LMFDB - Embedded newform 966.2.y.c.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	966.25
Dual form			966.2.y.c.541.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.167516 - 0.690511i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-2.01446 - 1.71521i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.167516 - 0.690511i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-2.01446 - 1.71521i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.697700 + 0.134471i) q^{10} +(0.177614 + 3.72857i) q^{11} +(0.888835 + 0.458227i) q^{12} +(0.811507 + 0.936529i) q^{13} +(-1.80912 + 1.93056i) q^{14} +(-0.101120 + 0.703308i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-0.450816 - 0.633082i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-4.98735 + 7.00375i) q^{19} +(0.101120 + 0.703308i) q^{20} +(1.23268 + 2.34105i) q^{21} +3.73280 q^{22} +(-4.79285 + 0.169076i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.99543 - 2.05979i) q^{25} +(0.974082 - 0.766026i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(1.84230 + 1.89893i) q^{28} +(1.47949 - 3.23962i) q^{29} +(0.697700 + 0.134471i) q^{30} +(4.42185 + 3.47738i) q^{31} +(0.235759 - 0.971812i) q^{32} +(1.22088 - 3.52750i) q^{33} +(-0.653816 + 0.420182i) q^{34} +(-0.846919 + 1.67833i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.873315 - 0.832704i) q^{37} +(6.75851 + 5.31495i) q^{38} +(-0.405304 - 1.17105i) q^{39} +(0.707323 - 0.0675412i) q^{40} +(6.63468 + 1.94812i) q^{41} +(2.39705 - 1.11989i) q^{42} +(-0.577413 - 4.01599i) q^{43} +(0.177614 - 3.72857i) q^{44} +(0.355270 - 0.615346i) q^{45} +(-0.0591690 + 4.79547i) q^{46} +(6.33543 + 10.9733i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(1.11609 + 6.91045i) q^{49} +(-1.86735 - 4.08892i) q^{50} +(0.183230 + 0.755284i) q^{51} +(-0.718810 - 1.00943i) q^{52} +(2.02989 + 5.86499i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(2.54487 - 0.747241i) q^{55} +(1.98444 - 1.74985i) q^{56} +(7.23312 - 4.64845i) q^{57} +(-3.16555 - 1.63196i) q^{58} +(9.32488 - 1.79722i) q^{59} +(0.167516 - 0.690511i) q^{60} +(-13.5794 + 5.43635i) q^{61} +(3.68384 - 4.25138i) q^{62} +(-0.274300 - 2.63149i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.510743 - 0.717239i) q^{65} +(-3.46541 - 1.38734i) q^{66} +(5.16374 - 2.66209i) q^{67} +(0.388596 + 0.673068i) q^{68} +(4.51237 + 1.62436i) q^{69} +(1.63613 + 0.925818i) q^{70} +(12.1678 + 7.81980i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-14.7744 - 1.41079i) q^{73} +(-0.873315 + 0.832704i) q^{74} +(-4.47478 + 0.427290i) q^{75} +(5.63051 - 6.49796i) q^{76} +(6.03750 - 7.81570i) q^{77} +(-1.18901 + 0.349125i) q^{78} +(-4.23893 + 12.2476i) q^{79} +(-0.0338089 - 0.709736i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.26160 - 6.53447i) q^{82} +(-10.6051 + 3.11395i) q^{83} +(-1.00457 - 2.44762i) q^{84} +(-0.361631 + 0.417345i) q^{85} +(-4.03892 + 0.385670i) q^{86} +(-2.57755 + 2.45769i) q^{87} +(-3.71590 - 0.354825i) q^{88} +(4.41346 - 3.47079i) q^{89} +(-0.597745 - 0.384147i) q^{90} +(-0.0284011 - 3.27851i) q^{91} +(4.78722 + 0.287279i) q^{92} +(-2.81269 - 4.87172i) q^{93} +(11.2623 - 5.80613i) q^{94} +(5.67163 + 2.27058i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.60141 - 2.52560i) q^{97} +(6.95573 - 0.786014i) q^{98} +(-2.44447 + 2.82106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	−0.167516	−	0.690511i	−0.0749155	−	0.308806i	0.922009	−	0.387167i	$-0.126546\pi$
$5$	−0.167516	−	0.690511i	−0.0749155	−	0.308806i	−0.996925	+	0.0783612i	$0.975031\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−2.01446	−	1.71521i	−0.761394	−	0.648289i
$7$	−2.01446	−	1.71521i	−0.761394	−	0.648289i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−0.697700	+	0.134471i	−0.220632	+	0.0425234i
$11$	0.177614	+	3.72857i	0.0535526	+	1.12421i	0.852473	+	0.522771i	$0.175102\pi$
$11$	0.177614	+	3.72857i	0.0535526	+	1.12421i	−0.798921	+	0.601436i	$0.794595\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	0.811507	+	0.936529i	0.225072	+	0.259746i	0.857043	−	0.515246i	$-0.172299\pi$
$13$	0.811507	+	0.936529i	0.225072	+	0.259746i	−0.631971	+	0.774992i	$0.717754\pi$
$14$	−1.80912	+	1.93056i	−0.483508	+	0.515965i
$15$	−0.101120	+	0.703308i	−0.0261092	+	0.181593i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−0.450816	−	0.633082i	−0.109339	−	0.153545i	0.756281	−	0.654247i	$-0.227014\pi$
$17$	−0.450816	−	0.633082i	−0.109339	−	0.153545i	−0.865619	+	0.500702i	$0.833075\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	−4.98735	+	7.00375i	−1.14418	+	1.60677i	−0.437528	+	0.899205i	$0.644146\pi$
$19$	−4.98735	+	7.00375i	−1.14418	+	1.60677i	−0.706648	+	0.707565i	$0.749793\pi$
$20$	0.101120	+	0.703308i	0.0226112	+	0.157264i
$21$	1.23268	+	2.34105i	0.268993	+	0.510858i
$22$	3.73280			0.795836
$23$	−4.79285	+	0.169076i	−0.999378	+	0.0352547i
$23$	−4.79285	+	0.169076i	−0.999378	+	0.0352547i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	3.99543	−	2.05979i	0.799087	−	0.411958i
$26$	0.974082	−	0.766026i	0.191033	−	0.150230i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	1.84230	+	1.89893i	0.348161	+	0.358865i
$29$	1.47949	−	3.23962i	0.274734	−	0.601583i	−0.721094	−	0.692837i	$-0.756360\pi$
$29$	1.47949	−	3.23962i	0.274734	−	0.601583i	0.995828	+	0.0912547i	$0.0290877\pi$
$30$	0.697700	+	0.134471i	0.127382	+	0.0245509i
$31$	4.42185	+	3.47738i	0.794187	+	0.624556i	0.930576	−	0.366100i	$-0.119307\pi$
$31$	4.42185	+	3.47738i	0.794187	+	0.624556i	−0.136389	+	0.990655i	$0.543550\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	1.22088	−	3.52750i	0.212528	−	0.614059i
$34$	−0.653816	+	0.420182i	−0.112128	+	0.0720606i
$35$	−0.846919	+	1.67833i	−0.143155	+	0.283690i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−0.873315	−	0.832704i	−0.143572	−	0.136896i	0.614890	−	0.788613i	$-0.289200\pi$
$37$	−0.873315	−	0.832704i	−0.143572	−	0.136896i	−0.758462	+	0.651717i	$0.774049\pi$
$38$	6.75851	+	5.31495i	1.09637	+	0.862199i
$39$	−0.405304	−	1.17105i	−0.0649007	−	0.187518i
$40$	0.707323	−	0.0675412i	0.111838	−	0.0106792i
$41$	6.63468	+	1.94812i	1.03616	+	0.304245i	0.755214	−	0.655478i	$-0.227533\pi$
$41$	6.63468	+	1.94812i	1.03616	+	0.304245i	0.280949	+	0.959723i	$0.409351\pi$
$42$	2.39705	−	1.11989i	0.369873	−	0.172803i
$43$	−0.577413	−	4.01599i	−0.0880546	−	0.612433i	−0.985291	−	0.170883i	$-0.945338\pi$
$43$	−0.577413	−	4.01599i	−0.0880546	−	0.612433i	0.897237	−	0.441550i	$-0.145571\pi$
$44$	0.177614	−	3.72857i	0.0267763	−	0.562104i
$45$	0.355270	−	0.615346i	0.0529606	−	0.0917304i
$46$	−0.0591690	+	4.79547i	−0.00872399	+	0.707053i
$47$	6.33543	+	10.9733i	0.924118	+	1.60062i	0.792974	+	0.609256i	$0.208532\pi$
$47$	6.33543	+	10.9733i	0.924118	+	1.60062i	0.131144	+	0.991363i	$0.458135\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	1.11609	+	6.91045i	0.159441	+	0.987207i
$50$	−1.86735	−	4.08892i	−0.264083	−	0.578260i
$51$	0.183230	+	0.755284i	0.0256573	+	0.105761i
$52$	−0.718810	−	1.00943i	−0.0996810	−	0.139982i
$53$	2.02989	+	5.86499i	0.278827	+	0.805618i	0.994265	+	0.106942i	$0.0341059\pi$
$53$	2.02989	+	5.86499i	0.278827	+	0.805618i	−0.715438	+	0.698676i	$0.753773\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	2.54487	−	0.747241i	0.343150	−	0.100758i
$56$	1.98444	−	1.74985i	0.265182	−	0.233834i
$57$	7.23312	−	4.64845i	0.958051	−	0.615702i
$58$	−3.16555	−	1.63196i	−0.415658	−	0.214286i
$59$	9.32488	−	1.79722i	1.21400	−	0.233979i	0.458238	−	0.888829i	$-0.348481\pi$
$59$	9.32488	−	1.79722i	1.21400	−	0.233979i	0.755758	+	0.654851i	$0.227269\pi$
$60$	0.167516	−	0.690511i	0.0216263	−	0.0891446i
$61$	−13.5794	+	5.43635i	−1.73866	+	0.696054i	−0.738906	+	0.673809i	$0.764657\pi$
$61$	−13.5794	+	5.43635i	−1.73866	+	0.696054i	−0.999753	+	0.0222450i	$0.992919\pi$
$62$	3.68384	−	4.25138i	0.467848	−	0.539925i
$63$	−0.274300	−	2.63149i	−0.0345586	−	0.331537i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.510743	−	0.717239i	0.0633499	−	0.0889625i
$66$	−3.46541	−	1.38734i	−0.426563	−	0.170770i
$67$	5.16374	−	2.66209i	0.630851	−	0.325226i	−0.112977	−	0.993598i	$-0.536039\pi$
$67$	5.16374	−	2.66209i	0.630851	−	0.325226i	0.743828	+	0.668371i	$0.233008\pi$
$68$	0.388596	+	0.673068i	0.0471242	+	0.0816215i
$69$	4.51237	+	1.62436i	0.543225	+	0.195550i
$70$	1.63613	+	0.925818i	0.195555	+	0.110656i
$71$	12.1678	+	7.81980i	1.44406	+	0.928040i	0.999478	+	0.0323002i	$0.0102832\pi$
$71$	12.1678	+	7.81980i	1.44406	+	0.928040i	0.444580	+	0.895739i	$0.353353\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	−14.7744	−	1.41079i	−1.72922	−	0.165120i	−0.817497	−	0.575933i	$-0.804639\pi$
$73$	−14.7744	−	1.41079i	−1.72922	−	0.165120i	−0.911720	+	0.410812i	$0.865245\pi$
$74$	−0.873315	+	0.832704i	−0.101521	+	0.0967999i
$75$	−4.47478	+	0.427290i	−0.516703	+	0.0493391i
$76$	5.63051	−	6.49796i	0.645864	−	0.745367i
$77$	6.03750	−	7.81570i	0.688037	−	0.890682i
$78$	−1.18901	+	0.349125i	−0.134629	+	0.0395306i
$79$	−4.23893	+	12.2476i	−0.476917	+	1.37796i	0.408328	+	0.912835i	$0.366112\pi$
$79$	−4.23893	+	12.2476i	−0.476917	+	1.37796i	−0.885245	+	0.465125i	$0.846009\pi$
$80$	−0.0338089	−	0.709736i	−0.00377995	−	0.0793508i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	2.26160	−	6.53447i	0.249752	−	0.721612i
$83$	−10.6051	+	3.11395i	−1.16406	+	0.341800i	−0.806010	−	0.591901i	$-0.798377\pi$
$83$	−10.6051	+	3.11395i	−1.16406	+	0.341800i	−0.358053	+	0.933701i	$0.616559\pi$
$84$	−1.00457	−	2.44762i	−0.109607	−	0.267057i
$85$	−0.361631	+	0.417345i	−0.0392244	+	0.0452674i
$86$	−4.03892	+	0.385670i	−0.435528	+	0.0415879i
$87$	−2.57755	+	2.45769i	−0.276343	+	0.263492i
$88$	−3.71590	−	0.354825i	−0.396116	−	0.0378245i
$89$	4.41346	−	3.47079i	0.467826	−	0.367903i	−0.356241	−	0.934394i	$-0.615942\pi$
$89$	4.41346	−	3.47079i	0.467826	−	0.367903i	0.824068	+	0.566491i	$0.191700\pi$
$90$	−0.597745	−	0.384147i	−0.0630078	−	0.0404927i
$91$	−0.0284011	−	3.27851i	−0.00297724	−	0.343681i
$92$	4.78722	+	0.287279i	0.499102	+	0.0299510i
$93$	−2.81269	−	4.87172i	−0.291662	−	0.505174i
$94$	11.2623	−	5.80613i	1.16162	−	0.598856i
$95$	5.67163	+	2.27058i	0.581897	+	0.232956i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	−8.60141	−	2.52560i	−0.873341	−	0.256436i	−0.185805	−	0.982587i	$-0.559489\pi$
$97$	−8.60141	−	2.52560i	−0.873341	−	0.256436i	−0.687536	+	0.726150i	$0.741308\pi$
$98$	6.95573	−	0.786014i	0.702635	−	0.0793994i
$99$	−2.44447	+	2.82106i	−0.245678	+	0.283528i
$100$	−4.17314	+	1.67067i	−0.417314	+	0.167067i
$101$	−1.54548	+	6.37054i	−0.153781	+	0.633892i	0.841784	+	0.539814i	$0.181505\pi$
$101$	−1.54548	+	6.37054i	−0.153781	+	0.633892i	−0.995565	+	0.0940779i	$0.970010\pi$
$102$	0.763147	−	0.147085i	0.0755629	−	0.0145635i
$103$	1.92133	+	0.990516i	0.189314	+	0.0975984i	0.550278	−	0.834982i	$-0.314522\pi$
$103$	1.92133	+	0.990516i	0.189314	+	0.0975984i	−0.360963	+	0.932580i	$0.617552\pi$
$104$	−1.04249	+	0.669965i	−0.102224	+	0.0656955i
$105$	1.41003	−	1.24334i	0.137604	−	0.121338i
$106$	5.95493	−	1.74853i	0.578394	−	0.169832i
$107$	−2.32426	+	0.930493i	−0.224695	+	0.0899541i	−0.481278	−	0.876568i	$-0.659827\pi$
$107$	−2.32426	+	0.930493i	−0.224695	+	0.0899541i	0.256584	+	0.966522i	$0.417403\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	2.42911	+	3.41121i	0.232667	+	0.326735i	0.914359	−	0.404904i	$-0.132695\pi$
$109$	2.42911	+	3.41121i	0.232667	+	0.326735i	−0.681692	+	0.731639i	$0.738756\pi$
$110$	−0.625305	−	2.57754i	−0.0596205	−	0.245759i
$111$	0.501273	+	1.09763i	0.0475787	+	0.104183i
$112$	−1.65345	−	2.06546i	−0.156236	−	0.195167i
$113$	3.34910	+	2.15233i	0.315056	+	0.202474i	0.688606	−	0.725136i	$-0.258223\pi$
$113$	3.34910	+	2.15233i	0.315056	+	0.202474i	−0.373549	+	0.927610i	$0.621859\pi$
$114$	−4.29902	−	7.44611i	−0.402640	−	0.697392i
$115$	0.919629	+	3.28119i	0.0857558	+	0.305973i
$116$	−1.78073	+	3.08432i	−0.165337	+	0.286372i
$117$	−0.0589638	+	1.23780i	−0.00545120	+	0.114435i
$118$	−1.35149	−	9.39984i	−0.124415	−	0.865325i
$119$	−0.177721	+	2.04856i	−0.0162916	+	0.187791i
$120$	−0.681758	−	0.200182i	−0.0622357	−	0.0182741i
$121$	−2.92052	+	0.278876i	−0.265502	+	0.0253524i
$122$	4.78406	+	13.8226i	0.433129	+	1.25144i
$123$	−5.43538	−	4.27443i	−0.490092	−	0.385413i
$124$	−4.07128	−	3.88196i	−0.365612	−	0.348610i
$125$	−4.41813	−	5.09880i	−0.395170	−	0.456050i
$126$	−2.64156	+	0.148778i	−0.235329	+	0.0132542i
$127$	4.88246	−	3.13776i	0.433248	−	0.278431i	−0.305785	−	0.952100i	$-0.598919\pi$
$127$	4.88246	−	3.13776i	0.433248	−	0.278431i	0.739033	+	0.673669i	$0.235283\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	−0.956543	+	3.94292i	−0.0842189	+	0.347155i
$130$	−0.692124	−	0.544292i	−0.0607033	−	0.0477376i
$131$	−5.58933	−	1.07726i	−0.488342	−	0.0941202i	−0.0608643	−	0.998146i	$-0.519386\pi$
$131$	−5.58933	−	1.07726i	−0.488342	−	0.0941202i	−0.427478	+	0.904026i	$0.640598\pi$
$132$	−1.55066	+	3.39548i	−0.134968	+	0.295538i
$133$	22.0597	−	5.55440i	1.91282	−	0.481628i
$134$	−2.41338	−	5.28456i	−0.208484	−	0.456516i
$135$	−0.558522	+	0.439227i	−0.0480700	+	0.0378026i
$136$	0.690796	−	0.356130i	0.0592353	−	0.0305379i
$137$	10.0440	−	17.3968i	0.858119	−	1.48630i	−0.0156028	−	0.999878i	$-0.504967\pi$
$137$	10.0440	−	17.3968i	0.858119	−	1.48630i	0.873721	−	0.486427i	$-0.161700\pi$
$138$	1.83723	−	4.42997i	0.156395	−	0.377104i
$139$	−17.3207			−1.46912			−0.734562	−	0.678541i	$-0.762613\pi$
$139$	−17.3207			−1.46912			−0.734562	+	0.678541i	$0.762613\pi$
$140$	1.00262	−	1.59023i	0.0847369	−	0.134399i
$141$	−1.80325	−	12.5419i	−0.151861	−	1.05622i
$142$	8.38991	−	11.7820i	0.704066	−	0.988722i
$143$	−3.34778	+	3.19210i	−0.279956	+	0.266937i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−2.48483	−	0.478912i	−0.206354	−	0.0397715i
$146$	−2.11219	+	14.6906i	−0.174806	+	1.21580i
$147$	1.53221	−	6.83025i	0.126375	−	0.563350i
$148$	0.790207	+	0.911947i	0.0649546	+	0.0749616i
$149$	−2.97968	−	1.53613i	−0.244105	−	0.125845i	0.331833	−	0.943338i	$-0.392333\pi$
$149$	−2.97968	−	1.53613i	−0.244105	−	0.125845i	−0.575938	+	0.817493i	$0.695363\pi$
$150$	0.213887	+	4.49004i	0.0174638	+	0.366610i
$151$	−11.0971	+	2.13879i	−0.903069	+	0.174052i	−0.619589	−	0.784926i	$-0.712701\pi$
$151$	−11.0971	+	2.13879i	−0.903069	+	0.174052i	−0.283479	+	0.958978i	$0.591489\pi$
$152$	−6.22269	−	5.93332i	−0.504727	−	0.481256i
$153$	0.110606	−	0.769282i	0.00894196	−	0.0621927i
$154$	−7.51958	−	6.40255i	−0.605945	−	0.515932i
$155$	1.66044	−	3.63585i	0.133370	−	0.292039i
$156$	0.292154	+	1.20427i	0.0233910	+	0.0964191i
$157$	−14.2913	−	1.36466i	−1.14057	−	0.108912i	−0.492375	−	0.870383i	$-0.663871\pi$
$157$	−14.2913	−	1.36466i	−1.14057	−	0.108912i	−0.648198	+	0.761472i	$0.724477\pi$
$158$	12.0320	+	4.81689i	0.957215	+	0.383211i
$159$	0.295309	−	6.19930i	0.0234195	−	0.491637i
$160$	−0.710540			−0.0561731
$161$	9.94500	+	7.88016i	0.783776	+	0.621044i
$162$	1.00000			0.0785674
$163$	0.637899	−	13.3912i	0.0499641	−	1.04888i	−0.825136	−	0.564934i	$-0.808902\pi$
$163$	0.637899	−	13.3912i	0.0499641	−	1.04888i	0.875100	−	0.483942i	$-0.160795\pi$
$164$	−6.41946	−	2.56996i	−0.501275	−	0.200680i
$165$	−2.64030	−	0.252118i	−0.205547	−	0.0196273i
$166$	2.60581	+	10.7413i	0.202250	+	0.833685i
$167$	−8.47146	+	18.5499i	−0.655542	+	1.43544i	0.231077	+	0.972935i	$0.425775\pi$
$167$	−8.47146	+	18.5499i	−0.655542	+	1.43544i	−0.886619	+	0.462501i	$0.846952\pi$
$168$	−2.49265	+	0.886966i	−0.192312	+	0.0684309i
$169$	1.63155	−	11.3477i	0.125504	−	0.872898i
$170$	0.399665	+	0.381080i	0.0306529	+	0.0292275i
$171$	−8.44265	+	1.62719i	−0.645626	+	0.124434i
$172$	0.193054	+	4.05270i	0.0147202	+	0.309015i
$173$	4.90692	+	2.52969i	0.373066	+	0.192329i	0.634555	−	0.772878i	$-0.281183\pi$
$173$	4.90692	+	2.52969i	0.373066	+	0.192329i	−0.261489	+	0.965206i	$0.584214\pi$
$174$	2.33226	+	2.69157i	0.176808	+	0.204048i
$175$	−11.5816	−	2.70366i	−0.875488	−	0.204377i
$176$	−0.531233	+	3.69481i	−0.0400432	+	0.278507i
$177$	−9.32488	−	1.79722i	−0.700901	−	0.135088i
$178$	−3.25685	−	4.57361i	−0.244112	−	0.342807i
$179$	−16.2965	+	15.5387i	−1.21806	+	1.16142i	−0.236222	+	0.971699i	$0.575909\pi$
$179$	−16.2965	+	15.5387i	−1.21806	+	1.16142i	−0.981838	+	0.189719i	$0.939242\pi$
$180$	−0.412154	+	0.578789i	−0.0307201	+	0.0431404i
$181$	1.28822	+	8.95978i	0.0957528	+	0.665975i	0.980006	+	0.198968i	$0.0637588\pi$
$181$	1.28822	+	8.95978i	0.0957528	+	0.665975i	−0.884253	+	0.467008i	$0.845332\pi$
$182$	−3.27615	−	0.127629i	−0.242844	−	0.00946047i
$183$	14.6271			1.08127
$184$	0.514739	−	4.76813i	0.0379471	−	0.351511i
$185$	−0.428697	+	0.742525i	−0.0315184	+	0.0545915i
$186$	−5.00004	+	2.57770i	−0.366620	+	0.189006i
$187$	2.28042	−	1.79334i	0.166761	−	0.131142i
$188$	−5.26367	−	11.5258i	−0.383892	−	0.840607i
$189$	−0.723376	+	2.54494i	−0.0526179	+	0.185117i
$190$	2.53787	−	5.55717i	0.184117	−	0.403159i
$191$	10.0313	+	1.93338i	0.725840	+	0.139894i	0.538771	−	0.842453i	$-0.318889\pi$
$191$	10.0313	+	1.93338i	0.725840	+	0.139894i	0.187069	+	0.982347i	$0.440101\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	−6.08481	+	25.0819i	−0.437994	+	1.80544i	0.140890	+	0.990025i	$0.455004\pi$
$193$	−6.08481	+	25.0819i	−0.437994	+	1.80544i	−0.578884	+	0.815410i	$0.696511\pi$
$194$	−2.93201	+	8.47150i	−0.210506	+	0.608218i
$195$	−0.740729	+	0.476037i	−0.0530447	+	0.0340897i
$196$	−0.454156	−	6.98525i	−0.0324397	−	0.498947i
$197$	−7.10626	−	8.20107i	−0.506300	−	0.584302i	0.443847	−	0.896102i	$-0.353613\pi$
$197$	−7.10626	−	8.20107i	−0.506300	−	0.584302i	−0.950148	+	0.311801i	$0.899068\pi$
$198$	2.70156	+	2.57593i	0.191991	+	0.183063i
$199$	−4.61035	−	3.62562i	−0.326819	−	0.257013i	0.441244	−	0.897387i	$-0.354537\pi$
$199$	−4.61035	−	3.62562i	−0.326819	−	0.257013i	−0.768064	+	0.640373i	$0.778780\pi$
$200$	1.47021	+	4.24790i	0.103960	+	0.300372i
$201$	−5.78325	+	0.552233i	−0.407919	+	0.0389515i
$202$	6.28978	+	1.84685i	0.442548	+	0.129944i
$203$	−8.53700	+	3.98845i	−0.599180	+	0.279934i
$204$	−0.110606	−	0.769282i	−0.00774397	−	0.0538605i
$205$	0.233781	−	4.90766i	0.0163280	−	0.342766i
$206$	1.08081	−	1.87203i	0.0753039	−	0.130430i
$207$	−3.58542	−	3.18508i	−0.249204	−	0.221378i
$208$	0.619603	+	1.07318i	0.0429617	+	0.0744119i
$209$	−26.9998	−	17.3517i	−1.86762	−	1.20024i
$210$	−1.17484	−	1.46759i	−0.0810718	−	0.101273i
$211$	−2.71823	−	5.95209i	−0.187131	−	0.409759i	0.792694	−	0.609620i	$-0.208678\pi$
$211$	−2.71823	−	5.95209i	−0.187131	−	0.409759i	−0.979824	+	0.199861i	$0.935951\pi$
$212$	−1.46320	−	6.03138i	−0.100493	−	0.414237i
$213$	−8.38991	−	11.7820i	−0.574867	−	0.807288i
$214$	0.818846	+	2.36590i	0.0559752	+	0.161730i
$215$	−2.67636	+	1.07145i	−0.182526	+	0.0730726i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−2.94318	−	14.5894i	−0.199796	−	0.990396i
$218$	3.52293	−	2.26405i	0.238603	−	0.153341i
$219$	13.1918	+	6.80083i	0.891418	+	0.459558i
$220$	−2.60438	+	0.501952i	−0.175587	+	0.0338416i
$221$	0.227060	−	0.935953i	0.0152737	−	0.0629590i
$222$	1.12024	−	0.448477i	0.0751857	−	0.0300998i
$223$	−14.8301	+	17.1148i	−0.993094	+	1.14609i	−0.00382398	+	0.999993i	$0.501217\pi$
$223$	−14.8301	+	17.1148i	−0.993094	+	1.14609i	−0.989270	+	0.146099i	$0.953328\pi$
$224$	−2.14179	+	1.55330i	−0.143104	+	0.103784i
$225$	4.31305	+	1.26643i	0.287537	+	0.0844283i
$226$	2.30925	−	3.24289i	0.153609	−	0.215714i
$227$	6.54039	+	2.61838i	0.434101	+	0.173788i	0.578412	−	0.815744i	$-0.303672\pi$
$227$	6.54039	+	2.61838i	0.434101	+	0.173788i	−0.144311	+	0.989532i	$0.546097\pi$
$228$	−7.64223	+	3.93985i	−0.506119	+	0.260923i
$229$	11.9701	+	20.7329i	0.791009	+	1.37007i	0.925343	+	0.379131i	$0.123777\pi$
$229$	11.9701	+	20.7329i	0.791009	+	1.37007i	−0.134334	+	0.990936i	$0.542889\pi$
$230$	3.32124	−	0.762462i	0.218996	−	0.0502752i
$231$	−8.50983	+	5.01194i	−0.559905	+	0.329761i
$232$	2.99609	+	1.92547i	0.196703	+	0.126413i
$233$	−4.10489	+	3.22812i	−0.268920	+	0.211481i	−0.743508	−	0.668727i	$-0.766840\pi$
$233$	−4.10489	+	3.22812i	−0.268920	+	0.211481i	0.474588	+	0.880208i	$0.342597\pi$
$234$	1.23359	+	0.117794i	0.0806426	+	0.00770043i
$235$	6.51589	−	6.21289i	0.425050	−	0.405284i
$236$	−9.45350	+	0.902699i	−0.615370	+	0.0587607i
$237$	8.48725	−	9.79481i	0.551306	−	0.636241i
$238$	2.03779	+	0.274994i	0.132090	+	0.0178252i
$239$	3.59796	−	1.05646i	0.232733	−	0.0683365i	−0.163287	−	0.986579i	$-0.552210\pi$
$239$	3.59796	−	1.05646i	0.232733	−	0.0683365i	0.396019	+	0.918242i	$0.370391\pi$
$240$	−0.232395	+	0.671461i	−0.0150010	+	0.0433426i
$241$	0.204916	+	4.30171i	0.0131998	+	0.277098i	0.995812	+	0.0914268i	$0.0291427\pi$
$241$	0.204916	+	4.30171i	0.0131998	+	0.277098i	−0.982612	+	0.185671i	$0.940554\pi$
$242$	0.139596	+	2.93048i	0.00897358	+	0.188379i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	14.0346	−	4.12094i	0.898475	−	0.263816i
$245$	4.58478	−	1.92829i	0.292911	−	0.123194i
$246$	−4.52822	+	5.22584i	−0.288709	+	0.333187i
$247$	−10.6065	+	1.01280i	−0.674874	+	0.0644427i
$248$	−4.07128	+	3.88196i	−0.258526	+	0.246504i
$249$	11.0028	+	1.05064i	0.697274	+	0.0665816i
$250$	−5.30324	+	4.17052i	−0.335407	+	0.263767i
$251$	−11.5794	−	7.44165i	−0.730887	−	0.469713i	0.121522	−	0.992589i	$-0.461223\pi$
$251$	−11.5794	−	7.44165i	−0.730887	−	0.469713i	−0.852409	+	0.522876i	$0.824859\pi$
$252$	0.0229188	+	2.64565i	0.00144375	+	0.166660i
$253$	−1.48169	−	17.8405i	−0.0931529	−	1.12162i
$254$	−2.90189	−	5.02623i	−0.182081	−	0.315373i
$255$	0.490838	−	0.253045i	0.0307375	−	0.0158463i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	16.1572	−	22.6896i	1.00786	−	1.41534i	0.100523	−	0.994935i	$-0.467949\pi$
$257$	16.1572	−	22.6896i	1.00786	−	1.41534i	0.907336	−	0.420405i	$-0.138112\pi$
$258$	3.89294	+	1.14307i	0.242364	+	0.0711645i
$259$	0.330992	+	3.17537i	0.0205669	+	0.197308i
$260$	−0.576609	+	0.665442i	−0.0357597	+	0.0412689i
$261$	3.30635	−	1.32366i	0.204658	−	0.0819326i
$262$	−1.34199	+	5.53174i	−0.0829082	+	0.341752i
$263$	1.50718	−	0.290485i	0.0929368	−	0.0179121i	−0.142571	−	0.989785i	$-0.545537\pi$
$263$	1.50718	−	0.290485i	0.0929368	−	0.0179121i	0.235508	+	0.971873i	$0.424325\pi$
$264$	3.31785	+	1.71047i	0.204199	+	0.105272i
$265$	3.70980	−	2.38414i	0.227891	−	0.146457i
$266$	−4.49847	−	22.2990i	−0.275819	−	1.36724i
$267$	−5.38728	+	1.58185i	−0.329696	+	0.0968075i
$268$	−5.39340	+	2.15919i	−0.329455	+	0.131894i
$269$	7.14372	+	20.6404i	0.435561	+	1.25847i	0.922826	+	0.385216i	$0.125873\pi$
$269$	7.14372	+	20.6404i	0.435561	+	1.25847i	−0.487266	+	0.873254i	$0.662006\pi$
$270$	0.412154	+	0.578789i	0.0250829	+	0.0352240i
$271$	−5.03975	−	20.7741i	−0.306143	−	1.26194i	−0.892189	−	0.451661i	$-0.850832\pi$
$271$	−5.03975	−	20.7741i	−0.306143	−	1.26194i	0.586046	−	0.810277i	$-0.300684\pi$
$272$	−0.322857	−	0.706959i	−0.0195761	−	0.0428657i
$273$	−1.19213	+	3.05422i	−0.0721511	+	0.184850i
$274$	−16.8991	−	10.8604i	−1.02091	−	0.656102i
$275$	8.38972	+	14.5314i	0.505919	+	0.876277i
$276$	−4.33753	−	2.04593i	−0.261089	−	0.123151i
$277$	−13.9962	+	24.2422i	−0.840952	+	1.45657i	0.0481394	+	0.998841i	$0.484671\pi$
$277$	−13.9962	+	24.2422i	−0.840952	+	1.45657i	−0.889091	+	0.457730i	$0.848663\pi$
$278$	−0.824153	+	17.3011i	−0.0494294	+	1.03765i
$279$	0.800575	+	5.56812i	0.0479292	+	0.333355i
$280$	−1.54072	−	1.07715i	−0.0920757	−	0.0643721i
$281$	28.7935	+	8.45455i	1.71768	+	0.504356i	0.984456	−	0.175633i	$-0.0561971\pi$
$281$	28.7935	+	8.45455i	1.71768	+	0.504356i	0.733223	+	0.679989i	$0.238015\pi$
$282$	−12.6135	+	1.20444i	−0.751122	+	0.0717235i
$283$	5.60933	+	16.2071i	0.333440	+	0.963412i	0.979730	+	0.200321i	$0.0641984\pi$
$283$	5.60933	+	16.2071i	0.333440	+	0.963412i	−0.646290	+	0.763092i	$0.723680\pi$
$284$	−11.3694	−	8.94102i	−0.674652	−	0.530552i
$285$	−4.42147	−	4.21586i	−0.261905	−	0.249726i
$286$	3.02920	+	3.49588i	0.179120	+	0.206716i
$287$	−10.0239	−	15.3043i	−0.591689	−	0.903384i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	5.36260	−	15.4942i	0.315447	−	0.911424i
$290$	−0.596603	+	2.45923i	−0.0350337	+	0.144411i
$291$	7.04660	+	5.54151i	0.413079	+	0.324849i
$292$	14.5734	+	2.80880i	0.852846	+	0.164373i
$293$	3.47589	−	7.61114i	0.203064	−	0.444648i	−0.780513	−	0.625140i	$-0.785042\pi$
$293$	3.47589	−	7.61114i	0.203064	−	0.444648i	0.983576	+	0.180492i	$0.0577691\pi$
$294$	−6.74961	−	1.85547i	−0.393645	−	0.108213i
$295$	−2.80307	−	6.13787i	−0.163201	−	0.357361i
$296$	0.948514	−	0.745920i	0.0551313	−	0.0433557i
$297$	3.31785	−	1.71047i	0.192521	−	0.0992515i
$298$	−1.67617	+	2.90321i	−0.0970979	+	0.168178i
$299$	−4.04778	−	4.35144i	−0.234089	−	0.251650i
$300$	4.49513			0.259527
$301$	−5.72511	+	9.08044i	−0.329990	+	0.523388i
$302$	1.60835	+	11.1863i	0.0925499	+	0.643699i
$303$	3.80246	−	5.33981i	0.218446	−	0.306764i
$304$	−6.22269	+	5.93332i	−0.356896	+	0.340299i
$305$	6.02863	+	8.46602i	0.345198	+	0.484763i
$306$	−0.763147	−	0.147085i	−0.0436262	−	0.00840827i
$307$	−0.0755016	+	0.525125i	−0.00430910	+	0.0299705i	−0.991863	−	0.127313i	$-0.959365\pi$
$307$	−0.0755016	+	0.525125i	−0.00430910	+	0.0299705i	0.987553	+	0.157284i	$0.0502737\pi$
$308$	−6.75309	+	7.20641i	−0.384793	+	0.410623i
$309$	−1.41557	−	1.63365i	−0.0805287	−	0.0929351i
$310$	−3.55273	−	1.83156i	−0.201781	−	0.104026i
$311$	1.34905	+	28.3201i	0.0764977	+	1.60588i	0.632403	+	0.774639i	$0.282069\pi$
$311$	1.34905	+	28.3201i	0.0764977	+	1.60588i	−0.555906	+	0.831245i	$0.687628\pi$
$312$	1.21681	−	0.234521i	0.0688884	−	0.0132771i
$313$	2.78454	+	2.65505i	0.157392	+	0.150073i	0.764683	−	0.644407i	$-0.222896\pi$
$313$	2.78454	+	2.65505i	0.157392	+	0.150073i	−0.607292	+	0.794479i	$0.707744\pi$
$314$	−2.04312	+	14.2102i	−0.115300	+	0.801929i
$315$	−1.77113	+	0.630225i	−0.0997917	+	0.0355092i
$316$	5.38394	−	11.7892i	0.302870	−	0.663193i
$317$	3.28215	+	13.5292i	0.184344	+	0.759877i	0.986635	+	0.162944i	$0.0520990\pi$
$317$	3.28215	+	13.5292i	0.184344	+	0.759877i	−0.802291	+	0.596933i	$0.796386\pi$
$318$	−6.17823	−	0.589949i	−0.346458	−	0.0330827i
$319$	12.3419	+	4.94097i	0.691016	+	0.276641i
$320$	−0.0338089	+	0.709736i	−0.00188997	+	0.0396754i
$321$	2.50360			0.139737
$322$	8.34444	−	9.55878i	0.465017	−	0.532690i
$323$	6.68232			0.371814
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	5.17138	+	2.07031i	0.286856	+	0.114840i
$326$	−13.3456	−	1.27435i	−0.739146	−	0.0705799i
$327$	−0.987291	−	4.06967i	−0.0545973	−	0.225053i
$328$	−2.87250	+	6.28990i	−0.158607	+	0.347302i
$329$	6.05906	−	32.9719i	0.334047	−	1.81780i
$330$	−0.377463	+	2.62531i	−0.0207786	+	0.144519i
$331$	−9.05721	−	8.63603i	−0.497829	−	0.474679i	0.399066	−	0.916922i	$-0.369334\pi$
$331$	−9.05721	−	8.63603i	−0.497829	−	0.474679i	−0.896895	+	0.442243i	$0.854183\pi$
$332$	10.8531	−	2.09176i	0.595641	−	0.114800i
$333$	−0.0574161	−	1.20531i	−0.00314638	−	0.0660507i
$334$	18.1258	+	9.34451i	0.991801	+	0.511309i
$335$	−2.70321	−	3.11968i	−0.147692	−	0.170446i
$336$	0.767357	+	2.53203i	0.0418627	+	0.138133i
$337$	−2.24644	+	15.6243i	−0.122371	+	0.851111i	0.832486	+	0.554046i	$0.186917\pi$
$337$	−2.24644	+	15.6243i	−0.122371	+	0.851111i	−0.954857	+	0.297065i	$0.903992\pi$
$338$	−11.2572	−	2.16965i	−0.612311	−	0.118013i
$339$	−2.30925	−	3.24289i	−0.125421	−	0.176130i
$340$	0.399665	−	0.381080i	0.0216749	−	0.0206670i
$341$	−12.1803	+	17.1048i	−0.659599	+	0.926277i
$342$	1.22363	+	8.51051i	0.0661662	+	0.460196i
$343$	9.60458	−	15.8352i	0.518598	−	0.855018i
$344$	4.05729			0.218754
$345$	0.365743	−	3.38795i	0.0196909	−	0.182401i
$346$	2.76031	−	4.78099i	0.148395	−	0.257028i
$347$	21.3395	−	11.0013i	1.14556	−	0.590578i	0.222387	−	0.974958i	$-0.428615\pi$
$347$	21.3395	−	11.0013i	1.14556	−	0.590578i	0.923175	+	0.384380i	$0.125585\pi$
$348$	2.79950	−	2.20155i	0.150069	−	0.118015i
$349$	0.624835	+	1.36820i	0.0334466	+	0.0732379i	0.925618	−	0.378459i	$-0.123546\pi$
$349$	0.624835	+	1.36820i	0.0334466	+	0.0732379i	−0.892171	+	0.451697i	$0.850819\pi$
$350$	−3.25167	+	11.4398i	−0.173809	+	0.611486i
$351$	0.514785	−	1.12722i	0.0274772	−	0.0601666i
$352$	3.66534	+	0.706437i	0.195364	+	0.0376532i
$353$	−12.0480	−	9.47465i	−0.641250	−	0.504285i	0.243773	−	0.969832i	$-0.421615\pi$
$353$	−12.0480	−	9.47465i	−0.641250	−	0.504285i	−0.885023	+	0.465548i	$0.845857\pi$
$354$	−2.23888	+	9.22881i	−0.118995	+	0.490506i
$355$	3.36135	−	9.71198i	0.178402	−	0.515458i
$356$	−4.72340	+	3.03554i	−0.250340	+	0.160884i
$357$	0.926364	−	1.83577i	0.0490284	−	0.0971592i
$358$	14.7457	+	17.0174i	0.779334	+	0.899400i
$359$	−16.1115	−	15.3623i	−0.850334	−	0.810792i	0.133280	−	0.991078i	$-0.457449\pi$
$359$	−16.1115	−	15.3623i	−0.850334	−	0.810792i	−0.983614	+	0.180287i	$0.942297\pi$
$360$	0.558522	+	0.439227i	0.0294367	+	0.0231493i
$361$	−17.9646	−	51.9052i	−0.945504	−	2.73185i
$362$	9.01093	−	0.860439i	0.473604	−	0.0452237i
$363$	2.81497	+	0.826549i	0.147747	+	0.0433826i
$364$	−0.283369	+	3.26636i	−0.0148526	+	0.171204i
$365$	1.50079	+	10.4382i	0.0785551	+	0.546363i
$366$	0.695987	−	14.6106i	0.0363798	−	0.763706i
$367$	6.70633	−	11.6157i	0.350068	−	0.606335i	−0.636193	−	0.771530i	$-0.719492\pi$
$367$	6.70633	−	11.6157i	0.350068	−	0.606335i	0.986261	+	0.165195i	$0.0528253\pi$
$368$	−4.73823	−	0.741033i	−0.246998	−	0.0386290i
$369$	3.45739	+	5.98837i	0.179984	+	0.311742i
$370$	0.721286	+	0.463542i	0.0374979	+	0.0240984i
$371$	5.97057	−	15.2965i	0.309976	−	0.794153i
$372$	2.33687	+	5.11702i	0.121161	+	0.265305i
$373$	1.27692	+	5.26353i	0.0661163	+	0.272535i	0.995269	−	0.0971622i	$-0.0309766\pi$
$373$	1.27692	+	5.26353i	0.0661163	+	0.272535i	−0.929152	+	0.369697i	$0.879461\pi$
$374$	−1.68281	−	2.36317i	−0.0870158	−	0.122197i
$375$	2.20662	+	6.37561i	0.113949	+	0.329235i
$376$	−11.7632	+	4.70928i	−0.606642	+	0.242863i
$377$	4.23461	−	1.24339i	0.218094	−	0.0640381i
$378$	2.50764	+	0.843650i	0.128979	+	0.0433927i
$379$	−6.57223	+	4.22372i	−0.337593	+	0.216958i	−0.698442	−	0.715666i	$-0.746123\pi$
$379$	−6.57223	+	4.22372i	−0.337593	+	0.216958i	0.360849	+	0.932624i	$0.382487\pi$
$380$	−5.43012	−	2.79942i	−0.278559	−	0.143607i
$381$	−5.69890	+	1.09837i	−0.291964	+	0.0562714i
$382$	2.40849	−	9.92795i	0.123229	−	0.507958i
$383$	9.17305	−	3.67234i	0.468721	−	0.187648i	−0.125264	−	0.992123i	$-0.539978\pi$
$383$	9.17305	−	3.67234i	0.468721	−	0.187648i	0.593985	+	0.804476i	$0.297554\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−6.40821	−	2.85971i	−0.326593	−	0.145744i
$386$	24.7640	+	7.27136i	1.26045	+	0.370102i
$387$	2.35346	−	3.30497i	0.119633	−	0.168001i
$388$	8.32239	+	3.33178i	0.422505	+	0.169146i
$389$	−26.6833	+	13.7562i	−1.35290	+	0.697467i	−0.973697	−	0.227847i	$-0.926831\pi$
$389$	−26.6833	+	13.7562i	−1.35290	+	0.697467i	−0.379201	+	0.925314i	$0.623801\pi$
$390$	0.440253	+	0.762540i	0.0222931	+	0.0386127i
$391$	2.26773	+	2.95805i	0.114684	+	0.149595i
$392$	−6.99895	+	0.121270i	−0.353500	+	0.00612507i
$393$	4.78858	+	3.07743i	0.241552	+	0.155236i
$394$	−8.52991	+	6.70799i	−0.429730	+	0.337944i
$395$	9.16718	+	0.875360i	0.461251	+	0.0440441i
$396$	2.70156	−	2.57593i	0.135758	−	0.129445i
$397$	23.1098	−	2.20672i	1.15985	−	0.110752i	0.502664	−	0.864482i	$-0.332353\pi$
$397$	23.1098	−	2.20672i	1.15985	−	0.110752i	0.657184	+	0.753730i	$0.271747\pi$
$398$	−3.84088	+	4.43262i	−0.192526	+	0.222187i
$399$	−22.5439	−	3.04224i	−1.12861	−	0.152303i
$400$	4.31305	−	1.26643i	0.215652	−	0.0633213i
$401$	−3.80699	+	10.9996i	−0.190112	+	0.549292i	−0.999266	−	0.0383040i	$-0.987804\pi$
$401$	−3.80699	+	10.9996i	−0.190112	+	0.549292i	0.809154	+	0.587596i	$0.199926\pi$
$402$	0.276430	+	5.80297i	0.0137871	+	0.289426i
$403$	0.331694	+	6.96310i	0.0165228	+	0.346857i
$404$	2.14404	−	6.19478i	0.106670	−	0.308202i
$405$	0.681758	−	0.200182i	0.0338769	−	0.00994714i
$406$	3.57773	+	8.71711i	0.177560	+	0.432623i
$407$	2.94969	−	3.40412i	0.146210	−	0.168736i
$408$	−0.773673	+	0.0738768i	−0.0383025	+	0.00365745i
$409$	6.95718	−	6.63366i	0.344011	−	0.328013i	−0.498301	−	0.867004i	$-0.666043\pi$
$409$	6.95718	−	6.63366i	0.344011	−	0.328013i	0.842312	+	0.538991i	$0.181194\pi$
$410$	−4.89098	−	0.467032i	−0.241548	−	0.0230651i
$411$	−15.7903	+	12.4176i	−0.778876	+	0.612515i
$412$	−1.81848	−	1.16866i	−0.0895900	−	0.0575760i
$413$	−21.8672	−	12.3737i	−1.07602	−	0.608871i
$414$	−3.35207	+	3.42981i	−0.164745	+	0.168566i
$415$	3.92674	+	6.80132i	0.192756	+	0.333864i
$416$	1.10145	−	0.567837i	0.0540030	−	0.0278405i
$417$	16.0800	+	6.43746i	0.787441	+	0.315244i
$418$	−18.6168	+	26.1436i	−0.910576	+	1.27873i
$419$	1.32280	+	0.388409i	0.0646229	+	0.0189750i	0.313884	−	0.949461i	$-0.398370\pi$
$419$	1.32280	+	0.388409i	0.0646229	+	0.0189750i	−0.249261	+	0.968436i	$0.580188\pi$
$420$	−1.52183	+	1.10368i	−0.0742576	+	0.0538541i
$421$	16.7072	−	19.2811i	0.814258	−	0.939703i	−0.184814	−	0.982773i	$-0.559168\pi$
$421$	16.7072	−	19.2811i	0.814258	−	0.939703i	0.999072	+	0.0430700i	$0.0137139\pi$
$422$	−6.07469	+	2.43194i	−0.295711	+	0.118385i
$423$	−2.98727	+	12.3137i	−0.145246	+	0.598712i
$424$	−6.09417	+	1.17456i	−0.295959	+	0.0570415i
$425$	−3.10522	−	1.60085i	−0.150625	−	0.0776527i
$426$	−12.1678	+	7.81980i	−0.589534	+	0.378871i
$427$	36.6796	+	12.3402i	1.77505	+	0.597183i
$428$	2.40218	−	0.705345i	0.116114	−	0.0340941i
$429$	4.29436	−	1.71920i	0.207334	−	0.0830039i
$430$	0.942894	+	2.72431i	0.0454704	+	0.131378i
$431$	−15.0534	−	21.1396i	−0.725097	−	1.01826i	−0.998412	−	0.0563322i	$-0.982059\pi$
$431$	−15.0534	−	21.1396i	−0.725097	−	1.01826i	0.273315	−	0.961925i	$-0.411880\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	−2.97997	−	6.52522i	−0.143208	−	0.313582i	0.824413	−	0.565988i	$-0.191505\pi$
$433$	−2.97997	−	6.52522i	−0.143208	−	0.313582i	−0.967621	+	0.252406i	$0.918778\pi$
$434$	−14.7130	+	2.24566i	−0.706245	+	0.107795i
$435$	2.12885	+	1.36813i	0.102070	+	0.0655966i
$436$	−2.09386	−	3.62667i	−0.100278	−	0.173686i
$437$	22.7194	−	34.4112i	1.08682	−	1.64611i
$438$	7.42082	−	12.8532i	0.354581	−	0.614151i
$439$	1.04344	−	21.9046i	0.0498008	−	1.04545i	−0.826273	−	0.563270i	$-0.809543\pi$
$439$	1.04344	−	21.9046i	0.0498008	−	1.04545i	0.876074	−	0.482177i	$-0.160154\pi$
$440$	0.377463	+	2.62531i	0.0179948	+	0.125157i
$441$	−3.96101	+	5.77152i	−0.188619	+	0.274834i
$442$	−0.924089	−	0.271337i	−0.0439544	−	0.0129062i
$443$	−3.57993	+	0.341842i	−0.170088	+	0.0162414i	−0.179752	−	0.983712i	$-0.557530\pi$
$443$	−3.57993	+	0.341842i	−0.170088	+	0.0162414i	0.00966471	+	0.999953i	$0.496924\pi$
$444$	−0.394666	−	1.14031i	−0.0187300	−	0.0541169i
$445$	−3.13594	−	2.46613i	−0.148658	−	0.116906i
$446$	16.3898	+	15.6276i	0.776078	+	0.739989i
$447$	2.19531	+	2.53353i	0.103835	+	0.119832i
$448$	1.44963	+	2.21327i	0.0684885	+	0.104567i
$449$	18.5742	−	11.9369i	0.876570	−	0.563337i	−0.0231859	−	0.999731i	$-0.507381\pi$
$449$	18.5742	−	11.9369i	0.876570	−	0.563337i	0.899756	+	0.436394i	$0.143745\pi$
$450$	1.47021	−	4.24790i	0.0693065	−	0.200248i
$451$	−6.08529	+	25.0839i	−0.286545	+	1.18116i
$452$	−3.12934	−	2.46094i	−0.147192	−	0.115753i
$453$	11.0971	+	2.13879i	0.521387	+	0.100489i
$454$	2.92662	−	6.40840i	0.137353	−	0.300761i
$455$	−2.25909	+	0.568814i	−0.105908	+	0.0266664i
$456$	3.57175	+	7.82104i	0.167263	+	0.366254i
$457$	22.3907	−	17.6083i	1.04739	−	0.823680i	0.0627113	−	0.998032i	$-0.480025\pi$
$457$	22.3907	−	17.6083i	1.04739	−	0.823680i	0.984684	+	0.174351i	$0.0557828\pi$
$458$	21.2790	−	10.9701i	0.994301	−	0.512598i
$459$	−0.388596	+	0.673068i	−0.0181381	+	0.0314161i
$460$	−0.603567	−	3.35375i	−0.0281415	−	0.156370i
$461$	35.6167			1.65883			0.829416	−	0.558631i	$-0.188673\pi$
$461$	35.6167			1.65883			0.829416	+	0.558631i	$0.188673\pi$
$462$	4.60135	+	8.73866i	0.214074	+	0.406559i
$463$	1.02660	+	7.14013i	0.0477099	+	0.331830i	0.999672	+	0.0256137i	$0.00815398\pi$
$463$	1.02660	+	7.14013i	0.0477099	+	0.331830i	−0.951962	+	0.306216i	$0.900937\pi$
$464$	2.06585	−	2.90108i	0.0959047	−	0.134679i
$465$	−2.89281	+	2.75829i	−0.134151	+	0.127912i
$466$	3.02915	+	4.25384i	0.140323	+	0.197055i
$467$	−15.3875	−	2.96570i	−0.712050	−	0.137236i	−0.179651	−	0.983730i	$-0.557497\pi$
$467$	−15.3875	−	2.96570i	−0.712050	−	0.137236i	−0.532398	+	0.846494i	$0.678709\pi$
$468$	0.176357	−	1.22659i	0.00815212	−	0.0566993i
$469$	−14.9682	−	3.49423i	−0.691167	−	0.161349i
$470$	−5.89582	−	6.80413i	−0.271954	−	0.313851i
$471$	12.7604	+	6.57846i	0.587970	+	0.303119i
$472$	0.451862	+	9.48574i	0.0207986	+	0.436617i
$473$	14.8714	−	2.86622i	0.683786	−	0.131789i
$474$	−9.37987	−	8.94369i	−0.430832	−	0.410797i
$475$	−5.50037	+	38.2559i	−0.252374	+	1.75530i
$476$	0.371644	−	2.02239i	0.0170343	−	0.0926963i
$477$	−2.57820	+	5.64548i	−0.118048	+	0.258489i
$478$	−0.884062	−	3.64415i	−0.0404361	−	0.166680i
$479$	−1.97574	−	0.188660i	−0.0902739	−	0.00862011i	0.0498213	−	0.998758i	$-0.484135\pi$
$479$	−1.97574	−	0.188660i	−0.0902739	−	0.00862011i	−0.140095	+	0.990138i	$0.544741\pi$
$480$	0.659643	+	0.264081i	0.0301084	+	0.0120536i
$481$	0.0711504	−	1.49363i	0.00324418	−	0.0681037i
$482$	4.30659			0.196160
$483$	−6.30386	−	11.0119i	−0.286836	−	0.501058i
$484$	2.93381			0.133355
$485$	−0.303081	+	6.36245i	−0.0137622	+	0.288904i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	18.1715	+	1.73517i	0.823430	+	0.0786280i	0.498260	−	0.867028i	$-0.333973\pi$
$487$	18.1715	+	1.73517i	0.823430	+	0.0786280i	0.325170	+	0.945656i	$0.394579\pi$
$488$	−3.44848	−	14.2148i	−0.156105	−	0.643474i
$489$	−5.56920	+	12.1948i	−0.251848	+	0.551470i
$490$	−1.70795	−	4.67134i	−0.0771573	−	0.211030i
$491$	−0.346328	+	2.40876i	−0.0156296	+	0.108706i	−0.996143	−	0.0877472i	$-0.972033\pi$
$491$	−0.346328	+	2.40876i	−0.0156296	+	0.108706i	0.980513	+	0.196453i	$0.0629423\pi$
$492$	5.00446	+	4.77174i	0.225618	+	0.215127i
$493$	−2.71792	+	0.523836i	−0.122409	+	0.0235924i
$494$	0.506972	+	10.6427i	0.0228098	+	0.478836i
$495$	2.35746	+	1.21536i	0.105960	+	0.0546262i
$496$	3.68384	+	4.25138i	0.165409	+	0.190892i
$497$	−11.0990	−	36.6231i	−0.497859	−	1.64277i
$498$	1.57298	−	10.9403i	0.0704871	−	0.490248i
$499$	−11.7914	−	2.27260i	−0.527855	−	0.101736i	−0.0816408	−	0.996662i	$-0.526016\pi$
$499$	−11.7914	−	2.27260i	−0.527855	−	0.101736i	−0.446214	+	0.894926i	$0.647228\pi$
$500$	3.91346	+	5.49568i	0.175015	+	0.245774i
$501$	14.7589	−	14.0726i	0.659381	−	0.628719i
$502$	−7.98419	+	11.2122i	−0.356352	+	0.500426i
$503$	−5.53844	−	38.5207i	−0.246947	−	1.71755i	−0.615663	−	0.788010i	$-0.711112\pi$
$503$	−5.53844	−	38.5207i	−0.246947	−	1.71755i	0.368716	−	0.929542i	$-0.379798\pi$
$504$	2.64375	+	0.102992i	0.117762	+	0.00458764i
$505$	4.65782			0.207270
$506$	−17.8908	+	0.631125i	−0.795341	+	0.0280569i
$507$	−5.73218	+	9.92843i	−0.254575	+	0.440937i
$508$	−5.15861	+	2.65945i	−0.228876	+	0.117994i
$509$	4.67505	−	3.67650i	0.207218	−	0.162958i	−0.509157	−	0.860674i	$-0.670043\pi$
$509$	4.67505	−	3.67650i	0.207218	−	0.162958i	0.716375	+	0.697716i	$0.245800\pi$
$510$	−0.229403	−	0.502323i	−0.0101581	−	0.0222432i
$511$	27.3427	+	28.1833i	1.20957	+	1.24675i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	8.44265	+	1.62719i	0.372752	+	0.0718421i
$514$	−21.8951	−	17.2185i	−0.965753	−	0.759477i
$515$	0.362108	−	1.49263i	0.0159564	−	0.0657731i
$516$	1.32701	−	3.83414i	0.0584184	−	0.168789i
$517$	−39.7895	+	25.5711i	−1.74994	+	1.12462i
$518$	3.18752	−	0.179527i	0.140052	−	0.00788798i
$519$	−3.61523	−	4.17220i	−0.158691	−	0.183139i
$520$	0.637252	+	0.607618i	0.0279453	+	0.0266458i
$521$	−19.3372	−	15.2069i	−0.847176	−	0.666227i	0.0971382	−	0.995271i	$-0.469031\pi$
$521$	−19.3372	−	15.2069i	−0.847176	−	0.666227i	−0.944315	+	0.329044i	$0.893274\pi$
$522$	−1.16484	−	3.36559i	−0.0509837	−	0.147308i
$523$	33.2768	−	3.17755i	1.45509	−	0.138945i	0.662668	−	0.748913i	$-0.269424\pi$
$523$	33.2768	−	3.17755i	1.45509	−	0.138945i	0.792425	+	0.609969i	$0.208818\pi$
$524$	5.46162	+	1.60368i	0.238592	+	0.0700570i
$525$	9.74715	+	6.81444i	0.425400	+	0.297407i
$526$	−0.218442	−	1.51930i	−0.00952452	−	0.0662445i
$527$	0.208028	−	4.36705i	0.00906185	−	0.190232i
$528$	1.86640	−	3.23270i	0.0812247	−	0.140685i
$529$	22.9428	−	1.62071i	0.997514	−	0.0704655i
$530$	−2.20492	−	3.81904i	−0.0957758	−	0.165889i
$531$	7.98896	+	5.13419i	0.346691	+	0.222805i
$532$	−22.4878	+	3.43234i	−0.974971	+	0.148811i
$533$	3.55962	+	7.79448i	0.154184	+	0.337617i
$534$	1.32372	+	5.45645i	0.0572829	+	0.236123i
$535$	1.03187	+	1.44905i	0.0446115	+	0.0626481i
$536$	1.90012	+	5.49003i	0.0820726	+	0.237133i
$537$	20.9043	−	8.36884i	0.902089	−	0.361142i
$538$	20.9570	−	6.15352i	0.903519	−	0.265297i
$539$	−25.5679	+	5.38882i	−1.10129	+	0.232113i
$540$	0.597745	−	0.384147i	0.0257228	−	0.0165311i
$541$	38.4229	+	19.8084i	1.65193	+	0.851629i	0.995238	+	0.0974698i	$0.0310750\pi$
$541$	38.4229	+	19.8084i	1.65193	+	0.851629i	0.656692	+	0.754159i	$0.271955\pi$
$542$	−20.9904	+	4.04557i	−0.901615	+	0.173772i
$543$	2.13407	−	8.79676i	0.0915817	−	0.377505i
$544$	−0.721520	+	0.288853i	−0.0309349	+	0.0123845i
$545$	1.94856	−	2.24876i	0.0834673	−	0.0963264i
$546$	2.99403	+	1.33611i	0.128133	+	0.0571801i
$547$	23.0566	+	6.77002i	0.985828	+	0.289465i	0.734628	−	0.678470i	$-0.237357\pi$
$547$	23.0566	+	6.77002i	0.985828	+	0.289465i	0.251200	+	0.967935i	$0.419175\pi$
$548$	−11.6522	+	16.3632i	−0.497758	+	0.699003i
$549$	−13.5794	−	5.43635i	−0.579553	−	0.232018i
$550$	14.9142	−	7.68878i	0.635942	−	0.327851i
$551$	15.3108	+	26.5191i	0.652261	+	1.12975i
$552$	−2.25000	+	4.23527i	−0.0957664	+	0.180265i
$553$	29.5463	−	17.4016i	1.25644	−	0.739990i
$554$	23.5487	+	15.1339i	1.00049	+	0.642976i
$555$	0.673958	−	0.530006i	0.0286079	−	0.0224975i
$556$	17.2423	+	1.64644i	0.731236	+	0.0698246i
$557$	13.8326	−	13.1894i	0.586108	−	0.558853i	−0.337922	−	0.941174i	$-0.609724\pi$
$557$	13.8326	−	13.1894i	0.586108	−	0.558853i	0.924029	+	0.382322i	$0.124875\pi$
$558$	5.59991	−	0.534726i	0.237063	−	0.0226368i
$559$	3.29252	−	3.79977i	0.139259	−	0.160713i
$560$	−1.14924	+	1.48772i	−0.0485643	+	0.0628678i
$561$	−2.78359	+	0.817336i	−0.117523	+	0.0345079i
$562$	9.81502	−	28.3586i	0.414022	−	1.19624i
$563$	0.997335	+	20.9366i	0.0420326	+	0.882374i	0.917169	+	0.398498i	$0.130468\pi$
$563$	0.997335	+	20.9366i	0.0420326	+	0.882374i	−0.875137	+	0.483876i	$0.839229\pi$
$564$	0.602904	+	12.6565i	0.0253868	+	0.532935i
$565$	0.925183	−	2.67314i	0.0389227	−	0.112460i
$566$	16.4556	−	4.83181i	0.691682	−	0.203096i
$567$	1.61742	−	2.09379i	0.0679252	−	0.0879309i
$568$	−9.47187	+	10.9311i	−0.397431	+	0.458660i
$569$	−29.2009	+	2.78835i	−1.22416	+	0.116894i	−0.687047	−	0.726613i	$-0.741093\pi$
$569$	−29.2009	+	2.78835i	−1.22416	+	0.116894i	−0.537118	+	0.843507i	$0.680487\pi$
$570$	−4.42147	+	4.21586i	−0.185195	+	0.176583i
$571$	29.4959	+	2.81652i	1.23436	+	0.117867i	0.691764	−	0.722124i	$-0.256834\pi$
$571$	29.4959	+	2.81652i	1.23436	+	0.117867i	0.542600	+	0.839991i	$0.317440\pi$
$572$	3.63605	−	2.85942i	0.152031	−	0.119559i
$573$	−8.59418	−	5.52314i	−0.359027	−	0.230733i
$574$	−15.7639	+	9.28429i	−0.657973	+	0.387519i
$575$	−18.8013	+	10.5478i	−0.784066	+	0.439873i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−15.9722	+	8.23423i	−0.664931	+	0.342796i	−0.757429	−	0.652917i	$-0.773545\pi$
$577$	−15.9722	+	8.23423i	−0.664931	+	0.342796i	0.0924986	+	0.995713i	$0.470515\pi$
$578$	−15.2215	−	6.09377i	−0.633131	−	0.253467i
$579$	14.9709	−	21.0237i	0.622171	−	0.873717i
$580$	2.42806	+	0.712942i	0.100820	+	0.0296033i
$581$	26.7047	+	11.9171i	1.10790	+	0.494406i
$582$	5.87053	−	6.77495i	0.243341	−	0.280831i
$583$	−21.5075	+	8.61030i	−0.890750	+	0.356602i
$584$	3.49905	−	14.4233i	0.144792	−	0.596840i
$585$	0.864594	−	0.166637i	0.0357466	−	0.00688958i
$586$	−7.43713	−	3.83411i	−0.307225	−	0.158385i
$587$	−13.6712	+	8.78596i	−0.564272	+	0.362635i	−0.791465	−	0.611214i	$-0.790681\pi$
$587$	−13.6712	+	8.78596i	−0.564272	+	0.362635i	0.227194	+	0.973850i	$0.427045\pi$
$588$	−2.17453	+	6.65368i	−0.0896762	+	0.274393i
$589$	−46.4080	+	13.6266i	−1.91221	+	0.561475i
$590$	−6.26430	+	2.50785i	−0.257897	+	0.103246i
$591$	3.54920	+	10.2547i	0.145995	+	0.421824i
$592$	−0.699943	−	0.982932i	−0.0287675	−	0.0403983i
$593$	3.43080	+	14.1420i	0.140886	+	0.580741i	0.997860	+	0.0653815i	$0.0208264\pi$
$593$	3.43080	+	14.1420i	0.140886	+	0.580741i	−0.856974	+	0.515359i	$0.827658\pi$
$594$	−1.55066	−	3.39548i	−0.0636244	−	0.139318i
$595$	1.44433	−	0.220449i	0.0592116	−	0.00903754i
$596$	2.82017	+	1.81241i	0.115519	+	0.0742392i
$597$	2.93260	+	5.07941i	0.120023	+	0.207886i
$598$	−4.53911	+	3.83614i	−0.185618	+	0.156872i
$599$	3.84356	−	6.65725i	0.157044	−	0.272008i	−0.776758	−	0.629800i	$-0.783137\pi$
$599$	3.84356	−	6.65725i	0.157044	−	0.272008i	0.933801	+	0.357792i	$0.116470\pi$
$600$	0.213887	−	4.49004i	0.00873190	−	0.183305i
$601$	−0.654052	−	4.54903i	−0.0266793	−	0.185559i	0.972124	−	0.234468i	$-0.0753347\pi$
$601$	−0.654052	−	4.54903i	−0.0266793	−	0.185559i	−0.998803	+	0.0489089i	$0.984426\pi$
$602$	8.79774	+	6.15069i	0.358569	+	0.250683i
$603$	5.57423	+	1.63674i	0.227000	+	0.0666532i
$604$	11.2501	−	1.07426i	0.457762	−	0.0437110i
$605$	0.681802	+	1.96994i	0.0277192	+	0.0800893i
$606$	−5.15283	−	4.05223i	−0.209319	−	0.164611i
$607$	−3.82105	−	3.64337i	−0.155092	−	0.147880i	0.608560	−	0.793507i	$-0.291747\pi$
$607$	−3.82105	−	3.64337i	−0.155092	−	0.147880i	−0.763652	+	0.645628i	$0.776596\pi$
$608$	5.63051	+	6.49796i	0.228347	+	0.263527i
$609$	9.40784	−	0.529867i	0.381225	−	0.0214713i
$610$	8.74329	−	5.61897i	0.354005	−	0.227505i
$611$	−5.13556	+	14.8382i	−0.207762	+	0.600290i
$612$	−0.183230	+	0.755284i	−0.00740663	+	0.0305306i
$613$	−36.8062	−	28.9447i	−1.48659	−	1.16907i	−0.944396	−	0.328810i	$-0.893353\pi$
$613$	−36.8062	−	28.9447i	−1.48659	−	1.16907i	−0.542191	−	0.840255i	$-0.682405\pi$
$614$	0.520938	+	0.100402i	0.0210233	+	0.00405191i
$615$	−2.04103	+	4.46923i	−0.0823022	+	0.180217i
$616$	6.87693	+	7.08834i	0.277079	+	0.285597i
$617$	18.1089	+	39.6529i	0.729035	+	1.59636i	0.800793	+	0.598942i	$0.204412\pi$
$617$	18.1089	+	39.6529i	0.729035	+	1.59636i	−0.0717576	+	0.997422i	$0.522861\pi$
$618$	−1.69915	+	1.33623i	−0.0683500	+	0.0537511i
$619$	−27.6657	+	14.2626i	−1.11198	+	0.573264i	−0.913499	−	0.406841i	$-0.866630\pi$
$619$	−27.6657	+	14.2626i	−1.11198	+	0.573264i	−0.198478	+	0.980105i	$0.563600\pi$
$620$	−1.99853	+	3.46155i	−0.0802629	+	0.139019i
$621$	2.14482	+	4.28949i	0.0860686	+	0.172131i
$622$	28.3522			1.13682
$623$	−14.8439	−	0.578273i	−0.594708	−	0.0231680i
$624$	−0.176357	−	1.22659i	−0.00705994	−	0.0491030i
$625$	10.2565	−	14.4032i	0.410260	−	0.576129i
$626$	2.78454	−	2.65505i	0.111293	−	0.106117i
$627$	18.6168	+	26.1436i	0.743482	+	1.04407i
$628$	14.0969	+	2.71696i	0.562528	+	0.108418i
$629$	−0.133466	+	0.928276i	−0.00532164	+	0.0370128i
$630$	0.545238	+	1.79911i	0.0217228	+	0.0716782i
$631$	−25.2601	−	29.1517i	−1.00559	−	1.16051i	−0.987006	−	0.160684i	$-0.948630\pi$
$631$	−25.2601	−	29.1517i	−1.00559	−	1.16051i	−0.0185828	−	0.999827i	$-0.505915\pi$
$632$	−11.5197	−	5.93879i	−0.458227	−	0.236233i
$633$	0.311348	+	6.53599i	0.0123750	+	0.259782i
$634$	13.6701	−	2.63469i	0.542908	−	0.104637i
$635$	−2.98455	−	2.84576i	−0.118438	−	0.112931i
$636$	−0.883253	+	6.14316i	−0.0350233	+	0.243592i
$637$	−5.56612	+	6.65313i	−0.220538	+	0.263607i
$638$	5.52262	−	12.0929i	0.218643	−	0.478761i
$639$	3.41000	+	14.0562i	0.134898	+	0.556056i
$640$	0.707323	+	0.0675412i	0.0279594	+	0.00266980i
$641$	5.12445	+	2.05152i	0.202404	+	0.0810302i	0.470649	−	0.882320i	$-0.344020\pi$
$641$	5.12445	+	2.05152i	0.202404	+	0.0810302i	−0.268246	+	0.963351i	$0.586444\pi$
$642$	0.119126	−	2.50076i	0.00470152	−	0.0986971i
$643$	17.9810			0.709100			0.354550	−	0.935037i	$-0.384634\pi$
$643$	17.9810			0.709100			0.354550	+	0.935037i	$0.384634\pi$
$644$	−9.15091	−	8.78981i	−0.360596	−	0.346367i
$645$	2.88287			0.113513
$646$	0.317958	−	6.67475i	0.0125099	−	0.262615i
$647$	30.4861	+	12.2048i	1.19853	+	0.479820i	0.883125	−	0.469137i	$-0.155435\pi$
$647$	30.4861	+	12.2048i	1.19853	+	0.479820i	0.315406	+	0.948957i	$0.397859\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	8.35731	+	34.4493i	0.328053	+	1.35225i
$650$	2.31403	−	5.06701i	0.0907635	−	0.198744i
$651$	−2.68999	+	14.6382i	−0.105429	+	0.573718i
$652$	−1.90792	+	13.2699i	−0.0747200	+	0.519689i
$653$	−7.47922	−	7.13142i	−0.292684	−	0.279074i	0.529482	−	0.848321i	$-0.322386\pi$
$653$	−7.47922	−	7.13142i	−0.292684	−	0.279074i	−0.822166	+	0.569247i	$0.807235\pi$
$654$	−4.11204	+	0.792530i	−0.160793	+	0.0309904i
$655$	0.192447	+	4.03995i	0.00751952	+	0.157854i
$656$	6.14610	+	3.16853i	0.239965	+	0.123710i
$657$	−9.71921	−	11.2166i	−0.379182	−	0.437600i
$658$	−32.6462	−	7.62106i	−1.27268	−	0.297100i
$659$	−2.01179	+	13.9923i	−0.0783681	+	0.545062i	0.912380	+	0.409345i	$0.134243\pi$
$659$	−2.01179	+	13.9923i	−0.0783681	+	0.545062i	−0.990748	+	0.135717i	$0.956666\pi$
$660$	2.60438	+	0.501952i	0.101375	+	0.0195385i
$661$	2.73742	+	3.84417i	0.106473	+	0.149521i	0.864375	−	0.502848i	$-0.167715\pi$
$661$	2.73742	+	3.84417i	0.106473	+	0.149521i	−0.757901	+	0.652369i	$0.773775\pi$
$662$	−9.05721	+	8.63603i	−0.352019	+	0.335649i
$663$	−0.558653	+	0.784519i	−0.0216963	+	0.0304682i
$664$	−1.57298	−	10.9403i	−0.0610436	−	0.424567i
$665$	−7.53074	−	14.3020i	−0.292030	−	0.554609i
$666$	−1.20668			−0.0467579
$667$	−6.54321	+	15.7772i	−0.253354	+	0.610894i
$668$	10.1964	−	17.6607i	0.394510	−	0.683311i
$669$	20.1287	−	10.3771i	0.778220	−	0.401200i
$670$	−3.24477	+	2.55171i	−0.125356	+	0.0985813i
$671$	−22.6817	−	49.6661i	−0.875618	−	1.91734i
$672$	2.56567	−	0.646009i	0.0989729	−	0.0249203i
$673$	−6.85420	+	15.0086i	−0.264210	+	0.578540i	−0.994516	−	0.104580i	$-0.966650\pi$
$673$	−6.85420	+	15.0086i	−0.264210	+	0.578540i	0.730306	+	0.683120i	$0.239377\pi$
$674$	15.4997	+	2.98733i	0.597028	+	0.115068i
$675$	−3.53341	−	2.77871i	−0.136001	−	0.106952i
$676$	−2.70283	+	11.1412i	−0.103955	+	0.428508i
$677$	−3.04700	+	8.80373i	−0.117106	+	0.338355i	−0.988287	−	0.152607i	$-0.951233\pi$
$677$	−3.04700	+	8.80373i	−0.117106	+	0.338355i	0.871181	+	0.490961i	$0.163354\pi$
$678$	−3.34910	+	2.15233i	−0.128621	+	0.0826599i
$679$	12.9952	+	19.8410i	0.498712	+	0.761427i
$680$	−0.361631	−	0.417345i	−0.0138679	−	0.0160044i
$681$	−5.09874	−	4.86164i	−0.195384	−	0.186298i
$682$	16.5059	+	12.9804i	0.632043	+	0.497044i
$683$	−16.5581	−	47.8414i	−0.633577	−	1.83060i	−0.551845	−	0.833947i	$-0.686076\pi$
$683$	−16.5581	−	47.8414i	−0.633577	−	1.83060i	−0.0817321	−	0.996654i	$-0.526045\pi$
$684$	8.55910	−	0.817295i	0.327265	−	0.0312500i
$685$	−13.6952	−	4.02127i	−0.523266	−	0.153645i
$686$	−15.3602	−	10.3472i	−0.586456	−	0.395057i
$687$	−3.40706	−	23.6966i	−0.129987	−	0.904081i
$688$	0.193054	−	4.05270i	0.00736010	−	0.154508i
$689$	−3.84546	+	6.66053i	−0.146500	+	0.253746i
$690$	−3.36671	−	0.526534i	−0.128168	−	0.0200448i
$691$	−0.973985	−	1.68699i	−0.0370521	−	0.0641762i	0.846905	−	0.531745i	$-0.178463\pi$
$691$	−0.973985	−	1.68699i	−0.0370521	−	0.0641762i	−0.883957	+	0.467569i	$0.845130\pi$
$692$	−4.64423	−	2.98467i	−0.176547	−	0.113460i
$693$	9.76300	−	1.49014i	0.370866	−	0.0566057i
$694$	−9.97342	−	21.8387i	−0.378586	−	0.828987i
$695$	2.90150	+	11.9602i	0.110060	+	0.453675i
$696$	−2.06585	−	2.90108i	−0.0783059	−	0.109965i
$697$	−1.75770	−	5.07854i	−0.0665776	−	0.192363i
$698$	1.39638	−	0.559026i	0.0528537	−	0.0211594i
$699$	5.01062	−	1.47125i	0.189519	−	0.0556478i
$700$	11.2722	+	3.79232i	0.426048	+	0.143336i
$701$	8.61985	−	5.53964i	0.325567	−	0.209229i	−0.367639	−	0.929969i	$-0.619834\pi$
$701$	8.61985	−	5.53964i	0.325567	−	0.209229i	0.693206	+	0.720739i	$0.256197\pi$
$702$	−1.10145	−	0.567837i	−0.0415716	−	0.0214316i
$703$	10.1876	−	1.96349i	0.384232	−	0.0740546i
$704$	0.880041	−	3.62758i	0.0331678	−	0.136720i
$705$	−8.35825	+	3.34614i	−0.314790	+	0.126023i
$706$	−10.0372	+	11.5835i	−0.377754	+	0.435952i
$707$	14.0401	−	10.1824i	0.528033	−	0.382947i
$708$	9.11182	+	2.67547i	0.342443	+	0.100550i
$709$	−11.2486	+	15.7964i	−0.422450	+	0.593248i	−0.969874	−	0.243608i	$-0.921669\pi$
$709$	−11.2486	+	15.7964i	−0.422450	+	0.593248i	0.547424	+	0.836855i	$0.315609\pi$
$710$	−9.54104	−	3.81966i	−0.358069	−	0.143349i
$711$	−11.5197	+	5.93879i	−0.432021	+	0.222722i
$712$	2.80736	+	4.86249i	0.105210	+	0.182229i
$713$	−21.7812	−	15.9189i	−0.815712	−	0.596168i
$714$	−1.78961	−	1.01266i	−0.0669745	−	0.0378980i
$715$	2.76499	+	1.77695i	0.103405	+	0.0664543i
$716$	17.6998	−	13.9193i	0.661472	−	0.520188i
$717$	−3.73288	−	0.356446i	−0.139407	−	0.0133117i
$718$	−16.1115	+	15.3623i	−0.601277	+	0.573316i
$719$	−29.4397	+	2.81115i	−1.09791	+	0.104838i	−0.628253	−	0.778009i	$-0.716230\pi$
$719$	−29.4397	+	2.81115i	−1.09791	+	0.104838i	−0.469661	+	0.882847i	$0.655624\pi$
$720$	0.465305	−	0.536991i	0.0173409	−	0.0200125i
$721$	−2.17150	−	5.29085i	−0.0808709	−	0.197041i
$722$	−52.7012	+	15.4745i	−1.96134	+	0.575900i
$723$	1.40855	−	4.06973i	0.0523844	−	0.151355i
$724$	−0.430707	−	9.04166i	−0.0160071	−	0.336031i
$725$	−0.761751	−	15.9911i	−0.0282907	−	0.593895i
$726$	0.959554	−	2.77245i	0.0356124	−	0.102895i
$727$	3.58059	−	1.05136i	0.132797	−	0.0389927i	−0.214659	−	0.976689i	$-0.568864\pi$
$727$	3.58059	−	1.05136i	0.132797	−	0.0389927i	0.347456	+	0.937696i	$0.387046\pi$
$728$	3.24918	+	0.438468i	0.120423	+	0.0162507i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	10.4978	−	1.00242i	0.388542	−	0.0371013i
$731$	−2.28215	+	2.17602i	−0.0844083	+	0.0804831i
$732$	−14.5609	−	1.39040i	−0.538186	−	0.0513905i
$733$	−28.4983	+	22.4113i	−1.05261	+	0.827782i	−0.985451	−	0.169961i	$-0.945636\pi$
$733$	−28.4983	+	22.4113i	−1.05261	+	0.827782i	−0.0671591	+	0.997742i	$0.521394\pi$
$734$	−11.2834	−	7.25143i	−0.416480	−	0.267655i
$735$	−4.97304	+	0.0861674i	−0.183433	+	0.00317833i
$736$	−0.965648	+	4.69761i	−0.0355942	+	0.173156i
$737$	10.8430	+	18.7806i	0.399405	+	0.691791i
$738$	6.14610	−	3.16853i	0.226241	−	0.116635i
$739$	−26.5707	−	10.6373i	−0.977419	−	0.391299i	−0.172712	−	0.984972i	$-0.555253\pi$
$739$	−26.5707	−	10.6373i	−0.977419	−	0.391299i	−0.804706	+	0.593673i	$0.797677\pi$
$740$	0.497338	−	0.698413i	0.0182825	−	0.0256742i
$741$	10.2231	+	3.00178i	0.375556	+	0.110273i
$742$	−14.9951	−	6.69164i	−0.550486	−	0.245658i
$743$	14.4085	−	16.6283i	0.528596	−	0.610032i	−0.427166	−	0.904173i	$-0.640488\pi$
$743$	14.4085	−	16.6283i	0.528596	−	0.610032i	0.955762	+	0.294141i	$0.0950336\pi$
$744$	5.22242	−	2.09074i	0.191463	−	0.0766503i
$745$	−0.561571	+	2.31483i	−0.0205744	+	0.0848087i
$746$	5.31832	−	1.02502i	0.194718	−	0.0375287i
$747$	−9.82416	−	5.06470i	−0.359447	−	0.185308i
$748$	−2.44056	+	1.56846i	−0.0892359	+	0.0573484i
$749$	6.27812	+	2.11216i	0.229397	+	0.0771766i
$750$	6.47339	−	1.90076i	0.236375	−	0.0694059i
$751$	−22.3639	+	8.95316i	−0.816071	+	0.326705i	−0.741875	−	0.670538i	$-0.766063\pi$
$751$	−22.3639	+	8.95316i	−0.816071	+	0.326705i	−0.0741958	+	0.997244i	$0.523639\pi$
$752$	4.14423	+	11.9740i	0.151125	+	0.436646i
$753$	7.98419	+	11.2122i	0.290960	+	0.408596i
$754$	−1.04050	−	4.28898i	−0.0378926	−	0.156195i
$755$	3.33580	+	7.30439i	0.121402	+	0.265834i
$756$	0.962012	−	2.46466i	0.0349881	−	0.0896387i
$757$	−9.60693	−	6.17400i	−0.349170	−	0.224398i	0.354285	−	0.935137i	$-0.384724\pi$
$757$	−9.60693	−	6.17400i	−0.349170	−	0.224398i	−0.703455	+	0.710739i	$0.748360\pi$
$758$	3.90622	+	6.76576i	0.141880	+	0.245744i
$759$	−5.25508	+	17.1132i	−0.190747	+	0.621170i
$760$	−3.05462	+	5.29076i	−0.110803	+	0.191916i
$761$	0.879857	−	18.4705i	0.0318948	−	0.669554i	−0.925148	−	0.379607i	$-0.876059\pi$
$761$	0.879857	−	18.4705i	0.0318948	−	0.669554i	0.957043	−	0.289947i	$-0.0936378\pi$
$762$	0.825965	+	5.74471i	0.0299215	+	0.208109i
$763$	0.957606	−	11.0382i	0.0346677	−	0.399609i
$764$	−9.80210	−	2.87816i	−0.354628	−	0.104128i
$765$	−0.549726	+	0.0524925i	−0.0198754	+	0.00189787i
$766$	−3.23170	−	9.33740i	−0.116766	−	0.337374i
$767$	9.25036	+	7.27457i	0.334011	+	0.262669i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	24.0530	+	27.7586i	0.867373	+	1.00100i	0.999952	+	0.00982931i	$0.00312882\pi$
$769$	24.0530	+	27.7586i	0.867373	+	1.00100i	−0.132579	+	0.991172i	$0.542326\pi$
$770$	−3.16138	+	6.26488i	−0.113928	+	0.225771i
$771$	−23.4327	+	15.0593i	−0.843909	+	0.542347i
$772$	8.44144	−	24.3899i	0.303814	−	0.877813i
$773$	−0.971733	+	4.00554i	−0.0349508	+	0.144069i	−0.986614	−	0.163076i	$-0.947858\pi$
$773$	−0.971733	+	4.00554i	−0.0349508	+	0.144069i	0.951663	+	0.307145i	$0.0993736\pi$
$774$	−3.18925	−	2.50805i	−0.114635	−	0.0901500i
$775$	24.8299	+	4.78556i	0.891915	+	0.171902i
$776$	3.72400	−	8.15443i	0.133684	−	0.292727i
$777$	0.872883	−	3.07093i	0.0313145	−	0.110169i
$778$	12.4710	+	27.3076i	0.447106	+	0.979026i
$779$	−46.7336	+	36.7517i	−1.67440	+	1.31677i
$780$	0.782625	−	0.403471i	0.0280225	−	0.0144466i
$781$	−26.9955	+	46.7576i	−0.965976	+	1.67312i
$782$	3.06260	−	2.12441i	0.109518	−	0.0759689i
$783$	−3.56146			−0.127276
$784$	−0.211891	+	6.99679i	−0.00756752	+	0.249885i
$785$	1.45172	+	10.0969i	0.0518141	+	0.360375i
$786$	3.30180	−	4.63673i	0.117771	−	0.165387i
$787$	18.3899	−	17.5347i	0.655529	−	0.625046i	−0.287490	−	0.957784i	$-0.592821\pi$
$787$	18.3899	−	17.5347i	0.655529	−	0.625046i	0.943019	+	0.332738i	$0.107972\pi$
$788$	6.29453	+	8.83942i	0.224233	+	0.314891i
$789$	−1.50718	−	0.290485i	−0.0536571	−	0.0103416i
$790$	1.31056	−	9.11515i	0.0466276	−	0.324302i
$791$	−3.05491	−	10.0802i	−0.108620	−	0.358411i
$792$	−2.44447	−	2.82106i	−0.0868603	−	0.100242i
$793$	−16.1110	−	8.30582i	−0.572120	−	0.294948i
$794$	−1.10461	−	23.1886i	−0.0392012	−	0.822934i
$795$	−4.33016	+	0.834569i	−0.153575	+	0.0295991i
$796$	4.24484	+	4.04745i	0.150454	+	0.143458i
$797$	3.09073	−	21.4965i	0.109479	−	0.761445i	−0.858933	−	0.512089i	$-0.828872\pi$
$797$	3.09073	−	21.4965i	0.109479	−	0.761445i	0.968412	−	0.249356i	$-0.0802190\pi$
$798$	−4.11148	+	22.3736i	−0.145545	+	0.792017i
$799$	4.09088	−	8.95778i	0.144725	−	0.316904i
$800$	−1.05977	−	4.36842i	−0.0374684	−	0.154447i
$801$	5.58929	+	0.533713i	0.197488	+	0.0188578i
$802$	10.8060	+	4.32606i	0.381572	+	0.152758i
$803$	2.63608	−	55.3381i	0.0930253	−	1.95284i
$804$	5.80955			0.204887
$805$	3.77539	−	8.18719i	0.133065	−	0.288561i
$806$	6.97100			0.245543
$807$	1.03927	−	21.8170i	0.0365841	−	0.767994i
$808$	−6.08575	−	2.43637i	−0.214096	−	0.0857111i
$809$	8.01858	+	0.765681i	0.281918	+	0.0269199i	0.235057	−	0.971982i	$-0.424472\pi$
$809$	8.01858	+	0.765681i	0.281918	+	0.0269199i	0.0468608	+	0.998901i	$0.485078\pi$
$810$	−0.167516	−	0.690511i	−0.00588592	−	0.0242621i
$811$	7.32391	−	16.0371i	0.257177	−	0.563140i	−0.736367	−	0.676582i	$-0.763460\pi$
$811$	7.32391	−	16.0371i	0.257177	−	0.563140i	0.993545	+	0.113442i	$0.0361877\pi$
$812$	8.87747	−	3.15890i	0.311538	−	0.110856i
$813$	−3.04222	+	21.1591i	−0.106695	+	0.742083i
$814$	−3.25991	−	3.10832i	−0.114260	−	0.108947i
$815$	−9.35360	+	1.80276i	−0.327642	+	0.0631479i
$816$	0.0369803	+	0.776312i	0.00129457	+	0.0271764i
$817$	31.0068	+	15.9851i	1.08479	+	0.559248i
$818$	−6.29511	−	7.26495i	−0.220103	−	0.254013i
$819$	2.24187	−	2.39237i	0.0783374	−	0.0835960i
$820$	−0.699225	+	4.86322i	−0.0244180	+	0.169831i
$821$	21.8610	+	4.21336i	0.762954	+	0.147047i	0.555862	−	0.831274i	$-0.312388\pi$
$821$	21.8610	+	4.21336i	0.762954	+	0.147047i	0.207091	+	0.978322i	$0.433600\pi$
$822$	11.6522	+	16.3632i	0.406417	+	0.570733i
$823$	−0.862620	+	0.822506i	−0.0300690	+	0.0286708i	−0.704965	−	0.709242i	$-0.749037\pi$
$823$	−0.862620	+	0.822506i	−0.0300690	+	0.0286708i	0.674896	+	0.737913i	$0.264189\pi$
$824$	−1.25387	+	1.76081i	−0.0436805	+	0.0613407i
$825$	−2.38796	−	16.6086i	−0.0831382	−	0.578239i
$826$	−13.4002	+	21.2537i	−0.466252	+	0.739510i
$827$	−12.2116			−0.424639			−0.212319	−	0.977200i	$-0.568102\pi$
$827$	−12.2116			−0.424639			−0.212319	+	0.977200i	$0.568102\pi$
$828$	3.26643	+	3.51147i	0.113516	+	0.122032i
$829$	−19.2386	+	33.3223i	−0.668186	+	1.15733i	0.310225	+	0.950663i	$0.399595\pi$
$829$	−19.2386	+	33.3223i	−0.668186	+	1.15733i	−0.978411	+	0.206669i	$0.933738\pi$
$830$	6.98046	−	3.59868i	0.242295	−	0.124912i
$831$	22.0036	−	17.3038i	0.763295	−	0.600262i
$832$	−0.514785	−	1.12722i	−0.0178469	−	0.0390794i
$833$	3.87173	−	3.82192i	0.134148	−	0.132422i
$834$	7.19529	−	15.7555i	0.249153	−	0.545568i
$835$	14.2280	+	2.74223i	0.492382	+	0.0948988i
$836$	25.2282	+	19.8397i	0.872534	+	0.686169i
$837$	1.32623	−	5.46681i	0.0458413	−	0.188961i
$838$	0.450910	−	1.30282i	0.0155764	−	0.0450051i
$839$	25.5856	−	16.4428i	0.883311	−	0.567670i	−0.0184859	−	0.999829i	$-0.505885\pi$
$839$	25.5856	−	16.4428i	0.883311	−	0.567670i	0.901797	+	0.432159i	$0.142248\pi$
$840$	1.03002	+	1.57262i	0.0355390	+	0.0542605i
$841$	10.6847	+	12.3308i	0.368438	+	0.425200i
$842$	−18.4643	−	17.6057i	−0.636322	−	0.606732i
$843$	−23.5888	−	18.5504i	−0.812440	−	0.638910i
$844$	2.14014	+	6.18352i	0.0736666	+	0.212846i
$845$	−8.10901	+	0.774317i	−0.278958	+	0.0266373i
$846$	12.1576	+	3.56980i	0.417987	+	0.122732i
$847$	6.36160	+	4.44753i	0.218587	+	0.152819i
$848$	0.883253	+	6.14316i	0.0303310	+	0.210957i
$849$	0.816047	−	17.1309i	0.0280067	−	0.587932i
$850$	−1.74679	+	3.02553i	−0.0599144	+	0.103775i
$851$	4.32646	+	3.84337i	0.148309	+	0.131749i
$852$	7.23197	+	12.5261i	0.247763	+	0.429139i
$853$	−42.8133	−	27.5145i	−1.46590	−	0.942077i	−0.998309	−	0.0581326i	$-0.981485\pi$
$853$	−42.8133	−	27.5145i	−1.46590	−	0.942077i	−0.467592	−	0.883945i	$-0.654878\pi$
$854$	14.0715	−	36.0508i	0.481516	−	1.23363i
$855$	2.53787	+	5.55717i	0.0867934	+	0.190051i
$856$	−0.590245	−	2.43302i	−0.0201742	−	0.0831590i
$857$	15.9780	+	22.4380i	0.545798	+	0.766466i	0.991694	−	0.128619i	$-0.0410543\pi$
$857$	15.9780	+	22.4380i	0.545798	+	0.766466i	−0.445896	+	0.895085i	$0.647115\pi$
$858$	−1.51292	−	4.37130i	−0.0516503	−	0.149234i
$859$	−6.58509	+	2.63627i	−0.224680	+	0.0899485i	−0.481272	−	0.876572i	$-0.659825\pi$
$859$	−6.58509	+	2.63627i	−0.224680	+	0.0899485i	0.256591	+	0.966520i	$0.417401\pi$
$860$	2.76609	−	0.812198i	0.0943230	−	0.0276957i
$861$	3.61779	+	17.9335i	0.123294	+	0.611172i
$862$	−21.8319	+	14.0305i	−0.743597	+	0.477881i
$863$	25.1255	+	12.9531i	0.855282	+	0.440928i	0.829346	−	0.558735i	$-0.188713\pi$
$863$	25.1255	+	12.9531i	0.855282	+	0.440928i	0.0259356	+	0.999664i	$0.491744\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	0.924792	−	3.81204i	0.0314439	−	0.129613i
$866$	−6.65962	+	2.66611i	−0.226303	+	0.0905981i
$867$	−10.7371	+	12.3912i	−0.364650	+	0.420829i
$868$	1.54304	+	14.8031i	0.0523743	+	0.502452i
$869$	−46.4189	−	13.6298i	−1.57465	−	0.462360i
$870$	1.46787	−	2.06134i	0.0497655	−	0.0698858i
$871$	6.68354	+	2.67568i	0.226463	+	0.0906621i
$872$	−3.72219	+	1.91892i	−0.126049	+	0.0649829i
$873$	−4.48227	−	7.76352i	−0.151702	−	0.262755i
$874$	−33.2911	−	24.3311i	−1.12609	−	0.823010i
$875$	0.154626	+	17.8494i	0.00522730	+	0.603418i
$876$	−12.4856	−	8.02400i	−0.421849	−	0.271106i
$877$	1.40443	−	1.10445i	0.0474241	−	0.0372947i	−0.594166	−	0.804343i	$-0.702518\pi$
$877$	1.40443	−	1.10445i	0.0474241	−	0.0372947i	0.641590	+	0.767048i	$0.278275\pi$
$878$	−21.8301	−	2.08452i	−0.736730	−	0.0703492i
$879$	−6.05568	+	5.77408i	−0.204253	+	0.194755i
$880$	2.64030	−	0.252118i	0.0890044	−	0.00849889i
$881$	7.58343	−	8.75174i	0.255492	−	0.294854i	−0.613484	−	0.789707i	$-0.710233\pi$
$881$	7.58343	−	8.75174i	0.255492	−	0.294854i	0.868977	+	0.494853i	$0.164778\pi$
$882$	5.57651	+	4.23114i	0.187771	+	0.142470i
$883$	4.14653	−	1.21753i	0.139542	−	0.0409732i	−0.211216	−	0.977439i	$-0.567742\pi$
$883$	4.14653	−	1.21753i	0.139542	−	0.0409732i	0.350758	+	0.936466i	$0.385924\pi$
$884$	−0.315000	+	0.910131i	−0.0105946	+	0.0306110i
$885$	0.321066	+	6.74000i	0.0107925	+	0.226563i
$886$	0.171115	+	3.59214i	0.00574871	+	0.120680i
$887$	1.61929	−	4.67863i	0.0543705	−	0.157093i	−0.914546	−	0.404483i	$-0.867452\pi$
$887$	1.61929	−	4.67863i	0.0543705	−	0.157093i	0.968916	+	0.247390i	$0.0795728\pi$
$888$	−1.15780	+	0.339961i	−0.0388532	+	0.0114083i
$889$	−15.2174	−	2.05355i	−0.510376	−	0.0688740i
$890$	−2.61256	+	3.01505i	−0.0875730	+	0.101065i
$891$	−3.71590	+	0.354825i	−0.124487	+	0.0118871i
$892$	16.3898	−	15.6276i	0.548770	−	0.523251i
$893$	−108.451	−	10.3558i	−3.62918	−	0.346545i
$894$	2.63512	−	2.07228i	0.0881314	−	0.0693073i
$895$	13.4596	+	8.64996i	0.449905	+	0.289136i
$896$	2.27974	−	1.34267i	0.0761609	−	0.0448556i
$897$	2.14056	+	5.54414i	0.0714712	+	0.185114i
$898$	−11.0396	−	19.1211i	−0.368396	−	0.638080i
$899$	17.8074	−	9.18037i	0.593911	−	0.306183i
$900$	−4.17314	−	1.67067i	−0.139105	−	0.0556891i
$901$	2.79791	−	3.92912i	0.0932119	−	0.130898i
$902$	24.7659	+	7.27194i	0.824616	+	0.242129i
$903$	8.68987	−	6.30218i	0.289181	−	0.209723i
$904$	−2.60705	+	3.00870i	−0.0867092	+	0.100068i
$905$	5.97103	−	2.39044i	0.198484	−	0.0794609i
$906$	2.66439	−	10.9828i	0.0885183	−	0.364878i
$907$	50.8666	−	9.80373i	1.68900	−	0.325528i	0.747938	−	0.663769i	$-0.231044\pi$
$907$	50.8666	−	9.80373i	1.68900	−	0.325528i	0.941059	+	0.338241i	$0.109832\pi$
$908$	−6.26188	−	3.22823i	−0.207808	−	0.107132i
$909$	−5.51469	+	3.54407i	−0.182911	+	0.117549i
$910$	0.460678	+	2.28360i	0.0152713	+	0.0757004i
$911$	25.5938	−	7.51501i	0.847960	−	0.248983i	0.171245	−	0.985229i	$-0.445221\pi$
$911$	25.5938	−	7.51501i	0.847960	−	0.248983i	0.676715	+	0.736245i	$0.263403\pi$
$912$	7.98214	−	3.19557i	0.264315	−	0.105816i
$913$	−13.4942	−	38.9889i	−0.446592	−	1.29034i
$914$	−16.5229	−	23.2032i	−0.546530	−	0.767494i
$915$	−2.45028	−	10.1002i	−0.0810038	−	0.333902i
$916$	−9.94515	−	21.7768i	−0.328597	−	0.719527i
$917$	9.41176	+	11.7570i	0.310804	+	0.388250i
$918$	0.653816	+	0.420182i	0.0215791	+	0.0138681i
$919$	−18.1664	−	31.4651i	−0.599254	−	1.03794i	−0.992931	−	0.118690i	$-0.962130\pi$
$919$	−18.1664	−	31.4651i	−0.599254	−	1.03794i	0.393677	−	0.919249i	$-0.371203\pi$
$920$	−3.37867	+	0.443306i	−0.111392	+	0.0146154i
$921$	0.265262	−	0.459448i	0.00874069	−	0.0151393i
$922$	1.69471	−	35.5763i	0.0558123	−	1.17164i
$923$	2.55082	+	17.7414i	0.0839614	+	0.583964i
$924$	8.94771	−	4.18033i	0.294358	−	0.137523i
$925$	−5.20447	−	1.52817i	−0.171122	−	0.0502459i
$926$	7.18089	−	0.685692i	0.235979	−	0.0225332i
$927$	0.706999	+	2.04274i	0.0232209	+	0.0670924i
$928$	−2.79950	−	2.20155i	−0.0918981	−	0.0722694i
$929$	−0.843530	−	0.804304i	−0.0276753	−	0.0263884i	0.676115	−	0.736796i	$-0.263662\pi$
$929$	−0.843530	−	0.804304i	−0.0276753	−	0.0263884i	−0.703791	+	0.710408i	$0.748511\pi$
$930$	2.61752	+	3.02077i	0.0858317	+	0.0990551i
$931$	−53.9654	−	26.6480i	−1.76864	−	0.873353i
$932$	4.39316	−	2.82331i	0.143903	−	0.0924806i
$933$	9.27310	−	26.7928i	0.303588	−	0.877158i
$934$	−3.69451	+	15.2290i	−0.120888	+	0.498307i
$935$	−1.62033	−	1.27424i	−0.0529905	−	0.0416722i
$936$	−1.21681	−	0.234521i	−0.0397727	−	0.00766557i
$937$	5.74542	−	12.5807i	0.187695	−	0.410994i	−0.792269	−	0.610173i	$-0.791100\pi$
$937$	5.74542	−	12.5807i	0.187695	−	0.410994i	0.979963	+	0.199179i	$0.0638274\pi$
$938$	−4.20249	+	14.7850i	−0.137216	+	0.482747i
$939$	−1.59829	−	3.49978i	−0.0521584	−	0.114211i
$940$	−7.07696	+	5.56538i	−0.230825	+	0.181523i
$941$	−2.80150	+	1.44427i	−0.0913262	+	0.0470819i	−0.503285	−	0.864121i	$-0.667875\pi$
$941$	−2.80150	+	1.44427i	−0.0913262	+	0.0470819i	0.411958	+	0.911203i	$0.364845\pi$
$942$	7.17818	−	12.4330i	0.233878	−	0.405088i
$943$	−32.1284	−	8.21528i	−1.04624	−	0.267526i
$944$	9.49650			0.309085
$945$	1.87849	+	0.0731802i	0.0611072	+	0.00238055i
$946$	−2.15537	−	14.9909i	−0.0700770	−	0.487396i
$947$	−13.1708	+	18.4958i	−0.427993	+	0.601032i	−0.971112	−	0.238624i	$-0.923304\pi$
$947$	−13.1708	+	18.4958i	−0.427993	+	0.601032i	0.543119	+	0.839656i	$0.317243\pi$
$948$	−9.37987	+	8.94369i	−0.304644	+	0.290478i
$949$	−10.6683	−	14.9816i	−0.346308	−	0.486322i
$950$	37.9508	+	7.31443i	1.23129	+	0.237311i
$951$	1.98126	−	13.7799i	0.0642467	−	0.446845i
$952$	−2.00242	−	0.467453i	−0.0648988	−	0.0151502i
$953$	−20.8790	−	24.0957i	−0.676338	−	0.780536i	0.309016	−	0.951057i	$-0.400000\pi$
$953$	−20.8790	−	24.0957i	−0.676338	−	0.780536i	−0.985354	+	0.170521i	$0.945455\pi$
$954$	5.51641	+	2.84391i	0.178600	+	0.0920748i
$955$	−0.345389	−	7.25060i	−0.0111765	−	0.234624i
$956$	−3.68209	+	0.709665i	−0.119087	+	0.0229522i
$957$	−9.62149	−	9.17407i	−0.311019	−	0.296556i
$958$	−0.282456	+	1.96453i	−0.00912574	+	0.0634709i
$959$	−50.0724	+	17.8174i	−1.61692	+	0.575354i
$960$	0.295169	−	0.646330i	0.00952654	−	0.0208602i
$961$	0.152036	+	0.626700i	0.00490438	+	0.0202161i
$962$	−1.48855	−	0.142140i	−0.0479929	−	0.00458276i
$963$	−2.32426	−	0.930493i	−0.0748982	−	0.0299847i
$964$	0.204916	−	4.30171i	0.00659989	−	0.138549i
$965$	18.3386			0.590342
$966$	−11.2994	+	5.77275i	−0.363551	+	0.185735i
$967$	−40.9236			−1.31601			−0.658007	−	0.753012i	$-0.728600\pi$
$967$	−40.9236			−1.31601			−0.658007	+	0.753012i	$0.728600\pi$
$968$	0.139596	−	2.93048i	0.00448679	−	0.0941893i
$969$	−6.20365	−	2.48357i	−0.199290	−	0.0797837i
$970$	6.34083	+	0.605475i	0.203592	+	0.0194406i
$971$	9.24107	+	38.0922i	0.296560	+	1.22244i	0.903813	+	0.427928i	$0.140756\pi$
$971$	9.24107	+	38.0922i	0.296560	+	1.22244i	−0.607253	+	0.794509i	$0.707729\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	34.8919	+	29.7087i	1.11858	+	0.952418i
$974$	2.59784	−	18.0684i	0.0832401	−	0.578948i
$975$	−4.03148	−	3.84401i	−0.129111	−	0.123107i
$976$	−14.3628	+	2.76820i	−0.459742	+	0.0886080i
$977$	0.341300	+	7.16477i	0.0109192	+	0.229221i	0.997730	+	0.0673430i	$0.0214522\pi$
$977$	0.341300	+	7.16477i	0.0109192	+	0.229221i	−0.986811	+	0.161878i	$0.948245\pi$
$978$	11.9160	+	6.14314i	0.381033	+	0.196436i
$979$	13.7250	+	15.8395i	0.438652	+	0.506232i
$980$	−4.74732	+	1.48374i	−0.151647	+	0.0473964i
$981$	−0.595974	+	4.14509i	−0.0190280	+	0.132343i
$982$	2.38956	+	0.460549i	0.0762538	+	0.0146967i
$983$	0.175055	+	0.245830i	0.00558338	+	0.00784076i	0.817358	−	0.576130i	$-0.195438\pi$
$983$	0.175055	+	0.245830i	0.00558338	+	0.00784076i	−0.811775	+	0.583971i	$0.801498\pi$
$984$	5.00446	−	4.77174i	0.159536	−	0.152118i
$985$	−4.47251	+	6.28077i	−0.142506	+	0.200122i
$986$	0.393919	+	2.73977i	0.0125449	+	0.0872520i
$987$	−17.8794	+	28.3581i	−0.569109	+	0.902648i
$988$	10.6547			0.338972
$989$	3.44646	+	19.1504i	0.109591	+	0.608948i
$990$	1.32615	−	2.29696i	0.0421479	−	0.0730023i
$991$	−42.1421	+	21.7258i	−1.33869	+	0.690142i	−0.970836	−	0.239743i	$-0.922937\pi$
$991$	−42.1421	+	21.7258i	−1.33869	+	0.690142i	−0.367851	+	0.929885i	$0.619907\pi$
$992$	4.42185	−	3.47738i	0.140394	−	0.110407i
$993$	5.19874	+	11.3836i	0.164977	+	0.361249i
$994$	−37.1097	+	9.34384i	−1.17705	+	0.296369i
$995$	−1.73122	+	3.79085i	−0.0548835	+	0.120178i
$996$	−10.8531	−	2.09176i	−0.343894	−	0.0662801i
$997$	−1.49752	−	1.17766i	−0.0474269	−	0.0372969i	0.594164	−	0.804344i	$-0.297483\pi$
$997$	−1.49752	−	1.17766i	−0.0474269	−	0.0372969i	−0.641591	+	0.767047i	$0.721725\pi$
$998$	−2.83109	+	11.6699i	−0.0896165	+	0.369404i
$999$	−0.394666	+	1.14031i	−0.0124867	+	0.0360779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.25.5	✓	160
7.2	even	3	inner	966.2.y.c.163.5	yes	160
23.12	even	11	inner	966.2.y.c.403.5	yes	160
161.58	even	33	inner	966.2.y.c.541.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.25.5	✓	160	1.1	even	1	trivial
966.2.y.c.163.5	yes	160	7.2	even	3	inner
966.2.y.c.403.5	yes	160	23.12	even	11	inner
966.2.y.c.541.5	yes	160	161.58	even	33	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.167516 - 0.690511i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-2.01446 - 1.71521i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.167516 - 0.690511i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-2.01446 - 1.71521i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.697700 + 0.134471i) q^{10} +(0.177614 + 3.72857i) q^{11} +(0.888835 + 0.458227i) q^{12} +(0.811507 + 0.936529i) q^{13} +(-1.80912 + 1.93056i) q^{14} +(-0.101120 + 0.703308i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-0.450816 - 0.633082i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-4.98735 + 7.00375i) q^{19} +(0.101120 + 0.703308i) q^{20} +(1.23268 + 2.34105i) q^{21} +3.73280 q^{22} +(-4.79285 + 0.169076i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.99543 - 2.05979i) q^{25} +(0.974082 - 0.766026i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(1.84230 + 1.89893i) q^{28} +(1.47949 - 3.23962i) q^{29} +(0.697700 + 0.134471i) q^{30} +(4.42185 + 3.47738i) q^{31} +(0.235759 - 0.971812i) q^{32} +(1.22088 - 3.52750i) q^{33} +(-0.653816 + 0.420182i) q^{34} +(-0.846919 + 1.67833i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.873315 - 0.832704i) q^{37} +(6.75851 + 5.31495i) q^{38} +(-0.405304 - 1.17105i) q^{39} +(0.707323 - 0.0675412i) q^{40} +(6.63468 + 1.94812i) q^{41} +(2.39705 - 1.11989i) q^{42} +(-0.577413 - 4.01599i) q^{43} +(0.177614 - 3.72857i) q^{44} +(0.355270 - 0.615346i) q^{45} +(-0.0591690 + 4.79547i) q^{46} +(6.33543 + 10.9733i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(1.11609 + 6.91045i) q^{49} +(-1.86735 - 4.08892i) q^{50} +(0.183230 + 0.755284i) q^{51} +(-0.718810 - 1.00943i) q^{52} +(2.02989 + 5.86499i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(2.54487 - 0.747241i) q^{55} +(1.98444 - 1.74985i) q^{56} +(7.23312 - 4.64845i) q^{57} +(-3.16555 - 1.63196i) q^{58} +(9.32488 - 1.79722i) q^{59} +(0.167516 - 0.690511i) q^{60} +(-13.5794 + 5.43635i) q^{61} +(3.68384 - 4.25138i) q^{62} +(-0.274300 - 2.63149i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.510743 - 0.717239i) q^{65} +(-3.46541 - 1.38734i) q^{66} +(5.16374 - 2.66209i) q^{67} +(0.388596 + 0.673068i) q^{68} +(4.51237 + 1.62436i) q^{69} +(1.63613 + 0.925818i) q^{70} +(12.1678 + 7.81980i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(-14.7744 - 1.41079i) q^{73} +(-0.873315 + 0.832704i) q^{74} +(-4.47478 + 0.427290i) q^{75} +(5.63051 - 6.49796i) q^{76} +(6.03750 - 7.81570i) q^{77} +(-1.18901 + 0.349125i) q^{78} +(-4.23893 + 12.2476i) q^{79} +(-0.0338089 - 0.709736i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.26160 - 6.53447i) q^{82} +(-10.6051 + 3.11395i) q^{83} +(-1.00457 - 2.44762i) q^{84} +(-0.361631 + 0.417345i) q^{85} +(-4.03892 + 0.385670i) q^{86} +(-2.57755 + 2.45769i) q^{87} +(-3.71590 - 0.354825i) q^{88} +(4.41346 - 3.47079i) q^{89} +(-0.597745 - 0.384147i) q^{90} +(-0.0284011 - 3.27851i) q^{91} +(4.78722 + 0.287279i) q^{92} +(-2.81269 - 4.87172i) q^{93} +(11.2623 - 5.80613i) q^{94} +(5.67163 + 2.27058i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.60141 - 2.52560i) q^{97} +(6.95573 - 0.786014i) q^{98} +(-2.44447 + 2.82106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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