LMFDB - Embedded newform 966.2.be.b.19.2

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			19.2
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.11320 + 1.08943i) q^{5} +(0.755750 - 0.654861i) q^{6} +(0.852549 - 2.50463i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.11320 + 1.08943i) q^{5} +(0.755750 - 0.654861i) q^{6} +(0.852549 - 2.50463i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(2.20719 - 0.883624i) q^{10} +(0.0226529 + 0.237232i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(2.58628 + 0.371851i) q^{13} +(-1.08677 + 2.41225i) q^{14} +(0.669817 - 2.28119i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-2.25427 + 6.51328i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(-1.71053 - 4.94226i) q^{19} +(-2.28119 + 0.669817i) q^{20} +(1.22436 + 2.34541i) q^{21} -0.238311i q^{22} +(4.77013 + 0.495842i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.378466 - 0.531481i) q^{25} +(-2.53922 - 0.616009i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.31115 - 2.29802i) q^{28} +(3.12541 + 3.60692i) q^{29} +(-0.883624 + 2.20719i) q^{30} +(-7.33477 + 1.77940i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-0.187325 - 0.147314i) q^{33} +(2.86319 - 6.26950i) q^{34} +(0.927011 + 6.22157i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-2.38039 + 0.113392i) q^{37} +(1.23300 + 5.08248i) q^{38} +(-2.05386 + 1.61517i) q^{39} +(2.33453 - 0.449943i) q^{40} +(-2.56058 + 3.98434i) q^{41} +(-0.995869 - 2.45117i) q^{42} +(2.13456 + 7.26966i) q^{43} +(-0.0226529 + 0.237232i) q^{44} +(1.18875 + 2.05897i) q^{45} +(-4.70140 - 0.947026i) q^{46} +(-9.49140 - 5.47986i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-5.54632 - 4.27063i) q^{49} +(-0.427273 + 0.493099i) q^{50} +(-3.15826 - 6.12616i) q^{51} +(2.46917 + 0.854588i) q^{52} +(-6.19714 - 7.88030i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.306317 - 0.476639i) q^{55} +(-1.52365 + 2.16298i) q^{56} +(4.75729 + 2.17258i) q^{57} +(-2.76840 - 3.88767i) q^{58} +(-5.15185 - 12.8687i) q^{59} +(1.08943 - 2.11320i) q^{60} +(-6.34870 + 6.05348i) q^{61} +(7.47070 - 1.07413i) q^{62} +(-2.54236 - 0.732408i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-5.87043 + 2.03177i) q^{65} +(0.172474 + 0.164453i) q^{66} +(-0.169718 - 0.120855i) q^{67} +(-3.44617 + 5.96895i) q^{68} +(-3.65062 + 3.11014i) q^{69} +(-0.331416 - 6.28151i) q^{70} +(6.37028 + 13.9490i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.912261 - 4.73326i) q^{73} +(2.38039 + 0.113392i) q^{74} +(0.123479 + 0.640672i) q^{75} +(-0.744293 - 5.17667i) q^{76} +(0.613490 + 0.145515i) q^{77} +(2.19809 - 1.41263i) q^{78} +(-10.1063 + 12.8512i) q^{79} +(-2.36673 + 0.225995i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(2.92772 - 3.72290i) q^{82} +(-0.362795 + 0.233154i) q^{83} +(0.758361 + 2.53474i) q^{84} +(-2.33204 - 16.2197i) q^{85} +(-1.43387 - 7.43965i) q^{86} +(-4.76723 - 0.227091i) q^{87} +(0.0451006 - 0.234004i) q^{88} +(-1.22296 + 5.04112i) q^{89} +(-0.987645 - 2.16264i) q^{90} +(3.13628 - 6.16065i) q^{91} +(4.59009 + 1.38963i) q^{92} +(3.77376 - 6.53635i) q^{93} +(8.92752 + 6.35726i) q^{94} +(8.99894 + 8.58047i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-2.39659 - 1.54019i) q^{97} +(5.11526 + 4.77851i) q^{98} +(0.235885 - 0.0339152i) 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
$5$	−2.11320	+	1.08943i	−0.945051	+	0.487208i	−0.860635	−	0.509223i	$-0.829933\pi$
$5$	−2.11320	+	1.08943i	−0.945051	+	0.487208i	−0.0844163	+	0.996431i	$0.526903\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	0.852549	−	2.50463i	0.322233	−	0.946660i
$7$	0.852549	−	2.50463i	0.322233	−	0.946660i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	2.20719	−	0.883624i	0.697974	−	0.279426i
$11$	0.0226529	+	0.237232i	0.00683010	+	0.0715281i	0.998244	−	0.0592306i	$-0.0188647\pi$
$11$	0.0226529	+	0.237232i	0.00683010	+	0.0715281i	−0.991414	+	0.130759i	$0.958259\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	2.58628	+	0.371851i	0.717305	+	0.103133i	0.491296	−	0.870992i	$-0.336523\pi$
$13$	2.58628	+	0.371851i	0.717305	+	0.103133i	0.226009	+	0.974125i	$0.427432\pi$
$14$	−1.08677	+	2.41225i	−0.290451	+	0.644700i
$15$	0.669817	−	2.28119i	0.172946	−	0.589000i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−2.25427	+	6.51328i	−0.546740	+	1.57970i	0.245439	+	0.969412i	$0.421068\pi$
$17$	−2.25427	+	6.51328i	−0.546740	+	1.57970i	−0.792179	+	0.610289i	$0.791053\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	−1.71053	−	4.94226i	−0.392423	−	1.13383i	−0.952275	−	0.305240i	$-0.901263\pi$
$19$	−1.71053	−	4.94226i	−0.392423	−	1.13383i	0.559852	−	0.828593i	$-0.310858\pi$
$20$	−2.28119	+	0.669817i	−0.510089	+	0.149776i
$21$	1.22436	+	2.34541i	0.267177	+	0.511810i
$22$		−	0.238311i		−	0.0508081i
$23$	4.77013	+	0.495842i	0.994641	+	0.103390i
$23$	4.77013	+	0.495842i	0.994641	+	0.103390i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.378466	−	0.531481i	0.0756932	−	0.106296i
$26$	−2.53922	−	0.616009i	−0.497983	−	0.120809i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	1.31115	−	2.29802i	0.247783	−	0.434285i
$29$	3.12541	+	3.60692i	0.580374	+	0.669788i	0.967685	−	0.252161i	$-0.0811414\pi$
$29$	3.12541	+	3.60692i	0.580374	+	0.669788i	−0.387311	+	0.921949i	$0.626596\pi$
$30$	−0.883624	+	2.20719i	−0.161327	+	0.402975i
$31$	−7.33477	+	1.77940i	−1.31736	+	0.319589i	−0.832026	−	0.554737i	$-0.812819\pi$
$31$	−7.33477	+	1.77940i	−1.31736	+	0.319589i	−0.485339	+	0.874326i	$0.661304\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	−0.187325	−	0.147314i	−0.0326091	−	0.0256441i
$34$	2.86319	−	6.26950i	0.491032	−	1.07521i
$35$	0.927011	+	6.22157i	0.156693	+	1.05164i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−2.38039	+	0.113392i	−0.391333	+	0.0186415i	−0.242327	−	0.970195i	$-0.577911\pi$
$37$	−2.38039	+	0.113392i	−0.391333	+	0.0186415i	−0.149007	+	0.988836i	$0.547608\pi$
$38$	1.23300	+	5.08248i	0.200018	+	0.824487i
$39$	−2.05386	+	1.61517i	−0.328881	+	0.258635i
$40$	2.33453	−	0.449943i	0.369121	−	0.0711423i
$41$	−2.56058	+	3.98434i	−0.399896	+	0.622250i	−0.981554	−	0.191183i	$-0.938768\pi$
$41$	−2.56058	+	3.98434i	−0.399896	+	0.622250i	0.581659	+	0.813433i	$0.302404\pi$
$42$	−0.995869	−	2.45117i	−0.153666	−	0.378224i
$43$	2.13456	+	7.26966i	0.325518	+	1.10861i	0.945939	+	0.324344i	$0.105144\pi$
$43$	2.13456	+	7.26966i	0.325518	+	1.10861i	−0.620421	+	0.784269i	$0.713038\pi$
$44$	−0.0226529	+	0.237232i	−0.00341505	+	0.0357640i
$45$	1.18875	+	2.05897i	0.177208	+	0.306933i
$46$	−4.70140	−	0.947026i	−0.693183	−	0.139631i
$47$	−9.49140	−	5.47986i	−1.38446	−	0.799320i	−0.391778	−	0.920060i	$-0.628140\pi$
$47$	−9.49140	−	5.47986i	−1.38446	−	0.799320i	−0.992684	+	0.120740i	$0.961473\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	−5.54632	−	4.27063i	−0.792332	−	0.610091i
$50$	−0.427273	+	0.493099i	−0.0604255	+	0.0697347i
$51$	−3.15826	−	6.12616i	−0.442245	−	0.857835i
$52$	2.46917	+	0.854588i	0.342412	+	0.118510i
$53$	−6.19714	−	7.88030i	−0.851243	−	1.08244i	−0.995673	−	0.0929281i	$-0.970377\pi$
$53$	−6.19714	−	7.88030i	−0.851243	−	1.08244i	0.144430	−	0.989515i	$-0.453865\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−0.306317	−	0.476639i	−0.0413038	−	0.0642700i
$56$	−1.52365	+	2.16298i	−0.203606	+	0.289041i
$57$	4.75729	+	2.17258i	0.630118	+	0.287765i
$58$	−2.76840	−	3.88767i	−0.363509	−	0.510477i
$59$	−5.15185	−	12.8687i	−0.670713	−	1.67536i	−0.735555	−	0.677466i	$-0.763078\pi$
$59$	−5.15185	−	12.8687i	−0.670713	−	1.67536i	0.0648411	−	0.997896i	$-0.479346\pi$
$60$	1.08943	−	2.11320i	0.140645	−	0.272813i
$61$	−6.34870	+	6.05348i	−0.812868	+	0.775068i	−0.977421	−	0.211300i	$-0.932230\pi$
$61$	−6.34870	+	6.05348i	−0.812868	+	0.775068i	0.164553	+	0.986368i	$0.447382\pi$
$62$	7.47070	−	1.07413i	0.948780	−	0.136414i
$63$	−2.54236	−	0.732408i	−0.320307	−	0.0922748i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−5.87043	+	2.03177i	−0.728137	+	0.252011i
$66$	0.172474	+	0.164453i	0.0212300	+	0.0202428i
$67$	−0.169718	−	0.120855i	−0.0207343	−	0.0147648i	0.569643	−	0.821892i	$-0.307082\pi$
$67$	−0.169718	−	0.120855i	−0.0207343	−	0.0147648i	−0.590377	+	0.807128i	$0.701021\pi$
$68$	−3.44617	+	5.96895i	−0.417910	+	0.723842i
$69$	−3.65062	+	3.11014i	−0.439484	+	0.374416i
$70$	−0.331416	−	6.28151i	−0.0396117	−	0.750784i
$71$	6.37028	+	13.9490i	0.756013	+	1.65544i	0.755249	+	0.655438i	$0.227516\pi$
$71$	6.37028	+	13.9490i	0.756013	+	1.65544i	0.000763658		1.00000i	$0.499757\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	0.912261	−	4.73326i	0.106772	−	0.553986i	−0.888664	−	0.458558i	$-0.848366\pi$
$73$	0.912261	−	4.73326i	0.106772	−	0.553986i	0.995436	−	0.0954277i	$-0.0304219\pi$
$74$	2.38039	+	0.113392i	0.276714	+	0.0131815i
$75$	0.123479	+	0.640672i	0.0142582	+	0.0739785i
$76$	−0.744293	−	5.17667i	−0.0853762	−	0.593805i
$77$	0.613490	+	0.145515i	0.0699137	+	0.0165829i
$78$	2.19809	−	1.41263i	0.248885	−	0.159949i
$79$	−10.1063	+	12.8512i	−1.13705	+	1.44588i	−0.259918	+	0.965631i	$0.583696\pi$
$79$	−10.1063	+	12.8512i	−1.13705	+	1.44588i	−0.877133	+	0.480247i	$0.840547\pi$
$80$	−2.36673	+	0.225995i	−0.264608	+	0.0252670i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	2.92772	−	3.72290i	0.323313	−	0.411126i
$83$	−0.362795	+	0.233154i	−0.0398219	+	0.0255920i	−0.560400	−	0.828222i	$-0.689353\pi$
$83$	−0.362795	+	0.233154i	−0.0398219	+	0.0255920i	0.520578	+	0.853814i	$0.325716\pi$
$84$	0.758361	+	2.53474i	0.0827440	+	0.276562i
$85$	−2.33204	−	16.2197i	−0.252945	−	1.75927i
$86$	−1.43387	−	7.43965i	−0.154619	−	0.802238i
$87$	−4.76723	−	0.227091i	−0.511101	−	0.0243467i
$88$	0.0451006	−	0.234004i	0.00480774	−	0.0249449i
$89$	−1.22296	+	5.04112i	−0.129634	+	0.534358i	0.869546	+	0.493853i	$0.164412\pi$
$89$	−1.22296	+	5.04112i	−0.129634	+	0.534358i	−0.999179	+	0.0405051i	$0.987103\pi$
$90$	−0.987645	−	2.16264i	−0.104107	−	0.227962i
$91$	3.13628	−	6.16065i	0.328771	−	0.645811i
$92$	4.59009	+	1.38963i	0.478550	+	0.144879i
$93$	3.77376	−	6.53635i	0.391321	−	0.677788i
$94$	8.92752	+	6.35726i	0.920804	+	0.655701i
$95$	8.99894	+	8.58047i	0.923272	+	0.880338i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	−2.39659	−	1.54019i	−0.243337	−	0.156383i	0.413288	−	0.910600i	$-0.364380\pi$
$97$	−2.39659	−	1.54019i	−0.243337	−	0.156383i	−0.656625	+	0.754217i	$0.728017\pi$
$98$	5.11526	+	4.77851i	0.516719	+	0.482702i
$99$	0.235885	−	0.0339152i	0.0237074	−	0.00340860i
$100$	0.472210	−	0.450251i	0.0472210	−	0.0450251i
$101$	−8.53158	+	16.5490i	−0.848924	+	1.64668i	−0.0895919	+	0.995979i	$0.528556\pi$
$101$	−8.53158	+	16.5490i	−0.848924	+	1.64668i	−0.759332	+	0.650704i	$0.774474\pi$
$102$	2.56163	+	6.39864i	0.253639	+	0.633559i
$103$	5.69643	+	7.99952i	0.561286	+	0.788216i	0.993534	−	0.113539i	$-0.0362186\pi$
$103$	5.69643	+	7.99952i	0.561286	+	0.788216i	−0.432247	+	0.901755i	$0.642279\pi$
$104$	−2.37676	−	1.08543i	−0.233060	−	0.106435i
$105$	−5.14247	−	3.62246i	−0.501854	−	0.353516i
$106$	5.42001	+	8.43370i	0.526438	+	0.819153i
$107$	−13.7257	−	14.3951i	−1.32692	−	1.39163i	−0.862537	−	0.505994i	$-0.831126\pi$
$107$	−13.7257	−	14.3951i	−1.32692	−	1.39163i	−0.464380	−	0.885636i	$-0.653723\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	−1.43763	−	0.497569i	−0.137700	−	0.0476585i	0.257349	−	0.966319i	$-0.417151\pi$
$109$	−1.43763	−	0.497569i	−0.137700	−	0.0476585i	−0.395049	+	0.918660i	$0.629272\pi$
$110$	0.259623	+	0.503598i	0.0247541	+	0.0480162i
$111$	1.56059	−	1.80102i	0.148125	−	0.170945i
$112$	1.72236	−	2.00836i	0.162747	−	0.189772i
$113$	−15.0894	+	6.89111i	−1.41949	+	0.648261i	−0.969572	−	0.244807i	$-0.921276\pi$
$113$	−15.0894	+	6.89111i	−1.41949	+	0.648261i	−0.449922	+	0.893068i	$0.648548\pi$
$114$	−4.52923	−	2.61495i	−0.424201	−	0.244913i
$115$	−10.6204	+	4.14891i	−0.990359	+	0.386888i
$116$	2.38632	+	4.13322i	0.221564	+	0.383760i
$117$	0.248370	−	2.60104i	0.0229618	−	0.240467i
$118$	3.90527	+	13.3001i	0.359509	+	1.22438i
$119$	14.3915	+	11.1990i	1.31926	+	1.02661i
$120$	−1.28537	+	2.00007i	−0.117338	+	0.182581i
$121$	10.7454	−	2.07102i	0.976859	−	0.188274i
$122$	6.89538	−	5.42258i	0.624278	−	0.490938i
$123$	−1.11660	−	4.60269i	−0.100681	−	0.415011i
$124$	−7.53898	+	0.359126i	−0.677020	+	0.0322504i
$125$	1.47100	−	10.2310i	0.131570	−	0.915090i
$126$	2.46123	+	0.970758i	0.219263	+	0.0864820i
$127$	1.94391	−	4.25658i	0.172494	−	0.377710i	−0.803564	−	0.595218i	$-0.797066\pi$
$127$	1.94391	−	4.25658i	0.172494	−	0.377710i	0.976059	+	0.217508i	$0.0697929\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	−6.73432	−	3.47178i	−0.592924	−	0.305673i
$130$	6.03698	−	1.46456i	0.529478	−	0.128450i
$131$	−6.47296	+	16.1687i	−0.565545	+	1.41266i	0.319690	+	0.947522i	$0.396421\pi$
$131$	−6.47296	+	16.1687i	−0.565545	+	1.41266i	−0.885236	+	0.465142i	$0.846003\pi$
$132$	−0.156060	−	0.180103i	−0.0135833	−	0.0156760i
$133$	−13.8368	+	0.0707304i	−1.19981	+	0.00613311i
$134$	0.157461	+	0.136441i	0.0136026	+	0.0117867i
$135$	−2.31047	−	0.560515i	−0.198854	−	0.0482414i
$136$	3.99796	−	5.61434i	0.342822	−	0.481426i
$137$	1.65329	−	0.954529i	0.141250	−	0.0815509i	−0.427709	−	0.903916i	$-0.640679\pi$
$137$	1.65329	−	0.954529i	0.141250	−	0.0815509i	0.568960	+	0.822365i	$0.307346\pi$
$138$	3.92973	−	2.74904i	0.334521	−	0.234014i
$139$			19.7429i			1.67457i	0.546768	+	0.837284i	$0.315858\pi$
$139$			19.7429i			1.67457i	−0.546768	+	0.837284i	$0.684142\pi$
$140$	−0.267181	+	6.28457i	−0.0225809	+	0.531143i
$141$	10.5158	−	3.08771i	0.885588	−	0.260032i
$142$	−5.01550	−	14.4913i	−0.420891	−	1.21609i
$143$	−0.0296282	+	0.621972i	−0.00247763	+	0.0520119i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−10.5341	−	4.21722i	−0.874809	−	0.350221i
$146$	−1.35806	+	4.62511i	−0.112393	+	0.382777i
$147$	6.91820	−	1.06699i	0.570604	−	0.0880035i
$148$	−2.35883	−	0.339149i	−0.193895	−	0.0278778i
$149$	0.780902	−	0.556078i	0.0639740	−	0.0455557i	−0.547623	−	0.836726i	$-0.684467\pi$
$149$	0.780902	−	0.556078i	0.0639740	−	0.0455557i	0.611597	+	0.791170i	$0.290528\pi$
$150$	−0.0620206	−	0.649509i	−0.00506396	−	0.0530322i
$151$	19.3449	−	7.74455i	1.57427	−	0.630242i	0.590077	−	0.807347i	$-0.299097\pi$
$151$	19.3449	−	7.74455i	1.57427	−	0.630242i	0.984192	+	0.177104i	$0.0566730\pi$
$152$	0.248849	+	5.22398i	0.0201843	+	0.423721i
$153$	6.61316	+	1.94180i	0.534642	+	0.156985i
$154$	−0.596880	−	0.203172i	−0.0480980	−	0.0163720i
$155$	13.5613	−	11.7509i	1.08927	−	0.943858i
$156$	−2.32242	+	1.19729i	−0.185942	+	0.0958598i
$157$	5.55954	+	1.07151i	0.443699	+	0.0855161i	0.406207	−	0.913781i	$-0.366851\pi$
$157$	5.55954	+	1.07151i	0.443699	+	0.0855161i	0.0374919	+	0.999297i	$0.488063\pi$
$158$	11.2822	−	11.8324i	0.897560	−	0.941334i
$159$	9.97976	+	0.952952i	0.791446	+	0.0755740i
$160$	2.37749			0.187957
$161$	5.30867	−	11.5247i	0.418382	−	0.908271i
$162$	1.00000			0.0785674
$163$	−9.65608	−	0.922044i	−0.756323	−	0.0722201i	−0.290231	−	0.956957i	$-0.593732\pi$
$163$	−9.65608	−	0.922044i	−0.756323	−	0.0722201i	−0.466092	+	0.884736i	$0.654338\pi$
$164$	−3.26835	+	3.42775i	−0.255215	+	0.267662i
$165$	0.556343	+	0.107226i	0.0433113	+	0.00834756i
$166$	0.383315	−	0.197613i	0.0297510	−	0.0153377i
$167$	8.48345	−	7.35095i	0.656469	−	0.568834i	−0.261638	−	0.965166i	$-0.584263\pi$
$167$	8.48345	−	7.35095i	0.656469	−	0.568834i	0.918107	+	0.396332i	$0.129717\pi$
$168$	−0.513985	−	2.59535i	−0.0396548	−	0.200235i
$169$	−5.92284	−	1.73910i	−0.455603	−	0.133777i
$170$	0.779701	+	16.3679i	0.0598003	+	1.25536i
$171$	−4.85527	+	1.94376i	−0.371292	+	0.148643i
$172$	0.720198	+	7.54226i	0.0549146	+	0.575092i
$173$	−9.11300	+	6.48934i	−0.692849	+	0.493375i	−0.871411	−	0.490553i	$-0.836795\pi$
$173$	−9.11300	+	6.48934i	−0.692849	+	0.493375i	0.178563	+	0.983929i	$0.442855\pi$
$174$	4.72406	+	0.679217i	0.358130	+	0.0514913i
$175$	−1.00850	−	1.40103i	−0.0762355	−	0.105908i
$176$	−0.0671400	+	0.228658i	−0.00506086	+	0.0172357i
$177$	12.8687	+	5.15185i	0.967270	+	0.387237i
$178$	1.69661	−	4.90205i	0.127167	−	0.367424i
$179$	−0.178400	+	3.74508i	−0.0133342	+	0.279920i	0.982346	+	0.187073i	$0.0599000\pi$
$179$	−0.178400	+	3.74508i	−0.0133342	+	0.279920i	−0.995680	+	0.0928476i	$0.970403\pi$
$180$	0.777601	+	2.24673i	0.0579590	+	0.167461i
$181$	−7.55960	+	2.21970i	−0.561901	+	0.164989i	−0.550335	−	0.834944i	$-0.685500\pi$
$181$	−7.55960	+	2.21970i	−0.561901	+	0.164989i	−0.0115660	+	0.999933i	$0.503682\pi$
$182$	−3.70768	+	5.83463i	−0.274832	+	0.432492i
$183$		−	8.77215i		−	0.648456i
$184$	−4.43721	−	1.81966i	−0.327116	−	0.134147i
$185$	4.90670	−	2.83288i	0.360748	−	0.208278i
$186$	−4.37800	+	6.14803i	−0.321010	+	0.450796i
$187$	−1.59622	−	0.387239i	−0.116727	−	0.0283177i
$188$	−8.28280	−	7.17709i	−0.604085	−	0.523443i
$189$	2.28450	−	1.33457i	0.166173	−	0.0970757i
$190$	−8.14257	−	9.39702i	−0.590724	−	0.681732i
$191$	4.18148	−	10.4448i	0.302561	−	0.755761i	−0.696701	−	0.717361i	$-0.745350\pi$
$191$	4.18148	−	10.4448i	0.302561	−	0.755761i	0.999262	−	0.0383999i	$-0.0122261\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	19.1038	+	9.84869i	1.37512	+	0.708924i	0.977954	−	0.208822i	$-0.0669630\pi$
$193$	19.1038	+	9.84869i	1.37512	+	0.708924i	0.397167	+	0.917746i	$0.369993\pi$
$194$	2.23933	+	1.76103i	0.160775	+	0.126435i
$195$	2.58059	−	5.65071i	0.184800	−	0.404656i
$196$	−4.63787	−	5.24311i	−0.331276	−	0.374508i
$197$	−1.09531	+	7.61802i	−0.0780373	+	0.542762i	0.912874	+	0.408242i	$0.133858\pi$
$197$	−1.09531	+	7.61802i	−0.0780373	+	0.542762i	−0.990911	+	0.134519i	$0.957051\pi$
$198$	−0.238041	+	0.0113393i	−0.0169168	+	0.000805848i
$199$	0.210549	+	0.867897i	0.0149255	+	0.0615236i	0.978787	−	0.204879i	$-0.0656801\pi$
$199$	0.210549	+	0.867897i	0.0149255	+	0.0615236i	−0.963862	+	0.266403i	$0.914165\pi$
$200$	−0.512871	+	0.403326i	−0.0362654	+	0.0285195i
$201$	0.204586	−	0.0394307i	0.0144304	−	0.00278122i
$202$	10.0660	−	15.6630i	0.708243	−	1.10205i
$203$	11.6986	−	4.75292i	0.821077	−	0.333590i
$204$	−1.94180	−	6.61316i	−0.135953	−	0.463014i
$205$	1.07036	−	11.2093i	0.0747569	−	0.782890i
$206$	−4.91024	−	8.50478i	−0.342112	−	0.592556i
$207$	0.268308	−	4.78832i	0.0186487	−	0.332811i
$208$	2.26282	+	1.30644i	0.156898	+	0.0905852i
$209$	1.13371	−	0.517750i	0.0784206	−	0.0358135i
$210$	4.77485	+	4.09488i	0.329496	+	0.282574i
$211$	13.6770	−	15.7841i	0.941566	−	1.08663i	−0.0545442	−	0.998511i	$-0.517371\pi$
$211$	13.6770	−	15.7841i	0.941566	−	1.08663i	0.996110	−	0.0881140i	$-0.0280840\pi$
$212$	−4.59379	−	8.91071i	−0.315503	−	0.611990i
$213$	−14.4913	−	5.01550i	−0.992930	−	0.343656i
$214$	12.2952	+	15.6347i	0.840485	+	1.06876i
$215$	−12.4305	−	13.0368i	−0.847756	−	0.889101i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	−1.79653	+	19.8879i	−0.121956	+	1.35008i
$218$	1.38382	+	0.631972i	0.0937245	+	0.0428025i
$219$	2.79609	+	3.92656i	0.188942	+	0.265332i
$220$	−0.210577	−	0.525997i	−0.0141971	−	0.0354627i
$221$	−8.25213	+	16.0069i	−0.555099	+	1.07674i
$222$	−1.72472	+	1.64452i	−0.115756	+	0.110373i
$223$	15.2669	−	2.19506i	1.02235	−	0.146992i	0.389307	−	0.921108i	$-0.372715\pi$
$223$	15.2669	−	2.19506i	1.02235	−	0.146992i	0.633043	+	0.774116i	$0.281805\pi$
$224$	−1.90546	+	1.83554i	−0.127314	+	0.122642i
$225$	−0.548887	−	0.352748i	−0.0365925	−	0.0235165i
$226$	15.6761	−	5.42557i	1.04276	−	0.360903i
$227$	−2.61577	−	2.49413i	−0.173615	−	0.165541i	0.598290	−	0.801280i	$-0.295847\pi$
$227$	−2.61577	−	2.49413i	−0.173615	−	0.165541i	−0.771904	+	0.635739i	$0.780696\pi$
$228$	4.26015	+	3.03364i	0.282135	+	0.200908i
$229$	−9.97047	+	17.2694i	−0.658867	+	1.14119i	0.322042	+	0.946725i	$0.395631\pi$
$229$	−9.97047	+	17.2694i	−0.658867	+	1.14119i	−0.980909	+	0.194466i	$0.937703\pi$
$230$	10.9667	−	3.12059i	0.723123	−	0.205765i
$231$	−0.528671	+	0.343587i	−0.0347840	+	0.0226064i
$232$	−1.98262	−	4.34134i	−0.130166	−	0.285023i
$233$	0.378972	−	1.56214i	0.0248273	−	0.102339i	−0.958050	−	0.286602i	$-0.907474\pi$
$233$	0.378972	−	1.56214i	0.0248273	−	0.102339i	0.982877	+	0.184262i	$0.0589896\pi$
$234$	−0.494490	+	2.56566i	−0.0323258	+	0.167722i
$235$	26.0271	+	1.23982i	1.69782	+	0.0808772i
$236$	−2.62333	−	13.6111i	−0.170764	−	0.886009i
$237$	−2.32672	−	16.1827i	−0.151136	−	1.05118i
$238$	−13.2618	−	12.5163i	−0.859632	−	0.811309i
$239$	1.01165	−	0.650150i	0.0654384	−	0.0420547i	−0.507513	−	0.861644i	$-0.669435\pi$
$239$	1.01165	−	0.650150i	0.0654384	−	0.0420547i	0.572951	+	0.819590i	$0.305799\pi$
$240$	1.46967	−	1.86883i	0.0948666	−	0.120633i
$241$	13.5154	−	1.29057i	0.870605	−	0.0831327i	0.349816	−	0.936818i	$-0.386244\pi$
$241$	13.5154	−	1.29057i	0.870605	−	0.0831327i	0.520789	+	0.853686i	$0.325638\pi$
$242$	−10.8937	+	1.04022i	−0.700271	+	0.0668677i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	−7.37960	+	4.74258i	−0.472431	+	0.303613i
$245$	16.3730	+	2.98237i	1.04603	+	0.190537i
$246$	0.674031	+	4.68799i	0.0429747	+	0.298895i
$247$	−2.58613	−	13.4181i	−0.164552	−	0.853776i
$248$	7.53898	+	0.359126i	0.478726	+	0.0228045i
$249$	0.0816156	−	0.423462i	0.00517218	−	0.0268358i
$250$	−2.43686	+	10.0449i	−0.154120	+	0.635293i
$251$	−3.09839	−	6.78452i	−0.195568	−	0.428235i	0.786288	−	0.617860i	$-0.212000\pi$
$251$	−3.09839	−	6.78452i	−0.195568	−	0.428235i	−0.981857	+	0.189625i	$0.939273\pi$
$252$	−2.35780	−	1.20032i	−0.148528	−	0.0756128i
$253$	−0.00957222	+	1.14286i	−0.000601800	+	0.0718509i
$254$	−2.33972	+	4.05252i	−0.146807	+	0.254278i
$255$	13.3480	+	9.50510i	0.835887	+	0.595233i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	17.0999	−	5.91834i	1.06666	−	0.369176i	0.263331	−	0.964706i	$-0.415179\pi$
$257$	17.0999	−	5.91834i	1.06666	−	0.369176i	0.803334	+	0.595529i	$0.203058\pi$
$258$	6.37381	+	4.09620i	0.396816	+	0.255018i
$259$	−1.74539	+	6.05866i	−0.108453	+	0.376467i
$260$	−6.14886	+	0.884072i	−0.381336	+	0.0548278i
$261$	3.45412	−	3.29350i	0.213805	−	0.203862i
$262$	7.98058	−	15.4802i	0.493042	−	0.956368i
$263$	3.22103	+	8.04574i	0.198617	+	0.496122i	0.993922	−	0.110088i	$-0.0351134\pi$
$263$	3.22103	+	8.04574i	0.198617	+	0.496122i	−0.795305	+	0.606210i	$0.792689\pi$
$264$	0.138234	+	0.194122i	0.00850771	+	0.0119474i
$265$	21.6808	+	9.90130i	1.33184	+	0.608232i
$266$	13.7809	+	1.24487i	0.844962	+	0.0763276i
$267$	−2.80449	−	4.36387i	−0.171632	−	0.267065i
$268$	−0.143779	−	0.150791i	−0.00878267	−	0.00921100i
$269$	−15.1130	−	19.2177i	−0.921453	−	1.17172i	−0.984793	−	0.173731i	$-0.944418\pi$
$269$	−15.1130	−	19.2177i	−0.921453	−	1.17172i	0.0633398	−	0.997992i	$-0.479825\pi$
$270$	2.24673	+	0.777601i	0.136732	+	0.0473233i
$271$	9.65337	+	18.7249i	0.586400	+	1.13746i	0.976264	+	0.216585i	$0.0694920\pi$
$271$	9.65337	+	18.7249i	0.586400	+	1.13746i	−0.389863	+	0.920873i	$0.627478\pi$
$272$	−4.51353	+	5.20889i	−0.273673	+	0.315835i
$273$	2.29439	+	6.52117i	0.138863	+	0.394679i
$274$	−1.73654	+	0.793051i	−0.104908	+	0.0479100i
$275$	0.134658	+	0.0777446i	0.00812015	+	0.00468817i
$276$	−4.17325	+	2.36305i	−0.251200	+	0.142239i
$277$	−11.1738	−	19.3537i	−0.671371	−	1.16285i	−0.977515	−	0.210864i	$-0.932372\pi$
$277$	−11.1738	−	19.3537i	−0.671371	−	1.16285i	0.306144	−	0.951985i	$-0.400961\pi$
$278$	1.87668	−	19.6535i	0.112556	−	1.17874i
$279$	2.12638	+	7.24180i	0.127303	+	0.433555i
$280$	0.863358	−	6.23072i	0.0515955	−	0.372357i
$281$	−3.28447	+	5.11073i	−0.195935	+	0.304880i	−0.925294	−	0.379250i	$-0.876182\pi$
$281$	−3.28447	+	5.11073i	−0.195935	+	0.304880i	0.729359	+	0.684131i	$0.239818\pi$
$282$	−10.7617	+	2.07414i	−0.640848	+	0.123513i
$283$	18.1145	−	14.2454i	1.07680	−	0.846801i	0.0880062	−	0.996120i	$-0.471950\pi$
$283$	18.1145	−	14.2454i	1.07680	−	0.846801i	0.988789	+	0.149319i	$0.0477080\pi$
$284$	3.61530	+	14.9025i	0.214529	+	0.884299i
$285$	−12.4200	+	0.591636i	−0.735695	+	0.0350455i
$286$	0.0886162	−	0.616339i	0.00523998	−	0.0364449i
$287$	7.79628	+	9.81015i	0.460200	+	0.579075i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	−23.9781	−	18.8566i	−1.41048	−	1.10921i
$290$	10.0855	+	5.19945i	0.592242	+	0.305322i
$291$	2.76853	−	0.671637i	0.162294	−	0.0393721i
$292$	1.79155	−	4.47508i	0.104843	−	0.261884i
$293$	−14.7517	−	17.0243i	−0.861801	−	0.994571i	−0.999991	−	0.00416532i	$-0.998674\pi$
$293$	−14.7517	−	17.0243i	−0.861801	−	0.994571i	0.138191	−	0.990406i	$-0.455871\pi$
$294$	−6.98830	+	0.404538i	−0.407566	+	0.0235931i
$295$	24.9064	+	21.5815i	1.45011	+	1.25652i
$296$	2.31591	+	0.561834i	0.134610	+	0.0326559i
$297$	−0.138234	+	0.194122i	−0.00802114	+	0.0112641i
$298$	−0.830225	+	0.479331i	−0.0480936	+	0.0277669i
$299$	12.1525	+	3.05616i	0.702798	+	0.176742i
$300$			0.652463i			0.0376700i
$301$	20.0276	+	0.851449i	1.15437	+	0.0490767i
$302$	−19.9935	+	5.87063i	−1.15050	+	0.337817i
$303$	−6.08958	−	17.5947i	−0.349837	−	1.01079i
$304$	0.248849	−	5.22398i	0.0142725	−	0.299616i
$305$	6.82123	−	19.7087i	0.390583	−	1.12851i
$306$	−6.39864	−	2.56163i	−0.365786	−	0.146439i
$307$	0.696403	−	2.37173i	0.0397458	−	0.135362i	−0.937230	−	0.348712i	$-0.886619\pi$
$307$	0.696403	−	2.37173i	0.0397458	−	0.135362i	0.976976	+	0.213350i	$0.0684374\pi$
$308$	0.574865	+	0.258989i	0.0327560	+	0.0147573i
$309$	−9.72052	−	1.39760i	−0.552981	−	0.0795066i
$310$	−14.6169	+	10.4086i	−0.830184	+	0.591171i
$311$	2.63653	+	27.6110i	0.149504	+	1.56568i	0.689674	+	0.724120i	$0.257754\pi$
$311$	2.63653	+	27.6110i	0.149504	+	1.56568i	−0.540171	+	0.841556i	$0.681640\pi$
$312$	2.42571	−	0.971108i	0.137329	−	0.0549782i
$313$	0.535270	+	11.2367i	0.0302552	+	0.635135i	0.962169	+	0.272455i	$0.0878354\pi$
$313$	0.535270	+	11.2367i	0.0302552	+	0.635135i	−0.931913	+	0.362681i	$0.881862\pi$
$314$	−5.43251	−	1.59513i	−0.306574	−	0.0900183i
$315$	6.17041	−	1.22199i	0.347663	−	0.0688516i
$316$	−12.3558	+	10.7064i	−0.695069	+	0.602280i
$317$	−11.8088	+	6.08787i	−0.663250	+	0.341929i	−0.756763	−	0.653689i	$-0.773220\pi$
$317$	−11.8088	+	6.08787i	−0.663250	+	0.341929i	0.0935137	+	0.995618i	$0.470190\pi$
$318$	−9.84399	−	1.89727i	−0.552023	−	0.106394i
$319$	−0.784876	+	0.823154i	−0.0439446	+	0.0460878i
$320$	−2.36673	−	0.225995i	−0.132304	−	0.0126335i
$321$	19.8901			1.11016
$322$	−6.38012	+	10.9679i	−0.355550	+	0.611215i
$323$	36.0463			2.00567
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	1.17645	−	1.23383i	0.0652577	−	0.0684403i
$326$	9.52471	+	1.83574i	0.527525	+	0.101672i
$327$	1.35219	−	0.697101i	0.0747761	−	0.0385498i
$328$	3.57938	−	3.10155i	0.197638	−	0.171254i
$329$	−21.8169	+	19.1006i	−1.20280	+	1.05305i
$330$	−0.543632	−	0.159625i	−0.0299259	−	0.00878705i
$331$	0.960217	+	20.1574i	0.0527783	+	1.10795i	0.857561	+	0.514383i	$0.171979\pi$
$331$	0.960217	+	20.1574i	0.0527783	+	1.10795i	−0.804782	+	0.593570i	$0.797718\pi$
$332$	−0.400363	+	0.160281i	−0.0219728	+	0.00879658i
$333$	0.226527	+	2.37230i	0.0124136	+	0.130001i
$334$	−9.14379	+	6.51126i	−0.500326	+	0.356280i
$335$	0.490310	+	0.0704960i	0.0267885	+	0.00385161i
$336$	0.264954	+	2.63245i	0.0144544	+	0.143612i
$337$	−0.181933	+	0.619608i	−0.00991054	+	0.0337522i	−0.964300	−	0.264813i	$-0.914690\pi$
$337$	−0.181933	+	0.619608i	−0.00991054	+	0.0337522i	0.954389	+	0.298565i	$0.0965080\pi$
$338$	5.73070	+	2.29423i	0.311709	+	0.124790i
$339$	5.42557	−	15.6761i	0.294676	−	0.851411i
$340$	0.779701	−	16.3679i	0.0422852	−	0.887676i
$341$	−0.588283	−	1.69973i	−0.0318573	−	0.0920457i
$342$	5.01805	−	1.47343i	0.271345	−	0.0796742i
$343$	−15.4249	+	10.2505i	−0.832864	+	0.553477i
$344$		−	7.57656i		−	0.408501i
$345$	4.32622	−	10.5494i	0.232916	−	0.567962i
$346$	9.68859	−	5.59371i	0.520862	−	0.300720i
$347$	11.6462	−	16.3549i	0.625203	−	0.877975i	−0.373565	−	0.927604i	$-0.621865\pi$
$347$	11.6462	−	16.3549i	0.625203	−	0.877975i	0.998768	+	0.0496295i	$0.0158040\pi$
$348$	−4.63810	−	1.12519i	−0.248628	−	0.0603166i
$349$	−10.3350	−	8.95536i	−0.553222	−	0.479370i	0.332810	−	0.942994i	$-0.392003\pi$
$349$	−10.3350	−	8.95536i	−0.553222	−	0.479370i	−0.886032	+	0.463624i	$0.846549\pi$
$350$	0.870758	+	1.49055i	0.0465440	+	0.0796732i
$351$	1.71107	+	1.97468i	0.0913301	+	0.105401i
$352$	0.0885712	−	0.221240i	0.00472086	−	0.0117921i
$353$	5.04391	−	1.22364i	0.268460	−	0.0651277i	−0.0992691	−	0.995061i	$-0.531650\pi$
$353$	5.04391	−	1.22364i	0.268460	−	0.0651277i	0.367729	+	0.929933i	$0.380135\pi$
$354$	−12.3207	−	6.35177i	−0.654838	−	0.337593i
$355$	−28.6581	−	22.5370i	−1.52101	−	1.19614i
$356$	−2.15490	+	4.71858i	−0.114210	+	0.250084i
$357$	−18.0363	+	2.68741i	−0.954584	+	0.142233i
$358$	0.533584	−	3.71116i	0.0282008	−	0.196141i
$359$	1.67542	−	0.0798100i	0.0884252	−	0.00421221i	−0.00332271	−	0.999994i	$-0.501058\pi$
$359$	1.67542	−	0.0798100i	0.0884252	−	0.00421221i	0.0917479	+	0.995782i	$0.470755\pi$
$360$	−0.560515	−	2.31047i	−0.0295417	−	0.121773i
$361$	−6.56502	+	5.16279i	−0.345527	+	0.271726i
$362$	7.73636	−	1.49106i	0.406614	−	0.0783685i
$363$	−5.91634	+	9.20601i	−0.310528	+	0.483190i
$364$	4.24551	−	5.45577i	0.222525	−	0.285960i
$365$	3.22876	+	10.9962i	0.169001	+	0.575565i
$366$	−0.833846	+	8.73243i	−0.0435858	+	0.456451i
$367$	−5.72719	−	9.91979i	−0.298957	−	0.517809i	0.676941	−	0.736038i	$-0.263305\pi$
$367$	−5.72719	−	9.91979i	−0.298957	−	0.517809i	−0.975898	+	0.218229i	$0.929972\pi$
$368$	4.24415	+	2.23320i	0.221242	+	0.116414i
$369$	4.10167	+	2.36810i	0.213524	+	0.123278i
$370$	−5.15376	+	2.35364i	−0.267931	+	0.122360i
$371$	−25.0206	+	8.80319i	−1.29900	+	0.457039i
$372$	4.94258	−	5.70404i	0.256261	−	0.295741i
$373$	−2.92131	−	5.66655i	−0.151260	−	0.293403i	0.801016	−	0.598643i	$-0.204293\pi$
$373$	−2.92131	−	5.66655i	−0.151260	−	0.293403i	−0.952275	+	0.305241i	$0.901263\pi$
$374$	1.55218	+	0.537216i	0.0802616	+	0.0277788i
$375$	6.38943	+	8.12483i	0.329949	+	0.419564i
$376$	7.56307	+	7.93192i	0.390036	+	0.409058i
$377$	6.74196	+	10.4907i	0.347228	+	0.540298i
$378$	−2.40101	+	1.11137i	−0.123495	+	0.0571628i
$379$	−1.99801	−	0.912463i	−0.102631	−	0.0468701i	0.363438	−	0.931618i	$-0.381603\pi$
$379$	−1.99801	−	0.912463i	−0.102631	−	0.0468701i	−0.466069	+	0.884748i	$0.654330\pi$
$380$	7.21245	+	10.1285i	0.369991	+	0.519580i
$381$	1.73918	+	4.34425i	0.0891007	+	0.222563i
$382$	−5.15539	+	10.0001i	−0.263773	+	0.511648i
$383$	10.4861	−	9.99850i	0.535816	−	0.510899i	−0.373149	−	0.927771i	$-0.621722\pi$
$383$	10.4861	−	9.99850i	0.535816	−	0.510899i	0.908965	+	0.416872i	$0.136874\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	−1.45495	+	0.360853i	−0.0741513	+	0.0183908i
$386$	−18.0811	−	11.6200i	−0.920304	−	0.591444i
$387$	7.15986	−	2.47805i	0.363956	−	0.125966i
$388$	−2.06179	−	1.96592i	−0.104672	−	0.0998043i
$389$	−11.6472	−	8.29393i	−0.590536	−	0.420519i	0.245340	−	0.969437i	$-0.421100\pi$
$389$	−11.6472	−	8.29393i	−0.590536	−	0.420519i	−0.835876	+	0.548918i	$0.815040\pi$
$390$	−3.10604	+	5.37983i	−0.157281	+	0.272418i
$391$	−13.9827	+	29.9514i	−0.707136	+	1.51471i
$392$	4.11848	+	5.66022i	0.208015	+	0.285884i
$393$	−7.23497	−	15.8424i	−0.364956	−	0.799142i
$394$	1.81449	−	7.47941i	0.0914125	−	0.376807i
$395$	7.35616	−	38.1674i	0.370128	−	1.92041i
$396$	0.238041	+	0.0113393i	0.0119620	+	0.000569821i
$397$	0.519984	+	2.69793i	0.0260972	+	0.135405i	0.992641	−	0.121098i	$-0.0386416\pi$
$397$	0.519984	+	2.69793i	0.0260972	+	0.135405i	−0.966543	+	0.256504i	$0.917429\pi$
$398$	−0.127097	−	0.883981i	−0.00637081	−	0.0443100i
$399$	9.49732	−	10.0630i	0.475461	−	0.503780i
$400$	0.548887	−	0.352748i	0.0274443	−	0.0176374i
$401$	−1.52349	+	1.93727i	−0.0760794	+	0.0967429i	−0.822603	−	0.568616i	$-0.807479\pi$
$401$	−1.52349	+	1.93727i	−0.0760794	+	0.0967429i	0.746524	+	0.665359i	$0.231721\pi$
$402$	−0.207407	+	0.0198050i	−0.0103445	+	0.000987784i
$403$	−19.6315	+	1.87458i	−0.977912	+	0.0933793i
$404$	−11.5093	+	14.6353i	−0.572610	+	0.728132i
$405$	2.00007	−	1.28537i	0.0993844	−	0.0638705i
$406$	−12.0974	+	3.61938i	−0.600383	+	0.179627i
$407$	−0.0808228	−	0.562135i	−0.00400624	−	0.0278640i
$408$	1.30439	+	6.76780i	0.0645767	+	0.335056i
$409$	−2.26119	−	0.107714i	−0.111809	−	0.00532610i	−0.00839699	−	0.999965i	$-0.502673\pi$
$409$	−2.26119	−	0.107714i	−0.111809	−	0.00532610i	−0.103412	+	0.994639i	$0.532976\pi$
$410$	−2.13102	+	11.0568i	−0.105244	+	0.546055i
$411$	−0.450077	+	1.85524i	−0.0222007	+	0.0915124i
$412$	4.07957	+	8.93302i	0.200986	+	0.440098i
$413$	−36.6235	+	1.93227i	−1.80212	+	0.0950809i
$414$	−0.722252	+	4.74113i	−0.0354968	+	0.233014i
$415$	0.512653	−	0.887940i	0.0251651	−	0.0435873i
$416$	−2.12839	−	1.51562i	−0.104353	−	0.0743092i
$417$	−14.2886	−	13.6241i	−0.699715	−	0.667177i
$418$	−1.17780	+	0.407639i	−0.0576078	+	0.0199383i
$419$	1.33906	+	0.860559i	0.0654172	+	0.0420411i	0.572941	−	0.819597i	$-0.305803\pi$
$419$	1.33906	+	0.860559i	0.0654172	+	0.0420411i	−0.507523	+	0.861638i	$0.669439\pi$
$420$	−4.36398	−	4.53022i	−0.212941	−	0.221052i
$421$	−21.8356	+	3.13948i	−1.06420	+	0.153009i	−0.652103	−	0.758131i	$-0.726113\pi$
$421$	−21.8356	+	3.13948i	−1.06420	+	0.153009i	−0.412098	+	0.911140i	$0.635204\pi$
$422$	−15.1155	+	14.4126i	−0.735810	+	0.701594i
$423$	−5.02203	+	9.74139i	−0.244180	+	0.473642i
$424$	3.72597	+	9.30703i	0.180949	+	0.451989i
$425$	2.60852	+	3.66315i	0.126532	+	0.177689i
$426$	13.9490	+	6.37028i	0.675829	+	0.308641i
$427$	9.74913	+	21.0620i	0.471793	+	1.01926i
$428$	−10.7534	−	16.7326i	−0.519785	−	0.808801i
$429$	−0.429696	−	0.450652i	−0.0207459	−	0.0217577i
$430$	11.1350	+	14.1593i	0.536979	+	0.682824i
$431$	8.56554	+	2.96456i	0.412587	+	0.142798i	0.525473	−	0.850810i	$-0.323888\pi$
$431$	8.56554	+	2.96456i	0.412587	+	0.142798i	−0.112886	+	0.993608i	$0.536009\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	−10.1537	+	11.7180i	−0.487956	+	0.563131i	−0.945318	−	0.326150i	$-0.894249\pi$
$433$	−10.1537	+	11.7180i	−0.487956	+	0.563131i	0.457363	+	0.889280i	$0.348794\pi$
$434$	3.67886	−	19.6271i	0.176591	−	0.942130i
$435$	10.3215	−	4.71367i	0.494878	−	0.226003i
$436$	−1.31749	−	0.760651i	−0.0630961	−	0.0364286i
$437$	−5.70889	−	24.4234i	−0.273093	−	1.16833i
$438$	−2.41018	−	4.17456i	−0.115163	−	0.199468i
$439$	−1.97072	+	20.6383i	−0.0940572	+	0.985011i	0.818074	+	0.575113i	$0.195042\pi$
$439$	−1.97072	+	20.6383i	−0.0940572	+	0.985011i	−0.912131	+	0.409898i	$0.865564\pi$
$440$	0.159625	+	0.543632i	0.00760981	+	0.0259166i
$441$	−4.00189	+	5.74324i	−0.190566	+	0.273488i
$442$	9.73632	−	15.1500i	0.463110	−	0.720613i
$443$	10.6240	−	2.04760i	0.504760	−	0.0972844i	0.0694865	−	0.997583i	$-0.477864\pi$
$443$	10.6240	−	2.04760i	0.504760	−	0.0972844i	0.435273	+	0.900298i	$0.356652\pi$
$444$	1.87323	−	1.47313i	0.0888997	−	0.0699115i
$445$	−2.90758	−	11.9852i	−0.137833	−	0.568154i
$446$	−15.4065	+	0.733901i	−0.729518	+	0.0347512i
$447$	−0.136432	+	0.948903i	−0.00645300	+	0.0448816i
$448$	2.07131	−	1.64610i	0.0978604	−	0.0777711i
$449$	−10.1201	+	22.1599i	−0.477596	+	1.04579i	0.505522	+	0.862814i	$0.331300\pi$
$449$	−10.1201	+	22.1599i	−0.477596	+	1.04579i	−0.983118	+	0.182975i	$0.941427\pi$
$450$	0.512871	+	0.403326i	0.0241770	+	0.0190130i
$451$	−1.00322	−	0.517195i	−0.0472397	−	0.0243537i
$452$	−16.1209	+	3.91089i	−0.758263	+	0.183953i
$453$	−7.74455	+	19.3449i	−0.363871	+	0.908905i
$454$	2.36684	+	2.73148i	0.111081	+	0.128195i
$455$	0.0840137	+	16.4354i	0.00393863	+	0.770505i
$456$	−3.95250	−	3.42486i	−0.185093	−	0.160384i
$457$	−3.57693	−	0.867755i	−0.167322	−	0.0405918i	0.151223	−	0.988500i	$-0.451679\pi$
$457$	−3.57693	−	0.867755i	−0.167322	−	0.0405918i	−0.318545	+	0.947908i	$0.603194\pi$
$458$	11.5669	−	16.2434i	0.540485	−	0.759005i
$459$	−5.96895	+	3.44617i	−0.278607	+	0.160854i
$460$	−11.2137	+	2.06400i	−0.522840	+	0.0962347i
$461$		−	33.6897i		−	1.56908i	−0.620075	−	0.784542i	$-0.712898\pi$
$461$		−	33.6897i		−	1.56908i	0.620075	−	0.784542i	$-0.287102\pi$
$462$	0.558937	−	0.291778i	0.0260041	−	0.0135747i
$463$	−18.1281	+	5.32289i	−0.842484	+	0.247376i	−0.674371	−	0.738392i	$-0.735585\pi$
$463$	−18.1281	+	5.32289i	−0.842484	+	0.247376i	−0.168112	+	0.985768i	$0.553767\pi$
$464$	1.56098	+	4.51015i	0.0724665	+	0.209378i
$465$	−0.853818	+	17.9239i	−0.0395949	+	0.831199i
$466$	−0.525747	+	1.51905i	−0.0243547	+	0.0703684i
$467$	10.9129	+	4.36886i	0.504988	+	0.202167i	0.610146	−	0.792289i	$-0.291111\pi$
$467$	10.9129	+	4.36886i	0.504988	+	0.202167i	−0.105159	+	0.994455i	$0.533535\pi$
$468$	0.736132	−	2.50704i	0.0340277	−	0.115888i
$469$	−0.447390	+	0.322044i	−0.0206586	+	0.0148706i
$470$	−25.7914	−	3.70825i	−1.18967	−	0.171049i
$471$	−4.61201	+	3.28420i	−0.212510	+	0.151328i
$472$	1.31763	+	13.7989i	0.0606489	+	0.635144i
$473$	−1.67624	+	0.671066i	−0.0770736	+	0.0308556i
$474$	0.777921	+	16.3306i	0.0357311	+	0.750088i
$475$	−3.27410	−	0.961361i	−0.150226	−	0.0441103i
$476$	12.0120	+	13.7202i	0.550568	+	0.628865i
$477$	−7.57651	+	6.56508i	−0.346904	+	0.300594i
$478$	−1.06887	+	0.551043i	−0.0488891	+	0.0252041i
$479$	−38.7695	−	7.47220i	−1.77142	−	0.341414i	−0.804009	−	0.594617i	$-0.797304\pi$
$479$	−38.7695	−	7.47220i	−1.77142	−	0.341414i	−0.967413	+	0.253203i	$0.918516\pi$
$480$	−1.64066	+	1.72067i	−0.0748854	+	0.0785375i
$481$	−6.19851	−	0.591886i	−0.282628	−	0.0269877i
$482$	−13.5769			−0.618411
$483$	4.67740	+	11.7950i	0.212829	+	0.536691i
$484$	10.9432			0.497419
$485$	6.74240	+	0.643821i	0.306157	+	0.0292344i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	−21.1995	−	4.08587i	−0.960640	−	0.185148i	−0.315256	−	0.949007i	$-0.602091\pi$
$487$	−21.1995	−	4.08587i	−0.960640	−	0.185148i	−0.645384	+	0.763858i	$0.723303\pi$
$488$	7.79700	−	4.01963i	0.352954	−	0.181960i
$489$	7.33077	−	6.35215i	0.331509	−	0.287254i
$490$	−16.0154	−	4.52522i	−0.723502	−	0.204429i
$491$	24.8608	+	7.29979i	1.12195	+	0.329435i	0.789540	−	0.613700i	$-0.210319\pi$
$491$	24.8608	+	7.29979i	1.12195	+	0.329435i	0.332412	+	0.943134i	$0.392138\pi$
$492$	−0.225357	−	4.73083i	−0.0101599	−	0.213282i
$493$	−30.5384	+	12.2257i	−1.37538	+	0.550619i
$494$	1.29895	+	13.6032i	0.0584425	+	0.612037i
$495$	−0.461524	+	0.328650i	−0.0207440	+	0.0147717i
$496$	−7.47070	−	1.07413i	−0.335445	−	0.0482296i
$497$	40.3679	−	4.06300i	1.81075	−	0.182251i
$498$	−0.121499	+	0.413786i	−0.00544448	+	0.0185422i
$499$	7.78372	+	3.11613i	0.348447	+	0.139497i	0.539283	−	0.842125i	$-0.318695\pi$
$499$	7.78372	+	3.11613i	0.348447	+	0.139497i	−0.190836	+	0.981622i	$0.561120\pi$
$500$	3.38065	−	9.76775i	0.151187	−	0.436827i
$501$	−0.534117	+	11.2125i	−0.0238626	+	0.500938i
$502$	2.43945	+	7.04832i	0.108878	+	0.314582i
$503$	2.25917	−	0.663353i	0.100732	−	0.0295775i	−0.230978	−	0.972959i	$-0.574193\pi$
$503$	2.25917	−	0.663353i	0.100732	−	0.0295775i	0.331710	+	0.943381i	$0.392374\pi$
$504$	2.23303	+	1.41901i	0.0994671	+	0.0632075i
$505$		−	44.2658i		−	1.96980i
$506$	0.118165	−	1.13677i	0.00525305	−	0.0505358i
$507$	5.34587	−	3.08644i	0.237419	−	0.137074i
$508$	2.71435	−	3.81177i	0.120430	−	0.169120i
$509$	18.6640	+	4.52783i	0.827266	+	0.200693i	0.626971	−	0.779043i	$-0.284295\pi$
$509$	18.6640	+	4.52783i	0.827266	+	0.200693i	0.200296	+	0.979735i	$0.435810\pi$
$510$	−12.3841	−	10.7309i	−0.548377	−	0.475171i
$511$	−11.0773	−	6.32021i	−0.490031	−	0.279590i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	1.94376	−	4.85527i	0.0858190	−	0.214366i
$514$	−17.5851	+	4.26609i	−0.775644	+	0.188169i
$515$	−20.7526	−	10.6987i	−0.914469	−	0.471442i
$516$	−5.95558	−	4.68352i	−0.262180	−	0.206181i
$517$	1.08499	−	2.37580i	0.0477178	−	0.104487i
$518$	2.31340	−	5.86531i	0.101645	−	0.257707i
$519$	1.59214	−	11.0735i	0.0698870	−	0.486075i
$520$	6.20505	−	0.295583i	0.272110	−	0.0129622i
$521$	4.49515	+	18.5293i	0.196936	+	0.811782i	0.981457	+	0.191680i	$0.0613936\pi$
$521$	4.49515	+	18.5293i	0.196936	+	0.811782i	−0.784521	+	0.620102i	$0.787091\pi$
$522$	−3.75155	+	2.95025i	−0.164201	+	0.129129i
$523$	−26.4473	+	5.09730i	−1.15646	+	0.222889i	−0.731188	−	0.682176i	$-0.761034\pi$
$523$	−26.4473	+	5.09730i	−1.15646	+	0.222889i	−0.425272	+	0.905066i	$0.639822\pi$
$524$	−9.41593	+	14.6515i	−0.411337	+	0.640053i
$525$	1.70992	+	0.236934i	0.0746269	+	0.0103407i
$526$	−2.44165	−	8.31549i	−0.106461	−	0.362572i
$527$	4.94483	−	51.7846i	0.215400	−	2.25577i
$528$	−0.119155	−	0.206383i	−0.00518558	−	0.00898168i
$529$	22.5083	+	4.73046i	0.978621	+	0.205672i
$530$	−20.6415	−	11.9174i	−0.896608	−	0.517657i
$531$	−12.6090	+	5.75833i	−0.547183	+	0.249890i
$532$	−13.6002	−	2.54919i	−0.589642	−	0.110521i
$533$	−8.10396	+	9.35247i	−0.351022	+	0.405101i
$534$	2.37698	+	4.61070i	0.102862	+	0.199524i
$535$	44.6877	+	15.4666i	1.93202	+	0.668678i
$536$	0.128794	+	0.163775i	0.00556305	+	0.00707399i
$537$	−2.58733	−	2.71351i	−0.111652	−	0.117097i
$538$	13.2178	+	20.5672i	0.569858	+	0.886717i
$539$	0.887490	−	1.41251i	0.0382269	−	0.0608410i
$540$	−2.16264	−	0.987645i	−0.0930653	−	0.0425015i
$541$	4.29881	+	6.03683i	0.184820	+	0.259544i	0.896583	−	0.442877i	$-0.146042\pi$
$541$	4.29881	+	6.03683i	0.184820	+	0.259544i	−0.711762	+	0.702420i	$0.752103\pi$
$542$	−7.82974	−	19.5577i	−0.336316	−	0.840077i
$543$	3.61025	−	7.00291i	0.154931	−	0.300523i
$544$	4.98823	−	4.75627i	0.213869	−	0.203923i
$545$	3.58007	−	0.514736i	0.153353	−	0.0220489i
$546$	−1.66413	−	6.70973i	−0.0712180	−	0.287150i
$547$	20.0894	+	12.9107i	0.858960	+	0.552020i	0.894357	−	0.447353i	$-0.147633\pi$
$547$	20.0894	+	12.9107i	0.858960	+	0.552020i	−0.0353971	+	0.999373i	$0.511270\pi$
$548$	1.80406	−	0.624392i	0.0770657	−	0.0266727i
$549$	6.34870	+	6.05348i	0.270956	+	0.258356i
$550$	−0.126658	−	0.0901925i	−0.00540070	−	0.00384582i
$551$	12.4802	−	21.6164i	0.531675	−	0.920888i
$552$	4.37897	−	1.95565i	0.186382	−	0.0832381i
$553$	23.5714	+	36.2689i	1.00236	+	1.54231i
$554$	9.28357	+	20.3282i	0.394421	+	0.863662i
$555$	−1.33576	+	5.50606i	−0.0566996	+	0.233719i
$556$	−3.73636	+	19.3861i	−0.158457	+	0.822154i
$557$	17.3976	+	0.828749i	0.737159	+	0.0351152i	0.412804	−	0.910820i	$-0.364550\pi$
$557$	17.3976	+	0.828749i	0.737159	+	0.0351152i	0.324355	+	0.945935i	$0.394853\pi$
$558$	−1.42838	−	7.41113i	−0.0604681	−	0.313738i
$559$	2.81735	+	19.5951i	0.119161	+	0.828785i
$560$	−1.45172	+	6.12044i	−0.0613462	+	0.258636i
$561$	1.38178	−	0.888015i	0.0583387	−	0.0374920i
$562$	3.75540	−	4.77538i	0.158412	−	0.201437i
$563$	24.0165	−	2.29329i	1.01217	−	0.0966508i	0.424231	−	0.905554i	$-0.360544\pi$
$563$	24.0165	−	2.29329i	1.01217	−	0.0966508i	0.587942	+	0.808903i	$0.299938\pi$
$564$	10.9101	−	1.04179i	0.459398	−	0.0438672i
$565$	24.3796	−	31.0012i	1.02566	−	1.30423i
$566$	−19.3866	+	12.4590i	−0.814879	+	0.523691i
$567$	−0.610608	+	2.57433i	−0.0256431	+	0.108112i
$568$	−2.18236	−	15.1786i	−0.0915698	−	0.636882i
$569$	3.05039	+	15.8269i	0.127879	+	0.663499i	0.988129	+	0.153626i	$0.0490952\pi$
$569$	3.05039	+	15.8269i	0.127879	+	0.663499i	−0.860250	+	0.509872i	$0.829693\pi$
$570$	12.4200	+	0.591636i	0.520215	+	0.0247809i
$571$	0.915319	−	4.74912i	0.0383049	−	0.198745i	−0.957735	−	0.287652i	$-0.907125\pi$
$571$	0.915319	−	4.74912i	0.0383049	−	0.198745i	0.996040	+	0.0889073i	$0.0283375\pi$
$572$	−0.146802	+	0.605125i	−0.00613808	+	0.0253015i
$573$	4.67373	+	10.2340i	0.195248	+	0.427533i
$574$	−6.82846	−	10.5068i	−0.285014	−	0.438546i
$575$	2.06886	−	2.34757i	0.0862775	−	0.0979006i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	24.4027	+	17.3771i	1.01590	+	0.723416i	0.961416	−	0.275099i	$-0.0887105\pi$
$577$	24.4027	+	17.3771i	1.01590	+	0.723416i	0.0544799	+	0.998515i	$0.482650\pi$
$578$	22.0771	+	21.0505i	0.918288	+	0.875586i
$579$	−20.3110	+	7.02969i	−0.844095	+	0.292144i
$580$	−9.54562	−	6.13460i	−0.396360	−	0.254725i
$581$	0.274664	+	1.10744i	0.0113950	+	0.0459444i
$582$	−2.81983	+	0.405431i	−0.116886	+	0.0168056i
$583$	1.72908	−	1.64867i	0.0716110	−	0.0682810i
$584$	−2.20882	+	4.28452i	−0.0914017	+	0.177295i
$585$	2.30880	+	5.76710i	0.0954571	+	0.238440i
$586$	13.0666	+	18.3495i	0.539776	+	0.758009i
$587$	−1.71014	−	0.780995i	−0.0705851	−	0.0322351i	0.379810	−	0.925065i	$-0.375989\pi$
$587$	−1.71014	−	0.780995i	−0.0705851	−	0.0322351i	−0.450395	+	0.892830i	$0.648717\pi$
$588$	6.99511	+	0.261574i	0.288474	+	0.0107871i
$589$	21.3406	+	33.2067i	0.879325	+	1.36826i
$590$	−22.7422	−	23.8513i	−0.936281	−	0.981943i
$591$	−4.75757	−	6.04975i	−0.195700	−	0.248853i
$592$	−2.25202	−	0.779431i	−0.0925574	−	0.0320344i
$593$	−3.40344	−	6.60176i	−0.139763	−	0.271102i	0.808557	−	0.588417i	$-0.200249\pi$
$593$	−3.40344	−	6.60176i	−0.139763	−	0.271102i	−0.948320	+	0.317316i	$0.897219\pi$
$594$	0.156060	−	0.180103i	0.00640324	−	0.00738973i
$595$	−42.6125	−	7.98720i	−1.74694	−	0.327443i
$596$	0.872029	−	0.398242i	0.0357197	−	0.0163126i
$597$	−0.773422	−	0.446535i	−0.0316541	−	0.0182755i
$598$	−11.8070	−	4.19749i	−0.482823	−	0.171648i
$599$	4.13547	+	7.16284i	0.168971	+	0.292666i	0.938058	−	0.346478i	$-0.112622\pi$
$599$	4.13547	+	7.16284i	0.168971	+	0.292666i	−0.769088	+	0.639143i	$0.779289\pi$
$600$	0.0620206	−	0.649509i	0.00253198	−	0.0265161i
$601$	−6.06125	−	20.6427i	−0.247244	−	0.842035i	−0.985812	−	0.167856i	$-0.946316\pi$
$601$	−6.06125	−	20.6427i	−0.247244	−	0.842035i	0.738568	−	0.674179i	$-0.235502\pi$
$602$	−19.8560	−	2.75134i	−0.809270	−	0.112136i
$603$	−0.112643	+	0.175276i	−0.00458718	+	0.00713778i
$604$	20.4610	−	3.94354i	0.832547	−	0.160460i
$605$	−20.4510	+	16.0829i	−0.831453	+	0.653862i
$606$	4.38952	+	18.0939i	0.178312	+	0.735013i
$607$	−15.6898	+	0.747399i	−0.636831	+	0.0303360i	−0.363515	−	0.931588i	$-0.618424\pi$
$607$	−15.6898	+	0.747399i	−0.636831	+	0.0303360i	−0.273316	+	0.961924i	$0.588120\pi$
$608$	−0.744293	+	5.17667i	−0.0301851	+	0.209942i
$609$	−4.63308	+	11.7465i	−0.187742	+	0.475993i
$610$	−8.66378	+	18.9710i	−0.350786	+	0.768114i
$611$	−22.5097	−	17.7018i	−0.910646	−	0.716140i
$612$	6.12616	+	3.15826i	0.247636	+	0.127665i
$613$	−11.0874	+	2.68977i	−0.447815	+	0.108639i	−0.453323	−	0.891346i	$-0.649762\pi$
$613$	−11.0874	+	2.68977i	−0.447815	+	0.108639i	0.00550872	+	0.999985i	$0.498247\pi$
$614$	−0.918698	+	2.29480i	−0.0370756	+	0.0926104i
$615$	7.37391	+	8.50994i	0.297345	+	0.343154i
$616$	−0.547643	−	0.312460i	−0.0220652	−	0.0125894i
$617$	21.4578	+	18.5933i	0.863858	+	0.748537i	0.969298	−	0.245888i	$-0.0790796\pi$
$617$	21.4578	+	18.5933i	0.863858	+	0.748537i	−0.105440	+	0.994426i	$0.533625\pi$
$618$	9.54365	+	2.31526i	0.383902	+	0.0931336i
$619$	−6.83850	+	9.60334i	−0.274863	+	0.385991i	−0.928814	−	0.370546i	$-0.879171\pi$
$619$	−6.83850	+	9.60334i	−0.274863	+	0.385991i	0.653951	+	0.756536i	$0.273110\pi$
$620$	15.5401	−	8.97209i	0.624106	−	0.360328i
$621$	3.28032	+	3.49850i	0.131635	+	0.140390i
$622$		−	27.7366i		−	1.11214i
$623$	11.5835	+	7.36087i	0.464083	+	0.294907i
$624$	−2.50704	+	0.736132i	−0.100362	+	0.0294689i
$625$	9.10446	+	26.3056i	0.364179	+	1.05222i
$626$	0.535270	−	11.2367i	0.0213937	−	0.449108i
$627$	−0.407639	+	1.17780i	−0.0162795	+	0.0470366i
$628$	5.25628	+	2.10430i	0.209749	+	0.0839707i
$629$	4.62748	−	15.7597i	0.184510	−	0.628382i
$630$	−6.25863	+	0.629927i	−0.249350	+	0.0250969i
$631$	−39.4752	−	5.67568i	−1.57148	−	0.225945i	−0.699194	−	0.714932i	$-0.746457\pi$
$631$	−39.4752	−	5.67568i	−1.57148	−	0.225945i	−0.872291	+	0.488987i	$0.837367\pi$
$632$	13.3176	−	9.48340i	0.529744	−	0.377229i
$633$	1.98529	+	20.7908i	0.0789080	+	0.826362i
$634$	12.3340	−	4.93780i	0.489847	−	0.196105i
$635$	0.529365	+	11.1127i	0.0210072	+	0.440996i
$636$	9.61907	+	2.82441i	0.381421	+	0.111995i
$637$	−12.7563	−	13.1075i	−0.505423	−	0.519337i
$638$	0.859568	−	0.744820i	0.0340306	−	0.0294877i
$639$	13.6301	−	7.02678i	0.539197	−	0.277975i
$640$	2.33453	+	0.449943i	0.0922803	+	0.0177856i
$641$	2.37384	−	2.48961i	0.0937609	−	0.0983336i	−0.675182	−	0.737652i	$-0.735935\pi$
$641$	2.37384	−	2.48961i	0.0937609	−	0.0983336i	0.768943	+	0.639318i	$0.220783\pi$
$642$	−19.8000	−	1.89067i	−0.781445	−	0.0746189i
$643$	30.4109			1.19929			0.599645	−	0.800266i	$-0.295308\pi$
$643$	30.4109			1.19929			0.599645	+	0.800266i	$0.295308\pi$
$644$	7.39379	−	10.3117i	0.291356	−	0.406339i
$645$	18.0132			0.709270
$646$	−35.8831	−	3.42642i	−1.41180	−	0.134811i
$647$	5.21720	−	5.47164i	0.205109	−	0.215112i	−0.613143	−	0.789972i	$-0.710095\pi$
$647$	5.21720	−	5.47164i	0.205109	−	0.215112i	0.818252	+	0.574860i	$0.194943\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	2.93616	−	1.51370i	0.115254	−	0.0594177i
$650$	−1.28841	+	1.11641i	−0.0505354	+	0.0437892i
$651$	−13.1538	−	15.0244i	−0.515538	−	0.588854i
$652$	−9.30709	−	2.73281i	−0.364494	−	0.107025i
$653$	−0.564653	−	11.8535i	−0.0220966	−	0.463864i	−0.982616	−	0.185651i	$-0.940561\pi$
$653$	−0.564653	−	11.8535i	−0.0220966	−	0.463864i	0.960519	−	0.278213i	$-0.0897423\pi$
$654$	−1.41233	+	0.565411i	−0.0552264	+	0.0221093i
$655$	−3.93598	−	41.2195i	−0.153792	−	1.61058i
$656$	−3.85799	+	2.74726i	−0.150629	+	0.107263i
$657$	−4.77131	−	0.686010i	−0.186146	−	0.0267638i
$658$	23.5337	−	16.9402i	0.917440	−	0.660400i
$659$	13.1065	−	44.6365i	0.510555	−	1.73879i	−0.150651	−	0.988587i	$-0.548137\pi$
$659$	13.1065	−	44.6365i	0.510555	−	1.73879i	0.661206	−	0.750204i	$-0.270045\pi$
$660$	0.525997	+	0.210577i	0.0204744	+	0.00819671i
$661$	−7.80880	+	22.5620i	−0.303727	+	0.877562i	0.685094	+	0.728455i	$0.259761\pi$
$661$	−7.80880	+	22.5620i	−0.303727	+	0.877562i	−0.988821	+	0.149107i	$0.952360\pi$
$662$	0.960217	−	20.1574i	0.0373199	−	0.783441i
$663$	−5.89012	−	17.0184i	−0.228753	−	0.660939i
$664$	0.413786	−	0.121499i	0.0160580	−	0.00471506i
$665$	29.1629	−	15.2237i	1.13089	−	0.590351i
$666$		−	2.38309i		−	0.0923427i
$667$	13.1202	+	18.7552i	0.508015	+	0.726203i
$668$	9.72132	−	5.61261i	0.376129	−	0.217158i
$669$	−8.94676	+	12.5640i	−0.345902	+	0.485751i
$670$	−0.481389	−	0.116784i	−0.0185977	−	0.00451175i
$671$	−1.57989	−	1.36899i	−0.0609911	−	0.0528491i
$672$	−0.0135242	−	2.64572i	−0.000521709	−	0.102061i
$673$	0.411802	+	0.475245i	0.0158738	+	0.0183194i	0.763631	−	0.645653i	$-0.223415\pi$
$673$	0.411802	+	0.475245i	0.0158738	+	0.0183194i	−0.747757	+	0.663972i	$0.768869\pi$
$674$	0.240007	−	0.599508i	0.00924472	−	0.0230922i
$675$	0.634071	−	0.153824i	0.0244054	−	0.00592069i
$676$	−5.48668	−	2.82858i	−0.211026	−	0.108791i
$677$	−31.4362	−	24.7217i	−1.20819	−	0.950132i	−0.208580	−	0.978005i	$-0.566884\pi$
$677$	−31.4362	−	24.7217i	−1.20819	−	0.950132i	−0.999611	+	0.0278735i	$0.991126\pi$
$678$	−6.89111	+	15.0894i	−0.264652	+	0.579506i
$679$	−5.90082	+	4.68947i	−0.226453	+	0.179965i
$680$	−2.33204	+	16.2197i	−0.0894297	+	0.621997i
$681$	3.61017	−	0.171974i	0.138342	−	0.00659004i
$682$	0.424050	+	1.74796i	0.0162377	+	0.0669327i
$683$	32.1094	−	25.2511i	1.22863	−	0.966207i	0.228658	−	0.973507i	$-0.426566\pi$
$683$	32.1094	−	25.2511i	1.22863	−	0.966207i	0.999973	+	0.00730026i	$0.00232377\pi$
$684$	−5.13539	+	0.989765i	−0.196357	+	0.0378446i
$685$	−2.45384	+	3.81825i	−0.0937565	+	0.145888i
$686$	16.3294	−	8.73790i	0.623459	−	0.333615i
$687$	−5.61801	−	19.1332i	−0.214340	−	0.729977i
$688$	−0.720198	+	7.54226i	−0.0274573	+	0.287546i
$689$	−13.0972	−	22.6851i	−0.498965	−	0.864233i
$690$	−5.30942	+	10.0904i	−0.202126	+	0.384136i
$691$	−36.9300	−	21.3215i	−1.40488	−	0.811110i	−0.409994	−	0.912088i	$-0.634469\pi$
$691$	−36.9300	−	21.3215i	−1.40488	−	0.811110i	−0.994889	+	0.100978i	$0.967803\pi$
$692$	−10.1764	+	4.64742i	−0.386850	+	0.176668i
$693$	0.116159	−	0.619719i	0.00441251	−	0.0235412i
$694$	−13.1481	+	15.1738i	−0.499096	+	0.575988i
$695$	−21.5085	−	41.7206i	−0.815863	−	1.58255i
$696$	4.51015	+	1.56098i	0.170957	+	0.0591687i
$697$	−20.1789	−	25.6595i	−0.764330	−	0.971925i
$698$	9.43698	+	9.89722i	0.357195	+	0.374615i
$699$	0.869055	+	1.35228i	0.0328707	+	0.0511478i
$700$	−0.725130	−	1.56657i	−0.0274073	−	0.0592108i
$701$	−13.3218	−	6.08387i	−0.503158	−	0.229785i	0.147632	−	0.989042i	$-0.452835\pi$
$701$	−13.3218	−	6.08387i	−0.503158	−	0.229785i	−0.650790	+	0.759258i	$0.725562\pi$
$702$	−1.51562	−	2.12839i	−0.0572033	−	0.0803307i
$703$	4.63214	+	11.5705i	0.174705	+	0.436391i
$704$	−0.109200	+	0.211819i	−0.00411564	+	0.00798324i
$705$	−18.8581	+	17.9811i	−0.710236	+	0.677209i
$706$	−5.13738	+	0.738644i	−0.193348	+	0.0277992i
$707$	34.1754	+	35.4772i	1.28530	+	1.33426i
$708$	11.6611	+	7.49416i	0.438253	+	0.281648i
$709$	−3.83991	+	1.32901i	−0.144211	+	0.0499118i	−0.398220	−	0.917290i	$-0.630372\pi$
$709$	−3.83991	+	1.32901i	−0.144211	+	0.0499118i	0.254009	+	0.967202i	$0.418251\pi$
$710$	26.3860	+	25.1590i	0.990250	+	0.944202i
$711$	13.3176	+	9.48340i	0.499448	+	0.355655i
$712$	2.59367	−	4.49237i	0.0972020	−	0.168359i
$713$	−35.8701	+	4.85107i	−1.34335	+	0.181674i
$714$	18.2101	−	0.960774i	0.681496	−	0.0359561i
$715$	−0.614984	−	1.34663i	−0.0229991	−	0.0503610i
$716$	−0.883937	+	3.64364i	−0.0330343	+	0.136169i
$717$	−0.227585	+	1.18082i	−0.00849932	+	0.0440986i
$718$	−1.67542	−	0.0798100i	−0.0625260	−	0.00297848i
$719$	−2.35132	−	12.1998i	−0.0876893	−	0.454975i	−0.999058	−	0.0433852i	$-0.986186\pi$
$719$	−2.35132	−	12.1998i	−0.0876893	−	0.454975i	0.911369	−	0.411590i	$-0.135026\pi$
$720$	0.338352	+	2.35329i	0.0126096	+	0.0877020i
$721$	24.8923	−	7.44746i	0.927038	−	0.277358i
$722$	7.02604	−	4.51536i	0.261482	−	0.168044i
$723$	−8.39268	+	10.6722i	−0.312127	+	0.396902i
$724$	−7.84307	+	0.748922i	−0.291485	+	0.0278335i
$725$	3.09987	−	0.296002i	0.115126	−	0.0109932i
$726$	6.76464	−	8.60194i	0.251059	−	0.319248i
$727$	33.7883	−	21.7144i	1.25314	−	0.805344i	0.265810	−	0.964025i	$-0.414361\pi$
$727$	33.7883	−	21.7144i	1.25314	−	0.805344i	0.987330	+	0.158681i	$0.0507243\pi$
$728$	−4.74489	+	5.02751i	−0.175857	+	0.186332i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−2.16889	−	11.2533i	−0.0802743	−	0.416503i
$731$	−52.1612	−	2.48474i	−1.92925	−	0.0919016i
$732$	1.66014	−	8.61363i	0.0613606	−	0.318369i
$733$	−7.33417	+	30.2319i	−0.270894	+	1.11664i	0.659975	+	0.751287i	$0.270567\pi$
$733$	−7.33417	+	30.2319i	−0.270894	+	1.11664i	−0.930869	+	0.365352i	$0.880948\pi$
$734$	4.75832	+	10.4193i	0.175633	+	0.384582i
$735$	−13.4571	+	9.79165i	−0.496374	+	0.361170i
$736$	−4.01265	−	2.62652i	−0.147908	−	0.0968149i
$737$	0.0248261	−	0.0430001i	0.000914483	−	0.00158393i
$738$	−3.85799	−	2.74726i	−0.142015	−	0.101128i
$739$	−30.2338	−	28.8279i	−1.11217	−	1.06045i	−0.997752	−	0.0670192i	$-0.978651\pi$
$739$	−30.2338	−	28.8279i	−1.11217	−	1.06045i	−0.114418	−	0.993433i	$-0.536500\pi$
$740$	5.35415	−	1.85309i	0.196823	−	0.0681210i
$741$	11.4958	+	7.38790i	0.422309	+	0.271401i
$742$	25.7441	−	6.38497i	0.945095	−	0.234399i
$743$	−25.5126	+	3.66815i	−0.935965	+	0.134571i	−0.593386	−	0.804918i	$-0.702209\pi$
$743$	−25.5126	+	3.66815i	−0.935965	+	0.134571i	−0.342578	+	0.939489i	$0.611300\pi$
$744$	−5.46240	+	5.20839i	−0.200261	+	0.190949i
$745$	−1.04439	+	2.02584i	−0.0382636	+	0.0742211i
$746$	2.36944	+	5.91857i	0.0867514	+	0.216694i
$747$	0.250153	+	0.351290i	0.00915260	+	0.0128530i
$748$	−1.49409	−	0.682328i	−0.0546294	−	0.0249484i
$749$	−47.7563	+	22.1053i	−1.74498	+	0.807710i
$750$	−5.58819	−	8.69539i	−0.204052	−	0.317511i
$751$	7.43990	+	7.80275i	0.271486	+	0.284726i	0.845337	−	0.534233i	$-0.179400\pi$
$751$	7.43990	+	7.80275i	0.271486	+	0.284726i	−0.573851	+	0.818960i	$0.694551\pi$
$752$	−6.77485	−	8.61492i	−0.247053	−	0.314154i
$753$	7.04832	+	2.43945i	0.256855	+	0.0888984i
$754$	−5.71422	−	11.0840i	−0.208100	−	0.403657i
$755$	−32.4426	+	37.4407i	−1.18071	+	1.36261i
$756$	2.49578	−	0.878110i	0.0907707	−	0.0319365i
$757$	46.8036	−	21.3745i	1.70111	−	0.776869i	0.703285	−	0.710908i	$-0.251716\pi$
$757$	46.8036	−	21.3745i	1.70111	−	0.776869i	0.997822	−	0.0659611i	$-0.0210113\pi$
$758$	1.90223	+	1.09825i	0.0690922	+	0.0398904i
$759$	−0.820520	−	0.795591i	−0.0297830	−	0.0288781i
$760$	−6.21702	−	10.7682i	−0.225515	−	0.390604i
$761$	1.82437	−	19.1056i	0.0661333	−	0.692579i	−0.900233	−	0.435409i	$-0.856604\pi$
$761$	1.82437	−	19.1056i	0.0661333	−	0.692579i	0.966366	−	0.257170i	$-0.0827901\pi$
$762$	−1.31835	−	4.48990i	−0.0477589	−	0.162652i
$763$	−2.47188	+	3.17653i	−0.0894879	+	0.114998i
$764$	6.08261	−	9.46473i	0.220061	−	0.342422i
$765$	−16.0904	+	3.10117i	−0.581749	+	0.112123i
$766$	−11.3891	+	8.95646i	−0.411503	+	0.323610i
$767$	−8.53889	−	35.1978i	−0.308321	−	1.27092i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	−1.39012	+	9.66850i	−0.0501290	+	0.348655i	0.949285	+	0.314418i	$0.101809\pi$
$769$	−1.39012	+	9.66850i	−0.0501290	+	0.348655i	−0.999414	+	0.0342373i	$0.989100\pi$
$770$	1.48267	−	0.220917i	0.0534316	−	0.00796129i
$771$	−7.51700	+	16.4599i	−0.270718	+	0.592790i
$772$	16.8947	+	13.2861i	0.608053	+	0.478178i
$773$	−16.1506	−	8.32619i	−0.580895	−	0.299472i	0.142624	−	0.989777i	$-0.454446\pi$
$773$	−16.1506	−	8.32619i	−0.580895	−	0.299472i	−0.723519	+	0.690305i	$0.757476\pi$
$774$	−7.36299	+	1.78624i	−0.264657	+	0.0642052i
$775$	−1.83025	+	4.57173i	−0.0657444	+	0.164221i
$776$	1.86559	+	2.15300i	0.0669707	+	0.0772883i
$777$	−3.18040	−	5.44415i	−0.114096	−	0.195308i
$778$	10.8061	+	9.36351i	0.387416	+	0.335698i
$779$	24.0716	+	5.83971i	0.862456	+	0.209229i
$780$	3.60336	−	5.06022i	0.129021	−	0.181185i
$781$	−3.16483	+	1.82722i	−0.113247	+	0.0653830i
$782$	16.7664	−	28.4867i	0.599567	−	1.01868i
$783$			4.77264i			0.170560i
$784$	−3.56179	−	6.02608i	−0.127207	−	0.215217i
$785$	−12.9157	+	3.79240i	−0.460983	+	0.135357i
$786$	5.69630	+	16.4584i	0.203180	+	0.587050i
$787$	0.586396	−	12.3100i	0.0209028	−	0.438803i	−0.964022	−	0.265821i	$-0.914357\pi$
$787$	0.586396	−	12.3100i	0.0209028	−	0.438803i	0.984925	−	0.172982i	$-0.0553401\pi$
$788$	−2.51723	+	7.27307i	−0.0896727	+	0.259092i
$789$	−8.04574	−	3.22103i	−0.286436	−	0.114672i
$790$	−10.9509	+	37.2953i	−0.389615	+	1.32691i
$791$	4.39520	+	43.6684i	0.156275	+	1.55267i
$792$	−0.235885	−	0.0339152i	−0.00838182	−	0.00120512i
$793$	−18.6705	+	13.2952i	−0.663010	+	0.472127i
$794$	−0.261175	−	2.73514i	−0.00926874	−	0.0970666i
$795$	−22.1274	+	8.85847i	−0.784778	+	0.314178i
$796$	0.0424940	+	0.892059i	0.00150616	+	0.0316182i
$797$	0.111803	+	0.0328283i	0.00396026	+	0.00116284i	0.283712	−	0.958910i	$-0.408434\pi$
$797$	0.111803	+	0.0328283i	0.00396026	+	0.00116284i	−0.279752	+	0.960072i	$0.590252\pi$
$798$	−10.4109	+	9.11466i	−0.368541	+	0.322655i
$799$	57.0880	−	49.4670i	2.01963	−	1.75002i
$800$	−0.579932	+	0.298976i	−0.0205037	+	0.0105704i
$801$	5.09360	+	0.981712i	0.179974	+	0.0346871i
$802$	1.70074	−	1.78369i	0.0600552	−	0.0629841i
$803$	1.14355	+	0.109195i	0.0403548	+	0.00385342i
$804$	0.208351			0.00734797
$805$	1.33705	+	30.1373i	0.0471248	+	1.06220i
$806$	19.7207			0.694634
$807$	24.3376	+	2.32396i	0.856725	+	0.0818073i
$808$	12.8484	−	13.4750i	0.452004	−	0.474048i
$809$	31.3420	+	6.04068i	1.10193	+	0.212379i	0.707615	−	0.706598i	$-0.249771\pi$
$809$	31.3420	+	6.04068i	1.10193	+	0.212379i	0.394311	+	0.918977i	$0.370983\pi$
$810$	−2.11320	+	1.08943i	−0.0742502	+	0.0382786i
$811$	−27.4320	+	23.7700i	−0.963268	+	0.834676i	−0.986284	−	0.165059i	$-0.947219\pi$
$811$	−27.4320	+	23.7700i	−0.963268	+	0.834676i	0.0230157	+	0.999735i	$0.492673\pi$
$812$	12.3866	−	2.45306i	0.434686	−	0.0860857i
$813$	−20.2135	−	5.93521i	−0.708917	−	0.208157i
$814$	0.0270225	+	0.567272i	0.000947139	+	0.0198829i
$815$	21.4097	−	8.57116i	0.749950	−	0.300235i
$816$	−0.655159	−	6.86114i	−0.0229352	−	0.240188i
$817$	32.2773	−	22.9846i	1.12924	−	0.804129i
$818$	2.24071	+	0.322166i	0.0783447	+	0.0112643i
$819$	−6.30290	−	2.83959i	−0.220241	−	0.0992233i
$820$	3.17238	−	10.8041i	0.110784	−	0.377297i
$821$	0.386440	+	0.154707i	0.0134868	+	0.00539932i	0.378396	−	0.925644i	$-0.376476\pi$
$821$	0.386440	+	0.154707i	0.0134868	+	0.00539932i	−0.364909	+	0.931043i	$0.618900\pi$
$822$	0.624392	−	1.80406i	0.0217782	−	0.0629238i
$823$	0.200595	−	4.21100i	0.00699229	−	0.146786i	−0.992671	−	0.120846i	$-0.961439\pi$
$823$	0.200595	−	4.21100i	0.00699229	−	0.146786i	0.999664	−	0.0259398i	$-0.00825782\pi$
$824$	−3.21196	−	9.28036i	−0.111894	−	0.323297i
$825$	−0.149191	+	0.0438063i	−0.00519415	+	0.00152514i
$826$	36.6413	+	1.55776i	1.27491	+	0.0542014i
$827$			12.2614i			0.426369i	0.977012	+	0.213185i	$0.0683835\pi$
$827$			12.2614i			0.426369i	−0.977012	+	0.213185i	$0.931616\pi$
$828$	1.16966	−	4.65101i	0.0406483	−	0.161634i
$829$	20.9668	−	12.1052i	0.728207	−	0.420431i	−0.0895586	−	0.995982i	$-0.528546\pi$
$829$	20.9668	−	12.1052i	0.728207	−	0.420431i	0.817766	+	0.575551i	$0.195212\pi$
$830$	−0.594735	+	0.835189i	−0.0206436	+	0.0289898i
$831$	21.7177	+	5.26867i	0.753380	+	0.182768i
$832$	1.97468	+	1.71107i	0.0684597	+	0.0593207i
$833$	40.3187	−	26.4976i	1.39696	−	0.918086i
$834$	12.9288	+	14.9207i	0.447689	+	0.516660i
$835$	−9.91887	+	24.7761i	−0.343257	+	0.857414i
$836$	1.21121	−	0.293836i	0.0418906	−	0.0101625i
$837$	−6.70851	−	3.45848i	−0.231880	−	0.119542i
$838$	−1.25119	−	0.983948i	−0.0432217	−	0.0339899i
$839$	−5.66923	+	12.4139i	−0.195723	+	0.428575i	−0.981893	−	0.189436i	$-0.939334\pi$
$839$	−5.66923	+	12.4139i	−0.195723	+	0.428575i	0.786170	+	0.618011i	$0.212061\pi$
$840$	3.91360	+	4.92453i	0.135032	+	0.169912i
$841$	0.885475	−	6.15861i	0.0305336	−	0.212366i
$842$	22.0351	−	1.04966i	0.759380	−	0.0361737i
$843$	−1.43227	−	5.90389i	−0.0493299	−	0.203341i
$844$	16.4170	−	12.9105i	0.565098	−	0.444398i
$845$	14.4108	−	2.77745i	0.495745	−	0.0955470i
$846$	5.92527	−	9.21990i	0.203715	−	0.316987i
$847$	3.97390	−	28.6790i	0.136545	−	0.985422i
$848$	−2.82441	−	9.61907i	−0.0969907	−	0.330320i
$849$	−2.19056	+	22.9405i	−0.0751797	+	0.787317i
$850$	−2.24850	−	3.89452i	−0.0771230	−	0.133581i
$851$	−11.4110	−	0.639402i	−0.391163	−	0.0219184i
$852$	−13.2803	−	7.66737i	−0.454974	−	0.262680i
$853$	18.6066	−	8.49733i	0.637076	−	0.290943i	−0.0705732	−	0.997507i	$-0.522483\pi$
$853$	18.6066	−	8.49733i	0.637076	−	0.290943i	0.707650	+	0.706564i	$0.249756\pi$
$854$	−7.70291	−	21.8934i	−0.263588	−	0.749176i
$855$	8.14257	−	9.39702i	0.278470	−	0.321371i
$856$	9.11417	+	17.6790i	0.311516	+	0.604256i
$857$	42.3548	+	14.6591i	1.44681	+	0.500746i	0.933850	−	0.357666i	$-0.116427\pi$
$857$	42.3548	+	14.6591i	1.44681	+	0.500746i	0.512961	+	0.858412i	$0.328548\pi$
$858$	0.384913	+	0.489457i	0.0131407	+	0.0167098i
$859$	9.48293	+	9.94541i	0.323553	+	0.339333i	0.865342	−	0.501182i	$-0.167101\pi$
$859$	9.48293	+	9.94541i	0.323553	+	0.339333i	−0.541789	+	0.840515i	$0.682253\pi$
$860$	−9.73868	−	15.1537i	−0.332086	−	0.516736i
$861$	−12.4800	−	1.12735i	−0.425317	−	0.0384200i
$862$	−8.24495	−	3.76534i	−0.280824	−	0.128248i
$863$	16.8669	+	23.6862i	0.574154	+	0.806287i	0.994897	−	0.100893i	$-0.0321699\pi$
$863$	16.8669	+	23.6862i	0.574154	+	0.806287i	−0.420743	+	0.907180i	$0.638231\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	12.1879	−	23.6412i	0.414401	−	0.803826i
$866$	11.2216	−	10.6998i	0.381325	−	0.363593i
$867$	30.1940	−	4.34124i	1.02544	−	0.147436i
$868$	−5.52787	+	19.1885i	−0.187628	+	0.651300i
$869$	−3.27766	−	2.10643i	−0.111187	−	0.0714556i
$870$	−10.7228	+	3.71121i	−0.363538	+	0.125822i
$871$	−0.393997	−	0.375675i	−0.0133501	−	0.0127293i
$872$	1.23922	+	0.882442i	0.0419651	+	0.0298832i
$873$	−1.42441	+	2.46716i	−0.0482091	+	0.0835007i
$874$	3.36145	+	24.8555i	0.113703	+	0.840748i
$875$	−24.3708	−	12.4067i	−0.823884	−	0.419425i
$876$	2.00245	+	4.38476i	0.0676566	+	0.148147i
$877$	9.27038	−	38.2130i	0.313038	−	1.29036i	−0.570226	−	0.821488i	$-0.693145\pi$
$877$	9.27038	−	38.2130i	0.313038	−	1.29036i	0.883265	−	0.468874i	$-0.155340\pi$
$878$	3.92359	−	20.3575i	0.132415	−	0.687032i
$879$	22.5009	+	1.07185i	0.758936	+	0.0361526i
$880$	−0.107226	−	0.556343i	−0.00361460	−	0.0187543i
$881$	−1.09223	−	7.59663i	−0.0367982	−	0.255937i	0.963115	−	0.269089i	$-0.0867226\pi$
$881$	−1.09223	−	7.59663i	−0.0367982	−	0.255937i	−0.999914	+	0.0131520i	$0.995813\pi$
$882$	4.52970	−	5.33683i	0.152523	−	0.179701i
$883$	6.73482	−	4.32821i	0.226645	−	0.145656i	−0.422391	−	0.906414i	$-0.638809\pi$
$883$	6.73482	−	4.32821i	0.226645	−	0.145656i	0.649036	+	0.760758i	$0.275173\pi$
$884$	−11.1323	+	14.1559i	−0.374421	+	0.476115i
$885$	−32.8067	+	3.13266i	−1.10278	+	0.105303i
$886$	−10.7705	+	1.02846i	−0.361842	+	0.0345517i
$887$	20.4882	−	26.0529i	0.687928	−	0.874771i	−0.309162	−	0.951009i	$-0.600048\pi$
$887$	20.4882	−	26.0529i	0.687928	−	0.874771i	0.997090	+	0.0762380i	$0.0242909\pi$
$888$	−2.00478	+	1.28839i	−0.0672760	+	0.0432357i
$889$	−9.00386	−	8.49772i	−0.301980	−	0.285004i
$890$	1.75515	+	12.2073i	0.0588328	+	0.409191i
$891$	−0.0451006	−	0.234004i	−0.00151093	−	0.00783944i
$892$	15.4065	+	0.733901i	0.515847	+	0.0245728i
$893$	−10.8476	+	56.2824i	−0.362999	+	1.88342i
$894$	0.226013	−	0.931638i	0.00755900	−	0.0311586i
$895$	−3.70300	−	8.10845i	−0.123778	−	0.271035i
$896$	−2.21841	+	1.44176i	−0.0741118	+	0.0481658i
$897$	−10.5980	+	6.68619i	−0.353858	+	0.223246i
$898$	12.1807	−	21.0976i	0.406475	−	0.704035i
$899$	−29.3423	−	20.8946i	−0.978621	−	0.696873i
$900$	−0.472210	−	0.450251i	−0.0157403	−	0.0150084i
$901$	65.2966	−	22.5994i	2.17535	−	0.752894i
$902$	0.949513	+	0.610215i	0.0316153	+	0.0203179i
$903$	−14.4369	+	13.9071i	−0.480429	+	0.462799i
$904$	16.4197	−	2.36079i	0.546109	−	0.0785187i
$905$	13.5567	−	12.9263i	0.450641	−	0.429685i
$906$	9.54833	−	18.5212i	0.317222	−	0.615325i
$907$	−6.65098	−	16.6133i	−0.220842	−	0.551637i	0.776028	−	0.630699i	$-0.217232\pi$
$907$	−6.65098	−	16.6133i	−0.220842	−	0.551637i	−0.996870	+	0.0790620i	$0.974808\pi$
$908$	−2.09648	−	2.94409i	−0.0695741	−	0.0977032i
$909$	16.9362	+	7.73448i	0.561737	+	0.256537i
$910$	1.47865	−	16.3690i	0.0490169	−	0.542627i
$911$	8.17897	+	12.7267i	0.270982	+	0.421655i	0.949898	−	0.312560i	$-0.101187\pi$
$911$	8.17897	+	12.7267i	0.270982	+	0.421655i	−0.678916	+	0.734216i	$0.737550\pi$
$912$	3.60905	+	3.78506i	0.119507	+	0.125336i
$913$	−0.0635299	−	0.0807849i	−0.00210253	−	0.00267359i
$914$	3.47825	+	1.20383i	0.115050	+	0.0398193i
$915$	9.55664	+	18.5373i	0.315933	+	0.612824i
$916$	−13.0585	+	15.0704i	−0.431466	+	0.497938i
$917$	34.9780	+	29.9970i	1.15508	+	0.990587i
$918$	6.26950	−	2.86319i	0.206924	−	0.0944992i
$919$	−38.8382	−	22.4233i	−1.28115	−	0.739675i	−0.304095	−	0.952642i	$-0.598354\pi$
$919$	−38.8382	−	22.4233i	−1.28115	−	0.739675i	−0.977059	+	0.212967i	$0.931687\pi$
$920$	11.3591	−	0.988731i	0.374498	−	0.0325975i
$921$	1.23593	+	2.14069i	0.0407253	+	0.0705383i
$922$	−3.20241	+	33.5371i	−0.105466	+	1.10449i
$923$	11.2884	+	38.4447i	0.371562	+	1.26542i
$924$	−0.584141	+	0.237326i	−0.0192168	+	0.00780747i
$925$	−0.840630	+	1.30805i	−0.0276397	+	0.0430083i
$926$	18.5520	−	3.57560i	0.609656	−	0.117502i
$927$	7.71941	−	6.07061i	0.253539	−	0.199385i
$928$	−1.12519	−	4.63810i	−0.0369362	−	0.152253i
$929$	45.4989	−	2.16738i	1.49277	−	0.0711095i	0.714765	−	0.699365i	$-0.246534\pi$
$929$	45.4989	−	2.16738i	1.49277	−	0.0711095i	0.778007	+	0.628256i	$0.216231\pi$
$930$	2.55372	−	17.7615i	0.0837399	−	0.582424i
$931$	−11.6194	+	34.7164i	−0.380811	+	1.13779i
$932$	0.667760	−	1.46219i	0.0218732	−	0.0478957i
$933$	−21.8024	−	17.1456i	−0.713779	−	0.561322i
$934$	−10.4482	−	5.38641i	−0.341875	−	0.176249i
$935$	3.79500	−	0.920658i	0.124110	−	0.0301087i
$936$	−0.971108	+	2.42571i	−0.0317417	+	0.0792868i
$937$	−32.9657	−	38.0445i	−1.07694	−	1.24286i	−0.968568	−	0.248749i	$-0.919981\pi$
$937$	−32.9657	−	38.0445i	−1.07694	−	1.24286i	−0.108375	−	0.994110i	$-0.534565\pi$
$938$	0.475977	−	0.278059i	0.0155412	−	0.00907894i
$939$	−8.50175	−	7.36681i	−0.277444	−	0.240407i
$940$	25.3221	+	6.14308i	0.825917	+	0.200365i
$941$	−6.18701	+	8.68844i	−0.201691	+	0.283235i	−0.903016	−	0.429606i	$-0.858652\pi$
$941$	−6.18701	+	8.68844i	−0.201691	+	0.283235i	0.701326	+	0.712841i	$0.252592\pi$
$942$	4.90331	−	2.83093i	0.159758	−	0.0922366i
$943$	−14.1899	+	17.7362i	−0.462087	+	0.577570i
$944$		−	13.8616i		−	0.451158i
$945$	−3.37367	+	5.30901i	−0.109746	+	0.172702i
$946$	1.73244	−	0.508690i	0.0563265	−	0.0165389i
$947$	−6.11020	−	17.6543i	−0.198555	−	0.573686i	0.801138	−	0.598480i	$-0.204228\pi$
$947$	−6.11020	−	17.6543i	−0.198555	−	0.573686i	−0.999693	+	0.0247936i	$0.992107\pi$
$948$	0.777921	−	16.3306i	0.0252657	−	0.530392i
$949$	4.11943	−	11.9023i	0.133722	−	0.386365i
$950$	3.16789	+	1.26823i	0.102780	+	0.0411468i
$951$	3.74302	−	12.7476i	0.121376	−	0.413368i
$952$	−10.6534	−	14.7999i	−0.345278	−	0.479667i
$953$	−31.4527	−	4.52222i	−1.01885	−	0.146489i	−0.387407	−	0.921909i	$-0.626629\pi$
$953$	−31.4527	−	4.52222i	−1.01885	−	0.146489i	−0.631446	+	0.775420i	$0.717538\pi$
$954$	8.16625	−	5.81516i	0.264392	−	0.188273i
$955$	2.54261	+	26.6274i	0.0822769	+	0.861643i
$956$	1.11641	−	0.446945i	0.0361074	−	0.0144552i
$957$	−0.0541183	−	1.13608i	−0.00174940	−	0.0367244i
$958$	37.8836	+	11.1236i	1.22396	+	0.359389i
$959$	−0.981227	−	4.95466i	−0.0316855	−	0.159994i
$960$	1.79679	−	1.55693i	0.0579911	−	0.0502496i
$961$	23.0788	−	11.8979i	0.744476	−	0.383804i
$962$	6.11418	+	1.17841i	0.197129	+	0.0379935i
$963$	−13.7257	+	14.3951i	−0.442306	+	0.463877i
$964$	13.5154	+	1.29057i	0.435302	+	0.0415663i
$965$	−51.0995			−1.64495
$966$	−3.53503	−	12.1862i	−0.113738	−	0.392085i
$967$	25.9224			0.833609			0.416805	−	0.908996i	$-0.363150\pi$
$967$	25.9224			0.833609			0.416805	+	0.908996i	$0.363150\pi$
$968$	−10.8937	−	1.04022i	−0.350135	−	0.0334339i
$969$	−24.8748	+	26.0879i	−0.799094	+	0.838066i
$970$	−6.65067	−	1.28181i	−0.213540	−	0.0411565i
$971$	44.3450	−	22.8614i	1.42310	−	0.733658i	0.436944	−	0.899489i	$-0.356061\pi$
$971$	44.3450	−	22.8614i	1.42310	−	0.733658i	0.986154	+	0.165831i	$0.0530306\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	49.4486	+	16.8318i	1.58525	+	0.539602i
$974$	20.7151	+	6.08250i	0.663755	+	0.194896i
$975$	0.0811179	+	1.70287i	0.00259785	+	0.0545356i
$976$	−8.14378	+	3.26028i	−0.260676	+	0.104359i
$977$	−0.489006	−	5.12110i	−0.0156447	−	0.163838i	0.984273	−	0.176653i	$-0.0565270\pi$
$977$	−0.489006	−	5.12110i	−0.0156447	−	0.163838i	−0.999918	+	0.0128144i	$0.995921\pi$
$978$	−7.90139	+	5.62656i	−0.252659	+	0.179917i
$979$	−1.22362	−	0.175930i	−0.0391070	−	0.00562274i
$980$	15.5127	+	6.02709i	0.495536	+	0.192528i
$981$	−0.428600	+	1.45968i	−0.0136842	+	0.0466040i
$982$	−24.0543	−	9.62990i	−0.767604	−	0.307302i
$983$	0.249309	−	0.720332i	0.00795173	−	0.0229750i	−0.940955	−	0.338531i	$-0.890070\pi$
$983$	0.249309	−	0.720332i	0.00795173	−	0.0229750i	0.948907	+	0.315556i	$0.102191\pi$
$984$	−0.225357	+	4.73083i	−0.00718413	+	0.150813i
$985$	−5.98470	−	17.2917i	−0.190688	−	0.550958i
$986$	31.5622	−	9.26750i	1.00515	−	0.295137i
$987$	1.23165	−	28.9705i	0.0392037	−	0.922142i
$988$		−	13.6651i		−	0.434744i
$989$	6.57755	+	35.7356i	0.209154	+	1.13633i
$990$	0.490674	−	0.283291i	0.0155947	−	0.00900358i
$991$	−18.3329	+	25.7450i	−0.582365	+	0.817817i	−0.995688	−	0.0927678i	$-0.970429\pi$
$991$	−18.3329	+	25.7450i	−0.582365	+	0.817817i	0.413323	+	0.910584i	$0.364368\pi$
$992$	7.33477	+	1.77940i	0.232879	+	0.0564959i
$993$	−15.2513	−	13.2153i	−0.483984	−	0.419374i
$994$	−40.5714	+	0.207391i	−1.28685	+	0.00657803i
$995$	−1.39044	−	1.60466i	−0.0440801	−	0.0508711i
$996$	0.160281	−	0.400363i	0.00507871	−	0.0126860i
$997$	3.13045	−	0.759440i	0.0991425	−	0.0240517i	−0.185881	−	0.982572i	$-0.559514\pi$
$997$	3.13045	−	0.759440i	0.0991425	−	0.0240517i	0.285023	+	0.958521i	$0.407999\pi$
$998$	−7.45227	−	3.84191i	−0.235897	−	0.121614i
$999$	−1.87323	−	1.47313i	−0.0592665	−	0.0466077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.2	✓	320
7.3	odd	6	inner	966.2.be.b.157.2	yes	320
23.17	odd	22	inner	966.2.be.b.523.2	yes	320
161.17	even	66	inner	966.2.be.b.661.2	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.2	✓	320	1.1	even	1	trivial
966.2.be.b.157.2	yes	320	7.3	odd	6	inner
966.2.be.b.523.2	yes	320	23.17	odd	22	inner
966.2.be.b.661.2	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)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.11320 + 1.08943i) q^{5} +(0.755750 - 0.654861i) q^{6} +(0.852549 - 2.50463i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.11320 + 1.08943i) q^{5} +(0.755750 - 0.654861i) q^{6} +(0.852549 - 2.50463i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(2.20719 - 0.883624i) q^{10} +(0.0226529 + 0.237232i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(2.58628 + 0.371851i) q^{13} +(-1.08677 + 2.41225i) q^{14} +(0.669817 - 2.28119i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-2.25427 + 6.51328i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(-1.71053 - 4.94226i) q^{19} +(-2.28119 + 0.669817i) q^{20} +(1.22436 + 2.34541i) q^{21} -0.238311i q^{22} +(4.77013 + 0.495842i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.378466 - 0.531481i) q^{25} +(-2.53922 - 0.616009i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.31115 - 2.29802i) q^{28} +(3.12541 + 3.60692i) q^{29} +(-0.883624 + 2.20719i) q^{30} +(-7.33477 + 1.77940i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-0.187325 - 0.147314i) q^{33} +(2.86319 - 6.26950i) q^{34} +(0.927011 + 6.22157i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-2.38039 + 0.113392i) q^{37} +(1.23300 + 5.08248i) q^{38} +(-2.05386 + 1.61517i) q^{39} +(2.33453 - 0.449943i) q^{40} +(-2.56058 + 3.98434i) q^{41} +(-0.995869 - 2.45117i) q^{42} +(2.13456 + 7.26966i) q^{43} +(-0.0226529 + 0.237232i) q^{44} +(1.18875 + 2.05897i) q^{45} +(-4.70140 - 0.947026i) q^{46} +(-9.49140 - 5.47986i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-5.54632 - 4.27063i) q^{49} +(-0.427273 + 0.493099i) q^{50} +(-3.15826 - 6.12616i) q^{51} +(2.46917 + 0.854588i) q^{52} +(-6.19714 - 7.88030i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-0.306317 - 0.476639i) q^{55} +(-1.52365 + 2.16298i) q^{56} +(4.75729 + 2.17258i) q^{57} +(-2.76840 - 3.88767i) q^{58} +(-5.15185 - 12.8687i) q^{59} +(1.08943 - 2.11320i) q^{60} +(-6.34870 + 6.05348i) q^{61} +(7.47070 - 1.07413i) q^{62} +(-2.54236 - 0.732408i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-5.87043 + 2.03177i) q^{65} +(0.172474 + 0.164453i) q^{66} +(-0.169718 - 0.120855i) q^{67} +(-3.44617 + 5.96895i) q^{68} +(-3.65062 + 3.11014i) q^{69} +(-0.331416 - 6.28151i) q^{70} +(6.37028 + 13.9490i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.912261 - 4.73326i) q^{73} +(2.38039 + 0.113392i) q^{74} +(0.123479 + 0.640672i) q^{75} +(-0.744293 - 5.17667i) q^{76} +(0.613490 + 0.145515i) q^{77} +(2.19809 - 1.41263i) q^{78} +(-10.1063 + 12.8512i) q^{79} +(-2.36673 + 0.225995i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(2.92772 - 3.72290i) q^{82} +(-0.362795 + 0.233154i) q^{83} +(0.758361 + 2.53474i) q^{84} +(-2.33204 - 16.2197i) q^{85} +(-1.43387 - 7.43965i) q^{86} +(-4.76723 - 0.227091i) q^{87} +(0.0451006 - 0.234004i) q^{88} +(-1.22296 + 5.04112i) q^{89} +(-0.987645 - 2.16264i) q^{90} +(3.13628 - 6.16065i) q^{91} +(4.59009 + 1.38963i) q^{92} +(3.77376 - 6.53635i) q^{93} +(8.92752 + 6.35726i) q^{94} +(8.99894 + 8.58047i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-2.39659 - 1.54019i) q^{97} +(5.11526 + 4.77851i) q^{98} +(0.235885 - 0.0339152i) 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

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Database

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