LMFDB - Embedded newform 966.2.be.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-0.0836058 + 0.0431018i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-1.37599 - 2.25979i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-0.0836058 + 0.0431018i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-1.37599 - 2.25979i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(0.0873243 - 0.0349594i) q^{10} +(-0.490848 - 5.14040i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-5.69238 - 0.818441i) q^{13} +(1.15495 + 2.38036i) q^{14} +(-0.0265004 + 0.0902520i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-0.866278 + 2.50294i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(2.59137 + 7.48728i) q^{19} +(-0.0902520 + 0.0265004i) q^{20} +(-2.58503 - 0.563587i) q^{21} +5.16378i q^{22} +(-3.19069 - 3.58043i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.89515 + 4.06567i) q^{25} +(5.58881 + 1.35583i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.923452 - 2.47936i) q^{28} +(6.00173 + 6.92636i) q^{29} +(0.0349594 - 0.0873243i) q^{30} +(-10.2032 + 2.47528i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-4.05900 - 3.19204i) q^{33} +(1.10028 - 2.40927i) q^{34} +(0.212442 + 0.129624i) q^{35} +(0.142315 - 0.989821i) q^{36} +(5.37699 - 0.256138i) q^{37} +(-1.86793 - 7.69970i) q^{38} +(-4.52053 + 3.55498i) q^{39} +(0.0923624 - 0.0178014i) q^{40} +(1.21650 - 1.89291i) q^{41} +(2.51975 + 0.806757i) q^{42} +(-2.35976 - 8.03659i) q^{43} +(0.490848 - 5.14040i) q^{44} +(0.0470311 + 0.0814603i) q^{45} +(2.83590 + 3.86751i) q^{46} +(-2.69188 - 1.55416i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-3.21332 + 6.21889i) q^{49} +(3.26851 - 3.77206i) q^{50} +(1.21367 + 2.35418i) q^{51} +(-5.43462 - 1.88094i) q^{52} +(-4.31754 - 5.49020i) q^{53} +(0.690079 + 0.723734i) q^{54} +(0.262598 + 0.408611i) q^{55} +(0.683592 + 2.55591i) q^{56} +(7.20705 + 3.29135i) q^{57} +(-5.31616 - 7.46550i) q^{58} +(-1.05934 - 2.64611i) q^{59} +(-0.0431018 + 0.0836058i) q^{60} +(-5.18214 + 4.94116i) q^{61} +(10.3923 - 1.49419i) q^{62} +(-2.19176 + 1.48195i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.511192 - 0.176925i) q^{65} +(3.73720 + 3.56342i) q^{66} +(5.77852 + 4.11487i) q^{67} +(-1.32431 + 2.29377i) q^{68} +(-4.79311 - 0.161567i) q^{69} +(-0.199158 - 0.149231i) q^{70} +(-5.71890 - 12.5226i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.0651002 - 0.337772i) q^{73} +(-5.37699 - 0.256138i) q^{74} +(0.944582 + 4.90096i) q^{75} +(1.12757 + 7.84240i) q^{76} +(-10.9408 + 8.18233i) q^{77} +(4.83798 - 3.10918i) q^{78} +(-2.00705 + 2.55217i) q^{79} +(-0.0936363 + 0.00894118i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-1.39092 + 1.76870i) q^{82} +(8.25379 - 5.30439i) q^{83} +(-2.43165 - 1.04262i) q^{84} +(-0.0354556 - 0.246599i) q^{85} +(1.58514 + 8.22451i) q^{86} +(9.15451 + 0.436083i) q^{87} +(-0.977251 + 5.07046i) q^{88} +(0.806693 - 3.32523i) q^{89} +(-0.0390749 - 0.0855620i) q^{90} +(5.98313 + 13.9898i) q^{91} +(-2.45543 - 4.11957i) q^{92} +(-5.24960 + 9.09258i) q^{93} +(2.53196 + 1.80300i) q^{94} +(-0.539369 - 0.514287i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(-6.19819 - 3.98334i) q^{97} +(3.78991 - 5.88528i) q^{98} +(-5.11122 + 0.734882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−0.0836058	+	0.0431018i	−0.0373897	+	0.0192757i	−0.476820	−	0.879001i	$-0.658211\pi$
$5$	−0.0836058	+	0.0431018i	−0.0373897	+	0.0192757i	0.439430	+	0.898277i	$0.355180\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	−1.37599	−	2.25979i	−0.520074	−	0.854121i
$7$	−1.37599	−	2.25979i	−0.520074	−	0.854121i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	0.0873243	−	0.0349594i	0.0276144	−	0.0110551i
$11$	−0.490848	−	5.14040i	−0.147996	−	1.54989i	−0.698839	−	0.715279i	$-0.746300\pi$
$11$	−0.490848	−	5.14040i	−0.147996	−	1.54989i	0.550843	−	0.834609i	$-0.314306\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	−5.69238	−	0.818441i	−1.57878	−	0.226995i	−0.703531	−	0.710664i	$-0.748395\pi$
$13$	−5.69238	−	0.818441i	−1.57878	−	0.226995i	−0.875251	+	0.483670i	$0.839304\pi$
$14$	1.15495	+	2.38036i	0.308673	+	0.636177i
$15$	−0.0265004	+	0.0902520i	−0.00684237	+	0.0233030i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−0.866278	+	2.50294i	−0.210103	+	0.607053i	−0.999981	−	0.00621133i	$-0.998023\pi$
$17$	−0.866278	+	2.50294i	−0.210103	+	0.607053i	0.789878	+	0.613265i	$0.210144\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	2.59137	+	7.48728i	0.594502	+	1.71770i	0.691463	+	0.722412i	$0.256967\pi$
$19$	2.59137	+	7.48728i	0.594502	+	1.71770i	−0.0969610	+	0.995288i	$0.530912\pi$
$20$	−0.0902520	+	0.0265004i	−0.0201810	+	0.00592567i
$21$	−2.58503	−	0.563587i	−0.564099	−	0.122985i
$22$			5.16378i			1.10092i
$23$	−3.19069	−	3.58043i	−0.665305	−	0.746571i
$23$	−3.19069	−	3.58043i	−0.665305	−	0.746571i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−2.89515	+	4.06567i	−0.579030	+	0.813135i
$26$	5.58881	+	1.35583i	1.09606	+	0.265900i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−0.923452	−	2.47936i	−0.174516	−	0.468555i
$29$	6.00173	+	6.92636i	1.11449	+	1.28619i	0.954215	+	0.299122i	$0.0966936\pi$
$29$	6.00173	+	6.92636i	1.11449	+	1.28619i	0.160278	+	0.987072i	$0.448761\pi$
$30$	0.0349594	−	0.0873243i	0.00638268	−	0.0159432i
$31$	−10.2032	+	2.47528i	−1.83256	+	0.444574i	−0.994834	−	0.101520i	$-0.967629\pi$
$31$	−10.2032	+	2.47528i	−1.83256	+	0.444574i	−0.837724	+	0.546094i	$0.816114\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	−4.05900	−	3.19204i	−0.706582	−	0.555662i
$34$	1.10028	−	2.40927i	0.188696	−	0.413186i
$35$	0.212442	+	0.129624i	0.0359092	+	0.0219105i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	5.37699	−	0.256138i	0.883972	−	0.0421088i	0.399315	−	0.916814i	$-0.369248\pi$
$37$	5.37699	−	0.256138i	0.883972	−	0.0421088i	0.484656	+	0.874705i	$0.338945\pi$
$38$	−1.86793	−	7.69970i	−0.303018	−	1.24906i
$39$	−4.52053	+	3.55498i	−0.723863	+	0.569252i
$40$	0.0923624	−	0.0178014i	0.0146038	−	0.00281465i
$41$	1.21650	−	1.89291i	0.189985	−	0.295622i	−0.733174	−	0.680041i	$-0.761962\pi$
$41$	1.21650	−	1.89291i	0.189985	−	0.295622i	0.923159	+	0.384419i	$0.125598\pi$
$42$	2.51975	+	0.806757i	0.388806	+	0.124485i
$43$	−2.35976	−	8.03659i	−0.359860	−	1.22557i	−0.918254	−	0.395993i	$-0.870400\pi$
$43$	−2.35976	−	8.03659i	−0.359860	−	1.22557i	0.558394	−	0.829576i	$-0.311418\pi$
$44$	0.490848	−	5.14040i	0.0739982	−	0.774944i
$45$	0.0470311	+	0.0814603i	0.00701098	+	0.0121434i
$46$	2.83590	+	3.86751i	0.418131	+	0.570234i
$47$	−2.69188	−	1.55416i	−0.392651	−	0.226697i	0.290657	−	0.956827i	$-0.406126\pi$
$47$	−2.69188	−	1.55416i	−0.392651	−	0.226697i	−0.683308	+	0.730130i	$0.739459\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	−3.21332	+	6.21889i	−0.459046	+	0.888413i
$50$	3.26851	−	3.77206i	0.462237	−	0.533450i
$51$	1.21367	+	2.35418i	0.169947	+	0.329652i
$52$	−5.43462	−	1.88094i	−0.753646	−	0.260840i
$53$	−4.31754	−	5.49020i	−0.593060	−	0.754137i	0.393179	−	0.919462i	$-0.371375\pi$
$53$	−4.31754	−	5.49020i	−0.593060	−	0.754137i	−0.986239	+	0.165325i	$0.947133\pi$
$54$	0.690079	+	0.723734i	0.0939079	+	0.0984877i
$55$	0.262598	+	0.408611i	0.0354087	+	0.0550970i
$56$	0.683592	+	2.55591i	0.0913489	+	0.341549i
$57$	7.20705	+	3.29135i	0.954597	+	0.435950i
$58$	−5.31616	−	7.46550i	−0.698046	−	0.980268i
$59$	−1.05934	−	2.64611i	−0.137915	−	0.344494i	0.843291	−	0.537457i	$-0.180615\pi$
$59$	−1.05934	−	2.64611i	−0.137915	−	0.344494i	−0.981206	+	0.192962i	$0.938191\pi$
$60$	−0.0431018	+	0.0836058i	−0.00556442	+	0.0107935i
$61$	−5.18214	+	4.94116i	−0.663505	+	0.632650i	−0.945061	−	0.326894i	$-0.893998\pi$
$61$	−5.18214	+	4.94116i	−0.663505	+	0.632650i	0.281556	+	0.959545i	$0.409149\pi$
$62$	10.3923	−	1.49419i	1.31983	−	0.189763i
$63$	−2.19176	+	1.48195i	−0.276136	+	0.186709i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	0.511192	−	0.176925i	0.0634056	−	0.0219449i
$66$	3.73720	+	3.56342i	0.460018	+	0.438626i
$67$	5.77852	+	4.11487i	0.705959	+	0.502711i	0.875747	−	0.482770i	$-0.160369\pi$
$67$	5.77852	+	4.11487i	0.705959	+	0.502711i	−0.169789	+	0.985480i	$0.554309\pi$
$68$	−1.32431	+	2.29377i	−0.160596	+	0.278160i
$69$	−4.79311	−	0.161567i	−0.577023	−	0.0194503i
$70$	−0.199158	−	0.149231i	−0.0238039	−	0.0178365i
$71$	−5.71890	−	12.5226i	−0.678708	−	1.48616i	−0.864006	−	0.503481i	$-0.832052\pi$
$71$	−5.71890	−	12.5226i	−0.678708	−	1.48616i	0.185298	−	0.982682i	$-0.440675\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	0.0651002	−	0.337772i	0.00761941	−	0.0395332i	−0.977920	−	0.208980i	$-0.932986\pi$
$73$	0.0651002	−	0.337772i	0.00761941	−	0.0395332i	0.985539	+	0.169446i	$0.0541979\pi$
$74$	−5.37699	−	0.256138i	−0.625062	−	0.0297754i
$75$	0.944582	+	4.90096i	0.109071	+	0.565914i
$76$	1.12757	+	7.84240i	0.129341	+	0.899585i
$77$	−10.9408	+	8.18233i	−1.24682	+	0.932463i
$78$	4.83798	−	3.10918i	0.547793	−	0.352045i
$79$	−2.00705	+	2.55217i	−0.225811	+	0.287142i	−0.885736	−	0.464190i	$-0.846346\pi$
$79$	−2.00705	+	2.55217i	−0.225811	+	0.287142i	0.659925	+	0.751331i	$0.270588\pi$
$80$	−0.0936363	+	0.00894118i	−0.0104689	+	0.000999654i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−1.39092	+	1.76870i	−0.153601	+	0.195320i
$83$	8.25379	−	5.30439i	0.905971	−	0.582232i	−0.00258450	−	0.999997i	$-0.500823\pi$
$83$	8.25379	−	5.30439i	0.905971	−	0.582232i	0.908555	+	0.417765i	$0.137186\pi$
$84$	−2.43165	−	1.04262i	−0.265315	−	0.113759i
$85$	−0.0354556	−	0.246599i	−0.00384570	−	0.0267474i
$86$	1.58514	+	8.22451i	0.170931	+	0.886872i
$87$	9.15451	+	0.436083i	0.981467	+	0.0467530i
$88$	−0.977251	+	5.07046i	−0.104175	+	0.540513i
$89$	0.806693	−	3.32523i	0.0855093	−	0.352474i	−0.912943	−	0.408087i	$-0.866196\pi$
$89$	0.806693	−	3.32523i	0.0855093	−	0.352474i	0.998452	+	0.0556127i	$0.0177112\pi$
$90$	−0.0390749	−	0.0855620i	−0.00411885	−	0.00901903i
$91$	5.98313	+	13.9898i	0.627203	+	1.46653i
$92$	−2.45543	−	4.11957i	−0.255996	−	0.429495i
$93$	−5.24960	+	9.09258i	−0.544358	+	0.942857i
$94$	2.53196	+	1.80300i	0.261152	+	0.185965i
$95$	−0.539369	−	0.514287i	−0.0553381	−	0.0527648i
$96$	−0.945001	+	0.327068i	−0.0964487	+	0.0333812i
$97$	−6.19819	−	3.98334i	−0.629331	−	0.404446i	0.186731	−	0.982411i	$-0.440211\pi$
$97$	−6.19819	−	3.98334i	−0.629331	−	0.404446i	−0.816062	+	0.577965i	$0.803847\pi$
$98$	3.78991	−	5.88528i	0.382839	−	0.594503i
$99$	−5.11122	+	0.734882i	−0.513697	+	0.0738584i
$100$	−3.61227	+	3.44429i	−0.361227	+	0.344429i
$101$	3.01397	−	5.84628i	0.299901	−	0.581727i	−0.689947	−	0.723860i	$-0.742366\pi$
$101$	3.01397	−	5.84628i	0.299901	−	0.581727i	0.989847	+	0.142134i	$0.0453963\pi$
$102$	−0.984391	−	2.45889i	−0.0974693	−	0.243466i
$103$	4.02173	+	5.64772i	0.396272	+	0.556487i	0.963717	−	0.266925i	$-0.0860074\pi$
$103$	4.02173	+	5.64772i	0.396272	+	0.556487i	−0.567445	+	0.823411i	$0.692068\pi$
$104$	5.23122	+	2.38902i	0.512963	+	0.234262i
$105$	0.240415	−	0.0643002i	0.0234621	−	0.00627506i
$106$	3.77611	+	5.87575i	0.366769	+	0.570703i
$107$	−6.43238	−	6.74608i	−0.621841	−	0.652168i	0.335191	−	0.942150i	$-0.391199\pi$
$107$	−6.43238	−	6.74608i	−0.621841	−	0.652168i	−0.957032	+	0.289982i	$0.906351\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	−10.0841	−	3.49013i	−0.965879	−	0.334294i	−0.201807	−	0.979425i	$-0.564682\pi$
$109$	−10.0841	−	3.49013i	−0.965879	−	0.334294i	−0.764072	+	0.645131i	$0.776803\pi$
$110$	−0.222568	−	0.431722i	−0.0212210	−	0.0411631i
$111$	3.52517	−	4.06826i	0.334594	−	0.386143i
$112$	−0.437542	−	2.60932i	−0.0413438	−	0.246558i
$113$	−10.3335	+	4.71916i	−0.972095	+	0.443941i	−0.837187	−	0.546917i	$-0.815801\pi$
$113$	−10.3335	+	4.71916i	−0.972095	+	0.443941i	−0.134908	+	0.990858i	$0.543074\pi$
$114$	−6.86156	−	3.96152i	−0.642644	−	0.371030i
$115$	0.421083	+	0.161820i	0.0392662	+	0.0150898i
$116$	4.58245	+	7.93703i	0.425470	+	0.736935i
$117$	−0.546659	+	5.72488i	−0.0505387	+	0.529265i
$118$	0.803018	+	2.73483i	0.0739238	+	0.251761i
$119$	6.84812	−	1.48641i	0.627766	−	0.136259i
$120$	0.0508539	−	0.0791302i	0.00464230	−	0.00722356i
$121$	−15.3815	+	2.96455i	−1.39832	+	0.269504i
$122$	5.62836	−	4.42619i	0.509568	−	0.400728i
$123$	−0.530482	−	2.18667i	−0.0478319	−	0.197166i
$124$	−10.4873	+	0.499572i	−0.941789	+	0.0448629i
$125$	0.133746	−	0.930224i	0.0119626	−	0.0832018i
$126$	2.32270	−	1.26690i	0.206923	−	0.112865i
$127$	5.90943	−	12.9399i	0.524377	−	1.14823i	−0.443378	−	0.896335i	$-0.646220\pi$
$127$	5.90943	−	12.9399i	0.524377	−	1.14823i	0.967755	−	0.251892i	$-0.0810527\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	−7.44477	−	3.83805i	−0.655476	−	0.337921i
$130$	−0.525695	+	0.127532i	−0.0461065	+	0.0111853i
$131$	0.0441027	−	0.110163i	0.00385327	−	0.00962500i	−0.926429	−	0.376470i	$-0.877138\pi$
$131$	0.0441027	−	0.110163i	0.00385327	−	0.00962500i	0.930282	+	0.366845i	$0.119562\pi$
$132$	−3.38156	−	3.90252i	−0.294327	−	0.339671i
$133$	13.3540	−	16.1584i	1.15794	−	1.40111i
$134$	−5.36121	−	4.64552i	−0.463138	−	0.401312i
$135$	0.0914107	+	0.0221760i	0.00786738	+	0.00190861i
$136$	1.53635	−	2.15750i	0.131741	−	0.185004i
$137$	11.1474	−	6.43593i	0.952384	−	0.549859i	0.0585630	−	0.998284i	$-0.481348\pi$
$137$	11.1474	−	6.43593i	0.952384	−	0.549859i	0.893821	+	0.448425i	$0.148015\pi$
$138$	4.75605	+	0.616449i	0.404862	+	0.0524756i
$139$		−	9.39677i		−	0.797024i	−0.917163	−	0.398512i	$-0.869527\pi$
$139$		−	9.39677i		−	0.797024i	0.917163	−	0.398512i	$-0.130473\pi$
$140$	0.184071	+	0.167487i	0.0155568	+	0.0141552i
$141$	−2.98241	+	0.875713i	−0.251164	+	0.0737484i
$142$	4.50265	+	13.0096i	0.377854	+	1.09174i
$143$	−1.41301	+	29.6628i	−0.118162	+	2.48053i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−0.800318	−	0.320399i	−0.0664628	−	0.0266077i
$146$	−0.0969127	+	0.330054i	−0.00802055	+	0.0273155i
$147$	2.28337	+	6.61711i	0.188330	+	0.545770i
$148$	5.32829	+	0.766093i	0.437983	+	0.0629725i
$149$	−13.1795	+	9.38508i	−1.07971	+	0.768856i	−0.974228	−	0.225566i	$-0.927577\pi$
$149$	−13.1795	+	9.38508i	−1.07971	+	0.768856i	−0.105479	+	0.994422i	$0.533638\pi$
$150$	−0.474439	−	4.96855i	−0.0387378	−	0.405681i
$151$	−0.746984	+	0.299047i	−0.0607887	+	0.0243361i	−0.401858	−	0.915702i	$-0.631635\pi$
$151$	−0.746984	+	0.299047i	−0.0607887	+	0.0243361i	0.341069	+	0.940038i	$0.389211\pi$
$152$	−0.376994	−	7.91407i	−0.0305782	−	0.641916i
$153$	2.54133	+	0.746202i	0.205454	+	0.0603268i
$154$	11.6691	−	7.10529i	0.940320	−	0.572561i
$155$	0.746362	−	0.646726i	0.0599492	−	0.0519463i
$156$	−5.11162	+	2.63522i	−0.409257	+	0.210987i
$157$	−17.0518	−	3.28647i	−1.36088	−	0.262289i	−0.543998	−	0.839087i	$-0.683090\pi$
$157$	−17.0518	−	3.28647i	−1.36088	−	0.262289i	−0.816887	+	0.576798i	$0.804302\pi$
$158$	2.24056	−	2.34983i	0.178249	−	0.186943i
$159$	−6.95289	−	0.663920i	−0.551400	−	0.0526523i
$160$	0.0940622			0.00743627
$161$	−3.70068	+	12.1369i	−0.291654	+	0.956524i
$162$	1.00000			0.0785674
$163$	−13.2404	−	1.26431i	−1.03707	−	0.0990281i	−0.437392	−	0.899271i	$-0.644098\pi$
$163$	−13.2404	−	1.26431i	−1.03707	−	0.0990281i	−0.599676	+	0.800243i	$0.704704\pi$
$164$	1.55275	−	1.62848i	0.121249	−	0.127163i
$165$	0.476939	+	0.0919224i	0.0371296	+	0.00715615i
$166$	−8.72063	+	4.49580i	−0.676852	+	0.348941i
$167$	3.01015	−	2.60831i	0.232932	−	0.201837i	−0.530572	−	0.847640i	$-0.678023\pi$
$167$	3.01015	−	2.60831i	0.232932	−	0.201837i	0.763504	+	0.645803i	$0.223477\pi$
$168$	2.32154	+	1.26904i	0.179110	+	0.0979089i
$169$	19.2599	+	5.65523i	1.48153	+	0.435017i
$170$	0.0118543	+	0.248853i	0.000909184	+	0.0190861i
$171$	7.35550	−	2.94470i	0.562489	−	0.225187i
$172$	−0.796177	−	8.33795i	−0.0607080	−	0.635763i
$173$	2.35031	−	1.67365i	0.178691	−	0.127245i	−0.487212	−	0.873284i	$-0.661986\pi$
$173$	2.35031	−	1.67365i	0.178691	−	0.127245i	0.665903	+	0.746039i	$0.268047\pi$
$174$	−9.07161	−	1.30430i	−0.687717	−	0.0988788i
$175$	13.1713	+	0.948132i	0.995654	+	0.0716720i
$176$	1.45480	−	4.95461i	0.109660	−	0.373468i
$177$	−2.64611	−	1.05934i	−0.198894	−	0.0796251i
$178$	−1.11912	+	3.23350i	−0.0838819	+	0.242361i
$179$	−0.250825	+	5.26547i	−0.0187476	+	0.393560i	0.969919	+	0.243429i	$0.0782724\pi$
$179$	−0.250825	+	5.26547i	−0.0187476	+	0.393560i	−0.988666	+	0.150130i	$0.952031\pi$
$180$	0.0307647	+	0.0888889i	0.00229307	+	0.00662538i
$181$	0.583691	−	0.171387i	0.0433854	−	0.0127391i	−0.259968	−	0.965617i	$-0.583712\pi$
$181$	0.583691	−	0.171387i	0.0433854	−	0.0127391i	0.303353	+	0.952878i	$0.401894\pi$
$182$	−4.62623	−	14.4951i	−0.342919	−	1.07445i
$183$			7.16028i			0.529303i
$184$	2.05272	+	4.33432i	0.151329	+	0.319530i
$185$	−0.438508	+	0.253172i	−0.0322397	+	0.0186136i
$186$	6.09014	−	8.55240i	0.446550	−	0.627092i
$187$	13.2913	+	3.22444i	0.971959	+	0.235795i
$188$	−2.34911	−	2.03551i	−0.171326	−	0.148455i
$189$	−0.439948	+	2.60892i	−0.0320015	+	0.189771i
$190$	0.488041	+	0.563229i	0.0354062	+	0.0408609i
$191$	0.170417	−	0.425681i	0.0123309	−	0.0308012i	−0.922075	−	0.387012i	$-0.873507\pi$
$191$	0.170417	−	0.425681i	0.0123309	−	0.0308012i	0.934406	+	0.356211i	$0.115931\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	9.95729	+	5.13334i	0.716742	+	0.369506i	0.777701	−	0.628634i	$-0.216386\pi$
$193$	9.95729	+	5.13334i	0.716742	+	0.369506i	−0.0609595	+	0.998140i	$0.519416\pi$
$194$	5.79148	+	4.55447i	0.415804	+	0.326992i
$195$	0.224716	−	0.492060i	0.0160923	−	0.0352371i
$196$	−4.33219	+	5.49838i	−0.309442	+	0.392741i
$197$	2.09822	−	14.5935i	0.149492	−	1.03974i	−0.767561	−	0.640976i	$-0.778530\pi$
$197$	2.09822	−	14.5935i	0.149492	−	1.03974i	0.917053	−	0.398765i	$-0.130561\pi$
$198$	5.15793	−	0.245702i	0.366558	−	0.0174613i
$199$	−2.04815	−	8.44260i	−0.145190	−	0.598480i	−0.997188	−	0.0749361i	$-0.976125\pi$
$199$	−2.04815	−	8.44260i	−0.145190	−	0.598480i	0.851999	−	0.523544i	$-0.175390\pi$
$200$	3.92331	−	3.08533i	0.277420	−	0.218165i
$201$	6.96571	−	1.34253i	0.491323	−	0.0946947i
$202$	−3.55604	+	5.53331i	−0.250202	+	0.389322i
$203$	7.39385	−	23.0932i	0.518946	−	1.62083i
$204$	0.746202	+	2.54133i	0.0522446	+	0.177929i
$205$	−0.0201186	+	0.210691i	−0.00140514	+	0.0147153i
$206$	−3.46666	−	6.00444i	−0.241534	−	0.418349i
$207$	−3.42456	+	3.35744i	−0.238023	+	0.233358i
$208$	−4.98044	−	2.87546i	−0.345331	−	0.199377i
$209$	37.2156	−	16.9958i	2.57426	−	1.17562i
$210$	−0.245438	+	0.0411562i	−0.0169369	+	0.00284004i
$211$	2.48837	−	2.87173i	0.171306	−	0.197698i	−0.663604	−	0.748084i	$-0.730974\pi$
$211$	2.48837	−	2.87173i	0.171306	−	0.197698i	0.834910	+	0.550386i	$0.185519\pi$
$212$	−3.20049	−	6.20808i	−0.219811	−	0.426373i
$213$	−13.0096	−	4.50265i	−0.891400	−	0.308516i
$214$	5.76199	+	7.32697i	0.393882	+	0.500862i
$215$	0.543681	+	0.570196i	0.0370787	+	0.0388871i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	19.6332	+	19.6513i	1.33279	+	1.33402i
$218$	9.70666	+	4.43288i	0.657418	+	0.300233i
$219$	−0.199533	−	0.280205i	−0.0134832	−	0.0189345i
$220$	0.180523	+	0.450923i	0.0121708	+	0.0304013i
$221$	6.97969	−	13.5387i	0.469505	−	0.910713i
$222$	−3.89592	+	3.71475i	−0.261477	+	0.249318i
$223$	15.4962	−	2.22801i	1.03770	−	0.149199i	0.397654	−	0.917535i	$-0.369824\pi$
$223$	15.4962	−	2.22801i	1.03770	−	0.149199i	0.640046	+	0.768336i	$0.278915\pi$
$224$	0.187529	+	2.63910i	0.0125298	+	0.176332i
$225$	4.19882	+	2.69842i	0.279922	+	0.179895i
$226$	10.7353	−	3.71552i	0.714102	−	0.247153i
$227$	11.0169	+	10.5046i	0.731218	+	0.697215i	0.961161	−	0.275989i	$-0.0890055\pi$
$227$	11.0169	+	10.5046i	0.731218	+	0.697215i	−0.229943	+	0.973204i	$0.573854\pi$
$228$	6.45392	+	4.59582i	0.427421	+	0.304365i
$229$	7.17503	−	12.4275i	0.474139	−	0.821233i	−0.525422	−	0.850841i	$-0.676093\pi$
$229$	7.17503	−	12.4275i	0.474139	−	0.821233i	0.999562	+	0.0296085i	$0.00942605\pi$
$230$	−0.403795	−	0.201114i	−0.0266254	−	0.0132611i
$231$	−1.62820	+	13.5647i	−0.107128	+	0.892492i
$232$	−3.80723	−	8.33668i	−0.249957	−	0.547330i
$233$	5.98578	−	24.6737i	0.392142	−	1.61643i	−0.343564	−	0.939129i	$-0.611634\pi$
$233$	5.98578	−	24.6737i	0.392142	−	1.61643i	0.735706	−	0.677301i	$-0.236850\pi$
$234$	1.08837	−	5.64699i	0.0711488	−	0.369155i
$235$	0.292044	+	0.0139118i	0.0190508	+	0.000907503i
$236$	−0.539420	−	2.79877i	−0.0351132	−	0.182185i
$237$	0.462070	+	3.21377i	0.0300147	+	0.208757i
$238$	−6.95841	+	0.828725i	−0.451046	+	0.0537183i
$239$	1.68986	−	1.08601i	0.109308	−	0.0702480i	−0.484845	−	0.874600i	$-0.661124\pi$
$239$	1.68986	−	1.08601i	0.109308	−	0.0702480i	0.594153	+	0.804352i	$0.297487\pi$
$240$	−0.0581454	+	0.0739379i	−0.00375327	+	0.00477267i
$241$	14.4720	−	1.38191i	0.932226	−	0.0890168i	0.382121	−	0.924112i	$-0.375194\pi$
$241$	14.4720	−	1.38191i	0.932226	−	0.0890168i	0.550105	+	0.835095i	$0.314588\pi$
$242$	15.5937	−	1.48902i	1.00240	−	0.0957175i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	−6.02361	+	3.87114i	−0.385622	+	0.247824i
$245$	0.000607187	−	0.658435i	3.87918e−5	−	0.0420659i
$246$	0.320223	+	2.22720i	0.0204167	+	0.142001i
$247$	−8.62319	−	44.7413i	−0.548680	−	2.84682i
$248$	10.4873	+	0.499572i	0.665945	+	0.0317229i
$249$	1.85680	−	9.63399i	0.117670	−	0.610529i
$250$	−0.221564	+	0.913299i	−0.0140129	+	0.0577621i
$251$	9.46008	+	20.7147i	0.597115	+	1.30750i	0.931046	+	0.364902i	$0.118898\pi$
$251$	9.46008	+	20.7147i	0.597115	+	1.30750i	−0.333931	+	0.942598i	$0.608375\pi$
$252$	−2.43261	+	1.04038i	−0.153240	+	0.0655377i
$253$	−16.8387	+	18.1589i	−1.05864	+	1.14164i
$254$	−7.11269	+	12.3195i	−0.446290	+	0.772996i
$255$	−0.202939	−	0.144512i	−0.0127085	−	0.00904971i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	−22.2734	+	7.70889i	−1.38937	+	0.480867i	−0.916419	−	0.400219i	$-0.868934\pi$
$257$	−22.2734	+	7.70889i	−1.38937	+	0.480867i	−0.472955	+	0.881087i	$0.656813\pi$
$258$	7.04623	+	4.52834i	0.438679	+	0.281922i
$259$	−7.97748	−	11.7984i	−0.495697	−	0.733119i
$260$	0.535438	−	0.0769843i	0.0332064	−	0.00477437i
$261$	6.63295	−	6.32450i	0.410569	−	0.391477i
$262$	−0.0543747	+	0.105472i	−0.00335928	+	0.00651609i
$263$	9.24413	+	23.0907i	0.570017	+	1.42383i	0.880862	+	0.473374i	$0.156964\pi$
$263$	9.24413	+	23.0907i	0.570017	+	1.42383i	−0.310844	+	0.950461i	$0.600612\pi$
$264$	2.99529	+	4.20629i	0.184347	+	0.258879i
$265$	0.597609	+	0.272919i	0.0367108	+	0.0167653i
$266$	−14.8295	+	14.8158i	−0.909254	+	0.908416i
$267$	−1.84990	−	2.87851i	−0.113212	−	0.176162i
$268$	4.89535	+	5.13410i	0.299031	+	0.313615i
$269$	−5.99641	−	7.62505i	−0.365607	−	0.464908i	0.568092	−	0.822965i	$-0.307682\pi$
$269$	−5.99641	−	7.62505i	−0.365607	−	0.464908i	−0.933700	+	0.358057i	$0.883439\pi$
$270$	−0.0888889	−	0.0307647i	−0.00540960	−	0.00187228i
$271$	−1.78615	−	3.46464i	−0.108501	−	0.210462i	0.828334	−	0.560235i	$-0.189289\pi$
$271$	−1.78615	−	3.46464i	−0.108501	−	0.210462i	−0.936835	+	0.349773i	$0.886259\pi$
$272$	−1.73448	+	2.00169i	−0.105168	+	0.121370i
$273$	14.2537	+	5.32384i	0.862673	+	0.322214i
$274$	−11.7087	+	5.34717i	−0.707346	+	0.323034i
$275$	22.3202	+	12.8866i	1.34596	+	0.777091i
$276$	−4.67591	−	1.06575i	−0.281457	−	0.0641505i
$277$	−9.64082	−	16.6984i	−0.579261	−	1.00331i	−0.995564	−	0.0940834i	$-0.970008\pi$
$277$	−9.64082	−	16.6984i	−0.579261	−	1.00331i	0.416304	−	0.909226i	$-0.363325\pi$
$278$	−0.893220	+	9.35422i	−0.0535718	+	0.561029i
$279$	2.95797	+	10.0739i	0.177089	+	0.603109i
$280$	−0.167317	−	0.184225i	−0.00999909	−	0.0110096i
$281$	15.6900	−	24.4141i	0.935985	−	1.45642i	0.0467845	−	0.998905i	$-0.485103\pi$
$281$	15.6900	−	24.4141i	0.935985	−	1.45642i	0.889201	−	0.457517i	$-0.151261\pi$
$282$	3.05214	−	0.588252i	0.181752	−	0.0350299i
$283$	−19.5051	+	15.3390i	−1.15946	+	0.911807i	−0.997188	−	0.0749400i	$-0.976123\pi$
$283$	−19.5051	+	15.3390i	−1.15946	+	0.911807i	−0.162268	+	0.986747i	$0.551881\pi$
$284$	−3.24562	−	13.3786i	−0.192592	−	0.793877i
$285$	−0.744415	+	0.0354608i	−0.0440953	+	0.00210052i
$286$	4.22625	−	29.3942i	0.249903	−	1.73811i
$287$	−5.95146	−	0.144417i	−0.351303	−	0.00852465i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	7.84861	+	6.17221i	0.461683	+	0.363071i
$290$	0.766238	+	0.395023i	0.0449951	+	0.0231966i
$291$	−7.16012	+	1.73703i	−0.419733	+	0.101826i
$292$	0.127848	−	0.319348i	0.00748171	−	0.0186884i
$293$	3.65309	+	4.21590i	0.213416	+	0.246295i	0.852357	−	0.522961i	$-0.175173\pi$
$293$	3.65309	+	4.21590i	0.213416	+	0.246295i	−0.638941	+	0.769256i	$0.720627\pi$
$294$	−1.64404	−	6.80420i	−0.0958823	−	0.396829i
$295$	0.202619	+	0.175571i	0.0117970	+	0.0102221i
$296$	−5.23135	−	1.26911i	−0.304066	−	0.0737656i
$297$	−2.99529	+	4.20629i	−0.173804	+	0.244074i
$298$	14.0119	−	8.08979i	0.811689	−	0.468629i
$299$	15.2323	+	22.9926i	0.880905	+	1.32969i
$300$			4.99115i			0.288164i
$301$	−14.9140	+	16.3908i	−0.859631	+	0.944750i
$302$	0.772028	−	0.226688i	0.0444252	−	0.0130444i
$303$	−2.15128	−	6.21571i	−0.123588	−	0.357083i
$304$	−0.376994	+	7.91407i	−0.0216221	+	0.453903i
$305$	0.220284	−	0.636469i	0.0126134	−	0.0364441i
$306$	−2.45889	−	0.984391i	−0.140565	−	0.0562739i
$307$	8.19637	−	27.9143i	0.467791	−	1.59315i	−0.300982	−	0.953630i	$-0.597314\pi$
$307$	8.19637	−	27.9143i	0.467791	−	1.59315i	0.768773	−	0.639521i	$-0.220867\pi$
$308$	−12.2916	+	5.96390i	−0.700381	+	0.339825i
$309$	6.86276	+	0.986716i	0.390409	+	0.0561323i
$310$	−0.804458	+	0.572852i	−0.0456901	+	0.0325358i
$311$	−0.0820198	−	0.858950i	−0.00465091	−	0.0487066i	0.992849	−	0.119381i	$-0.0380910\pi$
$311$	−0.0820198	−	0.858950i	−0.00465091	−	0.0487066i	−0.997499	+	0.0706743i	$0.977485\pi$
$312$	5.33897	−	2.13740i	0.302259	−	0.121006i
$313$	0.0479698	+	1.00701i	0.00271141	+	0.0569196i	0.999818	−	0.0191028i	$-0.00608098\pi$
$313$	0.0479698	+	1.00701i	0.00271141	+	0.0569196i	−0.997106	+	0.0760224i	$0.975778\pi$
$314$	16.6622	+	4.89247i	0.940304	+	0.276098i
$315$	0.119369	−	0.218369i	0.00672569	−	0.0123037i
$316$	−2.45378	+	2.12621i	−0.138036	+	0.119609i
$317$	−26.7497	+	13.7904i	−1.50241	+	0.774548i	−0.996136	−	0.0878224i	$-0.972009\pi$
$317$	−26.7497	+	13.7904i	−1.50241	+	0.774548i	−0.506278	+	0.862371i	$0.668979\pi$
$318$	6.85829	+	1.32183i	0.384594	+	0.0741244i
$319$	32.6583	−	34.2511i	1.82851	−	1.91769i
$320$	−0.0936363	−	0.00894118i	−0.00523443	−	0.000499827i
$321$	−9.32122			−0.520260
$322$	4.83761	−	11.7302i	0.269589	−	0.653698i
$323$	−20.9851			−1.16764
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	19.8078	−	20.7738i	1.09874	−	1.15233i
$326$	13.0603	+	2.51716i	0.723342	+	0.139413i
$327$	−9.48474	+	4.88972i	−0.524507	+	0.270402i
$328$	−1.70051	+	1.47350i	−0.0938951	+	0.0813606i
$329$	0.191917	+	8.22159i	0.0105807	+	0.453271i
$330$	−0.466041	−	0.136842i	−0.0256547	−	0.00753291i
$331$	0.794768	+	16.6842i	0.0436844	+	0.917048i	0.909249	+	0.416252i	$0.136656\pi$
$331$	0.794768	+	16.6842i	0.0436844	+	0.917048i	−0.865565	+	0.500796i	$0.833041\pi$
$332$	9.10849	−	3.64649i	0.499893	−	0.200127i
$333$	−0.511695	−	5.35871i	−0.0280407	−	0.293656i
$334$	−3.24445	+	2.31036i	−0.177528	+	0.126417i
$335$	−0.660476	−	0.0949621i	−0.0360857	−	0.00518834i
$336$	−2.19039	−	1.48397i	−0.119496	−	0.0809574i
$337$	−5.28979	+	18.0154i	−0.288153	+	0.981360i	0.680460	+	0.732785i	$0.261780\pi$
$337$	−5.28979	+	18.0154i	−0.288153	+	0.981360i	−0.968613	+	0.248574i	$0.920038\pi$
$338$	−18.6352	−	7.46039i	−1.01362	−	0.405792i
$339$	−3.71552	+	10.7353i	−0.201800	+	0.583062i
$340$	0.0118543	−	0.248853i	0.000642890	−	0.0134959i
$341$	17.7322	+	51.2338i	0.960251	+	2.77446i
$342$	−7.60210	+	2.23218i	−0.411075	+	0.120702i
$343$	18.4749	−	1.29567i	0.997550	−	0.0699594i
$344$			8.37587i			0.451597i
$345$	0.407696	−	0.193084i	0.0219496	−	0.0103953i
$346$	−2.49876	+	1.44266i	−0.134334	+	0.0775579i
$347$	13.2270	−	18.5747i	0.710060	−	0.997140i	−0.289145	−	0.957285i	$-0.593371\pi$
$347$	13.2270	−	18.5747i	0.710060	−	0.997140i	0.999205	−	0.0398547i	$-0.0126895\pi$
$348$	8.90655	+	2.16071i	0.477441	+	0.115826i
$349$	3.82406	+	3.31357i	0.204697	+	0.177371i	0.751176	−	0.660102i	$-0.229487\pi$
$349$	3.82406	+	3.31357i	0.204697	+	0.177371i	−0.546479	+	0.837473i	$0.684032\pi$
$350$	−13.0215	−	2.19585i	−0.696028	−	0.117373i
$351$	3.76605	+	4.34625i	0.201017	+	0.231986i
$352$	−1.91918	+	4.79389i	−0.102293	+	0.255515i
$353$	−14.8020	+	3.59092i	−0.787831	+	0.191126i	−0.609438	−	0.792834i	$-0.708605\pi$
$353$	−14.8020	+	3.59092i	−0.787831	+	0.191126i	−0.178393	+	0.983959i	$0.557090\pi$
$354$	2.53343	+	1.30608i	0.134650	+	0.0694171i
$355$	1.01788	+	0.800471i	0.0540235	+	0.0424846i
$356$	1.42142	−	3.11248i	0.0753351	−	0.164961i
$357$	3.64998	−	5.98196i	0.193177	−	0.316599i
$358$	0.750205	−	5.21779i	0.0396495	−	0.275769i
$359$	1.11910	−	0.0533092i	0.0590637	−	0.00281355i	−0.0180293	−	0.999837i	$-0.505739\pi$
$359$	1.11910	−	0.0533092i	0.0590637	−	0.00281355i	0.0770930	+	0.997024i	$0.475436\pi$
$360$	−0.0221760	−	0.0914107i	−0.00116878	−	0.00481777i
$361$	−34.4092	+	27.0597i	−1.81101	+	1.42419i
$362$	−0.597339	+	0.115128i	−0.0313955	+	0.00605098i
$363$	−8.46893	+	13.1779i	−0.444503	+	0.691661i
$364$	3.22743	+	14.8693i	0.169163	+	0.779361i
$365$	0.00911582	+	0.0310456i	0.000477144	+	0.00162500i
$366$	0.680628	−	7.12786i	0.0355770	−	0.372579i
$367$	1.03237	+	1.78812i	0.0538894	+	0.0933392i	0.891712	−	0.452604i	$-0.149505\pi$
$367$	1.03237	+	1.78812i	0.0538894	+	0.0933392i	−0.837822	+	0.545943i	$0.816171\pi$
$368$	−1.63143	−	4.50982i	−0.0850439	−	0.235090i
$369$	−1.94865	−	1.12505i	−0.101442	−	0.0585678i
$370$	0.460588	−	0.210343i	0.0239448	−	0.0109352i
$371$	−6.46583	+	17.3112i	−0.335689	+	0.898752i
$372$	−6.87552	+	7.93477i	−0.356479	+	0.411399i
$373$	−16.5458	−	32.0943i	−0.856708	−	1.66178i	−0.744027	−	0.668150i	$-0.767086\pi$
$373$	−16.5458	−	32.0943i	−0.856708	−	1.66178i	−0.112681	−	0.993631i	$-0.535944\pi$
$374$	−12.9247	−	4.47327i	−0.668318	−	0.231307i
$375$	−0.580940	−	0.738725i	−0.0299996	−	0.0381476i
$376$	2.14498	+	2.24959i	0.110619	+	0.116014i
$377$	−28.4953	−	44.3396i	−1.46758	−	2.28360i
$378$	0.685949	−	2.55528i	0.0352814	−	0.131430i
$379$	13.1519	+	6.00628i	0.675568	+	0.308522i	0.723495	−	0.690329i	$-0.242534\pi$
$379$	13.1519	+	6.00628i	0.675568	+	0.308522i	−0.0479272	+	0.998851i	$0.515262\pi$
$380$	−0.432293	−	0.607070i	−0.0221761	−	0.0311420i
$381$	−5.28704	−	13.2064i	−0.270863	−	0.676583i
$382$	−0.210109	+	0.407554i	−0.0107501	+	0.0208523i
$383$	−7.18225	+	6.84826i	−0.366996	+	0.349930i	−0.851028	−	0.525120i	$-0.824020\pi$
$383$	−7.18225	+	6.84826i	−0.366996	+	0.349930i	0.484032	+	0.875050i	$0.339172\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	0.562044	−	1.15566i	0.0286444	−	0.0588979i
$386$	−9.42425	−	6.05660i	−0.479682	−	0.308273i
$387$	−7.91521	+	2.73948i	−0.402353	+	0.139256i
$388$	−5.33233	−	5.08437i	−0.270708	−	0.258120i
$389$	−7.16941	−	5.10532i	−0.363504	−	0.258850i	0.383682	−	0.923465i	$-0.374656\pi$
$389$	−7.16941	−	5.10532i	−0.363504	−	0.258850i	−0.747185	+	0.664616i	$0.768595\pi$
$390$	−0.270472	+	0.468471i	−0.0136959	+	0.0237220i
$391$	11.7256	−	4.88448i	0.592991	−	0.247019i
$392$	4.83522	−	5.06168i	0.244216	−	0.255654i
$393$	−0.0492945	−	0.107940i	−0.00248658	−	0.00544485i
$394$	−3.47592	+	14.3279i	−0.175114	+	0.721831i
$395$	0.0577978	−	0.299884i	0.00290812	−	0.0150888i
$396$	−5.15793	−	0.245702i	−0.259196	−	0.0123470i
$397$	3.51226	+	18.2234i	0.176275	+	0.914604i	0.957079	+	0.289827i	$0.0935979\pi$
$397$	3.51226	+	18.2234i	0.176275	+	0.914604i	−0.780803	+	0.624777i	$0.785190\pi$
$398$	1.23636	+	8.59906i	0.0619731	+	0.431032i
$399$	−2.47904	−	20.8153i	−0.124107	−	1.04207i
$400$	−4.19882	+	2.69842i	−0.209941	+	0.134921i
$401$	−7.71874	+	9.81518i	−0.385456	+	0.490147i	−0.939600	−	0.342274i	$-0.888803\pi$
$401$	−7.71874	+	9.81518i	−0.385456	+	0.490147i	0.554145	+	0.832420i	$0.313045\pi$
$402$	−7.06178	+	0.674318i	−0.352210	+	0.0336319i
$403$	60.1066	−	5.73949i	2.99413	−	0.285904i
$404$	4.06592	−	5.17023i	0.202287	−	0.257229i
$405$	0.0791302	−	0.0508539i	0.00393201	−	0.00252695i
$406$	−9.55552	+	22.2858i	−0.474232	+	1.10603i
$407$	−3.95593	−	27.5141i	−0.196088	−	1.36382i
$408$	−0.501254	−	2.60075i	−0.0248158	−	0.128756i
$409$	0.191025	+	0.00909962i	0.00944556	+	0.000449947i	0.0523042	−	0.998631i	$-0.483343\pi$
$409$	0.191025	+	0.00909962i	0.00944556	+	0.000449947i	−0.0428586	+	0.999081i	$0.513646\pi$
$410$	0.0400549	−	0.207825i	0.00197817	−	0.0102637i
$411$	3.03466	−	12.5090i	0.149689	−	0.617025i
$412$	2.88021	+	6.30678i	0.141898	+	0.310713i
$413$	−4.52202	+	6.03491i	−0.222514	+	0.296959i
$414$	3.72819	−	3.01672i	0.183231	−	0.148263i
$415$	−0.461436	+	0.799231i	−0.0226510	+	0.0392327i
$416$	4.68456	+	3.33586i	0.229679	+	0.163554i
$417$	−6.80076	−	6.48451i	−0.333035	−	0.317548i
$418$	−38.6627	+	13.3813i	−1.89105	+	0.654500i
$419$	−28.3307	−	18.2071i	−1.38405	−	0.889473i	−0.384612	−	0.923078i	$-0.625665\pi$
$419$	−28.3307	−	18.2071i	−1.38405	−	0.889473i	−0.999435	+	0.0336054i	$0.989301\pi$
$420$	0.248239	−	0.0176394i	0.0121128	−	0.000860714i
$421$	−7.96659	+	1.14542i	−0.388268	+	0.0558245i	−0.333685	−	0.942685i	$-0.608292\pi$
$421$	−7.96659	+	1.14542i	−0.388268	+	0.0558245i	−0.0545833	+	0.998509i	$0.517383\pi$
$422$	−2.75007	+	2.62219i	−0.133872	+	0.127646i
$423$	−1.42431	+	2.76278i	−0.0692524	+	0.134331i
$424$	2.59588	+	6.48420i	0.126067	+	0.314901i
$425$	−7.66815	−	10.7684i	−0.371960	−	0.522345i
$426$	12.5226	+	5.71890i	0.606724	+	0.277081i
$427$	18.2965	+	4.91159i	0.885432	+	0.237688i
$428$	−5.03943	−	7.84151i	−0.243590	−	0.379034i
$429$	20.4929	+	21.4923i	0.989407	+	1.03766i
$430$	−0.487019	−	0.619294i	−0.0234861	−	0.0298650i
$431$	4.34241	+	1.50292i	0.209166	+	0.0723932i	0.429642	−	0.902999i	$-0.358640\pi$
$431$	4.34241	+	1.50292i	0.209166	+	0.0723932i	−0.220476	+	0.975392i	$0.570761\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	−7.24072	+	8.35623i	−0.347967	+	0.401575i	−0.902572	−	0.430538i	$-0.858324\pi$
$433$	−7.24072	+	8.35623i	−0.347967	+	0.401575i	0.554606	+	0.832113i	$0.312869\pi$
$434$	−17.6763	−	21.4285i	−0.848489	−	1.02860i
$435$	−0.784167	+	0.358117i	−0.0375979	+	0.0171704i
$436$	−9.24133	−	5.33549i	−0.442580	−	0.255523i
$437$	18.5394	−	33.1678i	0.886860	−	1.58663i
$438$	0.171994	+	0.297903i	0.00821820	+	0.0142343i
$439$	2.82952	−	29.6320i	0.135045	−	1.41426i	−0.633142	−	0.774036i	$-0.718235\pi$
$439$	2.82952	−	29.6320i	0.135045	−	1.41426i	0.768188	−	0.640225i	$-0.221159\pi$
$440$	−0.136842	−	0.466041i	−0.00652369	−	0.0222177i
$441$	6.36474	+	2.91378i	0.303083	+	0.138751i
$442$	−8.23503	+	12.8140i	−0.391700	+	0.609497i
$443$	−16.8886	+	3.25500i	−0.802400	+	0.154650i	−0.573933	−	0.818902i	$-0.694583\pi$
$443$	−16.8886	+	3.25500i	−0.802400	+	0.154650i	−0.228466	+	0.973552i	$0.573371\pi$
$444$	4.23139	−	3.32760i	0.200813	−	0.157921i
$445$	0.0758793	+	0.312779i	0.00359703	+	0.0148271i
$446$	−15.6378	+	0.744920i	−0.740471	+	0.0352730i
$447$	−2.30260	+	16.0149i	−0.108909	+	0.757479i
$448$	0.0641823	−	2.64497i	0.00303233	−	0.124963i
$449$	4.60949	−	10.0934i	0.217535	−	0.476335i	−0.769131	−	0.639091i	$-0.779311\pi$
$449$	4.60949	−	10.0934i	0.217535	−	0.476335i	0.986666	+	0.162755i	$0.0520381\pi$
$450$	−3.92331	−	3.08533i	−0.184947	−	0.145444i
$451$	−10.3274	−	5.32415i	−0.486298	−	0.250704i
$452$	−11.0399	+	2.67825i	−0.519272	+	0.125974i
$453$	−0.299047	+	0.746984i	−0.0140505	+	0.0350964i
$454$	−9.96850	−	11.5043i	−0.467845	−	0.539922i
$455$	−1.10321	−	0.911742i	−0.0517192	−	0.0427431i
$456$	−5.98784	−	5.18849i	−0.280406	−	0.242973i
$457$	3.16971	+	0.768962i	0.148273	+	0.0359705i	0.309208	−	0.950994i	$-0.399936\pi$
$457$	3.16971	+	0.768962i	0.148273	+	0.0359705i	−0.160936	+	0.986965i	$0.551451\pi$
$458$	−8.32385	+	11.6892i	−0.388948	+	0.546201i
$459$	2.29377	−	1.32431i	0.107064	−	0.0618134i
$460$	0.382849	+	0.238586i	0.0178504	+	0.0111242i
$461$			23.6434i			1.10119i	0.834774	+	0.550593i	$0.185598\pi$
$461$			23.6434i			1.10119i	−0.834774	+	0.550593i	$0.814402\pi$
$462$	2.91024	−	13.3485i	0.135397	−	0.621029i
$463$	35.1311	−	10.3154i	1.63268	−	0.479398i	0.668293	−	0.743898i	$-0.267025\pi$
$463$	35.1311	−	10.3154i	1.63268	−	0.479398i	0.964386	+	0.264500i	$0.0852069\pi$
$464$	2.99754	+	8.66083i	0.139157	+	0.402069i
$465$	0.0469909	−	0.986460i	0.00217915	−	0.0457460i
$466$	−8.30407	+	23.9930i	−0.384678	+	1.11146i
$467$	6.58144	+	2.63481i	0.304553	+	0.121925i	0.518905	−	0.854832i	$-0.326340\pi$
$467$	6.58144	+	2.63481i	0.304553	+	0.121925i	−0.214352	+	0.976756i	$0.568764\pi$
$468$	−1.62022	+	5.51796i	−0.0748947	+	0.255068i
$469$	1.34758	−	18.7203i	0.0622252	−	0.864421i
$470$	−0.289399	−	0.0416093i	−0.0133490	−	0.00191929i
$471$	−14.1456	+	10.0731i	−0.651797	+	0.464142i
$472$	0.270937	+	2.83738i	0.0124709	+	0.130601i
$473$	−40.1530	+	16.0748i	−1.84624	+	0.739122i
$474$	−0.154490	−	3.24314i	−0.00709595	−	0.148962i
$475$	−37.9433	−	11.1411i	−1.74096	−	0.511191i
$476$	7.00567	−	0.163534i	0.321104	−	0.00749557i
$477$	−5.27854	+	4.57388i	−0.241688	+	0.209424i
$478$	−1.78544	+	0.920458i	−0.0816641	+	0.0421008i
$479$	−13.0386	−	2.51298i	−0.595748	−	0.114821i	−0.117541	−	0.993068i	$-0.537501\pi$
$479$	−13.0386	−	2.51298i	−0.595748	−	0.114821i	−0.478207	+	0.878247i	$0.658713\pi$
$480$	0.0649104	−	0.0680760i	0.00296274	−	0.00310723i
$481$	−30.8175	−	2.94271i	−1.40516	−	0.134176i
$482$	−14.5379			−0.662182
$483$	6.23015	+	11.0537i	0.283482	+	0.502963i
$484$	−15.6646			−0.712028
$485$	0.689894	+	0.0658769i	0.0313265	+	0.00299131i
$486$	0.690079	−	0.723734i	0.0313026	−	0.0328292i
$487$	−4.88724	−	0.941938i	−0.221462	−	0.0426833i	0.0773131	−	0.997007i	$-0.475366\pi$
$487$	−4.88724	−	0.941938i	−0.221462	−	0.0426833i	−0.298775	+	0.954324i	$0.596578\pi$
$488$	6.36431	−	3.28103i	0.288099	−	0.148525i
$489$	−10.0519	+	8.71006i	−0.454565	+	0.393883i
$490$	−0.0631927	+	0.655396i	−0.00285475	+	0.0296078i
$491$	9.53356	+	2.79931i	0.430244	+	0.126331i	0.489682	−	0.871901i	$-0.337113\pi$
$491$	9.53356	+	2.79931i	0.430244	+	0.126331i	−0.0594385	+	0.998232i	$0.518931\pi$
$492$	−0.107064	−	2.24755i	−0.00482682	−	0.101328i
$493$	−22.5355	+	9.02184i	−1.01495	+	0.406323i
$494$	4.33120	+	45.3584i	0.194870	+	2.04077i
$495$	0.395653	−	0.281743i	0.0177833	−	0.0126634i
$496$	−10.3923	−	1.49419i	−0.466630	−	0.0670912i
$497$	−20.4294	+	30.1545i	−0.916385	+	1.35261i
$498$	−2.76416	+	9.41387i	−0.123865	+	0.421846i
$499$	−5.25559	−	2.10402i	−0.235273	−	0.0941889i	0.251030	−	0.967979i	$-0.419231\pi$
$499$	−5.25559	−	2.10402i	−0.235273	−	0.0941889i	−0.486303	+	0.873790i	$0.661655\pi$
$500$	0.307375	−	0.888102i	0.0137462	−	0.0397171i
$501$	0.189518	−	3.97848i	0.00846706	−	0.177746i
$502$	−7.44819	−	21.5201i	−0.332429	−	0.960491i
$503$	−16.8186	+	4.93839i	−0.749905	+	0.220192i	−0.634282	−	0.773101i	$-0.718704\pi$
$503$	−16.8186	+	4.93839i	−0.749905	+	0.220192i	−0.115622	+	0.993293i	$0.536886\pi$
$504$	2.52049	−	0.804433i	0.112272	−	0.0358323i
$505$			0.618690i			0.0275314i
$506$	18.4885	−	16.4760i	0.821916	−	0.732449i
$507$	17.3838	−	10.0365i	0.772040	−	0.445737i
$508$	8.25153	−	11.5876i	0.366102	−	0.514119i
$509$	24.0277	+	5.82905i	1.06501	+	0.258368i	0.729719	−	0.683748i	$-0.239651\pi$
$509$	24.0277	+	5.82905i	1.06501	+	0.258368i	0.335288	+	0.942116i	$0.391166\pi$
$510$	0.188283	+	0.163149i	0.00833733	+	0.00722434i
$511$	−0.852872	+	0.317657i	−0.0377288	+	0.0140523i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	2.94470	−	7.35550i	0.130012	−	0.324753i
$514$	22.9053	−	5.55676i	1.01031	−	0.245098i
$515$	−0.579667	−	0.298839i	−0.0255432	−	0.0131684i
$516$	−6.58388	−	5.17762i	−0.289839	−	0.227932i
$517$	−6.66768	+	14.6002i	−0.293244	+	0.642115i
$518$	6.81985	+	12.5033i	0.299647	+	0.549364i
$519$	0.410624	−	2.85595i	0.0180244	−	0.125362i
$520$	−0.540331	+	0.0257391i	−0.0236951	+	0.00112874i
$521$	6.97774	+	28.7626i	0.305700	+	1.26011i	0.892746	+	0.450560i	$0.148776\pi$
$521$	6.97774	+	28.7626i	0.305700	+	1.26011i	−0.587046	+	0.809554i	$0.699709\pi$
$522$	−7.20409	+	5.66536i	−0.315315	+	0.247966i
$523$	−18.3796	+	3.54238i	−0.803683	+	0.154897i	−0.574520	−	0.818491i	$-0.694811\pi$
$523$	−18.3796	+	3.54238i	−0.803683	+	0.154897i	−0.229164	+	0.973388i	$0.573599\pi$
$524$	0.0641542	−	0.0998259i	0.00280259	−	0.00436091i
$525$	9.77541	−	8.87821i	0.426634	−	0.387477i
$526$	−7.00736	−	23.8649i	−0.305535	−	1.04056i
$527$	2.64335	−	27.6825i	0.115146	−	1.20587i
$528$	−2.58189	−	4.47196i	−0.112362	−	0.194617i
$529$	−2.63896	+	22.8481i	−0.114737	+	0.993396i
$530$	−0.568960	−	0.328489i	−0.0247141	−	0.0142687i
$531$	−2.59271	+	1.18405i	−0.112514	+	0.0513834i
$532$	16.1707	−	13.3391i	0.701088	−	0.578323i
$533$	−8.47399	+	9.77951i	−0.367049	+	0.423598i
$534$	1.56791	+	3.04132i	0.0678500	+	0.131611i
$535$	0.828552	+	0.286765i	0.0358214	+	0.0123979i
$536$	−4.38516	−	5.57618i	−0.189410	−	0.240854i
$537$	3.63771	+	3.81512i	0.156979	+	0.164635i
$538$	5.24445	+	8.16052i	0.226104	+	0.351825i
$539$	33.5448	+	13.4652i	1.44488	+	0.579988i
$540$	0.0855620	+	0.0390749i	0.00368200	+	0.00168151i
$541$	−17.6719	−	24.8167i	−0.759773	−	1.06695i	−0.995465	−	0.0951244i	$-0.969675\pi$
$541$	−17.6719	−	24.8167i	−0.759773	−	1.06695i	0.235692	−	0.971828i	$-0.424264\pi$
$542$	1.44872	+	3.61874i	0.0622280	+	0.155438i
$543$	0.278754	−	0.540708i	0.0119625	−	0.0232040i
$544$	1.91689	−	1.82775i	0.0821862	−	0.0783643i
$545$	0.993518	−	0.142846i	0.0425577	−	0.00611887i
$546$	−13.6831	−	6.65464i	−0.585582	−	0.284792i
$547$	25.2456	+	16.2244i	1.07942	+	0.693704i	0.954424	−	0.298452i	$-0.0964704\pi$
$547$	25.2456	+	16.2244i	1.07942	+	0.693704i	0.125000	+	0.992157i	$0.460107\pi$
$548$	12.1639	−	4.20998i	0.519617	−	0.179841i
$549$	5.18214	+	4.94116i	0.221168	+	0.210883i
$550$	−20.9942	−	14.9499i	−0.895197	−	0.637467i
$551$	−36.3069	+	62.8854i	−1.54673	+	2.67901i
$552$	4.55344	+	1.50540i	0.193807	+	0.0640739i
$553$	8.52905	+	1.02376i	0.362692	+	0.0435348i
$554$	8.00988	+	17.5392i	0.340307	+	0.745169i
$555$	−0.119375	+	0.492072i	−0.00506720	+	0.0208873i
$556$	1.77835	−	9.22696i	0.0754189	−	0.391310i
$557$	−8.05070	−	0.383502i	−0.341119	−	0.0162495i	−0.123676	−	0.992323i	$-0.539468\pi$
$557$	−8.05070	−	0.383502i	−0.341119	−	0.0162495i	−0.217443	+	0.976073i	$0.569771\pi$
$558$	−1.98699	−	10.3095i	−0.0841159	−	0.436435i
$559$	6.85516	+	47.6787i	0.289942	+	2.01659i
$560$	0.149047	+	0.199296i	0.00629841	+	0.00842178i
$561$	11.5057	−	7.39427i	0.485772	−	0.312186i
$562$	−17.9396	+	22.8121i	−0.756738	+	0.962270i
$563$	39.1994	−	3.74309i	1.65206	−	0.157752i	0.772980	−	0.634430i	$-0.218765\pi$
$563$	39.1994	−	3.74309i	1.65206	−	0.157752i	0.879078	+	0.476677i	$0.158159\pi$
$564$	−3.09424	+	0.295464i	−0.130291	+	0.0124413i
$565$	0.660538	−	0.839942i	0.0277890	−	0.0353366i
$566$	20.8748	−	13.4154i	0.877434	−	0.563893i
$567$	1.58456	+	2.11876i	0.0665454	+	0.0889797i
$568$	1.95921	+	13.6266i	0.0822065	+	0.571759i
$569$	1.15307	+	5.98270i	0.0483392	+	0.250808i	0.998058	−	0.0622976i	$-0.0198428\pi$
$569$	1.15307	+	5.98270i	0.0483392	+	0.250808i	−0.949718	+	0.313105i	$0.898631\pi$
$570$	0.744415	+	0.0354608i	0.0311801	+	0.00148529i
$571$	0.225900	−	1.17208i	0.00945364	−	0.0490501i	−0.976896	−	0.213717i	$-0.931443\pi$
$571$	0.225900	−	1.17208i	0.00945364	−	0.0490501i	0.986349	+	0.164667i	$0.0526550\pi$
$572$	−7.00120	+	28.8594i	−0.292735	+	1.20667i
$573$	−0.190479	−	0.417090i	−0.00795736	−	0.0174242i
$574$	5.91078	+	0.709485i	0.246711	+	0.0296133i
$575$	23.7944	−	2.60642i	0.992295	−	0.108695i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	29.2037	+	20.7959i	1.21577	+	0.865744i	0.994003	−	0.109357i	$-0.0348791\pi$
$577$	29.2037	+	20.7959i	1.21577	+	0.865744i	0.221764	+	0.975100i	$0.428818\pi$
$578$	−7.22636	−	6.89032i	−0.300577	−	0.286600i
$579$	10.5865	−	3.66402i	0.439960	−	0.152271i
$580$	−0.725219	−	0.466070i	−0.0301131	−	0.0193525i
$581$	−23.3439	−	11.3531i	−0.968469	−	0.471005i
$582$	7.29281	−	1.04855i	0.302297	−	0.0434637i
$583$	−26.1025	+	24.8887i	−1.08106	+	1.03079i
$584$	−0.157625	+	0.305749i	−0.00652255	+	0.0126520i
$585$	−0.201049	−	0.502195i	−0.00831233	−	0.0207632i
$586$	−3.23581	−	4.54405i	−0.133670	−	0.187713i
$587$	5.17840	+	2.36489i	0.213735	+	0.0976096i	0.519406	−	0.854528i	$-0.326153\pi$
$587$	5.17840	+	2.36489i	0.213735	+	0.0976096i	−0.305670	+	0.952137i	$0.598881\pi$
$588$	0.989814	+	6.92967i	0.0408192	+	0.285775i
$589$	−44.9736	−	69.9802i	−1.85310	−	2.88348i
$590$	−0.185013	−	0.194036i	−0.00761686	−	0.00798833i
$591$	−9.11384	−	11.5892i	−0.374893	−	0.476716i
$592$	5.08702	+	1.76063i	0.209075	+	0.0723617i
$593$	−14.0716	−	27.2951i	−0.577851	−	1.12087i	−0.978808	−	0.204778i	$-0.934353\pi$
$593$	−14.0716	−	27.2951i	−0.577851	−	1.12087i	0.400957	−	0.916097i	$-0.368678\pi$
$594$	3.38156	−	3.90252i	0.138747	−	0.160122i
$595$	−0.508476	+	0.419439i	−0.0208455	+	0.0171953i
$596$	−14.7175	+	6.72124i	−0.602851	+	0.275313i
$597$	−7.52359	−	4.34374i	−0.307920	−	0.177778i
$598$	−12.9777	−	24.3364i	−0.530698	−	0.995188i
$599$	−14.5797	−	25.2529i	−0.595712	−	1.03180i	−0.993446	−	0.114303i	$-0.963537\pi$
$599$	−14.5797	−	25.2529i	−0.595712	−	1.03180i	0.397734	−	0.917501i	$-0.369797\pi$
$600$	0.474439	−	4.96855i	0.0193689	−	0.202840i
$601$	−3.21197	−	10.9390i	−0.131019	−	0.446210i	0.867684	−	0.497115i	$-0.165607\pi$
$601$	−3.21197	−	10.9390i	−0.131019	−	0.446210i	−0.998703	+	0.0509056i	$0.983789\pi$
$602$	16.4045	−	14.8989i	0.668600	−	0.607234i
$603$	3.83525	−	5.96777i	0.156184	−	0.243026i
$604$	−0.790081	+	0.152276i	−0.0321479	+	0.00619600i
$605$	1.15821	−	0.910825i	0.0470878	−	0.0370303i
$606$	1.55070	+	6.39205i	0.0629927	+	0.259659i
$607$	29.6361	−	1.41174i	1.20289	−	0.0573007i	0.563456	−	0.826146i	$-0.309471\pi$
$607$	29.6361	−	1.41174i	1.20289	−	0.0573007i	0.639435	+	0.768845i	$0.279168\pi$
$608$	1.12757	−	7.84240i	0.0457289	−	0.318051i
$609$	−11.6110	−	21.2873i	−0.470503	−	0.862607i
$610$	−0.279787	+	0.612648i	−0.0113282	+	0.0248054i
$611$	14.0512	+	11.0500i	0.568451	+	0.447035i
$612$	2.35418	+	1.21367i	0.0951623	+	0.0490596i
$613$	24.2795	−	5.89014i	0.980638	−	0.237900i	0.286768	−	0.958000i	$-0.407419\pi$
$613$	24.2795	−	5.89014i	0.980638	−	0.237900i	0.693871	+	0.720100i	$0.255904\pi$
$614$	−10.8127	+	27.0087i	−0.436364	+	1.08998i
$615$	0.138601	+	0.159954i	0.00558893	+	0.00644997i
$616$	12.8029	−	4.76850i	0.515843	−	0.192128i
$617$	−17.7327	−	15.3654i	−0.713890	−	0.618589i	0.220272	−	0.975439i	$-0.429306\pi$
$617$	−17.7327	−	15.3654i	−0.713890	−	0.618589i	−0.934162	+	0.356849i	$0.883851\pi$
$618$	−6.73789	−	1.63459i	−0.271038	−	0.0657530i
$619$	−19.1099	+	26.8361i	−0.768093	+	1.07864i	0.226421	+	0.974030i	$0.427298\pi$
$619$	−19.1099	+	26.8361i	−0.768093	+	1.07864i	−0.994514	+	0.104606i	$0.966642\pi$
$620$	0.855268	−	0.493789i	0.0343484	−	0.0198311i
$621$	0.0666817	+	4.79537i	0.00267584	+	0.192431i
$622$			0.862857i			0.0345974i
$623$	−8.62434	+	2.75252i	−0.345527	+	0.110277i
$624$	−5.51796	+	1.62022i	−0.220895	+	0.0648607i
$625$	−8.13332	−	23.4997i	−0.325333	−	0.939987i
$626$	0.0479698	−	1.00701i	0.00191726	−	0.0402482i
$627$	13.3813	−	38.6627i	0.534397	−	1.54404i
$628$	−16.1217	−	6.45416i	−0.643327	−	0.257549i
$629$	−4.01687	+	13.6802i	−0.160163	+	0.545465i
$630$	−0.139586	+	0.206033i	−0.00556123	+	0.00820856i
$631$	1.16196	+	0.167065i	0.0462569	+	0.00665074i	0.165404	−	0.986226i	$-0.447107\pi$
$631$	1.16196	+	0.167065i	0.0462569	+	0.00665074i	−0.119148	+	0.992877i	$0.538016\pi$
$632$	2.64478	−	1.88334i	0.105204	−	0.0749152i
$633$	−0.361198	−	3.78264i	−0.0143563	−	0.150346i
$634$	27.9395	−	11.1853i	1.10962	−	0.444224i
$635$	0.0636679	+	1.33655i	0.00252658	+	0.0530395i
$636$	−6.70159	−	1.96776i	−0.265735	−	0.0780270i
$637$	23.3812	−	32.7704i	0.926398	−	1.29841i
$638$	−35.7662	+	30.9916i	−1.41600	+	1.22697i
$639$	−12.2363	+	6.30827i	−0.484062	+	0.249551i
$640$	0.0923624	+	0.0178014i	0.00365094	+	0.000703662i
$641$	10.0175	−	10.5061i	0.395668	−	0.414965i	−0.495521	−	0.868596i	$-0.665023\pi$
$641$	10.0175	−	10.5061i	0.395668	−	0.414965i	0.891190	+	0.453631i	$0.149871\pi$
$642$	9.27901	+	0.886038i	0.366213	+	0.0349691i
$643$	−2.58093			−0.101782			−0.0508910	−	0.998704i	$-0.516206\pi$
$643$	−2.58093			−0.101782			−0.0508910	+	0.998704i	$0.516206\pi$
$644$	−5.93073	+	11.2172i	−0.233703	+	0.442021i
$645$	0.787853			0.0310217
$646$	20.8901	+	1.99476i	0.821909	+	0.0784828i
$647$	−17.9634	+	18.8395i	−0.706214	+	0.740656i	−0.974917	−	0.222567i	$-0.928556\pi$
$647$	−17.9634	+	18.8395i	−0.706214	+	0.740656i	0.268704	+	0.963223i	$0.413405\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	−13.0821	+	6.74428i	−0.513517	+	0.264736i
$650$	−21.6928	+	18.7969i	−0.850862	+	0.737276i
$651$	27.7707	−	0.648255i	1.08842	−	0.0254071i
$652$	−12.7619	−	3.74722i	−0.499793	−	0.146753i
$653$	−0.766453	−	16.0898i	−0.0299936	−	0.629644i	−0.962954	−	0.269665i	$-0.913087\pi$
$653$	−0.766453	−	16.0898i	−0.0299936	−	0.629644i	0.932961	−	0.359979i	$-0.117216\pi$
$654$	9.90659	−	3.96600i	0.387378	−	0.155083i
$655$	0.00106099	+	0.0111112i	4.14563e−5	+	0.000434150i
$656$	1.83288	−	1.30519i	0.0715619	−	0.0509590i
$657$	−0.340487	−	0.0489547i	−0.0132837	−	0.00190990i
$658$	0.590463	−	8.20260i	0.0230187	−	0.319771i
$659$	−6.17449	+	21.0284i	−0.240524	+	0.819149i	0.747422	+	0.664350i	$0.231291\pi$
$659$	−6.17449	+	21.0284i	−0.240524	+	0.819149i	−0.987946	+	0.154800i	$0.950527\pi$
$660$	0.450923	+	0.180523i	0.0175522	+	0.00702683i
$661$	−15.2416	+	44.0378i	−0.592831	+	1.71287i	0.103014	+	0.994680i	$0.467151\pi$
$661$	−15.2416	+	44.0378i	−0.592831	+	1.71287i	−0.695845	+	0.718192i	$0.744970\pi$
$662$	0.794768	−	16.6842i	0.0308895	−	0.648451i
$663$	−4.98189	−	14.3942i	−0.193481	−	0.559025i
$664$	−9.41387	+	2.76416i	−0.365329	+	0.107270i
$665$	−0.420018	+	1.92651i	−0.0162876	+	0.0747070i
$666$			5.38309i			0.208590i
$667$	5.64969	−	43.5887i	0.218757	−	1.68776i
$668$	3.44937	−	1.99150i	0.133460	−	0.0770533i
$669$	9.08110	−	12.7526i	0.351095	−	0.493045i
$670$	0.648459	+	0.157314i	0.0250521	+	0.00607759i
$671$	27.9432	+	24.2129i	1.07873	+	0.934728i
$672$	2.03941	+	1.68546i	0.0786721	+	0.0650182i
$673$	−3.54567	−	4.09192i	−0.136676	−	0.157732i	0.683285	−	0.730151i	$-0.260550\pi$
$673$	−3.54567	−	4.09192i	−0.136676	−	0.157732i	−0.819961	+	0.572419i	$0.806005\pi$
$674$	6.97831	−	17.4310i	0.268794	−	0.671416i
$675$	4.85046	−	1.17671i	0.186694	−	0.0452915i
$676$	17.8416	+	9.19800i	0.686216	+	0.353769i
$677$	25.9181	+	20.3822i	0.996115	+	0.783353i	0.976294	−	0.216450i	$-0.0694479\pi$
$677$	25.9181	+	20.3822i	0.996115	+	0.783353i	0.0198212	+	0.999804i	$0.493690\pi$
$678$	4.71916	−	10.3335i	0.181238	−	0.396856i
$679$	−0.472883	+	19.4876i	−0.0181476	+	0.747867i
$680$	−0.0354556	+	0.246599i	−0.00135966	+	0.00945664i
$681$	15.2051	−	0.724307i	0.582660	−	0.0277555i
$682$	−12.7818	−	52.6873i	−0.489441	−	2.01750i
$683$	−15.3115	+	12.0411i	−0.585879	+	0.460740i	−0.866568	−	0.499058i	$-0.833679\pi$
$683$	−15.3115	+	12.0411i	−0.585879	+	0.460740i	0.280689	+	0.959799i	$0.409437\pi$
$684$	7.77986	−	1.49945i	0.297470	−	0.0573327i
$685$	−0.654584	+	1.01855i	−0.0250104	+	0.0389169i
$686$	−18.5144	−	0.466350i	−0.706883	−	0.0178053i
$687$	−4.04288	−	13.7688i	−0.154245	−	0.525312i
$688$	0.796177	−	8.33795i	0.0303540	−	0.317881i
$689$	20.0837	+	34.7859i	0.765127	+	1.32524i
$690$	−0.424203	+	0.153455i	−0.0161491	+	0.00584195i
$691$	13.7754	+	7.95324i	0.524041	+	0.302555i	0.738587	−	0.674159i	$-0.235494\pi$
$691$	13.7754	+	7.95324i	0.524041	+	0.302555i	−0.214545	+	0.976714i	$0.568827\pi$
$692$	2.62458	−	1.19861i	0.0997716	−	0.0455641i
$693$	8.69365	+	10.5391i	0.330244	+	0.400347i
$694$	−14.9327	+	17.2332i	−0.566837	+	0.654165i
$695$	0.405018	+	0.785625i	0.0153632	+	0.0298004i
$696$	−8.66083	−	2.99754i	−0.328288	−	0.113622i
$697$	3.68402	+	4.68461i	0.139542	+	0.177442i
$698$	−3.49177	−	3.66206i	−0.132165	−	0.138611i
$699$	−13.7266	−	21.3589i	−0.519186	−	0.807869i
$700$	12.7538	+	3.42368i	0.482049	+	0.129403i
$701$	−9.80565	−	4.47809i	−0.370354	−	0.169135i	0.221539	−	0.975152i	$-0.428892\pi$
$701$	−9.80565	−	4.47809i	−0.370354	−	0.169135i	−0.591893	+	0.806016i	$0.701619\pi$
$702$	−3.33586	−	4.68456i	−0.125904	−	0.176807i
$703$	15.8516	+	39.5953i	0.597853	+	1.49336i
$704$	2.36618	−	4.58975i	0.0891788	−	0.172983i
$705$	0.211602	−	0.201762i	0.00796938	−	0.00759879i
$706$	15.0763	−	2.16765i	0.567404	−	0.0815804i
$707$	−17.3586	+	1.23346i	−0.652836	+	0.0463892i
$708$	−2.39781	−	1.54098i	−0.0901153	−	0.0579136i
$709$	11.6028	−	4.01575i	0.435751	−	0.150815i	−0.100381	−	0.994949i	$-0.532006\pi$
$709$	11.6028	−	4.01575i	0.435751	−	0.150815i	0.536132	+	0.844134i	$0.319885\pi$
$710$	−0.937183	−	0.893602i	−0.0351718	−	0.0335363i
$711$	2.64478	+	1.88334i	0.0991869	+	0.0706307i
$712$	−1.71084	+	2.96327i	−0.0641166	+	0.111053i
$713$	41.4180	+	28.6342i	1.55112	+	1.07236i
$714$	−4.20207	+	5.60792i	−0.157259	+	0.209871i
$715$	−1.16038	−	2.54089i	−0.0433959	−	0.0950238i
$716$	−1.24279	+	5.12285i	−0.0464452	+	0.191450i
$717$	0.380157	−	1.97244i	0.0141972	−	0.0736621i
$718$	−1.11910	−	0.0533092i	−0.0417643	−	0.00198948i
$719$	2.76628	+	14.3528i	0.103165	+	0.535270i	0.996334	+	0.0855489i	$0.0272644\pi$
$719$	2.76628	+	14.3528i	0.103165	+	0.535270i	−0.893169	+	0.449721i	$0.851524\pi$
$720$	0.0133864	+	0.0931048i	0.000498883	+	0.00346981i
$721$	7.22884	−	16.8595i	0.269216	−	0.627879i
$722$	36.8255	−	23.6663i	1.37050	−	0.880770i
$723$	8.98672	−	11.4275i	0.334220	−	0.424995i
$724$	0.605578	−	0.0578257i	0.0225061	−	0.00214908i
$725$	−45.5362	+	4.34818i	−1.69117	+	0.161488i
$726$	9.68322	−	12.3132i	0.359378	−	0.456986i
$727$	−8.38058	+	5.38587i	−0.310819	+	0.199751i	−0.686745	−	0.726899i	$-0.740961\pi$
$727$	−8.38058	+	5.38587i	−0.310819	+	0.199751i	0.375926	+	0.926650i	$0.377325\pi$
$728$	−1.79940	−	15.1087i	−0.0666903	−	0.559966i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−0.00612347	−	0.0317716i	−0.000226640	−	0.00117592i
$731$	22.1594	+	1.05558i	0.819593	+	0.0390420i
$732$	−1.35509	+	7.03088i	−0.0500856	+	0.259869i
$733$	−3.67966	+	15.1678i	−0.135911	+	0.560234i	0.862610	+	0.505870i	$0.168828\pi$
$733$	−3.67966	+	15.1678i	−0.135911	+	0.560234i	−0.998521	+	0.0543643i	$0.982687\pi$
$734$	−0.857726	−	1.87816i	−0.0316593	−	0.0693241i
$735$	−0.476113	−	0.454812i	−0.0175617	−	0.0167760i
$736$	1.19535	+	4.64447i	0.0440613	+	0.171198i
$737$	18.3157	−	31.7237i	0.674666	−	1.16856i
$738$	1.83288	+	1.30519i	0.0674692	+	0.0480446i
$739$	−1.67070	−	1.59301i	−0.0614578	−	0.0585999i	0.658728	−	0.752381i	$-0.271095\pi$
$739$	−1.67070	−	1.59301i	−0.0614578	−	0.0585999i	−0.720186	+	0.693781i	$0.755943\pi$
$740$	−0.478496	+	0.165609i	−0.0175899	+	0.00608792i
$741$	−38.3315	−	24.6342i	−1.40814	−	0.904959i
$742$	8.08209	−	16.6182i	0.296703	−	0.610073i
$743$	−10.2585	+	1.47494i	−0.376347	+	0.0541105i	−0.327893	−	0.944715i	$-0.606338\pi$
$743$	−10.2585	+	1.47494i	−0.376347	+	0.0541105i	−0.0484538	+	0.998825i	$0.515429\pi$
$744$	7.59863	−	7.24528i	0.278579	−	0.265625i
$745$	0.697369	−	1.35271i	0.0255496	−	0.0495594i
$746$	13.4201	+	33.5218i	0.491345	+	1.22732i
$747$	−5.69111	−	7.99205i	−0.208227	−	0.292414i
$748$	12.4409	+	5.68158i	0.454885	+	0.207739i
$749$	−6.39388	+	23.8184i	−0.233627	+	0.870304i
$750$	0.508089	+	0.790601i	0.0185528	+	0.0288687i
$751$	−1.83864	−	1.92831i	−0.0670930	−	0.0703651i	0.689332	−	0.724446i	$-0.257904\pi$
$751$	−1.83864	−	1.92831i	−0.0670930	−	0.0703651i	−0.756425	+	0.654081i	$0.773056\pi$
$752$	−1.92143	−	2.44330i	−0.0700674	−	0.0890980i
$753$	21.5201	+	7.44819i	0.784237	+	0.271427i
$754$	24.1515	+	46.8474i	0.879547	+	1.70608i
$755$	0.0495628	−	0.0571985i	0.00180377	−	0.00208167i
$756$	−0.925738	+	2.47851i	−0.0336688	+	0.0901425i
$757$	30.6757	−	14.0091i	1.11493	−	0.509171i	0.229202	−	0.973379i	$-0.426388\pi$
$757$	30.6757	−	14.0091i	1.11493	−	0.509171i	0.885726	+	0.464208i	$0.153661\pi$
$758$	−12.5214	−	7.22925i	−0.454799	−	0.262578i
$759$	1.52217	+	24.7178i	0.0552514	+	0.897199i
$760$	0.372629	+	0.645413i	0.0135167	+	0.0234116i
$761$	2.01352	−	21.0866i	0.0729901	−	0.764387i	−0.882685	−	0.469965i	$-0.844267\pi$
$761$	2.01352	−	21.0866i	0.0729901	−	0.764387i	0.955675	−	0.294422i	$-0.0951272\pi$
$762$	4.00775	+	13.6491i	0.145185	+	0.494456i
$763$	5.98858	+	27.5903i	0.216801	+	0.998836i
$764$	0.247898	−	0.385737i	0.00896863	−	0.0139555i
$765$	−0.244633	+	0.0471491i	−0.00884471	+	0.00170468i
$766$	7.80070	−	6.13454i	0.281851	−	0.221650i
$767$	3.86450	+	15.9297i	0.139539	+	0.575188i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	1.18623	−	8.25040i	0.0427765	−	0.297517i	−0.957191	−	0.289457i	$-0.906525\pi$
$769$	1.18623	−	8.25040i	0.0427765	−	0.297517i	0.999968	−	0.00806001i	$-0.00256561\pi$
$770$	−0.669351	+	1.09700i	−0.0241217	+	0.0395332i
$771$	−9.79120	+	21.4397i	−0.352621	+	0.772133i
$772$	8.80586	+	6.92500i	0.316930	+	0.249236i
$773$	−11.0732	−	5.70865i	−0.398277	−	0.205326i	0.247440	−	0.968903i	$-0.420411\pi$
$773$	−11.0732	−	5.70865i	−0.398277	−	0.205326i	−0.645716	+	0.763577i	$0.723441\pi$
$774$	8.13977	−	1.97469i	0.292578	−	0.0709787i
$775$	19.4763	−	48.6494i	0.699609	−	1.74754i
$776$	4.82489	+	5.56821i	0.173203	+	0.199887i
$777$	−14.0440	−	2.36828i	−0.503826	−	0.0849615i
$778$	6.65166	+	5.76369i	0.238473	+	0.206638i
$779$	17.3251	+	4.20303i	0.620737	+	0.150589i
$780$	0.313778	−	0.440640i	0.0112351	−	0.0157774i
$781$	−61.5642	+	35.5441i	−2.20294	+	1.27187i
$782$	−12.1368	+	3.74777i	−0.434013	+	0.134020i
$783$		−	9.16489i		−	0.327527i
$784$	−5.29447	+	4.57914i	−0.189088	+	0.163541i
$785$	1.56729	−	0.460197i	0.0559388	−	0.0164251i
$786$	0.0388110	+	0.112137i	0.00138434	+	0.00399979i
$787$	−0.591515	+	12.4174i	−0.0210852	+	0.442634i	0.963498	+	0.267716i	$0.0862689\pi$
$787$	−0.591515	+	12.4174i	−0.0210852	+	0.442634i	−0.984583	+	0.174918i	$0.944034\pi$
$788$	4.82213	−	13.9326i	0.171781	−	0.496330i
$789$	23.0907	+	9.24413i	0.822051	+	0.329100i
$790$	−0.0860419	+	0.293032i	−0.00306123	+	0.0104256i
$791$	24.8831	+	16.8581i	0.884741	+	0.599405i
$792$	5.11122	+	0.734882i	0.181619	+	0.0261129i
$793$	33.5427	−	23.8857i	1.19114	−	0.848205i
$794$	−1.76412	−	18.4747i	−0.0626063	−	0.655643i
$795$	0.609918	−	0.244174i	0.0216316	−	0.00865997i
$796$	−0.413367	−	8.67765i	−0.0146514	−	0.307571i
$797$	12.2808	+	3.60596i	0.435008	+	0.127730i	0.491902	−	0.870650i	$-0.336302\pi$
$797$	12.2808	+	3.60596i	0.435008	+	0.127730i	−0.0568947	+	0.998380i	$0.518120\pi$
$798$	0.489194	+	20.9567i	0.0173173	+	0.741859i
$799$	6.22188	−	5.39129i	0.220114	−	0.190730i
$800$	4.43631	−	2.28708i	0.156847	−	0.0808604i
$801$	−3.35985	−	0.647558i	−0.118715	−	0.0228804i
$802$	8.61679	−	9.03703i	0.304269	−	0.319108i
$803$	−1.76824	−	0.168846i	−0.0623997	−	0.00595845i
$804$	7.09390			0.250183
$805$	−0.213725	−	1.17422i	−0.00753282	−	0.0413859i
$806$	−60.3801			−2.12680
$807$	−9.65651	−	0.922084i	−0.339925	−	0.0324589i
$808$	−4.53897	+	4.76033i	−0.159680	+	0.167468i
$809$	−4.35229	−	0.838834i	−0.153018	−	0.0294918i	0.112167	−	0.993689i	$-0.464221\pi$
$809$	−4.35229	−	0.838834i	−0.153018	−	0.0294918i	−0.265185	+	0.964198i	$0.585433\pi$
$810$	−0.0836058	+	0.0431018i	−0.00293761	+	0.00151444i
$811$	37.1845	−	32.2206i	1.30573	−	1.13142i	0.322990	−	0.946402i	$-0.395312\pi$
$811$	37.1845	−	32.2206i	1.30573	−	1.13142i	0.982736	−	0.185016i	$-0.0592335\pi$
$812$	11.6307	−	21.2766i	0.408156	−	0.746663i
$813$	−3.74006	−	1.09818i	−0.131170	−	0.0385149i
$814$	1.32264	+	27.7656i	0.0463584	+	0.973183i
$815$	1.16147	−	0.464982i	0.0406845	−	0.0162876i
$816$	0.251767	+	2.63662i	0.00881361	+	0.0923003i
$817$	54.0572	−	38.4940i	1.89122	−	1.34673i
$818$	−0.189295	−	0.0272165i	−0.00661853	−	0.000951601i
$819$	13.6892	−	6.64202i	0.478340	−	0.232091i
$820$	−0.0596286	+	0.203076i	−0.00208232	+	0.00709173i
$821$	24.9780	+	9.99968i	0.871738	+	0.348991i	0.764022	−	0.645190i	$-0.223222\pi$
$821$	24.9780	+	9.99968i	0.871738	+	0.348991i	0.107716	+	0.994182i	$0.465646\pi$
$822$	−4.20998	+	12.1639i	−0.146840	+	0.424266i
$823$	1.03254	−	21.6756i	0.0359920	−	0.755565i	−0.906675	−	0.421830i	$-0.861388\pi$
$823$	1.03254	−	21.6756i	0.0359920	−	0.755565i	0.942667	−	0.333735i	$-0.108309\pi$
$824$	−2.26767	−	6.55200i	−0.0789980	−	0.228250i
$825$	24.7292	−	7.26115i	0.860961	−	0.252801i
$826$	5.07520	−	5.57774i	0.176589	−	0.194074i
$827$		−	45.8670i		−	1.59495i	−0.603350	−	0.797477i	$-0.706168\pi$
$827$		−	45.8670i		−	1.59495i	0.603350	−	0.797477i	$-0.293832\pi$
$828$	−3.99807	+	2.64867i	−0.138943	+	0.0920476i
$829$	−12.5972	+	7.27301i	−0.437520	+	0.252602i	−0.702545	−	0.711639i	$-0.747953\pi$
$829$	−12.5972	+	7.27301i	−0.437520	+	0.252602i	0.265025	+	0.964241i	$0.414620\pi$
$830$	0.535318	−	0.751749i	0.0185812	−	0.0260936i
$831$	−18.7381	−	4.54582i	−0.650018	−	0.157693i
$832$	−4.34625	−	3.76605i	−0.150679	−	0.130564i
$833$	−12.7819	−	13.4301i	−0.442867	−	0.465324i
$834$	6.15358	+	7.10160i	0.213081	+	0.245908i
$835$	−0.139243	+	0.347812i	−0.00481870	+	0.0120365i
$836$	39.7596	−	9.64557i	1.37511	−	0.333599i
$837$	9.33207	+	4.81101i	0.322563	+	0.166293i
$838$	26.4718	+	20.8176i	0.914452	+	0.719133i
$839$	19.3447	−	42.3590i	0.667853	−	1.46239i	−0.207165	−	0.978306i	$-0.566424\pi$
$839$	19.3447	−	42.3590i	0.667853	−	1.46239i	0.875019	−	0.484089i	$-0.160849\pi$
$840$	−0.248792	−	0.00603713i	−0.00858414	−	0.000208301i
$841$	−7.82664	+	54.4355i	−0.269884	+	1.87709i
$842$	8.03940	−	0.382964i	0.277056	−	0.0131978i
$843$	−6.84198	−	28.2030i	−0.235650	−	0.971363i
$844$	2.98688	−	2.34891i	0.102813	−	0.0808527i
$845$	−1.85399	+	0.357328i	−0.0637793	+	0.0122925i
$846$	1.68048	−	2.61488i	0.0577761	−	0.0899014i
$847$	27.8640	+	30.6799i	0.957419	+	1.05417i
$848$	−1.96776	−	6.70159i	−0.0675733	−	0.230134i
$849$	−2.35872	+	24.7016i	−0.0809509	+	0.847756i
$850$	6.60982	+	11.4486i	0.226715	+	0.392682i
$851$	−18.0734	−	18.4347i	−0.619548	−	0.631933i
$852$	−11.9223	−	6.88335i	−0.408452	−	0.235820i
$853$	−44.1121	+	20.1453i	−1.51037	+	0.689763i	−0.986759	−	0.162194i	$-0.948143\pi$
$853$	−44.1121	+	20.1453i	−1.51037	+	0.689763i	−0.523612	+	0.851957i	$0.675416\pi$
$854$	−17.7468	−	6.62854i	−0.607284	−	0.226824i
$855$	−0.488041	+	0.563229i	−0.0166906	+	0.0192620i
$856$	4.27123	+	8.28503i	0.145988	+	0.283176i
$857$	31.6410	+	10.9510i	1.08083	+	0.374081i	0.808726	−	0.588186i	$-0.200158\pi$
$857$	31.6410	+	10.9510i	1.08083	+	0.374081i	0.272109	+	0.962266i	$0.412279\pi$
$858$	−18.3571	−	23.3430i	−0.626702	−	0.796917i
$859$	−30.1781	−	31.6499i	−1.02966	−	1.07988i	−0.996761	−	0.0804213i	$-0.974373\pi$
$859$	−30.1781	−	31.6499i	−1.02966	−	1.07988i	−0.0329024	−	0.999459i	$-0.510475\pi$
$860$	0.425946	+	0.662784i	0.0145246	+	0.0226008i
$861$	−4.21150	+	4.20761i	−0.143527	+	0.143395i
$862$	−4.17988	−	1.90889i	−0.142367	−	0.0650170i
$863$	1.92446	+	2.70252i	0.0655093	+	0.0919949i	0.846031	−	0.533134i	$-0.178986\pi$
$863$	1.92446	+	2.70252i	0.0655093	+	0.0919949i	−0.780522	+	0.625129i	$0.785046\pi$
$864$	0.371662	+	0.928368i	0.0126442	+	0.0315837i
$865$	−0.124362	+	0.241230i	−0.00422845	+	0.00820205i
$866$	8.00224	−	7.63012i	0.271927	−	0.259282i
$867$	9.88320	−	1.42099i	0.335651	−	0.0482593i
$868$	15.5593	+	23.0117i	0.528118	+	0.781070i
$869$	14.1043	+	9.06430i	0.478456	+	0.307485i
$870$	0.814657	−	0.281956i	0.0276195	−	0.00955919i
$871$	−29.5258	−	28.1528i	−1.00044	−	0.953920i
$872$	8.69232	+	6.18977i	0.294359	+	0.209612i
$873$	−3.68390	+	6.38070i	−0.124681	+	0.215954i
$874$	−21.6083	+	31.2554i	−0.730911	+	1.05723i
$875$	−2.28615	+	0.977738i	−0.0772858	+	0.0330536i
$876$	−0.142898	−	0.312903i	−0.00482807	−	0.0105720i
$877$	−11.8307	+	48.7667i	−0.399494	+	1.64674i	0.316473	+	0.948602i	$0.397501\pi$
$877$	−11.8307	+	48.7667i	−0.399494	+	1.64674i	−0.715967	+	0.698134i	$0.754014\pi$
$878$	−5.63341	+	29.2289i	−0.190118	+	0.986428i
$879$	5.57211	+	0.265432i	0.187943	+	0.00895281i
$880$	0.0919224	+	0.476939i	0.00309870	+	0.0160776i
$881$	−3.82904	−	26.6316i	−0.129004	−	0.897241i	−0.946821	−	0.321762i	$-0.895725\pi$
$881$	−3.82904	−	26.6316i	−0.129004	−	0.897241i	0.817817	−	0.575479i	$-0.195184\pi$
$882$	−6.05895	−	3.50559i	−0.204015	−	0.118039i
$883$	−12.7630	+	8.20227i	−0.429508	+	0.276028i	−0.737482	−	0.675367i	$-0.763985\pi$
$883$	−12.7630	+	8.20227i	−0.429508	+	0.276028i	0.307974	+	0.951395i	$0.400349\pi$
$884$	9.41578	−	11.9731i	0.316687	−	0.402700i
$885$	0.266890	−	0.0254849i	0.00897141	−	0.000856665i
$886$	17.1215	−	1.63490i	0.575208	−	0.0549257i
$887$	−12.8194	+	16.3012i	−0.430434	+	0.547341i	−0.952091	−	0.305814i	$-0.901071\pi$
$887$	−12.8194	+	16.3012i	−0.430434	+	0.547341i	0.521657	+	0.853155i	$0.325314\pi$
$888$	−4.52854	+	2.91032i	−0.151968	+	0.0976638i
$889$	−37.3727	+	4.45097i	−1.25344	+	0.149281i
$890$	−0.0458042	−	0.318575i	−0.00153536	−	0.0106787i
$891$	0.977251	+	5.07046i	0.0327392	+	0.169867i
$892$	15.6378	+	0.744920i	0.523592	+	0.0249418i
$893$	4.66075	−	24.1823i	0.155966	−	0.809228i
$894$	3.81448	−	15.7235i	0.127575	−	0.525873i
$895$	−0.205981	−	0.451035i	−0.00688518	−	0.0150764i
$896$	−0.315312	+	2.62690i	−0.0105338	+	0.0877584i
$897$	27.1520	+	4.84257i	0.906578	+	0.161689i
$898$	−5.54805	+	9.60950i	−0.185141	+	0.320673i
$899$	−78.3818	−	55.8155i	−2.61418	−	1.86155i
$900$	3.61227	+	3.44429i	0.120409	+	0.114810i
$901$	17.4819	−	6.05053i	0.582405	−	0.201572i
$902$	9.77455	+	6.28172i	0.325457	+	0.209158i
$903$	1.57072	+	22.1047i	0.0522702	+	0.735600i
$904$	11.2445	−	1.61671i	0.373986	−	0.0537710i
$905$	−0.0414129	+	0.0394871i	−0.00137661	+	0.00131260i
$906$	0.368699	−	0.715176i	0.0122492	−	0.0237601i
$907$	−5.26526	−	13.1520i	−0.174830	−	0.436705i	0.814909	−	0.579588i	$-0.196787\pi$
$907$	−5.26526	−	13.1520i	−0.174830	−	0.436705i	−0.989739	+	0.142884i	$0.954362\pi$
$908$	8.82981	+	12.3997i	0.293027	+	0.411500i
$909$	−5.98307	−	2.73238i	−0.198446	−	0.0906272i
$910$	1.01155	+	1.01248i	0.0335324	+	0.0335634i
$911$	−16.6496	−	25.9073i	−0.551627	−	0.858348i	0.447731	−	0.894168i	$-0.352232\pi$
$911$	−16.6496	−	25.9073i	−0.551627	−	0.858348i	−0.999358	+	0.0358200i	$0.988596\pi$
$912$	5.46753	+	5.73418i	0.181048	+	0.189878i
$913$	−31.3180	−	39.8241i	−1.03647	−	1.31798i
$914$	−3.08226	−	1.06678i	−0.101952	−	0.0352859i
$915$	−0.308621	−	0.598641i	−0.0102027	−	0.0197905i
$916$	9.39729	−	10.8450i	0.310495	−	0.358330i
$917$	−0.309631	+	0.0519202i	−0.0102249	+	0.00171455i
$918$	−2.40927	+	1.10028i	−0.0795176	+	0.0363145i
$919$	45.6905	+	26.3794i	1.50719	+	0.870177i	0.999965	+	0.00836414i	$0.00266242\pi$
$919$	45.6905	+	26.3794i	1.50719	+	0.870177i	0.507226	+	0.861813i	$0.330671\pi$
$920$	−0.358437	−	0.273898i	−0.0118173	−	0.00903016i
$921$	−14.5464	−	25.1950i	−0.479319	−	0.830205i
$922$	2.24745	−	23.5364i	0.0740159	−	0.775130i
$923$	22.3051	+	75.9642i	0.734181	+	2.50039i
$924$	−4.16592	+	13.0114i	−0.137049	+	0.428045i
$925$	−14.5258	+	22.6026i	−0.477606	+	0.743170i
$926$	−35.9525	+	6.92928i	−1.18147	+	0.227710i
$927$	5.44997	−	4.28590i	0.179000	−	0.140767i
$928$	−2.16071	−	8.90655i	−0.0709286	−	0.292372i
$929$	33.4145	−	1.59173i	1.09630	−	0.0522230i	0.508371	−	0.861138i	$-0.330248\pi$
$929$	33.4145	−	1.59173i	1.09630	−	0.0522230i	0.587925	+	0.808915i	$0.299945\pi$
$930$	−0.140547	+	0.977526i	−0.00460872	+	0.0320543i
$931$	−54.8895	−	7.94359i	−1.79893	−	0.260341i
$932$	10.5471	−	23.0950i	0.345483	−	0.756503i
$933$	−0.678251	−	0.533383i	−0.0222049	−	0.0174622i
$934$	−6.30119	−	3.24849i	−0.206181	−	0.106294i
$935$	−1.25021	+	0.303298i	−0.0408863	+	0.00991892i
$936$	2.13740	−	5.33897i	0.0698631	−	0.174510i
$937$	8.47568	+	9.78145i	0.276888	+	0.319546i	0.877112	−	0.480286i	$-0.159467\pi$
$937$	8.47568	+	9.78145i	0.276888	+	0.319546i	−0.600224	+	0.799832i	$0.704922\pi$
$938$	−3.12095	+	18.5074i	−0.101903	+	0.604288i
$939$	0.761910	+	0.660199i	0.0248640	+	0.0215448i
$940$	0.284133	+	0.0689300i	0.00926741	+	0.00224825i
$941$	9.84129	−	13.8202i	0.320817	−	0.450524i	−0.622401	−	0.782698i	$-0.713843\pi$
$941$	9.84129	−	13.8202i	0.320817	−	0.450524i	0.943218	+	0.332174i	$0.107782\pi$
$942$	15.0391	−	8.68283i	0.490000	−	0.282902i
$943$	−10.6589	+	1.68410i	−0.347101	+	0.0548418i
$944$		−	2.85028i		−	0.0927688i
$945$	−0.0756668	−	0.237083i	−0.00246144	−	0.00771232i
$946$	41.4992	−	12.1853i	1.34925	−	0.396177i
$947$	−10.2310	−	29.5606i	−0.332464	−	0.960591i	−0.980076	−	0.198621i	$-0.936354\pi$
$947$	−10.2310	−	29.5606i	−0.332464	−	0.960591i	0.647613	−	0.761970i	$-0.275767\pi$
$948$	−0.154490	+	3.24314i	−0.00501759	+	0.105332i
$949$	−0.647022	+	1.86945i	−0.0210032	+	0.0606848i
$950$	36.7124	+	14.6974i	1.19111	+	0.476848i
$951$	−8.47881	+	28.8762i	−0.274944	+	0.936374i
$952$	−6.98950	−	0.503138i	−0.226531	−	0.0163068i
$953$	20.7480	+	2.98311i	0.672092	+	0.0966323i	0.469908	−	0.882715i	$-0.344287\pi$
$953$	20.7480	+	2.98311i	0.672092	+	0.0966323i	0.202184	+	0.979348i	$0.435196\pi$
$954$	5.68942	−	4.05142i	0.184202	−	0.131169i
$955$	0.00409977	+	0.0429347i	0.000132665	+	0.00138933i
$956$	1.86485	−	0.746574i	0.0603136	−	0.0241459i
$957$	−2.25184	−	47.2719i	−0.0727915	−	1.52808i
$958$	12.7407	+	3.74100i	0.411632	+	0.120866i
$959$	−29.8825	−	16.3350i	−0.964956	−	0.527484i
$960$	−0.0710875	+	0.0615976i	−0.00229434	+	0.00198806i
$961$	70.4254	−	36.3068i	2.27179	−	1.17119i
$962$	30.3982	+	5.85878i	0.980078	+	0.188895i
$963$	−6.43238	+	6.74608i	−0.207280	+	0.217389i
$964$	14.4720	+	1.38191i	0.466113	+	0.0445084i
$965$	−1.05374			−0.0339212
$966$	−5.15121	−	11.5959i	−0.165738	−	0.373092i
$967$	−35.9639			−1.15652			−0.578260	−	0.815852i	$-0.696268\pi$
$967$	−35.9639			−1.15652			−0.578260	+	0.815852i	$0.696268\pi$
$968$	15.5937	+	1.48902i	0.501200	+	0.0478588i
$969$	−14.4814	+	15.1876i	−0.465209	+	0.487897i
$970$	−0.680508	−	0.131157i	−0.0218498	−	0.00421120i
$971$	−47.5204	+	24.4985i	−1.52500	+	0.786193i	−0.997972	−	0.0636535i	$-0.979725\pi$
$971$	−47.5204	+	24.4985i	−1.52500	+	0.786193i	−0.527030	+	0.849847i	$0.676694\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	−21.2347	+	12.9298i	−0.680755	+	0.414511i
$974$	4.77557	+	1.40223i	0.153019	+	0.0449305i
$975$	−1.36578	−	28.6712i	−0.0437399	−	0.918213i
$976$	−6.64737	+	2.66121i	−0.212777	+	0.0851832i
$977$	3.80784	+	39.8775i	0.121824	+	1.27579i	0.825145	+	0.564921i	$0.191094\pi$
$977$	3.80784	+	39.8775i	0.121824	+	1.27579i	−0.703321	+	0.710872i	$0.748300\pi$
$978$	10.8344	−	7.71512i	0.346445	−	0.246702i
$979$	−17.4890	−	2.51454i	−0.558950	−	0.0803649i
$980$	0.125206	−	0.646421i	0.00399956	−	0.0206492i
$981$	−3.00636	+	10.2387i	−0.0959857	+	0.326897i
$982$	−9.22430	−	3.69285i	−0.294359	−	0.117844i
$983$	18.8243	−	54.3893i	0.600402	−	1.73475i	−0.0748837	−	0.997192i	$-0.523859\pi$
$983$	18.8243	−	54.3893i	0.600402	−	1.73475i	0.675286	−	0.737556i	$-0.264020\pi$
$984$	−0.107064	+	2.24755i	−0.00341308	+	0.0716494i
$985$	0.453581	+	1.31054i	0.0144523	+	0.0417571i
$986$	23.2910	−	6.83886i	0.741737	−	0.217794i
$987$	6.08268	+	5.53465i	0.193614	+	0.176170i
$988$		−	45.5648i		−	1.44961i
$989$	−21.2452	+	34.0912i	−0.675558	+	1.08404i
$990$	−0.420643	+	0.242858i	−0.0133689	+	0.00771854i
$991$	22.3965	−	31.4514i	0.711447	−	0.999088i	−0.287697	−	0.957722i	$-0.592890\pi$
$991$	22.3965	−	31.4514i	0.711447	−	0.999088i	0.999144	−	0.0413664i	$-0.0131711\pi$
$992$	10.2032	+	2.47528i	0.323953	+	0.0785903i
$993$	12.6234	+	10.9382i	0.400591	+	0.347114i
$994$	23.2033	−	28.0760i	0.735964	−	0.890517i
$995$	0.535129	+	0.617572i	0.0169647	+	0.0195783i
$996$	3.64649	−	9.10849i	0.115543	−	0.288614i
$997$	−51.8127	+	12.5696i	−1.64092	+	0.398084i	−0.946813	−	0.321784i	$-0.895718\pi$
$997$	−51.8127	+	12.5696i	−1.64092	+	0.398084i	−0.694111	+	0.719868i	$0.744202\pi$
$998$	5.03179	+	2.59407i	0.159279	+	0.0821138i
$999$	−4.23139	−	3.32760i	−0.133875	−	0.105281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.12	✓	320
7.3	odd	6	inner	966.2.be.b.157.12	yes	320
23.17	odd	22	inner	966.2.be.b.523.12	yes	320
161.17	even	66	inner	966.2.be.b.661.12	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.12	✓	320	1.1	even	1	trivial
966.2.be.b.157.12	yes	320	7.3	odd	6	inner
966.2.be.b.523.12	yes	320	23.17	odd	22	inner
966.2.be.b.661.12	yes	320	161.17	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-0.0836058 + 0.0431018i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-1.37599 - 2.25979i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-0.0836058 + 0.0431018i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-1.37599 - 2.25979i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(0.0873243 - 0.0349594i) q^{10} +(-0.490848 - 5.14040i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-5.69238 - 0.818441i) q^{13} +(1.15495 + 2.38036i) q^{14} +(-0.0265004 + 0.0902520i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-0.866278 + 2.50294i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(2.59137 + 7.48728i) q^{19} +(-0.0902520 + 0.0265004i) q^{20} +(-2.58503 - 0.563587i) q^{21} +5.16378i q^{22} +(-3.19069 - 3.58043i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.89515 + 4.06567i) q^{25} +(5.58881 + 1.35583i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.923452 - 2.47936i) q^{28} +(6.00173 + 6.92636i) q^{29} +(0.0349594 - 0.0873243i) q^{30} +(-10.2032 + 2.47528i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-4.05900 - 3.19204i) q^{33} +(1.10028 - 2.40927i) q^{34} +(0.212442 + 0.129624i) q^{35} +(0.142315 - 0.989821i) q^{36} +(5.37699 - 0.256138i) q^{37} +(-1.86793 - 7.69970i) q^{38} +(-4.52053 + 3.55498i) q^{39} +(0.0923624 - 0.0178014i) q^{40} +(1.21650 - 1.89291i) q^{41} +(2.51975 + 0.806757i) q^{42} +(-2.35976 - 8.03659i) q^{43} +(0.490848 - 5.14040i) q^{44} +(0.0470311 + 0.0814603i) q^{45} +(2.83590 + 3.86751i) q^{46} +(-2.69188 - 1.55416i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-3.21332 + 6.21889i) q^{49} +(3.26851 - 3.77206i) q^{50} +(1.21367 + 2.35418i) q^{51} +(-5.43462 - 1.88094i) q^{52} +(-4.31754 - 5.49020i) q^{53} +(0.690079 + 0.723734i) q^{54} +(0.262598 + 0.408611i) q^{55} +(0.683592 + 2.55591i) q^{56} +(7.20705 + 3.29135i) q^{57} +(-5.31616 - 7.46550i) q^{58} +(-1.05934 - 2.64611i) q^{59} +(-0.0431018 + 0.0836058i) q^{60} +(-5.18214 + 4.94116i) q^{61} +(10.3923 - 1.49419i) q^{62} +(-2.19176 + 1.48195i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.511192 - 0.176925i) q^{65} +(3.73720 + 3.56342i) q^{66} +(5.77852 + 4.11487i) q^{67} +(-1.32431 + 2.29377i) q^{68} +(-4.79311 - 0.161567i) q^{69} +(-0.199158 - 0.149231i) q^{70} +(-5.71890 - 12.5226i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.0651002 - 0.337772i) q^{73} +(-5.37699 - 0.256138i) q^{74} +(0.944582 + 4.90096i) q^{75} +(1.12757 + 7.84240i) q^{76} +(-10.9408 + 8.18233i) q^{77} +(4.83798 - 3.10918i) q^{78} +(-2.00705 + 2.55217i) q^{79} +(-0.0936363 + 0.00894118i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-1.39092 + 1.76870i) q^{82} +(8.25379 - 5.30439i) q^{83} +(-2.43165 - 1.04262i) q^{84} +(-0.0354556 - 0.246599i) q^{85} +(1.58514 + 8.22451i) q^{86} +(9.15451 + 0.436083i) q^{87} +(-0.977251 + 5.07046i) q^{88} +(0.806693 - 3.32523i) q^{89} +(-0.0390749 - 0.0855620i) q^{90} +(5.98313 + 13.9898i) q^{91} +(-2.45543 - 4.11957i) q^{92} +(-5.24960 + 9.09258i) q^{93} +(2.53196 + 1.80300i) q^{94} +(-0.539369 - 0.514287i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(-6.19819 - 3.98334i) q^{97} +(3.78991 - 5.88528i) q^{98} +(-5.11122 + 0.734882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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