LMFDB - Embedded newform 750.2.l.c.143.8

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			143.8
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(-0.00452789 + 1.73204i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.99996 - 0.0156850i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(-0.00452789 + 1.73204i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.99996 - 0.0156850i) q^{9} +(-4.88609 + 1.58759i) q^{11} +(1.40392 - 1.01441i) 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} +(-1.37593 + 2.66586i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(-0.263823 - 0.265206i) q^{21} +(-0.803689 + 5.07429i) q^{22} +(2.38239 + 1.21389i) q^{23} +(-0.266479 - 1.71143i) q^{24} +1.48636i q^{26} +(0.0407506 - 5.19599i) 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} +(-2.72765 - 8.47012i) q^{33} +(4.63684 + 1.50660i) q^{34} +(1.75064 + 2.43624i) q^{36} +(-1.95441 - 3.83574i) q^{37} +(0.218606 + 0.429039i) q^{38} +(-1.16278 - 2.29691i) q^{39} +(-5.95547 - 1.93505i) q^{41} +(-0.356073 + 0.114667i) 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} +(-1.64587 - 0.539538i) q^{48} +6.95335i q^{49} +(-8.34400 + 1.29921i) q^{51} +(1.32436 + 0.674795i) q^{52} +(-1.20325 + 7.59700i) q^{53} +(-4.61116 - 2.39524i) q^{54} +(0.126947 - 0.174728i) q^{56} +(-0.673453 - 0.491987i) 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} +(0.460543 - 0.455752i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-8.78526 - 1.41500i) q^{66} +(14.8405 - 2.35050i) q^{67} +(3.44747 - 3.44747i) q^{68} +(-2.11330 + 4.12092i) q^{69} +(7.13100 + 9.81498i) q^{71} +(2.96548 - 0.453805i) q^{72} +(-4.26070 + 8.36209i) q^{73} -4.30495 q^{74} +0.481522 q^{76} +(0.503741 - 0.988647i) q^{77} +(-2.57445 - 0.00673009i) q^{78} +(1.28502 + 1.76867i) q^{79} +(8.99951 + 0.0941087i) q^{81} +(-4.42787 + 4.42787i) q^{82} +(-4.93895 + 0.782253i) q^{83} +(-0.0594848 + 0.369321i) q^{84} +(-3.66142 + 1.18967i) q^{86} +(-9.52222 - 13.1785i) 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} +(2.32404 - 3.18124i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.22794 + 1.22154i) 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
$3$	−0.00452789	+	1.73204i	−0.00261418	+	0.999997i
$3$	−0.00452789	+	1.73204i	−0.00261418	+	0.999997i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	1.54121	+	0.790366i	0.629195	+	0.322666i
$7$	−0.152718	+	0.152718i	−0.0577219	+	0.0577219i	−0.735379	−	0.677657i	$-0.762996\pi$
$7$	−0.152718	+	0.152718i	−0.0577219	+	0.0577219i	0.677657	+	0.735379i	$0.262996\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$	−2.99996	−	0.0156850i	−0.999986	−	0.00522833i
$10$		0			0
$11$	−4.88609	+	1.58759i	−1.47321	+	0.478676i	−0.932077	−	0.362259i	$-0.882005\pi$
$11$	−4.88609	+	1.58759i	−1.47321	+	0.478676i	−0.541136	+	0.840935i	$0.682005\pi$
$12$	1.40392	−	1.01441i	0.405275	−	0.292834i
$13$	−1.32436	+	0.674795i	−0.367312	+	0.187155i	−0.627897	−	0.778296i	$-0.716084\pi$
$13$	−1.32436	+	0.674795i	−0.367312	+	0.187155i	0.260586	+	0.965451i	$0.416084\pi$
$14$	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	$0.748640\pi$
$18$	−1.37593	+	2.66586i	−0.324309	+	0.628350i
$19$	−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
$21$	−0.263823	−	0.265206i	−0.0575708	−	0.0578726i
$22$	−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
$27$	0.0407506	−	5.19599i	0.00784246	−	0.999969i
$28$	0.213317	+	0.0337860i	0.0403130	+	0.00638496i
$29$	−7.59423	+	5.51753i	−1.41021	+	1.02458i	−0.416921	+	0.908943i	$0.636891\pi$
$29$	−7.59423	+	5.51753i	−1.41021	+	1.02458i	−0.993292	+	0.115637i	$0.963109\pi$
$30$		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
$33$	−2.72765	−	8.47012i	−0.474823	−	1.47446i
$34$	4.63684	+	1.50660i	0.795211	+	0.258380i
$35$		0			0
$36$	1.75064	+	2.43624i	0.291774	+	0.406040i
$37$	−1.95441	−	3.83574i	−0.321303	−	0.630592i	0.672704	−	0.739912i	$-0.265133\pi$
$37$	−1.95441	−	3.83574i	−0.321303	−	0.630592i	−0.994007	+	0.109320i	$0.965133\pi$
$38$	0.218606	+	0.429039i	0.0354627	+	0.0695994i
$39$	−1.16278	−	2.29691i	−0.186194	−	0.367800i
$40$		0			0
$41$	−5.95547	−	1.93505i	−0.930087	−	0.302204i	−0.195489	−	0.980706i	$-0.562629\pi$
$41$	−5.95547	−	1.93505i	−0.930087	−	0.302204i	−0.734598	+	0.678502i	$0.762629\pi$
$42$	−0.356073	+	0.114667i	−0.0549432	+	0.0176935i
$43$	−2.72225	−	2.72225i	−0.415139	−	0.415139i	0.468385	−	0.883524i	$-0.344836\pi$
$43$	−2.72225	−	2.72225i	−0.415139	−	0.415139i	−0.883524	+	0.468385i	$0.844836\pi$
$44$	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	$0.284628\pi$
$48$	−1.64587	−	0.539538i	−0.237561	−	0.0778755i
$49$			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	$0.872842\pi$
$54$	−4.61116	−	2.39524i	−0.627500	−	0.325951i
$55$		0			0
$56$	0.126947	−	0.174728i	0.0169640	−	0.0233490i
$57$	−0.673453	−	0.491987i	−0.0892011	−	0.0651653i
$58$	1.46845	+	9.27141i	0.192817	+	1.21740i
$59$	−1.54130	+	4.74363i	−0.200660	+	0.617569i	0.799204	+	0.601061i	$0.205255\pi$
$59$	−1.54130	+	4.74363i	−0.200660	+	0.617569i	−0.999864	+	0.0165081i	$0.994745\pi$
$60$		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
$63$	0.460543	−	0.455752i	0.0580229	−	0.0574193i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−8.78526	−	1.41500i	−1.08139	−	0.174175i
$67$	14.8405	−	2.35050i	1.81305	−	0.287159i	0.844425	−	0.535673i	$-0.179942\pi$
$67$	14.8405	−	2.35050i	1.81305	−	0.287159i	0.968628	+	0.248514i	$0.0799422\pi$
$68$	3.44747	−	3.44747i	0.418067	−	0.418067i
$69$	−2.11330	+	4.12092i	−0.254411	+	0.496100i
$70$		0			0
$71$	7.13100	+	9.81498i	0.846294	+	1.16482i	0.984667	+	0.174444i	$0.0558128\pi$
$71$	7.13100	+	9.81498i	0.846294	+	1.16482i	−0.138373	+	0.990380i	$0.544187\pi$
$72$	2.96548	−	0.453805i	0.349485	−	0.0534814i
$73$	−4.26070	+	8.36209i	−0.498677	+	0.978708i	0.495259	+	0.868745i	$0.335073\pi$
$73$	−4.26070	+	8.36209i	−0.498677	+	0.978708i	−0.993936	+	0.109963i	$0.964927\pi$
$74$	−4.30495			−0.500441
$75$		0			0
$76$	0.481522			0.0552344
$77$	0.503741	−	0.988647i	0.0574066	−	0.112667i
$78$	−2.57445	−	0.00673009i	−0.291499	−	0.000762033i
$79$	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
$81$	8.99951	+	0.0941087i	0.999945	+	0.0104565i
$82$	−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	$0.538492\pi$
$84$	−0.0594848	+	0.369321i	−0.00649032	+	0.0402962i
$85$		0			0
$86$	−3.66142	+	1.18967i	−0.394821	+	0.128285i
$87$	−9.52222	−	13.1785i	−1.02089	−	1.41289i
$88$	4.57759	−	2.33240i	0.487972	−	0.248634i
$89$	−3.38311	−	10.4121i	−0.358609	−	1.10368i	−0.953887	−	0.300165i	$-0.902958\pi$
$89$	−3.38311	−	10.4121i	−0.358609	−	1.10368i	0.595279	−	0.803519i	$-0.297042\pi$
$90$		0			0
$91$	0.0992002	−	0.305307i	0.0103990	−	0.0320048i
$92$	−0.418278	−	2.64090i	−0.0436085	−	0.275333i
$93$	2.32404	−	3.18124i	0.240991	−	0.329879i
$94$	5.96725	−	8.21321i	0.615475	−	0.847128i
$95$		0			0
$96$	−1.22794	+	1.22154i	−0.125326	+	0.124673i
$97$	−1.57877	+	9.96799i	−0.160300	+	1.01210i	0.768050	+	0.640390i	$0.221227\pi$
$97$	−1.57877	+	9.96799i	−0.160300	+	1.01210i	−0.928350	+	0.371706i	$0.878773\pi$
$98$	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	$-0.842635\pi$
$101$		−	9.53700i		−	0.948967i	0.880264	−	0.474483i	$-0.157365\pi$
$102$	−2.63049	+	8.02438i	−0.260458	+	0.794533i
$103$	9.98929	+	1.58215i	0.984274	+	0.155894i	0.627769	−	0.778400i	$-0.283968\pi$
$103$	9.98929	+	1.58215i	0.984274	+	0.155894i	0.356505	+	0.934293i	$0.383968\pi$
$104$	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	$0.929234\pi$
$108$	−4.22760	+	3.02116i	−0.406801	+	0.290711i
$109$	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
$111$	6.65253	−	3.36776i	0.631430	−	0.319653i
$112$	−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	$-0.322855\pi$
$114$	−0.744105	+	0.376694i	−0.0696918	+	0.0352806i
$115$		0			0
$116$	8.92755	+	2.90074i	0.828902	+	0.269327i
$117$	3.98361	−	2.00359i	0.368285	−	0.185232i
$118$	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
$123$	3.37856	−	10.3064i	0.304634	−	0.929294i
$124$			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	0.932624	−	0.360850i	$-0.117513\pi$
$127$	13.3979	+	6.82658i	1.18887	+	0.605761i	0.256249	+	0.966611i	$0.417513\pi$
$128$	0.156434	−	0.987688i	0.0138270	−	0.0873001i
$129$	4.72738	−	4.70273i	0.416223	−	0.414052i
$130$		0			0
$131$	5.12870	−	7.05905i	0.448097	−	0.616752i	−0.523891	−	0.851785i	$-0.675520\pi$
$131$	5.12870	−	7.05905i	0.448097	−	0.616752i	0.971987	+	0.235034i	$0.0755200\pi$
$132$	−5.24920	+	7.18533i	−0.456884	+	0.625403i
$133$	−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	$0.388485\pi$
$138$	2.71235	+	3.75382i	0.230890	+	0.319546i
$139$	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
$141$	−2.79613	+	17.3602i	−0.235476	+	1.46199i
$142$	11.9826	−	1.89786i	1.00556	−	0.159265i
$143$	5.39965	−	5.39965i	0.451542	−	0.451542i
$144$	0.941956	−	2.84828i	0.0784963	−	0.237357i
$145$		0			0
$146$	5.51636	+	7.59261i	0.456537	+	0.628369i
$147$	−12.0435	−	0.0314840i	−0.993333	−	0.00259676i
$148$	−1.95441	+	3.83574i	−0.160651	+	0.315296i
$149$	7.72360			0.632742			0.316371	−	0.948635i	$-0.397535\pi$
$149$	7.72360			0.632742			0.316371	+	0.948635i	$0.397535\pi$
$150$		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
$153$	−2.21251	−	14.4581i	−0.178871	−	1.16887i
$154$	−0.652197	−	0.897673i	−0.0525556	−	0.0723365i
$155$		0			0
$156$	−1.17477	+	2.29080i	−0.0940571	+	0.183411i
$157$	−11.5941	+	11.5941i	−0.925312	+	0.925312i	−0.997398	−	0.0720863i	$-0.977034\pi$
$157$	−11.5941	+	11.5941i	−0.925312	+	0.925312i	0.0720863	+	0.997398i	$0.477034\pi$
$158$	2.15928	−	0.341997i	0.171783	−	0.0272078i
$159$	−13.1529	−	2.11847i	−1.04309	−	0.168006i
$160$		0			0
$161$	−0.549217	+	0.178451i	−0.0432843	+	0.0140639i
$162$	4.16954	−	7.97590i	0.327590	−	0.626646i
$163$	3.61543	−	1.84215i	0.283182	−	0.144289i	−0.306630	−	0.951829i	$-0.599202\pi$
$163$	3.61543	−	1.84215i	0.283182	−	0.144289i	0.589813	+	0.807540i	$0.299202\pi$
$164$	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	$0.770114\pi$
$168$	0.302062	+	0.220670i	0.0233046	+	0.0170250i
$169$	−6.34263	+	8.72988i	−0.487894	+	0.671529i
$170$		0			0
$171$	0.855194	−	1.16422i	0.0653983	−	0.0890304i
$172$	−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
$177$	−8.20921	−	2.69108i	−0.617042	−	0.202274i
$178$	−10.8132	−	1.71264i	−0.810482	−	0.128368i
$179$	9.58645	−	6.96496i	0.716525	−	0.520586i	−0.168747	−	0.985659i	$-0.553972\pi$
$179$	9.58645	−	6.96496i	0.716525	−	0.520586i	0.885272	+	0.465074i	$0.153972\pi$
$180$		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
$183$	22.4975	−	7.24492i	1.66306	−	0.535560i
$184$	−2.54296	−	0.826257i	−0.187469	−	0.0609125i
$185$		0			0
$186$	−1.77942	−	3.51498i	−0.130473	−	0.257731i
$187$	−11.3715	−	22.3178i	−0.831566	−	1.63204i
$188$	−4.60895	−	9.04558i	−0.336142	−	0.659716i
$189$	0.787297	+	0.799744i	0.0572675	+	0.0581728i
$190$		0			0
$191$	4.70151	+	1.52761i	0.340189	+	0.110534i	0.474129	−	0.880455i	$-0.342763\pi$
$191$	4.70151	+	1.52761i	0.340189	+	0.110534i	−0.133940	+	0.990989i	$0.542763\pi$
$192$	0.530925	+	1.64867i	0.0383162	+	0.118983i
$193$	2.38356	+	2.38356i	0.171572	+	0.171572i	0.787670	−	0.616098i	$-0.211287\pi$
$193$	2.38356	+	2.38356i	0.171572	+	0.171572i	−0.616098	+	0.787670i	$0.711287\pi$
$194$	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	$0.634112\pi$
$198$	2.49062	−	15.2101i	0.177001	−	1.08093i
$199$		−	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
$204$	5.95556	+	5.98678i	0.416973	+	0.419158i
$205$		0			0
$206$	5.94475	−	8.18224i	0.414190	−	0.570084i
$207$	−7.12804	−	3.67899i	−0.495433	−	0.255707i
$208$	−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
$213$	−17.0323	+	12.3068i	−1.16703	+	0.843246i
$214$	−10.5027	+	3.41254i	−0.717951	+	0.233276i
$215$		0			0
$216$	0.772583	+	5.13840i	0.0525676	+	0.349624i
$217$	0.485210	−	0.0768498i	0.0329382	−	0.00521690i
$218$	4.33602	−	4.33602i	0.293672	−	0.293672i
$219$	−14.4642	−	7.41758i	−0.977401	−	0.501233i
$220$		0			0
$221$	−4.25951	−	5.86271i	−0.286525	−	0.394369i
$222$	0.0194923	−	7.45637i	0.00130824	−	0.500439i
$223$	−0.331831	+	0.651256i	−0.0222211	+	0.0436113i	−0.901850	−	0.432049i	$-0.857791\pi$
$223$	−0.331831	+	0.651256i	−0.0222211	+	0.0436113i	0.879629	+	0.475660i	$0.157791\pi$
$224$	−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	$0.114957\pi$
$228$	−0.00218028	+	0.834018i	−0.000144392	+	0.0552342i
$229$	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
$231$	1.71010	+	0.876978i	0.112516	+	0.0577009i
$232$	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	$0.585297\pi$
$234$	0.0233136	−	4.45903i	0.00152406	−	0.291496i
$235$		0			0
$236$	4.74363	−	1.54130i	0.308784	−	0.100330i
$237$	−3.06924	+	2.21770i	−0.199369	+	0.144055i
$238$	−0.938212	+	0.478043i	−0.0608152	+	0.0309869i
$239$	3.62951	+	11.1705i	0.234773	+	0.722558i	0.997151	+	0.0754263i	$0.0240318\pi$
$239$	3.62951	+	11.1705i	0.234773	+	0.722558i	−0.762378	+	0.647132i	$0.775968\pi$
$240$		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
$243$	−0.203749	+	15.5871i	−0.0130705	+	0.999915i
$244$	−8.02083	+	11.0397i	−0.513481	+	0.706746i
$245$		0			0
$246$	−7.64921	−	7.68931i	−0.487696	−	0.490253i
$247$	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	$-0.747046\pi$
$251$		−	22.6123i		−	1.42728i	0.700515	−	0.713638i	$-0.252954\pi$
$252$	−0.639411	−	0.104703i	−0.0402791	−	0.00659564i
$253$	−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	$0.707978\pi$
$258$	−2.04398	−	6.34713i	−0.127252	−	0.395155i
$259$	0.884259	+	0.287313i	0.0549452	+	0.0178528i
$260$		0			0
$261$	22.8689	−	16.4332i	1.41555	−	1.01719i
$262$	−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	$0.824734\pi$
$264$	4.01909	+	7.93914i	0.247358	+	0.488621i
$265$		0			0
$266$	−0.0989071	−	0.0321369i	−0.00606438	−	0.00197044i
$267$	18.0496	−	5.81255i	1.10462	−	0.355722i
$268$	−10.6246	−	10.6246i	−0.649002	−	0.649002i
$269$	−19.5493	−	14.2034i	−1.19194	−	0.865996i	−0.198473	−	0.980106i	$-0.563598\pi$
$269$	−19.5493	−	14.2034i	−1.19194	−	0.865996i	−0.993468	+	0.114110i	$0.963598\pi$
$270$		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
$273$	0.528356	+	0.173202i	0.0319776	+	0.0104826i
$274$			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	0.240482	−	0.970654i	$-0.422695\pi$
$277$	−6.71461	−	3.42126i	−0.403442	−	0.205564i	−0.643924	+	0.765090i	$0.722695\pi$
$278$	1.08891	−	6.87513i	0.0653087	−	0.412343i
$279$	5.49953	+	4.03974i	0.329248	+	0.241853i
$280$		0			0
$281$	−13.8790	+	19.1028i	−0.827952	+	1.13958i	0.160349	+	0.987060i	$0.448738\pi$
$281$	−13.8790	+	19.1028i	−0.827952	+	1.13958i	−0.988301	+	0.152517i	$0.951262\pi$
$282$	14.1986	+	10.3727i	0.845516	+	0.617687i
$283$	1.54005	+	9.72347i	0.0915463	+	0.578000i	0.990234	+	0.139412i	$0.0445213\pi$
$283$	1.54005	+	9.72347i	0.0915463	+	0.578000i	−0.898688	+	0.438588i	$0.855479\pi$
$284$	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
$288$	−2.11020	−	2.13238i	−0.124345	−	0.125652i
$289$	−6.43873	+	2.09207i	−0.378749	+	0.123063i
$290$		0			0
$291$	−17.2579	−	2.77964i	−1.01167	−	0.162945i
$292$	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	$0.294052\pi$
$294$	−5.49570	+	10.7166i	−0.320516	+	0.625003i
$295$		0			0
$296$	2.53039	+	3.48278i	0.147076	+	0.202433i
$297$	8.04999	+	25.4528i	0.467108	+	1.47692i
$298$	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
$303$	16.5185	+	0.0431824i	0.948964	+	0.00248077i
$304$	−0.283032	−	0.389560i	−0.0162330	−	0.0223428i
$305$		0			0
$306$	−13.8867	−	4.59246i	−0.793849	−	0.262534i
$307$	−11.8133	+	11.8133i	−0.674221	+	0.674221i	−0.958686	−	0.284465i	$-0.908184\pi$
$307$	−11.8133	+	11.8133i	−0.674221	+	0.674221i	0.284465	+	0.958686i	$0.408184\pi$
$308$	−1.09592	+	0.173577i	−0.0624460	+	0.00989048i
$309$	−2.78558	+	17.2947i	−0.158466	+	0.983863i
$310$		0			0
$311$	−28.7239	+	9.33296i	−1.62878	+	0.529224i	−0.973991	−	0.226586i	$-0.927244\pi$
$311$	−28.7239	+	9.33296i	−1.62878	+	0.529224i	−0.654791	+	0.755810i	$0.727244\pi$
$312$	1.50778	+	2.08673i	0.0853612	+	0.118138i
$313$	14.8624	−	7.57278i	0.840073	−	0.428039i	0.0196580	−	0.999807i	$-0.493742\pi$
$313$	14.8624	−	7.57278i	0.840073	−	0.428039i	0.820415	+	0.571768i	$0.193742\pi$
$314$	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	$-0.148522\pi$
$318$	−7.85886	+	10.7575i	−0.440703	+	0.603253i
$319$	28.3466	−	39.0157i	1.58710	−	2.18446i
$320$		0			0
$321$	13.5604	−	13.4897i	0.756869	−	0.752922i
$322$	−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
$327$	−3.30848	+	10.0926i	−0.182959	+	0.558122i
$328$	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
$333$	5.80298	+	11.5377i	0.318001	+	0.632263i
$334$	13.1635	+	4.27710i	0.720277	+	0.234032i
$335$		0			0
$336$	0.333751	−	0.168957i	0.0182076	−	0.00921737i
$337$	12.7818	+	25.0858i	0.696272	+	1.36651i	0.920023	+	0.391864i	$0.128170\pi$
$337$	12.7818	+	25.0858i	0.696272	+	1.36651i	−0.223752	+	0.974646i	$0.571830\pi$
$338$	4.89888	+	9.61460i	0.266464	+	0.522965i
$339$	16.9769	−	8.59436i	0.922061	−	0.466782i
$340$		0			0
$341$	11.1139	+	3.61113i	0.601852	+	0.195554i
$342$	−0.649081	−	1.29053i	−0.0350983	−	0.0697838i
$343$	−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	$0.376548\pi$
$348$	−5.06463	+	15.4498i	−0.271493	+	0.828195i
$349$			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	$0.668300\pi$
$354$	−6.12467	+	6.09273i	−0.325523	+	0.323825i
$355$		0			0
$356$	−6.43505	+	8.85709i	−0.341057	+	0.469425i
$357$	1.07586	−	1.47269i	0.0569408	−	0.0779430i
$358$	−1.85367	−	11.7036i	−0.0979695	−	0.618555i
$359$	−10.6846	+	32.8840i	−0.563914	+	1.73555i	0.107242	+	0.994233i	$0.465798\pi$
$359$	−10.6846	+	32.8840i	−0.563914	+	1.73555i	−0.671156	+	0.741316i	$0.734202\pi$
$360$		0			0
$361$	5.79967	+	17.8496i	0.305246	+	0.939450i
$362$	15.3170	−	7.80442i	0.805045	−	0.410191i
$363$	15.6161	+	21.6124i	0.819635	+	1.13436i
$364$	−0.305307	+	0.0992002i	−0.0160024	+	0.00519950i
$365$		0			0
$366$	3.75839	−	23.3346i	0.196454	−	1.21972i
$367$	3.18996	−	0.505240i	0.166514	−	0.0263733i	−0.0726205	−	0.997360i	$-0.523136\pi$
$367$	3.18996	−	0.505240i	0.166514	−	0.0263733i	0.239135	+	0.970986i	$0.423136\pi$
$368$	−1.89068	+	1.89068i	−0.0985584	+	0.0985584i
$369$	17.8358	+	5.89848i	0.928495	+	0.307062i
$370$		0			0
$371$	−0.976440	−	1.34395i	−0.0506942	−	0.0697746i
$372$	−3.93971	−	0.0102991i	−0.204265	−	0.000533985i
$373$	−4.91900	+	9.65408i	−0.254696	+	0.499869i	−0.982582	−	0.185829i	$-0.940503\pi$
$373$	−4.91900	+	9.65408i	−0.254696	+	0.499869i	0.727886	+	0.685698i	$0.240503\pi$
$374$	−25.0479			−1.29519
$375$		0			0
$376$	−10.1521			−0.523554
$377$	6.33429	−	12.4317i	0.326233	−	0.640268i
$378$	1.07000	−	0.338411i	0.0550350	−	0.0174060i
$379$	−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
$381$	−11.8846	+	23.1749i	−0.608867	+	1.18729i
$382$	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	$0.586263\pi$
$384$	1.71001	+	0.275424i	0.0872637	+	0.0140552i
$385$		0			0
$386$	3.20588	−	1.04165i	0.163175	−	0.0530187i
$387$	8.12394	+	8.20933i	0.412963	+	0.417304i
$388$	8.99225	−	4.58178i	0.456512	−	0.232605i
$389$	−0.804900	−	2.47723i	−0.0408101	−	0.125600i	0.928576	−	0.371143i	$-0.121034\pi$
$389$	−0.804900	−	2.47723i	−0.0408101	−	0.125600i	−0.969386	+	0.245542i	$0.921034\pi$
$390$		0			0
$391$	−4.02838	+	12.3981i	−0.203724	+	0.626998i
$392$	−1.08774	−	6.86775i	−0.0549394	−	0.346874i
$393$	12.2034	+	8.91510i	0.615578	+	0.449707i
$394$	−4.30947	+	5.93148i	−0.217108	+	0.298824i
$395$		0			0
$396$	−12.4215	−	9.12439i	−0.624206	−	0.458518i
$397$	0.295160	−	1.86357i	0.0148137	−	0.0935298i	−0.979174	−	0.203024i	$-0.934923\pi$
$397$	0.295160	−	1.86357i	0.0148137	−	0.0935298i	0.993987	+	0.109494i	$0.0349231\pi$
$398$	−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	$-0.942715\pi$
$401$		−	7.16880i		−	0.357993i	0.983850	−	0.178996i	$-0.0572850\pi$
$402$	24.7300	+	8.10681i	1.23342	+	0.404331i
$403$	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
$408$	8.03803	−	2.58850i	0.397942	−	0.128150i
$409$	−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
$411$	−2.20874	−	4.36305i	−0.108949	−	0.215214i
$412$	−4.59157	−	9.01147i	−0.226211	−	0.443963i
$413$	−0.489054	−	0.959822i	−0.0240648	−	0.0472297i
$414$	−6.51407	+	4.68091i	−0.320149	+	0.230054i
$415$		0			0
$416$	−1.41362	−	0.459312i	−0.0693083	−	0.0225196i
$417$	3.69568	+	11.4761i	0.180978	+	0.561988i
$418$	−1.74927	−	1.74927i	−0.0855596	−	0.0855596i
$419$	1.81333	+	1.31746i	0.0885872	+	0.0643624i	0.631197	−	0.775622i	$-0.282564\pi$
$419$	1.81333	+	1.31746i	0.0885872	+	0.0643624i	−0.542610	+	0.839985i	$0.682564\pi$
$420$		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
$423$	−30.0560	−	4.92162i	−1.46137	−	0.239297i
$424$		−	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
$429$	9.32799	+	9.37689i	0.450360	+	0.452721i
$430$		0			0
$431$	0.661426	−	0.910375i	0.0318598	−	0.0438512i	−0.792790	−	0.609495i	$-0.791372\pi$
$431$	0.661426	−	0.910375i	0.0318598	−	0.0438512i	0.824650	+	0.565644i	$0.191372\pi$
$432$	4.92909	+	1.64441i	0.237151	+	0.0791165i
$433$	3.21125	+	20.2750i	0.154323	+	0.974355i	0.936339	+	0.351097i	$0.114191\pi$
$433$	3.21125	+	20.2750i	0.154323	+	0.974355i	−0.782016	+	0.623258i	$0.785809\pi$
$434$	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
$438$	−13.1757	+	9.52020i	−0.629561	+	0.454893i
$439$	−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
$441$	0.109063	−	20.8598i	0.00519350	−	0.993323i
$442$	−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	$0.401242\pi$
$444$	−6.63483	−	3.40249i	−0.314875	−	0.161475i
$445$		0			0
$446$	0.429625	+	0.591328i	0.0203433	+	0.0280002i
$447$	−0.0349716	+	13.3776i	−0.00165410	+	0.632740i
$448$	−0.0980509	+	0.192436i	−0.00463247	+	0.00909173i
$449$	19.2184			0.906973			0.453487	−	0.891263i	$-0.350180\pi$
$449$	19.2184			0.906973			0.453487	+	0.891263i	$0.350180\pi$
$450$		0			0
$451$	32.1710			1.51487
$452$	−4.98756	+	9.78864i	−0.234595	+	0.460419i
$453$	0.0669530	−	25.6114i	0.00314573	−	1.20333i
$454$	−1.94595	−	2.67837i	−0.0913281	−	0.125702i
$455$		0			0
$456$	0.742126	+	0.380579i	0.0347532	+	0.0178222i
$457$	15.9563	−	15.9563i	0.746405	−	0.746405i	−0.227397	−	0.973802i	$-0.573021\pi$
$457$	15.9563	−	15.9563i	0.746405	−	0.746405i	0.973802	+	0.227397i	$0.0730215\pi$
$458$	10.4220	−	1.65068i	0.486986	−	0.0771311i
$459$	25.0520	−	3.76670i	1.16933	−	0.175814i
$460$		0			0
$461$	−15.2184	+	4.94475i	−0.708790	+	0.230300i	−0.641156	−	0.767410i	$-0.721545\pi$
$461$	−15.2184	+	4.94475i	−0.708790	+	0.230300i	−0.0676337	+	0.997710i	$0.521545\pi$
$462$	1.55776	−	1.12557i	0.0724737	−	0.0523663i
$463$	5.51675	−	2.81092i	0.256385	−	0.130635i	−0.321075	−	0.947054i	$-0.604044\pi$
$463$	5.51675	−	2.81092i	0.256385	−	0.130635i	0.577460	+	0.816419i	$0.304044\pi$
$464$	−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	$0.769528\pi$
$468$	−3.96244	−	2.04513i	−0.183164	−	0.0945362i
$469$	−1.90744	+	2.62537i	−0.0880775	+	0.121228i
$470$		0			0
$471$	−20.0291	−	20.1340i	−0.922890	−	0.927728i
$472$	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
$477$	3.72885	−	22.7718i	0.170732	−	1.04265i
$478$	11.6007	+	1.83738i	0.530605	+	0.0840396i
$479$	−18.1330	+	13.1744i	−0.828519	+	0.601954i	−0.919140	−	0.393931i	$-0.871115\pi$
$479$	−18.1330	+	13.1744i	−0.828519	+	0.601954i	0.0906212	+	0.995885i	$0.471115\pi$
$480$		0			0
$481$	5.17668	+	3.76108i	0.236036	+	0.171491i
$482$	−0.860035	−	0.860035i	−0.0391735	−	0.0391735i
$483$	−0.306599	−	0.952076i	−0.0139507	−	0.0433210i
$484$	−14.6409	−	4.75712i	−0.665496	−	0.216233i
$485$		0			0
$486$	13.7957	+	7.25795i	0.625787	+	0.329227i
$487$	−9.62881	−	18.8976i	−0.436323	−	0.856332i	−0.999549	−	0.0300294i	$-0.990440\pi$
$487$	−9.62881	−	18.8976i	−0.436323	−	0.856332i	0.563226	−	0.826303i	$-0.309560\pi$
$488$	6.19509	+	12.1585i	0.280438	+	0.550391i
$489$	3.17432	+	6.27042i	0.143548	+	0.283558i
$490$		0			0
$491$	29.6177	+	9.62339i	1.33663	+	0.434297i	0.888174	−	0.459507i	$-0.151974\pi$
$491$	29.6177	+	9.62339i	1.33663	+	0.434297i	0.448456	+	0.893805i	$0.351974\pi$
$492$	−10.3239	+	3.32462i	−0.465437	+	0.149886i
$493$	−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
$498$	−8.23021	−	2.69796i	−0.368805	−	0.120899i
$499$			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	$-0.149419\pi$
$504$	−0.383577	+	0.522186i	−0.0170859	+	0.0232600i
$505$		0			0
$506$	−8.07434	+	11.1134i	−0.358948	+	0.494050i
$507$	−15.0918	−	11.0252i	−0.670251	−	0.489648i
$508$	−2.35228	−	14.8517i	−0.104366	−	0.658938i
$509$	−5.31690	+	16.3637i	−0.235668	+	0.725310i	0.761365	+	0.648324i	$0.224530\pi$
$509$	−5.31690	+	16.3637i	−0.235668	+	0.725310i	−0.997032	+	0.0769863i	$0.975470\pi$
$510$		0			0
$511$	−0.626355	−	1.92772i	−0.0277083	−	0.0852775i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	2.01262	+	1.48651i	0.0888591	+	0.0656308i
$514$	4.01395	−	1.30421i	0.177048	−	0.0575263i
$515$		0			0
$516$	−6.58328	−	1.06034i	−0.289813	−	0.0466788i
$517$	−51.5147	+	8.15912i	−2.26561	+	0.358838i
$518$	0.657443	−	0.657443i	0.0288864	−	0.0288864i
$519$	−0.717747	+	1.39960i	−0.0315056	+	0.0614357i
$520$		0			0
$521$	−7.91212	−	10.8901i	−0.346636	−	0.477104i	0.599729	−	0.800203i	$-0.295275\pi$
$521$	−7.91212	−	10.8901i	−0.346636	−	0.477104i	−0.946365	+	0.323099i	$0.895275\pi$
$522$	−4.25986	−	27.8369i	−0.186449	−	1.21839i
$523$	11.6979	−	22.9585i	0.511514	−	1.00390i	−0.480407	−	0.877046i	$-0.659511\pi$
$523$	11.6979	−	22.9585i	0.511514	−	1.00390i	0.991921	−	0.126858i	$-0.0404891\pi$
$524$	−8.72546			−0.381174
$525$		0			0
$526$	2.57177			0.112134
$527$	5.03463	−	9.88101i	0.219312	−	0.430424i
$528$	8.89846	+	0.0232622i	0.387256	+	0.00101236i
$529$	−9.31679	−	12.8235i	−0.405078	−	0.557542i
$530$		0			0
$531$	4.69824	−	14.2065i	0.203886	−	0.616511i
$532$	−0.0735370	+	0.0735370i	−0.00318823	+	0.00318823i
$533$	9.19295	−	1.45602i	0.398191	−	0.0630672i
$534$	3.01533	−	18.7212i	0.130486	−	0.810144i
$535$		0			0
$536$	−14.2901	+	4.64313i	−0.617237	+	0.200553i
$537$	12.0202	+	16.6357i	0.518711	+	0.717883i
$538$	−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
$543$	−17.5643	+	24.0428i	−0.753757	+	1.03177i
$544$	−2.86572	+	3.94433i	−0.122867	+	0.169112i
$545$		0			0
$546$	0.394192	−	0.392137i	0.0168699	−	0.0167819i
$547$	6.82585	−	43.0967i	0.291852	−	1.84268i	−0.209965	−	0.977709i	$-0.567335\pi$
$547$	6.82585	−	43.0967i	0.291852	−	1.84268i	0.501817	−	0.864974i	$-0.332665\pi$
$548$	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
$552$	1.44263	−	4.40077i	0.0614023	−	0.187309i
$553$	−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	$0.964139\pi$
$558$	6.09617	−	3.06611i	0.258071	−	0.129799i
$559$	5.44220	+	1.76828i	0.230181	+	0.0747902i
$560$		0			0
$561$	38.7070	−	19.5949i	1.63421	−	0.827297i
$562$	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	$0.957532\pi$
$564$	15.6882	−	7.94195i	0.660593	−	0.334417i
$565$		0			0
$566$	9.36284	+	3.04217i	0.393550	+	0.127872i
$567$	−1.38876	+	1.36001i	−0.0583223	+	0.0571152i
$568$	−8.57861	−	8.57861i	−0.359950	−	0.359950i
$569$	−3.20445	−	2.32817i	−0.134338	−	0.0976021i	0.518587	−	0.855025i	$-0.326458\pi$
$569$	−3.20445	−	2.32817i	−0.134338	−	0.0976021i	−0.652925	+	0.757423i	$0.726458\pi$
$570$		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
$573$	−2.66718	+	8.13631i	−0.111423	+	0.339899i
$574$		−	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	0.767511	−	0.641036i	$-0.221495\pi$
$577$	16.8154	+	8.56788i	0.700034	+	0.356685i	−0.0674769	+	0.997721i	$0.521495\pi$
$578$	−1.05907	+	6.68673i	−0.0440517	+	0.278131i
$579$	−4.13922	+	4.11763i	−0.172020	+	0.171123i
$580$		0			0
$581$	0.634802	−	0.873729i	0.0263360	−	0.0362484i
$582$	−10.3116	+	14.1149i	−0.427429	+	0.585083i
$583$	−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	$0.380641\pi$
$588$	7.05353	+	9.76192i	0.290883	+	0.402575i
$589$	1.04166	−	0.338457i	0.0429210	−	0.0139459i
$590$		0			0
$591$	2.01933	−	12.5373i	0.0830640	−	0.515716i
$592$	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	$-0.141825\pi$
$594$	26.3332	+	4.38274i	1.08047	+	0.179826i
$595$		0			0
$596$	−4.53982	−	6.24853i	−0.185958	−	0.255950i
$597$	14.4484	+	0.0377708i	0.591334	+	0.00154586i
$598$	−1.80428	+	3.54111i	−0.0737826	+	0.144807i
$599$	18.2921			0.747393			0.373697	−	0.927551i	$-0.378090\pi$
$599$	18.2921			0.747393			0.373697	+	0.927551i	$0.378090\pi$
$600$		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
$603$	−44.5577	+	6.81864i	−1.81453	+	0.277676i
$604$	8.69147	+	11.9628i	0.353651	+	0.486759i
$605$		0			0
$606$	7.53772	−	14.6985i	0.306199	−	0.597086i
$607$	−2.39455	+	2.39455i	−0.0971917	+	0.0971917i	−0.754031	−	0.656839i	$-0.771893\pi$
$607$	−2.39455	+	2.39455i	−0.0971917	+	0.0971917i	0.656839	+	0.754031i	$0.271893\pi$
$608$	−0.475594	+	0.0753267i	−0.0192879	+	0.00305490i
$609$	3.46681	+	0.558383i	0.140482	+	0.0226268i
$610$		0			0
$611$	−14.3512	+	4.66298i	−0.580586	+	0.188644i
$612$	−10.3963	+	10.2882i	−0.420247	+	0.415875i
$613$	−12.2470	+	6.24017i	−0.494653	+	0.252038i	−0.683476	−	0.729973i	$-0.739533\pi$
$613$	−12.2470	+	6.24017i	−0.494653	+	0.252038i	0.188823	+	0.982011i	$0.439533\pi$
$614$	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	$-0.116186\pi$
$618$	14.1451	+	10.3336i	0.568999	+	0.415679i
$619$	−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
$621$	6.40445	−	12.3294i	0.257002	−	0.494763i
$622$	−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
$627$	4.07163	+	1.33473i	0.162605	+	0.0533040i
$628$	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
$633$	−7.06846	+	2.27627i	−0.280946	+	0.0904736i
$634$	−10.3155	−	3.35172i	−0.409683	−	0.133114i
$635$		0			0
$636$	6.01719	+	11.8861i	0.238597	+	0.471315i
$637$	−4.69209	−	9.20875i	−0.185907	−	0.364864i
$638$	−21.8942	−	42.9697i	−0.866798	−	1.70119i
$639$	−21.2388	−	29.5564i	−0.840193	−	1.16923i
$640$		0			0
$641$	−0.702023	−	0.228101i	−0.0277282	−	0.00900945i	0.295120	−	0.955460i	$-0.404640\pi$
$641$	−0.702023	−	0.228101i	−0.0277282	−	0.00900945i	−0.322848	+	0.946451i	$0.604640\pi$
$642$	−5.86312	−	18.2066i	−0.231399	−	0.718558i
$643$	17.1573	+	17.1573i	0.676616	+	0.676616i	0.959233	−	0.282617i	$-0.0912025\pi$
$643$	17.1573	+	17.1573i	0.676616	+	0.676616i	−0.282617	+	0.959233i	$0.591203\pi$
$644$	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	$0.587815\pi$
$648$	−8.90343	+	1.31488i	−0.349760	+	0.0516535i
$649$		−	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	$0.986686\pi$
$654$	7.49055	+	7.52982i	0.292904	+	0.294439i
$655$		0			0
$656$	3.68068	−	5.06602i	0.143706	−	0.197795i
$657$	12.9131	−	25.0191i	0.503787	−	0.976087i
$658$	0.342999	+	2.16561i	0.0133715	+	0.0844242i
$659$	3.59331	−	11.0591i	0.139975	−	0.430800i	−0.856355	−	0.516387i	$-0.827277\pi$
$659$	3.59331	−	11.0591i	0.139975	−	0.430800i	0.996331	+	0.0855871i	$0.0272766\pi$
$660$		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
$663$	10.1738	−	7.35111i	0.395116	−	0.285494i
$664$	4.75577	−	1.54524i	0.184560	−	0.0599671i
$665$		0			0
$666$	12.9147	+	0.0675232i	0.500434	+	0.00261647i
$667$	−24.7901	+	3.92637i	−0.959877	+	0.152030i
$668$	9.78704	−	9.78704i	0.378672	−	0.378672i
$669$	−1.12650	−	0.577696i	−0.0435531	−	0.0223350i
$670$		0			0
$671$	41.2074	+	56.7171i	1.59079	+	2.18954i
$672$	0.000977913	−	0.374079i	3.77238e−5	−	0.0144304i
$673$	12.1800	−	23.9046i	0.469504	−	0.921454i	−0.527890	−	0.849313i	$-0.677017\pi$
$673$	12.1800	−	23.9046i	0.469504	−	0.921454i	0.997394	−	0.0721411i	$-0.0229832\pi$
$674$	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	$0.289395\pi$
$678$	0.0497436	−	19.0283i	0.00191039	−	0.730779i
$679$	−1.28118	−	1.76340i	−0.0491673	−	0.0676729i
$680$		0			0
$681$	5.10240	+	2.61663i	0.195524	+	0.100269i
$682$	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	$0.327786\pi$
$684$	−1.44455	−	0.00755268i	−0.0552336	−	0.000288784i
$685$		0			0
$686$	−2.86609	+	0.931249i	−0.109428	+	0.0355552i
$687$	−14.8139	+	10.7039i	−0.565187	+	0.408379i
$688$	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
$693$	−1.52671	+	2.95800i	−0.0579949	+	0.112365i
$694$	11.3510	−	15.6232i	0.430876	−	0.593050i
$695$		0			0
$696$	11.4666	+	11.5267i	0.434639	+	0.436917i
$697$	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	$-0.991908\pi$
$701$		−	1.34594i		−	0.0508356i	0.999677	−	0.0254178i	$-0.00809161\pi$
$702$	7.72314	+	0.0605703i	0.291491	+	0.00228608i
$703$	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
$708$	2.64812	+	8.22317i	0.0995225	+	0.309046i
$709$	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
$711$	−3.82725	−	5.32610i	−0.143533	−	0.199744i
$712$	4.97027	+	9.75471i	0.186269	+	0.365573i
$713$	−2.76112	−	5.41900i	−0.103405	−	0.202943i
$714$	−0.823744	−	1.62719i	−0.0308278	−	0.0608960i
$715$		0			0
$716$	−11.2695	−	3.66170i	−0.421163	−	0.136844i
$717$	−19.3642	+	6.23589i	−0.723170	+	0.232884i
$718$	24.4491	+	24.4491i	0.912432	+	0.912432i
$719$	15.2779	+	11.1001i	0.569770	+	0.413962i	0.835022	−	0.550217i	$-0.185455\pi$
$719$	15.2779	+	11.1001i	0.569770	+	0.413962i	−0.265251	+	0.964179i	$0.585455\pi$
$720$		0			0
$721$	−1.76717	+	1.28392i	−0.0658127	+	0.0478157i
$722$	18.5371	+	2.93598i	0.689878	+	0.109266i
$723$	2.00183	+	0.656225i	0.0744490	+	0.0244053i
$724$		−	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	0.646597	−	0.762832i	$-0.276192\pi$
$727$	11.0417	+	5.62601i	0.409513	+	0.208657i	−0.237084	+	0.971489i	$0.576192\pi$
$728$	−0.0502184	+	0.317066i	−0.00186122	+	0.0117513i
$729$	−26.9967	−	0.423480i	−0.999877	−	0.0156844i
$730$		0			0
$731$	11.0326	−	15.1850i	0.408055	−	0.561639i
$732$	−19.0850	−	13.9424i	−0.705401	−	0.515327i
$733$	1.46889	+	9.27418i	0.0542545	+	0.342550i	0.999852	+	0.0172103i	$0.00547849\pi$
$733$	1.46889	+	9.27418i	0.0542545	+	0.342550i	−0.945597	+	0.325339i	$0.894522\pi$
$734$	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
$738$	13.3529	−	13.2140i	0.491526	−	0.486413i
$739$	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
$741$	1.22389	+	0.197126i	0.0449606	+	0.00724159i
$742$	−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	$0.0444997\pi$
$744$	−1.79777	+	3.50563i	−0.0659094	+	0.128523i
$745$		0			0
$746$	6.36867	+	8.76572i	0.233174	+	0.320936i
$747$	14.8289	−	2.26926i	0.542562	−	0.0830278i
$748$	−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
$753$	39.1655	+	0.102386i	1.42727	+	0.00373115i
$754$	−8.20106	−	11.2878i	−0.298665	−	0.411077i
$755$		0			0
$756$	0.184245	−	1.10701i	0.00670092	−	0.0402617i
$757$	20.0652	−	20.0652i	0.729283	−	0.729283i	−0.241194	−	0.970477i	$-0.577539\pi$
$757$	20.0652	−	20.0652i	0.729283	−	0.729283i	0.970477	+	0.241194i	$0.0775389\pi$
$758$	−33.0785	+	5.23911i	−1.20146	+	0.190293i
$759$	3.78346	−	23.4902i	0.137331	−	0.852642i
$760$		0			0
$761$	30.4666	−	9.89919i	1.10441	−	0.358845i	0.300613	−	0.953746i	$-0.402809\pi$
$761$	30.4666	−	9.89919i	1.10441	−	0.358845i	0.803799	+	0.594901i	$0.202809\pi$
$762$	15.2535	+	21.1104i	0.552575	+	0.764751i
$763$	−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
$768$	1.02173	−	1.39859i	0.0368686	−	0.0504674i
$769$	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
$771$	−5.18256	+	5.15553i	−0.186645	+	0.185672i
$772$	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
$777$	−0.501643	+	1.53028i	−0.0179964	+	0.0548983i
$778$	−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
$783$	28.3596	+	39.6844i	1.01349	+	1.41820i
$784$	−6.61303	−	2.14870i	−0.236180	−	0.0767395i
$785$		0			0
$786$	13.4836	−	6.82591i	0.480945	−	0.243472i
$787$	23.2927	+	45.7145i	0.830295	+	1.62955i	0.775755	+	0.631035i	$0.217369\pi$
$787$	23.2927	+	45.7145i	0.830295	+	1.62955i	0.0545406	+	0.998512i	$0.482631\pi$
$788$	3.32853	+	6.53260i	0.118574	+	0.232714i
$789$	−3.97420	+	2.01189i	−0.141485	+	0.0716251i
$790$		0			0
$791$	2.25659	+	0.733210i	0.0802351	+	0.0260700i
$792$	−13.7692	+	6.92529i	−0.489265	+	0.246080i
$793$	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	$0.532495\pi$
$798$	0.0561103	−	0.171166i	0.00198628	−	0.00605921i
$799$			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
$804$	18.4504	−	18.3542i	0.650696	−	0.647303i
$805$		0			0
$806$	1.98724	−	2.73520i	0.0699974	−	0.0963431i
$807$	24.6894	−	33.7959i	0.869109	−	1.18967i
$808$	1.49192	+	9.41958i	0.0524854	+	0.331380i
$809$	4.71934	−	14.5246i	0.165923	−	0.510659i	−0.833180	−	0.553002i	$-0.813482\pi$
$809$	4.71934	−	14.5246i	0.165923	−	0.510659i	0.999103	+	0.0423432i	$0.0134823\pi$
$810$		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
$813$	−11.7421	−	16.2508i	−0.411814	−	0.569940i
$814$	21.0344	−	6.83450i	0.737256	−	0.239549i
$815$		0			0
$816$	1.34282	−	8.33709i	0.0470080	−	0.291857i
$817$	1.83096	−	0.289996i	0.0640572	−	0.0101457i
$818$	−11.3634	+	11.3634i	−0.397313	+	0.397313i
$819$	−0.302385	+	0.914352i	−0.0105662	+	0.0319500i
$820$		0			0
$821$	−18.3359	−	25.2372i	−0.639927	−	0.880784i	0.358685	−	0.933459i	$-0.383225\pi$
$821$	−18.3359	−	25.2372i	−0.639927	−	0.880784i	−0.998612	+	0.0526750i	$0.983225\pi$
$822$	−4.89026	−	0.0127840i	−0.170567	−	0.000445895i
$823$	−7.08420	+	13.9035i	−0.246940	+	0.484647i	−0.980892	−	0.194555i	$-0.937674\pi$
$823$	−7.08420	+	13.9035i	−0.246940	+	0.484647i	0.733952	+	0.679202i	$0.237674\pi$
$824$	−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	$0.170132\pi$
$828$	1.21339	+	7.92916i	0.0421684	+	0.275557i
$829$	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
$831$	5.95618	−	11.6145i	0.206618	−	0.402903i
$832$	−1.05102	+	1.05102i	−0.0364375	+	0.0364375i
$833$	−33.4834	+	5.30325i	−1.16013	+	0.183747i
$834$	11.9031	+	1.91718i	0.412171	+	0.0663864i
$835$		0			0
$836$	−2.35276	+	0.764459i	−0.0813720	+	0.0264394i
$837$	−7.02191	+	9.50714i	−0.242713	+	0.328615i
$838$	1.99711	−	1.01758i	0.0689889	−	0.0351516i
$839$	5.55073	+	17.0834i	0.191632	+	0.589784i	0.999999	+	0.00110507i	$0.000351754\pi$
$839$	5.55073	+	17.0834i	0.191632	+	0.589784i	−0.808367	+	0.588679i	$0.799648\pi$
$840$		0			0
$841$	18.2677	−	56.2221i	0.629920	−	1.93869i
$842$	−0.405096	−	2.55767i	−0.0139605	−	0.0881433i
$843$	−33.0241	−	24.1255i	−1.13741	−	0.830928i
$844$	2.52005	−	3.46855i	0.0867437	−	0.119392i
$845$		0			0
$846$	−18.0303	+	24.5457i	−0.619895	+	0.843899i
$847$	−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
$852$	19.9677	+	6.54566i	0.684083	+	0.224251i
$853$	−31.1950	−	4.94081i	−1.06810	−	0.169170i	−0.402454	−	0.915440i	$-0.631843\pi$
$853$	−31.1950	−	4.94081i	−1.06810	−	0.169170i	−0.665643	+	0.746270i	$0.731843\pi$
$854$	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	$0.816390\pi$
$858$	12.5897	−	4.05428i	0.429805	−	0.138411i
$859$	−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
$861$	1.05800	+	2.08993i	0.0360566	+	0.0712247i
$862$	−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	$0.687413\pi$
$864$	3.70294	−	3.64531i	0.125976	−	0.124016i
$865$		0			0
$866$	19.5231	+	6.34342i	0.663420	+	0.215558i
$867$	−3.59441	−	11.1616i	−0.122072	−	0.379069i
$868$	−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
$873$	4.89261	−	29.8788i	0.165590	−	1.01124i
$874$			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	0.174648	−	0.984631i	$-0.444121\pi$
$877$	−15.3780	−	7.83550i	−0.519279	−	0.264586i	−0.693927	+	0.720045i	$0.744121\pi$
$878$	−3.68012	+	23.2354i	−0.124198	+	0.784156i
$879$	−5.76893	−	5.79917i	−0.194581	−	0.195601i
$880$		0			0
$881$	11.5046	−	15.8347i	0.387600	−	0.533485i	−0.569978	−	0.821660i	$-0.693048\pi$
$881$	11.5046	−	15.8347i	0.387600	−	0.533485i	0.957578	+	0.288175i	$0.0930484\pi$
$882$	−18.5367	−	9.56732i	−0.624163	−	0.322148i
$883$	2.11040	+	13.3245i	0.0710206	+	0.448406i	0.997415	+	0.0718524i	$0.0228910\pi$
$883$	2.11040	+	13.3245i	0.0710206	+	0.448406i	−0.926395	+	0.376554i	$0.877109\pi$
$884$	−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	$0.00747579\pi$
$888$	−6.04379	+	4.36698i	−0.202816	+	0.146546i
$889$	−3.08864	+	1.00356i	−0.103590	+	0.0336583i
$890$		0			0
$891$	−44.1219	+	13.8277i	−1.47814	+	0.463245i
$892$	0.721923	−	0.114341i	0.0241718	−	0.00382843i
$893$	−3.45666	+	3.45666i	−0.115673	+	0.115673i
$894$	11.9037	+	6.10448i	0.398119	+	0.204164i
$895$		0			0
$896$	0.126947	+	0.174728i	0.00424101	+	0.00583725i
$897$	0.0179951	−	6.88362i	0.000600838	−	0.229838i
$898$	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
$903$	−0.00376481	+	1.44015i	−0.000125285	+	0.0479251i
$904$	6.45744	+	8.88790i	0.214771	+	0.295607i
$905$		0			0
$906$	−22.7896	−	11.6870i	−0.757132	−	0.388275i
$907$	7.30011	−	7.30011i	0.242396	−	0.242396i	−0.575445	−	0.817841i	$-0.695171\pi$
$907$	7.30011	−	7.30011i	0.242396	−	0.242396i	0.817841	+	0.575445i	$0.195171\pi$
$908$	−3.26989	+	0.517900i	−0.108515	+	0.0171871i
$909$	−0.149588	+	28.6106i	−0.00496152	+	0.948954i
$910$		0			0
$911$	−26.9954	+	8.77133i	−0.894397	+	0.290607i	−0.719922	−	0.694055i	$-0.755823\pi$
$911$	−26.9954	+	8.77133i	−0.894397	+	0.290607i	−0.174474	+	0.984662i	$0.555823\pi$
$912$	0.676016	−	0.488460i	0.0223851	−	0.0161745i
$913$	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
$918$	8.01723	−	24.0316i	0.264608	−	0.793160i
$919$	−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
$921$	−20.4077	−	20.5147i	−0.672457	−	0.675982i
$922$	−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
$927$	−29.9427	−	4.90306i	−0.983446	−	0.161038i
$928$	−9.27141	−	1.46845i	−0.304349	−	0.0482041i
$929$	5.66314	−	4.11451i	0.185802	−	0.134993i	−0.490996	−	0.871162i	$-0.663367\pi$
$929$	5.66314	−	4.11451i	0.185802	−	0.134993i	0.676798	+	0.736169i	$0.263367\pi$
$930$		0			0
$931$	−2.70875	−	1.96802i	−0.0887756	−	0.0644992i
$932$	8.90175	+	8.90175i	0.291586	+	0.291586i
$933$	−16.0350	−	49.7933i	−0.524964	−	1.63016i
$934$	22.0766	+	7.17313i	0.722369	+	0.234712i
$935$		0			0
$936$	−3.62114	+	2.60209i	−0.118361	+	0.0850521i
$937$	18.0852	+	35.4943i	0.590819	+	1.15955i	0.971986	+	0.235040i	$0.0755223\pi$
$937$	18.0852	+	35.4943i	0.590819	+	1.15955i	−0.381167	+	0.924506i	$0.624478\pi$
$938$	1.47326	+	2.89144i	0.0481037	+	0.0944088i
$939$	13.0491	+	25.7767i	0.425841	+	0.841189i
$940$		0			0
$941$	−0.912873	−	0.296610i	−0.0297588	−	0.00966922i	0.294100	−	0.955775i	$-0.404980\pi$
$941$	−0.912873	−	0.296610i	−0.0297588	−	0.00966922i	−0.323859	+	0.946106i	$0.604980\pi$
$942$	−27.0326	+	8.70535i	−0.880769	+	0.283636i
$943$	−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	$0.762250\pi$
$948$	3.59821	+	1.17954i	0.116864	+	0.0383096i
$949$		−	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	$0.671095\pi$
$954$	−18.5970	−	13.6606i	−0.602099	−	0.442279i
$955$		0			0
$956$	6.90374	−	9.50218i	0.223283	−	0.307322i
$957$	67.4486	+	49.2742i	2.18030	+	1.59281i
$958$	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
$963$	23.3034	+	23.5483i	0.750941	+	0.758835i
$964$	−1.15675	+	0.375849i	−0.0372563	+	0.0121053i
$965$		0			0
$966$	−0.987499	−	0.159052i	−0.0317723	−	0.00511741i
$967$	−43.6488	+	6.91329i	−1.40365	+	0.222316i	−0.811896	−	0.583802i	$-0.801565\pi$
$967$	−43.6488	+	6.91329i	−1.40365	+	0.222316i	−0.591755	+	0.806118i	$0.701565\pi$
$968$	−10.8855	+	10.8855i	−0.349872	+	0.349872i
$969$	1.85550	−	3.61820i	0.0596071	−	0.116233i
$970$		0			0
$971$	32.4405	+	44.6505i	1.04107	+	1.43290i	0.896306	+	0.443437i	$0.146241\pi$
$971$	32.4405	+	44.6505i	1.04107	+	1.43290i	0.144760	+	0.989467i	$0.453759\pi$
$972$	12.7300	−	8.99705i	0.408315	−	0.288580i
$973$	−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	$-0.0276079\pi$
$978$	7.02810	+	0.0183728i	0.224734	+	0.000587496i
$979$	33.0604	+	45.5037i	1.05661	+	1.45430i
$980$		0			0
$981$	−17.4658	−	5.77613i	−0.557642	−	0.184418i
$982$	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	$0.349350\pi$
$984$	−1.72469	+	10.7080i	−0.0549811	+	0.341359i
$985$		0			0
$986$	−43.5259	+	14.1424i	−1.38615	+	0.450386i
$987$	−2.22419	−	3.07823i	−0.0707968	−	0.0979811i
$988$	−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
$993$	9.84420	−	13.4752i	0.312396	−	0.427621i
$994$	−1.54012	+	2.11980i	−0.0488497	+	0.0672359i
$995$		0			0
$996$	−6.14034	+	6.10832i	−0.194564	+	0.193550i
$997$	7.20864	−	45.5136i	0.228300	−	1.44143i	−0.561201	−	0.827680i	$-0.689660\pi$
$997$	7.20864	−	45.5136i	0.228300	−	1.44143i	0.789501	−	0.613750i	$-0.210340\pi$
$998$	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.c.143.8		80
3.2	odd	2	inner	750.2.l.c.143.4		80
5.2	odd	4		150.2.l.a.17.10	yes	80
5.3	odd	4		750.2.l.b.107.1		80
5.4	even	2		750.2.l.a.143.3		80
15.2	even	4		150.2.l.a.17.1	✓	80
15.8	even	4		750.2.l.b.107.10		80
15.14	odd	2		750.2.l.a.143.7		80
25.3	odd	20		750.2.l.a.257.7		80
25.4	even	10		750.2.l.b.743.10		80
25.21	even	5		150.2.l.a.53.1	yes	80
25.22	odd	20	inner	750.2.l.c.257.4		80
75.29	odd	10		750.2.l.b.743.1		80
75.47	even	20	inner	750.2.l.c.257.8		80
75.53	even	20		750.2.l.a.257.3		80
75.71	odd	10		150.2.l.a.53.10	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(-0.00452789 + 1.73204i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.99996 - 0.0156850i) q^{9} +O(q^{10})\)	\(q+(0.453990 - 0.891007i) q^{2} +(-0.00452789 + 1.73204i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-2.99996 - 0.0156850i) q^{9} +(-4.88609 + 1.58759i) q^{11} +(1.40392 - 1.01441i) 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} +(-1.37593 + 2.66586i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(-0.263823 - 0.265206i) q^{21} +(-0.803689 + 5.07429i) q^{22} +(2.38239 + 1.21389i) q^{23} +(-0.266479 - 1.71143i) q^{24} +1.48636i q^{26} +(0.0407506 - 5.19599i) 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} +(-2.72765 - 8.47012i) q^{33} +(4.63684 + 1.50660i) q^{34} +(1.75064 + 2.43624i) q^{36} +(-1.95441 - 3.83574i) q^{37} +(0.218606 + 0.429039i) q^{38} +(-1.16278 - 2.29691i) q^{39} +(-5.95547 - 1.93505i) q^{41} +(-0.356073 + 0.114667i) 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} +(-1.64587 - 0.539538i) q^{48} +6.95335i q^{49} +(-8.34400 + 1.29921i) q^{51} +(1.32436 + 0.674795i) q^{52} +(-1.20325 + 7.59700i) q^{53} +(-4.61116 - 2.39524i) q^{54} +(0.126947 - 0.174728i) q^{56} +(-0.673453 - 0.491987i) 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} +(0.460543 - 0.455752i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-8.78526 - 1.41500i) q^{66} +(14.8405 - 2.35050i) q^{67} +(3.44747 - 3.44747i) q^{68} +(-2.11330 + 4.12092i) q^{69} +(7.13100 + 9.81498i) q^{71} +(2.96548 - 0.453805i) q^{72} +(-4.26070 + 8.36209i) q^{73} -4.30495 q^{74} +0.481522 q^{76} +(0.503741 - 0.988647i) q^{77} +(-2.57445 - 0.00673009i) q^{78} +(1.28502 + 1.76867i) q^{79} +(8.99951 + 0.0941087i) q^{81} +(-4.42787 + 4.42787i) q^{82} +(-4.93895 + 0.782253i) q^{83} +(-0.0594848 + 0.369321i) q^{84} +(-3.66142 + 1.18967i) q^{86} +(-9.52222 - 13.1785i) 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} +(2.32404 - 3.18124i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.22794 + 1.22154i) 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

Fields

Representations

Groups

Database

Properties

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