23	−	4.52070e22i	1.05193	−	0.0501516i
$659$	1.31488e24			1.43999			0.719997	−	0.693977i	$-0.244143\pi$
$659$	1.31488e24			1.43999			0.719997	+	0.693977i	$0.244143\pi$
$660$	−1.41154e23	+	2.44486e23i	−0.152605	+	0.264320i
$661$	−1.40218e23	−	2.42865e23i	−0.149655	−	0.259210i	0.781445	−	0.623974i	$-0.214483\pi$
$661$	−1.40218e23	−	2.42865e23i	−0.149655	−	0.259210i	−0.931100	+	0.364764i	$0.881150\pi$
$662$	−1.08128e24	−	1.87283e24i	−1.13931	−	1.97335i
$663$	1.72373e23	−	2.98558e23i	0.179310	−	0.310574i
$664$	−9.84104e23			−1.01068
$665$	−7.38321e23	+	3.52000e22i	−0.748620	+	0.0356910i
$666$	−4.91238e24			−4.91769
$667$	3.06557e23	−	5.30973e23i	0.303000	−	0.524811i
$668$	4.21740e23	+	7.30475e23i	0.411571	+	0.712862i
$669$	−5.81267e23	−	1.00678e24i	−0.560085	−	0.970096i
$670$	−2.25018e23	+	3.89742e23i	−0.214082	+	0.370801i
$671$	1.73206e23			0.162713
$672$	1.42930e24	+	2.22383e24i	1.32582	+	2.06283i
$673$	−1.90660e24			−1.74635			−0.873176	−	0.487405i	$-0.837944\pi$
$673$	−1.90660e24			−1.74635			−0.873176	+	0.487405i	$0.837944\pi$
$674$	8.04165e23	−	1.39286e24i	0.727338	−	1.25979i
$675$	−1.15747e24	−	2.00479e24i	−1.03378	−	1.79055i
$676$	2.81068e23	+	4.86824e23i	0.247893	+	0.429364i
$677$	7.80141e23	−	1.35124e24i	0.679469	−	1.17687i	−0.295672	−	0.955289i	$-0.595544\pi$
$677$	7.80141e23	−	1.35124e24i	0.679469	−	1.17687i	0.975141	−	0.221585i	$-0.0711231\pi$
$678$	−2.81469e23			−0.242090
$679$	−3.07518e23	+	5.96559e23i	−0.261202	+	0.506711i
$680$	−1.16490e23			−0.0977154
$681$	−1.53829e24	+	2.66439e24i	−1.27435	+	2.20723i
$682$	2.02762e21	+	3.51194e21i	0.00165890	+	0.00287329i
$683$	8.08952e23	+	1.40115e24i	0.653652	+	1.13216i	0.982230	+	0.187682i	$0.0600974\pi$
$683$	8.08952e23	+	1.40115e24i	0.653652	+	1.13216i	−0.328578	+	0.944477i	$0.606569\pi$
$684$	2.96283e24	−	5.13178e24i	2.36445	−	4.09535i
$685$	7.14504e23			0.563164
$686$	7.44907e23	−	1.86133e24i	0.579892	−	1.44900i
$687$	−9.99514e23			−0.768522
$688$	−4.20831e22	+	7.28901e22i	−0.0319599	+	0.0553562i
$689$	−9.39779e22	−	1.62774e23i	−0.0704956	−	0.122102i
$690$	6.76510e23	+	1.17175e24i	0.501253	+	0.868195i
$691$	5.43719e23	−	9.41749e23i	0.397934	−	0.689242i	−0.595537	−	0.803328i	$-0.703061\pi$
$691$	5.43719e23	−	9.41749e23i	0.397934	−	0.689242i	0.993471	+	0.114086i	$0.0363939\pi$
$692$	−1.01060e24			−0.730596
$693$	3.08972e23	−	5.99380e23i	0.220641	−	0.428026i
$694$	1.11843e24			0.788957
$695$	3.91392e23	−	6.77912e23i	0.272735	−	0.472392i
$696$	−1.10257e24	−	1.90971e24i	−0.758976	−	1.31459i
$697$	−4.59405e22	−	7.95713e22i	−0.0312404	−	0.0541100i
$698$	−1.56403e24	+	2.70899e24i	−1.05069	+	1.81985i
$699$	−2.60840e24			−1.73109
$700$	7.16179e23	+	1.11430e24i	0.469557	+	0.730581i
$701$	6.07925e22			0.0393774			0.0196887	−	0.999806i	$-0.493732\pi$
$701$	6.07925e22			0.0393774			0.0196887	+	0.999806i	$0.493732\pi$
$702$	−3.37297e24	+	5.84215e24i	−2.15847	+	3.73858i
$703$	1.07549e24	+	1.86281e24i	0.679967	+	1.17774i
$704$	−2.23118e23	−	3.86452e23i	−0.139369	−	0.241395i
$705$	−6.66579e23	+	1.15455e24i	−0.411381	+	0.712533i
$706$	3.09918e24			1.88976
$707$	−1.22223e24	+	5.82708e22i	−0.736358	+	0.0351064i
$708$	5.51040e24			3.28020
$709$	2.67729e23	−	4.63720e23i	0.157471	−	0.272749i	−0.776485	−	0.630136i	$-0.782999\pi$
$709$	2.67729e23	−	4.63720e23i	0.157471	−	0.272749i	0.933956	+	0.357387i	$0.116332\pi$
$710$	−4.59285e23	−	7.95505e23i	−0.266923	−	0.462325i
$711$	−1.89581e24	−	3.28364e24i	−1.08869	−	1.88566i
$712$	−8.04803e23	+	1.39396e24i	−0.456678	+	0.790989i
$713$	1.14567e22			0.00642390
$714$	1.24703e24	−	5.94530e22i	0.690943	−	0.0329412i
$715$	−1.61949e23			−0.0886703
$716$	−1.28108e24	+	2.21889e24i	−0.693130	+	1.20054i
$717$	−1.21755e24	−	2.10885e24i	−0.650988	−	1.12754i
$718$	1.20782e24	+	2.09201e24i	0.638183	+	1.10536i
$719$	−9.97302e23	+	1.72738e24i	−0.520752	+	0.901970i	0.478956	+	0.877839i	$0.341015\pi$
$719$	−9.97302e23	+	1.72738e24i	−0.520752	+	0.901970i	−0.999709	+	0.0241309i	$0.992318\pi$
$720$	−1.25898e24			−0.649669
$721$	3.39474e23	+	5.28185e23i	0.173124	+	0.269362i
$722$	−1.30504e24			−0.657745
$723$	2.65445e24	−	4.59763e24i	1.32220	−	2.29012i
$724$	1.30402e24	+	2.25864e24i	0.641960	+	1.11191i
$725$	7.15010e23	+	1.23843e24i	0.347887	+	0.602559i
$726$	3.05201e24	−	5.28624e24i	1.46766	−	2.54206i
$727$	−2.29680e24			−1.09164			−0.545822	−	0.837901i	$-0.683783\pi$
$727$	−2.29680e24			−1.09164			−0.545822	+	0.837901i	$0.683783\pi$
$728$	5.36888e23	−	1.04152e24i	0.252213	−	0.489273i
$729$	8.73287e24			4.05484
$730$	1.36220e24	−	2.35939e24i	0.625166	−	1.08282i
$731$	4.30288e22	+	7.45280e22i	0.0195192	+	0.0338082i
$732$	−2.89884e24	−	5.02093e24i	−1.29981	−	2.25134i
$733$	8.74436e23	−	1.51457e24i	0.387565	−	0.671282i	−0.604557	−	0.796562i	$-0.706650\pi$
$733$	8.74436e23	−	1.51457e24i	0.387565	−	0.671282i	0.992121	+	0.125280i	$0.0399830\pi$
$734$	−5.79748e24			−2.53993
$735$	1.63336e24	+	2.29335e24i	0.707359	+	0.993179i
$736$	−1.55567e24			−0.665972
$737$	−8.98868e22	+	1.55688e23i	−0.0380384	+	0.0658844i
$738$	1.40905e24	+	2.44054e24i	0.589449	+	1.02096i
$739$	1.70808e24	+	2.95848e24i	0.706366	+	1.22346i	0.966196	+	0.257807i	$0.0829999\pi$
$739$	1.70808e24	+	2.95848e24i	0.706366	+	1.22346i	−0.259831	+	0.965654i	$0.583667\pi$
$740$	−1.25922e24	+	2.18104e24i	−0.514794	+	0.891650i
$741$	4.62993e24			1.87120
$742$	3.11870e23	−	6.05003e23i	0.124606	−	0.241726i
$743$	−4.86402e24			−1.92128			−0.960640	−	0.277796i	$-0.910396\pi$
$743$	−4.86402e24			−1.92128			−0.960640	+	0.277796i	$0.910396\pi$
$744$	2.06027e22	−	3.56850e22i	0.00804553	−	0.0139353i
$745$	−1.59829e24	−	2.76833e24i	−0.617062	−	1.06878i
$746$	2.52645e24	+	4.37594e24i	0.964342	+	1.67029i
$747$	−5.43741e24	+	9.41787e24i	−2.05195	+	3.55408i
$748$	−1.53292e23			−0.0571948
$749$	−1.23515e24	−	1.92177e24i	−0.455644	−	0.708934i
$750$	−8.37334e24			−3.05406
$751$	1.11963e24	−	1.93925e24i	0.403771	−	0.699351i	−0.590407	−	0.807106i	$-0.701033\pi$
$751$	1.11963e24	−	1.93925e24i	0.403771	−	0.699351i	0.994178	+	0.107754i	$0.0343660\pi$
$752$	−3.53995e23	−	6.13138e23i	−0.126225	−	0.218628i
$753$	−1.10275e24	−	1.91002e24i	−0.388795	−	0.673412i
$754$	2.08360e24	−	3.60891e24i	0.726371	−	1.25811i
$755$	3.55926e24			1.22690
$756$	−1.43841e25	+	6.85771e23i	−4.90283	+	0.233746i
$757$	−2.78220e24			−0.937719			−0.468860	−	0.883273i	$-0.655335\pi$
$757$	−2.78220e24			−0.937719			−0.468860	+	0.883273i	$0.655335\pi$
$758$	2.15359e24	−	3.73014e24i	0.717754	−	1.24319i
$759$	2.70242e23	+	4.68074e23i	0.0890632	+	0.154262i
$760$	−7.82229e23	−	1.35486e24i	−0.254929	−	0.441549i
$761$	−2.61709e22	+	4.53293e22i	−0.00843429	+	0.0146086i	−0.870212	−	0.492678i	$-0.836018\pi$
$761$	−2.61709e22	+	4.53293e22i	−0.00843429	+	0.0146086i	0.861777	+	0.507287i	$0.169351\pi$
$762$	1.31112e25			4.17854
$763$	−9.00652e23	+	4.29392e22i	−0.283856	+	0.0135330i
$764$	2.59149e24			0.807711
$765$	−6.43635e23	+	1.11481e24i	−0.198389	+	0.343620i
$766$	2.77480e24	+	4.80609e24i	0.845837	+	1.46503i
$767$	1.58056e24	+	2.73760e24i	0.476485	+	0.825296i
$768$	−1.05010e24	+	1.81883e24i	−0.313085	+	0.542279i
$769$	−2.39234e24			−0.705421			−0.352710	−	0.935733i	$-0.614740\pi$
$769$	−2.39234e24			−0.705421			−0.352710	+	0.935733i	$0.614740\pi$
$770$	−3.17093e23	−	4.93363e23i	−0.0924730	−	0.143878i
$771$	9.74333e24			2.81025
$772$	3.57908e24	−	6.19916e24i	1.02100	−	1.76842i
$773$	−2.57010e24	−	4.45155e24i	−0.725144	−	1.25599i	−0.958915	−	0.283695i	$-0.908440\pi$
$773$	−2.57010e24	−	4.45155e24i	−0.725144	−	1.25599i	0.233770	−	0.972292i	$-0.424894\pi$
$774$	−1.31974e24	−	2.28586e24i	−0.368290	−	0.637898i
$775$	−1.33607e22	+	2.31414e22i	−0.00368778	+	0.00638743i
$776$	−1.42053e24			−0.387815
$777$	3.75413e24	−	7.28271e24i	1.01375	−	1.96659i
$778$	−5.92486e22			−0.0158253
$779$	6.16980e23	−	1.06864e24i	0.163006	−	0.282334i
$780$	2.71044e24	+	4.69461e24i	0.708329	+	1.22686i
$781$	−1.83469e23	−	3.17777e23i	−0.0474273	−	0.0821464i
$782$	−3.67342e23	+	6.36256e23i	−0.0939320	+	0.162695i
$783$	−1.55465e25			−3.93239
$784$	−1.48845e24	+	1.42249e23i	−0.372433	+	0.0355929i
$785$	2.76766e24			0.685048
$786$	−1.40613e24	+	2.43548e24i	−0.344296	+	0.596339i
$787$	1.18630e24	+	2.05472e24i	0.287348	+	0.497701i	0.973176	−	0.230063i	$-0.0738931\pi$
$787$	1.18630e24	+	2.05472e24i	0.287348	+	0.497701i	−0.685828	+	0.727764i	$0.740560\pi$
$788$	7.40070e23	+	1.28184e24i	0.177337	+	0.307157i
$789$	−1.57738e24	+	2.73210e24i	−0.373922	+	0.647652i
$790$	−3.29764e24			−0.773345
$791$	1.57931e23	−	3.06373e23i	0.0366409	−	0.0710804i
$792$	1.42724e24			0.327592
$793$	1.66295e24	−	2.88032e24i	0.377623	−	0.654062i
$794$	−8.90488e23	−	1.54237e24i	−0.200057	−	0.346509i
$795$	4.77944e23	+	8.27824e23i	0.106232	+	0.184000i
$796$	−3.29206e23	+	5.70201e23i	−0.0723946	+	0.125391i
$797$	−1.06588e24			−0.231907			−0.115953	−	0.993255i	$-0.536992\pi$
$797$	−1.06588e24			−0.231907			−0.115953	+	0.993255i	$0.536992\pi$
$798$	9.06528e24	+	1.41046e25i	1.95145	+	3.03624i
$799$	−7.23900e23			−0.154181
$800$	1.81421e24	−	3.14230e24i	0.382316	−	0.662191i
$801$	8.89346e24	+	1.54039e25i	1.85436	+	3.21185i
$802$	−4.68502e24	−	8.11469e24i	−0.966561	−	1.67413i
$803$	5.44151e23	−	9.42497e23i	0.111080	−	0.192397i
$804$	6.01749e24			1.21546
$805$	−1.65501e24	+	7.89038e22i	−0.330778	+	0.0157700i
$806$	7.78687e22			0.0153998
$807$	−9.34359e24	+	1.61836e25i	−1.82847	+	3.16701i
$808$	−1.29492e24	−	2.24287e24i	−0.250753	−	0.434317i
$809$	−9.38923e23	−	1.62626e24i	−0.179915	−	0.311622i	0.761936	−	0.647652i	$-0.224249\pi$
$809$	−9.38923e23	−	1.62626e24i	−0.179915	−	0.311622i	−0.941851	+	0.336030i	$0.890916\pi$
$810$	1.00075e25	−	1.73334e25i	1.89759	−	3.28672i
$811$	−1.32958e23			−0.0249481			−0.0124741	−	0.999922i	$-0.503971\pi$
$811$	−1.32958e23			−0.0249481			−0.0124741	+	0.999922i	$0.503971\pi$
$812$	8.88557e24	−	4.23626e23i	1.64991	−	0.0786604i
$813$	5.36637e23			0.0986078
$814$	−8.53337e23	+	1.47802e24i	−0.155172	+	0.268766i
$815$	1.71011e23	+	2.96200e23i	0.0307741	+	0.0533022i
$816$	−4.65550e23	−	8.06356e23i	−0.0829086	−	0.143602i
$817$	−5.77876e23	+	1.00091e24i	−0.101847	+	0.176404i
$818$	−1.24069e25			−2.16401
$819$	−7.00090e24	−	1.08927e25i	−1.20848	−	1.88027i
$820$	1.44476e24			0.246819
$821$	−2.55714e24	+	4.42910e24i	−0.432352	+	0.748856i	−0.997075	−	0.0764245i	$-0.975650\pi$
$821$	−2.55714e24	+	4.42910e24i	−0.432352	+	0.748856i	0.564723	+	0.825280i	$0.308983\pi$
$822$	−8.10366e24	−	1.40360e25i	−1.35604	−	2.34872i
$823$	6.41010e23	+	1.11026e24i	0.106161	+	0.183877i	0.914212	−	0.405236i	$-0.132811\pi$
$823$	6.41010e23	+	1.11026e24i	0.106161	+	0.183877i	−0.808051	+	0.589113i	$0.799477\pi$
$824$	−6.64456e23	+	1.15087e24i	−0.108914	+	0.188645i
$825$	−1.26062e24			−0.204515
$826$	−5.24515e24	+	1.01752e25i	−0.842224	+	1.63385i
$827$	5.26751e24			0.837160			0.418580	−	0.908180i	$-0.362528\pi$
$827$	5.26751e24			0.837160			0.418580	+	0.908180i	$0.362528\pi$
$828$	6.64145e24	−	1.15033e25i	1.04473	−	1.80953i
$829$	3.06477e24	+	5.30834e24i	0.477182	+	0.826504i	0.999658	−	0.0261500i	$-0.00832476\pi$
$829$	3.06477e24	+	5.30834e24i	0.477182	+	0.826504i	−0.522476	+	0.852654i	$0.674991\pi$
$830$	4.72902e24	+	8.19090e24i	0.728798	+	1.26231i
$831$	1.05274e25	−	1.82340e25i	1.60588	−	2.78147i
$832$	−8.56862e24			−1.29379
$833$	−6.34990e23	+	1.39073e24i	−0.0949040	+	0.207854i
$834$	−1.77562e25			−2.62687
$835$	1.23042e24	−	2.13115e24i	0.180185	−	0.312089i
$836$	−1.02936e24	−	1.78290e24i	−0.149215	−	0.258448i
$837$	−1.45251e23	−	2.51582e23i	−0.0208426	−	0.0361005i
$838$	−4.63194e24	+	8.02275e24i	−0.657944	+	1.13959i
$839$	8.26057e24			1.16154			0.580769	−	0.814069i	$-0.302752\pi$
$839$	8.26057e24			1.16154			0.580769	+	0.814069i	$0.302752\pi$
$840$	−2.73046e24	+	5.29687e24i	−0.380068	+	0.737302i
$841$	2.34646e24			0.323331
$842$	−8.08619e24	+	1.40057e25i	−1.10304	+	1.91052i
$843$	−1.21238e25	−	2.09990e25i	−1.63721	−	2.83573i
$844$	−5.23838e24	−	9.07315e24i	−0.700304	−	1.21296i
$845$	8.20011e23	−	1.42030e24i	0.108527	−	0.187974i
$846$	2.22028e25			2.90911
$847$	4.04150e24	+	6.28814e24i	0.524244	+	0.815668i
$848$	−5.07637e23			−0.0651911
$849$	3.08551e24	−	5.34426e24i	0.392294	−	0.679474i
$850$	−8.56783e23	−	1.48399e24i	−0.107848	−	0.186797i
$851$	2.41082e24	+	4.17565e24i	0.300443	+	0.520383i
$852$	−6.14118e24	+	1.06368e25i	−0.757731	+	1.31243i
$853$	2.16190e24			0.264101			0.132050	−	0.991243i	$-0.457844\pi$
$853$	2.16190e24			0.264101			0.132050	+	0.991243i	$0.457844\pi$
$854$	1.20306e25	−	5.73569e23i	1.45511	−	0.0693735i
$855$	−1.72880e25			−2.07030
$856$	2.41758e24	−	4.18737e24i	0.286651	−	0.496495i
$857$	−1.06421e24	−	1.84327e24i	−0.124937	−	0.216398i	0.796771	−	0.604281i	$-0.206540\pi$
$857$	−1.06421e24	−	1.84327e24i	−0.124937	−	0.216398i	−0.921708	+	0.387883i	$0.873206\pi$
$858$	1.83678e24	+	3.18139e24i	0.213508	+	0.369807i
$859$	−2.67319e24	+	4.63011e24i	−0.307672	+	0.532904i	−0.977853	−	0.209294i	$-0.932883\pi$
$859$	−2.67319e24	+	4.63011e24i	−0.307672	+	0.532904i	0.670180	+	0.742198i	$0.266217\pi$
$860$	−1.35319e24			−0.154214
$861$	−4.69497e24	+	2.23836e23i	−0.529793	+	0.0252582i
$862$	1.95264e25			2.18178
$863$	7.15675e23	−	1.23959e24i	0.0791816	−	0.137147i	−0.823715	−	0.567003i	$-0.808103\pi$
$863$	7.15675e23	−	1.23959e24i	0.0791816	−	0.137147i	0.902897	+	0.429857i	$0.141436\pi$
$864$	1.97232e25	+	3.41615e25i	2.16078	+	3.74258i
$865$	1.47420e24	+	2.55339e24i	0.159926	+	0.277001i
$866$	5.79701e24	−	1.00407e25i	0.622734	−	1.07861i
$867$	1.72824e25			1.83841
$868$	8.98736e22	+	1.39834e23i	0.00946704	+	0.0147297i
$869$	−1.31729e24			−0.137409
$870$	−1.05966e25	+	1.83538e25i	−1.09459	+	1.89589i
$871$	1.72601e24	+	2.98953e24i	0.176558	+	0.305808i
$872$	−9.54213e23	−	1.65275e24i	−0.0966619	−	0.167423i
$873$	−7.84874e24	+	1.35944e25i	−0.787370	+	1.36377i
$874$	−9.86680e24			−0.980233
$875$	4.69825e24	−	9.11421e24i	0.462240	−	0.896707i
$876$	−3.64283e25			−3.54939
$877$	3.39347e24	−	5.87766e24i	0.327452	−	0.567163i	−0.654554	−	0.756016i	$-0.727143\pi$
$877$	3.39347e24	−	5.87766e24i	0.327452	−	0.567163i	0.982006	+	0.188852i	$0.0604767\pi$
$878$	−1.15477e24	−	2.00013e24i	−0.110355	−	0.191141i
$879$	−2.29330e24	−	3.97212e24i	−0.217048	−	0.375938i
$880$	−2.18699e23	+	3.78798e23i	−0.0204995	+	0.0355062i
$881$	−7.68562e24			−0.713483			−0.356742	−	0.934203i	$-0.616112\pi$
$881$	−7.68562e24			−0.713483			−0.356742	+	0.934203i	$0.616112\pi$
$882$	1.94758e25	−	4.26551e25i	1.79066	−	3.92183i
$883$	1.33906e25			1.21936			0.609682	−	0.792646i	$-0.291297\pi$
$883$	1.33906e25			1.21936			0.609682	+	0.792646i	$0.291297\pi$
$884$	−1.47176e24	+	2.54916e24i	−0.132737	+	0.229907i
$885$	−8.03825e24	−	1.39227e25i	−0.718032	−	1.24367i
$886$	−8.42453e24	−	1.45917e25i	−0.745348	−	1.29098i
$887$	7.11026e24	−	1.23153e25i	0.623067	−	1.07918i	−0.365845	−	0.930676i	$-0.619220\pi$
$887$	7.11026e24	−	1.23153e25i	0.623067	−	1.07918i	0.988911	−	0.148507i	$-0.0474468\pi$
$888$	1.73416e25			1.50515
$889$	−7.35663e24	+	1.42713e25i	−0.632432	+	1.22687i
$890$	1.54696e25			1.31724
$891$	3.99764e24	−	6.92412e24i	0.337166	−	0.583988i
$892$	4.96299e24	+	8.59615e24i	0.414612	+	0.718130i
$893$	−4.86098e24	−	8.41947e24i	−0.402241	−	0.696702i
$894$	−3.62547e25	+	6.27949e25i	−2.97163	+	5.14702i
$895$	7.47504e24			0.606901
$896$	−8.27806e24	−	1.28798e25i	−0.665749	−	1.03584i
$897$	1.03784e25			0.826788
$898$	2.23236e24	−	3.86656e24i	0.176163	−	0.305123i
$899$	8.97268e22	+	1.55411e23i	0.00701399	+	0.0121486i
$900$	1.54904e25	+	2.68302e25i	1.19950	+	2.07760i
$901$	−2.59522e23	+	4.49505e23i	−0.0199074	+	0.0344806i
$902$	9.79069e23			0.0743974
$903$	4.39740e24	−	2.09649e23i	0.331017	−	0.0157815i
$904$	7.29534e23			0.0544019
$905$	3.80447e24	−	6.58953e24i	0.281048	−	0.486790i
$906$	−4.03680e25	−	6.99194e25i	−2.95425	−	5.11691i
$907$	1.13753e25	+	1.97026e25i	0.824709	+	1.42844i	0.902142	+	0.431440i	$0.141994\pi$
$907$	1.13753e25	+	1.97026e25i	0.824709	+	1.42844i	−0.0774333	+	0.996998i	$0.524672\pi$
$908$	1.31342e25	−	2.27492e25i	0.943355	−	1.63394i
$909$	−2.86190e25			−2.03639
$910$	−1.12487e25	+	5.36292e23i	−0.792962	+	0.0378050i
$911$	−2.21449e25			−1.54656			−0.773282	−	0.634062i	$-0.781386\pi$
$911$	−2.21449e25			−1.54656			−0.773282	+	0.634062i	$0.781386\pi$
$912$	6.25232e24	−	1.08293e25i	0.432599	−	0.749283i
$913$	1.88908e24	+	3.27198e24i	0.129494	+	0.224290i
$914$	1.00961e25	+	1.74869e25i	0.685661	+	1.18760i
$915$	−8.45730e24	+	1.46485e25i	−0.569053	+	0.985629i
$916$	8.53407e24			0.568912
$917$	−1.86200e24	−	2.89708e24i	−0.122982	−	0.191347i
$918$	1.86290e25			1.21907
$919$	−5.22419e24	+	9.04857e24i	−0.338717	+	0.586676i	−0.984192	−	0.177106i	$-0.943326\pi$
$919$	−5.22419e24	+	9.04857e24i	−0.338717	+	0.586676i	0.645474	+	0.763782i	$0.276660\pi$
$920$	−1.75344e24	−	3.03704e24i	−0.112640	−	0.195098i
$921$	2.38100e25	+	4.12401e25i	1.51549	+	2.62490i
$922$	6.15558e24	−	1.06618e25i	0.388200	−	0.672383i
$923$	−7.04593e24			−0.440275
$924$	−3.59308e24	+	6.97028e24i	−0.222462	+	0.431557i
$925$	−1.12459e25			−0.689905
$926$	−2.22104e25	+	3.84696e25i	−1.35009	+	2.33843i
$927$	7.34256e24	+	1.27177e25i	0.442252	+	0.766003i
$928$	−1.21837e25	−	2.11028e25i	−0.727147	−	1.25946i
$929$	1.43310e25	−	2.48221e25i	0.847509	−	1.46793i	−0.0359162	−	0.999355i	$-0.511435\pi$
$929$	1.43310e25	−	2.48221e25i	0.847509	−	1.46793i	0.883425	−	0.468573i	$-0.155232\pi$
$930$	−3.96018e23			−0.0232065
$931$	−2.04391e25	+	1.95333e24i	−1.18683	+	0.113424i
$932$	2.22711e25			1.28146
$933$	2.91036e24	−	5.04089e24i	0.165941	−	0.287418i
$934$	1.46311e24	+	2.53418e24i	0.0826661	+	0.143182i
$935$	2.23614e23	+	3.87310e23i	0.0125199	+	0.0216850i
$936$	1.37030e25	−	2.37342e25i	0.760273	−	1.31683i
$937$	−1.68452e25			−0.926166			−0.463083	−	0.886315i	$-0.653257\pi$
$937$	−1.68452e25			−0.926166			−0.463083	+	0.886315i	$0.653257\pi$
$938$	−5.72783e24	+	1.11115e25i	−0.312080	+	0.605410i
$939$	1.34024e25			0.723645
$940$	5.69140e24	−	9.85779e24i	0.304532	−	0.527464i
$941$	−6.83322e24	−	1.18355e25i	−0.362338	−	0.627588i	0.626007	−	0.779817i	$-0.284688\pi$
$941$	−6.83322e24	−	1.18355e25i	−0.362338	−	0.627588i	−0.988345	+	0.152230i	$0.951355\pi$
$942$	−3.13899e25	−	5.43689e25i	−1.64952	−	2.85705i
$943$	1.38301e24	−	2.39545e24i	0.0720240	−	0.124749i
$944$	8.53763e24			0.440631
$945$	2.27153e25	+	3.53427e25i	1.16185	+	1.80771i
$946$	−9.17016e23			−0.0464838
$947$	−1.02608e25	+	1.77722e25i	−0.515472	+	0.892825i	0.484366	+	0.874865i	$0.339050\pi$
$947$	−1.02608e25	+	1.77722e25i	−0.515472	+	0.892825i	−0.999839	+	0.0179592i	$0.994283\pi$
$948$	2.20467e25	+	3.81859e25i	1.09767	+	1.90122i
$949$	−1.04488e25	−	1.80978e25i	−0.515588	−	0.893025i
$950$	1.15066e25	−	1.99300e25i	0.562724	−	0.974667i
$951$	5.56576e25			2.69768
$952$	−3.23216e24	+	1.54095e23i	−0.155267	+	0.00740246i
$953$	−3.67636e25			−1.75037			−0.875183	−	0.483793i	$-0.839259\pi$
$953$	−3.67636e25			−1.75037			−0.875183	+	0.483793i	$0.839259\pi$
$954$	7.95983e24	−	1.37868e25i	0.375615	−	0.650584i
$955$	−3.78031e24	−	6.54770e24i	−0.176807	−	0.306239i
$956$	1.03957e25	+	1.80059e25i	0.481905	+	0.834683i
$957$	−4.23298e24	+	7.33173e24i	−0.194489	+	0.336864i
$958$	3.83771e25			1.74769
$959$	1.98248e25	−	9.45160e23i	0.894850	−	0.0426626i
$960$	4.35775e25			1.94965
$961$	1.12734e25	−	1.95261e25i	0.499926	−	0.865897i
$962$	1.63858e25	+	2.83810e25i	0.720243	+	1.24750i
$963$	−2.67154e25	−	4.62725e25i	−1.16396	−	2.01604i
$964$	−2.26642e25	+	3.92556e25i	−0.978783	+	1.69530i
$965$	−2.08838e25			−0.893980
$966$	2.03206e25	+	3.16167e25i	0.862246	+	1.34156i
$967$	1.72741e25			0.726558			0.363279	−	0.931680i	$-0.381657\pi$
$967$	1.72741e25			0.726558			0.363279	+	0.931680i	$0.381657\pi$
$968$	−7.91047e24	+	1.37013e25i	−0.329808	+	0.571245i
$969$	−6.39283e24	−	1.10727e25i	−0.264205	−	0.457616i
$970$	6.82620e24	+	1.18233e25i	0.279653	+	0.484373i
$971$	−1.59740e25	+	2.76677e25i	−0.648708	+	1.12360i	0.334723	+	0.942316i	$0.391357\pi$
$971$	−1.59740e25	+	2.76677e25i	−0.648708	+	1.12360i	−0.983432	+	0.181279i	$0.941976\pi$
$972$	−1.45695e26			−5.86518
$973$	9.96291e24	−	1.93272e25i	0.397582	−	0.771278i
$974$	9.19846e24			0.363885
$975$	−1.21032e25	+	2.09633e25i	−0.474636	+	0.822094i
$976$	−4.49136e24	−	7.77926e24i	−0.174604	−	0.302423i
$977$	−1.96759e24	−	3.40797e24i	−0.0758283	−	0.131338i	0.825618	−	0.564230i	$-0.190827\pi$
$977$	−1.96759e24	−	3.40797e24i	−0.0758283	−	0.131338i	−0.901446	+	0.432891i	$0.857493\pi$
$978$	3.87911e24	−	6.71881e24i	0.148201	−	0.256692i
$979$	6.17958e24			0.234049
$980$	−1.39460e25	−	1.95811e25i	−0.523634	−	0.735218i
$981$	−2.10890e25			−0.785001
$982$	−2.40154e23	+	4.15958e23i	−0.00886220	+	0.0153498i
$983$	2.20473e25	+	3.81871e25i	0.806587	+	1.39705i	0.915214	+	0.402967i	$0.132021\pi$
$983$	2.20473e25	+	3.81871e25i	0.806587	+	1.39705i	−0.108627	+	0.994083i	$0.534645\pi$
$984$	−4.97418e24	−	8.61553e24i	−0.180411	−	0.312481i
$985$	2.15914e24	−	3.73974e24i	0.0776377	−	0.134473i
$986$	−1.15078e25			−0.410242
$987$	−1.69678e25	+	3.29162e25i	−0.599694	+	1.16336i
$988$	−3.95314e25			−1.38518
$989$	−1.29536e24	+	2.24363e24i	−0.0450010	+	0.0779439i
$990$	−6.85848e24	−	1.18792e25i	−0.236226	−	0.409156i
$991$	−1.44605e25	−	2.50463e25i	−0.493806	−	0.855298i	0.506168	−	0.862435i	$-0.331061\pi$
$991$	−1.44605e25	−	2.50463e25i	−0.493806	−	0.855298i	−0.999975	+	0.00713714i	$0.997728\pi$
$992$	2.27666e23	−	3.94329e23i	0.00770812	−	0.0133509i
$993$	8.43615e25			2.83188
$994$	−1.37958e25	−	2.14647e25i	−0.459157	−	0.714400i
$995$	1.92090e24			0.0633883
$996$	6.32325e25	−	1.09522e26i	2.06888	−	3.58341i
$997$	1.86675e25	+	3.23331e25i	0.605589	+	1.04891i	0.991958	+	0.126567i	$0.0403957\pi$
$997$	1.86675e25	+	3.23331e25i	0.605589	+	1.04891i	−0.386369	+	0.922344i	$0.626271\pi$
$998$	1.58901e25	+	2.75225e25i	0.511115	+	0.885276i
$999$	6.11299e25	−	1.05880e26i	1.94961	−	3.37682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.c.a.2.9	✓	20
7.2	even	3		49.18.a.f.1.2		10
7.4	even	3	inner	7.18.c.a.4.9	yes	20
7.5	odd	6		49.18.a.g.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.c.a.2.9	✓	20	1.1	even	1	trivial
7.18.c.a.4.9	yes	20	7.4	even	3	inner
49.18.a.f.1.2		10	7.2	even	3
49.18.a.g.1.2		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)

\(f(q)\)	\(=\)	\(q+(282.522 - 489.343i) q^{2} +(11021.2 + 19089.3i) q^{3} +(-94101.8 - 162989. i) q^{4} +(-274540. + 475518. i) q^{5} +1.24550e7 q^{6} +(-6.98844e6 + 1.35570e7i) q^{7} -3.22819e7 q^{8} +(-1.78365e8 + 3.08938e8i) q^{9} +O(q^{10})\)	\(q+(282.522 - 489.343i) q^{2} +(11021.2 + 19089.3i) q^{3} +(-94101.8 - 162989. i) q^{4} +(-274540. + 475518. i) q^{5} +1.24550e7 q^{6} +(-6.98844e6 + 1.35570e7i) q^{7} -3.22819e7 q^{8} +(-1.78365e8 + 3.08938e8i) q^{9} +(1.55128e8 + 2.68689e8i) q^{10} +(6.19681e7 + 1.07332e8i) q^{11} +(2.07424e9 - 3.59268e9i) q^{12} +2.37982e9 q^{13} +(4.65963e9 + 7.24990e9i) q^{14} -1.21031e10 q^{15} +(3.21375e9 - 5.56638e9i) q^{16} +(-3.28597e9 - 5.69147e9i) q^{17} +(1.00784e11 + 1.74564e11i) q^{18} +(4.41305e10 - 7.64363e10i) q^{19} +1.03339e11 q^{20} +(-3.35815e11 + 1.60102e10i) q^{21} +7.00295e10 q^{22} +(9.89224e10 - 1.71339e11i) q^{23} +(-3.55786e11 - 6.16240e11i) q^{24} +(2.30725e11 + 3.99627e11i) q^{25} +(6.72354e11 - 1.16455e12i) q^{26} -5.01665e12 q^{27} +(2.86727e12 - 1.36699e11i) q^{28} +3.09897e12 q^{29} +(-3.41940e12 + 5.92257e12i) q^{30} +(2.89538e10 + 5.01494e10i) q^{31} +(-3.93154e12 - 6.80963e12i) q^{32} +(-1.36593e12 + 2.36586e12i) q^{33} -3.71344e12 q^{34} +(-4.52799e12 - 7.04507e12i) q^{35} +6.71380e13 q^{36} +(-1.21854e13 + 2.11057e13i) q^{37} +(-2.49357e13 - 4.31899e13i) q^{38} +(2.62286e13 + 4.54293e13i) q^{39} +(8.86268e12 - 1.53506e13i) q^{40} +1.39808e13 q^{41} +(-8.70409e13 + 1.68852e14i) q^{42} -1.30947e13 q^{43} +(1.16626e13 - 2.02003e13i) q^{44} +(-9.79369e13 - 1.69632e14i) q^{45} +(-5.58956e13 - 9.68140e13i) q^{46} +(5.50751e13 - 9.53928e13i) q^{47} +1.41678e14 q^{48} +(-1.34954e14 - 1.89485e14i) q^{49} +2.60740e14 q^{50} +(7.24309e13 - 1.25454e14i) q^{51} +(-2.23946e14 - 3.87885e14i) q^{52} +(-3.94894e13 - 6.83977e13i) q^{53} +(-1.41732e15 + 2.45487e15i) q^{54} -6.80510e13 q^{55} +(2.25600e14 - 4.37646e14i) q^{56} +1.94549e15 q^{57} +(8.75528e14 - 1.51646e15i) q^{58} +(6.64148e14 + 1.15034e15i) q^{59} +(1.13892e15 + 1.97267e15i) q^{60} +(6.98772e14 - 1.21031e15i) q^{61} +3.27204e13 q^{62} +(-2.94177e15 - 4.57709e15i) q^{63} -3.60053e15 q^{64} +(-6.53358e14 + 1.13165e15i) q^{65} +(7.71812e14 + 1.33682e15i) q^{66} +(7.25266e14 + 1.25620e15i) q^{67} +(-6.18431e14 + 1.07115e15i) q^{68} +4.36099e15 q^{69} +(-4.72671e15 + 2.25349e14i) q^{70} -2.96069e15 q^{71} +(5.75797e15 - 9.97309e15i) q^{72} +(-4.39057e15 - 7.60469e15i) q^{73} +(6.88529e15 + 1.19257e16i) q^{74} +(-5.08575e15 + 8.80878e15i) q^{75} -1.66110e16 q^{76} +(-1.88816e15 + 9.00193e13i) q^{77} +2.96407e16 q^{78} +(-5.31440e15 + 9.20482e15i) q^{79} +(1.76461e15 + 3.05639e15i) q^{80} +(-3.22556e16 - 5.58684e16i) q^{81} +(3.94989e15 - 6.84141e15i) q^{82} +3.04847e16 q^{83} +(3.42103e16 + 5.32277e16i) q^{84} +3.60852e15 q^{85} +(-3.69955e15 + 6.40780e15i) q^{86} +(3.41545e16 + 5.91573e16i) q^{87} +(-2.00045e15 - 3.46488e15i) q^{88} +(2.49305e16 - 4.31808e16i) q^{89} -1.10677e17 q^{90} +(-1.66313e16 + 3.22633e16i) q^{91} -3.72351e16 q^{92} +(-6.38213e14 + 1.10542e15i) q^{93} +(-3.11199e16 - 5.39012e16i) q^{94} +(2.42312e16 + 4.19697e16i) q^{95} +(8.66609e16 - 1.50101e17i) q^{96} +4.40038e16 q^{97} +(-1.30850e17 + 1.25052e16i) q^{98} -4.42118e16 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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