LMFDB - Embedded newform 966.2.q.h.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.3
Character	$\chi$	$=$	966.211
Dual form			966.2.q.h.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(3.27138 + 2.10239i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(3.27138 + 2.10239i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.553420 - 3.84912i) q^{10} +(2.21508 - 4.85036i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.760593 + 5.29004i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(3.73118 + 1.09557i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.865263 - 0.998567i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(3.77172 - 4.35280i) q^{19} +(-3.73118 + 1.09557i) q^{20} +(-0.415415 - 0.909632i) q^{21} -5.33222 q^{22} +(-4.52292 - 1.59475i) q^{23} +1.00000 q^{24} +(4.20483 + 9.20729i) q^{25} +(5.12795 - 1.50570i) q^{26} +(0.654861 - 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(3.33455 + 3.84828i) q^{29} +(-0.553420 - 3.84912i) q^{30} +(-2.44691 - 0.718479i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.758854 - 5.27794i) q^{33} +(-0.548885 + 1.20189i) q^{34} +(1.61542 - 3.53729i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(4.15319 - 2.66909i) q^{37} +(-5.52627 - 1.62266i) q^{38} +(0.760593 + 5.29004i) q^{39} +(2.54656 + 2.93888i) q^{40} +(4.00725 + 2.57530i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(-8.92892 + 2.62177i) q^{43} +(2.21508 + 4.85036i) q^{44} +3.88870 q^{45} +(0.428249 + 4.77667i) q^{46} +8.51654 q^{47} +(-0.415415 - 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(6.62849 - 7.64969i) q^{50} +(-1.11154 - 0.714345i) q^{51} +(-3.49986 - 4.03906i) q^{52} +(0.716087 + 4.98049i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(17.4437 - 11.2104i) q^{55} +(0.142315 - 0.989821i) q^{56} +(2.39261 - 5.23909i) q^{57} +(2.11529 - 4.63185i) q^{58} +(-2.11461 + 14.7074i) q^{59} +(-3.27138 + 2.10239i) q^{60} +(8.35103 + 2.45208i) q^{61} +(0.362933 + 2.52426i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-13.6099 + 15.7067i) q^{65} +(-5.11623 + 1.50226i) q^{66} +(-4.27206 - 9.35451i) q^{67} +1.32129 q^{68} +(-4.78900 - 0.255902i) q^{69} -3.88870 q^{70} +(-4.14453 - 9.07525i) q^{71} +(0.959493 - 0.281733i) q^{72} +(5.47547 - 6.31903i) q^{73} +(-4.15319 - 2.66909i) q^{74} +(6.62849 + 7.64969i) q^{75} +(0.819673 + 5.70095i) q^{76} +(-5.11623 - 1.50226i) q^{77} +(4.49603 - 2.88942i) q^{78} +(-0.0994686 + 0.691819i) q^{79} +(1.61542 - 3.53729i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.677907 - 4.71494i) q^{82} +(-7.26612 + 4.66965i) q^{83} +(0.959493 + 0.281733i) q^{84} +(-0.731230 - 5.08582i) q^{85} +(6.09405 + 7.03291i) q^{86} +(4.28367 + 2.75294i) q^{87} +(3.49186 - 4.02982i) q^{88} +(-5.61333 + 1.64822i) q^{89} +(-1.61542 - 3.53729i) q^{90} +5.34444 q^{91} +(4.16711 - 2.37385i) q^{92} -2.55022 q^{93} +(-3.53790 - 7.74692i) q^{94} +(21.4900 - 6.31004i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-15.6312 - 10.0455i) q^{97} +(0.654861 + 0.755750i) q^{98} +(-0.758854 - 5.27794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	3.27138	+	2.10239i	1.46301	+	0.940217i	0.998506	+	0.0546449i	$0.0174027\pi$
$5$	3.27138	+	2.10239i	1.46301	+	0.940217i	0.464501	+	0.885573i	$0.346234\pi$
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.553420	−	3.84912i	0.175007	−	1.21720i
$11$	2.21508	−	4.85036i	0.667873	−	1.46244i	−0.207127	−	0.978314i	$-0.566411\pi$
$11$	2.21508	−	4.85036i	0.667873	−	1.46244i	0.875000	−	0.484124i	$-0.160861\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	−0.760593	+	5.29004i	−0.210951	+	1.46719i	0.559041	+	0.829140i	$0.311169\pi$
$13$	−0.760593	+	5.29004i	−0.210951	+	1.46719i	−0.769992	+	0.638054i	$0.779740\pi$
$14$	−0.841254	+	0.540641i	−0.224834	+	0.144492i
$15$	3.73118	+	1.09557i	0.963387	+	0.282876i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−0.865263	−	0.998567i	−0.209857	−	0.242188i	0.641056	−	0.767494i	$-0.278496\pi$
$17$	−0.865263	−	0.998567i	−0.209857	−	0.242188i	−0.850914	+	0.525306i	$0.823951\pi$
$18$	−0.841254	−	0.540641i	−0.198285	−	0.127430i
$19$	3.77172	−	4.35280i	0.865292	−	0.998600i	−0.134679	−	0.990889i	$-0.543000\pi$
$19$	3.77172	−	4.35280i	0.865292	−	0.998600i	0.999970	−	0.00771057i	$-0.00245438\pi$
$20$	−3.73118	+	1.09557i	−0.834317	+	0.244978i
$21$	−0.415415	−	0.909632i	−0.0906510	−	0.198498i
$22$	−5.33222			−1.13683
$23$	−4.52292	−	1.59475i	−0.943093	−	0.332529i
$23$	−4.52292	−	1.59475i	−0.943093	−	0.332529i
$24$	1.00000			0.204124
$25$	4.20483	+	9.20729i	0.840965	+	1.84146i
$26$	5.12795	−	1.50570i	1.00567	−	0.295293i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	0.841254	+	0.540641i	0.158982	+	0.102172i
$29$	3.33455	+	3.84828i	0.619211	+	0.714607i	0.975557	−	0.219747i	$-0.0705230\pi$
$29$	3.33455	+	3.84828i	0.619211	+	0.714607i	−0.356346	+	0.934354i	$0.615978\pi$
$30$	−0.553420	−	3.84912i	−0.101040	−	0.702750i
$31$	−2.44691	−	0.718479i	−0.439479	−	0.129043i	0.0545055	−	0.998513i	$-0.482642\pi$
$31$	−2.44691	−	0.718479i	−0.439479	−	0.129043i	−0.493984	+	0.869471i	$0.664460\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	0.758854	−	5.27794i	0.132100	−	0.918772i
$34$	−0.548885	+	1.20189i	−0.0941330	+	0.206123i
$35$	1.61542	−	3.53729i	0.273057	−	0.597911i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	4.15319	−	2.66909i	0.682780	−	0.438796i	−0.152732	−	0.988268i	$-0.548807\pi$
$37$	4.15319	−	2.66909i	0.682780	−	0.438796i	0.835513	+	0.549471i	$0.185171\pi$
$38$	−5.52627	−	1.62266i	−0.896480	−	0.263230i
$39$	0.760593	+	5.29004i	0.121792	+	0.847085i
$40$	2.54656	+	2.93888i	0.402646	+	0.464678i
$41$	4.00725	+	2.57530i	0.625828	+	0.402195i	0.814763	−	0.579795i	$-0.196867\pi$
$41$	4.00725	+	2.57530i	0.625828	+	0.402195i	−0.188935	+	0.981990i	$0.560504\pi$
$42$	−0.654861	+	0.755750i	−0.101047	+	0.116615i
$43$	−8.92892	+	2.62177i	−1.36165	+	0.399816i	−0.879343	−	0.476188i	$-0.842018\pi$
$43$	−8.92892	+	2.62177i	−1.36165	+	0.399816i	−0.482304	+	0.876004i	$0.660200\pi$
$44$	2.21508	+	4.85036i	0.333936	+	0.731219i
$45$	3.88870			0.579693
$46$	0.428249	+	4.77667i	0.0631418	+	0.704282i
$47$	8.51654			1.24226			0.621132	−	0.783706i	$-0.286673\pi$
$47$	8.51654			1.24226			0.621132	+	0.783706i	$0.286673\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	6.62849	−	7.64969i	0.937411	−	1.08183i
$51$	−1.11154	−	0.714345i	−0.155647	−	0.100028i
$52$	−3.49986	−	4.03906i	−0.485344	−	0.560117i
$53$	0.716087	+	4.98049i	0.0983621	+	0.684123i	0.978019	+	0.208515i	$0.0668630\pi$
$53$	0.716087	+	4.98049i	0.0983621	+	0.684123i	−0.879657	+	0.475608i	$0.842228\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	17.4437	−	11.2104i	2.35211	−	1.51161i
$56$	0.142315	−	0.989821i	0.0190176	−	0.132270i
$57$	2.39261	−	5.23909i	0.316909	−	0.693935i
$58$	2.11529	−	4.63185i	0.277752	−	0.608192i
$59$	−2.11461	+	14.7074i	−0.275299	+	1.91475i	0.113712	+	0.993514i	$0.463726\pi$
$59$	−2.11461	+	14.7074i	−0.275299	+	1.91475i	−0.389011	+	0.921233i	$0.627183\pi$
$60$	−3.27138	+	2.10239i	−0.422334	+	0.271417i
$61$	8.35103	+	2.45208i	1.06924	+	0.313957i	0.768566	−	0.639770i	$-0.220970\pi$
$61$	8.35103	+	2.45208i	1.06924	+	0.313957i	0.300674	+	0.953727i	$0.402789\pi$
$62$	0.362933	+	2.52426i	0.0460926	+	0.320581i
$63$	−0.654861	−	0.755750i	−0.0825047	−	0.0952155i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−13.6099	+	15.7067i	−1.68810	+	1.94818i
$66$	−5.11623	+	1.50226i	−0.629764	+	0.184915i
$67$	−4.27206	−	9.35451i	−0.521915	−	1.14284i	−0.968709	−	0.248198i	$-0.920162\pi$
$67$	−4.27206	−	9.35451i	−0.521915	−	1.14284i	0.446794	−	0.894637i	$-0.352566\pi$
$68$	1.32129			0.160230
$69$	−4.78900	−	0.255902i	−0.576528	−	0.0308069i
$70$	−3.88870			−0.464789
$71$	−4.14453	−	9.07525i	−0.491865	−	1.07703i	−0.979028	−	0.203723i	$-0.934696\pi$
$71$	−4.14453	−	9.07525i	−0.491865	−	1.07703i	0.487163	−	0.873311i	$-0.338032\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	5.47547	−	6.31903i	0.640855	−	0.739586i	−0.338671	−	0.940905i	$-0.609977\pi$
$73$	5.47547	−	6.31903i	0.640855	−	0.739586i	0.979526	+	0.201319i	$0.0645227\pi$
$74$	−4.15319	−	2.66909i	−0.482799	−	0.310276i
$75$	6.62849	+	7.64969i	0.765393	+	0.883310i
$76$	0.819673	+	5.70095i	0.0940229	+	0.653944i
$77$	−5.11623	−	1.50226i	−0.583048	−	0.171198i
$78$	4.49603	−	2.88942i	0.509075	−	0.327163i
$79$	−0.0994686	+	0.691819i	−0.0111911	+	0.0778358i	−0.994652	−	0.103287i	$-0.967064\pi$
$79$	−0.0994686	+	0.691819i	−0.0111911	+	0.0778358i	0.983461	+	0.181123i	$0.0579731\pi$
$80$	1.61542	−	3.53729i	0.180610	−	0.395481i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.677907	−	4.71494i	0.0748623	−	0.520679i
$83$	−7.26612	+	4.66965i	−0.797561	+	0.512561i	−0.874819	−	0.484450i	$-0.839020\pi$
$83$	−7.26612	+	4.66965i	−0.797561	+	0.512561i	0.0772583	+	0.997011i	$0.475383\pi$
$84$	0.959493	+	0.281733i	0.104689	+	0.0307395i
$85$	−0.731230	−	5.08582i	−0.0793130	−	0.551634i
$86$	6.09405	+	7.03291i	0.657138	+	0.758378i
$87$	4.28367	+	2.75294i	0.459257	+	0.295147i
$88$	3.49186	−	4.02982i	0.372234	−	0.429581i
$89$	−5.61333	+	1.64822i	−0.595012	+	0.174711i	−0.565353	−	0.824849i	$-0.691260\pi$
$89$	−5.61333	+	1.64822i	−0.595012	+	0.174711i	−0.0296584	+	0.999560i	$0.509442\pi$
$90$	−1.61542	−	3.53729i	−0.170281	−	0.372863i
$91$	5.34444			0.560250
$92$	4.16711	−	2.37385i	0.434452	−	0.247491i
$93$	−2.55022			−0.264445
$94$	−3.53790	−	7.74692i	−0.364906	−	0.799033i
$95$	21.4900	−	6.31004i	2.20483	−	0.647396i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	−15.6312	−	10.0455i	−1.58711	−	1.01997i	−0.973017	−	0.230734i	$-0.925887\pi$
$97$	−15.6312	−	10.0455i	−1.58711	−	1.01997i	−0.614089	−	0.789237i	$-0.710476\pi$
$98$	0.654861	+	0.755750i	0.0661509	+	0.0763422i
$99$	−0.758854	−	5.27794i	−0.0762677	−	0.530453i
$100$	−9.71198	−	2.85169i	−0.971198	−	0.285169i
$101$	0.911096	−	0.585526i	0.0906574	−	0.0582620i	−0.494527	−	0.869162i	$-0.664659\pi$
$101$	0.911096	−	0.585526i	0.0906574	−	0.0582620i	0.585184	+	0.810900i	$0.301022\pi$
$102$	−0.188040	+	1.30784i	−0.0186187	+	0.129496i
$103$	2.83607	−	6.21013i	0.279447	−	0.611903i	−0.716912	−	0.697164i	$-0.754445\pi$
$103$	2.83607	−	6.21013i	0.279447	−	0.611903i	0.996359	+	0.0852610i	$0.0271724\pi$
$104$	−2.22016	+	4.86148i	−0.217705	+	0.476707i
$105$	0.553420	−	3.84912i	0.0540082	−	0.375636i
$106$	4.23294	−	2.72035i	0.411140	−	0.264223i
$107$	−6.03355	−	1.77161i	−0.583285	−	0.171268i	−0.0232397	−	0.999730i	$-0.507398\pi$
$107$	−6.03355	−	1.77161i	−0.583285	−	0.171268i	−0.560045	+	0.828462i	$0.689216\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	−8.91826	−	10.2922i	−0.854214	−	0.985816i	0.145780	−	0.989317i	$-0.453431\pi$
$109$	−8.91826	−	10.2922i	−0.854214	−	0.985816i	−0.999994	+	0.00350137i	$0.998885\pi$
$110$	−17.4437	−	11.2104i	−1.66319	−	1.06887i
$111$	3.23299	−	3.73107i	0.306862	−	0.354137i
$112$	−0.959493	+	0.281733i	−0.0906636	+	0.0266212i
$113$	−2.57852	−	5.64618i	−0.242567	−	0.531148i	0.748717	−	0.662890i	$-0.230670\pi$
$113$	−2.57852	−	5.64618i	−0.242567	−	0.531148i	−0.991284	+	0.131742i	$0.957943\pi$
$114$	−5.75957			−0.539434
$115$	−11.4434	−	14.7260i	−1.06710	−	1.37320i
$116$	−5.09200			−0.472781
$117$	2.22016	+	4.86148i	0.205254	+	0.449444i
$118$	14.2568	−	4.18618i	1.31245	−	0.385369i
$119$	−0.865263	+	0.998567i	−0.0793185	+	0.0915385i
$120$	3.27138	+	2.10239i	0.298635	+	0.191921i
$121$	−11.4159	−	13.1747i	−1.03781	−	1.19770i
$122$	−1.23865	−	8.61500i	−0.112142	−	0.779965i
$123$	4.57048	+	1.34201i	0.412106	+	0.121005i
$124$	2.14538	−	1.37875i	0.192661	−	0.123815i
$125$	−2.83461	+	19.7152i	−0.253535	+	1.76338i
$126$	−0.415415	+	0.909632i	−0.0370081	+	0.0810365i
$127$	0.836017	−	1.83062i	0.0741845	−	0.162441i	−0.868906	−	0.494976i	$-0.835177\pi$
$127$	0.836017	−	1.83062i	0.0741845	−	0.162441i	0.943091	+	0.332535i	$0.107904\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	−7.82860	+	5.03113i	−0.689270	+	0.442967i
$130$	19.9411	+	5.85523i	1.74895	+	0.513538i
$131$	2.60054	+	18.0871i	0.227210	+	1.58028i	0.709781	+	0.704422i	$0.248794\pi$
$131$	2.60054	+	18.0871i	0.227210	+	1.58028i	−0.482571	+	0.875857i	$0.660297\pi$
$132$	3.49186	+	4.02982i	0.303927	+	0.350751i
$133$	−4.84526	−	3.11386i	−0.420138	−	0.270006i
$134$	−6.73448	+	7.77201i	−0.581771	+	0.671399i
$135$	3.73118	−	1.09557i	0.321129	−	0.0942920i
$136$	−0.548885	−	1.20189i	−0.0470665	−	0.103061i
$137$	−2.30215			−0.196686			−0.0983430	−	0.995153i	$-0.531354\pi$
$137$	−2.30215			−0.196686			−0.0983430	+	0.995153i	$0.531354\pi$
$138$	1.75665	+	4.46253i	0.149536	+	0.379876i
$139$	3.90467			0.331190			0.165595	−	0.986194i	$-0.447046\pi$
$139$	3.90467			0.331190			0.165595	+	0.986194i	$0.447046\pi$
$140$	1.61542	+	3.53729i	0.136528	+	0.298955i
$141$	8.17156	−	2.39939i	0.688169	−	0.202065i
$142$	−6.53344	+	7.53999i	−0.548274	+	0.632742i
$143$	23.9738	+	15.4070i	2.00479	+	1.28840i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	2.81802	+	19.5997i	0.234023	+	1.62767i
$146$	−8.02258	−	2.35564i	−0.663954	−	0.194954i
$147$	−0.841254	+	0.540641i	−0.0693854	+	0.0445913i
$148$	−0.702595	+	4.88666i	−0.0577530	+	0.401681i
$149$	−5.93350	+	12.9925i	−0.486091	+	1.06439i	0.494652	+	0.869091i	$0.335295\pi$
$149$	−5.93350	+	12.9925i	−0.486091	+	1.06439i	−0.980744	+	0.195300i	$0.937432\pi$
$150$	4.20483	−	9.20729i	0.343323	−	0.751772i
$151$	−2.58324	+	17.9669i	−0.210221	+	1.46212i	0.562194	+	0.827005i	$0.309957\pi$
$151$	−2.58324	+	17.9669i	−0.210221	+	1.46212i	−0.772416	+	0.635117i	$0.780952\pi$
$152$	4.84526	−	3.11386i	0.393003	−	0.252567i
$153$	−1.26777	−	0.372251i	−0.102493	−	0.0300947i
$154$	0.758854	+	5.27794i	0.0611502	+	0.425309i
$155$	−6.49427	−	7.49479i	−0.521632	−	0.601996i
$156$	−4.49603	−	2.88942i	−0.359971	−	0.231339i
$157$	−0.958078	+	1.10568i	−0.0764630	+	0.0882430i	−0.792692	−	0.609622i	$-0.791321\pi$
$157$	−0.958078	+	1.10568i	−0.0764630	+	0.0882430i	0.716229	+	0.697865i	$0.245867\pi$
$158$	0.670622	−	0.196912i	0.0533518	−	0.0156655i
$159$	2.09025	+	4.57700i	0.165767	+	0.362980i
$160$	−3.88870			−0.307429
$161$	−0.934843	+	4.70384i	−0.0736759	+	0.370714i
$162$	−1.00000			−0.0785674
$163$	0.298710	+	0.654085i	0.0233968	+	0.0512319i	0.920970	−	0.389634i	$-0.127399\pi$
$163$	0.298710	+	0.654085i	0.0233968	+	0.0512319i	−0.897573	+	0.440866i	$0.854671\pi$
$164$	−4.57048	+	1.34201i	−0.356894	+	0.104794i
$165$	13.5788	−	15.6708i	1.05711	−	1.21997i
$166$	7.26612	+	4.66965i	0.563961	+	0.362435i
$167$	−13.3307	−	15.3845i	−1.03156	−	1.19048i	−0.981446	−	0.191741i	$-0.938587\pi$
$167$	−13.3307	−	15.3845i	−1.03156	−	1.19048i	−0.0501152	−	0.998743i	$-0.515959\pi$
$168$	−0.142315	−	0.989821i	−0.0109798	−	0.0763664i
$169$	−14.9326	−	4.38462i	−1.14866	−	0.337278i
$170$	−4.32246	+	2.77787i	−0.331517	+	0.213053i
$171$	0.819673	−	5.70095i	0.0626820	−	0.435963i
$172$	3.86580	−	8.46492i	0.294764	−	0.645444i
$173$	−2.76871	+	6.06263i	−0.210501	+	0.460933i	−0.985203	−	0.171394i	$-0.945173\pi$
$173$	−2.76871	+	6.06263i	−0.210501	+	0.460933i	0.774701	+	0.632327i	$0.217900\pi$
$174$	0.724668	−	5.04017i	0.0549369	−	0.382095i
$175$	8.51516	−	5.47236i	0.643686	−	0.413672i
$176$	−5.11623	−	1.50226i	−0.385650	−	0.113237i
$177$	2.11461	+	14.7074i	0.158944	+	1.10548i
$178$	3.83114	+	4.42137i	0.287156	+	0.331395i
$179$	15.2725	+	9.81501i	1.14152	+	0.733608i	0.967932	−	0.251211i	$-0.0808288\pi$
$179$	15.2725	+	9.81501i	1.14152	+	0.733608i	0.173584	+	0.984819i	$0.444465\pi$
$180$	−2.54656	+	2.93888i	−0.189809	+	0.219051i
$181$	15.5470	−	4.56502i	1.15560	−	0.339315i	0.352879	−	0.935669i	$-0.385203\pi$
$181$	15.5470	−	4.56502i	1.15560	−	0.339315i	0.802722	+	0.596354i	$0.203384\pi$
$182$	−2.22016	−	4.86148i	−0.164569	−	0.360357i
$183$	8.70359			0.643388
$184$	−3.89041	−	2.80441i	−0.286805	−	0.206744i
$185$	19.1982			1.41148
$186$	1.05940	+	2.31976i	0.0776788	+	0.170093i
$187$	−6.76004	+	1.98493i	−0.494343	+	0.145152i
$188$	−5.57715	+	6.43637i	−0.406755	+	0.469421i
$189$	−0.841254	−	0.540641i	−0.0611922	−	0.0393258i
$190$	−14.6671	−	16.9267i	−1.06406	−	1.22799i
$191$	−2.65613	−	18.4738i	−0.192191	−	1.33672i	−0.826193	−	0.563387i	$-0.809498\pi$
$191$	−2.65613	−	18.4738i	−0.192191	−	1.33672i	0.634002	−	0.773331i	$-0.281411\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	−17.6144	+	11.3201i	−1.26791	+	0.814839i	−0.989347	−	0.145578i	$-0.953496\pi$
$193$	−17.6144	+	11.3201i	−1.26791	+	0.814839i	−0.278568	+	0.960417i	$0.589860\pi$
$194$	−2.64433	+	18.3917i	−0.189852	+	1.32045i
$195$	−8.63354	+	18.9048i	−0.618261	+	1.35380i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−2.38903	+	16.6161i	−0.170211	+	1.18384i	0.708226	+	0.705986i	$0.249496\pi$
$197$	−2.38903	+	16.6161i	−0.170211	+	1.18384i	−0.878437	+	0.477859i	$0.841413\pi$
$198$	−4.48575	+	2.88282i	−0.318788	+	0.204873i
$199$	−7.23242	−	2.12363i	−0.512692	−	0.150540i	0.0151453	−	0.999885i	$-0.495179\pi$
$199$	−7.23242	−	2.12363i	−0.512692	−	0.150540i	−0.527838	+	0.849345i	$0.676997\pi$
$200$	1.44051	+	10.0190i	0.101859	+	0.708448i
$201$	−6.73448	−	7.77201i	−0.475014	−	0.548195i
$202$	−0.911096	−	0.585526i	−0.0641045	−	0.0411975i
$203$	3.33455	−	3.84828i	0.234040	−	0.270096i
$204$	1.26777	−	0.372251i	0.0887618	−	0.0260628i
$205$	7.69496	+	16.8496i	0.537439	+	1.17683i
$206$	−6.82708			−0.475665
$207$	−4.66711	+	1.10368i	−0.324386	+	0.0767111i
$208$	5.34444			0.370570
$209$	−12.7579	−	27.9360i	−0.882485	−	1.93237i
$210$	−3.73118	+	1.09557i	−0.257476	+	0.0756018i
$211$	−1.22967	+	1.41912i	−0.0846543	+	0.0976962i	−0.796496	−	0.604643i	$-0.793316\pi$
$211$	−1.22967	+	1.41912i	−0.0846543	+	0.0976962i	0.711842	+	0.702340i	$0.247861\pi$
$212$	−4.23294	−	2.72035i	−0.290720	−	0.186834i
$213$	−6.53344	−	7.53999i	−0.447664	−	0.516632i
$214$	0.894913	+	6.22426i	0.0611750	+	0.425482i
$215$	−34.7219	−	10.1953i	−2.36801	−	0.695312i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.362933	+	2.52426i	−0.0246375	+	0.171358i
$218$	−5.65735	+	12.3879i	−0.383164	+	0.839013i
$219$	3.47340	−	7.60568i	0.234710	−	0.513944i
$220$	−2.95096	+	20.5243i	−0.198953	+	1.38375i
$221$	5.94058	−	3.81778i	0.399606	−	0.256811i
$222$	−4.73693	−	1.39089i	−0.317922	−	0.0933503i
$223$	0.234510	+	1.63106i	0.0157040	+	0.109224i	0.996166	−	0.0874863i	$-0.0278834\pi$
$223$	0.234510	+	1.63106i	0.0157040	+	0.109224i	−0.980462	+	0.196710i	$0.936974\pi$
$224$	0.654861	+	0.755750i	0.0437547	+	0.0504956i
$225$	8.51516	+	5.47236i	0.567677	+	0.364824i
$226$	−4.06479	+	4.69102i	−0.270386	+	0.312042i
$227$	−19.9215	+	5.84948i	−1.32224	+	0.388244i	−0.865299	−	0.501255i	$-0.832872\pi$
$227$	−19.9215	+	5.84948i	−1.32224	+	0.388244i	−0.456937	+	0.889499i	$0.651054\pi$
$228$	2.39261	+	5.23909i	0.158455	+	0.346967i
$229$	14.6171			0.965925			0.482962	−	0.875641i	$-0.339561\pi$
$229$	14.6171			0.965925			0.482962	+	0.875641i	$0.339561\pi$
$230$	−8.64146	+	16.5267i	−0.569801	+	1.08974i
$231$	−5.33222			−0.350834
$232$	2.11529	+	4.63185i	0.138876	+	0.304096i
$233$	10.1209	−	2.97177i	0.663042	−	0.194687i	0.0671399	−	0.997744i	$-0.478613\pi$
$233$	10.1209	−	2.97177i	0.663042	−	0.194687i	0.595903	+	0.803057i	$0.296794\pi$
$234$	3.49986	−	4.03906i	0.228793	−	0.264042i
$235$	27.8609	+	17.9051i	1.81744	+	1.16800i
$236$	−9.73037	−	11.2294i	−0.633393	−	0.730975i
$237$	0.0994686	+	0.691819i	0.00646118	+	0.0449385i
$238$	1.26777	+	0.372251i	0.0821774	+	0.0241295i
$239$	−20.4710	+	13.1559i	−1.32416	+	0.850984i	−0.995619	−	0.0935062i	$-0.970193\pi$
$239$	−20.4710	+	13.1559i	−1.32416	+	0.850984i	−0.328539	+	0.944491i	$0.606556\pi$
$240$	0.553420	−	3.84912i	0.0357231	−	0.248460i
$241$	12.1149	−	26.5280i	0.780391	−	1.70882i	0.0780796	−	0.996947i	$-0.475121\pi$
$241$	12.1149	−	26.5280i	0.780391	−	1.70882i	0.702311	−	0.711870i	$-0.252152\pi$
$242$	−7.24175	+	15.8572i	−0.465517	+	1.01934i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−7.32192	+	4.70551i	−0.468738	+	0.301240i
$245$	−3.73118	−	1.09557i	−0.238376	−	0.0699936i
$246$	−0.677907	−	4.71494i	−0.0432218	−	0.300614i
$247$	20.1577	+	23.2633i	1.28261	+	1.48021i
$248$	−2.14538	−	1.37875i	−0.136232	−	0.0875507i
$249$	−5.65620	+	6.52760i	−0.358447	+	0.413670i
$250$	19.1111	−	5.61152i	1.20869	−	0.354903i
$251$	0.918241	+	2.01067i	0.0579589	+	0.126912i	0.936395	−	0.350947i	$-0.114140\pi$
$251$	0.918241	+	2.01067i	0.0579589	+	0.126912i	−0.878437	+	0.477859i	$0.841413\pi$
$252$	1.00000			0.0629941
$253$	−17.7538	+	18.4052i	−1.11617	+	1.15713i
$254$	−2.01249			−0.126275
$255$	−2.13445	−	4.67379i	−0.133664	−	0.292684i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	8.08851	−	9.33463i	0.504547	−	0.582278i	−0.445147	−	0.895458i	$-0.646849\pi$
$257$	8.08851	−	9.33463i	0.504547	−	0.582278i	0.949694	+	0.313179i	$0.101394\pi$
$258$	7.82860	+	5.03113i	0.487387	+	0.313225i
$259$	−3.23299	−	3.73107i	−0.200888	−	0.231837i
$260$	−2.95772	−	20.5714i	−0.183430	−	1.27578i
$261$	4.88574	+	1.43458i	0.302420	+	0.0887985i
$262$	15.3723	−	9.87919i	0.949705	−	0.610338i
$263$	−3.10441	+	21.5916i	−0.191426	+	1.33140i	0.636812	+	0.771019i	$0.280253\pi$
$263$	−3.10441	+	21.5916i	−0.191426	+	1.33140i	−0.828238	+	0.560377i	$0.810656\pi$
$264$	2.21508	−	4.85036i	0.136329	−	0.298519i
$265$	−8.12835	+	17.7986i	−0.499320	+	1.09336i
$266$	−0.819673	+	5.70095i	−0.0502574	+	0.349548i
$267$	−4.92159	+	3.16291i	−0.301196	+	0.193567i
$268$	9.86727	+	2.89729i	0.602740	+	0.176980i
$269$	0.708237	+	4.92590i	0.0431820	+	0.300337i	0.999955	+	0.00950118i	$0.00302437\pi$
$269$	0.708237	+	4.92590i	0.0431820	+	0.300337i	−0.956773	+	0.290836i	$0.906067\pi$
$270$	−2.54656	−	2.93888i	−0.154979	−	0.178855i
$271$	−3.27855	−	2.10699i	−0.199157	−	0.127991i	0.437261	−	0.899335i	$-0.355949\pi$
$271$	−3.27855	−	2.10699i	−0.199157	−	0.127991i	−0.636419	+	0.771344i	$0.719585\pi$
$272$	−0.865263	+	0.998567i	−0.0524643	+	0.0605470i
$273$	5.12795	−	1.50570i	0.310358	−	0.0911293i
$274$	0.956348	+	2.09411i	0.0577751	+	0.126510i
$275$	53.9727			3.25467
$276$	3.32953	−	3.45170i	0.200414	−	0.207768i
$277$	−4.92092			−0.295670			−0.147835	−	0.989012i	$-0.547230\pi$
$277$	−4.92092			−0.295670			−0.147835	+	0.989012i	$0.547230\pi$
$278$	−1.62206	−	3.55181i	−0.0972846	−	0.213024i
$279$	−2.44691	+	0.718479i	−0.146493	+	0.0430142i
$280$	2.54656	−	2.93888i	0.152186	−	0.175632i
$281$	−5.70778	−	3.66816i	−0.340497	−	0.218824i	0.359205	−	0.933259i	$-0.383048\pi$
$281$	−5.70778	−	3.66816i	−0.340497	−	0.218824i	−0.699703	+	0.714434i	$0.746684\pi$
$282$	−5.57715	−	6.43637i	−0.332114	−	0.383280i
$283$	3.67703	+	25.5743i	0.218577	+	1.52023i	0.743299	+	0.668960i	$0.233260\pi$
$283$	3.67703	+	25.5743i	0.218577	+	1.52023i	−0.524722	+	0.851273i	$0.675831\pi$
$284$	9.57271	+	2.81080i	0.568036	+	0.166790i
$285$	18.8418	−	12.1089i	1.11609	−	0.717268i
$286$	4.05565	−	28.2077i	0.239816	−	1.66795i
$287$	1.97880	−	4.33297i	0.116805	−	0.255767i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	2.17090	−	15.0989i	0.127700	−	0.888172i
$290$	16.6579	−	10.7054i	0.978185	−	0.628641i
$291$	−17.8282	−	5.23482i	−1.04511	−	0.306871i
$292$	1.18993	+	8.27617i	0.0696356	+	0.484326i
$293$	−18.1836	−	20.9850i	−1.06230	−	1.22596i	−0.973206	−	0.229936i	$-0.926148\pi$
$293$	−18.1836	−	20.9850i	−1.06230	−	1.22596i	−0.0890945	−	0.996023i	$-0.528397\pi$
$294$	0.841254	+	0.540641i	0.0490629	+	0.0315308i
$295$	−37.8385	+	43.6680i	−2.20304	+	2.54245i
$296$	4.73693	−	1.39089i	0.275328	−	0.0808437i
$297$	−2.21508	−	4.85036i	−0.128532	−	0.281446i
$298$	14.2833			0.827410
$299$	11.8764	−	22.7135i	0.686831	−	1.31355i
$300$	−10.1220			−0.584393
$301$	3.86580	+	8.46492i	0.222821	+	0.487910i
$302$	17.4164	−	5.11390i	1.00220	−	0.294272i
$303$	0.709229	−	0.818493i	0.0407441	−	0.0470212i
$304$	−4.84526	−	3.11386i	−0.277895	−	0.178592i
$305$	22.1642	+	25.5788i	1.26912	+	1.46464i
$306$	0.188040	+	1.30784i	0.0107495	+	0.0747645i
$307$	−25.4628	−	7.47656i	−1.45324	−	0.426710i	−0.542629	−	0.839973i	$-0.682571\pi$
$307$	−25.4628	−	7.47656i	−1.45324	−	0.426710i	−0.910612	+	0.413263i	$0.864389\pi$
$308$	4.48575	−	2.88282i	0.255599	−	0.164264i
$309$	0.971595	−	6.75759i	0.0552721	−	0.384426i
$310$	−4.11968	+	9.02084i	−0.233982	+	0.512349i
$311$	−3.90122	+	8.54247i	−0.221218	+	0.484399i	−0.987404	−	0.158219i	$-0.949425\pi$
$311$	−3.90122	+	8.54247i	−0.221218	+	0.484399i	0.766186	+	0.642618i	$0.222152\pi$
$312$	−0.760593	+	5.29004i	−0.0430601	+	0.299490i
$313$	−15.2104	+	9.77513i	−0.859743	+	0.552523i	−0.894599	−	0.446869i	$-0.852539\pi$
$313$	−15.2104	+	9.77513i	−0.859743	+	0.552523i	0.0348566	+	0.999392i	$0.488903\pi$
$314$	1.40376	+	0.412182i	0.0792189	+	0.0232608i
$315$	−0.553420	−	3.84912i	−0.0311817	−	0.216873i
$316$	−0.457704	−	0.528219i	−0.0257479	−	0.0297146i
$317$	4.12396	+	2.65031i	0.231625	+	0.148856i	0.651306	−	0.758816i	$-0.274222\pi$
$317$	4.12396	+	2.65031i	0.231625	+	0.148856i	−0.419681	+	0.907672i	$0.637858\pi$
$318$	3.29507	−	3.80271i	0.184778	−	0.213245i
$319$	26.0518	−	7.64951i	1.45862	−	0.428290i
$320$	1.61542	+	3.53729i	0.0903050	+	0.197740i
$321$	−6.28827			−0.350977
$322$	4.66711	−	1.10368i	0.260088	−	0.0615057i
$323$	−7.61009			−0.423437
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	−51.9051	+	15.2407i	−2.87918	+	0.845403i
$326$	0.470887	−	0.543433i	0.0260800	−	0.0300980i
$327$	−11.4567	−	7.36275i	−0.633555	−	0.407161i
$328$	3.11938	+	3.59996i	0.172239	+	0.198775i
$329$	−1.21203	−	8.42985i	−0.0668214	−	0.464753i
$330$	−19.8955	−	5.84184i	−1.09521	−	0.321583i
$331$	−10.8739	+	6.98824i	−0.597684	+	0.384108i	−0.804221	−	0.594331i	$-0.797417\pi$
$331$	−10.8739	+	6.98824i	−0.597684	+	0.384108i	0.206537	+	0.978439i	$0.433781\pi$
$332$	1.22921	−	8.54934i	0.0674617	−	0.469206i
$333$	2.05087	−	4.49077i	0.112387	−	0.246093i
$334$	−8.45641	+	18.5170i	−0.462714	+	1.01320i
$335$	5.69128	−	39.5837i	0.310948	−	2.16269i
$336$	−0.841254	+	0.540641i	−0.0458941	+	0.0294944i
$337$	−18.7379	−	5.50194i	−1.02072	−	0.299710i	−0.271787	−	0.962357i	$-0.587615\pi$
$337$	−18.7379	−	5.50194i	−1.02072	−	0.299710i	−0.748931	+	0.662648i	$0.769433\pi$
$338$	2.21485	+	15.4046i	0.120472	+	0.837902i
$339$	−4.06479	−	4.69102i	−0.220769	−	0.254781i
$340$	4.32246	+	2.77787i	0.234418	+	0.150651i
$341$	−8.90500	+	10.2769i	−0.482233	+	0.556526i
$342$	−5.52627	+	1.62266i	−0.298827	+	0.0877434i
$343$	0.415415	+	0.909632i	0.0224303	+	0.0491155i
$344$	−9.30587			−0.501739
$345$	−15.1286	−	10.9055i	−0.814499	−	0.587132i
$346$	6.66493			0.358309
$347$	4.62137	+	10.1194i	0.248088	+	0.543237i	0.992176	−	0.124844i	$-0.0398431\pi$
$347$	4.62137	+	10.1194i	0.248088	+	0.543237i	−0.744088	+	0.668081i	$0.767116\pi$
$348$	−4.88574	+	1.43458i	−0.261903	+	0.0769017i
$349$	7.87401	−	9.08709i	0.421486	−	0.486421i	−0.504803	−	0.863235i	$-0.668435\pi$
$349$	7.87401	−	9.08709i	0.421486	−	0.486421i	0.926289	+	0.376814i	$0.122980\pi$
$350$	−8.51516	−	5.47236i	−0.455154	−	0.292510i
$351$	3.49986	+	4.03906i	0.186809	+	0.215589i
$352$	0.758854	+	5.27794i	0.0404471	+	0.281315i
$353$	2.65231	+	0.778787i	0.141168	+	0.0414507i	0.351553	−	0.936168i	$-0.385654\pi$
$353$	2.65231	+	0.778787i	0.141168	+	0.0414507i	−0.210385	+	0.977619i	$0.567472\pi$
$354$	12.4999	−	8.03321i	0.664364	−	0.426961i
$355$	5.52138	−	38.4020i	0.293044	−	2.03817i
$356$	2.43031	−	5.32163i	0.128806	−	0.282046i
$357$	−0.548885	+	1.20189i	−0.0290501	+	0.0636108i
$358$	2.58364	−	17.9696i	0.136550	−	0.949724i
$359$	15.2880	−	9.82501i	0.806870	−	0.518544i	−0.0709809	−	0.997478i	$-0.522613\pi$
$359$	15.2880	−	9.82501i	0.806870	−	0.518544i	0.877851	+	0.478934i	$0.158977\pi$
$360$	3.73118	+	1.09557i	0.196650	+	0.0577418i
$361$	−2.01699	−	14.0284i	−0.106157	−	0.738339i
$362$	−10.6110	−	12.2457i	−0.557699	−	0.643619i
$363$	−14.6652	−	9.42475i	−0.769724	−	0.494671i
$364$	−3.49986	+	4.03906i	−0.183443	+	0.211704i
$365$	31.1974	−	9.16039i	1.63295	−	0.479477i
$366$	−3.61560	−	7.91706i	−0.188990	−	0.413831i
$367$	10.4688			0.546465			0.273232	−	0.961948i	$-0.411907\pi$
$367$	10.4688			0.546465			0.273232	+	0.961948i	$0.411907\pi$
$368$	−0.934843	+	4.70384i	−0.0487320	+	0.245204i
$369$	4.76343			0.247974
$370$	−7.97520	−	17.4633i	−0.414611	−	0.907872i
$371$	4.82789	−	1.41760i	0.250652	−	0.0735979i
$372$	1.67004	−	1.92732i	0.0865873	−	0.0999271i
$373$	−2.70224	−	1.73663i	−0.139917	−	0.0899192i	0.468810	−	0.883299i	$-0.344683\pi$
$373$	−2.70224	−	1.73663i	−0.139917	−	0.0899192i	−0.608727	+	0.793380i	$0.708319\pi$
$374$	4.61377	+	5.32458i	0.238573	+	0.275327i
$375$	2.83461	+	19.7152i	0.146379	+	1.01809i
$376$	8.17156	+	2.39939i	0.421416	+	0.123739i
$377$	−22.8938	+	14.7130i	−1.17909	+	0.757756i
$378$	−0.142315	+	0.989821i	−0.00731989	+	0.0509109i
$379$	3.81596	−	8.35578i	0.196013	−	0.429208i	−0.785948	−	0.618292i	$-0.787825\pi$
$379$	3.81596	−	8.35578i	0.196013	−	0.429208i	0.981961	+	0.189085i	$0.0605520\pi$
$380$	−9.30416	+	20.3733i	−0.477293	+	1.04513i
$381$	0.286407	−	1.99200i	0.0146731	−	0.102053i
$382$	−15.7010	+	10.0904i	−0.803332	+	0.516270i
$383$	−29.7195	−	8.72644i	−1.51860	−	0.445900i	−0.587059	−	0.809544i	$-0.699714\pi$
$383$	−29.7195	−	8.72644i	−1.51860	−	0.445900i	−0.931538	+	0.363644i	$0.881533\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−13.5788	−	15.6708i	−0.692040	−	0.798656i
$386$	17.6144	+	11.3201i	0.896551	+	0.576178i
$387$	−6.09405	+	7.03291i	−0.309778	+	0.357503i
$388$	17.8282	−	5.23482i	0.905088	−	0.265758i
$389$	1.09142	+	2.38987i	0.0553371	+	0.121171i	0.935281	−	0.353907i	$-0.115147\pi$
$389$	1.09142	+	2.38987i	0.0553371	+	0.121171i	−0.879944	+	0.475078i	$0.842420\pi$
$390$	20.7829			1.05238
$391$	2.32104	+	5.89631i	0.117380	+	0.298189i
$392$	−1.00000			−0.0505076
$393$	7.59093	+	16.6218i	0.382912	+	0.838459i
$394$	16.1069	−	4.72942i	0.811456	−	0.238265i
$395$	−1.77987	+	2.05408i	−0.0895552	+	0.103352i
$396$	4.48575	+	2.88282i	0.225417	+	0.144867i
$397$	4.96915	+	5.73470i	0.249394	+	0.287816i	0.866619	−	0.498971i	$-0.166288\pi$
$397$	4.96915	+	5.73470i	0.249394	+	0.287816i	−0.617225	+	0.786787i	$0.711743\pi$
$398$	1.07273	+	7.46102i	0.0537713	+	0.373987i
$399$	−5.52627	−	1.62266i	−0.276660	−	0.0812346i
$400$	8.51516	−	5.47236i	0.425758	−	0.273618i
$401$	1.92990	−	13.4228i	0.0963748	−	0.670301i	−0.883167	−	0.469059i	$-0.844593\pi$
$401$	1.92990	−	13.4228i	0.0963748	−	0.670301i	0.979542	−	0.201242i	$-0.0644978\pi$
$402$	−4.27206	+	9.35451i	−0.213071	+	0.466561i
$403$	5.66189	−	12.3978i	0.282039	−	0.617579i
$404$	−0.154130	+	1.07200i	−0.00766826	+	0.0533339i
$405$	3.27138	−	2.10239i	0.162556	−	0.104469i
$406$	−4.88574	−	1.43458i	−0.242475	−	0.0711972i
$407$	−3.74639	−	26.0567i	−0.185702	−	1.29158i
$408$	−0.865263	−	0.998567i	−0.0428369	−	0.0494364i
$409$	−12.2521	−	7.87393i	−0.605826	−	0.389341i	0.201464	−	0.979496i	$-0.435430\pi$
$409$	−12.2521	−	7.87393i	−0.605826	−	0.389341i	−0.807290	+	0.590155i	$0.799067\pi$
$410$	12.1303	−	13.9992i	0.599075	−	0.691369i
$411$	−2.20890	+	0.648591i	−0.108957	+	0.0319926i
$412$	2.83607	+	6.21013i	0.139723	+	0.305951i
$413$	14.8587			0.731148
$414$	2.94273	+	3.78686i	0.144627	+	0.186114i
$415$	−33.5877			−1.64876
$416$	−2.22016	−	4.86148i	−0.108852	−	0.238353i
$417$	3.74650	−	1.10007i	0.183467	−	0.0538708i
$418$	−20.1116	+	23.2101i	−0.983692	+	1.13524i
$419$	−12.8174	−	8.23725i	−0.626171	−	0.402416i	0.188719	−	0.982031i	$-0.439566\pi$
$419$	−12.8174	−	8.23725i	−0.626171	−	0.402416i	−0.814890	+	0.579615i	$0.803203\pi$
$420$	2.54656	+	2.93888i	0.124259	+	0.143403i
$421$	2.60899	+	18.1460i	0.127155	+	0.884380i	0.949136	+	0.314866i	$0.101959\pi$
$421$	2.60899	+	18.1460i	0.127155	+	0.884380i	−0.821982	+	0.569514i	$0.807131\pi$
$422$	1.80170	+	0.529027i	0.0877055	+	0.0257527i
$423$	7.16457	−	4.60439i	0.348353	−	0.223873i
$424$	−0.716087	+	4.98049i	−0.0347762	+	0.241874i
$425$	5.55581	−	12.1655i	0.269496	−	0.590115i
$426$	−4.14453	+	9.07525i	−0.200803	+	0.439697i
$427$	1.23865	−	8.61500i	0.0599425	−	0.416909i
$428$	5.29003	−	3.39969i	0.255703	−	0.164330i
$429$	27.3434	+	8.02874i	1.32015	+	0.387631i
$430$	5.15005	+	35.8194i	0.248358	+	1.72737i
$431$	0.00134136	+	0.00154802i	6.46112e−5	+	7.45653e-5i	0.755782	−	0.654823i	$-0.227257\pi$
$431$	0.00134136	+	0.00154802i	6.46112e−5	+	7.45653e-5i	−0.755717	+	0.654898i	$0.772712\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	1.37492	−	1.58674i	0.0660743	−	0.0762538i	−0.721750	−	0.692154i	$-0.756662\pi$
$433$	1.37492	−	1.58674i	0.0660743	−	0.0762538i	0.787824	+	0.615900i	$0.211207\pi$
$434$	2.44691	−	0.718479i	0.117456	−	0.0344881i
$435$	8.22575	+	18.0119i	0.394394	+	0.863603i
$436$	13.6186			0.652211
$437$	−24.0008	+	13.6724i	−1.14811	+	0.654038i
$438$	−8.36127			−0.399517
$439$	1.46592	+	3.20992i	0.0699645	+	0.153201i	0.941383	−	0.337339i	$-0.109527\pi$
$439$	1.46592	+	3.20992i	0.0699645	+	0.153201i	−0.871419	+	0.490540i	$0.836800\pi$
$440$	19.8955	−	5.84184i	0.948479	−	0.278499i
$441$	−0.654861	+	0.755750i	−0.0311838	+	0.0359881i
$442$	−5.94058	−	3.81778i	−0.282564	−	0.181593i
$443$	6.55216	+	7.56160i	0.311303	+	0.359262i	0.889743	−	0.456462i	$-0.150884\pi$
$443$	6.55216	+	7.56160i	0.311303	+	0.359262i	−0.578440	+	0.815725i	$0.696338\pi$
$444$	0.702595	+	4.88666i	0.0333437	+	0.231911i
$445$	−21.8286	−	6.40944i	−1.03477	−	0.303837i
$446$	1.38624	−	0.890883i	0.0656404	−	0.0421845i
$447$	−2.03273	+	14.1379i	−0.0961446	+	0.668701i
$448$	0.415415	−	0.909632i	0.0196265	−	0.0429761i
$449$	3.64178	−	7.97438i	0.171866	−	0.376334i	−0.804024	−	0.594597i	$-0.797312\pi$
$449$	3.64178	−	7.97438i	0.171866	−	0.376334i	0.975890	+	0.218263i	$0.0700389\pi$
$450$	1.44051	−	10.0190i	0.0679063	−	0.472298i
$451$	21.3675	−	13.7321i	1.00616	−	0.646619i
$452$	5.95567	+	1.74874i	0.280131	+	0.0822540i
$453$	2.58324	+	17.9669i	0.121371	+	0.844157i
$454$	13.5966	+	15.6913i	0.638118	+	0.736428i
$455$	17.4837	+	11.2361i	0.819649	+	0.526757i
$456$	3.77172	−	4.35280i	0.176627	−	0.203838i
$457$	0.229668	−	0.0674365i	0.0107434	−	0.00315455i	−0.276356	−	0.961055i	$-0.589127\pi$
$457$	0.229668	−	0.0674365i	0.0107434	−	0.00315455i	0.287100	+	0.957901i	$0.407309\pi$
$458$	−6.07216	−	13.2962i	−0.283733	−	0.621290i
$459$	−1.32129			−0.0616727
$460$	18.6230	+	0.995125i	0.868301	+	0.0463979i
$461$	11.3943			0.530686			0.265343	−	0.964154i	$-0.414515\pi$
$461$	11.3943			0.530686			0.265343	+	0.964154i	$0.414515\pi$
$462$	2.21508	+	4.85036i	0.103055	+	0.225659i
$463$	11.7448	−	3.44859i	0.545829	−	0.160270i	0.00281867	−	0.999996i	$-0.499103\pi$
$463$	11.7448	−	3.44859i	0.545829	−	0.160270i	0.543010	+	0.839726i	$0.317285\pi$
$464$	3.33455	−	3.84828i	0.154803	−	0.178652i
$465$	−8.34273	−	5.36155i	−0.386885	−	0.248636i
$466$	−6.90759	−	7.97178i	−0.319988	−	0.369286i
$467$	2.96789	+	20.6421i	0.137337	+	0.955202i	0.935642	+	0.352949i	$0.114821\pi$
$467$	2.96789	+	20.6421i	0.137337	+	0.955202i	−0.798305	+	0.602253i	$0.794270\pi$
$468$	−5.12795	−	1.50570i	−0.237040	−	0.0696012i
$469$	−8.65132	+	5.55986i	−0.399481	+	0.256731i
$470$	4.71322	−	32.7812i	0.217405	−	1.51208i
$471$	−0.607763	+	1.33082i	−0.0280042	+	0.0613207i
$472$	−6.17252	+	13.5159i	−0.284113	+	0.622122i
$473$	−7.06180	+	49.1159i	−0.324702	+	2.25835i
$474$	0.587980	−	0.377872i	0.0270068	−	0.0173562i
$475$	55.9369	+	16.4245i	2.56656	+	0.753610i
$476$	−0.188040	−	1.30784i	−0.00861878	−	0.0599450i
$477$	3.29507	+	3.80271i	0.150871	+	0.174114i
$478$	20.4710	+	13.1559i	0.936321	+	0.601737i
$479$	12.7784	−	14.7471i	0.583861	−	0.673812i	−0.384569	−	0.923096i	$-0.625650\pi$
$479$	12.7784	−	14.7471i	0.583861	−	0.673812i	0.968430	+	0.249284i	$0.0801954\pi$
$480$	−3.73118	+	1.09557i	−0.170304	+	0.0500059i
$481$	10.9607	+	24.0007i	0.499766	+	1.09434i
$482$	−29.1634			−1.32836
$483$	0.428249	+	4.77667i	0.0194860	+	0.217346i
$484$	17.4326			0.792389
$485$	−30.0159	−	65.7257i	−1.36295	−	2.98445i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	20.4131	−	23.5580i	0.925008	−	1.06752i	−0.0725286	−	0.997366i	$-0.523107\pi$
$487$	20.4131	−	23.5580i	0.925008	−	1.06752i	0.997536	−	0.0701497i	$-0.0223477\pi$
$488$	7.32192	+	4.70551i	0.331448	+	0.213009i
$489$	0.470887	+	0.543433i	0.0212943	+	0.0245749i
$490$	0.553420	+	3.84912i	0.0250010	+	0.173885i
$491$	1.40420	+	0.412310i	0.0633706	+	0.0186073i	0.313264	−	0.949666i	$-0.398577\pi$
$491$	1.40420	+	0.412310i	0.0633706	+	0.0186073i	−0.249894	+	0.968273i	$0.580396\pi$
$492$	−4.00725	+	2.57530i	−0.180661	+	0.116104i
$493$	0.957498	−	6.65955i	0.0431236	−	0.299931i
$494$	12.7872	−	28.0000i	0.575323	−	1.25978i
$495$	8.61380	−	18.8616i	0.387161	−	0.847765i
$496$	−0.362933	+	2.52426i	−0.0162962	+	0.113343i
$497$	−8.39305	+	5.39389i	−0.376480	+	0.241949i
$498$	8.28739	+	2.43340i	0.371367	+	0.109043i
$499$	−4.94825	−	34.4158i	−0.221514	−	1.54066i	−0.732315	−	0.680966i	$-0.761560\pi$
$499$	−4.94825	−	34.4158i	−0.221514	−	1.54066i	0.510801	−	0.859699i	$-0.329349\pi$
$500$	−13.0434	−	15.0529i	−0.583320	−	0.673188i
$501$	−17.1250	−	11.0056i	−0.765089	−	0.491693i
$502$	1.44752	−	1.67052i	0.0646058	−	0.0745591i
$503$	39.8718	−	11.7074i	1.77779	−	0.522007i	0.782829	−	0.622236i	$-0.213776\pi$
$503$	39.8718	−	11.7074i	1.77779	−	0.522007i	0.994964	+	0.100229i	$0.0319575\pi$
$504$	−0.415415	−	0.909632i	−0.0185041	−	0.0405182i
$505$	4.21155			0.187411
$506$	24.1172	+	8.50357i	1.07214	+	0.378030i
$507$	−15.5631			−0.691180
$508$	0.836017	+	1.83062i	0.0370923	+	0.0812207i
$509$	−29.9907	+	8.80607i	−1.32932	+	0.390322i	−0.867846	−	0.496834i	$-0.834496\pi$
$509$	−29.9907	+	8.80607i	−1.32932	+	0.390322i	−0.461470	+	0.887156i	$0.652678\pi$
$510$	−3.36475	+	3.88313i	−0.148994	+	0.171948i
$511$	−7.03395	−	4.52045i	−0.311164	−	0.199973i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−0.819673	−	5.70095i	−0.0361894	−	0.251703i
$514$	−11.8512	−	3.47982i	−0.522733	−	0.153488i
$515$	22.3340	−	14.3532i	0.984154	−	0.632477i
$516$	1.32436	−	9.21115i	0.0583019	−	0.405498i
$517$	18.8648	−	41.3083i	0.829675	−	1.81674i
$518$	−2.05087	+	4.49077i	−0.0901099	+	0.197313i
$519$	−0.948518	+	6.59709i	−0.0416353	+	0.289580i
$520$	−17.4837	+	11.2361i	−0.766712	+	0.492736i
$521$	20.2819	+	5.95530i	0.888566	+	0.260906i	0.693993	−	0.719982i	$-0.255850\pi$
$521$	20.2819	+	5.95530i	0.888566	+	0.260906i	0.194573	+	0.980888i	$0.437668\pi$
$522$	−0.724668	−	5.04017i	−0.0317178	−	0.220602i
$523$	−26.0091	−	30.0161i	−1.13730	−	1.31251i	−0.943464	−	0.331476i	$-0.892453\pi$
$523$	−26.0091	−	30.0161i	−1.13730	−	1.31251i	−0.193833	−	0.981035i	$-0.562092\pi$
$524$	−15.3723	−	9.87919i	−0.671543	−	0.431574i
$525$	6.62849	−	7.64969i	0.289291	−	0.333860i
$526$	20.9301	−	6.14562i	0.912594	−	0.267962i
$527$	1.39978	+	3.06508i	0.0609752	+	0.133517i
$528$	−5.33222			−0.232055
$529$	17.9135	+	14.4259i	0.778849	+	0.627211i
$530$	19.5668			0.849928
$531$	6.17252	+	13.5159i	0.267865	+	0.586542i
$532$	5.52627	−	1.62266i	0.239594	−	0.0703512i
$533$	−16.6714	+	19.2398i	−0.722117	+	0.833367i
$534$	4.92159	+	3.16291i	0.212978	+	0.136873i
$535$	−16.0134	−	18.4805i	−0.692321	−	0.798981i
$536$	−1.46354	−	10.1792i	−0.0632154	−	0.439673i
$537$	17.4190	+	5.11468i	0.751686	+	0.220715i
$538$	4.18654	−	2.69053i	0.180495	−	0.115997i
$539$	−0.758854	+	5.27794i	−0.0326862	+	0.227337i
$540$	−1.61542	+	3.53729i	−0.0695168	+	0.152221i
$541$	−14.6584	+	32.0974i	−0.630213	+	1.37997i	0.277639	+	0.960685i	$0.410448\pi$
$541$	−14.6584	+	32.0974i	−0.630213	+	1.37997i	−0.907853	+	0.419289i	$0.862279\pi$
$542$	−0.554631	+	3.85755i	−0.0238235	+	0.165696i
$543$	13.6311	−	8.76021i	0.584968	−	0.375936i
$544$	1.26777	+	0.372251i	0.0543553	+	0.0159601i
$545$	−7.53678	−	52.4194i	−0.322840	−	2.24540i
$546$	−3.49986	−	4.03906i	−0.149780	−	0.172856i
$547$	26.4414	+	16.9928i	1.13055	+	0.726561i	0.965675	−	0.259753i	$-0.0836413\pi$
$547$	26.4414	+	16.9928i	1.13055	+	0.726561i	0.164876	+	0.986314i	$0.447278\pi$
$548$	1.50759	−	1.73985i	0.0644010	−	0.0743227i
$549$	8.35103	−	2.45208i	0.356413	−	0.104652i
$550$	−22.4211	−	49.0953i	−0.956037	−	2.09343i
$551$	29.3278			1.24941
$552$	−4.52292	−	1.59475i	−0.192508	−	0.0678772i
$553$	0.698933			0.0297217
$554$	2.04423	+	4.47623i	0.0868508	+	0.190177i
$555$	18.4205	−	5.40875i	0.781907	−	0.229588i
$556$	−2.55702	+	2.95095i	−0.108442	+	0.125148i
$557$	−15.1429	−	9.73178i	−0.641627	−	0.412349i	0.178971	−	0.983854i	$-0.442723\pi$
$557$	−15.1429	−	9.73178i	−0.641627	−	0.412349i	−0.820598	+	0.571506i	$0.806360\pi$
$558$	1.67004	+	1.92732i	0.0706983	+	0.0815901i
$559$	−7.07799	−	49.2285i	−0.299367	−	2.08214i
$560$	−3.73118	−	1.09557i	−0.157671	−	0.0462964i
$561$	−5.92699	+	3.80904i	−0.250238	+	0.160818i
$562$	−0.965584	+	6.71579i	−0.0407307	+	0.283288i
$563$	−7.46280	+	16.3413i	−0.314520	+	0.688702i	−0.999194	−	0.0401474i	$-0.987217\pi$
$563$	−7.46280	+	16.3413i	−0.314520	+	0.688702i	0.684674	+	0.728849i	$0.259945\pi$
$564$	−3.53790	+	7.74692i	−0.148972	+	0.326204i
$565$	3.43513	−	23.8919i	0.144517	−	1.00514i
$566$	21.7357	−	13.9687i	0.913619	−	0.587147i
$567$	−0.959493	−	0.281733i	−0.0402949	−	0.0118317i
$568$	−1.41985	−	9.87529i	−0.0595757	−	0.414358i
$569$	−4.77210	−	5.50730i	−0.200057	−	0.230878i	0.646853	−	0.762615i	$-0.276085\pi$
$569$	−4.77210	−	5.50730i	−0.200057	−	0.230878i	−0.846910	+	0.531737i	$0.821539\pi$
$570$	−18.8418	−	12.1089i	−0.789195	−	0.507185i
$571$	12.0236	−	13.8760i	0.503172	−	0.580692i	−0.446165	−	0.894951i	$-0.647211\pi$
$571$	12.0236	−	13.8760i	0.503172	−	0.580692i	0.949337	+	0.314259i	$0.101756\pi$
$572$	−27.3434	+	8.02874i	−1.14328	+	0.335698i
$573$	−7.75321	−	16.9772i	−0.323895	−	0.709232i
$574$	−4.76343			−0.198822
$575$	−4.33473	−	48.3494i	−0.180771	−	2.01631i
$576$	1.00000			0.0416667
$577$	−17.7934	−	38.9620i	−0.740747	−	1.62201i	−0.782322	−	0.622875i	$-0.785965\pi$
$577$	−17.7934	−	38.9620i	−0.740747	−	1.62201i	0.0415747	−	0.999135i	$-0.486763\pi$
$578$	−14.6363	+	4.29760i	−0.608789	+	0.178757i
$579$	−13.7117	+	15.8241i	−0.569838	+	0.657628i
$580$	−16.6579	−	10.7054i	−0.691681	−	0.444517i
$581$	5.65620	+	6.52760i	0.234659	+	0.270811i
$582$	2.64433	+	18.3917i	0.109611	+	0.762360i
$583$	25.7434	+	7.55893i	1.06618	+	0.313059i
$584$	7.03395	−	4.52045i	0.291067	−	0.187057i
$585$	−2.95772	+	20.5714i	−0.122287	+	0.850522i
$586$	−11.5349	+	25.2579i	−0.476503	+	1.04340i
$587$	−17.4922	+	38.3025i	−0.721979	+	1.58091i	0.0891309	+	0.996020i	$0.471591\pi$
$587$	−17.4922	+	38.3025i	−0.721979	+	1.58091i	−0.811110	+	0.584894i	$0.801136\pi$
$588$	0.142315	−	0.989821i	0.00586897	−	0.0408195i
$589$	−12.3565	+	7.94102i	−0.509139	+	0.327204i
$590$	55.4405	+	16.2788i	2.28245	+	0.670187i
$591$	2.38903	+	16.6161i	0.0982715	+	0.683493i
$592$	−3.23299	−	3.73107i	−0.132875	−	0.153346i
$593$	31.3893	+	20.1727i	1.28900	+	0.828392i	0.991970	−	0.126475i	$-0.0403664\pi$
$593$	31.3893	+	20.1727i	1.28900	+	0.828392i	0.297033	+	0.954867i	$0.404003\pi$
$594$	−3.49186	+	4.02982i	−0.143273	+	0.165346i
$595$	−4.92998	+	1.44757i	−0.202110	+	0.0593447i
$596$	−5.93350	−	12.9925i	−0.243046	−	0.532196i
$597$	−7.53775			−0.308499
$598$	−25.5945	−	1.36765i	−1.04664	−	0.0559274i
$599$	16.6169			0.678947			0.339474	−	0.940616i	$-0.389751\pi$
$599$	16.6169			0.678947			0.339474	+	0.940616i	$0.389751\pi$
$600$	4.20483	+	9.20729i	0.171661	+	0.375886i
$601$	−11.9374	+	3.50513i	−0.486936	+	0.142977i	−0.515980	−	0.856601i	$-0.672572\pi$
$601$	−11.9374	+	3.50513i	−0.486936	+	0.142977i	0.0290436	+	0.999578i	$0.490754\pi$
$602$	6.09405	−	7.03291i	0.248375	−	0.286640i
$603$	−8.65132	−	5.55986i	−0.352309	−	0.226415i
$604$	−11.8868	−	13.7181i	−0.483666	−	0.558181i
$605$	−9.64752	−	67.1000i	−0.392228	−	2.72800i
$606$	−1.03915	−	0.305123i	−0.0422127	−	0.0123948i
$607$	8.47456	−	5.44627i	0.343972	−	0.221057i	−0.357236	−	0.934014i	$-0.616281\pi$
$607$	8.47456	−	5.44627i	0.343972	−	0.221057i	0.701208	+	0.712957i	$0.252644\pi$
$608$	−0.819673	+	5.70095i	−0.0332421	+	0.231204i
$609$	2.11529	−	4.63185i	0.0857161	−	0.187692i
$610$	14.0600	−	30.7871i	0.569272	−	1.24653i
$611$	−6.47762	+	45.0529i	−0.262057	+	1.82264i
$612$	1.11154	−	0.714345i	0.0449315	−	0.0288757i
$613$	27.1227	+	7.96396i	1.09548	+	0.321661i	0.779054	−	0.626957i	$-0.215700\pi$
$613$	27.1227	+	7.96396i	1.09548	+	0.321661i	0.316423	+	0.948618i	$0.397518\pi$
$614$	3.77672	+	26.2677i	0.152416	+	1.06008i
$615$	12.1303	+	13.9992i	0.489143	+	0.564501i
$616$	−4.48575	−	2.88282i	−0.180736	−	0.116152i
$617$	−15.3797	+	17.7491i	−0.619162	+	0.714551i	−0.975548	−	0.219788i	$-0.929463\pi$
$617$	−15.3797	+	17.7491i	−0.619162	+	0.714551i	0.356386	+	0.934339i	$0.384009\pi$
$618$	−6.55054	+	1.92341i	−0.263501	+	0.0773710i
$619$	6.57158	+	14.3898i	0.264134	+	0.578373i	0.994506	−	0.104676i	$-0.0333806\pi$
$619$	6.57158	+	14.3898i	0.264134	+	0.578373i	−0.730372	+	0.683050i	$0.760653\pi$
$620$	9.91702			0.398277
$621$	−4.16711	+	2.37385i	−0.167221	+	0.0952593i
$622$	9.39113			0.376550
$623$	2.43031	+	5.32163i	0.0973681	+	0.213206i
$624$	5.12795	−	1.50570i	0.205282	−	0.0602764i
$625$	−17.5796	+	20.2879i	−0.703183	+	0.811516i
$626$	15.2104	+	9.77513i	0.607930	+	0.390693i
$627$	−20.1116	−	23.2101i	−0.803181	−	0.926921i
$628$	−0.208210	−	1.44813i	−0.00830850	−	0.0577869i
$629$	−6.25887	−	1.83777i	−0.249558	−	0.0732767i
$630$	−3.27138	+	2.10239i	−0.130335	+	0.0837612i
$631$	4.55127	−	31.6548i	0.181183	−	1.26016i	−0.672788	−	0.739835i	$-0.734903\pi$
$631$	4.55127	−	31.6548i	0.181183	−	1.26016i	0.853971	−	0.520321i	$-0.174188\pi$
$632$	−0.290347	+	0.635772i	−0.0115494	+	0.0252897i
$633$	−0.780052	+	1.70807i	−0.0310043	+	0.0678899i
$634$	0.697651	−	4.85227i	0.0277072	−	0.192708i
$635$	6.58361	−	4.23103i	0.261263	−	0.167903i
$636$	−4.82789	−	1.41760i	−0.191438	−	0.0562113i
$637$	−0.760593	−	5.29004i	−0.0301358	−	0.209599i
$638$	−17.7806	−	20.5199i	−0.703939	−	0.812389i
$639$	−8.39305	−	5.39389i	−0.332024	−	0.213379i
$640$	2.54656	−	2.93888i	0.100662	−	0.116170i
$641$	20.8270	−	6.11536i	0.822617	−	0.241542i	0.156775	−	0.987634i	$-0.449890\pi$
$641$	20.8270	−	6.11536i	0.822617	−	0.241542i	0.665843	+	0.746092i	$0.268072\pi$
$642$	2.61224	+	5.72001i	0.103097	+	0.225751i
$643$	−3.67317			−0.144856			−0.0724279	−	0.997374i	$-0.523075\pi$
$643$	−3.67317			−0.144856			−0.0724279	+	0.997374i	$0.523075\pi$
$644$	−2.94273	−	3.78686i	−0.115960	−	0.149223i
$645$	−36.1878			−1.42489
$646$	3.16134	+	6.92238i	0.124381	+	0.272357i
$647$	−11.2348	+	3.29885i	−0.441687	+	0.129691i	−0.495012	−	0.868886i	$-0.664836\pi$
$647$	−11.2348	+	3.29885i	−0.441687	+	0.129691i	0.0533248	+	0.998577i	$0.483018\pi$
$648$	0.654861	−	0.755750i	0.0257254	−	0.0296886i
$649$	66.6523	+	42.8349i	2.61633	+	1.68142i
$650$	35.4256	+	40.8833i	1.38951	+	1.60358i
$651$	0.362933	+	2.52426i	0.0142245	+	0.0989335i
$652$	−0.689938	−	0.202584i	−0.0270201	−	0.00793380i
$653$	36.9040	−	23.7168i	1.44416	−	0.928108i	0.444691	−	0.895684i	$-0.353314\pi$
$653$	36.9040	−	23.7168i	1.44416	−	0.928108i	0.999474	−	0.0324243i	$-0.0103228\pi$
$654$	−1.93812	+	13.4799i	−0.0757866	+	0.527107i
$655$	−29.5188	+	64.6372i	−1.15340	+	2.52559i
$656$	1.97880	−	4.33297i	0.0772592	−	0.169174i
$657$	1.18993	−	8.27617i	0.0464237	−	0.322884i
$658$	−7.16457	+	4.60439i	−0.279304	+	0.179498i
$659$	26.3485	+	7.73663i	1.02639	+	0.301376i	0.751244	−	0.660025i	$-0.229454\pi$
$659$	26.3485	+	7.73663i	1.02639	+	0.301376i	0.275150	+	0.961401i	$0.411273\pi$
$660$	2.95096	+	20.5243i	0.114866	+	0.798909i
$661$	−17.0838	−	19.7158i	−0.664484	−	0.766855i	0.319019	−	0.947748i	$-0.396647\pi$
$661$	−17.0838	−	19.7158i	−0.664484	−	0.766855i	−0.983503	+	0.180893i	$0.942101\pi$
$662$	10.8739	+	6.98824i	0.422627	+	0.271606i
$663$	4.62435	−	5.33678i	0.179595	−	0.207263i
$664$	−8.28739	+	2.43340i	−0.321613	+	0.0944341i
$665$	−9.30416	−	20.3733i	−0.360800	−	0.790041i
$666$	−4.93691			−0.191301
$667$	−8.94485	−	22.7232i	−0.346346	−	0.879847i
$668$	20.3565			0.787618
$669$	0.684532	+	1.49892i	0.0264656	+	0.0579515i
$670$	−38.3709	+	11.2667i	−1.48240	+	0.435271i
$671$	30.3917	−	35.0739i	1.17326	−	1.35401i
$672$	0.841254	+	0.540641i	0.0324521	+	0.0208557i
$673$	4.03733	+	4.65933i	0.155628	+	0.179604i	0.828209	−	0.560419i	$-0.189360\pi$
$673$	4.03733	+	4.65933i	0.155628	+	0.179604i	−0.672581	+	0.740023i	$0.734814\pi$
$674$	2.77926	+	19.3302i	0.107053	+	0.744571i
$675$	9.71198	+	2.85169i	0.373814	+	0.109762i
$676$	13.0925	−	8.41402i	0.503557	−	0.323616i
$677$	3.33635	−	23.2048i	0.128226	−	0.891833i	−0.819575	−	0.572972i	$-0.805790\pi$
$677$	3.33635	−	23.2048i	0.128226	−	0.891833i	0.947801	−	0.318861i	$-0.103300\pi$
$678$	−2.57852	+	5.64618i	−0.0990276	+	0.216840i
$679$	−7.71875	+	16.9017i	−0.296218	+	0.648628i
$680$	0.731230	−	5.08582i	0.0280414	−	0.195032i
$681$	−17.4665	+	11.2251i	−0.669320	+	0.430146i
$682$	13.0475	+	3.83109i	0.499614	+	0.146700i
$683$	1.77236	+	12.3270i	0.0678174	+	0.471681i	0.995223	+	0.0976241i	$0.0311243\pi$
$683$	1.77236	+	12.3270i	0.0678174	+	0.471681i	−0.927406	+	0.374056i	$0.877967\pi$
$684$	3.77172	+	4.35280i	0.144215	+	0.166433i
$685$	−7.53121	−	4.84002i	−0.287753	−	0.184928i
$686$	0.654861	−	0.755750i	0.0250027	−	0.0288547i
$687$	14.0250	−	4.11811i	0.535087	−	0.157116i
$688$	3.86580	+	8.46492i	0.147382	+	0.322722i
$689$	−26.8917			−1.02449
$690$	−3.63532	+	18.2918i	−0.138394	+	0.696357i
$691$	7.09007			0.269719			0.134859	−	0.990865i	$-0.456942\pi$
$691$	7.09007			0.269719			0.134859	+	0.990865i	$0.456942\pi$
$692$	−2.76871	−	6.06263i	−0.105251	−	0.230467i
$693$	−5.11623	+	1.50226i	−0.194349	+	0.0570661i
$694$	7.28513	−	8.40749i	0.276540	−	0.319144i
$695$	12.7737	+	8.20914i	0.484533	+	0.311390i
$696$	3.33455	+	3.84828i	0.126396	+	0.145869i
$697$	−0.895714	−	6.22982i	−0.0339276	−	0.235971i
$698$	−11.5369	−	3.38754i	−0.436678	−	0.128220i
$699$	8.87369	−	5.70278i	0.335634	−	0.215699i
$700$	−1.44051	+	10.0190i	−0.0544461	+	0.378681i
$701$	−1.51506	+	3.31751i	−0.0572228	+	0.125301i	−0.936083	−	0.351778i	$-0.885577\pi$
$701$	−1.51506	+	3.31751i	−0.0572228	+	0.125301i	0.878861	+	0.477079i	$0.158304\pi$
$702$	2.22016	−	4.86148i	0.0837946	−	0.183485i
$703$	4.04665	−	28.1451i	0.152622	−	1.06151i
$704$	4.48575	−	2.88282i	0.169063	−	0.108650i
$705$	31.7767	+	9.33049i	1.19678	+	0.351407i
$706$	−0.393398	−	2.73614i	−0.0148057	−	0.102976i
$707$	−0.709229	−	0.818493i	−0.0266733	−	0.0307826i
$708$	−12.4999	−	8.03321i	−0.469776	−	0.301907i
$709$	12.5387	−	14.4705i	0.470902	−	0.543450i	−0.469760	−	0.882794i	$-0.655660\pi$
$709$	12.5387	−	14.4705i	0.470902	−	0.543450i	0.940662	+	0.339344i	$0.110205\pi$
$710$	−37.2254	+	10.9304i	−1.39704	+	0.410209i
$711$	0.290347	+	0.635772i	0.0108889	+	0.0238433i
$712$	−5.85031			−0.219250
$713$	9.92139	+	7.15184i	0.371559	+	0.267839i
$714$	1.32129			0.0494482
$715$	46.0359	+	100.805i	1.72165	+	3.76988i
$716$	−17.4190	+	5.11468i	−0.650979	+	0.191145i
$717$	−15.9353	+	18.3903i	−0.595115	+	0.686800i
$718$	−15.2880	−	9.82501i	−0.570543	−	0.366666i
$719$	0.334707	+	0.386273i	0.0124825	+	0.0144055i	0.761956	−	0.647628i	$-0.224239\pi$
$719$	0.334707	+	0.386273i	0.0124825	+	0.0144055i	−0.749474	+	0.662034i	$0.769694\pi$
$720$	−0.553420	−	3.84912i	−0.0206247	−	0.143448i
$721$	−6.55054	−	1.92341i	−0.243955	−	0.0716316i
$722$	−11.9228	+	7.66234i	−0.443722	+	0.285163i
$723$	4.15039	−	28.8666i	0.154355	−	1.07356i
$724$	−6.73112	+	14.7391i	−0.250160	+	0.547775i
$725$	−21.4110	+	46.8835i	−0.795184	+	1.74121i
$726$	−2.48091	+	17.2551i	−0.0920753	+	0.640398i
$727$	−34.2814	+	22.0313i	−1.27143	+	0.817097i	−0.989805	−	0.142428i	$-0.954509\pi$
$727$	−34.2814	+	22.0313i	−1.27143	+	0.817097i	−0.281623	+	0.959525i	$0.590873\pi$
$728$	5.12795	+	1.50570i	0.190055	+	0.0558051i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−21.2925	−	24.5728i	−0.788069	−	0.909480i
$731$	10.3439	+	6.64761i	0.382582	+	0.245871i
$732$	−5.69964	+	6.57773i	−0.210665	+	0.243120i
$733$	2.53365	−	0.743947i	0.0935825	−	0.0274783i	−0.234606	−	0.972091i	$-0.575380\pi$
$733$	2.53365	−	0.743947i	0.0935825	−	0.0274783i	0.328189	+	0.944612i	$0.393562\pi$
$734$	−4.34888	−	9.52272i	−0.160520	−	0.351490i
$735$	−3.88870			−0.143437
$736$	4.66711	−	1.10368i	0.172032	−	0.0406822i
$737$	−54.8357			−2.01990
$738$	−1.97880	−	4.33297i	−0.0728406	−	0.159499i
$739$	−19.8560	+	5.83024i	−0.730413	+	0.214469i	−0.625733	−	0.780037i	$-0.715200\pi$
$739$	−19.8560	+	5.83024i	−0.730413	+	0.214469i	−0.104680	+	0.994506i	$0.533382\pi$
$740$	−12.5721	+	14.5090i	−0.462160	+	0.533361i
$741$	25.8952	+	16.6418i	0.951285	+	0.611354i
$742$	−3.29507	−	3.80271i	−0.120966	−	0.139602i
$743$	2.32410	+	16.1645i	0.0852631	+	0.593018i	0.986998	+	0.160730i	$0.0513847\pi$
$743$	2.32410	+	16.1645i	0.0852631	+	0.593018i	−0.901735	+	0.432289i	$0.857706\pi$
$744$	−2.44691	−	0.718479i	−0.0897082	−	0.0263407i
$745$	−46.7262	+	30.0291i	−1.71191	+	1.10018i
$746$	−0.457139	+	3.17947i	−0.0167370	+	0.116409i
$747$	−3.58805	+	7.85673i	−0.131280	+	0.287463i
$748$	2.92678	−	6.40875i	0.107014	−	0.234327i
$749$	−0.894913	+	6.22426i	−0.0326994	+	0.227429i
$750$	16.7560	−	10.7684i	0.611842	−	0.393207i
$751$	−17.6879	−	5.19364i	−0.645441	−	0.189519i	−0.0574019	−	0.998351i	$-0.518282\pi$
$751$	−17.6879	−	5.19364i	−0.645441	−	0.189519i	−0.588039	+	0.808833i	$0.700100\pi$
$752$	−1.21203	−	8.42985i	−0.0441982	−	0.307405i
$753$	1.44752	+	1.67052i	0.0527504	+	0.0608772i
$754$	22.8938	+	14.7130i	0.833743	+	0.535814i
$755$	−46.2241	+	53.3455i	−1.68227	+	1.94144i
$756$	0.959493	−	0.281733i	0.0348964	−	0.0102465i
$757$	8.73405	+	19.1249i	0.317444	+	0.695106i	0.999339	−	0.0363437i	$-0.0115711\pi$
$757$	8.73405	+	19.1249i	0.317444	+	0.695106i	−0.681895	+	0.731450i	$0.738844\pi$
$758$	−9.18590			−0.333647
$759$	−11.8492	+	22.6615i	−0.430101	+	0.822561i
$760$	22.3973			0.812434
$761$	−6.31487	−	13.8276i	−0.228914	−	0.501251i	0.759967	−	0.649962i	$-0.225215\pi$
$761$	−6.31487	−	13.8276i	−0.228914	−	0.501251i	−0.988881	+	0.148710i	$0.952488\pi$
$762$	−1.93097	+	0.566983i	−0.0699516	+	0.0205396i
$763$	−8.91826	+	10.2922i	−0.322863	+	0.372603i
$764$	15.7010	+	10.0904i	0.568041	+	0.365058i
$765$	−3.36475	−	3.88313i	−0.121653	−	0.140395i
$766$	4.40809	+	30.6589i	0.159271	+	1.10775i
$767$	−76.1947	−	22.3728i	−2.75123	−	0.807834i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	−4.23422	+	29.4496i	−0.152690	+	1.06198i	0.758997	+	0.651094i	$0.225690\pi$
$769$	−4.23422	+	29.4496i	−0.152690	+	1.06198i	−0.911687	+	0.410886i	$0.865219\pi$
$770$	−8.61380	+	18.8616i	−0.310420	+	0.679724i
$771$	5.13099	−	11.2353i	0.184788	−	0.404630i
$772$	2.97983	−	20.7252i	0.107247	−	0.745916i
$773$	35.8477	−	23.0379i	1.28935	−	0.828616i	0.297341	−	0.954771i	$-0.403900\pi$
$773$	35.8477	−	23.0379i	1.28935	−	0.828616i	0.992010	+	0.126155i	$0.0402638\pi$
$774$	8.92892	+	2.62177i	0.320943	+	0.0942375i
$775$	−3.67361	−	25.5505i	−0.131960	−	0.917802i
$776$	−12.1678	−	14.0424i	−0.436800	−	0.504094i
$777$	−4.15319	−	2.66909i	−0.148995	−	0.0957532i
$778$	1.72051	−	1.98558i	0.0616834	−	0.0711864i
$779$	26.3240	−	7.72942i	0.943155	−	0.276935i
$780$	−8.63354	−	18.9048i	−0.309130	−	0.676901i
$781$	−53.1987			−1.90360
$782$	4.39928	−	4.56071i	0.157318	−	0.163091i
$783$	5.09200			0.181973
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	−5.45881	+	1.60285i	−0.194833	+	0.0572083i
$786$	11.9663	−	13.8099i	0.426825	−	0.492583i
$787$	34.9870	+	22.4848i	1.24715	+	0.801496i	0.986472	−	0.163929i	$-0.0524168\pi$
$787$	34.9870	+	22.4848i	1.24715	+	0.801496i	0.260680	+	0.965425i	$0.416053\pi$
$788$	−10.9931	−	12.6867i	−0.391613	−	0.451945i
$789$	3.10441	+	21.5916i	0.110520	+	0.768682i
$790$	2.60785	+	0.765733i	0.0927830	+	0.0272436i
$791$	−5.22175	+	3.35581i	−0.185664	+	0.119319i
$792$	0.758854	−	5.27794i	0.0269647	−	0.187544i
$793$	−19.3234	+	42.3123i	−0.686193	+	1.50255i
$794$	3.15221	−	6.90237i	0.111868	−	0.244956i
$795$	−2.78465	+	19.3676i	−0.0987612	+	0.686900i
$796$	6.34116	−	4.07521i	0.224756	−	0.144442i
$797$	32.2360	+	9.46535i	1.14186	+	0.335280i	0.797358	−	0.603507i	$-0.206230\pi$
$797$	32.2360	+	9.46535i	1.14186	+	0.335280i	0.344500	+	0.938786i	$0.388048\pi$
$798$	0.819673	+	5.70095i	0.0290161	+	0.201811i
$799$	−7.36905	−	8.50433i	−0.260698	−	0.300862i
$800$	−8.51516	−	5.47236i	−0.301056	−	0.193477i
$801$	−3.83114	+	4.42137i	−0.135367	+	0.156221i
$802$	−13.0115	+	3.82052i	−0.459452	+	0.134907i
$803$	−18.5209	−	40.5552i	−0.653589	−	1.43116i
$804$	10.2838			0.362683
$805$	−12.9475	+	13.4226i	−0.456340	+	0.473086i
$806$	−13.6295			−0.480078
$807$	2.06733	+	4.52683i	0.0727736	+	0.159352i
$808$	1.03915	−	0.305123i	0.0365572	−	0.0107342i
$809$	22.3129	−	25.7504i	0.784479	−	0.905337i	−0.212945	−	0.977064i	$-0.568306\pi$
$809$	22.3129	−	25.7504i	0.784479	−	0.905337i	0.997424	+	0.0717268i	$0.0228510\pi$
$810$	−3.27138	−	2.10239i	−0.114945	−	0.0738705i
$811$	−23.5319	−	27.1572i	−0.826316	−	0.953620i	0.173195	−	0.984888i	$-0.444591\pi$
$811$	−23.5319	−	27.1572i	−0.826316	−	0.953620i	−0.999511	+	0.0312678i	$0.990046\pi$
$812$	0.724668	+	5.04017i	0.0254308	+	0.176875i
$813$	−3.73935	−	1.09797i	−0.131145	−	0.0385076i
$814$	−22.1457	+	14.2322i	−0.776207	+	0.498838i
$815$	−0.397945	+	2.76777i	−0.0139394	+	0.0969506i
$816$	−0.548885	+	1.20189i	−0.0192148	+	0.0420746i
$817$	−22.2654	+	48.7543i	−0.778966	+	1.70570i
$818$	−2.07268	+	14.4158i	−0.0724696	+	0.504037i
$819$	4.49603	−	2.88942i	0.157104	−	0.100965i
$820$	−17.7732	−	5.21869i	−0.620668	−	0.182244i
$821$	7.00348	+	48.7103i	0.244423	+	1.70000i	0.629406	+	0.777076i	$0.283298\pi$
$821$	7.00348	+	48.7103i	0.244423	+	1.70000i	−0.384983	+	0.922924i	$0.625793\pi$
$822$	1.50759	+	1.73985i	0.0525832	+	0.0606842i
$823$	−10.3692	−	6.66388i	−0.361448	−	0.232288i	0.347294	−	0.937756i	$-0.387101\pi$
$823$	−10.3692	−	6.66388i	−0.361448	−	0.232288i	−0.708742	+	0.705468i	$0.750737\pi$
$824$	4.47079	−	5.15956i	0.155747	−	0.179742i
$825$	51.7864	−	15.2059i	1.80297	−	0.529400i
$826$	−6.17252	−	13.5159i	−0.214770	−	0.470280i
$827$	−44.6214			−1.55164			−0.775819	−	0.630955i	$-0.782663\pi$
$827$	−44.6214			−1.55164			−0.775819	+	0.630955i	$0.782663\pi$
$828$	2.22220	−	4.24992i	0.0772267	−	0.147695i
$829$	−11.5338			−0.400587			−0.200293	−	0.979736i	$-0.564190\pi$
$829$	−11.5338			−0.400587			−0.200293	+	0.979736i	$0.564190\pi$
$830$	13.9528	+	30.5525i	0.484310	+	1.06049i
$831$	−4.72159	+	1.38638i	−0.163790	+	0.0480932i
$832$	−3.49986	+	4.03906i	−0.121336	+	0.140029i
$833$	1.11154	+	0.714345i	0.0385127	+	0.0247506i
$834$	−2.55702	−	2.95095i	−0.0885422	−	0.102183i
$835$	−11.2657	−	78.3548i	−0.389866	−	2.71158i
$836$	29.4673	+	8.65238i	1.01915	+	0.299249i
$837$	−2.14538	+	1.37875i	−0.0741551	+	0.0476566i
$838$	−2.16832	+	15.0810i	−0.0749034	+	0.520964i
$839$	−10.3534	+	22.6708i	−0.357440	+	0.782683i	0.642427	+	0.766347i	$0.277928\pi$
$839$	−10.3534	+	22.6708i	−0.357440	+	0.782683i	−0.999867	+	0.0163366i	$0.994800\pi$
$840$	1.61542	−	3.53729i	0.0557374	−	0.122048i
$841$	0.437121	−	3.04024i	0.0150731	−	0.104836i
$842$	15.4223	−	9.91133i	0.531488	−	0.341567i
$843$	−6.51001	−	1.91151i	−0.224217	−	0.0658360i
$844$	−0.267234	−	1.85865i	−0.00919856	−	0.0639774i
$845$	−39.6322	−	45.7380i	−1.36339	−	1.57344i
$846$	−7.16457	−	4.60439i	−0.246323	−	0.158302i
$847$	−11.4159	+	13.1747i	−0.392255	+	0.452686i
$848$	4.82789	−	1.41760i	0.165790	−	0.0486804i
$849$	10.7332	+	23.5024i	0.368362	+	0.806600i
$850$	−13.3741			−0.458728
$851$	−23.0411	+	5.44877i	−0.789838	+	0.186782i
$852$	9.97684			0.341801
$853$	−11.2388	−	24.6096i	−0.384810	−	0.842617i	−0.998587	−	0.0531372i	$-0.983078\pi$
$853$	−11.2388	−	24.6096i	−0.384810	−	0.842617i	0.613777	−	0.789479i	$-0.289649\pi$
$854$	−8.35103	+	2.45208i	−0.285766	+	0.0839086i
$855$	14.6671	−	16.9267i	0.501604	−	0.578882i
$856$	−5.29003	−	3.39969i	−0.180809	−	0.116199i
$857$	19.0262	+	21.9574i	0.649923	+	0.750051i	0.981097	−	0.193519i	$-0.0619902\pi$
$857$	19.0262	+	21.9574i	0.649923	+	0.750051i	−0.331174	+	0.943570i	$0.607445\pi$
$858$	−4.05565	−	28.2077i	−0.138458	−	0.962994i
$859$	12.5611	+	3.68827i	0.428579	+	0.125842i	0.488906	−	0.872337i	$-0.337396\pi$
$859$	12.5611	+	3.68827i	0.428579	+	0.125842i	−0.0603270	+	0.998179i	$0.519214\pi$
$860$	30.4431	−	19.5646i	1.03810	−	0.667147i
$861$	0.677907	−	4.71494i	0.0231030	−	0.160685i
$862$	0.000850903	−	0.00186322i	2.89819e−5	−	6.34614e-5i
$863$	−2.82594	+	6.18795i	−0.0961962	+	0.210640i	−0.951612	−	0.307301i	$-0.900574\pi$
$863$	−2.82594	+	6.18795i	−0.0961962	+	0.210640i	0.855416	+	0.517941i	$0.173301\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	−21.8035	+	14.0123i	−0.741342	+	0.476432i
$866$	−2.01451	−	0.591513i	−0.0684558	−	0.0201004i
$867$	−2.17090	−	15.0989i	−0.0737275	−	0.512786i
$868$	−1.67004	−	1.92732i	−0.0566847	−	0.0654176i
$869$	3.13524	+	2.01490i	0.106356	+	0.0683507i
$870$	12.9671	−	14.9648i	0.439625	−	0.507354i
$871$	52.7351	−	15.4844i	1.78686	−	0.524669i
$872$	−5.65735	−	12.3879i	−0.191582	−	0.419506i
$873$	−18.5808			−0.628865
$874$	22.4071	+	16.1522i	0.757932	+	0.546356i
$875$	19.9179			0.673347
$876$	3.47340	+	7.60568i	0.117355	+	0.256972i
$877$	−10.0526	+	2.95171i	−0.339453	+	0.0996723i	−0.447016	−	0.894526i	$-0.647513\pi$
$877$	−10.0526	+	2.95171i	−0.339453	+	0.0996723i	0.107563	+	0.994198i	$0.465695\pi$
$878$	2.31088	−	2.66690i	0.0779884	−	0.0900034i
$879$	−23.3593	−	15.0121i	−0.787888	−	0.506345i
$880$	−13.5788	−	15.6708i	−0.457741	−	0.528262i
$881$	2.88932	+	20.0957i	0.0973438	+	0.677041i	0.978806	+	0.204787i	$0.0656503\pi$
$881$	2.88932	+	20.0957i	0.0973438	+	0.677041i	−0.881463	+	0.472254i	$0.843441\pi$
$882$	0.959493	+	0.281733i	0.0323078	+	0.00948643i
$883$	38.8883	−	24.9920i	1.30869	−	0.841047i	0.314564	−	0.949236i	$-0.398142\pi$
$883$	38.8883	−	24.9920i	1.30869	−	0.841047i	0.994130	+	0.108189i	$0.0345052\pi$
$884$	−1.00497	+	6.98970i	−0.0338007	+	0.235089i
$885$	−24.0031	+	52.5594i	−0.806855	+	1.76677i
$886$	4.15641	−	9.10126i	0.139637	−	0.305763i
$887$	2.28383	−	15.8844i	0.0766836	−	0.533346i	−0.914880	−	0.403726i	$-0.867715\pi$
$887$	2.28383	−	15.8844i	0.0766836	−	0.533346i	0.991564	−	0.129620i	$-0.0413758\pi$
$888$	4.15319	−	2.66909i	0.139372	−	0.0895689i
$889$	−1.93097	−	0.566983i	−0.0647626	−	0.0190160i
$890$	3.23768	+	22.5185i	0.108527	+	0.754823i
$891$	−3.49186	−	4.02982i	−0.116982	−	0.135004i
$892$	−1.38624	−	0.890883i	−0.0464148	−	0.0298290i
$893$	32.1220	−	37.0708i	1.07492	−	1.24053i
$894$	13.7047	−	4.02407i	0.458355	−	0.134585i
$895$	29.3271	+	64.2173i	0.980295	+	2.14655i
$896$	−1.00000			−0.0334077
$897$	4.99621	−	25.1394i	0.166819	−	0.839379i
$898$	−8.76660			−0.292545
$899$	−5.39446	−	11.8122i	−0.179915	−	0.393959i
$900$	−9.71198	+	2.85169i	−0.323733	+	0.0950565i
$901$	4.35375	−	5.02450i	0.145045	−	0.167390i
$902$	−21.3675	−	13.7321i	−0.711461	−	0.457228i
$903$	6.09405	+	7.03291i	0.202797	+	0.234041i
$904$	−0.883363	−	6.14393i	−0.0293802	−	0.204344i
$905$	60.4577	+	17.7520i	2.00968	+	0.590096i
$906$	15.2701	−	9.81351i	0.507316	−	0.326032i
$907$	2.89261	−	20.1185i	0.0960476	−	0.668025i	−0.883739	−	0.467980i	$-0.844982\pi$
$907$	2.89261	−	20.1185i	0.0960476	−	0.668025i	0.979787	−	0.200045i	$-0.0641090\pi$
$908$	8.62507	−	18.8863i	0.286233	−	0.626763i
$909$	0.449904	−	0.985151i	0.0149224	−	0.0326754i
$910$	2.95772	−	20.5714i	0.0980475	−	0.681935i
$911$	−27.4666	+	17.6517i	−0.910010	+	0.584828i	−0.909743	−	0.415172i	$-0.863721\pi$
$911$	−27.4666	+	17.6517i	−0.910010	+	0.584828i	−0.000266968		1.00000i	$0.500085\pi$
$912$	−5.52627	−	1.62266i	−0.182993	−	0.0537316i
$913$	6.55442	+	45.5870i	0.216920	+	1.50871i
$914$	−0.156750	−	0.180899i	−0.00518482	−	0.00598361i
$915$	28.4728	+	18.2983i	0.941281	+	0.604924i
$916$	−9.57216	+	11.0469i	−0.316273	+	0.364999i
$917$	17.5329	−	5.14813i	0.578988	−	0.170006i
$918$	0.548885	+	1.20189i	0.0181159	+	0.0396683i
$919$	21.1305			0.697033			0.348516	−	0.937303i	$-0.386686\pi$
$919$	21.1305			0.697033			0.348516	+	0.937303i	$0.386686\pi$
$920$	−6.83107	−	17.3535i	−0.225214	−	0.572126i
$921$	−26.5378			−0.874450
$922$	−4.73337	−	10.3646i	−0.155885	−	0.341341i
$923$	51.1608	−	15.0222i	1.68398	−	0.494460i
$924$	3.49186	−	4.02982i	0.114874	−	0.132571i
$925$	42.0386	+	27.0165i	1.38222	+	0.888299i
$926$	−8.01593	−	9.25088i	−0.263420	−	0.304003i
$927$	−0.971595	−	6.75759i	−0.0319114	−	0.221948i
$928$	−4.88574	−	1.43458i	−0.160382	−	0.0470925i
$929$	5.04172	−	3.24012i	0.165413	−	0.106305i	−0.455315	−	0.890330i	$-0.650473\pi$
$929$	5.04172	−	3.24012i	0.165413	−	0.106305i	0.620728	+	0.784026i	$0.286837\pi$
$930$	−1.41134	+	9.81608i	−0.0462796	+	0.321882i
$931$	−2.39261	+	5.23909i	−0.0784148	+	0.171704i
$932$	−4.38187	+	9.59496i	−0.143533	+	0.314293i
$933$	−1.33650	+	9.29554i	−0.0437549	+	0.304322i
$934$	17.5438	−	11.2747i	0.574051	−	0.368920i
$935$	−26.2878	−	7.71878i	−0.859702	−	0.252431i
$936$	0.760593	+	5.29004i	0.0248608	+	0.172910i
$937$	−1.41691	−	1.63520i	−0.0462884	−	0.0534197i	0.732133	−	0.681161i	$-0.238525\pi$
$937$	−1.41691	−	1.63520i	−0.0462884	−	0.0534197i	−0.778422	+	0.627742i	$0.783979\pi$
$938$	8.65132	+	5.55986i	0.282476	+	0.181536i
$939$	−11.8403	+	13.6644i	−0.386394	+	0.445922i
$940$	−31.7767	+	9.33049i	−1.03644	+	0.304327i
$941$	0.357785	+	0.783439i	0.0116634	+	0.0255394i	0.915374	−	0.402604i	$-0.131895\pi$
$941$	0.357785	+	0.783439i	0.0116634	+	0.0255394i	−0.903711	+	0.428144i	$0.859168\pi$
$942$	1.46303			0.0476680
$943$	−14.0175	−	18.0385i	−0.456472	−	0.587413i
$944$	14.8587			0.483609
$945$	−1.61542	−	3.53729i	−0.0525498	−	0.115068i
$946$	47.6110	−	13.9798i	1.54797	−	0.454524i
$947$	27.4315	−	31.6576i	0.891404	−	1.02873i	−0.107998	−	0.994151i	$-0.534444\pi$
$947$	27.4315	−	31.6576i	0.891404	−	1.02873i	0.999402	−	0.0345835i	$-0.0110105\pi$
$948$	−0.587980	−	0.377872i	−0.0190967	−	0.0122727i
$949$	29.2633	+	33.7717i	0.949928	+	1.09628i
$950$	−8.29672	−	57.7050i	−0.269181	−	1.87220i
$951$	4.70359	+	1.38110i	0.152524	+	0.0447852i
$952$	−1.11154	+	0.714345i	−0.0360253	+	0.0231521i
$953$	−3.43317	+	23.8782i	−0.111211	+	0.773491i	0.855533	+	0.517748i	$0.173229\pi$
$953$	−3.43317	+	23.8782i	−0.111211	+	0.773491i	−0.966745	+	0.255744i	$0.917680\pi$
$954$	2.09025	−	4.57700i	0.0676743	−	0.148186i
$955$	30.1499	−	66.0191i	0.975629	−	2.13633i
$956$	3.46307	−	24.0862i	0.112004	−	0.779004i
$957$	22.8414	−	14.6793i	0.738359	−	0.474515i
$958$	−18.7228	−	5.49750i	−0.604906	−	0.177616i
$959$	0.327630	+	2.27872i	0.0105797	+	0.0735836i
$960$	2.54656	+	2.93888i	0.0821898	+	0.0948521i
$961$	−20.6077	−	13.2438i	−0.664764	−	0.427218i
$962$	17.2785	−	19.9405i	0.557082	−	0.642906i
$963$	−6.03355	+	1.77161i	−0.194428	+	0.0570893i
$964$	12.1149	+	26.5280i	0.390195	+	0.854409i
$965$	−81.4228			−2.62109
$966$	4.16711	−	2.37385i	0.134075	−	0.0763774i
$967$	59.0110			1.89767			0.948834	−	0.315777i	$-0.102265\pi$
$967$	59.0110			1.89767			0.948834	+	0.315777i	$0.102265\pi$
$968$	−7.24175	−	15.8572i	−0.232759	−	0.509670i
$969$	−7.30183	+	2.14401i	−0.234568	+	0.0688755i
$970$	−47.3171	+	54.6069i	−1.51926	+	1.75332i
$971$	−28.6559	−	18.4160i	−0.919612	−	0.590999i	−0.00706697	−	0.999975i	$-0.502250\pi$
$971$	−28.6559	−	18.4160i	−0.919612	−	0.590999i	−0.912545	+	0.408976i	$0.865886\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	−0.555693	−	3.86493i	−0.0178147	−	0.123904i
$974$	−29.9091	−	8.78209i	−0.958348	−	0.281396i
$975$	−45.5088	+	29.2467i	−1.45745	+	0.936644i
$976$	1.23865	−	8.61500i	0.0396482	−	0.275759i
$977$	−3.63242	+	7.95390i	−0.116211	+	0.254468i	−0.958795	−	0.284097i	$-0.908306\pi$
$977$	−3.63242	+	7.95390i	−0.116211	+	0.254468i	0.842584	+	0.538565i	$0.181033\pi$
$978$	0.298710	−	0.654085i	0.00955171	−	0.0209153i
$979$	−4.43953	+	30.8776i	−0.141888	+	0.986852i
$980$	3.27138	−	2.10239i	0.104500	−	0.0671584i
$981$	−13.0669	−	3.83679i	−0.417194	−	0.122499i
$982$	−0.208275	−	1.44858i	−0.00664632	−	0.0462261i
$983$	27.2038	+	31.3949i	0.867667	+	1.00134i	0.999949	+	0.0101290i	$0.00322421\pi$
$983$	27.2038	+	31.3949i	0.867667	+	1.00134i	−0.132282	+	0.991212i	$0.542230\pi$
$984$	4.00725	+	2.57530i	0.127747	+	0.0820977i
$985$	−42.7489	+	49.3348i	−1.36209	+	1.57194i
$986$	−6.45550	+	1.89551i	−0.205585	+	0.0603652i
$987$	−3.53790	−	7.74692i	−0.112613	−	0.246587i
$988$	−30.7817			−0.979297
$989$	44.5658	+	2.38139i	1.41711	+	0.0757237i
$990$	−20.7354			−0.659014
$991$	20.1847	+	44.1982i	0.641187	+	1.40400i	0.899060	+	0.437825i	$0.144251\pi$
$991$	20.1847	+	44.1982i	0.641187	+	1.40400i	−0.257874	+	0.966179i	$0.583022\pi$
$992$	2.44691	−	0.718479i	0.0776896	−	0.0228117i
$993$	−8.46463	+	9.76870i	−0.268617	+	0.310000i
$994$	8.39305	+	5.39389i	0.266211	+	0.171084i
$995$	−19.1953	−	22.1526i	−0.608532	−	0.702284i
$996$	−1.22921	−	8.54934i	−0.0389490	−	0.270896i
$997$	−15.5093	−	4.55394i	−0.491184	−	0.144225i	0.0267553	−	0.999642i	$-0.491483\pi$
$997$	−15.5093	−	4.55394i	−0.491184	−	0.144225i	−0.517939	+	0.855417i	$0.673301\pi$
$998$	−29.2502	+	18.7979i	−0.925898	+	0.595039i
$999$	0.702595	−	4.88666i	0.0222291	−	0.154607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.211.3	✓	30
23.6	even	11	inner	966.2.q.h.673.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.211.3	✓	30	1.1	even	1	trivial
966.2.q.h.673.3	yes	30	23.6	even	11	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(3.27138 + 2.10239i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(3.27138 + 2.10239i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.553420 - 3.84912i) q^{10} +(2.21508 - 4.85036i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.760593 + 5.29004i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(3.73118 + 1.09557i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.865263 - 0.998567i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(3.77172 - 4.35280i) q^{19} +(-3.73118 + 1.09557i) q^{20} +(-0.415415 - 0.909632i) q^{21} -5.33222 q^{22} +(-4.52292 - 1.59475i) q^{23} +1.00000 q^{24} +(4.20483 + 9.20729i) q^{25} +(5.12795 - 1.50570i) q^{26} +(0.654861 - 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(3.33455 + 3.84828i) q^{29} +(-0.553420 - 3.84912i) q^{30} +(-2.44691 - 0.718479i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.758854 - 5.27794i) q^{33} +(-0.548885 + 1.20189i) q^{34} +(1.61542 - 3.53729i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(4.15319 - 2.66909i) q^{37} +(-5.52627 - 1.62266i) q^{38} +(0.760593 + 5.29004i) q^{39} +(2.54656 + 2.93888i) q^{40} +(4.00725 + 2.57530i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(-8.92892 + 2.62177i) q^{43} +(2.21508 + 4.85036i) q^{44} +3.88870 q^{45} +(0.428249 + 4.77667i) q^{46} +8.51654 q^{47} +(-0.415415 - 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(6.62849 - 7.64969i) q^{50} +(-1.11154 - 0.714345i) q^{51} +(-3.49986 - 4.03906i) q^{52} +(0.716087 + 4.98049i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(17.4437 - 11.2104i) q^{55} +(0.142315 - 0.989821i) q^{56} +(2.39261 - 5.23909i) q^{57} +(2.11529 - 4.63185i) q^{58} +(-2.11461 + 14.7074i) q^{59} +(-3.27138 + 2.10239i) q^{60} +(8.35103 + 2.45208i) q^{61} +(0.362933 + 2.52426i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-13.6099 + 15.7067i) q^{65} +(-5.11623 + 1.50226i) q^{66} +(-4.27206 - 9.35451i) q^{67} +1.32129 q^{68} +(-4.78900 - 0.255902i) q^{69} -3.88870 q^{70} +(-4.14453 - 9.07525i) q^{71} +(0.959493 - 0.281733i) q^{72} +(5.47547 - 6.31903i) q^{73} +(-4.15319 - 2.66909i) q^{74} +(6.62849 + 7.64969i) q^{75} +(0.819673 + 5.70095i) q^{76} +(-5.11623 - 1.50226i) q^{77} +(4.49603 - 2.88942i) q^{78} +(-0.0994686 + 0.691819i) q^{79} +(1.61542 - 3.53729i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.677907 - 4.71494i) q^{82} +(-7.26612 + 4.66965i) q^{83} +(0.959493 + 0.281733i) q^{84} +(-0.731230 - 5.08582i) q^{85} +(6.09405 + 7.03291i) q^{86} +(4.28367 + 2.75294i) q^{87} +(3.49186 - 4.02982i) q^{88} +(-5.61333 + 1.64822i) q^{89} +(-1.61542 - 3.53729i) q^{90} +5.34444 q^{91} +(4.16711 - 2.37385i) q^{92} -2.55022 q^{93} +(-3.53790 - 7.74692i) q^{94} +(21.4900 - 6.31004i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-15.6312 - 10.0455i) q^{97} +(0.654861 + 0.755750i) q^{98} +(-0.758854 - 5.27794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more