LMFDB - Embedded newform 690.2.m.h.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.2
Character	$\chi$	$=$	690.361
Dual form			690.2.m.h.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.94609 - 0.571424i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.94609 - 0.571424i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-3.23188 - 3.72979i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(6.08173 + 1.78576i) q^{13} +(0.842565 - 1.84496i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.738737 + 5.13803i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.914645 - 6.36150i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(1.32822 - 1.53285i) q^{21} -4.93521 q^{22} +(-4.78923 - 0.251457i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(5.33228 - 3.42685i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.842565 - 1.84496i) q^{28} +(0.160429 - 1.11581i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(1.29286 + 0.830872i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-4.73530 - 1.39041i) q^{33} +(3.39930 + 3.92300i) q^{34} +(-1.32822 - 1.53285i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.68615 - 8.07155i) q^{37} +(-5.40667 - 3.47465i) q^{38} +(6.08173 - 1.78576i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(2.21966 + 4.86037i) q^{41} +(-0.288650 - 2.00760i) q^{42} +(-6.99089 + 4.49277i) q^{43} +(-3.23188 + 3.72979i) q^{44} -1.00000 q^{45} +(-3.32632 + 3.45479i) q^{46} +11.5747 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-2.42803 + 1.56040i) q^{49} +(0.142315 + 0.989821i) q^{50} +(2.15636 + 4.72178i) q^{51} +(0.902061 - 6.27397i) q^{52} +(2.01899 - 0.592829i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-2.05016 + 4.48923i) q^{55} +(-1.94609 - 0.571424i) q^{56} +(-4.20873 - 4.85714i) q^{57} +(-0.738214 - 0.851945i) q^{58} +(1.34640 + 0.395340i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(0.181974 + 0.116948i) q^{61} +(1.47458 - 0.432975i) q^{62} +(0.288650 - 2.00760i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.902061 - 6.27397i) q^{65} +(-4.15177 + 2.66818i) q^{66} +(2.92544 - 3.37614i) q^{67} +5.19087 q^{68} +(-4.16491 + 2.37772i) q^{69} -2.02825 q^{70} +(-10.1035 + 11.6600i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.620858 + 4.31816i) q^{73} +(-3.68615 - 8.07155i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(-6.16658 + 1.81067i) q^{76} +(-8.42081 - 5.41173i) q^{77} +(2.63310 - 5.76569i) q^{78} +(14.8120 + 4.34918i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(5.12679 + 1.50536i) q^{82} +(0.0838378 - 0.183579i) q^{83} +(-1.70627 - 1.09655i) q^{84} +(4.98060 - 1.46244i) q^{85} +(-1.18265 + 8.22550i) q^{86} +(-0.468291 - 1.02541i) q^{87} +(0.702354 + 4.88498i) q^{88} +(7.42991 - 4.77491i) q^{89} +(-0.654861 + 0.755750i) q^{90} +12.8560 q^{91} +(0.432682 + 4.77627i) q^{92} +1.53683 q^{93} +(7.57982 - 8.74758i) q^{94} +(-5.40667 + 3.47465i) q^{95} +(0.142315 + 0.989821i) q^{96} +(5.87005 + 12.8536i) q^{97} +(-0.410750 + 2.85683i) q^{98} +(-4.73530 + 1.39041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	1.94609	−	0.571424i	0.735553	−	0.215978i	0.107562	−	0.994198i	$-0.465696\pi$
$7$	1.94609	−	0.571424i	0.735553	−	0.215978i	0.627991	+	0.778221i	$0.283877\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.959493	−	0.281733i	−0.303418	−	0.0890917i
$11$	−3.23188	−	3.72979i	−0.974448	−	1.12457i	−0.992191	−	0.124730i	$-0.960194\pi$
$11$	−3.23188	−	3.72979i	−0.974448	−	1.12457i	0.0177430	−	0.999843i	$-0.494352\pi$
$12$	−0.654861	−	0.755750i	−0.189042	−	0.218166i
$13$	6.08173	+	1.78576i	1.68677	+	0.495280i	0.977726	−	0.209884i	$-0.0673088\pi$
$13$	6.08173	+	1.78576i	1.68677	+	0.495280i	0.709044	+	0.705165i	$0.249127\pi$
$14$	0.842565	−	1.84496i	0.225185	−	0.493086i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.738737	+	5.13803i	−0.179170	+	1.24616i	0.679519	+	0.733658i	$0.262189\pi$
$17$	−0.738737	+	5.13803i	−0.179170	+	1.24616i	−0.858689	+	0.512497i	$0.828720\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	−0.914645	−	6.36150i	−0.209834	−	1.45943i	−0.773695	−	0.633558i	$-0.781594\pi$
$19$	−0.914645	−	6.36150i	−0.209834	−	1.45943i	0.563861	−	0.825870i	$-0.309315\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	1.32822	−	1.53285i	0.289841	−	0.334495i
$22$	−4.93521			−1.05219
$23$	−4.78923	−	0.251457i	−0.998624	−	0.0524323i
$23$	−4.78923	−	0.251457i	−0.998624	−	0.0524323i
$24$	−1.00000			−0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	5.33228	−	3.42685i	1.04575	−	0.672060i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	−0.842565	−	1.84496i	−0.159230	−	0.348665i
$29$	0.160429	−	1.11581i	0.0297910	−	0.207201i	−0.969489	−	0.245134i	$-0.921168\pi$
$29$	0.160429	−	1.11581i	0.0297910	−	0.207201i	0.999280	+	0.0379328i	$0.0120773\pi$
$30$	−0.959493	+	0.281733i	−0.175179	+	0.0514371i
$31$	1.29286	+	0.830872i	0.232205	+	0.149229i	0.651570	−	0.758589i	$-0.274111\pi$
$31$	1.29286	+	0.830872i	0.232205	+	0.149229i	−0.419365	+	0.907818i	$0.637747\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−4.73530	−	1.39041i	−0.824310	−	0.242039i
$34$	3.39930	+	3.92300i	0.582974	+	0.672788i
$35$	−1.32822	−	1.53285i	−0.224510	−	0.259099i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	3.68615	−	8.07155i	0.606000	−	1.32695i	−0.319277	−	0.947662i	$-0.603440\pi$
$37$	3.68615	−	8.07155i	0.606000	−	1.32695i	0.925276	−	0.379293i	$-0.123833\pi$
$38$	−5.40667	−	3.47465i	−0.877077	−	0.563663i
$39$	6.08173	−	1.78576i	0.973857	−	0.285950i
$40$	−0.142315	+	0.989821i	−0.0225020	+	0.156505i
$41$	2.21966	+	4.86037i	0.346652	+	0.759062i	0.999998	+	0.00200255i	$0.000637431\pi$
$41$	2.21966	+	4.86037i	0.346652	+	0.759062i	−0.653346	+	0.757059i	$0.726635\pi$
$42$	−0.288650	−	2.00760i	−0.0445396	−	0.309780i
$43$	−6.99089	+	4.49277i	−1.06610	+	0.685141i	−0.951306	−	0.308248i	$-0.900257\pi$
$43$	−6.99089	+	4.49277i	−1.06610	+	0.685141i	−0.114795	+	0.993389i	$0.536621\pi$
$44$	−3.23188	+	3.72979i	−0.487224	+	0.562286i
$45$	−1.00000			−0.149071
$46$	−3.32632	+	3.45479i	−0.490439	+	0.509381i
$47$	11.5747			1.68834			0.844172	−	0.536072i	$-0.180092\pi$
$47$	11.5747			1.68834			0.844172	+	0.536072i	$0.180092\pi$
$48$	−0.654861	+	0.755750i	−0.0945210	+	0.109083i
$49$	−2.42803	+	1.56040i	−0.346862	+	0.222915i
$50$	0.142315	+	0.989821i	0.0201264	+	0.139982i
$51$	2.15636	+	4.72178i	0.301951	+	0.661181i
$52$	0.902061	−	6.27397i	0.125093	−	0.870043i
$53$	2.01899	−	0.592829i	0.277330	−	0.0814314i	−0.140110	−	0.990136i	$-0.544746\pi$
$53$	2.01899	−	0.592829i	0.277330	−	0.0814314i	0.417440	+	0.908705i	$0.362927\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	−2.05016	+	4.48923i	−0.276444	+	0.605327i
$56$	−1.94609	−	0.571424i	−0.260057	−	0.0763597i
$57$	−4.20873	−	4.85714i	−0.557461	−	0.643344i
$58$	−0.738214	−	0.851945i	−0.0969323	−	0.111866i
$59$	1.34640	+	0.395340i	0.175287	+	0.0514689i	0.368198	−	0.929747i	$-0.379975\pi$
$59$	1.34640	+	0.395340i	0.175287	+	0.0514689i	−0.192911	+	0.981216i	$0.561793\pi$
$60$	−0.415415	+	0.909632i	−0.0536298	+	0.117433i
$61$	0.181974	+	0.116948i	0.0232994	+	0.0149736i	0.552239	−	0.833686i	$-0.313774\pi$
$61$	0.181974	+	0.116948i	0.0232994	+	0.0149736i	−0.528939	+	0.848660i	$0.677410\pi$
$62$	1.47458	−	0.432975i	0.187271	−	0.0549878i
$63$	0.288650	−	2.00760i	0.0363665	−	0.252934i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.902061	−	6.27397i	−0.111887	−	0.778190i
$66$	−4.15177	+	2.66818i	−0.511047	+	0.328430i
$67$	2.92544	−	3.37614i	0.357400	−	0.412461i	−0.548367	−	0.836238i	$-0.684750\pi$
$67$	2.92544	−	3.37614i	0.357400	−	0.412461i	0.905767	+	0.423777i	$0.139296\pi$
$68$	5.19087			0.629485
$69$	−4.16491	+	2.37772i	−0.501396	+	0.286243i
$70$	−2.02825			−0.242422
$71$	−10.1035	+	11.6600i	−1.19906	+	1.38379i	−0.295491	+	0.955346i	$0.595483\pi$
$71$	−10.1035	+	11.6600i	−1.19906	+	1.38379i	−0.903569	+	0.428443i	$0.859062\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	0.620858	+	4.31816i	0.0726659	+	0.505403i	0.993354	+	0.115103i	$0.0367197\pi$
$73$	0.620858	+	4.31816i	0.0726659	+	0.505403i	−0.920688	+	0.390300i	$0.872371\pi$
$74$	−3.68615	−	8.07155i	−0.428507	−	0.938299i
$75$	−0.142315	+	0.989821i	−0.0164331	+	0.114295i
$76$	−6.16658	+	1.81067i	−0.707355	+	0.207698i
$77$	−8.42081	−	5.41173i	−0.959641	−	0.616724i
$78$	2.63310	−	5.76569i	0.298140	−	0.652836i
$79$	14.8120	+	4.34918i	1.66647	+	0.489321i	0.972931	−	0.231094i	$-0.0742304\pi$
$79$	14.8120	+	4.34918i	1.66647	+	0.489321i	0.693543	+	0.720415i	$0.256049\pi$
$80$	0.654861	+	0.755750i	0.0732157	+	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	5.12679	+	1.50536i	0.566159	+	0.166239i
$83$	0.0838378	−	0.183579i	0.00920239	−	0.0201504i	−0.904975	−	0.425465i	$-0.860111\pi$
$83$	0.0838378	−	0.183579i	0.00920239	−	0.0201504i	0.914177	+	0.405314i	$0.132838\pi$
$84$	−1.70627	−	1.09655i	−0.186169	−	0.119644i
$85$	4.98060	−	1.46244i	0.540222	−	0.158623i
$86$	−1.18265	+	8.22550i	−0.127528	+	0.886979i
$87$	−0.468291	−	1.02541i	−0.0502060	−	0.109936i
$88$	0.702354	+	4.88498i	0.0748712	+	0.520741i
$89$	7.42991	−	4.77491i	0.787568	−	0.506140i	−0.0839690	−	0.996468i	$-0.526760\pi$
$89$	7.42991	−	4.77491i	0.787568	−	0.506140i	0.871538	+	0.490329i	$0.163123\pi$
$90$	−0.654861	+	0.755750i	−0.0690284	+	0.0796630i
$91$	12.8560			1.34768
$92$	0.432682	+	4.77627i	0.0451102	+	0.497961i
$93$	1.53683			0.159362
$94$	7.57982	−	8.74758i	0.781799	−	0.902244i
$95$	−5.40667	+	3.47465i	−0.554712	+	0.356492i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	5.87005	+	12.8536i	0.596013	+	1.30509i	0.931739	+	0.363128i	$0.118291\pi$
$97$	5.87005	+	12.8536i	0.596013	+	1.30509i	−0.335726	+	0.941960i	$0.608982\pi$
$98$	−0.410750	+	2.85683i	−0.0414921	+	0.288584i
$99$	−4.73530	+	1.39041i	−0.475916	+	0.139741i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−6.09055	+	13.3364i	−0.606032	+	1.32703i	0.319223	+	0.947680i	$0.396578\pi$
$101$	−6.09055	+	13.3364i	−0.606032	+	1.32703i	−0.925255	+	0.379346i	$0.876149\pi$
$102$	4.98060	+	1.46244i	0.493153	+	0.144803i
$103$	8.12109	+	9.37224i	0.800195	+	0.923474i	0.998392	−	0.0566878i	$-0.0180540\pi$
$103$	8.12109	+	9.37224i	0.800195	+	0.923474i	−0.198197	+	0.980162i	$0.563509\pi$
$104$	−4.15083	−	4.79031i	−0.407022	−	0.469729i
$105$	−1.94609	−	0.571424i	−0.189919	−	0.0557652i
$106$	0.874128	−	1.91407i	0.0849028	−	0.185911i
$107$	−1.93295	−	1.24223i	−0.186866	−	0.120091i	0.443863	−	0.896095i	$-0.353608\pi$
$107$	−1.93295	−	1.24223i	−0.186866	−	0.120091i	−0.630729	+	0.776003i	$0.717244\pi$
$108$	−0.959493	+	0.281733i	−0.0923273	+	0.0271097i
$109$	0.686723	−	4.77626i	0.0657762	−	0.457483i	−0.930140	−	0.367204i	$-0.880315\pi$
$109$	0.686723	−	4.77626i	0.0657762	−	0.457483i	0.995917	−	0.0902790i	$-0.0287759\pi$
$110$	2.05016	+	4.48923i	0.195475	+	0.428031i
$111$	−1.26282	−	8.78311i	−0.119862	−	0.833656i
$112$	−1.70627	+	1.09655i	−0.161227	+	0.103615i
$113$	0.0161081	−	0.0185897i	0.00151532	−	0.00174877i	−0.754991	−	0.655735i	$-0.772359\pi$
$113$	0.0161081	−	0.0185897i	0.00151532	−	0.00174877i	0.756507	+	0.653986i	$0.226904\pi$
$114$	−6.42692			−0.601936
$115$	1.76079	+	4.46090i	0.164194	+	0.415981i
$116$	−1.12728			−0.104666
$117$	4.15083	−	4.79031i	0.383744	−	0.442864i
$118$	1.18049	−	0.758652i	0.108672	−	0.0698396i
$119$	1.49834	+	10.4212i	0.137353	+	0.955310i
$120$	0.415415	+	0.909632i	0.0379220	+	0.0830377i
$121$	−1.90080	+	13.2204i	−0.172800	+	1.20185i
$122$	0.207551	−	0.0609425i	0.0187908	−	0.00551747i
$123$	4.49501	+	2.88877i	0.405301	+	0.260471i
$124$	0.638421	−	1.39795i	0.0573319	−	0.125539i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−1.32822	−	1.53285i	−0.118327	−	0.136557i
$127$	−12.6249	−	14.5699i	−1.12028	−	1.29287i	−0.951648	−	0.307191i	$-0.900611\pi$
$127$	−12.6249	−	14.5699i	−1.12028	−	1.29287i	−0.168630	−	0.985679i	$-0.553934\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−3.45214	+	7.55912i	−0.303944	+	0.665544i
$130$	−5.33228	−	3.42685i	−0.467672	−	0.300554i
$131$	4.27008	−	1.25381i	0.373078	−	0.109546i	−0.0898178	−	0.995958i	$-0.528628\pi$
$131$	4.27008	−	1.25381i	0.373078	−	0.109546i	0.462896	+	0.886413i	$0.346810\pi$
$132$	−0.702354	+	4.88498i	−0.0611321	+	0.425183i
$133$	−5.41509	−	11.8574i	−0.469548	−	1.02817i
$134$	−0.635759	−	4.42180i	−0.0549212	−	0.381986i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	3.39930	−	3.92300i	0.291487	−	0.336394i
$137$	2.56610			0.219237			0.109619	−	0.993974i	$-0.465037\pi$
$137$	2.56610			0.219237			0.109619	+	0.993974i	$0.465037\pi$
$138$	−0.930476	+	4.70470i	−0.0792074	+	0.400491i
$139$	11.2598			0.955046			0.477523	−	0.878619i	$-0.341535\pi$
$139$	11.2598			0.955046			0.477523	+	0.878619i	$0.341535\pi$
$140$	−1.32822	+	1.53285i	−0.112255	+	0.129549i
$141$	9.73726	−	6.25776i	0.820026	−	0.526998i
$142$	2.19569	+	15.2714i	0.184258	+	1.28154i
$143$	−12.9949	−	28.4549i	−1.08669	−	2.37952i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−1.08162	+	0.317593i	−0.0898238	+	0.0263746i
$146$	3.67002	+	2.35858i	0.303733	+	0.195198i
$147$	−1.19897	+	2.62539i	−0.0988898	+	0.216538i
$148$	−8.51399	−	2.49993i	−0.699846	−	0.205493i
$149$	−2.93589	−	3.38819i	−0.240517	−	0.277572i	0.622638	−	0.782510i	$-0.286061\pi$
$149$	−2.93589	−	3.38819i	−0.240517	−	0.277572i	−0.863156	+	0.504938i	$0.831515\pi$
$150$	0.654861	+	0.755750i	0.0534692	+	0.0617067i
$151$	−1.64794	−	0.483879i	−0.134107	−	0.0393775i	0.213990	−	0.976836i	$-0.431354\pi$
$151$	−1.64794	−	0.483879i	−0.134107	−	0.0393775i	−0.348097	+	0.937458i	$0.613172\pi$
$152$	−2.66984	+	5.84613i	−0.216552	+	0.474184i
$153$	4.36684	+	2.80639i	0.353038	+	0.226884i
$154$	−9.60437	+	2.82010i	−0.773942	+	0.227250i
$155$	0.218713	−	1.52119i	0.0175675	−	0.122185i
$156$	−2.63310	−	5.76569i	−0.210817	−	0.461625i
$157$	1.48526	+	10.3302i	0.118537	+	0.824442i	0.959169	+	0.282835i	$0.0912749\pi$
$157$	1.48526	+	10.3302i	0.118537	+	0.824442i	−0.840632	+	0.541607i	$0.817816\pi$
$158$	12.9867	−	8.34602i	1.03316	−	0.663974i
$159$	1.37798	−	1.59027i	0.109281	−	0.126117i
$160$	1.00000			0.0790569
$161$	−9.46397	+	2.24732i	−0.745865	+	0.177114i
$162$	−1.00000			−0.0785674
$163$	−11.3731	+	13.1253i	−0.890813	+	1.02805i	0.108610	+	0.994084i	$0.465360\pi$
$163$	−11.3731	+	13.1253i	−0.890813	+	1.02805i	−0.999423	+	0.0339686i	$0.989185\pi$
$164$	4.49501	−	2.88877i	0.351001	−	0.225575i
$165$	0.702354	+	4.88498i	0.0546782	+	0.380295i
$166$	−0.0838378	−	0.183579i	−0.00650707	−	0.0142485i
$167$	2.85180	−	19.8347i	0.220679	−	1.53486i	−0.514800	−	0.857310i	$-0.672134\pi$
$167$	2.85180	−	19.8347i	0.220679	−	1.53486i	0.735479	−	0.677547i	$-0.236957\pi$
$168$	−1.94609	+	0.571424i	−0.150144	+	0.0440863i
$169$	22.8623	+	14.6927i	1.75864	+	1.13021i
$170$	2.15636	−	4.72178i	0.165386	−	0.362144i
$171$	−6.16658	−	1.81067i	−0.471570	−	0.138466i
$172$	5.44195	+	6.28034i	0.414945	+	0.478872i
$173$	15.3428	+	17.7065i	1.16649	+	1.34620i	0.926893	+	0.375326i	$0.122469\pi$
$173$	15.3428	+	17.7065i	1.16649	+	1.34620i	0.239595	+	0.970873i	$0.422985\pi$
$174$	−1.08162	−	0.317593i	−0.0819975	−	0.0240766i
$175$	−0.842565	+	1.84496i	−0.0636919	+	0.139466i
$176$	4.15177	+	2.66818i	0.312951	+	0.201121i
$177$	1.34640	−	0.395340i	0.101202	−	0.0297156i
$178$	1.25692	−	8.74205i	0.0942099	−	0.655244i
$179$	−2.14917	−	4.70603i	−0.160637	−	0.351746i	0.812150	−	0.583449i	$-0.198297\pi$
$179$	−2.14917	−	4.70603i	−0.160637	−	0.351746i	−0.972786	+	0.231704i	$0.925570\pi$
$180$	0.142315	+	0.989821i	0.0106075	+	0.0737769i
$181$	−11.8677	+	7.62689i	−0.882118	+	0.566903i	−0.901437	−	0.432911i	$-0.857487\pi$
$181$	−11.8677	+	7.62689i	−0.882118	+	0.566903i	0.0193191	+	0.999813i	$0.493850\pi$
$182$	8.41891	−	9.71594i	0.624051	−	0.720193i
$183$	0.216313			0.0159903
$184$	3.89301	+	2.80079i	0.286997	+	0.206477i
$185$	−8.87343			−0.652387
$186$	1.00641	−	1.16146i	0.0737934	−	0.0851622i
$187$	21.5513	−	13.8502i	1.57598	−	1.01282i
$188$	−1.64725	−	11.4569i	−0.120138	−	0.835580i
$189$	−0.842565	−	1.84496i	−0.0612876	−	0.134201i
$190$	−0.914645	+	6.36150i	−0.0663554	+	0.461512i
$191$	−12.7522	+	3.74438i	−0.922715	+	0.270934i	−0.708384	−	0.705827i	$-0.750575\pi$
$191$	−12.7522	+	3.74438i	−0.922715	+	0.270934i	−0.214331	+	0.976761i	$0.568757\pi$
$192$	0.841254	+	0.540641i	0.0607122	+	0.0390174i
$193$	1.90007	−	4.16058i	0.136770	−	0.299485i	−0.828837	−	0.559490i	$-0.810997\pi$
$193$	1.90007	−	4.16058i	0.136770	−	0.299485i	0.965607	+	0.260005i	$0.0837242\pi$
$194$	13.5582	+	3.98104i	0.973421	+	0.285822i
$195$	−4.15083	−	4.79031i	−0.297247	−	0.343041i
$196$	1.89007	+	2.18125i	0.135005	+	0.155804i
$197$	12.2974	+	3.61083i	0.876150	+	0.257261i	0.688729	−	0.725019i	$-0.258169\pi$
$197$	12.2974	+	3.61083i	0.876150	+	0.257261i	0.187421	+	0.982280i	$0.439987\pi$
$198$	−2.05016	+	4.48923i	−0.145699	+	0.319036i
$199$	3.74207	+	2.40488i	0.265268	+	0.170478i	0.666513	−	0.745493i	$-0.267786\pi$
$199$	3.74207	+	2.40488i	0.265268	+	0.170478i	−0.401245	+	0.915971i	$0.631422\pi$
$200$	0.959493	−	0.281733i	0.0678464	−	0.0199215i
$201$	0.635759	−	4.42180i	0.0448430	−	0.311890i
$202$	6.09055	+	13.3364i	0.428530	+	0.938349i
$203$	−0.325390	−	2.26314i	−0.0228379	−	0.158841i
$204$	4.36684	−	2.80639i	0.305740	−	0.196487i
$205$	3.49907	−	4.03814i	0.244386	−	0.282036i
$206$	12.4013			0.864036
$207$	−2.21825	+	4.25198i	−0.154179	+	0.295533i
$208$	−6.33849			−0.439495
$209$	−20.7710	+	23.9710i	−1.43676	+	1.65811i
$210$	−1.70627	+	1.09655i	−0.117744	+	0.0756694i
$211$	2.06155	+	14.3384i	0.141923	+	0.987097i	0.928957	+	0.370187i	$0.120706\pi$
$211$	2.06155	+	14.3384i	0.141923	+	0.987097i	−0.787034	+	0.616909i	$0.788384\pi$
$212$	−0.874128	−	1.91407i	−0.0600353	−	0.131459i
$213$	−2.19569	+	15.2714i	−0.150446	+	1.04638i
$214$	−2.20463	+	0.647339i	−0.150706	+	0.0442512i
$215$	6.99089	+	4.49277i	0.476775	+	0.306405i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	2.99081	+	0.878180i	0.203029	+	0.0596147i
$218$	−3.15995	−	3.64678i	−0.214019	−	0.246991i
$219$	2.85687	+	3.29701i	0.193050	+	0.222791i
$220$	4.73530	+	1.39041i	0.319254	+	0.0937414i
$221$	−13.6681	+	29.9289i	−0.919415	+	2.01324i
$222$	−7.46480	−	4.79734i	−0.501005	−	0.321976i
$223$	−18.2019	+	5.34455i	−1.21889	+	0.357898i	−0.827046	−	0.562135i	$-0.809980\pi$
$223$	−18.2019	+	5.34455i	−1.21889	+	0.357898i	−0.391842	+	0.920033i	$0.628162\pi$
$224$	−0.288650	+	2.00760i	−0.0192862	+	0.134139i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	−0.00350062	−	0.0243473i	−0.000232858	−	0.00161956i
$227$	2.86981	−	1.84432i	0.190476	−	0.122412i	−0.441927	−	0.897051i	$-0.645705\pi$
$227$	2.86981	−	1.84432i	0.190476	−	0.122412i	0.632403	+	0.774639i	$0.282069\pi$
$228$	−4.20873	+	4.85714i	−0.278730	+	0.321672i
$229$	−2.59100			−0.171218			−0.0856090	−	0.996329i	$-0.527284\pi$
$229$	−2.59100			−0.171218			−0.0856090	+	0.996329i	$0.527284\pi$
$230$	4.52439	+	1.59055i	0.298330	+	0.104878i
$231$	−10.0098			−0.658599
$232$	−0.738214	+	0.851945i	−0.0484661	+	0.0559329i
$233$	2.51252	−	1.61470i	0.164601	−	0.105783i	−0.455747	−	0.890109i	$-0.650628\pi$
$233$	2.51252	−	1.61470i	0.164601	−	0.105783i	0.620348	+	0.784327i	$0.286991\pi$
$234$	−0.902061	−	6.27397i	−0.0589696	−	0.410142i
$235$	−4.80831	−	10.5287i	−0.313659	−	0.686818i
$236$	0.199703	−	1.38896i	0.0129995	−	0.0904138i
$237$	14.8120	−	4.34918i	0.962140	−	0.282510i
$238$	8.85703	+	5.69207i	0.574116	+	0.368962i
$239$	3.64261	−	7.97620i	0.235621	−	0.515938i	−0.754475	−	0.656328i	$-0.772109\pi$
$239$	3.64261	−	7.97620i	0.235621	−	0.515938i	0.990096	+	0.140391i	$0.0448358\pi$
$240$	0.959493	+	0.281733i	0.0619350	+	0.0181858i
$241$	−14.0577	−	16.2235i	−0.905536	−	1.04504i	−0.998779	−	0.0494012i	$-0.984269\pi$
$241$	−14.0577	−	16.2235i	−0.905536	−	1.04504i	0.0932427	−	0.995643i	$-0.470277\pi$
$242$	8.74654	+	10.0940i	0.562249	+	0.648870i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	0.0898597	−	0.196765i	0.00575268	−	0.0125966i
$245$	2.42803	+	1.56040i	0.155121	+	0.0996905i
$246$	5.12679	−	1.50536i	0.326872	−	0.0959783i
$247$	5.79747	−	40.3223i	0.368884	−	2.56565i
$248$	−0.638421	−	1.39795i	−0.0405398	−	0.0887698i
$249$	−0.0287215	−	0.199763i	−0.00182015	−	0.0126594i
$250$	0.841254	−	0.540641i	0.0532055	−	0.0341931i
$251$	13.3919	−	15.4551i	0.845290	−	0.975517i	−0.154633	−	0.987972i	$-0.549419\pi$
$251$	13.3919	−	15.4551i	0.845290	−	0.975517i	0.999922	+	0.0124555i	$0.00396482\pi$
$252$	−2.02825			−0.127768
$253$	14.5403	+	18.6755i	0.914143	+	1.17412i
$254$	−19.2787			−1.20966
$255$	3.39930	−	3.92300i	0.212872	−	0.245668i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−3.18229	−	22.1333i	−0.198506	−	1.38064i	−0.808622	−	0.588328i	$-0.799786\pi$
$257$	−3.18229	−	22.1333i	−0.198506	−	1.38064i	0.610116	−	0.792312i	$-0.291123\pi$
$258$	3.45214	+	7.55912i	0.214921	+	0.470610i
$259$	2.56131	−	17.8143i	0.159152	−	1.10693i
$260$	−6.08173	+	1.78576i	−0.377173	+	0.110748i
$261$	−0.948332	−	0.609456i	−0.0587003	−	0.0377244i
$262$	1.84874	−	4.04818i	0.114216	−	0.250097i
$263$	−18.6216	−	5.46780i	−1.14826	−	0.337159i	−0.348399	−	0.937346i	$-0.613275\pi$
$263$	−18.6216	−	5.46780i	−1.14826	−	0.337159i	−0.799859	+	0.600187i	$0.795093\pi$
$264$	3.23188	+	3.72979i	0.198908	+	0.229552i
$265$	−1.37798	−	1.59027i	−0.0846484	−	0.0976895i
$266$	−12.5074	−	3.67249i	−0.766875	−	0.225175i
$267$	3.66892	−	8.03382i	0.224534	−	0.491662i
$268$	−3.75811	−	2.41519i	−0.229563	−	0.147531i
$269$	−29.1131	+	8.54839i	−1.77506	+	0.521205i	−0.994580	−	0.103976i	$-0.966843\pi$
$269$	−29.1131	+	8.54839i	−1.77506	+	0.521205i	−0.780480	+	0.625181i	$0.785025\pi$
$270$	−0.142315	+	0.989821i	−0.00866101	+	0.0602386i
$271$	7.09375	+	15.5331i	0.430914	+	0.943571i	0.993177	+	0.116613i	$0.0372036\pi$
$271$	7.09375	+	15.5331i	0.430914	+	0.943571i	−0.562263	+	0.826958i	$0.690069\pi$
$272$	−0.738737	−	5.13803i	−0.0447925	−	0.311539i
$273$	10.8152	−	6.95049i	0.654564	−	0.420663i
$274$	1.68044	−	1.93933i	0.101519	−	0.117159i
$275$	4.93521			0.297605
$276$	2.94624	+	3.78413i	0.177343	+	0.227778i
$277$	−9.69805			−0.582700			−0.291350	−	0.956617i	$-0.594104\pi$
$277$	−9.69805			−0.582700			−0.291350	+	0.956617i	$0.594104\pi$
$278$	7.37362	−	8.50961i	0.442240	−	0.510372i
$279$	1.29286	−	0.830872i	0.0774016	−	0.0497430i
$280$	0.288650	+	2.00760i	0.0172501	+	0.119977i
$281$	0.900686	+	1.97223i	0.0537304	+	0.117653i	0.934593	−	0.355719i	$-0.115764\pi$
$281$	0.900686	+	1.97223i	0.0537304	+	0.117653i	−0.880863	+	0.473372i	$0.843037\pi$
$282$	1.64725	−	11.4569i	0.0980925	−	0.682248i
$283$	5.96710	−	1.75210i	0.354707	−	0.104151i	−0.0995244	−	0.995035i	$-0.531732\pi$
$283$	5.96710	−	1.75210i	0.354707	−	0.104151i	0.454231	+	0.890884i	$0.349914\pi$
$284$	12.9792	+	8.34123i	0.770174	+	0.494961i
$285$	−2.66984	+	5.84613i	−0.158148	+	0.346295i
$286$	−30.0147	−	8.81310i	−1.77480	−	0.521129i
$287$	7.09698	+	8.19035i	0.418921	+	0.483461i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	−9.54226	−	2.80186i	−0.561309	−	0.164815i
$290$	−0.468291	+	1.02541i	−0.0274990	+	0.0602144i
$291$	11.8874	+	7.63956i	0.696851	+	0.447839i
$292$	4.18585	−	1.22908i	0.244958	−	0.0719263i
$293$	4.43061	−	30.8156i	0.258839	−	1.80027i	−0.282292	−	0.959329i	$-0.591095\pi$
$293$	4.43061	−	30.8156i	0.258839	−	1.80027i	0.541131	−	0.840938i	$-0.317996\pi$
$294$	1.19897	+	2.62539i	0.0699256	+	0.153116i
$295$	−0.199703	−	1.38896i	−0.0116271	−	0.0808685i
$296$	−7.46480	+	4.79734i	−0.433883	+	0.278839i
$297$	−3.23188	+	3.72979i	−0.187533	+	0.216424i
$298$	−4.48322			−0.259706
$299$	−28.6778	−	10.0817i	−1.65848	−	0.583040i
$300$	1.00000			0.0577350
$301$	−11.0376	+	12.7381i	−0.636198	+	0.734212i
$302$	−1.44486	+	0.928557i	−0.0831425	+	0.0534324i
$303$	2.08653	+	14.5121i	0.119868	+	0.833700i
$304$	2.66984	+	5.84613i	0.153126	+	0.335298i
$305$	0.0307846	−	0.214111i	0.00176272	−	0.0122600i
$306$	4.98060	−	1.46244i	0.284722	−	0.0836019i
$307$	−8.66626	−	5.56947i	−0.494610	−	0.317866i	0.269447	−	0.963015i	$-0.413159\pi$
$307$	−8.66626	−	5.56947i	−0.494610	−	0.317866i	−0.764057	+	0.645149i	$0.776795\pi$
$308$	−4.15824	+	9.10527i	−0.236938	+	0.518821i
$309$	11.8989	+	3.49384i	0.676906	+	0.198757i
$310$	−1.00641	−	1.16146i	−0.0571602	−	0.0659663i
$311$	−10.9479	−	12.6345i	−0.620797	−	0.716438i	0.355061	−	0.934843i	$-0.384460\pi$
$311$	−10.9479	−	12.6345i	−0.620797	−	0.716438i	−0.975858	+	0.218405i	$0.929915\pi$
$312$	−6.08173	−	1.78576i	−0.344310	−	0.101099i
$313$	−12.9306	+	28.3141i	−0.730882	+	1.60041i	0.0671133	+	0.997745i	$0.478621\pi$
$313$	−12.9306	+	28.3141i	−0.730882	+	1.60041i	−0.797995	+	0.602663i	$0.794106\pi$
$314$	8.77971	+	5.64238i	0.495468	+	0.318418i
$315$	−1.94609	+	0.571424i	−0.109650	+	0.0321961i
$316$	2.19695	−	15.2801i	0.123588	−	0.859575i
$317$	6.30373	+	13.8032i	0.354053	+	0.775267i	0.999930	+	0.0118259i	$0.00376438\pi$
$317$	6.30373	+	13.8032i	0.354053	+	0.775267i	−0.645878	+	0.763441i	$0.723508\pi$
$318$	−0.299463	−	2.08281i	−0.0167930	−	0.116798i
$319$	−4.68022	+	3.00780i	−0.262042	+	0.168404i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	−2.29771			−0.128245
$322$	−4.49917	+	8.62408i	−0.250729	+	0.480601i
$323$	33.3613			1.85627
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−5.33228	+	3.42685i	−0.295781	+	0.190087i
$326$	2.47162	+	17.1905i	0.136890	+	0.952093i
$327$	−2.00454	−	4.38932i	−0.110851	−	0.242730i
$328$	0.760420	−	5.28884i	0.0419872	−	0.292027i
$329$	22.5254	−	6.61406i	1.24187	−	0.364645i
$330$	4.15177	+	2.66818i	0.228547	+	0.146878i
$331$	6.19164	−	13.5578i	0.340323	−	0.745204i	−0.659656	−	0.751567i	$-0.729298\pi$
$331$	6.19164	−	13.5578i	0.340323	−	0.745204i	0.999980	+	0.00636315i	$0.00202547\pi$
$332$	−0.193642	−	0.0568584i	−0.0106275	−	0.00312051i
$333$	−5.81086	−	6.70609i	−0.318433	−	0.367491i
$334$	−13.1226	−	15.1442i	−0.718034	−	0.828656i
$335$	−4.28632	−	1.25858i	−0.234187	−	0.0687634i
$336$	−0.842565	+	1.84496i	−0.0459657	+	0.100651i
$337$	−26.5698	−	17.0754i	−1.44735	−	0.930157i	−0.999347	−	0.0361254i	$-0.988498\pi$
$337$	−26.5698	−	17.0754i	−1.44735	−	0.930157i	−0.448005	−	0.894031i	$-0.647865\pi$
$338$	26.0756	−	7.65649i	1.41833	−	0.416458i
$339$	0.00350062	−	0.0243473i	0.000190127	−	0.00132237i
$340$	−2.15636	−	4.72178i	−0.116945	−	0.256074i
$341$	−1.07940	−	7.50737i	−0.0584527	−	0.406547i
$342$	−5.40667	+	3.47465i	−0.292359	+	0.187888i
$343$	−13.1311	+	15.1541i	−0.709011	+	0.818242i
$344$	8.31009			0.448050
$345$	3.89301	+	2.80079i	0.209593	+	0.150790i
$346$	23.4290			1.25955
$347$	2.47626	−	2.85776i	0.132933	−	0.153412i	−0.685380	−	0.728185i	$-0.740364\pi$
$347$	2.47626	−	2.85776i	0.132933	−	0.153412i	0.818313	+	0.574773i	$0.194910\pi$
$348$	−0.948332	+	0.609456i	−0.0508359	+	0.0326703i
$349$	−3.18772	−	22.1711i	−0.170635	−	1.18679i	−0.877548	−	0.479489i	$-0.840822\pi$
$349$	−3.18772	−	22.1711i	−0.170635	−	1.18679i	0.706913	−	0.707300i	$-0.250087\pi$
$350$	0.842565	+	1.84496i	0.0450370	+	0.0986172i
$351$	0.902061	−	6.27397i	0.0481485	−	0.334880i
$352$	4.73530	−	1.39041i	0.252392	−	0.0741091i
$353$	−8.38169	−	5.38659i	−0.446112	−	0.286699i	0.298234	−	0.954493i	$-0.403602\pi$
$353$	−8.38169	−	5.38659i	−0.446112	−	0.286699i	−0.744346	+	0.667794i	$0.767239\pi$
$354$	0.582929	−	1.27644i	0.0309823	−	0.0678419i
$355$	14.8034	+	4.34668i	0.785685	+	0.230698i
$356$	−5.78369	−	6.67474i	−0.306535	−	0.353761i
$357$	6.89461	+	7.95681i	0.364902	+	0.421119i
$358$	−4.96399	−	1.45756i	−0.262355	−	0.0770344i
$359$	0.735189	−	1.60984i	0.0388018	−	0.0849640i	−0.889239	−	0.457444i	$-0.848765\pi$
$359$	0.735189	−	1.60984i	0.0388018	−	0.0849640i	0.928040	+	0.372480i	$0.121492\pi$
$360$	0.841254	+	0.540641i	0.0443380	+	0.0284943i
$361$	−21.4017	+	6.28411i	−1.12641	+	0.330743i
$362$	−2.00766	+	13.9635i	−0.105520	+	0.733908i
$363$	5.54842	+	12.1493i	0.291217	+	0.637675i
$364$	−1.82960	−	12.7252i	−0.0958973	−	0.666980i
$365$	3.67002	−	2.35858i	0.192098	−	0.123454i
$366$	0.141655	−	0.163479i	0.00740442	−	0.00854516i
$367$	−17.0427			−0.889624			−0.444812	−	0.895624i	$-0.646729\pi$
$367$	−17.0427			−0.889624			−0.444812	+	0.895624i	$0.646729\pi$
$368$	4.66608	−	1.10801i	0.243236	−	0.0577591i
$369$	5.34322			0.278157
$370$	−5.81086	+	6.70609i	−0.302092	+	0.348633i
$371$	3.59038	−	2.30740i	0.186403	−	0.119794i
$372$	−0.218713	−	1.52119i	−0.0113398	−	0.0788698i
$373$	−12.5716	−	27.5279i	−0.650931	−	1.42534i	−0.890737	−	0.454519i	$-0.849811\pi$
$373$	−12.5716	−	27.5279i	−0.650931	−	1.42534i	0.239807	−	0.970821i	$-0.422916\pi$
$374$	3.64583	−	25.3573i	0.188521	−	1.31119i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	−9.73726	−	6.25776i	−0.502161	−	0.322719i
$377$	2.96826	−	6.49957i	0.152873	−	0.334745i
$378$	−1.94609	−	0.571424i	−0.100096	−	0.0293909i
$379$	−18.6727	−	21.5495i	−0.959153	−	1.10692i	−0.994201	−	0.107536i	$-0.965704\pi$
$379$	−18.6727	−	21.5495i	−0.959153	−	1.10692i	0.0350481	−	0.999386i	$-0.488842\pi$
$380$	4.20873	+	4.85714i	0.215904	+	0.249166i
$381$	−18.4978	−	5.43145i	−0.947672	−	0.278262i
$382$	−5.52109	+	12.0895i	−0.282483	+	0.618552i
$383$	−19.1266	−	12.2919i	−0.977323	−	0.628087i	−0.0485829	−	0.998819i	$-0.515471\pi$
$383$	−19.1266	−	12.2919i	−0.977323	−	0.628087i	−0.928740	+	0.370732i	$0.879107\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	−1.42455	+	9.90795i	−0.0726017	+	0.504956i
$386$	−1.90007	−	4.16058i	−0.0967112	−	0.211768i
$387$	1.18265	+	8.22550i	0.0601174	+	0.418126i
$388$	11.8874	−	7.63956i	0.603491	−	0.387840i
$389$	−5.92628	+	6.83929i	−0.300474	+	0.346766i	−0.885829	−	0.464011i	$-0.846410\pi$
$389$	−5.92628	+	6.83929i	−0.300474	+	0.346766i	0.585355	+	0.810777i	$0.300955\pi$
$390$	−6.33849			−0.320962
$391$	4.82998	−	24.4215i	0.244263	−	1.23505i
$392$	2.88621			0.145776
$393$	2.91436	−	3.36335i	0.147010	−	0.169658i
$394$	10.7819	−	6.92913i	0.543186	−	0.349085i
$395$	−2.19695	−	15.2801i	−0.110541	−	0.768827i
$396$	2.05016	+	4.48923i	0.103025	+	0.225592i
$397$	0.370615	−	2.57769i	0.0186007	−	0.129370i	−0.978405	−	0.206696i	$-0.933729\pi$
$397$	0.370615	−	2.57769i	0.0186007	−	0.129370i	0.997006	+	0.0773254i	$0.0246380\pi$
$398$	4.26802	−	1.25320i	0.213937	−	0.0628175i
$399$	−10.9661	−	7.04746i	−0.548990	−	0.352814i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	5.58308	+	1.63934i	0.278806	+	0.0818647i	0.418146	−	0.908380i	$-0.362680\pi$
$401$	5.58308	+	1.63934i	0.278806	+	0.0818647i	−0.139340	+	0.990245i	$0.544498\pi$
$402$	−2.92544	−	3.37614i	−0.145908	−	0.168387i
$403$	6.37911	+	7.36188i	0.317766	+	0.366722i
$404$	14.0675	+	4.13058i	0.699883	+	0.205504i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−1.92345	−	1.23613i	−0.0954593	−	0.0613480i
$407$	−42.0184	+	12.3377i	−2.08277	+	0.611557i
$408$	0.738737	−	5.13803i	0.0365730	−	0.254370i
$409$	6.22402	+	13.6287i	0.307758	+	0.673896i	0.998803	−	0.0489159i	$-0.0155766\pi$
$409$	6.22402	+	13.6287i	0.307758	+	0.673896i	−0.691045	+	0.722812i	$0.742849\pi$
$410$	−0.760420	−	5.28884i	−0.0375545	−	0.261197i
$411$	2.15874	−	1.38734i	0.106483	−	0.0684325i
$412$	8.12109	−	9.37224i	0.400098	−	0.461737i
$413$	2.84613			0.140049
$414$	1.76079	+	4.46090i	0.0865380	+	0.219241i
$415$	−0.201817			−0.00990680
$416$	−4.15083	+	4.79031i	−0.203511	+	0.234864i
$417$	9.47237	−	6.08752i	0.463864	−	0.298107i
$418$	4.51397	+	31.3954i	0.220786	+	1.53560i
$419$	13.6720	+	29.9374i	0.667919	+	1.46254i	0.874955	+	0.484205i	$0.160891\pi$
$419$	13.6720	+	29.9374i	0.667919	+	1.46254i	−0.207036	+	0.978333i	$0.566382\pi$
$420$	−0.288650	+	2.00760i	−0.0140847	+	0.0979610i
$421$	−23.1925	+	6.80993i	−1.13033	+	0.331896i	−0.792839	−	0.609432i	$-0.791398\pi$
$421$	−23.1925	+	6.80993i	−1.13033	+	0.331896i	−0.337495	+	0.941327i	$0.609580\pi$
$422$	12.1863	+	7.83164i	0.593219	+	0.381238i
$423$	4.80831	−	10.5287i	0.233788	−	0.511924i
$424$	−2.01899	−	0.592829i	−0.0980509	−	0.0287903i
$425$	−3.39930	−	3.92300i	−0.164890	−	0.190293i
$426$	10.1035	+	11.6600i	0.489514	+	0.564929i
$427$	0.420965	+	0.123606i	0.0203719	+	0.00598173i
$428$	−0.954502	+	2.09007i	−0.0461376	+	0.101027i
$429$	−26.3159	−	16.9122i	−1.27054	−	0.816529i
$430$	7.97347	−	2.34122i	0.384515	−	0.112904i
$431$	−0.827633	+	5.75631i	−0.0398657	+	0.277272i	−0.999997	−	0.00227612i	$-0.999275\pi$
$431$	−0.827633	+	5.75631i	−0.0398657	+	0.277272i	0.960132	+	0.279548i	$0.0901846\pi$
$432$	0.415415	+	0.909632i	0.0199867	+	0.0437647i
$433$	−4.53705	−	31.5559i	−0.218037	−	1.51648i	−0.745273	−	0.666759i	$-0.767681\pi$
$433$	−4.53705	−	31.5559i	−0.218037	−	1.51648i	0.527237	−	0.849718i	$-0.323228\pi$
$434$	2.62225	−	1.68521i	0.125872	−	0.0808929i
$435$	−0.738214	+	0.851945i	−0.0353947	+	0.0408476i
$436$	−4.82538			−0.231094
$437$	2.78081	+	30.6967i	0.133024	+	1.46842i
$438$	4.36257			0.208451
$439$	−20.7506	+	23.9475i	−0.990373	+	1.14295i	−0.000643090		1.00000i	$0.500205\pi$
$439$	−20.7506	+	23.9475i	−0.990373	+	1.14295i	−0.989730	+	0.142951i	$0.954341\pi$
$440$	4.15177	−	2.66818i	0.197928	−	0.127200i
$441$	0.410750	+	2.85683i	0.0195595	+	0.136040i
$442$	13.6681	+	29.9289i	0.650125	+	1.42357i
$443$	3.41850	−	23.7762i	0.162418	−	1.12964i	−0.731641	−	0.681691i	$-0.761245\pi$
$443$	3.41850	−	23.7762i	0.162418	−	1.12964i	0.894058	−	0.447950i	$-0.147846\pi$
$444$	−8.51399	+	2.49993i	−0.404056	+	0.118642i
$445$	−7.42991	−	4.77491i	−0.352211	−	0.226352i
$446$	−7.88055	+	17.2560i	−0.373155	+	0.817095i
$447$	−4.30162	−	1.26307i	−0.203460	−	0.0597412i
$448$	1.32822	+	1.53285i	0.0627525	+	0.0724202i
$449$	16.5641	+	19.1160i	0.781707	+	0.902138i	0.997231	−	0.0743601i	$-0.0236914\pi$
$449$	16.5641	+	19.1160i	0.781707	+	0.902138i	−0.215524	+	0.976499i	$0.569146\pi$
$450$	0.959493	+	0.281733i	0.0452309	+	0.0132810i
$451$	10.9545	−	23.9870i	0.515826	−	1.12950i
$452$	−0.0206929	−	0.0132985i	−0.000973312	−	0.000625510i
$453$	−1.64794	+	0.483879i	−0.0774270	+	0.0227346i
$454$	0.485486	−	3.37663i	0.0227850	−	0.158473i
$455$	−5.34059	−	11.6943i	−0.250371	−	0.548235i
$456$	0.914645	+	6.36150i	0.0428322	+	0.297904i
$457$	16.6349	−	10.6906i	0.778148	−	0.500086i	−0.0902703	−	0.995917i	$-0.528773\pi$
$457$	16.6349	−	10.6906i	0.778148	−	0.500086i	0.868419	+	0.495832i	$0.165137\pi$
$458$	−1.69674	+	1.95815i	−0.0792836	+	0.0914982i
$459$	5.19087			0.242289
$460$	4.16491	−	2.37772i	0.194190	−	0.110862i
$461$	−23.1599			−1.07866			−0.539332	−	0.842093i	$-0.681323\pi$
$461$	−23.1599			−1.07866			−0.539332	+	0.842093i	$0.681323\pi$
$462$	−6.55505	+	7.56493i	−0.304969	+	0.351952i
$463$	27.3622	−	17.5846i	1.27163	−	0.817227i	0.281799	−	0.959473i	$-0.409069\pi$
$463$	27.3622	−	17.5846i	1.27163	−	0.817227i	0.989831	+	0.142246i	$0.0454324\pi$
$464$	0.160429	+	1.11581i	0.00744774	+	0.0518002i
$465$	−0.638421	−	1.39795i	−0.0296061	−	0.0648283i
$466$	0.425044	−	2.95624i	0.0196898	−	0.136945i
$467$	−24.3801	+	7.15864i	−1.12818	+	0.331262i	−0.791990	−	0.610533i	$-0.790955\pi$
$467$	−24.3801	+	7.15864i	−1.12818	+	0.331262i	−0.336185	+	0.941796i	$0.609137\pi$
$468$	−5.33228	−	3.42685i	−0.246485	−	0.158406i
$469$	3.76397	−	8.24194i	0.173804	−	0.380577i
$470$	−11.1059	−	3.26097i	−0.512275	−	0.150417i
$471$	6.83443	+	7.88735i	0.314914	+	0.363430i
$472$	−0.918930	−	1.06050i	−0.0422972	−	0.0488136i
$473$	39.3508	+	11.5544i	1.80935	+	0.531273i
$474$	6.41287	−	14.0422i	0.294553	−	0.644981i
$475$	5.40667	+	3.47465i	0.248075	+	0.159428i
$476$	10.1019	−	2.96618i	0.463020	−	0.135955i
$477$	0.299463	−	2.08281i	0.0137115	−	0.0953653i
$478$	−3.64261	−	7.97620i	−0.166609	−	0.364823i
$479$	1.53819	+	10.6984i	0.0702819	+	0.488821i	0.994312	+	0.106503i	$0.0339653\pi$
$479$	1.53819	+	10.6984i	0.0702819	+	0.488821i	−0.924031	+	0.382319i	$0.875126\pi$
$480$	0.841254	−	0.540641i	0.0383978	−	0.0246768i
$481$	36.8321	−	42.5065i	1.67940	−	1.93813i
$482$	−21.4667			−0.977782
$483$	−6.74660	+	7.00718i	−0.306981	+	0.318838i
$484$	13.3563			0.607106
$485$	9.25356	−	10.6792i	0.420182	−	0.484916i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	3.75954	+	26.1482i	0.170361	+	1.18489i	0.878122	+	0.478436i	$0.158796\pi$
$487$	3.75954	+	26.1482i	0.170361	+	1.18489i	−0.707761	+	0.706452i	$0.750295\pi$
$488$	−0.0898597	−	0.196765i	−0.00406776	−	0.00890715i
$489$	−2.47162	+	17.1905i	−0.111770	+	0.777381i
$490$	2.76930	−	0.813139i	0.125104	−	0.0367339i
$491$	25.7769	+	16.5658i	1.16330	+	0.747605i	0.972243	−	0.233974i	$-0.0751731\pi$
$491$	25.7769	+	16.5658i	1.16330	+	0.747605i	0.191054	+	0.981580i	$0.438810\pi$
$492$	2.21966	−	4.86037i	0.100070	−	0.219122i
$493$	5.61455	+	1.64858i	0.252867	+	0.0742484i
$494$	−26.6770	−	30.7869i	−1.20026	−	1.38517i
$495$	3.23188	+	3.72979i	0.145262	+	0.167641i
$496$	−1.47458	−	0.432975i	−0.0662104	−	0.0194411i
$497$	−12.9994	+	28.4648i	−0.583104	+	1.27682i
$498$	−0.169779	−	0.109110i	−0.00760799	−	0.00488936i
$499$	1.86661	−	0.548085i	0.0835608	−	0.0245357i	−0.239685	−	0.970851i	$-0.577044\pi$
$499$	1.86661	−	0.548085i	0.0835608	−	0.0245357i	0.323246	+	0.946315i	$0.395226\pi$
$500$	0.142315	−	0.989821i	0.00636451	−	0.0442662i
$501$	−8.32437	−	18.2278i	−0.371906	−	0.814360i
$502$	−2.91034	−	20.2419i	−0.129895	−	0.903438i
$503$	25.7503	−	16.5487i	1.14815	−	0.737871i	0.178880	−	0.983871i	$-0.442753\pi$
$503$	25.7503	−	16.5487i	1.14815	−	0.737871i	0.969270	+	0.246000i	$0.0791163\pi$
$504$	−1.32822	+	1.53285i	−0.0591636	+	0.0682785i
$505$	14.6614			0.652422
$506$	23.6359	+	1.24099i	1.05074	+	0.0551688i
$507$	27.1764			1.20695
$508$	−12.6249	+	14.5699i	−0.560139	+	0.646435i
$509$	−1.10969	+	0.713156i	−0.0491862	+	0.0316101i	−0.565003	−	0.825089i	$-0.691125\pi$
$509$	−1.10969	+	0.713156i	−0.0491862	+	0.0316101i	0.515817	+	0.856699i	$0.327489\pi$
$510$	−0.738737	−	5.13803i	−0.0327118	−	0.227516i
$511$	3.67574	+	8.04876i	0.162605	+	0.356056i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−6.16658	+	1.81067i	−0.272261	+	0.0799431i
$514$	−18.8112	−	12.0892i	−0.829727	−	0.533233i
$515$	5.15167	−	11.2806i	0.227010	−	0.497082i
$516$	7.97347	+	2.34122i	0.351012	+	0.103067i
$517$	−37.4080	−	43.1712i	−1.64520	−	1.89867i
$518$	−11.7859	−	13.6016i	−0.517841	−	0.597620i
$519$	22.4800	+	6.60072i	0.986762	+	0.289740i
$520$	−2.63310	+	5.76569i	−0.115469	+	0.252842i
$521$	5.32096	+	3.41958i	0.233116	+	0.149814i	0.651984	−	0.758233i	$-0.273937\pi$
$521$	5.32096	+	3.41958i	0.233116	+	0.149814i	−0.418869	+	0.908047i	$0.637573\pi$
$522$	−1.08162	+	0.317593i	−0.0473413	+	0.0139007i
$523$	−4.06702	+	28.2867i	−0.177838	+	1.23689i	0.683914	+	0.729563i	$0.260276\pi$
$523$	−4.06702	+	28.2867i	−0.177838	+	1.23689i	−0.861752	+	0.507329i	$0.830633\pi$
$524$	−1.84874	−	4.04818i	−0.0807626	−	0.176846i
$525$	0.288650	+	2.00760i	0.0125977	+	0.0876190i
$526$	−16.3269	+	10.4926i	−0.711885	+	0.457501i
$527$	−5.22413	+	6.02897i	−0.227567	+	0.262626i
$528$	4.93521			0.214778
$529$	22.8735	+	2.40857i	0.994502	+	0.104720i
$530$	−2.10423			−0.0914018
$531$	0.918930	−	1.06050i	0.0398782	−	0.0460219i
$532$	−10.9661	+	7.04746i	−0.475439	+	0.305546i
$533$	4.81991	+	33.5232i	0.208774	+	1.45205i
$534$	−3.66892	−	8.03382i	−0.158770	−	0.347657i
$535$	−0.326998	+	2.27432i	−0.0141373	+	0.0983274i
$536$	−4.28632	+	1.25858i	−0.185141	+	0.0543622i
$537$	−4.35227	−	2.79704i	−0.187815	−	0.120701i
$538$	−12.6046	+	27.6002i	−0.543423	+	1.18993i
$539$	13.6671	+	4.01302i	0.588683	+	0.172853i
$540$	0.654861	+	0.755750i	0.0281807	+	0.0325223i
$541$	−15.4670	−	17.8499i	−0.664980	−	0.767427i	0.318603	−	0.947888i	$-0.396786\pi$
$541$	−15.4670	−	17.8499i	−0.664980	−	0.767427i	−0.983582	+	0.180461i	$0.942241\pi$
$542$	16.3846	+	4.81095i	0.703778	+	0.206648i
$543$	−5.86032	+	12.8323i	−0.251490	+	0.550687i
$544$	−4.36684	−	2.80639i	−0.187227	−	0.120323i
$545$	−4.62992	+	1.35947i	−0.198324	+	0.0582332i
$546$	1.82960	−	12.7252i	0.0782998	−	0.544587i
$547$	−1.74880	−	3.82933i	−0.0747732	−	0.163730i	0.868554	−	0.495594i	$-0.165050\pi$
$547$	−1.74880	−	3.82933i	−0.0747732	−	0.163730i	−0.943327	+	0.331864i	$0.892322\pi$
$548$	−0.365195	−	2.53999i	−0.0156003	−	0.108503i
$549$	0.181974	−	0.116948i	0.00776647	−	0.00499121i
$550$	3.23188	−	3.72979i	0.137808	−	0.159039i
$551$	−7.24496			−0.308646
$552$	4.78923	+	0.251457i	0.203843	+	0.0107027i
$553$	31.3106			1.33146
$554$	−6.35087	+	7.32930i	−0.269823	+	0.311392i
$555$	−7.46480	+	4.79734i	−0.316863	+	0.203636i
$556$	−1.60244	−	11.1452i	−0.0679586	−	0.472662i
$557$	−7.61801	−	16.6811i	−0.322785	−	0.706801i	0.676783	−	0.736183i	$-0.263374\pi$
$557$	−7.61801	−	16.6811i	−0.322785	−	0.706801i	−0.999568	+	0.0293813i	$0.990646\pi$
$558$	0.218713	−	1.52119i	0.00925888	−	0.0643969i
$559$	−50.5397	+	14.8398i	−2.13760	+	0.627657i
$560$	1.70627	+	1.09655i	0.0721031	+	0.0463379i
$561$	10.6421	−	23.3030i	0.449311	−	0.983853i
$562$	2.08033	+	0.610841i	0.0877536	+	0.0257668i
$563$	−12.9846	−	14.9850i	−0.547236	−	0.631544i	0.413001	−	0.910731i	$-0.364481\pi$
$563$	−12.9846	−	14.9850i	−0.547236	−	0.631544i	−0.960237	+	0.279187i	$0.909935\pi$
$564$	−7.57982	−	8.74758i	−0.319168	−	0.368340i
$565$	−0.0236013	−	0.00692997i	−0.000992915	−	0.000291546i
$566$	2.58347	−	5.65701i	0.108591	−	0.237782i
$567$	−1.70627	−	1.09655i	−0.0716566	−	0.0460509i
$568$	14.8034	−	4.34668i	0.621139	−	0.182383i
$569$	−4.46490	+	31.0541i	−0.187178	+	1.30185i	0.652092	+	0.758140i	$0.273892\pi$
$569$	−4.46490	+	31.0541i	−0.187178	+	1.30185i	−0.839270	+	0.543714i	$0.817017\pi$
$570$	2.66984	+	5.84613i	0.111827	+	0.244867i
$571$	1.83657	+	12.7736i	0.0768579	+	0.534559i	0.991481	+	0.130251i	$0.0415784\pi$
$571$	1.83657	+	12.7736i	0.0768579	+	0.534559i	−0.914623	+	0.404308i	$0.867513\pi$
$572$	−26.3159	+	16.9122i	−1.10032	+	0.707135i
$573$	−8.70345	+	10.0443i	−0.363592	+	0.419607i
$574$	10.8374			0.452344
$575$	3.32632	−	3.45479i	0.138717	−	0.144075i
$576$	1.00000			0.0416667
$577$	−1.07260	+	1.23785i	−0.0446531	+	0.0515324i	−0.777637	−	0.628714i	$-0.783582\pi$
$577$	−1.07260	+	1.23785i	−0.0446531	+	0.0515324i	0.732984	+	0.680246i	$0.238127\pi$
$578$	−8.36636	+	5.37673i	−0.347995	+	0.223642i
$579$	−0.650936	−	4.52736i	−0.0270520	−	0.188151i
$580$	0.468291	+	1.02541i	0.0194447	+	0.0425780i
$581$	0.0582544	−	0.405168i	0.00241680	−	0.0168092i
$582$	13.5582	−	3.98104i	0.562005	−	0.165020i
$583$	−8.73626	−	5.61445i	−0.361819	−	0.232527i
$584$	1.81228	−	3.96833i	0.0749925	−	0.164211i
$585$	−6.08173	−	1.78576i	−0.251449	−	0.0738320i
$586$	−20.3874	−	23.5284i	−0.842198	−	0.971948i
$587$	−20.5839	−	23.7550i	−0.849587	−	0.980475i	0.150380	−	0.988628i	$-0.451950\pi$
$587$	−20.5839	−	23.7550i	−0.849587	−	0.980475i	−0.999967	+	0.00815302i	$0.997405\pi$
$588$	2.76930	+	0.813139i	0.114204	+	0.0335333i
$589$	4.10308	−	8.98449i	0.169065	−	0.370200i
$590$	−1.18049	−	0.758652i	−0.0485998	−	0.0312332i
$591$	12.2974	−	3.61083i	0.505846	−	0.148530i
$592$	−1.26282	+	8.78311i	−0.0519016	+	0.360983i
$593$	13.9898	+	30.6334i	0.574492	+	1.25796i	0.944371	+	0.328882i	$0.106672\pi$
$593$	13.9898	+	30.6334i	0.574492	+	1.25796i	−0.369879	+	0.929080i	$0.620601\pi$
$594$	0.702354	+	4.88498i	0.0288179	+	0.200433i
$595$	8.85703	−	5.69207i	0.363103	−	0.233352i
$596$	−2.93589	+	3.38819i	−0.120259	+	0.138786i
$597$	4.44821			0.182053
$598$	−26.3992	+	15.0711i	−1.07954	+	0.616304i
$599$	−1.95186			−0.0797509			−0.0398755	−	0.999205i	$-0.512696\pi$
$599$	−1.95186			−0.0797509			−0.0398755	+	0.999205i	$0.512696\pi$
$600$	0.654861	−	0.755750i	0.0267346	−	0.0308533i
$601$	−12.6204	+	8.11063i	−0.514796	+	0.330839i	−0.772110	−	0.635488i	$-0.780799\pi$
$601$	−12.6204	+	8.11063i	−0.514796	+	0.330839i	0.257314	+	0.966328i	$0.417162\pi$
$602$	2.39871	+	16.6834i	0.0977639	+	0.679963i
$603$	−1.85577	−	4.06357i	−0.0755729	−	0.165482i
$604$	−0.244427	+	1.70003i	−0.00994561	+	0.0691732i
$605$	12.8153	−	3.76291i	0.521016	−	0.152984i
$606$	12.3339	+	7.92653i	0.501031	+	0.321993i
$607$	9.74878	−	21.3468i	0.395691	−	0.866442i	−0.601998	−	0.798497i	$-0.705629\pi$
$607$	9.74878	−	21.3468i	0.395691	−	0.866442i	0.997689	−	0.0679446i	$-0.0216441\pi$
$608$	6.16658	+	1.81067i	0.250088	+	0.0734324i
$609$	−1.49728	−	1.72796i	−0.0606729	−	0.0700203i
$610$	−0.141655	−	0.163479i	−0.00573544	−	0.00661905i
$611$	70.3943	+	20.6696i	2.84785	+	0.836204i
$612$	2.15636	−	4.72178i	0.0871659	−	0.190867i
$613$	18.3115	+	11.7681i	0.739594	+	0.475308i	0.855403	−	0.517963i	$-0.173310\pi$
$613$	18.3115	+	11.7681i	0.739594	+	0.475308i	−0.115809	+	0.993272i	$0.536946\pi$
$614$	−9.88432	+	2.90230i	−0.398899	+	0.117127i
$615$	0.760420	−	5.28884i	0.0306631	−	0.213267i
$616$	4.15824	+	9.10527i	0.167540	+	0.366862i
$617$	2.15387	+	14.9805i	0.0867114	+	0.603091i	0.986126	+	0.165996i	$0.0530838\pi$
$617$	2.15387	+	14.9805i	0.0867114	+	0.603091i	−0.899415	+	0.437096i	$0.856007\pi$
$618$	10.4326	−	6.70462i	0.419661	−	0.269700i
$619$	5.57499	−	6.43388i	0.224078	−	0.258599i	−0.632568	−	0.774505i	$-0.717999\pi$
$619$	5.57499	−	6.43388i	0.224078	−	0.258599i	0.856645	+	0.515906i	$0.172544\pi$
$620$	−1.53683			−0.0617205
$621$	0.432682	+	4.77627i	0.0173629	+	0.191665i
$622$	−16.7179			−0.670325
$623$	11.7308	−	13.5380i	0.469983	−	0.542390i
$624$	−5.33228	+	3.42685i	−0.213462	+	0.137184i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	12.9306	+	28.3141i	0.516812	+	1.13166i
$627$	−4.51397	+	31.3954i	−0.180271	+	1.25381i
$628$	10.0137	−	2.94029i	0.399591	−	0.117330i
$629$	38.7488	+	24.9023i	1.54502	+	0.992921i
$630$	−0.842565	+	1.84496i	−0.0335686	+	0.0735049i
$631$	2.08293	+	0.611603i	0.0829201	+	0.0243475i	0.322929	−	0.946423i	$-0.395332\pi$
$631$	2.08293	+	0.611603i	0.0829201	+	0.0243475i	−0.240009	+	0.970771i	$0.577151\pi$
$632$	−10.1093	−	11.6667i	−0.402125	−	0.464077i
$633$	9.48622	+	10.9477i	0.377043	+	0.435131i
$634$	14.5599	+	4.27516i	0.578246	+	0.169788i
$635$	−8.00868	+	17.5366i	−0.317815	+	0.695917i
$636$	−1.77019	−	1.13763i	−0.0701926	−	0.0451100i
$637$	−17.5532	+	5.15407i	−0.695482	+	0.204212i
$638$	−0.791753	+	5.50676i	−0.0313458	+	0.218015i
$639$	6.40919	+	14.0342i	0.253544	+	0.555183i
$640$	−0.142315	−	0.989821i	−0.00562549	−	0.0391261i
$641$	−11.1941	+	7.19403i	−0.442142	+	0.284147i	−0.742710	−	0.669613i	$-0.766460\pi$
$641$	−11.1941	+	7.19403i	−0.442142	+	0.284147i	0.300568	+	0.953760i	$0.402824\pi$
$642$	−1.50468	+	1.73649i	−0.0593849	+	0.0685338i
$643$	−12.8431			−0.506481			−0.253241	−	0.967403i	$-0.581496\pi$
$643$	−12.8431			−0.506481			−0.253241	+	0.967403i	$0.581496\pi$
$644$	3.57131	+	9.04781i	0.140729	+	0.356534i
$645$	8.31009			0.327209
$646$	21.8470	−	25.2128i	0.859558	−	0.991983i
$647$	25.6035	−	16.4544i	1.00658	−	0.646889i	0.0700730	−	0.997542i	$-0.477677\pi$
$647$	25.6035	−	16.4544i	1.00658	−	0.646889i	0.936505	+	0.350653i	$0.114040\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−2.87688	−	6.29949i	−0.112927	−	0.247277i
$650$	−0.902061	+	6.27397i	−0.0353817	+	0.246085i
$651$	2.99081	−	0.878180i	0.117219	−	0.0344186i
$652$	14.6103	+	9.38945i	0.572182	+	0.367719i
$653$	−5.58791	+	12.2358i	−0.218672	+	0.478824i	−0.986896	−	0.161356i	$-0.948413\pi$
$653$	−5.58791	+	12.2358i	−0.218672	+	0.478824i	0.768224	+	0.640181i	$0.221140\pi$
$654$	−4.62992	−	1.35947i	−0.181044	−	0.0531594i
$655$	−2.91436	−	3.36335i	−0.113873	−	0.131417i
$656$	−3.49907	−	4.03814i	−0.136616	−	0.157663i
$657$	4.18585	+	1.22908i	0.163306	+	0.0479509i
$658$	9.75244	−	21.3549i	0.380190	−	0.832499i
$659$	−6.21226	−	3.99238i	−0.241995	−	0.155521i	0.414022	−	0.910267i	$-0.364124\pi$
$659$	−6.21226	−	3.99238i	−0.241995	−	0.155521i	−0.656017	+	0.754746i	$0.727760\pi$
$660$	4.73530	−	1.39041i	0.184321	−	0.0541216i
$661$	−4.27448	+	29.7296i	−0.166258	+	1.15635i	0.720277	+	0.693687i	$0.244015\pi$
$661$	−4.27448	+	29.7296i	−0.166258	+	1.15635i	−0.886535	+	0.462662i	$0.846894\pi$
$662$	−6.19164	−	13.5578i	−0.240645	−	0.526939i
$663$	4.68248	+	32.5674i	0.181852	+	1.26481i
$664$	−0.169779	+	0.109110i	−0.00658871	+	0.00423431i
$665$	−8.53636	+	9.85148i	−0.331026	+	0.382024i
$666$	−8.87343			−0.343838
$667$	−1.04891	+	5.30354i	−0.0406140	+	0.205354i
$668$	−20.0387			−0.775320
$669$	−12.4229	+	14.3368i	−0.480297	+	0.554293i
$670$	−3.75811	+	2.41519i	−0.145188	+	0.0933069i
$671$	−0.151928	−	1.05669i	−0.00586513	−	0.0407929i
$672$	0.842565	+	1.84496i	0.0325026	+	0.0711709i
$673$	−1.13804	+	7.91521i	−0.0438680	+	0.305109i	0.956061	+	0.293169i	$0.0947098\pi$
$673$	−1.13804	+	7.91521i	−0.0438680	+	0.305109i	−0.999929	+	0.0119401i	$0.996199\pi$
$674$	−30.3043	+	8.89814i	−1.16728	+	0.342744i
$675$	0.841254	+	0.540641i	0.0323799	+	0.0208093i
$676$	11.2895	−	24.7206i	0.434211	−	0.950791i
$677$	31.7738	+	9.32961i	1.22116	+	0.358566i	0.827909	−	0.560863i	$-0.189531\pi$
$677$	31.7738	+	9.32961i	1.22116	+	0.358566i	0.393256	+	0.919429i	$0.371349\pi$
$678$	−0.0161081	−	0.0185897i	−0.000618627	−	0.000713933i
$679$	18.7685	+	21.6600i	0.720269	+	0.831235i
$680$	−4.98060	−	1.46244i	−0.190997	−	0.0560819i
$681$	1.41713	−	3.10308i	0.0543045	−	0.118910i
$682$	−6.38055	−	4.10053i	−0.244324	−	0.157017i
$683$	28.7993	−	8.45625i	1.10198	−	0.323569i	0.320339	−	0.947303i	$-0.396203\pi$
$683$	28.7993	−	8.45625i	1.10198	−	0.323569i	0.781637	+	0.623733i	$0.214385\pi$
$684$	−0.914645	+	6.36150i	−0.0349723	+	0.243238i
$685$	−1.06600	−	2.33421i	−0.0407297	−	0.0891856i
$686$	2.85365	+	19.8476i	0.108953	+	0.757784i
$687$	−2.17969	+	1.40080i	−0.0831603	+	0.0534439i
$688$	5.44195	−	6.28034i	0.207472	−	0.239436i
$689$	13.3376			0.508123
$690$	4.66608	−	1.10801i	0.177635	−	0.0421813i
$691$	46.2149			1.75810			0.879050	−	0.476730i	$-0.158178\pi$
$691$	46.2149			1.75810			0.879050	+	0.476730i	$0.158178\pi$
$692$	15.3428	−	17.7065i	0.583244	−	0.673099i
$693$	−8.42081	+	5.41173i	−0.319880	+	0.205575i
$694$	−0.538143	−	3.74286i	−0.0204276	−	0.142077i
$695$	−4.67750	−	10.2423i	−0.177428	−	0.388512i
$696$	−0.160429	+	1.11581i	−0.00608106	+	0.0422947i
$697$	−26.6125	+	7.81413i	−1.00802	+	0.295981i
$698$	−18.8433	−	12.1098i	−0.713229	−	0.458364i
$699$	1.24070	−	2.71675i	0.0469275	−	0.102757i
$700$	1.94609	+	0.571424i	0.0735553	+	0.0215978i
$701$	14.7127	+	16.9794i	0.555691	+	0.641302i	0.962200	−	0.272345i	$-0.0877993\pi$
$701$	14.7127	+	16.9794i	0.555691	+	0.641302i	−0.406508	+	0.913647i	$0.633254\pi$
$702$	−4.15083	−	4.79031i	−0.156663	−	0.180799i
$703$	−54.7187	−	16.0669i	−2.06375	−	0.605973i
$704$	2.05016	−	4.48923i	0.0772684	−	0.169194i
$705$	−9.73726	−	6.25776i	−0.366727	−	0.235681i
$706$	−9.55975	+	2.80700i	−0.359786	+	0.105643i
$707$	−4.23200	+	29.4342i	−0.159161	+	1.10699i
$708$	−0.582929	−	1.27644i	−0.0219078	−	0.0479714i
$709$	1.33825	+	9.30771i	0.0502589	+	0.349558i	0.999398	+	0.0347005i	$0.0110477\pi$
$709$	1.33825	+	9.30771i	0.0502589	+	0.349558i	−0.949139	+	0.314858i	$0.898043\pi$
$710$	12.9792	−	8.34123i	0.487101	−	0.313041i
$711$	10.1093	−	11.6667i	0.379127	−	0.437536i
$712$	−8.83195			−0.330991
$713$	−5.98289	−	4.30434i	−0.224061	−	0.161199i
$714$	10.5284			0.394014
$715$	−20.4852	+	23.6412i	−0.766104	+	0.884131i
$716$	−4.35227	+	2.79704i	−0.162652	+	0.104530i
$717$	−1.24790	−	8.67935i	−0.0466038	−	0.324136i
$718$	−0.735189	−	1.60984i	−0.0274370	−	0.0600786i
$719$	4.79256	−	33.3330i	0.178732	−	1.24311i	−0.680969	−	0.732312i	$-0.738441\pi$
$719$	4.79256	−	33.3330i	0.178732	−	1.24311i	0.859701	−	0.510797i	$-0.170650\pi$
$720$	0.959493	−	0.281733i	0.0357582	−	0.0104996i
$721$	21.1599	+	13.5986i	0.788036	+	0.506440i
$722$	−9.26593	+	20.2896i	−0.344842	+	0.755099i
$723$	−20.5972	−	6.04787i	−0.766016	−	0.224923i
$724$	9.23821	+	10.6615i	0.343335	+	0.396230i
$725$	0.738214	+	0.851945i	0.0274166	+	0.0316404i
$726$	12.8153	+	3.76291i	0.475621	+	0.139655i
$727$	−10.0333	+	21.9698i	−0.372114	+	0.814816i	0.627238	+	0.778828i	$0.284185\pi$
$727$	−10.0333	+	21.9698i	−0.372114	+	0.814816i	−0.999352	+	0.0359888i	$0.988542\pi$
$728$	−10.8152	−	6.95049i	−0.400837	−	0.257602i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.620858	−	4.31816i	0.0229790	−	0.159822i
$731$	−17.9196	−	39.2384i	−0.662779	−	1.45128i
$732$	−0.0307846	−	0.214111i	−0.00113783	−	0.00791378i
$733$	−28.7405	+	18.4704i	−1.06155	+	0.682219i	−0.950225	−	0.311564i	$-0.899147\pi$
$733$	−28.7405	+	18.4704i	−1.06155	+	0.682219i	−0.111329	+	0.993784i	$0.535511\pi$
$734$	−11.1606	+	12.8800i	−0.411946	+	0.475411i
$735$	2.88621			0.106459
$736$	2.21825	−	4.25198i	0.0817659	−	0.156730i
$737$	−22.0469			−0.812110
$738$	3.49907	−	4.03814i	0.128802	−	0.148646i
$739$	4.14173	−	2.66173i	0.152356	−	0.0979132i	−0.462242	−	0.886754i	$-0.652955\pi$
$739$	4.14173	−	2.66173i	0.152356	−	0.0979132i	0.614598	+	0.788841i	$0.289318\pi$
$740$	1.26282	+	8.78311i	0.0464222	+	0.322873i
$741$	−16.9227	−	37.0556i	−0.621672	−	1.36127i
$742$	0.607385	−	4.22445i	0.0222978	−	0.155085i
$743$	−27.6160	+	8.10879i	−1.01313	+	0.297483i	−0.745835	−	0.666131i	$-0.767949\pi$
$743$	−27.6160	+	8.10879i	−1.01313	+	0.297483i	−0.267298	+	0.963614i	$0.586131\pi$
$744$	−1.29286	−	0.830872i	−0.0473986	−	0.0304612i
$745$	−1.86240	+	4.07808i	−0.0682330	+	0.149409i
$746$	−29.0368	−	8.52597i	−1.06311	−	0.312158i
$747$	−0.132162	−	0.152523i	−0.00483555	−	0.00558053i
$748$	−16.7762	−	19.3608i	−0.613400	−	0.707902i
$749$	−4.47154	−	1.31296i	−0.163387	−	0.0479747i
$750$	0.415415	−	0.909632i	0.0151688	−	0.0332151i
$751$	17.3748	+	11.1661i	0.634014	+	0.407456i	0.817794	−	0.575511i	$-0.195197\pi$
$751$	17.3748	+	11.1661i	0.634014	+	0.407456i	−0.183780	+	0.982967i	$0.558833\pi$
$752$	−11.1059	+	3.26097i	−0.404989	+	0.118915i
$753$	2.91034	−	20.2419i	0.106059	−	0.737654i
$754$	−2.96826	−	6.49957i	−0.108098	−	0.236701i
$755$	0.244427	+	1.70003i	0.00889562	+	0.0618704i
$756$	−1.70627	+	1.09655i	−0.0620565	+	0.0398813i
$757$	0.920468	−	1.06228i	0.0334550	−	0.0386091i	−0.738776	−	0.673952i	$-0.764596\pi$
$757$	0.920468	−	1.06228i	0.0334550	−	0.0386091i	0.772230	+	0.635343i	$0.219141\pi$
$758$	−28.5140			−1.03568
$759$	22.3288	+	7.84972i	0.810486	+	0.284927i
$760$	6.42692			0.233129
$761$	−0.389962	+	0.450040i	−0.0141361	+	0.0163139i	−0.762774	−	0.646666i	$-0.776163\pi$
$761$	−0.389962	+	0.450040i	−0.0141361	+	0.0163139i	0.748637	+	0.662980i	$0.230708\pi$
$762$	−16.2183	+	10.4229i	−0.587528	+	0.377581i
$763$	−1.39285	−	9.68745i	−0.0504244	−	0.350709i
$764$	5.52109	+	12.0895i	0.199746	+	0.437383i
$765$	0.738737	−	5.13803i	0.0267091	−	0.185766i
$766$	−21.8149	+	6.40542i	−0.788203	+	0.231437i
$767$	7.48249	+	4.80871i	0.270177	+	0.173632i
$768$	0.415415	−	0.909632i	0.0149900	−	0.0328235i
$769$	−37.6717	−	11.0614i	−1.35848	−	0.398885i	−0.480251	−	0.877131i	$-0.659454\pi$
$769$	−37.6717	−	11.0614i	−1.35848	−	0.398885i	−0.878226	+	0.478247i	$0.841273\pi$
$770$	6.55505	+	7.56493i	0.236228	+	0.272621i
$771$	−14.6433	−	16.8993i	−0.527366	−	0.608612i
$772$	−4.38864	−	1.28862i	−0.157951	−	0.0463785i
$773$	−4.36247	+	9.55247i	−0.156907	+	0.343578i	−0.971717	−	0.236150i	$-0.924114\pi$
$773$	−4.36247	+	9.55247i	−0.156907	+	0.343578i	0.814810	+	0.579729i	$0.196841\pi$
$774$	6.99089	+	4.49277i	0.251282	+	0.161489i
$775$	−1.47458	+	0.432975i	−0.0529683	+	0.0155529i
$776$	2.01099	−	13.9867i	0.0721903	−	0.502095i
$777$	−7.47644	−	16.3711i	−0.268216	−	0.587310i
$778$	1.28790	+	8.95757i	0.0461736	+	0.321144i
$779$	28.8890	−	18.5659i	1.03506	−	0.665191i
$780$	−4.15083	+	4.79031i	−0.148623	+	0.171521i
$781$	76.1425			2.72459
$782$	−15.2936	−	19.6429i	−0.546897	−	0.702430i
$783$	−1.12728			−0.0402859
$784$	1.89007	−	2.18125i	0.0675023	−	0.0779018i
$785$	8.77971	−	5.64238i	0.313361	−	0.201385i
$786$	−0.633351	−	4.40505i	−0.0225909	−	0.157123i
$787$	11.7222	+	25.6680i	0.417851	+	0.914966i	0.995144	+	0.0984290i	$0.0313817\pi$
$787$	11.7222	+	25.6680i	0.417851	+	0.914966i	−0.577293	+	0.816537i	$0.695891\pi$
$788$	1.82398	−	12.6861i	0.0649766	−	0.451922i
$789$	−18.6216	+	5.46780i	−0.662947	+	0.194659i
$790$	−12.9867	−	8.34602i	−0.462045	−	0.296938i
$791$	0.0207252	−	0.0453818i	0.000736902	−	0.00161359i
$792$	4.73530	+	1.39041i	0.168262	+	0.0494061i
$793$	0.897878	+	1.03621i	0.0318846	+	0.0367968i
$794$	−1.70538	−	1.96812i	−0.0605218	−	0.0698459i
$795$	−2.01899	−	0.592829i	−0.0716063	−	0.0210255i
$796$	1.84785	−	4.04623i	0.0654954	−	0.143415i
$797$	15.0449	+	9.66876i	0.532917	+	0.342485i	0.779263	−	0.626697i	$-0.215594\pi$
$797$	15.0449	+	9.66876i	0.532917	+	0.342485i	−0.246346	+	0.969182i	$0.579230\pi$
$798$	−12.5074	+	3.67249i	−0.442756	+	0.130005i
$799$	−8.55067	+	59.4712i	−0.302501	+	2.10394i
$800$	−0.415415	−	0.909632i	−0.0146871	−	0.0321603i
$801$	−1.25692	−	8.74205i	−0.0444110	−	0.308885i
$802$	4.89507	−	3.14587i	0.172851	−	0.111085i
$803$	14.0993	−	16.2714i	0.497553	−	0.574207i
$804$	−4.46727			−0.157549
$805$	5.97571	+	7.67516i	0.210616	+	0.270514i
$806$	9.74117			0.343118
$807$	−19.8699	+	22.9311i	−0.699454	+	0.807214i
$808$	12.3339	−	7.92653i	0.433906	−	0.278854i
$809$	1.53117	+	10.6495i	0.0538331	+	0.374417i	0.998873	+	0.0474624i	$0.0151134\pi$
$809$	1.53117	+	10.6495i	0.0538331	+	0.374417i	−0.945040	+	0.326955i	$0.893977\pi$
$810$	0.415415	+	0.909632i	0.0145962	+	0.0319612i
$811$	1.00594	−	6.99646i	0.0353233	−	0.245679i	−0.964508	−	0.264054i	$-0.914940\pi$
$811$	1.00594	−	6.99646i	0.0353233	−	0.245679i	0.999831	+	0.0183752i	$0.00584934\pi$
$812$	−2.19380	+	0.644157i	−0.0769872	+	0.0226055i
$813$	14.3655	+	9.23214i	0.503820	+	0.323785i
$814$	−18.1920	+	39.8348i	−0.637628	+	1.39621i
$815$	16.6638	+	4.89292i	0.583706	+	0.171392i
$816$	−3.39930	−	3.92300i	−0.118999	−	0.137332i
$817$	34.9750	+	40.3632i	1.22362	+	1.41213i
$818$	14.3758	+	4.22110i	0.502636	+	0.147587i
$819$	5.34059	−	11.6943i	0.186615	−	0.408630i
$820$	−4.49501	−	2.88877i	−0.156972	−	0.100880i
$821$	5.89859	−	1.73198i	0.205862	−	0.0604466i	−0.177176	−	0.984179i	$-0.556696\pi$
$821$	5.89859	−	1.73198i	0.205862	−	0.0604466i	0.383038	+	0.923733i	$0.374878\pi$
$822$	0.365195	−	2.53999i	0.0127376	−	0.0885922i
$823$	7.90610	+	17.3119i	0.275589	+	0.603457i	0.995927	−	0.0901674i	$-0.0287402\pi$
$823$	7.90610	+	17.3119i	0.275589	+	0.603457i	−0.720337	+	0.693624i	$0.756013\pi$
$824$	−1.76488	−	12.2750i	−0.0614826	−	0.427621i
$825$	4.15177	−	2.66818i	0.144546	−	0.0928940i
$826$	1.86382	−	2.15096i	0.0648506	−	0.0748415i
$827$	37.0920			1.28981			0.644907	−	0.764261i	$-0.276896\pi$
$827$	37.0920			1.28981			0.644907	+	0.764261i	$0.276896\pi$
$828$	4.52439	+	1.59055i	0.157234	+	0.0552756i
$829$	42.9192			1.49065			0.745323	−	0.666704i	$-0.232295\pi$
$829$	42.9192			1.49065			0.745323	+	0.666704i	$0.232295\pi$
$830$	−0.132162	+	0.152523i	−0.00458741	+	0.00529415i
$831$	−8.15852	+	5.24316i	−0.283016	+	0.181883i
$832$	0.902061	+	6.27397i	0.0312733	+	0.217511i
$833$	−6.22372	−	13.6280i	−0.215639	−	0.472184i
$834$	1.60244	−	11.1452i	0.0554880	−	0.385927i
$835$	−19.2270	+	5.64555i	−0.665377	+	0.195372i
$836$	26.6830	+	17.1482i	0.922853	+	0.593081i
$837$	0.638421	−	1.39795i	0.0220671	−	0.0483202i
$838$	31.5784	+	9.27226i	1.09086	+	0.320305i
$839$	1.05531	+	1.21790i	0.0364335	+	0.0420465i	0.773674	−	0.633584i	$-0.218417\pi$
$839$	1.05531	+	1.21790i	0.0364335	+	0.0420465i	−0.737240	+	0.675631i	$0.763871\pi$
$840$	1.32822	+	1.53285i	0.0458279	+	0.0528883i
$841$	26.6060	+	7.81223i	0.917448	+	0.269387i
$842$	−10.0413	+	21.9873i	−0.346044	+	0.757732i
$843$	1.82397	+	1.17220i	0.0628209	+	0.0403725i
$844$	13.8991	−	4.08114i	0.478426	−	0.140478i
$845$	3.86761	−	26.8998i	0.133050	−	0.925382i
$846$	−4.80831	−	10.5287i	−0.165313	−	0.361985i
$847$	3.85530	+	26.8142i	0.132470	+	0.921347i
$848$	−1.77019	+	1.13763i	−0.0607885	+	0.0390664i
$849$	4.07258	−	4.70001i	0.139771	−	0.161304i
$850$	−5.19087			−0.178045
$851$	−19.6835	+	37.7296i	−0.674742	+	1.29336i
$852$	15.4284			0.528568
$853$	−7.41569	+	8.55816i	−0.253908	+	0.293026i	−0.868366	−	0.495924i	$-0.834829\pi$
$853$	−7.41569	+	8.55816i	−0.253908	+	0.293026i	0.614458	+	0.788950i	$0.289375\pi$
$854$	0.369089	−	0.237199i	0.0126300	−	0.00811678i
$855$	0.914645	+	6.36150i	0.0312802	+	0.217559i
$856$	0.954502	+	2.09007i	0.0326242	+	0.0714370i
$857$	−3.32036	+	23.0936i	−0.113421	+	0.788862i	0.851128	+	0.524958i	$0.175919\pi$
$857$	−3.32036	+	23.0936i	−0.113421	+	0.788862i	−0.964549	+	0.263903i	$0.914990\pi$
$858$	−30.0147	+	8.81310i	−1.02468	+	0.300874i
$859$	−4.49373	−	2.88795i	−0.153324	−	0.0985355i	0.461729	−	0.887021i	$-0.347229\pi$
$859$	−4.49373	−	2.88795i	−0.153324	−	0.0985355i	−0.615053	+	0.788485i	$0.710866\pi$
$860$	3.45214	−	7.55912i	0.117717	−	0.257764i
$861$	10.3984	+	3.05324i	0.354376	+	0.104054i
$862$	3.80835	+	4.39507i	0.129713	+	0.149697i
$863$	−18.2520	−	21.0639i	−0.621304	−	0.717023i	0.354650	−	0.934999i	$-0.384600\pi$
$863$	−18.2520	−	21.0639i	−0.621304	−	0.717023i	−0.975954	+	0.217976i	$0.930055\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	9.73277	−	21.3118i	0.330924	−	0.724623i
$866$	−26.8195	−	17.2358i	−0.911362	−	0.585697i
$867$	−9.54226	+	2.80186i	−0.324072	+	0.0951562i
$868$	0.443605	−	3.08534i	0.0150569	−	0.104723i
$869$	−31.6489	−	69.3014i	−1.07362	−	2.35089i
$870$	0.160429	+	1.11581i	0.00543906	+	0.0378295i
$871$	23.8207	−	15.3087i	0.807135	−	0.518714i
$872$	−3.15995	+	3.64678i	−0.107009	+	0.123496i
$873$	14.1306			0.478247
$874$	25.0201	+	18.0005i	0.846316	+	0.608875i
$875$	2.02825			0.0685673
$876$	2.85687	−	3.29701i	0.0965248	−	0.111396i
$877$	2.20122	−	1.41464i	0.0743299	−	0.0477689i	−0.502948	−	0.864317i	$-0.667751\pi$
$877$	2.20122	−	1.41464i	0.0743299	−	0.0477689i	0.577278	+	0.816548i	$0.304115\pi$
$878$	4.50954	+	31.3645i	0.152190	+	1.05850i
$879$	−12.9329	−	28.3191i	−0.436216	−	0.955180i
$880$	0.702354	−	4.88498i	0.0236764	−	0.164673i
$881$	5.35405	−	1.57209i	0.180382	−	0.0529651i	−0.190294	−	0.981727i	$-0.560944\pi$
$881$	5.35405	−	1.57209i	0.180382	−	0.0529651i	0.370676	+	0.928762i	$0.379126\pi$
$882$	2.42803	+	1.56040i	0.0817561	+	0.0525415i
$883$	6.90047	−	15.1099i	0.232219	−	0.508489i	−0.757269	−	0.653103i	$-0.773467\pi$
$883$	6.90047	−	15.1099i	0.232219	−	0.508489i	0.989488	+	0.144614i	$0.0461940\pi$
$884$	31.5695	+	9.26964i	1.06180	+	0.311772i
$885$	−0.918930	−	1.06050i	−0.0308895	−	0.0356484i
$886$	−15.7302	−	18.1536i	−0.528467	−	0.609883i
$887$	−23.6120	−	6.93310i	−0.792813	−	0.232791i	−0.139842	−	0.990174i	$-0.544659\pi$
$887$	−23.6120	−	6.93310i	−0.792813	−	0.232791i	−0.652971	+	0.757383i	$0.726478\pi$
$888$	−3.68615	+	8.07155i	−0.123699	+	0.270864i
$889$	−32.8948	−	21.1402i	−1.10325	−	0.709019i
$890$	−8.47419	+	2.48825i	−0.284056	+	0.0834062i
$891$	−0.702354	+	4.88498i	−0.0235297	+	0.163653i
$892$	7.88055	+	17.2560i	0.263860	+	0.577773i
$893$	−10.5868	−	73.6325i	−0.354272	−	2.46402i
$894$	−3.77153	+	2.42381i	−0.126139	+	0.0810644i
$895$	−3.38796	+	3.90991i	−0.113247	+	0.130694i
$896$	2.02825			0.0677590
$897$	−29.5759	+	7.02312i	−0.987510	+	0.234495i
$898$	25.2941			0.844073
$899$	1.13451	−	1.30929i	0.0378380	−	0.0436674i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	1.55447	+	10.8116i	0.0517870	+	0.360186i
$902$	−10.9545	−	23.9870i	−0.364744	−	0.798678i
$903$	−2.39871	+	16.6834i	−0.0798239	+	0.555187i
$904$	−0.0236013	+	0.00692997i	−0.000784968	+	0.000230488i
$905$	11.8677	+	7.62689i	0.394495	+	0.253527i
$906$	−0.713480	+	1.56230i	−0.0237038	+	0.0519041i
$907$	−14.1736	−	4.16174i	−0.470626	−	0.138188i	0.0378157	−	0.999285i	$-0.487960\pi$
$907$	−14.1736	−	4.16174i	−0.470626	−	0.138188i	−0.508442	+	0.861097i	$0.669778\pi$
$908$	−2.23396	−	2.57813i	−0.0741366	−	0.0855582i
$909$	9.60115	+	11.0803i	0.318450	+	0.367511i
$910$	−12.3353	−	3.62196i	−0.408910	−	0.120067i
$911$	1.99249	−	4.36294i	0.0660141	−	0.144551i	−0.873749	−	0.486377i	$-0.838318\pi$
$911$	1.99249	−	4.36294i	0.0660141	−	0.144551i	0.939763	+	0.341826i	$0.111045\pi$
$912$	5.40667	+	3.47465i	0.179033	+	0.115057i
$913$	−0.955664	+	0.280608i	−0.0316279	+	0.00928678i
$914$	2.81413	−	19.5727i	0.0930831	−	0.647407i
$915$	−0.0898597	−	0.196765i	−0.00297067	−	0.00650486i
$916$	0.368738	+	2.56463i	0.0121834	+	0.0847377i
$917$	7.59350	−	4.88005i	0.250759	−	0.161153i
$918$	3.39930	−	3.92300i	0.112193	−	0.129478i
$919$	−42.8419			−1.41322			−0.706612	−	0.707602i	$-0.749777\pi$
$919$	−42.8419			−1.41322			−0.706612	+	0.707602i	$0.749777\pi$
$920$	0.930476	−	4.70470i	0.0306769	−	0.155109i
$921$	−10.3016			−0.339449
$922$	−15.1665	+	17.5031i	−0.499482	+	0.576434i
$923$	−82.2685	+	52.8708i	−2.70790	+	1.74026i
$924$	1.42455	+	9.90795i	0.0468642	+	0.325948i
$925$	3.68615	+	8.07155i	0.121200	+	0.265391i
$926$	4.62887	−	32.1945i	0.152114	−	1.05798i
$927$	11.8989	−	3.49384i	0.390812	−	0.114753i
$928$	0.948332	+	0.609456i	0.0311305	+	0.0200064i
$929$	0.333873	−	0.731080i	0.0109540	−	0.0239859i	−0.904076	−	0.427372i	$-0.859440\pi$
$929$	0.333873	−	0.731080i	0.0109540	−	0.0239859i	0.915030	+	0.403386i	$0.132167\pi$
$930$	−1.47458	−	0.432975i	−0.0483532	−	0.0141978i
$931$	12.1473	+	14.0187i	0.398111	+	0.459445i
$932$	−1.95584	−	2.25715i	−0.0640655	−	0.0739356i
$933$	−16.0407	−	4.70997i	−0.525148	−	0.154197i
$934$	−10.5554	+	23.1132i	−0.345384	+	0.756285i
$935$	−21.5513	−	13.8502i	−0.704802	−	0.452949i
$936$	−6.08173	+	1.78576i	−0.198788	+	0.0583693i
$937$	2.73276	−	19.0068i	0.0892755	−	0.620925i	−0.895234	−	0.445596i	$-0.852992\pi$
$937$	2.73276	−	19.0068i	0.0892755	−	0.620925i	0.984510	−	0.175329i	$-0.0560990\pi$
$938$	−3.76397	−	8.24194i	−0.122898	−	0.269109i
$939$	4.42983	+	30.8102i	0.144562	+	1.00545i
$940$	−9.73726	+	6.25776i	−0.317595	+	0.204106i
$941$	31.4976	−	36.3502i	1.02679	−	1.18498i	0.0442361	−	0.999021i	$-0.485915\pi$
$941$	31.4976	−	36.3502i	1.02679	−	1.18498i	0.982557	−	0.185961i	$-0.0595399\pi$
$942$	10.4365			0.340038
$943$	−9.40828	−	23.8356i	−0.306376	−	0.776194i
$944$	−1.40325			−0.0456717
$945$	−1.32822	+	1.53285i	−0.0432070	+	0.0498635i
$946$	34.5015	−	22.1728i	1.12174	−	0.720900i
$947$	6.95367	+	48.3638i	0.225964	+	1.57161i	0.714858	+	0.699270i	$0.246491\pi$
$947$	6.95367	+	48.3638i	0.225964	+	1.57161i	−0.488894	+	0.872343i	$0.662600\pi$
$948$	−6.41287	−	14.0422i	−0.208280	−	0.456071i
$949$	−3.93530	+	27.3706i	−0.127745	+	0.888488i
$950$	6.16658	−	1.81067i	0.200070	−	0.0587459i
$951$	12.7656	+	8.20397i	0.413954	+	0.266032i
$952$	4.37364	−	9.57694i	0.141751	−	0.310390i
$953$	−0.524432	−	0.153987i	−0.0169880	−	0.00498813i	0.273228	−	0.961949i	$-0.411909\pi$
$953$	−0.524432	−	0.153987i	−0.0169880	−	0.00498813i	−0.290216	+	0.956961i	$0.593727\pi$
$954$	−1.37798	−	1.59027i	−0.0446136	−	0.0514869i
$955$	8.70345	+	10.0443i	0.281637	+	0.325026i
$956$	−8.41342	−	2.47040i	−0.272109	−	0.0798985i
$957$	−2.31112	+	5.06064i	−0.0747077	+	0.163587i
$958$	9.09260	+	5.84346i	0.293768	+	0.188794i
$959$	4.99387	−	1.46633i	0.161260	−	0.0473503i
$960$	0.142315	−	0.989821i	0.00459319	−	0.0319463i
$961$	−11.8967	−	26.0502i	−0.383765	−	0.840329i
$962$	−8.00437	−	55.6716i	−0.258071	−	1.79493i
$963$	−1.93295	+	1.24223i	−0.0622886	+	0.0400304i
$964$	−14.0577	+	16.2235i	−0.452768	+	0.522522i
$965$	−4.57392			−0.147240
$966$	0.877586	+	9.68747i	0.0282359	+	0.311689i
$967$	13.5829			0.436797			0.218399	−	0.975860i	$-0.429917\pi$
$967$	13.5829			0.436797			0.218399	+	0.975860i	$0.429917\pi$
$968$	8.74654	−	10.0940i	0.281124	−	0.324435i
$969$	28.0653	−	18.0365i	0.901587	−	0.579415i
$970$	−2.01099	−	13.9867i	−0.0645690	−	0.449087i
$971$	−17.8180	−	39.0161i	−0.571808	−	1.25209i	−0.945829	−	0.324665i	$-0.894748\pi$
$971$	−17.8180	−	39.0161i	−0.571808	−	1.25209i	0.374021	−	0.927420i	$-0.377979\pi$
$972$	−0.142315	+	0.989821i	−0.00456475	+	0.0317485i
$973$	21.9126	−	6.43413i	0.702487	−	0.206269i
$974$	22.2235	+	14.2822i	0.712086	+	0.457630i
$975$	−2.63310	+	5.76569i	−0.0843268	+	0.184650i
$976$	−0.207551	−	0.0609425i	−0.00664354	−	0.00195072i
$977$	−13.8994	−	16.0408i	−0.444682	−	0.513190i	0.488515	−	0.872555i	$-0.337539\pi$
$977$	−13.8994	−	16.0408i	−0.444682	−	0.513190i	−0.933197	+	0.359365i	$0.882993\pi$
$978$	11.3731	+	13.1253i	0.363673	+	0.419701i
$979$	−41.8219	−	12.2800i	−1.33663	−	0.392471i
$980$	1.19897	−	2.62539i	0.0382998	−	0.0838650i
$981$	−4.05937	−	2.60880i	−0.129606	−	0.0832925i
$982$	29.3999	−	8.63259i	0.938189	−	0.275477i
$983$	−7.55609	+	52.5538i	−0.241002	+	1.67620i	0.406122	+	0.913819i	$0.366881\pi$
$983$	−7.55609	+	52.5538i	−0.241002	+	1.67620i	−0.647123	+	0.762385i	$0.724028\pi$
$984$	−2.21966	−	4.86037i	−0.0707600	−	0.154943i
$985$	−1.82398	−	12.6861i	−0.0581168	−	0.404212i
$986$	4.92267	−	3.16361i	0.156770	−	0.100750i
$987$	15.3738	−	17.7423i	0.489352	−	0.564743i
$988$	−40.7369			−1.29601
$989$	34.6108	−	19.7590i	1.10056	−	0.628301i
$990$	4.93521			0.156851
$991$	−1.41100	+	1.62838i	−0.0448219	+	0.0517273i	−0.777718	−	0.628614i	$-0.783623\pi$
$991$	−1.41100	+	1.62838i	−0.0448219	+	0.0517273i	0.732896	+	0.680341i	$0.238168\pi$
$992$	−1.29286	+	0.830872i	−0.0410484	+	0.0263802i
$993$	−2.12116	−	14.7530i	−0.0673130	−	0.468172i
$994$	12.9994	+	28.4648i	0.412317	+	0.902848i
$995$	0.633046	−	4.40293i	0.0200689	−	0.139582i
$996$	−0.193642	+	0.0568584i	−0.00613578	+	0.00180163i
$997$	−44.7958	−	28.7885i	−1.41870	−	0.911742i	−0.999993	−	0.00361936i	$-0.998848\pi$
$997$	−44.7958	−	28.7885i	−1.41870	−	0.911742i	−0.418705	−	0.908122i	$-0.637516\pi$
$998$	0.808152	−	1.76961i	0.0255816	−	0.0560159i
$999$	−8.51399	−	2.49993i	−0.269371	−	0.0790944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.361.2	yes	30
23.13	even	11	inner	690.2.m.h.151.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.151.2	✓	30	23.13	even	11	inner
690.2.m.h.361.2	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.94609 - 0.571424i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.94609 - 0.571424i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-3.23188 - 3.72979i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(6.08173 + 1.78576i) q^{13} +(0.842565 - 1.84496i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.738737 + 5.13803i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.914645 - 6.36150i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(1.32822 - 1.53285i) q^{21} -4.93521 q^{22} +(-4.78923 - 0.251457i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(5.33228 - 3.42685i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.842565 - 1.84496i) q^{28} +(0.160429 - 1.11581i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(1.29286 + 0.830872i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-4.73530 - 1.39041i) q^{33} +(3.39930 + 3.92300i) q^{34} +(-1.32822 - 1.53285i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.68615 - 8.07155i) q^{37} +(-5.40667 - 3.47465i) q^{38} +(6.08173 - 1.78576i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(2.21966 + 4.86037i) q^{41} +(-0.288650 - 2.00760i) q^{42} +(-6.99089 + 4.49277i) q^{43} +(-3.23188 + 3.72979i) q^{44} -1.00000 q^{45} +(-3.32632 + 3.45479i) q^{46} +11.5747 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-2.42803 + 1.56040i) q^{49} +(0.142315 + 0.989821i) q^{50} +(2.15636 + 4.72178i) q^{51} +(0.902061 - 6.27397i) q^{52} +(2.01899 - 0.592829i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-2.05016 + 4.48923i) q^{55} +(-1.94609 - 0.571424i) q^{56} +(-4.20873 - 4.85714i) q^{57} +(-0.738214 - 0.851945i) q^{58} +(1.34640 + 0.395340i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(0.181974 + 0.116948i) q^{61} +(1.47458 - 0.432975i) q^{62} +(0.288650 - 2.00760i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.902061 - 6.27397i) q^{65} +(-4.15177 + 2.66818i) q^{66} +(2.92544 - 3.37614i) q^{67} +5.19087 q^{68} +(-4.16491 + 2.37772i) q^{69} -2.02825 q^{70} +(-10.1035 + 11.6600i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.620858 + 4.31816i) q^{73} +(-3.68615 - 8.07155i) q^{74} +(-0.142315 + 0.989821i) q^{75} +(-6.16658 + 1.81067i) q^{76} +(-8.42081 - 5.41173i) q^{77} +(2.63310 - 5.76569i) q^{78} +(14.8120 + 4.34918i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(5.12679 + 1.50536i) q^{82} +(0.0838378 - 0.183579i) q^{83} +(-1.70627 - 1.09655i) q^{84} +(4.98060 - 1.46244i) q^{85} +(-1.18265 + 8.22550i) q^{86} +(-0.468291 - 1.02541i) q^{87} +(0.702354 + 4.88498i) q^{88} +(7.42991 - 4.77491i) q^{89} +(-0.654861 + 0.755750i) q^{90} +12.8560 q^{91} +(0.432682 + 4.77627i) q^{92} +1.53683 q^{93} +(7.57982 - 8.74758i) q^{94} +(-5.40667 + 3.47465i) q^{95} +(0.142315 + 0.989821i) q^{96} +(5.87005 + 12.8536i) q^{97} +(-0.410750 + 2.85683i) q^{98} +(-4.73530 + 1.39041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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