LMFDB - Embedded newform 875.2.bb.a.243.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([27, 50]))

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

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

chi := DirichletCharacter("875.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			243.13
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.a.857.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31913 + 0.0691326i) q^{2} +(-0.985411 - 1.21688i) q^{3} +(-0.253721 - 0.0266672i) q^{4} +(-1.21576 - 1.67335i) q^{6} +(2.58371 + 0.569615i) q^{7} +(-2.94220 - 0.465999i) q^{8} +(0.113970 - 0.536187i) q^{9} +(0.468564 - 0.0995964i) q^{11} +(0.217569 + 0.335027i) q^{12} +(-0.195060 - 0.0993879i) q^{13} +(3.36886 + 0.930015i) q^{14} +(-3.34984 - 0.712030i) q^{16} +(-1.72008 - 4.48096i) q^{17} +(0.187409 - 0.699421i) q^{18} +(-0.561217 - 5.33963i) q^{19} +(-1.85286 - 3.70537i) q^{21} +(0.624982 - 0.0989874i) q^{22} +(0.0278939 - 0.532247i) q^{23} +(2.33221 + 4.03951i) q^{24} +(-0.250438 - 0.144591i) q^{26} +(-4.95029 + 2.52230i) q^{27} +(-0.640352 - 0.213424i) q^{28} +(2.22883 - 3.06772i) q^{29} +(1.36200 - 3.05910i) q^{31} +(1.38510 + 0.371137i) q^{32} +(-0.582925 - 0.472043i) q^{33} +(-1.95922 - 6.02987i) q^{34} +(-0.0432152 + 0.133003i) q^{36} +(-6.39160 + 4.15075i) q^{37} +(-0.371176 - 7.08245i) q^{38} +(0.0712708 + 0.335303i) q^{39} +(-2.67924 + 0.870538i) q^{41} +(-2.18800 - 5.01595i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(-0.121541 + 0.0127744i) q^{44} +(0.0735913 - 0.700174i) q^{46} +(-6.98550 - 2.68148i) q^{47} +(2.43451 + 4.77800i) q^{48} +(6.35108 + 2.94344i) q^{49} +(-3.75781 + 6.50871i) q^{51} +(0.0468405 + 0.0304185i) q^{52} +(-3.76438 + 3.04833i) q^{53} +(-6.70444 + 2.98501i) q^{54} +(-7.33634 - 2.87993i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(3.15219 - 3.89263i) q^{58} +(3.58205 - 3.97827i) q^{59} +(6.61519 - 5.95635i) q^{61} +(2.00814 - 3.94119i) q^{62} +(0.599885 - 1.32043i) q^{63} +(8.31559 + 2.70190i) q^{64} +(-0.736320 - 0.662985i) q^{66} +(12.1287 - 4.65578i) q^{67} +(0.316926 + 1.18278i) q^{68} +(-0.675168 + 0.490538i) q^{69} +(3.80548 + 2.76485i) q^{71} +(-0.585185 + 1.52446i) q^{72} +(7.14378 - 11.0005i) q^{73} +(-8.71829 + 5.03351i) q^{74} +1.36974i q^{76} +(1.26736 + 0.00957352i) q^{77} +(0.0708350 + 0.447234i) q^{78} +(3.76871 + 8.46467i) q^{79} +(6.44508 + 2.86953i) q^{81} +(-3.59445 + 0.963129i) q^{82} +(-1.48616 + 9.38322i) q^{83} +(0.371298 + 0.989542i) q^{84} +(-7.54123 - 8.37538i) q^{86} +(-5.92936 + 0.310744i) q^{87} +(-1.42502 + 0.0746822i) q^{88} +(3.91910 + 4.35260i) q^{89} +(-0.447364 - 0.367898i) q^{91} +(-0.0212708 + 0.134299i) q^{92} +(-5.06469 + 1.35708i) q^{93} +(-9.02940 - 4.02015i) q^{94} +(-0.913264 - 2.05122i) q^{96} +(-1.50690 - 9.51421i) q^{97} +(8.17440 + 4.32184i) q^{98} -0.262589i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.31913	+	0.0691326i	0.932765	+	0.0488842i	0.512660	−	0.858591i	$-0.328660\pi$
$2$	1.31913	+	0.0691326i	0.932765	+	0.0488842i	0.420105	+	0.907476i	$0.361993\pi$
$3$	−0.985411	−	1.21688i	−0.568927	−	0.702567i	0.408758	−	0.912643i	$-0.365962\pi$
$3$	−0.985411	−	1.21688i	−0.568927	−	0.702567i	−0.977685	+	0.210076i	$0.932629\pi$
$4$	−0.253721	−	0.0266672i	−0.126861	−	0.0133336i
$5$		0			0
$5$		0			0
$6$	−1.21576	−	1.67335i	−0.496331	−	0.683141i
$7$	2.58371	+	0.569615i	0.976549	+	0.215294i
$7$	2.58371	+	0.569615i	0.976549	+	0.215294i
$8$	−2.94220	−	0.465999i	−1.04023	−	0.164755i
$9$	0.113970	−	0.536187i	0.0379900	−	0.178729i
$10$		0			0
$11$	0.468564	−	0.0995964i	0.141277	−	0.0300294i	−0.136730	−	0.990608i	$-0.543659\pi$
$11$	0.468564	−	0.0995964i	0.141277	−	0.0300294i	0.278008	+	0.960579i	$0.410326\pi$
$12$	0.217569	+	0.335027i	0.0628068	+	0.0967140i
$13$	−0.195060	−	0.0993879i	−0.0540999	−	0.0275653i	0.426731	−	0.904378i	$-0.359665\pi$
$13$	−0.195060	−	0.0993879i	−0.0540999	−	0.0275653i	−0.480831	+	0.876813i	$0.659665\pi$
$14$	3.36886	+	0.930015i	0.900367	+	0.248557i
$15$		0			0
$16$	−3.34984	−	0.712030i	−0.837460	−	0.178008i
$17$	−1.72008	−	4.48096i	−0.417180	−	1.08679i	−0.967730	−	0.251989i	$-0.918915\pi$
$17$	−1.72008	−	4.48096i	−0.417180	−	1.08679i	0.550550	−	0.834802i	$-0.314418\pi$
$18$	0.187409	−	0.699421i	0.0441728	−	0.164855i
$19$	−0.561217	−	5.33963i	−0.128752	−	1.22499i	−0.847907	−	0.530145i	$-0.822138\pi$
$19$	−0.561217	−	5.33963i	−0.128752	−	1.22499i	0.719155	−	0.694849i	$-0.244529\pi$
$20$		0			0
$21$	−1.85286	−	3.70537i	−0.404327	−	0.808578i
$22$	0.624982	−	0.0989874i	0.133247	−	0.0211042i
$23$	0.0278939	−	0.532247i	0.00581628	−	0.110981i	−0.994178	−	0.107746i	$-0.965637\pi$
$23$	0.0278939	−	0.532247i	0.00581628	−	0.110981i	0.999995	−	0.00323548i	$-0.00102989\pi$
$24$	2.33221	+	4.03951i	0.476061	+	0.824561i
$25$		0			0
$26$	−0.250438	−	0.144591i	−0.0491150	−	0.0283565i
$27$	−4.95029	+	2.52230i	−0.952683	+	0.485416i
$28$	−0.640352	−	0.213424i	−0.121015	−	0.0403333i
$29$	2.22883	−	3.06772i	0.413883	−	0.569661i	−0.550277	−	0.834982i	$-0.685478\pi$
$29$	2.22883	−	3.06772i	0.413883	−	0.569661i	0.964160	+	0.265321i	$0.0854780\pi$
$30$		0			0
$31$	1.36200	−	3.05910i	0.244622	−	0.549431i	−0.748950	−	0.662626i	$-0.769442\pi$
$31$	1.36200	−	3.05910i	0.244622	−	0.549431i	0.993573	+	0.113195i	$0.0361086\pi$
$32$	1.38510	+	0.371137i	0.244853	+	0.0656083i
$33$	−0.582925	−	0.472043i	−0.101474	−	0.0821722i
$34$	−1.95922	−	6.02987i	−0.336004	−	1.03411i
$35$		0			0
$36$	−0.0432152	+	0.133003i	−0.00720254	+	0.0221671i
$37$	−6.39160	+	4.15075i	−1.05077	+	0.682379i	−0.949911	−	0.312521i	$-0.898826\pi$
$37$	−6.39160	+	4.15075i	−1.05077	+	0.682379i	−0.100861	+	0.994901i	$0.532160\pi$
$38$	−0.371176	−	7.08245i	−0.0602126	−	1.14893i
$39$	0.0712708	+	0.335303i	0.0114125	+	0.0536914i
$40$		0			0
$41$	−2.67924	+	0.870538i	−0.418427	+	0.135955i	−0.510661	−	0.859782i	$-0.670599\pi$
$41$	−2.67924	+	0.870538i	−0.418427	+	0.135955i	0.0922339	+	0.995737i	$0.470599\pi$
$42$	−2.18800	−	5.01595i	−0.337615	−	0.773978i
$43$	−6.03300	−	6.03300i	−0.920024	−	0.920024i	0.0770067	−	0.997031i	$-0.475464\pi$
$43$	−6.03300	−	6.03300i	−0.920024	−	0.920024i	−0.997031	+	0.0770067i	$0.975464\pi$
$44$	−0.121541	+	0.0127744i	−0.0183229	+	0.00192582i
$45$		0			0
$46$	0.0735913	−	0.700174i	0.0108504	−	0.103235i
$47$	−6.98550	−	2.68148i	−1.01894	−	0.391135i	−0.209169	−	0.977880i	$-0.567076\pi$
$47$	−6.98550	−	2.68148i	−1.01894	−	0.391135i	−0.809772	+	0.586745i	$0.800409\pi$
$48$	2.43451	+	4.77800i	0.351391	+	0.689645i
$49$	6.35108	+	2.94344i	0.907297	+	0.420491i
$50$		0			0
$51$	−3.75781	+	6.50871i	−0.526198	+	0.911402i
$52$	0.0468405	+	0.0304185i	0.00649560	+	0.00421829i
$53$	−3.76438	+	3.04833i	−0.517077	+	0.418721i	−0.852013	−	0.523520i	$-0.824619\pi$
$53$	−3.76438	+	3.04833i	−0.517077	+	0.418721i	0.334936	+	0.942241i	$0.391285\pi$
$54$	−6.70444	+	2.98501i	−0.912359	+	0.406208i
$55$		0			0
$56$	−7.33634	−	2.87993i	−0.980360	−	0.384846i
$57$	−5.94466	+	5.94466i	−0.787389	+	0.787389i
$58$	3.15219	−	3.89263i	0.413903	−	0.511127i
$59$	3.58205	−	3.97827i	0.466343	−	0.517927i	−0.463393	−	0.886153i	$-0.653368\pi$
$59$	3.58205	−	3.97827i	0.466343	−	0.517927i	0.929736	+	0.368226i	$0.120035\pi$
$60$		0			0
$61$	6.61519	−	5.95635i	0.846989	−	0.762632i	−0.126355	−	0.991985i	$-0.540328\pi$
$61$	6.61519	−	5.95635i	0.846989	−	0.762632i	0.973343	+	0.229353i	$0.0736611\pi$
$62$	2.00814	−	3.94119i	0.255034	−	0.500532i
$63$	0.599885	−	1.32043i	0.0755785	−	0.166359i
$64$	8.31559	+	2.70190i	1.03945	+	0.337737i
$65$		0			0
$66$	−0.736320	−	0.662985i	−0.0906347	−	0.0816079i
$67$	12.1287	−	4.65578i	1.48176	−	0.568794i	0.522829	−	0.852437i	$-0.324877\pi$
$67$	12.1287	−	4.65578i	1.48176	−	0.568794i	0.958930	+	0.283644i	$0.0915432\pi$
$68$	0.316926	+	1.18278i	0.0384329	+	0.143434i
$69$	−0.675168	+	0.490538i	−0.0812807	+	0.0590539i
$70$		0			0
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	0.790238	−	0.612800i	$-0.209957\pi$
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	−0.338610	+	0.940927i	$0.609957\pi$
$72$	−0.585185	+	1.52446i	−0.0689647	+	0.179659i
$73$	7.14378	−	11.0005i	0.836117	−	1.28751i	−0.119482	−	0.992836i	$-0.538124\pi$
$73$	7.14378	−	11.0005i	0.836117	−	1.28751i	0.955599	−	0.294670i	$-0.0952098\pi$
$74$	−8.71829	+	5.03351i	−1.01348	+	0.585133i
$75$		0			0
$76$			1.36974i			0.157120i
$77$	1.26736	+	0.00957352i	0.144429	+	0.00109100i
$78$	0.0708350	+	0.447234i	0.00802048	+	0.0506393i
$79$	3.76871	+	8.46467i	0.424013	+	0.952349i	0.991637	+	0.129061i	$0.0411963\pi$
$79$	3.76871	+	8.46467i	0.424013	+	0.952349i	−0.567623	+	0.823288i	$0.692137\pi$
$80$		0			0
$81$	6.44508	+	2.86953i	0.716120	+	0.318837i
$82$	−3.59445	+	0.963129i	−0.396940	+	0.106360i
$83$	−1.48616	+	9.38322i	−0.163127	+	1.02994i	0.761249	+	0.648459i	$0.224586\pi$
$83$	−1.48616	+	9.38322i	−0.163127	+	1.02994i	−0.924376	+	0.381482i	$0.875414\pi$
$84$	0.371298	+	0.989542i	0.0405119	+	0.107968i
$85$		0			0
$86$	−7.54123	−	8.37538i	−0.813192	−	0.903141i
$87$	−5.92936	+	0.310744i	−0.635694	+	0.0333153i
$88$	−1.42502	+	0.0746822i	−0.151908	+	0.00796115i
$89$	3.91910	+	4.35260i	0.415424	+	0.461375i	0.914145	−	0.405388i	$-0.132864\pi$
$89$	3.91910	+	4.35260i	0.415424	+	0.461375i	−0.498721	+	0.866762i	$0.666197\pi$
$90$		0			0
$91$	−0.447364	−	0.367898i	−0.0468965	−	0.0385662i
$92$	−0.0212708	+	0.134299i	−0.00221764	+	0.0140016i
$93$	−5.06469	+	1.35708i	−0.525184	+	0.140723i
$94$	−9.02940	−	4.02015i	−0.931312	−	0.414647i
$95$		0			0
$96$	−0.913264	−	2.05122i	−0.0932096	−	0.209352i
$97$	−1.50690	−	9.51421i	−0.153003	−	0.966022i	−0.938028	−	0.346558i	$-0.887350\pi$
$97$	−1.50690	−	9.51421i	−0.153003	−	0.966022i	0.785026	−	0.619463i	$-0.212650\pi$
$98$	8.17440	+	4.32184i	0.825739	+	0.436572i
$99$		−	0.262589i		−	0.0263912i
$100$		0			0
$101$	15.0410	−	8.68390i	1.49663	−	0.864080i	0.496638	−	0.867958i	$-0.334568\pi$
$101$	15.0410	−	8.68390i	1.49663	−	0.864080i	0.999992	+	0.00387741i	$0.00123422\pi$
$102$	−5.40700	+	8.32605i	−0.535373	+	0.824402i
$103$	−2.81276	+	7.32748i	−0.277149	+	0.721998i	0.722386	+	0.691491i	$0.243046\pi$
$103$	−2.81276	+	7.32748i	−0.277149	+	0.721998i	−0.999535	+	0.0305073i	$0.990288\pi$
$104$	0.527590	+	0.383317i	0.0517345	+	0.0375873i
$105$		0			0
$106$	−5.17644	+	3.76090i	−0.502780	+	0.365291i
$107$	0.556205	+	2.07579i	0.0537704	+	0.200674i	0.987586	−	0.157082i	$-0.0502087\pi$
$107$	0.556205	+	2.07579i	0.0537704	+	0.200674i	−0.933815	+	0.357756i	$0.883542\pi$
$108$	1.32326	−	0.507951i	0.127330	−	0.0488776i
$109$	8.12435	+	7.31520i	0.778171	+	0.700669i	0.959175	−	0.282814i	$-0.0912678\pi$
$109$	8.12435	+	7.31520i	0.778171	+	0.700669i	−0.181003	+	0.983482i	$0.557935\pi$
$110$		0			0
$111$	11.3493	+	3.68762i	1.07723	+	0.350013i
$112$	−8.24942	−	3.74780i	−0.779497	−	0.354133i
$113$	−8.07135	+	15.8409i	−0.759289	+	1.49019i	0.108952	+	0.994047i	$0.465250\pi$
$113$	−8.07135	+	15.8409i	−0.759289	+	1.49019i	−0.868241	+	0.496142i	$0.834750\pi$
$114$	−8.25274	+	7.43080i	−0.772940	+	0.695959i
$115$		0			0
$116$	−0.647308	+	0.718909i	−0.0601011	+	0.0667490i
$117$	−0.0755215	+	0.0932613i	−0.00698196	+	0.00862201i
$118$	5.00022	−	5.00022i	0.460307	−	0.460307i
$119$	−1.89175	−	12.5573i	−0.173417	−	1.15112i
$120$		0			0
$121$	−9.83937	+	4.38077i	−0.894488	+	0.398252i
$122$	9.13807	−	7.39986i	0.827322	−	0.669952i
$123$	3.69949	+	2.40248i	0.333572	+	0.216624i
$124$	−0.427146	+	0.739839i	−0.0383589	+	0.0664395i
$125$		0			0
$126$	0.882611	−	1.70035i	0.0786293	−	0.151479i
$127$	8.47711	+	16.6373i	0.752222	+	1.47632i	0.875124	+	0.483899i	$0.160780\pi$
$127$	8.47711	+	16.6373i	0.752222	+	1.47632i	−0.122902	+	0.992419i	$0.539220\pi$
$128$	8.10511	+	3.11126i	0.716397	+	0.274999i
$129$	−1.39646	+	13.2864i	−0.122951	+	1.16980i
$130$		0			0
$131$	0.505966	−	0.0531792i	0.0442064	−	0.00464628i	−0.0823994	−	0.996599i	$-0.526258\pi$
$131$	0.505966	−	0.0531792i	0.0442064	−	0.00464628i	0.126606	+	0.991953i	$0.459592\pi$
$132$	0.135313	+	0.135313i	0.0117774	+	0.0117774i
$133$	1.59151	−	14.1157i	0.138002	−	1.22399i
$134$	16.3212	−	5.30308i	1.40994	−	0.458117i
$135$		0			0
$136$	2.97269	+	13.9854i	0.254906	+	1.19924i
$137$	0.227695	+	4.34468i	0.0194533	+	0.371191i	0.990958	+	0.134171i	$0.0428373\pi$
$137$	0.227695	+	4.34468i	0.0194533	+	0.371191i	−0.971505	+	0.237020i	$0.923829\pi$
$138$	−0.924546	+	0.600407i	−0.0787026	+	0.0511101i
$139$	6.71334	−	20.6615i	0.569418	−	1.75249i	−0.0850255	−	0.996379i	$-0.527097\pi$
$139$	6.71334	−	20.6615i	0.569418	−	1.75249i	0.654444	−	0.756111i	$-0.272903\pi$
$140$		0			0
$141$	3.62054	+	11.1429i	0.304905	+	0.938401i
$142$	4.82878	+	3.91027i	0.405222	+	0.328143i
$143$	−0.101297	−	0.0271424i	−0.00847085	−	0.00226976i
$144$	−0.763563	+	1.71499i	−0.0636302	+	0.142916i
$145$		0			0
$146$	10.1841	−	14.0172i	0.842839	−	1.16007i
$147$	−2.67661	−	10.6290i	−0.220763	−	0.876665i
$148$	1.73237	−	0.882688i	0.142400	−	0.0725565i
$149$	−10.0097	−	5.77912i	−0.820030	−	0.473444i	0.0303970	−	0.999538i	$-0.490323\pi$
$149$	−10.0097	−	5.77912i	−0.820030	−	0.473444i	−0.850427	+	0.526094i	$0.823656\pi$
$150$		0			0
$151$	8.08621	+	14.0057i	0.658046	+	1.13977i	0.981121	+	0.193396i	$0.0619502\pi$
$151$	8.08621	+	14.0057i	0.658046	+	1.13977i	−0.323075	+	0.946373i	$0.604716\pi$
$152$	−0.837045	+	15.9718i	−0.0678933	+	1.29548i
$153$	−2.59867	+	0.411589i	−0.210090	+	0.0332750i
$154$	1.67115	+	0.100245i	0.134665	+	0.00807796i
$155$		0			0
$156$	−0.00914134	−	0.0869740i	−0.000731893	−	0.00696350i
$157$	1.04591	−	3.90339i	0.0834728	−	0.311525i	−0.911548	−	0.411194i	$-0.865112\pi$
$157$	1.04591	−	3.90339i	0.0834728	−	0.311525i	0.995021	+	0.0996695i	$0.0317785\pi$
$158$	4.38623	+	11.4265i	0.348950	+	0.909046i
$159$	7.41892	+	1.57694i	0.588359	+	0.125059i
$160$		0			0
$161$	0.375246	−	1.35928i	0.0295735	−	0.107126i
$162$	8.30351	+	4.23085i	0.652386	+	0.332407i
$163$	9.09407	+	14.0036i	0.712303	+	1.09685i	0.990658	+	0.136372i	$0.0435441\pi$
$163$	9.09407	+	14.0036i	0.712303	+	1.09685i	−0.278355	+	0.960478i	$0.589789\pi$
$164$	0.702996	−	0.149426i	0.0548947	−	0.0116682i
$165$		0			0
$166$	−2.60912	+	12.2749i	−0.202507	+	0.952719i
$167$	23.5551	+	3.73076i	1.82275	+	0.288695i	0.971669	−	0.236344i	$-0.0759492\pi$
$167$	23.5551	+	3.73076i	1.82275	+	0.288695i	0.851078	+	0.525039i	$0.175949\pi$
$168$	3.72478	+	11.7654i	0.287373	+	0.907718i
$169$	−7.61304	−	10.4784i	−0.585618	−	0.806034i
$170$		0			0
$171$	−2.92700	−	0.307640i	−0.223833	−	0.0235258i
$172$	1.36982	+	1.69158i	0.104448	+	0.128982i
$173$	−24.4441	−	1.28106i	−1.85845	−	0.0973971i	−0.910053	−	0.414492i	$-0.863959\pi$
$173$	−24.4441	−	1.28106i	−1.85845	−	0.0973971i	−0.948394	+	0.317095i	$0.897293\pi$
$174$	−7.84307			−0.594581
$175$		0			0
$176$	−1.64053			−0.123660
$177$	−8.37088	−	0.438699i	−0.629194	−	0.0329746i
$178$	4.86889	+	6.01258i	0.364939	+	0.450662i
$179$	−17.6041	−	1.85027i	−1.31579	−	0.138295i	−0.579507	−	0.814967i	$-0.696755\pi$
$179$	−17.6041	−	1.85027i	−1.31579	−	0.138295i	−0.736285	+	0.676672i	$0.763422\pi$
$180$		0			0
$181$	0.557581	+	0.767444i	0.0414447	+	0.0570437i	0.829236	−	0.558898i	$-0.188776\pi$
$181$	0.557581	+	0.767444i	0.0414447	+	0.0570437i	−0.787792	+	0.615942i	$0.788776\pi$
$182$	−0.564698	−	0.516233i	−0.0418582	−	0.0382657i
$183$	−13.7668	−	2.18045i	−1.01767	−	0.161184i
$184$	−0.330096	+	1.55298i	−0.0243350	+	0.114487i
$185$		0			0
$186$	−6.77480	+	1.44003i	−0.496753	+	0.105588i
$187$	−1.25225	−	1.92830i	−0.0915739	−	0.141011i
$188$	1.70086	+	0.866634i	0.124048	+	0.0632058i
$189$	−14.2268	+	3.69712i	−1.03485	+	0.268926i
$190$		0			0
$191$	10.2434	+	2.17730i	0.741184	+	0.157544i	0.563004	−	0.826454i	$-0.309646\pi$
$191$	10.2434	+	2.17730i	0.741184	+	0.157544i	0.178180	+	0.983998i	$0.442979\pi$
$192$	−4.90638	−	12.7816i	−0.354088	−	0.922430i
$193$	5.09648	−	19.0203i	0.366852	−	1.36911i	−0.498040	−	0.867154i	$-0.665947\pi$
$193$	5.09648	−	19.0203i	0.366852	−	1.36911i	0.864892	−	0.501957i	$-0.167387\pi$
$194$	−1.33006	−	12.6546i	−0.0954925	−	0.908551i
$195$		0			0
$196$	−1.53291	−	0.916179i	−0.109494	−	0.0654413i
$197$	14.1083	−	2.23453i	1.00517	−	0.159204i	0.367920	−	0.929858i	$-0.380070\pi$
$197$	14.1083	−	2.23453i	1.00517	−	0.159204i	0.637254	+	0.770654i	$0.280070\pi$
$198$	0.0181535	−	0.346389i	0.00129011	−	0.0246168i
$199$	3.58928	+	6.21681i	0.254437	+	0.440698i	0.964742	−	0.263196i	$-0.0847765\pi$
$199$	3.58928	+	6.21681i	0.254437	+	0.440698i	−0.710305	+	0.703894i	$0.751443\pi$
$200$		0			0
$201$	−17.6173	−	10.1714i	−1.24263	−	0.717432i
$202$	20.4413	−	10.4154i	1.43824	−	0.732822i
$203$	7.50605	−	6.65650i	0.526821	−	0.467195i
$204$	1.12701	−	1.55119i	0.0789062	−	0.108605i
$205$		0			0
$206$	−4.21696	+	9.47144i	−0.293809	+	0.659906i
$207$	−0.282205	−	0.0756165i	−0.0196146	−	0.00525571i
$208$	0.582652	+	0.471822i	0.0403996	+	0.0327150i
$209$	−0.794773	−	2.44606i	−0.0549756	−	0.169198i
$210$		0			0
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	−0.983271	−	0.182150i	$-0.941694\pi$
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	0.902548	+	0.430590i	$0.141694\pi$
$212$	1.03639	−	0.673042i	0.0711798	−	0.0462247i
$213$	−0.385476	−	7.35533i	−0.0264124	−	0.503979i
$214$	0.590202	+	2.77668i	0.0403454	+	0.189810i
$215$		0			0
$216$	15.7401	−	5.11428i	1.07098	−	0.347982i
$217$	5.26152	−	7.12800i	0.357175	−	0.483880i
$218$	10.2113	+	10.2113i	0.691600	+	0.691600i
$219$	−20.4258	+	2.14684i	−1.38025	+	0.145070i
$220$		0			0
$221$	−0.109835	+	1.04501i	−0.00738830	+	0.0702949i
$222$	14.7163	+	5.64905i	0.987692	+	0.379139i
$223$	1.74330	+	3.42142i	0.116740	+	0.229115i	0.941981	−	0.335665i	$-0.108961\pi$
$223$	1.74330	+	3.42142i	0.116740	+	0.229115i	−0.825242	+	0.564780i	$0.808961\pi$
$224$	3.36729	+	1.74788i	0.224986	+	0.116785i
$225$		0			0
$226$	−11.7423	+	20.3382i	−0.781085	+	1.35288i
$227$	1.63746	+	1.06338i	0.108682	+	0.0705788i	0.597836	−	0.801619i	$-0.296028\pi$
$227$	1.63746	+	1.06338i	0.108682	+	0.0705788i	−0.489154	+	0.872198i	$0.662694\pi$
$228$	1.66682	−	1.34976i	0.110388	−	0.0893901i
$229$	−10.0729	+	4.48475i	−0.665637	+	0.296361i	−0.711603	−	0.702582i	$-0.752030\pi$
$229$	−10.0729	+	4.48475i	−0.665637	+	0.296361i	0.0459653	+	0.998943i	$0.485364\pi$
$230$		0			0
$231$	−1.23722	−	1.55166i	−0.0814034	−	0.102092i
$232$	−7.98721	+	7.98721i	−0.524386	+	0.524386i
$233$	12.3061	−	15.1967i	0.806198	−	0.995571i	−0.193697	−	0.981061i	$-0.562048\pi$
$233$	12.3061	−	15.1967i	0.806198	−	0.995571i	0.999895	−	0.0145098i	$-0.00461877\pi$
$234$	−0.106070	+	0.117803i	−0.00693401	+	0.00770100i
$235$		0			0
$236$	−1.01493	+	0.913849i	−0.0660665	+	0.0594865i
$237$	6.58676	−	12.9273i	0.427856	−	0.839715i
$238$	−1.62735	−	16.6954i	−0.105486	−	1.08220i
$239$	−9.20533	−	2.99099i	−0.595443	−	0.193471i	−0.00423616	−	0.999991i	$-0.501348\pi$
$239$	−9.20533	−	2.99099i	−0.595443	−	0.193471i	−0.591207	+	0.806520i	$0.701348\pi$
$240$		0			0
$241$	−9.32794	−	8.39891i	−0.600865	−	0.541021i	0.311580	−	0.950220i	$-0.399142\pi$
$241$	−9.32794	−	8.39891i	−0.600865	−	0.541021i	−0.912445	+	0.409198i	$0.865808\pi$
$242$	−13.2822	+	5.09858i	−0.853815	+	0.327749i
$243$	1.45470	+	5.42901i	0.0933190	+	0.348271i
$244$	−1.83726	+	1.33484i	−0.117618	+	0.0854546i
$245$		0			0
$246$	4.71402	+	3.42494i	0.300555	+	0.218366i
$247$	−0.421223	+	1.09732i	−0.0268018	+	0.0698211i
$248$	−5.43281	+	8.36580i	−0.344984	+	0.531229i
$249$	12.8827	−	7.43785i	0.816410	−	0.471354i
$250$		0			0
$251$		−	15.3215i		−	0.967086i	−0.875321	−	0.483543i	$-0.839350\pi$
$251$		−	15.3215i		−	0.967086i	0.875321	−	0.483543i	$-0.160650\pi$
$252$	−0.187416	+	0.319024i	−0.0118061	+	0.0200966i
$253$	−0.0399398	−	0.252170i	−0.00251099	−	0.0158538i
$254$	10.0322	+	22.5327i	0.629478	+	1.41383i
$255$		0			0
$256$	−5.49862	−	2.44814i	−0.343664	−	0.153009i
$257$	−5.05092	+	1.35339i	−0.315068	+	0.0844221i	−0.412888	−	0.910782i	$-0.635480\pi$
$257$	−5.05092	+	1.35339i	−0.315068	+	0.0844221i	0.0978199	+	0.995204i	$0.468813\pi$
$258$	−2.76064	+	17.4300i	−0.171870	+	1.08514i
$259$	−18.8783	+	7.08357i	−1.17304	+	0.440152i
$260$		0			0
$261$	−1.39085	−	1.54470i	−0.0860914	−	0.0956142i
$262$	0.671111	−	0.0351714i	0.0414614	−	0.00217290i
$263$	11.6229	−	0.609132i	0.716701	−	0.0375607i	0.309500	−	0.950899i	$-0.399838\pi$
$263$	11.6229	−	0.609132i	0.716701	−	0.0375607i	0.407201	+	0.913339i	$0.366505\pi$
$264$	1.49511	+	1.66049i	0.0920177	+	0.102196i
$265$		0			0
$266$	3.07527	−	18.5104i	0.188557	−	1.13495i
$267$	1.43467	−	9.05817i	0.0878006	−	0.554351i
$268$	−3.20147	+	0.857832i	−0.195561	+	0.0524004i
$269$	−11.0120	−	4.90285i	−0.671412	−	0.298932i	0.0425725	−	0.999093i	$-0.486445\pi$
$269$	−11.0120	−	4.90285i	−0.671412	−	0.298932i	−0.713984	+	0.700162i	$0.753111\pi$
$270$		0			0
$271$	5.95538	+	13.3760i	0.361764	+	0.812535i	0.999119	+	0.0419648i	$0.0133617\pi$
$271$	5.95538	+	13.3760i	0.361764	+	0.812535i	−0.637355	+	0.770570i	$0.719972\pi$
$272$	2.57141	+	16.2352i	0.155915	+	0.984405i
$273$	−0.00685078	+	0.906920i	−0.000414628	+	0.0548893i
$274$			5.74694i			0.347185i
$275$		0			0
$276$	0.184386	−	0.106455i	0.0110987	−	0.00640785i
$277$	3.30097	−	5.08305i	0.198336	−	0.305411i	−0.725483	−	0.688240i	$-0.758384\pi$
$277$	3.30097	−	5.08305i	0.198336	−	0.305411i	0.923819	+	0.382829i	$0.125050\pi$
$278$	10.2842	−	26.7911i	0.616803	−	1.60683i
$279$	−1.48502	−	1.07893i	−0.0889060	−	0.0645940i
$280$		0			0
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	−0.693612	−	0.720349i	$-0.743982\pi$
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	0.470755	+	0.882264i	$0.343982\pi$
$282$	4.00563	+	14.9492i	0.238532	+	0.890212i
$283$	3.61407	−	1.38731i	0.214834	−	0.0824672i	−0.248571	−	0.968614i	$-0.579961\pi$
$283$	3.61407	−	1.38731i	0.214834	−	0.0824672i	0.463405	+	0.886147i	$0.346628\pi$
$284$	−0.891802	−	0.802982i	−0.0529187	−	0.0476482i
$285$		0			0
$286$	−0.131747	−	0.0428072i	−0.00779036	−	0.00253124i
$287$	−7.41824	+	0.723078i	−0.437885	+	0.0426820i
$288$	0.356858	−	0.700374i	0.0210281	−	0.0412699i
$289$	−4.48684	+	4.03997i	−0.263932	+	0.237645i
$290$		0			0
$291$	−10.0927	+	11.2091i	−0.591647	+	0.657091i
$292$	−2.10588	+	2.60055i	−0.123237	+	0.152186i
$293$	−10.8232	+	10.8232i	−0.632300	+	0.632300i	−0.948644	−	0.316344i	$-0.897545\pi$
$293$	−10.8232	+	10.8232i	−0.632300	+	0.632300i	0.316344	+	0.948644i	$0.397545\pi$
$294$	−2.79598	−	14.2061i	−0.163065	−	0.828515i
$295$		0			0
$296$	20.7396	−	9.23387i	1.20546	−	0.536708i
$297$	−2.06831	+	1.67489i	−0.120016	+	0.0971869i
$298$	−12.8046	−	8.31541i	−0.741751	−	0.481699i
$299$	−0.0583399	+	0.101048i	−0.00337388	+	0.00584374i
$300$		0			0
$301$	−12.1510	−	19.0240i	−0.700373	−	1.09652i
$302$	9.69850	+	19.0344i	0.558086	+	1.09531i
$303$	−25.3888	−	9.74584i	−1.45855	−	0.559884i
$304$	−1.92199	+	18.2865i	−0.110234	+	1.04880i
$305$		0			0
$306$	−3.45643	+	0.363286i	−0.197591	+	0.0207677i
$307$	−3.99596	−	3.99596i	−0.228061	−	0.228061i	0.583821	−	0.811882i	$-0.301557\pi$
$307$	−3.99596	−	3.99596i	−0.228061	−	0.228061i	−0.811882	+	0.583821i	$0.801557\pi$
$308$	−0.321302	−	0.0362260i	−0.0183079	−	0.00206417i
$309$	11.6884	−	3.79779i	0.664929	−	0.216049i
$310$		0			0
$311$	0.200656	+	0.944012i	0.0113782	+	0.0535300i	0.983470	−	0.181069i	$-0.0579557\pi$
$311$	0.200656	+	0.944012i	0.0113782	+	0.0535300i	−0.972092	+	0.234599i	$0.924622\pi$
$312$	−0.0534423	−	1.01974i	−0.00302557	−	0.0577314i
$313$	0.327398	−	0.212615i	0.0185056	−	0.0120177i	−0.535353	−	0.844628i	$-0.679821\pi$
$313$	0.327398	−	0.212615i	0.0185056	−	0.0120177i	0.553859	+	0.832611i	$0.313155\pi$
$314$	1.64954	−	5.07677i	0.0930891	−	0.286499i
$315$		0			0
$316$	−0.730474	−	2.24817i	−0.0410924	−	0.126469i
$317$	−23.3828	−	18.9350i	−1.31331	−	1.06350i	−0.993237	−	0.116105i	$-0.962959\pi$
$317$	−23.3828	−	18.9350i	−1.31331	−	1.06350i	−0.320073	−	0.947393i	$-0.603707\pi$
$318$	9.67749	+	2.59308i	0.542687	+	0.145413i
$319$	0.738814	−	1.65940i	0.0413657	−	0.0929088i
$320$		0			0
$321$	1.97789	−	2.72234i	0.110395	−	0.151946i
$322$	0.588968	−	1.76713i	0.0328219	−	0.0984781i
$323$	−22.9613	+	11.6994i	−1.27760	+	0.650970i
$324$	−1.55873	−	0.899935i	−0.0865962	−	0.0499964i
$325$		0			0
$326$	11.0281	+	19.1013i	0.610792	+	1.05792i
$327$	0.895903	−	17.0948i	0.0495435	−	0.945347i
$328$	8.28853	−	1.31277i	0.457658	−	0.0724859i
$329$	−16.5211	−	10.9072i	−0.910836	−	0.601334i
$330$		0			0
$331$	0.925838	+	8.80876i	0.0508887	+	0.484173i	0.990052	+	0.140702i	$0.0449360\pi$
$331$	0.925838	+	8.80876i	0.0508887	+	0.484173i	−0.939163	+	0.343471i	$0.888397\pi$
$332$	0.627294	−	2.34109i	0.0344272	−	0.128484i
$333$	1.49713	+	3.90015i	0.0820421	+	0.213727i
$334$	30.8143	+	6.54978i	1.68608	+	0.358388i
$335$		0			0
$336$	3.56844	+	13.7317i	0.194674	+	0.749125i
$337$	−17.6659	−	9.00124i	−0.962324	−	0.490329i	−0.0990602	−	0.995081i	$-0.531584\pi$
$337$	−17.6659	−	9.00124i	−0.962324	−	0.490329i	−0.863264	+	0.504753i	$0.831584\pi$
$338$	−9.31818	−	14.3487i	−0.506842	−	0.780468i
$339$	27.2301	−	5.78794i	1.47894	−	0.314358i
$340$		0			0
$341$	0.333509	−	1.56903i	0.0180605	−	0.0849680i
$342$	−3.83982	−	0.608168i	−0.207634	−	0.0328860i
$343$	14.7327	+	11.2226i	0.795490	+	0.605966i
$344$	14.9389	+	20.5617i	0.805453	+	1.10861i
$345$		0			0
$346$	−32.1563	−	3.37976i	−1.72873	−	0.181697i
$347$	0.632254	+	0.780769i	0.0339412	+	0.0419139i	0.793834	−	0.608135i	$-0.208082\pi$
$347$	0.632254	+	0.780769i	0.0339412	+	0.0419139i	−0.759893	+	0.650048i	$0.774749\pi$
$348$	1.51269	+	0.0792768i	0.0810888	+	0.00424968i
$349$	22.8601			1.22367			0.611835	−	0.790985i	$-0.290431\pi$
$349$	22.8601			1.22367			0.611835	+	0.790985i	$0.290431\pi$
$350$		0			0
$351$	1.21629			0.0649206
$352$	0.685972	+	0.0359503i	0.0365624	+	0.00191616i
$353$	11.0455	+	13.6401i	0.587893	+	0.725988i	0.981108	−	0.193459i	$-0.0619705\pi$
$353$	11.0455	+	13.6401i	0.587893	+	0.725988i	−0.393215	+	0.919447i	$0.628637\pi$
$354$	−11.0119	−	1.15740i	−0.585278	−	0.0615152i
$355$		0			0
$356$	−0.878288	−	1.20886i	−0.0465491	−	0.0640694i
$357$	−13.4165	+	14.6761i	−0.710078	+	0.776742i
$358$	−23.0942	−	3.65776i	−1.22056	−	0.193318i
$359$	6.02179	−	28.3303i	0.317818	−	1.49522i	−0.471848	−	0.881680i	$-0.656413\pi$
$359$	6.02179	−	28.3303i	0.317818	−	1.49522i	0.789666	−	0.613537i	$-0.210254\pi$
$360$		0			0
$361$	−9.61183	+	2.04306i	−0.505886	+	0.107529i
$362$	0.682466	+	1.05091i	0.0358696	+	0.0552344i
$363$	15.0267	+	7.65648i	0.788697	+	0.401861i
$364$	0.103695	+	0.105274i	0.00543510	+	0.00551784i
$365$		0			0
$366$	−18.0095	−	3.82804i	−0.941372	−	0.200095i
$367$	5.94229	+	15.4802i	0.310185	+	0.808060i	0.996717	+	0.0809605i	$0.0257987\pi$
$367$	5.94229	+	15.4802i	0.310185	+	0.808060i	−0.686532	+	0.727099i	$0.740868\pi$
$368$	−0.472416	+	1.76308i	−0.0246264	+	0.0919069i
$369$	0.161418	+	1.53579i	0.00840308	+	0.0799500i
$370$		0			0
$371$	−11.4624	+	5.73175i	−0.595100	+	0.297578i
$372$	1.32121	−	0.209259i	0.0685016	−	0.0108496i
$373$	1.53470	−	29.2838i	0.0794637	−	1.51626i	−0.610269	−	0.792194i	$-0.708939\pi$
$373$	1.53470	−	29.2838i	0.0794637	−	1.51626i	0.689733	−	0.724064i	$-0.257728\pi$
$374$	−1.51858	−	2.63025i	−0.0785237	−	0.136007i
$375$		0			0
$376$	19.3032	+	11.1447i	0.995486	+	0.574744i
$377$	−0.739648	+	0.376870i	−0.0380938	+	0.0194098i
$378$	−19.0226	+	3.89343i	−0.978418	+	0.200257i
$379$	10.6445	−	14.6509i	0.546773	−	0.752568i	−0.442797	−	0.896622i	$-0.646014\pi$
$379$	10.6445	−	14.6509i	0.546773	−	0.752568i	0.989570	+	0.144054i	$0.0460137\pi$
$380$		0			0
$381$	11.8921	−	26.7102i	0.609253	−	1.36840i
$382$	13.3618	+	3.58028i	0.683649	+	0.183183i
$383$	23.1844	+	18.7744i	1.18467	+	0.959326i	0.999726	−	0.0234230i	$-0.00745644\pi$
$383$	23.1844	+	18.7744i	1.18467	+	0.959326i	0.184944	+	0.982749i	$0.440790\pi$
$384$	−4.20083	−	12.9288i	−0.214373	−	0.659771i
$385$		0			0
$386$	8.03783	−	24.7379i	0.409115	−	1.25913i
$387$	−3.92240	+	2.54723i	−0.199387	+	0.129483i
$388$	0.128616	+	2.45414i	0.00652950	+	0.124590i
$389$	2.34616	+	11.0378i	0.118955	+	0.559639i	0.996747	+	0.0805966i	$0.0256826\pi$
$389$	2.34616	+	11.0378i	0.118955	+	0.559639i	−0.877792	+	0.479042i	$0.840984\pi$
$390$		0			0
$391$	−2.43296	+	0.790515i	−0.123040	+	0.0399781i
$392$	−17.3145	−	11.6198i	−0.874515	−	0.586887i
$393$	−0.563297	−	0.563297i	−0.0284146	−	0.0284146i
$394$	18.7651	−	1.97230i	0.945374	−	0.0993628i
$395$		0			0
$396$	−0.00700251	+	0.0666244i	−0.000351889	+	0.00334800i
$397$	−4.63333	−	1.77857i	−0.232540	−	0.0892638i	0.239308	−	0.970944i	$-0.423080\pi$
$397$	−4.63333	−	1.77857i	−0.232540	−	0.0892638i	−0.471848	+	0.881680i	$0.656413\pi$
$398$	4.30493	+	8.44891i	0.215787	+	0.423505i
$399$	−18.7454	+	11.9731i	−0.938445	+	0.599404i
$400$		0			0
$401$	2.20052	−	3.81142i	0.109889	−	0.190333i	−0.805836	−	0.592139i	$-0.798284\pi$
$401$	2.20052	−	3.81142i	0.109889	−	0.190333i	0.915725	+	0.401805i	$0.131617\pi$
$402$	−22.5363	−	14.6353i	−1.12401	−	0.729940i
$403$	−0.569709	+	0.461341i	−0.0283792	+	0.0229810i
$404$	−4.04779	+	1.80219i	−0.201385	+	0.0896624i
$405$		0			0
$406$	10.3616	−	8.26188i	0.514239	−	0.410030i
$407$	−2.58147	+	2.58147i	−0.127959	+	0.127959i
$408$	14.0893	−	17.3988i	0.697523	−	0.861369i
$409$	−0.144146	+	0.160091i	−0.00712759	+	0.00791599i	−0.746698	−	0.665163i	$-0.768362\pi$
$409$	−0.144146	+	0.160091i	−0.00712759	+	0.00791599i	0.739570	+	0.673079i	$0.235029\pi$
$410$		0			0
$411$	5.06259	−	4.55837i	0.249719	−	0.224848i
$412$	0.909060	−	1.78413i	0.0447862	−	0.0878978i
$413$	11.5211	−	8.23829i	0.566914	−	0.405380i
$414$	−0.367037	−	0.119258i	−0.0180389	−	0.00586119i
$415$		0			0
$416$	−0.233291	−	0.210056i	−0.0114380	−	0.0102988i
$417$	−31.7580	+	12.1908i	−1.55520	+	0.596985i
$418$	−0.879306	−	3.28162i	−0.0430083	−	0.160509i
$419$	−28.0621	+	20.3883i	−1.37092	+	0.996034i	−0.373259	+	0.927727i	$0.621760\pi$
$419$	−28.0621	+	20.3883i	−1.37092	+	0.996034i	−0.997664	+	0.0683067i	$0.978240\pi$
$420$		0			0
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.992723	−	0.120419i	$-0.0384239\pi$
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.192243	+	0.981347i	$0.438424\pi$
$422$	−1.79626	+	4.67942i	−0.0874405	+	0.227790i
$423$	−2.23391	+	3.43993i	−0.108617	+	0.167255i
$424$	12.4961	−	7.21461i	0.606863	−	0.350373i
$425$		0			0
$426$		−	9.72928i		−	0.471385i
$427$	20.4845	−	11.6213i	0.991316	−	0.562396i
$428$	−0.0857658	−	0.541504i	−0.00414565	−	0.0261746i
$429$	0.0667898	+	0.150012i	0.00322464	+	0.00724267i
$430$		0			0
$431$	31.9852	+	14.2407i	1.54067	+	0.685952i	0.988974	−	0.148092i	$-0.0473130\pi$
$431$	31.9852	+	14.2407i	1.54067	+	0.685952i	0.551699	+	0.834043i	$0.313980\pi$
$432$	18.3786	−	4.92453i	0.884241	−	0.236932i
$433$	−0.905859	+	5.71937i	−0.0435328	+	0.274855i	−0.999847	−	0.0174852i	$-0.994434\pi$
$433$	−0.905859	+	5.71937i	−0.0435328	+	0.274855i	0.956314	+	0.292340i	$0.0944340\pi$
$434$	7.43340	−	9.03901i	0.356815	−	0.433887i
$435$		0			0
$436$	−1.86625	−	2.07268i	−0.0893770	−	0.0992632i
$437$	−2.85765	+	0.149763i	−0.136700	+	0.00716415i
$438$	−27.0927	+	1.41987i	−1.29454	+	0.0678439i
$439$	12.8713	+	14.2950i	0.614312	+	0.682263i	0.967379	−	0.253335i	$-0.0815276\pi$
$439$	12.8713	+	14.2950i	0.614312	+	0.682263i	−0.353066	+	0.935598i	$0.614861\pi$
$440$		0			0
$441$	2.30207	−	3.06990i	0.109622	−	0.146186i
$442$	−0.217131	+	1.37091i	−0.0103279	+	0.0652075i
$443$	−14.8917	+	3.99023i	−0.707527	+	0.189581i	−0.594600	−	0.804022i	$-0.702689\pi$
$443$	−14.8917	+	3.99023i	−0.707527	+	0.189581i	−0.112928	+	0.993603i	$0.536023\pi$
$444$	−2.78123	−	1.23828i	−0.131991	−	0.0587663i
$445$		0			0
$446$	2.06310	+	4.63381i	0.0976908	+	0.219417i
$447$	2.83120	+	17.8755i	0.133911	+	0.845481i
$448$	19.9460	+	11.7176i	0.942360	+	0.553605i
$449$			14.1182i			0.666281i	0.942877	+	0.333140i	$0.108108\pi$
$449$			14.1182i			0.666281i	−0.942877	+	0.333140i	$0.891892\pi$
$450$		0			0
$451$	−1.16869	+	0.674745i	−0.0550316	+	0.0317725i
$452$	2.47031	−	3.80394i	0.116194	−	0.178922i
$453$	9.07506	−	23.6413i	0.426384	−	1.11077i
$454$	2.08650	+	1.51593i	0.0979245	+	0.0711463i
$455$		0			0
$456$	20.2606	−	14.7202i	0.948789	−	0.689335i
$457$	−7.49556	−	27.9738i	−0.350627	−	1.30856i	−0.885899	−	0.463879i	$-0.846457\pi$
$457$	−7.49556	−	27.9738i	−0.350627	−	1.30856i	0.535271	−	0.844680i	$-0.320209\pi$
$458$	−13.5975	+	5.21960i	−0.635371	+	0.243896i
$459$	19.8172	+	17.8435i	0.924987	+	0.832862i
$460$		0			0
$461$	−30.3418	−	9.85863i	−1.41316	−	0.459162i	−0.499735	−	0.866178i	$-0.666569\pi$
$461$	−30.3418	−	9.85863i	−1.41316	−	0.459162i	−0.913421	+	0.407016i	$0.866569\pi$
$462$	−1.52479	−	2.13238i	−0.0709395	−	0.0992072i
$463$	1.68874	−	3.31433i	0.0784822	−	0.154030i	−0.848431	−	0.529306i	$-0.822452\pi$
$463$	1.68874	−	3.31433i	0.0784822	−	0.154030i	0.926913	+	0.375276i	$0.122452\pi$
$464$	−9.65052	+	8.68936i	−0.448014	+	0.403394i
$465$		0			0
$466$	17.2839	−	19.1957i	0.800661	−	0.889224i
$467$	−4.47456	+	5.52562i	−0.207058	+	0.255695i	−0.870087	−	0.492899i	$-0.835937\pi$
$467$	−4.47456	+	5.52562i	−0.207058	+	0.255695i	0.663029	+	0.748594i	$0.269271\pi$
$468$	0.0216484	−	0.0216484i	0.00100070	−	0.00100070i
$469$	33.9891	−	5.12046i	1.56947	−	0.236441i
$470$		0			0
$471$	−5.78062	+	2.57370i	−0.266357	+	0.118590i
$472$	−12.3930	+	10.0356i	−0.570433	+	0.461928i
$473$	−3.42771	−	2.22598i	−0.157606	−	0.102351i
$474$	9.58249	−	16.5974i	0.440138	−	0.762342i
$475$		0			0
$476$	0.145112	+	3.23649i	0.00665119	+	0.148344i
$477$	1.20545	+	2.36583i	0.0551938	+	0.108324i
$478$	−11.9362	−	4.58189i	−0.545951	−	0.209571i
$479$	1.20444	−	11.4595i	0.0550324	−	0.523598i	−0.931929	−	0.362641i	$-0.881875\pi$
$479$	1.20444	−	11.4595i	0.0550324	−	0.523598i	0.986961	−	0.160957i	$-0.0514581\pi$
$480$		0			0
$481$	1.65928	−	0.174397i	0.0756566	−	0.00795182i
$482$	−11.7241	−	11.7241i	−0.534019	−	0.534019i
$483$	−2.02385	+	0.882821i	−0.0920886	+	0.0401697i
$484$	2.61328	−	0.849107i	0.118786	−	0.0385958i
$485$		0			0
$486$	1.54361	+	7.26214i	0.0700198	+	0.329417i
$487$	−0.229004	−	4.36966i	−0.0103772	−	0.198008i	−0.998898	−	0.0469259i	$-0.985058\pi$
$487$	−0.229004	−	4.36966i	−0.0103772	−	0.198008i	0.988521	−	0.151082i	$-0.0482758\pi$
$488$	−22.2389	+	14.4421i	−1.00671	+	0.653763i
$489$	8.07937	−	24.8657i	0.365362	−	1.12447i
$490$		0			0
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	0.995545	−	0.0942867i	$-0.0300570\pi$
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	−0.860833	+	0.508887i	$0.830057\pi$
$492$	−0.874574	−	0.708216i	−0.0394288	−	0.0319288i
$493$	−17.5801	−	4.71056i	−0.791766	−	0.212153i
$494$	−0.631509	+	1.41839i	−0.0284129	+	0.0638165i
$495$		0			0
$496$	−6.74065	+	9.27771i	−0.302664	+	0.416582i
$497$	8.25735	+	9.31121i	0.370393	+	0.417665i
$498$	17.5082	−	8.92087i	0.784561	−	0.399754i
$499$	4.09112	+	2.36201i	0.183144	+	0.105738i	0.588769	−	0.808301i	$-0.299613\pi$
$499$	4.09112	+	2.36201i	0.183144	+	0.105738i	−0.405625	+	0.914040i	$0.632946\pi$
$500$		0			0
$501$	−18.6716	−	32.3401i	−0.834184	−	1.44485i
$502$	1.05922	−	20.2111i	0.0472752	−	0.902064i
$503$	−3.93410	+	0.623100i	−0.175413	+	0.0277826i	−0.243523	−	0.969895i	$-0.578303\pi$
$503$	−3.93410	+	0.623100i	−0.175413	+	0.0277826i	0.0681101	+	0.997678i	$0.478303\pi$
$504$	−2.38030	+	3.60543i	−0.106027	+	0.160598i
$505$		0			0
$506$	−0.0352526	−	0.335406i	−0.00156717	−	0.0149106i
$507$	−5.24905	+	19.5897i	−0.233119	+	0.870011i
$508$	−1.70716	−	4.44729i	−0.0757428	−	0.197317i
$509$	−2.23882	−	0.475875i	−0.0992337	−	0.0210928i	0.158027	−	0.987435i	$-0.449487\pi$
$509$	−2.23882	−	0.475875i	−0.0992337	−	0.0210928i	−0.257261	+	0.966342i	$0.582820\pi$
$510$		0			0
$511$	24.7235	−	24.3528i	1.09370	−	1.07730i
$512$	−22.5551	−	11.4924i	−0.996806	−	0.507898i
$513$	16.2463	+	25.0171i	0.717292	+	1.10453i
$514$	−6.75638	+	1.43611i	−0.298011	+	0.0633442i
$515$		0			0
$516$	0.708624	−	3.33381i	0.0311954	−	0.146763i
$517$	−3.54022	−	0.560716i	−0.155699	−	0.0246603i
$518$	−25.3927	+	8.03903i	−1.11569	+	0.353215i
$519$	22.5285	+	31.0079i	0.988893	+	1.36109i
$520$		0			0
$521$	−13.4075	−	1.40918i	−0.587391	−	0.0617373i	−0.193829	−	0.981035i	$-0.562091\pi$
$521$	−13.4075	−	1.40918i	−0.587391	−	0.0617373i	−0.393562	+	0.919298i	$0.628757\pi$
$522$	−1.72792	−	2.13381i	−0.0756291	−	0.0933941i
$523$	6.81583	+	0.357203i	0.298036	+	0.0156194i	0.200768	−	0.979639i	$-0.435656\pi$
$523$	6.81583	+	0.357203i	0.298036	+	0.0156194i	0.0972678	+	0.995258i	$0.468990\pi$
$524$	−0.129793			−0.00567001
$525$		0			0
$526$	15.3743			0.670350
$527$	−16.0504	−	0.841168i	−0.699168	−	0.0366419i
$528$	1.61660	+	1.99633i	0.0703533	+	0.0868791i
$529$	22.5915	+	2.37446i	0.982239	+	0.103237i
$530$		0			0
$531$	−1.72485	−	2.37405i	−0.0748521	−	0.103025i
$532$	−0.780227	+	3.53902i	−0.0338271	+	0.153436i
$533$	0.609133	+	0.0964772i	0.0263845	+	0.00417889i
$534$	2.51874	−	11.8497i	0.108996	−	0.512788i
$535$		0			0
$536$	−37.8547	+	8.04627i	−1.63507	+	0.347546i
$537$	15.0957	+	23.2454i	0.651428	+	1.00311i
$538$	−14.1873	−	7.22877i	−0.611657	−	0.311655i
$539$	3.26904	+	0.746645i	0.140808	+	0.0321603i
$540$		0			0
$541$	7.46757	+	1.58728i	0.321056	+	0.0682425i	0.365621	−	0.930764i	$-0.380857\pi$
$541$	7.46757	+	1.58728i	0.321056	+	0.0682425i	−0.0445647	+	0.999006i	$0.514190\pi$
$542$	6.93120	+	18.0564i	0.297721	+	0.775589i
$543$	0.384442	−	1.43476i	0.0164980	−	0.0615714i
$544$	−0.719434	−	6.84496i	−0.0308455	−	0.293475i
$545$		0			0
$546$	−0.0717348	+	1.19587i	−0.00306997	+	0.0511786i
$547$	41.0298	−	6.49848i	1.75431	−	0.277855i	0.805244	−	0.592944i	$-0.202034\pi$
$547$	41.0298	−	6.49848i	1.75431	−	0.277855i	0.949062	+	0.315089i	$0.102034\pi$
$548$	0.0580893	−	1.10841i	0.00248145	−	0.0473490i
$549$	−2.43978	−	4.22582i	−0.104127	−	0.180354i
$550$		0			0
$551$	−17.6313	−	10.1794i	−0.751119	−	0.433659i
$552$	2.21507	−	1.12863i	0.0942797	−	0.0480379i
$553$	4.91564	+	24.0169i	0.209034	+	1.02130i
$554$	4.70581	−	6.47699i	0.199931	−	0.275181i
$555$		0			0
$556$	−2.25430	+	5.06325i	−0.0956038	+	0.214730i
$557$	−13.7087	−	3.67322i	−0.580855	−	0.155640i	−0.0435845	−	0.999050i	$-0.513878\pi$
$557$	−13.7087	−	3.67322i	−0.580855	−	0.155640i	−0.537270	+	0.843410i	$0.680544\pi$
$558$	−1.88435	−	1.52591i	−0.0797708	−	0.0645971i
$559$	0.577188	+	1.77640i	0.0244125	+	0.0751338i
$560$		0			0
$561$	−1.11253	+	3.42401i	−0.0469710	+	0.144562i
$562$	−5.11560	+	3.32211i	−0.215789	+	0.140135i
$563$	−2.19797	−	41.9397i	−0.0926332	−	1.76755i	−0.511295	−	0.859405i	$-0.670834\pi$
$563$	−2.19797	−	41.9397i	−0.0926332	−	1.76755i	0.418662	−	0.908142i	$-0.362499\pi$
$564$	−0.621460	−	2.92374i	−0.0261682	−	0.123112i
$565$		0			0
$566$	4.86334	−	1.58019i	0.204421	−	0.0664205i
$567$	15.0177	+	11.0852i	0.630682	+	0.465537i
$568$	−9.90808	−	9.90808i	−0.415734	−	0.415734i
$569$	23.3390	−	2.45303i	0.978423	−	0.102836i	0.398204	−	0.917297i	$-0.369634\pi$
$569$	23.3390	−	2.45303i	0.978423	−	0.102836i	0.580219	+	0.814460i	$0.302967\pi$
$570$		0			0
$571$	1.01109	−	9.61986i	0.0423127	−	0.402579i	−0.952782	−	0.303654i	$-0.901793\pi$
$571$	1.01109	−	9.61986i	0.0423127	−	0.402579i	0.995095	−	0.0989242i	$-0.0315401\pi$
$572$	0.0249773	+	0.00958790i	0.00104435	+	0.000400890i
$573$	−7.44442	−	14.6105i	−0.310995	−	0.610362i
$574$	−9.83561	+	0.440991i	−0.410530	+	0.0184066i
$575$		0			0
$576$	2.39645	−	4.15077i	0.0998521	−	0.172949i
$577$	1.40202	+	0.910483i	0.0583669	+	0.0379039i	0.573493	−	0.819211i	$-0.305588\pi$
$577$	1.40202	+	0.910483i	0.0583669	+	0.0379039i	−0.515126	+	0.857115i	$0.672255\pi$
$578$	−6.19802	+	5.01906i	−0.257804	+	0.208765i
$579$	−28.1676	+	12.5410i	−1.17060	+	0.521187i
$580$		0			0
$581$	−9.18461	+	23.3969i	−0.381042	+	0.970668i
$582$	−14.0886	+	14.0886i	−0.583989	+	0.583989i
$583$	−1.46025	+	1.80326i	−0.0604774	+	0.0746833i
$584$	−26.1446	+	29.0366i	−1.08187	+	1.20154i
$585$		0			0
$586$	−15.0255	+	13.5290i	−0.620697	+	0.558878i
$587$	−0.277321	+	0.544273i	−0.0114463	+	0.0224646i	−0.896659	−	0.442722i	$-0.854013\pi$
$587$	−0.277321	+	0.544273i	−0.0114463	+	0.0224646i	0.885213	+	0.465187i	$0.154013\pi$
$588$	0.395667	+	2.76818i	0.0163170	+	0.114158i
$589$	−17.0988	−	5.55575i	−0.704545	−	0.228921i
$590$		0			0
$591$	−16.6216	−	14.9662i	−0.683722	−	0.615626i
$592$	24.3663	−	9.35334i	1.00145	−	0.384420i
$593$	−6.55597	−	24.4672i	−0.269221	−	1.00475i	−0.959616	−	0.281314i	$-0.909230\pi$
$593$	−6.55597	−	24.4672i	−0.269221	−	1.00475i	0.690394	−	0.723433i	$-0.257437\pi$
$594$	−2.84416	+	2.06641i	−0.116697	+	0.0847857i
$595$		0			0
$596$	2.38557	+	1.73322i	0.0977168	+	0.0709954i
$597$	4.02820	−	10.4938i	0.164863	−	0.429484i
$598$	−0.0839435	+	0.129262i	−0.00343271	+	0.00528591i
$599$	2.55964	−	1.47781i	0.104584	−	0.0603816i	−0.446796	−	0.894636i	$-0.647435\pi$
$599$	2.55964	−	1.47781i	0.104584	−	0.0603816i	0.551380	+	0.834254i	$0.314102\pi$
$600$		0			0
$601$			2.33505i			0.0952489i	0.998865	+	0.0476244i	$0.0151651\pi$
$601$			2.33505i			0.0952489i	−0.998865	+	0.0476244i	$0.984835\pi$
$602$	−14.7136	−	25.9351i	−0.599681	−	1.05704i
$603$	−1.11406	−	7.03388i	−0.0453679	−	0.286442i
$604$	−1.67815	−	3.76919i	−0.0682830	−	0.153366i
$605$		0			0
$606$	−32.8173	−	14.6112i	−1.33311	−	0.593540i
$607$	18.6437	−	4.99555i	0.756723	−	0.202763i	0.140225	−	0.990120i	$-0.455218\pi$
$607$	18.6437	−	4.99555i	0.756723	−	0.202763i	0.616498	+	0.787356i	$0.288551\pi$
$608$	1.20439	−	7.60420i	0.0488444	−	0.308391i
$609$	−15.4967	−	2.57458i	−0.627959	−	0.104327i
$610$		0			0
$611$	1.09608	+	1.21732i	0.0443428	+	0.0492477i
$612$	0.670314	−	0.0351296i	0.0270958	−	0.00142003i
$613$	9.88907	−	0.518264i	0.399416	−	0.0209325i	0.148429	−	0.988923i	$-0.452578\pi$
$613$	9.88907	−	0.518264i	0.399416	−	0.0209325i	0.250987	+	0.967991i	$0.419245\pi$
$614$	−4.99493	−	5.54743i	−0.201579	−	0.223876i
$615$		0			0
$616$	−3.72438	−	0.618757i	−0.150059	−	0.0249304i
$617$	−0.868493	+	5.48345i	−0.0349642	+	0.220755i	−0.998984	−	0.0450769i	$-0.985647\pi$
$617$	−0.868493	+	5.48345i	−0.0349642	+	0.220755i	0.964019	+	0.265832i	$0.0856467\pi$
$618$	15.6810	−	4.20172i	0.630784	−	0.169018i
$619$	−34.8010	−	15.4944i	−1.39877	−	0.622772i	−0.437710	−	0.899116i	$-0.644210\pi$
$619$	−34.8010	−	15.4944i	−1.39877	−	0.622772i	−0.961059	+	0.276344i	$0.910877\pi$
$620$		0			0
$621$	1.20440	+	2.70513i	0.0483310	+	0.108553i
$622$	0.199429	+	1.25915i	0.00799638	+	0.0504872i
$623$	7.64649	+	13.4782i	0.306350	+	0.539993i
$624$		−	1.17396i		−	0.0469959i
$625$		0			0
$626$	0.446579	−	0.257833i	0.0178489	−	0.0103051i
$627$	−2.19339	+	3.37752i	−0.0875954	+	0.134885i
$628$	−0.369462	+	0.962483i	−0.0147432	+	0.0384072i
$629$	29.5934	+	21.5008i	1.17997	+	0.857295i
$630$		0			0
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	−0.791623	−	0.611010i	$-0.790764\pi$
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	0.336480	+	0.941691i	$0.390764\pi$
$632$	−7.14378	−	26.6610i	−0.284164	−	1.06052i
$633$	5.54695	−	2.12927i	0.220471	−	0.0846311i
$634$	−29.5359	−	26.5943i	−1.17302	−	1.05619i
$635$		0			0
$636$	−1.84029	−	0.597945i	−0.0729721	−	0.0237101i
$637$	−0.946298	−	1.20537i	−0.0374937	−	0.0477584i
$638$	1.08931	−	2.13789i	0.0431262	−	0.0846400i
$639$	1.91618	−	1.72534i	0.0758031	−	0.0682534i
$640$		0			0
$641$	5.18908	−	5.76306i	0.204956	−	0.227627i	−0.631900	−	0.775050i	$-0.717724\pi$
$641$	5.18908	−	5.76306i	0.204956	−	0.227627i	0.836856	+	0.547423i	$0.184391\pi$
$642$	2.79730	−	3.45438i	0.110401	−	0.136333i
$643$	16.8674	−	16.8674i	0.665185	−	0.665185i	−0.291412	−	0.956598i	$-0.594125\pi$
$643$	16.8674	−	16.8674i	0.665185	−	0.665185i	0.956598	+	0.291412i	$0.0941251\pi$
$644$	−0.131456	+	0.334872i	−0.00518010	+	0.0131958i
$645$		0			0
$646$	−31.0977	+	13.8456i	−1.22352	+	0.544748i
$647$	−23.5210	+	19.0469i	−0.924704	+	0.748811i	−0.968183	−	0.250244i	$-0.919489\pi$
$647$	−23.5210	+	19.0469i	−0.924704	+	0.748811i	0.0434786	+	0.999054i	$0.486156\pi$
$648$	−17.6255	−	11.4461i	−0.692396	−	0.449647i
$649$	1.28220	−	2.22083i	0.0503307	−	0.0871754i
$650$		0			0
$651$	−13.8587	+	0.621370i	−0.543165	+	0.0243534i
$652$	−1.93392	−	3.79554i	−0.0757383	−	0.148645i
$653$	−31.3427	−	12.0313i	−1.22654	−	0.470823i	−0.343066	−	0.939311i	$-0.611465\pi$
$653$	−31.3427	−	12.0313i	−1.22654	−	0.470823i	−0.883470	+	0.468488i	$0.844799\pi$
$654$	2.36362	−	22.4884i	0.0924250	−	0.879365i
$655$		0			0
$656$	9.59487	−	1.00846i	0.374617	−	0.0393738i
$657$	−5.08413	−	5.08413i	−0.198351	−	0.198351i
$658$	−21.0394	−	15.5302i	−0.820201	−	0.605429i
$659$	−45.9853	+	14.9415i	−1.79133	+	0.582039i	−0.999585	−	0.0288108i	$-0.990828\pi$
$659$	−45.9853	+	14.9415i	−1.79133	+	0.582039i	−0.791747	+	0.610850i	$0.790828\pi$
$660$		0			0
$661$	1.42228	+	6.69130i	0.0553203	+	0.260262i	0.997113	−	0.0759328i	$-0.0241934\pi$
$661$	1.42228	+	6.69130i	0.0553203	+	0.260262i	−0.941793	+	0.336194i	$0.890860\pi$
$662$	0.612327	+	11.6839i	0.0237988	+	0.454108i
$663$	1.37988	−	0.896108i	0.0535903	−	0.0348019i
$664$	8.74513	−	26.9148i	0.339377	−	1.04450i
$665$		0			0
$666$	1.70528	+	5.24830i	0.0660781	+	0.203368i
$667$	−1.57061	−	1.27186i	−0.0608143	−	0.0492465i
$668$	−5.87694	−	1.57472i	−0.227386	−	0.0609278i
$669$	2.44559	−	5.49289i	0.0945520	−	0.212367i
$670$		0			0
$671$	2.50641	−	3.44978i	0.0967589	−	0.133177i
$672$	−1.19120	−	5.81997i	−0.0459514	−	0.224510i
$673$	25.2746	−	12.8780i	0.974263	−	0.496412i	0.106999	−	0.994259i	$-0.465876\pi$
$673$	25.2746	−	12.8780i	0.974263	−	0.496412i	0.867265	+	0.497847i	$0.165876\pi$
$674$	−22.6814	−	13.0951i	−0.873653	−	0.504404i
$675$		0			0
$676$	1.65216	+	2.86163i	0.0635446	+	0.110063i
$677$	0.659688	−	12.5876i	0.0253539	−	0.483780i	−0.956214	−	0.292668i	$-0.905457\pi$
$677$	0.659688	−	12.5876i	0.0253539	−	0.483780i	0.981568	−	0.191113i	$-0.0612096\pi$
$678$	36.3202	−	5.75255i	1.39487	−	0.220925i
$679$	1.52605	−	25.4403i	0.0585643	−	0.976308i
$680$		0			0
$681$	−0.319565	−	3.04046i	−0.0122457	−	0.116510i
$682$	0.548413	−	2.04670i	0.0209998	−	0.0783723i
$683$	−1.82579	−	4.75634i	−0.0698619	−	0.181996i	0.894204	−	0.447660i	$-0.147742\pi$
$683$	−1.82579	−	4.75634i	−0.0698619	−	0.181996i	−0.964066	+	0.265663i	$0.914409\pi$
$684$	0.734439	+	0.156110i	0.0280820	+	0.00596900i
$685$		0			0
$686$	18.6585	+	15.8226i	0.712384	+	0.604111i
$687$	15.3834	+	7.83822i	0.586912	+	0.299047i
$688$	15.9139	+	24.5053i	0.606712	+	0.934254i
$689$	1.03725	−	0.220474i	0.0395159	−	0.00839937i
$690$		0			0
$691$	2.60404	−	12.2510i	0.0990622	−	0.466051i	−0.900454	−	0.434951i	$-0.856766\pi$
$691$	2.60404	−	12.2510i	0.0990622	−	0.466051i	0.999516	−	0.0310999i	$-0.00990101\pi$
$692$	6.16782	+	0.976886i	0.234465	+	0.0371356i
$693$	0.149575	−	0.678453i	0.00568187	−	0.0257723i
$694$	0.780048	+	1.07364i	0.0296102	+	0.0407550i
$695$		0			0
$696$	17.5902	+	1.84880i	0.666753	+	0.0700786i
$697$	8.50935	+	10.5082i	0.322315	+	0.398025i
$698$	30.1554	+	1.58038i	1.14140	+	0.0598181i
$699$	−30.6192			−1.15812
$700$		0			0
$701$	−38.5281			−1.45519			−0.727594	−	0.686008i	$-0.759361\pi$
$701$	−38.5281			−1.45519			−0.727594	+	0.686008i	$0.759361\pi$
$702$	1.60444	+	0.0840852i	0.0605557	+	0.00317359i
$703$	25.7505	+	31.7993i	0.971199	+	1.19933i
$704$	4.16549	+	0.437810i	0.156993	+	0.0165006i
$705$		0			0
$706$	13.6275	+	18.7566i	0.512877	+	0.705915i
$707$	43.8079	−	13.8691i	1.64757	−	0.521601i
$708$	2.11217	+	0.334535i	0.0793803	+	0.0125726i
$709$	−7.37634	+	34.7029i	−0.277024	+	1.30330i	0.590959	+	0.806702i	$0.298750\pi$
$709$	−7.37634	+	34.7029i	−0.277024	+	1.30330i	−0.867983	+	0.496594i	$0.834584\pi$
$710$		0			0
$711$	4.96816	−	1.05602i	0.186321	−	0.0396037i
$712$	−9.50247	−	14.6325i	−0.356120	−	0.548377i
$713$	−1.59021	−	0.810250i	−0.0595537	−	0.0303441i
$714$	−18.7127	+	18.4322i	−0.700307	+	0.689806i
$715$		0			0
$716$	4.41720	+	0.938904i	0.165078	+	0.0350885i
$717$	5.43135	+	14.1491i	0.202837	+	0.528410i
$718$	9.90207	−	36.9550i	0.369542	−	1.37915i
$719$	1.43210	+	13.6255i	0.0534082	+	0.508145i	0.988224	+	0.153013i	$0.0488975\pi$
$719$	1.43210	+	13.6255i	0.0534082	+	0.508145i	−0.934816	+	0.355132i	$0.884436\pi$
$720$		0			0
$721$	−11.4412	+	17.3299i	−0.426092	+	0.645398i
$722$	−12.8205	+	2.03057i	−0.477129	+	0.0755698i
$723$	−1.02863	+	19.6274i	−0.0382550	+	0.729950i
$724$	−0.121005	−	0.209586i	−0.00449710	−	0.00778921i
$725$		0			0
$726$	19.2928	+	11.1387i	0.716024	+	0.413397i
$727$	−36.6967	+	18.6979i	−1.36101	+	0.693467i	−0.973561	−	0.228425i	$-0.926642\pi$
$727$	−36.6967	+	18.6979i	−1.36101	+	0.693467i	−0.387445	+	0.921893i	$0.626642\pi$
$728$	1.14480	+	1.29090i	0.0424289	+	0.0478440i
$729$	17.6135	−	24.2429i	0.652352	−	0.897885i
$730$		0			0
$731$	−16.6564	+	37.4108i	−0.616058	+	1.38369i
$732$	3.43480	+	0.920351i	0.126954	+	0.0340172i
$733$	22.4407	+	18.1721i	0.828867	+	0.671203i	0.946802	−	0.321818i	$-0.104294\pi$
$733$	22.4407	+	18.1721i	0.828867	+	0.671203i	−0.117934	+	0.993021i	$0.537627\pi$
$734$	6.76846	+	20.8312i	0.249829	+	0.768893i
$735$		0			0
$736$	0.236172	−	0.726863i	0.00870542	−	0.0267925i
$737$	5.21938	−	3.38951i	0.192258	−	0.124854i
$738$	0.106758	+	2.03706i	0.00392982	+	0.0749853i
$739$	3.80274	+	17.8905i	0.139886	+	0.658113i	0.991081	+	0.133263i	$0.0425454\pi$
$739$	3.80274	+	17.8905i	0.139886	+	0.658113i	−0.851195	+	0.524850i	$0.824121\pi$
$740$		0			0
$741$	1.75039	−	0.568737i	0.0643022	−	0.0208931i
$742$	−15.5167	+	6.76849i	−0.569635	+	0.248479i
$743$	18.6958	+	18.6958i	0.685883	+	0.685883i	0.961319	−	0.275437i	$-0.0888224\pi$
$743$	18.6958	+	18.6958i	0.685883	+	0.685883i	−0.275437	+	0.961319i	$0.588822\pi$
$744$	15.5337	−	1.63266i	0.569494	−	0.0598563i
$745$		0			0
$746$	4.04893	−	38.5230i	0.148242	−	1.41043i
$747$	4.86178	+	1.86626i	0.177883	+	0.0682830i
$748$	0.266301	+	0.522646i	0.00973694	+	0.0191098i
$749$	0.254671	+	5.68005i	0.00930549	+	0.207544i
$750$		0			0
$751$	14.6728	−	25.4141i	0.535418	−	0.927372i	−0.463724	−	0.885979i	$-0.653487\pi$
$751$	14.6728	−	25.4141i	0.535418	−	0.927372i	0.999143	−	0.0413925i	$-0.0131794\pi$
$752$	21.4910	+	13.9564i	0.783697	+	0.508938i
$753$	−18.6445	+	15.0980i	−0.679442	+	0.550201i
$754$	−1.00175	+	0.446006i	−0.0364814	+	0.0162426i
$755$		0			0
$756$	3.70824	−	0.558648i	0.134867	−	0.0203178i
$757$	26.5318	−	26.5318i	0.964316	−	0.964316i	−0.0350687	−	0.999385i	$-0.511165\pi$
$757$	26.5318	−	26.5318i	0.964316	−	0.964316i	0.999385	+	0.0350687i	$0.0111650\pi$
$758$	15.0544	−	18.5906i	0.546799	−	0.675241i
$759$	−0.267504	+	0.297093i	−0.00970977	+	0.0107838i
$760$		0			0
$761$	−0.760199	+	0.684487i	−0.0275572	+	0.0248126i	−0.682794	−	0.730611i	$-0.739235\pi$
$761$	−0.760199	+	0.684487i	−0.0275572	+	0.0248126i	0.655237	+	0.755423i	$0.272569\pi$
$762$	17.5338	−	34.4120i	0.635183	−	1.24662i
$763$	16.8241	+	23.5281i	0.609073	+	0.851773i
$764$	−2.54090	−	0.825588i	−0.0919265	−	0.0298687i
$765$		0			0
$766$	29.2853	+	26.3686i	1.05812	+	0.952738i
$767$	−1.09411	+	0.419988i	−0.0395059	+	0.0151649i
$768$	2.43930	+	9.10360i	0.0880207	+	0.328498i
$769$	16.8522	−	12.2439i	0.607708	−	0.441525i	−0.240899	−	0.970550i	$-0.577442\pi$
$769$	16.8522	−	12.2439i	0.607708	−	0.441525i	0.848606	+	0.529025i	$0.177442\pi$
$770$		0			0
$771$	6.62415	+	4.81272i	0.238563	+	0.173326i
$772$	−1.80030	+	4.68995i	−0.0647943	+	0.168795i
$773$	−14.1583	+	21.8018i	−0.509238	+	0.784158i	−0.995998	−	0.0893781i	$-0.971512\pi$
$773$	−14.1583	+	21.8018i	−0.509238	+	0.784158i	0.486760	+	0.873536i	$0.338179\pi$
$774$	−5.35024	+	3.08897i	−0.192311	+	0.111031i
$775$		0			0
$776$			28.6949i			1.03009i
$777$	27.2228	+	15.9925i	0.976612	+	0.573726i
$778$	2.33181	+	14.7225i	0.0835995	+	0.527827i
$779$	6.15198	+	13.8176i	0.220418	+	0.495066i
$780$		0			0
$781$	2.05848	+	0.916495i	0.0736582	+	0.0327948i
$782$	−3.26403	+	0.874595i	−0.116722	+	0.0312754i
$783$	−3.29564	+	20.8078i	−0.117776	+	0.743611i
$784$	−19.1793	−	14.3822i	−0.684974	−	0.513650i
$785$		0			0
$786$	−0.704119	−	0.782004i	−0.0251151	−	0.0278931i
$787$	48.4809	−	2.54078i	1.72816	−	0.0905689i	0.837842	−	0.545912i	$-0.183817\pi$
$787$	48.4809	−	2.54078i	1.72816	−	0.0905689i	0.890316	+	0.455343i	$0.150483\pi$
$788$	−3.63916	+	0.190721i	−0.129640	+	0.00679414i
$789$	−12.1946	−	13.5435i	−0.434140	−	0.482161i
$790$		0			0
$791$	−29.8772	+	36.3307i	−1.06231	+	1.29177i
$792$	−0.122366	+	0.772589i	−0.00434809	+	0.0274528i
$793$	−1.88235	+	0.504373i	−0.0668441	+	0.0179108i
$794$	−5.98900	−	2.66647i	−0.212542	−	0.0946296i
$795$		0			0
$796$	−0.744891	−	1.67305i	−0.0264020	−	0.0592998i
$797$	−1.60051	−	10.1052i	−0.0566929	−	0.357945i	−0.999684	−	0.0251277i	$-0.992001\pi$
$797$	−1.60051	−	10.1052i	−0.0566929	−	0.357945i	0.942991	−	0.332817i	$-0.107999\pi$
$798$	−25.5554	+	14.4981i	−0.904650	+	0.513228i
$799$			35.9141i			1.27055i
$800$		0			0
$801$	2.78047	−	1.60530i	0.0982429	−	0.0567206i
$802$	3.16627	−	4.87563i	0.111805	−	0.172164i
$803$	2.25171	−	5.86591i	0.0794613	−	0.207004i
$804$	4.19865	+	3.05049i	0.148075	+	0.107583i
$805$		0			0
$806$	−0.783414	+	0.569183i	−0.0275946	+	0.0200486i
$807$	4.88514	+	18.2316i	0.171965	+	0.641782i
$808$	−48.3002	+	18.5407i	−1.69919	+	0.652260i
$809$	31.3375	+	28.2164i	1.10177	+	0.992036i	0.999996	−	0.00277189i	$-0.000882320\pi$
$809$	31.3375	+	28.2164i	1.10177	+	0.992036i	0.101771	+	0.994808i	$0.467549\pi$
$810$		0			0
$811$	30.4344	+	9.88872i	1.06869	+	0.347240i	0.789979	−	0.613134i	$-0.210091\pi$
$811$	30.4344	+	9.88872i	1.06869	+	0.347240i	0.278716	+	0.960374i	$0.410091\pi$
$812$	−2.08196	+	1.48873i	−0.0730623	+	0.0522443i
$813$	10.4085	−	20.4279i	0.365043	−	0.716436i
$814$	−3.58376	+	3.22683i	−0.125611	+	0.113100i
$815$		0			0
$816$	17.2225	−	19.1275i	0.602906	−	0.669595i
$817$	−28.8281	+	35.5998i	−1.00857	+	1.24548i
$818$	−0.201215	+	0.201215i	−0.00703533	+	0.00703533i
$819$	−0.248248	+	0.197942i	−0.00867450	+	0.00691664i
$820$		0			0
$821$	44.4213	−	19.7776i	1.55031	−	0.690244i	0.559924	−	0.828544i	$-0.310830\pi$
$821$	44.4213	−	19.7776i	1.55031	−	0.690244i	0.990390	+	0.138300i	$0.0441638\pi$
$822$	6.99334	−	5.66309i	0.243921	−	0.197523i
$823$	−1.50708	−	0.978707i	−0.0525334	−	0.0341156i	0.518105	−	0.855317i	$-0.326638\pi$
$823$	−1.50708	−	0.978707i	−0.0525334	−	0.0341156i	−0.570639	+	0.821201i	$0.693304\pi$
$824$	11.6903	−	20.2482i	0.407250	−	0.705378i
$825$		0			0
$826$	15.7673	−	10.0709i	0.548614	−	0.350411i
$827$	−8.07790	−	15.8538i	−0.280896	−	0.551290i	0.706849	−	0.707364i	$-0.250116\pi$
$827$	−8.07790	−	15.8538i	−0.280896	−	0.551290i	−0.987745	+	0.156075i	$0.950116\pi$
$828$	0.0695849	+	0.0267111i	0.00241824	+	0.000928277i
$829$	5.29689	−	50.3966i	0.183969	−	1.75035i	−0.380400	−	0.924822i	$-0.624214\pi$
$829$	5.29689	−	50.3966i	0.183969	−	1.75035i	0.564369	−	0.825523i	$-0.309120\pi$
$830$		0			0
$831$	−9.43827	+	0.992002i	−0.327410	+	0.0344122i
$832$	−1.35350	−	1.35350i	−0.0469242	−	0.0469242i
$833$	2.26507	−	33.5218i	0.0784800	−	1.16146i
$834$	−42.7357	+	13.8857i	−1.47982	+	0.480822i
$835$		0			0
$836$	0.136421	+	0.641813i	0.00471824	+	0.0221976i
$837$	0.973673	+	18.5788i	0.0336551	+	0.642177i
$838$	−38.4270	+	24.9548i	−1.32744	+	0.862049i
$839$	−2.38981	+	7.35507i	−0.0825053	+	0.253925i	−0.983797	−	0.179288i	$-0.942620\pi$
$839$	−2.38981	+	7.35507i	−0.0825053	+	0.253925i	0.901291	+	0.433214i	$0.142620\pi$
$840$		0			0
$841$	4.51828	+	13.9058i	0.155803	+	0.479511i
$842$	30.8514	+	24.9830i	1.06321	+	0.860970i
$843$	6.98412	+	1.87139i	0.240546	+	0.0644541i
$844$	0.393743	−	0.884362i	0.0135532	−	0.0304410i
$845$		0			0
$846$	−3.18463	+	4.38327i	−0.109490	+	0.150700i
$847$	−27.9174	+	5.71396i	−0.959253	+	0.196334i
$848$	14.7806	−	7.53108i	0.507567	−	0.258618i
$849$	−5.24954	−	3.03082i	−0.180164	−	0.104018i
$850$		0			0
$851$	2.03094	+	3.51769i	0.0696197	+	0.120585i
$852$	−0.0983424	+	1.87648i	−0.00336915	+	0.0642873i
$853$	−11.6162	+	1.83983i	−0.397732	+	0.0629946i	−0.352097	−	0.935964i	$-0.614531\pi$
$853$	−11.6162	+	1.83983i	−0.397732	+	0.0629946i	−0.0456353	+	0.998958i	$0.514531\pi$
$854$	27.8252	−	13.9139i	0.952158	−	0.476124i
$855$		0			0
$856$	−0.669154	−	6.36657i	−0.0228712	−	0.217605i
$857$	0.0986197	−	0.368054i	0.00336878	−	0.0125725i	−0.964221	−	0.265100i	$-0.914595\pi$
$857$	0.0986197	−	0.368054i	0.00336878	−	0.0125725i	0.967590	+	0.252527i	$0.0812618\pi$
$858$	0.0777336	+	0.202503i	0.00265378	+	0.00691334i
$859$	−9.45007	−	2.00867i	−0.322432	−	0.0685351i	0.0438522	−	0.999038i	$-0.486037\pi$
$859$	−9.45007	−	2.00867i	−0.322432	−	0.0685351i	−0.366284	+	0.930503i	$0.619370\pi$
$860$		0			0
$861$	8.18992	+	8.31459i	0.279112	+	0.283361i
$862$	41.2081	+	20.9966i	1.40355	+	0.715146i
$863$	−2.74016	−	4.21948i	−0.0932762	−	0.143633i	0.788952	−	0.614455i	$-0.210624\pi$
$863$	−2.74016	−	4.21948i	−0.0932762	−	0.143633i	−0.882228	+	0.470822i	$0.843957\pi$
$864$	−7.79276	+	1.65640i	−0.265115	+	0.0563519i
$865$		0			0
$866$	−1.59034	+	7.48196i	−0.0540419	+	0.254247i
$867$	9.33755	+	1.47892i	0.317120	+	0.0502268i
$868$	−1.52504	+	1.66822i	−0.0517634	+	0.0566230i
$869$	2.60893	+	3.59089i	0.0885020	+	0.121813i
$870$		0			0
$871$	−2.82855	−	0.297293i	−0.0958419	−	0.0100734i
$872$	−20.4946	−	25.3087i	−0.694034	−	0.857061i
$873$	−5.27314	−	0.276353i	−0.178469	−	0.00935315i
$874$	−3.77997			−0.127859
$875$		0			0
$876$	5.23972			0.177034
$877$	21.5953	+	1.13176i	0.729223	+	0.0382169i	0.413334	−	0.910579i	$-0.364364\pi$
$877$	21.5953	+	1.13176i	0.729223	+	0.0382169i	0.315888	+	0.948796i	$0.397697\pi$
$878$	15.9906	+	19.7468i	0.539657	+	0.666421i
$879$	23.8359	+	2.50526i	0.803966	+	0.0845002i
$880$		0			0
$881$	−15.8503	−	21.8160i	−0.534009	−	0.735001i	0.453725	−	0.891142i	$-0.350095\pi$
$881$	−15.8503	−	21.8160i	−0.534009	−	0.735001i	−0.987735	+	0.156141i	$0.950095\pi$
$882$	3.24895	−	3.89045i	0.109398	−	0.130998i
$883$	−0.656476	−	0.103976i	−0.0220922	−	0.00349906i	0.145379	−	0.989376i	$-0.453560\pi$
$883$	−0.656476	−	0.103976i	−0.0220922	−	0.00349906i	−0.167471	+	0.985877i	$0.553560\pi$
$884$	0.0557349	−	0.262212i	0.00187457	−	0.00881915i
$885$		0			0
$886$	−19.9200	+	4.23412i	−0.669224	+	0.142248i
$887$	16.6676	+	25.6659i	0.559644	+	0.861775i	0.999338	−	0.0363718i	$-0.0115801\pi$
$887$	16.6676	+	25.6659i	0.559644	+	0.861775i	−0.439695	+	0.898147i	$0.644913\pi$
$888$	−31.6735	−	16.1385i	−1.06289	−	0.541572i
$889$	12.4255	+	47.8145i	0.416739	+	1.60365i
$890$		0			0
$891$	3.30573	+	0.702654i	0.110746	+	0.0235398i
$892$	−0.351073	−	0.914576i	−0.0117548	−	0.0306223i
$893$	−10.3977	+	38.8049i	−0.347947	+	1.29856i
$894$	2.49894	+	23.7758i	0.0835769	+	0.795181i
$895$		0			0
$896$	19.1690	+	12.6554i	0.640391	+	0.422787i
$897$	0.180452	−	0.0285808i	0.00602511	−	0.000954284i
$898$	−0.976031	+	18.6238i	−0.0325706	+	0.621484i
$899$	−6.34879	−	10.9964i	−0.211744	−	0.366752i
$900$		0			0
$901$	20.1345	+	11.6246i	0.670777	+	0.387273i
$902$	−1.58830	+	0.809282i	−0.0528848	+	0.0269461i
$903$	−11.1762	+	33.5328i	−0.371921	+	1.11590i
$904$	31.1294	−	42.8459i	1.03535	−	1.42503i
$905$		0			0
$906$	13.6056	−	30.5586i	0.452015	−	1.01524i
$907$	−32.6459	−	8.74745i	−1.08399	−	0.290454i	−0.327760	−	0.944761i	$-0.606294\pi$
$907$	−32.6459	−	8.74745i	−1.08399	−	0.290454i	−0.756229	+	0.654307i	$0.772961\pi$
$908$	−0.387101	−	0.313468i	−0.0128464	−	0.0104028i
$909$	−2.94197	−	9.05447i	−0.0975791	−	0.300318i
$910$		0			0
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	−0.791847	−	0.610719i	$-0.790880\pi$
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	0.999590	−	0.0286459i	$-0.00911953\pi$
$912$	24.1464	−	15.6809i	0.799568	−	0.519246i
$913$	0.238175	+	4.54465i	0.00788245	+	0.150406i
$914$	−7.95370	−	37.4192i	−0.263085	−	1.23772i
$915$		0			0
$916$	2.67531	−	0.869261i	0.0883948	−	0.0287212i
$917$	1.33756	+	0.150807i	0.0441701	+	0.00498007i
$918$	24.9079	+	24.9079i	0.822082	+	0.822082i
$919$	−31.8299	+	3.34546i	−1.04997	+	0.110357i	−0.613764	−	0.789489i	$-0.710346\pi$
$919$	−31.8299	+	3.34546i	−1.04997	+	0.110357i	−0.436208	+	0.899846i	$0.643679\pi$
$920$		0			0
$921$	−0.924945	+	8.80026i	−0.0304780	+	0.289979i
$922$	−39.3431	−	15.1024i	−1.29570	−	0.497372i
$923$	−0.467504	−	0.917529i	−0.0153881	−	0.0302008i
$924$	0.272532	+	0.426684i	0.00896563	+	0.0140369i
$925$		0			0
$926$	2.45679	−	4.25528i	0.0807351	−	0.139837i
$927$	3.60833	+	2.34328i	0.118513	+	0.0769633i
$928$	4.22569	−	3.42190i	0.138715	−	0.112329i
$929$	−38.4664	+	17.1263i	−1.26204	+	0.561897i	−0.925134	−	0.379641i	$-0.876048\pi$
$929$	−38.4664	+	17.1263i	−1.26204	+	0.561897i	−0.336908	+	0.941538i	$0.609381\pi$
$930$		0			0
$931$	12.1525	−	35.5643i	0.398283	−	1.16557i
$932$	−3.52757	+	3.52757i	−0.115549	+	0.115549i
$933$	0.951022	−	1.17441i	0.0311351	−	0.0384486i
$934$	−6.28452	+	6.97967i	−0.205636	+	0.228382i
$935$		0			0
$936$	0.265659	−	0.239200i	0.00868334	−	0.00781851i
$937$	7.54518	−	14.8083i	0.246490	−	0.483765i	−0.734301	−	0.678824i	$-0.762490\pi$
$937$	7.54518	−	14.8083i	0.246490	−	0.483765i	0.980791	+	0.195059i	$0.0624900\pi$
$938$	45.1899	−	4.40480i	1.47550	−	0.143822i
$939$	−0.581349	−	0.188892i	−0.0189716	−	0.00616425i
$940$		0			0
$941$	8.12267	+	7.31369i	0.264791	+	0.238419i	0.790822	−	0.612047i	$-0.209653\pi$
$941$	8.12267	+	7.31369i	0.264791	+	0.238419i	−0.526030	+	0.850466i	$0.676320\pi$
$942$	−7.80330	+	2.99541i	−0.254245	+	0.0975957i
$943$	0.388607	+	1.45030i	0.0126548	+	0.0472283i
$944$	−14.8319	+	10.7760i	−0.482739	+	0.350730i
$945$		0			0
$946$	−4.36771	−	3.17332i	−0.142006	−	0.103174i
$947$	−11.7372	+	30.5764i	−0.381407	+	0.993599i	0.599716	+	0.800213i	$0.295280\pi$
$947$	−11.7372	+	30.5764i	−0.381407	+	0.993599i	−0.981123	+	0.193386i	$0.938053\pi$
$948$	−2.01594	+	3.10427i	−0.0654746	+	0.100822i
$949$	−2.48678	+	1.43574i	−0.0807242	+	0.0466062i
$950$		0			0
$951$			47.1129i			1.52774i
$952$	−0.285745	+	37.8275i	−0.00926105	+	1.22600i
$953$	4.85130	+	30.6299i	0.157149	+	0.992200i	0.932631	+	0.360831i	$0.117507\pi$
$953$	4.85130	+	30.6299i	0.157149	+	0.992200i	−0.775482	+	0.631369i	$0.782493\pi$
$954$	1.42659	+	3.20417i	0.0461875	+	0.103739i
$955$		0			0
$956$	2.25583	+	1.00436i	0.0729587	+	0.0324833i
$957$	−2.74733	+	0.736146i	−0.0888087	+	0.0237962i
$958$	2.38104	−	15.0333i	0.0769279	−	0.485704i
$959$	−1.88650	+	11.3551i	−0.0609182	+	0.366675i
$960$		0			0
$961$	13.2400	+	14.7045i	0.427097	+	0.474339i
$962$	2.20086	−	0.115342i	0.0709585	−	0.00371878i
$963$	1.17640	−	0.0616525i	0.0379090	−	0.00198673i
$964$	2.14272	+	2.37973i	0.0690124	+	0.0766461i
$965$		0			0
$966$	−2.73076	+	1.02464i	−0.0878607	+	0.0329673i
$967$	5.19736	−	32.8149i	0.167136	−	1.05525i	−0.751380	−	0.659870i	$-0.770611\pi$
$967$	5.19736	−	32.8149i	0.167136	−	1.05525i	0.918516	−	0.395385i	$-0.129389\pi$
$968$	30.9908	−	8.30397i	0.996083	−	0.266900i
$969$	36.8630	+	16.4125i	1.18421	+	0.527245i
$970$		0			0
$971$	−3.93520	−	8.83860i	−0.126287	−	0.283644i	0.839327	−	0.543628i	$-0.182950\pi$
$971$	−3.93520	−	8.83860i	−0.126287	−	0.283644i	−0.965613	+	0.259983i	$0.916283\pi$
$972$	−0.224312	−	1.41625i	−0.00719481	−	0.0454262i
$973$	29.1144	−	49.5593i	0.933366	−	1.58880i
$974$		−	5.77998i		−	0.185202i
$975$		0			0
$976$	−26.4009	+	15.2426i	−0.845073	+	0.487903i
$977$	2.27910	−	3.50951i	0.0729149	−	0.112279i	−0.800332	−	0.599557i	$-0.795343\pi$
$977$	2.27910	−	3.50951i	0.0729149	−	0.112279i	0.873247	+	0.487278i	$0.162010\pi$
$978$	12.3768	−	32.2426i	0.395765	−	1.03100i
$979$	2.26985	+	1.64914i	0.0725448	+	0.0527069i
$980$		0			0
$981$	4.84824	−	3.52246i	0.154793	−	0.112463i
$982$	3.30250	+	12.3251i	0.105387	+	0.393310i
$983$	11.3765	−	4.36704i	0.362855	−	0.139287i	−0.170108	−	0.985425i	$-0.554412\pi$
$983$	11.3765	−	4.36704i	0.362855	−	0.139287i	0.532963	+	0.846138i	$0.321078\pi$
$984$	−9.76510	−	8.79254i	−0.311300	−	0.280296i
$985$		0			0
$986$	−22.8647	−	7.42920i	−0.728161	−	0.236594i
$987$	3.00726	+	30.8523i	0.0957222	+	0.982039i
$988$	0.136136	−	0.267182i	0.00433106	−	0.00850019i
$989$	−3.37933	+	3.04276i	−0.107456	+	0.0967542i
$990$		0			0
$991$	−26.7684	+	29.7294i	−0.850327	+	0.944384i	−0.999009	−	0.0445008i	$-0.985830\pi$
$991$	−26.7684	+	29.7294i	−0.850327	+	0.944384i	0.148682	+	0.988885i	$0.452497\pi$
$992$	3.02185	−	3.73167i	0.0959438	−	0.118481i
$993$	9.80688	−	9.80688i	0.311212	−	0.311212i
$994$	10.2488	+	12.8535i	0.325072	+	0.407690i
$995$		0			0
$996$	−3.46697	+	1.54360i	−0.109855	+	0.0489107i
$997$	0.300574	−	0.243400i	0.00951926	−	0.00770855i	−0.624549	−	0.780986i	$-0.714717\pi$
$997$	0.300574	−	0.243400i	0.00951926	−	0.00770855i	0.634068	+	0.773277i	$0.281384\pi$
$998$	5.23343	+	3.39863i	0.165661	+	0.107582i
$999$	21.1708	−	36.6689i	0.669815	−	1.16015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.243.13		288
5.2	odd	4		875.2.bb.c.257.6		288
5.3	odd	4		175.2.x.a.47.13	yes	288
5.4	even	2		875.2.bb.b.243.6		288
7.3	odd	6	inner	875.2.bb.a.493.6		288
25.6	even	5		875.2.bb.c.768.6		288
25.8	odd	20		875.2.bb.b.607.13		288
25.17	odd	20	inner	875.2.bb.a.607.6		288
25.19	even	10		175.2.x.a.33.13	✓	288
35.3	even	12		175.2.x.a.122.13	yes	288
35.17	even	12		875.2.bb.c.507.6		288
35.24	odd	6		875.2.bb.b.493.13		288
175.17	even	60	inner	875.2.bb.a.857.13		288
175.31	odd	30		875.2.bb.c.143.6		288
175.94	odd	30		175.2.x.a.108.13	yes	288
175.108	even	60		875.2.bb.b.857.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	25.19	even	10
175.2.x.a.47.13	yes	288	5.3	odd	4
175.2.x.a.108.13	yes	288	175.94	odd	30
175.2.x.a.122.13	yes	288	35.3	even	12
875.2.bb.a.243.13		288	1.1	even	1	trivial
875.2.bb.a.493.6		288	7.3	odd	6	inner
875.2.bb.a.607.6		288	25.17	odd	20	inner
875.2.bb.a.857.13		288	175.17	even	60	inner
875.2.bb.b.243.6		288	5.4	even	2
875.2.bb.b.493.13		288	35.24	odd	6
875.2.bb.b.607.13		288	25.8	odd	20
875.2.bb.b.857.6		288	175.108	even	60
875.2.bb.c.143.6		288	175.31	odd	30
875.2.bb.c.257.6		288	5.2	odd	4
875.2.bb.c.507.6		288	35.17	even	12
875.2.bb.c.768.6		288	25.6	even	5

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31913 + 0.0691326i) q^{2} +(-0.985411 - 1.21688i) q^{3} +(-0.253721 - 0.0266672i) q^{4} +(-1.21576 - 1.67335i) q^{6} +(2.58371 + 0.569615i) q^{7} +(-2.94220 - 0.465999i) q^{8} +(0.113970 - 0.536187i) q^{9} +(0.468564 - 0.0995964i) q^{11} +(0.217569 + 0.335027i) q^{12} +(-0.195060 - 0.0993879i) q^{13} +(3.36886 + 0.930015i) q^{14} +(-3.34984 - 0.712030i) q^{16} +(-1.72008 - 4.48096i) q^{17} +(0.187409 - 0.699421i) q^{18} +(-0.561217 - 5.33963i) q^{19} +(-1.85286 - 3.70537i) q^{21} +(0.624982 - 0.0989874i) q^{22} +(0.0278939 - 0.532247i) q^{23} +(2.33221 + 4.03951i) q^{24} +(-0.250438 - 0.144591i) q^{26} +(-4.95029 + 2.52230i) q^{27} +(-0.640352 - 0.213424i) q^{28} +(2.22883 - 3.06772i) q^{29} +(1.36200 - 3.05910i) q^{31} +(1.38510 + 0.371137i) q^{32} +(-0.582925 - 0.472043i) q^{33} +(-1.95922 - 6.02987i) q^{34} +(-0.0432152 + 0.133003i) q^{36} +(-6.39160 + 4.15075i) q^{37} +(-0.371176 - 7.08245i) q^{38} +(0.0712708 + 0.335303i) q^{39} +(-2.67924 + 0.870538i) q^{41} +(-2.18800 - 5.01595i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(-0.121541 + 0.0127744i) q^{44} +(0.0735913 - 0.700174i) q^{46} +(-6.98550 - 2.68148i) q^{47} +(2.43451 + 4.77800i) q^{48} +(6.35108 + 2.94344i) q^{49} +(-3.75781 + 6.50871i) q^{51} +(0.0468405 + 0.0304185i) q^{52} +(-3.76438 + 3.04833i) q^{53} +(-6.70444 + 2.98501i) q^{54} +(-7.33634 - 2.87993i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(3.15219 - 3.89263i) q^{58} +(3.58205 - 3.97827i) q^{59} +(6.61519 - 5.95635i) q^{61} +(2.00814 - 3.94119i) q^{62} +(0.599885 - 1.32043i) q^{63} +(8.31559 + 2.70190i) q^{64} +(-0.736320 - 0.662985i) q^{66} +(12.1287 - 4.65578i) q^{67} +(0.316926 + 1.18278i) q^{68} +(-0.675168 + 0.490538i) q^{69} +(3.80548 + 2.76485i) q^{71} +(-0.585185 + 1.52446i) q^{72} +(7.14378 - 11.0005i) q^{73} +(-8.71829 + 5.03351i) q^{74} +1.36974i q^{76} +(1.26736 + 0.00957352i) q^{77} +(0.0708350 + 0.447234i) q^{78} +(3.76871 + 8.46467i) q^{79} +(6.44508 + 2.86953i) q^{81} +(-3.59445 + 0.963129i) q^{82} +(-1.48616 + 9.38322i) q^{83} +(0.371298 + 0.989542i) q^{84} +(-7.54123 - 8.37538i) q^{86} +(-5.92936 + 0.310744i) q^{87} +(-1.42502 + 0.0746822i) q^{88} +(3.91910 + 4.35260i) q^{89} +(-0.447364 - 0.367898i) q^{91} +(-0.0212708 + 0.134299i) q^{92} +(-5.06469 + 1.35708i) q^{93} +(-9.02940 - 4.02015i) q^{94} +(-0.913264 - 2.05122i) q^{96} +(-1.50690 - 9.51421i) q^{97} +(8.17440 + 4.32184i) q^{98} -0.262589i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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