LMFDB - Embedded newform 644.2.bc.a.493.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.10
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.274085 + 0.531650i) q^{3} +(3.06381 - 0.292558i) q^{5} +(1.85568 + 1.88586i) q^{7} +(1.53264 - 2.15229i) q^{9} +O(q^{10})$	\(q+(0.274085 + 0.531650i) q^{3} +(3.06381 - 0.292558i) q^{5} +(1.85568 + 1.88586i) q^{7} +(1.53264 - 2.15229i) q^{9} +(2.28661 - 0.791402i) q^{11} +(-0.939799 - 3.20066i) q^{13} +(0.995282 + 1.54869i) q^{15} +(-2.74331 - 1.09826i) q^{17} +(-4.33377 + 1.73498i) q^{19} +(-0.494006 + 1.50346i) q^{21} +(-4.66078 + 1.13011i) q^{23} +(4.39168 - 0.846427i) q^{25} +(3.34050 + 0.480292i) q^{27} +(0.466657 + 3.24567i) q^{29} +(8.12585 - 0.387082i) q^{31} +(1.04747 + 0.998764i) q^{33} +(6.23716 + 5.23502i) q^{35} +(-1.05222 - 0.749284i) q^{37} +(1.44405 - 1.37690i) q^{39} +(-7.14425 - 3.26267i) q^{41} +(-0.939375 + 1.46170i) q^{43} +(4.06605 - 7.04260i) q^{45} +(-1.61823 + 0.934288i) q^{47} +(-0.112935 + 6.99909i) q^{49} +(-0.168012 - 1.75950i) q^{51} +(-1.44514 - 1.51562i) q^{53} +(6.77419 - 3.09367i) q^{55} +(-2.11022 - 1.82852i) q^{57} +(2.93607 + 0.712284i) q^{59} +(4.86207 + 2.50657i) q^{61} +(6.90301 - 1.10361i) q^{63} +(-3.81574 - 9.53127i) q^{65} +(0.395822 + 2.05372i) q^{67} +(-1.87827 - 2.16816i) q^{69} +(7.43408 + 8.57939i) q^{71} +(-7.25130 + 9.22078i) q^{73} +(1.65370 + 2.10285i) q^{75} +(5.73567 + 2.84363i) q^{77} +(-6.39301 + 6.70479i) q^{79} +(-1.93233 - 5.58309i) q^{81} +(-1.95415 - 4.27900i) q^{83} +(-8.72628 - 2.56227i) q^{85} +(-1.59766 + 1.13769i) q^{87} +(-0.209028 + 4.38803i) q^{89} +(4.29204 - 7.71172i) q^{91} +(2.43296 + 4.21402i) q^{93} +(-12.7703 + 6.58353i) q^{95} +(4.22277 - 9.24658i) q^{97} +(1.80122 - 6.13438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.274085	+	0.531650i	0.158243	+	0.306949i	0.954607	−	0.297870i	$-0.0962761\pi$
$3$	0.274085	+	0.531650i	0.158243	+	0.306949i	−0.796364	+	0.604818i	$0.793246\pi$
$4$		0			0
$5$	3.06381	−	0.292558i	1.37018	−	0.130836i	0.616123	−	0.787650i	$-0.288702\pi$
$5$	3.06381	−	0.292558i	1.37018	−	0.130836i	0.754053	+	0.656814i	$0.228096\pi$
$6$		0			0
$7$	1.85568	+	1.88586i	0.701379	+	0.712788i
$7$	1.85568	+	1.88586i	0.701379	+	0.712788i
$8$		0			0
$9$	1.53264	−	2.15229i	0.510880	−	0.717431i
$10$		0			0
$11$	2.28661	−	0.791402i	0.689438	−	0.238617i	0.0401882	−	0.999192i	$-0.487204\pi$
$11$	2.28661	−	0.791402i	0.689438	−	0.238617i	0.649250	+	0.760575i	$0.275083\pi$
$12$		0			0
$13$	−0.939799	−	3.20066i	−0.260653	−	0.887704i	−0.980987	−	0.194076i	$-0.937829\pi$
$13$	−0.939799	−	3.20066i	−0.260653	−	0.887704i	0.720333	−	0.693628i	$-0.243989\pi$
$14$		0			0
$15$	0.995282	+	1.54869i	0.256981	+	0.399870i
$16$		0			0
$17$	−2.74331	−	1.09826i	−0.665351	−	0.266366i	0.0143048	−	0.999898i	$-0.495446\pi$
$17$	−2.74331	−	1.09826i	−0.665351	−	0.266366i	−0.679656	+	0.733531i	$0.737871\pi$
$18$		0			0
$19$	−4.33377	+	1.73498i	−0.994235	+	0.398032i	−0.811006	−	0.585038i	$-0.801079\pi$
$19$	−4.33377	+	1.73498i	−0.994235	+	0.398032i	−0.183230	+	0.983070i	$0.558655\pi$
$20$		0			0
$21$	−0.494006	+	1.50346i	−0.107801	+	0.328081i
$22$		0			0
$23$	−4.66078	+	1.13011i	−0.971839	+	0.235645i
$23$	−4.66078	+	1.13011i	−0.971839	+	0.235645i
$24$		0			0
$25$	4.39168	−	0.846427i	0.878336	−	0.169285i
$26$		0			0
$27$	3.34050	+	0.480292i	0.642880	+	0.0924323i
$28$		0			0
$29$	0.466657	+	3.24567i	0.0866560	+	0.602706i	0.986160	+	0.165794i	$0.0530187\pi$
$29$	0.466657	+	3.24567i	0.0866560	+	0.602706i	−0.899504	+	0.436912i	$0.856072\pi$
$30$		0			0
$31$	8.12585	−	0.387082i	1.45945	−	0.0695220i	0.697231	−	0.716846i	$-0.254415\pi$
$31$	8.12585	−	0.387082i	1.45945	−	0.0695220i	0.762215	+	0.647324i	$0.224112\pi$
$32$		0			0
$33$	1.04747	+	0.998764i	0.182342	+	0.173862i
$34$		0			0
$35$	6.23716	+	5.23502i	1.05427	+	0.884879i
$36$		0			0
$37$	−1.05222	−	0.749284i	−0.172984	−	0.123182i	0.490286	−	0.871562i	$-0.336892\pi$
$37$	−1.05222	−	0.749284i	−0.172984	−	0.123182i	−0.663270	+	0.748380i	$0.730832\pi$
$38$		0			0
$39$	1.44405	−	1.37690i	0.231233	−	0.220480i
$40$		0			0
$41$	−7.14425	−	3.26267i	−1.11574	−	0.509543i	−0.229755	−	0.973249i	$-0.573792\pi$
$41$	−7.14425	−	3.26267i	−1.11574	−	0.509543i	−0.885989	+	0.463705i	$0.846520\pi$
$42$		0			0
$43$	−0.939375	+	1.46170i	−0.143253	+	0.222906i	−0.905465	−	0.424422i	$-0.860477\pi$
$43$	−0.939375	+	1.46170i	−0.143253	+	0.222906i	0.762211	+	0.647328i	$0.224114\pi$
$44$		0			0
$45$	4.06605	−	7.04260i	0.606130	−	1.04985i
$46$		0			0
$47$	−1.61823	+	0.934288i	−0.236044	+	0.136280i	−0.613357	−	0.789806i	$-0.710181\pi$
$47$	−1.61823	+	0.934288i	−0.236044	+	0.136280i	0.377313	+	0.926086i	$0.376848\pi$
$48$		0			0
$49$	−0.112935	+	6.99909i	−0.0161336	+	0.999870i
$50$		0			0
$51$	−0.168012	−	1.75950i	−0.0235263	−	0.246379i
$52$		0			0
$53$	−1.44514	−	1.51562i	−0.198505	−	0.208186i	0.616957	−	0.786997i	$-0.288365\pi$
$53$	−1.44514	−	1.51562i	−0.198505	−	0.208186i	−0.815462	+	0.578811i	$0.803517\pi$
$54$		0			0
$55$	6.77419	−	3.09367i	0.913432	−	0.417150i
$56$		0			0
$57$	−2.11022	−	1.82852i	−0.279506	−	0.242193i
$58$		0			0
$59$	2.93607	+	0.712284i	0.382244	+	0.0927315i	0.422277	−	0.906467i	$-0.361231\pi$
$59$	2.93607	+	0.712284i	0.382244	+	0.0927315i	−0.0400326	+	0.999198i	$0.512746\pi$
$60$		0			0
$61$	4.86207	+	2.50657i	0.622524	+	0.320933i	0.740473	−	0.672086i	$-0.234602\pi$
$61$	4.86207	+	2.50657i	0.622524	+	0.320933i	−0.117949	+	0.993020i	$0.537632\pi$
$62$		0			0
$63$	6.90301	−	1.10361i	0.869697	−	0.139042i
$64$		0			0
$65$	−3.81574	−	9.53127i	−0.473285	−	1.18221i
$66$		0			0
$67$	0.395822	+	2.05372i	0.0483574	+	0.250902i	0.998061	−	0.0622494i	$-0.0198274\pi$
$67$	0.395822	+	2.05372i	0.0483574	+	0.250902i	−0.949703	+	0.313151i	$0.898615\pi$
$68$		0			0
$69$	−1.87827	−	2.16816i	−0.226118	−	0.261015i
$70$		0			0
$71$	7.43408	+	8.57939i	0.882263	+	1.01819i	0.999685	+	0.0251040i	$0.00799168\pi$
$71$	7.43408	+	8.57939i	0.882263	+	1.01819i	−0.117422	+	0.993082i	$0.537463\pi$
$72$		0			0
$73$	−7.25130	+	9.22078i	−0.848700	+	1.07921i	0.147232	+	0.989102i	$0.452964\pi$
$73$	−7.25130	+	9.22078i	−0.848700	+	1.07921i	−0.995932	+	0.0901083i	$0.971279\pi$
$74$		0			0
$75$	1.65370	+	2.10285i	0.190952	+	0.242816i
$76$		0			0
$77$	5.73567	+	2.84363i	0.653641	+	0.324062i
$78$		0			0
$79$	−6.39301	+	6.70479i	−0.719269	+	0.754348i	−0.977316	−	0.211784i	$-0.932073\pi$
$79$	−6.39301	+	6.70479i	−0.719269	+	0.754348i	0.258047	+	0.966132i	$0.416921\pi$
$80$		0			0
$81$	−1.93233	−	5.58309i	−0.214703	−	0.620344i
$82$		0			0
$83$	−1.95415	−	4.27900i	−0.214496	−	0.469681i	0.771547	−	0.636173i	$-0.219483\pi$
$83$	−1.95415	−	4.27900i	−0.214496	−	0.469681i	−0.986043	+	0.166491i	$0.946756\pi$
$84$		0			0
$85$	−8.72628	−	2.56227i	−0.946498	−	0.277917i
$86$		0			0
$87$	−1.59766	+	1.13769i	−0.171287	+	0.121973i
$88$		0			0
$89$	−0.209028	+	4.38803i	−0.0221569	+	0.465130i	0.960338	+	0.278839i	$0.0899497\pi$
$89$	−0.209028	+	4.38803i	−0.0221569	+	0.465130i	−0.982495	+	0.186291i	$0.940353\pi$
$90$		0			0
$91$	4.29204	−	7.71172i	0.449928	−	0.808408i
$92$		0			0
$93$	2.43296	+	4.21402i	0.252287	+	0.436973i
$94$		0			0
$95$	−12.7703	+	6.58353i	−1.31020	+	0.675455i
$96$		0			0
$97$	4.22277	−	9.24658i	0.428758	−	0.938848i	−0.564769	−	0.825249i	$-0.691035\pi$
$97$	4.22277	−	9.24658i	0.428758	−	0.938848i	0.993527	−	0.113599i	$-0.0362380\pi$
$98$		0			0
$99$	1.80122	−	6.13438i	0.181029	−	0.616529i
$100$		0			0
$101$	0.361743	−	3.78834i	0.0359948	−	0.376954i	−0.959469	−	0.281814i	$-0.909064\pi$
$101$	0.361743	−	3.78834i	0.0359948	−	0.376954i	0.995464	−	0.0951405i	$-0.0303300\pi$
$102$		0			0
$103$	−16.8280	−	3.24333i	−1.65811	−	0.319575i	−0.727646	−	0.685953i	$-0.759386\pi$
$103$	−16.8280	−	3.24333i	−1.65811	−	0.319575i	−0.930466	+	0.366378i	$0.880598\pi$
$104$		0			0
$105$	−1.07369	+	4.75083i	−0.104781	+	0.463633i
$106$		0			0
$107$	0.331004	−	0.642058i	0.0319993	−	0.0620701i	−0.872294	−	0.488982i	$-0.837368\pi$
$107$	0.331004	−	0.642058i	0.0319993	−	0.0620701i	0.904293	+	0.426912i	$0.140399\pi$
$108$		0			0
$109$	−6.35899	+	15.8840i	−0.609080	+	1.52141i	0.227621	+	0.973750i	$0.426905\pi$
$109$	−6.35899	+	15.8840i	−0.609080	+	1.52141i	−0.836701	+	0.547660i	$0.815519\pi$
$110$		0			0
$111$	0.109959	−	0.764782i	0.0104368	−	0.0725899i
$112$		0			0
$113$	12.6638	−	10.9733i	1.19131	−	1.03228i	0.192615	−	0.981275i	$-0.438303\pi$
$113$	12.6638	−	10.9733i	1.19131	−	1.03228i	0.998698	−	0.0510040i	$-0.0162421\pi$
$114$		0			0
$115$	−13.9491	+	4.82600i	−1.30076	+	0.450026i
$116$		0			0
$117$	−8.32914	−	2.88274i	−0.770029	−	0.266510i
$118$		0			0
$119$	−3.01954	−	7.21151i	−0.276801	−	0.661078i
$120$		0			0
$121$	−4.04433	+	3.18050i	−0.367667	+	0.289136i
$122$		0			0
$123$	−0.223531	−	4.69249i	−0.0201551	−	0.423108i
$124$		0			0
$125$	−1.55774	+	0.457393i	−0.139328	+	0.0409105i
$126$		0			0
$127$	7.63668	−	8.81320i	0.677646	−	0.782045i	−0.307907	−	0.951417i	$-0.599628\pi$
$127$	7.63668	−	8.81320i	0.677646	−	0.782045i	0.985552	+	0.169372i	$0.0541739\pi$
$128$		0			0
$129$	−1.03458	−	0.0987903i	−0.0910896	−	0.00869800i
$130$		0			0
$131$	−11.5358	+	2.79857i	−1.00789	+	0.244512i	−0.705529	−	0.708681i	$-0.749290\pi$
$131$	−11.5358	+	2.79857i	−1.00789	+	0.244512i	−0.302363	+	0.953193i	$0.597775\pi$
$132$		0			0
$133$	−11.3140	−	4.95333i	−0.981049	−	0.429508i
$134$		0			0
$135$	10.3752	+	0.494230i	0.892953	+	0.0425366i
$136$		0			0
$137$	−6.70343	−	3.87023i	−0.572713	−	0.330656i	0.185519	−	0.982641i	$-0.440603\pi$
$137$	−6.70343	−	3.87023i	−0.572713	−	0.330656i	−0.758232	+	0.651985i	$0.773937\pi$
$138$		0			0
$139$			0.456172i			0.0386920i	0.999813	+	0.0193460i	$0.00615841\pi$
$139$			0.456172i			0.0386920i	−0.999813	+	0.0193460i	$0.993842\pi$
$140$		0			0
$141$	−0.940248	−	0.604261i	−0.0791832	−	0.0508879i
$142$		0			0
$143$	−4.68196	−	6.57490i	−0.391525	−	0.549821i
$144$		0			0
$145$	2.37929	+	9.80758i	0.197590	+	0.814475i
$146$		0			0
$147$	−3.75202	+	1.85830i	−0.309462	+	0.153270i
$148$		0			0
$149$	1.82808	−	9.48498i	0.149762	−	0.777040i	−0.826915	−	0.562327i	$-0.809906\pi$
$149$	1.82808	−	9.48498i	0.149762	−	0.777040i	0.976677	−	0.214713i	$-0.0688816\pi$
$150$		0			0
$151$	−0.789479	+	3.25428i	−0.0642469	+	0.264829i	−0.994872	−	0.101146i	$-0.967749\pi$
$151$	−0.789479	+	3.25428i	−0.0642469	+	0.264829i	0.930625	+	0.365975i	$0.119264\pi$
$152$		0			0
$153$	−6.56828	+	4.22118i	−0.531014	+	0.341262i
$154$		0			0
$155$	24.7828	−	3.56323i	1.99060	−	0.286205i
$156$		0			0
$157$	−15.9894	−	12.5742i	−1.27609	−	1.00353i	−0.999090	−	0.0426589i	$-0.986417\pi$
$157$	−15.9894	−	12.5742i	−1.27609	−	1.00353i	−0.277001	−	0.960870i	$-0.589340\pi$
$158$		0			0
$159$	0.409689	−	1.18372i	0.0324904	−	0.0938749i
$160$		0			0
$161$	−10.7801	−	6.69245i	−0.849593	−	0.527439i
$162$		0			0
$163$	−4.44918	+	12.8551i	−0.348487	+	1.00689i	0.625488	+	0.780233i	$0.284900\pi$
$163$	−4.44918	+	12.8551i	−0.348487	+	1.00689i	−0.973975	+	0.226654i	$0.927221\pi$
$164$		0			0
$165$	3.50145	+	2.75357i	0.272588	+	0.214365i
$166$		0			0
$167$	−12.5962	+	1.81106i	−0.974725	+	0.140144i	−0.611231	−	0.791452i	$-0.709325\pi$
$167$	−12.5962	+	1.81106i	−0.974725	+	0.140144i	−0.363494	+	0.931596i	$0.618416\pi$
$168$		0			0
$169$	1.57528	−	1.01237i	0.121175	−	0.0778745i
$170$		0			0
$171$	−2.90793	+	11.9867i	−0.222375	+	0.916642i
$172$		0			0
$173$	0.781229	−	4.05340i	0.0593957	−	0.308174i	−0.940066	−	0.340994i	$-0.889236\pi$
$173$	0.781229	−	4.05340i	0.0593957	−	0.308174i	0.999461	+	0.0328194i	$0.0104486\pi$
$174$		0			0
$175$	9.74577	+	6.71140i	0.736711	+	0.507334i
$176$		0			0
$177$	0.426047	+	1.75619i	0.0320237	+	0.132003i
$178$		0			0
$179$	5.33573	+	7.49298i	0.398811	+	0.560052i	0.964337	−	0.264679i	$-0.0852660\pi$
$179$	5.33573	+	7.49298i	0.398811	+	0.560052i	−0.565526	+	0.824731i	$0.691327\pi$
$180$		0			0
$181$	−11.8107	−	7.59029i	−0.877884	−	0.564182i	0.0222708	−	0.999752i	$-0.492910\pi$
$181$	−11.8107	−	7.59029i	−0.877884	−	0.564182i	−0.900155	+	0.435570i	$0.856547\pi$
$182$		0			0
$183$			3.27193i			0.241868i
$184$		0			0
$185$	−3.44301	−	1.98783i	−0.253135	−	0.146148i
$186$		0			0
$187$	−7.14204	−	0.340217i	−0.522277	−	0.0248791i
$188$		0			0
$189$	5.29313	+	7.19099i	0.385019	+	0.523068i
$190$		0			0
$191$	18.6988	−	4.53628i	1.35300	−	0.328234i	0.507243	−	0.861803i	$-0.330665\pi$
$191$	18.6988	−	4.53628i	1.35300	−	0.328234i	0.845756	+	0.533569i	$0.179150\pi$
$192$		0			0
$193$	12.1672	+	1.16183i	0.875814	+	0.0836301i	0.523272	−	0.852166i	$-0.324711\pi$
$193$	12.1672	+	1.16183i	0.875814	+	0.0836301i	0.352542	+	0.935796i	$0.385317\pi$
$194$		0			0
$195$	4.02146	−	4.64102i	0.287983	−	0.332350i
$196$		0			0
$197$	25.1059	−	7.37175i	1.78872	−	0.525215i	0.792328	−	0.610096i	$-0.208869\pi$
$197$	25.1059	−	7.37175i	1.78872	−	0.525215i	0.996391	+	0.0848802i	$0.0270508\pi$
$198$		0			0
$199$	0.156271	+	3.28053i	0.0110778	+	0.232551i	0.997615	+	0.0690169i	$0.0219862\pi$
$199$	0.156271	+	3.28053i	0.0110778	+	0.232551i	−0.986538	+	0.163534i	$0.947711\pi$
$200$		0			0
$201$	−0.983373	+	0.773333i	−0.0693618	+	0.0545467i
$202$		0			0
$203$	−5.25491	+	6.90296i	−0.368823	+	0.484493i
$204$		0			0
$205$	−22.8431	−	7.90608i	−1.59543	−	0.552185i
$206$		0			0
$207$	−4.71096	+	11.7634i	−0.327435	+	0.817614i
$208$		0			0
$209$	−8.53656	+	7.39697i	−0.590486	+	0.511659i
$210$		0			0
$211$	−1.65363	+	11.5013i	−0.113841	+	0.791780i	0.850283	+	0.526326i	$0.176431\pi$
$211$	−1.65363	+	11.5013i	−0.113841	+	0.791780i	−0.964124	+	0.265454i	$0.914478\pi$
$212$		0			0
$213$	−2.52367	+	6.30381i	−0.172919	+	0.431930i
$214$		0			0
$215$	−2.45043	+	4.75317i	−0.167118	+	0.324164i
$216$		0			0
$217$	15.8089	+	14.6059i	1.07318	+	0.991514i
$218$		0			0
$219$	−6.88970	−	1.32788i	−0.465563	−	0.0897299i
$220$		0			0
$221$	−0.936985	+	9.81255i	−0.0630285	+	0.660064i
$222$		0			0
$223$	7.18332	−	24.4642i	0.481031	−	1.63824i	−0.259153	−	0.965836i	$-0.583443\pi$
$223$	7.18332	−	24.4642i	0.481031	−	1.63824i	0.740184	−	0.672404i	$-0.234738\pi$
$224$		0			0
$225$	4.90911	−	10.7494i	0.327274	−	0.716630i
$226$		0			0
$227$	2.32595	−	1.19911i	0.154379	−	0.0795879i	−0.379306	−	0.925271i	$-0.623837\pi$
$227$	2.32595	−	1.19911i	0.154379	−	0.0795879i	0.533685	+	0.845683i	$0.320807\pi$
$228$		0			0
$229$	2.47987	+	4.29526i	0.163874	+	0.283839i	0.936255	−	0.351321i	$-0.114268\pi$
$229$	2.47987	+	4.29526i	0.163874	+	0.283839i	−0.772381	+	0.635160i	$0.780934\pi$
$230$		0			0
$231$	0.0602422	+	3.82877i	0.00396365	+	0.251915i
$232$		0			0
$233$	0.332754	−	6.98537i	0.0217995	−	0.457627i	−0.961407	−	0.275130i	$-0.911279\pi$
$233$	0.332754	−	6.98537i	0.0217995	−	0.457627i	0.983206	−	0.182497i	$-0.0584179\pi$
$234$		0			0
$235$	−4.68462	+	3.33591i	−0.305591	+	0.217610i
$236$		0			0
$237$	−5.31683	−	1.56116i	−0.345365	−	0.101408i
$238$		0			0
$239$	−10.4783	−	22.9444i	−0.677788	−	1.48415i	−0.864970	−	0.501823i	$-0.832663\pi$
$239$	−10.4783	−	22.9444i	−0.677788	−	1.48415i	0.187183	−	0.982325i	$-0.440064\pi$
$240$		0			0
$241$	−5.55032	−	16.0366i	−0.357527	−	1.03301i	−0.970124	−	0.242611i	$-0.921996\pi$
$241$	−5.55032	−	16.0366i	−0.357527	−	1.03301i	0.612596	−	0.790396i	$-0.290125\pi$
$242$		0			0
$243$	9.42538	−	9.88506i	0.604639	−	0.634127i
$244$		0			0
$245$	1.70163	+	21.4769i	0.108713	+	1.37211i
$246$		0			0
$247$	9.62596	+	12.2404i	0.612485	+	0.778839i
$248$		0			0
$249$	1.73933	−	2.21174i	0.110225	−	0.140163i
$250$		0			0
$251$	16.7451	+	19.3249i	1.05694	+	1.21978i	0.974782	+	0.223160i	$0.0716371\pi$
$251$	16.7451	+	19.3249i	1.05694	+	1.21978i	0.0821622	+	0.996619i	$0.473817\pi$
$252$		0			0
$253$	−9.76299	+	6.27267i	−0.613794	+	0.394360i
$254$		0			0
$255$	−1.02951	−	5.34161i	−0.0644705	−	0.334505i
$256$		0			0
$257$	−4.92493	−	12.3019i	−0.307209	−	0.767371i	−0.998976	−	0.0452498i	$-0.985592\pi$
$257$	−4.92493	−	12.3019i	−0.307209	−	0.767371i	0.691767	−	0.722121i	$-0.256833\pi$
$258$		0			0
$259$	−0.539538	−	3.37477i	−0.0335253	−	0.209698i
$260$		0			0
$261$	7.70085	+	3.97006i	0.476671	+	0.245741i
$262$		0			0
$263$	−7.63996	−	1.85343i	−0.471100	−	0.114288i	−0.00682126	−	0.999977i	$-0.502171\pi$
$263$	−7.63996	−	1.85343i	−0.471100	−	0.114288i	−0.464279	+	0.885689i	$0.653686\pi$
$264$		0			0
$265$	−4.87104	−	4.22078i	−0.299225	−	0.259280i
$266$		0			0
$267$	−2.39019	+	1.09156i	−0.146277	+	0.0668026i
$268$		0			0
$269$	0.231648	+	0.242945i	0.0141238	+	0.0148126i	0.730758	−	0.682637i	$-0.239167\pi$
$269$	0.231648	+	0.242945i	0.0141238	+	0.0148126i	−0.716634	+	0.697449i	$0.754318\pi$
$270$		0			0
$271$	0.892860	+	9.35045i	0.0542374	+	0.567999i	0.981220	+	0.192894i	$0.0617874\pi$
$271$	0.892860	+	9.35045i	0.0542374	+	0.567999i	−0.926982	+	0.375105i	$0.877607\pi$
$272$		0			0
$273$	5.27632	+	0.168198i	0.319338	+	0.0101798i
$274$		0			0
$275$	9.37218	−	5.41103i	0.565164	−	0.326297i
$276$		0			0
$277$	2.49720	−	4.32528i	0.150042	−	0.259881i	−0.781201	−	0.624280i	$-0.785392\pi$
$277$	2.49720	−	4.32528i	0.150042	−	0.259881i	0.931243	+	0.364400i	$0.118726\pi$
$278$		0			0
$279$	11.6209	−	18.0825i	0.695725	−	1.08257i
$280$		0			0
$281$	20.2647	+	9.25459i	1.20889	+	0.552083i	0.914883	−	0.403720i	$-0.132283\pi$
$281$	20.2647	+	9.25459i	1.20889	+	0.552083i	0.294010	+	0.955802i	$0.405010\pi$
$282$		0			0
$283$	−23.4133	+	22.3246i	−1.39178	+	1.32706i	−0.506314	+	0.862349i	$0.668992\pi$
$283$	−23.4133	+	22.3246i	−1.39178	+	1.32706i	−0.885464	+	0.464709i	$0.846159\pi$
$284$		0			0
$285$	−7.00027	−	4.98487i	−0.414660	−	0.295278i
$286$		0			0
$287$	−7.10447	−	19.5275i	−0.419364	−	1.15267i
$288$		0			0
$289$	−5.98389	−	5.70563i	−0.351993	−	0.335625i
$290$		0			0
$291$	6.07335	−	0.289309i	0.356026	−	0.0169596i
$292$		0			0
$293$	−4.24205	−	29.5041i	−0.247823	−	1.72365i	−0.610745	−	0.791827i	$-0.709130\pi$
$293$	−4.24205	−	29.5041i	−0.247823	−	1.72365i	0.362922	−	0.931820i	$-0.381779\pi$
$294$		0			0
$295$	9.20395	+	1.32333i	0.535875	+	0.0770471i
$296$		0			0
$297$	8.01852	−	1.54544i	0.465282	−	0.0896757i
$298$		0			0
$299$	7.99731	+	13.8555i	0.462496	+	0.801284i
$300$		0			0
$301$	−4.49973	+	0.940904i	−0.259360	+	0.0542328i
$302$		0			0
$303$	2.11322	−	0.846007i	0.121402	−	0.0486018i
$304$		0			0
$305$	15.6297	+	6.25721i	0.894957	+	0.358287i
$306$		0			0
$307$	−9.10900	−	14.1739i	−0.519878	−	0.808946i	0.477699	−	0.878524i	$-0.341471\pi$
$307$	−9.10900	−	14.1739i	−0.519878	−	0.808946i	−0.997577	+	0.0695780i	$0.977835\pi$
$308$		0			0
$309$	−2.88798	−	9.83556i	−0.164292	−	0.559526i
$310$		0			0
$311$	15.2315	−	5.27168i	0.863701	−	0.298930i	0.140932	−	0.990019i	$-0.454990\pi$
$311$	15.2315	−	5.27168i	0.863701	−	0.298930i	0.722769	+	0.691090i	$0.242869\pi$
$312$		0			0
$313$	−16.4040	+	23.0361i	−0.927207	+	1.30208i	0.0259690	+	0.999663i	$0.491733\pi$
$313$	−16.4040	+	23.0361i	−0.927207	+	1.30208i	−0.953176	+	0.302417i	$0.902207\pi$
$314$		0			0
$315$	20.8266	−	5.40078i	1.17345	−	0.304300i
$316$		0			0
$317$	30.0144	−	2.86603i	1.68578	−	0.160972i	0.792315	−	0.610112i	$-0.208876\pi$
$317$	30.0144	−	2.86603i	1.68578	−	0.160972i	0.893462	+	0.449140i	$0.148269\pi$
$318$		0			0
$319$	3.63569	+	7.05226i	0.203560	+	0.394850i
$320$		0			0
$321$	0.432073			0.0241160
$322$		0			0
$323$	13.7943			0.767537
$324$		0			0
$325$	−6.83642	−	13.2608i	−0.379217	−	0.735578i
$326$		0			0
$327$	−10.1876	+	0.972800i	−0.563377	+	0.0537960i
$328$		0			0
$329$	−4.76485	−	1.31803i	−0.262695	−	0.0726652i
$330$		0			0
$331$	−2.81568	+	3.95408i	−0.154764	+	0.217336i	−0.884677	−	0.466204i	$-0.845621\pi$
$331$	−2.81568	+	3.95408i	−0.154764	+	0.217336i	0.729913	+	0.683540i	$0.239561\pi$
$332$		0			0
$333$	−3.22536	+	1.11631i	−0.176748	+	0.0611732i
$334$		0			0
$335$	1.81356	+	6.17640i	0.0990851	+	0.337453i
$336$		0			0
$337$	14.2585	+	22.1866i	0.776709	+	1.20858i	0.973623	+	0.228163i	$0.0732718\pi$
$337$	14.2585	+	22.1866i	0.776709	+	1.20858i	−0.196914	+	0.980421i	$0.563092\pi$
$338$		0			0
$339$	9.30491	+	3.72512i	0.505373	+	0.202321i
$340$		0			0
$341$	18.2743	−	7.31592i	0.989608	−	0.396179i
$342$		0			0
$343$	−13.4089	+	12.7751i	−0.724011	+	0.689788i
$344$		0			0
$345$	−6.38898	−	6.09331i	−0.343971	−	0.328053i
$346$		0			0
$347$	21.0986	−	4.06643i	1.13263	−	0.218297i	0.411712	−	0.911314i	$-0.364931\pi$
$347$	21.0986	−	4.06643i	1.13263	−	0.218297i	0.720922	+	0.693016i	$0.243719\pi$
$348$		0			0
$349$	8.17592	+	1.17552i	0.437647	+	0.0629241i	0.357617	−	0.933868i	$-0.383589\pi$
$349$	8.17592	+	1.17552i	0.437647	+	0.0629241i	0.0800300	+	0.996792i	$0.474498\pi$
$350$		0			0
$351$	−1.60215	−	11.1432i	−0.0855165	−	0.594780i
$352$		0			0
$353$	5.62762	−	0.268077i	0.299528	−	0.0142683i	0.102720	−	0.994710i	$-0.467245\pi$
$353$	5.62762	−	0.268077i	0.299528	−	0.0142683i	0.196808	+	0.980442i	$0.436942\pi$
$354$		0			0
$355$	25.2866	+	24.1107i	1.34207	+	1.27966i
$356$		0			0
$357$	3.00639	−	3.58190i	0.159115	−	0.189574i
$358$		0			0
$359$	−26.7095	−	19.0197i	−1.40967	−	1.00382i	−0.995612	−	0.0935739i	$-0.970171\pi$
$359$	−26.7095	−	19.0197i	−1.40967	−	1.00382i	−0.414060	−	0.910249i	$-0.635890\pi$
$360$		0			0
$361$	2.02048	−	1.92652i	0.106341	−	0.101396i
$362$		0			0
$363$	−2.79940	−	1.27844i	−0.146931	−	0.0671009i
$364$		0			0
$365$	−19.5190	+	30.3721i	−1.02167	+	1.58975i
$366$		0			0
$367$	1.77933	−	3.08189i	0.0928802	−	0.160873i	−0.815842	−	0.578275i	$-0.803726\pi$
$367$	1.77933	−	3.08189i	0.0928802	−	0.160873i	0.908722	+	0.417402i	$0.137059\pi$
$368$		0			0
$369$	−17.9718	+	10.3760i	−0.935574	+	0.540154i
$370$		0			0
$371$	0.176534	−	5.53783i	0.00916520	−	0.287510i
$372$		0			0
$373$	3.07785	+	32.2327i	0.159365	+	1.66894i	0.622472	+	0.782642i	$0.286128\pi$
$373$	3.07785	+	32.2327i	0.159365	+	1.66894i	−0.463108	+	0.886302i	$0.653266\pi$
$374$		0			0
$375$	−0.670125	−	0.702807i	−0.0346051	−	0.0362928i
$376$		0			0
$377$	9.94973	−	4.54389i	0.512437	−	0.234022i
$378$		0			0
$379$	15.1898	+	13.1621i	0.780250	+	0.676090i	0.950989	−	0.309226i	$-0.100070\pi$
$379$	15.1898	+	13.1621i	0.780250	+	0.676090i	−0.170739	+	0.985316i	$0.554615\pi$
$380$		0			0
$381$	6.77864	+	1.64448i	0.347280	+	0.0842493i
$382$		0			0
$383$	0.276754	+	0.142676i	0.0141414	+	0.00729042i	0.465283	−	0.885162i	$-0.345953\pi$
$383$	0.276754	+	0.142676i	0.0141414	+	0.00729042i	−0.451141	+	0.892453i	$0.648983\pi$
$384$		0			0
$385$	18.4049	+	7.03433i	0.938002	+	0.358502i
$386$		0			0
$387$	1.70627	+	4.26206i	0.0867347	+	0.216653i
$388$		0			0
$389$	−1.35447	−	7.02768i	−0.0686746	−	0.356318i	0.931294	−	0.364269i	$-0.118681\pi$
$389$	−1.35447	−	7.02768i	−0.0686746	−	0.356318i	−0.999968	+	0.00795134i	$0.997469\pi$
$390$		0			0
$391$	14.0271	+	2.01848i	0.709382	+	0.102079i
$392$		0			0
$393$	−4.64966	−	5.36599i	−0.234544	−	0.270678i
$394$		0			0
$395$	−17.6254	+	22.4125i	−0.886830	+	1.12770i
$396$		0			0
$397$	16.4048	+	20.8604i	0.823333	+	1.04695i	0.998055	+	0.0623356i	$0.0198549\pi$
$397$	16.4048	+	20.8604i	0.823333	+	1.04695i	−0.174722	+	0.984618i	$0.555903\pi$
$398$		0			0
$399$	−0.467560	−	7.37273i	−0.0234073	−	0.369098i
$400$		0			0
$401$	−3.15424	+	3.30807i	−0.157515	+	0.165197i	−0.797763	−	0.602971i	$-0.793983\pi$
$401$	−3.15424	+	3.30807i	−0.157515	+	0.165197i	0.640248	+	0.768169i	$0.278832\pi$
$402$		0			0
$403$	−8.87559	−	25.6443i	−0.442125	−	1.27744i
$404$		0			0
$405$	−7.55366	−	16.5402i	−0.375344	−	0.821889i
$406$		0			0
$407$	−2.99900	−	0.880587i	−0.148655	−	0.0436491i
$408$		0			0
$409$	31.3379	−	22.3156i	1.54956	−	1.10344i	0.595690	−	0.803215i	$-0.296879\pi$
$409$	31.3379	−	22.3156i	1.54956	−	1.10344i	0.953870	−	0.300221i	$-0.0970605\pi$
$410$		0			0
$411$	0.220299	−	4.62465i	0.0108666	−	0.228117i
$412$		0			0
$413$	4.10513	+	6.85879i	0.202000	+	0.337499i
$414$		0			0
$415$	−7.23901	−	12.5383i	−0.355349	−	0.615483i
$416$		0			0
$417$	−0.242524	+	0.125030i	−0.0118765	+	0.00612274i
$418$		0			0
$419$	7.43223	−	16.2743i	0.363088	−	0.795053i	−0.636626	−	0.771172i	$-0.719671\pi$
$419$	7.43223	−	16.2743i	0.363088	−	0.795053i	0.999715	−	0.0238804i	$-0.00760208\pi$
$420$		0			0
$421$	2.06431	−	7.03039i	0.100608	−	0.342640i	−0.893770	−	0.448525i	$-0.851949\pi$
$421$	2.06431	−	7.03039i	0.100608	−	0.342640i	0.994378	+	0.105885i	$0.0337675\pi$
$422$		0			0
$423$	−0.469311	+	4.91484i	−0.0228187	+	0.238968i
$424$		0			0
$425$	−12.9773	−	2.50118i	−0.629493	−	0.121325i
$426$		0			0
$427$	4.29538	+	13.8206i	0.207868	+	0.668824i
$428$		0			0
$429$	2.21229	−	4.29125i	0.106810	−	0.207183i
$430$		0			0
$431$	10.5798	−	26.4271i	0.509613	−	1.27295i	−0.421039	−	0.907043i	$-0.638334\pi$
$431$	10.5798	−	26.4271i	0.509613	−	1.27295i	0.930651	−	0.365908i	$-0.119241\pi$
$432$		0			0
$433$	−3.20824	+	22.3138i	−0.154178	+	1.07233i	0.754939	+	0.655795i	$0.227666\pi$
$433$	−3.20824	+	22.3138i	−0.154178	+	1.07233i	−0.909118	+	0.416539i	$0.863243\pi$
$434$		0			0
$435$	−4.56208	+	3.95306i	−0.218735	+	0.189535i
$436$		0			0
$437$	18.2380	−	12.9840i	0.872443	−	0.621109i
$438$		0			0
$439$	2.58354	+	0.894172i	0.123306	+	0.0426765i	0.388024	−	0.921649i	$-0.373158\pi$
$439$	2.58354	+	0.894172i	0.123306	+	0.0426765i	−0.264718	+	0.964326i	$0.585279\pi$
$440$		0			0
$441$	14.8910	+	10.9702i	0.709095	+	0.522389i
$442$		0			0
$443$	−14.0856	+	11.0770i	−0.669227	+	0.526286i	−0.893967	−	0.448133i	$-0.852089\pi$
$443$	−14.0856	+	11.0770i	−0.669227	+	0.526286i	0.224740	+	0.974419i	$0.427847\pi$
$444$		0			0
$445$	0.643333	+	13.5052i	0.0304969	+	0.640209i
$446$		0			0
$447$	5.54374	−	1.62779i	0.262210	−	0.0769918i
$448$		0			0
$449$	26.1228	−	30.1473i	1.23281	−	1.42274i	0.361238	−	0.932474i	$-0.382354\pi$
$449$	26.1228	−	30.1473i	1.23281	−	1.42274i	0.871573	−	0.490266i	$-0.163100\pi$
$450$		0			0
$451$	−18.9182	−	1.80647i	−0.890822	−	0.0850632i
$452$		0			0
$453$	−1.94652	+	0.472221i	−0.0914555	+	0.0221869i
$454$		0			0
$455$	10.8939	−	24.8829i	0.510712	−	1.16653i
$456$		0			0
$457$	−4.71487	−	0.224597i	−0.220552	−	0.0105062i	−0.0629851	−	0.998014i	$-0.520062\pi$
$457$	−4.71487	−	0.224597i	−0.220552	−	0.0105062i	−0.157567	+	0.987508i	$0.550365\pi$
$458$		0			0
$459$	−8.63656	−	4.98632i	−0.403120	−	0.232741i
$460$		0			0
$461$			23.2995i			1.08516i	0.840003	+	0.542582i	$0.182553\pi$
$461$			23.2995i			1.08516i	−0.840003	+	0.542582i	$0.817447\pi$
$462$		0			0
$463$	−29.3823	−	18.8828i	−1.36551	−	0.877560i	−0.366900	−	0.930260i	$-0.619581\pi$
$463$	−29.3823	−	18.8828i	−1.36551	−	0.877560i	−0.998610	+	0.0527002i	$0.983217\pi$
$464$		0			0
$465$	8.68698	+	12.1992i	0.402849	+	0.565722i
$466$		0			0
$467$	4.70107	+	19.3781i	0.217539	+	0.896710i	0.970974	+	0.239186i	$0.0768807\pi$
$467$	4.70107	+	19.3781i	0.217539	+	0.896710i	−0.753434	+	0.657523i	$0.771604\pi$
$468$		0			0
$469$	−3.13851	+	4.55750i	−0.144923	+	0.210446i
$470$		0			0
$471$	2.30262	−	11.9471i	0.106099	−	0.550495i
$472$		0			0
$473$	−0.991191	+	4.08574i	−0.0455750	+	0.187863i
$474$		0			0
$475$	−17.5640	+	11.2877i	−0.805892	+	0.517915i
$476$		0			0
$477$	−5.47694	+	0.787465i	−0.250772	+	0.0360555i
$478$		0			0
$479$	4.04064	+	3.17760i	0.184622	+	0.145188i	0.706192	−	0.708020i	$-0.250411\pi$
$479$	4.04064	+	3.17760i	0.184622	+	0.145188i	−0.521571	+	0.853208i	$0.674654\pi$
$480$		0			0
$481$	−1.40933	+	4.07198i	−0.0642598	+	0.185667i
$482$		0			0
$483$	0.603375	−	7.56556i	0.0274545	−	0.344245i
$484$		0			0
$485$	10.2326	−	29.5651i	0.464638	−	1.34248i
$486$		0			0
$487$	−20.9202	−	16.4518i	−0.947984	−	0.745503i	0.0191379	−	0.999817i	$-0.493908\pi$
$487$	−20.9202	−	16.4518i	−0.947984	−	0.745503i	−0.967122	+	0.254314i	$0.918150\pi$
$488$		0			0
$489$	−8.05386	+	1.15797i	−0.364208	+	0.0523652i
$490$		0			0
$491$	−28.1585	+	18.0964i	−1.27078	+	0.816679i	−0.989721	−	0.143013i	$-0.954321\pi$
$491$	−28.1585	+	18.0964i	−1.27078	+	0.816679i	−0.281056	+	0.959691i	$0.590685\pi$
$492$		0			0
$493$	2.28439	−	9.41639i	0.102884	−	0.424093i
$494$		0			0
$495$	3.72392	−	19.3215i	0.167378	−	0.868438i
$496$		0			0
$497$	−2.38428	+	29.9402i	−0.106950	+	1.34300i
$498$		0			0
$499$	4.58071	+	18.8820i	0.205061	+	0.845273i	0.977628	+	0.210340i	$0.0674571\pi$
$499$	4.58071	+	18.8820i	0.205061	+	0.845273i	−0.772567	+	0.634933i	$0.781028\pi$
$500$		0			0
$501$	−4.41529	−	6.20041i	−0.197261	−	0.277014i
$502$		0			0
$503$	−22.0462	−	14.1682i	−0.982991	−	0.631730i	−0.0527226	−	0.998609i	$-0.516790\pi$
$503$	−22.0462	−	14.1682i	−0.982991	−	0.631730i	−0.930269	+	0.366879i	$0.880426\pi$
$504$		0			0
$505$		−	11.7126i		−	0.521203i
$506$		0			0
$507$	0.969985	+	0.560021i	0.0430786	+	0.0248714i
$508$		0			0
$509$	−40.2439	−	1.91705i	−1.78378	−	0.0849718i	−0.870465	−	0.492231i	$-0.836182\pi$
$509$	−40.2439	−	1.91705i	−1.78378	−	0.0849718i	−0.913313	+	0.407259i	$0.866485\pi$
$510$		0			0
$511$	−30.8452	+	3.43584i	−1.36451	+	0.151993i
$512$		0			0
$513$	−15.3103	+	3.71423i	−0.675966	+	0.163987i
$514$		0			0
$515$	−52.5066	−	5.01377i	−2.31372	−	0.220933i
$516$		0			0
$517$	−2.96087	+	3.41702i	−0.130219	+	0.150280i
$518$		0			0
$519$	2.36912	−	0.695635i	0.103993	−	0.0305350i
$520$		0			0
$521$	0.753797	+	15.8241i	0.0330244	+	0.693268i	0.953305	+	0.302009i	$0.0976573\pi$
$521$	0.753797	+	15.8241i	0.0330244	+	0.693268i	−0.920281	+	0.391259i	$0.872040\pi$
$522$		0			0
$523$	−7.13284	+	5.60933i	−0.311897	+	0.245279i	−0.761820	−	0.647789i	$-0.775694\pi$
$523$	−7.13284	+	5.60933i	−0.311897	+	0.245279i	0.449923	+	0.893068i	$0.351452\pi$
$524$		0			0
$525$	−0.896948	+	7.02084i	−0.0391460	+	0.306414i
$526$		0			0
$527$	−22.7169	−	7.86238i	−0.989562	−	0.342491i
$528$		0			0
$529$	20.4457	−	10.5344i	0.888943	−	0.458018i
$530$		0			0
$531$	6.03299	−	5.22762i	0.261810	−	0.226859i
$532$		0			0
$533$	−3.72854	+	25.9326i	−0.161501	+	1.12326i
$534$		0			0
$535$	0.826292	−	2.06398i	0.0357237	−	0.0892336i
$536$		0			0
$537$	−2.52120	+	4.89045i	−0.108798	+	0.211039i
$538$		0			0
$539$	5.28086	+	16.0935i	0.227463	+	0.693198i
$540$		0			0
$541$	43.7124	+	8.42488i	1.87934	+	0.362214i	0.994593	−	0.103852i	$-0.0331168\pi$
$541$	43.7124	+	8.42488i	1.87934	+	0.362214i	0.884750	+	0.466066i	$0.154329\pi$
$542$		0			0
$543$	0.798241	−	8.35956i	0.0342558	−	0.358743i
$544$		0			0
$545$	−14.8357	+	50.5258i	−0.635492	+	2.16429i
$546$		0			0
$547$	−8.63674	+	18.9118i	−0.369280	+	0.808611i	0.630202	+	0.776431i	$0.282972\pi$
$547$	−8.63674	+	18.9118i	−0.369280	+	0.808611i	−0.999482	+	0.0321798i	$0.989755\pi$
$548$		0			0
$549$	12.8467	−	6.62292i	0.548283	−	0.282659i
$550$		0			0
$551$	−7.65356	−	13.2564i	−0.326053	−	0.564740i
$552$		0			0
$553$	−24.5076	+	0.385605i	−1.04217	+	0.0163976i
$554$		0			0
$555$	0.113150	−	2.37531i	0.00480295	−	0.100826i
$556$		0			0
$557$	1.63614	−	1.16509i	0.0693257	−	0.0493666i	−0.544869	−	0.838521i	$-0.683420\pi$
$557$	1.63614	−	1.16509i	0.0693257	−	0.0493666i	0.614194	+	0.789155i	$0.289481\pi$
$558$		0			0
$559$	5.56122	+	1.63292i	0.235214	+	0.0690652i
$560$		0			0
$561$	−1.77665	−	3.89031i	−0.0750101	−	0.164249i
$562$		0			0
$563$	1.69255	+	4.89030i	0.0713325	+	0.206102i	0.975031	−	0.222067i	$-0.0712803\pi$
$563$	1.69255	+	4.89030i	0.0713325	+	0.206102i	−0.903699	+	0.428168i	$0.859159\pi$
$564$		0			0
$565$	35.5892	−	37.3249i	1.49725	−	1.57027i
$566$		0			0
$567$	6.94316	−	14.0045i	0.291585	−	0.588134i
$568$		0			0
$569$	−5.67542	−	7.21688i	−0.237926	−	0.302548i	0.652397	−	0.757878i	$-0.273764\pi$
$569$	−5.67542	−	7.21688i	−0.237926	−	0.302548i	−0.890323	+	0.455330i	$0.849521\pi$
$570$		0			0
$571$	−13.4453	+	17.0971i	−0.562668	+	0.715490i	−0.981261	−	0.192684i	$-0.938281\pi$
$571$	−13.4453	+	17.0971i	−0.562668	+	0.715490i	0.418593	+	0.908174i	$0.362523\pi$
$572$		0			0
$573$	7.53678	+	8.69791i	0.314854	+	0.363360i
$574$		0			0
$575$	−19.5121	+	8.90810i	−0.813710	+	0.371493i
$576$		0			0
$577$	0.202550	+	1.05093i	0.00843227	+	0.0437508i	0.985901	−	0.167329i	$-0.0535142\pi$
$577$	0.202550	+	1.05093i	0.00843227	+	0.0437508i	−0.977469	+	0.211080i	$0.932302\pi$
$578$		0			0
$579$	2.71716	+	6.78714i	0.112921	+	0.282064i
$580$		0			0
$581$	4.44332	−	11.6257i	0.184340	−	0.482315i
$582$		0			0
$583$	−4.50393	−	2.32194i	−0.186534	−	0.0961648i
$584$		0			0
$585$	−26.3622	−	6.39541i	−1.08994	−	0.264418i
$586$		0			0
$587$	16.3967	+	14.2078i	0.676763	+	0.586418i	0.923933	−	0.382554i	$-0.124955\pi$
$587$	16.3967	+	14.2078i	0.676763	+	0.586418i	−0.247171	+	0.968972i	$0.579501\pi$
$588$		0			0
$589$	−34.5440	+	15.7757i	−1.42336	+	0.650027i
$590$		0			0
$591$	10.8003	+	11.3271i	0.444266	+	0.465933i
$592$		0			0
$593$	−3.16382	−	33.1330i	−0.129922	−	1.36061i	−0.791700	−	0.610910i	$-0.790804\pi$
$593$	−3.16382	−	33.1330i	−0.129922	−	1.36061i	0.661778	−	0.749700i	$-0.269802\pi$
$594$		0			0
$595$	−11.3611	−	21.2113i	−0.465758	−	0.869578i
$596$		0			0
$597$	−1.70126	+	0.982225i	−0.0696281	+	0.0401998i
$598$		0			0
$599$	21.9266	−	37.9780i	0.895896	−	1.55174i	0.0632041	−	0.998001i	$-0.479868\pi$
$599$	21.9266	−	37.9780i	0.895896	−	1.55174i	0.832692	−	0.553737i	$-0.186799\pi$
$600$		0			0
$601$	20.5685	−	32.0052i	0.839007	−	1.30552i	−0.111167	−	0.993802i	$-0.535459\pi$
$601$	20.5685	−	32.0052i	0.839007	−	1.30552i	0.950174	−	0.311719i	$-0.100905\pi$
$602$		0			0
$603$	5.02686	+	2.29569i	0.204710	+	0.0934878i
$604$		0			0
$605$	−11.4606	+	10.9276i	−0.465939	+	0.444272i
$606$		0			0
$607$	−4.03022	−	2.86991i	−0.163582	−	0.116486i	0.495335	−	0.868702i	$-0.335045\pi$
$607$	−4.03022	−	2.86991i	−0.163582	−	0.116486i	−0.658916	+	0.752216i	$0.728985\pi$
$608$		0			0
$609$	−5.11025	−	0.901781i	−0.207078	−	0.0365420i
$610$		0			0
$611$	4.51116	+	4.30138i	0.182502	+	0.174015i
$612$		0			0
$613$	16.2482	−	0.773995i	0.656257	−	0.0312614i	0.283187	−	0.959065i	$-0.408608\pi$
$613$	16.2482	−	0.773995i	0.656257	−	0.0312614i	0.373070	+	0.927803i	$0.378305\pi$
$614$		0			0
$615$	−2.05768	−	14.3115i	−0.0829737	−	0.577095i
$616$		0			0
$617$	41.8943	+	6.02349i	1.68660	+	0.242496i	0.917814	−	0.397011i	$-0.129952\pi$
$617$	41.8943	+	6.02349i	1.68660	+	0.242496i	0.768785	+	0.639507i	$0.220861\pi$
$618$		0			0
$619$	−27.7137	+	5.34137i	−1.11391	+	0.214688i	−0.712816	−	0.701351i	$-0.752581\pi$
$619$	−27.7137	+	5.34137i	−1.11391	+	0.214688i	−0.401090	+	0.916039i	$0.631369\pi$
$620$		0			0
$621$	−16.1121	+	1.53661i	−0.646558	+	0.0616622i
$622$		0			0
$623$	−8.66310	+	7.74857i	−0.347080	+	0.310440i
$624$		0			0
$625$	−25.3994	+	10.1684i	−1.01598	+	0.406736i
$626$		0			0
$627$	−6.27235	−	2.51107i	−0.250493	−	0.100282i
$628$		0			0
$629$	2.06367	+	3.21113i	0.0822838	+	0.128036i
$630$		0			0
$631$	−13.4477	−	45.7988i	−0.535346	−	1.82322i	−0.566994	−	0.823722i	$-0.691894\pi$
$631$	−13.4477	−	45.7988i	−0.535346	−	1.82322i	0.0316486	−	0.999499i	$-0.489924\pi$
$632$		0			0
$633$	−6.56789	+	2.27317i	−0.261050	+	0.0903504i
$634$		0			0
$635$	20.8189	−	29.2361i	0.826174	−	1.16020i
$636$		0			0
$637$	22.5079	−	6.21627i	0.891794	−	0.246298i
$638$		0			0
$639$	29.8591	−	2.85120i	1.18121	−	0.112792i
$640$		0			0
$641$	17.7170	+	34.3661i	0.699779	+	1.35738i	0.923830	+	0.382804i	$0.125041\pi$
$641$	17.7170	+	34.3661i	0.699779	+	1.35738i	−0.224051	+	0.974577i	$0.571928\pi$
$642$		0			0
$643$	−24.2818			−0.957580			−0.478790	−	0.877930i	$-0.658924\pi$
$643$	−24.2818			−0.957580			−0.478790	+	0.877930i	$0.658924\pi$
$644$		0			0
$645$	−3.19865			−0.125947
$646$		0			0
$647$	−22.6781	−	43.9894i	−0.891569	−	1.72940i	−0.651505	−	0.758645i	$-0.725862\pi$
$647$	−22.6781	−	43.9894i	−0.891569	−	1.72940i	−0.240064	−	0.970757i	$-0.577168\pi$
$648$		0			0
$649$	7.27735	−	0.694903i	0.285661	−	0.0272773i
$650$		0			0
$651$	−3.43226	+	12.4081i	−0.134521	+	0.486311i
$652$		0			0
$653$	−21.0445	+	29.5529i	−0.823535	+	1.15649i	0.161961	+	0.986797i	$0.448218\pi$
$653$	−21.0445	+	29.5529i	−0.823535	+	1.15649i	−0.985496	+	0.169696i	$0.945721\pi$
$654$		0			0
$655$	−34.5249	+	11.9492i	−1.34900	+	0.466893i
$656$		0			0
$657$	8.73218	+	29.7391i	0.340675	+	1.16023i
$658$		0			0
$659$	19.7772	+	30.7740i	0.770411	+	1.19878i	0.975491	+	0.220038i	$0.0706181\pi$
$659$	19.7772	+	30.7740i	0.770411	+	1.19878i	−0.205080	+	0.978745i	$0.565746\pi$
$660$		0			0
$661$	41.5954	+	16.6523i	1.61787	+	0.647699i	0.991295	−	0.131660i	$-0.0420307\pi$
$661$	41.5954	+	16.6523i	1.61787	+	0.647699i	0.626578	+	0.779359i	$0.284455\pi$
$662$		0			0
$663$	−5.47366	+	2.19132i	−0.212579	+	0.0851040i
$664$		0			0
$665$	−36.1131	−	11.8660i	−1.40040	−	0.460145i
$666$		0			0
$667$	−5.84296	−	14.6000i	−0.226240	−	0.565313i
$668$		0			0
$669$	14.9752	−	2.88624i	0.578975	−	0.111588i
$670$		0			0
$671$	13.1013	+	1.88369i	0.505771	+	0.0727190i
$672$		0			0
$673$	−0.838128	−	5.82931i	−0.0323074	−	0.224703i	0.967271	−	0.253747i	$-0.0816630\pi$
$673$	−0.838128	−	5.82931i	−0.0323074	−	0.224703i	−0.999578	+	0.0290435i	$0.990754\pi$
$674$		0			0
$675$	15.0770	−	0.718204i	0.580312	−	0.0276437i
$676$		0			0
$677$	−7.42546	−	7.08016i	−0.285384	−	0.272113i	0.533842	−	0.845584i	$-0.320748\pi$
$677$	−7.42546	−	7.08016i	−0.285384	−	0.272113i	−0.819225	+	0.573472i	$0.805596\pi$
$678$		0			0
$679$	25.2739	−	9.19510i	0.969921	−	0.352876i
$680$		0			0
$681$	1.27502	+	0.907936i	0.0488588	+	0.0347922i
$682$		0			0
$683$	−2.20150	+	2.09912i	−0.0842379	+	0.0803207i	−0.731028	−	0.682347i	$-0.760959\pi$
$683$	−2.20150	+	2.09912i	−0.0842379	+	0.0803207i	0.646790	+	0.762668i	$0.276111\pi$
$684$		0			0
$685$	−21.6703	−	9.89649i	−0.827979	−	0.378125i
$686$		0			0
$687$	−1.60388	+	2.49569i	−0.0611919	+	0.0952164i
$688$		0			0
$689$	−3.49284	+	6.04978i	−0.133067	+	0.230478i
$690$		0			0
$691$	25.4374	−	14.6863i	0.967683	−	0.558692i	0.0691537	−	0.997606i	$-0.477970\pi$
$691$	25.4374	−	14.6863i	0.967683	−	0.558692i	0.898529	+	0.438914i	$0.144637\pi$
$692$		0			0
$693$	14.9111	−	7.98658i	0.566424	−	0.303385i
$694$		0			0
$695$	0.133457	+	1.39762i	0.00506231	+	0.0530149i
$696$		0			0
$697$	16.0156	+	16.7967i	0.606636	+	0.636222i
$698$		0			0
$699$	3.80498	−	1.73768i	0.143918	−	0.0657249i
$700$		0			0
$701$	−31.0013	−	26.8628i	−1.17090	−	1.01459i	−0.999568	−	0.0293806i	$-0.990647\pi$
$701$	−31.0013	−	26.8628i	−1.17090	−	1.01459i	−0.171335	−	0.985213i	$-0.554808\pi$
$702$		0			0
$703$	5.86008	+	1.42164i	0.221017	+	0.0536182i
$704$		0			0
$705$	−3.05752	−	1.57626i	−0.115153	−	0.0593654i
$706$		0			0
$707$	7.81557	−	6.34774i	0.293935	−	0.238731i
$708$		0			0
$709$	9.24046	+	23.0815i	0.347033	+	0.866846i	0.994498	+	0.104751i	$0.0334046\pi$
$709$	9.24046	+	23.0815i	0.347033	+	0.866846i	−0.647466	+	0.762094i	$0.724171\pi$
$710$		0			0
$711$	4.63249	+	24.0357i	0.173732	+	0.901408i
$712$		0			0
$713$	−37.4353	+	10.9872i	−1.40196	+	0.411475i
$714$		0			0
$715$	−16.2682	−	18.7745i	−0.608395	−	0.702125i
$716$		0			0
$717$	9.32643	−	11.8595i	0.348302	−	0.442902i
$718$		0			0
$719$	7.28837	+	9.26791i	0.271810	+	0.345635i	0.902726	−	0.430217i	$-0.141563\pi$
$719$	7.28837	+	9.26791i	0.271810	+	0.345635i	−0.630915	+	0.775852i	$0.717320\pi$
$720$		0			0
$721$	−25.1108	−	37.7538i	−0.935177	−	1.40603i
$722$		0			0
$723$	7.00460	−	7.34621i	0.260504	−	0.273209i
$724$		0			0
$725$	4.79663	+	13.8589i	0.178142	+	0.514708i
$726$		0			0
$727$	13.5623	+	29.6972i	0.502996	+	1.10141i	0.975484	+	0.220071i	$0.0706289\pi$
$727$	13.5623	+	29.6972i	0.502996	+	1.10141i	−0.472488	+	0.881337i	$0.656644\pi$
$728$		0			0
$729$	−9.16739	−	2.69179i	−0.339533	−	0.0996959i
$730$		0			0
$731$	4.18231	−	2.97821i	0.154688	−	0.110153i
$732$		0			0
$733$	1.14611	−	24.0599i	0.0423327	−	0.888673i	−0.873429	−	0.486951i	$-0.838109\pi$
$733$	1.14611	−	24.0599i	0.0423327	−	0.888673i	0.915762	−	0.401721i	$-0.131588\pi$
$734$		0			0
$735$	−10.9518	+	6.79116i	−0.403964	+	0.250496i
$736$		0			0
$737$	2.53041	+	4.38280i	0.0932088	+	0.161442i
$738$		0			0
$739$	−30.4259	+	15.6857i	−1.11924	+	0.577006i	−0.915620	−	0.402044i	$-0.868300\pi$
$739$	−30.4259	+	15.6857i	−1.11924	+	0.577006i	−0.203616	+	0.979051i	$0.565269\pi$
$740$		0			0
$741$	−3.86929	+	8.47256i	−0.142142	+	0.311247i
$742$		0			0
$743$	−9.00142	+	30.6560i	−0.330230	+	1.12466i	0.612324	+	0.790607i	$0.290235\pi$
$743$	−9.00142	+	30.6560i	−0.330230	+	1.12466i	−0.942554	+	0.334053i	$0.891583\pi$
$744$		0			0
$745$	2.82598	−	29.5950i	0.103536	−	1.08428i
$746$		0			0
$747$	−12.2047	−	2.35226i	−0.446546	−	0.0860647i
$748$		0			0
$749$	1.82507	−	0.567224i	0.0666865	−	0.0207259i
$750$		0			0
$751$	13.2861	−	25.7714i	0.484816	−	0.940411i	−0.511870	−	0.859063i	$-0.671047\pi$
$751$	13.2861	−	25.7714i	0.484816	−	0.940411i	0.996686	−	0.0813483i	$-0.0259226\pi$
$752$		0			0
$753$	−5.68452	+	14.1992i	−0.207155	+	0.517449i
$754$		0			0
$755$	−1.46675	+	10.2014i	−0.0533803	+	0.371268i
$756$		0			0
$757$	8.22192	−	7.12433i	0.298831	−	0.258938i	−0.492520	−	0.870301i	$-0.663924\pi$
$757$	8.22192	−	7.12433i	0.298831	−	0.258938i	0.791350	+	0.611363i	$0.209379\pi$
$758$		0			0
$759$	−6.01076	−	3.47125i	−0.218177	−	0.125999i
$760$		0			0
$761$	−5.86898	−	2.03127i	−0.212750	−	0.0736336i	0.218614	−	0.975811i	$-0.429846\pi$
$761$	−5.86898	−	2.03127i	−0.212750	−	0.0736336i	−0.431364	+	0.902178i	$0.641968\pi$
$762$		0			0
$763$	−41.7552	+	17.4834i	−1.51164	+	0.632940i
$764$		0			0
$765$	−18.8890	+	14.8545i	−0.682933	+	0.537065i
$766$		0			0
$767$	−0.479540	−	10.0668i	−0.0173152	−	0.363491i
$768$		0			0
$769$	8.19263	−	2.40557i	0.295434	−	0.0867472i	−0.130657	−	0.991428i	$-0.541709\pi$
$769$	8.19263	−	2.40557i	0.295434	−	0.0867472i	0.426091	+	0.904680i	$0.359890\pi$
$770$		0			0
$771$	5.19046	−	5.99011i	0.186930	−	0.215728i
$772$		0			0
$773$	−35.6030	−	3.39967i	−1.28055	−	0.122278i	−0.567490	−	0.823380i	$-0.692085\pi$
$773$	−35.6030	−	3.39967i	−1.28055	−	0.122278i	−0.713060	+	0.701103i	$0.752691\pi$
$774$		0			0
$775$	35.3585	−	8.57788i	1.27011	−	0.308126i
$776$		0			0
$777$	1.64632	−	1.21182i	0.0590614	−	0.0434738i
$778$		0			0
$779$	36.6222	+	1.74453i	1.31213	+	0.0625043i
$780$		0			0
$781$	23.7886	+	13.7343i	0.851222	+	0.491453i
$782$		0			0
$783$			11.0663i			0.395477i
$784$		0			0
$785$	−52.6670	−	33.8470i	−1.87977	−	1.20805i
$786$		0			0
$787$	−14.4308	−	20.2653i	−0.514404	−	0.722379i	0.472919	−	0.881106i	$-0.343200\pi$
$787$	−14.4308	−	20.2653i	−0.514404	−	0.722379i	−0.987323	+	0.158727i	$0.949261\pi$
$788$		0			0
$789$	−1.10862	−	4.56979i	−0.0394679	−	0.162689i
$790$		0			0
$791$	44.1940	+	3.51938i	1.57136	+	0.125135i
$792$		0			0
$793$	3.45332	−	17.9175i	0.122631	−	0.636269i
$794$		0			0
$795$	0.908901	−	3.74654i	0.0322354	−	0.132876i
$796$		0			0
$797$	−30.7444	+	19.7582i	−1.08902	+	0.699873i	−0.956625	−	0.291324i	$-0.905904\pi$
$797$	−30.7444	+	19.7582i	−1.08902	+	0.699873i	−0.132399	+	0.991197i	$0.542268\pi$
$798$		0			0
$799$	5.46541	−	0.785807i	0.193352	−	0.0277998i
$800$		0			0
$801$	9.12396	+	7.17517i	0.322379	+	0.253522i
$802$		0			0
$803$	−9.28352	+	26.8230i	−0.327608	+	0.946562i
$804$		0			0
$805$	−34.9862	−	17.3506i	−1.23310	−	0.611527i
$806$		0			0
$807$	−0.0656708	+	0.189743i	−0.00231172	+	0.00667928i
$808$		0			0
$809$	21.6935	+	17.0600i	0.762704	+	0.599797i	0.921890	−	0.387452i	$-0.126645\pi$
$809$	21.6935	+	17.0600i	0.762704	+	0.599797i	−0.159186	+	0.987249i	$0.550887\pi$
$810$		0			0
$811$	53.1691	−	7.64456i	1.86702	−	0.268437i	0.886193	−	0.463316i	$-0.153341\pi$
$811$	53.1691	−	7.64456i	1.86702	−	0.268437i	0.980827	+	0.194879i	$0.0624315\pi$
$812$		0			0
$813$	−4.72645	+	3.03751i	−0.165764	+	0.106530i
$814$		0			0
$815$	−9.87058	+	40.6871i	−0.345751	+	1.42521i
$816$		0			0
$817$	1.53502	−	7.96445i	0.0537036	−	0.278641i
$818$		0			0
$819$	−10.0197	−	21.0570i	−0.350118	−	0.735792i
$820$		0			0
$821$	11.6135	+	47.8715i	0.405314	+	1.67073i	0.699230	+	0.714896i	$0.253526\pi$
$821$	11.6135	+	47.8715i	0.405314	+	1.67073i	−0.293916	+	0.955831i	$0.594959\pi$
$822$		0			0
$823$	−4.94768	−	6.94805i	−0.172465	−	0.242194i	0.719292	−	0.694708i	$-0.244466\pi$
$823$	−4.94768	−	6.94805i	−0.172465	−	0.242194i	−0.891757	+	0.452514i	$0.850527\pi$
$824$		0			0
$825$	5.44555	+	3.49964i	0.189590	+	0.121842i
$826$		0			0
$827$		−	7.28655i		−	0.253378i	−0.991942	−	0.126689i	$-0.959565\pi$
$827$		−	7.28655i		−	0.253378i	0.991942	−	0.126689i	$-0.0404350\pi$
$828$		0			0
$829$	2.42664	+	1.40102i	0.0842805	+	0.0486594i	0.541548	−	0.840670i	$-0.317838\pi$
$829$	2.42664	+	1.40102i	0.0842805	+	0.0486594i	−0.457267	+	0.889329i	$0.651172\pi$
$830$		0			0
$831$	2.98398	+	0.142144i	0.103513	+	0.00493094i
$832$		0			0
$833$	7.99661	−	19.0766i	0.277066	−	0.660967i
$834$		0			0
$835$	−38.0626	+	9.23388i	−1.31721	+	0.319552i
$836$		0			0
$837$	27.3304	+	2.60973i	0.944675	+	0.0902056i
$838$		0			0
$839$	−20.7256	+	23.9186i	−0.715526	+	0.825760i	−0.990761	−	0.135616i	$-0.956699\pi$
$839$	−20.7256	+	23.9186i	−0.715526	+	0.825760i	0.275236	+	0.961377i	$0.411244\pi$
$840$		0			0
$841$	17.5087	−	5.14102i	0.603748	−	0.177276i
$842$		0			0
$843$	0.634047	+	13.3103i	0.0218378	+	0.458431i
$844$		0			0
$845$	4.53016	−	3.56256i	0.155842	−	0.122556i
$846$		0			0
$847$	−13.5029	−	1.72507i	−0.463967	−	0.0592741i
$848$		0			0
$849$	−18.2861	−	6.32888i	−0.627577	−	0.217207i
$850$		0			0
$851$	5.75095	+	2.30312i	0.197140	+	0.0789498i
$852$		0			0
$853$	21.1459	−	18.3230i	0.724021	−	0.627368i	−0.212833	−	0.977089i	$-0.568269\pi$
$853$	21.1459	−	18.3230i	0.724021	−	0.627368i	0.936854	+	0.349721i	$0.113724\pi$
$854$		0			0
$855$	−5.40254	+	37.5755i	−0.184763	+	1.28506i
$856$		0			0
$857$	2.75772	−	6.88846i	0.0942020	−	0.235305i	−0.873782	−	0.486318i	$-0.838340\pi$
$857$	2.75772	−	6.88846i	0.0942020	−	0.235305i	0.967984	+	0.251013i	$0.0807638\pi$
$858$		0			0
$859$	−3.94336	+	7.64906i	−0.134546	+	0.260982i	−0.946477	−	0.322770i	$-0.895386\pi$
$859$	−3.94336	+	7.64906i	−0.134546	+	0.260982i	0.811932	+	0.583753i	$0.198416\pi$
$860$		0			0
$861$	8.43458	−	9.12929i	0.287450	−	0.311125i
$862$		0			0
$863$	12.2437	+	2.35977i	0.416779	+	0.0803275i	0.393330	−	0.919398i	$-0.371323\pi$
$863$	12.2437	+	2.35977i	0.416779	+	0.0803275i	0.0234491	+	0.999725i	$0.492535\pi$
$864$		0			0
$865$	1.20768	−	12.6474i	0.0410623	−	0.430024i
$866$		0			0
$867$	1.39331	−	4.74516i	0.0473191	−	0.161154i
$868$		0			0
$869$	−9.31210	+	20.3907i	−0.315891	+	0.691706i
$870$		0			0
$871$	6.20127	−	3.19698i	0.210122	−	0.108325i
$872$		0			0
$873$	−13.4294	−	23.2603i	−0.454515	−	0.787243i
$874$		0			0
$875$	−3.75323	−	2.08890i	−0.126882	−	0.0706178i
$876$		0			0
$877$	−1.92741	+	40.4614i	−0.0650841	+	1.36628i	0.696192	+	0.717855i	$0.254876\pi$
$877$	−1.92741	+	40.4614i	−0.0650841	+	1.36628i	−0.761276	+	0.648428i	$0.775427\pi$
$878$		0			0
$879$	14.5232	−	10.3419i	0.489855	−	0.348824i
$880$		0			0
$881$	0.843431	+	0.247654i	0.0284159	+	0.00834367i	0.295910	−	0.955216i	$-0.404377\pi$
$881$	0.843431	+	0.247654i	0.0284159	+	0.00834367i	−0.267494	+	0.963560i	$0.586195\pi$
$882$		0			0
$883$	−0.933268	−	2.04357i	−0.0314070	−	0.0687717i	0.893278	−	0.449504i	$-0.148399\pi$
$883$	−0.933268	−	2.04357i	−0.0314070	−	0.0687717i	−0.924685	+	0.380732i	$0.875672\pi$
$884$		0			0
$885$	1.81911	+	5.25599i	0.0611489	+	0.176678i
$886$		0			0
$887$	14.8313	−	15.5546i	0.497987	−	0.522274i	−0.425987	−	0.904729i	$-0.640073\pi$
$887$	14.8313	−	15.5546i	0.497987	−	0.522274i	0.923974	+	0.382455i	$0.124921\pi$
$888$		0			0
$889$	30.7917	−	1.95273i	1.03272	−	0.0654924i
$890$		0			0
$891$	−8.83695	−	11.2371i	−0.296049	−	0.376457i
$892$		0			0
$893$	5.39209	−	6.85660i	0.180439	−	0.229447i
$894$		0			0
$895$	18.5398	+	21.3960i	0.619716	+	0.715191i
$896$		0			0
$897$	−5.17434	+	8.04935i	−0.172766	+	0.268760i
$898$		0			0
$899$	5.04832	+	26.1932i	0.168371	+	0.873592i
$900$		0			0
$901$	2.29993	+	5.74495i	0.0766218	+	0.191392i
$902$		0			0
$903$	−1.73354	−	2.13439i	−0.0576886	−	0.0710282i
$904$		0			0
$905$	−38.4064	−	19.7999i	−1.27667	−	0.658170i
$906$		0			0
$907$	44.3957	+	10.7703i	1.47414	+	0.357621i	0.890720	−	0.454553i	$-0.150201\pi$
$907$	44.3957	+	10.7703i	1.47414	+	0.357621i	0.583415	+	0.812174i	$0.301716\pi$
$908$		0			0
$909$	−7.59921	−	6.58475i	−0.252050	−	0.218402i
$910$		0			0
$911$	42.2237	−	19.2829i	1.39893	−	0.638872i	0.433892	−	0.900965i	$-0.357140\pi$
$911$	42.2237	−	19.2829i	1.39893	−	0.638872i	0.965043	+	0.262093i	$0.0844126\pi$
$912$		0			0
$913$	−7.85479	−	8.23787i	−0.259956	−	0.272634i
$914$		0			0
$915$	0.957230	+	10.0246i	0.0316451	+	0.331402i
$916$		0			0
$917$	−26.6845	−	16.5618i	−0.881199	−	0.546917i
$918$		0			0
$919$	17.0444	−	9.84060i	0.562243	−	0.324611i	−0.191802	−	0.981434i	$-0.561433\pi$
$919$	17.0444	−	9.84060i	0.562243	−	0.324611i	0.754045	+	0.656822i	$0.228100\pi$
$920$		0			0
$921$	5.03891	−	8.72765i	0.166038	−	0.287586i
$922$		0			0
$923$	20.4732	−	31.8569i	0.673883	−	1.04858i
$924$		0			0
$925$	−5.25524	−	2.39999i	−0.172791	−	0.0789110i
$926$		0			0
$927$	−32.7719	+	31.2479i	−1.07637	+	1.02632i
$928$		0			0
$929$	−7.51432	−	5.35092i	−0.246537	−	0.175558i	0.450108	−	0.892974i	$-0.351385\pi$
$929$	−7.51432	−	5.35092i	−0.246537	−	0.175558i	−0.696645	+	0.717416i	$0.745325\pi$
$930$		0			0
$931$	−11.6538	−	30.5284i	−0.381939	−	1.00053i
$932$		0			0
$933$	6.97742	+	6.65296i	0.228431	+	0.217808i
$934$		0			0
$935$	−21.9813	+	1.04710i	−0.718867	+	0.0342439i
$936$		0			0
$937$	2.70127	+	18.7877i	0.0882466	+	0.613768i	0.985170	+	0.171582i	$0.0548879\pi$
$937$	2.70127	+	18.7877i	0.0882466	+	0.613768i	−0.896923	+	0.442186i	$0.854203\pi$
$938$		0			0
$939$	−16.7433	−	2.40732i	−0.546395	−	0.0785598i
$940$		0			0
$941$	−4.83870	+	0.932584i	−0.157737	+	0.0304014i	−0.267508	−	0.963556i	$-0.586200\pi$
$941$	−4.83870	+	0.932584i	−0.157737	+	0.0304014i	0.109771	+	0.993957i	$0.464988\pi$
$942$		0			0
$943$	36.9849	+	7.13277i	1.20440	+	0.232275i
$944$		0			0
$945$	18.3209	+	20.4833i	0.595979	+	0.666320i
$946$		0			0
$947$	44.2318	−	17.7077i	1.43734	−	0.575424i	0.483394	−	0.875403i	$-0.339404\pi$
$947$	44.2318	−	17.7077i	1.43734	−	0.575424i	0.953946	+	0.299979i	$0.0969798\pi$
$948$		0			0
$949$	36.3274	+	14.5433i	1.17924	+	0.472095i
$950$		0			0
$951$	9.75022	+	15.1716i	0.316172	+	0.491974i
$952$		0			0
$953$	2.49652	+	8.50236i	0.0808702	+	0.275418i	0.989994	−	0.141107i	$-0.0450660\pi$
$953$	2.49652	+	8.50236i	0.0808702	+	0.275418i	−0.909124	+	0.416525i	$0.863248\pi$
$954$		0			0
$955$	55.9624	−	19.3688i	1.81090	−	0.626759i
$956$		0			0
$957$	−2.75285	+	3.86583i	−0.0889869	+	0.124965i
$958$		0			0
$959$	−5.14069	−	19.8236i	−0.166001	−	0.640138i
$960$		0			0
$961$	35.0200	−	3.34400i	1.12968	−	0.107871i
$962$		0			0
$963$	−0.874586	−	1.69646i	−0.0281832	−	0.0546677i
$964$		0			0
$965$	37.6179			1.21096
$966$		0			0
$967$	−6.86472			−0.220755			−0.110377	−	0.993890i	$-0.535206\pi$
$967$	−6.86472			−0.220755			−0.110377	+	0.993890i	$0.535206\pi$
$968$		0			0
$969$	3.78082	+	7.33377i	0.121457	+	0.235594i
$970$		0			0
$971$	38.9122	−	3.71567i	1.24875	−	0.119241i	0.550343	−	0.834939i	$-0.314497\pi$
$971$	38.9122	−	3.71567i	1.24875	−	0.119241i	0.698411	+	0.715697i	$0.253891\pi$
$972$		0			0
$973$	−0.860277	+	0.846508i	−0.0275792	+	0.0271378i
$974$		0			0
$975$	5.17636	−	7.26918i	0.165776	−	0.232800i
$976$		0			0
$977$	11.6420	−	4.02935i	0.372462	−	0.128910i	−0.134423	−	0.990924i	$-0.542918\pi$
$977$	11.6420	−	4.02935i	0.372462	−	0.128910i	0.506885	+	0.862014i	$0.330797\pi$
$978$		0			0
$979$	2.99473	+	10.1991i	0.0957121	+	0.325965i
$980$		0			0
$981$	24.4409	+	38.0308i	0.780339	+	1.21423i
$982$		0			0
$983$	41.4141	+	16.5797i	1.32090	+	0.528810i	0.921647	−	0.388029i	$-0.126844\pi$
$983$	41.4141	+	16.5797i	1.32090	+	0.528810i	0.399257	+	0.916839i	$0.369268\pi$
$984$		0			0
$985$	74.7629	−	29.9305i	2.38214	−	0.953666i
$986$		0			0
$987$	−0.605244	−	2.89449i	−0.0192651	−	0.0921326i
$988$		0			0
$989$	2.72633	−	7.87424i	0.0866924	−	0.250386i
$990$		0			0
$991$	−48.2497	+	9.29937i	−1.53270	+	0.295404i	−0.884673	−	0.466211i	$-0.845619\pi$
$991$	−48.2497	+	9.29937i	−1.53270	+	0.295404i	−0.648029	+	0.761616i	$0.724406\pi$
$992$		0			0
$993$	−2.87392	−	0.413208i	−0.0912012	−	0.0131127i
$994$		0			0
$995$	1.43853	+	10.0052i	0.0456045	+	0.317186i
$996$		0			0
$997$	25.4859	−	1.21404i	0.807147	−	0.0384491i	0.360048	−	0.932934i	$-0.382760\pi$
$997$	25.4859	−	1.21404i	0.807147	−	0.0384491i	0.447099	+	0.894485i	$0.352457\pi$
$998$		0			0
$999$	−3.15508	−	3.00836i	−0.0998222	−	0.0951803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.10	yes	320
7.5	odd	6	inner	644.2.bc.a.33.10	✓	320
23.7	odd	22	inner	644.2.bc.a.605.10	yes	320
161.145	even	66	inner	644.2.bc.a.145.10	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.10	✓	320	7.5	odd	6	inner
644.2.bc.a.145.10	yes	320	161.145	even	66	inner
644.2.bc.a.493.10	yes	320	1.1	even	1	trivial
644.2.bc.a.605.10	yes	320	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.274085 + 0.531650i) q^{3} +(3.06381 - 0.292558i) q^{5} +(1.85568 + 1.88586i) q^{7} +(1.53264 - 2.15229i) q^{9} +O(q^{10})\)	\(q+(0.274085 + 0.531650i) q^{3} +(3.06381 - 0.292558i) q^{5} +(1.85568 + 1.88586i) q^{7} +(1.53264 - 2.15229i) q^{9} +(2.28661 - 0.791402i) q^{11} +(-0.939799 - 3.20066i) q^{13} +(0.995282 + 1.54869i) q^{15} +(-2.74331 - 1.09826i) q^{17} +(-4.33377 + 1.73498i) q^{19} +(-0.494006 + 1.50346i) q^{21} +(-4.66078 + 1.13011i) q^{23} +(4.39168 - 0.846427i) q^{25} +(3.34050 + 0.480292i) q^{27} +(0.466657 + 3.24567i) q^{29} +(8.12585 - 0.387082i) q^{31} +(1.04747 + 0.998764i) q^{33} +(6.23716 + 5.23502i) q^{35} +(-1.05222 - 0.749284i) q^{37} +(1.44405 - 1.37690i) q^{39} +(-7.14425 - 3.26267i) q^{41} +(-0.939375 + 1.46170i) q^{43} +(4.06605 - 7.04260i) q^{45} +(-1.61823 + 0.934288i) q^{47} +(-0.112935 + 6.99909i) q^{49} +(-0.168012 - 1.75950i) q^{51} +(-1.44514 - 1.51562i) q^{53} +(6.77419 - 3.09367i) q^{55} +(-2.11022 - 1.82852i) q^{57} +(2.93607 + 0.712284i) q^{59} +(4.86207 + 2.50657i) q^{61} +(6.90301 - 1.10361i) q^{63} +(-3.81574 - 9.53127i) q^{65} +(0.395822 + 2.05372i) q^{67} +(-1.87827 - 2.16816i) q^{69} +(7.43408 + 8.57939i) q^{71} +(-7.25130 + 9.22078i) q^{73} +(1.65370 + 2.10285i) q^{75} +(5.73567 + 2.84363i) q^{77} +(-6.39301 + 6.70479i) q^{79} +(-1.93233 - 5.58309i) q^{81} +(-1.95415 - 4.27900i) q^{83} +(-8.72628 - 2.56227i) q^{85} +(-1.59766 + 1.13769i) q^{87} +(-0.209028 + 4.38803i) q^{89} +(4.29204 - 7.71172i) q^{91} +(2.43296 + 4.21402i) q^{93} +(-12.7703 + 6.58353i) q^{95} +(4.22277 - 9.24658i) q^{97} +(1.80122 - 6.13438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more