LMFDB - Embedded newform 352.2.s.b.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(79,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 1]))

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

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

chi := DirichletCharacter("352.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.s (of order $10$, degree $4$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	352.271
Dual form			352.2.s.b.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.385688 + 1.18702i) q^{3} +(-2.03454 - 2.80031i) q^{5} +(0.442181 + 1.36089i) q^{7} +(1.16678 + 0.847714i) q^{9} +(1.18696 + 3.09695i) q^{11} +(5.33740 + 3.87785i) q^{13} +(4.10874 - 1.33501i) q^{15} +(0.442479 + 0.609020i) q^{17} +(2.61700 + 0.850314i) q^{19} -1.78596 q^{21} -4.40738i q^{23} +(-2.15728 + 6.63943i) q^{25} +(-4.48550 + 3.25891i) q^{27} +(-0.0386973 - 0.119098i) q^{29} +(-2.25749 + 3.10716i) q^{31} +(-4.13396 + 0.214498i) q^{33} +(2.91129 - 4.00704i) q^{35} +(1.91508 - 0.622247i) q^{37} +(-6.66167 + 4.83999i) q^{39} +(2.52037 + 0.818917i) q^{41} -4.68327i q^{43} -4.99205i q^{45} +(-4.39059 - 1.42659i) q^{47} +(4.00661 - 2.91097i) q^{49} +(-0.893581 + 0.290342i) q^{51} +(-3.06496 + 4.21856i) q^{53} +(6.25750 - 9.62476i) q^{55} +(-2.01869 + 2.77849i) q^{57} +(-1.90440 - 5.86114i) q^{59} +(-2.37790 + 1.72765i) q^{61} +(-0.637721 + 1.96270i) q^{63} -22.8360i q^{65} +10.7156 q^{67} +(5.23168 + 1.69987i) q^{69} +(6.91440 + 9.51686i) q^{71} +(-5.95032 + 1.93338i) q^{73} +(-7.04913 - 5.12150i) q^{75} +(-3.68977 + 2.98475i) q^{77} +(1.32581 + 0.963258i) q^{79} +(-0.801393 - 2.46643i) q^{81} +(-7.17988 - 9.88226i) q^{83} +(0.805202 - 2.47816i) q^{85} +0.156297 q^{87} +10.6955 q^{89} +(-2.91724 + 8.97834i) q^{91} +(-2.81760 - 3.87809i) q^{93} +(-2.94326 - 9.05841i) q^{95} +(-9.17200 - 6.66385i) q^{97} +(-1.24041 + 4.61966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} - 10 q^{9} + 18 q^{11} - 10 q^{17} + 6 q^{25} + 32 q^{27} + 32 q^{33} + 10 q^{35} - 10 q^{41} - 18 q^{49} - 60 q^{51} - 80 q^{57} - 28 q^{59} + 28 q^{67} - 10 q^{73} - 4 q^{75} + 28 q^{81}+ \cdots - 122 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 - 10 * q^9 + 18 * q^11 - 10 * q^17 + 6 * q^25 + 32 * q^27 + 32 * q^33 + 10 * q^35 - 10 * q^41 - 18 * q^49 - 60 * q^51 - 80 * q^57 - 28 * q^59 + 28 * q^67 - 10 * q^73 - 4 * q^75 + 28 * q^81 + 20 * q^89 - 78 * q^91 - 52 * q^97 - 122 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.385688	+	1.18702i	−0.222677	+	0.685329i	0.775842	+	0.630927i	$0.217325\pi$
$3$	−0.385688	+	1.18702i	−0.222677	+	0.685329i	−0.998519	+	0.0544021i	$0.982675\pi$
$4$		0			0
$5$	−2.03454	−	2.80031i	−0.909876	−	1.25234i	−0.967209	−	0.253982i	$-0.918260\pi$
$5$	−2.03454	−	2.80031i	−0.909876	−	1.25234i	0.0573329	−	0.998355i	$-0.481740\pi$
$6$		0			0
$7$	0.442181	+	1.36089i	0.167129	+	0.514370i	0.999187	−	0.0403190i	$-0.0128374\pi$
$7$	0.442181	+	1.36089i	0.167129	+	0.514370i	−0.832058	+	0.554689i	$0.812837\pi$
$8$		0			0
$9$	1.16678	+	0.847714i	0.388926	+	0.282571i
$10$		0			0
$11$	1.18696	+	3.09695i	0.357883	+	0.933766i
$11$	1.18696	+	3.09695i	0.357883	+	0.933766i
$12$		0			0
$13$	5.33740	+	3.87785i	1.48033	+	1.07552i	0.977451	+	0.211163i	$0.0677249\pi$
$13$	5.33740	+	3.87785i	1.48033	+	1.07552i	0.502876	+	0.864358i	$0.332275\pi$
$14$		0			0
$15$	4.10874	−	1.33501i	1.06087	−	0.344698i
$16$		0			0
$17$	0.442479	+	0.609020i	0.107317	+	0.147709i	0.859297	−	0.511476i	$-0.170901\pi$
$17$	0.442479	+	0.609020i	0.107317	+	0.147709i	−0.751980	+	0.659185i	$0.770901\pi$
$18$		0			0
$19$	2.61700	+	0.850314i	0.600381	+	0.195075i	0.593410	−	0.804900i	$-0.297781\pi$
$19$	2.61700	+	0.850314i	0.600381	+	0.195075i	0.00697046	+	0.999976i	$0.497781\pi$
$20$		0			0
$21$	−1.78596			−0.389728
$22$		0			0
$23$		−	4.40738i		−	0.919003i	−0.888177	−	0.459502i	$-0.848028\pi$
$23$		−	4.40738i		−	0.919003i	0.888177	−	0.459502i	$-0.151972\pi$
$24$		0			0
$25$	−2.15728	+	6.63943i	−0.431456	+	1.32789i
$26$		0			0
$27$	−4.48550	+	3.25891i	−0.863235	+	0.627177i
$28$		0			0
$29$	−0.0386973	−	0.119098i	−0.00718590	−	0.0221159i	0.947399	−	0.320054i	$-0.103701\pi$
$29$	−0.0386973	−	0.119098i	−0.00718590	−	0.0221159i	−0.954585	+	0.297938i	$0.903701\pi$
$30$		0			0
$31$	−2.25749	+	3.10716i	−0.405457	+	0.558063i	−0.962103	−	0.272686i	$-0.912088\pi$
$31$	−2.25749	+	3.10716i	−0.405457	+	0.558063i	0.556646	+	0.830750i	$0.312088\pi$
$32$		0			0
$33$	−4.13396	+	0.214498i	−0.719630	+	0.0373393i
$34$		0			0
$35$	2.91129	−	4.00704i	0.492098	−	0.677314i
$36$		0			0
$37$	1.91508	−	0.622247i	0.314837	−	0.102297i	−0.147336	−	0.989086i	$-0.547070\pi$
$37$	1.91508	−	0.622247i	0.314837	−	0.102297i	0.462173	+	0.886790i	$0.347070\pi$
$38$		0			0
$39$	−6.66167	+	4.83999i	−1.06672	+	0.775018i
$40$		0			0
$41$	2.52037	+	0.818917i	0.393615	+	0.127893i	0.499136	−	0.866524i	$-0.333651\pi$
$41$	2.52037	+	0.818917i	0.393615	+	0.127893i	−0.105521	+	0.994417i	$0.533651\pi$
$42$		0			0
$43$		−	4.68327i		−	0.714192i	−0.934068	−	0.357096i	$-0.883767\pi$
$43$		−	4.68327i		−	0.714192i	0.934068	−	0.357096i	$-0.116233\pi$
$44$		0			0
$45$		−	4.99205i		−	0.744171i
$46$		0			0
$47$	−4.39059	−	1.42659i	−0.640433	−	0.208089i	−0.0292421	−	0.999572i	$-0.509309\pi$
$47$	−4.39059	−	1.42659i	−0.640433	−	0.208089i	−0.611191	+	0.791483i	$0.709309\pi$
$48$		0			0
$49$	4.00661	−	2.91097i	0.572373	−	0.415853i
$50$		0			0
$51$	−0.893581	+	0.290342i	−0.125126	+	0.0406560i
$52$		0			0
$53$	−3.06496	+	4.21856i	−0.421005	+	0.579463i	−0.965859	−	0.259067i	$-0.916585\pi$
$53$	−3.06496	+	4.21856i	−0.421005	+	0.579463i	0.544854	+	0.838531i	$0.316585\pi$
$54$		0			0
$55$	6.25750	−	9.62476i	0.843761	−	1.29780i
$56$		0			0
$57$	−2.01869	+	2.77849i	−0.267382	+	0.368020i
$58$		0			0
$59$	−1.90440	−	5.86114i	−0.247932	−	0.763056i	−0.995140	−	0.0984660i	$-0.968606\pi$
$59$	−1.90440	−	5.86114i	−0.247932	−	0.763056i	0.747209	−	0.664590i	$-0.231394\pi$
$60$		0			0
$61$	−2.37790	+	1.72765i	−0.304460	+	0.221203i	−0.729516	−	0.683964i	$-0.760254\pi$
$61$	−2.37790	+	1.72765i	−0.304460	+	0.221203i	0.425056	+	0.905167i	$0.360254\pi$
$62$		0			0
$63$	−0.637721	+	1.96270i	−0.0803453	+	0.247277i
$64$		0			0
$65$		−	22.8360i		−	2.83246i
$66$		0			0
$67$	10.7156			1.30912			0.654559	−	0.756011i	$-0.272854\pi$
$67$	10.7156			1.30912			0.654559	+	0.756011i	$0.272854\pi$
$68$		0			0
$69$	5.23168	+	1.69987i	0.629820	+	0.204641i
$70$		0			0
$71$	6.91440	+	9.51686i	0.820588	+	1.12944i	0.989602	+	0.143829i	$0.0459417\pi$
$71$	6.91440	+	9.51686i	0.820588	+	1.12944i	−0.169014	+	0.985614i	$0.554058\pi$
$72$		0			0
$73$	−5.95032	+	1.93338i	−0.696433	+	0.226285i	−0.635776	−	0.771874i	$-0.719320\pi$
$73$	−5.95032	+	1.93338i	−0.696433	+	0.226285i	−0.0606571	+	0.998159i	$0.519320\pi$
$74$		0			0
$75$	−7.04913	−	5.12150i	−0.813964	−	0.591379i
$76$		0			0
$77$	−3.68977	+	2.98475i	−0.420489	+	0.340143i
$78$		0			0
$79$	1.32581	+	0.963258i	0.149165	+	0.108375i	0.659865	−	0.751384i	$-0.270614\pi$
$79$	1.32581	+	0.963258i	0.149165	+	0.108375i	−0.510700	+	0.859759i	$0.670614\pi$
$80$		0			0
$81$	−0.801393	−	2.46643i	−0.0890436	−	0.274048i
$82$		0			0
$83$	−7.17988	−	9.88226i	−0.788094	−	1.08472i	−0.994343	−	0.106219i	$-0.966126\pi$
$83$	−7.17988	−	9.88226i	−0.788094	−	1.08472i	0.206249	−	0.978500i	$-0.433874\pi$
$84$		0			0
$85$	0.805202	−	2.47816i	0.0873365	−	0.268794i
$86$		0			0
$87$	0.156297			0.0167568
$88$		0			0
$89$	10.6955			1.13372			0.566858	−	0.823815i	$-0.308159\pi$
$89$	10.6955			1.13372			0.566858	+	0.823815i	$0.308159\pi$
$90$		0			0
$91$	−2.91724	+	8.97834i	−0.305810	+	0.941186i
$92$		0			0
$93$	−2.81760	−	3.87809i	−0.292171	−	0.402139i
$94$		0			0
$95$	−2.94326	−	9.05841i	−0.301972	−	0.929373i
$96$		0			0
$97$	−9.17200	−	6.66385i	−0.931276	−	0.676611i	0.0150293	−	0.999887i	$-0.495216\pi$
$97$	−9.17200	−	6.66385i	−0.931276	−	0.676611i	−0.946305	+	0.323276i	$0.895216\pi$
$98$		0			0
$99$	−1.24041	+	4.61966i	−0.124666	+	0.464293i
$100$		0			0
$101$	−7.14622	−	5.19204i	−0.711076	−	0.516627i	0.172445	−	0.985019i	$-0.444833\pi$
$101$	−7.14622	−	5.19204i	−0.711076	−	0.516627i	−0.883521	+	0.468392i	$0.844833\pi$
$102$		0			0
$103$	−16.7264	+	5.43473i	−1.64810	+	0.535499i	−0.978327	−	0.207068i	$-0.933608\pi$
$103$	−16.7264	+	5.43473i	−1.64810	+	0.535499i	−0.669771	+	0.742567i	$0.733608\pi$
$104$		0			0
$105$	3.63361	+	5.00124i	0.354604	+	0.488071i
$106$		0			0
$107$	4.41132	+	1.43333i	0.426459	+	0.138565i	0.514379	−	0.857563i	$-0.328022\pi$
$107$	4.41132	+	1.43333i	0.426459	+	0.138565i	−0.0879209	+	0.996127i	$0.528022\pi$
$108$		0			0
$109$	−11.8543			−1.13544			−0.567718	−	0.823223i	$-0.692173\pi$
$109$	−11.8543			−1.13544			−0.567718	+	0.823223i	$0.692173\pi$
$110$		0			0
$111$			2.51324i			0.238546i
$112$		0			0
$113$	0.696722	−	2.14429i	0.0655421	−	0.201718i	−0.912922	−	0.408133i	$-0.866180\pi$
$113$	0.696722	−	2.14429i	0.0655421	−	0.201718i	0.978464	+	0.206415i	$0.0661798\pi$
$114$		0			0
$115$	−12.3420	+	8.96702i	−1.15090	+	0.836179i
$116$		0			0
$117$	2.94025	+	9.04917i	0.271826	+	0.836596i
$118$		0			0
$119$	−0.633156	+	0.871465i	−0.0580413	+	0.0798870i
$120$		0			0
$121$	−8.18224	+	7.35194i	−0.743840	+	0.668358i
$122$		0			0
$123$	−1.94415	+	2.67589i	−0.175298	+	0.241277i
$124$		0			0
$125$	6.52174	−	2.11904i	0.583323	−	0.189533i
$126$		0			0
$127$	11.2265	−	8.15650i	0.996187	−	0.723772i	0.0349194	−	0.999390i	$-0.488883\pi$
$127$	11.2265	−	8.15650i	0.996187	−	0.723772i	0.961267	+	0.275618i	$0.0888826\pi$
$128$		0			0
$129$	5.55916	+	1.80628i	0.489457	+	0.159034i
$130$		0			0
$131$		−	8.50766i		−	0.743317i	−0.928369	−	0.371659i	$-0.878789\pi$
$131$		−	8.50766i		−	0.743317i	0.928369	−	0.371659i	$-0.121211\pi$
$132$		0			0
$133$			3.93745i			0.341420i
$134$		0			0
$135$	18.2519	+	5.93040i	1.57087	+	0.510408i
$136$		0			0
$137$	−3.93506	+	2.85899i	−0.336195	+	0.244260i	−0.743055	−	0.669231i	$-0.766624\pi$
$137$	−3.93506	+	2.85899i	−0.336195	+	0.244260i	0.406860	+	0.913491i	$0.366624\pi$
$138$		0			0
$139$	15.2832	−	4.96581i	1.29630	−	0.421194i	0.422009	−	0.906592i	$-0.361325\pi$
$139$	15.2832	−	4.96581i	1.29630	−	0.421194i	0.874294	+	0.485397i	$0.161325\pi$
$140$		0			0
$141$	3.38679	−	4.66152i	0.285219	−	0.392571i
$142$		0			0
$143$	−5.67421	+	21.1325i	−0.474501	+	1.76719i
$144$		0			0
$145$	−0.254780	+	0.350674i	−0.0211583	+	0.0291219i
$146$		0			0
$147$	1.91010	+	5.87867i	0.157542	+	0.484865i
$148$		0			0
$149$	17.2096	−	12.5035i	1.40986	−	1.02433i	0.416520	−	0.909127i	$-0.363250\pi$
$149$	17.2096	−	12.5035i	1.40986	−	1.02433i	0.993342	−	0.115198i	$-0.0367504\pi$
$150$		0			0
$151$	4.91773	−	15.1352i	0.400199	−	1.23169i	−0.524639	−	0.851325i	$-0.675800\pi$
$151$	4.91773	−	15.1352i	0.400199	−	1.23169i	0.924838	−	0.380361i	$-0.124200\pi$
$152$		0			0
$153$			1.08569i			0.0877726i
$154$		0			0
$155$	13.2940			1.06780
$156$		0			0
$157$	1.98718	+	0.645673i	0.158594	+	0.0515303i	0.387238	−	0.921980i	$-0.373429\pi$
$157$	1.98718	+	0.645673i	0.158594	+	0.0515303i	−0.228644	+	0.973510i	$0.573429\pi$
$158$		0			0
$159$	−3.82542	−	5.26523i	−0.303375	−	0.417560i
$160$		0			0
$161$	5.99798	−	1.94886i	0.472707	−	0.153592i
$162$		0			0
$163$	−8.87445	−	6.44766i	−0.695100	−	0.505020i	0.183233	−	0.983070i	$-0.441344\pi$
$163$	−8.87445	−	6.44766i	−0.695100	−	0.505020i	−0.878333	+	0.478050i	$0.841344\pi$
$164$		0			0
$165$	9.01138	+	11.1400i	0.701535	+	0.867245i
$166$		0			0
$167$	−10.5048	−	7.63218i	−0.812885	−	0.590595i	0.101781	−	0.994807i	$-0.467546\pi$
$167$	−10.5048	−	7.63218i	−0.812885	−	0.590595i	−0.914666	+	0.404211i	$0.867546\pi$
$168$		0			0
$169$	9.43289	+	29.0315i	0.725607	+	2.23319i
$170$		0			0
$171$	2.33263	+	3.21059i	0.178381	+	0.245520i
$172$		0			0
$173$	−1.07620	+	3.31219i	−0.0818217	+	0.251821i	−0.983596	−	0.180386i	$-0.942265\pi$
$173$	−1.07620	+	3.31219i	−0.0818217	+	0.251821i	0.901774	+	0.432208i	$0.142265\pi$
$174$		0			0
$175$	−9.98947			−0.755133
$176$		0			0
$177$	7.69182			0.578153
$178$		0			0
$179$	−0.835692	+	2.57200i	−0.0624626	+	0.192240i	−0.977418	−	0.211315i	$-0.932226\pi$
$179$	−0.835692	+	2.57200i	−0.0624626	+	0.192240i	0.914956	+	0.403555i	$0.132226\pi$
$180$		0			0
$181$	6.52174	+	8.97641i	0.484757	+	0.667211i	0.979410	−	0.201879i	$-0.0647048\pi$
$181$	6.52174	+	8.97641i	0.484757	+	0.667211i	−0.494653	+	0.869091i	$0.664705\pi$
$182$		0			0
$183$	−1.13363	−	3.48897i	−0.0838006	−	0.257912i
$184$		0			0
$185$	−5.63880	−	4.09682i	−0.414572	−	0.301205i
$186$		0			0
$187$	−1.36090	+	2.09322i	−0.0995189	+	0.153072i
$188$		0			0
$189$	−6.41843	−	4.66326i	−0.466872	−	0.339203i
$190$		0			0
$191$	12.9352	−	4.20291i	0.935961	−	0.304112i	0.198963	−	0.980007i	$-0.436243\pi$
$191$	12.9352	−	4.20291i	0.935961	−	0.304112i	0.736998	+	0.675895i	$0.236243\pi$
$192$		0			0
$193$	−3.16835	−	4.36086i	−0.228063	−	0.313901i	0.679615	−	0.733569i	$-0.262147\pi$
$193$	−3.16835	−	4.36086i	−0.228063	−	0.313901i	−0.907678	+	0.419667i	$0.862147\pi$
$194$		0			0
$195$	27.1069	+	8.80757i	1.94117	+	0.630723i
$196$		0			0
$197$	−6.42744			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$197$	−6.42744			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$198$		0			0
$199$		−	3.62012i		−	0.256623i	−0.991734	−	0.128312i	$-0.959044\pi$
$199$		−	3.62012i		−	0.256623i	0.991734	−	0.128312i	$-0.0409558\pi$
$200$		0			0
$201$	−4.13288	+	12.7197i	−0.291511	+	0.897177i
$202$		0			0
$203$	0.144968	−	0.105326i	0.0101748	−	0.00739242i
$204$		0			0
$205$	−2.83458	−	8.72393i	−0.197976	−	0.609306i
$206$		0			0
$207$	3.73620	−	5.14244i	0.259684	−	0.357424i
$208$		0			0
$209$	0.472897	+	9.11401i	0.0327110	+	0.630430i
$210$		0			0
$211$	−12.3044	+	16.9355i	−0.847067	+	1.16589i	0.137434	+	0.990511i	$0.456114\pi$
$211$	−12.3044	+	16.9355i	−0.847067	+	1.16589i	−0.984501	+	0.175377i	$0.943886\pi$
$212$		0			0
$213$	−13.9635	+	4.53703i	−0.956766	+	0.310872i
$214$		0			0
$215$	−13.1146	+	9.52832i	−0.894409	+	0.649826i
$216$		0			0
$217$	−5.22674	−	1.69827i	−0.354814	−	0.115286i
$218$		0			0
$219$		−	7.80886i		−	0.527674i
$220$		0			0
$221$			4.96645i			0.334080i
$222$		0			0
$223$	2.52383	+	0.820041i	0.169008	+	0.0549140i	0.392299	−	0.919838i	$-0.371680\pi$
$223$	2.52383	+	0.820041i	0.169008	+	0.0549140i	−0.223291	+	0.974752i	$0.571680\pi$
$224$		0			0
$225$	−8.14541	+	5.91798i	−0.543027	+	0.394532i
$226$		0			0
$227$	3.31167	−	1.07603i	0.219803	−	0.0714184i	−0.197045	−	0.980394i	$-0.563135\pi$
$227$	3.31167	−	1.07603i	0.219803	−	0.0714184i	0.416848	+	0.908976i	$0.363135\pi$
$228$		0			0
$229$	7.74574	−	10.6611i	0.511853	−	0.704505i	−0.472377	−	0.881396i	$-0.656604\pi$
$229$	7.74574	−	10.6611i	0.511853	−	0.704505i	0.984230	+	0.176891i	$0.0566041\pi$
$230$		0			0
$231$	−2.11987	−	5.53103i	−0.139477	−	0.363915i
$232$		0			0
$233$	4.10254	−	5.64666i	0.268766	−	0.369925i	−0.653207	−	0.757180i	$-0.726577\pi$
$233$	4.10254	−	5.64666i	0.268766	−	0.369925i	0.921973	+	0.387255i	$0.126577\pi$
$234$		0			0
$235$	4.93796	+	15.1975i	0.322117	+	0.991374i
$236$		0			0
$237$	−1.65476	+	1.20225i	−0.107488	+	0.0780947i
$238$		0			0
$239$	0.736760	−	2.26751i	0.0476570	−	0.146673i	−0.924396	−	0.381434i	$-0.875431\pi$
$239$	0.736760	−	2.26751i	0.0476570	−	0.146673i	0.972053	+	0.234760i	$0.0754305\pi$
$240$		0			0
$241$		−	10.0044i		−	0.644440i	−0.946665	−	0.322220i	$-0.895571\pi$
$241$		−	10.0044i		−	0.644440i	0.946665	−	0.322220i	$-0.104429\pi$
$242$		0			0
$243$	−13.3963			−0.859376
$244$		0			0
$245$	−16.3033	−	5.29725i	−1.04158	−	0.338429i
$246$		0			0
$247$	10.6706	+	14.6868i	0.678952	+	0.934498i
$248$		0			0
$249$	14.4997	−	4.71123i	0.918880	−	0.298562i
$250$		0			0
$251$	−14.1273	−	10.2641i	−0.891709	−	0.647864i	0.0446141	−	0.999004i	$-0.485794\pi$
$251$	−14.1273	−	10.2641i	−0.891709	−	0.647864i	−0.936323	+	0.351140i	$0.885794\pi$
$252$		0			0
$253$	13.6495	−	5.23140i	0.858134	−	0.328896i
$254$		0			0
$255$	2.63108	+	1.91159i	0.164765	+	0.119708i
$256$		0			0
$257$	−2.52039	−	7.75695i	−0.157217	−	0.483865i	0.841162	−	0.540784i	$-0.181872\pi$
$257$	−2.52039	−	7.75695i	−0.157217	−	0.483865i	−0.998379	+	0.0569189i	$0.981872\pi$
$258$		0			0
$259$	1.69362	+	2.33107i	0.105237	+	0.144846i
$260$		0			0
$261$	0.0558098	−	0.171765i	0.00345454	−	0.0106320i
$262$		0			0
$263$	21.0996			1.30106			0.650530	−	0.759481i	$-0.274547\pi$
$263$	21.0996			1.30106			0.650530	+	0.759481i	$0.274547\pi$
$264$		0			0
$265$	18.0491			1.10875
$266$		0			0
$267$	−4.12511	+	12.6958i	−0.252453	+	0.776969i
$268$		0			0
$269$	12.3273	+	16.9671i	0.751610	+	1.03450i	0.997866	+	0.0652981i	$0.0207998\pi$
$269$	12.3273	+	16.9671i	0.751610	+	1.03450i	−0.246255	+	0.969205i	$0.579200\pi$
$270$		0			0
$271$	6.16426	+	18.9717i	0.374452	+	1.15245i	0.943847	+	0.330382i	$0.107178\pi$
$271$	6.16426	+	18.9717i	0.374452	+	1.15245i	−0.569395	+	0.822064i	$0.692822\pi$
$272$		0			0
$273$	−9.53237	−	6.92567i	−0.576925	−	0.419161i
$274$		0			0
$275$	−23.1226	+	1.19976i	−1.39435	+	0.0723482i
$276$		0			0
$277$	−0.866547	−	0.629583i	−0.0520658	−	0.0378280i	0.561448	−	0.827512i	$-0.310244\pi$
$277$	−0.866547	−	0.629583i	−0.0520658	−	0.0378280i	−0.613514	+	0.789684i	$0.710244\pi$
$278$		0			0
$279$	−5.26797	+	1.71167i	−0.315385	+	0.102475i
$280$		0			0
$281$	−2.05101	−	2.82297i	−0.122353	−	0.168404i	0.743447	−	0.668795i	$-0.233190\pi$
$281$	−2.05101	−	2.82297i	−0.122353	−	0.168404i	−0.865800	+	0.500391i	$0.833190\pi$
$282$		0			0
$283$	−19.4768	−	6.32839i	−1.15777	−	0.376184i	−0.333707	−	0.942677i	$-0.608300\pi$
$283$	−19.4768	−	6.32839i	−1.15777	−	0.376184i	−0.824066	+	0.566493i	$0.808300\pi$
$284$		0			0
$285$	11.8877			0.704169
$286$		0			0
$287$			3.79206i			0.223838i
$288$		0			0
$289$	5.07817	−	15.6290i	0.298716	−	0.919353i
$290$		0			0
$291$	11.4477	−	8.31723i	0.671075	−	0.487565i
$292$		0			0
$293$	−8.03179	−	24.7193i	−0.469222	−	1.44412i	−0.853594	−	0.520939i	$-0.825582\pi$
$293$	−8.03179	−	24.7193i	−0.469222	−	1.44412i	0.384372	−	0.923178i	$-0.374418\pi$
$294$		0			0
$295$	−12.5384	+	17.2577i	−0.730015	+	1.00478i
$296$		0			0
$297$	−15.4168	−	10.0232i	−0.894574	−	0.581604i
$298$		0			0
$299$	17.0912	−	23.5240i	0.988407	−	1.36043i
$300$		0			0
$301$	6.37343	−	2.07085i	0.367359	−	0.119362i
$302$		0			0
$303$	8.91929	−	6.48024i	0.512400	−	0.372280i
$304$		0			0
$305$	9.67591	+	3.14389i	0.554041	+	0.180019i
$306$		0			0
$307$		−	9.33420i		−	0.532731i	−0.963872	−	0.266366i	$-0.914177\pi$
$307$		−	9.33420i		−	0.532731i	0.963872	−	0.266366i	$-0.0858228\pi$
$308$		0			0
$309$		−	21.9507i		−	1.24873i
$310$		0			0
$311$	−18.5133	−	6.01534i	−1.04979	−	0.341099i	−0.267206	−	0.963639i	$-0.586101\pi$
$311$	−18.5133	−	6.01534i	−1.04979	−	0.341099i	−0.782588	+	0.622541i	$0.786101\pi$
$312$		0			0
$313$	−11.9727	+	8.69865i	−0.676735	+	0.491677i	−0.872273	−	0.489020i	$-0.837355\pi$
$313$	−11.9727	+	8.69865i	−0.676735	+	0.491677i	0.195538	+	0.980696i	$0.437355\pi$
$314$		0			0
$315$	6.79365	−	2.20739i	0.382779	−	0.124372i
$316$		0			0
$317$	−18.6496	+	25.6690i	−1.04747	+	1.44171i	−0.156480	+	0.987681i	$0.550015\pi$
$317$	−18.6496	+	25.6690i	−1.04747	+	1.44171i	−0.890986	+	0.454031i	$0.849985\pi$
$318$		0			0
$319$	0.322908	−	0.261208i	0.0180794	−	0.0146249i
$320$		0			0
$321$	−3.40279	+	4.68353i	−0.189925	+	0.261409i
$322$		0			0
$323$	0.640109	+	1.97005i	0.0356166	+	0.109617i
$324$		0			0
$325$	−37.2610	+	27.0717i	−2.06687	+	1.50167i
$326$		0			0
$327$	4.57206	−	14.0713i	0.252835	−	0.778147i
$328$		0			0
$329$		−	6.60594i		−	0.364197i
$330$		0			0
$331$	0.462745			0.0254347			0.0127174	−	0.999919i	$-0.495952\pi$
$331$	0.462745			0.0254347			0.0127174	+	0.999919i	$0.495952\pi$
$332$		0			0
$333$	2.76196	+	0.897414i	0.151354	+	0.0491780i
$334$		0			0
$335$	−21.8014	−	30.0070i	−1.19114	−	1.63946i
$336$		0			0
$337$	21.3704	−	6.94366i	1.16412	−	0.378245i	0.337675	−	0.941263i	$-0.390360\pi$
$337$	21.3704	−	6.94366i	1.16412	−	0.378245i	0.826445	+	0.563017i	$0.190360\pi$
$338$		0			0
$339$	2.27661	+	1.65405i	0.123648	+	0.0898358i
$340$		0			0
$341$	−12.3023	−	3.30324i	−0.666207	−	0.178881i
$342$		0			0
$343$	13.8367	+	10.0529i	0.747111	+	0.542808i
$344$		0			0
$345$	−5.88390	−	18.1088i	−0.316779	−	0.974944i
$346$		0			0
$347$	10.6270	+	14.6268i	0.570486	+	0.785207i	0.992612	−	0.121330i	$-0.0387159\pi$
$347$	10.6270	+	14.6268i	0.570486	+	0.785207i	−0.422126	+	0.906537i	$0.638716\pi$
$348$		0			0
$349$	0.0983383	−	0.302654i	0.00526393	−	0.0162007i	−0.948390	−	0.317106i	$-0.897289\pi$
$349$	0.0983383	−	0.302654i	0.00526393	−	0.0162007i	0.953654	+	0.300905i	$0.0972889\pi$
$350$		0			0
$351$	−36.5784			−1.95241
$352$		0			0
$353$	−35.8303			−1.90706			−0.953529	−	0.301303i	$-0.902579\pi$
$353$	−35.8303			−1.90706			−0.953529	+	0.301303i	$0.902579\pi$
$354$		0			0
$355$	12.5825	−	38.7249i	0.667810	−	2.05531i
$356$		0			0
$357$	−0.790250	−	1.08769i	−0.0418245	−	0.0575664i
$358$		0			0
$359$	−7.17559	−	22.0842i	−0.378713	−	1.16556i	−0.940939	−	0.338576i	$-0.890055\pi$
$359$	−7.17559	−	22.0842i	−0.378713	−	1.16556i	0.562226	−	0.826984i	$-0.309945\pi$
$360$		0			0
$361$	−9.24568	−	6.71738i	−0.486615	−	0.353546i
$362$		0			0
$363$	−5.57115	−	12.5481i	−0.292409	−	0.658603i
$364$		0			0
$365$	17.5203	+	12.7292i	0.917052	+	0.666277i
$366$		0			0
$367$	12.4753	−	4.05346i	0.651203	−	0.211589i	0.0352586	−	0.999378i	$-0.488775\pi$
$367$	12.4753	−	4.05346i	0.651203	−	0.211589i	0.615945	+	0.787789i	$0.288775\pi$
$368$		0			0
$369$	2.24650	+	3.09204i	0.116948	+	0.160965i
$370$		0			0
$371$	−7.09628	−	2.30572i	−0.368420	−	0.119707i
$372$		0			0
$373$	11.1209			0.575820			0.287910	−	0.957657i	$-0.407040\pi$
$373$	11.1209			0.575820			0.287910	+	0.957657i	$0.407040\pi$
$374$		0			0
$375$			8.55876i			0.441973i
$376$		0			0
$377$	0.255301	−	0.785735i	0.0131487	−	0.0404674i
$378$		0			0
$379$	3.56804	−	2.59234i	0.183278	−	0.133159i	−0.492363	−	0.870390i	$-0.663867\pi$
$379$	3.56804	−	2.59234i	0.183278	−	0.133159i	0.675641	+	0.737231i	$0.263867\pi$
$380$		0			0
$381$	5.35206	+	16.4719i	0.274194	+	0.843883i
$382$		0			0
$383$	1.05035	−	1.44568i	0.0536703	−	0.0738709i	−0.781338	−	0.624108i	$-0.785463\pi$
$383$	1.05035	−	1.44568i	0.0536703	−	0.0738709i	0.835009	+	0.550237i	$0.185463\pi$
$384$		0			0
$385$	15.8652	+	4.25991i	0.808567	+	0.217105i
$386$		0			0
$387$	3.97007	−	5.46434i	0.201810	−	0.277768i
$388$		0			0
$389$	17.8795	−	5.80939i	0.906525	−	0.294548i	0.181598	−	0.983373i	$-0.441873\pi$
$389$	17.8795	−	5.80939i	0.906525	−	0.294548i	0.724928	+	0.688825i	$0.241873\pi$
$390$		0			0
$391$	2.68419	−	1.95018i	0.135745	−	0.0986246i
$392$		0			0
$393$	10.0988	+	3.28130i	0.509417	+	0.165520i
$394$		0			0
$395$		−	5.67247i		−	0.285413i
$396$		0			0
$397$		−	16.9423i		−	0.850309i	−0.905121	−	0.425154i	$-0.860220\pi$
$397$		−	16.9423i		−	0.850309i	0.905121	−	0.425154i	$-0.139780\pi$
$398$		0			0
$399$	−4.67385	−	1.51863i	−0.233985	−	0.0760264i
$400$		0			0
$401$	−22.0372	+	16.0110i	−1.10049	+	0.799551i	−0.981139	−	0.193302i	$-0.938080\pi$
$401$	−22.0372	+	16.0110i	−1.10049	+	0.799551i	−0.119348	+	0.992853i	$0.538080\pi$
$402$		0			0
$403$	−24.0982	+	7.82998i	−1.20042	+	0.390039i
$404$		0			0
$405$	−5.27631	+	7.26222i	−0.262182	+	0.360862i
$406$		0			0
$407$	4.20020	+	5.19232i	0.208196	+	0.257374i
$408$		0			0
$409$	8.51572	−	11.7209i	0.421075	−	0.579560i	−0.544801	−	0.838565i	$-0.683395\pi$
$409$	8.51572	−	11.7209i	0.421075	−	0.579560i	0.965876	+	0.259005i	$0.0833947\pi$
$410$		0			0
$411$	−1.87599	−	5.77369i	−0.0925356	−	0.284795i
$412$		0			0
$413$	7.13430	−	5.18337i	0.351056	−	0.255057i
$414$		0			0
$415$	−13.0656	+	40.2118i	−0.641365	+	1.97392i
$416$		0			0
$417$			20.0568i			0.982184i
$418$		0			0
$419$	29.5266			1.44247			0.721234	−	0.692691i	$-0.243575\pi$
$419$	29.5266			1.44247			0.721234	+	0.692691i	$0.243575\pi$
$420$		0			0
$421$	25.1953	+	8.18646i	1.22795	+	0.398984i	0.849970	−	0.526831i	$-0.176620\pi$
$421$	25.1953	+	8.18646i	1.22795	+	0.398984i	0.377976	+	0.925815i	$0.376620\pi$
$422$		0			0
$423$	−3.91350	−	5.38648i	−0.190281	−	0.261899i
$424$		0			0
$425$	−4.99810	+	1.62398i	−0.242444	+	0.0787747i
$426$		0			0
$427$	−3.40261	−	2.47214i	−0.164664	−	0.119635i
$428$		0			0
$429$	−22.8964	−	14.8860i	−1.10545	−	0.718702i
$430$		0			0
$431$	15.6499	+	11.3703i	0.753827	+	0.547688i	0.897011	−	0.442008i	$-0.145734\pi$
$431$	15.6499	+	11.3703i	0.753827	+	0.547688i	−0.143183	+	0.989696i	$0.545734\pi$
$432$		0			0
$433$	2.01155	+	6.19091i	0.0966689	+	0.297516i	0.987685	−	0.156455i	$-0.0500067\pi$
$433$	2.01155	+	6.19091i	0.0966689	+	0.297516i	−0.891016	+	0.453972i	$0.850007\pi$
$434$		0			0
$435$	−0.317994	−	0.437681i	−0.0152466	−	0.0209852i
$436$		0			0
$437$	3.74766	−	11.5341i	0.179275	−	0.551752i
$438$		0			0
$439$	3.89313			0.185809			0.0929044	−	0.995675i	$-0.470385\pi$
$439$	3.89313			0.185809			0.0929044	+	0.995675i	$0.470385\pi$
$440$		0			0
$441$	7.14250			0.340119
$442$		0			0
$443$	−9.08528	+	27.9616i	−0.431655	+	1.32850i	0.464822	+	0.885404i	$0.346118\pi$
$443$	−9.08528	+	27.9616i	−0.431655	+	1.32850i	−0.896476	+	0.443092i	$0.853882\pi$
$444$		0			0
$445$	−21.7604	−	29.9506i	−1.03154	−	1.41979i
$446$		0			0
$447$	8.20442	+	25.2506i	0.388056	+	1.19431i
$448$		0			0
$449$	19.3694	+	14.0727i	0.914096	+	0.664130i	0.942048	−	0.335479i	$-0.108898\pi$
$449$	19.3694	+	14.0727i	0.914096	+	0.664130i	−0.0279511	+	0.999609i	$0.508898\pi$
$450$		0			0
$451$	0.455436	+	8.77748i	0.0214456	+	0.413316i
$452$		0			0
$453$	16.0692	+	11.6749i	0.754995	+	0.548536i
$454$		0			0
$455$	31.0774	−	10.0977i	1.45693	−	0.473386i
$456$		0			0
$457$	−19.8130	−	27.2702i	−0.926811	−	1.27565i	−0.961091	−	0.276233i	$-0.910914\pi$
$457$	−19.8130	−	27.2702i	−0.926811	−	1.27565i	0.0342799	−	0.999412i	$-0.489086\pi$
$458$		0			0
$459$	−3.96948	−	1.28976i	−0.185280	−	0.0602010i
$460$		0			0
$461$	1.14908			0.0535180			0.0267590	−	0.999642i	$-0.491481\pi$
$461$	1.14908			0.0535180			0.0267590	+	0.999642i	$0.491481\pi$
$462$		0			0
$463$		−	35.5695i		−	1.65305i	−0.562897	−	0.826527i	$-0.690313\pi$
$463$		−	35.5695i		−	1.65305i	0.562897	−	0.826527i	$-0.309687\pi$
$464$		0			0
$465$	−5.12733	+	15.7803i	−0.237774	+	0.731793i
$466$		0			0
$467$	−7.76496	+	5.64158i	−0.359320	+	0.261061i	−0.752768	−	0.658286i	$-0.771282\pi$
$467$	−7.76496	+	5.64158i	−0.359320	+	0.261061i	0.393449	+	0.919347i	$0.371282\pi$
$468$		0			0
$469$	4.73824	+	14.5828i	0.218792	+	0.673371i
$470$		0			0
$471$	−1.53286	+	2.10980i	−0.0706304	+	0.0972144i
$472$		0			0
$473$	14.5039	−	5.55887i	0.666889	−	0.255597i
$474$		0			0
$475$	−11.2912	+	15.5410i	−0.518076	+	0.713071i
$476$		0			0
$477$	−7.15226	+	2.32391i	−0.327479	+	0.106405i
$478$		0			0
$479$	10.6121	−	7.71014i	0.484879	−	0.352285i	−0.318332	−	0.947979i	$-0.603123\pi$
$479$	10.6121	−	7.71014i	0.484879	−	0.352285i	0.803212	+	0.595694i	$0.203123\pi$
$480$		0			0
$481$	12.6345	+	4.10520i	0.576084	+	0.187181i
$482$		0			0
$483$			7.87141i			0.358162i
$484$		0			0
$485$			39.2423i			1.78190i
$486$		0			0
$487$	−13.1809	−	4.28273i	−0.597283	−	0.194069i	−0.00525485	−	0.999986i	$-0.501673\pi$
$487$	−13.1809	−	4.28273i	−0.597283	−	0.194069i	−0.592028	+	0.805917i	$0.701673\pi$
$488$		0			0
$489$	11.0763	−	8.04740i	0.500888	−	0.363916i
$490$		0			0
$491$	−7.72819	+	2.51104i	−0.348768	+	0.113322i	−0.478162	−	0.878272i	$-0.658697\pi$
$491$	−7.72819	+	2.51104i	−0.348768	+	0.113322i	0.129394	+	0.991593i	$0.458697\pi$
$492$		0			0
$493$	0.0554103	−	0.0762658i	0.00249556	−	0.00343484i
$494$		0			0
$495$	15.4601	−	5.92538i	0.694882	−	0.266326i
$496$		0			0
$497$	−9.89402	+	13.6179i	−0.443807	+	0.610848i
$498$		0			0
$499$	2.03291	+	6.25665i	0.0910055	+	0.280086i	0.986192	−	0.165605i	$-0.0529578\pi$
$499$	2.03291	+	6.25665i	0.0910055	+	0.280086i	−0.895187	+	0.445692i	$0.852958\pi$
$500$		0			0
$501$	13.1112	−	9.52581i	0.585763	−	0.425582i
$502$		0			0
$503$	−11.1744	+	34.3912i	−0.498242	+	1.53343i	0.313602	+	0.949555i	$0.398464\pi$
$503$	−11.1744	+	34.3912i	−0.498242	+	1.53343i	−0.811843	+	0.583875i	$0.801536\pi$
$504$		0			0
$505$			30.5751i			1.36057i
$506$		0			0
$507$	−38.0992			−1.69205
$508$		0			0
$509$	−17.9333	−	5.82690i	−0.794881	−	0.258273i	−0.116700	−	0.993167i	$-0.537232\pi$
$509$	−17.9333	−	5.82690i	−0.794881	−	0.258273i	−0.678181	+	0.734895i	$0.737232\pi$
$510$		0			0
$511$	−5.26224	−	7.24286i	−0.232788	−	0.320405i
$512$		0			0
$513$	−14.5096	+	4.71447i	−0.640616	+	0.208149i
$514$		0			0
$515$	49.2495	+	35.7818i	2.17019	+	1.57674i
$516$		0			0
$517$	−0.793389	−	15.2908i	−0.0348932	−	0.672487i
$518$		0			0
$519$	−3.51658	−	2.55494i	−0.154361	−	0.112150i
$520$		0			0
$521$	−8.33018	−	25.6377i	−0.364952	−	1.12321i	−0.950011	−	0.312216i	$-0.898929\pi$
$521$	−8.33018	−	25.6377i	−0.364952	−	1.12321i	0.585059	−	0.810991i	$-0.301071\pi$
$522$		0			0
$523$	15.4730	+	21.2968i	0.676588	+	0.931243i	0.999887	−	0.0150535i	$-0.00479187\pi$
$523$	15.4730	+	21.2968i	0.676588	+	0.931243i	−0.323299	+	0.946297i	$0.604792\pi$
$524$		0			0
$525$	3.85282	−	11.8578i	0.168151	−	0.517515i
$526$		0			0
$527$	−2.89122			−0.125943
$528$		0			0
$529$	3.57496			0.155433
$530$		0			0
$531$	2.74656	−	8.45303i	0.119190	−	0.366830i
$532$		0			0
$533$	10.2766	+	14.1445i	0.445127	+	0.612665i
$534$		0			0
$535$	−4.96128	−	15.2692i	−0.214495	−	0.660147i
$536$		0			0
$537$	−2.73071	−	1.98397i	−0.117839	−	0.0856148i
$538$		0			0
$539$	13.7708	+	8.95307i	0.593152	+	0.385636i
$540$		0			0
$541$	−28.9843	−	21.0583i	−1.24613	−	0.905369i	−0.248142	−	0.968724i	$-0.579820\pi$
$541$	−28.9843	−	21.0583i	−1.24613	−	0.905369i	−0.997991	+	0.0633548i	$0.979820\pi$
$542$		0			0
$543$	−13.1706	+	4.27938i	−0.565204	+	0.183646i
$544$		0			0
$545$	24.1181	+	33.1957i	1.03311	+	1.42195i
$546$		0			0
$547$	2.46974	+	0.802466i	0.105598	+	0.0343110i	0.361340	−	0.932434i	$-0.382320\pi$
$547$	2.46974	+	0.802466i	0.105598	+	0.0343110i	−0.255741	+	0.966745i	$0.582320\pi$
$548$		0			0
$549$	−4.23904			−0.180918
$550$		0			0
$551$		−	0.344584i		−	0.0146798i
$552$		0			0
$553$	−0.724643	+	2.23022i	−0.0308150	+	0.0948387i
$554$		0			0
$555$	7.03785	−	5.11330i	0.298740	−	0.217047i
$556$		0			0
$557$	−5.74085	−	17.6685i	−0.243248	−	0.748639i	−0.995920	−	0.0902436i	$-0.971235\pi$
$557$	−5.74085	−	17.6685i	−0.243248	−	0.748639i	0.752672	−	0.658396i	$-0.228765\pi$
$558$		0			0
$559$	18.1610	−	24.9965i	0.768128	−	1.05724i
$560$		0			0
$561$	−1.95982	−	2.42275i	−0.0827438	−	0.102289i
$562$		0			0
$563$	−6.88635	+	9.47824i	−0.290225	+	0.399460i	−0.929087	−	0.369861i	$-0.879405\pi$
$563$	−6.88635	+	9.47824i	−0.290225	+	0.399460i	0.638862	+	0.769321i	$0.279405\pi$
$564$		0			0
$565$	−7.42219	+	2.41162i	−0.312254	+	0.101457i
$566$		0			0
$567$	3.00219	−	2.18122i	0.126080	−	0.0916027i
$568$		0			0
$569$	0.0584948	+	0.0190061i	0.00245223	+	0.000796778i	0.310243	−	0.950657i	$-0.399590\pi$
$569$	0.0584948	+	0.0190061i	0.00245223	+	0.000796778i	−0.307791	+	0.951454i	$0.599590\pi$
$570$		0			0
$571$		−	13.5141i		−	0.565549i	−0.959186	−	0.282775i	$-0.908745\pi$
$571$		−	13.5141i		−	0.565549i	0.959186	−	0.282775i	$-0.0912549\pi$
$572$		0			0
$573$			16.9755i			0.709160i
$574$		0			0
$575$	29.2625	+	9.50797i	1.22033	+	0.396510i
$576$		0			0
$577$	23.6007	−	17.1469i	0.982509	−	0.713834i	0.0242409	−	0.999706i	$-0.492283\pi$
$577$	23.6007	−	17.1469i	0.982509	−	0.713834i	0.958268	+	0.285872i	$0.0922831\pi$
$578$		0			0
$579$	6.39844	−	2.07898i	0.265910	−	0.0863994i
$580$		0			0
$581$	10.2739	−	14.1408i	0.426233	−	0.586659i
$582$		0			0
$583$	−16.7027	−	4.48477i	−0.691754	−	0.185740i
$584$		0			0
$585$	19.3584	−	26.6446i	0.800372	−	1.10162i
$586$		0			0
$587$	5.16224	+	15.8877i	0.213068	+	0.655757i	0.999285	+	0.0378060i	$0.0120369\pi$
$587$	5.16224	+	15.8877i	0.213068	+	0.655757i	−0.786217	+	0.617951i	$0.787963\pi$
$588$		0			0
$589$	−8.54991	+	6.21187i	−0.352293	+	0.255956i
$590$		0			0
$591$	2.47898	−	7.62953i	0.101972	−	0.313837i
$592$		0			0
$593$			25.8884i			1.06311i	0.847024	+	0.531555i	$0.178392\pi$
$593$			25.8884i			1.06311i	−0.847024	+	0.531555i	$0.821608\pi$
$594$		0			0
$595$	3.72856			0.152856
$596$		0			0
$597$	4.29717	+	1.39624i	0.175871	+	0.0571441i
$598$		0			0
$599$	20.0324	+	27.5722i	0.818500	+	1.12657i	0.989956	+	0.141377i	$0.0451528\pi$
$599$	20.0324	+	27.5722i	0.818500	+	1.12657i	−0.171456	+	0.985192i	$0.554847\pi$
$600$		0			0
$601$	−13.2879	+	4.31751i	−0.542026	+	0.176115i	−0.567218	−	0.823568i	$-0.691980\pi$
$601$	−13.2879	+	4.31751i	−0.542026	+	0.176115i	0.0251919	+	0.999683i	$0.491980\pi$
$602$		0			0
$603$	12.5027	+	9.08376i	0.509150	+	0.369919i
$604$		0			0
$605$	37.2348	+	7.95496i	1.51381	+	0.323415i
$606$		0			0
$607$	−14.8915	−	10.8193i	−0.604426	−	0.439141i	0.243021	−	0.970021i	$-0.421862\pi$
$607$	−14.8915	−	10.8193i	−0.604426	−	0.439141i	−0.847447	+	0.530880i	$0.821862\pi$
$608$		0			0
$609$	0.0691117	+	0.212704i	0.00280055	+	0.00861920i
$610$		0			0
$611$	−17.9022	−	24.6403i	−0.724247	−	0.996840i
$612$		0			0
$613$	−1.90751	+	5.87070i	−0.0770435	+	0.237115i	−0.982160	−	0.188049i	$-0.939784\pi$
$613$	−1.90751	+	5.87070i	−0.0770435	+	0.237115i	0.905116	+	0.425164i	$0.139784\pi$
$614$		0			0
$615$	11.4488			0.461660
$616$		0			0
$617$	1.39128			0.0560109			0.0280054	−	0.999608i	$-0.491084\pi$
$617$	1.39128			0.0560109			0.0280054	+	0.999608i	$0.491084\pi$
$618$		0			0
$619$	3.39184	−	10.4390i	0.136330	−	0.419580i	−0.859465	−	0.511195i	$-0.829203\pi$
$619$	3.39184	−	10.4390i	0.136330	−	0.419580i	0.995794	+	0.0916154i	$0.0292030\pi$
$620$		0			0
$621$	14.3633	+	19.7693i	0.576378	+	0.793316i
$622$		0			0
$623$	4.72933	+	14.5554i	0.189477	+	0.583149i
$624$		0			0
$625$	9.03643	+	6.56535i	0.361457	+	0.262614i
$626$		0			0
$627$	−11.0010	−	2.95382i	−0.439336	−	0.117964i
$628$		0			0
$629$	1.22634	+	0.890990i	0.0488975	+	0.0355261i
$630$		0			0
$631$	−1.93780	+	0.629628i	−0.0771425	+	0.0250651i	−0.347334	−	0.937741i	$-0.612913\pi$
$631$	−1.93780	+	0.629628i	−0.0771425	+	0.0250651i	0.270192	+	0.962807i	$0.412913\pi$
$632$		0			0
$633$	−15.3572	−	21.1374i	−0.610395	−	0.840136i
$634$		0			0
$635$	−45.6814	−	14.8428i	−1.81281	−	0.589019i
$636$		0			0
$637$	32.6732			1.29456
$638$		0			0
$639$			16.9655i			0.671144i
$640$		0			0
$641$	−1.03461	+	3.18420i	−0.0408646	+	0.125768i	−0.969408	−	0.245457i	$-0.921062\pi$
$641$	−1.03461	+	3.18420i	−0.0408646	+	0.125768i	0.928543	+	0.371225i	$0.121062\pi$
$642$		0			0
$643$	33.9880	−	24.6938i	1.34036	−	0.973827i	0.340927	−	0.940090i	$-0.389259\pi$
$643$	33.9880	−	24.6938i	1.34036	−	0.973827i	0.999431	−	0.0337372i	$-0.0107409\pi$
$644$		0			0
$645$	−6.25221	−	19.2423i	−0.246181	−	0.757666i
$646$		0			0
$647$	6.76639	−	9.31313i	0.266014	−	0.366137i	−0.655025	−	0.755607i	$-0.727342\pi$
$647$	6.76639	−	9.31313i	0.266014	−	0.366137i	0.921039	+	0.389470i	$0.127342\pi$
$648$		0			0
$649$	15.8912	−	12.8548i	0.623785	−	0.504595i
$650$		0			0
$651$	4.03178	−	5.54927i	0.158018	−	0.217493i
$652$		0			0
$653$	−39.9222	+	12.9715i	−1.56227	+	0.507614i	−0.957414	−	0.288718i	$-0.906771\pi$
$653$	−39.9222	+	12.9715i	−1.56227	+	0.507614i	−0.604860	+	0.796331i	$0.706771\pi$
$654$		0			0
$655$	−23.8241	+	17.3092i	−0.930884	+	0.676327i
$656$		0			0
$657$	−8.58166	−	2.78835i	−0.334802	−	0.108784i
$658$		0			0
$659$			38.3263i			1.49298i	0.665396	+	0.746490i	$0.268263\pi$
$659$			38.3263i			1.49298i	−0.665396	+	0.746490i	$0.731737\pi$
$660$		0			0
$661$		−	12.9209i		−	0.502563i	−0.967914	−	0.251281i	$-0.919148\pi$
$661$		−	12.9209i		−	0.502563i	0.967914	−	0.251281i	$-0.0808520\pi$
$662$		0			0
$663$	−5.89530	−	1.91550i	−0.228954	−	0.0743918i
$664$		0			0
$665$	11.0261	−	8.01092i	0.427573	−	0.310650i
$666$		0			0
$667$	−0.524910	+	0.170554i	−0.0203246	+	0.00660387i
$668$		0			0
$669$	−1.94682	+	2.67957i	−0.0752684	+	0.103598i
$670$		0			0
$671$	−8.17293	−	5.31360i	−0.315513	−	0.205129i
$672$		0			0
$673$	−24.8122	+	34.1511i	−0.956442	+	1.31643i	−0.00783601	+	0.999969i	$0.502494\pi$
$673$	−24.8122	+	34.1511i	−0.956442	+	1.31643i	−0.948606	+	0.316460i	$0.897506\pi$
$674$		0			0
$675$	−11.9608	−	36.8116i	−0.460371	−	1.41688i
$676$		0			0
$677$	6.94588	−	5.04648i	0.266952	−	0.193952i	−0.446254	−	0.894906i	$-0.647242\pi$
$677$	6.94588	−	5.04648i	0.266952	−	0.193952i	0.713206	+	0.700954i	$0.247242\pi$
$678$		0			0
$679$	5.01310	−	15.4287i	0.192385	−	0.592101i
$680$		0			0
$681$			4.34604i			0.166541i
$682$		0			0
$683$	−28.2213			−1.07986			−0.539928	−	0.841711i	$-0.681549\pi$
$683$	−28.2213			−1.07986			−0.539928	+	0.841711i	$0.681549\pi$
$684$		0			0
$685$	16.0121	+	5.20265i	0.611792	+	0.198783i
$686$		0			0
$687$	9.66755	+	13.3062i	0.368840	+	0.507665i
$688$		0			0
$689$	−32.7178	+	10.6307i	−1.24645	+	0.404996i
$690$		0			0
$691$	−8.43429	−	6.12787i	−0.320855	−	0.233115i	0.415685	−	0.909509i	$-0.363542\pi$
$691$	−8.43429	−	6.12787i	−0.320855	−	0.233115i	−0.736540	+	0.676394i	$0.763542\pi$
$692$		0			0
$693$	−6.83535	+	0.354665i	−0.259654	+	0.0134726i
$694$		0			0
$695$	−45.0001	−	32.6945i	−1.70695	−	1.24017i
$696$		0			0
$697$	0.616473	+	1.89731i	0.0233506	+	0.0718657i
$698$		0			0
$699$	5.12042	+	7.04766i	0.193672	+	0.266567i
$700$		0			0
$701$	6.36425	−	19.5871i	0.240374	−	0.739796i	−0.755989	−	0.654585i	$-0.772843\pi$
$701$	6.36425	−	19.5871i	0.240374	−	0.739796i	0.996363	−	0.0852113i	$-0.0271565\pi$
$702$		0			0
$703$	5.54086			0.208978
$704$		0			0
$705$	−19.9443			−0.751146
$706$		0			0
$707$	3.90588	−	12.0211i	0.146896	−	0.452099i
$708$		0			0
$709$	−10.4287	−	14.3539i	−0.391658	−	0.539071i	0.566968	−	0.823740i	$-0.308116\pi$
$709$	−10.4287	−	14.3539i	−0.391658	−	0.539071i	−0.958626	+	0.284669i	$0.908116\pi$
$710$		0			0
$711$	0.730359	+	2.24782i	0.0273906	+	0.0842996i
$712$		0			0
$713$	13.6945	+	9.94961i	0.512862	+	0.372616i
$714$		0			0
$715$	70.7221	−	27.1055i	2.64486	−	1.01369i
$716$		0			0
$717$	2.40744	+	1.74910i	0.0899074	+	0.0653215i
$718$		0			0
$719$	−39.9775	+	12.9895i	−1.49091	+	0.484426i	−0.937351	−	0.348385i	$-0.886730\pi$
$719$	−39.9775	+	12.9895i	−1.49091	+	0.484426i	−0.553557	+	0.832811i	$0.686730\pi$
$720$		0			0
$721$	−14.7922	−	20.3597i	−0.550889	−	0.758234i
$722$		0			0
$723$	11.8755	+	3.85858i	0.441654	+	0.143502i
$724$		0			0
$725$	0.874223			0.0324678
$726$		0			0
$727$			28.2673i			1.04838i	0.851602	+	0.524189i	$0.175631\pi$
$727$			28.2673i			1.04838i	−0.851602	+	0.524189i	$0.824369\pi$
$728$		0			0
$729$	7.57098	−	23.3011i	0.280407	−	0.863004i
$730$		0			0
$731$	2.85221	−	2.07225i	0.105493	−	0.0766449i
$732$		0			0
$733$	10.0445	+	30.9137i	0.371001	+	1.14182i	0.946137	+	0.323765i	$0.104949\pi$
$733$	10.0445	+	30.9137i	0.371001	+	1.14182i	−0.575137	+	0.818057i	$0.695051\pi$
$734$		0			0
$735$	12.5759	−	17.3093i	0.463870	−	0.638463i
$736$		0			0
$737$	12.7190	+	33.1857i	0.468511	+	1.22241i
$738$		0			0
$739$	−13.9205	+	19.1599i	−0.512075	+	0.704810i	−0.984267	−	0.176685i	$-0.943463\pi$
$739$	−13.9205	+	19.1599i	−0.512075	+	0.704810i	0.472193	+	0.881495i	$0.343463\pi$
$740$		0			0
$741$	−21.5491	+	7.00172i	−0.791625	+	0.257215i
$742$		0			0
$743$	10.1076	−	7.34362i	0.370813	−	0.269411i	−0.386735	−	0.922191i	$-0.626397\pi$
$743$	10.1076	−	7.34362i	0.370813	−	0.269411i	0.757548	+	0.652780i	$0.226397\pi$
$744$		0			0
$745$	−70.0273	−	22.7532i	−2.56560	−	0.833614i
$746$		0			0
$747$		−	17.6169i		−	0.644568i
$748$		0			0
$749$			6.63713i			0.242515i
$750$		0			0
$751$	−4.15146	−	1.34889i	−0.151489	−	0.0492217i	0.232291	−	0.972646i	$-0.425378\pi$
$751$	−4.15146	−	1.34889i	−0.151489	−	0.0492217i	−0.383780	+	0.923425i	$0.625378\pi$
$752$		0			0
$753$	17.6325	−	12.8108i	0.642563	−	0.466850i
$754$		0			0
$755$	−52.3886	+	17.0221i	−1.90662	+	0.619497i
$756$		0			0
$757$	−11.5578	+	15.9080i	−0.420076	+	0.578185i	−0.965640	−	0.259884i	$-0.916316\pi$
$757$	−11.5578	+	15.9080i	−0.420076	+	0.578185i	0.545564	+	0.838069i	$0.316316\pi$
$758$		0			0
$759$	0.945375	+	18.2199i	0.0343149	+	0.661342i
$760$		0			0
$761$	6.31497	−	8.69181i	0.228917	−	0.315078i	−0.679071	−	0.734072i	$-0.737617\pi$
$761$	6.31497	−	8.69181i	0.228917	−	0.315078i	0.907989	+	0.418995i	$0.137617\pi$
$762$		0			0
$763$	−5.24175	−	16.1324i	−0.189764	−	0.584034i
$764$		0			0
$765$	3.04026	−	2.20888i	0.109921	−	0.0798622i
$766$		0			0
$767$	12.5641	−	38.6682i	0.453662	−	1.39623i
$768$		0			0
$769$		−	28.3787i		−	1.02336i	−0.859176	−	0.511680i	$-0.829023\pi$
$769$		−	28.3787i		−	1.02336i	0.859176	−	0.511680i	$-0.170977\pi$
$770$		0			0
$771$	10.1798			0.366616
$772$		0			0
$773$	−12.7726	−	4.15006i	−0.459398	−	0.149267i	0.0701700	−	0.997535i	$-0.477646\pi$
$773$	−12.7726	−	4.15006i	−0.459398	−	0.149267i	−0.529568	+	0.848268i	$0.677646\pi$
$774$		0			0
$775$	−15.7598	−	21.6915i	−0.566108	−	0.779180i
$776$		0			0
$777$	−3.42025	+	1.11131i	−0.122701	+	0.0398679i
$778$		0			0
$779$	5.89946	+	4.28621i	0.211370	+	0.153569i
$780$		0			0
$781$	−21.2661	+	32.7097i	−0.760962	+	1.17045i
$782$		0			0
$783$	0.561706	+	0.408103i	0.0200737	+	0.0145844i
$784$		0			0
$785$	−2.23491	−	6.87836i	−0.0797675	−	0.245499i
$786$		0			0
$787$	−31.3392	−	43.1347i	−1.11712	−	1.53759i	−0.810486	−	0.585758i	$-0.800797\pi$
$787$	−31.3392	−	43.1347i	−1.11712	−	1.53759i	−0.306635	−	0.951827i	$-0.599203\pi$
$788$		0			0
$789$	−8.13787	+	25.0458i	−0.289716	+	0.891654i
$790$		0			0
$791$	3.22623			0.114712
$792$		0			0
$793$	−19.3914			−0.688608
$794$		0			0
$795$	−6.96131	+	21.4247i	−0.246892	+	0.759856i
$796$		0			0
$797$	−7.58342	−	10.4377i	−0.268619	−	0.369722i	0.653304	−	0.757096i	$-0.273382\pi$
$797$	−7.58342	−	10.4377i	−0.268619	−	0.369722i	−0.921923	+	0.387374i	$0.873382\pi$
$798$		0			0
$799$	−1.07392	−	3.30519i	−0.0379927	−	0.116929i
$800$		0			0
$801$	12.4792	+	9.06669i	0.440932	+	0.320356i
$802$		0			0
$803$	−13.0504	−	16.1330i	−0.460538	−	0.569322i
$804$		0			0
$805$	−17.6606	−	12.8312i	−0.622454	−	0.452239i
$806$		0			0
$807$	−24.8949	+	8.08884i	−0.876341	+	0.284741i
$808$		0			0
$809$	11.5869	+	15.9479i	0.407372	+	0.560700i	0.962575	−	0.271015i	$-0.0873594\pi$
$809$	11.5869	+	15.9479i	0.407372	+	0.560700i	−0.555203	+	0.831715i	$0.687359\pi$
$810$		0			0
$811$	−3.05542	−	0.992767i	−0.107290	−	0.0348608i	0.254880	−	0.966973i	$-0.417964\pi$
$811$	−3.05542	−	0.992767i	−0.107290	−	0.0348608i	−0.362170	+	0.932112i	$0.617964\pi$
$812$		0			0
$813$	−24.8973			−0.873187
$814$		0			0
$815$			37.9693i			1.33001i
$816$		0			0
$817$	3.98225	−	12.2561i	0.139321	−	0.428787i
$818$		0			0
$819$	−11.0148	+	8.00275i	−0.384889	+	0.279639i
$820$		0			0
$821$	10.5519	+	32.4755i	0.368265	+	1.13340i	0.947911	+	0.318534i	$0.103191\pi$
$821$	10.5519	+	32.4755i	0.368265	+	1.13340i	−0.579647	+	0.814868i	$0.696809\pi$
$822$		0			0
$823$	11.0334	−	15.1861i	0.384599	−	0.529355i	−0.572197	−	0.820116i	$-0.693909\pi$
$823$	11.0334	−	15.1861i	0.384599	−	0.529355i	0.956796	+	0.290762i	$0.0939087\pi$
$824$		0			0
$825$	7.49397	−	27.9099i	0.260907	−	0.971697i
$826$		0			0
$827$	28.3862	−	39.0702i	0.987084	−	1.35860i	0.0541588	−	0.998532i	$-0.482752\pi$
$827$	28.3862	−	39.0702i	0.987084	−	1.35860i	0.932925	−	0.360072i	$-0.117248\pi$
$828$		0			0
$829$	23.8963	−	7.76436i	0.829951	−	0.269668i	0.136926	−	0.990581i	$-0.456278\pi$
$829$	23.8963	−	7.76436i	0.829951	−	0.269668i	0.693025	+	0.720914i	$0.256278\pi$
$830$		0			0
$831$	1.08155	−	0.785790i	0.0375185	−	0.0272588i
$832$		0			0
$833$	3.54568	+	1.15206i	0.122851	+	0.0399166i
$834$		0			0
$835$			44.9447i			1.55537i
$836$		0			0
$837$		−	21.2941i		−	0.736033i
$838$		0			0
$839$	9.12336	+	2.96436i	0.314973	+	0.102341i	0.462238	−	0.886756i	$-0.347047\pi$
$839$	9.12336	+	2.96436i	0.314973	+	0.102341i	−0.147264	+	0.989097i	$0.547047\pi$
$840$		0			0
$841$	23.4488	−	17.0366i	0.808580	−	0.587467i
$842$		0			0
$843$	4.14199	−	1.34581i	0.142658	−	0.0463523i
$844$		0			0
$845$	62.1055	−	85.4808i	2.13649	−	2.94063i
$846$		0			0
$847$	−13.6232	−	7.88427i	−0.468100	−	0.270907i
$848$		0			0
$849$	15.0239	−	20.6786i	0.515619	−	0.709689i
$850$		0			0
$851$	−2.74248	−	8.44049i	−0.0940110	−	0.289336i
$852$		0			0
$853$	21.4801	−	15.6062i	0.735466	−	0.534347i	−0.155822	−	0.987785i	$-0.549803\pi$
$853$	21.4801	−	15.6062i	0.735466	−	0.534347i	0.891288	+	0.453438i	$0.149803\pi$
$854$		0			0
$855$	4.24481	−	13.0642i	0.145170	−	0.446786i
$856$		0			0
$857$		−	9.29115i		−	0.317380i	−0.987328	−	0.158690i	$-0.949273\pi$
$857$		−	9.29115i		−	0.317380i	0.987328	−	0.158690i	$-0.0507270\pi$
$858$		0			0
$859$	−0.473127			−0.0161429			−0.00807145	−	0.999967i	$-0.502569\pi$
$859$	−0.473127			−0.0161429			−0.00807145	+	0.999967i	$0.502569\pi$
$860$		0			0
$861$	−4.50127	−	1.46255i	−0.153403	−	0.0498436i
$862$		0			0
$863$	3.66396	+	5.04300i	0.124723	+	0.171666i	0.866812	−	0.498635i	$-0.166165\pi$
$863$	3.66396	+	5.04300i	0.124723	+	0.171666i	−0.742090	+	0.670301i	$0.766165\pi$
$864$		0			0
$865$	11.4647	−	3.72512i	0.389813	−	0.126658i
$866$		0			0
$867$	16.5934	+	12.0558i	0.563542	+	0.409437i
$868$		0			0
$869$	−1.40948	+	5.24932i	−0.0478132	+	0.178071i
$870$		0			0
$871$	57.1934	+	41.5534i	1.93792	+	1.40798i
$872$		0			0
$873$	−5.05265	−	15.5505i	−0.171006	−	0.526303i
$874$		0			0
$875$	5.76759	+	7.93840i	0.194980	+	0.268367i
$876$		0			0
$877$	−17.9712	+	55.3096i	−0.606844	+	1.86767i	−0.123262	+	0.992374i	$0.539336\pi$
$877$	−17.9712	+	55.3096i	−0.606844	+	1.86767i	−0.483582	+	0.875299i	$0.660664\pi$
$878$		0			0
$879$	32.4402			1.09418
$880$		0			0
$881$	−21.4583			−0.722949			−0.361475	−	0.932382i	$-0.617727\pi$
$881$	−21.4583			−0.722949			−0.361475	+	0.932382i	$0.617727\pi$
$882$		0			0
$883$	11.8139	−	36.3594i	0.397569	−	1.22359i	−0.529373	−	0.848389i	$-0.677573\pi$
$883$	11.8139	−	36.3594i	0.397569	−	1.22359i	0.926942	−	0.375204i	$-0.122427\pi$
$884$		0			0
$885$	−15.6494	−	21.5395i	−0.526047	−	0.724042i
$886$		0			0
$887$	11.8654	+	36.5179i	0.398400	+	1.22615i	0.926281	+	0.376832i	$0.122987\pi$
$887$	11.8654	+	36.5179i	0.398400	+	1.22615i	−0.527881	+	0.849318i	$0.677013\pi$
$888$		0			0
$889$	16.0643	+	11.6714i	0.538778	+	0.391445i
$890$		0			0
$891$	6.68720	−	5.40944i	0.224030	−	0.181223i
$892$		0			0
$893$	−10.2771	−	7.46676i	−0.343911	−	0.249866i
$894$		0			0
$895$	8.90264	−	2.89264i	0.297582	−	0.0966904i
$896$		0			0
$897$	21.3317	+	29.3605i	0.712244	+	0.980320i
$898$		0			0
$899$	0.457415	+	0.148623i	0.0152557	+	0.00495686i
$900$		0			0
$901$	−3.92537			−0.130773
$902$		0			0
$903$			8.36413i			0.278341i
$904$		0			0
$905$	11.8680	−	36.5258i	0.394504	−	1.21416i
$906$		0			0
$907$	0.530037	−	0.385095i	0.0175996	−	0.0127869i	−0.578951	−	0.815363i	$-0.696538\pi$
$907$	0.530037	−	0.385095i	0.0175996	−	0.0127869i	0.596550	+	0.802576i	$0.296538\pi$
$908$		0			0
$909$	−3.93670	−	12.1159i	−0.130572	−	0.401859i
$910$		0			0
$911$	−28.8473	+	39.7049i	−0.955754	+	1.31548i	−0.00683066	+	0.999977i	$0.502174\pi$
$911$	−28.8473	+	39.7049i	−0.955754	+	1.31548i	−0.948924	+	0.315506i	$0.897826\pi$
$912$		0			0
$913$	22.0826	−	33.9656i	0.730828	−	1.12410i
$914$		0			0
$915$	−7.46376	+	10.2730i	−0.246744	+	0.339614i
$916$		0			0
$917$	11.5780	−	3.76193i	0.382340	−	0.124230i
$918$		0			0
$919$	16.4110	−	11.9233i	0.541350	−	0.393314i	−0.283236	−	0.959050i	$-0.591408\pi$
$919$	16.4110	−	11.9233i	0.541350	−	0.393314i	0.824586	+	0.565736i	$0.191408\pi$
$920$		0			0
$921$	11.0799	+	3.60009i	0.365096	+	0.118627i
$922$		0			0
$923$			77.6082i			2.55451i
$924$		0			0
$925$			14.0574i			0.462204i
$926$		0			0
$927$	−24.1230	−	7.83805i	−0.792305	−	0.257435i
$928$		0			0
$929$	−20.9664	+	15.2330i	−0.687887	+	0.499779i	−0.875965	−	0.482375i	$-0.839774\pi$
$929$	−20.9664	+	15.2330i	−0.687887	+	0.499779i	0.188078	+	0.982154i	$0.439774\pi$
$930$		0			0
$931$	12.9605	−	4.21113i	0.424764	−	0.138014i
$932$		0			0
$933$	14.2807	−	19.6557i	0.467530	−	0.643500i
$934$		0			0
$935$	8.63049	−	0.447809i	0.282247	−	0.0146449i
$936$		0			0
$937$	−25.0688	+	34.5043i	−0.818962	+	1.12721i	0.170916	+	0.985286i	$0.445327\pi$
$937$	−25.0688	+	34.5043i	−0.818962	+	1.12721i	−0.989878	+	0.141920i	$0.954673\pi$
$938$		0			0
$939$	−5.70780	−	17.5668i	−0.186267	−	0.573271i
$940$		0			0
$941$	−2.92074	+	2.12204i	−0.0952134	+	0.0691766i	−0.634373	−	0.773027i	$-0.718742\pi$
$941$	−2.92074	+	2.12204i	−0.0952134	+	0.0691766i	0.539160	+	0.842203i	$0.318742\pi$
$942$		0			0
$943$	3.60928	−	11.1082i	0.117534	−	0.361734i
$944$		0			0
$945$			27.4612i			0.893314i
$946$		0			0
$947$	−24.5514			−0.797813			−0.398907	−	0.916992i	$-0.630610\pi$
$947$	−24.5514			−0.797813			−0.398907	+	0.916992i	$0.630610\pi$
$948$		0			0
$949$	−39.2566	−	12.7552i	−1.27432	−	0.414052i
$950$		0			0
$951$	−23.2768	−	32.0377i	−0.754801	−	1.03889i
$952$		0			0
$953$	−4.79500	+	1.55799i	−0.155325	+	0.0504682i	−0.385648	−	0.922646i	$-0.626022\pi$
$953$	−4.79500	+	1.55799i	−0.155325	+	0.0504682i	0.230322	+	0.973114i	$0.426022\pi$
$954$		0			0
$955$	−38.0868	−	27.6717i	−1.23246	−	0.895434i
$956$		0			0
$957$	0.185519	+	0.484045i	0.00599698	+	0.0156470i
$958$		0			0
$959$	−5.63079	−	4.09101i	−0.181828	−	0.132106i
$960$		0			0
$961$	5.02130	+	15.4540i	0.161978	+	0.498516i
$962$		0			0
$963$	3.93198	+	5.41191i	0.126706	+	0.174396i
$964$		0			0
$965$	−5.76561	+	17.7447i	−0.185602	+	0.571223i
$966$		0			0
$967$	−32.9415			−1.05933			−0.529664	−	0.848208i	$-0.677682\pi$
$967$	−32.9415			−1.05933			−0.529664	+	0.848208i	$0.677682\pi$
$968$		0			0
$969$	−2.58538			−0.0830545
$970$		0			0
$971$	−14.2466	+	43.8466i	−0.457196	+	1.40710i	0.411342	+	0.911481i	$0.365060\pi$
$971$	−14.2466	+	43.8466i	−0.457196	+	1.40710i	−0.868538	+	0.495623i	$0.834940\pi$
$972$		0			0
$973$	13.5159	+	18.6030i	0.433299	+	0.596385i
$974$		0			0
$975$	−17.7637	−	54.6709i	−0.568892	−	1.75087i
$976$		0			0
$977$	26.4008	+	19.1813i	0.844635	+	0.613664i	0.923662	−	0.383209i	$-0.125181\pi$
$977$	26.4008	+	19.1813i	0.844635	+	0.613664i	−0.0790263	+	0.996873i	$0.525181\pi$
$978$		0			0
$979$	12.6951	+	33.1233i	0.405738	+	1.05863i
$980$		0			0
$981$	−13.8313	−	10.0490i	−0.441600	−	0.320841i
$982$		0			0
$983$	8.03767	−	2.61160i	0.256362	−	0.0832970i	−0.178017	−	0.984027i	$-0.556968\pi$
$983$	8.03767	−	2.61160i	0.256362	−	0.0832970i	0.434378	+	0.900730i	$0.356968\pi$
$984$		0			0
$985$	13.0769	+	17.9988i	0.416665	+	0.573490i
$986$		0			0
$987$	7.84141	+	2.54783i	0.249595	+	0.0810983i
$988$		0			0
$989$	−20.6410			−0.656345
$990$		0			0
$991$		−	29.6890i		−	0.943104i	−0.881838	−	0.471552i	$-0.843694\pi$
$991$		−	29.6890i		−	0.943104i	0.881838	−	0.471552i	$-0.156306\pi$
$992$		0			0
$993$	−0.178475	+	0.549289i	−0.00566373	+	0.0174312i
$994$		0			0
$995$	−10.1375	+	7.36529i	−0.321379	+	0.233495i
$996$		0			0
$997$	−0.571855	−	1.75999i	−0.0181108	−	0.0557394i	0.941593	−	0.336754i	$-0.109329\pi$
$997$	−0.571855	−	1.75999i	−0.0181108	−	0.0557394i	−0.959703	+	0.281015i	$0.909329\pi$
$998$		0			0
$999$	−6.56224	+	9.03215i	−0.207620	+	0.285765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.s.b.271.3		32
4.3	odd	2		88.2.k.b.51.3	yes	32
8.3	odd	2	inner	352.2.s.b.271.4		32
8.5	even	2		88.2.k.b.51.5	yes	32
11.5	even	5		3872.2.g.d.1935.11		32
11.6	odd	10		3872.2.g.d.1935.12		32
11.8	odd	10	inner	352.2.s.b.239.4		32
12.11	even	2		792.2.bp.b.667.6		32
24.5	odd	2		792.2.bp.b.667.4		32
44.3	odd	10		968.2.k.h.723.4		32
44.7	even	10		968.2.k.i.475.7		32
44.15	odd	10		968.2.k.e.475.2		32
44.19	even	10		88.2.k.b.19.5	yes	32
44.27	odd	10		968.2.g.e.483.17		32
44.31	odd	10		968.2.k.i.699.8		32
44.35	even	10		968.2.k.e.699.1		32
44.39	even	10		968.2.g.e.483.16		32
44.43	even	2		968.2.k.h.403.6		32
88.5	even	10		968.2.g.e.483.15		32
88.13	odd	10		968.2.k.e.699.2		32
88.19	even	10	inner	352.2.s.b.239.3		32
88.21	odd	2		968.2.k.h.403.4		32
88.27	odd	10		3872.2.g.d.1935.9		32
88.29	odd	10		968.2.k.i.475.8		32
88.37	even	10		968.2.k.e.475.1		32
88.53	even	10		968.2.k.i.699.7		32
88.61	odd	10		968.2.g.e.483.18		32
88.69	even	10		968.2.k.h.723.6		32
88.83	even	10		3872.2.g.d.1935.10		32
88.85	odd	10		88.2.k.b.19.3	✓	32
132.107	odd	10		792.2.bp.b.19.4		32
264.173	even	10		792.2.bp.b.19.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.b.19.3	✓	32	88.85	odd	10
88.2.k.b.19.5	yes	32	44.19	even	10
88.2.k.b.51.3	yes	32	4.3	odd	2
88.2.k.b.51.5	yes	32	8.5	even	2
352.2.s.b.239.3		32	88.19	even	10	inner
352.2.s.b.239.4		32	11.8	odd	10	inner
352.2.s.b.271.3		32	1.1	even	1	trivial
352.2.s.b.271.4		32	8.3	odd	2	inner
792.2.bp.b.19.4		32	132.107	odd	10
792.2.bp.b.19.6		32	264.173	even	10
792.2.bp.b.667.4		32	24.5	odd	2
792.2.bp.b.667.6		32	12.11	even	2
968.2.g.e.483.15		32	88.5	even	10
968.2.g.e.483.16		32	44.39	even	10
968.2.g.e.483.17		32	44.27	odd	10
968.2.g.e.483.18		32	88.61	odd	10
968.2.k.e.475.1		32	88.37	even	10
968.2.k.e.475.2		32	44.15	odd	10
968.2.k.e.699.1		32	44.35	even	10
968.2.k.e.699.2		32	88.13	odd	10
968.2.k.h.403.4		32	88.21	odd	2
968.2.k.h.403.6		32	44.43	even	2
968.2.k.h.723.4		32	44.3	odd	10
968.2.k.h.723.6		32	88.69	even	10
968.2.k.i.475.7		32	44.7	even	10
968.2.k.i.475.8		32	88.29	odd	10
968.2.k.i.699.7		32	88.53	even	10
968.2.k.i.699.8		32	44.31	odd	10
3872.2.g.d.1935.9		32	88.27	odd	10
3872.2.g.d.1935.10		32	88.83	even	10
3872.2.g.d.1935.11		32	11.5	even	5
3872.2.g.d.1935.12		32	11.6	odd	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.s (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.385688 + 1.18702i) q^{3} +(-2.03454 - 2.80031i) q^{5} +(0.442181 + 1.36089i) q^{7} +(1.16678 + 0.847714i) q^{9} +(1.18696 + 3.09695i) q^{11} +(5.33740 + 3.87785i) q^{13} +(4.10874 - 1.33501i) q^{15} +(0.442479 + 0.609020i) q^{17} +(2.61700 + 0.850314i) q^{19} -1.78596 q^{21} -4.40738i q^{23} +(-2.15728 + 6.63943i) q^{25} +(-4.48550 + 3.25891i) q^{27} +(-0.0386973 - 0.119098i) q^{29} +(-2.25749 + 3.10716i) q^{31} +(-4.13396 + 0.214498i) q^{33} +(2.91129 - 4.00704i) q^{35} +(1.91508 - 0.622247i) q^{37} +(-6.66167 + 4.83999i) q^{39} +(2.52037 + 0.818917i) q^{41} -4.68327i q^{43} -4.99205i q^{45} +(-4.39059 - 1.42659i) q^{47} +(4.00661 - 2.91097i) q^{49} +(-0.893581 + 0.290342i) q^{51} +(-3.06496 + 4.21856i) q^{53} +(6.25750 - 9.62476i) q^{55} +(-2.01869 + 2.77849i) q^{57} +(-1.90440 - 5.86114i) q^{59} +(-2.37790 + 1.72765i) q^{61} +(-0.637721 + 1.96270i) q^{63} -22.8360i q^{65} +10.7156 q^{67} +(5.23168 + 1.69987i) q^{69} +(6.91440 + 9.51686i) q^{71} +(-5.95032 + 1.93338i) q^{73} +(-7.04913 - 5.12150i) q^{75} +(-3.68977 + 2.98475i) q^{77} +(1.32581 + 0.963258i) q^{79} +(-0.801393 - 2.46643i) q^{81} +(-7.17988 - 9.88226i) q^{83} +(0.805202 - 2.47816i) q^{85} +0.156297 q^{87} +10.6955 q^{89} +(-2.91724 + 8.97834i) q^{91} +(-2.81760 - 3.87809i) q^{93} +(-2.94326 - 9.05841i) q^{95} +(-9.17200 - 6.66385i) q^{97} +(-1.24041 + 4.61966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} - 10 q^{9} + 18 q^{11} - 10 q^{17} + 6 q^{25} + 32 q^{27} + 32 q^{33} + 10 q^{35} - 10 q^{41} - 18 q^{49} - 60 q^{51} - 80 q^{57} - 28 q^{59} + 28 q^{67} - 10 q^{73} - 4 q^{75} + 28 q^{81}+ \cdots - 122 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 - 10 * q^9 + 18 * q^11 - 10 * q^17 + 6 * q^25 + 32 * q^27 + 32 * q^33 + 10 * q^35 - 10 * q^41 - 18 * q^49 - 60 * q^51 - 80 * q^57 - 28 * q^59 + 28 * q^67 - 10 * q^73 - 4 * q^75 + 28 * q^81 + 20 * q^89 - 78 * q^91 - 52 * q^97 - 122 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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