LMFDB - Embedded newform 750.2.l.a.143.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.7
Character	$\chi$	$=$	750.143
Dual form			750.2.l.a.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(-0.530925 + 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 - 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(-0.530925 + 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 - 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +(4.88609 - 1.58759i) q^{11} +(1.64587 - 0.539538i) q^{12} +(1.32436 - 0.674795i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.762690 + 4.81543i) q^{17} +(-2.66586 + 1.37593i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(0.170700 + 0.332863i) q^{21} +(0.803689 - 5.07429i) q^{22} +(2.38239 + 1.21389i) q^{23} +(0.266479 - 1.71143i) q^{24} -1.48636i q^{26} +(4.17969 - 3.08710i) q^{27} +(-0.213317 - 0.0337860i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.0232622 + 8.89846i) q^{33} +(4.63684 + 1.50660i) q^{34} +(0.0156850 + 2.99996i) q^{36} +(1.95441 + 3.83574i) q^{37} +(0.218606 + 0.429039i) q^{38} +(0.409380 + 2.54170i) q^{39} +(5.95547 + 1.93505i) q^{41} +(0.374079 - 0.000977913i) q^{42} +(2.72225 + 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(10.0271 + 1.58814i) q^{47} +(-1.40392 - 1.01441i) q^{48} +6.95335i q^{49} +(-8.34400 - 1.29921i) q^{51} +(-1.32436 - 0.674795i) q^{52} +(-1.20325 + 7.59700i) q^{53} +(-0.853081 - 5.12565i) q^{54} +(-0.126947 + 0.174728i) q^{56} +(-0.491987 - 0.673453i) q^{57} +(-1.46845 - 9.27141i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(-2.02668 + 1.03265i) q^{62} +(-0.639411 + 0.104703i) q^{63} +(0.951057 - 0.309017i) q^{64} +(7.93914 + 4.01909i) q^{66} +(-14.8405 + 2.35050i) q^{67} +(3.44747 - 3.44747i) q^{68} +(-3.26618 + 3.28330i) q^{69} +(-7.13100 - 9.81498i) q^{71} +(2.68010 + 1.34798i) q^{72} +(4.26070 - 8.36209i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(0.503741 - 0.988647i) q^{77} +(2.45053 + 0.789148i) q^{78} +(1.28502 + 1.76867i) q^{79} +(2.87050 + 8.52996i) q^{81} +(4.42787 - 4.42787i) q^{82} +(-4.93895 + 0.782253i) q^{83} +(0.168957 - 0.333751i) q^{84} +(3.66142 - 1.18967i) q^{86} +(5.06463 + 15.4498i) q^{87} +(-4.57759 + 2.33240i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(-0.418278 - 2.64090i) q^{92} +(3.18124 - 2.32404i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.54121 + 0.790366i) q^{96} +(1.57877 - 9.96799i) q^{97} +(6.19548 + 3.15676i) q^{98} +(-14.6830 - 4.68606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$3$	−0.530925	+	1.64867i	−0.306530	+	0.951861i
$3$	−0.530925	+	1.64867i	−0.306530	+	0.951861i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	1.22794	+	1.22154i	0.501305	+	0.498691i
$7$	0.152718	−	0.152718i	0.0577219	−	0.0577219i	−0.677657	−	0.735379i	$-0.737004\pi$
$7$	0.152718	−	0.152718i	0.0577219	−	0.0577219i	0.735379	+	0.677657i	$0.237004\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$	−2.43624	−	1.75064i	−0.812079	−	0.583547i
$10$		0			0
$11$	4.88609	−	1.58759i	1.47321	−	0.478676i	0.541136	−	0.840935i	$-0.317995\pi$
$11$	4.88609	−	1.58759i	1.47321	−	0.478676i	0.932077	+	0.362259i	$0.117995\pi$
$12$	1.64587	−	0.539538i	0.475123	−	0.155751i
$13$	1.32436	−	0.674795i	0.367312	−	0.187155i	−0.260586	−	0.965451i	$-0.583916\pi$
$13$	1.32436	−	0.674795i	0.367312	−	0.187155i	0.627897	+	0.778296i	$0.283916\pi$
$14$	−0.0667401	−	0.205405i	−0.0178371	−	0.0548968i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.762690	+	4.81543i	0.184979	+	1.16791i	0.889059	+	0.457793i	$0.151360\pi$
$17$	0.762690	+	4.81543i	0.184979	+	1.16791i	−0.704080	+	0.710121i	$0.748640\pi$
$18$	−2.66586	+	1.37593i	−0.628350	+	0.324309i
$19$	−0.283032	+	0.389560i	−0.0649319	+	0.0893711i	−0.840248	−	0.542202i	$-0.817591\pi$
$19$	−0.283032	+	0.389560i	−0.0649319	+	0.0893711i	0.775316	+	0.631574i	$0.217591\pi$
$20$		0			0
$21$	0.170700	+	0.332863i	0.0372498	+	0.0726367i
$22$	0.803689	−	5.07429i	0.171347	−	1.08184i
$23$	2.38239	+	1.21389i	0.496763	+	0.253114i	0.684376	−	0.729130i	$-0.260075\pi$
$23$	2.38239	+	1.21389i	0.496763	+	0.253114i	−0.187612	+	0.982243i	$0.560075\pi$
$24$	0.266479	−	1.71143i	0.0543949	−	0.349344i
$25$		0			0
$26$		−	1.48636i		−	0.291500i
$27$	4.17969	−	3.08710i	0.804382	−	0.594112i
$28$	−0.213317	−	0.0337860i	−0.0403130	−	0.00638496i
$29$	7.59423	−	5.51753i	1.41021	−	1.02458i	0.416921	−	0.908943i	$-0.363109\pi$
$29$	7.59423	−	5.51753i	1.41021	−	1.02458i	0.993292	−	0.115637i	$-0.0368909\pi$
$30$		0			0
$31$	−1.84019	−	1.33698i	−0.330508	−	0.240128i	0.410138	−	0.912023i	$-0.365480\pi$
$31$	−1.84019	−	1.33698i	−0.330508	−	0.240128i	−0.740646	+	0.671895i	$0.765480\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.0232622	+	8.89846i	0.00404943	+	1.54902i
$34$	4.63684	+	1.50660i	0.795211	+	0.258380i
$35$		0			0
$36$	0.0156850	+	2.99996i	0.00261417	+	0.499993i
$37$	1.95441	+	3.83574i	0.321303	+	0.630592i	0.994007	−	0.109320i	$-0.0348672\pi$
$37$	1.95441	+	3.83574i	0.321303	+	0.630592i	−0.672704	+	0.739912i	$0.734867\pi$
$38$	0.218606	+	0.429039i	0.0354627	+	0.0695994i
$39$	0.409380	+	2.54170i	0.0655533	+	0.406998i
$40$		0			0
$41$	5.95547	+	1.93505i	0.930087	+	0.302204i	0.734598	−	0.678502i	$-0.237371\pi$
$41$	5.95547	+	1.93505i	0.930087	+	0.302204i	0.195489	+	0.980706i	$0.437371\pi$
$42$	0.374079		0.000977913i	0.0577217		0.000150895i
$43$	2.72225	+	2.72225i	0.415139	+	0.415139i	0.883524	−	0.468385i	$-0.155164\pi$
$43$	2.72225	+	2.72225i	0.415139	+	0.415139i	−0.468385	+	0.883524i	$0.655164\pi$
$44$	−4.15636	−	3.01977i	−0.626595	−	0.455248i
$45$		0			0
$46$	2.16317	−	1.57163i	0.318942	−	0.231725i
$47$	10.0271	+	1.58814i	1.46260	+	0.231654i	0.836448	−	0.548046i	$-0.184628\pi$
$47$	10.0271	+	1.58814i	1.46260	+	0.231654i	0.626154	+	0.779699i	$0.284628\pi$
$48$	−1.40392	−	1.01441i	−0.202638	−	0.146417i
$49$			6.95335i			0.993336i
$50$		0			0
$51$	−8.34400	−	1.29921i	−1.16839	−	0.181926i
$52$	−1.32436	−	0.674795i	−0.183656	−	0.0935773i
$53$	−1.20325	+	7.59700i	−0.165279	+	1.04353i	0.755985	+	0.654589i	$0.227158\pi$
$53$	−1.20325	+	7.59700i	−0.165279	+	1.04353i	−0.921264	+	0.388939i	$0.872842\pi$
$54$	−0.853081	−	5.12565i	−0.116090	−	0.697512i
$55$		0			0
$56$	−0.126947	+	0.174728i	−0.0169640	+	0.0233490i
$57$	−0.491987	−	0.673453i	−0.0651653	−	0.0892011i
$58$	−1.46845	−	9.27141i	−0.192817	−	1.21740i
$59$	1.54130	−	4.74363i	0.200660	−	0.617569i	−0.799204	−	0.601061i	$-0.794745\pi$
$59$	1.54130	−	4.74363i	0.200660	−	0.617569i	0.999864	−	0.0165081i	$-0.00525494\pi$
$60$		0			0
$61$	−4.21680	−	12.9780i	−0.539906	−	1.66166i	−0.732803	−	0.680440i	$-0.761789\pi$
$61$	−4.21680	−	12.9780i	−0.539906	−	1.66166i	0.192898	−	0.981219i	$-0.438211\pi$
$62$	−2.02668	+	1.03265i	−0.257389	+	0.131146i
$63$	−0.639411	+	0.104703i	−0.0805582	+	0.0131913i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	7.93914	+	4.01909i	0.977241	+	0.494716i
$67$	−14.8405	+	2.35050i	−1.81305	+	0.287159i	−0.968628	−	0.248514i	$-0.920058\pi$
$67$	−14.8405	+	2.35050i	−1.81305	+	0.287159i	−0.844425	+	0.535673i	$0.820058\pi$
$68$	3.44747	−	3.44747i	0.418067	−	0.418067i
$69$	−3.26618	+	3.28330i	−0.393202	+	0.395263i
$70$		0			0
$71$	−7.13100	−	9.81498i	−0.846294	−	1.16482i	−0.984667	−	0.174444i	$-0.944187\pi$
$71$	−7.13100	−	9.81498i	−0.846294	−	1.16482i	0.138373	−	0.990380i	$-0.455813\pi$
$72$	2.68010	+	1.34798i	0.315853	+	0.158861i
$73$	4.26070	−	8.36209i	0.498677	−	0.978708i	−0.495259	−	0.868745i	$-0.664927\pi$
$73$	4.26070	−	8.36209i	0.498677	−	0.978708i	0.993936	−	0.109963i	$-0.0350731\pi$
$74$	4.30495			0.500441
$75$		0			0
$76$	0.481522			0.0552344
$77$	0.503741	−	0.988647i	0.0574066	−	0.112667i
$78$	2.45053	+	0.789148i	0.277468	+	0.0893534i
$79$	1.28502	+	1.76867i	0.144576	+	0.198991i	0.875163	−	0.483828i	$-0.160754\pi$
$79$	1.28502	+	1.76867i	0.144576	+	0.198991i	−0.730588	+	0.682819i	$0.760754\pi$
$80$		0			0
$81$	2.87050	+	8.52996i	0.318945	+	0.947773i
$82$	4.42787	−	4.42787i	0.488976	−	0.488976i
$83$	−4.93895	+	0.782253i	−0.542120	+	0.0858634i	−0.421488	−	0.906834i	$-0.638492\pi$
$83$	−4.93895	+	0.782253i	−0.542120	+	0.0858634i	−0.120632	+	0.992697i	$0.538492\pi$
$84$	0.168957	−	0.333751i	0.0184347	−	0.0364152i
$85$		0			0
$86$	3.66142	−	1.18967i	0.394821	−	0.128285i
$87$	5.06463	+	15.4498i	0.542985	+	1.65639i
$88$	−4.57759	+	2.33240i	−0.487972	+	0.248634i
$89$	3.38311	+	10.4121i	0.358609	+	1.10368i	0.953887	+	0.300165i	$0.0970417\pi$
$89$	3.38311	+	10.4121i	0.358609	+	1.10368i	−0.595279	+	0.803519i	$0.702958\pi$
$90$		0			0
$91$	0.0992002	−	0.305307i	0.0103990	−	0.0320048i
$92$	−0.418278	−	2.64090i	−0.0436085	−	0.275333i
$93$	3.18124	−	2.32404i	0.329879	−	0.240991i
$94$	5.96725	−	8.21321i	0.615475	−	0.847128i
$95$		0			0
$96$	−1.54121	+	0.790366i	−0.157299	+	0.0806664i
$97$	1.57877	−	9.96799i	0.160300	−	1.01210i	−0.768050	−	0.640390i	$-0.778773\pi$
$97$	1.57877	−	9.96799i	0.160300	−	1.01210i	0.928350	−	0.371706i	$-0.121227\pi$
$98$	6.19548	+	3.15676i	0.625838	+	0.318881i
$99$	−14.6830	−	4.68606i	−1.47570	−	0.470967i
$100$		0			0
$101$			9.53700i			0.948967i	0.880264	+	0.474483i	$0.157365\pi$
$101$			9.53700i			0.948967i	−0.880264	+	0.474483i	$0.842635\pi$
$102$	−4.94570	+	6.84473i	−0.489697	+	0.677729i
$103$	−9.98929	−	1.58215i	−0.984274	−	0.155894i	−0.356505	−	0.934293i	$-0.616032\pi$
$103$	−9.98929	−	1.58215i	−0.984274	−	0.155894i	−0.627769	+	0.778400i	$0.716032\pi$
$104$	−1.20249	+	0.873663i	−0.117914	+	0.0856697i
$105$		0			0
$106$	6.22271	+	4.52106i	0.604403	+	0.439125i
$107$	−7.80873	−	7.80873i	−0.754898	−	0.754898i	0.220491	−	0.975389i	$-0.429234\pi$
$107$	−7.80873	−	7.80873i	−0.754898	−	0.754898i	−0.975389	+	0.220491i	$0.929234\pi$
$108$	−4.95428	−	1.56689i	−0.476725	−	0.150774i
$109$	5.83194	+	1.89491i	0.558598	+	0.181500i	0.574690	−	0.818371i	$-0.305123\pi$
$109$	5.83194	+	1.89491i	0.558598	+	0.181500i	−0.0160921	+	0.999871i	$0.505123\pi$
$110$		0			0
$111$	−7.36152	+	1.18569i	−0.698725	+	0.112540i
$112$	0.0980509	+	0.192436i	0.00926494	+	0.0181835i
$113$	−4.98756	−	9.78864i	−0.469190	−	0.920838i	−0.997423	−	0.0717385i	$-0.977145\pi$
$113$	−4.98756	−	9.78864i	−0.469190	−	0.920838i	0.528233	−	0.849099i	$-0.322855\pi$
$114$	−0.823409	+	0.132623i	−0.0771193	+	0.0124212i
$115$		0			0
$116$	−8.92755	−	2.90074i	−0.828902	−	0.269327i
$117$	−4.40778	−	0.674520i	−0.407500	−	0.0623594i
$118$	−3.52687	−	3.52687i	−0.324675	−	0.324675i
$119$	0.851879	+	0.618926i	0.0780916	+	0.0567369i
$120$		0			0
$121$	12.4543	−	9.04858i	1.13221	−	0.822598i
$122$	−13.4778	−	2.13468i	−1.22023	−	0.193265i
$123$	−6.35216	+	8.79124i	−0.572755	+	0.792680i
$124$			2.27460i			0.204265i
$125$		0			0
$126$	−0.196996	+	0.617253i	−0.0175498	+	0.0549893i
$127$	−13.3979	−	6.82658i	−1.18887	−	0.605761i	−0.256249	−	0.966611i	$-0.582487\pi$
$127$	−13.3979	−	6.82658i	−1.18887	−	0.605761i	−0.932624	+	0.360850i	$0.882487\pi$
$128$	0.156434	−	0.987688i	0.0138270	−	0.0873001i
$129$	−5.93341	+	3.04279i	−0.522407	+	0.267902i
$130$		0			0
$131$	−5.12870	+	7.05905i	−0.448097	+	0.616752i	−0.971987	−	0.235034i	$-0.924480\pi$
$131$	−5.12870	+	7.05905i	−0.448097	+	0.616752i	0.523891	+	0.851785i	$0.324480\pi$
$132$	7.18533	−	5.24920i	0.625403	−	0.456884i
$133$	0.0162687	+	0.102717i	0.00141068	+	0.00890667i
$134$	−4.64313	+	14.2901i	−0.401105	+	1.23447i
$135$		0			0
$136$	−1.50660	−	4.63684i	−0.129190	−	0.397605i
$137$	−2.51567	+	1.28180i	−0.214928	+	0.109511i	−0.558140	−	0.829747i	$-0.688485\pi$
$137$	−2.51567	+	1.28180i	−0.214928	+	0.109511i	0.343212	+	0.939258i	$0.388485\pi$
$138$	1.44263	+	4.40077i	0.122805	+	0.374619i
$139$	6.62014	−	2.15102i	0.561513	−	0.182447i	−0.0144887	−	0.999895i	$-0.504612\pi$
$139$	6.62014	−	2.15102i	0.561513	−	0.182447i	0.576002	+	0.817448i	$0.304612\pi$
$140$		0			0
$141$	−7.94195	+	15.6882i	−0.668833	+	1.32119i
$142$	−11.9826	+	1.89786i	−1.00556	+	0.159265i
$143$	5.39965	−	5.39965i	0.451542	−	0.451542i
$144$	2.41780	−	1.77602i	0.201483	−	0.148002i
$145$		0			0
$146$	−5.51636	−	7.59261i	−0.456537	−	0.628369i
$147$	−11.4638	−	3.69171i	−0.945518	−	0.304487i
$148$	1.95441	−	3.83574i	0.160651	−	0.315296i
$149$	−7.72360			−0.632742			−0.316371	−	0.948635i	$-0.602465\pi$
$149$	−7.72360			−0.632742			−0.316371	+	0.948635i	$0.602465\pi$
$150$		0			0
$151$	−14.7868			−1.20333			−0.601667	−	0.798747i	$-0.705497\pi$
$151$	−14.7868			−1.20333			−0.601667	+	0.798747i	$0.705497\pi$
$152$	0.218606	−	0.429039i	0.0177313	−	0.0347997i
$153$	6.57201	−	13.0667i	0.531315	−	1.05638i
$154$	−0.652197	−	0.897673i	−0.0525556	−	0.0723365i
$155$		0			0
$156$	1.81565	−	1.82517i	0.145369	−	0.146131i
$157$	11.5941	−	11.5941i	0.925312	−	0.925312i	−0.0720863	−	0.997398i	$-0.522966\pi$
$157$	11.5941	−	11.5941i	0.925312	−	0.925312i	0.997398	+	0.0720863i	$0.0229657\pi$
$158$	2.15928	−	0.341997i	0.171783	−	0.0272078i
$159$	−11.8861	−	6.01719i	−0.942630	−	0.477194i
$160$		0			0
$161$	0.549217	−	0.178451i	0.0432843	−	0.0140639i
$162$	8.90343	+	1.31488i	0.699520	+	0.103307i
$163$	−3.61543	+	1.84215i	−0.283182	+	0.144289i	−0.589813	−	0.807540i	$-0.700798\pi$
$163$	−3.61543	+	1.84215i	−0.283182	+	0.144289i	0.306630	+	0.951829i	$0.400798\pi$
$164$	−1.93505	−	5.95547i	−0.151102	−	0.465044i
$165$		0			0
$166$	−1.54524	+	4.75577i	−0.119934	+	0.369119i
$167$	2.16520	+	13.6706i	0.167549	+	1.05786i	0.917897	+	0.396818i	$0.129886\pi$
$167$	2.16520	+	13.6706i	0.167549	+	1.05786i	−0.750349	+	0.661042i	$0.770114\pi$
$168$	−0.220670	−	0.302062i	−0.0170250	−	0.0233046i
$169$	−6.34263	+	8.72988i	−0.487894	+	0.671529i
$170$		0			0
$171$	1.37151	−	0.453573i	0.104882	−	0.0346856i
$172$	0.602248	−	3.80244i	0.0459210	−	0.289934i
$173$	0.809140	+	0.412278i	0.0615178	+	0.0313449i	0.484479	−	0.874803i	$-0.339009\pi$
$173$	0.809140	+	0.412278i	0.0615178	+	0.0313449i	−0.422961	+	0.906148i	$0.639009\pi$
$174$	16.0652	+	2.50144i	1.21790	+	0.189633i
$175$		0			0
$176$			5.13754i			0.387257i
$177$	7.00238	+	5.05961i	0.526331	+	0.380304i
$178$	10.8132	+	1.71264i	0.810482	+	0.128368i
$179$	−9.58645	+	6.96496i	−0.716525	+	0.520586i	−0.885272	−	0.465074i	$-0.846028\pi$
$179$	−9.58645	+	6.96496i	−0.716525	+	0.520586i	0.168747	+	0.985659i	$0.446028\pi$
$180$		0			0
$181$	13.9076	+	10.1044i	1.03374	+	0.751057i	0.969054	−	0.246848i	$-0.0793949\pi$
$181$	13.9076	+	10.1044i	1.03374	+	0.751057i	0.0646876	+	0.997906i	$0.479395\pi$
$182$	−0.226994	−	0.226994i	−0.0168259	−	0.0168259i
$183$	23.6352	−	0.0617869i	1.74717	−	0.00456742i
$184$	−2.54296	−	0.826257i	−0.187469	−	0.0609125i
$185$		0			0
$186$	−0.626479	−	3.88960i	−0.0459357	−	0.285199i
$187$	11.3715	+	22.3178i	0.831566	+	1.63204i
$188$	−4.60895	−	9.04558i	−0.336142	−	0.659716i
$189$	0.166859	−	1.10977i	0.0121372	−	0.0807238i
$190$		0			0
$191$	−4.70151	−	1.52761i	−0.340189	−	0.110534i	0.133940	−	0.990989i	$-0.457237\pi$
$191$	−4.70151	−	1.52761i	−0.340189	−	0.110534i	−0.474129	+	0.880455i	$0.657237\pi$
$192$	0.00452789	+	1.73204i	0.000326772	+	0.125000i
$193$	−2.38356	−	2.38356i	−0.171572	−	0.171572i	0.616098	−	0.787670i	$-0.288713\pi$
$193$	−2.38356	−	2.38356i	−0.171572	−	0.171572i	−0.787670	+	0.616098i	$0.788713\pi$
$194$	−8.16479	−	5.93207i	−0.586198	−	0.425898i
$195$		0			0
$196$	5.62538	−	4.08708i	0.401813	−	0.291934i
$197$	−7.24145	−	1.14693i	−0.515932	−	0.0817156i	−0.106961	−	0.994263i	$-0.534112\pi$
$197$	−7.24145	−	1.14693i	−0.515932	−	0.0817156i	−0.408970	+	0.912548i	$0.634112\pi$
$198$	−10.8412	+	10.9552i	−0.770454	+	0.778553i
$199$		−	8.34182i		−	0.591336i	−0.955291	−	0.295668i	$-0.904458\pi$
$199$		−	8.34182i		−	0.591336i	0.955291	−	0.295668i	$-0.0955422\pi$
$200$		0			0
$201$	4.00398	−	25.7150i	0.282419	−	1.81380i
$202$	8.49753	+	4.32971i	0.597884	+	0.304637i
$203$	0.317149	−	2.00240i	0.0222595	−	0.140541i
$204$	3.85340	+	7.51409i	0.269792	+	0.526092i
$205$		0			0
$206$	−5.94475	+	8.18224i	−0.414190	+	0.570084i
$207$	−3.67899	−	7.12804i	−0.255707	−	0.495433i
$208$	0.232519	+	1.46807i	0.0161223	+	0.101792i
$209$	−0.764459	+	2.35276i	−0.0528787	+	0.162744i
$210$		0			0
$211$	1.32487	+	4.07753i	0.0912078	+	0.280709i	0.986247	−	0.165279i	$-0.0528525\pi$
$211$	1.32487	+	4.07753i	0.0912078	+	0.280709i	−0.895039	+	0.445988i	$0.852852\pi$
$212$	6.85335	−	3.49196i	0.470690	−	0.239828i
$213$	19.9677	−	6.54566i	1.36817	−	0.448501i
$214$	−10.5027	+	3.41254i	−0.717951	+	0.233276i
$215$		0			0
$216$	−3.64531	+	3.70294i	−0.248032	+	0.251953i
$217$	−0.485210	+	0.0768498i	−0.0329382	+	0.00521690i
$218$	4.33602	−	4.33602i	0.293672	−	0.293672i
$219$	11.5242	+	11.4641i	0.778735	+	0.774674i
$220$		0			0
$221$	4.25951	+	5.86271i	0.286525	+	0.394369i
$222$	−2.28561	+	7.09746i	−0.153400	+	0.476350i
$223$	0.331831	−	0.651256i	0.0222211	−	0.0436113i	−0.879629	−	0.475660i	$-0.842209\pi$
$223$	0.331831	−	0.651256i	0.0222211	−	0.0436113i	0.901850	+	0.432049i	$0.142209\pi$
$224$	0.215976			0.0144305
$225$		0			0
$226$	−10.9860			−0.730781
$227$	1.50300	−	2.94981i	0.0997579	−	0.195786i	−0.835734	−	0.549135i	$-0.814957\pi$
$227$	1.50300	−	2.94981i	0.0997579	−	0.195786i	0.935492	+	0.353349i	$0.114957\pi$
$228$	−0.255652	+	0.793872i	−0.0169310	+	0.0525755i
$229$	6.20224	+	8.53665i	0.409855	+	0.564117i	0.963183	−	0.268846i	$-0.0866423\pi$
$229$	6.20224	+	8.53665i	0.409855	+	0.564117i	−0.553328	+	0.832964i	$0.686642\pi$
$230$		0			0
$231$	1.36251	+	1.35540i	0.0896463	+	0.0891788i
$232$	−6.63760	+	6.63760i	−0.435780	+	0.435780i
$233$	−12.4340	+	1.96935i	−0.814577	+	0.129016i	−0.549803	−	0.835294i	$-0.685297\pi$
$233$	−12.4340	+	1.96935i	−0.814577	+	0.129016i	−0.264774	+	0.964311i	$0.585297\pi$
$234$	−2.60209	+	3.62114i	−0.170104	+	0.236721i
$235$		0			0
$236$	−4.74363	+	1.54130i	−0.308784	+	0.100330i
$237$	−3.59821	+	1.17954i	−0.233729	+	0.0766192i
$238$	0.938212	−	0.478043i	0.0608152	−	0.0309869i
$239$	−3.62951	−	11.1705i	−0.234773	−	0.722558i	−0.997151	−	0.0754263i	$-0.975968\pi$
$239$	−3.62951	−	11.1705i	−0.234773	−	0.722558i	0.762378	−	0.647132i	$-0.224032\pi$
$240$		0			0
$241$	0.375849	−	1.15675i	0.0242106	−	0.0745125i	−0.938221	−	0.346036i	$-0.887527\pi$
$241$	0.375849	−	1.15675i	0.0242106	−	0.0745125i	0.962432	+	0.271524i	$0.0875275\pi$
$242$	−2.40821	−	15.2048i	−0.154805	−	0.977403i
$243$	−15.5871	+	0.203749i	−0.999915	+	0.0130705i
$244$	−8.02083	+	11.0397i	−0.513481	+	0.706746i
$245$		0			0
$246$	4.94923	+	9.65096i	0.315552	+	0.615323i
$247$	−0.111963	+	0.706906i	−0.00712403	+	0.0449793i
$248$	2.02668	+	1.03265i	0.128695	+	0.0655732i
$249$	1.33253	−	8.55802i	0.0844459	−	0.542343i
$250$		0			0
$251$			22.6123i			1.42728i	0.700515	+	0.713638i	$0.252954\pi$
$251$			22.6123i			1.42728i	−0.700515	+	0.713638i	$0.747046\pi$
$252$	0.460543	+	0.455752i	0.0290115	+	0.0287097i
$253$	13.5678	+	2.14892i	0.852998	+	0.135102i
$254$	−12.1651	+	8.83843i	−0.763304	+	0.554573i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.98436	+	2.98436i	0.186159	+	0.186159i	0.794033	−	0.607874i	$-0.207978\pi$
$257$	2.98436	+	2.98436i	0.186159	+	0.186159i	−0.607874	+	0.794033i	$0.707978\pi$
$258$	0.0174316	+	6.66810i	0.00108525	+	0.415138i
$259$	0.884259	+	0.287313i	0.0549452	+	0.0178528i
$260$		0			0
$261$	−28.1606	+	0.147235i	−1.74309	+	0.00911361i
$262$	3.96128	+	7.77445i	0.244729	+	0.480307i
$263$	1.16756	+	2.29146i	0.0719947	+	0.141298i	0.924199	−	0.381912i	$-0.124734\pi$
$263$	1.16756	+	2.29146i	0.0719947	+	0.141298i	−0.852204	+	0.523210i	$0.824734\pi$
$264$	−1.41500	−	8.78526i	−0.0870873	−	0.540696i
$265$		0			0
$266$	0.0989071	+	0.0321369i	0.00606438	+	0.00197044i
$267$	−18.9624	+	0.0495712i	−1.16048	+	0.00303371i
$268$	10.6246	+	10.6246i	0.649002	+	0.649002i
$269$	19.5493	+	14.2034i	1.19194	+	0.865996i	0.993468	−	0.114110i	$-0.0364018\pi$
$269$	19.5493	+	14.2034i	1.19194	+	0.865996i	0.198473	+	0.980106i	$0.436402\pi$
$270$		0			0
$271$	−9.36464	+	6.80381i	−0.568861	+	0.413302i	−0.834691	−	0.550718i	$-0.814354\pi$
$271$	−9.36464	+	6.80381i	−0.568861	+	0.413302i	0.265830	+	0.964020i	$0.414354\pi$
$272$	−4.81543	−	0.762690i	−0.291978	−	0.0462448i
$273$	0.450683	+	0.325644i	0.0272766	+	0.0197088i
$274$			2.82340i			0.170568i
$275$		0			0
$276$	4.57606	+	0.712519i	0.275446	+	0.0428886i
$277$	6.71461	+	3.42126i	0.403442	+	0.205564i	0.643924	−	0.765090i	$-0.277305\pi$
$277$	6.71461	+	3.42126i	0.403442	+	0.205564i	−0.240482	+	0.970654i	$0.577305\pi$
$278$	1.08891	−	6.87513i	0.0653087	−	0.412343i
$279$	2.14257	+	6.47871i	0.128273	+	0.387870i
$280$		0			0
$281$	13.8790	−	19.1028i	0.827952	−	1.13958i	−0.160349	−	0.987060i	$-0.551262\pi$
$281$	13.8790	−	19.1028i	0.827952	−	1.13958i	0.988301	−	0.152517i	$-0.0487380\pi$
$282$	10.3727	+	14.1986i	0.617687	+	0.845516i
$283$	−1.54005	−	9.72347i	−0.0915463	−	0.578000i	−0.990234	−	0.139412i	$-0.955479\pi$
$283$	−1.54005	−	9.72347i	−0.0915463	−	0.578000i	0.898688	−	0.438588i	$-0.144521\pi$
$284$	−3.74899	+	11.5382i	−0.222462	+	0.684667i
$285$		0			0
$286$	−2.35974	−	7.26252i	−0.139534	−	0.429442i
$287$	1.20502	−	0.613989i	0.0711302	−	0.0362426i
$288$	−0.484789	−	2.96057i	−0.0285665	−	0.174453i
$289$	−6.43873	+	2.09207i	−0.378749	+	0.123063i
$290$		0			0
$291$	15.5957	+	7.89513i	0.914238	+	0.462821i
$292$	−9.26944	+	1.46814i	−0.542453	+	0.0859161i
$293$	−3.33944	+	3.33944i	−0.195092	+	0.195092i	−0.797892	−	0.602800i	$-0.794052\pi$
$293$	−3.33944	+	3.33944i	−0.195092	+	0.195092i	0.602800	+	0.797892i	$0.294052\pi$
$294$	−8.49379	+	8.53832i	−0.495368	+	0.497965i
$295$		0			0
$296$	−2.53039	−	3.48278i	−0.147076	−	0.202433i
$297$	15.5213	−	21.7195i	0.900640	−	1.26029i
$298$	−3.50644	+	6.88178i	−0.203123	+	0.398651i
$299$	3.97428			0.229838
$300$		0			0
$301$	0.831472			0.0479252
$302$	−6.71307	+	13.1751i	−0.386294	+	0.758145i
$303$	−15.7234	−	5.06343i	−0.903285	−	0.290887i
$304$	−0.283032	−	0.389560i	−0.0162330	−	0.0223428i
$305$		0			0
$306$	−8.65891	−	11.7879i	−0.494997	−	0.673868i
$307$	11.8133	−	11.8133i	0.674221	−	0.674221i	−0.284465	−	0.958686i	$-0.591816\pi$
$307$	11.8133	−	11.8133i	0.674221	−	0.674221i	0.958686	+	0.284465i	$0.0918160\pi$
$308$	−1.09592	+	0.173577i	−0.0624460	+	0.00989048i
$309$	7.91201	−	15.6291i	0.450098	−	0.889106i
$310$		0			0
$311$	28.7239	−	9.33296i	1.62878	−	0.529224i	0.654791	−	0.755810i	$-0.272756\pi$
$311$	28.7239	−	9.33296i	1.62878	−	0.529224i	0.973991	+	0.226586i	$0.0727564\pi$
$312$	−0.801950	−	2.44637i	−0.0454015	−	0.138498i
$313$	−14.8624	+	7.57278i	−0.840073	+	0.428039i	−0.820415	−	0.571768i	$-0.806258\pi$
$313$	−14.8624	+	7.57278i	−0.840073	+	0.428039i	−0.0196580	+	0.999807i	$0.506258\pi$
$314$	−5.06682	−	15.5941i	−0.285937	−	0.880024i
$315$		0			0
$316$	0.675573	−	2.07920i	0.0380040	−	0.116964i
$317$	−1.69675	−	10.7129i	−0.0952991	−	0.601695i	−0.988404	−	0.151847i	$-0.951478\pi$
$317$	−1.69675	−	10.7129i	−0.0952991	−	0.601695i	0.893105	−	0.449848i	$-0.148522\pi$
$318$	−10.7575	+	7.85886i	−0.603253	+	0.440703i
$319$	28.3466	−	39.0157i	1.58710	−	2.18446i
$320$		0			0
$321$	17.0199	−	8.72818i	0.949957	−	0.487160i
$322$	0.0903379	−	0.570371i	0.00503433	−	0.0317855i
$323$	−2.09176	−	1.06581i	−0.116389	−	0.0593031i
$324$	5.21364	−	7.33607i	0.289647	−	0.407559i
$325$		0			0
$326$			4.05769i			0.224735i
$327$	−6.22041	+	8.60889i	−0.343989	+	0.476073i
$328$	−6.18485	−	0.979584i	−0.341501	−	0.0540885i
$329$	1.77385	−	1.28878i	0.0977957	−	0.0710527i
$330$		0			0
$331$	−7.79472	−	5.66319i	−0.428436	−	0.311277i	0.352587	−	0.935779i	$-0.385302\pi$
$331$	−7.79472	−	5.66319i	−0.428436	−	0.311277i	−0.781023	+	0.624502i	$0.785302\pi$
$332$	3.53590	+	3.53590i	0.194058	+	0.194058i
$333$	1.95361	−	12.7662i	0.107057	−	0.699586i
$334$	13.1635	+	4.27710i	0.720277	+	0.234032i
$335$		0			0
$336$	−0.369321	+	0.0594848i	−0.0201481	+	0.00324516i
$337$	−12.7818	−	25.0858i	−0.696272	−	1.36651i	−0.920023	−	0.391864i	$-0.871830\pi$
$337$	−12.7818	−	25.0858i	−0.696272	−	1.36651i	0.223752	−	0.974646i	$-0.428170\pi$
$338$	4.89888	+	9.61460i	0.266464	+	0.522965i
$339$	18.7863	−	3.02582i	1.02033	−	0.164340i
$340$		0			0
$341$	−11.1139	−	3.61113i	−0.601852	−	0.195554i
$342$	0.218517	−	1.42794i	0.0118161	−	0.0772143i
$343$	2.13093	+	2.13093i	0.115059	+	0.115059i
$344$	−3.11459	−	2.26288i	−0.167927	−	0.122006i
$345$		0			0
$346$	0.734684	−	0.533779i	0.0394969	−	0.0286962i
$347$	19.0736	+	3.02097i	1.02393	+	0.162174i	0.645742	−	0.763556i	$-0.276548\pi$
$347$	19.0736	+	3.02097i	1.02393	+	0.162174i	0.378185	+	0.925730i	$0.376548\pi$
$348$	9.52222	−	13.1785i	0.510445	−	0.706443i
$349$			14.4119i			0.771451i	0.922614	+	0.385725i	$0.126049\pi$
$349$			14.4119i			0.771451i	−0.922614	+	0.385725i	$0.873951\pi$
$350$		0			0
$351$	3.45226	−	6.90887i	0.184268	−	0.368768i
$352$	4.57759	+	2.33240i	0.243986	+	0.124317i
$353$	−5.47696	+	34.5802i	−0.291509	+	1.84052i	0.212929	+	0.977068i	$0.431700\pi$
$353$	−5.47696	+	34.5802i	−0.291509	+	1.84052i	−0.504438	+	0.863448i	$0.668300\pi$
$354$	7.68716	−	3.94215i	0.408568	−	0.209523i
$355$		0			0
$356$	6.43505	−	8.85709i	0.341057	−	0.469425i
$357$	−1.47269	+	1.07586i	−0.0779430	+	0.0569408i
$358$	1.85367	+	11.7036i	0.0979695	+	0.618555i
$359$	10.6846	−	32.8840i	0.563914	−	1.73555i	−0.107242	−	0.994233i	$-0.534202\pi$
$359$	10.6846	−	32.8840i	0.563914	−	1.73555i	0.671156	−	0.741316i	$-0.265798\pi$
$360$		0			0
$361$	5.79967	+	17.8496i	0.305246	+	0.939450i
$362$	15.3170	−	7.80442i	0.805045	−	0.410191i
$363$	8.30583	+	25.3372i	0.435943	+	1.32986i
$364$	−0.305307	+	0.0992002i	−0.0160024	+	0.00519950i
$365$		0			0
$366$	10.6751	−	21.0872i	0.557997	−	1.10224i
$367$	−3.18996	+	0.505240i	−0.166514	+	0.0263733i	−0.239135	−	0.970986i	$-0.576864\pi$
$367$	−3.18996	+	0.505240i	−0.166514	+	0.0263733i	0.0726205	+	0.997360i	$0.476864\pi$
$368$	−1.89068	+	1.89068i	−0.0985584	+	0.0985584i
$369$	−11.1214	−	15.1401i	−0.578954	−	0.788163i
$370$		0			0
$371$	0.976440	+	1.34395i	0.0506942	+	0.0697746i
$372$	−3.75007	−	1.20764i	−0.194432	−	0.0626134i
$373$	4.91900	−	9.65408i	0.254696	−	0.499869i	−0.727886	−	0.685698i	$-0.759497\pi$
$373$	4.91900	−	9.65408i	0.254696	−	0.499869i	0.982582	+	0.185829i	$0.0594970\pi$
$374$	25.0479			1.29519
$375$		0			0
$376$	−10.1521			−0.523554
$377$	6.33429	−	12.4317i	0.326233	−	0.640268i
$378$	−0.913058	−	0.652497i	−0.0469627	−	0.0335608i
$379$	−19.6854	−	27.0946i	−1.01117	−	1.39176i	−0.918213	−	0.396087i	$-0.870368\pi$
$379$	−19.6854	−	27.0946i	−1.01117	−	1.39176i	−0.0929573	−	0.995670i	$-0.529632\pi$
$380$		0			0
$381$	18.3681	−	18.4644i	0.941025	−	0.945958i
$382$	−3.49555	+	3.49555i	−0.178848	+	0.178848i
$383$	−16.0484	+	2.54182i	−0.820034	+	0.129881i	−0.552335	−	0.833622i	$-0.686263\pi$
$383$	−16.0484	+	2.54182i	−0.820034	+	0.129881i	−0.267699	+	0.963503i	$0.586263\pi$
$384$	1.54532	+	0.782298i	0.0788592	+	0.0399215i
$385$		0			0
$386$	−3.20588	+	1.04165i	−0.163175	+	0.0530187i
$387$	−1.86636	−	11.3977i	−0.0948724	−	0.579379i
$388$	−8.99225	+	4.58178i	−0.456512	+	0.232605i
$389$	0.804900	+	2.47723i	0.0408101	+	0.125600i	0.969386	−	0.245542i	$-0.0789660\pi$
$389$	0.804900	+	2.47723i	0.0408101	+	0.125600i	−0.928576	+	0.371143i	$0.878966\pi$
$390$		0			0
$391$	−4.02838	+	12.3981i	−0.203724	+	0.626998i
$392$	−1.08774	−	6.86775i	−0.0549394	−	0.346874i
$393$	−8.91510	−	12.2034i	−0.449707	−	0.615578i
$394$	−4.30947	+	5.93148i	−0.217108	+	0.298824i
$395$		0			0
$396$	4.83934	+	14.6332i	0.243186	+	0.735345i
$397$	−0.295160	+	1.86357i	−0.0148137	+	0.0935298i	−0.993987	−	0.109494i	$-0.965077\pi$
$397$	−0.295160	+	1.86357i	−0.0148137	+	0.0935298i	0.979174	+	0.203024i	$0.0650769\pi$
$398$	−7.43262	−	3.78711i	−0.372563	−	0.189831i
$399$	−0.177984	−	0.0277131i	−0.00891032	−	0.00138739i
$400$		0			0
$401$			7.16880i			0.357993i	0.983850	+	0.178996i	$0.0572850\pi$
$401$			7.16880i			0.357993i	−0.983850	+	0.178996i	$0.942715\pi$
$402$	−21.0945	−	15.2419i	−1.05210	−	0.760199i
$403$	−3.33926	−	0.528887i	−0.166341	−	0.0263458i
$404$	7.71559	−	5.60571i	0.383865	−	0.278894i
$405$		0			0
$406$	−1.64017	−	1.19165i	−0.0814002	−	0.0591407i
$407$	15.6390	+	15.6390i	0.775197	+	0.775197i
$408$	8.44451	−	0.0220755i	0.418066	−	0.00109290i
$409$	−15.2838	−	4.96600i	−0.755734	−	0.245553i	−0.0942874	−	0.995545i	$-0.530057\pi$
$409$	−15.2838	−	4.96600i	−0.755734	−	0.245553i	−0.661447	+	0.749992i	$0.730057\pi$
$410$		0			0
$411$	−0.777631	−	4.82805i	−0.0383577	−	0.238150i
$412$	4.59157	+	9.01147i	0.226211	+	0.443963i
$413$	−0.489054	−	0.959822i	−0.0240648	−	0.0472297i
$414$	−8.02136	+	0.0419389i	−0.394228	+	0.00206119i
$415$		0			0
$416$	1.41362	+	0.459312i	0.0693083	+	0.0225196i
$417$	0.0315179	+	12.0565i	0.00154344	+	0.590408i
$418$	1.74927	+	1.74927i	0.0855596	+	0.0855596i
$419$	−1.81333	−	1.31746i	−0.0885872	−	0.0643624i	0.542610	−	0.839985i	$-0.317436\pi$
$419$	−1.81333	−	1.31746i	−0.0885872	−	0.0643624i	−0.631197	+	0.775622i	$0.717436\pi$
$420$		0			0
$421$	2.09500	−	1.52210i	0.102104	−	0.0741828i	−0.535562	−	0.844496i	$-0.679900\pi$
$421$	2.09500	−	1.52210i	0.102104	−	0.0741828i	0.637666	+	0.770313i	$0.279900\pi$
$422$	4.23458	+	0.670692i	0.206136	+	0.0326488i
$423$	−21.6481	−	21.4229i	−1.05257	−	1.04162i
$424$		−	7.69169i		−	0.373542i
$425$		0			0
$426$	3.23292	−	20.7630i	0.156636	−	1.00597i
$427$	−2.62595	−	1.33799i	−0.127079	−	0.0647498i
$428$	−1.72754	+	10.9072i	−0.0835037	+	0.527222i
$429$	6.03545	+	11.7691i	0.291394	+	0.568216i
$430$		0			0
$431$	−0.661426	+	0.910375i	−0.0318598	+	0.0438512i	−0.824650	−	0.565644i	$-0.808628\pi$
$431$	−0.661426	+	0.910375i	−0.0318598	+	0.0438512i	0.792790	+	0.609495i	$0.208628\pi$
$432$	1.64441	+	4.92909i	0.0791165	+	0.237151i
$433$	−3.21125	−	20.2750i	−0.154323	−	0.974355i	−0.936339	−	0.351097i	$-0.885809\pi$
$433$	−3.21125	−	20.2750i	−0.154323	−	0.974355i	0.782016	−	0.623258i	$-0.214191\pi$
$434$	−0.151807	+	0.467215i	−0.00728698	+	0.0224270i
$435$		0			0
$436$	−1.89491	−	5.83194i	−0.0907498	−	0.279299i
$437$	−1.14718	+	0.584515i	−0.0548768	+	0.0279611i
$438$	15.4465	−	5.06355i	0.738062	−	0.241946i
$439$	−22.3736	+	7.26963i	−1.06783	+	0.346960i	−0.789644	−	0.613565i	$-0.789735\pi$
$439$	−22.3736	+	7.26963i	−1.06783	+	0.346960i	−0.278191	+	0.960526i	$0.589735\pi$
$440$		0			0
$441$	12.1728	−	16.9400i	0.579659	−	0.806668i
$442$	7.15749	−	1.13363i	0.340447	−	0.0539215i
$443$	−13.6168	+	13.6168i	−0.646952	+	0.646952i	−0.952255	−	0.305303i	$-0.901242\pi$
$443$	−13.6168	+	13.6168i	−0.646952	+	0.646952i	0.305303	+	0.952255i	$0.401242\pi$
$444$	5.28624	+	5.25867i	0.250874	+	0.249565i
$445$		0			0
$446$	−0.429625	−	0.591328i	−0.0203433	−	0.0280002i
$447$	4.10066	−	12.7337i	0.193954	−	0.602283i
$448$	0.0980509	−	0.192436i	0.00463247	−	0.00909173i
$449$	−19.2184			−0.906973			−0.453487	−	0.891263i	$-0.649820\pi$
$449$	−19.2184			−0.906973			−0.453487	+	0.891263i	$0.649820\pi$
$450$		0			0
$451$	32.1710			1.51487
$452$	−4.98756	+	9.78864i	−0.234595	+	0.460419i
$453$	7.85069	−	24.3786i	0.368858	−	1.14541i
$454$	−1.94595	−	2.67837i	−0.0913281	−	0.125702i
$455$		0			0
$456$	0.591281	+	0.588198i	0.0276893	+	0.0275449i
$457$	−15.9563	+	15.9563i	−0.746405	+	0.746405i	−0.973802	−	0.227397i	$-0.926979\pi$
$457$	−15.9563	+	15.9563i	−0.746405	+	0.746405i	0.227397	+	0.973802i	$0.426979\pi$
$458$	10.4220	−	1.65068i	0.486986	−	0.0771311i
$459$	18.0535	+	17.7725i	0.842666	+	0.829551i
$460$		0			0
$461$	15.2184	−	4.94475i	0.708790	−	0.230300i	0.0676337	−	0.997710i	$-0.478455\pi$
$461$	15.2184	−	4.94475i	0.708790	−	0.230300i	0.641156	+	0.767410i	$0.278455\pi$
$462$	1.82624	−	0.598662i	0.0849642	−	0.0278523i
$463$	−5.51675	+	2.81092i	−0.256385	+	0.130635i	−0.577460	−	0.816419i	$-0.695956\pi$
$463$	−5.51675	+	2.81092i	−0.256385	+	0.130635i	0.321075	+	0.947054i	$0.395956\pi$
$464$	2.90074	+	8.92755i	0.134663	+	0.414451i
$465$		0			0
$466$	−3.89021	+	11.9728i	−0.180210	+	0.554630i
$467$	3.63127	+	22.9270i	0.168035	+	1.06093i	0.917164	+	0.398509i	$0.130472\pi$
$467$	3.63127	+	22.9270i	0.168035	+	1.06093i	−0.749129	+	0.662424i	$0.769528\pi$
$468$	2.04513	+	3.96244i	0.0945362	+	0.183164i
$469$	−1.90744	+	2.62537i	−0.0880775	+	0.121228i
$470$		0			0
$471$	12.9593	+	25.2705i	0.597133	+	1.16440i
$472$	−0.780256	+	4.92635i	−0.0359142	+	0.226753i
$473$	17.6230	+	8.97936i	0.810305	+	0.412871i
$474$	−0.582577	+	3.74153i	−0.0267587	+	0.171854i
$475$		0			0
$476$		−	1.05298i		−	0.0482633i
$477$	16.2310	−	16.4016i	0.743167	−	0.750979i
$478$	−11.6007	−	1.83738i	−0.530605	−	0.0840396i
$479$	18.1330	−	13.1744i	0.828519	−	0.601954i	−0.0906212	−	0.995885i	$-0.528885\pi$
$479$	18.1330	−	13.1744i	0.828519	−	0.601954i	0.919140	+	0.393931i	$0.128885\pi$
$480$		0			0
$481$	5.17668	+	3.76108i	0.236036	+	0.171491i
$482$	−0.860035	−	0.860035i	−0.0391735	−	0.0391735i
$483$	0.00261477	+	1.00022i	0.000118976	+	0.0455117i
$484$	−14.6409	−	4.75712i	−0.665496	−	0.216233i
$485$		0			0
$486$	−6.89486	+	13.9807i	−0.312757	+	0.634179i
$487$	9.62881	+	18.8976i	0.436323	+	0.856332i	0.999549	+	0.0300294i	$0.00956009\pi$
$487$	9.62881	+	18.8976i	0.436323	+	0.856332i	−0.563226	+	0.826303i	$0.690440\pi$
$488$	6.19509	+	12.1585i	0.280438	+	0.550391i
$489$	−1.11758	−	6.93870i	−0.0505389	−	0.313779i
$490$		0			0
$491$	−29.6177	−	9.62339i	−1.33663	−	0.434297i	−0.448456	−	0.893805i	$-0.648026\pi$
$491$	−29.6177	−	9.62339i	−1.33663	−	0.434297i	−0.888174	+	0.459507i	$0.848026\pi$
$492$	10.8460	−	0.0283534i	0.488974	−	0.00127827i
$493$	32.3613	+	32.3613i	1.45748	+	1.45748i
$494$	0.579028	+	0.420688i	0.0260517	+	0.0189277i
$495$		0			0
$496$	1.84019	−	1.33698i	0.0826270	−	0.0600320i
$497$	−2.58795	−	0.409892i	−0.116086	−	0.0183862i
$498$	−7.02030	−	5.07256i	−0.314587	−	0.227307i
$499$			1.25659i			0.0562528i	0.999604	+	0.0281264i	$0.00895410\pi$
$499$			1.25659i			0.0562528i	−0.999604	+	0.0281264i	$0.991046\pi$
$500$		0			0
$501$	−23.6878	−	3.68833i	−1.05829	−	0.164783i
$502$	20.1477	+	10.2658i	0.899236	+	0.458184i
$503$	4.11407	−	25.9752i	0.183437	−	1.15818i	−0.708397	−	0.705815i	$-0.750581\pi$
$503$	4.11407	−	25.9752i	0.183437	−	1.15818i	0.891834	−	0.452363i	$-0.149419\pi$
$504$	0.615160	−	0.203439i	0.0274014	−	0.00906191i
$505$		0			0
$506$	8.07434	−	11.1134i	0.358948	−	0.494050i
$507$	−11.0252	−	15.0918i	−0.489648	−	0.670251i
$508$	2.35228	+	14.8517i	0.104366	+	0.658938i
$509$	5.31690	−	16.3637i	0.235668	−	0.725310i	−0.761365	−	0.648324i	$-0.775470\pi$
$509$	5.31690	−	16.3637i	0.235668	−	0.725310i	0.997032	−	0.0769863i	$-0.0245298\pi$
$510$		0			0
$511$	−0.626355	−	1.92772i	−0.0277083	−	0.0852775i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	0.0196223	+	2.50199i	0.000866347	+	0.110465i
$514$	4.01395	−	1.30421i	0.177048	−	0.0575263i
$515$		0			0
$516$	5.94923	+	3.01172i	0.261900	+	0.132584i
$517$	51.5147	−	8.15912i	2.26561	−	0.358838i
$518$	0.657443	−	0.657443i	0.0288864	−	0.0288864i
$519$	−1.10930	+	1.11512i	−0.0486930	+	0.0489483i
$520$		0			0
$521$	7.91212	+	10.8901i	0.346636	+	0.477104i	0.946365	−	0.323099i	$-0.104725\pi$
$521$	7.91212	+	10.8901i	0.346636	+	0.477104i	−0.599729	+	0.800203i	$0.704725\pi$
$522$	−12.6534	+	25.1581i	−0.553826	+	1.10114i
$523$	−11.6979	+	22.9585i	−0.511514	+	1.00390i	0.480407	+	0.877046i	$0.340489\pi$
$523$	−11.6979	+	22.9585i	−0.511514	+	1.00390i	−0.991921	+	0.126858i	$0.959511\pi$
$524$	8.72546			0.381174
$525$		0			0
$526$	2.57177			0.112134
$527$	5.03463	−	9.88101i	0.219312	−	0.430424i
$528$	−8.47012	−	2.72765i	−0.368615	−	0.118706i
$529$	−9.31679	−	12.8235i	−0.405078	−	0.557542i
$530$		0			0
$531$	−12.0594	+	8.85835i	−0.523333	+	0.384420i
$532$	0.0735370	−	0.0735370i	0.00318823	−	0.00318823i
$533$	9.19295	−	1.45602i	0.398191	−	0.0630672i
$534$	−8.56457	+	16.9181i	−0.370625	+	0.732118i
$535$		0			0
$536$	14.2901	−	4.64313i	0.617237	−	0.200553i
$537$	−6.39325	−	19.5028i	−0.275889	−	0.841607i
$538$	21.5305	−	10.9703i	0.928246	−	0.472965i
$539$	11.0391	+	33.9747i	0.475486	+	1.46340i
$540$		0			0
$541$	−6.47364	+	19.9238i	−0.278323	+	0.856591i	0.709998	+	0.704204i	$0.248696\pi$
$541$	−6.47364	+	19.9238i	−0.278323	+	0.856591i	−0.988321	+	0.152387i	$0.951304\pi$
$542$	1.81078	+	11.4328i	0.0777797	+	0.491082i
$543$	−24.0428	+	17.5643i	−1.03177	+	0.753757i
$544$	−2.86572	+	3.94433i	−0.122867	+	0.169112i
$545$		0			0
$546$	0.494756	−	0.253722i	0.0211736	−	0.0108583i
$547$	−6.82585	+	43.0967i	−0.291852	+	1.84268i	0.209965	+	0.977709i	$0.432665\pi$
$547$	−6.82585	+	43.0967i	−0.291852	+	1.84268i	−0.501817	+	0.864974i	$0.667335\pi$
$548$	2.51567	+	1.28180i	0.107464	+	0.0547557i
$549$	−12.4467	+	38.9995i	−0.531211	+	1.66446i
$550$		0			0
$551$			4.52004i			0.192560i
$552$	2.71235	−	3.75382i	0.115445	−	0.159773i
$553$	0.466353	+	0.0738630i	0.0198313	+	0.00314098i
$554$	6.09674	−	4.42954i	0.259025	−	0.188193i
$555$		0			0
$556$	−5.63143	−	4.09147i	−0.238826	−	0.173517i
$557$	−20.7979	−	20.7979i	−0.881236	−	0.881236i	0.112424	−	0.993660i	$-0.464139\pi$
$557$	−20.7979	−	20.7979i	−0.881236	−	0.881236i	−0.993660	+	0.112424i	$0.964139\pi$
$558$	6.74528	+	1.03223i	0.285551	+	0.0436976i
$559$	5.44220	+	1.76828i	0.230181	+	0.0747902i
$560$		0			0
$561$	−42.8322	+	6.89878i	−1.80838	+	0.291267i
$562$	−10.7198	−	21.0388i	−0.452187	−	0.887467i
$563$	−7.14045	−	14.0139i	−0.300934	−	0.590616i	0.690179	−	0.723639i	$-0.257532\pi$
$563$	−7.14045	−	14.0139i	−0.300934	−	0.590616i	−0.991113	+	0.133022i	$0.957532\pi$
$564$	17.3602	−	2.79613i	0.730996	−	0.117738i
$565$		0			0
$566$	−9.36284	−	3.04217i	−0.393550	−	0.127872i
$567$	1.74105	+	0.864300i	0.0731174	+	0.0362972i
$568$	8.57861	+	8.57861i	0.359950	+	0.359950i
$569$	3.20445	+	2.32817i	0.134338	+	0.0976021i	0.652925	−	0.757423i	$-0.273542\pi$
$569$	3.20445	+	2.32817i	0.134338	+	0.0976021i	−0.518587	+	0.855025i	$0.673542\pi$
$570$		0			0
$571$	−31.7943	+	23.0999i	−1.33055	+	0.966702i	−0.330815	+	0.943696i	$0.607324\pi$
$571$	−31.7943	+	23.0999i	−1.33055	+	0.966702i	−0.999735	+	0.0230060i	$0.992676\pi$
$572$	−7.54225	−	1.19457i	−0.315357	−	0.0499477i
$573$	5.01468	−	6.94020i	0.209491	−	0.289931i
$574$		−	1.35243i		−	0.0564492i
$575$		0			0
$576$	−2.85798	−	0.912121i	−0.119082	−	0.0380050i
$577$	−16.8154	−	8.56788i	−0.700034	−	0.356685i	0.0674769	−	0.997721i	$-0.478505\pi$
$577$	−16.8154	−	8.56788i	−0.700034	−	0.356685i	−0.767511	+	0.641036i	$0.778505\pi$
$578$	−1.05907	+	6.68673i	−0.0440517	+	0.278131i
$579$	5.19519	−	2.66421i	0.215905	−	0.110721i
$580$		0			0
$581$	−0.634802	+	0.873729i	−0.0263360	+	0.0362484i
$582$	14.1149	−	10.3116i	0.585083	−	0.427429i
$583$	6.18173	+	39.0299i	0.256021	+	1.61645i
$584$	−2.90012	+	8.92565i	−0.120008	+	0.369346i
$585$		0			0
$586$	1.45939	+	4.49153i	0.0602867	+	0.185543i
$587$	−4.14963	+	2.11434i	−0.171274	+	0.0872683i	−0.537526	−	0.843247i	$-0.680641\pi$
$587$	−4.14963	+	2.11434i	−0.171274	+	0.0872683i	0.366252	+	0.930516i	$0.380641\pi$
$588$	3.75160	+	11.4443i	0.154713	+	0.471957i
$589$	1.04166	−	0.338457i	0.0429210	−	0.0139459i
$590$		0			0
$591$	5.73558	−	11.3298i	0.235930	−	0.466047i
$592$	−4.25195	+	0.673443i	−0.174754	+	0.0276783i
$593$	32.4687	−	32.4687i	1.33333	−	1.33333i	0.430960	−	0.902371i	$-0.358175\pi$
$593$	32.4687	−	32.4687i	1.33333	−	1.33333i	0.902371	−	0.430960i	$-0.141825\pi$
$594$	−12.3057	−	23.6901i	−0.504907	−	0.972015i
$595$		0			0
$596$	4.53982	+	6.24853i	0.185958	+	0.255950i
$597$	13.7529	+	4.42888i	0.562870	+	0.181262i
$598$	1.80428	−	3.54111i	0.0737826	−	0.144807i
$599$	−18.2921			−0.747393			−0.373697	−	0.927551i	$-0.621910\pi$
$599$	−18.2921			−0.747393			−0.373697	+	0.927551i	$0.621910\pi$
$600$		0			0
$601$	−0.981781			−0.0400477			−0.0200238	−	0.999800i	$-0.506374\pi$
$601$	−0.981781			−0.0400477			−0.0200238	+	0.999800i	$0.506374\pi$
$602$	0.377480	−	0.740847i	0.0153850	−	0.0301947i
$603$	40.2698	+	20.2540i	1.63991	+	0.824807i
$604$	8.69147	+	11.9628i	0.353651	+	0.486759i
$605$		0			0
$606$	−11.6498	+	11.7109i	−0.473241	+	0.475722i
$607$	2.39455	−	2.39455i	0.0971917	−	0.0971917i	−0.656839	−	0.754031i	$-0.728107\pi$
$607$	2.39455	−	2.39455i	0.0971917	−	0.0971917i	0.754031	+	0.656839i	$0.228107\pi$
$608$	−0.475594	+	0.0753267i	−0.0192879	+	0.00305490i
$609$	3.13292	+	1.58600i	0.126952	+	0.0642679i
$610$		0			0
$611$	14.3512	−	4.66298i	0.580586	−	0.188644i
$612$	−14.4341	+	2.36357i	−0.583465	+	0.0955415i
$613$	12.2470	−	6.24017i	0.494653	−	0.252038i	−0.188823	−	0.982011i	$-0.560467\pi$
$613$	12.2470	−	6.24017i	0.494653	−	0.252038i	0.683476	+	0.729973i	$0.260467\pi$
$614$	−5.16261	−	15.8889i	−0.208346	−	0.641223i
$615$		0			0
$616$	−0.342880	+	1.05528i	−0.0138150	+	0.0425183i
$617$	−1.60431	−	10.1292i	−0.0645872	−	0.407787i	−0.998707	−	0.0508287i	$-0.983814\pi$
$617$	−1.60431	−	10.1292i	−0.0645872	−	0.407787i	0.934120	−	0.356959i	$-0.116186\pi$
$618$	−10.3336	−	14.1451i	−0.415679	−	0.568999i
$619$	−27.3325	+	37.6199i	−1.09859	+	1.51207i	−0.261338	+	0.965247i	$0.584164\pi$
$619$	−27.3325	+	37.6199i	−1.09859	+	1.51207i	−0.837247	+	0.546825i	$0.815836\pi$
$620$		0			0
$621$	13.7051	−	2.28099i	0.549966	−	0.0915329i
$622$	4.72465	−	29.8303i	0.189441	−	1.19608i
$623$	2.10678	+	1.07346i	0.0844063	+	0.0430072i
$624$	−2.54381	−	0.396086i	−0.101834	−	0.0158561i
$625$		0			0
$626$			16.6805i			0.666686i
$627$	−3.47306	−	2.50948i	−0.138701	−	0.100219i
$628$	−16.1947	−	2.56499i	−0.646239	−	0.102354i
$629$	−16.9802	+	12.3368i	−0.677043	+	0.491900i
$630$		0			0
$631$	−20.6748	−	15.0211i	−0.823051	−	0.597981i	0.0945340	−	0.995522i	$-0.469864\pi$
$631$	−20.6748	−	15.0211i	−0.823051	−	0.597981i	−0.917585	+	0.397540i	$0.869864\pi$
$632$	−1.54588	−	1.54588i	−0.0614917	−	0.0614917i
$633$	−7.42591	+	0.0194127i	−0.295153	+	0.000771586i
$634$	−10.3155	−	3.35172i	−0.409683	−	0.133114i
$635$		0			0
$636$	2.11847	+	13.1529i	0.0840030	+	0.521546i
$637$	4.69209	+	9.20875i	0.185907	+	0.364864i
$638$	−21.8942	−	42.9697i	−0.866798	−	1.70119i
$639$	0.190290	+	36.3955i	0.00752777	+	1.43978i
$640$		0			0
$641$	0.702023	+	0.228101i	0.0277282	+	0.00900945i	0.322848	−	0.946451i	$-0.395360\pi$
$641$	0.702023	+	0.228101i	0.0277282	+	0.00900945i	−0.295120	+	0.955460i	$0.595360\pi$
$642$	−0.0500024	−	19.1273i	−0.00197344	−	0.754896i
$643$	−17.1573	−	17.1573i	−0.676616	−	0.676616i	0.282617	−	0.959233i	$-0.408797\pi$
$643$	−17.1573	−	17.1573i	−0.676616	−	0.676616i	−0.959233	+	0.282617i	$0.908797\pi$
$644$	−0.467192	−	0.339435i	−0.0184099	−	0.0133756i
$645$		0			0
$646$	−1.89928	+	1.37991i	−0.0747262	+	0.0542918i
$647$	−5.95524	−	0.943217i	−0.234125	−	0.0370817i	0.0382696	−	0.999267i	$-0.487815\pi$
$647$	−5.95524	−	0.943217i	−0.234125	−	0.0370817i	−0.272394	+	0.962186i	$0.587815\pi$
$648$	−4.16954	−	7.97590i	−0.163795	−	0.313323i
$649$		−	25.6248i		−	1.00586i
$650$		0			0
$651$	0.130910	−	0.840754i	0.00513078	−	0.0329517i
$652$	3.61543	+	1.84215i	0.141591	+	0.0721443i
$653$	−1.57981	+	9.97451i	−0.0618226	+	0.390333i	0.937303	+	0.348516i	$0.113314\pi$
$653$	−1.57981	+	9.97451i	−0.0618226	+	0.390333i	−0.999125	+	0.0418163i	$0.986686\pi$
$654$	4.84657	+	9.45078i	0.189516	+	0.369555i
$655$		0			0
$656$	−3.68068	+	5.06602i	−0.143706	+	0.197795i
$657$	−25.0191	+	12.9131i	−0.976087	+	0.503787i
$658$	−0.342999	−	2.16561i	−0.0133715	−	0.0844242i
$659$	−3.59331	+	11.0591i	−0.139975	+	0.430800i	−0.996331	−	0.0855871i	$-0.972723\pi$
$659$	−3.59331	+	11.0591i	−0.139975	+	0.430800i	0.856355	+	0.516387i	$0.172723\pi$
$660$		0			0
$661$	12.8291	+	39.4838i	0.498993	+	1.53574i	0.810641	+	0.585544i	$0.199119\pi$
$661$	12.8291	+	39.4838i	0.498993	+	1.53574i	−0.311648	+	0.950197i	$0.600881\pi$
$662$	−8.58467	+	4.37411i	−0.333653	+	0.170005i
$663$	−11.9272	+	3.90987i	−0.463213	+	0.151847i
$664$	4.75577	−	1.54524i	0.184560	−	0.0599671i
$665$		0			0
$666$	−10.4879	−	7.53643i	−0.406397	−	0.292031i
$667$	24.7901	−	3.92637i	0.959877	−	0.152030i
$668$	9.78704	−	9.78704i	0.378672	−	0.378672i
$669$	0.897530	+	0.892849i	0.0347005	+	0.0345195i
$670$		0			0
$671$	−41.2074	−	56.7171i	−1.59079	−	2.18954i
$672$	−0.114667	+	0.356073i	−0.00442337	+	0.0137358i
$673$	−12.1800	+	23.9046i	−0.469504	+	0.921454i	0.527890	+	0.849313i	$0.322983\pi$
$673$	−12.1800	+	23.9046i	−0.469504	+	0.921454i	−0.997394	+	0.0721411i	$0.977017\pi$
$674$	−28.1544			−1.08447
$675$		0			0
$676$	10.7907			0.415028
$677$	−10.0184	+	19.6621i	−0.385037	+	0.755677i	−0.999445	−	0.0333112i	$-0.989395\pi$
$677$	−10.0184	+	19.6621i	−0.385037	+	0.755677i	0.614408	+	0.788988i	$0.289395\pi$
$678$	5.83277	−	18.1124i	0.224006	−	0.695602i
$679$	−1.28118	−	1.76340i	−0.0491673	−	0.0676729i
$680$		0			0
$681$	4.06529	+	4.04409i	0.155782	+	0.154970i
$682$	−8.26315	+	8.26315i	−0.316413	+	0.316413i
$683$	19.3379	−	3.06282i	0.739944	−	0.117196i	0.224927	−	0.974376i	$-0.427786\pi$
$683$	19.3379	−	3.06282i	0.739944	−	0.117196i	0.515017	+	0.857180i	$0.327786\pi$
$684$	−1.17310	−	0.842973i	−0.0448547	−	0.0322319i
$685$		0			0
$686$	2.86609	−	0.931249i	0.109428	−	0.0355552i
$687$	−17.3670	+	5.69313i	−0.662594	+	0.217207i
$688$	−3.43023	+	1.74779i	−0.130776	+	0.0666339i
$689$	3.53289	+	10.8731i	0.134592	+	0.414232i
$690$		0			0
$691$	12.6136	−	38.8206i	0.479843	−	1.47681i	−0.359469	−	0.933157i	$-0.617042\pi$
$691$	12.6136	−	38.8206i	0.479843	−	1.47681i	0.839313	−	0.543649i	$-0.182958\pi$
$692$	−0.142061	−	0.896939i	−0.00540036	−	0.0340965i
$693$	−2.95800	+	1.52671i	−0.112365	+	0.0579949i
$694$	11.3510	−	15.6232i	0.430876	−	0.593050i
$695$		0			0
$696$	−7.41915	−	14.4673i	−0.281222	−	0.548381i
$697$	−4.77592	+	30.1540i	−0.180901	+	1.14216i
$698$	12.8411	+	6.54286i	0.486042	+	0.247651i
$699$	3.35470	−	21.5451i	0.126886	−	0.814912i
$700$		0			0
$701$			1.34594i			0.0508356i	0.999677	+	0.0254178i	$0.00809161\pi$
$701$			1.34594i			0.0508356i	−0.999677	+	0.0254178i	$0.991908\pi$
$702$	−4.58855	−	6.21255i	−0.173184	−	0.234478i
$703$	−2.04741	−	0.324278i	−0.0772195	−	0.0122304i
$704$	4.15636	−	3.01977i	0.156649	−	0.113812i
$705$		0			0
$706$	28.3247	+	20.5791i	1.06601	+	0.774503i
$707$	1.45647	+	1.45647i	0.0547762	+	0.0547762i
$708$	−0.0225840	−	8.63901i	−0.000848758	−	0.324674i
$709$	5.99345	+	1.94739i	0.225089	+	0.0731358i	0.419390	−	0.907806i	$-0.362244\pi$
$709$	5.99345	+	1.94739i	0.225089	+	0.0731358i	−0.194301	+	0.980942i	$0.562244\pi$
$710$		0			0
$711$	−0.0342906	−	6.55851i	−0.00128600	−	0.245963i
$712$	−4.97027	−	9.75471i	−0.186269	−	0.365573i
$713$	−2.76112	−	5.41900i	−0.103405	−	0.202943i
$714$	0.290016	+	1.80061i	0.0108536	+	0.0673861i
$715$		0			0
$716$	11.2695	+	3.66170i	0.421163	+	0.136844i
$717$	20.3435	−	0.0531816i	0.759740	−	0.00198610i
$718$	−24.4491	−	24.4491i	−0.912432	−	0.912432i
$719$	−15.2779	−	11.1001i	−0.569770	−	0.413962i	0.265251	−	0.964179i	$-0.414545\pi$
$719$	−15.2779	−	11.1001i	−0.569770	−	0.413962i	−0.835022	+	0.550217i	$0.814545\pi$
$720$		0			0
$721$	−1.76717	+	1.28392i	−0.0658127	+	0.0478157i
$722$	18.5371	+	2.93598i	0.689878	+	0.109266i
$723$	1.70755	+	1.23380i	0.0635043	+	0.0458854i
$724$		−	17.1907i		−	0.638888i
$725$		0			0
$726$	26.3463	+	4.10228i	0.977805	+	0.152250i
$727$	−11.0417	−	5.62601i	−0.409513	−	0.208657i	0.237084	−	0.971489i	$-0.423808\pi$
$727$	−11.0417	−	5.62601i	−0.409513	−	0.208657i	−0.646597	+	0.762832i	$0.723808\pi$
$728$	−0.0502184	+	0.317066i	−0.00186122	+	0.0117513i
$729$	7.93968	−	25.8062i	0.294062	−	0.955786i
$730$		0			0
$731$	−11.0326	+	15.1850i	−0.408055	+	0.561639i
$732$	−13.9424	−	19.0850i	−0.515327	−	0.705401i
$733$	−1.46889	−	9.27418i	−0.0542545	−	0.342550i	−0.999852	−	0.0172103i	$-0.994522\pi$
$733$	−1.46889	−	9.27418i	−0.0542545	−	0.342550i	0.945597	−	0.325339i	$-0.105478\pi$
$734$	−0.998039	+	3.07165i	−0.0368383	+	0.113377i
$735$		0			0
$736$	0.826257	+	2.54296i	0.0304562	+	0.0937346i
$737$	−68.7804	+	35.0454i	−2.53356	+	1.29091i
$738$	−18.5389	+	3.03572i	−0.682428	+	0.111746i
$739$	18.0916	−	5.87832i	0.665511	−	0.216238i	0.0432699	−	0.999063i	$-0.486222\pi$
$739$	18.0916	−	5.87832i	0.665511	−	0.216238i	0.622241	+	0.782826i	$0.286222\pi$
$740$		0			0
$741$	−1.10601	−	0.559904i	−0.0406304	−	0.0205686i
$742$	1.64077	−	0.259872i	0.0602344	−	0.00954019i
$743$	23.1938	−	23.1938i	0.850899	−	0.850899i	−0.139345	−	0.990244i	$-0.544500\pi$
$743$	23.1938	−	23.1938i	0.850899	−	0.850899i	0.990244	+	0.139345i	$0.0444997\pi$
$744$	−2.77851	+	2.79308i	−0.101865	+	0.102399i
$745$		0			0
$746$	−6.36867	−	8.76572i	−0.233174	−	0.320936i
$747$	13.4019	+	6.74058i	0.490350	+	0.246625i
$748$	11.3715	−	22.3178i	0.415783	−	0.816020i
$749$	−2.38506			−0.0871483
$750$		0			0
$751$	35.1267			1.28179			0.640895	−	0.767628i	$-0.278563\pi$
$751$	35.1267			1.28179			0.640895	+	0.767628i	$0.278563\pi$
$752$	−4.60895	+	9.04558i	−0.168071	+	0.329858i
$753$	−37.2803	−	12.0054i	−1.35857	−	0.437502i
$754$	−8.20106	−	11.2878i	−0.298665	−	0.411077i
$755$		0			0
$756$	−0.995899	+	0.517314i	−0.0362205	+	0.0188145i
$757$	−20.0652	+	20.0652i	−0.729283	+	0.729283i	−0.970477	−	0.241194i	$-0.922461\pi$
$757$	−20.0652	+	20.0652i	−0.729283	+	0.729283i	0.241194	+	0.970477i	$0.422461\pi$
$758$	−33.0785	+	5.23911i	−1.20146	+	0.190293i
$759$	−10.7463	+	21.2279i	−0.390067	+	0.770523i
$760$		0			0
$761$	−30.4666	+	9.89919i	−1.10441	+	0.358845i	−0.803799	−	0.594901i	$-0.797191\pi$
$761$	−30.4666	+	9.89919i	−1.10441	+	0.358845i	−0.300613	+	0.953746i	$0.597191\pi$
$762$	−8.11294	−	24.7487i	−0.293901	−	0.896552i
$763$	1.18003	−	0.601254i	0.0427199	−	0.0217669i
$764$	1.52761	+	4.70151i	0.0552671	+	0.170095i
$765$		0			0
$766$	−5.02104	+	15.4532i	−0.181418	+	0.558346i
$767$	−1.15975	−	7.32235i	−0.0418760	−	0.264395i
$768$	1.39859	−	1.02173i	0.0504674	−	0.0368686i
$769$	8.74366	−	12.0346i	0.315305	−	0.433980i	−0.621722	−	0.783238i	$-0.713567\pi$
$769$	8.74366	−	12.0346i	0.315305	−	0.433980i	0.937026	+	0.349259i	$0.113567\pi$
$770$		0			0
$771$	−6.50470	+	3.33576i	−0.234261	+	0.120134i
$772$	−0.527318	+	3.32936i	−0.0189786	+	0.119826i
$773$	19.8204	+	10.0990i	0.712889	+	0.363235i	0.772524	−	0.634985i	$-0.218994\pi$
$773$	19.8204	+	10.0990i	0.712889	+	0.363235i	−0.0596354	+	0.998220i	$0.518994\pi$
$774$	−11.0028	−	3.51152i	−0.395486	−	0.126219i
$775$		0			0
$776$			10.0922i			0.362290i
$777$	−0.943161	+	1.30531i	−0.0338357	+	0.0468278i
$778$	2.57264	+	0.407467i	0.0922337	+	0.0146084i
$779$	−2.43940	+	1.77233i	−0.0874006	+	0.0635003i
$780$		0			0
$781$	−50.4249	−	36.6358i	−1.80435	−	1.31093i
$782$	9.21792	+	9.21792i	0.329632	+	0.329632i
$783$	14.7084	−	46.5057i	0.525635	−	1.66198i
$784$	−6.61303	−	2.14870i	−0.236180	−	0.0767395i
$785$		0			0
$786$	−14.9207	+	2.40320i	−0.532202	+	0.0857193i
$787$	−23.2927	−	45.7145i	−0.830295	−	1.62955i	−0.775755	−	0.631035i	$-0.782631\pi$
$787$	−23.2927	−	45.7145i	−0.830295	−	1.62955i	−0.0545406	−	0.998512i	$-0.517369\pi$
$788$	3.32853	+	6.53260i	0.118574	+	0.232714i
$789$	−4.39775	+	0.708326i	−0.156564	+	0.0252171i
$790$		0			0
$791$	−2.25659	−	0.733210i	−0.0802351	−	0.0260700i
$792$	15.2353	+	2.33144i	0.541362	+	0.0828442i
$793$	−14.3420	−	14.3420i	−0.509301	−	0.509301i
$794$	1.52645	+	1.10903i	0.0541717	+	0.0393580i
$795$		0			0
$796$	−6.74867	+	4.90320i	−0.239200	+	0.173789i
$797$	3.06529	+	0.485494i	0.108578	+	0.0171971i	0.210487	−	0.977597i	$-0.432495\pi$
$797$	3.06529	+	0.485494i	0.108578	+	0.0171971i	−0.101909	+	0.994794i	$0.532495\pi$
$798$	−0.105495	+	0.146003i	−0.00373450	+	0.00516845i
$799$			49.4961i			1.75105i
$800$		0			0
$801$	9.98587	−	31.2890i	0.352833	−	1.10554i
$802$	6.38745	+	3.25457i	0.225549	+	0.114923i
$803$	7.54261	−	47.6222i	0.266173	−	1.68055i
$804$	−23.1574	+	11.8756i	−0.816698	+	0.418821i
$805$		0			0
$806$	−1.98724	+	2.73520i	−0.0699974	+	0.0963431i
$807$	−33.7959	+	24.6894i	−1.18967	+	0.869109i
$808$	−1.49192	−	9.41958i	−0.0524854	−	0.331380i
$809$	−4.71934	+	14.5246i	−0.165923	+	0.510659i	−0.999103	−	0.0423432i	$-0.986518\pi$
$809$	−4.71934	+	14.5246i	−0.165923	+	0.510659i	0.833180	+	0.553002i	$0.186518\pi$
$810$		0			0
$811$	1.02202	+	3.14544i	0.0358879	+	0.110451i	0.967396	−	0.253270i	$-0.0815060\pi$
$811$	1.02202	+	3.14544i	0.0358879	+	0.110451i	−0.931508	+	0.363721i	$0.881506\pi$
$812$	−1.80639	+	0.920402i	−0.0633919	+	0.0322998i
$813$	−6.24533	−	19.0515i	−0.219033	−	0.668166i
$814$	21.0344	−	6.83450i	0.737256	−	0.239549i
$815$		0			0
$816$	3.81406	−	7.53414i	0.133519	−	0.263748i
$817$	−1.83096	+	0.289996i	−0.0640572	+	0.0101457i
$818$	−11.3634	+	11.3634i	−0.397313	+	0.397313i
$819$	−0.776158	+	0.570136i	−0.0271212	+	0.0199222i
$820$		0			0
$821$	18.3359	+	25.2372i	0.639927	+	0.880784i	0.998612	−	0.0526750i	$-0.0167748\pi$
$821$	18.3359	+	25.2372i	0.639927	+	0.880784i	−0.358685	+	0.933459i	$0.616775\pi$
$822$	−4.65486	−	1.49901i	−0.162357	−	0.0522841i
$823$	7.08420	−	13.9035i	0.246940	−	0.484647i	−0.733952	−	0.679202i	$-0.762326\pi$
$823$	7.08420	−	13.9035i	0.246940	−	0.484647i	0.980892	+	0.194555i	$0.0623262\pi$
$824$	10.1138			0.352331
$825$		0			0
$826$	−1.07723			−0.0374817
$827$	−1.65039	+	3.23908i	−0.0573898	+	0.112634i	−0.917920	−	0.396766i	$-0.870132\pi$
$827$	−1.65039	+	3.23908i	−0.0573898	+	0.112634i	0.860530	+	0.509400i	$0.170132\pi$
$828$	−3.60425	+	7.16612i	−0.125256	+	0.249040i
$829$	14.6691	+	20.1903i	0.509480	+	0.701239i	0.983832	−	0.179096i	$-0.0573174\pi$
$829$	14.6691	+	20.1903i	0.509480	+	0.701239i	−0.474351	+	0.880336i	$0.657317\pi$
$830$		0			0
$831$	−9.20549	+	9.25375i	−0.319335	+	0.321009i
$832$	1.05102	−	1.05102i	0.0364375	−	0.0364375i
$833$	−33.4834	+	5.30325i	−1.16013	+	0.183747i
$834$	10.7567	+	5.44544i	0.372474	+	0.188560i
$835$		0			0
$836$	2.35276	−	0.764459i	0.0813720	−	0.0264394i
$837$	−11.8188	+	0.0926914i	−0.408518	+	0.00320388i
$838$	−1.99711	+	1.01758i	−0.0689889	+	0.0351516i
$839$	−5.55073	−	17.0834i	−0.191632	−	0.589784i	−0.999999	−	0.00110507i	$-0.999648\pi$
$839$	−5.55073	−	17.0834i	−0.191632	−	0.589784i	0.808367	−	0.588679i	$-0.200352\pi$
$840$		0			0
$841$	18.2677	−	56.2221i	0.629920	−	1.93869i
$842$	−0.405096	−	2.55767i	−0.0139605	−	0.0881433i
$843$	24.1255	+	33.0241i	0.830928	+	1.13741i
$844$	2.52005	−	3.46855i	0.0867437	−	0.119392i
$845$		0			0
$846$	−28.9160	+	9.56282i	−0.994153	+	0.328776i
$847$	0.520114	−	3.28387i	0.0178713	−	0.112835i
$848$	−6.85335	−	3.49196i	−0.235345	−	0.119914i
$849$	16.8485	+	2.62340i	0.578238	+	0.0900350i
$850$		0			0
$851$			11.5107i			0.394581i
$852$	−17.0323	−	12.3068i	−0.583516	−	0.421623i
$853$	31.1950	+	4.94081i	1.06810	+	0.169170i	0.665643	−	0.746270i	$-0.268157\pi$
$853$	31.1950	+	4.94081i	1.06810	+	0.169170i	0.402454	+	0.915440i	$0.368157\pi$
$854$	−2.38431	+	1.73230i	−0.0815894	+	0.0592782i
$855$		0			0
$856$	8.93414	+	6.49104i	0.305363	+	0.221859i
$857$	−8.57240	−	8.57240i	−0.292828	−	0.292828i	0.545369	−	0.838196i	$-0.316390\pi$
$857$	−8.57240	−	8.57240i	−0.292828	−	0.292828i	−0.838196	+	0.545369i	$0.816390\pi$
$858$	13.2264	−	0.0345761i	0.451540	−	0.00118041i
$859$	−1.99366	−	0.647780i	−0.0680228	−	0.0221020i	0.274808	−	0.961499i	$-0.411386\pi$
$859$	−1.99366	−	0.647780i	−0.0680228	−	0.0221020i	−0.342831	+	0.939397i	$0.611386\pi$
$860$		0			0
$861$	0.372491	+	2.31267i	0.0126944	+	0.0788155i
$862$	0.510869	+	1.00264i	0.0174003	+	0.0341500i
$863$	13.0397	+	25.5918i	0.443876	+	0.871155i	0.999218	+	0.0395333i	$0.0125871\pi$
$863$	13.0397	+	25.5918i	0.443876	+	0.871155i	−0.555343	+	0.831622i	$0.687413\pi$
$864$	5.13840	+	0.772583i	0.174812	+	0.0262838i
$865$		0			0
$866$	−19.5231	−	6.34342i	−0.663420	−	0.215558i
$867$	−0.0306542	−	11.7261i	−0.00104107	−	0.398239i
$868$	0.347372	+	0.347372i	0.0117906	+	0.0117906i
$869$	9.08664	+	6.60183i	0.308243	+	0.223952i
$870$		0			0
$871$	−18.0680	+	13.1272i	−0.612212	+	0.444798i
$872$	−6.05656	−	0.959266i	−0.205101	−	0.0324848i
$873$	−21.2966	+	21.5205i	−0.720782	+	0.728359i
$874$			1.28751i			0.0435505i
$875$		0			0
$876$	2.50091	−	16.0617i	0.0844978	−	0.542676i
$877$	15.3780	+	7.83550i	0.519279	+	0.264586i	0.693927	−	0.720045i	$-0.255879\pi$
$877$	15.3780	+	7.83550i	0.519279	+	0.264586i	−0.174648	+	0.984631i	$0.555879\pi$
$878$	−3.68012	+	23.2354i	−0.124198	+	0.784156i
$879$	−3.73264	−	7.27862i	−0.125899	−	0.245502i
$880$		0			0
$881$	−11.5046	+	15.8347i	−0.387600	+	0.533485i	−0.957578	−	0.288175i	$-0.906952\pi$
$881$	−11.5046	+	15.8347i	−0.387600	+	0.533485i	0.569978	+	0.821660i	$0.306952\pi$
$882$	−9.56732	−	18.5367i	−0.322148	−	0.624163i
$883$	−2.11040	−	13.3245i	−0.0710206	−	0.448406i	−0.997415	−	0.0718524i	$-0.977109\pi$
$883$	−2.11040	−	13.3245i	−0.0710206	−	0.448406i	0.926395	−	0.376554i	$-0.122891\pi$
$884$	2.23936	−	6.89203i	0.0753177	−	0.231804i
$885$		0			0
$886$	5.95075	+	18.3145i	0.199919	+	0.615288i
$887$	46.7094	−	23.7996i	1.56835	−	0.799114i	0.568624	−	0.822597i	$-0.307476\pi$
$887$	46.7094	−	23.7996i	1.56835	−	0.799114i	0.999724	+	0.0234837i	$0.00747579\pi$
$888$	7.08541	−	2.32268i	0.237771	−	0.0779442i
$889$	−3.08864	+	1.00356i	−0.103590	+	0.0336583i
$890$		0			0
$891$	27.5676	+	37.1210i	0.923550	+	1.24360i
$892$	−0.721923	+	0.114341i	−0.0241718	+	0.00382843i
$893$	−3.45666	+	3.45666i	−0.115673	+	0.115673i
$894$	−9.48414	−	9.43468i	−0.317197	−	0.315543i
$895$		0			0
$896$	−0.126947	−	0.174728i	−0.00424101	−	0.00583725i
$897$	−2.11004	+	6.55228i	−0.0704523	+	0.218774i
$898$	−8.72498	+	17.1237i	−0.291156	+	0.571426i
$899$	−21.3516			−0.712117
$900$		0			0
$901$	−37.5005			−1.24932
$902$	14.6053	−	28.6646i	0.486305	−	0.954427i
$903$	−0.441449	+	1.37082i	−0.0146905	+	0.0456182i
$904$	6.45744	+	8.88790i	0.214771	+	0.295607i
$905$		0			0
$906$	−18.1574	−	18.0627i	−0.603238	−	0.600092i
$907$	−7.30011	+	7.30011i	−0.242396	+	0.242396i	−0.817841	−	0.575445i	$-0.804829\pi$
$907$	−7.30011	+	7.30011i	−0.242396	+	0.242396i	0.575445	+	0.817841i	$0.304829\pi$
$908$	−3.26989	+	0.517900i	−0.108515	+	0.0171871i
$909$	16.6959	−	23.2344i	0.553767	−	0.770636i
$910$		0			0
$911$	26.9954	−	8.77133i	0.894397	−	0.290607i	0.174474	−	0.984662i	$-0.444177\pi$
$911$	26.9954	−	8.77133i	0.894397	−	0.290607i	0.719922	+	0.694055i	$0.244177\pi$
$912$	0.792525	−	0.259799i	0.0262431	−	0.00860281i
$913$	−22.8903	+	11.6632i	−0.757557	+	0.385995i
$914$	6.97317	+	21.4612i	0.230652	+	0.709874i
$915$		0			0
$916$	3.26071	−	10.0354i	0.107737	−	0.331580i
$917$	0.294799	+	1.86129i	0.00973511	+	0.0614651i
$918$	24.0316	−	8.01723i	0.793160	−	0.264608i
$919$	−4.27526	+	5.88440i	−0.141028	+	0.194108i	−0.873688	−	0.486486i	$-0.838278\pi$
$919$	−4.27526	+	5.88440i	−0.141028	+	0.194108i	0.732660	+	0.680594i	$0.238278\pi$
$920$		0			0
$921$	13.2043	+	25.7483i	0.435096	+	0.848434i
$922$	2.50319	−	15.8045i	0.0824382	−	0.520494i
$923$	−16.0671	−	8.18661i	−0.528856	−	0.269466i
$924$	0.295681	−	1.89897i	0.00972720	−	0.0624717i
$925$		0			0
$926$			6.19159i			0.203468i
$927$	21.5665	+	21.3422i	0.708337	+	0.700969i
$928$	9.27141	+	1.46845i	0.304349	+	0.0482041i
$929$	−5.66314	+	4.11451i	−0.185802	+	0.134993i	−0.676798	−	0.736169i	$-0.736633\pi$
$929$	−5.66314	+	4.11451i	−0.185802	+	0.134993i	0.490996	+	0.871162i	$0.336633\pi$
$930$		0			0
$931$	−2.70875	−	1.96802i	−0.0887756	−	0.0644992i
$932$	8.90175	+	8.90175i	0.291586	+	0.291586i
$933$	0.136752	+	52.3114i	0.00447705	+	1.71260i
$934$	22.0766	+	7.17313i	0.722369	+	0.234712i
$935$		0			0
$936$	4.45903	−	0.0233136i	0.145748	−	0.000762030i
$937$	−18.0852	−	35.4943i	−0.590819	−	1.15955i	−0.971986	−	0.235040i	$-0.924478\pi$
$937$	−18.0852	−	35.4943i	−0.590819	−	1.15955i	0.381167	−	0.924506i	$-0.375522\pi$
$938$	1.47326	+	2.89144i	0.0481037	+	0.0944088i
$939$	−4.59420	−	28.5238i	−0.149926	−	0.930840i
$940$		0			0
$941$	0.912873	+	0.296610i	0.0297588	+	0.00966922i	0.323859	−	0.946106i	$-0.395020\pi$
$941$	0.912873	+	0.296610i	0.0297588	+	0.00966922i	−0.294100	+	0.955775i	$0.595020\pi$
$942$	28.3996	−	0.0742418i	0.925309	−	0.00241893i
$943$	11.8393	+	11.8393i	0.385542	+	0.385542i
$944$	4.03518	+	2.93173i	0.131334	+	0.0954196i
$945$		0			0
$946$	16.0013	−	11.6256i	0.520248	−	0.377982i
$947$	−37.5965	−	5.95470i	−1.22172	−	0.193502i	−0.487935	−	0.872880i	$-0.662250\pi$
$947$	−37.5965	−	5.95470i	−1.22172	−	0.193502i	−0.733788	+	0.679378i	$0.762250\pi$
$948$	3.06924	+	2.21770i	0.0996843	+	0.0720275i
$949$		−	13.9495i		−	0.452820i
$950$		0			0
$951$	18.5629	+	2.89034i	0.601942	+	0.0937258i
$952$	−0.938212	−	0.478043i	−0.0304076	−	0.0154935i
$953$	−8.96795	+	56.6214i	−0.290500	+	1.83415i	0.221499	+	0.975161i	$0.428905\pi$
$953$	−8.96795	+	56.6214i	−0.290500	+	1.83415i	−0.511999	+	0.858986i	$0.671095\pi$
$954$	−7.24523	−	21.9081i	−0.234573	−	0.709302i
$955$		0			0
$956$	−6.90374	+	9.50218i	−0.223283	+	0.307322i
$957$	49.2742	+	67.4486i	1.59281	+	2.18030i
$958$	−3.50627	−	22.1377i	−0.113282	−	0.715236i
$959$	−0.188434	+	0.579941i	−0.00608486	+	0.0187273i
$960$		0			0
$961$	−7.98073	−	24.5622i	−0.257443	−	0.792328i
$962$	5.70131	−	2.90496i	0.183818	−	0.0936598i
$963$	5.35363	+	32.6942i	0.172518	+	1.05356i
$964$	−1.15675	+	0.375849i	−0.0372563	+	0.0121053i
$965$		0			0
$966$	0.892392	+	0.451762i	0.0287122	+	0.0145352i
$967$	43.6488	−	6.91329i	1.40365	−	0.222316i	0.591755	−	0.806118i	$-0.298435\pi$
$967$	43.6488	−	6.91329i	1.40365	−	0.222316i	0.811896	+	0.583802i	$0.198435\pi$
$968$	−10.8855	+	10.8855i	−0.349872	+	0.349872i
$969$	2.86773	−	2.88277i	0.0921249	−	0.0926078i
$970$		0			0
$971$	−32.4405	−	44.6505i	−1.04107	−	1.43290i	−0.896306	−	0.443437i	$-0.853759\pi$
$971$	−32.4405	−	44.6505i	−1.04107	−	1.43290i	−0.144760	−	0.989467i	$-0.546241\pi$
$972$	9.32672	+	12.4905i	0.299155	+	0.400633i
$973$	0.682516	−	1.33951i	0.0218804	−	0.0429428i
$974$	21.2093			0.679589
$975$		0			0
$976$	13.6458			0.436793
$977$	15.0267	−	29.4915i	0.480746	−	0.943516i	−0.515496	−	0.856892i	$-0.672392\pi$
$977$	15.0267	−	29.4915i	0.480746	−	0.943516i	0.996241	−	0.0866240i	$-0.0276079\pi$
$978$	−6.68980	−	2.15433i	−0.213916	−	0.0688878i
$979$	33.0604	+	45.5037i	1.05661	+	1.45430i
$980$		0			0
$981$	−10.8907	−	14.8261i	−0.347712	−	0.473360i
$982$	−22.0207	+	22.0207i	−0.702708	+	0.702708i
$983$	19.2588	−	3.05030i	0.614261	−	0.0972894i	0.158451	−	0.987367i	$-0.449350\pi$
$983$	19.2588	−	3.05030i	0.614261	−	0.0972894i	0.455809	+	0.890077i	$0.349350\pi$
$984$	4.89871	−	9.67671i	0.156165	−	0.308482i
$985$		0			0
$986$	43.5259	−	14.1424i	1.38615	−	0.450386i
$987$	1.18299	+	3.60875i	0.0376550	+	0.114868i
$988$	0.637709	−	0.324929i	0.0202882	−	0.0103374i
$989$	3.18096	+	9.78998i	0.101149	+	0.311303i
$990$		0			0
$991$	10.9360	−	33.6576i	0.347394	−	1.06917i	−0.612896	−	0.790164i	$-0.709995\pi$
$991$	10.9360	−	33.6576i	0.347394	−	1.06917i	0.960290	−	0.279005i	$-0.0900046\pi$
$992$	−0.355826	−	2.24660i	−0.0112975	−	0.0713295i
$993$	13.4752	−	9.84420i	0.427621	−	0.312396i
$994$	−1.54012	+	2.11980i	−0.0488497	+	0.0672359i
$995$		0			0
$996$	−7.70683	+	3.95224i	−0.244200	+	0.125231i
$997$	−7.20864	+	45.5136i	−0.228300	+	1.44143i	0.561201	+	0.827680i	$0.310340\pi$
$997$	−7.20864	+	45.5136i	−0.228300	+	1.44143i	−0.789501	+	0.613750i	$0.789660\pi$
$998$	1.11963	+	0.570481i	0.0354414	+	0.0180583i
$999$	20.0101	+	9.99878i	0.633093	+	0.316347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.143.7		80
3.2	odd	2	inner	750.2.l.a.143.3		80
5.2	odd	4		750.2.l.b.107.10		80
5.3	odd	4		150.2.l.a.17.1	✓	80
5.4	even	2		750.2.l.c.143.4		80
15.2	even	4		750.2.l.b.107.1		80
15.8	even	4		150.2.l.a.17.10	yes	80
15.14	odd	2		750.2.l.c.143.8		80
25.3	odd	20		750.2.l.c.257.8		80
25.4	even	10		150.2.l.a.53.10	yes	80
25.21	even	5		750.2.l.b.743.1		80
25.22	odd	20	inner	750.2.l.a.257.3		80
75.29	odd	10		150.2.l.a.53.1	yes	80
75.47	even	20	inner	750.2.l.a.257.7		80
75.53	even	20		750.2.l.c.257.4		80
75.71	odd	10		750.2.l.b.743.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.1	✓	80	5.3	odd	4
150.2.l.a.17.10	yes	80	15.8	even	4
150.2.l.a.53.1	yes	80	75.29	odd	10
150.2.l.a.53.10	yes	80	25.4	even	10
750.2.l.a.143.3		80	3.2	odd	2	inner
750.2.l.a.143.7		80	1.1	even	1	trivial
750.2.l.a.257.3		80	25.22	odd	20	inner
750.2.l.a.257.7		80	75.47	even	20	inner
750.2.l.b.107.1		80	15.2	even	4
750.2.l.b.107.10		80	5.2	odd	4
750.2.l.b.743.1		80	25.21	even	5
750.2.l.b.743.10		80	75.71	odd	10
750.2.l.c.143.4		80	5.4	even	2
750.2.l.c.143.8		80	15.14	odd	2
750.2.l.c.257.4		80	75.53	even	20
750.2.l.c.257.8		80	25.3	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(-0.530925 + 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 - 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +O(q^{10})\)	\(q+(0.453990 - 0.891007i) q^{2} +(-0.530925 + 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 - 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +(4.88609 - 1.58759i) q^{11} +(1.64587 - 0.539538i) q^{12} +(1.32436 - 0.674795i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.762690 + 4.81543i) q^{17} +(-2.66586 + 1.37593i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(0.170700 + 0.332863i) q^{21} +(0.803689 - 5.07429i) q^{22} +(2.38239 + 1.21389i) q^{23} +(0.266479 - 1.71143i) q^{24} -1.48636i q^{26} +(4.17969 - 3.08710i) q^{27} +(-0.213317 - 0.0337860i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.0232622 + 8.89846i) q^{33} +(4.63684 + 1.50660i) q^{34} +(0.0156850 + 2.99996i) q^{36} +(1.95441 + 3.83574i) q^{37} +(0.218606 + 0.429039i) q^{38} +(0.409380 + 2.54170i) q^{39} +(5.95547 + 1.93505i) q^{41} +(0.374079 - 0.000977913i) q^{42} +(2.72225 + 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(10.0271 + 1.58814i) q^{47} +(-1.40392 - 1.01441i) q^{48} +6.95335i q^{49} +(-8.34400 - 1.29921i) q^{51} +(-1.32436 - 0.674795i) q^{52} +(-1.20325 + 7.59700i) q^{53} +(-0.853081 - 5.12565i) q^{54} +(-0.126947 + 0.174728i) q^{56} +(-0.491987 - 0.673453i) q^{57} +(-1.46845 - 9.27141i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(-2.02668 + 1.03265i) q^{62} +(-0.639411 + 0.104703i) q^{63} +(0.951057 - 0.309017i) q^{64} +(7.93914 + 4.01909i) q^{66} +(-14.8405 + 2.35050i) q^{67} +(3.44747 - 3.44747i) q^{68} +(-3.26618 + 3.28330i) q^{69} +(-7.13100 - 9.81498i) q^{71} +(2.68010 + 1.34798i) q^{72} +(4.26070 - 8.36209i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(0.503741 - 0.988647i) q^{77} +(2.45053 + 0.789148i) q^{78} +(1.28502 + 1.76867i) q^{79} +(2.87050 + 8.52996i) q^{81} +(4.42787 - 4.42787i) q^{82} +(-4.93895 + 0.782253i) q^{83} +(0.168957 - 0.333751i) q^{84} +(3.66142 - 1.18967i) q^{86} +(5.06463 + 15.4498i) q^{87} +(-4.57759 + 2.33240i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(-0.418278 - 2.64090i) q^{92} +(3.18124 - 2.32404i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.54121 + 0.790366i) q^{96} +(1.57877 - 9.96799i) q^{97} +(6.19548 + 3.15676i) q^{98} +(-14.6830 - 4.68606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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