LMFDB - Embedded newform 440.2.v.b.417.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(153,440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("440.153"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			417.11
Character	$\chi$	$=$	440.417
Dual form			440.2.v.b.153.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395428 - 0.395428i) q^{3} +(-0.0577165 + 2.23532i) q^{5} +(-2.57694 + 2.57694i) q^{7} +2.68727i q^{9} +(-2.35988 - 2.33045i) q^{11} +(-1.81117 - 1.81117i) q^{13} +(0.861087 + 0.906733i) q^{15} +(-2.63935 + 2.63935i) q^{17} -4.84582 q^{19} +2.03799i q^{21} +(-0.648703 + 0.648703i) q^{23} +(-4.99334 - 0.258030i) q^{25} +(2.24891 + 2.24891i) q^{27} +9.19512 q^{29} +9.88551 q^{31} +(-1.85469 + 0.0116379i) q^{33} +(-5.61155 - 5.90901i) q^{35} +(7.37845 + 7.37845i) q^{37} -1.43238 q^{39} +5.37784i q^{41} +(2.39070 + 2.39070i) q^{43} +(-6.00692 - 0.155100i) q^{45} +(-2.29033 - 2.29033i) q^{47} -6.28119i q^{49} +2.08734i q^{51} +(-3.34356 + 3.34356i) q^{53} +(5.34550 - 5.14058i) q^{55} +(-1.91618 + 1.91618i) q^{57} -11.1958i q^{59} +6.46922i q^{61} +(-6.92493 - 6.92493i) q^{63} +(4.15309 - 3.94402i) q^{65} +(-0.909029 - 0.909029i) q^{67} +0.513031i q^{69} -5.95422 q^{71} +(1.99610 + 1.99610i) q^{73} +(-2.07654 + 1.87247i) q^{75} +(12.0867 - 0.0758421i) q^{77} +7.61472 q^{79} -6.28326 q^{81} +(4.50707 + 4.50707i) q^{83} +(-5.74746 - 6.05212i) q^{85} +(3.63601 - 3.63601i) q^{87} -2.85642i q^{89} +9.33455 q^{91} +(3.90901 - 3.90901i) q^{93} +(0.279684 - 10.8320i) q^{95} +(-8.73192 - 8.73192i) q^{97} +(6.26254 - 6.34163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5} - 8 q^{11} + 24 q^{15} - 28 q^{23} + 4 q^{25} - 4 q^{27} + 24 q^{31} - 12 q^{33} + 4 q^{37} - 28 q^{45} + 8 q^{47} + 24 q^{53} + 12 q^{55} - 52 q^{67} + 48 q^{71} - 24 q^{75} + 56 q^{77}+ \cdots - 36 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 - 8 * q^11 + 24 * q^15 - 28 * q^23 + 4 * q^25 - 4 * q^27 + 24 * q^31 - 12 * q^33 + 4 * q^37 - 28 * q^45 + 8 * q^47 + 24 * q^53 + 12 * q^55 - 52 * q^67 + 48 * q^71 - 24 * q^75 + 56 * q^77 - 24 * q^81 - 16 * q^91 - 76 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	0.395428	−	0.395428i	0.228301	−	0.228301i	−0.583682	−	0.811982i	$-0.698388\pi$
$3$	0.395428	−	0.395428i	0.228301	−	0.228301i	0.811982	+	0.583682i	$0.198388\pi$
$4$		0			0
$5$	−0.0577165	+	2.23532i	−0.0258116	+	0.999667i
$5$	−0.0577165	+	2.23532i	−0.0258116	+	0.999667i
$6$		0			0
$7$	−2.57694	+	2.57694i	−0.973990	+	0.973990i	−0.999670	−	0.0256803i	$-0.991825\pi$
$7$	−2.57694	+	2.57694i	−0.973990	+	0.973990i	0.0256803	+	0.999670i	$0.491825\pi$
$8$		0			0
$9$			2.68727i			0.895758i
$10$		0			0
$11$	−2.35988	−	2.33045i	−0.711530	−	0.702656i
$11$	−2.35988	−	2.33045i	−0.711530	−	0.702656i
$12$		0			0
$13$	−1.81117	−	1.81117i	−0.502329	−	0.502329i	0.409832	−	0.912161i	$-0.365587\pi$
$13$	−1.81117	−	1.81117i	−0.502329	−	0.502329i	−0.912161	+	0.409832i	$0.865587\pi$
$14$		0			0
$15$	0.861087	+	0.906733i	0.222332	+	0.234117i
$16$		0			0
$17$	−2.63935	+	2.63935i	−0.640135	+	0.640135i	−0.950589	−	0.310453i	$-0.899519\pi$
$17$	−2.63935	+	2.63935i	−0.640135	+	0.640135i	0.310453	+	0.950589i	$0.399519\pi$
$18$		0			0
$19$	−4.84582			−1.11171			−0.555854	−	0.831280i	$-0.687609\pi$
$19$	−4.84582			−1.11171			−0.555854	+	0.831280i	$0.687609\pi$
$20$		0			0
$21$			2.03799i			0.444725i
$22$		0			0
$23$	−0.648703	+	0.648703i	−0.135264	+	0.135264i	−0.771497	−	0.636233i	$-0.780492\pi$
$23$	−0.648703	+	0.648703i	−0.135264	+	0.135264i	0.636233	+	0.771497i	$0.280492\pi$
$24$		0			0
$25$	−4.99334	−	0.258030i	−0.998668	−	0.0516060i
$26$		0			0
$27$	2.24891	+	2.24891i	0.432803	+	0.432803i
$28$		0			0
$29$	9.19512			1.70749			0.853746	−	0.520690i	$-0.174325\pi$
$29$	9.19512			1.70749			0.853746	+	0.520690i	$0.174325\pi$
$30$		0			0
$31$	9.88551			1.77549			0.887745	−	0.460335i	$-0.152271\pi$
$31$	9.88551			1.77549			0.887745	+	0.460335i	$0.152271\pi$
$32$		0			0
$33$	−1.85469	+	0.0116379i	−0.322859	+	0.00202590i
$34$		0			0
$35$	−5.61155	−	5.90901i	−0.948525	−	0.998806i
$36$		0			0
$37$	7.37845	+	7.37845i	1.21301	+	1.21301i	0.970032	+	0.242978i	$0.0781242\pi$
$37$	7.37845	+	7.37845i	1.21301	+	1.21301i	0.242978	+	0.970032i	$0.421876\pi$
$38$		0			0
$39$	−1.43238			−0.229364
$40$		0			0
$41$			5.37784i			0.839877i	0.907553	+	0.419939i	$0.137948\pi$
$41$			5.37784i			0.839877i	−0.907553	+	0.419939i	$0.862052\pi$
$42$		0			0
$43$	2.39070	+	2.39070i	0.364578	+	0.364578i	0.865495	−	0.500917i	$-0.167004\pi$
$43$	2.39070	+	2.39070i	0.364578	+	0.364578i	−0.500917	+	0.865495i	$0.667004\pi$
$44$		0			0
$45$	−6.00692	−	0.155100i	−0.895459	−	0.0231209i
$46$		0			0
$47$	−2.29033	−	2.29033i	−0.334079	−	0.334079i	0.520054	−	0.854133i	$-0.325912\pi$
$47$	−2.29033	−	2.29033i	−0.334079	−	0.334079i	−0.854133	+	0.520054i	$0.825912\pi$
$48$		0			0
$49$		−	6.28119i		−	0.897313i
$50$		0			0
$51$			2.08734i			0.292287i
$52$		0			0
$53$	−3.34356	+	3.34356i	−0.459274	+	0.459274i	−0.898417	−	0.439143i	$-0.855282\pi$
$53$	−3.34356	+	3.34356i	−0.459274	+	0.459274i	0.439143	+	0.898417i	$0.355282\pi$
$54$		0			0
$55$	5.34550	−	5.14058i	0.720788	−	0.693156i
$56$		0			0
$57$	−1.91618	+	1.91618i	−0.253804	+	0.253804i
$58$		0			0
$59$		−	11.1958i		−	1.45757i	−0.684742	−	0.728786i	$-0.740085\pi$
$59$		−	11.1958i		−	1.45757i	0.684742	−	0.728786i	$-0.259915\pi$
$60$		0			0
$61$			6.46922i			0.828299i	0.910209	+	0.414149i	$0.135921\pi$
$61$			6.46922i			0.828299i	−0.910209	+	0.414149i	$0.864079\pi$
$62$		0			0
$63$	−6.92493	−	6.92493i	−0.872459	−	0.872459i
$64$		0			0
$65$	4.15309	−	3.94402i	0.515128	−	0.489196i
$66$		0			0
$67$	−0.909029	−	0.909029i	−0.111056	−	0.111056i	0.649395	−	0.760451i	$-0.275022\pi$
$67$	−0.909029	−	0.909029i	−0.111056	−	0.111056i	−0.760451	+	0.649395i	$0.775022\pi$
$68$		0			0
$69$			0.513031i			0.0617616i
$70$		0			0
$71$	−5.95422			−0.706636			−0.353318	−	0.935503i	$-0.614947\pi$
$71$	−5.95422			−0.706636			−0.353318	+	0.935503i	$0.614947\pi$
$72$		0			0
$73$	1.99610	+	1.99610i	0.233626	+	0.233626i	0.814205	−	0.580578i	$-0.197173\pi$
$73$	1.99610	+	1.99610i	0.233626	+	0.233626i	−0.580578	+	0.814205i	$0.697173\pi$
$74$		0			0
$75$	−2.07654	+	1.87247i	−0.239778	+	0.216215i
$76$		0			0
$77$	12.0867	−	0.0758421i	1.37740	−	0.00864301i
$78$		0			0
$79$	7.61472			0.856723			0.428361	−	0.903608i	$-0.359091\pi$
$79$	7.61472			0.856723			0.428361	+	0.903608i	$0.359091\pi$
$80$		0			0
$81$	−6.28326			−0.698139
$82$		0			0
$83$	4.50707	+	4.50707i	0.494716	+	0.494716i	0.909788	−	0.415073i	$-0.136244\pi$
$83$	4.50707	+	4.50707i	0.494716	+	0.494716i	−0.415073	+	0.909788i	$0.636244\pi$
$84$		0			0
$85$	−5.74746	−	6.05212i	−0.623399	−	0.656445i
$86$		0			0
$87$	3.63601	−	3.63601i	0.389821	−	0.389821i
$88$		0			0
$89$		−	2.85642i		−	0.302780i	−0.988474	−	0.151390i	$-0.951625\pi$
$89$		−	2.85642i		−	0.302780i	0.988474	−	0.151390i	$-0.0483749\pi$
$90$		0			0
$91$	9.33455			0.978527
$92$		0			0
$93$	3.90901	−	3.90901i	0.405346	−	0.405346i
$94$		0			0
$95$	0.279684	−	10.8320i	0.0286949	−	1.11134i
$96$		0			0
$97$	−8.73192	−	8.73192i	−0.886592	−	0.886592i	0.107602	−	0.994194i	$-0.465683\pi$
$97$	−8.73192	−	8.73192i	−0.886592	−	0.886592i	−0.994194	+	0.107602i	$0.965683\pi$
$98$		0			0
$99$	6.26254	−	6.34163i	0.629409	−	0.637358i
$100$		0			0
$101$		−	10.9116i		−	1.08574i	−0.839816	−	0.542871i	$-0.817337\pi$
$101$		−	10.9116i		−	1.08574i	0.839816	−	0.542871i	$-0.182663\pi$
$102$		0			0
$103$	−11.2923	+	11.2923i	−1.11267	+	1.11267i	−0.119877	+	0.992789i	$0.538250\pi$
$103$	−11.2923	+	11.2923i	−1.11267	+	1.11267i	−0.992789	+	0.119877i	$0.961750\pi$
$104$		0			0
$105$	−4.55556	−	0.117625i	−0.444577	−	0.0114791i
$106$		0			0
$107$	−10.0693	+	10.0693i	−0.973433	+	0.973433i	−0.999656	−	0.0262235i	$-0.991652\pi$
$107$	−10.0693	+	10.0693i	−0.973433	+	0.973433i	0.0262235	+	0.999656i	$0.491652\pi$
$108$		0			0
$109$	20.1342			1.92851			0.964254	−	0.264979i	$-0.0853652\pi$
$109$	20.1342			1.92851			0.964254	+	0.264979i	$0.0853652\pi$
$110$		0			0
$111$	5.83530			0.553862
$112$		0			0
$113$	1.80030	−	1.80030i	0.169358	−	0.169358i	−0.617339	−	0.786697i	$-0.711789\pi$
$113$	1.80030	−	1.80030i	0.169358	−	0.169358i	0.786697	+	0.617339i	$0.211789\pi$
$114$		0			0
$115$	−1.41262	−	1.48750i	−0.131727	−	0.138710i
$116$		0			0
$117$	4.86712	−	4.86712i	0.449965	−	0.449965i
$118$		0			0
$119$		−	13.6028i		−	1.24697i
$120$		0			0
$121$	0.138042	+	10.9991i	0.0125492	+	0.999921i
$122$		0			0
$123$	2.12655	+	2.12655i	0.191744	+	0.191744i
$124$		0			0
$125$	0.864978	−	11.1468i	0.0773660	−	0.997003i
$126$		0			0
$127$	−6.52447	+	6.52447i	−0.578953	+	0.578953i	−0.934615	−	0.355662i	$-0.884256\pi$
$127$	−6.52447	+	6.52447i	−0.578953	+	0.578953i	0.355662	+	0.934615i	$0.384256\pi$
$128$		0			0
$129$	1.89070			0.166467
$130$		0			0
$131$		−	2.86084i		−	0.249952i	−0.992160	−	0.124976i	$-0.960115\pi$
$131$		−	2.86084i		−	0.249952i	0.992160	−	0.124976i	$-0.0398855\pi$
$132$		0			0
$133$	12.4874	−	12.4874i	1.08279	−	1.08279i
$134$		0			0
$135$	−5.15684	+	4.89724i	−0.443830	+	0.421487i
$136$		0			0
$137$	0.844340	+	0.844340i	0.0721368	+	0.0721368i	0.742255	−	0.670118i	$-0.233756\pi$
$137$	0.844340	+	0.844340i	0.0721368	+	0.0721368i	−0.670118	+	0.742255i	$0.733756\pi$
$138$		0			0
$139$	16.5684			1.40532			0.702658	−	0.711528i	$-0.251996\pi$
$139$	16.5684			1.40532			0.702658	+	0.711528i	$0.251996\pi$
$140$		0			0
$141$	−1.81132			−0.152541
$142$		0			0
$143$	0.0533049	+	8.49499i	0.00445758	+	0.710386i
$144$		0			0
$145$	−0.530710	+	20.5541i	−0.0440730	+	1.70692i
$146$		0			0
$147$	−2.48376	−	2.48376i	−0.204857	−	0.204857i
$148$		0			0
$149$	−14.7385			−1.20743			−0.603713	−	0.797202i	$-0.706313\pi$
$149$	−14.7385			−1.20743			−0.603713	+	0.797202i	$0.706313\pi$
$150$		0			0
$151$			14.5028i			1.18022i	0.807321	+	0.590112i	$0.200917\pi$
$151$			14.5028i			1.18022i	−0.807321	+	0.590112i	$0.799083\pi$
$152$		0			0
$153$	−7.09264	−	7.09264i	−0.573406	−	0.573406i
$154$		0			0
$155$	−0.570557	+	22.0973i	−0.0458282	+	1.77490i
$156$		0			0
$157$	9.02952	+	9.02952i	0.720634	+	0.720634i	0.968734	−	0.248100i	$-0.0798062\pi$
$157$	9.02952	+	9.02952i	0.720634	+	0.720634i	−0.248100	+	0.968734i	$0.579806\pi$
$158$		0			0
$159$			2.64428i			0.209705i
$160$		0			0
$161$		−	3.34333i		−	0.263491i
$162$		0			0
$163$	5.48598	−	5.48598i	0.429695	−	0.429695i	−0.458829	−	0.888524i	$-0.651731\pi$
$163$	5.48598	−	5.48598i	0.429695	−	0.429695i	0.888524	+	0.458829i	$0.151731\pi$
$164$		0			0
$165$	0.0810314	−	4.14649i	0.00630829	−	0.322804i
$166$		0			0
$167$	−7.46180	+	7.46180i	−0.577411	+	0.577411i	−0.934189	−	0.356778i	$-0.883875\pi$
$167$	−7.46180	+	7.46180i	−0.577411	+	0.577411i	0.356778	+	0.934189i	$0.383875\pi$
$168$		0			0
$169$		−	6.43931i		−	0.495331i
$170$		0			0
$171$		−	13.0221i		−	0.995821i
$172$		0			0
$173$	−18.2946	−	18.2946i	−1.39091	−	1.39091i	−0.823288	−	0.567624i	$-0.807863\pi$
$173$	−18.2946	−	18.2946i	−1.39091	−	1.39091i	−0.567624	−	0.823288i	$-0.692137\pi$
$174$		0			0
$175$	13.5324	−	12.2026i	1.02296	−	0.922428i
$176$		0			0
$177$	−4.42714	−	4.42714i	−0.332764	−	0.332764i
$178$		0			0
$179$		−	2.61564i		−	0.195502i	−0.995211	−	0.0977510i	$-0.968835\pi$
$179$		−	2.61564i		−	0.195502i	0.995211	−	0.0977510i	$-0.0311649\pi$
$180$		0			0
$181$	13.1841			0.979967			0.489983	−	0.871732i	$-0.337003\pi$
$181$	13.1841			0.979967			0.489983	+	0.871732i	$0.337003\pi$
$182$		0			0
$183$	2.55811	+	2.55811i	0.189101	+	0.189101i
$184$		0			0
$185$	−16.9191	+	16.0674i	−1.24392	+	1.18130i
$186$		0			0
$187$	12.3794	−	0.0776789i	0.905270	−	0.00568045i
$188$		0			0
$189$	−11.5906			−0.843091
$190$		0			0
$191$	6.10951			0.442069			0.221034	−	0.975266i	$-0.429057\pi$
$191$	6.10951			0.442069			0.221034	+	0.975266i	$0.429057\pi$
$192$		0			0
$193$	−10.8980	−	10.8980i	−0.784458	−	0.784458i	0.196122	−	0.980580i	$-0.437165\pi$
$193$	−10.8980	−	10.8980i	−0.784458	−	0.784458i	−0.980580	+	0.196122i	$0.937165\pi$
$194$		0			0
$195$	0.0826718	−	3.20183i	0.00592025	−	0.229288i
$196$		0			0
$197$	3.06310	−	3.06310i	0.218237	−	0.218237i	−0.589518	−	0.807755i	$-0.700682\pi$
$197$	3.06310	−	3.06310i	0.218237	−	0.218237i	0.807755	+	0.589518i	$0.200682\pi$
$198$		0			0
$199$			7.73120i			0.548050i	0.961722	+	0.274025i	$0.0883552\pi$
$199$			7.73120i			0.548050i	−0.961722	+	0.274025i	$0.911645\pi$
$200$		0			0
$201$	−0.718911			−0.0507081
$202$		0			0
$203$	−23.6952	+	23.6952i	−1.66308	+	1.66308i
$204$		0			0
$205$	−12.0212	−	0.310390i	−0.839597	−	0.0216786i
$206$		0			0
$207$	−1.74324	−	1.74324i	−0.121164	−	0.121164i
$208$		0			0
$209$	11.4355	+	11.2929i	0.791014	+	0.781148i
$210$		0			0
$211$			10.1385i			0.697962i	0.937130	+	0.348981i	$0.113472\pi$
$211$			10.1385i			0.697962i	−0.937130	+	0.348981i	$0.886528\pi$
$212$		0			0
$213$	−2.35447	+	2.35447i	−0.161326	+	0.161326i
$214$		0			0
$215$	−5.48197	+	5.20600i	−0.373867	+	0.355046i
$216$		0			0
$217$	−25.4743	+	25.4743i	−1.72931	+	1.72931i
$218$		0			0
$219$	1.57863			0.106674
$220$		0			0
$221$	9.56062			0.643117
$222$		0			0
$223$	4.06971	−	4.06971i	0.272528	−	0.272528i	−0.557589	−	0.830117i	$-0.688274\pi$
$223$	4.06971	−	4.06971i	0.272528	−	0.272528i	0.830117	+	0.557589i	$0.188274\pi$
$224$		0			0
$225$	0.693397	−	13.4185i	0.0462264	−	0.894564i
$226$		0			0
$227$	−5.82126	+	5.82126i	−0.386370	+	0.386370i	−0.873391	−	0.487020i	$-0.838084\pi$
$227$	−5.82126	+	5.82126i	−0.386370	+	0.386370i	0.487020	+	0.873391i	$0.338084\pi$
$228$		0			0
$229$			11.7765i			0.778212i	0.921193	+	0.389106i	$0.127216\pi$
$229$			11.7765i			0.778212i	−0.921193	+	0.389106i	$0.872784\pi$
$230$		0			0
$231$	4.74942	−	4.80940i	0.312489	−	0.316435i
$232$		0			0
$233$	2.29149	+	2.29149i	0.150121	+	0.150121i	0.778172	−	0.628051i	$-0.216147\pi$
$233$	2.29149	+	2.29149i	0.150121	+	0.150121i	−0.628051	+	0.778172i	$0.716147\pi$
$234$		0			0
$235$	5.25182	−	4.98744i	0.342591	−	0.325345i
$236$		0			0
$237$	3.01107	−	3.01107i	0.195590	−	0.195590i
$238$		0			0
$239$	−17.2852			−1.11809			−0.559043	−	0.829138i	$-0.688831\pi$
$239$	−17.2852			−1.11809			−0.559043	+	0.829138i	$0.688831\pi$
$240$		0			0
$241$		−	0.971908i		−	0.0626061i	−0.999510	−	0.0313030i	$-0.990034\pi$
$241$		−	0.971908i		−	0.0626061i	0.999510	−	0.0313030i	$-0.00996570\pi$
$242$		0			0
$243$	−9.23130	+	9.23130i	−0.592188	+	0.592188i
$244$		0			0
$245$	14.0405	+	0.362528i	0.897014	+	0.0231611i
$246$		0			0
$247$	8.77663	+	8.77663i	0.558443	+	0.558443i
$248$		0			0
$249$	3.56445			0.225888
$250$		0			0
$251$	−7.96516			−0.502756			−0.251378	−	0.967889i	$-0.580884\pi$
$251$	−7.96516			−0.502756			−0.251378	+	0.967889i	$0.580884\pi$
$252$		0			0
$253$	3.04263	−	0.0190921i	0.191288	−	0.00120031i
$254$		0			0
$255$	−4.66589	−	0.120474i	−0.292189	−	0.00754438i
$256$		0			0
$257$	7.86800	+	7.86800i	0.490792	+	0.490792i	0.908556	−	0.417764i	$-0.137186\pi$
$257$	7.86800	+	7.86800i	0.490792	+	0.490792i	−0.417764	+	0.908556i	$0.637186\pi$
$258$		0			0
$259$	−38.0276			−2.36292
$260$		0			0
$261$			24.7098i			1.52950i
$262$		0			0
$263$	17.0117	+	17.0117i	1.04899	+	1.04899i	0.998737	+	0.0502505i	$0.0160020\pi$
$263$	17.0117	+	17.0117i	1.04899	+	1.04899i	0.0502505	+	0.998737i	$0.483998\pi$
$264$		0			0
$265$	−7.28097	−	7.66692i	−0.447266	−	0.470975i
$266$		0			0
$267$	−1.12951	−	1.12951i	−0.0691249	−	0.0691249i
$268$		0			0
$269$		−	8.80868i		−	0.537074i	−0.963269	−	0.268537i	$-0.913460\pi$
$269$		−	8.80868i		−	0.537074i	0.963269	−	0.268537i	$-0.0865402\pi$
$270$		0			0
$271$			6.56619i			0.398868i	0.979911	+	0.199434i	$0.0639103\pi$
$271$			6.56619i			0.398868i	−0.979911	+	0.199434i	$0.936090\pi$
$272$		0			0
$273$	3.69115	−	3.69115i	0.223398	−	0.223398i
$274$		0			0
$275$	11.1823	+	12.2456i	0.674320	+	0.738439i
$276$		0			0
$277$	20.8316	−	20.8316i	1.25165	−	1.25165i	0.296673	−	0.954979i	$-0.404123\pi$
$277$	20.8316	−	20.8316i	1.25165	−	1.25165i	0.954979	−	0.296673i	$-0.0958771\pi$
$278$		0			0
$279$			26.5651i			1.59041i
$280$		0			0
$281$		−	17.2721i		−	1.03037i	−0.857080	−	0.515183i	$-0.827724\pi$
$281$		−	17.2721i		−	1.03037i	0.857080	−	0.515183i	$-0.172276\pi$
$282$		0			0
$283$	7.15505	+	7.15505i	0.425324	+	0.425324i	0.887032	−	0.461708i	$-0.152763\pi$
$283$	7.15505	+	7.15505i	0.425324	+	0.425324i	−0.461708	+	0.887032i	$0.652763\pi$
$284$		0			0
$285$	−4.17268	−	4.39387i	−0.247168	−	0.260270i
$286$		0			0
$287$	−13.8583	−	13.8583i	−0.818032	−	0.818032i
$288$		0			0
$289$			3.06771i			0.180453i
$290$		0			0
$291$	−6.90569			−0.404819
$292$		0			0
$293$	−0.0672710	−	0.0672710i	−0.00393001	−	0.00393001i	0.705139	−	0.709069i	$-0.250885\pi$
$293$	−0.0672710	−	0.0672710i	−0.00393001	−	0.00393001i	−0.709069	+	0.705139i	$0.750885\pi$
$294$		0			0
$295$	25.0263	+	0.646183i	1.45709	+	0.0376222i
$296$		0			0
$297$	−0.0661879	−	10.5481i	−0.00384061	−	0.612063i
$298$		0			0
$299$	2.34983			0.135894
$300$		0			0
$301$	−12.3214			−0.710191
$302$		0			0
$303$	−4.31475	−	4.31475i	−0.247876	−	0.247876i
$304$		0			0
$305$	−14.4608	−	0.373380i	−0.828023	−	0.0213797i
$306$		0			0
$307$	17.5587	−	17.5587i	1.00213	−	1.00213i	0.00212927	−	0.999998i	$-0.499322\pi$
$307$	17.5587	−	17.5587i	1.00213	−	1.00213i	0.999998	−	0.00212927i	$-0.000677768\pi$
$308$		0			0
$309$			8.93061i			0.508045i
$310$		0			0
$311$	−22.9373			−1.30065			−0.650326	−	0.759655i	$-0.725368\pi$
$311$	−22.9373			−1.30065			−0.650326	+	0.759655i	$0.725368\pi$
$312$		0			0
$313$	14.0106	−	14.0106i	0.791925	−	0.791925i	−0.189882	−	0.981807i	$-0.560811\pi$
$313$	14.0106	−	14.0106i	0.791925	−	0.791925i	0.981807	+	0.189882i	$0.0608106\pi$
$314$		0			0
$315$	15.8791	−	15.0798i	0.894688	−	0.849649i
$316$		0			0
$317$	19.1316	+	19.1316i	1.07454	+	1.07454i	0.996988	+	0.0775510i	$0.0247101\pi$
$317$	19.1316	+	19.1316i	1.07454	+	1.07454i	0.0775510	+	0.996988i	$0.475290\pi$
$318$		0			0
$319$	−21.6994	−	21.4287i	−1.21493	−	1.19978i
$320$		0			0
$321$			7.96334i			0.444471i
$322$		0			0
$323$	12.7898	−	12.7898i	0.711644	−	0.711644i
$324$		0			0
$325$	8.57646	+	9.51113i	0.475736	+	0.527583i
$326$		0			0
$327$	7.96164	−	7.96164i	0.440280	−	0.440280i
$328$		0			0
$329$	11.8041			0.650779
$330$		0			0
$331$	2.47486			0.136031			0.0680153	−	0.997684i	$-0.478333\pi$
$331$	2.47486			0.136031			0.0680153	+	0.997684i	$0.478333\pi$
$332$		0			0
$333$	−19.8279	+	19.8279i	−1.08656	+	1.08656i
$334$		0			0
$335$	2.08444	−	1.97951i	0.113885	−	0.108152i
$336$		0			0
$337$	−9.40834	+	9.40834i	−0.512505	+	0.512505i	−0.915293	−	0.402788i	$-0.868041\pi$
$337$	−9.40834	+	9.40834i	−0.512505	+	0.512505i	0.402788	+	0.915293i	$0.368041\pi$
$338$		0			0
$339$		−	1.42378i		−	0.0773291i
$340$		0			0
$341$	−23.3286	−	23.0377i	−1.26331	−	1.24756i
$342$		0			0
$343$	−1.85233	−	1.85233i	−0.100016	−	0.100016i
$344$		0			0
$345$	−1.14679	−	0.0296103i	−0.0617411	−	0.00159417i
$346$		0			0
$347$	−4.53292	+	4.53292i	−0.243340	+	0.243340i	−0.818230	−	0.574891i	$-0.805045\pi$
$347$	−4.53292	+	4.53292i	−0.243340	+	0.243340i	0.574891	+	0.818230i	$0.305045\pi$
$348$		0			0
$349$	6.49260			0.347541			0.173770	−	0.984786i	$-0.444405\pi$
$349$	6.49260			0.347541			0.173770	+	0.984786i	$0.444405\pi$
$350$		0			0
$351$		−	8.14632i		−	0.434819i
$352$		0			0
$353$	10.9322	−	10.9322i	0.581860	−	0.581860i	−0.353554	−	0.935414i	$-0.615027\pi$
$353$	10.9322	−	10.9322i	0.581860	−	0.581860i	0.935414	+	0.353554i	$0.115027\pi$
$354$		0			0
$355$	0.343657	−	13.3096i	0.0182394	−	0.706401i
$356$		0			0
$357$	−5.37895	−	5.37895i	−0.284684	−	0.284684i
$358$		0			0
$359$	28.2077			1.48875			0.744373	−	0.667764i	$-0.232749\pi$
$359$	28.2077			1.48875			0.744373	+	0.667764i	$0.232749\pi$
$360$		0			0
$361$	4.48201			0.235895
$362$		0			0
$363$	4.40395	+	4.29478i	0.231148	+	0.225418i
$364$		0			0
$365$	−4.57715	+	4.34673i	−0.239579	+	0.227518i
$366$		0			0
$367$	2.28005	+	2.28005i	0.119018	+	0.119018i	0.764107	−	0.645089i	$-0.223180\pi$
$367$	2.28005	+	2.28005i	0.119018	+	0.119018i	−0.645089	+	0.764107i	$0.723180\pi$
$368$		0			0
$369$	−14.4517			−0.752326
$370$		0			0
$371$		−	17.2323i		−	0.894656i
$372$		0			0
$373$	18.0890	+	18.0890i	0.936613	+	0.936613i	0.998107	−	0.0614946i	$-0.0195867\pi$
$373$	18.0890	+	18.0890i	0.936613	+	0.936613i	−0.0614946	+	0.998107i	$0.519587\pi$
$374$		0			0
$375$	−4.06573	−	4.74981i	−0.209954	−	0.245279i
$376$		0			0
$377$	−16.6540	−	16.6540i	−0.857722	−	0.857722i
$378$		0			0
$379$			17.3714i			0.892310i	0.894956	+	0.446155i	$0.147207\pi$
$379$			17.3714i			0.892310i	−0.894956	+	0.446155i	$0.852793\pi$
$380$		0			0
$381$			5.15992i			0.264351i
$382$		0			0
$383$	19.3670	−	19.3670i	0.989607	−	0.989607i	−0.0103394	−	0.999947i	$-0.503291\pi$
$383$	19.3670	−	19.3670i	0.989607	−	0.989607i	0.999947	+	0.0103394i	$0.00329118\pi$
$384$		0			0
$385$	−0.528067	+	27.0220i	−0.0269128	+	1.37717i
$386$		0			0
$387$	−6.42446	+	6.42446i	−0.326574	+	0.326574i
$388$		0			0
$389$		−	2.40286i		−	0.121830i	−0.998143	−	0.0609149i	$-0.980598\pi$
$389$		−	2.40286i		−	0.121830i	0.998143	−	0.0609149i	$-0.0194018\pi$
$390$		0			0
$391$		−	3.42430i		−	0.173174i
$392$		0			0
$393$	−1.13126	−	1.13126i	−0.0570643	−	0.0570643i
$394$		0			0
$395$	−0.439495	+	17.0214i	−0.0221134	+	0.856437i
$396$		0			0
$397$	−5.43031	−	5.43031i	−0.272539	−	0.272539i	0.557582	−	0.830122i	$-0.311729\pi$
$397$	−5.43031	−	5.43031i	−0.272539	−	0.272539i	−0.830122	+	0.557582i	$0.811729\pi$
$398$		0			0
$399$		−	9.87572i		−	0.494404i
$400$		0			0
$401$	−5.18454			−0.258903			−0.129452	−	0.991586i	$-0.541322\pi$
$401$	−5.18454			−0.258903			−0.129452	+	0.991586i	$0.541322\pi$
$402$		0			0
$403$	−17.9044	−	17.9044i	−0.891880	−	0.891880i
$404$		0			0
$405$	0.362647	−	14.0451i	0.0180201	−	0.697907i
$406$		0			0
$407$	−0.217156	−	34.6073i	−0.0107640	−	1.71542i
$408$		0			0
$409$	−8.58105			−0.424306			−0.212153	−	0.977237i	$-0.568047\pi$
$409$	−8.58105			−0.424306			−0.212153	+	0.977237i	$0.568047\pi$
$410$		0			0
$411$	0.667752			0.0329378
$412$		0			0
$413$	28.8509	+	28.8509i	1.41966	+	1.41966i
$414$		0			0
$415$	−10.3349	+	9.81463i	−0.507320	+	0.481781i
$416$		0			0
$417$	6.55163	−	6.55163i	0.320835	−	0.320835i
$418$		0			0
$419$		−	6.16560i		−	0.301209i	−0.988594	−	0.150605i	$-0.951878\pi$
$419$		−	6.16560i		−	0.301209i	0.988594	−	0.150605i	$-0.0481220\pi$
$420$		0			0
$421$	−15.5610			−0.758398			−0.379199	−	0.925315i	$-0.623800\pi$
$421$	−15.5610			−0.758398			−0.379199	+	0.925315i	$0.623800\pi$
$422$		0			0
$423$	6.15474	−	6.15474i	0.299254	−	0.299254i
$424$		0			0
$425$	13.8602	−	12.4981i	0.672317	−	0.606248i
$426$		0			0
$427$	−16.6708	−	16.6708i	−0.806755	−	0.806755i
$428$		0			0
$429$	3.38024	+	3.33808i	0.163199	+	0.161164i
$430$		0			0
$431$		−	23.0868i		−	1.11205i	−0.831165	−	0.556026i	$-0.812325\pi$
$431$		−	23.0868i		−	1.11205i	0.831165	−	0.556026i	$-0.187675\pi$
$432$		0			0
$433$	9.07268	−	9.07268i	0.436005	−	0.436005i	−0.454660	−	0.890665i	$-0.650239\pi$
$433$	9.07268	−	9.07268i	0.436005	−	0.436005i	0.890665	+	0.454660i	$0.150239\pi$
$434$		0			0
$435$	7.91780	+	8.33752i	0.379630	+	0.399753i
$436$		0			0
$437$	3.14350	−	3.14350i	0.150374	−	0.150374i
$438$		0			0
$439$	1.80353			0.0860779			0.0430390	−	0.999073i	$-0.486296\pi$
$439$	1.80353			0.0860779			0.0430390	+	0.999073i	$0.486296\pi$
$440$		0			0
$441$	16.8793			0.803775
$442$		0			0
$443$	22.8468	−	22.8468i	1.08549	−	1.08549i	0.0894981	−	0.995987i	$-0.471474\pi$
$443$	22.8468	−	22.8468i	1.08549	−	1.08549i	0.995987	−	0.0894981i	$-0.0285263\pi$
$444$		0			0
$445$	6.38502	+	0.164862i	0.302679	+	0.00781523i
$446$		0			0
$447$	−5.82802	+	5.82802i	−0.275656	+	0.275656i
$448$		0			0
$449$			32.1905i			1.51916i	0.650413	+	0.759581i	$0.274596\pi$
$449$			32.1905i			1.51916i	−0.650413	+	0.759581i	$0.725404\pi$
$450$		0			0
$451$	12.5328	−	12.6910i	0.590145	−	0.597598i
$452$		0			0
$453$	5.73483	+	5.73483i	0.269446	+	0.269446i
$454$		0			0
$455$	−0.538757	+	20.8657i	−0.0252573	+	0.978201i
$456$		0			0
$457$	10.7891	−	10.7891i	0.504691	−	0.504691i	−0.408201	−	0.912892i	$-0.633844\pi$
$457$	10.7891	−	10.7891i	0.504691	−	0.504691i	0.912892	+	0.408201i	$0.133844\pi$
$458$		0			0
$459$	−11.8713			−0.554105
$460$		0			0
$461$		−	0.553181i		−	0.0257642i	−0.999917	−	0.0128821i	$-0.995899\pi$
$461$		−	0.553181i		−	0.0257642i	0.999917	−	0.0128821i	$-0.00410061\pi$
$462$		0			0
$463$	−17.8695	+	17.8695i	−0.830468	+	0.830468i	−0.987581	−	0.157112i	$-0.949782\pi$
$463$	−17.8695	+	17.8695i	−0.830468	+	0.830468i	0.157112	+	0.987581i	$0.449782\pi$
$464$		0			0
$465$	8.51229	+	8.96352i	0.394748	+	0.415673i
$466$		0			0
$467$	3.56303	+	3.56303i	0.164877	+	0.164877i	0.784723	−	0.619846i	$-0.212805\pi$
$467$	3.56303	+	3.56303i	0.164877	+	0.164877i	−0.619846	+	0.784723i	$0.712805\pi$
$468$		0			0
$469$	4.68502			0.216334
$470$		0			0
$471$	7.14106			0.329043
$472$		0			0
$473$	−0.0703610	−	11.2132i	−0.00323520	−	0.515581i
$474$		0			0
$475$	24.1968	+	1.25037i	1.11023	+	0.0573708i
$476$		0			0
$477$	−8.98507	−	8.98507i	−0.411398	−	0.411398i
$478$		0			0
$479$	−9.40996			−0.429952			−0.214976	−	0.976619i	$-0.568967\pi$
$479$	−9.40996			−0.429952			−0.214976	+	0.976619i	$0.568967\pi$
$480$		0			0
$481$		−	26.7273i		−	1.21866i
$482$		0			0
$483$	−1.32205	−	1.32205i	−0.0601552	−	0.0601552i
$484$		0			0
$485$	20.0226	−	19.0147i	0.909181	−	0.863412i
$486$		0			0
$487$	−1.73414	−	1.73414i	−0.0785816	−	0.0785816i	0.666724	−	0.745305i	$-0.267696\pi$
$487$	−1.73414	−	1.73414i	−0.0785816	−	0.0785816i	−0.745305	+	0.666724i	$0.767696\pi$
$488$		0			0
$489$		−	4.33862i		−	0.196199i
$490$		0			0
$491$			17.3458i			0.782807i	0.920219	+	0.391403i	$0.128010\pi$
$491$			17.3458i			0.782807i	−0.920219	+	0.391403i	$0.871990\pi$
$492$		0			0
$493$	−24.2691	+	24.2691i	−1.09303	+	1.09303i
$494$		0			0
$495$	13.8141	+	14.3648i	0.620900	+	0.645651i
$496$		0			0
$497$	15.3436	−	15.3436i	0.688257	−	0.688257i
$498$		0			0
$499$		−	10.3889i		−	0.465071i	−0.972588	−	0.232536i	$-0.925298\pi$
$499$		−	10.3889i		−	0.465071i	0.972588	−	0.232536i	$-0.0747023\pi$
$500$		0			0
$501$			5.90121i			0.263647i
$502$		0			0
$503$	−3.91147	−	3.91147i	−0.174404	−	0.174404i	0.614507	−	0.788911i	$-0.289355\pi$
$503$	−3.91147	−	3.91147i	−0.174404	−	0.174404i	−0.788911	+	0.614507i	$0.789355\pi$
$504$		0			0
$505$	24.3909	+	0.629778i	1.08538	+	0.0280247i
$506$		0			0
$507$	−2.54628	−	2.54628i	−0.113084	−	0.113084i
$508$		0			0
$509$		−	2.44868i		−	0.108536i	−0.998526	−	0.0542680i	$-0.982717\pi$
$509$		−	2.44868i		−	0.108536i	0.998526	−	0.0542680i	$-0.0172825\pi$
$510$		0			0
$511$	−10.2877			−0.455099
$512$		0			0
$513$	−10.8978	−	10.8978i	−0.481150	−	0.481150i
$514$		0			0
$515$	−24.5902	−	25.8938i	−1.08358	−	1.14102i
$516$		0			0
$517$	0.0674070	+	10.7424i	0.00296456	+	0.472450i
$518$		0			0
$519$	−14.4684			−0.635092
$520$		0			0
$521$	−7.52889			−0.329847			−0.164923	−	0.986306i	$-0.552738\pi$
$521$	−7.52889			−0.329847			−0.164923	+	0.986306i	$0.552738\pi$
$522$		0			0
$523$	20.8756	+	20.8756i	0.912826	+	0.912826i	0.996494	−	0.0836673i	$-0.0266633\pi$
$523$	20.8756	+	20.8756i	0.912826	+	0.912826i	−0.0836673	+	0.996494i	$0.526663\pi$
$524$		0			0
$525$	0.525861	−	10.1764i	0.0229505	−	0.444132i
$526$		0			0
$527$	−26.0913	+	26.0913i	−1.13655	+	1.13655i
$528$		0			0
$529$			22.1584i			0.963407i
$530$		0			0
$531$	30.0862			1.30563
$532$		0			0
$533$	9.74020	−	9.74020i	0.421895	−	0.421895i
$534$		0			0
$535$	−21.9269	−	23.0892i	−0.947982	−	0.998234i
$536$		0			0
$537$	−1.03430	−	1.03430i	−0.0446332	−	0.0446332i
$538$		0			0
$539$	−14.6380	+	14.8228i	−0.630502	+	0.638465i
$540$		0			0
$541$			4.59976i			0.197759i	0.995099	+	0.0988795i	$0.0315258\pi$
$541$			4.59976i			0.197759i	−0.995099	+	0.0988795i	$0.968474\pi$
$542$		0			0
$543$	5.21337	−	5.21337i	0.223727	−	0.223727i
$544$		0			0
$545$	−1.16208	+	45.0065i	−0.0497778	+	1.92787i
$546$		0			0
$547$	−2.64220	+	2.64220i	−0.112972	+	0.112972i	−0.761333	−	0.648361i	$-0.775455\pi$
$547$	−2.64220	+	2.64220i	−0.112972	+	0.112972i	0.648361	+	0.761333i	$0.275455\pi$
$548$		0			0
$549$	−17.3846			−0.741955
$550$		0			0
$551$	−44.5579			−1.89823
$552$		0			0
$553$	−19.6226	+	19.6226i	−0.834439	+	0.834439i
$554$		0			0
$555$	−0.336793	+	13.0438i	−0.0142960	+	0.553677i
$556$		0			0
$557$	4.66152	−	4.66152i	0.197515	−	0.197515i	−0.601419	−	0.798934i	$-0.705398\pi$
$557$	4.66152	−	4.66152i	0.197515	−	0.197515i	0.798934	+	0.601419i	$0.205398\pi$
$558$		0			0
$559$		−	8.65994i		−	0.366276i
$560$		0			0
$561$	4.86444	−	4.92588i	0.205377	−	0.207971i
$562$		0			0
$563$	−25.8582	−	25.8582i	−1.08979	−	1.08979i	−0.995549	−	0.0942459i	$-0.969956\pi$
$563$	−25.8582	−	25.8582i	−1.08979	−	1.08979i	−0.0942459	−	0.995549i	$-0.530044\pi$
$564$		0			0
$565$	3.92035	+	4.12816i	0.164930	+	0.173673i
$566$		0			0
$567$	16.1915	−	16.1915i	0.679981	−	0.679981i
$568$		0			0
$569$	41.4277			1.73674			0.868369	−	0.495919i	$-0.165169\pi$
$569$	41.4277			1.73674			0.868369	+	0.495919i	$0.165169\pi$
$570$		0			0
$571$		−	5.29324i		−	0.221515i	−0.993847	−	0.110758i	$-0.964672\pi$
$571$		−	5.29324i		−	0.221515i	0.993847	−	0.110758i	$-0.0353277\pi$
$572$		0			0
$573$	2.41587	−	2.41587i	0.100925	−	0.100925i
$574$		0			0
$575$	3.40658	−	3.07181i	0.142064	−	0.128103i
$576$		0			0
$577$	−30.6415	−	30.6415i	−1.27562	−	1.27562i	−0.943094	−	0.332527i	$-0.892099\pi$
$577$	−30.6415	−	30.6415i	−1.27562	−	1.27562i	−0.332527	−	0.943094i	$-0.607901\pi$
$578$		0			0
$579$	−8.61878			−0.358184
$580$		0			0
$581$	−23.2289			−0.963696
$582$		0			0
$583$	15.6824	−	0.0984049i	0.649498	−	0.00407551i
$584$		0			0
$585$	10.5987	+	11.1605i	0.438201	+	0.461429i
$586$		0			0
$587$	−18.3039	−	18.3039i	−0.755485	−	0.755485i	0.220012	−	0.975497i	$-0.429390\pi$
$587$	−18.3039	−	18.3039i	−0.755485	−	0.755485i	−0.975497	+	0.220012i	$0.929390\pi$
$588$		0			0
$589$	−47.9034			−1.97383
$590$		0			0
$591$		−	2.42248i		−	0.0996473i
$592$		0			0
$593$	1.46867	+	1.46867i	0.0603109	+	0.0603109i	0.736619	−	0.676308i	$-0.236421\pi$
$593$	1.46867	+	1.46867i	0.0603109	+	0.0603109i	−0.676308	+	0.736619i	$0.736421\pi$
$594$		0			0
$595$	30.4068	+	0.785108i	1.24656	+	0.0321863i
$596$		0			0
$597$	3.05714	+	3.05714i	0.125120	+	0.125120i
$598$		0			0
$599$			33.2549i			1.35876i	0.733788	+	0.679378i	$0.237750\pi$
$599$			33.2549i			1.35876i	−0.733788	+	0.679378i	$0.762250\pi$
$600$		0			0
$601$			16.2920i			0.664563i	0.943180	+	0.332282i	$0.107818\pi$
$601$			16.2920i			0.664563i	−0.943180	+	0.332282i	$0.892182\pi$
$602$		0			0
$603$	2.44281	−	2.44281i	0.0994789	−	0.0994789i
$604$		0			0
$605$	−24.5946	−	0.326264i	−0.999912	−	0.0132645i
$606$		0			0
$607$	17.8082	−	17.8082i	0.722814	−	0.722814i	−0.246363	−	0.969178i	$-0.579236\pi$
$607$	17.8082	−	17.8082i	0.722814	−	0.722814i	0.969178	+	0.246363i	$0.0792357\pi$
$608$		0			0
$609$			18.7395i			0.759364i
$610$		0			0
$611$			8.29637i			0.335635i
$612$		0			0
$613$	−2.71472	−	2.71472i	−0.109647	−	0.109647i	0.650155	−	0.759802i	$-0.274704\pi$
$613$	−2.71472	−	2.71472i	−0.109647	−	0.109647i	−0.759802	+	0.650155i	$0.774704\pi$
$614$		0			0
$615$	−4.87626	+	4.63079i	−0.196630	+	0.186731i
$616$		0			0
$617$	29.5807	+	29.5807i	1.19088	+	1.19088i	0.976822	+	0.214053i	$0.0686665\pi$
$617$	29.5807	+	29.5807i	1.19088	+	1.19088i	0.214053	+	0.976822i	$0.431333\pi$
$618$		0			0
$619$			36.8113i			1.47957i	0.672843	+	0.739786i	$0.265073\pi$
$619$			36.8113i			1.47957i	−0.672843	+	0.739786i	$0.734927\pi$
$620$		0			0
$621$	−2.91775			−0.117085
$622$		0			0
$623$	7.36081	+	7.36081i	0.294905	+	0.294905i
$624$		0			0
$625$	24.8668	+	2.57686i	0.994674	+	0.103074i
$626$		0			0
$627$	8.98748	−	0.0563952i	0.358926	−	0.00225221i
$628$		0			0
$629$	−38.9486			−1.55298
$630$		0			0
$631$	19.0420			0.758050			0.379025	−	0.925386i	$-0.376259\pi$
$631$	19.0420			0.758050			0.379025	+	0.925386i	$0.376259\pi$
$632$		0			0
$633$	4.00904	+	4.00904i	0.159345	+	0.159345i
$634$		0			0
$635$	−14.2077	−	14.9609i	−0.563817	−	0.593704i
$636$		0			0
$637$	−11.3763	+	11.3763i	−0.450746	+	0.450746i
$638$		0			0
$639$		−	16.0006i		−	0.632975i
$640$		0			0
$641$	34.0719			1.34576			0.672880	−	0.739751i	$-0.265057\pi$
$641$	34.0719			1.34576			0.672880	+	0.739751i	$0.265057\pi$
$642$		0			0
$643$	0.0858757	−	0.0858757i	0.00338661	−	0.00338661i	−0.705411	−	0.708798i	$-0.749238\pi$
$643$	0.0858757	−	0.0858757i	0.00338661	−	0.00338661i	0.708798	+	0.705411i	$0.249238\pi$
$644$		0			0
$645$	−0.109124	+	4.22632i	−0.00429677	+	0.166411i
$646$		0			0
$647$	25.7189	+	25.7189i	1.01111	+	1.01111i	0.999938	+	0.0111757i	$0.00355741\pi$
$647$	25.7189	+	25.7189i	1.01111	+	1.01111i	0.0111757	+	0.999938i	$0.496443\pi$
$648$		0			0
$649$	−26.0913	+	26.4208i	−1.02417	+	1.03711i
$650$		0			0
$651$			20.1465i			0.789605i
$652$		0			0
$653$	17.3115	−	17.3115i	0.677451	−	0.677451i	−0.281972	−	0.959423i	$-0.590989\pi$
$653$	17.3115	−	17.3115i	0.677451	−	0.677451i	0.959423	+	0.281972i	$0.0909885\pi$
$654$		0			0
$655$	6.39489	+	0.165117i	0.249869	+	0.00645167i
$656$		0			0
$657$	−5.36408	+	5.36408i	−0.209273	+	0.209273i
$658$		0			0
$659$	9.53243			0.371331			0.185665	−	0.982613i	$-0.440556\pi$
$659$	9.53243			0.371331			0.185665	+	0.982613i	$0.440556\pi$
$660$		0			0
$661$	−35.9333			−1.39764			−0.698821	−	0.715297i	$-0.746292\pi$
$661$	−35.9333			−1.39764			−0.698821	+	0.715297i	$0.746292\pi$
$662$		0			0
$663$	3.78054	−	3.78054i	0.146824	−	0.146824i
$664$		0			0
$665$	27.1926	+	28.6340i	1.05448	+	1.11038i
$666$		0			0
$667$	−5.96490	+	5.96490i	−0.230962	+	0.230962i
$668$		0			0
$669$		−	3.21855i		−	0.124436i
$670$		0			0
$671$	15.0762	−	15.2666i	0.582009	−	0.589359i
$672$		0			0
$673$	−5.75533	−	5.75533i	−0.221852	−	0.221852i	0.587426	−	0.809278i	$-0.300141\pi$
$673$	−5.75533	−	5.75533i	−0.221852	−	0.221852i	−0.809278	+	0.587426i	$0.800141\pi$
$674$		0			0
$675$	−10.6493	−	11.8098i	−0.409891	−	0.454561i
$676$		0			0
$677$	8.65872	−	8.65872i	0.332782	−	0.332782i	−0.520860	−	0.853642i	$-0.674389\pi$
$677$	8.65872	−	8.65872i	0.332782	−	0.332782i	0.853642	+	0.520860i	$0.174389\pi$
$678$		0			0
$679$	45.0032			1.72706
$680$		0			0
$681$			4.60378i			0.176417i
$682$		0			0
$683$	−10.8306	+	10.8306i	−0.414421	+	0.414421i	−0.883275	−	0.468855i	$-0.844667\pi$
$683$	−10.8306	+	10.8306i	−0.414421	+	0.414421i	0.468855	+	0.883275i	$0.344667\pi$
$684$		0			0
$685$	−1.93610	+	1.83864i	−0.0739748	+	0.0702508i
$686$		0			0
$687$	4.65675	+	4.65675i	0.177666	+	0.177666i
$688$		0			0
$689$	12.1115			0.461413
$690$		0			0
$691$	−25.8562			−0.983616			−0.491808	−	0.870704i	$-0.663664\pi$
$691$	−25.8562			−0.983616			−0.491808	+	0.870704i	$0.663664\pi$
$692$		0			0
$693$	0.203809	+	32.4802i	0.00774205	+	1.23382i
$694$		0			0
$695$	−0.956271	+	37.0358i	−0.0362734	+	1.40485i
$696$		0			0
$697$	−14.1940	−	14.1940i	−0.537635	−	0.537635i
$698$		0			0
$699$	1.81224			0.0685453
$700$		0			0
$701$			38.7467i			1.46344i	0.681604	+	0.731721i	$0.261283\pi$
$701$			38.7467i			1.46344i	−0.681604	+	0.731721i	$0.738717\pi$
$702$		0			0
$703$	−35.7547	−	35.7547i	−1.34851	−	1.34851i
$704$		0			0
$705$	0.104543	−	4.04889i	0.00393732	−	0.152490i
$706$		0			0
$707$	28.1184	+	28.1184i	1.05750	+	1.05750i
$708$		0			0
$709$		−	26.5481i		−	0.997036i	−0.866879	−	0.498518i	$-0.833878\pi$
$709$		−	26.5481i		−	0.997036i	0.866879	−	0.498518i	$-0.166122\pi$
$710$		0			0
$711$			20.4628i			0.767416i
$712$		0			0
$713$	−6.41276	+	6.41276i	−0.240160	+	0.240160i
$714$		0			0
$715$	−18.9921	−	0.371147i	−0.710265	−	0.0138801i
$716$		0			0
$717$	−6.83506	+	6.83506i	−0.255260	+	0.255260i
$718$		0			0
$719$			9.68228i			0.361088i	0.983567	+	0.180544i	$0.0577859\pi$
$719$			9.68228i			0.361088i	−0.983567	+	0.180544i	$0.942214\pi$
$720$		0			0
$721$		−	58.1992i		−	2.16745i
$722$		0			0
$723$	−0.384320	−	0.384320i	−0.0142930	−	0.0142930i
$724$		0			0
$725$	−45.9143	−	2.37262i	−1.70522	−	0.0881167i
$726$		0			0
$727$	37.2556	+	37.2556i	1.38173	+	1.38173i	0.841542	+	0.540191i	$0.181648\pi$
$727$	37.2556	+	37.2556i	1.38173	+	1.38173i	0.540191	+	0.841542i	$0.318352\pi$
$728$		0			0
$729$		−	11.5491i		−	0.427746i
$730$		0			0
$731$	−12.6198			−0.466759
$732$		0			0
$733$	−6.40249	−	6.40249i	−0.236481	−	0.236481i	0.578910	−	0.815391i	$-0.303478\pi$
$733$	−6.40249	−	6.40249i	−0.236481	−	0.236481i	−0.815391	+	0.578910i	$0.803478\pi$
$734$		0			0
$735$	5.69536	−	5.40865i	0.210076	−	0.199501i
$736$		0			0
$737$	0.0267538	+	4.26364i	0.000985487	+	0.157053i
$738$		0			0
$739$	−14.9922			−0.551498			−0.275749	−	0.961230i	$-0.588926\pi$
$739$	−14.9922			−0.551498			−0.275749	+	0.961230i	$0.588926\pi$
$740$		0			0
$741$	6.94105			0.254986
$742$		0			0
$743$	10.3814	+	10.3814i	0.380858	+	0.380858i	0.871411	−	0.490553i	$-0.163205\pi$
$743$	10.3814	+	10.3814i	0.380858	+	0.380858i	−0.490553	+	0.871411i	$0.663205\pi$
$744$		0			0
$745$	0.850654	−	32.9453i	0.0311656	−	1.20702i
$746$		0			0
$747$	−12.1117	+	12.1117i	−0.443145	+	0.443145i
$748$		0			0
$749$		−	51.8957i		−	1.89623i
$750$		0			0
$751$	−17.5794			−0.641481			−0.320740	−	0.947167i	$-0.603932\pi$
$751$	−17.5794			−0.641481			−0.320740	+	0.947167i	$0.603932\pi$
$752$		0			0
$753$	−3.14965	+	3.14965i	−0.114780	+	0.114780i
$754$		0			0
$755$	−32.4185	−	0.837053i	−1.17983	−	0.0304635i
$756$		0			0
$757$	−24.3374	−	24.3374i	−0.884556	−	0.884556i	0.109437	−	0.993994i	$-0.465095\pi$
$757$	−24.3374	−	24.3374i	−0.884556	−	0.884556i	−0.993994	+	0.109437i	$0.965095\pi$
$758$		0			0
$759$	1.19559	−	1.21069i	0.0433972	−	0.0439453i
$760$		0			0
$761$		−	49.2285i		−	1.78453i	−0.451511	−	0.892265i	$-0.649115\pi$
$761$		−	49.2285i		−	1.78453i	0.451511	−	0.892265i	$-0.350885\pi$
$762$		0			0
$763$	−51.8846	+	51.8846i	−1.87835	+	1.87835i
$764$		0			0
$765$	16.2637	−	15.4450i	0.588016	−	0.558415i
$766$		0			0
$767$	−20.2776	+	20.2776i	−0.732180	+	0.732180i
$768$		0			0
$769$	−35.1042			−1.26589			−0.632945	−	0.774197i	$-0.718154\pi$
$769$	−35.1042			−1.26589			−0.632945	+	0.774197i	$0.718154\pi$
$770$		0			0
$771$	6.22246			0.224096
$772$		0			0
$773$	−5.87447	+	5.87447i	−0.211290	+	0.211290i	−0.804815	−	0.593525i	$-0.797736\pi$
$773$	−5.87447	+	5.87447i	−0.211290	+	0.211290i	0.593525	+	0.804815i	$0.297736\pi$
$774$		0			0
$775$	−49.3617	−	2.55076i	−1.77312	−	0.0916259i
$776$		0			0
$777$	−15.0372	+	15.0372i	−0.539456	+	0.539456i
$778$		0			0
$779$		−	26.0601i		−	0.933698i
$780$		0			0
$781$	14.0512	+	13.8760i	0.502793	+	0.496522i
$782$		0			0
$783$	20.6790	+	20.6790i	0.739007	+	0.739007i
$784$		0			0
$785$	−20.7051	+	19.6627i	−0.738995	+	0.701794i
$786$		0			0
$787$	38.2443	−	38.2443i	1.36326	−	1.36326i	0.493538	−	0.869724i	$-0.335703\pi$
$787$	38.2443	−	38.2443i	1.36326	−	1.36326i	0.869724	−	0.493538i	$-0.164297\pi$
$788$		0			0
$789$	13.4538			0.478969
$790$		0			0
$791$			9.27852i			0.329906i
$792$		0			0
$793$	11.7169	−	11.7169i	0.416078	−	0.416078i
$794$		0			0
$795$	−5.91082	−	0.152618i	−0.209635	−	0.00541282i
$796$		0			0
$797$	3.66253	+	3.66253i	0.129733	+	0.129733i	0.768992	−	0.639258i	$-0.220759\pi$
$797$	3.66253	+	3.66253i	0.129733	+	0.129733i	−0.639258	+	0.768992i	$0.720759\pi$
$798$		0			0
$799$	12.0899			0.427712
$800$		0			0
$801$	7.67598			0.271218
$802$		0			0
$803$	−0.0587476	−	9.36238i	−0.00207316	−	0.330391i
$804$		0			0
$805$	7.47342	+	0.192965i	0.263404	+	0.00680113i
$806$		0			0
$807$	−3.48320	−	3.48320i	−0.122614	−	0.122614i
$808$		0			0
$809$	11.9386			0.419738			0.209869	−	0.977730i	$-0.432696\pi$
$809$	11.9386			0.419738			0.209869	+	0.977730i	$0.432696\pi$
$810$		0			0
$811$			20.8801i			0.733198i	0.930379	+	0.366599i	$0.119478\pi$
$811$			20.8801i			0.733198i	−0.930379	+	0.366599i	$0.880522\pi$
$812$		0			0
$813$	2.59646	+	2.59646i	0.0910618	+	0.0910618i
$814$		0			0
$815$	11.9463	+	12.5796i	0.418461	+	0.440643i
$816$		0			0
$817$	−11.5849	−	11.5849i	−0.405305	−	0.405305i
$818$		0			0
$819$			25.0845i			0.876523i
$820$		0			0
$821$			24.5208i			0.855782i	0.903830	+	0.427891i	$0.140743\pi$
$821$			24.5208i			0.855782i	−0.903830	+	0.427891i	$0.859257\pi$
$822$		0			0
$823$	−20.7314	+	20.7314i	−0.722653	+	0.722653i	−0.969145	−	0.246492i	$-0.920722\pi$
$823$	−20.7314	+	20.7314i	−0.722653	+	0.722653i	0.246492	+	0.969145i	$0.420722\pi$
$824$		0			0
$825$	9.26408	+	0.420452i	0.322534	+	0.0146383i
$826$		0			0
$827$	36.7933	−	36.7933i	1.27943	−	1.27943i	0.338440	−	0.940988i	$-0.390101\pi$
$827$	36.7933	−	36.7933i	1.27943	−	1.27943i	0.940988	−	0.338440i	$-0.109899\pi$
$828$		0			0
$829$		−	1.29408i		−	0.0449452i	−0.999747	−	0.0224726i	$-0.992846\pi$
$829$		−	1.29408i		−	0.0449452i	0.999747	−	0.0224726i	$-0.00715385\pi$
$830$		0			0
$831$		−	16.4748i		−	0.571506i
$832$		0			0
$833$	16.5782	+	16.5782i	0.574402	+	0.574402i
$834$		0			0
$835$	−16.2489	−	17.1102i	−0.562315	−	0.592123i
$836$		0			0
$837$	22.2316	+	22.2316i	0.768437	+	0.768437i
$838$		0			0
$839$			6.91488i			0.238728i	0.992851	+	0.119364i	$0.0380856\pi$
$839$			6.91488i			0.238728i	−0.992851	+	0.119364i	$0.961914\pi$
$840$		0			0
$841$	55.5503			1.91553
$842$		0			0
$843$	−6.82987	−	6.82987i	−0.235233	−	0.235233i
$844$		0			0
$845$	14.3939	+	0.371654i	0.495166	+	0.0127853i
$846$		0			0
$847$	−28.6998	−	27.9883i	−0.986136	−	0.961690i
$848$		0			0
$849$	5.65862			0.194203
$850$		0			0
$851$	−9.57284			−0.328153
$852$		0			0
$853$	−20.7065	−	20.7065i	−0.708976	−	0.708976i	0.257344	−	0.966320i	$-0.417153\pi$
$853$	−20.7065	−	20.7065i	−0.708976	−	0.708976i	−0.966320	+	0.257344i	$0.917153\pi$
$854$		0			0
$855$	29.1085	+	0.751587i	0.995489	+	0.0257037i
$856$		0			0
$857$	−18.9902	+	18.9902i	−0.648692	+	0.648692i	−0.952677	−	0.303985i	$-0.901683\pi$
$857$	−18.9902	+	18.9902i	−0.648692	+	0.648692i	0.303985	+	0.952677i	$0.401683\pi$
$858$		0			0
$859$			7.39810i			0.252420i	0.992004	+	0.126210i	$0.0402813\pi$
$859$			7.39810i			0.252420i	−0.992004	+	0.126210i	$0.959719\pi$
$860$		0			0
$861$	−10.9600			−0.373514
$862$		0			0
$863$	37.1731	−	37.1731i	1.26539	−	1.26539i	0.316942	−	0.948445i	$-0.397344\pi$
$863$	37.1731	−	37.1731i	1.26539	−	1.26539i	0.948445	−	0.316942i	$-0.102656\pi$
$864$		0			0
$865$	41.9502	−	39.8384i	1.42635	−	1.35455i
$866$		0			0
$867$	1.21306	+	1.21306i	0.0411976	+	0.0411976i
$868$		0			0
$869$	−17.9698	−	17.7457i	−0.609584	−	0.601981i
$870$		0			0
$871$			3.29282i			0.111573i
$872$		0			0
$873$	23.4650	−	23.4650i	0.794171	−	0.794171i
$874$		0			0
$875$	26.4957	+	30.9536i	0.895717	+	1.04642i
$876$		0			0
$877$	15.8146	−	15.8146i	0.534020	−	0.534020i	−0.387746	−	0.921766i	$-0.626746\pi$
$877$	15.8146	−	15.8146i	0.534020	−	0.534020i	0.921766	+	0.387746i	$0.126746\pi$
$878$		0			0
$879$	−0.0532017			−0.00179445
$880$		0			0
$881$	−19.4528			−0.655380			−0.327690	−	0.944785i	$-0.606270\pi$
$881$	−19.4528			−0.655380			−0.327690	+	0.944785i	$0.606270\pi$
$882$		0			0
$883$	37.2824	−	37.2824i	1.25465	−	1.25465i	0.301040	−	0.953612i	$-0.402666\pi$
$883$	37.2824	−	37.2824i	1.25465	−	1.25465i	0.953612	−	0.301040i	$-0.0973336\pi$
$884$		0			0
$885$	10.1516	−	9.64058i	0.341243	−	0.324064i
$886$		0			0
$887$	−24.4254	+	24.4254i	−0.820123	+	0.820123i	−0.986125	−	0.166002i	$-0.946914\pi$
$887$	−24.4254	+	24.4254i	−0.820123	+	0.820123i	0.166002	+	0.986125i	$0.446914\pi$
$888$		0			0
$889$		−	33.6263i		−	1.12779i
$890$		0			0
$891$	14.8277	+	14.6428i	0.496747	+	0.490552i
$892$		0			0
$893$	11.0985	+	11.0985i	0.371398	+	0.371398i
$894$		0			0
$895$	5.84680	+	0.150965i	0.195437	+	0.00504622i
$896$		0			0
$897$	0.929187	−	0.929187i	0.0310247	−	0.0310247i
$898$		0			0
$899$	90.8985			3.03163
$900$		0			0
$901$		−	17.6496i		−	0.587995i
$902$		0			0
$903$	−4.87221	+	4.87221i	−0.162137	+	0.162137i
$904$		0			0
$905$	−0.760940	+	29.4707i	−0.0252945	+	0.979640i
$906$		0			0
$907$	−15.6361	−	15.6361i	−0.519189	−	0.519189i	0.398137	−	0.917326i	$-0.369657\pi$
$907$	−15.6361	−	15.6361i	−0.519189	−	0.519189i	−0.917326	+	0.398137i	$0.869657\pi$
$908$		0			0
$909$	29.3224			0.972562
$910$		0			0
$911$	12.4412			0.412194			0.206097	−	0.978532i	$-0.433924\pi$
$911$	12.4412			0.412194			0.206097	+	0.978532i	$0.433924\pi$
$912$		0			0
$913$	−0.132648	−	21.1396i	−0.00439002	−	0.699620i
$914$		0			0
$915$	−5.86585	+	5.57056i	−0.193919	+	0.184157i
$916$		0			0
$917$	7.37219	+	7.37219i	0.243451	+	0.243451i
$918$		0			0
$919$	12.7375			0.420173			0.210086	−	0.977683i	$-0.432626\pi$
$919$	12.7375			0.420173			0.210086	+	0.977683i	$0.432626\pi$
$920$		0			0
$921$		−	13.8864i		−	0.457572i
$922$		0			0
$923$	10.7841	+	10.7841i	0.354964	+	0.354964i
$924$		0			0
$925$	−34.9392	−	38.7470i	−1.14879	−	1.27399i
$926$		0			0
$927$	−30.3456	−	30.3456i	−0.996679	−	0.996679i
$928$		0			0
$929$		−	47.3644i		−	1.55398i	−0.629515	−	0.776988i	$-0.716747\pi$
$929$		−	47.3644i		−	1.55398i	0.629515	−	0.776988i	$-0.283253\pi$
$930$		0			0
$931$			30.4375i			0.997550i
$932$		0			0
$933$	−9.07004	+	9.07004i	−0.296940	+	0.296940i
$934$		0			0
$935$	−0.540857	+	27.6764i	−0.0176879	+	0.905115i
$936$		0			0
$937$	−27.9413	+	27.9413i	−0.912802	+	0.912802i	−0.996492	−	0.0836899i	$-0.973329\pi$
$937$	−27.9413	+	27.9413i	−0.912802	+	0.912802i	0.0836899	+	0.996492i	$0.473329\pi$
$938$		0			0
$939$		−	11.0804i		−	0.361594i
$940$		0			0
$941$		−	10.6469i		−	0.347078i	−0.984827	−	0.173539i	$-0.944480\pi$
$941$		−	10.6469i		−	0.347078i	0.984827	−	0.173539i	$-0.0555203\pi$
$942$		0			0
$943$	−3.48862	−	3.48862i	−0.113605	−	0.113605i
$944$		0			0
$945$	0.668967	−	25.9087i	0.0217615	−	0.842810i
$946$		0			0
$947$	−2.81620	−	2.81620i	−0.0915143	−	0.0915143i	0.659868	−	0.751382i	$-0.270612\pi$
$947$	−2.81620	−	2.81620i	−0.0915143	−	0.0915143i	−0.751382	+	0.659868i	$0.770612\pi$
$948$		0			0
$949$		−	7.23058i		−	0.234715i
$950$		0			0
$951$	15.1304			0.490636
$952$		0			0
$953$	−13.4300	−	13.4300i	−0.435041	−	0.435041i	0.455298	−	0.890339i	$-0.349533\pi$
$953$	−13.4300	−	13.4300i	−0.435041	−	0.435041i	−0.890339	+	0.455298i	$0.849533\pi$
$954$		0			0
$955$	−0.352619	+	13.6567i	−0.0114105	+	0.441922i
$956$		0			0
$957$	−17.0541	+	0.107012i	−0.551280	+	0.00345920i
$958$		0			0
$959$	−4.35162			−0.140521
$960$		0			0
$961$	66.7233			2.15237
$962$		0			0
$963$	−27.0589	−	27.0589i	−0.871960	−	0.871960i
$964$		0			0
$965$	24.9896	−	23.7316i	0.804445	−	0.763948i
$966$		0			0
$967$	8.75445	−	8.75445i	0.281524	−	0.281524i	−0.552192	−	0.833717i	$-0.686209\pi$
$967$	8.75445	−	8.75445i	0.281524	−	0.281524i	0.833717	+	0.552192i	$0.186209\pi$
$968$		0			0
$969$		−	10.1149i		−	0.324937i
$970$		0			0
$971$	−31.5322			−1.01192			−0.505959	−	0.862558i	$-0.668861\pi$
$971$	−31.5322			−1.01192			−0.505959	+	0.862558i	$0.668861\pi$
$972$		0			0
$973$	−42.6958	+	42.6958i	−1.36876	+	1.36876i
$974$		0			0
$975$	7.15235	+	0.369596i	0.229058	+	0.0118366i
$976$		0			0
$977$	14.7311	+	14.7311i	0.471289	+	0.471289i	0.902332	−	0.431043i	$-0.141854\pi$
$977$	14.7311	+	14.7311i	0.471289	+	0.471289i	−0.431043	+	0.902332i	$0.641854\pi$
$978$		0			0
$979$	−6.65674	+	6.74080i	−0.212750	+	0.215437i
$980$		0			0
$981$			54.1061i			1.72748i
$982$		0			0
$983$	20.1070	−	20.1070i	0.641314	−	0.641314i	−0.309564	−	0.950878i	$-0.600183\pi$
$983$	20.1070	−	20.1070i	0.641314	−	0.641314i	0.950878	+	0.309564i	$0.100183\pi$
$984$		0			0
$985$	6.67024	+	7.02382i	0.212531	+	0.223797i
$986$		0			0
$987$	4.66766	−	4.66766i	0.148573	−	0.148573i
$988$		0			0
$989$	−3.10171			−0.0986285
$990$		0			0
$991$	−18.4167			−0.585026			−0.292513	−	0.956262i	$-0.594491\pi$
$991$	−18.4167			−0.585026			−0.292513	+	0.956262i	$0.594491\pi$
$992$		0			0
$993$	0.978630	−	0.978630i	0.0310559	−	0.0310559i
$994$		0			0
$995$	−17.2817	−	0.446218i	−0.547868	−	0.0141461i
$996$		0			0
$997$	−39.4630	+	39.4630i	−1.24981	+	1.24981i	−0.294002	+	0.955805i	$0.594987\pi$
$997$	−39.4630	+	39.4630i	−1.24981	+	1.24981i	−0.955805	+	0.294002i	$0.905013\pi$
$998$		0			0
$999$			33.1869i			1.04999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.v.b.417.11	yes	32
4.3	odd	2		880.2.bd.i.417.6		32
5.3	odd	4	inner	440.2.v.b.153.12	yes	32
11.10	odd	2	inner	440.2.v.b.417.12	yes	32
20.3	even	4		880.2.bd.i.593.5		32
44.43	even	2		880.2.bd.i.417.5		32
55.43	even	4	inner	440.2.v.b.153.11	✓	32
220.43	odd	4		880.2.bd.i.593.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.v.b.153.11	✓	32	55.43	even	4	inner
440.2.v.b.153.12	yes	32	5.3	odd	4	inner
440.2.v.b.417.11	yes	32	1.1	even	1	trivial
440.2.v.b.417.12	yes	32	11.10	odd	2	inner
880.2.bd.i.417.5		32	44.43	even	2
880.2.bd.i.417.6		32	4.3	odd	2
880.2.bd.i.593.5		32	20.3	even	4
880.2.bd.i.593.6		32	220.43	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395428 - 0.395428i) q^{3} +(-0.0577165 + 2.23532i) q^{5} +(-2.57694 + 2.57694i) q^{7} +2.68727i q^{9} +(-2.35988 - 2.33045i) q^{11} +(-1.81117 - 1.81117i) q^{13} +(0.861087 + 0.906733i) q^{15} +(-2.63935 + 2.63935i) q^{17} -4.84582 q^{19} +2.03799i q^{21} +(-0.648703 + 0.648703i) q^{23} +(-4.99334 - 0.258030i) q^{25} +(2.24891 + 2.24891i) q^{27} +9.19512 q^{29} +9.88551 q^{31} +(-1.85469 + 0.0116379i) q^{33} +(-5.61155 - 5.90901i) q^{35} +(7.37845 + 7.37845i) q^{37} -1.43238 q^{39} +5.37784i q^{41} +(2.39070 + 2.39070i) q^{43} +(-6.00692 - 0.155100i) q^{45} +(-2.29033 - 2.29033i) q^{47} -6.28119i q^{49} +2.08734i q^{51} +(-3.34356 + 3.34356i) q^{53} +(5.34550 - 5.14058i) q^{55} +(-1.91618 + 1.91618i) q^{57} -11.1958i q^{59} +6.46922i q^{61} +(-6.92493 - 6.92493i) q^{63} +(4.15309 - 3.94402i) q^{65} +(-0.909029 - 0.909029i) q^{67} +0.513031i q^{69} -5.95422 q^{71} +(1.99610 + 1.99610i) q^{73} +(-2.07654 + 1.87247i) q^{75} +(12.0867 - 0.0758421i) q^{77} +7.61472 q^{79} -6.28326 q^{81} +(4.50707 + 4.50707i) q^{83} +(-5.74746 - 6.05212i) q^{85} +(3.63601 - 3.63601i) q^{87} -2.85642i q^{89} +9.33455 q^{91} +(3.90901 - 3.90901i) q^{93} +(0.279684 - 10.8320i) q^{95} +(-8.73192 - 8.73192i) q^{97} +(6.26254 - 6.34163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5} - 8 q^{11} + 24 q^{15} - 28 q^{23} + 4 q^{25} - 4 q^{27} + 24 q^{31} - 12 q^{33} + 4 q^{37} - 28 q^{45} + 8 q^{47} + 24 q^{53} + 12 q^{55} - 52 q^{67} + 48 q^{71} - 24 q^{75} + 56 q^{77}+ \cdots - 36 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 - 8 * q^11 + 24 * q^15 - 28 * q^23 + 4 * q^25 - 4 * q^27 + 24 * q^31 - 12 * q^33 + 4 * q^37 - 28 * q^45 + 8 * q^47 + 24 * q^53 + 12 * q^55 - 52 * q^67 + 48 * q^71 - 24 * q^75 + 56 * q^77 - 24 * q^81 - 16 * q^91 - 76 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more