LMFDB - Embedded newform 644.2.bc.a.605.5

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			605.5
Character	$\chi$	$=$	644.605
Dual form			644.2.bc.a.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89530 + 0.0902843i) q^{3} +(-1.65070 + 2.31808i) q^{5} +(-1.26732 + 2.32248i) q^{7} +(0.597594 - 0.0570633i) q^{9} +(0.236397 + 1.22655i) q^{11} +(0.961267 - 3.27377i) q^{13} +(2.91928 - 4.54248i) q^{15} +(-2.70539 - 2.12754i) q^{17} +(-2.03189 + 1.59790i) q^{19} +(2.19227 - 4.51621i) q^{21} +(4.35585 + 2.00663i) q^{23} +(-1.01335 - 2.92788i) q^{25} +(4.50694 - 0.648000i) q^{27} +(1.15149 - 8.00878i) q^{29} +(-2.14781 - 4.16618i) q^{31} +(-0.558782 - 2.30333i) q^{33} +(-3.29172 - 6.77145i) q^{35} +(-0.792882 - 8.30344i) q^{37} +(-1.52632 + 6.29157i) q^{39} +(-8.85506 + 4.04397i) q^{41} +(-0.760372 - 1.18316i) q^{43} +(-0.854168 + 1.47946i) q^{45} +(-7.74681 + 4.47262i) q^{47} +(-3.78780 - 5.88665i) q^{49} +(5.31961 + 3.78808i) q^{51} +(4.66513 + 1.13175i) q^{53} +(-3.23345 - 1.47667i) q^{55} +(3.70678 - 3.21194i) q^{57} +(0.345155 + 0.361989i) q^{59} +(0.0209233 - 0.439234i) q^{61} +(-0.624815 + 1.46022i) q^{63} +(6.00210 + 7.63230i) q^{65} +(7.51285 - 2.60022i) q^{67} +(-8.43681 - 3.40991i) q^{69} +(-2.01845 + 2.32942i) q^{71} +(3.11745 - 7.78702i) q^{73} +(2.18494 + 5.45772i) q^{75} +(-3.14822 - 1.00540i) q^{77} +(-11.3625 + 2.75652i) q^{79} +(-10.2519 + 1.97589i) q^{81} +(2.97437 - 6.51296i) q^{83} +(9.39759 - 2.75938i) q^{85} +(-1.45935 + 15.2830i) q^{87} +(11.4035 + 5.87889i) q^{89} +(6.38503 + 6.38144i) q^{91} +(4.44689 + 7.70224i) q^{93} +(-0.350016 - 7.34773i) q^{95} +(-6.62960 - 14.5168i) q^{97} +(0.211260 + 0.719487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{22}\right)$	$1$

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
$3$	−1.89530	+	0.0902843i	−1.09425	+	0.0521256i	−0.586935	−	0.809634i	$-0.699666\pi$
$3$	−1.89530	+	0.0902843i	−1.09425	+	0.0521256i	−0.507317	+	0.861760i	$0.669363\pi$
$4$		0			0
$5$	−1.65070	+	2.31808i	−0.738214	+	1.03668i	0.259272	+	0.965804i	$0.416517\pi$
$5$	−1.65070	+	2.31808i	−0.738214	+	1.03668i	−0.997485	+	0.0708716i	$0.977422\pi$
$6$		0			0
$7$	−1.26732	+	2.32248i	−0.479002	+	0.877814i
$7$	−1.26732	+	2.32248i	−0.479002	+	0.877814i
$8$		0			0
$9$	0.597594	−	0.0570633i	0.199198	−	0.0190211i
$10$		0			0
$11$	0.236397	+	1.22655i	0.0712765	+	0.369818i	1.00000		0.000956533i	$-0.000304474\pi$
$11$	0.236397	+	1.22655i	0.0712765	+	0.369818i	−0.928723	+	0.370774i	$0.879092\pi$
$12$		0			0
$13$	0.961267	−	3.27377i	0.266607	−	0.907981i	−0.711989	−	0.702191i	$-0.752205\pi$
$13$	0.961267	−	3.27377i	0.266607	−	0.907981i	0.978596	−	0.205790i	$-0.0659765\pi$
$14$		0			0
$15$	2.91928	−	4.54248i	0.753754	−	1.17286i
$16$		0			0
$17$	−2.70539	−	2.12754i	−0.656154	−	0.516005i	0.233666	−	0.972317i	$-0.424928\pi$
$17$	−2.70539	−	2.12754i	−0.656154	−	0.516005i	−0.889820	+	0.456312i	$0.849170\pi$
$18$		0			0
$19$	−2.03189	+	1.59790i	−0.466148	+	0.366583i	−0.823434	−	0.567412i	$-0.807945\pi$
$19$	−2.03189	+	1.59790i	−0.466148	+	0.366583i	0.357286	+	0.933995i	$0.383702\pi$
$20$		0			0
$21$	2.19227	−	4.51621i	0.478392	−	0.985517i
$22$		0			0
$23$	4.35585	+	2.00663i	0.908257	+	0.418412i
$23$	4.35585	+	2.00663i	0.908257	+	0.418412i
$24$		0			0
$25$	−1.01335	−	2.92788i	−0.202670	−	0.585576i
$26$		0			0
$27$	4.50694	−	0.648000i	0.867361	−	0.124708i
$28$		0			0
$29$	1.15149	−	8.00878i	0.213826	−	1.48719i	−0.546394	−	0.837528i	$-0.684000\pi$
$29$	1.15149	−	8.00878i	0.213826	−	1.48719i	0.760220	−	0.649665i	$-0.225091\pi$
$30$		0			0
$31$	−2.14781	−	4.16618i	−0.385759	−	0.748267i	0.613379	−	0.789789i	$-0.289810\pi$
$31$	−2.14781	−	4.16618i	−0.385759	−	0.748267i	−0.999138	+	0.0415214i	$0.986780\pi$
$32$		0			0
$33$	−0.558782	−	2.30333i	−0.0972715	−	0.400958i
$34$		0			0
$35$	−3.29172	−	6.77145i	−0.556402	−	1.14458i
$36$		0			0
$37$	−0.792882	−	8.30344i	−0.130349	−	1.36508i	−0.789816	−	0.613344i	$-0.789824\pi$
$37$	−0.792882	−	8.30344i	−0.130349	−	1.36508i	0.659467	−	0.751733i	$-0.270782\pi$
$38$		0			0
$39$	−1.52632	+	6.29157i	−0.244407	+	1.00746i
$40$		0			0
$41$	−8.85506	+	4.04397i	−1.38293	+	0.631562i	−0.961375	−	0.275242i	$-0.911242\pi$
$41$	−8.85506	+	4.04397i	−1.38293	+	0.631562i	−0.421553	+	0.906804i	$0.638515\pi$
$42$		0			0
$43$	−0.760372	−	1.18316i	−0.115956	−	0.180431i	0.778424	−	0.627738i	$-0.216019\pi$
$43$	−0.760372	−	1.18316i	−0.115956	−	0.180431i	−0.894380	+	0.447308i	$0.852383\pi$
$44$		0			0
$45$	−0.854168	+	1.47946i	−0.127332	+	0.220545i
$46$		0			0
$47$	−7.74681	+	4.47262i	−1.12999	+	0.652399i	−0.943932	−	0.330140i	$-0.892904\pi$
$47$	−7.74681	+	4.47262i	−1.12999	+	0.652399i	−0.186056	+	0.982539i	$0.559571\pi$
$48$		0			0
$49$	−3.78780	−	5.88665i	−0.541114	−	0.840949i
$50$		0			0
$51$	5.31961	+	3.78808i	0.744895	+	0.530437i
$52$		0			0
$53$	4.66513	+	1.13175i	0.640805	+	0.155458i	0.542980	−	0.839746i	$-0.317296\pi$
$53$	4.66513	+	1.13175i	0.640805	+	0.155458i	0.0978257	+	0.995204i	$0.468811\pi$
$54$		0			0
$55$	−3.23345	−	1.47667i	−0.435998	−	0.199114i
$56$		0			0
$57$	3.70678	−	3.21194i	0.490975	−	0.425432i
$58$		0			0
$59$	0.345155	+	0.361989i	0.0449354	+	0.0471269i	0.745818	−	0.666150i	$-0.232059\pi$
$59$	0.345155	+	0.361989i	0.0449354	+	0.0471269i	−0.700883	+	0.713277i	$0.747210\pi$
$60$		0			0
$61$	0.0209233	−	0.439234i	0.00267896	−	0.0562382i	−0.997132	−	0.0756822i	$-0.975887\pi$
$61$	0.0209233	−	0.439234i	0.00267896	−	0.0562382i	0.999811	+	0.0194440i	$0.00618959\pi$
$62$		0			0
$63$	−0.624815	+	1.46022i	−0.0787193	+	0.183970i
$64$		0			0
$65$	6.00210	+	7.63230i	0.744469	+	0.946670i
$66$		0			0
$67$	7.51285	−	2.60022i	0.917840	−	0.317668i	0.173009	−	0.984920i	$-0.444651\pi$
$67$	7.51285	−	2.60022i	0.917840	−	0.317668i	0.744831	+	0.667253i	$0.232530\pi$
$68$		0			0
$69$	−8.43681	−	3.40991i	−1.01567	−	0.410505i
$70$		0			0
$71$	−2.01845	+	2.32942i	−0.239546	+	0.276451i	−0.862774	−	0.505589i	$-0.831275\pi$
$71$	−2.01845	+	2.32942i	−0.239546	+	0.276451i	0.623228	+	0.782040i	$0.285821\pi$
$72$		0			0
$73$	3.11745	−	7.78702i	0.364870	−	0.911402i	−0.626393	−	0.779507i	$-0.715470\pi$
$73$	3.11745	−	7.78702i	0.364870	−	0.911402i	0.991264	−	0.131895i	$-0.0421061\pi$
$74$		0			0
$75$	2.18494	+	5.45772i	0.252295	+	0.630203i
$76$		0			0
$77$	−3.14822	−	1.00540i	−0.358773	−	0.114576i
$78$		0			0
$79$	−11.3625	+	2.75652i	−1.27838	+	0.310132i	−0.816778	−	0.576953i	$-0.804242\pi$
$79$	−11.3625	+	2.75652i	−1.27838	+	0.310132i	−0.461606	+	0.887085i	$0.652727\pi$
$80$		0			0
$81$	−10.2519	+	1.97589i	−1.13910	+	0.219543i
$82$		0			0
$83$	2.97437	−	6.51296i	0.326479	−	0.714890i	−0.673219	−	0.739443i	$-0.735089\pi$
$83$	2.97437	−	6.51296i	0.326479	−	0.714890i	0.999699	+	0.0245531i	$0.00781629\pi$
$84$		0			0
$85$	9.39759	−	2.75938i	1.01931	−	0.299297i
$86$		0			0
$87$	−1.45935	+	15.2830i	−0.156459	+	1.63851i
$88$		0			0
$89$	11.4035	+	5.87889i	1.20876	+	0.623161i	0.940372	−	0.340148i	$-0.110477\pi$
$89$	11.4035	+	5.87889i	1.20876	+	0.623161i	0.268393	+	0.963310i	$0.413508\pi$
$90$		0			0
$91$	6.38503	+	6.38144i	0.669333	+	0.668957i
$92$		0			0
$93$	4.44689	+	7.70224i	0.461121	+	0.798685i
$94$		0			0
$95$	−0.350016	−	7.34773i	−0.0359108	−	0.753861i
$96$		0			0
$97$	−6.62960	−	14.5168i	−0.673134	−	1.47396i	−0.869758	−	0.493479i	$-0.835725\pi$
$97$	−6.62960	−	14.5168i	−0.673134	−	1.47396i	0.196624	−	0.980479i	$-0.437002\pi$
$98$		0			0
$99$	0.211260	+	0.719487i	0.0212325	+	0.0723112i
$100$		0			0
$101$	−6.18214	+	4.40228i	−0.615146	+	0.438043i	−0.844691	−	0.535255i	$-0.820216\pi$
$101$	−6.18214	+	4.40228i	−0.615146	+	0.438043i	0.229545	+	0.973298i	$0.426276\pi$
$102$		0			0
$103$	−3.55885	+	10.2826i	−0.350664	+	1.01318i	0.622411	+	0.782691i	$0.286153\pi$
$103$	−3.55885	+	10.2826i	−0.350664	+	1.01318i	−0.973075	+	0.230488i	$0.925968\pi$
$104$		0			0
$105$	6.85015	+	12.5367i	0.668507	+	1.22346i
$106$		0			0
$107$	11.1980	+	0.533425i	1.08255	+	0.0515681i	0.581264	−	0.813715i	$-0.302558\pi$
$107$	11.1980	+	0.533425i	1.08255	+	0.0515681i	0.501284	+	0.865283i	$0.332861\pi$
$108$		0			0
$109$	−0.855345	+	1.08766i	−0.0819272	+	0.104179i	−0.825289	−	0.564711i	$-0.808988\pi$
$109$	−0.855345	+	1.08766i	−0.0819272	+	0.104179i	0.743362	+	0.668890i	$0.233230\pi$
$110$		0			0
$111$	2.25242	+	15.6659i	0.213790	+	1.48694i
$112$		0			0
$113$	4.58463	+	3.97261i	0.431286	+	0.373711i	0.843279	−	0.537475i	$-0.180622\pi$
$113$	4.58463	+	3.97261i	0.431286	+	0.373711i	−0.411993	+	0.911187i	$0.635167\pi$
$114$		0			0
$115$	−11.8417	+	6.78485i	−1.10425	+	0.632691i
$116$		0			0
$117$	0.387635	−	2.01124i	0.0358368	−	0.185939i
$118$		0			0
$119$	8.36977	−	3.58693i	0.767256	−	0.328813i
$120$		0			0
$121$	8.76351	−	3.50838i	0.796683	−	0.318944i
$122$		0			0
$123$	16.4179	−	8.46401i	1.48035	−	0.763174i
$124$		0			0
$125$	−5.19259	−	1.52468i	−0.464440	−	0.136372i
$126$		0			0
$127$	−2.42478	−	2.79834i	−0.215164	−	0.248313i	0.637899	−	0.770120i	$-0.279804\pi$
$127$	−2.42478	−	2.79834i	−0.215164	−	0.248313i	−0.853064	+	0.521807i	$0.825258\pi$
$128$		0			0
$129$	1.54795	+	2.17380i	0.136290	+	0.191392i
$130$		0			0
$131$	−13.2367	+	13.8822i	−1.15649	+	1.21289i	−0.183261	+	0.983064i	$0.558666\pi$
$131$	−13.2367	+	13.8822i	−1.15649	+	1.21289i	−0.973231	+	0.229830i	$0.926183\pi$
$132$		0			0
$133$	−1.13602	−	6.74407i	−0.0985056	−	0.584785i
$134$		0			0
$135$	−5.93747	+	11.5171i	−0.511016	+	0.991233i
$136$		0			0
$137$	2.35330	+	1.35868i	0.201056	+	0.116079i	0.597148	−	0.802131i	$-0.296301\pi$
$137$	2.35330	+	1.35868i	0.201056	+	0.116079i	−0.396092	+	0.918211i	$0.629634\pi$
$138$		0			0
$139$		−	11.9523i		−	1.01378i	−0.862010	−	0.506892i	$-0.830794\pi$
$139$		−	11.9523i		−	1.01378i	0.862010	−	0.506892i	$-0.169206\pi$
$140$		0			0
$141$	14.2787	−	9.17638i	1.20249	−	0.772790i
$142$		0			0
$143$	4.24268	+	0.405127i	0.354790	+	0.0338784i
$144$		0			0
$145$	16.6642	+	15.8893i	1.38389	+	1.31954i
$146$		0			0
$147$	7.71048	+	10.8150i	0.635950	+	0.892004i
$148$		0			0
$149$	−14.8656	−	5.14505i	−1.21784	−	0.421499i	−0.358804	−	0.933413i	$-0.616815\pi$
$149$	−14.8656	−	5.14505i	−1.21784	−	0.421499i	−0.859037	+	0.511914i	$0.828937\pi$
$150$		0			0
$151$	−11.5255	+	10.9895i	−0.937930	+	0.894314i	−0.994569	−	0.104080i	$-0.966810\pi$
$151$	−11.5255	+	10.9895i	−0.937930	+	0.894314i	0.0566390	+	0.998395i	$0.481962\pi$
$152$		0			0
$153$	−1.73813	−	1.11703i	−0.140519	−	0.0903064i
$154$		0			0
$155$	13.2029	+	1.89829i	1.06048	+	0.152474i
$156$		0			0
$157$	6.97382	+	2.79190i	0.556571	+	0.222817i	0.632857	−	0.774268i	$-0.281882\pi$
$157$	6.97382	+	2.79190i	0.556571	+	0.222817i	−0.0762861	+	0.997086i	$0.524306\pi$
$158$		0			0
$159$	−8.94400	−	1.72382i	−0.709306	−	0.136707i
$160$		0			0
$161$	−10.1806	+	7.57331i	−0.802345	+	0.596860i
$162$		0			0
$163$	−20.4320	−	3.93794i	−1.60036	−	0.308443i	−0.690488	−	0.723343i	$-0.742604\pi$
$163$	−20.4320	−	3.93794i	−1.60036	−	0.308443i	−0.909867	+	0.414900i	$0.863816\pi$
$164$		0			0
$165$	6.26168	+	2.50680i	0.487471	+	0.195154i
$166$		0			0
$167$	−12.2336	−	1.75893i	−0.946665	−	0.136110i	−0.348344	−	0.937367i	$-0.613256\pi$
$167$	−12.2336	−	1.75893i	−0.946665	−	0.136110i	−0.598321	+	0.801257i	$0.704165\pi$
$168$		0			0
$169$	1.14274	+	0.734392i	0.0879028	+	0.0564917i
$170$		0			0
$171$	−1.12307	+	1.07084i	−0.0858830	+	0.0818892i
$172$		0			0
$173$	6.15108	+	2.12891i	0.467658	+	0.161858i	0.550726	−	0.834686i	$-0.314351\pi$
$173$	6.15108	+	2.12891i	0.467658	+	0.161858i	−0.0830685	+	0.996544i	$0.526472\pi$
$174$		0			0
$175$	8.08417	+	1.35708i	0.611106	+	0.102586i
$176$		0			0
$177$	−0.686855	−	0.654915i	−0.0516272	−	0.0492264i
$178$		0			0
$179$	1.54372	+	0.147408i	0.115383	+	0.0110178i	0.152588	−	0.988290i	$-0.451239\pi$
$179$	1.54372	+	0.147408i	0.115383	+	0.0110178i	−0.0372046	+	0.999308i	$0.511845\pi$
$180$		0			0
$181$	−13.5109	+	8.68295i	−1.00426	+	0.645398i	−0.935901	−	0.352263i	$-0.885412\pi$
$181$	−13.5109	+	8.68295i	−1.00426	+	0.645398i	−0.0683581	+	0.997661i	$0.521776\pi$
$182$		0			0
$183$			0.834370i			0.0616784i
$184$		0			0
$185$	20.5568	+	11.8685i	1.51137	+	0.872589i
$186$		0			0
$187$	1.96998	−	3.82124i	0.144059	−	0.279436i
$188$		0			0
$189$	−4.20677	+	11.2885i	−0.305998	+	0.821116i
$190$		0			0
$191$	−5.57404	+	5.84589i	−0.403324	+	0.422994i	−0.893803	−	0.448459i	$-0.851973\pi$
$191$	−5.57404	+	5.84589i	−0.403324	+	0.422994i	0.490480	+	0.871453i	$0.336822\pi$
$192$		0			0
$193$	−11.9844	−	16.8297i	−0.862653	−	1.21143i	−0.975978	−	0.217869i	$-0.930089\pi$
$193$	−11.9844	−	16.8297i	−0.862653	−	1.21143i	0.113325	−	0.993558i	$-0.463850\pi$
$194$		0			0
$195$	−12.0649	−	13.9236i	−0.863983	−	0.997089i
$196$		0			0
$197$	−4.22417	−	1.24033i	−0.300960	−	0.0883697i	0.127766	−	0.991804i	$-0.459219\pi$
$197$	−4.22417	−	1.24033i	−0.300960	−	0.0883697i	−0.428726	+	0.903435i	$0.641037\pi$
$198$		0			0
$199$	11.3716	−	5.86245i	0.806109	−	0.415578i	−0.00535105	−	0.999986i	$-0.501703\pi$
$199$	11.3716	−	5.86245i	0.806109	−	0.415578i	0.811460	+	0.584407i	$0.198673\pi$
$200$		0			0
$201$	−14.0043	+	5.60649i	−0.987790	+	0.395451i
$202$		0			0
$203$	17.1409	+	12.8240i	1.20306	+	0.900069i
$204$		0			0
$205$	5.24277	−	27.2021i	0.366171	−	1.89988i
$206$		0			0
$207$	2.71753	+	0.950593i	0.188882	+	0.0660708i
$208$		0			0
$209$	−2.44023	−	2.11447i	−0.168794	−	0.146261i
$210$		0			0
$211$	−3.21673	−	22.3728i	−0.221449	−	1.54021i	−0.732564	−	0.680698i	$-0.761677\pi$
$211$	−3.21673	−	22.3728i	−0.221449	−	1.54021i	0.511115	−	0.859512i	$-0.329232\pi$
$212$		0			0
$213$	3.61526	−	4.59717i	0.247713	−	0.314993i
$214$		0			0
$215$	3.99781	+	0.190439i	0.272648	+	0.0129878i
$216$		0			0
$217$	12.3978	+	0.291635i	0.841619	+	0.0197975i
$218$		0			0
$219$	−5.20546	+	15.0402i	−0.351753	+	1.01632i
$220$		0			0
$221$	−9.56570	+	6.81170i	−0.643459	+	0.458205i
$222$		0			0
$223$	0.923271	+	3.14437i	0.0618268	+	0.210563i	0.984613	−	0.174750i	$-0.0559117\pi$
$223$	0.923271	+	3.14437i	0.0618268	+	0.210563i	−0.922786	+	0.385313i	$0.874094\pi$
$224$		0			0
$225$	−0.772646	−	1.69186i	−0.0515097	−	0.112791i
$226$		0			0
$227$	−0.546929	−	11.4815i	−0.0363009	−	0.762051i	−0.941490	−	0.337041i	$-0.890574\pi$
$227$	−0.546929	−	11.4815i	−0.0363009	−	0.762051i	0.905189	−	0.425009i	$-0.139729\pi$
$228$		0			0
$229$	−7.62832	−	13.2126i	−0.504093	−	0.873115i	−0.999989	−	0.00473317i	$-0.998493\pi$
$229$	−7.62832	−	13.2126i	−0.504093	−	0.873115i	0.495895	−	0.868382i	$-0.334840\pi$
$230$		0			0
$231$	6.05759	+	1.62130i	0.398560	+	0.106674i
$232$		0			0
$233$	−21.9251	−	11.3032i	−1.43636	−	0.740496i	−0.448203	−	0.893932i	$-0.647936\pi$
$233$	−21.9251	−	11.3032i	−1.43636	−	0.740496i	−0.988159	+	0.153436i	$0.950966\pi$
$234$		0			0
$235$	2.41974	−	25.3407i	0.157846	−	1.65304i
$236$		0			0
$237$	21.2865	−	6.25028i	1.38271	−	0.406000i
$238$		0			0
$239$	1.59087	−	3.48353i	0.102905	−	0.225331i	−0.851175	−	0.524882i	$-0.824110\pi$
$239$	1.59087	−	3.48353i	0.102905	−	0.225331i	0.954080	+	0.299551i	$0.0968368\pi$
$240$		0			0
$241$	−17.9889	+	3.46708i	−1.15877	+	0.223334i	−0.732180	−	0.681112i	$-0.761497\pi$
$241$	−17.9889	+	3.46708i	−1.15877	+	0.223334i	−0.426588	+	0.904446i	$0.640285\pi$
$242$		0			0
$243$	5.97720	−	1.45005i	0.383438	−	0.0930210i
$244$		0			0
$245$	19.8982	+	0.936654i	1.27125	+	0.0598406i
$246$		0			0
$247$	3.27797	+	8.18797i	0.208572	+	0.520988i
$248$		0			0
$249$	−5.04930	+	12.6125i	−0.319986	+	0.799287i
$250$		0			0
$251$	13.9687	−	16.1207i	0.881696	−	1.01753i	−0.118004	−	0.993013i	$-0.537650\pi$
$251$	13.9687	−	16.1207i	0.881696	−	1.01753i	0.999699	−	0.0245178i	$-0.00780504\pi$
$252$		0			0
$253$	−1.43152	+	5.81702i	−0.0899988	+	0.365713i
$254$		0			0
$255$	−17.5621	+	6.07831i	−1.09978	+	0.380639i
$256$		0			0
$257$	8.78738	+	11.1741i	0.548142	+	0.697019i	0.978642	−	0.205571i	$-0.0659053\pi$
$257$	8.78738	+	11.1741i	0.548142	+	0.697019i	−0.430500	+	0.902590i	$0.641663\pi$
$258$		0			0
$259$	20.2894	+	8.68167i	1.26072	+	0.539453i
$260$		0			0
$261$	0.231115	−	4.85171i	0.0143057	−	0.300313i
$262$		0			0
$263$	8.66102	+	9.08341i	0.534061	+	0.560107i	0.934384	−	0.356267i	$-0.115951\pi$
$263$	8.66102	+	9.08341i	0.534061	+	0.560107i	−0.400323	+	0.916374i	$0.631102\pi$
$264$		0			0
$265$	−10.3242	+	8.94597i	−0.634210	+	0.549546i
$266$		0			0
$267$	−22.1437	−	10.1127i	−1.35518	−	0.618888i
$268$		0			0
$269$	−1.39655	−	0.338798i	−0.0851489	−	0.0206569i	0.192958	−	0.981207i	$-0.438192\pi$
$269$	−1.39655	−	0.338798i	−0.0851489	−	0.0206569i	−0.278107	+	0.960550i	$0.589707\pi$
$270$		0			0
$271$	−15.3941	−	10.9621i	−0.935124	−	0.665899i	0.00742293	−	0.999972i	$-0.497637\pi$
$271$	−15.3941	−	10.9621i	−0.935124	−	0.665899i	−0.942547	+	0.334074i	$0.891577\pi$
$272$		0			0
$273$	−12.6777	−	11.5183i	−0.767289	−	0.697118i
$274$		0			0
$275$	3.35163	−	1.93506i	0.202111	−	0.116689i
$276$		0			0
$277$	−1.46713	+	2.54114i	−0.0881511	+	0.152682i	−0.906730	−	0.421712i	$-0.861429\pi$
$277$	−1.46713	+	2.54114i	−0.0881511	+	0.152682i	0.818579	+	0.574395i	$0.194763\pi$
$278$		0			0
$279$	−1.52126	−	2.36712i	−0.0910752	−	0.141716i
$280$		0			0
$281$	−26.7076	+	12.1970i	−1.59324	+	0.727610i	−0.997160	−	0.0753115i	$-0.976005\pi$
$281$	−26.7076	+	12.1970i	−1.59324	+	0.727610i	−0.596084	+	0.802922i	$0.703278\pi$
$282$		0			0
$283$	1.66666	−	6.87006i	0.0990726	−	0.408383i	−0.900581	−	0.434687i	$-0.856859\pi$
$283$	1.66666	−	6.87006i	0.0990726	−	0.408383i	0.999654	+	0.0263046i	$0.00837398\pi$
$284$		0			0
$285$	1.32677	+	13.8946i	0.0785910	+	0.823042i
$286$		0			0
$287$	1.83017	−	25.6907i	0.108032	−	1.51647i
$288$		0			0
$289$	−1.21520	−	5.00912i	−0.0714823	−	0.294654i
$290$		0			0
$291$	13.8757	+	26.9151i	0.813409	+	1.57779i
$292$		0			0
$293$	−2.45980	+	17.1083i	−0.143703	+	0.999479i	0.782553	+	0.622584i	$0.213917\pi$
$293$	−2.45980	+	17.1083i	−0.143703	+	0.999479i	−0.926256	+	0.376895i	$0.876992\pi$
$294$		0			0
$295$	−1.40886	+	0.202564i	−0.0820273	+	0.0117937i
$296$		0			0
$297$	1.86023	+	5.37479i	0.107942	+	0.311877i
$298$		0			0
$299$	10.7564	−	12.3312i	0.622059	−	0.713129i
$300$		0			0
$301$	3.71150	−	0.266501i	0.213927	−	0.0153609i
$302$		0			0
$303$	11.3195	−	8.90179i	0.650291	−	0.511394i
$304$		0			0
$305$	0.983642	+	0.773544i	0.0563232	+	0.0442930i
$306$		0			0
$307$	−1.00209	+	1.55929i	−0.0571924	+	0.0889932i	−0.868672	−	0.495387i	$-0.835026\pi$
$307$	−1.00209	+	1.55929i	−0.0571924	+	0.0889932i	0.811480	+	0.584381i	$0.198662\pi$
$308$		0			0
$309$	5.81674	−	19.8100i	0.330903	−	1.12695i
$310$		0			0
$311$	−4.88412	−	25.3412i	−0.276953	−	1.43697i	−0.807778	−	0.589487i	$-0.799330\pi$
$311$	−4.88412	−	25.3412i	−0.276953	−	1.43697i	0.530825	−	0.847482i	$-0.321882\pi$
$312$		0			0
$313$	23.4784	−	2.24191i	1.32708	−	0.126720i	0.592677	−	0.805440i	$-0.298071\pi$
$313$	23.4784	−	2.24191i	1.32708	−	0.126720i	0.734398	+	0.678720i	$0.237465\pi$
$314$		0			0
$315$	−2.35351	−	3.85874i	−0.132605	−	0.217415i
$316$		0			0
$317$	7.82917	−	10.9945i	0.439730	−	0.617514i	−0.533928	−	0.845530i	$-0.679284\pi$
$317$	7.82917	−	10.9945i	0.439730	−	0.617514i	0.973657	+	0.228016i	$0.0732239\pi$
$318$		0			0
$319$	10.0954	−	0.480901i	0.565231	−	0.0269253i
$320$		0			0
$321$	−21.2717			−1.18727
$322$		0			0
$323$	8.89667			0.495024
$324$		0			0
$325$	−10.5593	+	0.503002i	−0.585725	+	0.0279015i
$326$		0			0
$327$	1.52294	−	2.13867i	0.0842186	−	0.118269i
$328$		0			0
$329$	−0.569870	−	23.6600i	−0.0314180	−	1.30442i
$330$		0			0
$331$	−30.4833	+	2.91081i	−1.67552	+	0.159992i	−0.889102	−	0.457708i	$-0.848670\pi$
$331$	−30.4833	+	2.91081i	−1.67552	+	0.159992i	−0.786413	+	0.617701i	$0.788064\pi$
$332$		0			0
$333$	−0.947643	−	4.91684i	−0.0519305	−	0.269441i
$334$		0			0
$335$	−6.37391	+	21.7075i	−0.348244	+	1.18601i
$336$		0			0
$337$	−10.8898	+	16.9448i	−0.593204	+	0.923043i	0.406751	+	0.913539i	$0.366662\pi$
$337$	−10.8898	+	16.9448i	−0.593204	+	0.923043i	−0.999955	+	0.00950428i	$0.996975\pi$
$338$		0			0
$339$	−9.04792	−	7.11536i	−0.491415	−	0.386453i
$340$		0			0
$341$	4.60227	−	3.61927i	0.249227	−	0.195994i
$342$		0			0
$343$	18.4720	−	1.33680i	0.997392	−	0.0721805i
$344$		0			0
$345$	21.8310	−	13.9285i	1.17534	−	0.749883i
$346$		0			0
$347$	3.20326	+	9.25520i	0.171960	+	0.496845i	0.997743	−	0.0671418i	$-0.0213880\pi$
$347$	3.20326	+	9.25520i	0.171960	+	0.496845i	−0.825784	+	0.563987i	$0.809267\pi$
$348$		0			0
$349$	22.9124	−	3.29430i	1.22647	−	0.176340i	0.501524	−	0.865144i	$-0.332773\pi$
$349$	22.9124	−	3.29430i	1.22647	−	0.176340i	0.724948	+	0.688804i	$0.241864\pi$
$350$		0			0
$351$	2.21096	−	15.3776i	0.118013	−	0.820796i
$352$		0			0
$353$	1.78301	+	3.45856i	0.0949001	+	0.184081i	0.931507	−	0.363723i	$-0.118494\pi$
$353$	1.78301	+	3.45856i	0.0949001	+	0.184081i	−0.836607	+	0.547803i	$0.815464\pi$
$354$		0			0
$355$	−2.06792	−	8.52408i	−0.109754	−	0.452411i
$356$		0			0
$357$	−15.5394	+	7.55396i	−0.822431	+	0.399798i
$358$		0			0
$359$	−0.193902	−	2.03063i	−0.0102338	−	0.107173i	0.988912	−	0.148505i	$-0.0474460\pi$
$359$	−0.193902	−	2.03063i	−0.0102338	−	0.107173i	−0.999145	+	0.0413319i	$0.986840\pi$
$360$		0			0
$361$	−2.90411	+	11.9709i	−0.152848	+	0.630047i
$362$		0			0
$363$	−16.2927	+	7.44064i	−0.855147	+	0.390532i
$364$		0			0
$365$	12.9050	+	20.0805i	0.675476	+	1.05106i
$366$		0			0
$367$	−12.5373	+	21.7152i	−0.654440	+	1.13352i	0.327594	+	0.944819i	$0.393762\pi$
$367$	−12.5373	+	21.7152i	−0.654440	+	1.13352i	−0.982034	+	0.188704i	$0.939571\pi$
$368$		0			0
$369$	−5.06097	+	2.92195i	−0.263463	+	0.152111i
$370$		0			0
$371$	−8.54068	+	9.40037i	−0.443410	+	0.488043i
$372$		0			0
$373$	−9.73698	−	6.93367i	−0.504162	−	0.359012i	0.299502	−	0.954096i	$-0.403180\pi$
$373$	−9.73698	−	6.93367i	−0.504162	−	0.359012i	−0.803664	+	0.595084i	$0.797119\pi$
$374$		0			0
$375$	9.97917	+	2.42092i	0.515322	+	0.125016i
$376$		0			0
$377$	−25.1121	−	11.4683i	−1.29334	−	0.590647i
$378$		0			0
$379$	−5.19533	+	4.50178i	−0.266866	+	0.231241i	−0.778006	−	0.628257i	$-0.783769\pi$
$379$	−5.19533	+	4.50178i	−0.266866	+	0.231241i	0.511140	+	0.859497i	$0.329223\pi$
$380$		0			0
$381$	4.84833	+	5.08478i	0.248387	+	0.260501i
$382$		0			0
$383$	−0.504017	+	10.5806i	−0.0257541	+	0.540645i	0.948716	+	0.316129i	$0.102383\pi$
$383$	−0.504017	+	10.5806i	−0.0257541	+	0.540645i	−0.974470	+	0.224516i	$0.927920\pi$
$384$		0			0
$385$	7.52735	−	5.63820i	0.383629	−	0.287349i
$386$		0			0
$387$	−0.521909	−	0.663661i	−0.0265301	−	0.0337358i
$388$		0			0
$389$	2.81532	−	0.974393i	0.142743	−	0.0494037i	−0.254763	−	0.967004i	$-0.581997\pi$
$389$	2.81532	−	0.974393i	0.142743	−	0.0494037i	0.397505	+	0.917600i	$0.369876\pi$
$390$		0			0
$391$	−7.51507	−	14.6960i	−0.380054	−	0.743208i
$392$		0			0
$393$	23.8341	−	27.5060i	1.20227	−	1.38749i
$394$		0			0
$395$	12.3662	−	30.8894i	0.622213	−	1.55421i
$396$		0			0
$397$	−3.71970	−	9.29137i	−0.186687	−	0.466320i	0.805269	−	0.592910i	$-0.202021\pi$
$397$	−3.71970	−	9.29137i	−0.186687	−	0.466320i	−0.991955	+	0.126590i	$0.959597\pi$
$398$		0			0
$399$	2.76199	+	12.6795i	0.138272	+	0.634768i
$400$		0			0
$401$	−18.9854	+	4.60580i	−0.948083	+	0.230002i	−0.679850	−	0.733351i	$-0.737955\pi$
$401$	−18.9854	+	4.60580i	−0.948083	+	0.230002i	−0.268233	+	0.963354i	$0.586440\pi$
$402$		0			0
$403$	−15.7037	+	3.02665i	−0.782259	+	0.150768i
$404$		0			0
$405$	12.3425	−	27.0263i	0.613303	−	1.34295i
$406$		0			0
$407$	9.99712	−	2.93542i	0.495539	−	0.145503i
$408$		0			0
$409$	−0.287476	+	3.01059i	−0.0142148	+	0.148864i	−0.999793	−	0.0203580i	$-0.993519\pi$
$409$	−0.287476	+	3.01059i	−0.0142148	+	0.148864i	0.985578	+	0.169222i	$0.0541255\pi$
$410$		0			0
$411$	−4.58287	−	2.36263i	−0.226056	−	0.116540i
$412$		0			0
$413$	−1.27813	+	0.342860i	−0.0628928	+	0.0168710i
$414$		0			0
$415$	10.1878	+	17.6457i	0.500098	+	0.866195i
$416$		0			0
$417$	1.07911	+	22.6532i	0.0528441	+	1.10933i
$418$		0			0
$419$	2.25711	+	4.94239i	0.110267	+	0.241452i	0.956719	−	0.291014i	$-0.0939927\pi$
$419$	2.25711	+	4.94239i	0.110267	+	0.241452i	−0.846451	+	0.532466i	$0.821265\pi$
$420$		0			0
$421$	−4.89997	−	16.6878i	−0.238810	−	0.813312i	−0.988461	−	0.151478i	$-0.951597\pi$
$421$	−4.89997	−	16.6878i	−0.238810	−	0.813312i	0.749651	−	0.661834i	$-0.230221\pi$
$422$		0			0
$423$	−4.37422	+	3.11487i	−0.212682	+	0.151450i
$424$		0			0
$425$	−3.48769	+	10.0770i	−0.169178	+	0.488807i
$426$		0			0
$427$	0.993595	+	0.605245i	0.0480834	+	0.0292898i
$428$		0			0
$429$	−8.07772	−	0.384789i	−0.389996	−	0.0185778i
$430$		0			0
$431$	−13.6808	+	17.3965i	−0.658981	+	0.837962i	−0.994573	−	0.104045i	$-0.966821\pi$
$431$	−13.6808	+	17.3965i	−0.658981	+	0.837962i	0.335592	+	0.942007i	$0.391064\pi$
$432$		0			0
$433$	−4.62142	−	32.1427i	−0.222091	−	1.54468i	−0.730108	−	0.683331i	$-0.760530\pi$
$433$	−4.62142	−	32.1427i	−0.222091	−	1.54468i	0.508017	−	0.861347i	$-0.330379\pi$
$434$		0			0
$435$	−33.0183	−	28.6105i	−1.58310	−	1.37177i
$436$		0			0
$437$	−12.0570	+	2.88294i	−0.576765	+	0.137910i
$438$		0			0
$439$	−3.16850	+	16.4398i	−0.151224	+	0.784627i	0.824540	+	0.565803i	$0.191434\pi$
$439$	−3.16850	+	16.4398i	−0.151224	+	0.784627i	−0.975765	+	0.218823i	$0.929778\pi$
$440$		0			0
$441$	−2.59948	−	3.30168i	−0.123785	−	0.157223i
$442$		0			0
$443$	27.4683	−	10.9966i	1.30506	−	0.522466i	0.388161	−	0.921592i	$-0.373110\pi$
$443$	27.4683	−	10.9966i	1.30506	−	0.522466i	0.916896	+	0.399126i	$0.130686\pi$
$444$		0			0
$445$	−32.4514	+	16.7298i	−1.53834	+	0.793071i
$446$		0			0
$447$	28.6394	+	8.40928i	1.35460	+	0.397745i
$448$		0			0
$449$	22.1561	+	25.5695i	1.04561	+	1.20670i	0.977917	+	0.208994i	$0.0670190\pi$
$449$	22.1561	+	25.5695i	1.04561	+	1.20670i	0.0676950	+	0.997706i	$0.478436\pi$
$450$		0			0
$451$	−7.05343	−	9.90516i	−0.332133	−	0.466416i
$452$		0			0
$453$	20.8520	−	21.8690i	0.979715	−	1.02750i
$454$		0			0
$455$	−25.3324	+	4.26718i	−1.18760	+	0.200048i
$456$		0			0
$457$	8.37882	−	16.2526i	0.391944	−	0.760266i	−0.607475	−	0.794339i	$-0.707817\pi$
$457$	8.37882	−	16.2526i	0.391944	−	0.760266i	0.999419	+	0.0340727i	$0.0108478\pi$
$458$		0			0
$459$	−13.5717	−	7.83562i	−0.633472	−	0.365735i
$460$		0			0
$461$			19.9289i			0.928183i	0.885787	+	0.464091i	$0.153619\pi$
$461$			19.9289i			0.928183i	−0.885787	+	0.464091i	$0.846381\pi$
$462$		0			0
$463$	30.8247	−	19.8098i	1.43254	−	0.920641i	0.432727	−	0.901525i	$-0.357551\pi$
$463$	30.8247	−	19.8098i	1.43254	−	0.920641i	0.999817	−	0.0191158i	$-0.00608512\pi$
$464$		0			0
$465$	−25.1949	−	2.40582i	−1.16838	−	0.111567i
$466$		0			0
$467$	−15.0879	−	14.3863i	−0.698184	−	0.665717i	0.255403	−	0.966835i	$-0.417792\pi$
$467$	−15.0879	−	14.3863i	−0.698184	−	0.665717i	−0.953587	+	0.301118i	$0.902640\pi$
$468$		0			0
$469$	−3.48223	+	20.7437i	−0.160795	+	0.957856i
$470$		0			0
$471$	−13.4695	−	4.66185i	−0.620644	−	0.214807i
$472$		0			0
$473$	1.27145	−	1.21233i	0.0584615	−	0.0557429i
$474$		0			0
$475$	6.73747	+	4.32991i	0.309136	+	0.198670i
$476$		0			0
$477$	2.85244	+	0.410118i	0.130604	+	0.0187780i
$478$		0			0
$479$	−7.46898	−	2.99013i	−0.341266	−	0.136622i	0.194698	−	0.980863i	$-0.437627\pi$
$479$	−7.46898	−	2.99013i	−0.341266	−	0.136622i	−0.535964	+	0.844241i	$0.680052\pi$
$480$		0			0
$481$	−27.9457	−	5.38610i	−1.27422	−	0.245585i
$482$		0			0
$483$	18.6116	−	15.2728i	0.846856	−	0.694938i
$484$		0			0
$485$	44.5945	+	8.59489i	2.02493	+	0.390274i
$486$		0			0
$487$	1.07726	+	0.431270i	0.0488154	+	0.0195427i	0.395942	−	0.918276i	$-0.370418\pi$
$487$	1.07726	+	0.431270i	0.0488154	+	0.0195427i	−0.347126	+	0.937818i	$0.612842\pi$
$488$		0			0
$489$	39.0802	+	5.61889i	1.76727	+	0.254095i
$490$		0			0
$491$	8.32596	+	5.35077i	0.375745	+	0.241477i	0.714859	−	0.699269i	$-0.246491\pi$
$491$	8.32596	+	5.35077i	0.375745	+	0.241477i	−0.339114	+	0.940745i	$0.610127\pi$
$492$		0			0
$493$	−20.1543	+	19.2171i	−0.907702	+	0.865492i
$494$		0			0
$495$	−2.01655	−	0.697936i	−0.0906374	−	0.0313699i
$496$		0			0
$497$	−2.85199	−	7.63992i	−0.127929	−	0.342697i
$498$		0			0
$499$	−8.69792	−	8.29345i	−0.389372	−	0.371266i	0.469956	−	0.882690i	$-0.344270\pi$
$499$	−8.69792	−	8.29345i	−0.389372	−	0.371266i	−0.859329	+	0.511424i	$0.829118\pi$
$500$		0			0
$501$	23.3452	+	2.22919i	1.04298	+	0.0995930i
$502$		0			0
$503$	−2.20005	+	1.41389i	−0.0980953	+	0.0630420i	−0.588769	−	0.808301i	$-0.700387\pi$
$503$	−2.20005	+	1.41389i	−0.0980953	+	0.0630420i	0.490673	+	0.871344i	$0.336751\pi$
$504$		0			0
$505$		−	21.5975i		−	0.961076i
$506$		0			0
$507$	−2.23213	−	1.28872i	−0.0991325	−	0.0572342i
$508$		0			0
$509$	11.0823	−	21.4967i	0.491215	−	0.952825i	−0.504765	−	0.863257i	$-0.668421\pi$
$509$	11.0823	−	21.4967i	0.491215	−	0.952825i	0.995981	−	0.0895681i	$-0.0285487\pi$
$510$		0			0
$511$	14.1344	+	17.1089i	0.625267	+	0.756852i
$512$		0			0
$513$	−8.12218	+	8.51830i	−0.358603	+	0.376092i
$514$		0			0
$515$	−17.9614	−	25.2232i	−0.791472	−	1.11147i
$516$		0			0
$517$	−7.31721	−	8.44451i	−0.321810	−	0.371389i
$518$		0			0
$519$	−11.8503	−	3.47957i	−0.520172	−	0.152736i
$520$		0			0
$521$	35.3508	−	18.2246i	1.54875	−	0.798435i	0.549436	−	0.835536i	$-0.314843\pi$
$521$	35.3508	−	18.2246i	1.54875	−	0.798435i	0.999312	+	0.0371007i	$0.0118122\pi$
$522$		0			0
$523$	20.9611	−	8.39154i	0.916563	−	0.366936i	0.135060	−	0.990837i	$-0.456877\pi$
$523$	20.9611	−	8.39154i	0.916563	−	0.366936i	0.781503	+	0.623901i	$0.214453\pi$
$524$		0			0
$525$	−15.4445	−	1.84221i	−0.674051	−	0.0804004i
$526$		0			0
$527$	−3.05305	+	15.8407i	−0.132993	+	0.690032i
$528$		0			0
$529$	14.9468	+	17.4812i	0.649862	+	0.760052i
$530$		0			0
$531$	0.226919	+	0.196626i	0.00984745	+	0.00853286i
$532$		0			0
$533$	4.72697	+	32.8768i	0.204748	+	1.42405i
$534$		0			0
$535$	−19.7210	+	25.0772i	−0.852611	+	1.08418i
$536$		0			0
$537$	−2.93913	−	0.140008i	−0.126833	−	0.00604179i
$538$		0			0
$539$	6.32482	−	6.03750i	0.272429	−	0.260053i
$540$		0			0
$541$	−11.3841	+	32.8923i	−0.489442	+	1.41415i	0.382233	+	0.924066i	$0.375155\pi$
$541$	−11.3841	+	32.8923i	−0.489442	+	1.41415i	−0.871675	+	0.490084i	$0.836966\pi$
$542$		0			0
$543$	24.8233	−	17.6766i	1.06527	−	0.758576i
$544$		0			0
$545$	−1.10937	−	3.77815i	−0.0475200	−	0.161838i
$546$		0			0
$547$	15.6043	+	34.1687i	0.667194	+	1.46095i	0.875664	+	0.482921i	$0.160424\pi$
$547$	15.6043	+	34.1687i	0.667194	+	1.46095i	−0.208470	+	0.978029i	$0.566848\pi$
$548$		0			0
$549$	−0.0125605	−	0.263678i	−0.000536070	−	0.0112535i
$550$		0			0
$551$	10.4575	+	18.1130i	0.445505	+	0.771638i
$552$		0			0
$553$	7.99801	−	29.8826i	0.340110	−	1.27074i
$554$		0			0
$555$	−40.0329	−	20.6384i	−1.69930	−	0.876051i
$556$		0			0
$557$	−0.383206	+	4.01312i	−0.0162370	+	0.170041i	−0.999953	−	0.00968808i	$-0.996916\pi$
$557$	−0.383206	+	4.01312i	−0.0162370	+	0.170041i	0.983716	+	0.179729i	$0.0575222\pi$
$558$		0			0
$559$	−4.60433	+	1.35195i	−0.194742	+	0.0571815i
$560$		0			0
$561$	−3.38871	+	7.42024i	−0.143072	+	0.313283i
$562$		0			0
$563$	22.0735	−	4.25431i	0.930286	−	0.179298i	0.298472	−	0.954418i	$-0.403523\pi$
$563$	22.0735	−	4.25431i	0.930286	−	0.179298i	0.631814	+	0.775120i	$0.282311\pi$
$564$		0			0
$565$	−16.7767	+	4.06997i	−0.705799	+	0.171225i
$566$		0			0
$567$	8.40347	−	26.3139i	0.352913	−	1.10508i
$568$		0			0
$569$	10.3019	+	25.7330i	0.431880	+	1.07878i	0.971535	+	0.236898i	$0.0761306\pi$
$569$	10.3019	+	25.7330i	0.431880	+	1.07878i	−0.539655	+	0.841887i	$0.681445\pi$
$570$		0			0
$571$	8.54835	−	21.3528i	0.357737	−	0.893585i	−0.634915	−	0.772582i	$-0.718965\pi$
$571$	8.54835	−	21.3528i	0.357737	−	0.893585i	0.992652	−	0.121003i	$-0.0386110\pi$
$572$		0			0
$573$	10.0367	−	11.5830i	0.419289	−	0.483885i
$574$		0			0
$575$	1.46119	−	14.7868i	0.0609358	−	0.616653i
$576$		0			0
$577$	31.9973	−	11.0744i	1.33206	−	0.461032i	0.434007	−	0.900910i	$-0.357099\pi$
$577$	31.9973	−	11.0744i	1.33206	−	0.461032i	0.898058	+	0.439877i	$0.144978\pi$
$578$		0			0
$579$	24.2334	+	30.8153i	1.00711	+	1.28064i
$580$		0			0
$581$	11.3567	+	15.1619i	0.471156	+	0.629022i
$582$		0			0
$583$	−0.285317	+	5.98955i	−0.0118166	+	0.248062i
$584$		0			0
$585$	4.02234	+	4.21851i	0.166303	+	0.174414i
$586$		0			0
$587$	−20.5031	+	17.7660i	−0.846253	+	0.733283i	−0.965728	−	0.259554i	$-0.916424\pi$
$587$	−20.5031	+	17.7660i	−0.846253	+	0.733283i	0.119475	+	0.992837i	$0.461879\pi$
$588$		0			0
$589$	11.0213	+	5.03324i	0.454123	+	0.207391i
$590$		0			0
$591$	8.11805	+	1.96942i	0.333932	+	0.0810110i
$592$		0			0
$593$	−4.53751	−	3.23115i	−0.186333	−	0.132687i	0.483084	−	0.875574i	$-0.339517\pi$
$593$	−4.53751	−	3.23115i	−0.186333	−	0.132687i	−0.669417	+	0.742887i	$0.733456\pi$
$594$		0			0
$595$	−5.50116	+	25.3227i	−0.225526	+	1.03813i
$596$		0			0
$597$	−21.0232	+	12.1378i	−0.860424	+	0.496766i
$598$		0			0
$599$	−18.4396	+	31.9383i	−0.753422	+	1.30496i	0.192734	+	0.981251i	$0.438265\pi$
$599$	−18.4396	+	31.9383i	−0.753422	+	1.30496i	−0.946155	+	0.323713i	$0.895069\pi$
$600$		0			0
$601$	15.3376	+	23.8658i	0.625635	+	0.973508i	0.998950	+	0.0458031i	$0.0145847\pi$
$601$	15.3376	+	23.8658i	0.625635	+	0.973508i	−0.373315	+	0.927705i	$0.621779\pi$
$602$		0			0
$603$	4.34125	−	1.98258i	0.176789	−	0.0807371i
$604$		0			0
$605$	−6.33319	+	26.1058i	−0.257481	+	1.06135i
$606$		0			0
$607$	−3.61264	−	37.8333i	−0.146633	−	1.53561i	−0.706912	−	0.707302i	$-0.749912\pi$
$607$	−3.61264	−	37.8333i	−0.146633	−	1.53561i	0.560279	−	0.828304i	$-0.310694\pi$
$608$		0			0
$609$	−33.6450	−	22.7578i	−1.36336	−	0.922192i
$610$		0			0
$611$	7.19561	+	29.6607i	0.291103	+	1.19994i
$612$		0			0
$613$	−2.42320	−	4.70035i	−0.0978721	−	0.189845i	0.834816	−	0.550529i	$-0.185574\pi$
$613$	−2.42320	−	4.70035i	−0.0978721	−	0.189845i	−0.932688	+	0.360683i	$0.882544\pi$
$614$		0			0
$615$	−7.48071	+	52.0294i	−0.301651	+	2.09803i
$616$		0			0
$617$	−22.7953	+	3.27748i	−0.917706	+	0.131946i	−0.584953	−	0.811068i	$-0.698887\pi$
$617$	−22.7953	+	3.27748i	−0.917706	+	0.131946i	−0.332754	+	0.943014i	$0.607978\pi$
$618$		0			0
$619$	5.12492	+	14.8075i	0.205988	+	0.595163i	0.999917	−	0.0128466i	$-0.00408932\pi$
$619$	5.12492	+	14.8075i	0.205988	+	0.595163i	−0.793929	+	0.608010i	$0.791968\pi$
$620$		0			0
$621$	20.9318	+	6.22119i	0.839966	+	0.249648i
$622$		0			0
$623$	−28.1054	+	19.0338i	−1.12602	+	0.762574i
$624$		0			0
$625$	24.2828	−	19.0962i	0.971312	−	0.763848i
$626$		0			0
$627$	4.81587	+	3.78725i	0.192327	+	0.151248i
$628$		0			0
$629$	−15.5209	+	24.1509i	−0.618858	+	0.962961i
$630$		0			0
$631$	−6.40276	+	21.8058i	−0.254890	+	0.868076i	0.728264	+	0.685297i	$0.240327\pi$
$631$	−6.40276	+	21.8058i	−0.254890	+	0.868076i	−0.983154	+	0.182779i	$0.941491\pi$
$632$		0			0
$633$	8.11658	+	42.1128i	0.322605	+	1.67383i
$634$		0			0
$635$	10.4894	−	1.00161i	0.416257	−	0.0397477i
$636$		0			0
$637$	−22.9126	+	6.74175i	−0.907831	+	0.267118i
$638$		0			0
$639$	−1.07329	+	1.50722i	−0.0424587	+	0.0596248i
$640$		0			0
$641$	27.7539	−	1.32208i	1.09621	−	0.0522190i	0.508328	−	0.861164i	$-0.330264\pi$
$641$	27.7539	−	1.32208i	1.09621	−	0.0522190i	0.587885	+	0.808945i	$0.299961\pi$
$642$		0			0
$643$	−7.88943			−0.311129			−0.155564	−	0.987826i	$-0.549720\pi$
$643$	−7.88943			−0.311129			−0.155564	+	0.987826i	$0.549720\pi$
$644$		0			0
$645$	−7.59424			−0.299023
$646$		0			0
$647$	−48.6850	+	2.31915i	−1.91400	+	0.0911753i	−0.970633	−	0.240563i	$-0.922668\pi$
$647$	−48.6850	+	2.31915i	−1.91400	+	0.0911753i	−0.943371	+	0.331738i	$0.892365\pi$
$648$		0			0
$649$	−0.362402	+	0.508922i	−0.0142255	+	0.0199770i
$650$		0			0
$651$	−23.5239	+	0.566591i	−0.921975	+	0.0222065i
$652$		0			0
$653$	−36.7570	+	3.50987i	−1.43841	+	0.137352i	−0.784928	−	0.619587i	$-0.787300\pi$
$653$	−36.7570	+	3.50987i	−1.43841	+	0.137352i	−0.653486	+	0.756939i	$0.726694\pi$
$654$		0			0
$655$	−10.3303	−	53.5989i	−0.403640	−	2.09428i
$656$		0			0
$657$	1.41862	−	4.83137i	0.0553455	−	0.188490i
$658$		0			0
$659$	−16.2401	+	25.2702i	−0.632626	+	0.984386i	0.365929	+	0.930643i	$0.380751\pi$
$659$	−16.2401	+	25.2702i	−0.632626	+	0.984386i	−0.998555	+	0.0537426i	$0.982885\pi$
$660$		0			0
$661$	27.3582	+	21.5147i	1.06411	+	0.836826i	0.987084	−	0.160203i	$-0.0512150\pi$
$661$	27.3582	+	21.5147i	1.06411	+	0.836826i	0.0770265	+	0.997029i	$0.475457\pi$
$662$		0			0
$663$	17.5149	−	13.7739i	0.680221	−	0.534932i
$664$		0			0
$665$	17.5085	+	8.49903i	0.678951	+	0.329578i
$666$		0			0
$667$	21.0864	−	32.5744i	0.816469	−	1.26129i
$668$		0			0
$669$	−2.03376	−	5.87617i	−0.0786298	−	0.227186i
$670$		0			0
$671$	0.543688	−	0.0781705i	0.0209888	−	0.00301774i
$672$		0			0
$673$	−5.49284	+	38.2035i	−0.211733	+	1.47264i	0.555633	+	0.831428i	$0.312476\pi$
$673$	−5.49284	+	38.2035i	−0.211733	+	1.47264i	−0.767366	+	0.641210i	$0.778433\pi$
$674$		0			0
$675$	−6.46437	−	12.5391i	−0.248814	−	0.482631i
$676$		0			0
$677$	9.90234	+	40.8180i	0.380578	+	1.56876i	0.764017	+	0.645197i	$0.223224\pi$
$677$	9.90234	+	40.8180i	0.380578	+	1.56876i	−0.383439	+	0.923566i	$0.625260\pi$
$678$		0			0
$679$	42.1168	+	3.00035i	1.61629	+	0.115143i
$680$		0			0
$681$	2.07319	+	21.7114i	0.0794448	+	0.831983i
$682$		0			0
$683$	7.36381	−	30.3540i	0.281768	−	1.16146i	−0.638326	−	0.769766i	$-0.720373\pi$
$683$	7.36381	−	30.3540i	0.281768	−	1.16146i	0.920094	−	0.391698i	$-0.128112\pi$
$684$		0			0
$685$	−7.03409	+	3.21236i	−0.268759	+	0.122738i
$686$		0			0
$687$	15.6508	+	24.3532i	0.597117	+	0.929132i
$688$		0			0
$689$	8.18953	−	14.1847i	0.311996	−	0.540393i
$690$		0			0
$691$	−21.8780	+	12.6312i	−0.832277	+	0.480515i	−0.854632	−	0.519235i	$-0.826217\pi$
$691$	−21.8780	+	12.6312i	−0.832277	+	0.480515i	0.0223547	+	0.999750i	$0.492884\pi$
$692$		0			0
$693$	−1.93873	−	0.421173i	−0.0736461	−	0.0159991i
$694$		0			0
$695$	27.7064	+	19.7297i	1.05096	+	0.748389i
$696$		0			0
$697$	32.5601	+	7.89900i	1.23330	+	0.299196i
$698$		0			0
$699$	42.5752	+	19.4434i	1.61034	+	0.735418i
$700$		0			0
$701$	−14.1484	+	12.2596i	−0.534377	+	0.463040i	−0.879758	−	0.475422i	$-0.842295\pi$
$701$	−14.1484	+	12.2596i	−0.534377	+	0.463040i	0.345381	+	0.938463i	$0.387750\pi$
$702$		0			0
$703$	14.8791	+	15.6048i	0.561176	+	0.588545i
$704$		0			0
$705$	−2.29827	+	48.2466i	−0.0865578	+	1.81707i
$706$		0			0
$707$	−2.38944	−	19.9370i	−0.0898642	−	0.749807i
$708$		0			0
$709$	10.9373	+	13.9079i	0.410759	+	0.522322i	0.946780	−	0.321882i	$-0.104316\pi$
$709$	10.9373	+	13.9079i	0.410759	+	0.522322i	−0.536021	+	0.844205i	$0.680073\pi$
$710$		0			0
$711$	−6.63288	+	2.29566i	−0.248752	+	0.0860940i
$712$		0			0
$713$	−0.995556	−	22.4571i	−0.0372839	−	0.841025i
$714$		0			0
$715$	−7.94248	+	9.16612i	−0.297032	+	0.342793i
$716$		0			0
$717$	−2.70068	+	6.74596i	−0.100859	+	0.251933i
$718$		0			0
$719$	−9.96475	−	24.8907i	−0.371622	−	0.928268i	−0.989830	−	0.142253i	$-0.954565\pi$
$719$	−9.96475	−	24.8907i	−0.371622	−	0.928268i	0.618208	−	0.786015i	$-0.287859\pi$
$720$		0			0
$721$	−19.3710	−	21.2968i	−0.721413	−	0.793133i
$722$		0			0
$723$	33.7814	−	8.19527i	1.25634	−	0.304785i
$724$		0			0
$725$	−24.6156	+	4.74427i	−0.914201	+	0.176198i
$726$		0			0
$727$	−3.94548	+	8.63940i	−0.146330	+	0.320418i	−0.968577	−	0.248712i	$-0.919993\pi$
$727$	−3.94548	+	8.63940i	−0.146330	+	0.320418i	0.822248	+	0.569130i	$0.192720\pi$
$728$		0			0
$729$	18.8553	−	5.53641i	0.698343	−	0.205052i
$730$		0			0
$731$	−0.460125	+	4.81864i	−0.0170183	+	0.178224i
$732$		0			0
$733$	−41.1332	−	21.2056i	−1.51929	−	0.783248i	−0.521732	−	0.853109i	$-0.674714\pi$
$733$	−41.1332	−	21.2056i	−1.51929	−	0.783248i	−0.997557	+	0.0698616i	$0.977744\pi$
$734$		0			0
$735$	−37.7976	+	0.0212554i	−1.39419	+	0.000784017i
$736$		0			0
$737$	4.96531	+	8.60017i	0.182900	+	0.316791i
$738$		0			0
$739$	−2.45510	−	51.5390i	−0.0903124	−	1.89589i	−0.360013	−	0.932947i	$-0.617228\pi$
$739$	−2.45510	−	51.5390i	−0.0903124	−	1.89589i	0.269701	−	0.962944i	$-0.413075\pi$
$740$		0			0
$741$	−6.95197	−	15.2227i	−0.255387	−	0.559220i
$742$		0			0
$743$	−12.1066	−	41.2311i	−0.444146	−	1.51262i	−0.812513	−	0.582943i	$-0.801901\pi$
$743$	−12.1066	−	41.2311i	−0.444146	−	1.51262i	0.368367	−	0.929681i	$-0.379917\pi$
$744$		0			0
$745$	36.4653	−	25.9668i	1.33598	−	0.951350i
$746$		0			0
$747$	1.40581	−	4.06183i	0.0514360	−	0.148615i
$748$		0			0
$749$	−15.4303	+	25.3310i	−0.563810	+	0.925574i
$750$		0			0
$751$	20.2466	+	0.964466i	0.738810	+	0.0351939i	0.413613	−	0.910453i	$-0.364267\pi$
$751$	20.2466	+	0.964466i	0.738810	+	0.0351939i	0.325196	+	0.945646i	$0.394570\pi$
$752$		0			0
$753$	−25.0194	+	31.8148i	−0.911757	+	1.15939i
$754$		0			0
$755$	−6.44951	−	44.8573i	−0.234722	−	1.63252i
$756$		0			0
$757$	−5.58172	−	4.83659i	−0.202871	−	0.175789i	0.547500	−	0.836806i	$-0.315580\pi$
$757$	−5.58172	−	4.83659i	−0.202871	−	0.175789i	−0.750371	+	0.661017i	$0.770125\pi$
$758$		0			0
$759$	2.18797	−	11.1542i	0.0794184	−	0.404873i
$760$		0			0
$761$	0.764051	−	3.96427i	0.0276968	−	0.143705i	−0.965448	−	0.260596i	$-0.916081\pi$
$761$	0.764051	−	3.96427i	0.0276968	−	0.143705i	0.993145	+	0.116892i	$0.0372930\pi$
$762$		0			0
$763$	−1.44207	−	3.36493i	−0.0522064	−	0.121819i
$764$		0			0
$765$	5.45848	−	2.18525i	0.197352	−	0.0790078i
$766$		0			0
$767$	1.51686	−	0.781993i	0.0547705	−	0.0282361i
$768$		0			0
$769$	39.0537	+	11.4672i	1.40831	+	0.413518i	0.895530	−	0.445001i	$-0.146797\pi$
$769$	39.0537	+	11.4672i	1.40831	+	0.413518i	0.512782	+	0.858519i	$0.328615\pi$
$770$		0			0
$771$	−17.6636	−	20.3848i	−0.636138	−	0.734142i
$772$		0			0
$773$	−17.1641	−	24.1036i	−0.617350	−	0.866947i	0.380988	−	0.924580i	$-0.375584\pi$
$773$	−17.1641	−	24.1036i	−0.617350	−	0.866947i	−0.998338	+	0.0576332i	$0.981645\pi$
$774$		0			0
$775$	−10.0216	+	10.5103i	−0.359986	+	0.377542i
$776$		0			0
$777$	−39.2383	−	14.6226i	−1.40767	−	0.524581i
$778$		0			0
$779$	11.5307	−	22.3664i	0.413130	−	0.801360i
$780$		0			0
$781$	−3.33429	−	1.92506i	−0.119310	−	0.0688839i
$782$		0			0
$783$		−	36.8413i		−	1.31660i
$784$		0			0
$785$	−17.9835	+	11.5573i	−0.641858	+	0.412497i
$786$		0			0
$787$	50.3237	+	4.80533i	1.79385	+	0.171292i	0.938160	−	0.346201i	$-0.112529\pi$
$787$	50.3237	+	4.80533i	1.79385	+	0.171292i	0.855687	+	0.517493i	$0.173135\pi$
$788$		0			0
$789$	−17.2353	−	16.4338i	−0.613593	−	0.585060i
$790$		0			0
$791$	−15.0365	+	5.61314i	−0.534636	+	0.199580i
$792$		0			0
$793$	−1.41784	−	0.490720i	−0.0503490	−	0.0174260i
$794$		0			0
$795$	18.7598	−	17.8874i	0.665340	−	0.634401i
$796$		0			0
$797$	14.2239	+	9.14114i	0.503836	+	0.323796i	0.767749	−	0.640751i	$-0.221377\pi$
$797$	14.2239	+	9.14114i	0.503836	+	0.323796i	−0.263913	+	0.964547i	$0.585013\pi$
$798$		0			0
$799$	30.4739	+	4.38148i	1.07809	+	0.155006i
$800$		0			0
$801$	7.15011	+	2.86247i	0.252637	+	0.101140i
$802$		0			0
$803$	10.2881	+	1.98287i	0.363059	+	0.0699739i
$804$		0			0
$805$	−0.750413	−	36.1007i	−0.0264486	−	1.27238i
$806$		0			0
$807$	2.67746	+	0.516038i	0.0942511	+	0.0181654i
$808$		0			0
$809$	−41.5014	−	16.6147i	−1.45911	−	0.584140i	−0.499712	−	0.866192i	$-0.666561\pi$
$809$	−41.5014	−	16.6147i	−1.45911	−	0.584140i	−0.959399	+	0.282051i	$0.908985\pi$
$810$		0			0
$811$	2.48801	+	0.357721i	0.0873658	+	0.0125613i	0.185859	−	0.982576i	$-0.440493\pi$
$811$	2.48801	+	0.357721i	0.0873658	+	0.0125613i	−0.0984933	+	0.995138i	$0.531402\pi$
$812$		0			0
$813$	30.1661	+	19.3866i	1.05797	+	0.679917i
$814$		0			0
$815$	42.8554	−	40.8626i	1.50116	−	1.43135i
$816$		0			0
$817$	3.43557	+	1.18906i	0.120195	+	0.0416000i
$818$		0			0
$819$	4.17980	+	3.44916i	0.146054	+	0.120523i
$820$		0			0
$821$	−11.3762	−	10.8472i	−0.397034	−	0.378571i	0.465094	−	0.885261i	$-0.346020\pi$
$821$	−11.3762	−	10.8472i	−0.397034	−	0.378571i	−0.862128	+	0.506690i	$0.830869\pi$
$822$		0			0
$823$	13.4968	+	1.28879i	0.470469	+	0.0449244i	0.327599	−	0.944817i	$-0.393761\pi$
$823$	13.4968	+	1.28879i	0.470469	+	0.0449244i	0.142871	+	0.989741i	$0.454367\pi$
$824$		0			0
$825$	−6.17763	+	3.97012i	−0.215078	+	0.138222i
$826$		0			0
$827$			25.0724i			0.871854i	0.899982	+	0.435927i	$0.143579\pi$
$827$			25.0724i			0.871854i	−0.899982	+	0.435927i	$0.856421\pi$
$828$		0			0
$829$	−32.6538	−	18.8527i	−1.13411	−	0.654780i	−0.189147	−	0.981949i	$-0.560572\pi$
$829$	−32.6538	−	18.8527i	−1.13411	−	0.654780i	−0.944966	+	0.327169i	$0.893905\pi$
$830$		0			0
$831$	2.55122	−	4.94868i	0.0885009	−	0.171668i
$832$		0			0
$833$	−2.27662	+	23.9844i	−0.0788803	+	0.831010i
$834$		0			0
$835$	24.2713	−	25.4550i	0.839943	−	0.880907i
$836$		0			0
$837$	−12.3797	−	17.3849i	−0.427907	−	0.600911i
$838$		0			0
$839$	−20.9380	−	24.1637i	−0.722860	−	0.834225i	0.268788	−	0.963199i	$-0.413377\pi$
$839$	−20.9380	−	24.1637i	−0.722860	−	0.834225i	−0.991648	+	0.128975i	$0.958831\pi$
$840$		0			0
$841$	−34.9894	−	10.2738i	−1.20653	−	0.354269i
$842$		0			0
$843$	49.5178	−	25.5282i	1.70548	−	0.879238i
$844$		0			0
$845$	−3.58869	+	1.43669i	−0.123455	+	0.0494238i
$846$		0			0
$847$	−2.95805	+	24.7993i	−0.101640	+	0.852114i
$848$		0			0
$849$	−2.53856	+	13.1713i	−0.0871232	+	0.452038i
$850$		0			0
$851$	13.2083	−	37.7595i	0.452774	−	1.29438i
$852$		0			0
$853$	3.43335	+	2.97502i	0.117556	+	0.101863i	0.711655	−	0.702529i	$-0.247946\pi$
$853$	3.43335	+	2.97502i	0.117556	+	0.101863i	−0.594099	+	0.804392i	$0.702491\pi$
$854$		0			0
$855$	−0.628453	−	4.37099i	−0.0214926	−	0.149485i
$856$		0			0
$857$	14.0249	−	17.8341i	0.479082	−	0.609203i	−0.485095	−	0.874462i	$-0.661215\pi$
$857$	14.0249	−	17.8341i	0.479082	−	0.609203i	0.964177	+	0.265259i	$0.0854574\pi$
$858$		0			0
$859$	−39.4896	−	1.88112i	−1.34737	−	0.0641830i	−0.638553	−	0.769578i	$-0.720467\pi$
$859$	−39.4896	−	1.88112i	−1.34737	−	0.0641830i	−0.708814	+	0.705395i	$0.750770\pi$
$860$		0			0
$861$	−1.14926	+	48.8568i	−0.0391668	+	1.66503i
$862$		0			0
$863$	0.681026	−	1.96770i	0.0231824	−	0.0669811i	−0.932816	−	0.360353i	$-0.882656\pi$
$863$	0.681026	−	1.96770i	0.0231824	−	0.0669811i	0.955998	+	0.293372i	$0.0947774\pi$
$864$		0			0
$865$	−15.0885	+	10.7445i	−0.513026	+	0.365324i
$866$		0			0
$867$	2.75541	+	9.38407i	0.0935787	+	0.318700i
$868$		0			0
$869$	−6.06707	−	13.2850i	−0.205811	−	0.450664i
$870$		0			0
$871$	−1.29069	−	27.0949i	−0.0437333	−	0.918074i
$872$		0			0
$873$	−4.79019	−	8.29684i	−0.162123	−	0.280806i
$874$		0			0
$875$	10.1217	−	10.1274i	0.342177	−	0.342369i
$876$		0			0
$877$	18.4134	+	9.49278i	0.621777	+	0.320548i	0.740171	−	0.672418i	$-0.234744\pi$
$877$	18.4134	+	9.49278i	0.621777	+	0.320548i	−0.118394	+	0.992967i	$0.537775\pi$
$878$		0			0
$879$	3.11746	−	32.6475i	0.105149	−	1.10117i
$880$		0			0
$881$	23.2276	−	6.82022i	0.782556	−	0.229779i	0.134036	−	0.990977i	$-0.457206\pi$
$881$	23.2276	−	6.82022i	0.782556	−	0.229779i	0.648520	+	0.761197i	$0.275388\pi$
$882$		0			0
$883$	−9.66357	+	21.1603i	−0.325205	+	0.712100i	−0.999656	−	0.0262198i	$-0.991653\pi$
$883$	−9.66357	+	21.1603i	−0.325205	+	0.712100i	0.674451	+	0.738319i	$0.264380\pi$
$884$		0			0
$885$	2.65193	−	0.511118i	0.0891437	−	0.0171810i
$886$		0			0
$887$	5.82464	−	1.41304i	0.195572	−	0.0474453i	−0.136776	−	0.990602i	$-0.543674\pi$
$887$	5.82464	−	1.41304i	0.195572	−	0.0474453i	0.332349	+	0.943157i	$0.392159\pi$
$888$		0			0
$889$	9.57206	−	2.08509i	0.321037	−	0.0699318i
$890$		0			0
$891$	−4.84704	−	12.1073i	−0.162382	−	0.405611i
$892$		0			0
$893$	8.59389	−	21.4665i	0.287584	−	0.718349i
$894$		0			0
$895$	−2.88992	+	3.33515i	−0.0965994	+	0.111482i
$896$		0			0
$897$	−19.2733	+	24.3424i	−0.643516	+	0.812768i
$898$		0			0
$899$	−35.8392	+	12.4041i	−1.19530	+	0.413699i
$900$		0			0
$901$	−10.2132	−	12.9871i	−0.340250	−	0.432663i
$902$		0			0
$903$	−7.01035	+	0.840189i	−0.233290	+	0.0279597i
$904$		0			0
$905$	2.17469	−	45.6523i	0.0722890	−	1.51753i
$906$		0			0
$907$	−2.37945	−	2.49549i	−0.0790083	−	0.0828615i	0.683043	−	0.730378i	$-0.260656\pi$
$907$	−2.37945	−	2.49549i	−0.0790083	−	0.0828615i	−0.762051	+	0.647517i	$0.775808\pi$
$908$		0			0
$909$	−3.44320	+	2.98355i	−0.114204	+	0.0989580i
$910$		0			0
$911$	−8.09030	−	3.69472i	−0.268044	−	0.122411i	0.276860	−	0.960910i	$-0.410706\pi$
$911$	−8.09030	−	3.69472i	−0.268044	−	0.122411i	−0.544903	+	0.838499i	$0.683434\pi$
$912$		0			0
$913$	8.69158	+	2.10855i	0.287649	+	0.0697829i
$914$		0			0
$915$	−1.93413	−	1.37729i	−0.0639405	−	0.0455318i
$916$		0			0
$917$	−15.4660	−	48.3350i	−0.510733	−	1.59616i
$918$		0			0
$919$	−25.1758	+	14.5353i	−0.830474	+	0.479474i	−0.854015	−	0.520249i	$-0.825839\pi$
$919$	−25.1758	+	14.5353i	−0.830474	+	0.479474i	0.0235411	+	0.999723i	$0.492506\pi$
$920$		0			0
$921$	1.75849	−	3.04579i	0.0579441	−	0.100362i
$922$		0			0
$923$	5.68571	+	8.84714i	0.187147	+	0.291207i
$924$		0			0
$925$	−23.5080	+	10.7357i	−0.772938	+	0.352989i
$926$		0			0
$927$	−1.53999	+	6.34792i	−0.0505799	+	0.208493i
$928$		0			0
$929$	−0.108984	−	1.14133i	−0.00357564	−	0.0374458i	0.993508	−	0.113762i	$-0.0362902\pi$
$929$	−0.108984	−	1.14133i	−0.00357564	−	0.0374458i	−0.997084	+	0.0763163i	$0.975684\pi$
$930$		0			0
$931$	17.1027	+	5.90852i	0.560517	+	0.193644i
$932$		0			0
$933$	11.5448	+	47.5883i	0.377959	+	1.55797i
$934$		0			0
$935$	5.60608	+	10.8743i	0.183338	+	0.355627i
$936$		0			0
$937$	−1.80041	+	12.5221i	−0.0588168	+	0.409080i	0.939049	+	0.343783i	$0.111708\pi$
$937$	−1.80041	+	12.5221i	−0.0588168	+	0.409080i	−0.997866	+	0.0652968i	$0.979201\pi$
$938$		0			0
$939$	−44.2961	+	6.36882i	−1.44555	+	0.207839i
$940$		0			0
$941$	11.0461	+	31.9155i	0.360092	+	1.04042i	0.968975	+	0.247157i	$0.0794964\pi$
$941$	11.0461	+	31.9155i	0.360092	+	1.04042i	−0.608884	+	0.793260i	$0.708382\pi$
$942$		0			0
$943$	−46.6861	−	0.153945i	−1.52031	−	0.00501314i
$944$		0			0
$945$	−19.2235	−	28.3855i	−0.625340	−	0.923380i
$946$		0			0
$947$	−39.8698	+	31.3540i	−1.29559	+	1.01887i	−0.297657	+	0.954673i	$0.596205\pi$
$947$	−39.8698	+	31.3540i	−1.29559	+	1.01887i	−0.997937	+	0.0641938i	$0.979552\pi$
$948$		0			0
$949$	−22.4962	−	17.6912i	−0.730259	−	0.574282i
$950$		0			0
$951$	−13.8460	+	21.5448i	−0.448987	+	0.698637i
$952$		0			0
$953$	15.8415	−	53.9511i	0.513155	−	1.74765i	−0.139730	−	0.990190i	$-0.544624\pi$
$953$	15.8415	−	53.9511i	0.513155	−	1.74765i	0.652885	−	0.757457i	$-0.273558\pi$
$954$		0			0
$955$	−4.35017	−	22.5709i	−0.140768	−	0.730376i
$956$		0			0
$957$	−19.0903	+	1.82290i	−0.617102	+	0.0589261i
$958$		0			0
$959$	−6.13787	+	3.74360i	−0.198202	+	0.120887i
$960$		0			0
$961$	5.23784	−	7.35552i	0.168963	−	0.237275i
$962$		0			0
$963$	6.72227	−	0.320221i	0.216622	−	0.0103190i
$964$		0			0
$965$	58.7950			1.89268
$966$		0			0
$967$	−20.4492			−0.657603			−0.328802	−	0.944399i	$-0.606645\pi$
$967$	−20.4492			−0.657603			−0.328802	+	0.944399i	$0.606645\pi$
$968$		0			0
$969$	−16.8618	+	0.803229i	−0.541681	+	0.0258034i
$970$		0			0
$971$	7.87926	−	11.0649i	0.252858	−	0.355089i	−0.668563	−	0.743656i	$-0.733090\pi$
$971$	7.87926	−	11.0649i	0.252858	−	0.355089i	0.921421	+	0.388567i	$0.127030\pi$
$972$		0			0
$973$	27.7590	+	15.1474i	0.889913	+	0.485604i
$974$		0			0
$975$	19.9677	−	1.90668i	0.639477	−	0.0610626i
$976$		0			0
$977$	−3.15643	−	16.3771i	−0.100983	−	0.523951i	−0.996828	−	0.0795839i	$-0.974641\pi$
$977$	−3.15643	−	16.3771i	−0.100983	−	0.523951i	0.895845	−	0.444367i	$-0.146571\pi$
$978$		0			0
$979$	−4.51499	+	15.3766i	−0.144300	+	0.491439i
$980$		0			0
$981$	−0.449084	+	0.698788i	−0.0143381	+	0.0223106i
$982$		0			0
$983$	−36.6991	−	28.8605i	−1.17052	−	0.920506i	−0.172600	−	0.984992i	$-0.555217\pi$
$983$	−36.6991	−	28.8605i	−1.17052	−	0.920506i	−0.997919	+	0.0644859i	$0.979459\pi$
$984$		0			0
$985$	9.84799	−	7.74455i	0.313783	−	0.246762i
$986$		0			0
$987$	3.21620	+	44.7914i	0.102373	+	1.42573i
$988$		0			0
$989$	−0.937892	−	6.67947i	−0.0298232	−	0.212395i
$990$		0			0
$991$	16.8388	+	48.6526i	0.534903	+	1.54550i	0.811403	+	0.584487i	$0.198704\pi$
$991$	16.8388	+	48.6526i	0.534903	+	1.54550i	−0.276500	+	0.961014i	$0.589174\pi$
$992$		0			0
$993$	57.5123	−	8.26902i	1.82510	−	0.262409i
$994$		0			0
$995$	−5.18138	+	36.0373i	−0.164261	+	1.14246i
$996$		0			0
$997$	9.39719	+	18.2280i	0.297612	+	0.577286i	0.989468	−	0.144748i	$-0.0462373\pi$
$997$	9.39719	+	18.2280i	0.297612	+	0.577286i	−0.691857	+	0.722035i	$0.743207\pi$
$998$		0			0
$999$	−8.95410	−	36.9093i	−0.283295	−	1.16776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.605.5	yes	320
7.5	odd	6	inner	644.2.bc.a.145.5	yes	320
23.10	odd	22	inner	644.2.bc.a.493.5	yes	320
161.33	even	66	inner	644.2.bc.a.33.5	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.5	✓	320	161.33	even	66	inner
644.2.bc.a.145.5	yes	320	7.5	odd	6	inner
644.2.bc.a.493.5	yes	320	23.10	odd	22	inner
644.2.bc.a.605.5	yes	320	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.89530 + 0.0902843i) q^{3} +(-1.65070 + 2.31808i) q^{5} +(-1.26732 + 2.32248i) q^{7} +(0.597594 - 0.0570633i) q^{9} +(0.236397 + 1.22655i) q^{11} +(0.961267 - 3.27377i) q^{13} +(2.91928 - 4.54248i) q^{15} +(-2.70539 - 2.12754i) q^{17} +(-2.03189 + 1.59790i) q^{19} +(2.19227 - 4.51621i) q^{21} +(4.35585 + 2.00663i) q^{23} +(-1.01335 - 2.92788i) q^{25} +(4.50694 - 0.648000i) q^{27} +(1.15149 - 8.00878i) q^{29} +(-2.14781 - 4.16618i) q^{31} +(-0.558782 - 2.30333i) q^{33} +(-3.29172 - 6.77145i) q^{35} +(-0.792882 - 8.30344i) q^{37} +(-1.52632 + 6.29157i) q^{39} +(-8.85506 + 4.04397i) q^{41} +(-0.760372 - 1.18316i) q^{43} +(-0.854168 + 1.47946i) q^{45} +(-7.74681 + 4.47262i) q^{47} +(-3.78780 - 5.88665i) q^{49} +(5.31961 + 3.78808i) q^{51} +(4.66513 + 1.13175i) q^{53} +(-3.23345 - 1.47667i) q^{55} +(3.70678 - 3.21194i) q^{57} +(0.345155 + 0.361989i) q^{59} +(0.0209233 - 0.439234i) q^{61} +(-0.624815 + 1.46022i) q^{63} +(6.00210 + 7.63230i) q^{65} +(7.51285 - 2.60022i) q^{67} +(-8.43681 - 3.40991i) q^{69} +(-2.01845 + 2.32942i) q^{71} +(3.11745 - 7.78702i) q^{73} +(2.18494 + 5.45772i) q^{75} +(-3.14822 - 1.00540i) q^{77} +(-11.3625 + 2.75652i) q^{79} +(-10.2519 + 1.97589i) q^{81} +(2.97437 - 6.51296i) q^{83} +(9.39759 - 2.75938i) q^{85} +(-1.45935 + 15.2830i) q^{87} +(11.4035 + 5.87889i) q^{89} +(6.38503 + 6.38144i) q^{91} +(4.44689 + 7.70224i) q^{93} +(-0.350016 - 7.34773i) q^{95} +(-6.62960 - 14.5168i) q^{97} +(0.211260 + 0.719487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71}+ \cdots + 242 q^{99}+O(q^{100}) \) 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

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