LMFDB - Embedded newform 7.18.c.a.4.2

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			4.2
Root			$-139.056 - 240.852i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.18.c.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-265.112 - 459.187i) q^{2} +(9523.58 - 16495.3i) q^{3} +(-75032.3 + 129960. i) q^{4} +(224503. + 388850. i) q^{5} -1.00992e7 q^{6} +(-1.05114e7 + 1.10518e7i) q^{7} +1.00703e7 q^{8} +(-1.16827e8 - 2.02350e8i) q^{9} +O(q^{10})$	\(q+(-265.112 - 459.187i) q^{2} +(9523.58 - 16495.3i) q^{3} +(-75032.3 + 129960. i) q^{4} +(224503. + 388850. i) q^{5} -1.00992e7 q^{6} +(-1.05114e7 + 1.10518e7i) q^{7} +1.00703e7 q^{8} +(-1.16827e8 - 2.02350e8i) q^{9} +(1.19037e8 - 2.06177e8i) q^{10} +(-5.29396e8 + 9.16941e8i) q^{11} +(1.42915e9 + 2.47536e9i) q^{12} -1.79049e9 q^{13} +(7.86151e9 + 1.89672e9i) q^{14} +8.55228e9 q^{15} +(7.16487e9 + 1.24099e10i) q^{16} +(2.07991e9 - 3.60250e9i) q^{17} +(-6.19444e10 + 1.07291e11i) q^{18} +(-4.53233e10 - 7.85022e10i) q^{19} -6.73799e10 q^{20} +(8.21968e10 + 2.78641e11i) q^{21} +5.61396e11 q^{22} +(-3.17674e11 - 5.50228e11i) q^{23} +(9.59057e10 - 1.66114e11i) q^{24} +(2.80667e11 - 4.86129e11i) q^{25} +(4.74678e11 + 8.22167e11i) q^{26} -1.99069e12 q^{27} +(-6.47595e11 - 2.19530e12i) q^{28} -1.62529e12 q^{29} +(-2.26731e12 - 3.92709e12i) q^{30} +(-1.43358e12 + 2.48304e12i) q^{31} +(4.45895e12 - 7.72313e12i) q^{32} +(1.00835e13 + 1.74651e13i) q^{33} -2.20563e12 q^{34} +(-6.65732e12 - 1.60619e12i) q^{35} +3.50632e13 q^{36} +(3.61127e11 + 6.25491e11i) q^{37} +(-2.40315e13 + 4.16237e13i) q^{38} +(-1.70518e13 + 2.95346e13i) q^{39} +(2.26082e12 + 3.91586e12i) q^{40} -8.70450e13 q^{41} +(1.06157e14 - 1.11615e14i) q^{42} +3.31253e13 q^{43} +(-7.94436e13 - 1.37600e14i) q^{44} +(5.24560e13 - 9.08564e13i) q^{45} +(-1.68438e14 + 2.91744e14i) q^{46} +(3.10754e13 + 5.38242e13i) q^{47} +2.72941e14 q^{48} +(-1.16530e13 - 2.32338e14i) q^{49} -2.97632e14 q^{50} +(-3.96163e13 - 6.86175e13i) q^{51} +(1.34344e14 - 2.32691e14i) q^{52} +(3.11897e14 - 5.40221e14i) q^{53} +(5.27755e14 + 9.14099e14i) q^{54} -4.75404e14 q^{55} +(-1.05853e14 + 1.11295e14i) q^{56} -1.72656e15 q^{57} +(4.30885e14 + 7.46314e14i) q^{58} +(2.18484e14 - 3.78425e14i) q^{59} +(-6.41698e14 + 1.11145e15i) q^{60} +(9.27168e14 + 1.60590e15i) q^{61} +1.52024e15 q^{62} +(3.46434e15 + 8.35832e14i) q^{63} -2.85025e15 q^{64} +(-4.01969e14 - 6.96231e14i) q^{65} +(5.34650e15 - 9.26041e15i) q^{66} +(-3.75721e14 + 6.50768e14i) q^{67} +(3.12120e14 + 5.40609e14i) q^{68} -1.21016e16 q^{69} +(1.02739e15 + 3.48277e15i) q^{70} -3.64485e15 q^{71} +(-1.17649e15 - 2.03774e15i) q^{72} +(-2.44389e15 + 4.23294e15i) q^{73} +(1.91478e14 - 3.31650e14i) q^{74} +(-5.34590e15 - 9.25937e15i) q^{75} +1.36028e16 q^{76} +(-4.56915e15 - 1.54891e16i) q^{77} +1.80826e16 q^{78} +(8.44607e15 + 1.46290e16i) q^{79} +(-3.21707e15 + 5.57213e15i) q^{80} +(-3.87145e15 + 6.70554e15i) q^{81} +(2.30767e16 + 3.99699e16i) q^{82} +1.74297e16 q^{83} +(-4.23795e16 - 1.02248e16i) q^{84} +1.86778e15 q^{85} +(-8.78190e15 - 1.52107e16i) q^{86} +(-1.54786e16 + 2.68098e16i) q^{87} +(-5.33120e15 + 9.23391e15i) q^{88} +(-2.22441e16 - 3.85280e16i) q^{89} -5.56268e16 q^{90} +(1.88204e16 - 1.97880e16i) q^{91} +9.53433e16 q^{92} +(2.73057e16 + 4.72948e16i) q^{93} +(1.64769e16 - 2.85389e16i) q^{94} +(2.03504e16 - 3.52479e16i) q^{95} +(-8.49303e16 - 1.47104e17i) q^{96} -9.07758e16 q^{97} +(-1.03597e17 + 6.69465e16i) q^{98} +2.47391e17 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 $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−265.112	−	459.187i	−0.732274	−	1.26834i	−0.955909	−	0.293663i	$-0.905126\pi$
$2$	−265.112	−	459.187i	−0.732274	−	1.26834i	0.223635	−	0.974673i	$-0.428208\pi$
$3$	9523.58	−	16495.3i	0.838049	−	1.45154i	−0.0534744	−	0.998569i	$-0.517030\pi$
$3$	9523.58	−	16495.3i	0.838049	−	1.45154i	0.891524	−	0.452974i	$-0.149637\pi$
$4$	−75032.3	+	129960.i	−0.572451	+	0.991515i
$5$	224503.	+	388850.i	0.257026	+	0.445182i	0.965444	−	0.260611i	$-0.0839241\pi$
$5$	224503.	+	388850.i	0.257026	+	0.445182i	−0.708418	+	0.705793i	$0.750591\pi$
$6$	−1.00992e7			−2.45473
$7$	−1.05114e7	+	1.10518e7i	−0.689169	+	0.724601i
$7$	−1.05114e7	+	1.10518e7i	−0.689169	+	0.724601i
$8$	1.00703e7			0.212217
$9$	−1.16827e8	−	2.02350e8i	−0.904653	−	1.56690i
$10$	1.19037e8	−	2.06177e8i	0.376427	−	0.651990i
$11$	−5.29396e8	+	9.16941e8i	−0.744634	+	1.28974i	0.205731	+	0.978608i	$0.434043\pi$
$11$	−5.29396e8	+	9.16941e8i	−0.744634	+	1.28974i	−0.950366	+	0.311136i	$0.899291\pi$
$12$	1.42915e9	+	2.47536e9i	0.959485	+	1.66188i
$13$	−1.79049e9			−0.608769			−0.304384	−	0.952549i	$-0.598451\pi$
$13$	−1.79049e9			−0.608769			−0.304384	+	0.952549i	$0.598451\pi$
$14$	7.86151e9	+	1.89672e9i	1.42370	+	0.343492i
$15$	8.55228e9			0.861601
$16$	7.16487e9	+	1.24099e10i	0.417050	+	0.722352i
$17$	2.07991e9	−	3.60250e9i	0.0723149	−	0.125253i	−0.827601	−	0.561317i	$-0.810295\pi$
$17$	2.07991e9	−	3.60250e9i	0.0723149	−	0.125253i	0.899915	+	0.436064i	$0.143628\pi$
$18$	−6.19444e10	+	1.07291e11i	−1.32491	+	2.29481i
$19$	−4.53233e10	−	7.85022e10i	−0.612231	−	1.06042i	−0.990863	−	0.134869i	$-0.956939\pi$
$19$	−4.53233e10	−	7.85022e10i	−0.612231	−	1.06042i	0.378632	−	0.925547i	$-0.376395\pi$
$20$	−6.73799e10			−0.588539
$21$	8.21968e10	+	2.78641e11i	0.474232	+	1.60761i
$22$	5.61396e11			2.18111
$23$	−3.17674e11	−	5.50228e11i	−0.845854	−	1.46506i	−0.884878	−	0.465823i	$-0.845758\pi$
$23$	−3.17674e11	−	5.50228e11i	−0.845854	−	1.46506i	0.0390240	−	0.999238i	$-0.487575\pi$
$24$	9.59057e10	−	1.66114e11i	0.177848	−	0.308042i
$25$	2.80667e11	−	4.86129e11i	0.367875	−	0.637179i
$26$	4.74678e11	+	8.22167e11i	0.445786	+	0.772123i
$27$	−1.99069e12			−1.35648
$28$	−6.47595e11	−	2.19530e12i	−0.323937	−	1.09812i
$29$	−1.62529e12			−0.603322			−0.301661	−	0.953415i	$-0.597541\pi$
$29$	−1.62529e12			−0.603322			−0.301661	+	0.953415i	$0.597541\pi$
$30$	−2.26731e12	−	3.92709e12i	−0.630928	−	1.09280i
$31$	−1.43358e12	+	2.48304e12i	−0.301890	+	0.522888i	−0.976564	−	0.215227i	$-0.930951\pi$
$31$	−1.43358e12	+	2.48304e12i	−0.301890	+	0.522888i	0.674674	+	0.738116i	$0.264284\pi$
$32$	4.45895e12	−	7.72313e12i	0.716899	−	1.24171i
$33$	1.00835e13	+	1.74651e13i	1.24808	+	2.16174i
$34$	−2.20563e12			−0.211817
$35$	−6.65732e12	−	1.60619e12i	−0.499713	−	0.120564i
$36$	3.50632e13			2.07148
$37$	3.61127e11	+	6.25491e11i	0.0169023	+	0.0292756i	0.874353	−	0.485291i	$-0.161286\pi$
$37$	3.61127e11	+	6.25491e11i	0.0169023	+	0.0292756i	−0.857451	+	0.514566i	$0.827953\pi$
$38$	−2.40315e13	+	4.16237e13i	−0.896643	+	1.55303i
$39$	−1.70518e13	+	2.95346e13i	−0.510178	+	0.883654i
$40$	2.26082e12	+	3.91586e12i	0.0545452	+	0.0944750i
$41$	−8.70450e13			−1.70248			−0.851239	−	0.524779i	$-0.824148\pi$
$41$	−8.70450e13			−1.70248			−0.851239	+	0.524779i	$0.824148\pi$
$42$	1.06157e14	−	1.11615e14i	1.69172	−	1.77870i
$43$	3.31253e13			0.432193			0.216097	−	0.976372i	$-0.430667\pi$
$43$	3.31253e13			0.432193			0.216097	+	0.976372i	$0.430667\pi$
$44$	−7.94436e13	−	1.37600e14i	−0.852533	−	1.47663i
$45$	5.24560e13	−	9.08564e13i	0.465038	−	0.805470i
$46$	−1.68438e14	+	2.91744e14i	−1.23879	+	2.14565i
$47$	3.10754e13	+	5.38242e13i	0.190364	+	0.329721i	0.945371	−	0.325996i	$-0.105700\pi$
$47$	3.10754e13	+	5.38242e13i	0.190364	+	0.329721i	−0.755007	+	0.655717i	$0.772366\pi$
$48$	2.72941e14			1.39803
$49$	−1.16530e13	−	2.32338e14i	−0.0500923	−	0.998745i
$50$	−2.97632e14			−1.07754
$51$	−3.96163e13	−	6.86175e13i	−0.121207	−	0.209937i
$52$	1.34344e14	−	2.32691e14i	0.348490	−	0.603603i
$53$	3.11897e14	−	5.40221e14i	0.688123	−	1.19186i	−0.284322	−	0.958729i	$-0.591768\pi$
$53$	3.11897e14	−	5.40221e14i	0.688123	−	1.19186i	0.972444	−	0.233135i	$-0.0748983\pi$
$54$	5.27755e14	+	9.14099e14i	0.993312	+	1.72047i
$55$	−4.75404e14			−0.765561
$56$	−1.05853e14	+	1.11295e14i	−0.146253	+	0.153772i
$57$	−1.72656e15			−2.05232
$58$	4.30885e14	+	7.46314e14i	0.441797	+	0.765215i
$59$	2.18484e14	−	3.78425e14i	0.193721	−	0.335535i	−0.752759	−	0.658296i	$-0.771278\pi$
$59$	2.18484e14	−	3.78425e14i	0.193721	−	0.335535i	0.946481	+	0.322761i	$0.104611\pi$
$60$	−6.41698e14	+	1.11145e15i	−0.493225	+	0.854290i
$61$	9.27168e14	+	1.60590e15i	0.619234	+	1.07254i	0.989626	+	0.143669i	$0.0458900\pi$
$61$	9.27168e14	+	1.60590e15i	0.619234	+	1.07254i	−0.370392	+	0.928876i	$0.620777\pi$
$62$	1.52024e15			0.884264
$63$	3.46434e15	+	8.35832e14i	1.75884	+	0.424350i
$64$	−2.85025e15			−1.26577
$65$	−4.01969e14	−	6.96231e14i	−0.156469	−	0.271013i
$66$	5.34650e15	−	9.26041e15i	1.82787	−	3.16597i
$67$	−3.75721e14	+	6.50768e14i	−0.113039	+	0.195790i	−0.916994	−	0.398900i	$-0.869392\pi$
$67$	−3.75721e14	+	6.50768e14i	−0.113039	+	0.195790i	0.803955	+	0.594690i	$0.202725\pi$
$68$	3.12120e14	+	5.40609e14i	0.0827936	+	0.143403i
$69$	−1.21016e16			−2.83547
$70$	1.02739e15	+	3.48277e15i	0.213011	+	0.722091i
$71$	−3.64485e15			−0.669859			−0.334930	−	0.942243i	$-0.608713\pi$
$71$	−3.64485e15			−0.669859			−0.334930	+	0.942243i	$0.608713\pi$
$72$	−1.17649e15	−	2.03774e15i	−0.191982	−	0.332523i
$73$	−2.44389e15	+	4.23294e15i	−0.354681	+	0.614325i	−0.987063	−	0.160331i	$-0.948744\pi$
$73$	−2.44389e15	+	4.23294e15i	−0.354681	+	0.614325i	0.632383	+	0.774656i	$0.282077\pi$
$74$	1.91478e14	−	3.31650e14i	0.0247542	−	0.0428756i
$75$	−5.34590e15	−	9.25937e15i	−0.616595	−	1.06797i
$76$	1.36028e16			1.40189
$77$	−4.56915e15	−	1.54891e16i	−0.421371	−	1.42841i
$78$	1.80826e16			1.49436
$79$	8.44607e15	+	1.46290e16i	0.626360	+	1.08489i	0.988276	+	0.152677i	$0.0487895\pi$
$79$	8.44607e15	+	1.46290e16i	0.626360	+	1.08489i	−0.361916	+	0.932211i	$0.617877\pi$
$80$	−3.21707e15	+	5.57213e15i	−0.214385	+	0.371327i
$81$	−3.87145e15	+	6.70554e15i	−0.232140	+	0.402079i
$82$	2.30767e16	+	3.99699e16i	1.24668	+	2.15931i
$83$	1.74297e16			0.849429			0.424715	−	0.905327i	$-0.360374\pi$
$83$	1.74297e16			0.849429			0.424715	+	0.905327i	$0.360374\pi$
$84$	−4.23795e16	−	1.02248e16i	−1.86544	−	0.450070i
$85$	1.86778e15			0.0743472
$86$	−8.78190e15	−	1.52107e16i	−0.316484	−	0.548166i
$87$	−1.54786e16	+	2.68098e16i	−0.505614	+	0.875748i
$88$	−5.33120e15	+	9.23391e15i	−0.158024	+	0.273705i
$89$	−2.22441e16	−	3.85280e16i	−0.598963	−	1.03743i	−0.992974	−	0.118329i	$-0.962246\pi$
$89$	−2.22441e16	−	3.85280e16i	−0.598963	−	1.03743i	0.394011	−	0.919106i	$-0.371087\pi$
$90$	−5.56268e16			−1.36214
$91$	1.88204e16	−	1.97880e16i	0.419544	−	0.441114i
$92$	9.53433e16			1.93684
$93$	2.73057e16	+	4.72948e16i	0.505997	+	0.876412i
$94$	1.64769e16	−	2.85389e16i	0.278798	−	0.482892i
$95$	2.03504e16	−	3.52479e16i	0.314719	−	0.545109i
$96$	−8.49303e16	−	1.47104e17i	−1.20159	−	2.08122i
$97$	−9.07758e16			−1.17601			−0.588004	−	0.808858i	$-0.700086\pi$
$97$	−9.07758e16			−1.17601			−0.588004	+	0.808858i	$0.700086\pi$
$98$	−1.03597e17	+	6.69465e16i	−1.23006	+	0.794889i
$99$	2.47391e17			2.69454
$100$	4.21181e16	+	7.29508e16i	0.421181	+	0.729508i
$101$	3.59698e16	−	6.23016e16i	0.330527	−	0.572489i	−0.652088	−	0.758143i	$-0.726107\pi$
$101$	3.59698e16	−	6.23016e16i	0.330527	−	0.572489i	0.982615	+	0.185654i	$0.0594402\pi$
$102$	−2.10055e16	+	3.63826e16i	−0.177513	+	0.307462i
$103$	6.29733e15	+	1.09073e16i	0.0489824	+	0.0848400i	0.889477	−	0.456980i	$-0.151069\pi$
$103$	6.29733e15	+	1.09073e16i	0.0489824	+	0.0848400i	−0.840495	+	0.541820i	$0.817736\pi$
$104$	−1.80308e16			−0.129191
$105$	−8.98961e16	+	9.45179e16i	−0.593789	+	0.624317i
$106$	−3.30750e17			−2.01558
$107$	4.05003e16	+	7.01486e16i	0.227875	+	0.394690i	0.957178	−	0.289500i	$-0.0934890\pi$
$107$	4.05003e16	+	7.01486e16i	0.227875	+	0.394690i	−0.729303	+	0.684190i	$0.760156\pi$
$108$	1.49366e17	−	2.58710e17i	0.776516	−	1.34497i
$109$	4.36056e16	−	7.55271e16i	0.209612	−	0.363059i	−0.741980	−	0.670422i	$-0.766113\pi$
$109$	4.36056e16	−	7.55271e16i	0.209612	−	0.363059i	0.951592	+	0.307363i	$0.0994465\pi$
$110$	1.26035e17	+	2.18299e17i	0.560601	+	0.970989i
$111$	1.37569e16			0.0566598
$112$	−2.12464e17	−	5.12606e16i	−0.810835	−	0.195628i
$113$	−2.13727e17			−0.756296			−0.378148	−	0.925745i	$-0.623439\pi$
$113$	−2.13727e17			−0.756296			−0.378148	+	0.925745i	$0.623439\pi$
$114$	4.57731e17	+	7.92813e17i	1.50286	+	2.60303i
$115$	1.42638e17	−	2.47055e17i	0.434813	−	0.753117i
$116$	1.21950e17	−	2.11223e17i	0.345372	−	0.598203i
$117$	2.09177e17	+	3.62305e17i	0.550724	+	0.953882i
$118$	−2.31690e17			−0.567428
$119$	1.79514e16	+	6.08539e16i	0.0409213	+	0.138720i
$120$	8.61245e16			0.182846
$121$	−3.07797e17	−	5.33120e17i	−0.608960	−	1.05475i
$122$	4.91606e17	−	8.51486e17i	0.906898	−	1.57079i
$123$	−8.28980e17	+	1.43584e18i	−1.42676	+	2.47122i
$124$	−2.15130e17	−	3.72616e17i	−0.345634	−	0.598656i
$125$	5.94606e17			0.892266
$126$	−5.34634e17	−	1.81237e18i	−0.749734	−	2.54154i
$127$	3.85004e17			0.504817			0.252408	−	0.967621i	$-0.418777\pi$
$127$	3.85004e17			0.504817			0.252408	+	0.967621i	$0.418777\pi$
$128$	1.71191e17	+	2.96511e17i	0.209989	+	0.363711i
$129$	3.15471e17	−	5.46412e17i	0.362199	−	0.627347i
$130$	−2.13133e17	+	3.69158e17i	−0.229157	+	0.396911i
$131$	−3.67864e17	−	6.37159e17i	−0.370580	−	0.641863i	0.619075	−	0.785332i	$-0.287508\pi$
$131$	−3.67864e17	−	6.37159e17i	−0.370580	−	0.641863i	−0.989655	+	0.143469i	$0.954174\pi$
$132$	−3.02635e18			−2.85786
$133$	1.34400e18	+	3.24263e17i	1.19031	+	0.287182i
$134$	3.98432e17			0.331103
$135$	−4.46916e17	−	7.74081e17i	−0.348649	−	0.603878i
$136$	2.09454e16	−	3.62785e16i	0.0153464	−	0.0265808i
$137$	−5.39211e17	+	9.33941e17i	−0.371222	+	0.642976i	−0.989754	−	0.142784i	$-0.954395\pi$
$137$	−5.39211e17	+	9.33941e17i	−0.371222	+	0.642976i	0.618532	+	0.785760i	$0.287728\pi$
$138$	3.20827e18	+	5.55688e18i	2.07634	+	3.59633i
$139$	−1.47814e18			−0.899686			−0.449843	−	0.893108i	$-0.648520\pi$
$139$	−1.47814e18			−0.899686			−0.449843	+	0.893108i	$0.648520\pi$
$140$	7.08255e17	−	7.44667e17i	0.405603	−	0.426456i
$141$	1.18380e18			0.638138
$142$	9.66292e17	+	1.67367e18i	0.490521	+	0.849607i
$143$	9.47876e17	−	1.64177e18i	0.453310	−	0.785156i
$144$	1.67410e18	−	2.89963e18i	0.754572	−	1.30696i
$145$	−3.64883e17	−	6.31997e17i	−0.155069	−	0.268588i
$146$	2.59161e18			1.03889
$147$	−3.94348e18	−	2.02047e18i	−1.49170	−	0.764286i
$148$	−1.08385e17			−0.0387030
$149$	1.94490e17	+	3.36867e17i	0.0655865	+	0.113599i	0.896954	−	0.442124i	$-0.145775\pi$
$149$	1.94490e17	+	3.36867e17i	0.0655865	+	0.113599i	−0.831368	+	0.555723i	$0.812442\pi$
$150$	−2.83452e18	+	4.90953e18i	−0.903034	+	1.56410i
$151$	−9.50995e17	+	1.64717e18i	−0.286335	+	0.495947i	−0.972932	−	0.231091i	$-0.925770\pi$
$151$	−9.50995e17	+	1.64717e18i	−0.286335	+	0.495947i	0.686597	+	0.727038i	$0.259104\pi$
$152$	−4.56421e17	−	7.90545e17i	−0.129926	−	0.225038i
$153$	−9.71957e17			−0.261680
$154$	−5.90104e18	+	6.20443e18i	−1.50315	+	1.58043i
$155$	−1.28737e18			−0.310374
$156$	−2.55888e18	−	4.43210e18i	−0.584104	−	1.01170i
$157$	1.14924e18	−	1.99054e18i	0.248464	−	0.430353i	−0.714636	−	0.699497i	$-0.753407\pi$
$157$	1.14924e18	−	1.99054e18i	0.248464	−	0.430353i	0.963100	+	0.269144i	$0.0867408\pi$
$158$	4.47830e18	−	7.75664e18i	0.917335	−	1.58887i
$159$	−5.94075e18	−	1.02897e19i	−1.15336	−	1.99768i
$160$	4.00419e18			0.737046
$161$	9.42018e18	+	2.27278e18i	1.64452	+	0.396769i
$162$	4.10546e18			0.679961
$163$	6.22300e18	+	1.07785e19i	0.978149	+	1.69420i	0.669127	+	0.743148i	$0.266668\pi$
$163$	6.22300e18	+	1.07785e19i	0.978149	+	1.69420i	0.309022	+	0.951055i	$0.399998\pi$
$164$	6.53119e18	−	1.13124e19i	0.974585	−	1.68803i
$165$	−4.52754e18	+	7.84194e18i	−0.641578	+	1.11125i
$166$	−4.62083e18	−	8.00351e18i	−0.622015	−	1.07736i
$167$	2.89662e16			0.00370511			0.00185255	−	0.999998i	$-0.499410\pi$
$167$	2.89662e16			0.00370511			0.00185255	+	0.999998i	$0.499410\pi$
$168$	8.27750e17	+	2.80601e18i	0.100640	+	0.341162i
$169$	−5.44458e18			−0.629401
$170$	−4.95170e17	−	8.57660e17i	−0.0544426	−	0.0942973i
$171$	−1.05900e19	+	1.83424e19i	−1.10771	+	1.91862i
$172$	−2.48547e18	+	4.30496e18i	−0.247410	+	0.428526i
$173$	−6.08582e18	−	1.05409e19i	−0.576669	−	0.998821i	−0.995858	−	0.0909216i	$-0.971019\pi$
$173$	−6.08582e18	−	1.05409e19i	−0.576669	−	0.998821i	0.419189	−	0.907899i	$-0.362315\pi$
$174$	1.64143e19			1.48099
$175$	2.42240e18	+	8.21174e18i	0.208172	+	0.705687i
$176$	−1.51722e19			−1.24220
$177$	−4.16149e18	−	7.20791e18i	−0.324695	−	0.562389i
$178$	−1.17944e19	+	2.04284e19i	−0.877211	+	1.51937i
$179$	5.79210e18	−	1.00322e19i	0.410758	−	0.711453i	−0.584215	−	0.811599i	$-0.698598\pi$
$179$	5.79210e18	−	1.00322e19i	0.410758	−	0.711453i	0.994973	+	0.100146i	$0.0319309\pi$
$180$	7.87179e18	+	1.36343e19i	0.532424	+	0.922185i
$181$	1.00923e19			0.651211			0.325605	−	0.945506i	$-0.394432\pi$
$181$	1.00923e19			0.651211			0.325605	+	0.945506i	$0.394432\pi$
$182$	−1.40759e19	−	3.39606e18i	−0.866703	−	0.209107i
$183$	3.53198e19			2.07579
$184$	−3.19909e18	−	5.54098e18i	−0.179504	−	0.310911i
$185$	−1.62148e17	+	2.80849e17i	−0.00868866	+	0.0150492i
$186$	1.44781e19	−	2.50768e19i	0.741057	−	1.28355i
$187$	2.20219e18	+	3.81430e18i	0.107696	+	0.186536i
$188$	−9.32665e18			−0.435897
$189$	2.09249e19	−	2.20007e19i	0.934841	−	0.982903i
$190$	−2.15805e19			−0.921842
$191$	9.06486e17	+	1.57008e18i	0.0370320	+	0.0641414i	0.883947	−	0.467586i	$-0.154876\pi$
$191$	9.06486e17	+	1.57008e18i	0.0370320	+	0.0641414i	−0.846915	+	0.531728i	$0.821543\pi$
$192$	−2.71446e19	+	4.70158e19i	−1.06077	+	1.83731i
$193$	3.72312e18	−	6.44864e18i	0.139210	−	0.241119i	−0.787988	−	0.615691i	$-0.788877\pi$
$193$	3.72312e18	−	6.44864e18i	0.139210	−	0.241119i	0.927198	+	0.374572i	$0.122210\pi$
$194$	2.40657e19	+	4.16830e19i	0.861161	+	1.49157i
$195$	−1.53127e19			−0.524516
$196$	3.10690e19	+	1.59185e19i	1.01895	+	0.522065i
$197$	−3.03773e19			−0.954083			−0.477041	−	0.878881i	$-0.658291\pi$
$197$	−3.03773e19			−0.954083			−0.477041	+	0.878881i	$0.658291\pi$
$198$	−6.55862e19	−	1.13599e20i	−1.97314	−	3.41758i
$199$	3.02623e19	−	5.24159e19i	0.872271	−	1.51082i	0.0126283	−	0.999920i	$-0.495980\pi$
$199$	3.02623e19	−	5.24159e19i	0.872271	−	1.51082i	0.859642	−	0.510897i	$-0.170686\pi$
$200$	2.82641e18	−	4.89549e18i	0.0780693	−	0.135220i
$201$	7.15642e18	+	1.23953e19i	0.189465	+	0.328163i
$202$	−3.81441e19			−0.968145
$203$	1.70841e19	−	1.79624e19i	0.415791	−	0.437168i
$204$	1.18900e19			0.277540
$205$	−1.95419e19	−	3.38475e19i	−0.437581	−	0.757912i
$206$	3.33899e18	−	5.78330e18i	0.0717371	−	0.124252i
$207$	−7.42258e19	+	1.28563e20i	−1.53041	+	2.65074i
$208$	−1.28286e19	−	2.22198e19i	−0.253887	−	0.439746i
$209$	9.59759e19			1.82355
$210$	6.72339e19	+	1.62213e19i	1.22666	+	0.295953i
$211$	−1.02619e19			−0.179816			−0.0899079	−	0.995950i	$-0.528657\pi$
$211$	−1.02619e19			−0.179816			−0.0899079	+	0.995950i	$0.528657\pi$
$212$	4.68047e19	+	8.10681e19i	0.787834	+	1.36457i
$213$	−3.47120e19	+	6.01229e19i	−0.561375	+	0.972330i
$214$	2.14742e19	−	3.71944e19i	0.333733	−	0.578043i
$215$	7.43672e18	+	1.28808e19i	0.111085	+	0.192405i
$216$	−2.00470e19			−0.287867
$217$	−1.23731e19	−	4.19438e19i	−0.170832	−	0.579108i
$218$	−4.62414e19			−0.613975
$219$	4.65492e19	+	8.06255e19i	0.594479	+	1.02967i
$220$	3.56707e19	−	6.17834e19i	0.438246	−	0.759065i
$221$	−3.72404e18	+	6.45023e18i	−0.0440231	+	0.0762502i
$222$	−3.64711e18	−	6.31699e18i	−0.0414905	−	0.0718637i
$223$	8.69465e19			0.952052			0.476026	−	0.879431i	$-0.342077\pi$
$223$	8.69465e19			0.952052			0.476026	+	0.879431i	$0.342077\pi$
$224$	3.84847e19	+	1.30460e20i	0.405676	+	1.37521i
$225$	−1.31158e20			−1.33120
$226$	5.66614e19	+	9.81405e19i	0.553816	+	0.959238i
$227$	−1.23489e19	+	2.13890e19i	−0.116255	+	0.201359i	−0.918281	−	0.395930i	$-0.870422\pi$
$227$	−1.23489e19	+	2.13890e19i	−0.116255	+	0.201359i	0.802026	+	0.597289i	$0.203755\pi$
$228$	1.29548e20	−	2.24383e20i	1.17485	−	2.03491i
$229$	−5.27769e19	−	9.14123e19i	−0.461150	−	0.798736i	0.537868	−	0.843029i	$-0.319230\pi$
$229$	−5.27769e19	−	9.14123e19i	−0.461150	−	0.798736i	−0.999019	+	0.0442931i	$0.985896\pi$
$230$	−1.51259e20			−1.27361
$231$	−2.99012e20	−	7.21417e19i	−2.42653	−	0.585443i
$232$	−1.63673e19			−0.128035
$233$	−7.08193e19	−	1.22663e20i	−0.534105	−	0.925096i	−0.999206	−	0.0398391i	$-0.987315\pi$
$233$	−7.08193e19	−	1.22663e20i	−0.534105	−	0.925096i	0.465101	−	0.885257i	$-0.346018\pi$
$234$	1.10911e20	−	1.92103e20i	0.806562	−	1.39701i
$235$	−1.39531e19	+	2.41674e19i	−0.0978571	+	0.169493i
$236$	3.27867e19	+	5.67882e19i	0.221792	+	0.384154i
$237$	3.21747e20			2.09968
$238$	2.31842e19	−	2.43761e19i	0.145978	−	0.153483i
$239$	−2.13318e20			−1.29612			−0.648060	−	0.761589i	$-0.724420\pi$
$239$	−2.13318e20			−1.29612			−0.648060	+	0.761589i	$0.724420\pi$
$240$	6.12760e19	+	1.06133e20i	0.359331	+	0.622380i
$241$	−3.49939e19	+	6.06113e19i	−0.198083	+	0.343090i	−0.947907	−	0.318547i	$-0.896805\pi$
$241$	−3.49939e19	+	6.06113e19i	−0.198083	+	0.343090i	0.749824	+	0.661638i	$0.230138\pi$
$242$	−1.63201e20	+	2.82673e20i	−0.891851	+	1.54473i
$243$	−5.47991e19	−	9.49148e19i	−0.289148	−	0.500819i
$244$	−2.78270e20			−1.41792
$245$	8.77288e19	−	5.66919e19i	0.431748	−	0.279003i
$246$	8.79089e20			4.17912
$247$	8.11507e19	+	1.40557e20i	0.372707	+	0.645548i
$248$	−1.44367e19	+	2.50051e19i	−0.0640660	+	0.110966i
$249$	1.65994e20	−	2.87509e20i	0.711864	−	1.23298i
$250$	−1.57637e20	−	2.73035e20i	−0.653383	−	1.13169i
$251$	−4.48445e20			−1.79673			−0.898365	−	0.439249i	$-0.855244\pi$
$251$	−4.48445e20			−1.79673			−0.898365	+	0.439249i	$0.855244\pi$
$252$	−3.68562e20	+	3.87511e20i	−1.42760	+	1.50099i
$253$	6.72702e20			2.51941
$254$	−1.02069e20	−	1.76789e20i	−0.369664	−	0.640278i
$255$	1.77879e19	−	3.08096e19i	0.0623066	−	0.107918i
$256$	−9.60246e19	+	1.66320e20i	−0.325344	+	0.563513i
$257$	8.20570e19	+	1.42127e20i	0.268958	+	0.465849i	0.968593	−	0.248652i	$-0.0799874\pi$
$257$	8.20570e19	+	1.42127e20i	0.268958	+	0.465849i	−0.699635	+	0.714500i	$0.746654\pi$
$258$	−3.34540e20			−1.06092
$259$	−1.07087e19	−	2.58366e18i	−0.0328617	−	0.00792845i
$260$	1.20643e20			0.358284
$261$	1.89878e20	+	3.28879e20i	0.545797	+	0.945348i
$262$	−1.95050e20	+	3.37837e20i	−0.542732	+	0.940039i
$263$	−9.15494e19	+	1.58568e20i	−0.246622	+	0.427162i	−0.962586	−	0.270975i	$-0.912654\pi$
$263$	−9.15494e19	+	1.58568e20i	−0.246622	+	0.427162i	0.715964	+	0.698137i	$0.245987\pi$
$264$	1.01544e20	+	1.75880e20i	0.264863	+	0.458757i
$265$	2.80087e20			0.707461
$266$	−2.07412e20	−	7.03112e20i	−0.507389	−	1.72001i
$267$	−8.47375e20			−2.00784
$268$	−5.63825e19	−	9.76573e19i	−0.129419	−	0.224160i
$269$	5.66545e19	−	9.81284e19i	0.125991	−	0.218223i	−0.796129	−	0.605127i	$-0.793122\pi$
$269$	5.66545e19	−	9.81284e19i	0.125991	−	0.218223i	0.922120	+	0.386904i	$0.126456\pi$
$270$	−2.36965e20	+	4.10436e20i	−0.510614	+	0.884409i
$271$	1.91792e20	+	3.32193e20i	0.400489	+	0.693667i	0.993785	−	0.111317i	$-0.0355070\pi$
$271$	1.91792e20	+	3.32193e20i	0.400489	+	0.693667i	−0.593296	+	0.804984i	$0.702174\pi$
$272$	5.96091e19			0.120636
$273$	−1.47172e20	−	4.98902e20i	−0.288698	−	0.978663i
$274$	5.71804e20			1.08735
$275$	2.97168e20	+	5.14709e20i	0.547865	+	0.948930i
$276$	9.08010e20	−	1.57272e21i	1.62317	−	2.81141i
$277$	3.43327e20	−	5.94659e20i	0.595154	−	1.03084i	−0.398371	−	0.917224i	$-0.630424\pi$
$277$	3.43327e20	−	5.94659e20i	0.595154	−	1.03084i	0.993525	−	0.113613i	$-0.0362424\pi$
$278$	3.91873e20	+	6.78744e20i	0.658817	+	1.14110i
$279$	6.69925e20			1.09242
$280$	−6.70415e19	−	1.61749e19i	−0.106048	−	0.0255858i
$281$	−7.31886e20			−1.12316			−0.561578	−	0.827424i	$-0.689805\pi$
$281$	−7.31886e20			−1.12316			−0.561578	+	0.827424i	$0.689805\pi$
$282$	−3.13838e20	−	5.43584e20i	−0.467292	−	0.809374i
$283$	−4.08485e20	+	7.07517e20i	−0.590190	+	1.02224i	0.404017	+	0.914752i	$0.367614\pi$
$283$	−4.08485e20	+	7.07517e20i	−0.590190	+	1.02224i	−0.994206	+	0.107487i	$0.965720\pi$
$284$	2.73481e20	−	4.73684e20i	0.383462	−	0.664175i
$285$	−3.87617e20	−	6.71373e20i	−0.527499	−	0.913656i
$286$	−1.00517e21			−1.32779
$287$	9.14962e20	−	9.62002e20i	1.17329	−	1.23362i
$288$	−2.08370e21			−2.59418
$289$	4.04968e20	+	7.01425e20i	0.489541	+	0.847910i
$290$	−1.93470e20	+	3.35099e20i	−0.227107	+	0.393360i
$291$	−8.64510e20	+	1.49738e21i	−0.985553	+	1.70703i
$292$	−3.66742e20	−	6.35215e20i	−0.406075	−	0.703342i
$293$	−3.82449e20			−0.411338			−0.205669	−	0.978622i	$-0.565937\pi$
$293$	−3.82449e20			−0.411338			−0.205669	+	0.978622i	$0.565937\pi$
$294$	1.17687e20	+	2.34644e21i	0.122963	+	2.45165i
$295$	1.96201e20			0.199165
$296$	3.63668e18	+	6.29891e18i	0.00358695	+	0.00621278i
$297$	1.05386e21	−	1.82535e21i	1.01008	−	1.74951i
$298$	1.03123e20	−	1.78615e20i	0.0960546	−	0.166371i
$299$	5.68791e20	+	9.85175e20i	0.514929	+	0.891884i
$300$	1.60446e21			1.41188
$301$	−3.48192e20	+	3.66093e20i	−0.297854	+	0.313167i
$302$	1.00848e21			0.838703
$303$	−6.85123e20	−	1.18667e21i	−0.553996	−	0.959548i
$304$	6.49471e20	−	1.12492e21i	0.510663	−	0.884494i
$305$	−4.16304e20	+	7.21059e20i	−0.318318	+	0.551343i
$306$	2.57677e20	+	4.46310e20i	0.191621	+	0.331898i
$307$	−9.59188e19			−0.0693789			−0.0346895	−	0.999398i	$-0.511044\pi$
$307$	−9.59188e19			−0.0693789			−0.0346895	+	0.999398i	$0.511044\pi$
$308$	2.35579e21	+	5.68375e20i	1.65751	+	0.399902i
$309$	2.39892e20			0.164199
$310$	3.41298e20	+	5.91145e20i	0.227279	+	0.393658i
$311$	−7.81712e19	+	1.35396e20i	−0.0506505	+	0.0877292i	−0.890239	−	0.455494i	$-0.849463\pi$
$311$	−7.81712e19	+	1.35396e20i	−0.0506505	+	0.0877292i	0.839589	+	0.543223i	$0.182796\pi$
$312$	−1.71718e20	+	2.97424e20i	−0.108268	+	0.187526i
$313$	5.35715e20	+	9.27885e20i	0.328705	+	0.569334i	0.982255	−	0.187549i	$-0.0600543\pi$
$313$	5.35715e20	+	9.27885e20i	0.328705	+	0.569334i	−0.653550	+	0.756883i	$0.726721\pi$
$314$	−1.21871e21			−0.727776
$315$	4.52741e20	+	1.53476e21i	0.263154	+	0.892072i
$316$	−2.53491e21			−1.43424
$317$	−9.04485e20	−	1.56661e21i	−0.498193	−	0.862896i	0.501805	−	0.864981i	$-0.332670\pi$
$317$	−9.04485e20	−	1.56661e21i	−0.498193	−	0.862896i	−0.999998	+	0.00208510i	$0.999336\pi$
$318$	−3.14992e21	+	5.45582e21i	−1.68915	+	2.92570i
$319$	8.60425e20	−	1.49030e21i	0.449254	−	0.778131i
$320$	−6.39890e20	−	1.10832e21i	−0.325335	−	0.563496i
$321$	1.54283e21			0.763881
$322$	−1.45377e21	−	4.92816e21i	−0.701004	−	2.37635i
$323$	−3.77073e20			−0.177094
$324$	−5.80967e20	−	1.00626e21i	−0.265778	−	0.460341i
$325$	−5.02530e20	+	8.70407e20i	−0.223951	+	0.387895i
$326$	3.29958e21	−	5.71504e21i	1.43255	−	2.48124i
$327$	−8.30563e20	−	1.43858e21i	−0.351331	−	0.608523i
$328$	−8.76574e20			−0.361294
$329$	−9.21499e20	−	2.22327e20i	−0.370109	−	0.0892951i
$330$	4.80122e21			1.87924
$331$	−1.50674e21	−	2.60975e21i	−0.574779	−	0.995547i	−0.996066	−	0.0886189i	$-0.971755\pi$
$331$	−1.50674e21	−	2.60975e21i	−0.574779	−	0.995547i	0.421287	−	0.906928i	$-0.361579\pi$
$332$	−1.30779e21	+	2.26517e21i	−0.486257	+	0.842222i
$333$	8.43789e19	−	1.46148e20i	0.0305814	−	0.0529686i
$334$	−7.67926e18	−	1.33009e19i	−0.00271315	−	0.00469932i
$335$	−3.37402e20			−0.116216
$336$	−2.86898e21	+	3.01648e21i	−0.963482	+	1.01302i
$337$	2.21341e21			0.724783			0.362392	−	0.932026i	$-0.381960\pi$
$337$	2.21341e21			0.724783			0.362392	+	0.932026i	$0.381960\pi$
$338$	1.44342e21	+	2.50008e21i	0.460894	+	0.798292i
$339$	−2.03544e21	+	3.52549e21i	−0.633813	+	1.09780i
$340$	−1.40144e20	+	2.42736e20i	−0.0425602	+	0.0737164i
$341$	−1.51787e21	−	2.62902e21i	−0.449595	−	0.778721i
$342$	1.12301e22			3.24460
$343$	2.69024e21	+	2.31341e21i	0.758213	+	0.652007i
$344$	3.33583e20			0.0917186
$345$	−2.71684e21	−	4.70570e21i	−0.728789	−	1.26230i
$346$	−3.22684e21	+	5.58905e21i	−0.844560	+	1.46282i
$347$	−3.10088e21	+	5.37088e21i	−0.791926	+	1.37166i	0.132847	+	0.991137i	$0.457588\pi$
$347$	−3.10088e21	+	5.37088e21i	−0.791926	+	1.37166i	−0.924773	+	0.380519i	$0.875745\pi$
$348$	−2.32279e21	−	4.02320e21i	−0.578878	−	1.00265i
$349$	−5.79344e21			−1.40903			−0.704515	−	0.709689i	$-0.748835\pi$
$349$	−5.79344e21			−1.40903			−0.704515	+	0.709689i	$0.748835\pi$
$350$	3.12852e21	−	3.28936e21i	0.742609	−	0.780788i
$351$	3.56430e21			0.825780
$352$	4.72110e21	+	8.17719e21i	1.06765	+	1.84923i
$353$	2.36627e21	−	4.09851e21i	0.522372	−	0.904775i	−0.477289	−	0.878746i	$-0.658381\pi$
$353$	2.36627e21	−	4.09851e21i	0.522372	−	0.904775i	0.999661	−	0.0260287i	$-0.00828613\pi$
$354$	−2.20652e21	+	3.82180e21i	−0.475532	+	0.823646i
$355$	−8.18279e20	−	1.41730e21i	−0.172171	−	0.298209i
$356$	6.67611e21			1.37151
$357$	1.17477e21	+	2.83432e20i	0.235652	+	0.0568551i
$358$	−6.14222e21			−1.20315
$359$	9.24327e20	+	1.60098e21i	0.176817	+	0.306255i	0.940788	−	0.338994i	$-0.110087\pi$
$359$	9.24327e20	+	1.60098e21i	0.176817	+	0.306255i	−0.763972	+	0.645250i	$0.776753\pi$
$360$	5.28250e20	−	9.14956e20i	0.0986889	−	0.170934i
$361$	−1.36820e21	+	2.36980e21i	−0.249655	+	0.432415i
$362$	−2.67558e21	−	4.63424e21i	−0.476865	−	0.825954i
$363$	−1.17253e22			−2.04135
$364$	1.15951e21	+	3.93064e21i	0.197202	+	0.668501i
$365$	−2.19464e21			−0.364648
$366$	−9.36369e21	−	1.62184e22i	−1.52005	−	2.63280i
$367$	4.65731e21	−	8.06670e21i	0.738709	−	1.27948i	−0.214367	−	0.976753i	$-0.568769\pi$
$367$	4.65731e21	−	8.06670e21i	0.738709	−	1.27948i	0.953077	−	0.302729i	$-0.0978977\pi$
$368$	4.55219e21	−	7.88462e21i	0.705527	−	1.22201i
$369$	1.01692e22	+	1.76136e22i	1.54015	+	2.66762i
$370$	1.71950e20			0.0254499
$371$	2.69194e21	+	9.12547e21i	0.389392	+	1.32001i
$372$	−8.19523e21			−1.15863
$373$	6.49406e21	+	1.12480e22i	0.897411	+	1.55436i	0.830792	+	0.556583i	$0.187888\pi$
$373$	6.49406e21	+	1.12480e22i	0.897411	+	1.55436i	0.0666194	+	0.997778i	$0.478779\pi$
$374$	1.16765e21	−	2.02243e21i	0.157727	−	0.273190i
$375$	5.66278e21	−	9.80822e21i	0.747763	−	1.29516i
$376$	3.12940e20	+	5.42029e20i	0.0403985	+	0.0699722i
$377$	2.91007e21			0.367284
$378$	−1.56498e22	−	3.77579e21i	−1.93121	−	0.465938i
$379$	−8.27873e20			−0.0998919			−0.0499460	−	0.998752i	$-0.515905\pi$
$379$	−8.27873e20			−0.0998919			−0.0499460	+	0.998752i	$0.515905\pi$
$380$	3.05388e21	+	5.28947e21i	0.360322	+	0.624096i
$381$	3.66662e21	−	6.35077e21i	0.423061	−	0.732764i
$382$	4.80640e20	−	8.32493e20i	0.0542352	−	0.0939381i
$383$	−4.39060e21	−	7.60474e21i	−0.484545	−	0.839257i	0.515297	−	0.857012i	$-0.327682\pi$
$383$	−4.39060e21	−	7.60474e21i	−0.484545	−	0.839257i	−0.999842	+	0.0177545i	$0.994348\pi$
$384$	6.52140e21			0.703924
$385$	4.99714e21	−	5.25406e21i	0.527601	−	0.554726i
$386$	−3.94817e21			−0.407759
$387$	−3.86993e21	−	6.70291e21i	−0.390985	−	0.677205i
$388$	6.81112e21	−	1.17972e22i	0.673207	−	1.16603i
$389$	3.53046e21	−	6.11494e21i	0.341397	−	0.591317i	−0.643295	−	0.765618i	$-0.722433\pi$
$389$	3.53046e21	−	6.11494e21i	0.341397	−	0.591317i	0.984692	+	0.174301i	$0.0557666\pi$
$390$	4.05958e21	+	7.03141e21i	0.384089	+	0.665263i
$391$	−2.64293e21			−0.244671
$392$	−1.17350e20	−	2.33973e21i	−0.0106304	−	0.211950i
$393$	−1.40135e22			−1.24226
$394$	8.05337e21	+	1.39489e22i	0.698650	+	1.21010i
$395$	−3.79233e21	+	6.56851e21i	−0.321982	+	0.557689i
$396$	−1.85623e22	+	3.21509e22i	−1.54249	+	2.67168i
$397$	7.81870e21	+	1.35424e22i	0.635939	+	1.10148i	0.986315	+	0.164869i	$0.0527203\pi$
$397$	7.81870e21	+	1.35424e22i	0.635939	+	1.10148i	−0.350377	+	0.936609i	$0.613946\pi$
$398$	−3.20916e22			−2.55497
$399$	1.81485e22	−	1.90815e22i	1.41440	−	1.48711i
$400$	8.04376e21			0.613690
$401$	−1.49004e21	−	2.58082e21i	−0.111294	−	0.192766i	0.804998	−	0.593277i	$-0.202166\pi$
$401$	−1.49004e21	−	2.58082e21i	−0.111294	−	0.192766i	−0.916292	+	0.400511i	$0.868833\pi$
$402$	3.79450e21	−	6.57227e21i	0.277481	−	0.480611i
$403$	2.56681e21	−	4.44584e21i	0.183781	−	0.318318i
$404$	5.39780e21	+	9.34927e21i	0.378421	+	0.655445i
$405$	−3.47660e21			−0.238664
$406$	−1.27773e22	−	3.08274e21i	−0.858948	−	0.207236i
$407$	−7.64718e20			−0.0503441
$408$	−3.98950e20	−	6.91002e20i	−0.0257221	−	0.0445521i
$409$	5.70327e21	−	9.87835e21i	0.360144	−	0.623787i	−0.627841	−	0.778342i	$-0.716061\pi$
$409$	5.70327e21	−	9.87835e21i	0.360144	−	0.623787i	0.987984	+	0.154555i	$0.0493944\pi$
$410$	−1.03615e22	+	1.79467e22i	−0.640858	+	1.11000i
$411$	1.02704e22	+	1.77889e22i	0.622205	+	1.07769i
$412$	−1.89001e21			−0.112160
$413$	1.88570e21	+	6.39239e21i	0.109622	+	0.371610i
$414$	7.87125e22			4.48271
$415$	3.91303e21	+	6.77756e21i	0.218325	+	0.378151i
$416$	−7.98369e21	+	1.38282e22i	−0.436426	+	0.755911i
$417$	−1.40772e22	+	2.43825e22i	−0.753981	+	1.30593i
$418$	−2.54443e22	−	4.40708e22i	−1.33534	−	2.31288i
$419$	1.07542e22			0.553042			0.276521	−	0.961008i	$-0.410818\pi$
$419$	1.07542e22			0.553042			0.276521	+	0.961008i	$0.410818\pi$
$420$	−5.53841e21	−	1.87748e22i	−0.279104	−	0.946141i
$421$	−6.35326e21			−0.313761			−0.156880	−	0.987618i	$-0.550144\pi$
$421$	−6.35326e21			−0.313761			−0.156880	+	0.987618i	$0.550144\pi$
$422$	2.72055e21	+	4.71214e21i	0.131674	+	0.228067i
$423$	7.26090e21	−	1.25762e22i	0.344427	−	0.596565i
$424$	3.14091e21	−	5.44021e21i	0.146031	−	0.252933i
$425$	−1.16752e21	−	2.02221e21i	−0.0532058	−	0.0921551i
$426$	3.68102e22			1.64432
$427$	−2.74939e22	−	6.63336e21i	−1.20392	−	0.290467i
$428$	−1.21553e22			−0.521788
$429$	−1.80543e22	−	3.12710e22i	−0.759792	−	1.31600i
$430$	3.94312e21	−	6.82969e21i	0.162689	−	0.281786i
$431$	1.42572e22	−	2.46942e22i	0.576738	−	0.998939i	−0.419113	−	0.907934i	$-0.637659\pi$
$431$	1.42572e22	−	2.46942e22i	0.576738	−	0.998939i	0.995850	−	0.0910049i	$-0.0290079\pi$
$432$	−1.42630e22	−	2.47043e22i	−0.565719	−	0.979853i
$433$	−4.82204e22			−1.87536			−0.937678	−	0.347505i	$-0.887029\pi$
$433$	−4.82204e22			−1.87536			−0.937678	+	0.347505i	$0.887029\pi$
$434$	−1.59798e22	+	1.68013e22i	−0.609408	+	0.640739i
$435$	−1.39000e22			−0.519823
$436$	6.54366e21	+	1.13339e22i	0.239986	+	0.415668i
$437$	−2.87961e22	+	4.98762e22i	−1.03572	+	1.79391i
$438$	2.46814e22	−	4.27495e22i	0.870644	−	1.50800i
$439$	1.50027e22	+	2.59855e22i	0.519066	+	0.899048i	0.999755	+	0.0221569i	$0.00705335\pi$
$439$	1.50027e22	+	2.59855e22i	0.519066	+	0.899048i	−0.480689	+	0.876891i	$0.659613\pi$
$440$	−4.78748e21			−0.162465
$441$	−4.56524e22	+	2.95014e22i	−1.51962	+	0.982007i
$442$	3.94915e21			0.128948
$443$	2.70795e22	+	4.69031e22i	0.867379	+	1.50235i	0.864665	+	0.502349i	$0.167531\pi$
$443$	2.70795e22	+	4.69031e22i	0.867379	+	1.50235i	0.00271446	+	0.999996i	$0.499136\pi$
$444$	−1.03221e21	+	1.78784e21i	−0.0324350	+	0.0561791i
$445$	9.98774e21	−	1.72993e22i	0.307898	−	0.533295i
$446$	−2.30505e22	−	3.99247e22i	−0.697163	−	1.20752i
$447$	7.40897e21			0.219859
$448$	2.99600e22	−	3.15003e22i	0.872326	−	0.917175i
$449$	1.51015e21			0.0431446			0.0215723	−	0.999767i	$-0.493133\pi$
$449$	1.51015e21			0.0431446			0.0215723	+	0.999767i	$0.493133\pi$
$450$	3.47714e22	+	6.02259e22i	0.974802	+	1.68841i
$451$	4.60813e22	−	7.98152e22i	1.26772	−	2.19576i
$452$	1.60364e22	−	2.77759e22i	0.432943	−	0.749879i
$453$	1.81138e22	+	3.13739e22i	0.479926	+	0.831255i
$454$	1.30954e22			0.340521
$455$	1.19198e22	+	2.87586e21i	0.304210	+	0.0733958i
$456$	−1.73870e22			−0.435537
$457$	−3.68717e22	−	6.38637e22i	−0.906579	−	1.57024i	−0.818784	−	0.574102i	$-0.805351\pi$
$457$	−3.68717e22	−	6.38637e22i	−0.906579	−	1.57024i	−0.0877949	−	0.996139i	$-0.527982\pi$
$458$	−2.79836e22	+	4.84689e22i	−0.675377	+	1.16979i
$459$	−4.14045e21	+	7.17147e21i	−0.0980934	+	0.169903i
$460$	2.14048e22	+	3.70743e22i	0.497818	+	0.862246i
$461$	6.54061e22			1.49335			0.746673	−	0.665191i	$-0.231650\pi$
$461$	6.54061e22			1.49335			0.746673	+	0.665191i	$0.231650\pi$
$462$	4.61450e22	+	1.56428e23i	1.03435	+	3.50637i
$463$	1.85653e22			0.408567			0.204284	−	0.978912i	$-0.434513\pi$
$463$	1.85653e22			0.408567			0.204284	+	0.978912i	$0.434513\pi$
$464$	−1.16450e22	−	2.01698e22i	−0.251616	−	0.435811i
$465$	−1.22604e22	+	2.12356e22i	−0.260109	+	0.450521i
$466$	−3.75500e22	+	6.50386e22i	−0.782222	+	1.35485i
$467$	−1.10054e22	−	1.90618e22i	−0.225118	−	0.389916i	0.731237	−	0.682124i	$-0.238943\pi$
$467$	−1.10054e22	−	1.90618e22i	−0.225118	−	0.389916i	−0.956355	+	0.292208i	$0.905610\pi$
$468$	−6.27802e22			−1.26105
$469$	−3.24280e21	−	1.09928e22i	−0.0639663	−	0.216841i
$470$	1.47965e22			0.286633
$471$	−2.18898e22	−	3.79142e22i	−0.416451	−	0.721314i
$472$	2.20021e21	−	3.81087e21i	0.0411108	−	0.0712061i
$473$	−1.75364e22	+	3.03739e22i	−0.321826	+	0.557419i
$474$	−8.52989e22	−	1.47742e23i	−1.53754	−	2.66310i
$475$	−5.08829e22			−0.900900
$476$	−9.25550e21	−	2.23305e21i	−0.160968	−	0.0388364i
$477$	−1.45752e23			−2.49005
$478$	5.65531e22	+	9.79528e22i	0.949116	+	1.64392i
$479$	1.06534e22	−	1.84522e22i	0.175645	−	0.304226i	−0.764739	−	0.644340i	$-0.777132\pi$
$479$	1.06534e22	−	1.84522e22i	0.175645	−	0.304226i	0.940384	+	0.340114i	$0.110466\pi$
$480$	3.81342e22	−	6.60504e22i	0.617681	−	1.06985i
$481$	−6.46594e20	−	1.11993e21i	−0.0102896	−	0.0178221i
$482$	3.71092e22			0.580205
$483$	1.27204e23	−	1.33744e23i	1.95412	−	2.05458i
$484$	9.23789e22			1.39440
$485$	−2.03794e22	−	3.52982e22i	−0.302265	−	0.523538i
$486$	−2.90557e22	+	5.03260e22i	−0.423471	+	0.733473i
$487$	−4.76368e22	+	8.25094e22i	−0.682255	+	1.18170i	0.292036	+	0.956407i	$0.405667\pi$
$487$	−4.76368e22	+	8.25094e22i	−0.682255	+	1.18170i	−0.974291	+	0.225293i	$0.927666\pi$
$488$	9.33690e21	+	1.61720e22i	0.131412	+	0.227612i
$489$	2.37061e23			3.27895
$490$	−4.92901e22	−	2.52542e22i	−0.670028	−	0.343295i
$491$	−1.61994e22			−0.216424			−0.108212	−	0.994128i	$-0.534513\pi$
$491$	−1.61994e22			−0.216424			−0.108212	+	0.994128i	$0.534513\pi$
$492$	−1.24401e23	−	2.15468e23i	−1.63350	−	2.82931i
$493$	−3.38046e21	+	5.85513e21i	−0.0436292	+	0.0755680i
$494$	4.30280e22	−	7.45266e22i	0.545848	−	0.945437i
$495$	5.55400e22	+	9.61981e22i	0.692567	+	1.19956i
$496$	−4.10857e22			−0.503613
$497$	3.83123e22	−	4.02820e22i	0.461646	−	0.485380i
$498$	−1.76027e23			−2.08512
$499$	4.98074e22	+	8.62689e22i	0.580015	+	1.00462i	0.995477	+	0.0950046i	$0.0302866\pi$
$499$	4.98074e22	+	8.62689e22i	0.580015	+	1.00462i	−0.415462	+	0.909611i	$0.636380\pi$
$500$	−4.46147e22	+	7.72749e22i	−0.510779	+	0.884695i
$501$	2.75861e20	−	4.77806e20i	0.00310506	−	0.00537812i
$502$	1.18888e23	+	2.05920e23i	1.31570	+	2.27886i
$503$	−7.64227e22			−0.831561			−0.415781	−	0.909465i	$-0.636492\pi$
$503$	−7.64227e22			−0.831561			−0.415781	+	0.909465i	$0.636492\pi$
$504$	3.48871e22	+	8.41711e21i	0.373255	+	0.0900541i
$505$	3.23013e22			0.339816
$506$	−1.78341e23	−	3.08896e23i	−1.84490	−	3.19545i
$507$	−5.18519e22	+	8.98101e22i	−0.527469	+	0.913603i
$508$	−2.88878e22	+	5.00351e22i	−0.288983	+	0.500533i
$509$	6.28615e22	+	1.08879e23i	0.618421	+	1.07114i	0.989774	+	0.142644i	$0.0455605\pi$
$509$	6.28615e22	+	1.08879e23i	0.618421	+	1.07114i	−0.371353	+	0.928492i	$0.621106\pi$
$510$	−1.88632e22			−0.182502
$511$	−2.10929e22	−	7.15033e22i	−0.200705	−	0.680375i
$512$	1.46706e23			1.37294
$513$	9.02246e22	+	1.56274e23i	0.830477	+	1.43843i
$514$	4.35085e22	−	7.53590e22i	0.393902	−	0.682258i
$515$	−2.82754e21	+	4.89744e21i	−0.0251795	+	0.0436121i
$516$	4.73411e22	+	8.19972e22i	0.414683	+	0.718251i
$517$	−6.58049e22			−0.567007
$518$	1.65262e21	+	5.60227e21i	0.0140078	+	0.0474855i
$519$	−2.31835e23			−1.93311
$520$	−4.04797e21	−	7.01129e21i	−0.0332054	−	0.0575134i
$521$	4.72238e22	−	8.17941e22i	0.381101	−	0.660087i	−0.610119	−	0.792310i	$-0.708878\pi$
$521$	4.72238e22	−	8.17941e22i	0.381101	−	0.660087i	0.991220	+	0.132223i	$0.0422116\pi$
$522$	1.00678e23	−	1.74379e23i	0.799346	−	1.38451i
$523$	−1.20993e23	−	2.09565e23i	−0.945137	−	1.63703i	−0.755477	−	0.655175i	$-0.772595\pi$
$523$	−1.20993e23	−	2.09565e23i	−0.945137	−	1.63703i	−0.189660	−	0.981850i	$-0.560739\pi$
$524$	1.10407e23			0.848555
$525$	1.58525e23	+	3.82469e22i	1.19879	+	0.289229i
$526$	9.70832e22			0.722379
$527$	5.96344e21	+	1.03290e22i	0.0436623	+	0.0756253i
$528$	−1.44494e23	+	2.50271e23i	−1.04102	+	1.80311i
$529$	−1.31309e23	+	2.27433e23i	−0.930937	+	1.61243i
$530$	−7.42543e22	−	1.28612e23i	−0.518056	−	0.897299i
$531$	−1.02099e23			−0.701001
$532$	−1.42984e23	+	1.50336e23i	−0.966140	+	1.01581i
$533$	1.55853e23			1.03641
$534$	2.24649e23	+	3.89103e23i	1.47029	+	2.54662i
$535$	−1.81849e22	+	3.14971e22i	−0.117139	+	0.202891i
$536$	−3.78364e21	+	6.55346e21i	−0.0239888	+	0.0415499i
$537$	−1.10323e23	−	1.91085e23i	−0.688470	−	1.19247i
$538$	−6.00790e22			−0.369040
$539$	2.19210e23	+	1.12314e23i	1.32543	+	0.679093i
$540$	1.34133e23			0.798339
$541$	−1.10782e23	−	1.91881e23i	−0.649074	−	1.12423i	−0.983345	−	0.181751i	$-0.941823\pi$
$541$	−1.10782e23	−	1.91881e23i	−0.649074	−	1.12423i	0.334271	−	0.942477i	$-0.391510\pi$
$542$	1.01692e23	−	1.76136e23i	0.586536	−	1.01591i
$543$	9.61147e22	−	1.66475e23i	0.545747	−	0.945261i
$544$	−1.85484e22	−	3.21268e22i	−0.103685	−	0.179588i
$545$	3.91583e22			0.215503
$546$	−1.90072e23	+	1.99844e23i	−1.02987	+	1.08282i
$547$	8.04277e22			0.429055			0.214528	−	0.976718i	$-0.431179\pi$
$547$	8.04277e22			0.429055			0.214528	+	0.976718i	$0.431179\pi$
$548$	−8.09165e22	−	1.40152e23i	−0.425013	−	0.736144i
$549$	2.16636e23	−	3.75225e23i	1.12038	−	1.94056i
$550$	1.57565e23	−	2.72911e23i	0.802375	−	1.38975i
$551$	7.36637e22	+	1.27589e23i	0.369373	+	0.639772i
$552$	−1.21867e23			−0.601734
$553$	−2.50456e23	−	6.04269e22i	−1.21778	−	0.293810i
$554$	−3.64080e23			−1.74326
$555$	3.08846e21	+	5.34938e21i	0.0145630	+	0.0252239i
$556$	1.10909e23	−	1.92099e23i	0.515027	−	0.892052i
$557$	−1.42925e23	+	2.47554e23i	−0.653642	+	1.13214i	0.328591	+	0.944472i	$0.393426\pi$
$557$	−1.42925e23	+	2.47554e23i	−0.653642	+	1.13214i	−0.982232	+	0.187668i	$0.939907\pi$
$558$	−1.77605e23	−	3.07621e23i	−0.799952	−	1.38556i
$559$	−5.93104e22			−0.263106
$560$	−2.77661e22	−	9.41250e22i	−0.121316	−	0.411251i
$561$	8.38909e22			0.361019
$562$	1.94032e23	+	3.36073e23i	0.822458	+	1.42454i
$563$	−1.20301e23	+	2.08368e23i	−0.502283	+	0.869979i	0.497714	+	0.867341i	$0.334173\pi$
$563$	−1.20301e23	+	2.08368e23i	−0.502283	+	0.869979i	−0.999997	+	0.00263786i	$0.999160\pi$
$564$	−8.88231e22	+	1.53846e23i	−0.365303	+	0.632724i
$565$	−4.79823e22	−	8.31077e22i	−0.194388	−	0.336689i
$566$	4.33177e23			1.72872
$567$	−3.34140e22	−	1.13271e23i	−0.131363	−	0.445309i
$568$	−3.67049e22			−0.142155
$569$	−3.34547e22	−	5.79452e22i	−0.127645	−	0.221087i	0.795119	−	0.606453i	$-0.207408\pi$
$569$	−3.34547e22	−	5.79452e22i	−0.127645	−	0.221087i	−0.922764	+	0.385366i	$0.874075\pi$
$570$	−2.05524e23	+	3.55978e23i	−0.772549	+	1.33809i
$571$	−4.99466e21	+	8.65100e21i	−0.0184969	+	0.0320376i	−0.875126	−	0.483896i	$-0.839221\pi$
$571$	−4.99466e21	+	8.65100e21i	−0.0184969	+	0.0320376i	0.856629	+	0.515933i	$0.172555\pi$
$572$	1.42243e23	+	2.46372e23i	0.518996	+	0.898927i
$573$	3.45320e22			0.124139
$574$	−6.84306e23	−	1.65101e23i	−2.42381	−	0.584786i
$575$	−3.56642e23			−1.24468
$576$	3.32986e23	+	5.76749e23i	1.14508	+	1.98333i
$577$	2.32099e23	−	4.02008e23i	0.786465	−	1.36220i	−0.141654	−	0.989916i	$-0.545242\pi$
$577$	2.32099e23	−	4.02008e23i	0.786465	−	1.36220i	0.928120	−	0.372282i	$-0.121425\pi$
$578$	2.14723e23	−	3.71912e23i	0.716957	−	1.24181i
$579$	−7.09149e22	−	1.22828e23i	−0.233330	−	0.404139i
$580$	1.09512e23			0.355079
$581$	−1.83210e23	+	1.92630e23i	−0.585400	+	0.615497i
$582$	9.16767e23			2.88678
$583$	3.30234e23	+	5.71982e23i	1.02480	+	1.77500i
$584$	−2.46108e22	+	4.26272e22i	−0.0752691	+	0.130370i
$585$	−9.39217e22	+	1.62677e23i	−0.283101	+	0.490345i
$586$	1.01392e23	+	1.75616e23i	0.301212	+	0.521715i
$587$	2.07221e23			0.606751			0.303376	−	0.952871i	$-0.401886\pi$
$587$	2.07221e23			0.606751			0.303376	+	0.952871i	$0.401886\pi$
$588$	5.58469e23	−	3.60893e23i	1.61173	−	1.04153i
$589$	2.59899e23			0.739306
$590$	−5.20151e22	−	9.00928e22i	−0.145844	−	0.252609i
$591$	−2.89301e23	+	5.01083e23i	−0.799568	+	1.38489i
$592$	−5.17486e21	+	8.96313e21i	−0.0140982	+	0.0244188i
$593$	1.47850e23	+	2.56083e23i	0.397060	+	0.687727i	0.993362	−	0.115033i	$-0.0366973\pi$
$593$	1.47850e23	+	2.56083e23i	0.397060	+	0.687727i	−0.596302	+	0.802760i	$0.703364\pi$
$594$	−1.11757e24			−2.95862
$595$	−1.96329e22	+	2.06423e22i	−0.0512378	+	0.0538721i
$596$	−5.83722e22			−0.150180
$597$	−5.76411e23	−	9.98374e23i	−1.46201	−	2.53228i
$598$	3.01586e23	−	5.22363e23i	0.754139	−	1.30621i
$599$	−2.48872e23	+	4.31058e23i	−0.613547	+	1.06269i	0.377091	+	0.926176i	$0.376924\pi$
$599$	−2.48872e23	+	4.31058e23i	−0.613547	+	1.06269i	−0.990638	+	0.136518i	$0.956409\pi$
$600$	−5.38351e22	−	9.32451e22i	−0.130852	−	0.226642i
$601$	1.89322e23			0.453699			0.226850	−	0.973930i	$-0.427157\pi$
$601$	1.89322e23			0.453699			0.226850	+	0.973930i	$0.427157\pi$
$602$	2.60415e23	+	6.28296e22i	0.615313	+	0.148455i
$603$	1.75577e23			0.409046
$604$	−1.42711e23	−	2.47182e23i	−0.327826	−	0.567811i
$605$	1.38203e23	−	2.39374e23i	0.313037	−	0.542196i
$606$	−3.63268e23	+	6.29199e23i	−0.811353	+	1.40531i
$607$	−3.01006e22	−	5.21358e22i	−0.0662936	−	0.114824i	0.830973	−	0.556312i	$-0.187784\pi$
$607$	−3.01006e22	−	5.21358e22i	−0.0662936	−	0.114824i	−0.897267	+	0.441488i	$0.854451\pi$
$608$	−8.08377e23			−1.75563
$609$	−1.33594e23	−	4.52873e23i	−0.286115	−	0.969906i
$610$	4.41468e23			0.932385
$611$	−5.56401e22	−	9.63715e22i	−0.115888	−	0.200724i
$612$	7.29282e22	−	1.26315e23i	0.149799	−	0.259459i
$613$	−1.01488e23	+	1.75783e23i	−0.205590	+	0.356092i	−0.950321	−	0.311273i	$-0.899245\pi$
$613$	−1.01488e23	+	1.75783e23i	−0.205590	+	0.356092i	0.744730	+	0.667365i	$0.232578\pi$
$614$	2.54292e22	+	4.40447e22i	0.0508044	+	0.0879958i
$615$	−7.44434e23			−1.46686
$616$	−4.60129e22	−	1.55980e23i	−0.0894219	−	0.303133i
$617$	−3.07131e23			−0.588707			−0.294354	−	0.955697i	$-0.595104\pi$
$617$	−3.07131e23			−0.588707			−0.294354	+	0.955697i	$0.595104\pi$
$618$	−6.35982e22	−	1.10155e23i	−0.120238	−	0.208259i
$619$	1.62169e23	−	2.80886e23i	0.302412	−	0.523792i	−0.674270	−	0.738485i	$-0.735542\pi$
$619$	1.62169e23	−	2.80886e23i	0.302412	−	0.523792i	0.976682	+	0.214693i	$0.0688749\pi$
$620$	9.65946e22	−	1.67307e23i	0.177674	−	0.307740i
$621$	6.32391e23	+	1.09533e24i	1.14738	+	1.98732i
$622$	8.28964e22			0.148360
$623$	6.59618e23	+	1.59144e23i	1.16451	+	0.280959i
$624$	−4.88697e23			−0.851080
$625$	−8.06409e22	−	1.39674e23i	−0.138540	−	0.239958i
$626$	2.84048e23	−	4.91986e23i	0.481405	−	0.833818i
$627$	9.14034e23	−	1.58315e24i	1.52823	−	2.64697i
$628$	1.72460e23	+	2.98710e23i	0.284467	+	0.492712i
$629$	3.00445e21			0.00488916
$630$	5.84713e23	−	6.14775e23i	0.938746	−	0.987009i
$631$	−5.87570e23			−0.930701			−0.465350	−	0.885127i	$-0.654072\pi$
$631$	−5.87570e23			−0.930701			−0.465350	+	0.885127i	$0.654072\pi$
$632$	8.50548e22	+	1.47319e23i	0.132924	+	0.230231i
$633$	−9.77302e22	+	1.69274e23i	−0.150694	+	0.261010i
$634$	−4.79579e23	+	8.30655e23i	−0.729628	+	1.26375i
$635$	8.64345e22	+	1.49709e23i	0.129751	+	0.224735i
$636$	1.78299e24			2.64097
$637$	2.08645e22	+	4.15999e23i	0.0304946	+	0.608004i
$638$	−9.12434e23			−1.31591
$639$	4.25817e23	+	7.37536e23i	0.605990	+	1.04961i
$640$	−7.68657e22	+	1.33135e23i	−0.107945	+	0.186966i
$641$	1.08847e23	−	1.88528e23i	0.150842	−	0.261265i	−0.780695	−	0.624912i	$-0.785135\pi$
$641$	1.08847e23	−	1.88528e23i	0.150842	−	0.261265i	0.931537	+	0.363646i	$0.118468\pi$
$642$	−4.09022e23	−	7.08447e23i	−0.559370	−	0.968857i
$643$	1.17300e23			0.158308			0.0791542	−	0.996862i	$-0.474778\pi$
$643$	1.17300e23			0.158308			0.0791542	+	0.996862i	$0.474778\pi$
$644$	−1.00219e24	+	1.05371e24i	−1.33481	+	1.40344i
$645$	2.83297e23			0.372378
$646$	9.99664e22	+	1.73147e23i	0.129681	+	0.224615i
$647$	−4.88631e23	+	8.46335e23i	−0.625598	+	1.08357i	0.362827	+	0.931856i	$0.381811\pi$
$647$	−4.88631e23	+	8.46335e23i	−0.625598	+	1.08357i	−0.988425	+	0.151710i	$0.951522\pi$
$648$	−3.89868e22	+	6.75271e22i	−0.0492640	+	0.0853278i
$649$	2.31329e23	+	4.00673e23i	0.288503	+	0.499701i
$650$	5.32906e23			0.655974
$651$	−8.09712e23	−	1.95357e23i	−0.983766	−	0.237350i
$652$	−1.86770e24			−2.23977
$653$	−2.42352e22	−	4.19766e22i	−0.0286869	−	0.0496873i	0.851326	−	0.524638i	$-0.175799\pi$
$653$	−2.42352e22	−	4.19766e22i	−0.0286869	−	0.0496873i	−0.880012	+	0.474951i	$0.842466\pi$
$654$	−4.40384e23	+	7.62767e23i	−0.514541	+	0.891212i
$655$	1.65173e23	−	2.86088e23i	0.190497	−	0.329951i
$656$	−6.23667e23	−	1.08022e24i	−0.710019	−	1.22979i
$657$	1.14205e24			1.28345
$658$	1.42210e23	+	4.82082e23i	0.157765	+	0.534811i
$659$	8.18831e23			0.896744			0.448372	−	0.893847i	$-0.352004\pi$
$659$	8.18831e23			0.896744			0.448372	+	0.893847i	$0.352004\pi$
$660$	−6.79424e23	−	1.17680e24i	−0.734544	−	1.27227i
$661$	6.96540e23	−	1.20644e24i	0.743419	−	1.28764i	−0.207511	−	0.978233i	$-0.566536\pi$
$661$	6.96540e23	−	1.20644e24i	0.743419	−	1.28764i	0.950930	−	0.309406i	$-0.100130\pi$
$662$	−7.98910e23	+	1.38375e24i	−0.841792	+	1.45803i
$663$	7.09324e22	+	1.22859e23i	0.0737870	+	0.127803i
$664$	1.75524e23			0.180263
$665$	1.75642e23	+	5.95412e23i	0.178092	+	0.603717i
$666$	−8.94793e22			−0.0895760
$667$	5.16314e23	+	8.94282e23i	0.510322	+	0.883904i
$668$	−2.17340e21	+	3.76444e21i	−0.00212099	+	0.00367367i
$669$	8.28042e23	−	1.43421e24i	0.797866	−	1.38195i
$670$	8.94492e22	+	1.54930e23i	0.0851021	+	0.147401i
$671$	−1.96336e24			−1.84441
$672$	2.51849e24	+	6.07629e23i	2.33615	+	0.563637i
$673$	1.26923e24			1.16255			0.581275	−	0.813707i	$-0.302554\pi$
$673$	1.26923e24			1.16255			0.581275	+	0.813707i	$0.302554\pi$
$674$	−5.86801e23	−	1.01637e24i	−0.530740	−	0.919269i
$675$	−5.58721e23	+	9.67732e23i	−0.499014	+	0.864317i
$676$	4.08519e23	−	7.07576e23i	0.360301	−	0.624060i
$677$	−9.17407e23	−	1.58900e24i	−0.799022	−	1.38395i	−0.920254	−	0.391322i	$-0.872018\pi$
$677$	−9.17407e23	−	1.58900e24i	−0.799022	−	1.38395i	0.121232	−	0.992624i	$-0.461315\pi$
$678$	2.15848e24			1.85650
$679$	9.54177e23	−	1.00323e24i	0.810468	−	0.852136i
$680$	1.88092e22			0.0157777
$681$	2.35212e23	+	4.07399e23i	0.194854	+	0.337497i
$682$	−8.04808e23	+	1.39397e24i	−0.658453	+	1.14047i
$683$	3.18425e23	−	5.51528e23i	0.257295	−	0.445648i	−0.708221	−	0.705990i	$-0.750502\pi$
$683$	3.18425e23	−	5.51528e23i	0.257295	−	0.445648i	0.965516	+	0.260343i	$0.0838355\pi$
$684$	−1.58918e24	−	2.75254e24i	−1.26822	−	2.19663i
$685$	−4.84218e23			−0.381655
$686$	3.49072e23	−	1.84863e24i	0.271744	−	1.43912i
$687$	−2.01050e24			−1.54587
$688$	2.37338e23	+	4.11082e23i	0.180246	+	0.312196i
$689$	−5.58447e23	+	9.67258e23i	−0.418908	+	0.725569i
$690$	−1.44053e24	+	2.49507e24i	−1.06735	+	1.84870i
$691$	−7.97491e23	−	1.38130e24i	−0.583664	−	1.01094i	−0.995041	−	0.0994698i	$-0.968285\pi$
$691$	−7.97491e23	−	1.38130e24i	−0.583664	−	1.01094i	0.411377	−	0.911465i	$-0.365048\pi$
$692$	1.82653e24			1.32046
$693$	−2.60042e24	+	2.73411e24i	−1.85699	+	1.95247i
$694$	3.28832e24			2.31963
$695$	−3.31848e23	−	5.74777e23i	−0.231243	−	0.400524i
$696$	−1.55875e23	+	2.69984e23i	−0.107300	+	0.185848i
$697$	−1.81046e23	+	3.13580e23i	−0.123115	+	0.213241i
$698$	1.53591e24	+	2.66027e24i	1.03180	+	1.78712i
$699$	−2.69781e24			−1.79042
$700$	−1.24895e24	−	3.01332e23i	−0.818867	−	0.197566i
$701$	1.18872e24			0.769972			0.384986	−	0.922923i	$-0.374206\pi$
$701$	1.18872e24			0.769972			0.384986	+	0.922923i	$0.374206\pi$
$702$	−9.44938e23	−	1.63668e24i	−0.604697	−	1.04737i
$703$	3.27350e22	−	5.66986e22i	0.0206962	−	0.0358469i
$704$	1.50891e24	−	2.61351e24i	0.942532	−	1.63251i
$705$	2.65766e23	+	4.60320e23i	0.164018	+	0.284088i
$706$	−2.50931e24			−1.53008
$707$	3.10451e23	+	1.05241e24i	0.187037	+	0.634042i
$708$	1.24899e24			0.743489
$709$	−1.48548e24	−	2.57293e24i	−0.873723	−	1.51333i	−0.858117	−	0.513455i	$-0.828365\pi$
$709$	−1.48548e24	−	2.57293e24i	−0.873723	−	1.51333i	−0.0156065	−	0.999878i	$-0.504968\pi$
$710$	−4.33870e23	+	7.51486e23i	−0.252153	+	0.436742i
$711$	1.97346e24	−	3.41813e24i	1.13328	−	1.96289i
$712$	−2.24006e23	−	3.87990e23i	−0.127110	−	0.220161i
$713$	1.82165e24			1.02142
$714$	−1.81296e23	−	6.14578e23i	−0.100451	−	0.340520i
$715$	8.51204e23			0.466050
$716$	8.69190e23	+	1.50548e24i	0.470277	+	0.814544i
$717$	−2.03155e24	+	3.51875e24i	−1.08621	+	1.88138i
$718$	4.90100e23	−	8.48877e23i	0.258956	−	0.448526i
$719$	1.28331e24	+	2.22276e24i	0.670094	+	1.16064i	0.977877	+	0.209180i	$0.0670795\pi$
$719$	1.28331e24	+	2.22276e24i	0.670094	+	1.16064i	−0.307783	+	0.951457i	$0.599587\pi$
$720$	1.50336e24			0.775778
$721$	−1.86738e23	−	4.50538e22i	−0.0952322	−	0.0229764i
$722$	1.45091e24			0.731263
$723$	6.66535e23	+	1.15447e24i	0.332007	+	0.575053i
$724$	−7.57248e23	+	1.31159e24i	−0.372786	+	0.645685i
$725$	−4.56166e23	+	7.90103e23i	−0.221947	+	0.384424i
$726$	3.10852e24	+	5.38411e24i	1.49483	+	2.58912i
$727$	2.35907e24			1.12124			0.560620	−	0.828073i	$-0.310563\pi$
$727$	2.35907e24			1.12124			0.560620	+	0.828073i	$0.310563\pi$
$728$	1.89528e23	−	1.99273e23i	0.0890344	−	0.0936118i
$729$	−3.08745e24			−1.43356
$730$	5.81825e23	+	1.00775e24i	0.267023	+	0.462497i
$731$	6.88975e22	−	1.19334e23i	0.0312540	−	0.0541336i
$732$	−2.65013e24	+	4.59016e24i	−1.18829	+	2.05818i
$733$	−6.03367e23	−	1.04506e24i	−0.267422	−	0.463189i	0.700773	−	0.713384i	$-0.252839\pi$
$733$	−6.03367e23	−	1.04506e24i	−0.267422	−	0.463189i	−0.968195	+	0.250195i	$0.919505\pi$
$734$	−4.93883e24			−2.16375
$735$	−9.96598e22	−	1.98702e24i	−0.0431596	−	0.860520i
$736$	−5.66597e24			−2.42557
$737$	−3.97811e23	−	6.89028e23i	−0.168346	−	0.291584i
$738$	5.39195e24	−	9.33913e24i	2.25563	−	3.90686i
$739$	−1.97118e24	+	3.41418e24i	−0.815170	+	1.41192i	0.0940350	+	0.995569i	$0.470023\pi$
$739$	−1.97118e24	+	3.41418e24i	−0.815170	+	1.41192i	−0.909205	+	0.416348i	$0.863310\pi$
$740$	−2.43327e22	−	4.21455e22i	−0.00994767	−	0.0172299i
$741$	3.09138e24			1.24939
$742$	3.47663e24	−	3.65537e24i	1.38907	−	1.46049i
$743$	4.32838e24			1.70970			0.854850	−	0.518875i	$-0.173649\pi$
$743$	4.32838e24			1.70970			0.854850	+	0.518875i	$0.173649\pi$
$744$	2.74978e23	+	4.76275e23i	0.107381	+	0.185989i
$745$	−8.73272e22	+	1.51255e23i	−0.0337148	+	0.0583958i
$746$	3.44330e24	−	5.96398e24i	1.31430	−	2.27644i
$747$	−2.03626e24	−	3.52691e24i	−0.768439	−	1.33097i
$748$	−6.60941e23			−0.246604
$749$	−1.20098e24	−	2.89757e23i	−0.443037	−	0.106890i
$750$	−6.00507e24			−2.19027
$751$	1.80694e23	+	3.12971e23i	0.0651635	+	0.112867i	0.896767	−	0.442504i	$-0.145910\pi$
$751$	1.80694e23	+	3.12971e23i	0.0651635	+	0.112867i	−0.831603	+	0.555371i	$0.812576\pi$
$752$	−4.45303e23	+	7.71287e23i	−0.158783	+	0.275020i
$753$	−4.27080e24	+	7.39725e24i	−1.50575	+	2.60803i
$754$	−7.71493e23	−	1.33626e24i	−0.268952	−	0.465839i
$755$	−8.54005e23			−0.294382
$756$	1.28916e24	+	4.37015e24i	0.439412	+	1.48957i
$757$	−4.19212e22			−0.0141292			−0.00706462	−	0.999975i	$-0.502249\pi$
$757$	−4.19212e22			−0.0141292			−0.00706462	+	0.999975i	$0.502249\pi$
$758$	2.19479e23	+	3.80148e23i	0.0731483	+	0.126697i
$759$	6.40653e24	−	1.10964e25i	2.11139	−	3.65703i
$760$	2.04936e23	−	3.54959e23i	0.0667886	−	0.115681i
$761$	−2.17990e24	−	3.77569e24i	−0.702532	−	1.21682i	−0.967575	−	0.252585i	$-0.918719\pi$
$761$	−2.17990e24	−	3.77569e24i	−0.702532	−	1.21682i	0.265043	−	0.964237i	$-0.414614\pi$
$762$	−3.88825e24			−1.23919
$763$	3.76354e23	+	1.27581e24i	0.118615	+	0.402094i
$764$	−2.72063e23			−0.0847961
$765$	−2.18207e23	−	3.77946e23i	−0.0672584	−	0.116495i
$766$	−2.32800e24	+	4.03221e24i	−0.709640	+	1.22913i
$767$	−3.91192e23	+	6.77564e23i	−0.117931	+	0.204263i
$768$	1.82900e24	+	3.16791e24i	0.545309	+	0.944502i
$769$	1.39210e23			0.0410484			0.0205242	−	0.999789i	$-0.493466\pi$
$769$	1.39210e23			0.0410484			0.0205242	+	0.999789i	$0.493466\pi$
$770$	−3.73739e24	−	9.01710e23i	−1.08993	−	0.262964i
$771$	3.12591e24			0.901599
$772$	5.58709e23	+	9.67713e23i	0.159382	+	0.276057i
$773$	2.01383e24	−	3.48805e24i	0.568194	−	0.984140i	−0.428551	−	0.903518i	$-0.640976\pi$
$773$	2.01383e24	−	3.48805e24i	0.568194	−	0.984140i	0.996745	−	0.0806225i	$-0.0256908\pi$
$774$	−2.05193e24	+	3.55404e24i	−0.572616	+	0.991800i
$775$	8.04718e23	+	1.39381e24i	0.222116	+	0.384716i
$776$	−9.14144e23			−0.249569
$777$	−1.44604e23	+	1.52038e23i	−0.0390482	+	0.0410558i
$778$	−3.74386e24			−0.999985
$779$	3.94517e24	+	6.83323e24i	1.04231	+	1.80533i
$780$	1.14895e24	−	1.99004e24i	0.300260	−	0.520065i
$781$	1.92957e24	−	3.34211e24i	0.498800	−	0.863947i
$782$	7.00671e23	+	1.21360e24i	0.179167	+	0.310326i
$783$	3.23546e24			0.818391
$784$	2.79981e24	−	1.80929e24i	0.700555	−	0.452711i
$785$	1.03203e24			0.255447
$786$	3.71515e24	+	6.43483e24i	0.909672	+	1.57560i
$787$	−3.77208e24	+	6.53344e24i	−0.913684	+	1.58255i	−0.104868	+	0.994486i	$0.533442\pi$
$787$	−3.77208e24	+	6.53344e24i	−0.913684	+	1.58255i	−0.808816	+	0.588061i	$0.799891\pi$
$788$	2.27928e24	−	3.94783e24i	0.546166	−	0.945987i
$789$	1.74376e24	+	3.02027e24i	0.413363	+	0.715965i
$790$	4.02157e24			0.943115
$791$	2.24656e24	−	2.36206e24i	0.521216	−	0.548013i
$792$	2.49131e24			0.571827
$793$	−1.66008e24	−	2.87534e24i	−0.376970	−	0.652931i
$794$	4.14566e24	−	7.18049e24i	0.931363	−	1.61317i
$795$	2.66743e24	−	4.62012e24i	0.592887	−	1.02691i
$796$	4.54131e24	+	7.86577e24i	0.998665	+	1.72974i
$797$	−8.89807e24			−1.93598			−0.967989	−	0.250994i	$-0.919243\pi$
$797$	−8.89807e24			−1.93598			−0.967989	+	0.250994i	$0.919243\pi$
$798$	−1.35734e25	−	3.27481e24i	−2.92188	−	0.704955i
$799$	2.58536e23			0.0550647
$800$	−2.50296e24	−	4.33525e24i	−0.527459	−	0.913586i
$801$	−5.19743e24	+	9.00221e24i	−1.08371	+	1.87704i
$802$	−7.90053e23	+	1.36841e24i	−0.162995	+	0.282316i
$803$	−2.58757e24	−	4.48181e24i	−0.528214	−	0.914894i
$804$	−2.14785e24			−0.433838
$805$	1.23109e24	+	4.17329e24i	0.246050	+	0.834091i
$806$	−2.72196e24			−0.538312
$807$	−1.07911e24	−	1.86907e24i	−0.211173	−	0.365763i
$808$	3.62229e23	−	6.27399e23i	0.0701433	−	0.121492i
$809$	−1.90949e24	+	3.30733e24i	−0.365894	+	0.633747i	−0.988919	−	0.148455i	$-0.952570\pi$
$809$	−1.90949e24	+	3.30733e24i	−0.365894	+	0.633747i	0.623025	+	0.782202i	$0.285903\pi$
$810$	9.21688e23	+	1.59641e24i	0.174768	+	0.302706i
$811$	−2.15654e24			−0.404650			−0.202325	−	0.979318i	$-0.564850\pi$
$811$	−2.15654e24			−0.404650			−0.202325	+	0.979318i	$0.564850\pi$
$812$	1.05253e24	+	3.56800e24i	0.195438	+	0.662520i
$813$	7.30617e24			1.34252
$814$	2.02736e23	+	3.51148e23i	0.0368657	+	0.0638533i
$815$	−2.79416e24	+	4.83963e24i	−0.502819	+	0.870908i
$816$	5.67691e23	−	9.83270e23i	0.101099	−	0.175108i
$817$	−1.50135e24	−	2.60041e24i	−0.264602	−	0.458305i
$818$	−6.04801e24			−1.05490
$819$	−6.20285e24	−	1.49654e24i	−1.07073	−	0.258331i
$820$	5.86509e24			1.00197
$821$	3.73866e24	+	6.47556e24i	0.632120	+	1.09486i	0.987117	+	0.159997i	$0.0511485\pi$
$821$	3.73866e24	+	6.47556e24i	0.632120	+	1.09486i	−0.354997	+	0.934867i	$0.615518\pi$
$822$	5.44562e24	−	9.43210e24i	0.911249	−	1.57833i
$823$	−2.44871e24	+	4.24129e24i	−0.405545	+	0.702424i	−0.994385	−	0.105826i	$-0.966251\pi$
$823$	−2.44871e24	+	4.24129e24i	−0.405545	+	0.702424i	0.588840	+	0.808250i	$0.299585\pi$
$824$	6.34163e22	+	1.09840e23i	0.0103949	+	0.0180045i
$825$	1.13204e25			1.83655
$826$	2.43538e24	−	2.56059e24i	0.391054	−	0.411159i
$827$	7.36666e24			1.17078			0.585388	−	0.810753i	$-0.300942\pi$
$827$	7.36666e24			1.17078			0.585388	+	0.810753i	$0.300942\pi$
$828$	−1.11387e25	−	1.92927e25i	−1.75217	−	3.03484i
$829$	8.95951e23	−	1.55183e24i	0.139499	−	0.241619i	−0.787808	−	0.615921i	$-0.788784\pi$
$829$	8.95951e23	−	1.55183e24i	0.139499	−	0.241619i	0.927307	+	0.374301i	$0.122117\pi$
$830$	2.07478e24	−	3.59362e24i	0.319748	−	0.553820i
$831$	−6.53940e24	−	1.13266e25i	−0.997537	−	1.72779i
$832$	5.10333e24			0.770559
$833$	−8.61237e23	−	4.41262e23i	−0.128718	−	0.0659499i
$834$	1.49281e25			2.20848
$835$	6.50298e21	+	1.12635e22i	0.000952308	+	0.00164945i
$836$	−7.20129e24	+	1.24730e25i	−1.04390	+	1.80808i
$837$	2.85382e24	−	4.94296e24i	0.409506	−	0.709285i
$838$	−2.85106e24	−	4.93818e24i	−0.404978	−	0.701443i
$839$	−1.96968e24			−0.276961			−0.138480	−	0.990365i	$-0.544222\pi$
$839$	−1.96968e24			−0.276961			−0.138480	+	0.990365i	$0.544222\pi$
$840$	−9.05285e23	+	9.51828e23i	−0.126012	+	0.132490i
$841$	−4.61556e24			−0.636002
$842$	1.68432e24	+	2.91733e24i	0.229759	+	0.397954i
$843$	−6.97018e24	+	1.20727e25i	−0.941260	+	1.63031i
$844$	7.69976e23	−	1.33364e24i	0.102936	−	0.178290i
$845$	−1.22232e24	−	2.11713e24i	−0.161772	−	0.280198i
$846$	−7.69980e24			−1.00886
$847$	9.12729e24	+	2.20211e24i	1.18395	+	0.285648i
$848$	8.93880e24			1.14793
$849$	7.78048e24	+	1.34762e25i	0.989216	+	1.71337i
$850$	−6.19047e23	+	1.07222e24i	−0.0779224	+	0.134966i
$851$	2.29442e23	−	3.97405e23i	0.0285938	−	0.0495258i
$852$	−5.20904e24	−	9.02233e24i	−0.642719	−	1.11322i
$853$	−2.79912e24			−0.341943			−0.170972	−	0.985276i	$-0.554691\pi$
$853$	−2.79912e24			−0.341943			−0.170972	+	0.985276i	$0.554691\pi$
$854$	4.24299e24	+	1.43834e25i	0.513192	+	1.73968i
$855$	−9.50991e24			−1.13884
$856$	4.07852e23	+	7.06420e23i	0.0483588	+	0.0837599i
$857$	6.84681e24	−	1.18590e25i	0.803806	−	1.39223i	−0.113288	−	0.993562i	$-0.536138\pi$
$857$	6.84681e24	−	1.18590e25i	0.803806	−	1.39223i	0.917094	−	0.398671i	$-0.130528\pi$
$858$	−9.57283e24	+	1.65806e25i	−1.11275	+	1.92734i
$859$	−8.20778e24	−	1.42163e25i	−0.944678	−	1.63623i	−0.756395	−	0.654115i	$-0.773041\pi$
$859$	−8.20778e24	−	1.42163e25i	−0.944678	−	1.63623i	−0.188282	−	0.982115i	$-0.560292\pi$
$860$	−2.23198e24			−0.254363
$861$	−7.15483e24	−	2.42543e25i	−0.807369	−	2.73692i
$862$	−1.51190e25			−1.68932
$863$	−3.48394e24	−	6.03435e24i	−0.385459	−	0.667635i	0.606374	−	0.795180i	$-0.292624\pi$
$863$	−3.48394e24	−	6.03435e24i	−0.385459	−	0.667635i	−0.991833	+	0.127545i	$0.959290\pi$
$864$	−8.87640e24	+	1.53744e25i	−0.972456	+	1.68434i
$865$	2.73257e24	−	4.73294e24i	0.296438	−	0.513446i
$866$	1.27838e25	+	2.21422e25i	1.37328	+	2.37858i
$867$	1.54270e25			1.64104
$868$	6.37938e24	+	1.53914e24i	0.671987	+	0.162128i
$869$	−1.78853e25			−1.86564
$870$	3.68505e24	+	6.38269e24i	0.380653	+	0.659310i
$871$	6.72723e23	−	1.16519e24i	0.0688148	−	0.119191i
$872$	4.39123e23	−	7.60584e23i	0.0444833	−	0.0770473i
$873$	1.06051e25	+	1.83685e25i	1.06388	+	1.84269i
$874$	3.05367e25			3.03371
$875$	−6.25012e24	+	6.57145e24i	−0.614922	+	0.646536i
$876$	−1.39708e25			−1.36124
$877$	−4.40734e24	−	7.63373e24i	−0.425285	−	0.736615i	0.571162	−	0.820837i	$-0.306493\pi$
$877$	−4.40734e24	−	7.63373e24i	−0.425285	−	0.736615i	−0.996447	+	0.0842224i	$0.973159\pi$
$878$	7.95480e24	−	1.37781e25i	0.760197	−	1.31670i
$879$	−3.64229e24	+	6.30863e24i	−0.344722	+	0.597076i
$880$	−3.40621e24	−	5.89972e24i	−0.319277	−	0.553005i
$881$	6.82777e24			0.633845			0.316923	−	0.948451i	$-0.397350\pi$
$881$	6.82777e24			0.633845			0.316923	+	0.948451i	$0.397350\pi$
$882$	2.56496e25	+	1.31418e25i	2.35829	+	1.20829i
$883$	−1.42622e25			−1.29874			−0.649368	−	0.760474i	$-0.724967\pi$
$883$	−1.42622e25			−1.29874			−0.649368	+	0.760474i	$0.724967\pi$
$884$	−5.58847e23	−	9.67952e23i	−0.0504021	−	0.0872990i
$885$	1.86853e24	−	3.23639e24i	0.166910	−	0.289097i
$886$	1.43582e25	−	2.48691e25i	1.27032	−	2.20026i
$887$	8.33443e24	+	1.44357e25i	0.730340	+	1.26499i	0.956738	+	0.290951i	$0.0939718\pi$
$887$	8.33443e24	+	1.44357e25i	0.730340	+	1.26499i	−0.226398	+	0.974035i	$0.572695\pi$
$888$	1.38537e23			0.0120242
$889$	−4.04692e24	+	4.25498e24i	−0.347904	+	0.365791i
$890$	−1.05915e25			−0.901864
$891$	−4.09906e24	−	7.09977e24i	−0.345719	−	0.598803i
$892$	−6.52380e24	+	1.12995e25i	−0.545003	+	0.943974i
$893$	2.81688e24	−	4.87898e24i	0.233094	−	0.403731i
$894$	−1.96420e24	−	3.40210e24i	−0.160997	−	0.278855i
$895$	5.20138e24			0.422301
$896$	−5.07643e24	−	1.22478e24i	−0.408263	−	0.0985005i
$897$	2.16677e25			1.72614
$898$	−4.00358e23	−	6.93441e23i	−0.0315936	−	0.0547218i
$899$	2.32999e24	−	4.03567e24i	0.182137	−	0.315470i
$900$	9.84107e24	−	1.70452e25i	0.762046	−	1.31990i
$901$	−1.29743e24	−	2.24722e24i	−0.0995231	−	0.172379i
$902$	−4.88668e25			−3.71328
$903$	2.72279e24	+	9.23006e24i	0.204960	+	0.694798i
$904$	−2.15230e24			−0.160499
$905$	2.26575e24	+	3.92439e24i	0.167378	+	0.289907i
$906$	9.60434e24	−	1.66352e25i	0.702874	−	1.21741i
$907$	−4.47309e23	+	7.74762e23i	−0.0324299	+	0.0561702i	−0.881785	−	0.471652i	$-0.843658\pi$
$907$	−4.47309e23	+	7.74762e23i	−0.0324299	+	0.0561702i	0.849355	+	0.527822i	$0.176991\pi$
$908$	−1.85314e24	−	3.20973e24i	−0.133100	−	0.230536i
$909$	−1.68090e25			−1.19605
$910$	−1.83953e24	−	6.23585e24i	−0.129674	−	0.439586i
$911$	−1.46523e25			−1.02329			−0.511646	−	0.859196i	$-0.670964\pi$
$911$	−1.46523e25			−1.02329			−0.511646	+	0.859196i	$0.670964\pi$
$912$	−1.23706e25	−	2.14265e25i	−0.855921	−	1.48250i
$913$	−9.22724e24	+	1.59820e25i	−0.632514	+	1.09555i
$914$	−1.95502e25	+	3.38620e25i	−1.32773	+	2.29969i
$915$	7.92940e24	+	1.37341e25i	0.533533	+	0.924106i
$916$	1.58399e25			1.05594
$917$	1.09085e25	+	2.63186e24i	0.720486	+	0.173830i
$918$	4.39073e24			0.287325
$919$	−7.20588e24	−	1.24810e25i	−0.467203	−	0.809219i	0.532095	−	0.846685i	$-0.321405\pi$
$919$	−7.20588e24	−	1.24810e25i	−0.467203	−	0.809219i	−0.999298	+	0.0374656i	$0.988072\pi$
$920$	1.43641e24	−	2.48793e24i	0.0922745	−	0.159824i
$921$	−9.13490e23	+	1.58221e24i	−0.0581430	+	0.100707i
$922$	−1.73399e25	−	3.00336e25i	−1.09354	−	1.89406i
$923$	6.52605e24			0.407789
$924$	3.18111e25	−	3.34466e25i	1.96955	−	2.07081i
$925$	4.05426e23			0.0248718
$926$	−4.92188e24	−	8.52494e24i	−0.299183	−	0.518201i
$927$	1.47140e24	−	2.54853e24i	0.0886241	−	0.153501i
$928$	−7.24711e24	+	1.25524e25i	−0.432521	+	0.749148i
$929$	−2.18919e24	−	3.79179e24i	−0.129464	−	0.224239i	0.794005	−	0.607911i	$-0.207992\pi$
$929$	−2.18919e24	−	3.79179e24i	−0.129464	−	0.224239i	−0.923469	+	0.383673i	$0.874659\pi$
$930$	1.30015e25			0.761883
$931$	−1.77109e25	+	1.14451e25i	−1.02842	+	0.664582i
$932$	2.12550e25			1.22300
$933$	1.48894e24	+	2.57892e24i	0.0848952	+	0.147043i
$934$	−5.83530e24	+	1.01070e25i	−0.329697	+	0.571051i
$935$	−9.88795e23	+	1.71264e24i	−0.0553615	+	0.0958889i
$936$	2.10649e24	+	3.64854e24i	0.116873	+	0.202430i
$937$	3.85849e24			0.212144			0.106072	−	0.994358i	$-0.466173\pi$
$937$	3.85849e24			0.212144			0.106072	+	0.994358i	$0.466173\pi$
$938$	−4.18807e24	+	4.40338e24i	−0.228186	+	0.239918i
$939$	2.04077e25			1.10189
$940$	−2.09386e24	−	3.62667e24i	−0.112037	−	0.194053i
$941$	1.39742e25	−	2.42040e25i	0.740995	−	1.28344i	−0.211047	−	0.977476i	$-0.567687\pi$
$941$	1.39742e25	−	2.42040e25i	0.740995	−	1.28344i	0.952042	−	0.305966i	$-0.0989794\pi$
$942$	−1.16065e25	+	2.01030e25i	−0.609912	+	1.05640i
$943$	2.76520e25	+	4.78946e25i	1.44005	+	2.49423i
$944$	6.26163e24			0.323166
$945$	1.32527e25	+	3.19743e24i	0.677849	+	0.163543i
$946$	1.85964e25			0.942659
$947$	−1.09613e25	−	1.89856e25i	−0.550666	−	0.953782i	−0.998227	−	0.0595281i	$-0.981040\pi$
$947$	−1.09613e25	−	1.89856e25i	−0.550666	−	0.953782i	0.447560	−	0.894254i	$-0.352293\pi$
$948$	−2.41414e25	+	4.18142e25i	−1.20197	+	2.08187i
$949$	4.37575e24	−	7.57902e24i	0.215918	−	0.373982i
$950$	1.34897e25	+	2.33648e25i	0.659706	+	1.14264i
$951$	−3.44557e25			−1.67004
$952$	1.80777e23	+	6.12820e23i	0.00868419	+	0.0294387i
$953$	−1.22289e25			−0.582236			−0.291118	−	0.956687i	$-0.594027\pi$
$953$	−1.22289e25			−0.582236			−0.291118	+	0.956687i	$0.594027\pi$
$954$	3.86405e25	+	6.69273e25i	1.82340	+	3.15822i
$955$	−4.07017e23	+	7.04975e23i	−0.0190364	+	0.0329720i
$956$	1.60058e25	−	2.77228e25i	0.741966	−	1.28512i
$957$	−1.63886e25	−	2.83860e25i	−0.752994	−	1.30422i
$958$	−1.12974e25			−0.514482
$959$	−4.65386e24	−	1.57762e25i	−0.210066	−	0.712107i
$960$	−2.43762e25			−1.09059
$961$	7.16474e24	+	1.24097e25i	0.317725	+	0.550316i
$962$	−3.42839e23	+	5.93814e23i	−0.0150696	+	0.0261013i
$963$	9.46305e24	−	1.63905e25i	0.412295	−	0.714116i
$964$	−5.25135e24	−	9.09561e24i	−0.226786	−	0.392805i
$965$	3.34341e24			0.143122
$966$	−9.51367e25	−	2.29534e25i	−4.03685	−	0.973959i
$967$	1.93475e25			0.813766			0.406883	−	0.913480i	$-0.366616\pi$
$967$	1.93475e25			0.813766			0.406883	+	0.913480i	$0.366616\pi$
$968$	−3.09962e24	−	5.36870e24i	−0.129231	−	0.223835i
$969$	−3.59108e24	+	6.21994e24i	−0.148413	+	0.257060i
$970$	−1.08056e25	+	1.87159e25i	−0.442681	+	0.766746i
$971$	1.33280e25	+	2.30847e25i	0.541254	+	0.937479i	0.998832	+	0.0483097i	$0.0153834\pi$
$971$	1.33280e25	+	2.30847e25i	0.541254	+	0.937479i	−0.457579	+	0.889169i	$0.651283\pi$
$972$	1.64468e25			0.662092
$973$	1.55373e25	−	1.63361e25i	0.620036	−	0.651913i
$974$	5.05163e25			1.99839
$975$	9.57176e24	+	1.65788e25i	0.375364	+	0.650149i
$976$	−1.32861e25	+	2.30122e25i	−0.516503	+	0.894610i
$977$	2.44503e25	−	4.23492e25i	0.942281	−	1.63208i	0.181176	−	0.983451i	$-0.442010\pi$
$977$	2.44503e25	−	4.23492e25i	0.942281	−	1.63208i	0.761105	−	0.648628i	$-0.224657\pi$
$978$	−6.28476e25	−	1.08855e26i	−2.40109	−	4.15881i
$979$	4.71038e25			1.78403
$980$	7.85178e23	+	1.56549e25i	0.0294813	+	0.587800i
$981$	−2.03772e25			−0.758506
$982$	4.29464e24	+	7.43853e24i	0.158482	+	0.274498i
$983$	4.14475e24	−	7.17891e24i	0.151633	−	0.262636i	−0.780195	−	0.625536i	$-0.784880\pi$
$983$	4.14475e24	−	7.17891e24i	0.151633	−	0.262636i	0.931828	+	0.362901i	$0.118214\pi$
$984$	−8.34812e24	+	1.44594e25i	−0.302782	+	0.524434i
$985$	−6.81979e24	−	1.18122e25i	−0.245224	−	0.424740i
$986$	3.58480e24			0.127794
$987$	−1.24433e25	+	1.30831e25i	−0.439785	+	0.462396i
$988$	−2.43557e25			−0.853427
$989$	−1.05231e25	−	1.82265e25i	−0.365572	−	0.633190i
$990$	2.94486e25	−	5.10065e25i	1.01430	−	1.75682i
$991$	−1.91099e25	+	3.30994e25i	−0.652579	+	1.13030i	0.329916	+	0.944010i	$0.392979\pi$
$991$	−1.91099e25	+	3.30994e25i	−0.652579	+	1.13030i	−0.982495	+	0.186289i	$0.940354\pi$
$992$	1.27846e25	+	2.21435e25i	0.432849	+	0.749716i
$993$	−5.73983e25			−1.92677
$994$	−2.86540e25	−	6.91327e24i	−0.953677	−	0.230091i
$995$	2.71759e25			0.896784
$996$	2.49098e25	+	4.31450e25i	0.815014	+	1.41165i
$997$	−4.75614e24	+	8.23787e24i	−0.154293	+	0.267243i	−0.932801	−	0.360391i	$-0.882643\pi$
$997$	−4.75614e24	+	8.23787e24i	−0.154293	+	0.267243i	0.778509	+	0.627634i	$0.215977\pi$
$998$	2.64090e25	−	4.57418e25i	0.849460	−	1.47131i
$999$	−7.18893e23	−	1.24516e24i	−0.0229276	−	0.0397117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.c.a.4.2	yes	20
7.2	even	3	inner	7.18.c.a.2.2	✓	20
7.3	odd	6		49.18.a.g.1.9		10
7.4	even	3		49.18.a.f.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.c.a.2.2	✓	20	7.2	even	3	inner
7.18.c.a.4.2	yes	20	1.1	even	1	trivial
49.18.a.f.1.9		10	7.4	even	3
49.18.a.g.1.9		10	7.3	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)

\(f(q)\)	\(=\)	\(q+(-265.112 - 459.187i) q^{2} +(9523.58 - 16495.3i) q^{3} +(-75032.3 + 129960. i) q^{4} +(224503. + 388850. i) q^{5} -1.00992e7 q^{6} +(-1.05114e7 + 1.10518e7i) q^{7} +1.00703e7 q^{8} +(-1.16827e8 - 2.02350e8i) q^{9} +O(q^{10})\)	\(q+(-265.112 - 459.187i) q^{2} +(9523.58 - 16495.3i) q^{3} +(-75032.3 + 129960. i) q^{4} +(224503. + 388850. i) q^{5} -1.00992e7 q^{6} +(-1.05114e7 + 1.10518e7i) q^{7} +1.00703e7 q^{8} +(-1.16827e8 - 2.02350e8i) q^{9} +(1.19037e8 - 2.06177e8i) q^{10} +(-5.29396e8 + 9.16941e8i) q^{11} +(1.42915e9 + 2.47536e9i) q^{12} -1.79049e9 q^{13} +(7.86151e9 + 1.89672e9i) q^{14} +8.55228e9 q^{15} +(7.16487e9 + 1.24099e10i) q^{16} +(2.07991e9 - 3.60250e9i) q^{17} +(-6.19444e10 + 1.07291e11i) q^{18} +(-4.53233e10 - 7.85022e10i) q^{19} -6.73799e10 q^{20} +(8.21968e10 + 2.78641e11i) q^{21} +5.61396e11 q^{22} +(-3.17674e11 - 5.50228e11i) q^{23} +(9.59057e10 - 1.66114e11i) q^{24} +(2.80667e11 - 4.86129e11i) q^{25} +(4.74678e11 + 8.22167e11i) q^{26} -1.99069e12 q^{27} +(-6.47595e11 - 2.19530e12i) q^{28} -1.62529e12 q^{29} +(-2.26731e12 - 3.92709e12i) q^{30} +(-1.43358e12 + 2.48304e12i) q^{31} +(4.45895e12 - 7.72313e12i) q^{32} +(1.00835e13 + 1.74651e13i) q^{33} -2.20563e12 q^{34} +(-6.65732e12 - 1.60619e12i) q^{35} +3.50632e13 q^{36} +(3.61127e11 + 6.25491e11i) q^{37} +(-2.40315e13 + 4.16237e13i) q^{38} +(-1.70518e13 + 2.95346e13i) q^{39} +(2.26082e12 + 3.91586e12i) q^{40} -8.70450e13 q^{41} +(1.06157e14 - 1.11615e14i) q^{42} +3.31253e13 q^{43} +(-7.94436e13 - 1.37600e14i) q^{44} +(5.24560e13 - 9.08564e13i) q^{45} +(-1.68438e14 + 2.91744e14i) q^{46} +(3.10754e13 + 5.38242e13i) q^{47} +2.72941e14 q^{48} +(-1.16530e13 - 2.32338e14i) q^{49} -2.97632e14 q^{50} +(-3.96163e13 - 6.86175e13i) q^{51} +(1.34344e14 - 2.32691e14i) q^{52} +(3.11897e14 - 5.40221e14i) q^{53} +(5.27755e14 + 9.14099e14i) q^{54} -4.75404e14 q^{55} +(-1.05853e14 + 1.11295e14i) q^{56} -1.72656e15 q^{57} +(4.30885e14 + 7.46314e14i) q^{58} +(2.18484e14 - 3.78425e14i) q^{59} +(-6.41698e14 + 1.11145e15i) q^{60} +(9.27168e14 + 1.60590e15i) q^{61} +1.52024e15 q^{62} +(3.46434e15 + 8.35832e14i) q^{63} -2.85025e15 q^{64} +(-4.01969e14 - 6.96231e14i) q^{65} +(5.34650e15 - 9.26041e15i) q^{66} +(-3.75721e14 + 6.50768e14i) q^{67} +(3.12120e14 + 5.40609e14i) q^{68} -1.21016e16 q^{69} +(1.02739e15 + 3.48277e15i) q^{70} -3.64485e15 q^{71} +(-1.17649e15 - 2.03774e15i) q^{72} +(-2.44389e15 + 4.23294e15i) q^{73} +(1.91478e14 - 3.31650e14i) q^{74} +(-5.34590e15 - 9.25937e15i) q^{75} +1.36028e16 q^{76} +(-4.56915e15 - 1.54891e16i) q^{77} +1.80826e16 q^{78} +(8.44607e15 + 1.46290e16i) q^{79} +(-3.21707e15 + 5.57213e15i) q^{80} +(-3.87145e15 + 6.70554e15i) q^{81} +(2.30767e16 + 3.99699e16i) q^{82} +1.74297e16 q^{83} +(-4.23795e16 - 1.02248e16i) q^{84} +1.86778e15 q^{85} +(-8.78190e15 - 1.52107e16i) q^{86} +(-1.54786e16 + 2.68098e16i) q^{87} +(-5.33120e15 + 9.23391e15i) q^{88} +(-2.22441e16 - 3.85280e16i) q^{89} -5.56268e16 q^{90} +(1.88204e16 - 1.97880e16i) q^{91} +9.53433e16 q^{92} +(2.73057e16 + 4.72948e16i) q^{93} +(1.64769e16 - 2.85389e16i) q^{94} +(2.03504e16 - 3.52479e16i) q^{95} +(-8.49303e16 - 1.47104e17i) q^{96} -9.07758e16 q^{97} +(-1.03597e17 + 6.69465e16i) q^{98} +2.47391e17 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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