LMFDB - Embedded newform 690.2.m.e.331.1

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
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} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			331.1
Root			$-0.462319 - 3.21550i$ of defining polynomial
Character	$\chi$	$=$	690.331
Dual form			690.2.m.e.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.63866 + 3.58816i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.63866 + 3.58816i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(4.05459 + 1.19054i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.877087 + 1.92055i) q^{13} +(-0.561379 + 3.90448i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(2.41720 + 1.55344i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-2.20746 + 1.41865i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-3.78484 + 1.11133i) q^{21} +4.22577 q^{22} +(-1.66031 - 4.49926i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.38264 + 1.59565i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.561379 + 3.90448i) q^{28} +(8.55007 + 5.49480i) q^{29} +(0.415415 - 0.909632i) q^{30} +(6.42298 - 7.41252i) q^{31} +(0.142315 - 0.989821i) q^{32} +(1.75545 + 3.84389i) q^{33} +(2.75694 + 0.809510i) q^{34} +(3.78484 + 1.11133i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.362134 + 2.51870i) q^{37} +(-1.71836 + 1.98310i) q^{38} +(-0.877087 + 1.92055i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(-0.513005 - 3.56803i) q^{41} +(-3.31843 + 2.13263i) q^{42} +(-8.19369 - 9.45602i) q^{43} +(4.05459 - 1.19054i) q^{44} +1.00000 q^{45} +(-2.86065 - 3.84925i) q^{46} -8.95443 q^{47} +(0.959493 - 0.281733i) q^{48} +(-5.60567 - 6.46928i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.408917 + 2.84408i) q^{51} +(1.77618 + 1.14148i) q^{52} +(-4.05870 + 8.88731i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.601389 - 4.18276i) q^{55} +(1.63866 + 3.58816i) q^{56} +(-2.51772 - 0.739270i) q^{57} +(9.75179 + 2.86339i) q^{58} +(-2.31958 - 5.07918i) q^{59} +(0.142315 - 0.989821i) q^{60} +(0.622802 - 0.718752i) q^{61} +(4.07446 - 8.92182i) q^{62} +(-3.31843 - 2.13263i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.77618 - 1.14148i) q^{65} +(2.76729 + 3.19362i) q^{66} +(0.480031 - 0.140950i) q^{67} +2.87333 q^{68} +(2.31304 - 4.20117i) q^{69} +3.94463 q^{70} +(-10.2180 + 3.00027i) q^{71} +(0.654861 + 0.755750i) q^{72} +(3.02217 - 1.94223i) q^{73} +(0.362134 + 2.51870i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-1.09005 + 2.38689i) q^{76} +(-10.9159 + 12.5977i) q^{77} +(-0.300477 + 2.08986i) q^{78} +(1.98127 + 4.33837i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.49745 - 3.27897i) q^{82} +(2.12692 - 14.7930i) q^{83} +(-2.58318 + 2.98115i) q^{84} +(1.19362 - 2.61367i) q^{85} +(-10.5259 - 6.76456i) q^{86} +(1.44641 + 10.0600i) q^{87} +(3.55494 - 2.28462i) q^{88} +(11.7645 + 13.5769i) q^{89} +(0.959493 - 0.281733i) q^{90} -8.32850 q^{91} +(-3.82923 - 2.88739i) q^{92} +9.80817 q^{93} +(-8.59171 + 2.52275i) q^{94} +(1.71836 + 1.98310i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-2.06884 - 14.3891i) q^{97} +(-7.20121 - 4.62793i) q^{98} +(-1.75545 + 3.84389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−1.63866	+	3.58816i	−0.619354	+	1.35620i	0.296634	+	0.954991i	$0.404136\pi$
$7$	−1.63866	+	3.58816i	−0.619354	+	1.35620i	−0.915988	+	0.401206i	$0.868591\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.415415	−	0.909632i	−0.131366	−	0.287651i
$11$	4.05459	+	1.19054i	1.22251	+	0.358960i	0.828417	−	0.560112i	$-0.189242\pi$
$11$	4.05459	+	1.19054i	1.22251	+	0.358960i	0.394089	+	0.919072i	$0.371060\pi$
$12$	0.959493	+	0.281733i	0.276982	+	0.0813292i
$13$	0.877087	+	1.92055i	0.243260	+	0.532666i	0.991399	−	0.130877i	$-0.0417793\pi$
$13$	0.877087	+	1.92055i	0.243260	+	0.532666i	−0.748138	+	0.663543i	$0.769052\pi$
$14$	−0.561379	+	3.90448i	−0.150035	+	1.04352i
$15$	0.654861	−	0.755750i	0.169084	−	0.195134i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	2.41720	+	1.55344i	0.586257	+	0.376764i	0.799887	−	0.600150i	$-0.204893\pi$
$17$	2.41720	+	1.55344i	0.586257	+	0.376764i	−0.213631	+	0.976914i	$0.568529\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	−2.20746	+	1.41865i	−0.506426	+	0.325460i	−0.768782	−	0.639511i	$-0.779137\pi$
$19$	−2.20746	+	1.41865i	−0.506426	+	0.325460i	0.262356	+	0.964971i	$0.415501\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	−3.78484	+	1.11133i	−0.825920	+	0.242512i
$22$	4.22577			0.900937
$23$	−1.66031	−	4.49926i	−0.346199	−	0.938161i
$23$	−1.66031	−	4.49926i	−0.346199	−	0.938161i
$24$	1.00000			0.204124
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	1.38264	+	1.59565i	0.271158	+	0.312933i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.561379	+	3.90448i	0.106091	+	0.737877i
$29$	8.55007	+	5.49480i	1.58771	+	1.02036i	0.972767	+	0.231785i	$0.0744565\pi$
$29$	8.55007	+	5.49480i	1.58771	+	1.02036i	0.614941	+	0.788573i	$0.289180\pi$
$30$	0.415415	−	0.909632i	0.0758441	−	0.166075i
$31$	6.42298	−	7.41252i	1.15360	−	1.33133i	0.218962	−	0.975733i	$-0.429733\pi$
$31$	6.42298	−	7.41252i	1.15360	−	1.33133i	0.934640	−	0.355594i	$-0.115721\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	1.75545	+	3.84389i	0.305584	+	0.669136i
$34$	2.75694	+	0.809510i	0.472811	+	0.138830i
$35$	3.78484	+	1.11133i	0.639755	+	0.187849i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−0.362134	+	2.51870i	−0.0595345	+	0.414071i	0.938160	+	0.346203i	$0.112529\pi$
$37$	−0.362134	+	2.51870i	−0.0595345	+	0.414071i	−0.997694	+	0.0678689i	$0.978380\pi$
$38$	−1.71836	+	1.98310i	−0.278755	+	0.321701i
$39$	−0.877087	+	1.92055i	−0.140446	+	0.307535i
$40$	−0.841254	−	0.540641i	−0.133014	−	0.0854828i
$41$	−0.513005	−	3.56803i	−0.0801179	−	0.557232i	−0.989859	−	0.142055i	$-0.954629\pi$
$41$	−0.513005	−	3.56803i	−0.0801179	−	0.557232i	0.909741	−	0.415177i	$-0.136280\pi$
$42$	−3.31843	+	2.13263i	−0.512045	+	0.329071i
$43$	−8.19369	−	9.45602i	−1.24953	−	1.44203i	−0.851247	−	0.524765i	$-0.824153\pi$
$43$	−8.19369	−	9.45602i	−1.24953	−	1.44203i	−0.398278	−	0.917265i	$-0.630392\pi$
$44$	4.05459	−	1.19054i	0.611253	−	0.179480i
$45$	1.00000			0.149071
$46$	−2.86065	−	3.84925i	−0.421779	−	0.567541i
$47$	−8.95443			−1.30614			−0.653069	−	0.757299i	$-0.726519\pi$
$47$	−8.95443			−1.30614			−0.653069	+	0.757299i	$0.726519\pi$
$48$	0.959493	−	0.281733i	0.138491	−	0.0406646i
$49$	−5.60567	−	6.46928i	−0.800809	−	0.924183i
$50$	−0.841254	+	0.540641i	−0.118971	+	0.0764582i
$51$	0.408917	+	2.84408i	0.0572599	+	0.398251i
$52$	1.77618	+	1.14148i	0.246312	+	0.158295i
$53$	−4.05870	+	8.88731i	−0.557505	+	1.22077i	0.395683	+	0.918387i	$0.370508\pi$
$53$	−4.05870	+	8.88731i	−0.557505	+	1.22077i	−0.953188	+	0.302379i	$0.902219\pi$
$54$	−0.654861	+	0.755750i	−0.0891153	+	0.102844i
$55$	0.601389	−	4.18276i	0.0810913	−	0.564003i
$56$	1.63866	+	3.58816i	0.218975	+	0.479488i
$57$	−2.51772	−	0.739270i	−0.333480	−	0.0979187i
$58$	9.75179	+	2.86339i	1.28047	+	0.375981i
$59$	−2.31958	−	5.07918i	−0.301984	−	0.661253i	0.696426	−	0.717629i	$-0.254773\pi$
$59$	−2.31958	−	5.07918i	−0.301984	−	0.661253i	−0.998410	+	0.0563762i	$0.982045\pi$
$60$	0.142315	−	0.989821i	0.0183728	−	0.127785i
$61$	0.622802	−	0.718752i	0.0797416	−	0.0920267i	−0.714477	−	0.699659i	$-0.753335\pi$
$61$	0.622802	−	0.718752i	0.0797416	−	0.0920267i	0.794218	+	0.607632i	$0.207881\pi$
$62$	4.07446	−	8.92182i	0.517457	−	1.13307i
$63$	−3.31843	−	2.13263i	−0.418083	−	0.268686i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	1.77618	−	1.14148i	0.220308	−	0.141584i
$66$	2.76729	+	3.19362i	0.340630	+	0.393108i
$67$	0.480031	−	0.140950i	0.0586451	−	0.0172198i	−0.252278	−	0.967655i	$-0.581180\pi$
$67$	0.480031	−	0.140950i	0.0586451	−	0.0172198i	0.310924	+	0.950435i	$0.399362\pi$
$68$	2.87333			0.348442
$69$	2.31304	−	4.20117i	0.278458	−	0.505761i
$70$	3.94463			0.471473
$71$	−10.2180	+	3.00027i	−1.21265	+	0.356067i	−0.824678	−	0.565603i	$-0.808644\pi$
$71$	−10.2180	+	3.00027i	−1.21265	+	0.356067i	−0.387975	+	0.921670i	$0.626825\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	3.02217	−	1.94223i	0.353718	−	0.227321i	−0.351699	−	0.936113i	$-0.614396\pi$
$73$	3.02217	−	1.94223i	0.353718	−	0.227321i	0.705417	+	0.708792i	$0.250760\pi$
$74$	0.362134	+	2.51870i	0.0420972	+	0.292793i
$75$	−0.841254	−	0.540641i	−0.0971396	−	0.0624278i
$76$	−1.09005	+	2.38689i	−0.125038	+	0.273795i
$77$	−10.9159	+	12.5977i	−1.24399	+	1.43564i
$78$	−0.300477	+	2.08986i	−0.0340223	+	0.236630i
$79$	1.98127	+	4.33837i	0.222910	+	0.488104i	0.987736	−	0.156132i	$-0.0499026\pi$
$79$	1.98127	+	4.33837i	0.222910	+	0.488104i	−0.764826	+	0.644236i	$0.777175\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−1.49745	−	3.27897i	−0.165366	−	0.362101i
$83$	2.12692	−	14.7930i	0.233459	−	1.62375i	−0.449494	−	0.893283i	$-0.648396\pi$
$83$	2.12692	−	14.7930i	0.233459	−	1.62375i	0.682954	−	0.730462i	$-0.260695\pi$
$84$	−2.58318	+	2.98115i	−0.281848	+	0.325270i
$85$	1.19362	−	2.61367i	0.129467	−	0.283492i
$86$	−10.5259	−	6.76456i	−1.13503	−	0.729441i
$87$	1.44641	+	10.0600i	0.155072	+	1.07855i
$88$	3.55494	−	2.28462i	0.378958	−	0.243542i
$89$	11.7645	+	13.5769i	1.24703	+	1.43915i	0.854532	+	0.519399i	$0.173844\pi$
$89$	11.7645	+	13.5769i	1.24703	+	1.43915i	0.392499	+	0.919752i	$0.371611\pi$
$90$	0.959493	−	0.281733i	0.101139	−	0.0296972i
$91$	−8.32850			−0.873064
$92$	−3.82923	−	2.88739i	−0.399225	−	0.301031i
$93$	9.80817			1.01706
$94$	−8.59171	+	2.52275i	−0.886167	+	0.260202i
$95$	1.71836	+	1.98310i	0.176300	+	0.203461i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−2.06884	−	14.3891i	−0.210059	−	1.46099i	−0.772953	−	0.634463i	$-0.781221\pi$
$97$	−2.06884	−	14.3891i	−0.210059	−	1.46099i	0.562894	−	0.826529i	$-0.309688\pi$
$98$	−7.20121	−	4.62793i	−0.727432	−	0.467492i
$99$	−1.75545	+	3.84389i	−0.176429	+	0.386326i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	1.29350	−	8.99650i	0.128708	−	0.895186i	−0.818486	−	0.574526i	$-0.805186\pi$
$101$	1.29350	−	8.99650i	0.128708	−	0.895186i	0.947195	−	0.320660i	$-0.103905\pi$
$102$	1.19362	+	2.61367i	0.118186	+	0.258792i
$103$	13.6593	+	4.01072i	1.34589	+	0.395188i	0.873767	−	0.486345i	$-0.161670\pi$
$103$	13.6593	+	4.01072i	1.34589	+	0.395188i	0.472121	+	0.881534i	$0.343488\pi$
$104$	2.02583	+	0.594837i	0.198649	+	0.0583285i
$105$	1.63866	+	3.58816i	0.159917	+	0.350169i
$106$	−1.39045	+	9.67078i	−0.135052	+	0.939309i
$107$	−6.91629	+	7.98182i	−0.668623	+	0.771632i	−0.984160	−	0.177281i	$-0.943270\pi$
$107$	−6.91629	+	7.98182i	−0.668623	+	0.771632i	0.315537	+	0.948913i	$0.397815\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	−12.3912	−	7.96332i	−1.18686	−	0.762748i	−0.210224	−	0.977653i	$-0.567419\pi$
$109$	−12.3912	−	7.96332i	−1.18686	−	0.762748i	−0.976635	+	0.214906i	$0.931056\pi$
$110$	−0.601389	−	4.18276i	−0.0573402	−	0.398810i
$111$	−2.14065	+	1.37571i	−0.203182	+	0.130577i
$112$	2.58318	+	2.98115i	0.244088	+	0.281692i
$113$	0.301614	−	0.0885619i	0.0283735	−	0.00833121i	−0.267515	−	0.963554i	$-0.586202\pi$
$113$	0.301614	−	0.0885619i	0.0283735	−	0.00833121i	0.295888	+	0.955222i	$0.404384\pi$
$114$	−2.62401			−0.245761
$115$	−4.21718	+	2.28372i	−0.393254	+	0.212958i
$116$	10.1635			0.943656
$117$	−2.02583	+	0.594837i	−0.187288	+	0.0549927i
$118$	−3.65659	−	4.21994i	−0.336617	−	0.388477i
$119$	−9.53494	+	6.12774i	−0.874067	+	0.561729i
$120$	−0.142315	−	0.989821i	−0.0129915	−	0.0903579i
$121$	5.76857	+	3.70724i	0.524416	+	0.337021i
$122$	0.395078	−	0.865101i	0.0357687	−	0.0783226i
$123$	2.36059	−	2.72426i	0.212847	−	0.245638i
$124$	1.39585	−	9.70834i	0.125351	−	0.871834i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	−3.78484	−	1.11133i	−0.337181	−	0.0990052i
$127$	−6.83559	−	2.00711i	−0.606560	−	0.178102i	−0.0359916	−	0.999352i	$-0.511459\pi$
$127$	−6.83559	−	2.00711i	−0.606560	−	0.178102i	−0.570569	+	0.821250i	$0.693277\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	1.78066	−	12.3848i	0.156778	−	1.09042i
$130$	1.38264	−	1.59565i	0.121266	−	0.139948i
$131$	9.10226	−	19.9312i	0.795268	−	1.74139i	0.134354	−	0.990933i	$-0.457104\pi$
$131$	9.10226	−	19.9312i	0.795268	−	1.74139i	0.660914	−	0.750462i	$-0.270169\pi$
$132$	3.55494	+	2.28462i	0.309418	+	0.198851i
$133$	−1.47307	−	10.2454i	−0.127731	−	0.888389i
$134$	0.420876	−	0.270481i	0.0363582	−	0.0233660i
$135$	0.654861	+	0.755750i	0.0563614	+	0.0650446i
$136$	2.75694	−	0.809510i	0.236406	−	0.0694149i
$137$	0.664710			0.0567900			0.0283950	−	0.999597i	$-0.490960\pi$
$137$	0.664710			0.0567900			0.0283950	+	0.999597i	$0.490960\pi$
$138$	1.03574	−	4.68265i	0.0881682	−	0.398614i
$139$	−5.95709			−0.505274			−0.252637	−	0.967561i	$-0.581298\pi$
$139$	−5.95709			−0.505274			−0.252637	+	0.967561i	$0.581298\pi$
$140$	3.78484	−	1.11133i	0.319878	−	0.0939245i
$141$	−5.86390	−	6.76730i	−0.493830	−	0.569910i
$142$	−8.95882	+	5.75748i	−0.751808	+	0.483157i
$143$	1.26975	+	8.83127i	0.106181	+	0.738508i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	4.22206	−	9.24503i	0.350623	−	0.767758i
$146$	2.35256	−	2.71500i	0.194699	−	0.224695i
$147$	1.21823	−	8.47296i	0.100478	−	0.698838i
$148$	1.05706	+	2.31465i	0.0868902	+	0.190263i
$149$	7.06196	+	2.07358i	0.578539	+	0.169874i	0.557893	−	0.829913i	$-0.311610\pi$
$149$	7.06196	+	2.07358i	0.578539	+	0.169874i	0.0206452	+	0.999787i	$0.493428\pi$
$150$	−0.959493	−	0.281733i	−0.0783423	−	0.0230034i
$151$	−5.93948	−	13.0057i	−0.483348	−	1.05838i	−0.981529	−	0.191312i	$-0.938726\pi$
$151$	−5.93948	−	13.0057i	−0.483348	−	1.05838i	0.498181	−	0.867073i	$-0.334001\pi$
$152$	−0.373436	+	2.59730i	−0.0302897	+	0.210669i
$153$	−1.88163	+	2.17152i	−0.152121	+	0.175557i
$154$	−6.92459	+	15.1627i	−0.557999	+	1.22185i
$155$	−8.25116	−	5.30270i	−0.662749	−	0.425923i
$156$	0.300477	+	2.08986i	0.0240574	+	0.167323i
$157$	−18.3488	+	11.7921i	−1.46440	+	0.941111i	−0.465984	+	0.884793i	$0.654299\pi$
$157$	−18.3488	+	11.7921i	−1.46440	+	0.941111i	−0.998413	+	0.0563172i	$0.982064\pi$
$158$	3.12327	+	3.60444i	0.248474	+	0.286754i
$159$	−9.37446	+	2.75259i	−0.743443	+	0.218295i
$160$	−1.00000			−0.0790569
$161$	18.8648	+	1.41529i	1.48675	+	0.111540i
$162$	−1.00000			−0.0785674
$163$	7.88312	−	2.31469i	0.617453	−	0.181301i	0.0419764	−	0.999119i	$-0.486635\pi$
$163$	7.88312	−	2.31469i	0.617453	−	0.181301i	0.575477	+	0.817818i	$0.304816\pi$
$164$	−2.36059	−	2.72426i	−0.184331	−	0.212729i
$165$	3.55494	−	2.28462i	0.276752	−	0.177858i
$166$	−2.12692	−	14.7930i	−0.165081	−	1.14816i
$167$	4.66082	+	2.99533i	0.360665	+	0.231785i	0.708406	−	0.705805i	$-0.249415\pi$
$167$	4.66082	+	2.99533i	0.360665	+	0.231785i	−0.347741	+	0.937591i	$0.613051\pi$
$168$	−1.63866	+	3.58816i	−0.126425	+	0.276833i
$169$	5.59395	−	6.45576i	0.430304	−	0.496597i
$170$	0.408917	−	2.84408i	0.0313625	−	0.218131i
$171$	−1.09005	−	2.38689i	−0.0833586	−	0.182530i
$172$	−12.0053	−	3.52507i	−0.915394	−	0.268784i
$173$	0.0473351	+	0.0138988i	0.00359882	+	0.00105671i	0.283531	−	0.958963i	$-0.408494\pi$
$173$	0.0473351	+	0.0138988i	0.00359882	+	0.00105671i	−0.279933	+	0.960020i	$0.590312\pi$
$174$	4.22206	+	9.24503i	0.320074	+	0.700864i
$175$	0.561379	−	3.90448i	0.0424363	−	0.295151i
$176$	2.76729	−	3.19362i	0.208592	−	0.240728i
$177$	2.31958	−	5.07918i	0.174351	−	0.381775i
$178$	15.1130	+	9.71253i	1.13277	+	0.727985i
$179$	1.05143	+	7.31283i	0.0785873	+	0.546587i	0.990639	+	0.136511i	$0.0435888\pi$
$179$	1.05143	+	7.31283i	0.0785873	+	0.546587i	−0.912051	+	0.410076i	$0.865502\pi$
$180$	0.841254	−	0.540641i	0.0627033	−	0.0402970i
$181$	−6.58854	−	7.60358i	−0.489723	−	0.565170i	0.456069	−	0.889944i	$-0.349257\pi$
$181$	−6.58854	−	7.60358i	−0.489723	−	0.565170i	−0.945791	+	0.324774i	$0.894712\pi$
$182$	−7.99114	+	2.34641i	−0.592342	+	0.173927i
$183$	0.951045			0.0703033
$184$	−4.48759	−	1.69161i	−0.330829	−	0.124707i
$185$	2.54460			0.187083
$186$	9.41087	−	2.76328i	0.690038	−	0.202614i
$187$	7.95133	+	9.17633i	0.581459	+	0.671039i
$188$	−7.53294	+	4.84113i	−0.549396	+	0.353076i
$189$	−0.561379	−	3.90448i	−0.0408343	−	0.284009i
$190$	2.20746	+	1.41865i	0.160146	+	0.102920i
$191$	−4.47057	+	9.78919i	−0.323479	+	0.708321i	−0.999595	−	0.0284750i	$-0.990935\pi$
$191$	−4.47057	+	9.78919i	−0.323479	+	0.708321i	0.676115	+	0.736796i	$0.263662\pi$
$192$	0.654861	−	0.755750i	0.0472605	−	0.0545415i
$193$	1.84276	−	12.8167i	0.132645	−	0.922566i	−0.809442	−	0.587199i	$-0.800231\pi$
$193$	1.84276	−	12.8167i	0.132645	−	0.922566i	0.942087	−	0.335367i	$-0.108860\pi$
$194$	−6.03892	−	13.2234i	−0.433569	−	0.949384i
$195$	2.02583	+	0.594837i	0.145073	+	0.0425971i
$196$	−8.21335	−	2.41166i	−0.586668	−	0.172261i
$197$	5.40173	+	11.8281i	0.384857	+	0.842719i	0.998584	+	0.0532009i	$0.0169424\pi$
$197$	5.40173	+	11.8281i	0.384857	+	0.842719i	−0.613727	+	0.789518i	$0.710330\pi$
$198$	−0.601389	+	4.18276i	−0.0427389	+	0.297256i
$199$	−2.01292	+	2.32303i	−0.142692	+	0.164675i	−0.822597	−	0.568625i	$-0.807476\pi$
$199$	−2.01292	+	2.32303i	−0.142692	+	0.164675i	0.679905	+	0.733300i	$0.262021\pi$
$200$	−0.415415	+	0.909632i	−0.0293743	+	0.0643207i
$201$	0.420876	+	0.270481i	0.0296863	+	0.0190782i
$202$	−1.29350	−	8.99650i	−0.0910105	−	0.632992i
$203$	−33.7268	+	21.6749i	−2.36716	+	1.52128i
$204$	1.88163	+	2.17152i	0.131740	+	0.152037i
$205$	−3.45870	+	1.01557i	−0.241566	+	0.0709302i
$206$	14.2359			0.991864
$207$	4.68975	−	1.00310i	0.325960	−	0.0697203i
$208$	2.11135			0.146396
$209$	−10.6393	+	3.12398i	−0.735937	+	0.216090i
$210$	2.58318	+	2.98115i	0.178256	+	0.205719i
$211$	8.55189	−	5.49596i	0.588736	−	0.378358i	−0.212094	−	0.977249i	$-0.568028\pi$
$211$	8.55189	−	5.49596i	0.588736	−	0.378358i	0.800830	+	0.598891i	$0.204392\pi$
$212$	1.39045	+	9.67078i	0.0954964	+	0.664192i
$213$	−8.95882	−	5.75748i	−0.613848	−	0.394496i
$214$	−4.38739	+	9.60705i	−0.299916	+	0.656724i
$215$	−8.19369	+	9.45602i	−0.558805	+	0.644895i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	16.0722	+	35.1933i	1.09105	+	2.38908i
$218$	−14.1328	−	4.14975i	−0.957192	−	0.281057i
$219$	3.44694	+	1.01211i	0.232922	+	0.0683922i
$220$	−1.75545	−	3.84389i	−0.118352	−	0.259155i
$221$	−0.863368	+	6.00486i	−0.0580764	+	0.403931i
$222$	−1.66636	+	1.92308i	−0.111839	+	0.129069i
$223$	−0.599509	+	1.31274i	−0.0401461	+	0.0879077i	−0.928642	−	0.370976i	$-0.879023\pi$
$223$	−0.599509	+	1.31274i	−0.0401461	+	0.0879077i	0.888496	+	0.458884i	$0.151751\pi$
$224$	3.31843	+	2.13263i	0.221722	+	0.142492i
$225$	−0.142315	−	0.989821i	−0.00948766	−	0.0659881i
$226$	0.264446	−	0.169949i	0.0175907	−	0.0113048i
$227$	7.50489	+	8.66111i	0.498117	+	0.574858i	0.948016	−	0.318221i	$-0.103086\pi$
$227$	7.50489	+	8.66111i	0.498117	+	0.574858i	−0.449899	+	0.893079i	$0.648540\pi$
$228$	−2.51772	+	0.739270i	−0.166740	+	0.0489594i
$229$	−9.49191			−0.627243			−0.313622	−	0.949548i	$-0.601542\pi$
$229$	−9.49191			−0.627243			−0.313622	+	0.949548i	$0.601542\pi$
$230$	−3.40295	+	3.37933i	−0.224384	+	0.222827i
$231$	−16.6691			−1.09675
$232$	9.75179	−	2.86339i	0.640237	−	0.187990i
$233$	−11.1896	−	12.9134i	−0.733052	−	0.845987i	0.259760	−	0.965673i	$-0.416357\pi$
$233$	−11.1896	−	12.9134i	−0.733052	−	0.845987i	−0.992812	+	0.119686i	$0.961811\pi$
$234$	−1.77618	+	1.14148i	−0.116113	+	0.0746211i
$235$	1.27435	+	8.86328i	0.0831293	+	0.578177i
$236$	−4.69737	−	3.01882i	−0.305773	−	0.196508i
$237$	−1.98127	+	4.33837i	−0.128697	+	0.281807i
$238$	−7.42233	+	8.56583i	−0.481118	+	0.555240i
$239$	1.14518	−	7.96488i	0.0740753	−	0.515205i	−0.918675	−	0.395013i	$-0.870740\pi$
$239$	1.14518	−	7.96488i	0.0740753	−	0.515205i	0.992751	−	0.120192i	$-0.0383510\pi$
$240$	−0.415415	−	0.909632i	−0.0268149	−	0.0587165i
$241$	2.58153	+	0.758004i	0.166291	+	0.0488273i	0.363818	−	0.931470i	$-0.381473\pi$
$241$	2.58153	+	0.758004i	0.166291	+	0.0488273i	−0.197527	+	0.980297i	$0.563291\pi$
$242$	6.57935	+	1.93187i	0.422937	+	0.124185i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	0.135348	−	0.941365i	0.00866476	−	0.0602647i
$245$	−5.60567	+	6.46928i	−0.358133	+	0.413307i
$246$	1.49745	−	3.27897i	0.0954741	−	0.209059i
$247$	−4.66073	−	2.99527i	−0.296555	−	0.190584i
$248$	−1.39585	−	9.70834i	−0.0886364	−	0.616480i
$249$	12.5727	−	8.07995i	0.796759	−	0.512046i
$250$	0.654861	+	0.755750i	0.0414170	+	0.0477978i
$251$	19.6013	−	5.75545i	1.23722	−	0.363281i	0.403250	−	0.915090i	$-0.367880\pi$
$251$	19.6013	−	5.75545i	1.23722	−	0.363281i	0.833970	+	0.551809i	$0.186062\pi$
$252$	−3.94463			−0.248488
$253$	−1.37536	−	20.2193i	−0.0864679	−	1.27118i
$254$	−7.12417			−0.447010
$255$	2.75694	−	0.809510i	0.172646	−	0.0506935i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	18.5448	−	11.9180i	1.15679	−	0.743426i	0.185812	−	0.982585i	$-0.440508\pi$
$257$	18.5448	−	11.9180i	1.15679	−	0.743426i	0.970980	+	0.239160i	$0.0768719\pi$
$258$	−1.78066	−	12.3848i	−0.110859	−	0.771041i
$259$	−8.44408	−	5.42668i	−0.524690	−	0.337197i
$260$	0.877087	−	1.92055i	0.0543947	−	0.119108i
$261$	−6.65567	+	7.68105i	−0.411976	+	0.475445i
$262$	3.11830	−	21.6882i	0.192649	−	1.33990i
$263$	10.4078	+	22.7900i	0.641774	+	1.40529i	0.898573	+	0.438825i	$0.144605\pi$
$263$	10.4078	+	22.7900i	0.641774	+	1.40529i	−0.256798	+	0.966465i	$0.582668\pi$
$264$	4.05459	+	1.19054i	0.249543	+	0.0732724i
$265$	9.37446	+	2.75259i	0.575869	+	0.169090i
$266$	−4.29986	−	9.41538i	−0.263641	−	0.577294i
$267$	−2.55666	+	17.7820i	−0.156465	+	1.08824i
$268$	0.327625	−	0.378099i	0.0200129	−	0.0230961i
$269$	2.46059	−	5.38794i	0.150025	−	0.328509i	−0.819667	−	0.572841i	$-0.805841\pi$
$269$	2.46059	−	5.38794i	0.150025	−	0.328509i	0.969692	+	0.244332i	$0.0785686\pi$
$270$	0.841254	+	0.540641i	0.0511971	+	0.0329024i
$271$	−0.411607	−	2.86279i	−0.0250033	−	0.173902i	0.973493	−	0.228716i	$-0.0734526\pi$
$271$	−0.411607	−	2.86279i	−0.0250033	−	0.173902i	−0.998497	+	0.0548137i	$0.982543\pi$
$272$	2.41720	−	1.55344i	0.146564	−	0.0941910i
$273$	−5.45401	−	6.29426i	−0.330092	−	0.380946i
$274$	0.637785	−	0.187270i	0.0385300	−	0.0113134i
$275$	−4.22577			−0.254823
$276$	−0.325469	−	4.78477i	−0.0195909	−	0.288010i
$277$	4.95969			0.297999			0.148999	−	0.988837i	$-0.452395\pi$
$277$	4.95969			0.297999			0.148999	+	0.988837i	$0.452395\pi$
$278$	−5.71579	+	1.67831i	−0.342810	+	0.100658i
$279$	6.42298	+	7.41252i	0.384534	+	0.443776i
$280$	3.31843	−	2.13263i	0.198314	−	0.127449i
$281$	2.63918	+	18.3559i	0.157440	+	1.09502i	0.903329	+	0.428949i	$0.141116\pi$
$281$	2.63918	+	18.3559i	0.157440	+	1.09502i	−0.745889	+	0.666071i	$0.767975\pi$
$282$	−7.53294	−	4.84113i	−0.448580	−	0.288285i
$283$	6.09788	−	13.3525i	0.362482	−	0.793724i	−0.637252	−	0.770655i	$-0.719929\pi$
$283$	6.09788	−	13.3525i	0.362482	−	0.793724i	0.999734	−	0.0230687i	$-0.00734365\pi$
$284$	−6.97385	+	8.04826i	−0.413822	+	0.477576i
$285$	−0.373436	+	2.59730i	−0.0221204	+	0.153851i
$286$	3.70637	+	8.11581i	0.219162	+	0.479898i
$287$	13.6433	+	4.00603i	0.805338	+	0.236468i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−3.63238	−	7.95381i	−0.213670	−	0.467871i
$290$	1.44641	−	10.0600i	0.0849364	−	0.590746i
$291$	9.51976	−	10.9864i	0.558058	−	0.644033i
$292$	1.49236	−	3.26781i	0.0873337	−	0.191234i
$293$	7.89628	+	5.07463i	0.461305	+	0.296463i	0.750576	−	0.660784i	$-0.229776\pi$
$293$	7.89628	+	5.07463i	0.461305	+	0.296463i	−0.289270	+	0.957247i	$0.593413\pi$
$294$	−1.21823	−	8.47296i	−0.0710485	−	0.494153i
$295$	−4.69737	+	3.01882i	−0.273491	+	0.175762i
$296$	1.66636	+	1.92308i	0.0968551	+	0.111777i
$297$	−4.05459	+	1.19054i	−0.235271	+	0.0690819i
$298$	7.36010			0.426359
$299$	7.18484	−	7.13496i	0.415510	−	0.412626i
$300$	−1.00000			−0.0577350
$301$	47.3564	−	13.9051i	2.72957	−	0.801475i
$302$	−9.36301	−	10.8055i	−0.538780	−	0.621786i
$303$	7.64617	−	4.91389i	0.439261	−	0.282296i
$304$	0.373436	+	2.59730i	0.0214180	+	0.148966i
$305$	−0.800070	−	0.514174i	−0.0458119	−	0.0294415i
$306$	−1.19362	+	2.61367i	−0.0682349	+	0.149414i
$307$	−13.0401	+	15.0490i	−0.744235	+	0.858893i	−0.993996	−	0.109414i	$-0.965102\pi$
$307$	−13.0401	+	15.0490i	−0.744235	+	0.858893i	0.249761	+	0.968307i	$0.419648\pi$
$308$	−2.37226	+	16.4994i	−0.135172	+	0.940141i
$309$	5.91382	+	12.9495i	0.336425	+	0.736669i
$310$	−9.41087	−	2.76328i	−0.534501	−	0.156944i
$311$	−6.52065	−	1.91463i	−0.369752	−	0.108569i	0.0915774	−	0.995798i	$-0.470809\pi$
$311$	−6.52065	−	1.91463i	−0.369752	−	0.108569i	−0.461329	+	0.887229i	$0.652627\pi$
$312$	0.877087	+	1.92055i	0.0496553	+	0.108730i
$313$	−3.00769	+	20.9190i	−0.170005	+	1.18241i	0.708864	+	0.705345i	$0.249208\pi$
$313$	−3.00769	+	20.9190i	−0.170005	+	1.18241i	−0.878869	+	0.477064i	$0.841701\pi$
$314$	−14.2834	+	16.4839i	−0.806057	+	0.930239i
$315$	−1.63866	+	3.58816i	−0.0923279	+	0.202170i
$316$	4.01224	+	2.57851i	0.225706	+	0.145053i
$317$	1.16453	+	8.09950i	0.0654067	+	0.454913i	0.996036	+	0.0889504i	$0.0283513\pi$
$317$	1.16453	+	8.09950i	0.0654067	+	0.454913i	−0.930629	+	0.365963i	$0.880740\pi$
$318$	−8.21924	+	5.28218i	−0.460912	+	0.296210i
$319$	28.1253	+	32.4583i	1.57471	+	1.81732i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	−10.5615			−0.589484
$322$	18.4993	−	3.95686i	1.03093	−	0.220507i
$323$	−7.53965			−0.419517
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−1.38264	−	1.59565i	−0.0766952	−	0.0885109i
$326$	6.91167	−	4.44186i	0.382802	−	0.246012i
$327$	−2.09621	−	14.5795i	−0.115921	−	0.806247i
$328$	−3.03248	−	1.94886i	−0.167441	−	0.107608i
$329$	14.6732	−	32.1299i	0.808962	−	1.77138i
$330$	2.76729	−	3.19362i	0.152334	−	0.175803i
$331$	−1.64970	+	11.4739i	−0.0906756	+	0.630663i	0.892912	+	0.450231i	$0.148658\pi$
$331$	−1.64970	+	11.4739i	−0.0906756	+	0.630663i	−0.983588	+	0.180431i	$0.942251\pi$
$332$	−6.20844	−	13.5946i	−0.340732	−	0.746099i
$333$	−2.44152	−	0.716896i	−0.133795	−	0.0392857i
$334$	5.31590	+	1.56089i	0.290873	+	0.0854081i
$335$	−0.207831	−	0.455086i	−0.0113550	−	0.0248640i
$336$	−0.561379	+	3.90448i	−0.0306257	+	0.213007i
$337$	−1.41401	+	1.63185i	−0.0770258	+	0.0888926i	−0.792954	−	0.609281i	$-0.791458\pi$
$337$	−1.41401	+	1.63185i	−0.0770258	+	0.0888926i	0.715929	+	0.698174i	$0.246004\pi$
$338$	3.54855	−	7.77025i	0.193016	−	0.422646i
$339$	0.264446	+	0.169949i	0.0143627	+	0.00923037i
$340$	−0.408917	−	2.84408i	−0.0221767	−	0.154242i
$341$	34.8675	−	22.4080i	1.88818	−	1.21346i
$342$	−1.71836	−	1.98310i	−0.0929185	−	0.107234i
$343$	5.90469	−	1.73377i	0.318823	−	0.0936150i
$344$	−12.5121			−0.674608
$345$	−4.48759	−	1.69161i	−0.241604	−	0.0910732i
$346$	0.0493334			0.00265218
$347$	14.9894	−	4.40129i	0.804674	−	0.236274i	0.146570	−	0.989200i	$-0.453177\pi$
$347$	14.9894	−	4.40129i	0.804674	−	0.236274i	0.658104	+	0.752927i	$0.271359\pi$
$348$	6.65567	+	7.68105i	0.356781	+	0.411748i
$349$	19.4302	−	12.4870i	1.04007	−	0.668415i	0.0950684	−	0.995471i	$-0.469693\pi$
$349$	19.4302	−	12.4870i	1.04007	−	0.668415i	0.945005	+	0.327056i	$0.106057\pi$
$350$	−0.561379	−	3.90448i	−0.0300070	−	0.208703i
$351$	−1.77618	−	1.14148i	−0.0948056	−	0.0609279i
$352$	1.75545	−	3.84389i	0.0935657	−	0.204880i
$353$	−9.43522	+	10.8888i	−0.502186	+	0.579554i	−0.949081	−	0.315033i	$-0.897984\pi$
$353$	−9.43522	+	10.8888i	−0.502186	+	0.579554i	0.446895	+	0.894587i	$0.352530\pi$
$354$	0.794654	−	5.52694i	0.0422354	−	0.293754i
$355$	4.42391	+	9.68701i	0.234797	+	0.514133i
$356$	17.2371	+	5.06128i	0.913567	+	0.268247i
$357$	−10.8751	−	3.19322i	−0.575571	−	0.169003i
$358$	3.06910	+	6.72039i	0.162207	+	0.355184i
$359$	2.94840	−	20.5065i	0.155610	−	1.08229i	−0.750993	−	0.660310i	$-0.770425\pi$
$359$	2.94840	−	20.5065i	0.155610	−	1.08229i	0.906603	−	0.421984i	$-0.138666\pi$
$360$	0.654861	−	0.755750i	0.0345142	−	0.0398315i
$361$	−5.03257	+	11.0198i	−0.264872	+	0.579989i
$362$	−8.46384	−	5.43938i	−0.444849	−	0.285887i
$363$	0.975869	+	6.78732i	0.0512198	+	0.356242i
$364$	−7.00638	+	4.50273i	−0.367234	+	0.236007i
$365$	−2.35256	−	2.71500i	−0.123138	−	0.142109i
$366$	0.912521	−	0.267940i	0.0476982	−	0.0140055i
$367$	−32.8148			−1.71292			−0.856460	−	0.516214i	$-0.827341\pi$
$367$	−32.8148			−1.71292			−0.856460	+	0.516214i	$0.827341\pi$
$368$	−4.78239	−	0.358788i	−0.249299	−	0.0187031i
$369$	3.60472			0.187654
$370$	2.44152	−	0.716896i	0.126929	−	0.0372697i
$371$	−25.2383	−	29.1265i	−1.31031	−	1.51217i
$372$	8.25116	−	5.30270i	0.427803	−	0.274932i
$373$	1.99032	+	13.8430i	0.103055	+	0.716761i	0.974192	+	0.225722i	$0.0724740\pi$
$373$	1.99032	+	13.8430i	0.103055	+	0.716761i	−0.871137	+	0.491040i	$0.836617\pi$
$374$	10.2145	+	6.56447i	0.528180	+	0.339441i
$375$	−0.415415	+	0.909632i	−0.0214519	+	0.0469732i
$376$	−5.86390	+	6.76730i	−0.302408	+	0.348997i
$377$	−3.05389	+	21.2403i	−0.157283	+	1.09393i
$378$	−1.63866	−	3.58816i	−0.0842835	−	0.184555i
$379$	−25.1882	−	7.39593i	−1.29383	−	0.379903i	−0.438850	−	0.898561i	$-0.644614\pi$
$379$	−25.1882	−	7.39593i	−1.29383	−	0.379903i	−0.854982	+	0.518657i	$0.826432\pi$
$380$	2.51772	+	0.739270i	0.129156	+	0.0379238i
$381$	−2.95949	−	6.48037i	−0.151619	−	0.331999i
$382$	−1.53155	+	10.6522i	−0.0783609	+	0.545012i
$383$	−20.4493	+	23.5997i	−1.04491	+	1.20589i	−0.0668081	+	0.997766i	$0.521282\pi$
$383$	−20.4493	+	23.5997i	−1.04491	+	1.20589i	−0.978102	+	0.208125i	$0.933264\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	14.0229	+	9.01199i	0.714674	+	0.459293i
$386$	−1.84276	−	12.8167i	−0.0937942	−	0.652353i
$387$	10.5259	−	6.76456i	0.535059	−	0.343862i
$388$	−9.51976	−	10.9864i	−0.483293	−	0.557749i
$389$	−3.67773	+	1.07988i	−0.186468	+	0.0547521i	−0.373634	−	0.927576i	$-0.621888\pi$
$389$	−3.67773	+	1.07988i	−0.186468	+	0.0547521i	0.187165	+	0.982328i	$0.440070\pi$
$390$	2.11135			0.106912
$391$	2.97603	−	13.4548i	0.150504	−	0.680438i
$392$	−8.56009			−0.432350
$393$	21.0237	−	6.17311i	1.06051	−	0.311392i
$394$	8.51529	+	9.82717i	0.428994	+	0.495085i
$395$	4.01224	−	2.57851i	0.201878	−	0.129739i
$396$	0.601389	+	4.18276i	0.0302210	+	0.210191i
$397$	31.0531	+	19.9566i	1.55851	+	1.00159i	0.982958	+	0.183831i	$0.0588500\pi$
$397$	31.0531	+	19.9566i	1.55851	+	1.00159i	0.575554	+	0.817764i	$0.304786\pi$
$398$	−1.27691	+	2.79604i	−0.0640055	+	0.140153i
$399$	6.77830	−	7.82258i	0.339340	−	0.391619i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	8.03120	+	17.5859i	0.401059	+	0.878197i	0.997162	+	0.0752886i	$0.0239878\pi$
$401$	8.03120	+	17.5859i	0.401059	+	0.878197i	−0.596103	+	0.802908i	$0.703285\pi$
$402$	0.480031	+	0.140950i	0.0239418	+	0.00702994i
$403$	19.8697	+	5.83426i	0.989778	+	0.290625i
$404$	−3.77571	−	8.26766i	−0.187849	−	0.411332i
$405$	−0.142315	+	0.989821i	−0.00707168	+	0.0491846i
$406$	−26.2541	+	30.2989i	−1.30297	+	1.50371i
$407$	−4.46691	+	9.78117i	−0.221416	+	0.484834i
$408$	2.41720	+	1.55344i	0.119669	+	0.0769067i
$409$	−0.731145	−	5.08522i	−0.0361528	−	0.251448i	0.963728	−	0.266886i	$-0.0859948\pi$
$409$	−0.731145	−	5.08522i	−0.0361528	−	0.251448i	−0.999881	+	0.0154381i	$0.995086\pi$
$410$	−3.03248	+	1.94886i	−0.149764	+	0.0962472i
$411$	0.435293	+	0.502354i	0.0214714	+	0.0247793i
$412$	13.6593	−	4.01072i	0.672944	−	0.197594i
$413$	22.0259			1.08382
$414$	4.21718	−	2.28372i	0.207263	−	0.112239i
$415$	−14.9451			−0.733628
$416$	2.02583	−	0.594837i	0.0993244	−	0.0291643i
$417$	−3.90106	−	4.50207i	−0.191036	−	0.220467i
$418$	−9.32822	+	5.99488i	−0.456258	+	0.293219i
$419$	−4.04776	−	28.1528i	−0.197746	−	1.37535i	−0.810804	−	0.585317i	$-0.800970\pi$
$419$	−4.04776	−	28.1528i	−0.197746	−	1.37535i	0.613058	−	0.790038i	$-0.289939\pi$
$420$	3.31843	+	2.13263i	0.161923	+	0.104062i
$421$	−6.72160	+	14.7183i	−0.327591	+	0.717324i	−0.999733	−	0.0230980i	$-0.992647\pi$
$421$	−6.72160	+	14.7183i	−0.327591	+	0.717324i	0.672142	+	0.740422i	$0.265374\pi$
$422$	6.65708	−	7.68268i	0.324062	−	0.373987i
$423$	1.27435	−	8.86328i	0.0619609	−	0.430948i
$424$	4.05870	+	8.88731i	0.197108	+	0.431606i
$425$	−2.75694	−	0.809510i	−0.133731	−	0.0392670i
$426$	−10.2180	−	3.00027i	−0.495064	−	0.145364i
$427$	1.55844	+	3.41250i	0.0754181	+	0.165143i
$428$	−1.50305	+	10.4540i	−0.0726528	+	0.505311i
$429$	−5.84272	+	6.74286i	−0.282089	+	0.325548i
$430$	−5.19772	+	11.3814i	−0.250656	+	0.548860i
$431$	12.9932	+	8.35025i	0.625863	+	0.402218i	0.814776	−	0.579776i	$-0.196860\pi$
$431$	12.9932	+	8.35025i	0.625863	+	0.402218i	−0.188913	+	0.981994i	$0.560496\pi$
$432$	0.142315	+	0.989821i	0.00684713	+	0.0476228i
$433$	−9.80247	+	6.29967i	−0.471077	+	0.302743i	−0.754556	−	0.656236i	$-0.772148\pi$
$433$	−9.80247	+	6.29967i	−0.471077	+	0.302743i	0.283479	+	0.958978i	$0.408511\pi$
$434$	25.3363	+	29.2396i	1.21618	+	1.40355i
$435$	9.75179	−	2.86339i	0.467563	−	0.137289i
$436$	−14.7294			−0.705411
$437$	10.0479	+	7.57655i	0.480658	+	0.362435i
$438$	3.59245			0.171654
$439$	−32.1036	+	9.42646i	−1.53222	+	0.449901i	−0.935729	−	0.352719i	$-0.885257\pi$
$439$	−32.1036	+	9.42646i	−1.53222	+	0.449901i	−0.596491	+	0.802620i	$0.703439\pi$
$440$	−2.76729	−	3.19362i	−0.131925	−	0.152250i
$441$	7.20121	−	4.62793i	0.342915	−	0.220378i
$442$	0.863368	+	6.00486i	0.0410662	+	0.285622i
$443$	3.29968	+	2.12058i	0.156773	+	0.100752i	0.616675	−	0.787218i	$-0.288479\pi$
$443$	3.29968	+	2.12058i	0.156773	+	0.100752i	−0.459902	+	0.887969i	$0.652116\pi$
$444$	−1.05706	+	2.31465i	−0.0501661	+	0.109848i
$445$	11.7645	−	13.5769i	0.557689	−	0.643608i
$446$	−0.205383	+	1.42847i	−0.00972515	+	0.0676399i
$447$	3.05750	+	6.69498i	0.144615	+	0.316662i
$448$	3.78484	+	1.11133i	0.178817	+	0.0525054i
$449$	27.9669	+	8.21183i	1.31984	+	0.387540i	0.864436	−	0.502744i	$-0.167676\pi$
$449$	27.9669	+	8.21183i	1.31984	+	0.387540i	0.455406	+	0.890284i	$0.349494\pi$
$450$	−0.415415	−	0.909632i	−0.0195829	−	0.0428805i
$451$	2.16784	−	15.0776i	0.102080	−	0.709979i
$452$	0.205854	−	0.237568i	0.00968255	−	0.0111743i
$453$	5.93948	−	13.0057i	0.279061	−	0.611059i
$454$	9.64101	+	6.19590i	0.452475	+	0.290788i
$455$	1.18527	+	8.24373i	0.0555663	+	0.386472i
$456$	−2.20746	+	1.41865i	−0.103374	+	0.0664343i
$457$	−2.32594	−	2.68427i	−0.108803	−	0.125565i	0.698736	−	0.715380i	$-0.253746\pi$
$457$	−2.32594	−	2.68427i	−0.108803	−	0.125565i	−0.807539	+	0.589815i	$0.799201\pi$
$458$	−9.10742	+	2.67418i	−0.425562	+	0.124956i
$459$	−2.87333			−0.134115
$460$	−2.31304	+	4.20117i	−0.107846	+	0.195881i
$461$	8.15995			0.380047			0.190023	−	0.981780i	$-0.439144\pi$
$461$	8.15995			0.380047			0.190023	+	0.981780i	$0.439144\pi$
$462$	−15.9939	+	4.69622i	−0.744102	+	0.218488i
$463$	12.6213	+	14.5657i	0.586560	+	0.676927i	0.969002	−	0.247053i	$-0.0794622\pi$
$463$	12.6213	+	14.5657i	0.586560	+	0.676927i	−0.382442	+	0.923980i	$0.624917\pi$
$464$	8.55007	−	5.49480i	0.396927	−	0.255089i
$465$	−1.39585	−	9.70834i	−0.0647309	−	0.450213i
$466$	−14.3744	−	9.23788i	−0.665883	−	0.427937i
$467$	9.67364	−	21.1823i	0.447643	−	0.980201i	−0.542489	−	0.840063i	$-0.682518\pi$
$467$	9.67364	−	21.1823i	0.447643	−	0.980201i	0.990132	−	0.140138i	$-0.0447546\pi$
$468$	−1.38264	+	1.59565i	−0.0639126	+	0.0737591i
$469$	−0.280856	+	1.95340i	−0.0129687	+	0.0901995i
$470$	3.71980	+	8.14523i	0.171582	+	0.375712i
$471$	−20.9278	−	6.14495i	−0.964302	−	0.283145i
$472$	−5.35759	−	1.57313i	−0.246603	−	0.0724092i
$473$	−21.9643	−	48.0952i	−1.00992	−	2.21142i
$474$	−0.678751	+	4.72082i	−0.0311761	+	0.216834i
$475$	1.71836	−	1.98310i	0.0788439	−	0.0909907i
$476$	−4.70840	+	10.3100i	−0.215809	+	0.472556i
$477$	−8.21924	−	5.28218i	−0.376333	−	0.241855i
$478$	−1.14518	−	7.96488i	−0.0523792	−	0.364305i
$479$	−0.638272	+	0.410193i	−0.0291634	+	0.0187422i	−0.555141	−	0.831756i	$-0.687336\pi$
$479$	−0.638272	+	0.410193i	−0.0291634	+	0.0187422i	0.525978	+	0.850498i	$0.323699\pi$
$480$	−0.654861	−	0.755750i	−0.0298902	−	0.0344951i
$481$	−5.15492	+	1.51362i	−0.235044	+	0.0690152i
$482$	2.69051			0.122549
$483$	11.2842	+	15.1838i	0.513448	+	0.690889i
$484$	6.85711			0.311687
$485$	−13.9482	+	4.09557i	−0.633356	+	0.185970i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−22.0430	+	14.1662i	−0.998863	+	0.641931i	−0.934488	−	0.355995i	$-0.884142\pi$
$487$	−22.0430	+	14.1662i	−0.998863	+	0.641931i	−0.0643756	+	0.997926i	$0.520506\pi$
$488$	−0.135348	−	0.941365i	−0.00612691	−	0.0426136i
$489$	6.91167	+	4.44186i	0.312557	+	0.200868i
$490$	−3.55599	+	7.78653i	−0.160643	+	0.351760i
$491$	−23.1736	+	26.7438i	−1.04581	+	1.20693i	−0.0679464	+	0.997689i	$0.521645\pi$
$491$	−23.1736	+	26.7438i	−1.04581	+	1.20693i	−0.977864	+	0.209241i	$0.932901\pi$
$492$	0.513005	−	3.56803i	0.0231280	−	0.160859i
$493$	12.1314	+	26.5640i	0.546370	+	1.19638i
$494$	−5.31580	−	1.56086i	−0.239169	−	0.0702264i
$495$	4.05459	+	1.19054i	0.182240	+	0.0535106i
$496$	−4.07446	−	8.92182i	−0.182949	−	0.400602i
$497$	5.97833	−	41.5802i	0.268165	−	1.86513i
$498$	9.78699	−	11.2948i	0.438565	−	0.506131i
$499$	−4.62321	+	10.1234i	−0.206963	+	0.453187i	−0.984439	−	0.175726i	$-0.943773\pi$
$499$	−4.62321	+	10.1234i	−0.206963	+	0.453187i	0.777476	+	0.628913i	$0.216500\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	0.788471	+	5.48393i	0.0352263	+	0.245004i
$502$	17.1858	−	11.0446i	0.767039	−	0.492946i
$503$	−6.03847	−	6.96877i	−0.269242	−	0.310722i	0.604987	−	0.796235i	$-0.293178\pi$
$503$	−6.03847	−	6.96877i	−0.269242	−	0.310722i	−0.874229	+	0.485513i	$0.838633\pi$
$504$	−3.78484	+	1.11133i	−0.168590	+	0.0495026i
$505$	−9.08902			−0.404456
$506$	−7.01609	−	19.0128i	−0.311903	−	0.845224i
$507$	8.54219			0.379372
$508$	−6.83559	+	2.00711i	−0.303280	+	0.0890511i
$509$	17.7472	+	20.4813i	0.786630	+	0.907819i	0.997569	−	0.0696800i	$-0.0221978\pi$
$509$	17.7472	+	20.4813i	0.786630	+	0.907819i	−0.210940	+	0.977499i	$0.567652\pi$
$510$	2.41720	−	1.55344i	0.107035	−	0.0687874i
$511$	2.01673	+	14.0267i	0.0892148	+	0.620503i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	1.09005	−	2.38689i	0.0481271	−	0.105384i
$514$	14.4359	−	16.6599i	0.636741	−	0.734838i
$515$	2.02598	−	14.0910i	0.0892755	−	0.620925i
$516$	−5.19772	−	11.3814i	−0.228817	−	0.501039i
$517$	−36.3066	−	10.6606i	−1.59676	−	0.468851i
$518$	−9.63091	−	2.82789i	−0.423158	−	0.124250i
$519$	0.0204938	+	0.0448753i	0.000899580	+	0.00196981i
$520$	0.300477	−	2.08986i	0.0131768	−	0.0916465i
$521$	−7.08823	+	8.18026i	−0.310541	+	0.358384i	−0.889469	−	0.456995i	$-0.848926\pi$
$521$	−7.08823	+	8.18026i	−0.310541	+	0.358384i	0.578928	+	0.815379i	$0.303471\pi$
$522$	−4.22206	+	9.24503i	−0.184795	+	0.404644i
$523$	30.8308	+	19.8138i	1.34814	+	0.866396i	0.997538	−	0.0701297i	$-0.0223413\pi$
$523$	30.8308	+	19.8138i	1.34814	+	0.866396i	0.350600	+	0.936525i	$0.385978\pi$
$524$	−3.11830	−	21.6882i	−0.136223	−	0.947455i
$525$	3.31843	−	2.13263i	0.144828	−	0.0930755i
$526$	16.4069	+	18.9346i	0.715376	+	0.825587i
$527$	27.0405	−	7.93981i	1.17790	−	0.345864i
$528$	4.22577			0.183903
$529$	−17.4867	+	14.9404i	−0.760293	+	0.649581i
$530$	9.77023			0.424391
$531$	5.35759	−	1.57313i	0.232500	−	0.0682681i
$532$	−6.77830	−	7.82258i	−0.293877	−	0.339152i
$533$	6.40263	−	4.11472i	0.277329	−	0.178228i
$534$	2.55666	+	17.7820i	0.110638	+	0.769502i
$535$	8.88487	+	5.70996i	0.384126	+	0.246863i
$536$	0.207831	−	0.455086i	0.00897692	−	0.0196567i
$537$	−4.83813	+	5.58350i	−0.208781	+	0.240946i
$538$	0.842961	−	5.86292i	0.0363426	−	0.252769i
$539$	−15.0268	−	32.9041i	−0.647250	−	1.41728i
$540$	0.959493	+	0.281733i	0.0412900	+	0.0121238i
$541$	29.7206	+	8.72674i	1.27779	+	0.375192i	0.849086	−	0.528255i	$-0.177153\pi$
$541$	29.7206	+	8.72674i	1.27779	+	0.375192i	0.428701	+	0.903447i	$0.358972\pi$
$542$	−1.20147	−	2.63086i	−0.0516077	−	0.113005i
$543$	1.43183	−	9.95858i	0.0614456	−	0.427363i
$544$	1.88163	−	2.17152i	0.0806742	−	0.0931030i
$545$	−6.11882	+	13.3983i	−0.262101	+	0.573922i
$546$	−7.00638	−	4.50273i	−0.299845	−	0.192699i
$547$	−0.726474	−	5.05274i	−0.0310618	−	0.216039i	0.968379	−	0.249485i	$-0.0802612\pi$
$547$	−0.726474	−	5.05274i	−0.0310618	−	0.216039i	−0.999441	+	0.0334451i	$0.989352\pi$
$548$	0.559190	−	0.359369i	0.0238874	−	0.0153515i
$549$	0.622802	+	0.718752i	0.0265805	+	0.0306756i
$550$	−4.05459	+	1.19054i	−0.172888	+	0.0507646i
$551$	−26.6691			−1.13614
$552$	−1.66031	−	4.49926i	−0.0706676	−	0.191501i
$553$	−18.8134			−0.800026
$554$	4.75879	−	1.39731i	0.202181	−	0.0593658i
$555$	1.66636	+	1.92308i	0.0707330	+	0.0816302i
$556$	−5.01142	+	3.22065i	−0.212532	+	0.136586i
$557$	−4.71905	−	32.8217i	−0.199952	−	1.39070i	−0.804416	−	0.594067i	$-0.797522\pi$
$557$	−4.71905	−	32.8217i	−0.199952	−	1.39070i	0.604464	−	0.796633i	$-0.293388\pi$
$558$	8.25116	+	5.30270i	0.349299	+	0.224481i
$559$	10.9742	−	24.0302i	0.464160	−	1.01637i
$560$	2.58318	−	2.98115i	0.109159	−	0.125977i
$561$	−1.72799	+	12.0184i	−0.0729558	+	0.507419i
$562$	7.70372	+	16.8688i	0.324962	+	0.711567i
$563$	−2.67583	−	0.785694i	−0.112773	−	0.0331130i	0.224859	−	0.974391i	$-0.427808\pi$
$563$	−2.67583	−	0.785694i	−0.112773	−	0.0331130i	−0.337632	+	0.941278i	$0.609626\pi$
$564$	−8.59171	−	2.52275i	−0.361776	−	0.106227i
$565$	−0.130585	−	0.285941i	−0.00549374	−	0.0120296i
$566$	2.08904	−	14.5296i	0.0878090	−	0.610725i
$567$	2.58318	−	2.98115i	0.108483	−	0.125197i
$568$	−4.42391	+	9.68701i	−0.185623	+	0.406458i
$569$	−5.30618	−	3.41007i	−0.222446	−	0.142958i	0.424672	−	0.905347i	$-0.360390\pi$
$569$	−5.30618	−	3.41007i	−0.222446	−	0.142958i	−0.647118	+	0.762390i	$0.724026\pi$
$570$	0.373436	+	2.59730i	0.0156415	+	0.108789i
$571$	−25.9411	+	16.6714i	−1.08560	+	0.697675i	−0.955845	−	0.293871i	$-0.905056\pi$
$571$	−25.9411	+	16.6714i	−1.08560	+	0.697675i	−0.129758	+	0.991546i	$0.541420\pi$
$572$	5.84272	+	6.74286i	0.244297	+	0.281933i
$573$	−10.3258	+	3.03192i	−0.431366	+	0.126660i
$574$	14.2193			0.593501
$575$	2.86065	+	3.84925i	0.119297	+	0.160525i
$576$	1.00000			0.0416667
$577$	−1.05384	+	0.309436i	−0.0438720	+	0.0128820i	−0.303595	−	0.952801i	$-0.598187\pi$
$577$	−1.05384	+	0.309436i	−0.0438720	+	0.0128820i	0.259723	+	0.965683i	$0.416369\pi$
$578$	−5.72609	−	6.60826i	−0.238174	−	0.274867i
$579$	10.8930	−	7.00049i	0.452696	−	0.290930i
$580$	−1.44641	−	10.0600i	−0.0600591	−	0.417720i
$581$	49.5944	+	31.8724i	2.05752	+	1.32229i
$582$	6.03892	−	13.2234i	0.250321	−	0.548127i
$583$	−27.0370	+	31.2024i	−1.11976	+	1.29227i
$584$	0.511260	−	3.55589i	0.0211561	−	0.147144i
$585$	0.877087	+	1.92055i	0.0362631	+	0.0794051i
$586$	9.00611	+	2.64443i	0.372039	+	0.109240i
$587$	−38.8782	−	11.4157i	−1.60468	−	0.471175i	−0.647833	−	0.761782i	$-0.724325\pi$
$587$	−38.8782	−	11.4157i	−1.60468	−	0.471175i	−0.956843	+	0.290607i	$0.906143\pi$
$588$	−3.55599	−	7.78653i	−0.146647	−	0.321111i
$589$	−3.66272	+	25.4748i	−0.150920	+	1.04967i
$590$	−3.65659	+	4.21994i	−0.150540	+	0.173732i
$591$	−5.40173	+	11.8281i	−0.222197	+	0.486544i
$592$	2.14065	+	1.37571i	0.0879803	+	0.0565415i
$593$	−2.45787	−	17.0949i	−0.100933	−	0.702003i	−0.975963	−	0.217935i	$-0.930068\pi$
$593$	−2.45787	−	17.0949i	−0.100933	−	0.702003i	0.875031	−	0.484068i	$-0.160841\pi$
$594$	−3.55494	+	2.28462i	−0.145861	+	0.0937392i
$595$	7.42233	+	8.56583i	0.304286	+	0.351165i
$596$	7.06196	−	2.07358i	0.289269	−	0.0849371i
$597$	−3.07381			−0.125803
$598$	4.88365	−	8.87015i	0.199707	−	0.362727i
$599$	−27.4057			−1.11977			−0.559883	−	0.828571i	$-0.689154\pi$
$599$	−27.4057			−1.11977			−0.559883	+	0.828571i	$0.689154\pi$
$600$	−0.959493	+	0.281733i	−0.0391711	+	0.0115017i
$601$	−11.1111	−	12.8229i	−0.453230	−	0.523056i	0.482441	−	0.875928i	$-0.339750\pi$
$601$	−11.1111	−	12.8229i	−0.453230	−	0.523056i	−0.935671	+	0.352873i	$0.885205\pi$
$602$	41.5206	−	26.6837i	1.69225	−	1.08754i
$603$	0.0711997	+	0.495204i	0.00289947	+	0.0201663i
$604$	−12.0280	−	7.72992i	−0.489412	−	0.314526i
$605$	2.84855	−	6.23745i	0.115810	−	0.253588i
$606$	5.95204	−	6.86902i	0.241785	−	0.279035i
$607$	−4.08614	+	28.4198i	−0.165851	+	1.15352i	0.721495	+	0.692419i	$0.243455\pi$
$607$	−4.08614	+	28.4198i	−0.165851	+	1.15352i	−0.887347	+	0.461103i	$0.847454\pi$
$608$	1.09005	+	2.38689i	0.0442076	+	0.0968010i
$609$	−38.4672	−	11.2950i	−1.55877	−	0.457696i
$610$	−0.912521	−	0.267940i	−0.0369469	−	0.0108486i
$611$	−7.85382	−	17.1975i	−0.317731	−	0.695735i
$612$	−0.408917	+	2.84408i	−0.0165295	+	0.114965i
$613$	6.14933	−	7.09670i	0.248369	−	0.286633i	−0.617852	−	0.786295i	$-0.711997\pi$
$613$	6.14933	−	7.09670i	0.248369	−	0.286633i	0.866221	+	0.499661i	$0.166542\pi$
$614$	−8.27204	+	18.1132i	−0.333832	+	0.730991i
$615$	−3.03248	−	1.94886i	−0.122281	−	0.0785855i
$616$	2.37226	+	16.4994i	0.0955810	+	0.664780i
$617$	−1.36275	+	0.875785i	−0.0548622	+	0.0352578i	−0.567784	−	0.823177i	$-0.692199\pi$
$617$	−1.36275	+	0.875785i	−0.0548622	+	0.0352578i	0.512922	+	0.858435i	$0.328563\pi$
$618$	9.32255	+	10.7588i	0.375008	+	0.432782i
$619$	39.7969	−	11.6854i	1.59957	−	0.469677i	0.644146	−	0.764903i	$-0.277213\pi$
$619$	39.7969	−	11.6854i	1.59957	−	0.469677i	0.955428	+	0.295226i	$0.0953949\pi$
$620$	−9.80817			−0.393906
$621$	3.82923	+	2.88739i	0.153662	+	0.115867i
$622$	−6.79593			−0.272492
$623$	−67.9941	+	19.9649i	−2.72413	+	0.799876i
$624$	1.38264	+	1.59565i	0.0553500	+	0.0638773i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	3.00769	+	20.9190i	0.120212	+	0.836090i
$627$	−9.32822	−	5.99488i	−0.372533	−	0.239412i
$628$	−9.06074	+	19.8403i	−0.361563	+	0.791713i
$629$	−4.78799	+	5.52564i	−0.190910	+	0.220322i
$630$	−0.561379	+	3.90448i	−0.0223659	+	0.155558i
$631$	−3.89199	−	8.52228i	−0.154938	−	0.339267i	0.816206	−	0.577761i	$-0.196073\pi$
$631$	−3.89199	−	8.52228i	−0.154938	−	0.339267i	−0.971144	+	0.238494i	$0.923346\pi$
$632$	4.57617	+	1.34369i	0.182030	+	0.0534489i
$633$	9.75387	+	2.86399i	0.387681	+	0.113834i
$634$	3.39925	+	7.44333i	0.135002	+	0.295612i
$635$	−1.01387	+	7.05165i	−0.0402344	+	0.279836i
$636$	−6.39814	+	7.38384i	−0.253703	+	0.292788i
$637$	7.50795	−	16.4401i	0.297476	−	0.651381i
$638$	36.1306	+	23.2197i	1.43042	+	0.919278i
$639$	−1.51556	−	10.5410i	−0.0599548	−	0.416995i
$640$	−0.841254	+	0.540641i	−0.0332535	+	0.0213707i
$641$	4.58130	+	5.28710i	0.180950	+	0.208828i	0.838977	−	0.544167i	$-0.183154\pi$
$641$	4.58130	+	5.28710i	0.180950	+	0.208828i	−0.658027	+	0.752995i	$0.728609\pi$
$642$	−10.1337	+	2.97551i	−0.399943	+	0.117434i
$643$	33.4391			1.31871			0.659356	−	0.751831i	$-0.270829\pi$
$643$	33.4391			1.31871			0.659356	+	0.751831i	$0.270829\pi$
$644$	16.6352	−	9.00844i	0.655519	−	0.354982i
$645$	−12.5121			−0.492664
$646$	−7.23424	+	2.12417i	−0.284627	+	0.0835742i
$647$	−16.4231	−	18.9533i	−0.645660	−	0.745131i	0.334705	−	0.942323i	$-0.391363\pi$
$647$	−16.4231	−	18.9533i	−0.645660	−	0.745131i	−0.980365	+	0.197192i	$0.936818\pi$
$648$	−0.841254	+	0.540641i	−0.0330476	+	0.0212384i
$649$	−3.35802	−	23.3556i	−0.131814	−	0.916786i
$650$	−1.77618	−	1.14148i	−0.0696676	−	0.0447727i
$651$	−16.0722	+	35.1933i	−0.629920	+	1.37933i
$652$	5.38028	−	6.20918i	0.210708	−	0.243170i
$653$	1.36594	−	9.50034i	0.0534535	−	0.371777i	−0.945483	−	0.325671i	$-0.894410\pi$
$653$	1.36594	−	9.50034i	0.0534535	−	0.371777i	0.998937	−	0.0461059i	$-0.0146812\pi$
$654$	−6.11882	−	13.3983i	−0.239265	−	0.523917i
$655$	−21.0237	−	6.17311i	−0.821464	−	0.241203i
$656$	−3.45870	−	1.01557i	−0.135040	−	0.0396512i
$657$	1.49236	+	3.26781i	0.0582225	+	0.127489i
$658$	5.02683	−	34.9624i	0.195966	−	1.36297i
$659$	−17.8394	+	20.5878i	−0.694926	+	0.801987i	−0.988058	−	0.154085i	$-0.950757\pi$
$659$	−17.8394	+	20.5878i	−0.694926	+	0.801987i	0.293132	+	0.956072i	$0.405303\pi$
$660$	1.75545	−	3.84389i	0.0683307	−	0.149623i
$661$	−10.4618	−	6.72341i	−0.406918	−	0.261510i	0.321132	−	0.947035i	$-0.395937\pi$
$661$	−10.4618	−	6.72341i	−0.406918	−	0.261510i	−0.728050	+	0.685524i	$0.759573\pi$
$662$	1.64970	+	11.4739i	0.0641174	+	0.445946i
$663$	−5.10356	+	3.27986i	−0.198206	+	0.127379i
$664$	−9.78699	−	11.2948i	−0.379809	−	0.438323i
$665$	−9.93148	+	2.91615i	−0.385126	+	0.113083i
$666$	−2.54460			−0.0986012
$667$	10.5267	−	47.5921i	0.407597	−	1.84277i
$668$	5.54033			0.214362
$669$	−1.38470	+	0.406584i	−0.0535356	+	0.0157195i
$670$	−0.327625	−	0.378099i	−0.0126572	−	0.0146072i
$671$	3.38091	−	2.17278i	0.130519	−	0.0838792i
$672$	0.561379	+	3.90448i	0.0216557	+	0.150618i
$673$	−32.7270	−	21.0324i	−1.26153	−	0.810738i	−0.273040	−	0.962003i	$-0.588029\pi$
$673$	−32.7270	−	21.0324i	−1.26153	−	0.810738i	−0.988493	+	0.151264i	$0.951666\pi$
$674$	−0.896984	+	1.96412i	−0.0345505	+	0.0756551i
$675$	0.654861	−	0.755750i	0.0252056	−	0.0290888i
$676$	1.21568	−	8.45524i	0.0467569	−	0.325202i
$677$	−3.46922	−	7.59654i	−0.133333	−	0.291959i	0.831176	−	0.556010i	$-0.187668\pi$
$677$	−3.46922	−	7.59654i	−0.133333	−	0.291959i	−0.964509	+	0.264051i	$0.914941\pi$
$678$	0.301614	+	0.0885619i	0.0115834	+	0.00340120i
$679$	55.0205	+	16.1555i	2.11149	+	0.619991i
$680$	−1.19362	−	2.61367i	−0.0457734	−	0.100230i
$681$	−1.63097	+	11.3436i	−0.0624989	+	0.434689i
$682$	27.1420	−	31.3236i	1.03932	−	1.19944i
$683$	17.9151	−	39.2287i	0.685504	−	1.50104i	−0.171201	−	0.985236i	$-0.554765\pi$
$683$	17.9151	−	39.2287i	0.685504	−	1.50104i	0.856705	−	0.515807i	$-0.172508\pi$
$684$	−2.20746	−	1.41865i	−0.0844044	−	0.0542434i
$685$	−0.0945981	−	0.657944i	−0.00361441	−	0.0251388i
$686$	5.17705	−	3.32709i	0.197661	−	0.127029i
$687$	−6.21588	−	7.17351i	−0.237151	−	0.273686i
$688$	−12.0053	+	3.52507i	−0.457697	+	0.134392i
$689$	−20.6284			−0.785879
$690$	−4.78239	−	0.358788i	−0.182063	−	0.0136588i
$691$	3.11978			0.118682			0.0593411	−	0.998238i	$-0.481100\pi$
$691$	3.11978			0.118682			0.0593411	+	0.998238i	$0.481100\pi$
$692$	0.0473351	−	0.0138988i	0.00179941	−	0.000528354i
$693$	−10.9159	−	12.5977i	−0.414662	−	0.478545i
$694$	13.1423	−	8.44601i	0.498873	−	0.320606i
$695$	0.847782	+	5.89646i	0.0321582	+	0.223665i
$696$	8.55007	+	5.49480i	0.324090	+	0.208280i
$697$	4.30267	−	9.42154i	0.162975	−	0.356866i
$698$	15.1251	−	17.4553i	0.572494	−	0.660693i
$699$	2.43172	−	16.9130i	0.0919762	−	0.639708i
$700$	−1.63866	−	3.58816i	−0.0619354	−	0.135620i
$701$	−22.3386	−	6.55920i	−0.843717	−	0.247738i	−0.168818	−	0.985647i	$-0.553995\pi$
$701$	−22.3386	−	6.55920i	−0.843717	−	0.247738i	−0.674900	+	0.737910i	$0.735813\pi$
$702$	−2.02583	−	0.594837i	−0.0764599	−	0.0224507i
$703$	−2.77375	−	6.07367i	−0.104614	−	0.229073i
$704$	0.601389	−	4.18276i	0.0226657	−	0.157644i
$705$	−5.86390	+	6.76730i	−0.220847	+	0.254871i
$706$	−5.98529	+	13.1060i	−0.225259	+	0.493249i
$707$	30.1613	+	19.3835i	1.13433	+	0.728991i
$708$	−0.794654	−	5.52694i	−0.0298649	−	0.207715i
$709$	−17.8295	+	11.4583i	−0.669601	+	0.430326i	−0.830782	−	0.556599i	$-0.812106\pi$
$709$	−17.8295	+	11.4583i	−0.669601	+	0.430326i	0.161181	+	0.986925i	$0.448470\pi$
$710$	6.97385	+	8.04826i	0.261724	+	0.302046i
$711$	−4.57617	+	1.34369i	−0.171620	+	0.0503921i
$712$	17.9648			0.673261
$713$	−44.0150	−	16.5916i	−1.64838	−	0.621360i
$714$	−11.3342			−0.424172
$715$	8.56068	−	2.51364i	0.320151	−	0.0940049i
$716$	4.83813	+	5.58350i	0.180809	+	0.208665i
$717$	6.76939	−	4.35042i	0.252807	−	0.162469i
$718$	−2.94840	−	20.5065i	−0.110033	−	0.765297i
$719$	17.3411	+	11.1444i	0.646712	+	0.415617i	0.822464	−	0.568818i	$-0.192599\pi$
$719$	17.3411	+	11.1444i	0.646712	+	0.415617i	−0.175751	+	0.984435i	$0.556235\pi$
$720$	0.415415	−	0.909632i	0.0154816	−	0.0339000i
$721$	−36.7740	+	42.4395i	−1.36954	+	1.58053i
$722$	−1.72408	+	11.9912i	−0.0641636	+	0.446268i
$723$	1.11768	+	2.44737i	0.0415669	+	0.0910188i
$724$	−9.65344	−	2.83451i	−0.358767	−	0.105344i
$725$	−9.75179	−	2.86339i	−0.362173	−	0.106343i
$726$	2.84855	+	6.23745i	0.105720	+	0.231494i
$727$	6.36307	−	44.2561i	0.235993	−	1.64137i	−0.435378	−	0.900248i	$-0.643385\pi$
$727$	6.36307	−	44.2561i	0.235993	−	1.64137i	0.671371	−	0.741121i	$-0.265706\pi$
$728$	−5.45401	+	6.29426i	−0.202139	+	0.233281i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−3.02217	−	1.94223i	−0.111855	−	0.0718851i
$731$	−5.11642	−	35.5855i	−0.189237	−	1.31618i
$732$	0.800070	−	0.514174i	0.0295714	−	0.0190044i
$733$	−19.7627	−	22.8074i	−0.729952	−	0.842410i	0.262514	−	0.964928i	$-0.415448\pi$
$733$	−19.7627	−	22.8074i	−0.729952	−	0.842410i	−0.992466	+	0.122518i	$0.960903\pi$
$734$	−31.4856	+	9.24500i	−1.16215	+	0.341239i
$735$	−8.56009			−0.315744
$736$	−4.68975	+	1.00310i	−0.172867	+	0.0369748i
$737$	2.11414			0.0778753
$738$	3.45870	−	1.01557i	0.127316	−	0.0373835i
$739$	−9.10480	−	10.5075i	−0.334926	−	0.386525i	0.563158	−	0.826349i	$-0.309586\pi$
$739$	−9.10480	−	10.5075i	−0.334926	−	0.386525i	−0.898084	+	0.439824i	$0.855041\pi$
$740$	2.14065	−	1.37571i	0.0786920	−	0.0505723i
$741$	−0.788455	−	5.48383i	−0.0289646	−	0.201453i
$742$	−32.4218	−	20.8362i	−1.19024	−	0.764923i
$743$	−6.61739	+	14.4901i	−0.242769	+	0.531589i	−0.991317	−	0.131491i	$-0.958024\pi$
$743$	−6.61739	+	14.4901i	−0.242769	+	0.531589i	0.748549	+	0.663080i	$0.230751\pi$
$744$	6.42298	−	7.41252i	0.235478	−	0.271756i
$745$	1.04745	−	7.28518i	0.0383757	−	0.266909i
$746$	5.80971	+	12.7215i	0.212709	+	0.465767i
$747$	14.3398	+	4.21053i	0.524664	+	0.154055i
$748$	11.6502	+	3.42080i	0.425973	+	0.125077i
$749$	−17.3066	−	37.8962i	−0.632370	−	1.38470i
$750$	−0.142315	+	0.989821i	−0.00519660	+	0.0361432i
$751$	23.7331	−	27.3894i	0.866032	−	0.999454i	−0.133932	−	0.990991i	$-0.542760\pi$
$751$	23.7331	−	27.3894i	0.866032	−	0.999454i	0.999964	−	0.00846392i	$-0.00269418\pi$
$752$	−3.71980	+	8.14523i	−0.135647	+	0.297026i
$753$	17.1858	+	11.0446i	0.626284	+	0.402489i
$754$	3.05389	+	21.2403i	0.111216	+	0.773525i
$755$	−12.0280	+	7.72992i	−0.437744	+	0.281321i
$756$	−2.58318	−	2.98115i	−0.0939494	−	0.108423i
$757$	−42.1763	+	12.3841i	−1.53292	+	0.450107i	−0.935944	−	0.352148i	$-0.885451\pi$
$757$	−42.1763	+	12.3841i	−1.53292	+	0.450107i	−0.596981	+	0.802256i	$0.703633\pi$
$758$	−26.2516			−0.953501
$759$	14.3801	−	14.2803i	0.521964	−	0.518341i
$760$	2.62401			0.0951830
$761$	−3.09147	+	0.907739i	−0.112066	+	0.0329055i	−0.337285	−	0.941403i	$-0.609508\pi$
$761$	−3.09147	+	0.907739i	−0.112066	+	0.0329055i	0.225219	+	0.974308i	$0.427690\pi$
$762$	−4.66534	−	5.38408i	−0.169007	−	0.195045i
$763$	48.8785	−	31.4123i	1.76952	−	1.13720i
$764$	1.53155	+	10.6522i	0.0554095	+	0.385382i
$765$	2.41720	+	1.55344i	0.0873940	+	0.0561647i
$766$	−12.9721	+	28.4050i	−0.468703	+	1.02632i
$767$	7.72036	−	8.90977i	0.278766	−	0.321713i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	−13.7934	−	30.2033i	−0.497402	−	1.08916i	−0.977305	−	0.211837i	$-0.932055\pi$
$769$	−13.7934	−	30.2033i	−0.497402	−	1.08916i	0.479903	−	0.877322i	$-0.340672\pi$
$770$	15.9939	+	4.69622i	0.576379	+	0.169240i
$771$	21.1513	+	6.21058i	0.761745	+	0.223669i
$772$	−5.37900	−	11.7784i	−0.193594	−	0.423913i
$773$	−1.51647	+	10.5473i	−0.0545437	+	0.379360i	0.944205	+	0.329357i	$0.106832\pi$
$773$	−1.51647	+	10.5473i	−0.0545437	+	0.379360i	−0.998749	+	0.0500025i	$0.984077\pi$
$774$	8.19369	−	9.45602i	0.294516	−	0.339890i
$775$	−4.07446	+	8.92182i	−0.146359	+	0.320481i
$776$	−12.2294	−	7.85934i	−0.439009	−	0.282134i
$777$	−1.42848	−	9.93533i	−0.0512466	−	0.356428i
$778$	−3.22452	+	2.07227i	−0.115605	+	0.0742946i
$779$	6.19421	+	7.14850i	0.221931	+	0.256122i
$780$	2.02583	−	0.594837i	0.0725363	−	0.0212986i
$781$	−45.0018			−1.61029
$782$	−0.935179	−	13.7482i	−0.0334419	−	0.491636i
$783$	−10.1635			−0.363213
$784$	−8.21335	+	2.41166i	−0.293334	+	0.0861306i
$785$	14.2834	+	16.4839i	0.509795	+	0.588335i
$786$	18.4329	−	11.8461i	0.657480	−	0.422537i
$787$	−1.19424	−	8.30609i	−0.0425699	−	0.296080i	−0.999973	−	0.00732590i	$-0.997668\pi$
$787$	−1.19424	−	8.30609i	−0.0425699	−	0.296080i	0.957403	−	0.288754i	$-0.0932410\pi$
$788$	10.9390	+	7.03006i	0.389685	+	0.250436i
$789$	−10.4078	+	22.7900i	−0.370529	+	0.811344i
$790$	3.12327	−	3.60444i	0.111121	−	0.128240i
$791$	−0.176468	+	1.22736i	−0.00627448	+	0.0436400i
$792$	1.75545	+	3.84389i	0.0623771	+	0.136587i
$793$	1.92665	+	0.565716i	0.0684175	+	0.0200892i
$794$	35.4177	+	10.3996i	1.25693	+	0.369067i
$795$	4.05870	+	8.88731i	0.143947	+	0.315200i
$796$	−0.437449	+	3.04252i	−0.0155050	+	0.107839i
$797$	18.8111	−	21.7092i	0.666324	−	0.768979i	−0.317473	−	0.948267i	$-0.602834\pi$
$797$	18.8111	−	21.7092i	0.666324	−	0.768979i	0.983796	+	0.179289i	$0.0573797\pi$
$798$	4.29986	−	9.41538i	0.152213	−	0.333301i
$799$	−21.6446	−	13.9102i	−0.765732	−	0.492106i
$800$	0.142315	+	0.989821i	0.00503159	+	0.0349955i
$801$	−15.1130	+	9.71253i	−0.533991	+	0.343175i
$802$	12.6604	+	14.6109i	0.447054	+	0.515928i
$803$	14.5659	−	4.27695i	0.514021	−	0.150930i
$804$	0.500297			0.0176441
$805$	−1.28385	−	18.8742i	−0.0452499	−	0.665227i
$806$	20.7085			0.729426
$807$	5.68328	−	1.66876i	0.200061	−	0.0587432i
$808$	−5.95204	−	6.86902i	−0.209392	−	0.241651i
$809$	−11.5071	+	7.39517i	−0.404569	+	0.260000i	−0.727063	−	0.686571i	$-0.759115\pi$
$809$	−11.5071	+	7.39517i	−0.404569	+	0.260000i	0.322494	+	0.946571i	$0.395479\pi$
$810$	0.142315	+	0.989821i	0.00500043	+	0.0347788i
$811$	−25.5337	−	16.4095i	−0.896608	−	0.576215i	0.00917467	−	0.999958i	$-0.497080\pi$
$811$	−25.5337	−	16.4095i	−0.896608	−	0.576215i	−0.905782	+	0.423743i	$0.860716\pi$
$812$	−16.6545	+	36.4682i	−0.584457	+	1.27978i
$813$	1.89400	−	2.18580i	0.0664256	−	0.0766593i
$814$	−1.53030	+	10.6434i	−0.0536368	+	0.373052i
$815$	−3.41302	−	7.47346i	−0.119553	−	0.261784i
$816$	2.75694	+	0.809510i	0.0965121	+	0.0283385i
$817$	31.5020	+	9.24982i	1.10212	+	0.323610i
$818$	−2.13420	−	4.67325i	−0.0746206	−	0.163396i
$819$	1.18527	−	8.24373i	0.0414167	−	0.288059i
$820$	−2.36059	+	2.72426i	−0.0824353	+	0.0951354i
$821$	0.623806	−	1.36594i	0.0217710	−	0.0476718i	−0.898434	−	0.439108i	$-0.855294\pi$
$821$	0.623806	−	1.36594i	0.0217710	−	0.0476718i	0.920205	+	0.391436i	$0.128022\pi$
$822$	0.559190	+	0.359369i	0.0195040	+	0.0125344i
$823$	5.86736	+	40.8084i	0.204523	+	1.42249i	0.790648	+	0.612271i	$0.209744\pi$
$823$	5.86736	+	40.8084i	0.204523	+	1.42249i	−0.586125	+	0.810221i	$0.699347\pi$
$824$	11.9760	−	7.69652i	0.417205	−	0.268121i
$825$	−2.76729	−	3.19362i	−0.0963447	−	0.111188i
$826$	21.1337	−	6.20542i	0.735336	−	0.215914i
$827$	14.7465			0.512787			0.256393	−	0.966572i	$-0.417466\pi$
$827$	14.7465			0.512787			0.256393	+	0.966572i	$0.417466\pi$
$828$	3.40295	−	3.37933i	0.118261	−	0.117440i
$829$	−30.0860			−1.04493			−0.522466	−	0.852660i	$-0.674988\pi$
$829$	−30.0860			−1.04493			−0.522466	+	0.852660i	$0.674988\pi$
$830$	−14.3398	+	4.21053i	−0.497740	+	0.146150i
$831$	3.24791	+	3.74828i	0.112669	+	0.130026i
$832$	1.77618	−	1.14148i	0.0615781	−	0.0395738i
$833$	−3.50037	−	24.3456i	−0.121281	−	0.843525i
$834$	−5.01142	−	3.22065i	−0.173531	−	0.111522i
$835$	2.30153	−	5.03966i	0.0796479	−	0.174405i
$836$	−7.26140	+	8.38011i	−0.251141	+	0.289832i
$837$	−1.39585	+	9.70834i	−0.0482476	+	0.335569i
$838$	−11.8154	−	25.8720i	−0.408155	−	0.893735i
$839$	−0.0671767	−	0.0197249i	−0.00231920	−	0.000680978i	0.280573	−	0.959833i	$-0.409476\pi$
$839$	−0.0671767	−	0.0197249i	−0.00231920	−	0.000680978i	−0.282892	+	0.959152i	$0.591294\pi$
$840$	3.78484	+	1.11133i	0.130589	+	0.0383445i
$841$	30.8639	+	67.5824i	1.06427	+	2.33043i
$842$	−2.30272	+	16.0158i	−0.0793569	+	0.551939i
$843$	−12.1442	+	14.0151i	−0.418267	+	0.482706i
$844$	4.22296	−	9.24700i	0.145360	−	0.318295i
$845$	−7.18615	−	4.61826i	−0.247211	−	0.158873i
$846$	−1.27435	−	8.86328i	−0.0438130	−	0.304726i
$847$	−22.7549	+	14.6237i	−0.781867	+	0.502475i
$848$	6.39814	+	7.38384i	0.219713	+	0.253562i
$849$	14.0844	−	4.13556i	0.483376	−	0.141932i
$850$	−2.87333			−0.0985543
$851$	11.9335	−	2.55249i	0.409077	−	0.0874982i
$852$	−10.6494			−0.364841
$853$	4.44074	−	1.30392i	0.152048	−	0.0446454i	−0.204823	−	0.978799i	$-0.565662\pi$
$853$	4.44074	−	1.30392i	0.152048	−	0.0446454i	0.356871	+	0.934154i	$0.383844\pi$
$854$	2.45672	+	2.83521i	0.0840673	+	0.0970188i
$855$	−2.20746	+	1.41865i	−0.0754936	+	0.0485168i
$856$	1.50305	+	10.4540i	0.0513733	+	0.357309i
$857$	−11.9413	−	7.67420i	−0.407907	−	0.262146i	0.320558	−	0.947229i	$-0.396130\pi$
$857$	−11.9413	−	7.67420i	−0.407907	−	0.262146i	−0.728465	+	0.685083i	$0.759766\pi$
$858$	−3.70637	+	8.11581i	−0.126533	+	0.277069i
$859$	−24.6993	+	28.5045i	−0.842730	+	0.972563i	−0.999887	−	0.0150110i	$-0.995222\pi$
$859$	−24.6993	+	28.5045i	−0.842730	+	0.972563i	0.157157	+	0.987574i	$0.449767\pi$
$860$	−1.78066	+	12.3848i	−0.0607199	+	0.422316i
$861$	5.90690	+	12.9343i	0.201306	+	0.440800i
$862$	14.8195	+	4.35139i	0.504753	+	0.148209i
$863$	−12.3481	−	3.62572i	−0.420333	−	0.123421i	0.0647245	−	0.997903i	$-0.479383\pi$
$863$	−12.3481	−	3.62572i	−0.420333	−	0.123421i	−0.485057	+	0.874482i	$0.661201\pi$
$864$	0.415415	+	0.909632i	0.0141327	+	0.0309463i
$865$	0.00702088	−	0.0488313i	0.000238717	−	0.00166031i
$866$	−7.63058	+	8.80616i	−0.259298	+	0.299246i
$867$	3.63238	−	7.95381i	0.123362	−	0.270125i
$868$	32.5477	+	20.9172i	1.10474	+	0.709975i
$869$	2.86825	+	19.9491i	0.0972986	+	0.676726i
$870$	8.55007	−	5.49480i	0.289874	−	0.186291i
$871$	0.691731	+	0.798300i	0.0234384	+	0.0270494i
$872$	−14.1328	+	4.14975i	−0.478596	+	0.140528i
$873$	14.5371			0.492005
$874$	11.7755	+	4.43881i	0.398312	+	0.150145i
$875$	−3.94463			−0.133353
$876$	3.44694	−	1.01211i	0.116461	−	0.0341961i
$877$	−12.0345	−	13.8885i	−0.406376	−	0.468982i	0.515263	−	0.857032i	$-0.327694\pi$
$877$	−12.0345	−	13.8885i	−0.406376	−	0.468982i	−0.921638	+	0.388050i	$0.873149\pi$
$878$	−28.1474	+	18.0893i	−0.949929	+	0.610483i
$879$	1.33581	+	9.29078i	0.0450558	+	0.313370i
$880$	−3.55494	−	2.28462i	−0.119837	−	0.0770146i
$881$	−10.2551	+	22.4555i	−0.345503	+	0.756546i	0.654497	+	0.756065i	$0.272880\pi$
$881$	−10.2551	+	22.4555i	−0.345503	+	0.756546i	−1.00000		0.000481287i	$0.999847\pi$
$882$	5.60567	−	6.46928i	0.188753	−	0.217832i
$883$	−2.42141	+	16.8413i	−0.0814870	+	0.566755i	0.907647	+	0.419735i	$0.137877\pi$
$883$	−2.42141	+	16.8413i	−0.0814870	+	0.566755i	−0.989134	+	0.147020i	$0.953032\pi$
$884$	2.52016	+	5.51838i	0.0847622	+	0.185603i
$885$	−5.35759	−	1.57313i	−0.180094	−	0.0528802i
$886$	3.76346	+	1.10505i	0.126436	+	0.0371249i
$887$	0.769090	+	1.68407i	0.0258235	+	0.0565456i	0.922104	−	0.386941i	$-0.126468\pi$
$887$	0.769090	+	1.68407i	0.0258235	+	0.0565456i	−0.896281	+	0.443487i	$0.853741\pi$
$888$	−0.362134	+	2.51870i	−0.0121524	+	0.0845220i
$889$	18.4030	−	21.2382i	0.617217	−	0.712307i
$890$	7.46287	−	16.3414i	0.250156	−	0.547765i
$891$	−3.55494	−	2.28462i	−0.119095	−	0.0765377i
$892$	0.205383	+	1.42847i	0.00687672	+	0.0478287i
$893$	19.7665	−	12.7032i	0.661462	−	0.425096i
$894$	4.81984	+	5.56239i	0.161200	+	0.186034i
$895$	7.08876	−	2.08145i	0.236951	−	0.0695752i
$896$	3.94463			0.131781
$897$	10.0973	+	0.757529i	0.337140	+	0.0252931i
$898$	29.1476			0.972669
$899$	95.6472	−	28.0846i	3.19001	−	0.936673i
$900$	−0.654861	−	0.755750i	−0.0218287	−	0.0251917i
$901$	−23.6166	+	15.1774i	−0.786782	+	0.505634i
$902$	−2.16784	−	15.0776i	−0.0721811	−	0.502031i
$903$	41.5206	+	26.6837i	1.38172	+	0.887976i
$904$	0.130585	−	0.285941i	0.00434318	−	0.00951024i
$905$	−6.58854	+	7.60358i	−0.219011	+	0.252752i
$906$	2.03478	−	14.1522i	0.0676009	−	0.470175i
$907$	1.83929	+	4.02748i	0.0610726	+	0.133730i	0.937707	−	0.347426i	$-0.112944\pi$
$907$	1.83929	+	4.02748i	0.0610726	+	0.133730i	−0.876635	+	0.481156i	$0.840217\pi$
$908$	10.9961	+	3.22874i	0.364917	+	0.107149i
$909$	8.72085	+	2.56067i	0.289252	+	0.0849321i
$910$	3.45978	+	7.57587i	0.114691	+	0.251138i
$911$	−2.91605	+	20.2816i	−0.0966131	+	0.671959i	0.882749	+	0.469845i	$0.155690\pi$
$911$	−2.91605	+	20.2816i	−0.0966131	+	0.671959i	−0.979362	+	0.202114i	$0.935219\pi$
$912$	−1.71836	+	1.98310i	−0.0569007	+	0.0656669i
$913$	26.2354	−	57.4475i	0.868265	−	1.90124i
$914$	−2.98797	−	1.92025i	−0.0988332	−	0.0635162i
$915$	−0.135348	−	0.941365i	−0.00447446	−	0.0311206i
$916$	−7.98510	+	5.13171i	−0.263835	+	0.169557i
$917$	56.6008	+	65.3207i	1.86912	+	2.15708i
$918$	−2.75694	+	0.809510i	−0.0909925	+	0.0267178i
$919$	−2.51361			−0.0829162			−0.0414581	−	0.999140i	$-0.513200\pi$
$919$	−2.51361			−0.0829162			−0.0414581	+	0.999140i	$0.513200\pi$
$920$	−1.03574	+	4.68265i	−0.0341474	+	0.154382i
$921$	−19.9127			−0.656146
$922$	7.82942	−	2.29892i	0.257848	−	0.0757110i
$923$	−14.7243	−	16.9927i	−0.484655	−	0.559322i
$924$	−14.0229	+	9.01199i	−0.461320	+	0.296473i
$925$	−0.362134	−	2.51870i	−0.0119069	−	0.0828143i
$926$	16.2137	+	10.4199i	0.532814	+	0.342419i
$927$	−5.91382	+	12.9495i	−0.194235	+	0.425316i
$928$	6.65567	−	7.68105i	0.218483	−	0.252143i
$929$	−5.72370	+	39.8092i	−0.187788	+	1.30610i	0.649930	+	0.759994i	$0.274798\pi$
$929$	−5.72370	+	39.8092i	−0.187788	+	1.30610i	−0.837718	+	0.546103i	$0.816111\pi$
$930$	−4.07446	−	8.92182i	−0.133607	−	0.292558i
$931$	21.5519	+	6.32822i	0.706336	+	0.207399i
$932$	−16.3948	−	4.81394i	−0.537029	−	0.157686i
$933$	−2.82313	−	6.18179i	−0.0924251	−	0.202383i
$934$	3.31404	−	23.0497i	0.108439	−	0.754208i
$935$	7.95133	−	9.17633i	0.260036	−	0.300098i
$936$	−0.877087	+	1.92055i	−0.0286685	+	0.0627753i
$937$	−4.09235	−	2.62999i	−0.133691	−	0.0859181i	0.472086	−	0.881553i	$-0.343501\pi$
$937$	−4.09235	−	2.62999i	−0.133691	−	0.0859181i	−0.605777	+	0.795635i	$0.707138\pi$
$938$	0.280856	+	1.95340i	0.00917028	+	0.0637807i
$939$	−17.7791	+	11.4259i	−0.580199	+	0.372872i
$940$	5.86390	+	6.76730i	0.191259	+	0.220725i
$941$	−7.80322	+	2.29123i	−0.254378	+	0.0746921i	−0.406435	−	0.913680i	$-0.633228\pi$
$941$	−7.80322	+	2.29123i	−0.254378	+	0.0746921i	0.152057	+	0.988372i	$0.451410\pi$
$942$	−21.8113			−0.710651
$943$	−15.2017	+	8.23218i	−0.495037	+	0.268077i
$944$	−5.58377			−0.181736
$945$	−3.78484	+	1.11133i	−0.123121	+	0.0361516i
$946$	−34.6246	−	39.9589i	−1.12574	−	1.29918i
$947$	−23.7596	+	15.2693i	−0.772082	+	0.496187i	−0.866397	−	0.499355i	$-0.833570\pi$
$947$	−23.7596	+	15.2693i	−0.772082	+	0.496187i	0.0943152	+	0.995542i	$0.469934\pi$
$948$	0.678751	+	4.72082i	0.0220448	+	0.153325i
$949$	6.38086	+	4.10073i	0.207131	+	0.133115i
$950$	1.09005	−	2.38689i	0.0353660	−	0.0774408i
$951$	−5.35859	+	6.18414i	−0.173764	+	0.200535i
$952$	−1.61303	+	11.2188i	−0.0522785	+	0.363605i
$953$	3.78253	+	8.28259i	0.122528	+	0.268299i	0.960950	−	0.276723i	$-0.0892485\pi$
$953$	3.78253	+	8.28259i	0.122528	+	0.268299i	−0.838422	+	0.545022i	$0.816521\pi$
$954$	−9.37446	−	2.75259i	−0.303509	−	0.0891184i
$955$	10.3258	+	3.03192i	0.334134	+	0.0981107i
$956$	−3.34276	−	7.31961i	−0.108112	−	0.236733i
$957$	−6.11221	+	42.5114i	−0.197580	+	1.37420i
$958$	−0.496853	+	0.573399i	−0.0160526	+	0.0185257i
$959$	−1.08923	+	2.38509i	−0.0351731	+	0.0770185i
$960$	−0.841254	−	0.540641i	−0.0271513	−	0.0174491i
$961$	−9.27895	−	64.5365i	−0.299321	−	2.08182i
$962$	−4.51967	+	2.90462i	−0.145720	+	0.0936486i
$963$	−6.91629	−	7.98182i	−0.222874	−	0.257211i
$964$	2.58153	−	0.758004i	0.0831453	−	0.0244137i
$965$	−12.9485			−0.416827
$966$	15.1049	+	11.3897i	0.485992	+	0.366457i
$967$	−15.7185			−0.505473			−0.252736	−	0.967535i	$-0.581331\pi$
$967$	−15.7185			−0.505473			−0.252736	+	0.967535i	$0.581331\pi$
$968$	6.57935	−	1.93187i	0.211468	−	0.0620927i
$969$	−4.93742	−	5.69809i	−0.158613	−	0.183049i
$970$	−12.2294	+	7.85934i	−0.392661	+	0.252348i
$971$	−2.11519	−	14.7115i	−0.0678798	−	0.472114i	−0.995201	−	0.0978487i	$-0.968804\pi$
$971$	−2.11519	−	14.7115i	−0.0678798	−	0.472114i	0.927322	−	0.374266i	$-0.122105\pi$
$972$	−0.841254	−	0.540641i	−0.0269832	−	0.0173411i
$973$	9.76163	−	21.3750i	0.312944	−	0.685251i
$974$	−17.1590	+	19.8026i	−0.549811	+	0.634515i
$975$	0.300477	−	2.08986i	0.00962296	−	0.0669291i
$976$	−0.395078	−	0.865101i	−0.0126462	−	0.0276912i
$977$	10.5872	+	3.10868i	0.338714	+	0.0994555i	0.446666	−	0.894701i	$-0.352611\pi$
$977$	10.5872	+	3.10868i	0.338714	+	0.0994555i	−0.107952	+	0.994156i	$0.534429\pi$
$978$	7.88312	+	2.31469i	0.252074	+	0.0740157i
$979$	31.5363	+	69.0549i	1.00791	+	2.20701i
$980$	−1.21823	+	8.47296i	−0.0389149	+	0.270659i
$981$	9.64571	−	11.1317i	0.307964	−	0.355409i
$982$	−14.7003	+	32.1892i	−0.469106	+	1.02720i
$983$	−4.52572	−	2.90850i	−0.144348	−	0.0927669i	0.466473	−	0.884535i	$-0.345524\pi$
$983$	−4.52572	−	2.90850i	−0.144348	−	0.0927669i	−0.610821	+	0.791768i	$0.709161\pi$
$984$	−0.513005	−	3.56803i	−0.0163540	−	0.113744i
$985$	10.9390	−	7.03006i	0.348545	−	0.223996i
$986$	19.1239	+	22.0702i	0.609030	+	0.702858i
$987$	33.8911	−	9.95132i	1.07877	−	0.316754i
$988$	−5.54022			−0.176258
$989$	−28.9410	+	52.5655i	−0.920271	+	1.67149i
$990$	4.22577			0.134304
$991$	−25.1963	+	7.39831i	−0.800388	+	0.235015i	−0.656251	−	0.754543i	$-0.727859\pi$
$991$	−25.1963	+	7.39831i	−0.800388	+	0.235015i	−0.144137	+	0.989558i	$0.546041\pi$
$992$	−6.42298	−	7.41252i	−0.203930	−	0.235348i
$993$	−9.75172	+	6.26705i	−0.309462	+	0.198879i
$994$	−5.97833	−	41.5802i	−0.189621	−	1.31884i
$995$	2.58585	+	1.66183i	0.0819771	+	0.0526835i
$996$	6.20844	−	13.5946i	0.196722	−	0.430761i
$997$	−0.452426	+	0.522128i	−0.0143285	+	0.0165360i	−0.762869	−	0.646554i	$-0.776210\pi$
$997$	−0.452426	+	0.522128i	−0.0143285	+	0.0165360i	0.748540	+	0.663090i	$0.230755\pi$
$998$	−1.58384	+	11.0159i	−0.0501357	+	0.348701i
$999$	−1.05706	−	2.31465i	−0.0334440	−	0.0732322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.331.1	yes	20
23.18	even	11	inner	690.2.m.e.271.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.271.1	✓	20	23.18	even	11	inner
690.2.m.e.331.1	yes	20	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)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.63866 + 3.58816i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.63866 + 3.58816i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(4.05459 + 1.19054i) q^{11} +(0.959493 + 0.281733i) q^{12} +(0.877087 + 1.92055i) q^{13} +(-0.561379 + 3.90448i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(2.41720 + 1.55344i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-2.20746 + 1.41865i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-3.78484 + 1.11133i) q^{21} +4.22577 q^{22} +(-1.66031 - 4.49926i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.38264 + 1.59565i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.561379 + 3.90448i) q^{28} +(8.55007 + 5.49480i) q^{29} +(0.415415 - 0.909632i) q^{30} +(6.42298 - 7.41252i) q^{31} +(0.142315 - 0.989821i) q^{32} +(1.75545 + 3.84389i) q^{33} +(2.75694 + 0.809510i) q^{34} +(3.78484 + 1.11133i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-0.362134 + 2.51870i) q^{37} +(-1.71836 + 1.98310i) q^{38} +(-0.877087 + 1.92055i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(-0.513005 - 3.56803i) q^{41} +(-3.31843 + 2.13263i) q^{42} +(-8.19369 - 9.45602i) q^{43} +(4.05459 - 1.19054i) q^{44} +1.00000 q^{45} +(-2.86065 - 3.84925i) q^{46} -8.95443 q^{47} +(0.959493 - 0.281733i) q^{48} +(-5.60567 - 6.46928i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.408917 + 2.84408i) q^{51} +(1.77618 + 1.14148i) q^{52} +(-4.05870 + 8.88731i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(0.601389 - 4.18276i) q^{55} +(1.63866 + 3.58816i) q^{56} +(-2.51772 - 0.739270i) q^{57} +(9.75179 + 2.86339i) q^{58} +(-2.31958 - 5.07918i) q^{59} +(0.142315 - 0.989821i) q^{60} +(0.622802 - 0.718752i) q^{61} +(4.07446 - 8.92182i) q^{62} +(-3.31843 - 2.13263i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.77618 - 1.14148i) q^{65} +(2.76729 + 3.19362i) q^{66} +(0.480031 - 0.140950i) q^{67} +2.87333 q^{68} +(2.31304 - 4.20117i) q^{69} +3.94463 q^{70} +(-10.2180 + 3.00027i) q^{71} +(0.654861 + 0.755750i) q^{72} +(3.02217 - 1.94223i) q^{73} +(0.362134 + 2.51870i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-1.09005 + 2.38689i) q^{76} +(-10.9159 + 12.5977i) q^{77} +(-0.300477 + 2.08986i) q^{78} +(1.98127 + 4.33837i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.49745 - 3.27897i) q^{82} +(2.12692 - 14.7930i) q^{83} +(-2.58318 + 2.98115i) q^{84} +(1.19362 - 2.61367i) q^{85} +(-10.5259 - 6.76456i) q^{86} +(1.44641 + 10.0600i) q^{87} +(3.55494 - 2.28462i) q^{88} +(11.7645 + 13.5769i) q^{89} +(0.959493 - 0.281733i) q^{90} -8.32850 q^{91} +(-3.82923 - 2.88739i) q^{92} +9.80817 q^{93} +(-8.59171 + 2.52275i) q^{94} +(1.71836 + 1.98310i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-2.06884 - 14.3891i) q^{97} +(-7.20121 - 4.62793i) q^{98} +(-1.75545 + 3.84389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Introduction

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