LMFDB - Embedded newform 864.2.bn.a.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00355 - 0.996435i) q^{2} +(0.0142344 + 1.99995i) q^{4} +(-2.06818 - 1.58697i) q^{5} +(3.83711 - 1.02815i) q^{7} +(1.97853 - 2.02124i) q^{8} +O(q^{10})$	\(q+(-1.00355 - 0.996435i) q^{2} +(0.0142344 + 1.99995i) q^{4} +(-2.06818 - 1.58697i) q^{5} +(3.83711 - 1.02815i) q^{7} +(1.97853 - 2.02124i) q^{8} +(0.494213 + 3.65341i) q^{10} +(-0.653532 + 4.96407i) q^{11} +(-1.16718 + 0.153662i) q^{13} +(-4.87523 - 2.79163i) q^{14} +(-3.99959 + 0.0569361i) q^{16} +7.05448 q^{17} +(1.06615 + 0.441612i) q^{19} +(3.14442 - 4.15884i) q^{20} +(5.60223 - 4.33050i) q^{22} +(-1.37678 + 5.13821i) q^{23} +(0.464792 + 1.73463i) q^{25} +(1.32444 + 1.00881i) q^{26} +(2.11087 + 7.65939i) q^{28} +(-2.22085 - 2.89427i) q^{29} +(-1.66613 + 0.961943i) q^{31} +(4.07054 + 3.92820i) q^{32} +(-7.07954 - 7.02933i) q^{34} +(-9.56747 - 3.96297i) q^{35} +(-0.612465 - 1.47862i) q^{37} +(-0.629895 - 1.50553i) q^{38} +(-7.29960 + 1.04040i) q^{40} +(7.20617 + 1.93089i) q^{41} +(10.2902 + 1.35473i) q^{43} +(-9.93719 - 1.23637i) q^{44} +(6.50157 - 3.78459i) q^{46} +(4.68935 + 2.70740i) q^{47} +(7.60416 - 4.39026i) q^{49} +(1.26200 - 2.20392i) q^{50} +(-0.323930 - 2.33211i) q^{52} +(-2.35419 - 5.68351i) q^{53} +(9.22943 - 9.22943i) q^{55} +(5.51372 - 9.78995i) q^{56} +(-0.655211 + 5.11748i) q^{58} +(8.24841 - 10.7495i) q^{59} +(1.60784 - 1.23374i) q^{61} +(2.63057 + 0.694834i) q^{62} +(-0.170801 - 7.99818i) q^{64} +(2.65778 + 1.53447i) q^{65} +(0.884289 - 0.116419i) q^{67} +(0.100416 + 14.1086i) q^{68} +(5.65261 + 13.5104i) q^{70} +(7.21124 - 7.21124i) q^{71} +(7.16896 + 7.16896i) q^{73} +(-0.858710 + 2.09416i) q^{74} +(-0.868026 + 2.13852i) q^{76} +(2.59614 + 19.7196i) q^{77} +(0.521243 - 0.902819i) q^{79} +(8.36222 + 6.22947i) q^{80} +(-5.30776 - 9.11822i) q^{82} +(-0.662598 - 0.863515i) q^{83} +(-14.5899 - 11.1952i) q^{85} +(-8.97688 - 11.6131i) q^{86} +(8.74053 + 11.1425i) q^{88} +(-7.64124 - 7.64124i) q^{89} +(-4.32060 + 1.78965i) q^{91} +(-10.2958 - 2.68035i) q^{92} +(-2.00826 - 7.38966i) q^{94} +(-1.50415 - 2.60527i) q^{95} +(-4.09467 + 7.09217i) q^{97} +(-12.0058 - 3.17119i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.00355	−	0.996435i	−0.709619	−	0.704586i
$2$	−1.00355	−	0.996435i	−0.709619	−	0.704586i
$3$		0			0
$3$		0			0
$4$	0.0142344	+	1.99995i	0.00711719	+	0.999975i
$5$	−2.06818	−	1.58697i	−0.924916	−	0.709713i	0.0321802	−	0.999482i	$-0.489755\pi$
$5$	−2.06818	−	1.58697i	−0.924916	−	0.709713i	−0.957097	+	0.289769i	$0.906422\pi$
$6$		0			0
$7$	3.83711	−	1.02815i	1.45029	−	0.388605i	0.554167	−	0.832406i	$-0.313037\pi$
$7$	3.83711	−	1.02815i	1.45029	−	0.388605i	0.896125	+	0.443801i	$0.146370\pi$
$8$	1.97853	−	2.02124i	0.699518	−	0.714615i
$9$		0			0
$10$	0.494213	+	3.65341i	0.156284	+	1.15531i
$11$	−0.653532	+	4.96407i	−0.197047	+	1.49672i	0.551798	+	0.833978i	$0.313942\pi$
$11$	−0.653532	+	4.96407i	−0.197047	+	1.49672i	−0.748845	+	0.662745i	$0.769391\pi$
$12$		0			0
$13$	−1.16718	+	0.153662i	−0.323717	+	0.0426181i	−0.290633	−	0.956834i	$-0.593866\pi$
$13$	−1.16718	+	0.153662i	−0.323717	+	0.0426181i	−0.0330833	+	0.999453i	$0.510533\pi$
$14$	−4.87523	−	2.79163i	−1.30296	−	0.746094i
$15$		0			0
$16$	−3.99959	+	0.0569361i	−0.999899	+	0.0142340i
$17$	7.05448			1.71096			0.855481	−	0.517834i	$-0.173262\pi$
$17$	7.05448			1.71096			0.855481	+	0.517834i	$0.173262\pi$
$18$		0			0
$19$	1.06615	+	0.441612i	0.244591	+	0.101313i	0.501611	−	0.865093i	$-0.332741\pi$
$19$	1.06615	+	0.441612i	0.244591	+	0.101313i	−0.257021	+	0.966406i	$0.582741\pi$
$20$	3.14442	−	4.15884i	0.703113	−	0.929944i
$21$		0			0
$22$	5.60223	−	4.33050i	1.19440	−	0.923266i
$23$	−1.37678	+	5.13821i	−0.287079	+	1.07139i	0.660229	+	0.751065i	$0.270459\pi$
$23$	−1.37678	+	5.13821i	−0.287079	+	1.07139i	−0.947307	+	0.320327i	$0.896207\pi$
$24$		0			0
$25$	0.464792	+	1.73463i	0.0929584	+	0.346925i
$26$	1.32444	+	1.00881i	0.259744	+	0.197844i
$27$		0			0
$28$	2.11087	+	7.65939i	0.398917	+	1.44749i
$29$	−2.22085	−	2.89427i	−0.412401	−	0.537452i	0.540255	−	0.841501i	$-0.318328\pi$
$29$	−2.22085	−	2.89427i	−0.412401	−	0.537452i	−0.952656	+	0.304049i	$0.901661\pi$
$30$		0			0
$31$	−1.66613	+	0.961943i	−0.299246	+	0.172770i	−0.642104	−	0.766617i	$-0.721938\pi$
$31$	−1.66613	+	0.961943i	−0.299246	+	0.172770i	0.342858	+	0.939387i	$0.388605\pi$
$32$	4.07054	+	3.92820i	0.719576	+	0.694414i
$33$		0			0
$34$	−7.07954	−	7.02933i	−1.21413	−	1.20552i
$35$	−9.56747	−	3.96297i	−1.61720	−	0.669865i
$36$		0			0
$37$	−0.612465	−	1.47862i	−0.100689	−	0.243084i	0.865506	−	0.500899i	$-0.166997\pi$
$37$	−0.612465	−	1.47862i	−0.100689	−	0.243084i	−0.966194	+	0.257815i	$0.916997\pi$
$38$	−0.629895	−	1.50553i	−0.102182	−	0.244228i
$39$		0			0
$40$	−7.29960	+	1.04040i	−1.15417	+	0.164502i
$41$	7.20617	+	1.93089i	1.12541	+	0.301554i	0.773073	−	0.634318i	$-0.218719\pi$
$41$	7.20617	+	1.93089i	1.12541	+	0.301554i	0.352342	+	0.935871i	$0.385385\pi$
$42$		0			0
$43$	10.2902	+	1.35473i	1.56924	+	0.206595i	0.864414	−	0.502780i	$-0.167690\pi$
$43$	10.2902	+	1.35473i	1.56924	+	0.206595i	0.704831	+	0.709375i	$0.251023\pi$
$44$	−9.93719	−	1.23637i	−1.49809	−	0.186390i
$45$		0			0
$46$	6.50157	−	3.78459i	0.958604	−	0.558008i
$47$	4.68935	+	2.70740i	0.684013	+	0.394915i	0.801365	−	0.598175i	$-0.204107\pi$
$47$	4.68935	+	2.70740i	0.684013	+	0.394915i	−0.117352	+	0.993090i	$0.537441\pi$
$48$		0			0
$49$	7.60416	−	4.39026i	1.08631	−	0.627180i
$50$	1.26200	−	2.20392i	0.178474	−	0.311682i
$51$		0			0
$52$	−0.323930	−	2.33211i	−0.0449210	−	0.323405i
$53$	−2.35419	−	5.68351i	−0.323372	−	0.780690i	−0.999054	−	0.0434961i	$-0.986150\pi$
$53$	−2.35419	−	5.68351i	−0.323372	−	0.780690i	0.675681	−	0.737194i	$-0.263850\pi$
$54$		0			0
$55$	9.22943	−	9.22943i	1.24450	−	1.24450i
$56$	5.51372	−	9.78995i	0.736802	−	1.30824i
$57$		0			0
$58$	−0.655211	+	5.11748i	−0.0860334	+	0.671958i
$59$	8.24841	−	10.7495i	1.07385	−	1.39947i	0.163054	−	0.986617i	$-0.447865\pi$
$59$	8.24841	−	10.7495i	1.07385	−	1.39947i	0.910797	−	0.412854i	$-0.135468\pi$
$60$		0			0
$61$	1.60784	−	1.23374i	0.205863	−	0.157964i	−0.500684	−	0.865630i	$-0.666918\pi$
$61$	1.60784	−	1.23374i	0.205863	−	0.157964i	0.706548	+	0.707666i	$0.250252\pi$
$62$	2.63057	+	0.694834i	0.334082	+	0.0882440i
$63$		0			0
$64$	−0.170801	−	7.99818i	−0.0213501	−	0.999772i
$65$	2.65778	+	1.53447i	0.329658	+	0.190328i
$66$		0			0
$67$	0.884289	−	0.116419i	0.108033	−	0.0142228i	−0.0763158	−	0.997084i	$-0.524316\pi$
$67$	0.884289	−	0.116419i	0.108033	−	0.0142228i	0.184349	+	0.982861i	$0.440982\pi$
$68$	0.100416	+	14.1086i	0.0121772	+	1.71092i
$69$		0			0
$70$	5.65261	+	13.5104i	0.675616	+	1.61480i
$71$	7.21124	−	7.21124i	0.855817	−	0.855817i	−0.135025	−	0.990842i	$-0.543112\pi$
$71$	7.21124	−	7.21124i	0.855817	−	0.855817i	0.990842	+	0.135025i	$0.0431115\pi$
$72$		0			0
$73$	7.16896	+	7.16896i	0.839063	+	0.839063i	0.988736	−	0.149672i	$-0.0478219\pi$
$73$	7.16896	+	7.16896i	0.839063	+	0.839063i	−0.149672	+	0.988736i	$0.547822\pi$
$74$	−0.858710	+	2.09416i	−0.0998230	+	0.243441i
$75$		0			0
$76$	−0.868026	+	2.13852i	−0.0995694	+	0.245305i
$77$	2.59614	+	19.7196i	0.295857	+	2.24726i
$78$		0			0
$79$	0.521243	−	0.902819i	0.0586444	−	0.101575i	−0.835213	−	0.549927i	$-0.814656\pi$
$79$	0.521243	−	0.902819i	0.0586444	−	0.101575i	0.893857	+	0.448352i	$0.147989\pi$
$80$	8.36222	+	6.22947i	0.934925	+	0.696476i
$81$		0			0
$82$	−5.30776	−	9.11822i	−0.586144	−	1.00694i
$83$	−0.662598	−	0.863515i	−0.0727296	−	0.0947831i	0.755572	−	0.655066i	$-0.227359\pi$
$83$	−0.662598	−	0.863515i	−0.0727296	−	0.0947831i	−0.828301	+	0.560283i	$0.810692\pi$
$84$		0			0
$85$	−14.5899	−	11.1952i	−1.58250	−	1.21429i
$86$	−8.97688	−	11.6131i	−0.968001	−	1.25227i
$87$		0			0
$88$	8.74053	+	11.1425i	0.931743	+	1.18780i
$89$	−7.64124	−	7.64124i	−0.809970	−	0.809970i	0.174659	−	0.984629i	$-0.444118\pi$
$89$	−7.64124	−	7.64124i	−0.809970	−	0.809970i	−0.984629	+	0.174659i	$0.944118\pi$
$90$		0			0
$91$	−4.32060	+	1.78965i	−0.452922	+	0.187606i
$92$	−10.2958	−	2.68035i	−1.07341	−	0.279446i
$93$		0			0
$94$	−2.00826	−	7.38966i	−0.207137	−	0.762185i
$95$	−1.50415	−	2.60527i	−0.154323	−	0.267295i
$96$		0			0
$97$	−4.09467	+	7.09217i	−0.415751	+	0.720101i	−0.995507	−	0.0946887i	$-0.969814\pi$
$97$	−4.09467	+	7.09217i	−0.415751	+	0.720101i	0.579756	+	0.814790i	$0.303148\pi$
$98$	−12.0058	−	3.17119i	−1.21277	−	0.320339i
$99$		0			0
$100$	−3.46255	+	0.954252i	−0.346255	+	0.0954252i
$101$	−0.257025	+	1.95230i	−0.0255750	+	0.194261i	−0.999463	−	0.0327677i	$-0.989568\pi$
$101$	−0.257025	+	1.95230i	−0.0255750	+	0.194261i	0.973888	+	0.227029i	$0.0729012\pi$
$102$		0			0
$103$	1.85921	−	6.93865i	0.183193	−	0.683686i	−0.811817	−	0.583912i	$-0.801521\pi$
$103$	1.85921	−	6.93865i	0.183193	−	0.683686i	0.995010	−	0.0997739i	$-0.0318119\pi$
$104$	−1.99871	+	2.66317i	−0.195990	+	0.261145i
$105$		0			0
$106$	−3.30070	+	8.04949i	−0.320592	+	0.781836i
$107$	1.15804	−	0.479677i	0.111952	−	0.0463722i	−0.326004	−	0.945368i	$-0.605702\pi$
$107$	1.15804	−	0.479677i	0.111952	−	0.0463722i	0.437957	+	0.898996i	$0.355702\pi$
$108$		0			0
$109$	−2.38543	+	5.75895i	−0.228483	+	0.551607i	−0.995993	−	0.0894298i	$-0.971496\pi$
$109$	−2.38543	+	5.75895i	−0.228483	+	0.551607i	0.767510	+	0.641037i	$0.221496\pi$
$110$	−18.4588	+	0.0656881i	−1.75997	+	0.00626311i
$111$		0			0
$112$	−15.2884	+	4.33066i	−1.44461	+	0.409209i
$113$	−1.10097	−	1.90693i	−0.103570	−	0.179389i	0.809583	−	0.587006i	$-0.199693\pi$
$113$	−1.10097	−	1.90693i	−0.103570	−	0.179389i	−0.913153	+	0.407617i	$0.866360\pi$
$114$		0			0
$115$	11.0016	−	8.44183i	1.02590	−	0.787204i
$116$	5.75678	−	4.48278i	0.534503	−	0.416216i
$117$		0			0
$118$	−18.9889	+	2.56872i	−1.74807	+	0.236470i
$119$	27.0688	−	7.25307i	2.48139	−	0.664888i
$120$		0			0
$121$	−13.5897	−	3.64135i	−1.23543	−	0.331032i
$122$	−2.84290	−	0.363987i	−0.257384	−	0.0329538i
$123$		0			0
$124$	−1.94755	−	3.31849i	−0.174895	−	0.298009i
$125$	−3.19652	+	7.71709i	−0.285906	+	0.690237i
$126$		0			0
$127$		−	18.0654i		−	1.60304i	−0.597966	−	0.801522i	$-0.704024\pi$
$127$		−	18.0654i		−	1.60304i	0.597966	−	0.801522i	$-0.295976\pi$
$128$	−7.79826	+	8.19678i	−0.689275	+	0.724500i
$129$		0			0
$130$	−1.13822	−	4.18823i	−0.0998288	−	0.367332i
$131$	1.54055	+	11.7017i	0.134599	+	1.02238i	0.916798	+	0.399351i	$0.130764\pi$
$131$	1.54055	+	11.7017i	0.134599	+	1.02238i	−0.782199	+	0.623028i	$0.785902\pi$
$132$		0			0
$133$	4.54496	+	0.598356i	0.394098	+	0.0518840i
$134$	−1.00343	−	0.764304i	−0.0866835	−	0.0660258i
$135$		0			0
$136$	13.9575	−	14.2588i	1.19685	−	1.22268i
$137$	2.16595	+	8.08342i	0.185049	+	0.690613i	0.994620	+	0.103591i	$0.0330333\pi$
$137$	2.16595	+	8.08342i	0.185049	+	0.690613i	−0.809571	+	0.587022i	$0.800300\pi$
$138$		0			0
$139$	−5.81901	+	7.58348i	−0.493562	+	0.643222i	−0.972023	−	0.234887i	$-0.924528\pi$
$139$	−5.81901	+	7.58348i	−0.493562	+	0.643222i	0.478461	+	0.878109i	$0.341195\pi$
$140$	7.78956	−	19.1909i	0.658338	−	1.62192i
$141$		0			0
$142$	−14.4224	+	0.0513241i	−1.21030	+	0.00430702i
$143$		−	5.89437i		−	0.492912i
$144$		0			0
$145$			9.51027i			0.789785i
$146$	−0.0510232	−	14.3378i	−0.00422271	−	1.18661i
$147$		0			0
$148$	2.94845	−	1.24595i	0.242361	−	0.102416i
$149$	−5.19198	+	6.76632i	−0.425343	+	0.554318i	−0.956037	−	0.293245i	$-0.905265\pi$
$149$	−5.19198	+	6.76632i	−0.425343	+	0.554318i	0.530694	+	0.847564i	$0.321931\pi$
$150$		0			0
$151$	0.0363502	+	0.135661i	0.00295814	+	0.0110399i	0.967389	−	0.253295i	$-0.0815143\pi$
$151$	0.0363502	+	0.135661i	0.00295814	+	0.0110399i	−0.964431	+	0.264335i	$0.914848\pi$
$152$	3.00201	−	1.28119i	0.243495	−	0.103918i
$153$		0			0
$154$	17.0440	−	22.3765i	1.37344	−	1.80315i
$155$	4.97243	+	0.654633i	0.399395	+	0.0525814i
$156$		0			0
$157$	1.16722	+	8.86591i	0.0931542	+	0.707577i	0.972750	+	0.231855i	$0.0744796\pi$
$157$	1.16722	+	8.86591i	0.0931542	+	0.707577i	−0.879596	+	0.475721i	$0.842187\pi$
$158$	−1.42270	+	0.386642i	−0.113184	+	0.0307595i
$159$		0			0
$160$	−2.18466	−	14.5840i	−0.172713	−	1.15297i
$161$			21.1314i			1.66539i
$162$		0			0
$163$	2.91057	−	7.02674i	0.227973	−	0.550376i	−0.767957	−	0.640501i	$-0.778727\pi$
$163$	2.91057	−	7.02674i	0.227973	−	0.550376i	0.995930	+	0.0901248i	$0.0287266\pi$
$164$	−3.75910	+	14.4395i	−0.293536	+	1.12753i
$165$		0			0
$166$	−0.195485	+	1.52682i	−0.0151725	+	0.118504i
$167$	0.664466	+	0.178043i	0.0514179	+	0.0137774i	0.284436	−	0.958695i	$-0.408194\pi$
$167$	0.664466	+	0.178043i	0.0514179	+	0.0137774i	−0.233018	+	0.972472i	$0.574860\pi$
$168$		0			0
$169$	−11.2183	+	3.00595i	−0.862950	+	0.231227i
$170$	3.48641	+	25.7729i	0.267396	+	1.97669i
$171$		0			0
$172$	−2.56292	+	20.5992i	−0.195421	+	1.57068i
$173$	13.7225	−	10.5296i	1.04330	−	0.800553i	0.0629906	−	0.998014i	$-0.479936\pi$
$173$	13.7225	−	10.5296i	1.04330	−	0.800553i	0.980311	+	0.197461i	$0.0632695\pi$
$174$		0			0
$175$	3.56692	+	6.17808i	0.269634	+	0.467019i
$176$	2.33123	−	19.8915i	0.175723	−	1.49938i
$177$		0			0
$178$	0.0543845	+	15.2824i	0.00407629	+	1.14546i
$179$	−2.83400	+	6.84188i	−0.211823	+	0.511386i	−0.993703	−	0.112042i	$-0.964261\pi$
$179$	−2.83400	+	6.84188i	−0.211823	+	0.511386i	0.781880	+	0.623429i	$0.214261\pi$
$180$		0			0
$181$	−12.3989	+	5.13577i	−0.921600	+	0.381739i	−0.792486	−	0.609891i	$-0.791213\pi$
$181$	−12.3989	+	5.13577i	−0.921600	+	0.381739i	−0.129114	+	0.991630i	$0.541213\pi$
$182$	6.11922	+	2.50919i	0.453587	+	0.185994i
$183$		0			0
$184$	7.66154	+	12.9489i	0.564816	+	0.954608i
$185$	−1.07984	+	4.03001i	−0.0793913	+	0.296292i
$186$		0			0
$187$	−4.61033	+	35.0189i	−0.337140	+	2.56084i
$188$	−5.34791	+	9.41701i	−0.390037	+	0.686806i
$189$		0			0
$190$	−1.08649	+	4.11331i	−0.0788220	+	0.298411i
$191$	2.88811	−	5.00235i	0.208976	−	0.361957i	−0.742416	−	0.669939i	$-0.766320\pi$
$191$	2.88811	−	5.00235i	0.208976	−	0.361957i	0.951392	+	0.307982i	$0.0996536\pi$
$192$		0			0
$193$	−4.36740	−	7.56457i	−0.314373	−	0.544509i	0.664931	−	0.746904i	$-0.268461\pi$
$193$	−4.36740	−	7.56457i	−0.314373	−	0.544509i	−0.979304	+	0.202395i	$0.935127\pi$
$194$	11.1761	−	3.03730i	0.802398	−	0.218065i
$195$		0			0
$196$	8.88854	+	15.1454i	0.634896	+	1.08182i
$197$	9.50609	−	3.93755i	0.677281	−	0.280539i	−0.0174090	−	0.999848i	$-0.505542\pi$
$197$	9.50609	−	3.93755i	0.677281	−	0.280539i	0.694690	+	0.719310i	$0.255542\pi$
$198$		0			0
$199$	12.9779	+	12.9779i	0.919982	+	0.919982i	0.997028	−	0.0770456i	$-0.0245487\pi$
$199$	12.9779	+	12.9779i	0.919982	+	0.919982i	−0.0770456	+	0.997028i	$0.524549\pi$
$200$	4.42570	+	2.49256i	0.312944	+	0.176251i
$201$		0			0
$202$	2.20328	−	1.70313i	0.155022	−	0.119832i
$203$	−11.4974	−	8.82226i	−0.806959	−	0.619201i
$204$		0			0
$205$	−11.8394	−	15.4294i	−0.826897	−	1.07763i
$206$	−8.77973	+	5.11072i	−0.611712	+	0.356081i
$207$		0			0
$208$	4.65949	−	0.681039i	0.323077	−	0.0472216i
$209$	−2.88895	+	5.00381i	−0.199833	+	0.346121i
$210$		0			0
$211$	2.08780	+	15.8584i	0.143730	+	1.09174i	0.899506	+	0.436908i	$0.143927\pi$
$211$	2.08780	+	15.8584i	0.143730	+	1.09174i	−0.755776	+	0.654830i	$0.772740\pi$
$212$	11.3332	−	4.78916i	0.778369	−	0.328921i
$213$		0			0
$214$	−1.64012	−	0.672534i	−0.112117	−	0.0459735i
$215$	−19.1321	−	19.1321i	−1.30480	−	1.30480i
$216$		0			0
$217$	−5.40412	+	5.40412i	−0.366856	+	0.366856i
$218$	8.13233	−	3.40248i	0.550791	−	0.230445i
$219$		0			0
$220$	18.5898	+	18.3270i	1.25332	+	1.23561i
$221$	−8.23382	+	1.08400i	−0.553867	+	0.0729180i
$222$		0			0
$223$	−18.4798	−	10.6693i	−1.23750	−	0.714469i	−0.268915	−	0.963164i	$-0.586665\pi$
$223$	−18.4798	−	10.6693i	−1.23750	−	0.714469i	−0.968582	+	0.248695i	$0.919998\pi$
$224$	19.6579	+	10.8878i	1.31345	+	0.727472i
$225$		0			0
$226$	−0.795255	+	3.01075i	−0.0528996	+	0.200272i
$227$	−18.8170	+	14.4388i	−1.24893	+	0.958335i	−0.999948	−	0.0101741i	$-0.996761\pi$
$227$	−18.8170	+	14.4388i	−1.24893	+	0.958335i	−0.248978	+	0.968509i	$0.580095\pi$
$228$		0			0
$229$	14.6379	−	19.0765i	0.967302	−	1.26061i	0.00185959	−	0.999998i	$-0.499408\pi$
$229$	14.6379	−	19.0765i	0.967302	−	1.26061i	0.965443	−	0.260615i	$-0.0839253\pi$
$230$	−19.4524	−	2.49057i	−1.28265	−	0.164223i
$231$		0			0
$232$	−10.2440	−	1.23754i	−0.672553	−	0.0812488i
$233$	−13.5549	+	13.5549i	−0.888011	+	0.888011i	−0.994332	−	0.106321i	$-0.966093\pi$
$233$	−13.5549	+	13.5549i	−0.888011	+	0.888011i	0.106321	+	0.994332i	$0.466093\pi$
$234$		0			0
$235$	−5.40186	−	13.0412i	−0.352378	−	0.850716i
$236$	21.6159	+	16.3434i	1.40708	+	1.06386i
$237$		0			0
$238$	−34.3922	−	19.6935i	−2.22931	−	1.27654i
$239$	−3.64977	+	2.10719i	−0.236084	+	0.136303i	−0.613375	−	0.789791i	$-0.710189\pi$
$239$	−3.64977	+	2.10719i	−0.236084	+	0.136303i	0.377292	+	0.926094i	$0.376855\pi$
$240$		0			0
$241$	15.0808	+	8.70690i	0.971440	+	0.560861i	0.899675	−	0.436561i	$-0.143804\pi$
$241$	15.0808	+	8.70690i	0.971440	+	0.560861i	0.0717649	+	0.997422i	$0.477137\pi$
$242$	10.0096	+	17.1955i	0.643441	+	1.10537i
$243$		0			0
$244$	2.49031	+	3.19804i	0.159426	+	0.204734i
$245$	−22.6939	−	2.98771i	−1.44986	−	0.190878i
$246$		0			0
$247$	−1.31224	−	0.351614i	−0.0834958	−	0.0223726i
$248$	−1.35219	+	5.27089i	−0.0858641	+	0.334702i
$249$		0			0
$250$	10.8975	−	4.55937i	0.689215	−	0.288360i
$251$	−8.23412	−	19.8789i	−0.519733	−	1.25475i	−0.938067	−	0.346454i	$-0.887386\pi$
$251$	−8.23412	−	19.8789i	−0.519733	−	1.25475i	0.418334	−	0.908293i	$-0.362614\pi$
$252$		0			0
$253$	−24.6067	−	10.1924i	−1.54701	−	0.640792i
$254$	−18.0010	+	18.1296i	−1.12948	+	1.13755i
$255$		0			0
$256$	15.9935	−	0.455443i	0.999595	−	0.0284652i
$257$	−15.6605	+	9.04157i	−0.976873	+	0.563998i	−0.901325	−	0.433144i	$-0.857404\pi$
$257$	−15.6605	+	9.04157i	−0.976873	+	0.563998i	−0.0755482	+	0.997142i	$0.524071\pi$
$258$		0			0
$259$	−3.87034	−	5.04393i	−0.240491	−	0.313415i
$260$	−3.03104	+	5.33728i	−0.187977	+	0.331004i
$261$		0			0
$262$	10.1139	−	13.2783i	0.624840	−	0.820336i
$263$	3.69457	+	13.7883i	0.227817	+	0.850225i	0.981256	+	0.192707i	$0.0617268\pi$
$263$	3.69457	+	13.7883i	0.227817	+	0.850225i	−0.753439	+	0.657518i	$0.771607\pi$
$264$		0			0
$265$	−4.15067	+	15.4905i	−0.254974	+	0.951575i
$266$	−3.96489	−	5.12924i	−0.243103	−	0.314494i
$267$		0			0
$268$	0.245419	+	1.76688i	0.0149914	+	0.107929i
$269$	8.03571	+	3.32850i	0.489946	+	0.202942i	0.613958	−	0.789338i	$-0.289576\pi$
$269$	8.03571	+	3.32850i	0.489946	+	0.202942i	−0.124012	+	0.992281i	$0.539576\pi$
$270$		0			0
$271$	−0.476222			−0.0289284			−0.0144642	−	0.999895i	$-0.504604\pi$
$271$	−0.476222			−0.0289284			−0.0144642	+	0.999895i	$0.504604\pi$
$272$	−28.2150	+	0.401654i	−1.71079	+	0.0243539i
$273$		0			0
$274$	5.88097	−	10.2704i	0.355282	−	0.620455i
$275$	−8.91456	+	1.17362i	−0.537568	+	0.0707722i
$276$		0			0
$277$	−1.59434	+	12.1102i	−0.0957947	+	0.727633i	0.874383	+	0.485237i	$0.161267\pi$
$277$	−1.59434	+	12.1102i	−0.0957947	+	0.727633i	−0.970177	+	0.242396i	$0.922067\pi$
$278$	13.3961	−	1.81215i	0.803446	−	0.108686i
$279$		0			0
$280$	−26.9397	+	11.4972i	−1.60995	+	0.687091i
$281$	1.12047	−	0.300229i	0.0668416	−	0.0179101i	−0.225243	−	0.974303i	$-0.572318\pi$
$281$	1.12047	−	0.300229i	0.0668416	−	0.0179101i	0.292085	+	0.956392i	$0.405651\pi$
$282$		0			0
$283$	−0.193522	−	0.148494i	−0.0115037	−	0.00882707i	0.602994	−	0.797746i	$-0.293974\pi$
$283$	−0.193522	−	0.148494i	−0.0115037	−	0.00882707i	−0.614497	+	0.788919i	$0.710641\pi$
$284$	14.5248	+	14.3195i	0.861886	+	0.849704i
$285$		0			0
$286$	−5.87336	+	5.91531i	−0.347299	+	0.349780i
$287$	29.6361			1.74936
$288$		0			0
$289$	32.7656			1.92739
$290$	9.47637	−	9.54405i	0.556471	−	0.560446i
$291$		0			0
$292$	−14.2355	+	14.4396i	−0.833070	+	0.845014i
$293$	−13.9642	−	10.7151i	−0.815795	−	0.625982i	0.114240	−	0.993453i	$-0.463557\pi$
$293$	−13.9642	−	10.7151i	−0.815795	−	0.625982i	−0.930035	+	0.367472i	$0.880224\pi$
$294$		0			0
$295$	−34.1183	+	9.14198i	−1.98645	+	0.532267i
$296$	−4.20043	−	1.68757i	−0.244145	−	0.0980878i
$297$		0			0
$298$	11.9526	−	1.61688i	0.692396	−	0.0936636i
$299$	0.817399	−	6.20876i	0.0472714	−	0.359062i
$300$		0			0
$301$	40.8776	−	5.38164i	2.35615	−	0.310193i
$302$	0.0986978	−	0.172363i	0.00567942	−	0.00991839i
$303$		0			0
$304$	−4.28929	−	1.70557i	−0.246008	−	0.0978210i
$305$	−5.28321			−0.302516
$306$		0			0
$307$	3.77457	+	1.56348i	0.215426	+	0.0892325i	0.487787	−	0.872963i	$-0.337804\pi$
$307$	3.77457	+	1.56348i	0.215426	+	0.0892325i	−0.272361	+	0.962195i	$0.587804\pi$
$308$	−39.4013	+	5.47284i	−2.24510	+	0.311844i
$309$		0			0
$310$	−4.33779	−	5.61166i	−0.246370	−	0.318721i
$311$	−2.77898	+	10.3713i	−0.157582	+	0.588103i	0.841289	+	0.540586i	$0.181797\pi$
$311$	−2.77898	+	10.3713i	−0.157582	+	0.588103i	−0.998870	+	0.0475168i	$0.984869\pi$
$312$		0			0
$313$	−3.30296	−	12.3268i	−0.186695	−	0.696754i	−0.994261	−	0.106978i	$-0.965883\pi$
$313$	−3.30296	−	12.3268i	−0.186695	−	0.696754i	0.807567	−	0.589776i	$-0.200784\pi$
$314$	7.66294	−	10.0605i	0.432445	−	0.567745i
$315$		0			0
$316$	1.81301	+	1.02961i	0.101990	+	0.0579200i
$317$	16.2827	+	21.2200i	0.914526	+	1.19183i	0.980993	+	0.194045i	$0.0621609\pi$
$317$	16.2827	+	21.2200i	0.914526	+	1.19183i	−0.0664662	+	0.997789i	$0.521172\pi$
$318$		0			0
$319$	15.8187	−	9.13295i	0.885679	−	0.511347i
$320$	−12.3396	+	16.8127i	−0.689805	+	0.939858i
$321$		0			0
$322$	21.0561	−	21.2065i	1.17341	−	1.18179i
$323$	7.52110	+	3.11534i	0.418485	+	0.173342i
$324$		0			0
$325$	−0.809040	−	1.95320i	−0.0448775	−	0.108344i
$326$	−9.92259	+	4.15150i	−0.549562	+	0.229931i
$327$		0			0
$328$	18.1604	−	10.7450i	1.00274	−	0.593296i
$329$	20.7772	+	5.56723i	1.14548	+	0.306931i
$330$		0			0
$331$	23.3964	+	3.08019i	1.28598	+	0.169303i	0.742345	−	0.670018i	$-0.233714\pi$
$331$	23.3964	+	3.08019i	1.28598	+	0.169303i	0.543637	+	0.839320i	$0.317047\pi$
$332$	1.71755	−	1.33746i	0.0942631	−	0.0734024i
$333$		0			0
$334$	−0.489418	−	0.840773i	−0.0267798	−	0.0460050i
$335$	−2.01362	−	1.16256i	−0.110016	−	0.0635176i
$336$		0			0
$337$	3.31031	−	1.91121i	0.180324	−	0.104110i	−0.407121	−	0.913374i	$-0.633467\pi$
$337$	3.31031	−	1.91121i	0.180324	−	0.104110i	0.587445	+	0.809264i	$0.300134\pi$
$338$	14.2534	+	8.16173i	0.775284	+	0.443939i
$339$		0			0
$340$	22.1822	−	29.3384i	1.20300	−	1.59110i
$341$	−3.68628	−	8.89946i	−0.199623	−	0.481933i
$342$		0			0
$343$	5.00142	−	5.00142i	0.270051	−	0.270051i
$344$	23.0978	−	18.1186i	1.24535	−	0.976890i
$345$		0			0
$346$	−24.2633	−	3.10653i	−1.30440	−	0.167008i
$347$	15.0455	−	19.6077i	0.807684	−	1.05259i	−0.189809	−	0.981821i	$-0.560787\pi$
$347$	15.0455	−	19.6077i	0.807684	−	1.05259i	0.997492	−	0.0707728i	$-0.0225465\pi$
$348$		0			0
$349$	−21.0632	+	16.1624i	−1.12749	+	0.865153i	−0.992076	−	0.125636i	$-0.959903\pi$
$349$	−21.0632	+	16.1624i	−1.12749	+	0.865153i	−0.135413	+	0.990789i	$0.543236\pi$
$350$	2.57647	−	9.75423i	0.137718	−	0.521385i
$351$		0			0
$352$	−22.1601	+	17.6392i	−1.18114	+	0.940173i
$353$	−4.99998	−	2.88674i	−0.266122	−	0.153646i	0.361002	−	0.932565i	$-0.382435\pi$
$353$	−4.99998	−	2.88674i	−0.266122	−	0.153646i	−0.627124	+	0.778919i	$0.715768\pi$
$354$		0			0
$355$	−26.3581	+	3.47011i	−1.39894	+	0.184174i
$356$	15.1733	−	15.3909i	0.804185	−	0.815714i
$357$		0			0
$358$	9.66156	−	4.04229i	0.510629	−	0.213642i
$359$	−20.4405	+	20.4405i	−1.07881	+	1.07881i	−0.0821923	+	0.996616i	$0.526192\pi$
$359$	−20.4405	+	20.4405i	−1.07881	+	1.07881i	−0.996616	+	0.0821923i	$0.973808\pi$
$360$		0			0
$361$	−12.4934	−	12.4934i	−0.657547	−	0.657547i
$362$	17.5604	+	7.20064i	0.922952	+	0.378457i
$363$		0			0
$364$	−3.64071	−	8.61551i	−0.190825	−	0.451575i
$365$	−3.44977	−	26.2036i	−0.180569	−	1.37156i
$366$		0			0
$367$	16.1409	−	27.9568i	0.842547	−	1.45933i	−0.0451884	−	0.998978i	$-0.514389\pi$
$367$	16.1409	−	27.9568i	0.842547	−	1.45933i	0.887735	−	0.460355i	$-0.152278\pi$
$368$	5.21401	−	20.6292i	0.271799	−	1.07537i
$369$		0			0
$370$	5.09932	−	2.96834i	0.265101	−	0.154317i
$371$	−14.8768	−	19.3878i	−0.772364	−	1.00656i
$372$		0			0
$373$	−8.11621	−	6.22779i	−0.420242	−	0.322463i	0.376901	−	0.926253i	$-0.376990\pi$
$373$	−8.11621	−	6.22779i	−0.420242	−	0.322463i	−0.797143	+	0.603791i	$0.793656\pi$
$374$	39.5208	−	30.5494i	2.04357	−	1.57967i
$375$		0			0
$376$	14.7504	−	4.12161i	0.760691	−	0.212556i
$377$	3.03686	+	3.03686i	0.156406	+	0.156406i
$378$		0			0
$379$	13.0140	−	5.39059i	0.668486	−	0.276896i	−0.0225185	−	0.999746i	$-0.507168\pi$
$379$	13.0140	−	5.39059i	0.668486	−	0.276896i	0.691004	+	0.722850i	$0.257168\pi$
$380$	5.18900	−	3.04531i	0.266190	−	0.156221i
$381$		0			0
$382$	−7.88288	+	2.14231i	−0.403323	+	0.109610i
$383$	−6.27026	−	10.8604i	−0.320395	−	0.554941i	0.660174	−	0.751112i	$-0.270482\pi$
$383$	−6.27026	−	10.8604i	−0.320395	−	0.554941i	−0.980570	+	0.196172i	$0.937149\pi$
$384$		0			0
$385$	25.9251	−	44.9036i	1.32127	−	2.28850i
$386$	−3.15468	+	11.9433i	−0.160569	+	0.607896i
$387$		0			0
$388$	−14.2423	−	8.08818i	−0.723042	−	0.410615i
$389$	4.44316	−	33.7492i	0.225277	−	1.71115i	−0.388315	−	0.921527i	$-0.626943\pi$
$389$	4.44316	−	33.7492i	0.225277	−	1.71115i	0.613592	−	0.789623i	$-0.289724\pi$
$390$		0			0
$391$	−9.71246	+	36.2474i	−0.491180	+	1.83311i
$392$	6.17133	−	24.0561i	0.311699	−	1.21502i
$393$		0			0
$394$	−13.4634	−	5.52066i	−0.678275	−	0.278127i
$395$	−2.51077	+	1.03999i	−0.126330	+	0.0523278i
$396$		0			0
$397$	−8.09249	+	19.5370i	−0.406150	+	0.980533i	0.579991	+	0.814623i	$0.303056\pi$
$397$	−8.09249	+	19.5370i	−0.406150	+	0.980533i	−0.986141	+	0.165910i	$0.946944\pi$
$398$	−0.0923671	−	25.9557i	−0.00462994	−	1.30104i
$399$		0			0
$400$	−1.95774	−	6.91134i	−0.0978871	−	0.345567i
$401$	−12.9161	−	22.3713i	−0.644999	−	1.11717i	−0.984302	−	0.176494i	$-0.943524\pi$
$401$	−12.9161	−	22.3713i	−0.644999	−	1.11717i	0.339303	−	0.940677i	$-0.389809\pi$
$402$		0			0
$403$	1.79686	−	1.37878i	0.0895079	−	0.0686819i
$404$	−3.90816	−	0.486248i	−0.194438	−	0.0241917i
$405$		0			0
$406$	2.74743	+	20.3100i	0.136352	+	1.00797i
$407$	7.74025	−	2.07399i	0.383670	−	0.102804i
$408$		0			0
$409$	−1.91976	−	0.514397i	−0.0949259	−	0.0254353i	0.211043	−	0.977477i	$-0.432314\pi$
$409$	−1.91976	−	0.514397i	−0.0949259	−	0.0254353i	−0.305969	+	0.952041i	$0.598981\pi$
$410$	−3.49294	+	27.2813i	−0.172504	+	1.34733i
$411$		0			0
$412$	13.9034	+	3.61955i	0.684972	+	0.178322i
$413$	20.5979	−	49.7278i	1.01356	−	2.44694i
$414$		0			0
$415$			2.83742i			0.139284i
$416$	−5.35465	−	3.95942i	−0.262533	−	0.194126i
$417$		0			0
$418$	7.88519	−	2.14293i	0.385677	−	0.104814i
$419$	0.558644	+	4.24332i	0.0272915	+	0.207300i	0.999658	−	0.0261610i	$-0.00832826\pi$
$419$	0.558644	+	4.24332i	0.0272915	+	0.207300i	−0.972366	+	0.233461i	$0.924995\pi$
$420$		0			0
$421$	−18.1597	−	2.39077i	−0.885049	−	0.116519i	−0.325721	−	0.945466i	$-0.605607\pi$
$421$	−18.1597	−	2.39077i	−0.885049	−	0.116519i	−0.559327	+	0.828947i	$0.688940\pi$
$422$	13.7067	−	17.9951i	0.667230	−	0.875988i
$423$		0			0
$424$	−16.1456	−	6.48665i	−0.784098	−	0.315020i
$425$	3.27886	+	12.2369i	0.159048	+	0.593576i
$426$		0			0
$427$	4.90100	−	6.38711i	0.237176	−	0.309094i
$428$	0.975815	+	2.30920i	0.0471678	+	0.111619i
$429$		0			0
$430$	0.136168	+	38.2639i	0.00656658	+	1.84525i
$431$		−	8.40470i		−	0.404840i	−0.979299	−	0.202420i	$-0.935119\pi$
$431$		−	8.40470i		−	0.404840i	0.979299	−	0.202420i	$-0.0648807\pi$
$432$		0			0
$433$			11.0814i			0.532540i	0.963899	+	0.266270i	$0.0857913\pi$
$433$			11.0814i			0.532540i	−0.963899	+	0.266270i	$0.914209\pi$
$434$	10.8082	−	0.0384624i	0.518809	−	0.00184625i
$435$		0			0
$436$	−11.5516	−	4.68877i	−0.553219	−	0.224552i
$437$	−3.73694	+	4.87008i	−0.178762	+	0.232968i
$438$		0			0
$439$	7.15619	+	26.7073i	0.341546	+	1.27467i	0.896595	+	0.442851i	$0.146033\pi$
$439$	7.15619	+	26.7073i	0.341546	+	1.27467i	−0.555049	+	0.831818i	$0.687300\pi$
$440$	−0.394122	−	36.9156i	−0.0187890	−	1.75988i
$441$		0			0
$442$	9.34321	+	7.11662i	0.444411	+	0.338503i
$443$	−20.6876	−	2.72357i	−0.982897	−	0.129401i	−0.378086	−	0.925770i	$-0.623418\pi$
$443$	−20.6876	−	2.72357i	−0.982897	−	0.129401i	−0.604810	+	0.796370i	$0.706751\pi$
$444$		0			0
$445$	3.67703	+	27.9298i	0.174308	+	1.32400i
$446$	7.91415	+	29.1211i	0.374746	+	1.37892i
$447$		0			0
$448$	−8.87872	−	30.5143i	−0.419480	−	1.44166i
$449$		−	15.1590i		−	0.715397i	−0.933837	−	0.357699i	$-0.883562\pi$
$449$		−	15.1590i		−	0.715397i	0.933837	−	0.357699i	$-0.116438\pi$
$450$		0			0
$451$	−14.2945	+	34.5100i	−0.673103	+	1.62501i
$452$	3.79809	−	2.22902i	0.178647	−	0.104844i
$453$		0			0
$454$	33.2711	+	4.25983i	1.56149	+	0.199924i
$455$	11.7759	+	3.15534i	0.552062	+	0.147925i
$456$		0			0
$457$	−19.0876	+	5.11451i	−0.892881	+	0.239247i	−0.675956	−	0.736942i	$-0.736269\pi$
$457$	−19.0876	+	5.11451i	−0.892881	+	0.239247i	−0.216924	+	0.976188i	$0.569602\pi$
$458$	−33.6985	+	4.55854i	−1.57463	+	0.213007i
$459$		0			0
$460$	17.0398	+	21.8825i	0.794486	+	1.02028i
$461$	−17.3404	+	13.3058i	−0.807625	+	0.619712i	−0.927816	−	0.373038i	$-0.878316\pi$
$461$	−17.3404	+	13.3058i	−0.807625	+	0.619712i	0.120191	+	0.992751i	$0.461649\pi$
$462$		0			0
$463$	−0.850272	−	1.47271i	−0.0395155	−	0.0684428i	0.845591	−	0.533831i	$-0.179248\pi$
$463$	−0.850272	−	1.47271i	−0.0395155	−	0.0684428i	−0.885107	+	0.465388i	$0.845915\pi$
$464$	9.04729	+	11.4495i	0.420010	+	0.531527i
$465$		0			0
$466$	27.1096	−	0.0964735i	1.25583	−	0.00446905i
$467$	0.645766	−	1.55902i	0.0298825	−	0.0721427i	−0.908234	−	0.418463i	$-0.862569\pi$
$467$	0.645766	−	1.55902i	0.0298825	−	0.0721427i	0.938116	+	0.346320i	$0.112569\pi$
$468$		0			0
$469$	3.27342	−	1.35589i	0.151152	−	0.0626094i
$470$	−7.57370	+	18.4702i	−0.349349	+	0.851965i
$471$		0			0
$472$	−5.40760	−	37.9403i	−0.248905	−	1.74635i
$473$	−13.4500	+	50.1960i	−0.618431	+	2.30802i
$474$		0			0
$475$	−0.270496	+	2.05462i	−0.0124112	+	0.0942725i
$476$	14.8911	+	54.0330i	0.682531	+	2.47660i
$477$		0			0
$478$	5.76241	+	1.52208i	0.263567	+	0.0696181i
$479$	20.2093	−	35.0035i	0.923387	−	1.59935i	0.129252	−	0.991612i	$-0.458743\pi$
$479$	20.2093	−	35.0035i	0.923387	−	1.59935i	0.794135	−	0.607741i	$-0.207924\pi$
$480$		0			0
$481$	0.942063	+	1.63170i	0.0429544	+	0.0743992i
$482$	−6.45851	−	23.7649i	−0.294177	−	1.08246i
$483$		0			0
$484$	7.08907	−	27.2305i	0.322230	−	1.23775i
$485$	19.7235	−	8.16976i	0.895600	−	0.370970i
$486$		0			0
$487$	−28.5548	−	28.5548i	−1.29394	−	1.29394i	−0.932329	−	0.361612i	$-0.882226\pi$
$487$	−28.5548	−	28.5548i	−1.29394	−	1.29394i	−0.361612	−	0.932329i	$-0.617774\pi$
$488$	0.687489	−	5.69083i	0.0311212	−	0.257612i
$489$		0			0
$490$	19.7975	+	25.6114i	0.894359	+	1.15700i
$491$	−1.72230	−	1.32157i	−0.0777262	−	0.0596414i	0.569167	−	0.822222i	$-0.307266\pi$
$491$	−1.72230	−	1.32157i	−0.0777262	−	0.0596414i	−0.646894	+	0.762580i	$0.723932\pi$
$492$		0			0
$493$	−15.6669	−	20.4175i	−0.705603	−	0.919560i
$494$	0.966541	+	1.66042i	0.0434867	+	0.0747060i
$495$		0			0
$496$	6.60909	−	3.94224i	0.296757	−	0.177012i
$497$	20.2561	−	35.0846i	0.908610	−	1.57376i
$498$		0			0
$499$	−3.38087	−	25.6803i	−0.151348	−	1.14961i	−0.883489	−	0.468452i	$-0.844812\pi$
$499$	−3.38087	−	25.6803i	−0.151348	−	1.14961i	0.732140	−	0.681154i	$-0.238521\pi$
$500$	−15.4793	−	6.28303i	−0.692255	−	0.280986i
$501$		0			0
$502$	−11.5447	+	28.1543i	−0.515265	+	1.25659i
$503$	14.9007	+	14.9007i	0.664388	+	0.664388i	0.956411	−	0.292023i	$-0.0943284\pi$
$503$	14.9007	+	14.9007i	0.664388	+	0.664388i	−0.292023	+	0.956411i	$0.594328\pi$
$504$		0			0
$505$	3.62981	−	3.62981i	0.161524	−	0.161524i
$506$	14.5380	+	34.7476i	0.646293	+	1.54472i
$507$		0			0
$508$	36.1298	−	0.257150i	1.60300	−	0.0114092i
$509$	−14.5082	+	1.91004i	−0.643065	+	0.0846612i	−0.445004	−	0.895529i	$-0.646798\pi$
$509$	−14.5082	+	1.91004i	−0.643065	+	0.0846612i	−0.198061	+	0.980190i	$0.563464\pi$
$510$		0			0
$511$	34.8789	+	20.1373i	1.54295	+	0.890823i
$512$	−16.5041	−	15.4794i	−0.729387	−	0.684101i
$513$		0			0
$514$	24.7254	+	6.53094i	1.09059	+	0.288068i
$515$	−14.8566	+	11.3999i	−0.654659	+	0.502338i
$516$		0			0
$517$	−16.5044	+	21.5089i	−0.725861	+	0.945961i
$518$	−1.14186	+	8.91839i	−0.0501703	+	0.391852i
$519$		0			0
$520$	8.36005	−	2.33601i	0.366612	−	0.102441i
$521$	−11.2961	+	11.2961i	−0.494892	+	0.494892i	−0.909843	−	0.414952i	$-0.863798\pi$
$521$	−11.2961	+	11.2961i	−0.494892	+	0.494892i	0.414952	+	0.909843i	$0.363798\pi$
$522$		0			0
$523$	8.98920	+	21.7018i	0.393070	+	0.948955i	0.989267	+	0.146117i	$0.0466776\pi$
$523$	8.98920	+	21.7018i	0.393070	+	0.948955i	−0.596197	+	0.802838i	$0.703322\pi$
$524$	−23.3808	+	3.24759i	−1.02140	+	0.141872i
$525$		0			0
$526$	10.0315	−	17.5187i	0.437393	−	0.763852i
$527$	−11.7537	+	6.78600i	−0.511999	+	0.295603i
$528$		0			0
$529$	−4.58713	−	2.64838i	−0.199441	−	0.115147i
$530$	19.6007	−	11.4097i	0.851400	−	0.495604i
$531$		0			0
$532$	−1.13199	+	9.09821i	−0.0490778	+	0.394458i
$533$	−8.70758	−	1.14637i	−0.377167	−	0.0496550i
$534$		0			0
$535$	−3.15627	−	0.845720i	−0.136457	−	0.0365637i
$536$	1.51429	−	2.01770i	0.0654072	−	0.0871512i
$537$		0			0
$538$	−4.74762	−	11.3474i	−0.204684	−	0.489221i
$539$	16.8240	+	40.6167i	0.724661	+	1.74949i
$540$		0			0
$541$	−0.000948429	0	0.000392852i	−4.07761e−5	0	1.68900e-5i	0.382663	−	0.923888i	$-0.375007\pi$
$541$	−0.000948429	0	0.000392852i	−4.07761e−5	0	1.68900e-5i	−0.382704	+	0.923871i	$0.625007\pi$
$542$	0.477914	+	0.474524i	0.0205282	+	0.0203826i
$543$		0			0
$544$	28.7155	+	27.7114i	1.23117	+	1.18812i
$545$	14.0728	−	8.12491i	0.602811	−	0.348033i
$546$		0			0
$547$	−7.98562	−	10.4071i	−0.341440	−	0.444974i	0.590797	−	0.806820i	$-0.298813\pi$
$547$	−7.98562	−	10.4071i	−0.341440	−	0.444974i	−0.932238	+	0.361846i	$0.882147\pi$
$548$	−16.1356	+	4.44685i	−0.689279	+	0.189960i
$549$		0			0
$550$	10.1157	+	7.70499i	0.431334	+	0.328542i
$551$	−1.08961	−	4.06646i	−0.0464188	−	0.173237i
$552$		0			0
$553$	1.07183	−	4.00013i	0.0455790	−	0.170103i
$554$	13.6671	−	10.5646i	0.580657	−	0.448846i
$555$		0			0
$556$	−15.2494	−	11.5298i	−0.646718	−	0.488971i
$557$	−17.4040	−	7.20896i	−0.737430	−	0.305453i	−0.0178286	−	0.999841i	$-0.505675\pi$
$557$	−17.4040	−	7.20896i	−0.737430	−	0.305453i	−0.719601	+	0.694388i	$0.755675\pi$
$558$		0			0
$559$	−12.2187			−0.516795
$560$	38.4916	+	15.3056i	1.62657	+	0.646778i
$561$		0			0
$562$	−1.42361	−	0.815179i	−0.0600513	−	0.0343863i
$563$	24.1925	−	3.18500i	1.01959	−	0.134232i	0.397847	−	0.917452i	$-0.369758\pi$
$563$	24.1925	−	3.18500i	1.01959	−	0.134232i	0.621744	+	0.783220i	$0.286424\pi$
$564$		0			0
$565$	−0.749243	+	5.69107i	−0.0315209	+	0.239425i
$566$	0.0462441	+	0.341854i	0.00194378	+	0.0143692i
$567$		0			0
$568$	−0.307940	−	28.8433i	−0.0129209	−	1.21024i
$569$	23.9009	−	6.40423i	1.00198	−	0.268479i	0.279705	−	0.960086i	$-0.409763\pi$
$569$	23.9009	−	6.40423i	1.00198	−	0.268479i	0.722274	+	0.691607i	$0.243097\pi$
$570$		0			0
$571$	−4.20949	−	3.23006i	−0.176162	−	0.135174i	0.516917	−	0.856036i	$-0.327080\pi$
$571$	−4.20949	−	3.23006i	−0.176162	−	0.135174i	−0.693079	+	0.720862i	$0.743746\pi$
$572$	11.7884	−	0.0839027i	0.492900	−	0.00350815i
$573$		0			0
$574$	−29.7414	−	29.5305i	−1.24138	−	1.23258i
$575$	−9.55280			−0.398379
$576$		0			0
$577$	−15.0291			−0.625668			−0.312834	−	0.949808i	$-0.601278\pi$
$577$	−15.0291			−0.625668			−0.312834	+	0.949808i	$0.601278\pi$
$578$	−32.8820	−	32.6488i	−1.36771	−	1.35801i
$579$		0			0
$580$	−19.0201	+	0.135373i	−0.789765	+	0.00562105i
$581$	−3.43029	−	2.63215i	−0.142312	−	0.109200i
$582$		0			0
$583$	29.7519	−	7.97199i	1.23220	−	0.330166i
$584$	28.6742	−	0.306134i	1.18655	−	0.0126679i
$585$		0			0
$586$	3.33689	+	24.6675i	0.137846	+	1.01901i
$587$	−1.39871	+	10.6243i	−0.0577309	+	0.438510i	0.938032	+	0.346549i	$0.112647\pi$
$587$	−1.39871	+	10.6243i	−0.0577309	+	0.438510i	−0.995763	+	0.0919606i	$0.970687\pi$
$588$		0			0
$589$	−2.20115	+	0.289786i	−0.0906967	+	0.0119404i
$590$	43.3489	+	24.8222i	1.78465	+	1.02192i
$591$		0			0
$592$	2.53380	+	5.87902i	0.104139	+	0.241626i
$593$	−7.89434			−0.324182			−0.162091	−	0.986776i	$-0.551824\pi$
$593$	−7.89434			−0.324182			−0.162091	+	0.986776i	$0.551824\pi$
$594$		0			0
$595$	−67.4935	−	27.9567i	−2.76696	−	1.14611i
$596$	−13.6062	−	10.2874i	−0.557331	−	0.421387i
$597$		0			0
$598$	−7.00693	+	5.41633i	−0.286535	+	0.221490i
$599$	−1.12852	+	4.21170i	−0.0461102	+	0.172086i	−0.985141	−	0.171747i	$-0.945059\pi$
$599$	−1.12852	+	4.21170i	−0.0461102	+	0.172086i	0.939031	+	0.343833i	$0.111725\pi$
$600$		0			0
$601$	−1.24796	−	4.65744i	−0.0509052	−	0.189981i	0.935791	−	0.352555i	$-0.114687\pi$
$601$	−1.24796	−	4.65744i	−0.0509052	−	0.189981i	−0.986696	+	0.162574i	$0.948020\pi$
$602$	−46.3853	−	35.3311i	−1.89052	−	1.43999i
$603$		0			0
$604$	−0.270797	+	0.0746296i	−0.0110186	+	0.00303664i
$605$	22.3272	+	29.0973i	0.907729	+	1.18298i
$606$		0			0
$607$	19.6779	−	11.3610i	0.798701	−	0.461130i	−0.0443158	−	0.999018i	$-0.514111\pi$
$607$	19.6779	−	11.3610i	0.798701	−	0.461130i	0.843017	+	0.537887i	$0.180777\pi$
$608$	2.60504	+	5.98563i	0.105648	+	0.242749i
$609$		0			0
$610$	5.30198	+	5.26437i	0.214671	+	0.213148i
$611$	−5.88933	−	2.43944i	−0.238257	−	0.0986892i
$612$		0			0
$613$	12.8808	+	31.0971i	0.520252	+	1.25600i	0.937747	+	0.347319i	$0.112908\pi$
$613$	12.8808	+	31.0971i	0.520252	+	1.25600i	−0.417495	+	0.908679i	$0.637092\pi$
$614$	−2.23008	−	5.33015i	−0.0899985	−	0.215107i
$615$		0			0
$616$	44.9946	+	33.7685i	1.81288	+	1.36057i
$617$	17.4594	+	4.67823i	0.702888	+	0.188338i	0.592524	−	0.805553i	$-0.298132\pi$
$617$	17.4594	+	4.67823i	0.702888	+	0.188338i	0.110364	+	0.993891i	$0.464798\pi$
$618$		0			0
$619$	−33.4351	−	4.40182i	−1.34387	−	0.176924i	−0.575958	−	0.817479i	$-0.695371\pi$
$619$	−33.4351	−	4.40182i	−1.34387	−	0.176924i	−0.767912	+	0.640555i	$0.778704\pi$
$620$	−1.23845	+	9.95393i	−0.0497375	+	0.399759i
$621$		0			0
$622$	13.1232	−	7.63907i	0.526192	−	0.306299i
$623$	−37.1767	−	21.4640i	−1.48945	−	0.859935i
$624$		0			0
$625$	26.6339	−	15.3771i	1.06535	−	0.615083i
$626$	−8.96819	+	15.6618i	−0.358441	+	0.625972i
$627$		0			0
$628$	−17.7148	+	2.46058i	−0.706896	+	0.0981879i
$629$	−4.32062	−	10.4309i	−0.172274	−	0.415907i
$630$		0			0
$631$	22.7155	−	22.7155i	0.904289	−	0.904289i	−0.0915149	−	0.995804i	$-0.529171\pi$
$631$	22.7155	−	22.7155i	0.904289	−	0.904289i	0.995804	+	0.0915149i	$0.0291709\pi$
$632$	−0.793515	−	2.83981i	−0.0315643	−	0.112962i
$633$		0			0
$634$	4.80383	−	37.5200i	0.190785	−	1.49011i
$635$	−28.6692	+	37.3624i	−1.13770	+	1.48268i
$636$		0			0
$637$	−8.20078	+	6.29268i	−0.324927	+	0.249325i
$638$	−24.9753	−	6.59695i	−0.988783	−	0.261176i
$639$		0			0
$640$	29.1362	−	4.57681i	1.15171	−	0.180914i
$641$	10.2324	+	5.90769i	0.404156	+	0.233340i	0.688276	−	0.725449i	$-0.258368\pi$
$641$	10.2324	+	5.90769i	0.404156	+	0.233340i	−0.284120	+	0.958789i	$0.591701\pi$
$642$		0			0
$643$	−38.8796	+	5.11860i	−1.53326	+	0.201858i	−0.849399	−	0.527752i	$-0.823035\pi$
$643$	−38.8796	+	5.11860i	−1.53326	+	0.201858i	−0.683864	+	0.729610i	$0.739702\pi$
$644$	−42.2618	+	0.300793i	−1.66535	+	0.0118529i
$645$		0			0
$646$	−4.44358	−	10.6207i	−0.174830	−	0.417866i
$647$	−33.9272	+	33.9272i	−1.33382	+	1.33382i	−0.431892	+	0.901925i	$0.642154\pi$
$647$	−33.9272	+	33.9272i	−1.33382	+	1.33382i	−0.901925	+	0.431892i	$0.857846\pi$
$648$		0			0
$649$	47.9708	+	47.9708i	1.88302	+	1.88302i
$650$	−1.13432	+	2.76629i	−0.0444916	+	0.108503i
$651$		0			0
$652$	14.0945	+	5.72097i	0.551985	+	0.224050i
$653$	−1.83455	−	13.9348i	−0.0717916	−	0.545311i	−0.989112	−	0.147162i	$-0.952986\pi$
$653$	−1.83455	−	13.9348i	−0.0717916	−	0.545311i	0.917321	−	0.398149i	$-0.130347\pi$
$654$		0			0
$655$	15.3840	−	26.6459i	0.601103	−	1.04114i
$656$	−28.9317	−	7.31247i	−1.12959	−	0.285504i
$657$		0			0
$658$	−15.3036	−	26.2901i	−0.596597	−	1.02490i
$659$	−1.14523	−	1.49249i	−0.0446118	−	0.0581392i	0.770515	−	0.637422i	$-0.219999\pi$
$659$	−1.14523	−	1.49249i	−0.0446118	−	0.0581392i	−0.815126	+	0.579283i	$0.803333\pi$
$660$		0			0
$661$	−12.6044	−	9.67166i	−0.490253	−	0.376184i	0.333848	−	0.942627i	$-0.391653\pi$
$661$	−12.6044	−	9.67166i	−0.490253	−	0.376184i	−0.824101	+	0.566443i	$0.808319\pi$
$662$	−20.4103	−	26.4041i	−0.793268	−	1.02623i
$663$		0			0
$664$	−3.05634	−	0.369226i	−0.118609	−	0.0143287i
$665$	−8.45021	−	8.45021i	−0.327685	−	0.327685i
$666$		0			0
$667$	17.9290	−	7.42643i	0.694213	−	0.287552i
$668$	−0.346619	+	1.33143i	−0.0134111	+	0.0515147i
$669$		0			0
$670$	0.862352	+	3.17313i	0.0333156	+	0.122589i
$671$	5.07360	+	8.78773i	0.195864	+	0.339247i
$672$		0			0
$673$	−16.2158	+	28.0865i	−0.625072	+	1.08266i	0.363455	+	0.931612i	$0.381597\pi$
$673$	−16.2158	+	28.0865i	−0.625072	+	1.08266i	−0.988527	+	0.151044i	$0.951736\pi$
$674$	−5.22646	−	1.38051i	−0.201316	−	0.0531753i
$675$		0			0
$676$	−6.17143	−	22.3933i	−0.237363	−	0.861282i
$677$	−3.66641	+	27.8491i	−0.140912	+	1.07033i	0.764147	+	0.645042i	$0.223160\pi$
$677$	−3.66641	+	27.8491i	−0.140912	+	1.07033i	−0.905058	+	0.425287i	$0.860173\pi$
$678$		0			0
$679$	−8.41988	+	31.4234i	−0.323125	+	1.20592i
$680$	−51.4948	+	7.33951i	−1.97474	+	0.281457i
$681$		0			0
$682$	−5.16836	+	12.6042i	−0.197907	+	0.482640i
$683$	17.0308	−	7.05439i	0.651666	−	0.269929i	−0.0322608	−	0.999479i	$-0.510271\pi$
$683$	17.0308	−	7.05439i	0.651666	−	0.269929i	0.683927	+	0.729551i	$0.260271\pi$
$684$		0			0
$685$	8.34857	−	20.1552i	0.318982	−	0.770092i
$686$	−10.0028	+	0.0355963i	−0.381908	+	0.00135907i
$687$		0			0
$688$	−41.2339	−	4.83250i	−1.57203	−	0.184237i
$689$	3.62109	+	6.27191i	0.137953	+	0.238941i
$690$		0			0
$691$	11.0321	−	8.46524i	0.419681	−	0.322033i	−0.377240	−	0.926115i	$-0.623127\pi$
$691$	11.0321	−	8.46524i	0.419681	−	0.322033i	0.796922	+	0.604083i	$0.206460\pi$
$692$	21.2541	+	27.2944i	0.807958	+	1.03758i
$693$		0			0
$694$	−34.6367	+	4.68546i	−1.31479	+	0.177858i
$695$	24.0695	−	6.44939i	0.913007	−	0.244639i
$696$		0			0
$697$	50.8357	+	13.6214i	1.92554	+	0.515947i
$698$	37.2428	+	4.76834i	1.40966	+	0.180485i
$699$		0			0
$700$	−12.3051	+	7.22159i	−0.465088	+	0.272951i
$701$	12.7941	−	30.8876i	0.483225	−	1.16661i	−0.474844	−	0.880070i	$-0.657496\pi$
$701$	12.7941	−	30.8876i	0.483225	−	1.16661i	0.958069	−	0.286538i	$-0.0925045\pi$
$702$		0			0
$703$		−	1.84690i		−	0.0696571i
$704$	39.8151	+	4.37920i	1.50059	+	0.165047i
$705$		0			0
$706$	2.14129	+	7.87915i	0.0805886	+	0.296536i
$707$	1.02103	+	7.75546i	0.0383996	+	0.291674i
$708$		0			0
$709$	0.290651	+	0.0382650i	0.0109156	+	0.00143707i	0.135982	−	0.990711i	$-0.456581\pi$
$709$	0.290651	+	0.0382650i	0.0109156	+	0.00143707i	−0.125066	+	0.992148i	$0.539914\pi$
$710$	29.9095	+	22.7817i	1.12248	+	0.854983i
$711$		0			0
$712$	−30.5632	+	0.326302i	−1.14541	+	0.0122287i
$713$	−2.64877	−	9.88533i	−0.0991971	−	0.370209i
$714$		0			0
$715$	−9.35417	+	12.1906i	−0.349826	+	0.455902i
$716$	−13.7238	−	5.57047i	−0.512881	−	0.208178i
$717$		0			0
$718$	40.8808	−	0.145480i	1.52566	−	0.00542926i
$719$			3.72978i			0.139097i	0.997579	+	0.0695487i	$0.0221559\pi$
$719$			3.72978i			0.139097i	−0.997579	+	0.0695487i	$0.977844\pi$
$720$		0			0
$721$		−	28.5359i		−	1.06273i
$722$	0.0889184	+	24.9866i	0.00330920	+	0.929905i
$723$		0			0
$724$	−10.4478	−	24.7240i	−0.388289	−	0.918859i
$725$	3.98824	−	5.19758i	0.148120	−	0.193033i
$726$		0			0
$727$	−7.19961	−	26.8693i	−0.267019	−	0.996528i	−0.961003	−	0.276538i	$-0.910813\pi$
$727$	−7.19961	−	26.8693i	−0.267019	−	0.996528i	0.693984	−	0.719990i	$-0.255854\pi$
$728$	−4.93115	+	12.2738i	−0.182761	+	0.454899i
$729$		0			0
$730$	−22.6481	+	29.7341i	−0.838245	+	1.10051i
$731$	72.5922	+	9.55694i	2.68492	+	0.353476i
$732$		0			0
$733$	−0.538597	−	4.09105i	−0.0198935	−	0.151106i	0.978615	−	0.205700i	$-0.0659470\pi$
$733$	−0.538597	−	4.09105i	−0.0198935	−	0.151106i	−0.998509	+	0.0545935i	$0.982614\pi$
$734$	−44.0553	+	11.9728i	−1.62611	+	0.441924i
$735$		0			0
$736$	−25.7882	+	15.5070i	−0.950564	+	0.571596i
$737$			4.46575i			0.164498i
$738$		0			0
$739$	−0.367059	+	0.886159i	−0.0135025	+	0.0325979i	−0.930487	−	0.366325i	$-0.880616\pi$
$739$	−0.367059	+	0.886159i	−0.0135025	+	0.0325979i	0.916985	+	0.398923i	$0.130616\pi$
$740$	−8.07519	−	2.10226i	−0.296850	−	0.0772805i
$741$		0			0
$742$	−4.38906	+	34.2804i	−0.161127	+	1.25847i
$743$	−7.55451	−	2.02422i	−0.277148	−	0.0742616i	0.117568	−	0.993065i	$-0.462490\pi$
$743$	−7.55451	−	2.02422i	−0.277148	−	0.0742616i	−0.394716	+	0.918803i	$0.629157\pi$
$744$		0			0
$745$	21.4758	−	5.75443i	0.786814	−	0.210826i
$746$	1.93946	+	14.3372i	0.0710086	+	0.524922i
$747$		0			0
$748$	−70.1017	−	8.72195i	−2.56317	−	0.318906i
$749$	3.95036	−	3.03122i	0.144343	−	0.110758i
$750$		0			0
$751$	−12.3305	−	21.3570i	−0.449945	−	0.779328i	0.548437	−	0.836192i	$-0.315223\pi$
$751$	−12.3305	−	21.3570i	−0.449945	−	0.779328i	−0.998382	+	0.0568642i	$0.981890\pi$
$752$	−18.9097	−	10.5615i	−0.689565	−	0.385139i
$753$		0			0
$754$	−0.0216141	−	6.07369i	−0.000787138	−	0.221191i
$755$	0.140111	−	0.338257i	0.00509915	−	0.0123104i
$756$		0			0
$757$	49.7610	−	20.6117i	1.80860	−	0.749145i	0.825926	−	0.563779i	$-0.190653\pi$
$757$	49.7610	−	20.6117i	1.80860	−	0.749145i	0.982670	−	0.185366i	$-0.0593471\pi$
$758$	−18.4316	−	7.55790i	−0.669467	−	0.274515i
$759$		0			0
$760$	−8.24189	−	2.11437i	−0.298965	−	0.0766961i
$761$	9.39307	−	35.0554i	0.340498	−	1.27076i	−0.557285	−	0.830321i	$-0.688157\pi$
$761$	9.39307	−	35.0554i	0.340498	−	1.27076i	0.897784	−	0.440436i	$-0.145176\pi$
$762$		0			0
$763$	−3.23211	+	24.5503i	−0.117010	+	0.888781i
$764$	10.0456	+	5.70486i	0.363435	+	0.206395i
$765$		0			0
$766$	−4.52915	+	17.1469i	−0.163645	+	0.619542i
$767$	−7.97556	+	13.8141i	−0.287981	+	0.498798i
$768$		0			0
$769$	19.3515	+	33.5177i	0.697832	+	1.20868i	0.969217	+	0.246209i	$0.0791850\pi$
$769$	19.3515	+	33.5177i	0.697832	+	1.20868i	−0.271385	+	0.962471i	$0.587482\pi$
$770$	−70.7608	+	19.2304i	−2.55004	+	0.693017i
$771$		0			0
$772$	15.0666	−	8.84226i	0.542258	−	0.318240i
$773$	−16.7885	+	6.95401i	−0.603839	+	0.250118i	−0.663592	−	0.748095i	$-0.730969\pi$
$773$	−16.7885	+	6.95401i	−0.603839	+	0.250118i	0.0597526	+	0.998213i	$0.480969\pi$
$774$		0			0
$775$	−2.44302	−	2.44302i	−0.0877558	−	0.0877558i
$776$	6.23352	+	22.3084i	0.223770	+	0.800825i
$777$		0			0
$778$	−38.0878	+	29.4417i	−1.36551	+	1.05554i
$779$	6.83012	+	5.24094i	0.244714	+	0.187776i
$780$		0			0
$781$	31.0843	+	40.5099i	1.11228	+	1.44956i
$782$	45.8652	−	26.6983i	1.64013	−	0.954730i
$783$		0			0
$784$	−30.1636	+	17.9922i	−1.07727	+	0.642579i
$785$	11.6559	−	20.1886i	0.416017	−	0.720562i
$786$		0			0
$787$	4.11614	+	31.2652i	0.146725	+	1.11448i	0.893389	+	0.449284i	$0.148321\pi$
$787$	4.11614	+	31.2652i	0.146725	+	1.11448i	−0.746664	+	0.665201i	$0.768346\pi$
$788$	8.01021	+	18.9556i	0.285352	+	0.675267i
$789$		0			0
$790$	3.55597	+	1.45813i	0.126516	+	0.0518779i
$791$	−6.18515	−	6.18515i	−0.219919	−	0.219919i
$792$		0			0
$793$	−1.68706	+	1.68706i	−0.0599092	+	0.0599092i
$794$	27.5886	−	11.5428i	0.979082	−	0.409637i
$795$		0			0
$796$	−25.7705	+	26.1400i	−0.913411	+	0.926506i
$797$	21.5071	−	2.83147i	0.761822	−	0.100296i	0.260403	−	0.965500i	$-0.416145\pi$
$797$	21.5071	−	2.83147i	0.761822	−	0.100296i	0.501420	+	0.865204i	$0.332811\pi$
$798$		0			0
$799$	33.0809	+	19.0993i	1.17032	+	0.675684i
$800$	−4.92201	+	8.88666i	−0.174019	+	0.314191i
$801$		0			0
$802$	−9.32960	+	35.3209i	−0.329440	+	1.24722i
$803$	−40.2724	+	30.9021i	−1.42118	+	1.09051i
$804$		0			0
$805$	33.5349	−	43.7035i	1.18195	−	1.54035i
$806$	−3.17711	−	0.406777i	−0.111909	−	0.0143281i
$807$		0			0
$808$	3.43753	+	4.38220i	0.120932	+	0.154165i
$809$	−39.8723	+	39.8723i	−1.40183	+	1.40183i	−0.607561	+	0.794273i	$0.707852\pi$
$809$	−39.8723	+	39.8723i	−1.40183	+	1.40183i	−0.794273	+	0.607561i	$0.792148\pi$
$810$		0			0
$811$	−4.37938	−	10.5728i	−0.153781	−	0.371260i	0.828148	−	0.560509i	$-0.189395\pi$
$811$	−4.37938	−	10.5728i	−0.153781	−	0.371260i	−0.981929	+	0.189249i	$0.939395\pi$
$812$	17.4804	−	23.1198i	0.613442	−	0.811345i
$813$		0			0
$814$	−9.83434	−	5.63129i	−0.344693	−	0.197377i
$815$	−17.1708	+	9.91355i	−0.601466	+	0.347256i
$816$		0			0
$817$	10.3726	+	5.98863i	0.362892	+	0.209516i
$818$	1.41401	+	2.42914i	0.0494398	+	0.0849328i
$819$		0			0
$820$	30.6894	−	23.8978i	1.07172	−	0.834546i
$821$	−19.9215	−	2.62271i	−0.695264	−	0.0915333i	−0.225393	−	0.974268i	$-0.572367\pi$
$821$	−19.9215	−	2.62271i	−0.695264	−	0.0915333i	−0.469872	+	0.882735i	$0.655700\pi$
$822$		0			0
$823$	−44.9659	−	12.0486i	−1.56741	−	0.419987i	−0.632411	−	0.774633i	$-0.717935\pi$
$823$	−44.9659	−	12.0486i	−1.56741	−	0.419987i	−0.935001	+	0.354646i	$0.884601\pi$
$824$	−10.3462	−	17.4863i	−0.360425	−	0.609163i
$825$		0			0
$826$	−70.2216	+	29.3799i	−2.44332	+	1.02226i
$827$	0.427005	+	1.03088i	0.0148484	+	0.0358473i	0.931130	−	0.364688i	$-0.118824\pi$
$827$	0.427005	+	1.03088i	0.0148484	+	0.0358473i	−0.916281	+	0.400535i	$0.868824\pi$
$828$		0			0
$829$	8.43363	+	3.49332i	0.292912	+	0.121328i	0.524301	−	0.851533i	$-0.324327\pi$
$829$	8.43363	+	3.49332i	0.292912	+	0.121328i	−0.231389	+	0.972861i	$0.574327\pi$
$830$	2.82731	−	2.84750i	0.0981373	−	0.0988383i
$831$		0			0
$832$	1.42837	+	9.30904i	0.0495198	+	0.322733i
$833$	53.6433	−	30.9710i	1.85863	−	1.07308i
$834$		0			0
$835$	−1.09168	−	1.42271i	−0.0377793	−	0.0492349i
$836$	−10.0485	−	5.70653i	−0.347534	−	0.197365i
$837$		0			0
$838$	3.66757	−	4.81505i	0.126694	−	0.166333i
$839$	7.11625	+	26.5582i	0.245680	+	0.916891i	0.973040	+	0.230635i	$0.0740804\pi$
$839$	7.11625	+	26.5582i	0.245680	+	0.916891i	−0.727360	+	0.686256i	$0.759253\pi$
$840$		0			0
$841$	4.06114	−	15.1564i	0.140039	−	0.522634i
$842$	15.8419	+	20.4942i	0.545949	+	0.706277i
$843$		0			0
$844$	−31.6863	+	4.40123i	−1.09069	+	0.151497i
$845$	27.9719	+	11.5863i	0.962261	+	0.398582i
$846$		0			0
$847$	−55.8890			−1.92037
$848$	9.73939	+	22.5977i	0.334452	+	0.776008i
$849$		0			0
$850$	8.90275	−	15.5475i	0.305362	−	0.533276i
$851$	8.44070	−	1.11124i	0.289344	−	0.0380928i
$852$		0			0
$853$	3.64438	−	27.6818i	0.124781	−	0.947807i	−0.808458	−	0.588553i	$-0.799698\pi$
$853$	3.64438	−	27.6818i	0.124781	−	0.947807i	0.933240	−	0.359254i	$-0.116969\pi$
$854$	−11.2827	+	1.52627i	−0.386088	+	0.0522278i
$855$		0			0
$856$	1.32169	−	3.28974i	0.0451744	−	0.112441i
$857$	−33.8594	+	9.07260i	−1.15662	+	0.309914i	−0.785613	−	0.618718i	$-0.787652\pi$
$857$	−33.8594	+	9.07260i	−1.15662	+	0.309914i	−0.371002	+	0.928632i	$0.620986\pi$
$858$		0			0
$859$	26.6473	+	20.4472i	0.909196	+	0.697650i	0.953508	−	0.301367i	$-0.0974431\pi$
$859$	26.6473	+	20.4472i	0.909196	+	0.697650i	−0.0443125	+	0.999018i	$0.514110\pi$
$860$	37.9909	−	38.5355i	1.29548	−	1.31405i
$861$		0			0
$862$	−8.37474	+	8.43456i	−0.285245	+	0.287282i
$863$	−25.5227			−0.868802			−0.434401	−	0.900720i	$-0.643040\pi$
$863$	−25.5227			−0.868802			−0.434401	+	0.900720i	$0.643040\pi$
$864$		0			0
$865$	−45.0907			−1.53313
$866$	11.0419	−	11.1208i	0.375220	−	0.377900i
$867$		0			0
$868$	−10.8849	−	10.7310i	−0.369457	−	0.364235i
$869$	4.14101	+	3.17751i	0.140474	+	0.107790i
$870$		0			0
$871$	−1.01423	+	0.271763i	−0.0343660	+	0.00920833i
$872$	6.92054	+	16.2158i	0.234359	+	0.549137i
$873$		0			0
$874$	8.60294	−	1.16376i	0.290999	−	0.0393647i
$875$	−4.33108	+	32.8978i	−0.146417	+	1.11215i
$876$		0			0
$877$	5.85318	−	0.770586i	0.197648	−	0.0260208i	−0.0310522	−	0.999518i	$-0.509886\pi$
$877$	5.85318	−	0.770586i	0.197648	−	0.0260208i	0.228700	+	0.973497i	$0.426552\pi$
$878$	19.4305	−	33.9328i	0.655746	−	1.14518i
$879$		0			0
$880$	−36.3885	+	37.4395i	−1.22666	+	1.26208i
$881$	−10.3855			−0.349896			−0.174948	−	0.984578i	$-0.555976\pi$
$881$	−10.3855			−0.349896			−0.174948	+	0.984578i	$0.555976\pi$
$882$		0			0
$883$	23.9356	+	9.91443i	0.805495	+	0.333647i	0.747155	−	0.664650i	$-0.231419\pi$
$883$	23.9356	+	9.91443i	0.805495	+	0.333647i	0.0583403	+	0.998297i	$0.481419\pi$
$884$	−2.28516	−	16.4518i	−0.0768581	−	0.553334i
$885$		0			0
$886$	18.0472	+	23.3471i	0.606308	+	0.784360i
$887$	−3.52355	+	13.1501i	−0.118309	+	0.441536i	−0.999513	−	0.0312001i	$-0.990067\pi$
$887$	−3.52355	+	13.1501i	−0.118309	+	0.441536i	0.881204	+	0.472736i	$0.156734\pi$
$888$		0			0
$889$	−18.5739	−	69.3189i	−0.622950	−	2.32488i
$890$	24.1402	−	31.6930i	0.809181	−	1.06235i
$891$		0			0
$892$	21.0750	−	37.1105i	0.705644	−	1.24255i
$893$	3.80391	+	4.95736i	0.127293	+	0.165892i
$894$		0			0
$895$	16.7191	−	9.65275i	0.558856	−	0.322656i
$896$	−21.4953	+	39.4697i	−0.718106	+	1.31859i
$897$		0			0
$898$	−15.1050	+	15.2128i	−0.504059	+	0.507659i
$899$	6.48435	+	2.68591i	0.216265	+	0.0895800i
$900$		0			0
$901$	−16.6076	−	40.0942i	−0.553278	−	1.33573i
$902$	48.7323	−	20.3890i	1.62261	−	0.678881i
$903$		0			0
$904$	−6.03266	−	1.54761i	−0.200643	−	0.0514729i
$905$	33.7933	+	9.05489i	1.12333	+	0.300995i
$906$		0			0
$907$	0.413202	+	0.0543991i	0.0137202	+	0.00180629i	0.137383	−	0.990518i	$-0.456131\pi$
$907$	0.413202	+	0.0543991i	0.0137202	+	0.00180629i	−0.123663	+	0.992324i	$0.539464\pi$
$908$	−29.1447	−	37.4275i	−0.967200	−	1.24207i
$909$		0			0
$910$	−8.67363	−	14.9005i	−0.287528	−	0.493945i
$911$	32.2573	+	18.6237i	1.06873	+	0.617032i	0.927834	−	0.372992i	$-0.121668\pi$
$911$	32.2573	+	18.6237i	1.06873	+	0.617032i	0.140896	+	0.990024i	$0.455002\pi$
$912$		0			0
$913$	4.71958	−	2.72485i	0.156195	−	0.0901794i
$914$	24.2517	+	13.8869i	0.802175	+	0.459337i
$915$		0			0
$916$	38.3605	+	29.0036i	1.26747	+	0.958306i
$917$	17.9424	+	43.3167i	0.592509	+	1.43044i
$918$		0			0
$919$	−37.8327	+	37.8327i	−1.24799	+	1.24799i	−0.291380	+	0.956608i	$0.594114\pi$
$919$	−37.8327	+	37.8327i	−1.24799	+	1.24799i	−0.956608	+	0.291380i	$0.905886\pi$
$920$	4.70412	−	38.9393i	0.155090	−	1.28379i
$921$		0			0
$922$	30.6604	+	3.92557i	1.00975	+	0.129282i
$923$	−7.30870	+	9.52489i	−0.240569	+	0.313516i
$924$		0			0
$925$	2.28019	−	1.74965i	0.0749721	−	0.0575281i
$926$	−0.614172	+	2.32519i	−0.0201829	+	0.0764104i
$927$		0			0
$928$	2.32921	−	20.5052i	0.0764600	−	0.673115i
$929$	−21.5926	−	12.4665i	−0.708431	−	0.409013i	0.102049	−	0.994779i	$-0.467460\pi$
$929$	−21.5926	−	12.4665i	−0.708431	−	0.409013i	−0.810480	+	0.585767i	$0.800793\pi$
$930$		0			0
$931$	10.0459	−	1.32257i	0.329242	−	0.0433455i
$932$	−27.3021	−	26.9162i	−0.894309	−	0.881669i
$933$		0			0
$934$	−2.20152	+	0.921091i	−0.0720359	+	0.0301390i
$935$	65.1088	−	65.1088i	2.12929	−	2.12929i
$936$		0			0
$937$	13.6878	+	13.6878i	0.447161	+	0.447161i	0.894410	−	0.447248i	$-0.147596\pi$
$937$	13.6878	+	13.6878i	0.447161	+	0.447161i	−0.447248	+	0.894410i	$0.647596\pi$
$938$	−4.63611	−	1.90104i	−0.151374	−	0.0620711i
$939$		0			0
$940$	26.0049	−	10.9891i	0.848187	−	0.358424i
$941$	−6.45386	−	49.0219i	−0.210390	−	1.59807i	−0.692142	−	0.721761i	$-0.743333\pi$
$941$	−6.45386	−	49.0219i	−0.210390	−	1.59807i	0.481753	−	0.876307i	$-0.340000\pi$
$942$		0			0
$943$	−19.8426	+	34.3684i	−0.646165	+	1.11919i
$944$	−32.3783	+	43.4634i	−1.05382	+	1.41461i
$945$		0			0
$946$	63.5149	−	36.9723i	2.06505	−	1.20207i
$947$	−12.0131	−	15.6558i	−0.390373	−	0.508744i	0.556282	−	0.830994i	$-0.312228\pi$
$947$	−12.0131	−	15.6558i	−0.390373	−	0.508744i	−0.946655	+	0.322250i	$0.895561\pi$
$948$		0			0
$949$	−9.46904	−	7.26585i	−0.307378	−	0.235860i
$950$	2.31876	−	1.79239i	0.0752303	−	0.0581528i
$951$		0			0
$952$	38.8964	−	69.0629i	1.26064	−	2.23834i
$953$	−10.9279	−	10.9279i	−0.353989	−	0.353989i	0.507602	−	0.861591i	$-0.330532\pi$
$953$	−10.9279	−	10.9279i	−0.353989	−	0.353989i	−0.861591	+	0.507602i	$0.830532\pi$
$954$		0			0
$955$	−13.9117	+	5.76241i	−0.450171	+	0.186467i
$956$	−4.26623	−	7.26935i	−0.137980	−	0.235108i
$957$		0			0
$958$	−55.1599	+	14.9906i	−1.78213	+	0.484325i
$959$	16.6220	+	28.7901i	0.536751	+	0.929680i
$960$		0			0
$961$	−13.6493	+	23.6413i	−0.440301	+	0.762624i
$962$	0.680475	−	2.57620i	0.0219394	−	0.0830601i
$963$		0			0
$964$	−17.1987	+	30.2848i	−0.553933	+	0.975407i
$965$	−2.97216	+	22.5758i	−0.0956771	+	0.726740i
$966$		0			0
$967$	−1.06241	+	3.96498i	−0.0341649	+	0.127505i	−0.980902	−	0.194502i	$-0.937691\pi$
$967$	−1.06241	+	3.96498i	−0.0341649	+	0.127505i	0.946737	+	0.322007i	$0.104358\pi$
$968$	−34.2477	+	20.2635i	−1.10076	+	0.651292i
$969$		0			0
$970$	−27.9342	−	11.4545i	−0.896915	−	0.367780i
$971$	33.6813	−	13.9513i	1.08089	−	0.447717i	0.230066	−	0.973175i	$-0.426106\pi$
$971$	33.6813	−	13.9513i	1.08089	−	0.447717i	0.850820	+	0.525458i	$0.176106\pi$
$972$		0			0
$973$	−14.5312	+	35.0815i	−0.465849	+	1.12466i
$974$	0.203231	+	57.1092i	0.00651195	+	1.82990i
$975$		0			0
$976$	−6.36047	+	5.02601i	−0.203594	+	0.160879i
$977$	1.76153	+	3.05105i	0.0563562	+	0.0976119i	0.892827	−	0.450399i	$-0.148718\pi$
$977$	1.76153	+	3.05105i	0.0563562	+	0.0976119i	−0.836471	+	0.548011i	$0.815385\pi$
$978$		0			0
$979$	42.9255	−	32.9379i	1.37190	−	1.05270i
$980$	5.65224	−	45.4292i	0.180554	−	1.45118i
$981$		0			0
$982$	0.411562	+	3.04242i	0.0131335	+	0.0970875i
$983$	−59.5138	+	15.9467i	−1.89820	+	0.508620i	−0.900996	+	0.433827i	$0.857163\pi$
$983$	−59.5138	+	15.9467i	−1.89820	+	0.508620i	−0.997199	+	0.0747931i	$0.976170\pi$
$984$		0			0
$985$	−25.9090	−	6.94230i	−0.825530	−	0.221200i
$986$	−4.62217	+	36.1011i	−0.147200	+	1.14969i
$987$		0			0
$988$	0.684530	−	2.62942i	0.0217778	−	0.0836529i
$989$	−21.1283	+	51.0082i	−0.671841	+	1.62197i
$990$		0			0
$991$			36.8951i			1.17201i	0.810307	+	0.586006i	$0.199301\pi$
$991$			36.8951i			1.17201i	−0.810307	+	0.586006i	$0.800699\pi$
$992$	−10.5608	−	2.62928i	−0.335304	−	0.0834798i
$993$		0			0
$994$	−55.2876	+	15.0253i	−1.75362	+	0.476575i
$995$	−6.24510	−	47.4362i	−0.197983	−	1.50383i
$996$		0			0
$997$	−15.7719	−	2.07641i	−0.499500	−	0.0657605i	−0.123433	−	0.992353i	$-0.539390\pi$
$997$	−15.7719	−	2.07641i	−0.499500	−	0.0657605i	−0.376067	+	0.926592i	$0.622724\pi$
$998$	−22.1958	+	29.1403i	−0.702597	+	0.922420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.11		368
3.2	odd	2		288.2.bf.a.227.36	yes	368
9.4	even	3		288.2.bf.a.131.42	yes	368
9.5	odd	6	inner	864.2.bn.a.611.5		368
32.11	odd	8	inner	864.2.bn.a.683.5		368
96.11	even	8		288.2.bf.a.11.42	✓	368
288.139	odd	24		288.2.bf.a.203.36	yes	368
288.203	even	24	inner	864.2.bn.a.395.11		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.42	✓	368	96.11	even	8
288.2.bf.a.131.42	yes	368	9.4	even	3
288.2.bf.a.203.36	yes	368	288.139	odd	24
288.2.bf.a.227.36	yes	368	3.2	odd	2
864.2.bn.a.35.11		368	1.1	even	1	trivial
864.2.bn.a.395.11		368	288.203	even	24	inner
864.2.bn.a.611.5		368	9.5	odd	6	inner
864.2.bn.a.683.5		368	32.11	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00355 - 0.996435i) q^{2} +(0.0142344 + 1.99995i) q^{4} +(-2.06818 - 1.58697i) q^{5} +(3.83711 - 1.02815i) q^{7} +(1.97853 - 2.02124i) q^{8} +O(q^{10})\)	\(q+(-1.00355 - 0.996435i) q^{2} +(0.0142344 + 1.99995i) q^{4} +(-2.06818 - 1.58697i) q^{5} +(3.83711 - 1.02815i) q^{7} +(1.97853 - 2.02124i) q^{8} +(0.494213 + 3.65341i) q^{10} +(-0.653532 + 4.96407i) q^{11} +(-1.16718 + 0.153662i) q^{13} +(-4.87523 - 2.79163i) q^{14} +(-3.99959 + 0.0569361i) q^{16} +7.05448 q^{17} +(1.06615 + 0.441612i) q^{19} +(3.14442 - 4.15884i) q^{20} +(5.60223 - 4.33050i) q^{22} +(-1.37678 + 5.13821i) q^{23} +(0.464792 + 1.73463i) q^{25} +(1.32444 + 1.00881i) q^{26} +(2.11087 + 7.65939i) q^{28} +(-2.22085 - 2.89427i) q^{29} +(-1.66613 + 0.961943i) q^{31} +(4.07054 + 3.92820i) q^{32} +(-7.07954 - 7.02933i) q^{34} +(-9.56747 - 3.96297i) q^{35} +(-0.612465 - 1.47862i) q^{37} +(-0.629895 - 1.50553i) q^{38} +(-7.29960 + 1.04040i) q^{40} +(7.20617 + 1.93089i) q^{41} +(10.2902 + 1.35473i) q^{43} +(-9.93719 - 1.23637i) q^{44} +(6.50157 - 3.78459i) q^{46} +(4.68935 + 2.70740i) q^{47} +(7.60416 - 4.39026i) q^{49} +(1.26200 - 2.20392i) q^{50} +(-0.323930 - 2.33211i) q^{52} +(-2.35419 - 5.68351i) q^{53} +(9.22943 - 9.22943i) q^{55} +(5.51372 - 9.78995i) q^{56} +(-0.655211 + 5.11748i) q^{58} +(8.24841 - 10.7495i) q^{59} +(1.60784 - 1.23374i) q^{61} +(2.63057 + 0.694834i) q^{62} +(-0.170801 - 7.99818i) q^{64} +(2.65778 + 1.53447i) q^{65} +(0.884289 - 0.116419i) q^{67} +(0.100416 + 14.1086i) q^{68} +(5.65261 + 13.5104i) q^{70} +(7.21124 - 7.21124i) q^{71} +(7.16896 + 7.16896i) q^{73} +(-0.858710 + 2.09416i) q^{74} +(-0.868026 + 2.13852i) q^{76} +(2.59614 + 19.7196i) q^{77} +(0.521243 - 0.902819i) q^{79} +(8.36222 + 6.22947i) q^{80} +(-5.30776 - 9.11822i) q^{82} +(-0.662598 - 0.863515i) q^{83} +(-14.5899 - 11.1952i) q^{85} +(-8.97688 - 11.6131i) q^{86} +(8.74053 + 11.1425i) q^{88} +(-7.64124 - 7.64124i) q^{89} +(-4.32060 + 1.78965i) q^{91} +(-10.2958 - 2.68035i) q^{92} +(-2.00826 - 7.38966i) q^{94} +(-1.50415 - 2.60527i) q^{95} +(-4.09467 + 7.09217i) q^{97} +(-12.0058 - 3.17119i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

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