LMFDB - Embedded newform 1078.2.i.d.1011.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.13
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.d.901.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(1.02581 - 1.77675i) q^{10} +(-3.14127 + 1.06416i) q^{11} +(-0.662827 + 0.382683i) q^{12} +6.59694 q^{13} -1.57024 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.80554 - 3.12729i) q^{17} +(-2.09077 - 1.20711i) q^{18} +(0.439269 + 0.760837i) q^{19} -2.05161i q^{20} +(-2.18834 + 2.49222i) q^{22} +(-3.30966 - 5.73249i) q^{23} +(-0.382683 + 0.662827i) q^{24} +(-0.395443 + 0.684927i) q^{25} +(5.71311 - 3.29847i) q^{26} +4.14386i q^{27} -6.18955i q^{29} +(-1.35986 + 0.785118i) q^{30} +(-5.61510 - 3.24188i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.48935 + 0.496755i) q^{33} -3.61108i q^{34} -2.41421 q^{36} +(5.52454 + 9.56878i) q^{37} +(0.760837 + 0.439269i) q^{38} +(-4.37263 - 2.52454i) q^{39} +(-1.02581 - 1.77675i) q^{40} -2.36864 q^{41} -7.81288i q^{43} +(-0.649042 + 3.25250i) q^{44} +(-4.28945 - 2.47652i) q^{45} +(-5.73249 - 3.30966i) q^{46} +(4.97716 - 2.87357i) q^{47} +0.765367i q^{48} +0.790886i q^{50} +(-2.39352 + 1.38190i) q^{51} +(3.29847 - 5.71311i) q^{52} +(-0.214882 + 0.372186i) q^{53} +(2.07193 + 3.58869i) q^{54} +(-4.48962 + 5.11308i) q^{55} -0.672404i q^{57} +(-3.09477 - 5.36031i) q^{58} +(-2.78725 - 1.60922i) q^{59} +(-0.785118 + 1.35986i) q^{60} +(5.66711 + 9.81572i) q^{61} -6.48376 q^{62} -1.00000 q^{64} +(11.7211 - 6.76718i) q^{65} +(2.40422 - 0.814474i) q^{66} +(-1.48123 + 2.56556i) q^{67} +(-1.80554 - 3.12729i) q^{68} +5.06620i q^{69} -2.13403 q^{71} +(-2.09077 + 1.20711i) q^{72} +(5.41262 - 9.37493i) q^{73} +(9.56878 + 5.52454i) q^{74} +(0.524221 - 0.302659i) q^{75} +0.878539 q^{76} -5.04908 q^{78} +(-7.34847 + 4.24264i) q^{79} +(-1.77675 - 1.02581i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(-2.05130 + 1.18432i) q^{82} +12.3153 q^{83} -7.40854i q^{85} +(-3.90644 - 6.76615i) q^{86} +(-2.36864 + 4.10260i) q^{87} +(1.06416 + 3.14127i) q^{88} +(-5.82684 + 3.36413i) q^{89} -4.95303 q^{90} -6.61931 q^{92} +(2.48123 + 4.29762i) q^{93} +(2.87357 - 4.97716i) q^{94} +(1.56094 + 0.901211i) q^{95} +(0.382683 + 0.662827i) q^{96} -9.23880i q^{97} +(6.01676 + 5.28311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^9	$ 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.662827	−	0.382683i	−0.382683	−	0.220942i	0.296302	−	0.955094i	$-0.404247\pi$
$3$	−0.662827	−	0.382683i	−0.382683	−	0.220942i	−0.678985	+	0.734152i	$0.737580\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.77675	−	1.02581i	0.794586	−	0.458755i	−0.0469885	−	0.998895i	$-0.514962\pi$
$5$	1.77675	−	1.02581i	0.794586	−	0.458755i	0.841575	+	0.540141i	$0.181629\pi$
$6$	−0.765367			−0.312460
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.20711	−	2.09077i	−0.402369	−	0.696923i
$10$	1.02581	−	1.77675i	0.324388	−	0.561857i
$11$	−3.14127	+	1.06416i	−0.947128	+	0.320857i
$11$	−3.14127	+	1.06416i	−0.947128	+	0.320857i
$12$	−0.662827	+	0.382683i	−0.191342	+	0.110471i
$13$	6.59694			1.82966			0.914830	−	0.403838i	$-0.132324\pi$
$13$	6.59694			1.82966			0.914830	+	0.403838i	$0.132324\pi$
$14$		0			0
$15$	−1.57024			−0.405433
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.80554	−	3.12729i	0.437908	−	0.758478i	−0.559620	−	0.828749i	$-0.689053\pi$
$17$	1.80554	−	3.12729i	0.437908	−	0.758478i	0.997528	+	0.0702708i	$0.0223863\pi$
$18$	−2.09077	−	1.20711i	−0.492799	−	0.284518i
$19$	0.439269	+	0.760837i	0.100775	+	0.174548i	0.912004	−	0.410181i	$-0.134534\pi$
$19$	0.439269	+	0.760837i	0.100775	+	0.174548i	−0.811229	+	0.584729i	$0.801201\pi$
$20$		−	2.05161i		−	0.458755i
$21$		0			0
$22$	−2.18834	+	2.49222i	−0.466555	+	0.531344i
$23$	−3.30966	−	5.73249i	−0.690111	−	1.19531i	−0.971801	−	0.235802i	$-0.924228\pi$
$23$	−3.30966	−	5.73249i	−0.690111	−	1.19531i	0.281690	−	0.959505i	$-0.409105\pi$
$24$	−0.382683	+	0.662827i	−0.0781149	+	0.135299i
$25$	−0.395443	+	0.684927i	−0.0790886	+	0.136985i
$26$	5.71311	−	3.29847i	1.12043	−	0.646883i
$27$			4.14386i			0.797486i
$28$		0			0
$29$		−	6.18955i		−	1.14937i	−0.818375	−	0.574685i	$-0.805124\pi$
$29$		−	6.18955i		−	1.14937i	0.818375	−	0.574685i	$-0.194876\pi$
$30$	−1.35986	+	0.785118i	−0.248276	+	0.143342i
$31$	−5.61510	−	3.24188i	−1.00850	−	0.582259i	−0.0977497	−	0.995211i	$-0.531164\pi$
$31$	−5.61510	−	3.24188i	−1.00850	−	0.582259i	−0.910753	+	0.412952i	$0.864498\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.48935	+	0.496755i	0.433341	+	0.0864740i
$34$		−	3.61108i		−	0.619295i
$35$		0			0
$36$	−2.41421			−0.402369
$37$	5.52454	+	9.56878i	0.908229	+	1.57310i	0.816524	+	0.577312i	$0.195898\pi$
$37$	5.52454	+	9.56878i	0.908229	+	1.57310i	0.0917046	+	0.995786i	$0.470768\pi$
$38$	0.760837	+	0.439269i	0.123424	+	0.0712589i
$39$	−4.37263	−	2.52454i	−0.700181	−	0.404250i
$40$	−1.02581	−	1.77675i	−0.162194	−	0.280929i
$41$	−2.36864			−0.369919			−0.184960	−	0.982746i	$-0.559215\pi$
$41$	−2.36864			−0.369919			−0.184960	+	0.982746i	$0.559215\pi$
$42$		0			0
$43$		−	7.81288i		−	1.19145i	−0.803188	−	0.595726i	$-0.796864\pi$
$43$		−	7.81288i		−	1.19145i	0.803188	−	0.595726i	$-0.203136\pi$
$44$	−0.649042	+	3.25250i	−0.0978468	+	0.490333i
$45$	−4.28945	−	2.47652i	−0.639434	−	0.369177i
$46$	−5.73249	−	3.30966i	−0.845210	−	0.487982i
$47$	4.97716	−	2.87357i	0.725994	−	0.419153i	−0.0909611	−	0.995854i	$-0.528994\pi$
$47$	4.97716	−	2.87357i	0.725994	−	0.419153i	0.816955	+	0.576702i	$0.195661\pi$
$48$			0.765367i			0.110471i
$49$		0			0
$50$			0.790886i			0.111848i
$51$	−2.39352	+	1.38190i	−0.335160	+	0.193505i
$52$	3.29847	−	5.71311i	0.457415	−	0.792266i
$53$	−0.214882	+	0.372186i	−0.0295163	+	0.0511237i	−0.880406	−	0.474220i	$-0.842730\pi$
$53$	−0.214882	+	0.372186i	−0.0295163	+	0.0511237i	0.850890	+	0.525344i	$0.176063\pi$
$54$	2.07193	+	3.58869i	0.281954	+	0.488359i
$55$	−4.48962	+	5.11308i	−0.605380	+	0.689448i
$56$		0			0
$57$		−	0.672404i		−	0.0890621i
$58$	−3.09477	−	5.36031i	−0.406364	−	0.703843i
$59$	−2.78725	−	1.60922i	−0.362870	−	0.209503i	0.307469	−	0.951558i	$-0.400518\pi$
$59$	−2.78725	−	1.60922i	−0.362870	−	0.209503i	−0.670339	+	0.742055i	$0.733851\pi$
$60$	−0.785118	+	1.35986i	−0.101358	+	0.175558i
$61$	5.66711	+	9.81572i	0.725599	+	1.25677i	0.958727	+	0.284328i	$0.0917704\pi$
$61$	5.66711	+	9.81572i	0.725599	+	1.25677i	−0.233129	+	0.972446i	$0.574896\pi$
$62$	−6.48376			−0.823439
$63$		0			0
$64$	−1.00000			−0.125000
$65$	11.7211	−	6.76718i	1.45382	−	0.839365i
$66$	2.40422	−	0.814474i	0.295939	−	0.100255i
$67$	−1.48123	+	2.56556i	−0.180961	+	0.313434i	−0.942208	−	0.335028i	$-0.891254\pi$
$67$	−1.48123	+	2.56556i	−0.180961	+	0.313434i	0.761247	+	0.648462i	$0.224587\pi$
$68$	−1.80554	−	3.12729i	−0.218954	−	0.379239i
$69$			5.06620i			0.609899i
$70$		0			0
$71$	−2.13403			−0.253263			−0.126631	−	0.991950i	$-0.540417\pi$
$71$	−2.13403			−0.253263			−0.126631	+	0.991950i	$0.540417\pi$
$72$	−2.09077	+	1.20711i	−0.246400	+	0.142259i
$73$	5.41262	−	9.37493i	0.633499	−	1.09725i	−0.353332	−	0.935498i	$-0.614951\pi$
$73$	5.41262	−	9.37493i	0.633499	−	1.09725i	0.986831	−	0.161754i	$-0.0517152\pi$
$74$	9.56878	+	5.52454i	1.11235	+	0.642215i
$75$	0.524221	−	0.302659i	0.0605318	−	0.0349480i
$76$	0.878539			0.100775
$77$		0			0
$78$	−5.04908			−0.571695
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	−0.852745	−	0.522328i	$-0.825064\pi$
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	0.0259772	+	0.999663i	$0.491730\pi$
$80$	−1.77675	−	1.02581i	−0.198647	−	0.114689i
$81$	−2.03553	+	3.52565i	−0.226170	+	0.391739i
$82$	−2.05130	+	1.18432i	−0.226528	+	0.130786i
$83$	12.3153			1.35178			0.675892	−	0.737001i	$-0.263759\pi$
$83$	12.3153			1.35178			0.675892	+	0.737001i	$0.263759\pi$
$84$		0			0
$85$		−	7.40854i		−	0.803569i
$86$	−3.90644	−	6.76615i	−0.421242	−	0.729613i
$87$	−2.36864	+	4.10260i	−0.253945	+	0.439845i
$88$	1.06416	+	3.14127i	0.113440	+	0.334860i
$89$	−5.82684	+	3.36413i	−0.617644	+	0.356597i	−0.775951	−	0.630793i	$-0.782730\pi$
$89$	−5.82684	+	3.36413i	−0.617644	+	0.356597i	0.158307	+	0.987390i	$0.449396\pi$
$90$	−4.95303			−0.522095
$91$		0			0
$92$	−6.61931			−0.690111
$93$	2.48123	+	4.29762i	0.257291	+	0.445642i
$94$	2.87357	−	4.97716i	0.296386	−	0.513355i
$95$	1.56094	+	0.901211i	0.160149	+	0.0924622i
$96$	0.382683	+	0.662827i	0.0390575	+	0.0676495i
$97$		−	9.23880i		−	0.938058i	−0.883183	−	0.469029i	$-0.844604\pi$
$97$		−	9.23880i		−	0.938058i	0.883183	−	0.469029i	$-0.155396\pi$
$98$		0			0
$99$	6.01676	+	5.28311i	0.604707	+	0.530973i
$100$	0.395443	+	0.684927i	0.0395443	+	0.0684927i
$101$	−0.929830	+	1.61051i	−0.0925216	+	0.160252i	−0.908572	−	0.417729i	$-0.862826\pi$
$101$	−0.929830	+	1.61051i	−0.0925216	+	0.160252i	0.816050	+	0.577981i	$0.196159\pi$
$102$	−1.38190	+	2.39352i	−0.136829	+	0.236994i
$103$	−5.81112	+	3.35505i	−0.572587	+	0.330583i	−0.758182	−	0.652043i	$-0.773912\pi$
$103$	−5.81112	+	3.35505i	−0.572587	+	0.330583i	0.185595	+	0.982626i	$0.440579\pi$
$104$		−	6.59694i		−	0.646883i
$105$		0			0
$106$			0.429764i			0.0417423i
$107$	12.7768	−	7.37667i	1.23518	−	0.713130i	0.267073	−	0.963676i	$-0.413944\pi$
$107$	12.7768	−	7.37667i	1.23518	−	0.713130i	0.968105	+	0.250547i	$0.0806103\pi$
$108$	3.58869	+	2.07193i	0.345322	+	0.199372i
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	0.230063	−	0.973176i	$-0.426107\pi$
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	−0.727764	+	0.685828i	$0.759440\pi$
$110$	−1.33158	+	6.67287i	−0.126961	+	0.636233i
$111$		−	8.45660i		−	0.802665i
$112$		0			0
$113$	−0.597322			−0.0561913			−0.0280956	−	0.999605i	$-0.508944\pi$
$113$	−0.597322			−0.0561913			−0.0280956	+	0.999605i	$0.508944\pi$
$114$	−0.336202	−	0.582319i	−0.0314882	−	0.0545392i
$115$	−11.7609	−	6.79013i	−1.09671	−	0.633183i
$116$	−5.36031	−	3.09477i	−0.497692	−	0.287343i
$117$	−7.96321	−	13.7927i	−0.736199	−	1.27513i
$118$	−3.21844			−0.296282
$119$		0			0
$120$			1.57024i			0.143342i
$121$	8.73512	−	6.68563i	0.794102	−	0.607785i
$122$	9.81572	+	5.66711i	0.888673	+	0.513076i
$123$	1.57000	+	0.906438i	0.141562	+	0.0817308i
$124$	−5.61510	+	3.24188i	−0.504251	+	0.291130i
$125$			11.8807i			1.06264i
$126$		0			0
$127$			7.33002i			0.650434i	0.945639	+	0.325217i	$0.105437\pi$
$127$			7.33002i			0.650434i	−0.945639	+	0.325217i	$0.894563\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.98986	+	5.17859i	−0.263242	+	0.455949i
$130$	6.76718	−	11.7211i	0.593521	−	1.02801i
$131$	4.41025	+	7.63878i	0.385325	+	0.667403i	0.991814	−	0.127689i	$-0.0407559\pi$
$131$	4.41025	+	7.63878i	0.385325	+	0.667403i	−0.606489	+	0.795092i	$0.707423\pi$
$132$	1.67488	−	1.90747i	0.145780	−	0.166024i
$133$		0			0
$134$			2.96246i			0.255917i
$135$	4.25080	+	7.36260i	0.365850	+	0.633671i
$136$	−3.12729	−	1.80554i	−0.268163	−	0.154824i
$137$	−1.61810	+	2.80263i	−0.138244	+	0.239445i	−0.926832	−	0.375477i	$-0.877479\pi$
$137$	−1.61810	+	2.80263i	−0.138244	+	0.239445i	0.788588	+	0.614922i	$0.210812\pi$
$138$	2.53310	+	4.38746i	0.215632	+	0.373485i
$139$	−2.47122			−0.209606			−0.104803	−	0.994493i	$-0.533421\pi$
$139$	−2.47122			−0.209606			−0.104803	+	0.994493i	$0.533421\pi$
$140$		0			0
$141$	−4.39866			−0.370434
$142$	−1.84813	+	1.06702i	−0.155091	+	0.0895420i
$143$	−20.7227	+	7.02021i	−1.73292	+	0.587059i
$144$	−1.20711	+	2.09077i	−0.100592	+	0.174231i
$145$	−6.34928	−	10.9973i	−0.527279	−	0.913274i
$146$		−	10.8252i		−	0.895903i
$147$		0			0
$148$	11.0491			0.908229
$149$	−3.38495	+	1.95430i	−0.277306	+	0.160103i	−0.632203	−	0.774803i	$-0.717849\pi$
$149$	−3.38495	+	1.95430i	−0.277306	+	0.160103i	0.354897	+	0.934905i	$0.384516\pi$
$150$	0.302659	−	0.524221i	0.0247120	−	0.0428024i
$151$	20.9488	+	12.0948i	1.70479	+	0.984259i	0.940760	+	0.339074i	$0.110114\pi$
$151$	20.9488	+	12.0948i	1.70479	+	0.984259i	0.764027	+	0.645185i	$0.223220\pi$
$152$	0.760837	−	0.439269i	0.0617120	−	0.0356294i
$153$	−8.71792			−0.704802
$154$		0			0
$155$	−13.3022			−1.06846
$156$	−4.37263	+	2.52454i	−0.350090	+	0.202125i
$157$	17.5828	+	10.1514i	1.40326	+	0.810172i	0.994726	−	0.102571i	$-0.0327068\pi$
$157$	17.5828	+	10.1514i	1.40326	+	0.810172i	0.408534	+	0.912743i	$0.366040\pi$
$158$	−4.24264	+	7.34847i	−0.337526	+	0.584613i
$159$	0.284859	−	0.164463i	0.0225908	−	0.0130428i
$160$	−2.05161			−0.162194
$161$		0			0
$162$			4.07107i			0.319853i
$163$	6.63031	+	11.4840i	0.519326	+	0.899499i	0.999748	+	0.0224612i	$0.00715023\pi$
$163$	6.63031	+	11.4840i	0.519326	+	0.899499i	−0.480422	+	0.877038i	$0.659516\pi$
$164$	−1.18432	+	2.05130i	−0.0924798	+	0.160180i
$165$	4.93253	−	1.67099i	0.383997	−	0.130086i
$166$	10.6654	−	6.15767i	0.827795	−	0.477928i
$167$	20.4160			1.57984			0.789920	−	0.613210i	$-0.210122\pi$
$167$	20.4160			1.57984			0.789920	+	0.613210i	$0.210122\pi$
$168$		0			0
$169$	30.5196			2.34766
$170$	−3.70427	−	6.41598i	−0.284104	−	0.492083i
$171$	1.06049	−	1.83682i	0.0810977	−	0.140465i
$172$	−6.76615	−	3.90644i	−0.515914	−	0.297863i
$173$	7.78809	+	13.4894i	0.592117	+	1.02558i	0.993947	+	0.109863i	$0.0350411\pi$
$173$	7.78809	+	13.4894i	0.592117	+	1.02558i	−0.401830	+	0.915714i	$0.631626\pi$
$174$			4.73728i			0.359132i
$175$		0			0
$176$	2.49222	+	2.18834i	0.187859	+	0.164952i
$177$	1.23165	+	2.13327i	0.0925761	+	0.160347i
$178$	−3.36413	+	5.82684i	−0.252152	+	0.436740i
$179$	2.25080	−	3.89850i	0.168232	−	0.291387i	−0.769566	−	0.638567i	$-0.779527\pi$
$179$	2.25080	−	3.89850i	0.168232	−	0.291387i	0.937798	+	0.347180i	$0.112861\pi$
$180$	−4.28945	+	2.47652i	−0.319717	+	0.184589i
$181$			8.18338i			0.608266i	0.952630	+	0.304133i	$0.0983667\pi$
$181$			8.18338i			0.608266i	−0.952630	+	0.304133i	$0.901633\pi$
$182$		0			0
$183$		−	8.67483i		−	0.641262i
$184$	−5.73249	+	3.30966i	−0.422605	+	0.243991i
$185$	19.6314	+	11.3342i	1.44333	+	0.833308i
$186$	4.29762	+	2.48123i	0.315116	+	0.181933i
$187$	−2.34374	+	11.7450i	−0.171391	+	0.858882i
$188$		−	5.74713i		−	0.419153i
$189$		0			0
$190$	1.80242			0.130761
$191$	−5.18311	−	8.97741i	−0.375037	−	0.649582i	0.615296	−	0.788296i	$-0.289037\pi$
$191$	−5.18311	−	8.97741i	−0.375037	−	0.649582i	−0.990333	+	0.138714i	$0.955703\pi$
$192$	0.662827	+	0.382683i	0.0478354	+	0.0276178i
$193$	1.40584	+	0.811664i	0.101195	+	0.0584248i	0.549743	−	0.835334i	$-0.314726\pi$
$193$	1.40584	+	0.811664i	0.101195	+	0.0584248i	−0.448549	+	0.893758i	$0.648059\pi$
$194$	−4.61940	−	8.00103i	−0.331653	−	0.574441i
$195$	−10.3587			−0.741805
$196$		0			0
$197$			4.38713i			0.312570i	0.987712	+	0.156285i	$0.0499518\pi$
$197$			4.38713i			0.312570i	−0.987712	+	0.156285i	$0.950048\pi$
$198$	7.85223	+	1.56693i	0.558033	+	0.111357i
$199$	17.3760	+	10.0320i	1.23175	+	0.711151i	0.967394	−	0.253275i	$-0.0815077\pi$
$199$	17.3760	+	10.0320i	1.23175	+	0.711151i	0.264355	+	0.964426i	$0.414841\pi$
$200$	0.684927	+	0.395443i	0.0484317	+	0.0279620i
$201$	1.96360	−	1.13368i	0.138502	−	0.0799639i
$202$			1.85966i			0.130845i
$203$		0			0
$204$			2.76380i			0.193505i
$205$	−4.20847	+	2.42976i	−0.293933	+	0.169702i
$206$	−3.35505	+	5.81112i	−0.233758	+	0.404880i
$207$	−7.99022	+	13.8395i	−0.555359	+	0.961909i
$208$	−3.29847	−	5.71311i	−0.228708	−	0.396133i
$209$	−2.18952	−	1.92254i	−0.151452	−	0.132985i
$210$		0			0
$211$			8.56380i			0.589556i	0.955566	+	0.294778i	$0.0952457\pi$
$211$			8.56380i			0.589556i	−0.955566	+	0.294778i	$0.904754\pi$
$212$	0.214882	+	0.372186i	0.0147581	+	0.0255619i
$213$	1.41449	+	0.816659i	0.0969195	+	0.0559565i
$214$	7.37667	−	12.7768i	0.504259	−	0.873402i
$215$	−8.01450	−	13.8815i	−0.546584	−	0.946712i
$216$	4.14386			0.281954
$217$		0			0
$218$	−6.00000			−0.406371
$219$	−7.17526	+	4.14264i	−0.484859	+	0.279934i
$220$	2.18325	+	6.44466i	0.147195	+	0.434499i
$221$	11.9110	−	20.6305i	0.801223	−	1.38776i
$222$	−4.22830	−	7.32363i	−0.283785	−	0.491530i
$223$			8.24084i			0.551848i	0.961180	+	0.275924i	$0.0889837\pi$
$223$			8.24084i			0.551848i	−0.961180	+	0.275924i	$0.911016\pi$
$224$		0			0
$225$	1.90937			0.127291
$226$	−0.517296	+	0.298661i	−0.0344100	+	0.0198666i
$227$	−13.7397	+	23.7979i	−0.911938	+	1.57952i	−0.100614	+	0.994926i	$0.532081\pi$
$227$	−13.7397	+	23.7979i	−0.911938	+	1.57952i	−0.811324	+	0.584597i	$0.801253\pi$
$228$	−0.582319	−	0.336202i	−0.0385650	−	0.0222655i
$229$	0.0903638	−	0.0521716i	0.00597141	−	0.00344759i	−0.497011	−	0.867744i	$-0.665569\pi$
$229$	0.0903638	−	0.0521716i	0.00597141	−	0.00344759i	0.502983	+	0.864296i	$0.332236\pi$
$230$	−13.5803			−0.895456
$231$		0			0
$232$	−6.18955			−0.406364
$233$	−13.1269	+	7.57884i	−0.859974	+	0.496507i	−0.864004	−	0.503485i	$-0.832051\pi$
$233$	−13.1269	+	7.57884i	−0.859974	+	0.496507i	0.00402925	+	0.999992i	$0.498717\pi$
$234$	−13.7927	−	7.96321i	−0.901656	−	0.520571i
$235$	5.89544	−	10.2112i	0.384576	−	0.666106i
$236$	−2.78725	+	1.60922i	−0.181435	+	0.104751i
$237$	6.49435			0.421854
$238$		0			0
$239$			25.9135i			1.67620i	0.545515	+	0.838101i	$0.316334\pi$
$239$			25.9135i			1.67620i	−0.545515	+	0.838101i	$0.683666\pi$
$240$	0.785118	+	1.35986i	0.0506792	+	0.0877789i
$241$	3.65554	−	6.33158i	0.235474	−	0.407853i	−0.723936	−	0.689867i	$-0.757669\pi$
$241$	3.65554	−	6.33158i	0.235474	−	0.407853i	0.959410	+	0.282014i	$0.0910024\pi$
$242$	4.22202	−	10.1575i	0.271402	−	0.652948i
$243$	13.4645	−	7.77372i	0.863747	−	0.498684i
$244$	11.3342			0.725599
$245$		0			0
$246$	1.81288			0.115585
$247$	2.89783	+	5.01919i	0.184385	+	0.319364i
$248$	−3.24188	+	5.61510i	−0.205860	+	0.356560i
$249$	−8.16294	−	4.71287i	−0.517305	−	0.298666i
$250$	5.94033	+	10.2889i	0.375699	+	0.650730i
$251$		−	10.0161i		−	0.632208i	−0.948724	−	0.316104i	$-0.897625\pi$
$251$		−	10.0161i		−	0.632208i	0.948724	−	0.316104i	$-0.102375\pi$
$252$		0			0
$253$	16.4968	+	14.4853i	1.03715	+	0.910682i
$254$	3.66501	+	6.34799i	0.229963	+	0.398308i
$255$	−2.83512	+	4.91058i	−0.177542	+	0.307512i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.1654	+	8.75577i	−0.945994	+	0.546170i	−0.891834	−	0.452362i	$-0.850581\pi$
$257$	−15.1654	+	8.75577i	−0.945994	+	0.546170i	−0.0541598	+	0.998532i	$0.517248\pi$
$258$			5.97972i			0.372281i
$259$		0			0
$260$		−	13.5344i		−	0.839365i
$261$	−12.9409	+	7.47145i	−0.801023	+	0.462471i
$262$	7.63878	+	4.41025i	0.471925	+	0.272466i
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	0.709150	−	0.705058i	$-0.249079\pi$
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	−0.256023	+	0.966671i	$0.582412\pi$
$264$	0.496755	−	2.48935i	0.0305732	−	0.153209i
$265$			0.881709i			0.0541629i
$266$		0			0
$267$	5.14958			0.315149
$268$	1.48123	+	2.56556i	0.0904805	+	0.156717i
$269$	5.85020	+	3.37761i	0.356693	+	0.205937i	0.667629	−	0.744494i	$-0.267309\pi$
$269$	5.85020	+	3.37761i	0.356693	+	0.205937i	−0.310936	+	0.950431i	$0.600643\pi$
$270$	7.36260	+	4.25080i	0.448073	+	0.258695i
$271$	−9.77158	−	16.9249i	−0.593581	−	1.02811i	−0.993745	−	0.111669i	$-0.964380\pi$
$271$	−9.77158	−	16.9249i	−0.593581	−	1.02811i	0.400164	−	0.916443i	$-0.368953\pi$
$272$	−3.61108			−0.218954
$273$		0			0
$274$			3.23620i			0.195506i
$275$	0.513318	−	2.57235i	0.0309543	−	0.155119i
$276$	4.38746	+	2.53310i	0.264094	+	0.152475i
$277$	−23.1011	−	13.3374i	−1.38801	−	0.801368i	−0.394919	−	0.918716i	$-0.629227\pi$
$277$	−23.1011	−	13.3374i	−1.38801	−	0.801368i	−0.993091	+	0.117348i	$0.962561\pi$
$278$	−2.14014	+	1.23561i	−0.128357	+	0.0741070i
$279$			15.6532i			0.937132i
$280$		0			0
$281$		−	20.9533i		−	1.24997i	−0.780636	−	0.624986i	$-0.785105\pi$
$281$		−	20.9533i		−	1.24997i	0.780636	−	0.624986i	$-0.214895\pi$
$282$	−3.80935	+	2.19933i	−0.226844	+	0.130968i
$283$	5.03147	−	8.71476i	0.299090	−	0.518039i	−0.676838	−	0.736132i	$-0.736650\pi$
$283$	5.03147	−	8.71476i	0.299090	−	0.518039i	0.975928	+	0.218093i	$0.0699836\pi$
$284$	−1.06702	+	1.84813i	−0.0633157	+	0.109666i
$285$	−0.689757	−	1.19469i	−0.0408577	−	0.0707675i
$286$	−14.4363	+	16.4410i	−0.853637	+	0.972180i
$287$		0			0
$288$			2.41421i			0.142259i
$289$	1.98005	+	3.42955i	0.116474	+	0.201738i
$290$	−10.9973	−	6.34928i	−0.645782	−	0.372842i
$291$	−3.53553	+	6.12372i	−0.207257	+	0.358979i
$292$	−5.41262	−	9.37493i	−0.316749	−	0.548626i
$293$	29.6429			1.73176			0.865879	−	0.500253i	$-0.166760\pi$
$293$	29.6429			1.73176			0.865879	+	0.500253i	$0.166760\pi$
$294$		0			0
$295$	−6.60300			−0.384442
$296$	9.56878	−	5.52454i	0.556174	−	0.321107i
$297$	−4.40974	−	13.0170i	−0.255879	−	0.755321i
$298$	−1.95430	+	3.38495i	−0.113210	+	0.196085i
$299$	−21.8336	−	37.8169i	−1.26267	−	2.18701i
$300$		−	0.605318i		−	0.0349480i
$301$		0			0
$302$	24.1895			1.39195
$303$	1.23263	−	0.711661i	0.0708129	−	0.0408839i
$304$	0.439269	−	0.760837i	0.0251938	−	0.0436370i
$305$	20.1380	+	11.6267i	1.15310	+	0.665743i
$306$	−7.54994	+	4.35896i	−0.431601	+	0.249185i
$307$	−16.1877			−0.923883			−0.461941	−	0.886910i	$-0.652847\pi$
$307$	−16.1877			−0.923883			−0.461941	+	0.886910i	$0.652847\pi$
$308$		0			0
$309$	5.13569			0.292159
$310$	−11.5200	+	6.65109i	−0.654293	+	0.377756i
$311$	1.23529	+	0.713195i	0.0700469	+	0.0404416i	0.534614	−	0.845096i	$-0.320457\pi$
$311$	1.23529	+	0.713195i	0.0700469	+	0.0404416i	−0.464568	+	0.885538i	$0.653790\pi$
$312$	−2.52454	+	4.37263i	−0.142924	+	0.247551i
$313$	−9.99982	+	5.77340i	−0.565223	+	0.326332i	−0.755239	−	0.655449i	$-0.772479\pi$
$313$	−9.99982	+	5.77340i	−0.565223	+	0.326332i	0.190016	+	0.981781i	$0.439146\pi$
$314$	20.3029			1.14576
$315$		0			0
$316$			8.48528i			0.477334i
$317$	−15.8620	−	27.4737i	−0.890896	−	1.54308i	−0.838803	−	0.544435i	$-0.816744\pi$
$317$	−15.8620	−	27.4737i	−0.890896	−	1.54308i	−0.0520931	−	0.998642i	$-0.516589\pi$
$318$	0.164463	−	0.284859i	0.00922265	−	0.0159741i
$319$	6.58668	+	19.4430i	0.368783	+	1.08860i
$320$	−1.77675	+	1.02581i	−0.0993233	+	0.0573443i
$321$	−11.2917			−0.630242
$322$		0			0
$323$	3.17247			0.176521
$324$	2.03553	+	3.52565i	0.113085	+	0.195869i
$325$	−2.60871	+	4.51842i	−0.144705	+	0.250637i
$326$	11.4840	+	6.63031i	0.636042	+	0.367219i
$327$	2.29610	+	3.97696i	0.126975	+	0.219927i
$328$			2.36864i			0.130786i
$329$		0			0
$330$	3.43620	−	3.91338i	0.189157	−	0.215425i
$331$	−15.9620	−	27.6469i	−0.877348	−	1.51961i	−0.854240	−	0.519879i	$-0.825977\pi$
$331$	−15.9620	−	27.6469i	−0.877348	−	1.51961i	−0.0231086	−	0.999733i	$-0.507356\pi$
$332$	6.15767	−	10.6654i	0.337946	−	0.585339i
$333$	13.3374	−	23.1011i	0.730886	−	1.26593i
$334$	17.6808	−	10.2080i	0.967450	−	0.558558i
$335$			6.07782i			0.332067i
$336$		0			0
$337$			1.40854i			0.0767278i	0.999264	+	0.0383639i	$0.0122146\pi$
$337$			1.40854i			0.0767278i	−0.999264	+	0.0383639i	$0.987785\pi$
$338$	26.4307	−	15.2598i	1.43764	−	0.830023i
$339$	0.395921	+	0.228585i	0.0215035	+	0.0124150i
$340$	−6.41598	−	3.70427i	−0.347955	−	0.200892i
$341$	21.0884	+	4.20824i	1.14200	+	0.227889i
$342$		−	2.12098i		−	0.114689i
$343$		0			0
$344$	−7.81288			−0.421242
$345$	5.19694	+	9.00137i	0.279794	+	0.484617i
$346$	13.4894	+	7.78809i	0.725193	+	0.418690i
$347$	9.55973	+	5.51931i	0.513193	+	0.296292i	0.734145	−	0.678993i	$-0.237583\pi$
$347$	9.55973	+	5.51931i	0.513193	+	0.296292i	−0.220952	+	0.975285i	$0.570916\pi$
$348$	2.36864	+	4.10260i	0.126972	+	0.219923i
$349$	−15.5762			−0.833773			−0.416887	−	0.908958i	$-0.636879\pi$
$349$	−15.5762			−0.833773			−0.416887	+	0.908958i	$0.636879\pi$
$350$		0			0
$351$			27.3368i			1.45913i
$352$	3.25250	+	0.649042i	0.173359	+	0.0345941i
$353$	5.44549	+	3.14396i	0.289834	+	0.167336i	0.637867	−	0.770146i	$-0.279817\pi$
$353$	5.44549	+	3.14396i	0.289834	+	0.167336i	−0.348033	+	0.937482i	$0.613150\pi$
$354$	2.13327	+	1.23165i	0.113382	+	0.0654612i
$355$	−3.79164	+	2.18910i	−0.201239	+	0.116186i
$356$			6.72825i			0.356597i
$357$		0			0
$358$		−	4.50159i		−	0.237917i
$359$	−8.90941	+	5.14385i	−0.470221	+	0.271482i	−0.716332	−	0.697759i	$-0.754180\pi$
$359$	−8.90941	+	5.14385i	−0.470221	+	0.271482i	0.246111	+	0.969242i	$0.420847\pi$
$360$	−2.47652	+	4.28945i	−0.130524	+	0.226074i
$361$	9.11408	−	15.7861i	0.479689	−	0.830845i
$362$	4.09169	+	7.08701i	0.215054	+	0.372485i
$363$	−8.34836	+	1.08864i	−0.438175	+	0.0571385i
$364$		0			0
$365$		−	22.2092i		−	1.16248i
$366$	−4.33742	−	7.51262i	−0.226720	−	0.392691i
$367$	−3.91575	−	2.26076i	−0.204401	−	0.118011i	0.394306	−	0.918979i	$-0.370985\pi$
$367$	−3.91575	−	2.26076i	−0.204401	−	0.118011i	−0.598706	+	0.800969i	$0.704318\pi$
$368$	−3.30966	+	5.73249i	−0.172528	+	0.298827i
$369$	2.85920	+	4.95228i	0.148844	+	0.257805i
$370$	22.6684			1.17848
$371$		0			0
$372$	4.96246			0.257291
$373$	17.0814	−	9.86195i	0.884442	−	0.510633i	0.0123213	−	0.999924i	$-0.496078\pi$
$373$	17.0814	−	9.86195i	0.884442	−	0.510633i	0.872120	+	0.489291i	$0.162745\pi$
$374$	3.84277	+	11.3434i	0.198705	+	0.586551i
$375$	4.54653	−	7.87482i	0.234782	−	0.406654i
$376$	−2.87357	−	4.97716i	−0.148193	−	0.256677i
$377$		−	40.8321i		−	2.10296i
$378$		0			0
$379$	−35.6268			−1.83003			−0.915014	−	0.403423i	$-0.867820\pi$
$379$	−35.6268			−1.83003			−0.915014	+	0.403423i	$0.867820\pi$
$380$	1.56094	−	0.901211i	0.0800747	−	0.0462311i
$381$	2.80508	−	4.85854i	0.143708	−	0.248910i
$382$	−8.97741	−	5.18311i	−0.459324	−	0.265191i
$383$	18.7384	−	10.8186i	0.957488	−	0.552806i	0.0620891	−	0.998071i	$-0.480224\pi$
$383$	18.7384	−	10.8186i	0.957488	−	0.552806i	0.895399	+	0.445265i	$0.146890\pi$
$384$	0.765367			0.0390575
$385$		0			0
$386$	1.62333			0.0826252
$387$	−16.3349	+	9.43098i	−0.830351	+	0.479403i
$388$	−8.00103	−	4.61940i	−0.406191	−	0.234514i
$389$	4.32349	−	7.48851i	0.219210	−	0.379682i	−0.735357	−	0.677680i	$-0.762985\pi$
$389$	4.32349	−	7.48851i	0.219210	−	0.379682i	0.954567	+	0.297998i	$0.0963188\pi$
$390$	−8.97094	+	5.17937i	−0.454261	+	0.262268i
$391$	−23.9029			−1.20882
$392$		0			0
$393$		−	6.75092i		−	0.340539i
$394$	2.19356	+	3.79936i	0.110510	+	0.191409i
$395$	−8.70426	+	15.0762i	−0.437959	+	0.758567i
$396$	7.58369	−	2.56911i	0.381095	−	0.129103i
$397$	−31.3257	+	18.0859i	−1.57219	+	0.907705i	−0.576292	+	0.817244i	$0.695501\pi$
$397$	−31.3257	+	18.0859i	−1.57219	+	0.907705i	−0.995900	+	0.0904617i	$0.971166\pi$
$398$	20.0640			1.00572
$399$		0			0
$400$	0.790886			0.0395443
$401$	4.49678	+	7.78865i	0.224558	+	0.388947i	0.956187	−	0.292757i	$-0.0945727\pi$
$401$	4.49678	+	7.78865i	0.224558	+	0.388947i	−0.731628	+	0.681704i	$0.761239\pi$
$402$	1.13368	−	1.96360i	0.0565430	−	0.0979354i
$403$	−37.0425	−	21.3865i	−1.84522	−	1.06534i
$404$	0.929830	+	1.61051i	0.0462608	+	0.0801260i
$405$			8.35225i			0.415027i
$406$		0			0
$407$	−27.5368	−	24.1791i	−1.36495	−	1.19851i
$408$	1.38190	+	2.39352i	0.0684143	+	0.118497i
$409$	4.79140	−	8.29894i	0.236919	−	0.410356i	−0.722909	−	0.690943i	$-0.757196\pi$
$409$	4.79140	−	8.29894i	0.236919	−	0.410356i	0.959829	+	0.280587i	$0.0905290\pi$
$410$	−2.42976	+	4.20847i	−0.119997	+	0.207842i
$411$	2.14504	−	1.23844i	0.105807	−	0.0610877i
$412$			6.71011i			0.330583i
$413$		0			0
$414$			15.9804i			0.785396i
$415$	21.8813	−	12.6331i	1.07411	−	0.620137i
$416$	−5.71311	−	3.29847i	−0.280108	−	0.161721i
$417$	1.63799	+	0.945695i	0.0802128	+	0.0463109i
$418$	−2.85745	−	0.570209i	−0.139762	−	0.0278898i
$419$		−	37.9064i		−	1.85185i	−0.377709	−	0.925924i	$-0.623288\pi$
$419$		−	37.9064i		−	1.85185i	0.377709	−	0.925924i	$-0.376712\pi$
$420$		0			0
$421$	2.88394			0.140555			0.0702774	−	0.997527i	$-0.477612\pi$
$421$	2.88394			0.140555			0.0702774	+	0.997527i	$0.477612\pi$
$422$	4.28190	+	7.41646i	0.208440	+	0.361028i
$423$	−12.0159	−	6.93740i	−0.584235	−	0.337308i
$424$	0.372186	+	0.214882i	0.0180750	+	0.0104356i
$425$	1.42798	+	2.47333i	0.0692670	+	0.119974i
$426$	1.63332			0.0791345
$427$		0			0
$428$		−	14.7533i		−	0.713130i
$429$	16.4221	+	3.27706i	0.792867	+	0.158218i
$430$	−13.8815	−	8.01450i	−0.669426	−	0.386493i
$431$	−28.0651	−	16.2034i	−1.35185	−	0.780490i	−0.363339	−	0.931657i	$-0.618363\pi$
$431$	−28.0651	−	16.2034i	−1.35185	−	0.780490i	−0.988508	+	0.151167i	$0.951697\pi$
$432$	3.58869	−	2.07193i	0.172661	−	0.0996858i
$433$		−	10.2319i		−	0.491714i	−0.969306	−	0.245857i	$-0.920931\pi$
$433$		−	10.2319i		−	0.491714i	0.969306	−	0.245857i	$-0.0790694\pi$
$434$		0			0
$435$			9.71905i			0.465993i
$436$	−5.19615	+	3.00000i	−0.248851	+	0.143674i
$437$	2.90766	−	5.03622i	0.139092	−	0.240915i
$438$	−4.14264	+	7.17526i	−0.197943	+	0.342847i
$439$	14.4363	+	25.0044i	0.689008	+	1.19340i	0.972159	+	0.234321i	$0.0752867\pi$
$439$	14.4363	+	25.0044i	0.689008	+	1.19340i	−0.283152	+	0.959075i	$0.591380\pi$
$440$	5.11308	+	4.48962i	0.243757	+	0.214034i
$441$		0			0
$442$		−	23.8221i		−	1.13310i
$443$	4.28018	+	7.41349i	0.203358	+	0.352226i	0.949608	−	0.313439i	$-0.101481\pi$
$443$	4.28018	+	7.41349i	0.203358	+	0.352226i	−0.746251	+	0.665665i	$0.768148\pi$
$444$	−7.32363	−	4.22830i	−0.347564	−	0.200666i
$445$	−6.90188	+	11.9544i	−0.327181	+	0.566694i
$446$	4.12042	+	7.13678i	0.195108	+	0.337936i
$447$	2.99152			0.141494
$448$		0			0
$449$	−10.8089			−0.510102			−0.255051	−	0.966928i	$-0.582092\pi$
$449$	−10.8089			−0.510102			−0.255051	+	0.966928i	$0.582092\pi$
$450$	1.65356	−	0.954684i	0.0779496	−	0.0450042i
$451$	7.44052	−	2.52061i	0.350361	−	0.118691i
$452$	−0.298661	+	0.517296i	−0.0140478	+	0.0243315i
$453$	−9.25694	−	16.0335i	−0.434929	−	0.753319i
$454$			27.4795i			1.28967i
$455$		0			0
$456$	−0.672404			−0.0314882
$457$	−21.1220	+	12.1948i	−0.988044	+	0.570448i	−0.904689	−	0.426072i	$-0.859897\pi$
$457$	−21.1220	+	12.1948i	−0.988044	+	0.570448i	−0.0833551	+	0.996520i	$0.526564\pi$
$458$	0.0521716	−	0.0903638i	0.00243782	−	0.00422242i
$459$	12.9590	+	7.48190i	0.604876	+	0.349225i
$460$	−11.7609	+	6.79013i	−0.548353	+	0.316592i
$461$	−1.13186			−0.0527158			−0.0263579	−	0.999653i	$-0.508391\pi$
$461$	−1.13186			−0.0527158			−0.0263579	+	0.999653i	$0.508391\pi$
$462$		0			0
$463$	6.38388			0.296684			0.148342	−	0.988936i	$-0.452606\pi$
$463$	6.38388			0.296684			0.148342	+	0.988936i	$0.452606\pi$
$464$	−5.36031	+	3.09477i	−0.248846	+	0.143671i
$465$	8.81704	+	5.09052i	0.408881	+	0.236067i
$466$	−7.57884	+	13.1269i	−0.351083	+	0.608094i
$467$	30.9033	−	17.8420i	1.43003	−	0.825629i	0.432910	−	0.901437i	$-0.357487\pi$
$467$	30.9033	−	17.8420i	1.43003	−	0.825629i	0.997122	+	0.0758078i	$0.0241536\pi$
$468$	−15.9264			−0.736199
$469$		0			0
$470$		−	11.7909i		−	0.543873i
$471$	−7.76957	−	13.4573i	−0.358003	−	0.620079i
$472$	−1.60922	+	2.78725i	−0.0740704	+	0.128294i
$473$	8.31417	+	24.5423i	0.382286	+	1.12846i
$474$	5.62427	−	3.24718i	0.258331	−	0.149148i
$475$	−0.694824			−0.0318807
$476$		0			0
$477$	1.03754			0.0475058
$478$	12.9567	+	22.4417i	0.592627	+	1.02646i
$479$	5.79094	−	10.0302i	0.264595	−	0.458291i	−0.702863	−	0.711325i	$-0.748095\pi$
$479$	5.79094	−	10.0302i	0.264595	−	0.458291i	0.967457	+	0.253034i	$0.0814285\pi$
$480$	1.35986	+	0.785118i	0.0620690	+	0.0358356i
$481$	36.4450	+	63.1246i	1.66175	+	2.87824i
$482$		−	7.31108i		−	0.333011i
$483$		0			0
$484$	−1.42237	−	10.9077i	−0.0646532	−	0.495802i
$485$	−9.47721	−	16.4150i	−0.430338	−	0.745368i
$486$	7.77372	−	13.4645i	0.352623	−	0.610761i
$487$	−20.0319	+	34.6963i	−0.907732	+	1.57224i	−0.0905248	+	0.995894i	$0.528854\pi$
$487$	−20.0319	+	34.6963i	−0.907732	+	1.57224i	−0.817207	+	0.576344i	$0.804479\pi$
$488$	9.81572	−	5.66711i	0.444337	−	0.256538i
$489$		−	10.1492i		−	0.458964i
$490$		0			0
$491$			19.7876i			0.893003i	0.894783	+	0.446502i	$0.147330\pi$
$491$			19.7876i			0.893003i	−0.894783	+	0.446502i	$0.852670\pi$
$492$	1.57000	−	0.906438i	0.0707810	−	0.0408654i
$493$	−19.3565	−	11.1755i	−0.871773	−	0.503318i
$494$	5.01919	+	2.89783i	0.225824	+	0.130380i
$495$	16.1097	+	3.21473i	0.724078	+	0.144491i
$496$			6.48376i			0.291130i
$497$		0			0
$498$	−9.42575			−0.422378
$499$	13.3276	+	23.0841i	0.596627	+	1.03339i	0.993315	+	0.115435i	$0.0368260\pi$
$499$	13.3276	+	23.0841i	0.596627	+	1.03339i	−0.396688	+	0.917953i	$0.629841\pi$
$500$	10.2889	+	5.94033i	0.460136	+	0.265660i
$501$	−13.5323	−	7.81288i	−0.604579	−	0.349054i
$502$	−5.00803	−	8.67417i	−0.223519	−	0.387147i
$503$	10.9142			0.486638			0.243319	−	0.969946i	$-0.421764\pi$
$503$	10.9142			0.486638			0.243319	+	0.969946i	$0.421764\pi$
$504$		0			0
$505$			3.81530i			0.169779i
$506$	21.5293	+	4.29621i	0.957094	+	0.190990i
$507$	−20.2292	−	11.6793i	−0.898410	−	0.518697i
$508$	6.34799	+	3.66501i	0.281646	+	0.162609i
$509$	−19.4284	+	11.2170i	−0.861149	+	0.497184i	−0.864397	−	0.502810i	$-0.832299\pi$
$509$	−19.4284	+	11.2170i	−0.861149	+	0.497184i	0.00324816	+	0.999995i	$0.498966\pi$
$510$			5.67025i			0.251083i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−3.15280	+	1.82027i	−0.139200	+	0.0803669i
$514$	−8.75577	+	15.1654i	−0.386200	+	0.668919i
$515$	−6.88327	+	11.9222i	−0.303313	+	0.525354i
$516$	2.98986	+	5.17859i	0.131621	+	0.227975i
$517$	−12.5767	+	14.3231i	−0.553121	+	0.629931i
$518$		0			0
$519$		−	11.9215i		−	0.523295i
$520$	−6.76718	−	11.7211i	−0.296760	−	0.514004i
$521$	33.9574	+	19.6053i	1.48770	+	0.858925i	0.999902	−	0.0140307i	$-0.00446624\pi$
$521$	33.9574	+	19.6053i	1.48770	+	0.858925i	0.487800	+	0.872955i	$0.337800\pi$
$522$	−7.47145	+	12.9409i	−0.327016	+	0.566409i
$523$	−9.04494	−	15.6663i	−0.395508	−	0.685039i	0.597658	−	0.801751i	$-0.296098\pi$
$523$	−9.04494	−	15.6663i	−0.395508	−	0.685039i	−0.993166	+	0.116712i	$0.962765\pi$
$524$	8.82050			0.385325
$525$		0			0
$526$	8.48528			0.369976
$527$	−20.2766	+	11.7067i	−0.883262	+	0.509952i
$528$	−0.814474	−	2.40422i	−0.0354454	−	0.104630i
$529$	−10.4077	+	18.0266i	−0.452507	+	0.783764i
$530$	0.440854	+	0.763582i	0.0191495	+	0.0331679i
$531$			7.77001i			0.337190i
$532$		0			0
$533$	−15.6258			−0.676827
$534$	4.45967	−	2.57479i	0.192989	−	0.111422i
$535$	15.1341	−	26.2130i	0.654303	−	1.13329i
$536$	2.56556	+	1.48123i	0.110816	+	0.0639794i
$537$	−2.98378	+	1.72269i	−0.128760	+	0.0743394i
$538$	6.75523			0.291238
$539$		0			0
$540$	8.50159			0.365850
$541$	−8.33615	+	4.81288i	−0.358399	+	0.206922i	−0.668378	−	0.743822i	$-0.733011\pi$
$541$	−8.33615	+	4.81288i	−0.358399	+	0.206922i	0.309979	+	0.950743i	$0.399678\pi$
$542$	−16.9249	−	9.77158i	−0.726985	−	0.419725i
$543$	3.13164	−	5.42416i	0.134392	−	0.232773i
$544$	−3.12729	+	1.80554i	−0.134081	+	0.0774119i
$545$	−12.3097			−0.527289
$546$		0			0
$547$			10.2834i			0.439685i	0.975535	+	0.219843i	$0.0705544\pi$
$547$			10.2834i			0.439685i	−0.975535	+	0.219843i	$0.929446\pi$
$548$	1.61810	+	2.80263i	0.0691218	+	0.119722i
$549$	13.6816	−	23.6972i	0.583917	−	1.01137i
$550$	−0.841631	−	2.48438i	−0.0358873	−	0.105934i
$551$	4.70924	−	2.71888i	0.200620	−	0.115828i
$552$	5.06620			0.215632
$553$		0			0
$554$	−26.6748			−1.13330
$555$	−8.67483	−	15.0252i	−0.368226	−	0.637786i
$556$	−1.23561	+	2.14014i	−0.0524016	+	0.0907622i
$557$	−32.2426	−	18.6153i	−1.36616	−	0.788755i	−0.375729	−	0.926730i	$-0.622608\pi$
$557$	−32.2426	−	18.6153i	−1.36616	−	0.788755i	−0.990436	+	0.137974i	$0.955941\pi$
$558$	7.82660	+	13.5561i	0.331326	+	0.573874i
$559$		−	51.5411i		−	2.17995i
$560$		0			0
$561$	6.04812	−	6.88801i	0.255352	−	0.290812i
$562$	−10.4767	−	18.1461i	−0.441932	−	0.765448i
$563$	8.09387	−	14.0190i	0.341116	−	0.590830i	−0.643524	−	0.765426i	$-0.722529\pi$
$563$	8.09387	−	14.0190i	0.341116	−	0.590830i	0.984640	+	0.174596i	$0.0558618\pi$
$564$	−2.19933	+	3.80935i	−0.0926086	+	0.160403i
$565$	−1.06129	+	0.612736i	−0.0446488	+	0.0257780i
$566$		−	10.0629i		−	0.422977i
$567$		0			0
$568$			2.13403i			0.0895420i
$569$	26.4052	−	15.2451i	1.10696	−	0.639106i	0.168923	−	0.985629i	$-0.445971\pi$
$569$	26.4052	−	15.2451i	1.10696	−	0.639106i	0.938042	+	0.346523i	$0.112638\pi$
$570$	−1.19469	−	0.689757i	−0.0500402	−	0.0288907i
$571$	35.0634	+	20.2439i	1.46736	+	0.847179i	0.999332	−	0.0365365i	$-0.0116325\pi$
$571$	35.0634	+	20.2439i	1.46736	+	0.847179i	0.468025	+	0.883715i	$0.344966\pi$
$572$	−4.28169	+	21.4565i	−0.179026	+	0.897142i
$573$			7.93396i			0.331446i
$574$		0			0
$575$	5.23512			0.218320
$576$	1.20711	+	2.09077i	0.0502961	+	0.0871154i
$577$	−22.1360	−	12.7802i	−0.921533	−	0.532047i	−0.0374092	−	0.999300i	$-0.511910\pi$
$577$	−22.1360	−	12.7802i	−0.921533	−	0.532047i	−0.884124	+	0.467253i	$0.845244\pi$
$578$	3.42955	+	1.98005i	0.142651	+	0.0823594i
$579$	−0.621221	−	1.07599i	−0.0258170	−	0.0447164i
$580$	−12.6986			−0.527279
$581$		0			0
$582$			7.07107i			0.293105i
$583$	0.278935	−	1.39781i	0.0115523	−	0.0578912i
$584$	−9.37493	−	5.41262i	−0.387937	−	0.223976i
$585$	−28.2972	−	16.3374i	−1.16995	−	0.675469i
$586$	25.6715	−	14.8215i	1.06048	−	0.612269i
$587$			7.18094i			0.296389i	0.988958	+	0.148195i	$0.0473462\pi$
$587$			7.18094i			0.296389i	−0.988958	+	0.148195i	$0.952654\pi$
$588$		0			0
$589$		−	5.69624i		−	0.234709i
$590$	−5.71837	+	3.30150i	−0.235421	+	0.135921i
$591$	1.67888	−	2.90791i	0.0690599	−	0.119615i
$592$	5.52454	−	9.56878i	0.227057	−	0.393274i
$593$	9.88857	+	17.1275i	0.406075	+	0.703343i	0.994446	−	0.105249i	$-0.0335638\pi$
$593$	9.88857	+	17.1275i	0.406075	+	0.703343i	−0.588371	+	0.808591i	$0.700230\pi$
$594$	−10.3274	−	9.06816i	−0.423740	−	0.372071i
$595$		0			0
$596$			3.90860i			0.160103i
$597$	−7.67817	−	13.2990i	−0.314247	−	0.544291i
$598$	−37.8169	−	21.8336i	−1.54645	−	0.892842i
$599$	6.87989	−	11.9163i	0.281105	−	0.486888i	−0.690552	−	0.723282i	$-0.742632\pi$
$599$	6.87989	−	11.9163i	0.281105	−	0.486888i	0.971657	+	0.236395i	$0.0759658\pi$
$600$	−0.302659	−	0.524221i	−0.0123560	−	0.0214012i
$601$	−11.0384			−0.450266			−0.225133	−	0.974328i	$-0.572282\pi$
$601$	−11.0384			−0.450266			−0.225133	+	0.974328i	$0.572282\pi$
$602$		0			0
$603$	7.15201			0.291252
$604$	20.9488	−	12.0948i	0.852393	−	0.492129i
$605$	8.66194	−	20.8392i	0.352158	−	0.847235i
$606$	0.711661	−	1.23263i	0.0289093	−	0.0500723i
$607$	−5.90718	−	10.2315i	−0.239765	−	0.415285i	0.720882	−	0.693058i	$-0.243737\pi$
$607$	−5.90718	−	10.2315i	−0.239765	−	0.415285i	−0.960647	+	0.277773i	$0.910404\pi$
$608$		−	0.878539i		−	0.0356294i
$609$		0			0
$610$	23.2534			0.941503
$611$	32.8340	−	18.9567i	1.32832	−	0.766907i
$612$	−4.35896	+	7.54994i	−0.176200	+	0.305188i
$613$	−18.3140	−	10.5736i	−0.739697	−	0.427064i	0.0822621	−	0.996611i	$-0.473786\pi$
$613$	−18.3140	−	10.5736i	−0.739697	−	0.427064i	−0.821959	+	0.569546i	$0.807119\pi$
$614$	−14.0190	+	8.09387i	−0.565760	+	0.326642i
$615$	3.71932			0.149978
$616$		0			0
$617$	−43.8743			−1.76631			−0.883157	−	0.469078i	$-0.844586\pi$
$617$	−43.8743			−1.76631			−0.883157	+	0.469078i	$0.844586\pi$
$618$	4.44764	−	2.56785i	0.178910	−	0.103294i
$619$	4.12964	+	2.38425i	0.165984	+	0.0958310i	0.580691	−	0.814124i	$-0.302782\pi$
$619$	4.12964	+	2.38425i	0.165984	+	0.0958310i	−0.414707	+	0.909955i	$0.636116\pi$
$620$	−6.65109	+	11.5200i	−0.267114	+	0.462655i
$621$	23.7546	−	13.7148i	0.953241	−	0.550354i
$622$	1.42639			0.0571931
$623$		0			0
$624$			5.04908i			0.202125i
$625$	10.2100	+	17.6843i	0.408401	+	0.707372i
$626$	−5.77340	+	9.99982i	−0.230751	+	0.399673i
$627$	0.715547	+	2.11220i	0.0285762	+	0.0843532i
$628$	17.5828	−	10.1514i	0.701630	−	0.405086i
$629$	39.8991			1.59088
$630$		0			0
$631$	−6.66195			−0.265208			−0.132604	−	0.991169i	$-0.542334\pi$
$631$	−6.66195			−0.265208			−0.132604	+	0.991169i	$0.542334\pi$
$632$	4.24264	+	7.34847i	0.168763	+	0.292306i
$633$	3.27722	−	5.67632i	0.130258	−	0.225613i
$634$	−27.4737	−	15.8620i	−1.09112	−	0.629959i
$635$	7.51918	+	13.0236i	0.298390	+	0.516826i
$636$		−	0.328927i		−	0.0130428i
$637$		0			0
$638$	15.4257	+	13.5448i	0.610711	+	0.536244i
$639$	2.57600	+	4.46177i	0.101905	+	0.176505i
$640$	−1.02581	+	1.77675i	−0.0405486	+	0.0702322i
$641$	5.76074	−	9.97789i	0.227535	−	0.394103i	−0.729542	−	0.683936i	$-0.760267\pi$
$641$	5.76074	−	9.97789i	0.227535	−	0.394103i	0.957077	+	0.289833i	$0.0935999\pi$
$642$	−9.77892	+	5.64586i	−0.385943	+	0.222824i
$643$			21.7793i			0.858892i	0.903093	+	0.429446i	$0.141291\pi$
$643$			21.7793i			0.858892i	−0.903093	+	0.429446i	$0.858709\pi$
$644$		0			0
$645$			12.2681i			0.483055i
$646$	2.74744	−	1.58624i	0.108097	−	0.0624096i
$647$	−15.2087	−	8.78075i	−0.597916	−	0.345207i	0.170306	−	0.985391i	$-0.445525\pi$
$647$	−15.2087	−	8.78075i	−0.597916	−	0.345207i	−0.768221	+	0.640185i	$0.778858\pi$
$648$	3.52565	+	2.03553i	0.138501	+	0.0799633i
$649$	10.4680	+	2.08891i	0.410904	+	0.0819967i
$650$			5.21742i			0.204644i
$651$		0			0
$652$	13.2606			0.519326
$653$	−13.2213	−	22.9000i	−0.517390	−	0.896146i	−0.999796	−	0.0201984i	$-0.993570\pi$
$653$	−13.2213	−	22.9000i	−0.517390	−	0.896146i	0.482406	−	0.875948i	$-0.339763\pi$
$654$	3.97696	+	2.29610i	0.155512	+	0.0897846i
$655$	15.6718	+	9.04812i	0.612348	+	0.353539i
$656$	1.18432	+	2.05130i	0.0462399	+	0.0800898i
$657$	−26.1344			−1.01960
$658$		0			0
$659$		−	38.9324i		−	1.51659i	−0.651910	−	0.758296i	$-0.726032\pi$
$659$		−	38.9324i		−	1.51659i	0.651910	−	0.758296i	$-0.273968\pi$
$660$	1.01915	−	5.10719i	0.0396703	−	0.198797i
$661$	10.2982	+	5.94569i	0.400555	+	0.231261i	0.686723	−	0.726919i	$-0.259048\pi$
$661$	10.2982	+	5.94569i	0.400555	+	0.231261i	−0.286168	+	0.958179i	$0.592382\pi$
$662$	−27.6469	−	15.9620i	−1.07453	−	0.620379i
$663$	−15.7899	+	9.11631i	−0.613229	+	0.354048i
$664$		−	12.3153i		−	0.477928i
$665$		0			0
$666$		−	26.6748i		−	1.03363i
$667$	−35.4815	+	20.4853i	−1.37385	+	0.793193i
$668$	10.2080	−	17.6808i	0.394960	−	0.684091i
$669$	3.15363	−	5.46225i	0.121927	−	0.211183i
$670$	3.03891	+	5.26354i	0.117403	+	0.203348i
$671$	−28.2474	−	24.8031i	−1.09048	−	0.957512i
$672$		0			0
$673$		−	17.4386i		−	0.672210i	−0.941825	−	0.336105i	$-0.890890\pi$
$673$		−	17.4386i		−	0.672210i	0.941825	−	0.336105i	$-0.109110\pi$
$674$	0.704268	+	1.21983i	0.0271274	+	0.0469860i
$675$	−2.83824	−	1.63866i	−0.109244	−	0.0630720i
$676$	15.2598	−	26.4307i	0.586915	−	1.01657i
$677$	−20.7150	−	35.8794i	−0.796141	−	1.37896i	−0.922112	−	0.386923i	$-0.873538\pi$
$677$	−20.7150	−	35.8794i	−0.796141	−	1.37896i	0.125970	−	0.992034i	$-0.459796\pi$
$678$	0.457170			0.0175575
$679$		0			0
$680$	−7.40854			−0.284104
$681$	18.2141	−	10.5159i	0.697967	−	0.402971i
$682$	20.3672	−	6.89978i	0.779902	−	0.264206i
$683$	−10.7076	+	18.5462i	−0.409717	+	0.709650i	−0.994858	−	0.101281i	$-0.967706\pi$
$683$	−10.7076	+	18.5462i	−0.409717	+	0.709650i	0.585141	+	0.810931i	$0.301039\pi$
$684$	−1.06049	−	1.83682i	−0.0405488	−	0.0702327i
$685$			6.63943i			0.253679i
$686$		0			0
$687$	−0.0798608			−0.00304688
$688$	−6.76615	+	3.90644i	−0.257957	+	0.148932i
$689$	−1.41756	+	2.45529i	−0.0540048	+	0.0935391i
$690$	9.00137	+	5.19694i	0.342676	+	0.197844i
$691$	11.6732	−	6.73955i	0.444071	−	0.256384i	−0.261252	−	0.965271i	$-0.584135\pi$
$691$	11.6732	−	6.73955i	0.444071	−	0.256384i	0.705323	+	0.708886i	$0.250802\pi$
$692$	15.5762			0.592117
$693$		0			0
$694$	11.0386			0.419020
$695$	−4.39074	+	2.53499i	−0.166550	+	0.0961578i
$696$	4.10260	+	2.36864i	0.155509	+	0.0897830i
$697$	−4.27667	+	7.40741i	−0.161990	+	0.280576i
$698$	−13.4894	+	7.78809i	−0.510580	+	0.294783i
$699$	11.6012			0.438797
$700$		0			0
$701$			26.4644i			0.999545i	0.866157	+	0.499773i	$0.166583\pi$
$701$			26.4644i			0.999545i	−0.866157	+	0.499773i	$0.833417\pi$
$702$	13.6684	+	23.6743i	0.515880	+	0.893531i
$703$	−4.85352	+	8.40654i	−0.183054	+	0.317059i
$704$	3.14127	−	1.06416i	0.118391	−	0.0401071i
$705$	−7.81532	+	4.51218i	−0.294342	+	0.169938i
$706$	6.28791			0.236649
$707$		0			0
$708$	2.46329			0.0925761
$709$	−9.38888	−	16.2620i	−0.352607	−	0.610733i	0.634099	−	0.773252i	$-0.281371\pi$
$709$	−9.38888	−	16.2620i	−0.352607	−	0.610733i	−0.986705	+	0.162519i	$0.948038\pi$
$710$	−2.18910	+	3.79164i	−0.0821556	+	0.142298i
$711$	17.7408	+	10.2426i	0.665331	+	0.384129i
$712$	3.36413	+	5.82684i	0.126076	+	0.218370i
$713$			42.9181i			1.60729i
$714$		0			0
$715$	−29.6177	+	33.7307i	−1.10764	+	1.26146i
$716$	−2.25080	−	3.89850i	−0.0841162	−	0.145694i
$717$	9.91665	−	17.1761i	0.370344	−	0.641455i
$718$	−5.14385	+	8.90941i	−0.191967	+	0.332496i
$719$	−3.00287	+	1.73371i	−0.111988	+	0.0646564i	−0.554948	−	0.831885i	$-0.687262\pi$
$719$	−3.00287	+	1.73371i	−0.111988	+	0.0646564i	0.442960	+	0.896542i	$0.353928\pi$
$720$			4.95303i			0.184589i
$721$		0			0
$722$		−	18.2282i		−	0.678382i
$723$	−4.84598	+	2.79783i	−0.180224	+	0.104052i
$724$	7.08701	+	4.09169i	0.263387	+	0.152066i
$725$	4.23939	+	2.44761i	0.157447	+	0.0909021i
$726$	−6.68557	+	5.11696i	−0.248125	+	0.189908i
$727$			21.6647i			0.803500i	0.915749	+	0.401750i	$0.131598\pi$
$727$			21.6647i			0.803500i	−0.915749	+	0.401750i	$0.868402\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$	−11.1046	−	19.2337i	−0.410999	−	0.711872i
$731$	−24.4331	−	14.1065i	−0.903691	−	0.521746i
$732$	−7.51262	−	4.33742i	−0.277675	−	0.160315i
$733$	−7.45423	−	12.9111i	−0.275328	−	0.476883i	0.694890	−	0.719116i	$-0.255453\pi$
$733$	−7.45423	−	12.9111i	−0.275328	−	0.476883i	−0.970218	+	0.242234i	$0.922120\pi$
$734$	−4.52152			−0.166892
$735$		0			0
$736$			6.61931i			0.243991i
$737$	1.92276	−	9.63539i	0.0708258	−	0.354924i
$738$	4.95228	+	2.85920i	0.182296	+	0.105249i
$739$	4.11862	+	2.37789i	0.151506	+	0.0874719i	0.573836	−	0.818970i	$-0.305455\pi$
$739$	4.11862	+	2.37789i	0.151506	+	0.0874719i	−0.422331	+	0.906442i	$0.638788\pi$
$740$	19.6314	−	11.3342i	0.721666	−	0.416654i
$741$		−	4.43581i		−	0.162954i
$742$		0			0
$743$		−	14.8792i		−	0.545864i	−0.962033	−	0.272932i	$-0.912007\pi$
$743$		−	14.8792i		−	0.545864i	0.962033	−	0.272932i	$-0.0879934\pi$
$744$	4.29762	−	2.48123i	0.157558	−	0.0909663i
$745$	−4.00947	+	6.94461i	−0.146896	+	0.254431i
$746$	9.86195	−	17.0814i	0.361072	−	0.625395i
$747$	−14.8659	−	25.7485i	−0.543916	−	0.942090i
$748$	8.99962	+	7.90226i	0.329059	+	0.288935i
$749$		0			0
$750$		−	9.09306i		−	0.332032i
$751$	−8.24101	−	14.2739i	−0.300719	−	0.520860i	0.675580	−	0.737287i	$-0.263893\pi$
$751$	−8.24101	−	14.2739i	−0.300719	−	0.520860i	−0.976299	+	0.216426i	$0.930560\pi$
$752$	−4.97716	−	2.87357i	−0.181498	−	0.104788i
$753$	−3.83298	+	6.63892i	−0.139682	+	0.241936i
$754$	−20.4160	−	35.3616i	−0.743508	−	1.28779i
$755$	49.6276			1.80613
$756$		0			0
$757$	−3.82008			−0.138843			−0.0694216	−	0.997587i	$-0.522115\pi$
$757$	−3.82008			−0.138843			−0.0694216	+	0.997587i	$0.522115\pi$
$758$	−30.8537	+	17.8134i	−1.12066	+	0.647012i
$759$	−5.39126	−	15.9143i	−0.195690	−	0.577652i
$760$	0.901211	−	1.56094i	0.0326903	−	0.0566213i
$761$	0.927001	+	1.60561i	0.0336038	+	0.0582034i	0.882338	−	0.470616i	$-0.155968\pi$
$761$	0.927001	+	1.60561i	0.0336038	+	0.0582034i	−0.848734	+	0.528819i	$0.822635\pi$
$762$		−	5.61016i		−	0.203235i
$763$		0			0
$764$	−10.3662			−0.375037
$765$	−15.4895	+	8.94289i	−0.560026	+	0.323331i
$766$	10.8186	−	18.7384i	0.390893	−	0.677046i
$767$	−18.3873	−	10.6159i	−0.663928	−	0.383319i
$768$	0.662827	−	0.382683i	0.0239177	−	0.0138089i
$769$	8.92308			0.321775			0.160887	−	0.986973i	$-0.448564\pi$
$769$	8.92308			0.321775			0.160887	+	0.986973i	$0.448564\pi$
$770$		0			0
$771$	13.4028			0.482688
$772$	1.40584	−	0.811664i	0.0505974	−	0.0292124i
$773$	17.6034	+	10.1633i	0.633151	+	0.365550i	0.781971	−	0.623315i	$-0.214214\pi$
$773$	17.6034	+	10.1633i	0.633151	+	0.365550i	−0.148821	+	0.988864i	$0.547548\pi$
$774$	−9.43098	+	16.3349i	−0.338989	+	0.587147i
$775$	4.44091	−	2.56396i	0.159522	−	0.0921001i
$776$	−9.23880			−0.331653
$777$		0			0
$778$		−	8.64698i		−	0.310009i
$779$	−1.04047	−	1.80215i	−0.0372787	−	0.0645686i
$780$	−5.17937	+	8.97094i	−0.185451	+	0.321211i
$781$	6.70356	−	2.27096i	0.239872	−	0.0812612i
$782$	−20.7005	+	11.9514i	−0.740248	+	0.427382i
$783$	25.6486			0.916607
$784$		0			0
$785$	41.6536			1.48668
$786$	−3.37546	−	5.84647i	−0.120399	−	0.208537i
$787$	−19.2008	+	33.2568i	−0.684435	+	1.18548i	0.289179	+	0.957275i	$0.406618\pi$
$787$	−19.2008	+	33.2568i	−0.684435	+	1.18548i	−0.973614	+	0.228201i	$0.926716\pi$
$788$	3.79936	+	2.19356i	0.135347	+	0.0781425i
$789$	−3.24718	−	5.62427i	−0.115603	−	0.200229i
$790$			17.4085i			0.619367i
$791$		0			0
$792$	5.28311	−	6.01676i	0.187727	−	0.213796i
$793$	37.3855	+	64.7537i	1.32760	+	2.29947i
$794$	−18.0859	+	31.3257i	−0.641845	+	1.11171i
$795$	0.337415	−	0.584420i	0.0119669	−	0.0207273i
$796$	17.3760	−	10.0320i	0.615875	−	0.355575i
$797$		−	42.5849i		−	1.50843i	−0.656625	−	0.754217i	$-0.728017\pi$
$797$		−	42.5849i		−	1.50843i	0.656625	−	0.754217i	$-0.271983\pi$
$798$		0			0
$799$		−	20.7533i		−	0.734201i
$800$	0.684927	−	0.395443i	0.0242158	−	0.0139810i
$801$	14.0672	+	8.12172i	0.497041	+	0.286967i
$802$	7.78865	+	4.49678i	0.275027	+	0.158787i
$803$	−7.02603	+	35.2091i	−0.247943	+	1.24250i
$804$		−	2.26737i		−	0.0799639i
$805$		0			0
$806$	−42.7730			−1.50661
$807$	−2.58511	−	4.47755i	−0.0910003	−	0.157617i
$808$	1.61051	+	0.929830i	0.0566577	+	0.0327113i
$809$	−6.42504	−	3.70950i	−0.225892	−	0.130419i	0.382783	−	0.923838i	$-0.374966\pi$
$809$	−6.42504	−	3.70950i	−0.225892	−	0.130419i	−0.608676	+	0.793419i	$0.708299\pi$
$810$	4.17613	+	7.23326i	0.146734	+	0.254151i
$811$	−43.2953			−1.52030			−0.760151	−	0.649746i	$-0.774875\pi$
$811$	−43.2953			−1.52030			−0.760151	+	0.649746i	$0.774875\pi$
$812$		0			0
$813$			14.9577i			0.524589i
$814$	−35.9371	−	7.17132i	−1.25959	−	0.251355i
$815$	23.5608	+	13.6028i	0.825298	+	0.476486i
$816$	2.39352	+	1.38190i	0.0837900	+	0.0483762i
$817$	5.94432	−	3.43196i	0.207966	−	0.120069i
$818$		−	9.58279i		−	0.335055i
$819$		0			0
$820$			4.85953i			0.169702i
$821$	−20.8680	+	12.0481i	−0.728297	+	0.420482i	−0.817799	−	0.575504i	$-0.804806\pi$
$821$	−20.8680	+	12.0481i	−0.728297	+	0.420482i	0.0895019	+	0.995987i	$0.471472\pi$
$822$	1.23844	−	2.14504i	0.0431956	−	0.0748169i
$823$	−1.25003	+	2.16512i	−0.0435735	+	0.0754714i	−0.886990	−	0.461789i	$-0.847208\pi$
$823$	−1.25003	+	2.16512i	−0.0435735	+	0.0754714i	0.843416	+	0.537261i	$0.180541\pi$
$824$	3.35505	+	5.81112i	0.116879	+	0.202440i
$825$	−1.32464	+	1.50859i	−0.0461180	+	0.0525223i
$826$		0			0
$827$		−	32.9902i		−	1.14718i	−0.819142	−	0.573591i	$-0.805550\pi$
$827$		−	32.9902i		−	1.14718i	0.819142	−	0.573591i	$-0.194450\pi$
$828$	7.99022	+	13.8395i	0.277679	+	0.480955i
$829$	24.6422	+	14.2272i	0.855858	+	0.494130i	0.862623	−	0.505847i	$-0.168820\pi$
$829$	24.6422	+	14.2272i	0.855858	+	0.494130i	−0.00676498	+	0.999977i	$0.502153\pi$
$830$	12.6331	−	21.8813i	0.438503	−	0.759509i
$831$	10.2080	+	17.6808i	0.354112	+	0.613340i
$832$	−6.59694			−0.228708
$833$		0			0
$834$	1.89139			0.0654935
$835$	36.2742	−	20.9429i	1.25532	−	0.724759i
$836$	−2.75972	+	0.934908i	−0.0954471	+	0.0323345i
$837$	13.4339	−	23.2682i	0.464344	−	0.804267i
$838$	−18.9532	−	32.8279i	−0.654727	−	1.13402i
$839$			26.5407i			0.916288i	0.888878	+	0.458144i	$0.151486\pi$
$839$			26.5407i			0.916288i	−0.888878	+	0.458144i	$0.848514\pi$
$840$		0			0
$841$	−9.31052			−0.321052
$842$	2.49757	−	1.44197i	0.0860719	−	0.0496937i
$843$	−8.01850	+	13.8884i	−0.276172	+	0.478344i
$844$	7.41646	+	4.28190i	0.255285	+	0.147389i
$845$	54.2256	−	31.3072i	1.86542	−	1.07700i
$846$	−13.8748			−0.477025
$847$		0			0
$848$	0.429764			0.0147581
$849$	−6.66999	+	3.85092i	−0.228913	+	0.132163i
$850$	2.47333	+	1.42798i	0.0848344	+	0.0489792i
$851$	36.5686	−	63.3388i	1.25356	−	2.17122i
$852$	1.41449	−	0.816659i	0.0484598	−	0.0279783i
$853$	−0.431373			−0.0147699			−0.00738496	−	0.999973i	$-0.502351\pi$
$853$	−0.431373			−0.0147699			−0.00738496	+	0.999973i	$0.502351\pi$
$854$		0			0
$855$		−	4.35143i		−	0.148816i
$856$	−7.37667	−	12.7768i	−0.252129	−	0.436701i
$857$	−8.75672	+	15.1671i	−0.299124	+	0.518098i	−0.975936	−	0.218058i	$-0.930028\pi$
$857$	−8.75672	+	15.1671i	−0.299124	+	0.518098i	0.676812	+	0.736156i	$0.263361\pi$
$858$	15.8605	−	5.37304i	0.541468	−	0.183432i
$859$	39.3879	−	22.7406i	1.34390	−	0.775901i	0.356522	−	0.934287i	$-0.383962\pi$
$859$	39.3879	−	22.7406i	1.34390	−	0.775901i	0.987377	+	0.158386i	$0.0506291\pi$
$860$	−16.0290			−0.546584
$861$		0			0
$862$	−32.4068			−1.10378
$863$	−11.8660	−	20.5525i	−0.403922	−	0.699614i	0.590273	−	0.807204i	$-0.299020\pi$
$863$	−11.8660	−	20.5525i	−0.403922	−	0.699614i	−0.994195	+	0.107590i	$0.965687\pi$
$864$	2.07193	−	3.58869i	0.0704885	−	0.122090i
$865$	27.6749	+	15.9781i	0.940976	+	0.543273i
$866$	−5.11596	−	8.86110i	−0.173847	−	0.301112i
$867$		−	3.03093i		−	0.102936i
$868$		0			0
$869$	18.5686	−	21.1472i	0.629898	−	0.717371i
$870$	4.85953	+	8.41695i	0.164753	+	0.285361i
$871$	−9.77158	+	16.9249i	−0.331097	+	0.573477i
$872$	−3.00000	+	5.19615i	−0.101593	+	0.175964i
$873$	−19.3162	+	11.1522i	−0.653754	+	0.377445i
$874$		−	5.81532i		−	0.196706i
$875$		0			0
$876$			8.28528i			0.279934i
$877$	28.8886	−	16.6788i	0.975499	−	0.563205i	0.0745907	−	0.997214i	$-0.476235\pi$
$877$	28.8886	−	16.6788i	0.975499	−	0.563205i	0.900908	+	0.434010i	$0.142902\pi$
$878$	25.0044	+	14.4363i	0.843859	+	0.487202i
$879$	−19.6481	−	11.3439i	−0.662715	−	0.382619i
$880$	6.67287	+	1.33158i	0.224942	+	0.0448877i
$881$			18.7347i			0.631187i	0.948895	+	0.315593i	$0.102204\pi$
$881$			18.7347i			0.631187i	−0.948895	+	0.315593i	$0.897796\pi$
$882$		0			0
$883$	26.0705			0.877342			0.438671	−	0.898648i	$-0.355449\pi$
$883$	26.0705			0.877342			0.438671	+	0.898648i	$0.355449\pi$
$884$	−11.9110	−	20.6305i	−0.400611	−	0.693879i
$885$	4.37665	+	2.52686i	0.147119	+	0.0849394i
$886$	7.41349	+	4.28018i	0.249061	+	0.143796i
$887$	−26.0619	−	45.1405i	−0.875073	−	1.51567i	−0.856685	−	0.515839i	$-0.827480\pi$
$887$	−26.0619	−	45.1405i	−0.875073	−	1.51567i	−0.0183874	−	0.999831i	$-0.505853\pi$
$888$	−8.45660			−0.283785
$889$		0			0
$890$			13.8038i			0.462703i
$891$	2.64229	−	13.2411i	0.0885202	−	0.443595i
$892$	7.13678	+	4.12042i	0.238957	+	0.137962i
$893$	4.37263	+	2.52454i	0.146324	+	0.0844805i
$894$	2.59073	−	1.49576i	0.0866469	−	0.0500256i
$895$		−	9.23553i		−	0.308710i
$896$		0			0
$897$			33.4214i			1.11591i
$898$	−9.36075	+	5.40443i	−0.312372	+	0.180348i
$899$	−20.0658	+	34.7550i	−0.669232	+	1.15914i
$900$	0.954684	−	1.65356i	0.0318228	−	0.0551187i
$901$	0.775955	+	1.34399i	0.0258508	+	0.0447749i
$902$	5.18338	−	5.90318i	0.172588	−	0.196554i
$903$		0			0
$904$			0.597322i			0.0198666i
$905$	8.39456	+	14.5398i	0.279045	+	0.483319i
$906$	−16.0335	−	9.25694i	−0.532677	−	0.307541i
$907$	−15.2867	+	26.4774i	−0.507587	+	0.879166i	0.492374	+	0.870383i	$0.336129\pi$
$907$	−15.2867	+	26.4774i	−0.507587	+	0.879166i	−0.999961	+	0.00878294i	$0.997204\pi$
$908$	13.7397	+	23.7979i	0.455969	+	0.789761i
$909$	4.48962			0.148911
$910$		0			0
$911$	0.343220			0.0113714			0.00568569	−	0.999984i	$-0.498190\pi$
$911$	0.343220			0.0113714			0.00568569	+	0.999984i	$0.498190\pi$
$912$	−0.582319	+	0.336202i	−0.0192825	+	0.0111328i
$913$	−38.6858	+	13.1055i	−1.28031	+	0.433729i
$914$	−12.1948	+	21.1220i	−0.403367	+	0.698653i
$915$	−8.89870	−	15.4130i	−0.294182	−	0.509538i
$916$		−	0.104343i		−	0.00344759i
$917$		0			0
$918$	14.9638			0.493879
$919$	−44.2268	+	25.5344i	−1.45891	+	0.842301i	−0.998958	−	0.0456441i	$-0.985466\pi$
$919$	−44.2268	+	25.5344i	−1.45891	+	0.842301i	−0.459950	+	0.887945i	$0.652133\pi$
$920$	−6.79013	+	11.7609i	−0.223864	+	0.387744i
$921$	10.7297	+	6.19478i	0.353555	+	0.204125i
$922$	−0.980215	+	0.565928i	−0.0322817	+	0.0186378i
$923$	−14.0781			−0.463385
$924$		0			0
$925$	−8.73856			−0.287322
$926$	5.52860	−	3.19194i	0.181681	−	0.104894i
$927$	14.0293	+	8.09982i	0.460783	+	0.266033i
$928$	−3.09477	+	5.36031i	−0.101591	+	0.175961i
$929$	−50.7827	+	29.3194i	−1.66613	+	0.961939i	−0.696433	+	0.717622i	$0.745230\pi$
$929$	−50.7827	+	29.3194i	−1.66613	+	0.961939i	−0.969695	+	0.244317i	$0.921436\pi$
$930$	10.1810			0.333850
$931$		0			0
$932$			15.1577i			0.496507i
$933$	−0.545856	−	0.945450i	−0.0178705	−	0.0309527i
$934$	17.8420	−	30.9033i	0.583808	−	1.01119i
$935$	7.88388	+	23.2722i	0.257831	+	0.761082i
$936$	−13.7927	+	7.96321i	−0.450828	+	0.260286i
$937$	40.2806			1.31591			0.657955	−	0.753057i	$-0.271422\pi$
$937$	40.2806			1.31591			0.657955	+	0.753057i	$0.271422\pi$
$938$		0			0
$939$	8.83754			0.288402
$940$	−5.89544	−	10.2112i	−0.192288	−	0.333053i
$941$	−1.37193	+	2.37625i	−0.0447236	+	0.0774636i	−0.887521	−	0.460768i	$-0.847574\pi$
$941$	−1.37193	+	2.37625i	−0.0447236	+	0.0774636i	0.842797	+	0.538231i	$0.180907\pi$
$942$	−13.4573	−	7.76957i	−0.438462	−	0.253146i
$943$	7.83938	+	13.5782i	0.255285	+	0.442167i
$944$			3.21844i			0.104751i
$945$		0			0
$946$	19.4714	+	17.0972i	0.633071	+	0.555878i
$947$	20.4229	+	35.3736i	0.663657	+	1.14949i	0.979648	+	0.200725i	$0.0643297\pi$
$947$	20.4229	+	35.3736i	0.663657	+	1.14949i	−0.315991	+	0.948762i	$0.602337\pi$
$948$	3.24718	−	5.62427i	0.105463	−	0.182668i
$949$	35.7067	−	61.8458i	1.15909	−	2.00760i
$950$	−0.601735	+	0.347412i	−0.0195229	+	0.0112715i
$951$			24.2804i			0.787347i
$952$		0			0
$953$		−	3.21096i		−	0.104013i	−0.998647	−	0.0520065i	$-0.983438\pi$
$953$		−	3.21096i		−	0.104013i	0.998647	−	0.0520065i	$-0.0165617\pi$
$954$	0.898537	−	0.518771i	0.0290912	−	0.0167958i
$955$	−18.4182	−	10.6337i	−0.595998	−	0.344099i
$956$	22.4417	+	12.9567i	0.725817	+	0.419051i
$957$	3.07469	−	15.4080i	0.0993907	−	0.498069i
$958$		−	11.5819i		−	0.374193i
$959$		0			0
$960$	1.57024			0.0506792
$961$	5.51960	+	9.56023i	0.178052	+	0.308395i
$962$	63.1246	+	36.4450i	2.03522	+	1.17503i
$963$	−30.8459	−	17.8089i	−0.993994	−	0.573883i
$964$	−3.65554	−	6.33158i	−0.117737	−	0.203927i
$965$	3.33044			0.107211
$966$		0			0
$967$			31.1521i			1.00178i	0.865510	+	0.500892i	$0.166995\pi$
$967$			31.1521i			1.00178i	−0.865510	+	0.500892i	$0.833005\pi$
$968$	−6.68563	−	8.73512i	−0.214884	−	0.280757i
$969$	−2.10280	−	1.21405i	−0.0675517	−	0.0390010i
$970$	−16.4150	−	9.47721i	−0.527054	−	0.304295i
$971$	−19.3805	+	11.1894i	−0.621951	+	0.359084i	−0.777628	−	0.628724i	$-0.783577\pi$
$971$	−19.3805	+	11.1894i	−0.621951	+	0.359084i	0.155677	+	0.987808i	$0.450244\pi$
$972$		−	15.5474i		−	0.498684i
$973$		0			0
$974$			40.0638i			1.28373i
$975$	3.45825	−	1.99662i	0.110753	−	0.0639431i
$976$	5.66711	−	9.81572i	0.181400	−	0.314193i
$977$	−8.83203	+	15.2975i	−0.282562	+	0.489411i	−0.972015	−	0.234919i	$-0.924518\pi$
$977$	−8.83203	+	15.2975i	−0.282562	+	0.489411i	0.689453	+	0.724330i	$0.257851\pi$
$978$	−5.07462	−	8.78950i	−0.162268	−	0.281057i
$979$	14.7237	−	16.7683i	0.470571	−	0.535918i
$980$		0			0
$981$			14.4853i			0.462479i
$982$	9.89382	+	17.1366i	0.315724	+	0.546851i
$983$	36.5871	+	21.1236i	1.16695	+	0.673737i	0.952959	−	0.303099i	$-0.0980213\pi$
$983$	36.5871	+	21.1236i	1.16695	+	0.673737i	0.213988	+	0.976836i	$0.431355\pi$
$984$	0.906438	−	1.57000i	0.0288962	−	0.0500497i
$985$	4.50034	+	7.79482i	0.143393	+	0.248364i
$986$	−22.3510			−0.711799
$987$		0			0
$988$	5.79566			0.184385
$989$	−44.7873	+	25.8579i	−1.42415	+	0.822235i
$990$	15.5588	−	5.27083i	0.494491	−	0.167518i
$991$	1.72788	−	2.99278i	0.0548881	−	0.0950689i	−0.837276	−	0.546781i	$-0.815853\pi$
$991$	1.72788	−	2.99278i	0.0548881	−	0.0950689i	0.892164	+	0.451712i	$0.149186\pi$
$992$	3.24188	+	5.61510i	0.102930	+	0.178280i
$993$			24.4335i			0.775374i
$994$		0			0
$995$	41.1636			1.30497
$996$	−8.16294	+	4.71287i	−0.258653	+	0.149333i
$997$	9.28384	−	16.0801i	0.294022	−	0.509262i	−0.680735	−	0.732530i	$-0.738339\pi$
$997$	9.28384	−	16.0801i	0.294022	−	0.509262i	0.974757	+	0.223269i	$0.0716727\pi$
$998$	23.0841	+	13.3276i	0.730716	+	0.421879i
$999$	−39.6517	+	22.8929i	−1.25452	+	0.724300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.d.1011.13		32
7.2	even	3	inner	1078.2.i.d.901.8		32
7.3	odd	6		1078.2.c.c.1077.11	yes	16
7.4	even	3		1078.2.c.c.1077.14	yes	16
7.5	odd	6	inner	1078.2.i.d.901.7		32
7.6	odd	2	inner	1078.2.i.d.1011.14		32
11.10	odd	2	inner	1078.2.i.d.1011.7		32
77.10	even	6		1078.2.c.c.1077.3	✓	16
77.32	odd	6		1078.2.c.c.1077.6	yes	16
77.54	even	6	inner	1078.2.i.d.901.13		32
77.65	odd	6	inner	1078.2.i.d.901.14		32
77.76	even	2	inner	1078.2.i.d.1011.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.3	✓	16	77.10	even	6
1078.2.c.c.1077.6	yes	16	77.32	odd	6
1078.2.c.c.1077.11	yes	16	7.3	odd	6
1078.2.c.c.1077.14	yes	16	7.4	even	3
1078.2.i.d.901.7		32	7.5	odd	6	inner
1078.2.i.d.901.8		32	7.2	even	3	inner
1078.2.i.d.901.13		32	77.54	even	6	inner
1078.2.i.d.901.14		32	77.65	odd	6	inner
1078.2.i.d.1011.7		32	11.10	odd	2	inner
1078.2.i.d.1011.8		32	77.76	even	2	inner
1078.2.i.d.1011.13		32	1.1	even	1	trivial
1078.2.i.d.1011.14		32	7.6	odd	2	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(1.02581 - 1.77675i) q^{10} +(-3.14127 + 1.06416i) q^{11} +(-0.662827 + 0.382683i) q^{12} +6.59694 q^{13} -1.57024 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.80554 - 3.12729i) q^{17} +(-2.09077 - 1.20711i) q^{18} +(0.439269 + 0.760837i) q^{19} -2.05161i q^{20} +(-2.18834 + 2.49222i) q^{22} +(-3.30966 - 5.73249i) q^{23} +(-0.382683 + 0.662827i) q^{24} +(-0.395443 + 0.684927i) q^{25} +(5.71311 - 3.29847i) q^{26} +4.14386i q^{27} -6.18955i q^{29} +(-1.35986 + 0.785118i) q^{30} +(-5.61510 - 3.24188i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.48935 + 0.496755i) q^{33} -3.61108i q^{34} -2.41421 q^{36} +(5.52454 + 9.56878i) q^{37} +(0.760837 + 0.439269i) q^{38} +(-4.37263 - 2.52454i) q^{39} +(-1.02581 - 1.77675i) q^{40} -2.36864 q^{41} -7.81288i q^{43} +(-0.649042 + 3.25250i) q^{44} +(-4.28945 - 2.47652i) q^{45} +(-5.73249 - 3.30966i) q^{46} +(4.97716 - 2.87357i) q^{47} +0.765367i q^{48} +0.790886i q^{50} +(-2.39352 + 1.38190i) q^{51} +(3.29847 - 5.71311i) q^{52} +(-0.214882 + 0.372186i) q^{53} +(2.07193 + 3.58869i) q^{54} +(-4.48962 + 5.11308i) q^{55} -0.672404i q^{57} +(-3.09477 - 5.36031i) q^{58} +(-2.78725 - 1.60922i) q^{59} +(-0.785118 + 1.35986i) q^{60} +(5.66711 + 9.81572i) q^{61} -6.48376 q^{62} -1.00000 q^{64} +(11.7211 - 6.76718i) q^{65} +(2.40422 - 0.814474i) q^{66} +(-1.48123 + 2.56556i) q^{67} +(-1.80554 - 3.12729i) q^{68} +5.06620i q^{69} -2.13403 q^{71} +(-2.09077 + 1.20711i) q^{72} +(5.41262 - 9.37493i) q^{73} +(9.56878 + 5.52454i) q^{74} +(0.524221 - 0.302659i) q^{75} +0.878539 q^{76} -5.04908 q^{78} +(-7.34847 + 4.24264i) q^{79} +(-1.77675 - 1.02581i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(-2.05130 + 1.18432i) q^{82} +12.3153 q^{83} -7.40854i q^{85} +(-3.90644 - 6.76615i) q^{86} +(-2.36864 + 4.10260i) q^{87} +(1.06416 + 3.14127i) q^{88} +(-5.82684 + 3.36413i) q^{89} -4.95303 q^{90} -6.61931 q^{92} +(2.48123 + 4.29762i) q^{93} +(2.87357 - 4.97716i) q^{94} +(1.56094 + 0.901211i) q^{95} +(0.382683 + 0.662827i) q^{96} -9.23880i q^{97} +(6.01676 + 5.28311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^9	\( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more