LMFDB - Embedded newform 875.2.bb.a.857.13

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			857.13
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.a.243.13

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

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	0.420105	−	0.907476i	$-0.361993\pi$
$2$	1.31913	−	0.0691326i	0.932765	−	0.0488842i	0.512660	+	0.858591i	$0.328660\pi$
$3$	−0.985411	+	1.21688i	−0.568927	+	0.702567i	−0.977685	−	0.210076i	$-0.932629\pi$
$3$	−0.985411	+	1.21688i	−0.568927	+	0.702567i	0.408758	+	0.912643i	$0.365962\pi$
$4$	−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	0.278008	−	0.960579i	$-0.410326\pi$
$11$	0.468564	+	0.0995964i	0.141277	+	0.0300294i	−0.136730	+	0.990608i	$0.543659\pi$
$12$	0.217569	−	0.335027i	0.0628068	−	0.0967140i
$13$	−0.195060	+	0.0993879i	−0.0540999	+	0.0275653i	−0.480831	−	0.876813i	$-0.659665\pi$
$13$	−0.195060	+	0.0993879i	−0.0540999	+	0.0275653i	0.426731	+	0.904378i	$0.359665\pi$
$14$	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	0.550550	+	0.834802i	$0.314418\pi$
$17$	−1.72008	+	4.48096i	−0.417180	+	1.08679i	−0.967730	+	0.251989i	$0.918915\pi$
$18$	0.187409	+	0.699421i	0.0441728	+	0.164855i
$19$	−0.561217	+	5.33963i	−0.128752	+	1.22499i	0.719155	+	0.694849i	$0.244529\pi$
$19$	−0.561217	+	5.33963i	−0.128752	+	1.22499i	−0.847907	+	0.530145i	$0.822138\pi$
$20$		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	0.999995	+	0.00323548i	$0.00102989\pi$
$23$	0.0278939	+	0.532247i	0.00581628	+	0.110981i	−0.994178	+	0.107746i	$0.965637\pi$
$24$	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	0.964160	−	0.265321i	$-0.0854780\pi$
$29$	2.22883	+	3.06772i	0.413883	+	0.569661i	−0.550277	+	0.834982i	$0.685478\pi$
$30$		0			0
$31$	1.36200	+	3.05910i	0.244622	+	0.549431i	0.993573	−	0.113195i	$-0.0361086\pi$
$31$	1.36200	+	3.05910i	0.244622	+	0.549431i	−0.748950	+	0.662626i	$0.769442\pi$
$32$	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	−0.100861	−	0.994901i	$-0.532160\pi$
$37$	−6.39160	−	4.15075i	−1.05077	−	0.682379i	−0.949911	+	0.312521i	$0.898826\pi$
$38$	−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	0.0922339	−	0.995737i	$-0.470599\pi$
$41$	−2.67924	−	0.870538i	−0.418427	−	0.135955i	−0.510661	+	0.859782i	$0.670599\pi$
$42$	−2.18800	+	5.01595i	−0.337615	+	0.773978i
$43$	−6.03300	+	6.03300i	−0.920024	+	0.920024i	−0.997031	−	0.0770067i	$-0.975464\pi$
$43$	−6.03300	+	6.03300i	−0.920024	+	0.920024i	0.0770067	+	0.997031i	$0.475464\pi$
$44$	−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	−0.809772	−	0.586745i	$-0.800409\pi$
$47$	−6.98550	+	2.68148i	−1.01894	+	0.391135i	−0.209169	+	0.977880i	$0.567076\pi$
$48$	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	0.334936	−	0.942241i	$-0.391285\pi$
$53$	−3.76438	−	3.04833i	−0.517077	−	0.418721i	−0.852013	+	0.523520i	$0.824619\pi$
$54$	−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	0.929736	−	0.368226i	$-0.120035\pi$
$59$	3.58205	+	3.97827i	0.466343	+	0.517927i	−0.463393	+	0.886153i	$0.653368\pi$
$60$		0			0
$61$	6.61519	+	5.95635i	0.846989	+	0.762632i	0.973343	−	0.229353i	$-0.0736611\pi$
$61$	6.61519	+	5.95635i	0.846989	+	0.762632i	−0.126355	+	0.991985i	$0.540328\pi$
$62$	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	0.958930	−	0.283644i	$-0.0915432\pi$
$67$	12.1287	+	4.65578i	1.48176	+	0.568794i	0.522829	+	0.852437i	$0.324877\pi$
$68$	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	−0.338610	−	0.940927i	$-0.609957\pi$
$71$	3.80548	−	2.76485i	0.451628	−	0.328127i	0.790238	+	0.612800i	$0.209957\pi$
$72$	−0.585185	−	1.52446i	−0.0689647	−	0.179659i
$73$	7.14378	+	11.0005i	0.836117	+	1.28751i	0.955599	+	0.294670i	$0.0952098\pi$
$73$	7.14378	+	11.0005i	0.836117	+	1.28751i	−0.119482	+	0.992836i	$0.538124\pi$
$74$	−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	−0.567623	−	0.823288i	$-0.692137\pi$
$79$	3.76871	−	8.46467i	0.424013	−	0.952349i	0.991637	−	0.129061i	$-0.0411963\pi$
$80$		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	−0.924376	−	0.381482i	$-0.875414\pi$
$83$	−1.48616	−	9.38322i	−0.163127	−	1.02994i	0.761249	−	0.648459i	$-0.224586\pi$
$84$	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	−0.498721	−	0.866762i	$-0.666197\pi$
$89$	3.91910	−	4.35260i	0.415424	−	0.461375i	0.914145	+	0.405388i	$0.132864\pi$
$90$		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	0.785026	+	0.619463i	$0.212650\pi$
$97$	−1.50690	+	9.51421i	−0.153003	+	0.966022i	−0.938028	+	0.346558i	$0.887350\pi$
$98$	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	0.999992	−	0.00387741i	$-0.00123422\pi$
$101$	15.0410	+	8.68390i	1.49663	+	0.864080i	0.496638	+	0.867958i	$0.334568\pi$
$102$	−5.40700	−	8.32605i	−0.535373	−	0.824402i
$103$	−2.81276	−	7.32748i	−0.277149	−	0.721998i	−0.999535	−	0.0305073i	$-0.990288\pi$
$103$	−2.81276	−	7.32748i	−0.277149	−	0.721998i	0.722386	−	0.691491i	$-0.243046\pi$
$104$	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	−0.933815	−	0.357756i	$-0.883542\pi$
$107$	0.556205	−	2.07579i	0.0537704	−	0.200674i	0.987586	+	0.157082i	$0.0502087\pi$
$108$	1.32326	+	0.507951i	0.127330	+	0.0488776i
$109$	8.12435	−	7.31520i	0.778171	−	0.700669i	−0.181003	−	0.983482i	$-0.557935\pi$
$109$	8.12435	−	7.31520i	0.778171	−	0.700669i	0.959175	+	0.282814i	$0.0912678\pi$
$110$		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	−0.868241	−	0.496142i	$-0.834750\pi$
$113$	−8.07135	−	15.8409i	−0.759289	−	1.49019i	0.108952	−	0.994047i	$-0.465250\pi$
$114$	−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	−0.122902	−	0.992419i	$-0.539220\pi$
$127$	8.47711	−	16.6373i	0.752222	−	1.47632i	0.875124	−	0.483899i	$-0.160780\pi$
$128$	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	0.126606	−	0.991953i	$-0.459592\pi$
$131$	0.505966	+	0.0531792i	0.0442064	+	0.00464628i	−0.0823994	+	0.996599i	$0.526258\pi$
$132$	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	−0.971505	−	0.237020i	$-0.923829\pi$
$137$	0.227695	−	4.34468i	0.0194533	−	0.371191i	0.990958	−	0.134171i	$-0.0428373\pi$
$138$	−0.924546	−	0.600407i	−0.0787026	−	0.0511101i
$139$	6.71334	+	20.6615i	0.569418	+	1.75249i	0.654444	+	0.756111i	$0.272903\pi$
$139$	6.71334	+	20.6615i	0.569418	+	1.75249i	−0.0850255	+	0.996379i	$0.527097\pi$
$140$		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	−0.850427	−	0.526094i	$-0.823656\pi$
$149$	−10.0097	+	5.77912i	−0.820030	+	0.473444i	0.0303970	+	0.999538i	$0.490323\pi$
$150$		0			0
$151$	8.08621	−	14.0057i	0.658046	−	1.13977i	−0.323075	−	0.946373i	$-0.604716\pi$
$151$	8.08621	−	14.0057i	0.658046	−	1.13977i	0.981121	−	0.193396i	$-0.0619502\pi$
$152$	−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	0.995021	−	0.0996695i	$-0.0317785\pi$
$157$	1.04591	+	3.90339i	0.0834728	+	0.311525i	−0.911548	+	0.411194i	$0.865112\pi$
$158$	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	−0.278355	−	0.960478i	$-0.589789\pi$
$163$	9.09407	−	14.0036i	0.712303	−	1.09685i	0.990658	−	0.136372i	$-0.0435441\pi$
$164$	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	0.851078	−	0.525039i	$-0.175949\pi$
$167$	23.5551	−	3.73076i	1.82275	−	0.288695i	0.971669	+	0.236344i	$0.0759492\pi$
$168$	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	−0.948394	−	0.317095i	$-0.897293\pi$
$173$	−24.4441	+	1.28106i	−1.85845	+	0.0973971i	−0.910053	+	0.414492i	$0.863959\pi$
$174$	−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	−0.736285	−	0.676672i	$-0.763422\pi$
$179$	−17.6041	+	1.85027i	−1.31579	+	0.138295i	−0.579507	+	0.814967i	$0.696755\pi$
$180$		0			0
$181$	0.557581	−	0.767444i	0.0414447	−	0.0570437i	−0.787792	−	0.615942i	$-0.788776\pi$
$181$	0.557581	−	0.767444i	0.0414447	−	0.0570437i	0.829236	+	0.558898i	$0.188776\pi$
$182$	−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	0.178180	−	0.983998i	$-0.442979\pi$
$191$	10.2434	−	2.17730i	0.741184	−	0.157544i	0.563004	+	0.826454i	$0.309646\pi$
$192$	−4.90638	+	12.7816i	−0.354088	+	0.922430i
$193$	5.09648	+	19.0203i	0.366852	+	1.36911i	0.864892	+	0.501957i	$0.167387\pi$
$193$	5.09648	+	19.0203i	0.366852	+	1.36911i	−0.498040	+	0.867154i	$0.665947\pi$
$194$	−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	0.637254	−	0.770654i	$-0.280070\pi$
$197$	14.1083	+	2.23453i	1.00517	+	0.159204i	0.367920	+	0.929858i	$0.380070\pi$
$198$	0.0181535	+	0.346389i	0.00129011	+	0.0246168i
$199$	3.58928	−	6.21681i	0.254437	−	0.440698i	−0.710305	−	0.703894i	$-0.751443\pi$
$199$	3.58928	−	6.21681i	0.254437	−	0.440698i	0.964742	+	0.263196i	$0.0847765\pi$
$200$		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	0.902548	−	0.430590i	$-0.141694\pi$
$211$	−1.17257	−	3.60880i	−0.0807231	−	0.248440i	−0.983271	+	0.182150i	$0.941694\pi$
$212$	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	−0.825242	−	0.564780i	$-0.808961\pi$
$223$	1.74330	−	3.42142i	0.116740	−	0.229115i	0.941981	+	0.335665i	$0.108961\pi$
$224$	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	−0.489154	−	0.872198i	$-0.662694\pi$
$227$	1.63746	−	1.06338i	0.108682	−	0.0705788i	0.597836	+	0.801619i	$0.296028\pi$
$228$	1.66682	+	1.34976i	0.110388	+	0.0893901i
$229$	−10.0729	−	4.48475i	−0.665637	−	0.296361i	0.0459653	−	0.998943i	$-0.485364\pi$
$229$	−10.0729	−	4.48475i	−0.665637	−	0.296361i	−0.711603	+	0.702582i	$0.752030\pi$
$230$		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	0.999895	+	0.0145098i	$0.00461877\pi$
$233$	12.3061	+	15.1967i	0.806198	+	0.995571i	−0.193697	+	0.981061i	$0.562048\pi$
$234$	−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	−0.591207	−	0.806520i	$-0.701348\pi$
$239$	−9.20533	+	2.99099i	−0.595443	+	0.193471i	−0.00423616	+	0.999991i	$0.501348\pi$
$240$		0			0
$241$	−9.32794	+	8.39891i	−0.600865	+	0.541021i	−0.912445	−	0.409198i	$-0.865808\pi$
$241$	−9.32794	+	8.39891i	−0.600865	+	0.541021i	0.311580	+	0.950220i	$0.399142\pi$
$242$	−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	$0.160650\pi$
$251$			15.3215i			0.967086i	−0.875321	+	0.483543i	$0.839350\pi$
$252$	−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	0.0978199	−	0.995204i	$-0.468813\pi$
$257$	−5.05092	−	1.35339i	−0.315068	−	0.0844221i	−0.412888	+	0.910782i	$0.635480\pi$
$258$	−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	0.407201	−	0.913339i	$-0.366505\pi$
$263$	11.6229	+	0.609132i	0.716701	+	0.0375607i	0.309500	+	0.950899i	$0.399838\pi$
$264$	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	−0.713984	−	0.700162i	$-0.753111\pi$
$269$	−11.0120	+	4.90285i	−0.671412	+	0.298932i	0.0425725	+	0.999093i	$0.486445\pi$
$270$		0			0
$271$	5.95538	−	13.3760i	0.361764	−	0.812535i	−0.637355	−	0.770570i	$-0.719972\pi$
$271$	5.95538	−	13.3760i	0.361764	−	0.812535i	0.999119	−	0.0419648i	$-0.0133617\pi$
$272$	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	0.923819	−	0.382829i	$-0.125050\pi$
$277$	3.30097	+	5.08305i	0.198336	+	0.305411i	−0.725483	+	0.688240i	$0.758384\pi$
$278$	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	0.470755	−	0.882264i	$-0.343982\pi$
$281$	−3.73577	−	2.71420i	−0.222857	−	0.161915i	−0.693612	+	0.720349i	$0.743982\pi$
$282$	4.00563	−	14.9492i	0.238532	−	0.890212i
$283$	3.61407	+	1.38731i	0.214834	+	0.0824672i	0.463405	−	0.886147i	$-0.346628\pi$
$283$	3.61407	+	1.38731i	0.214834	+	0.0824672i	−0.248571	+	0.968614i	$0.579961\pi$
$284$	−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	0.316344	−	0.948644i	$-0.397545\pi$
$293$	−10.8232	−	10.8232i	−0.632300	−	0.632300i	−0.948644	+	0.316344i	$0.897545\pi$
$294$	−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	−0.811882	−	0.583821i	$-0.801557\pi$
$307$	−3.99596	+	3.99596i	−0.228061	+	0.228061i	0.583821	+	0.811882i	$0.301557\pi$
$308$	−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	−0.972092	−	0.234599i	$-0.924622\pi$
$311$	0.200656	−	0.944012i	0.0113782	−	0.0535300i	0.983470	+	0.181069i	$0.0579557\pi$
$312$	−0.0534423	+	1.01974i	−0.00302557	+	0.0577314i
$313$	0.327398	+	0.212615i	0.0185056	+	0.0120177i	0.553859	−	0.832611i	$-0.313155\pi$
$313$	0.327398	+	0.212615i	0.0185056	+	0.0120177i	−0.535353	+	0.844628i	$0.679821\pi$
$314$	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	−0.320073	+	0.947393i	$0.603707\pi$
$317$	−23.3828	+	18.9350i	−1.31331	+	1.06350i	−0.993237	+	0.116105i	$0.962959\pi$
$318$	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	−0.939163	−	0.343471i	$-0.888397\pi$
$331$	0.925838	−	8.80876i	0.0508887	−	0.484173i	0.990052	−	0.140702i	$-0.0449360\pi$
$332$	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	−0.863264	−	0.504753i	$-0.831584\pi$
$337$	−17.6659	+	9.00124i	−0.962324	+	0.490329i	−0.0990602	+	0.995081i	$0.531584\pi$
$338$	−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	−0.759893	−	0.650048i	$-0.774749\pi$
$347$	0.632254	−	0.780769i	0.0339412	−	0.0419139i	0.793834	+	0.608135i	$0.208082\pi$
$348$	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	−0.393215	−	0.919447i	$-0.628637\pi$
$353$	11.0455	−	13.6401i	0.587893	−	0.725988i	0.981108	+	0.193459i	$0.0619705\pi$
$354$	−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	0.789666	+	0.613537i	$0.210254\pi$
$359$	6.02179	+	28.3303i	0.317818	+	1.49522i	−0.471848	+	0.881680i	$0.656413\pi$
$360$		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	−0.686532	−	0.727099i	$-0.740868\pi$
$367$	5.94229	−	15.4802i	0.310185	−	0.808060i	0.996717	−	0.0809605i	$-0.0257987\pi$
$368$	−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	0.689733	+	0.724064i	$0.257728\pi$
$373$	1.53470	+	29.2838i	0.0794637	+	1.51626i	−0.610269	+	0.792194i	$0.708939\pi$
$374$	−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	0.989570	−	0.144054i	$-0.0460137\pi$
$379$	10.6445	+	14.6509i	0.546773	+	0.752568i	−0.442797	+	0.896622i	$0.646014\pi$
$380$		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	0.184944	−	0.982749i	$-0.440790\pi$
$383$	23.1844	−	18.7744i	1.18467	−	0.959326i	0.999726	+	0.0234230i	$0.00745644\pi$
$384$	−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	−0.877792	−	0.479042i	$-0.840984\pi$
$389$	2.34616	−	11.0378i	0.118955	−	0.559639i	0.996747	−	0.0805966i	$-0.0256826\pi$
$390$		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	−0.471848	−	0.881680i	$-0.656413\pi$
$397$	−4.63333	+	1.77857i	−0.232540	+	0.0892638i	0.239308	+	0.970944i	$0.423080\pi$
$398$	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	0.915725	−	0.401805i	$-0.131617\pi$
$401$	2.20052	+	3.81142i	0.109889	+	0.190333i	−0.805836	+	0.592139i	$0.798284\pi$
$402$	−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	0.739570	−	0.673079i	$-0.235029\pi$
$409$	−0.144146	−	0.160091i	−0.00712759	−	0.00791599i	−0.746698	+	0.665163i	$0.768362\pi$
$410$		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	−0.997664	−	0.0683067i	$-0.978240\pi$
$419$	−28.0621	−	20.3883i	−1.37092	−	0.996034i	−0.373259	−	0.927727i	$-0.621760\pi$
$420$		0			0
$421$	24.3135	−	17.6648i	1.18497	−	0.860928i	0.192243	−	0.981347i	$-0.438424\pi$
$421$	24.3135	−	17.6648i	1.18497	−	0.860928i	0.992723	+	0.120419i	$0.0384239\pi$
$422$	−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	0.551699	−	0.834043i	$-0.313980\pi$
$431$	31.9852	−	14.2407i	1.54067	−	0.685952i	0.988974	+	0.148092i	$0.0473130\pi$
$432$	18.3786	+	4.92453i	0.884241	+	0.236932i
$433$	−0.905859	−	5.71937i	−0.0435328	−	0.274855i	0.956314	−	0.292340i	$-0.0944340\pi$
$433$	−0.905859	−	5.71937i	−0.0435328	−	0.274855i	−0.999847	+	0.0174852i	$0.994434\pi$
$434$	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	−0.353066	−	0.935598i	$-0.614861\pi$
$439$	12.8713	−	14.2950i	0.614312	−	0.682263i	0.967379	+	0.253335i	$0.0815276\pi$
$440$		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	−0.112928	−	0.993603i	$-0.536023\pi$
$443$	−14.8917	−	3.99023i	−0.707527	−	0.189581i	−0.594600	+	0.804022i	$0.702689\pi$
$444$	−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	$-0.891892\pi$
$449$		−	14.1182i		−	0.666281i	0.942877	−	0.333140i	$-0.108108\pi$
$450$		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	0.535271	+	0.844680i	$0.320209\pi$
$457$	−7.49556	+	27.9738i	−0.350627	+	1.30856i	−0.885899	+	0.463879i	$0.846457\pi$
$458$	−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	−0.913421	−	0.407016i	$-0.866569\pi$
$461$	−30.3418	+	9.85863i	−1.41316	+	0.459162i	−0.499735	+	0.866178i	$0.666569\pi$
$462$	−1.52479	+	2.13238i	−0.0709395	+	0.0992072i
$463$	1.68874	+	3.31433i	0.0784822	+	0.154030i	0.926913	−	0.375276i	$-0.122452\pi$
$463$	1.68874	+	3.31433i	0.0784822	+	0.154030i	−0.848431	+	0.529306i	$0.822452\pi$
$464$	−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	0.663029	−	0.748594i	$-0.269271\pi$
$467$	−4.47456	−	5.52562i	−0.207058	−	0.255695i	−0.870087	+	0.492899i	$0.835937\pi$
$468$	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	0.986961	+	0.160957i	$0.0514581\pi$
$479$	1.20444	+	11.4595i	0.0550324	+	0.523598i	−0.931929	+	0.362641i	$0.881875\pi$
$480$		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	0.988521	+	0.151082i	$0.0482758\pi$
$487$	−0.229004	+	4.36966i	−0.0103772	+	0.198008i	−0.998898	+	0.0469259i	$0.985058\pi$
$488$	−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	−0.860833	−	0.508887i	$-0.830057\pi$
$491$	2.98502	−	9.18693i	0.134712	−	0.414600i	0.995545	+	0.0942867i	$0.0300570\pi$
$492$	−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	−0.405625	−	0.914040i	$-0.632946\pi$
$499$	4.09112	−	2.36201i	0.183144	−	0.105738i	0.588769	+	0.808301i	$0.299613\pi$
$500$		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	0.0681101	−	0.997678i	$-0.478303\pi$
$503$	−3.93410	−	0.623100i	−0.175413	−	0.0277826i	−0.243523	+	0.969895i	$0.578303\pi$
$504$	−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	−0.257261	−	0.966342i	$-0.582820\pi$
$509$	−2.23882	+	0.475875i	−0.0992337	+	0.0210928i	0.158027	+	0.987435i	$0.449487\pi$
$510$		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	−0.393562	−	0.919298i	$-0.628757\pi$
$521$	−13.4075	+	1.40918i	−0.587391	+	0.0617373i	−0.193829	+	0.981035i	$0.562091\pi$
$522$	−1.72792	+	2.13381i	−0.0756291	+	0.0933941i
$523$	6.81583	−	0.357203i	0.298036	−	0.0156194i	0.0972678	−	0.995258i	$-0.468990\pi$
$523$	6.81583	−	0.357203i	0.298036	−	0.0156194i	0.200768	+	0.979639i	$0.435656\pi$
$524$	−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	−0.0445647	−	0.999006i	$-0.514190\pi$
$541$	7.46757	−	1.58728i	0.321056	−	0.0682425i	0.365621	+	0.930764i	$0.380857\pi$
$542$	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	0.949062	−	0.315089i	$-0.102034\pi$
$547$	41.0298	+	6.49848i	1.75431	+	0.277855i	0.805244	+	0.592944i	$0.202034\pi$
$548$	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	−0.537270	−	0.843410i	$-0.680544\pi$
$557$	−13.7087	+	3.67322i	−0.580855	+	0.155640i	−0.0435845	+	0.999050i	$0.513878\pi$
$558$	−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	0.418662	+	0.908142i	$0.362499\pi$
$563$	−2.19797	+	41.9397i	−0.0926332	+	1.76755i	−0.511295	+	0.859405i	$0.670834\pi$
$564$	−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	0.580219	−	0.814460i	$-0.302967\pi$
$569$	23.3390	+	2.45303i	0.978423	+	0.102836i	0.398204	+	0.917297i	$0.369634\pi$
$570$		0			0
$571$	1.01109	+	9.61986i	0.0423127	+	0.402579i	0.995095	+	0.0989242i	$0.0315401\pi$
$571$	1.01109	+	9.61986i	0.0423127	+	0.402579i	−0.952782	+	0.303654i	$0.901793\pi$
$572$	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	−0.515126	−	0.857115i	$-0.672255\pi$
$577$	1.40202	−	0.910483i	0.0583669	−	0.0379039i	0.573493	+	0.819211i	$0.305588\pi$
$578$	−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	0.885213	−	0.465187i	$-0.154013\pi$
$587$	−0.277321	−	0.544273i	−0.0114463	−	0.0224646i	−0.896659	+	0.442722i	$0.854013\pi$
$588$	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	0.690394	+	0.723433i	$0.257437\pi$
$593$	−6.55597	+	24.4672i	−0.269221	+	1.00475i	−0.959616	+	0.281314i	$0.909230\pi$
$594$	−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	0.551380	−	0.834254i	$-0.314102\pi$
$599$	2.55964	+	1.47781i	0.104584	+	0.0603816i	−0.446796	+	0.894636i	$0.647435\pi$
$600$		0			0
$601$		−	2.33505i		−	0.0952489i	−0.998865	−	0.0476244i	$-0.984835\pi$
$601$		−	2.33505i		−	0.0952489i	0.998865	−	0.0476244i	$-0.0151651\pi$
$602$	−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	0.616498	−	0.787356i	$-0.288551\pi$
$607$	18.6437	+	4.99555i	0.756723	+	0.202763i	0.140225	+	0.990120i	$0.455218\pi$
$608$	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	0.250987	−	0.967991i	$-0.419245\pi$
$613$	9.88907	+	0.518264i	0.399416	+	0.0209325i	0.148429	+	0.988923i	$0.452578\pi$
$614$	−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	0.964019	−	0.265832i	$-0.0856467\pi$
$617$	−0.868493	−	5.48345i	−0.0349642	−	0.220755i	−0.998984	+	0.0450769i	$0.985647\pi$
$618$	15.6810	+	4.20172i	0.630784	+	0.169018i
$619$	−34.8010	+	15.4944i	−1.39877	+	0.622772i	−0.961059	−	0.276344i	$-0.910877\pi$
$619$	−34.8010	+	15.4944i	−1.39877	+	0.622772i	−0.437710	+	0.899116i	$0.644210\pi$
$620$		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	0.336480	−	0.941691i	$-0.390764\pi$
$631$	−11.4331	−	8.30661i	−0.455143	−	0.330681i	−0.791623	+	0.611010i	$0.790764\pi$
$632$	−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	0.836856	−	0.547423i	$-0.184391\pi$
$641$	5.18908	+	5.76306i	0.204956	+	0.227627i	−0.631900	+	0.775050i	$0.717724\pi$
$642$	2.79730	+	3.45438i	0.110401	+	0.136333i
$643$	16.8674	+	16.8674i	0.665185	+	0.665185i	0.956598	−	0.291412i	$-0.0941251\pi$
$643$	16.8674	+	16.8674i	0.665185	+	0.665185i	−0.291412	+	0.956598i	$0.594125\pi$
$644$	−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	0.0434786	−	0.999054i	$-0.486156\pi$
$647$	−23.5210	−	19.0469i	−0.924704	−	0.748811i	−0.968183	+	0.250244i	$0.919489\pi$
$648$	−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	−0.883470	−	0.468488i	$-0.844799\pi$
$653$	−31.3427	+	12.0313i	−1.22654	+	0.470823i	−0.343066	+	0.939311i	$0.611465\pi$
$654$	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	−0.791747	−	0.610850i	$-0.790828\pi$
$659$	−45.9853	−	14.9415i	−1.79133	−	0.582039i	−0.999585	+	0.0288108i	$0.990828\pi$
$660$		0			0
$661$	1.42228	−	6.69130i	0.0553203	−	0.260262i	−0.941793	−	0.336194i	$-0.890860\pi$
$661$	1.42228	−	6.69130i	0.0553203	−	0.260262i	0.997113	+	0.0759328i	$0.0241934\pi$
$662$	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	0.867265	−	0.497847i	$-0.165876\pi$
$673$	25.2746	+	12.8780i	0.974263	+	0.496412i	0.106999	+	0.994259i	$0.465876\pi$
$674$	−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	0.981568	+	0.191113i	$0.0612096\pi$
$677$	0.659688	+	12.5876i	0.0253539	+	0.483780i	−0.956214	+	0.292668i	$0.905457\pi$
$678$	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	−0.964066	−	0.265663i	$-0.914409\pi$
$683$	−1.82579	+	4.75634i	−0.0698619	+	0.181996i	0.894204	+	0.447660i	$0.147742\pi$
$684$	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	0.999516	+	0.0310999i	$0.00990101\pi$
$691$	2.60404	+	12.2510i	0.0990622	+	0.466051i	−0.900454	+	0.434951i	$0.856766\pi$
$692$	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	−0.867983	−	0.496594i	$-0.834584\pi$
$709$	−7.37634	−	34.7029i	−0.277024	−	1.30330i	0.590959	−	0.806702i	$-0.298750\pi$
$710$		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	−0.934816	−	0.355132i	$-0.884436\pi$
$719$	1.43210	−	13.6255i	0.0534082	−	0.508145i	0.988224	−	0.153013i	$-0.0488975\pi$
$720$		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	−0.387445	−	0.921893i	$-0.626642\pi$
$727$	−36.6967	−	18.6979i	−1.36101	−	0.693467i	−0.973561	+	0.228425i	$0.926642\pi$
$728$	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	−0.117934	−	0.993021i	$-0.537627\pi$
$733$	22.4407	−	18.1721i	0.828867	−	0.671203i	0.946802	+	0.321818i	$0.104294\pi$
$734$	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	−0.851195	−	0.524850i	$-0.824121\pi$
$739$	3.80274	−	17.8905i	0.139886	−	0.658113i	0.991081	−	0.133263i	$-0.0425454\pi$
$740$		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	−0.275437	−	0.961319i	$-0.588822\pi$
$743$	18.6958	−	18.6958i	0.685883	−	0.685883i	0.961319	+	0.275437i	$0.0888224\pi$
$744$	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	0.999143	+	0.0413925i	$0.0131794\pi$
$751$	14.6728	+	25.4141i	0.535418	+	0.927372i	−0.463724	+	0.885979i	$0.653487\pi$
$752$	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	0.999385	−	0.0350687i	$-0.0111650\pi$
$757$	26.5318	+	26.5318i	0.964316	+	0.964316i	−0.0350687	+	0.999385i	$0.511165\pi$
$758$	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	0.655237	−	0.755423i	$-0.272569\pi$
$761$	−0.760199	−	0.684487i	−0.0275572	−	0.0248126i	−0.682794	+	0.730611i	$0.739235\pi$
$762$	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	0.848606	−	0.529025i	$-0.177442\pi$
$769$	16.8522	+	12.2439i	0.607708	+	0.441525i	−0.240899	+	0.970550i	$0.577442\pi$
$770$		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	0.486760	−	0.873536i	$-0.338179\pi$
$773$	−14.1583	−	21.8018i	−0.509238	−	0.784158i	−0.995998	+	0.0893781i	$0.971512\pi$
$774$	−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	0.890316	−	0.455343i	$-0.150483\pi$
$787$	48.4809	+	2.54078i	1.72816	+	0.0905689i	0.837842	+	0.545912i	$0.183817\pi$
$788$	−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	0.942991	+	0.332817i	$0.107999\pi$
$797$	−1.60051	+	10.1052i	−0.0566929	+	0.357945i	−0.999684	+	0.0251277i	$0.992001\pi$
$798$	−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	0.101771	−	0.994808i	$-0.467549\pi$
$809$	31.3375	−	28.2164i	1.10177	−	0.992036i	0.999996	+	0.00277189i	$0.000882320\pi$
$810$		0			0
$811$	30.4344	−	9.88872i	1.06869	−	0.347240i	0.278716	−	0.960374i	$-0.410091\pi$
$811$	30.4344	−	9.88872i	1.06869	−	0.347240i	0.789979	+	0.613134i	$0.210091\pi$
$812$	−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	0.990390	−	0.138300i	$-0.0441638\pi$
$821$	44.4213	+	19.7776i	1.55031	+	0.690244i	0.559924	+	0.828544i	$0.310830\pi$
$822$	6.99334	+	5.66309i	0.243921	+	0.197523i
$823$	−1.50708	+	0.978707i	−0.0525334	+	0.0341156i	−0.570639	−	0.821201i	$-0.693304\pi$
$823$	−1.50708	+	0.978707i	−0.0525334	+	0.0341156i	0.518105	+	0.855317i	$0.326638\pi$
$824$	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	−0.987745	−	0.156075i	$-0.950116\pi$
$827$	−8.07790	+	15.8538i	−0.280896	+	0.551290i	0.706849	+	0.707364i	$0.250116\pi$
$828$	0.0695849	−	0.0267111i	0.00241824	−	0.000928277i
$829$	5.29689	+	50.3966i	0.183969	+	1.75035i	0.564369	+	0.825523i	$0.309120\pi$
$829$	5.29689	+	50.3966i	0.183969	+	1.75035i	−0.380400	+	0.924822i	$0.624214\pi$
$830$		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	0.901291	−	0.433214i	$-0.142620\pi$
$839$	−2.38981	−	7.35507i	−0.0825053	−	0.253925i	−0.983797	+	0.179288i	$0.942620\pi$
$840$		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	−0.0456353	−	0.998958i	$-0.514531\pi$
$853$	−11.6162	−	1.83983i	−0.397732	−	0.0629946i	−0.352097	+	0.935964i	$0.614531\pi$
$854$	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	0.967590	−	0.252527i	$-0.0812618\pi$
$857$	0.0986197	+	0.368054i	0.00336878	+	0.0125725i	−0.964221	+	0.265100i	$0.914595\pi$
$858$	0.0777336	−	0.202503i	0.00265378	−	0.00691334i
$859$	−9.45007	+	2.00867i	−0.322432	+	0.0685351i	−0.366284	−	0.930503i	$-0.619370\pi$
$859$	−9.45007	+	2.00867i	−0.322432	+	0.0685351i	0.0438522	+	0.999038i	$0.486037\pi$
$860$		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	−0.882228	−	0.470822i	$-0.843957\pi$
$863$	−2.74016	+	4.21948i	−0.0932762	+	0.143633i	0.788952	+	0.614455i	$0.210624\pi$
$864$	−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	0.315888	−	0.948796i	$-0.397697\pi$
$877$	21.5953	−	1.13176i	0.729223	−	0.0382169i	0.413334	+	0.910579i	$0.364364\pi$
$878$	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	−0.987735	−	0.156141i	$-0.950095\pi$
$881$	−15.8503	+	21.8160i	−0.534009	+	0.735001i	0.453725	+	0.891142i	$0.350095\pi$
$882$	3.24895	+	3.89045i	0.109398	+	0.130998i
$883$	−0.656476	+	0.103976i	−0.0220922	+	0.00349906i	−0.167471	−	0.985877i	$-0.553560\pi$
$883$	−0.656476	+	0.103976i	−0.0220922	+	0.00349906i	0.145379	+	0.989376i	$0.453560\pi$
$884$	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	−0.439695	−	0.898147i	$-0.644913\pi$
$887$	16.6676	−	25.6659i	0.559644	−	0.861775i	0.999338	+	0.0363718i	$0.0115801\pi$
$888$	−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	−0.756229	−	0.654307i	$-0.772961\pi$
$907$	−32.6459	+	8.74745i	−1.08399	+	0.290454i	−0.327760	+	0.944761i	$0.606294\pi$
$908$	−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	0.999590	+	0.0286459i	$0.00911953\pi$
$911$	6.27024	+	19.2978i	0.207742	+	0.639365i	−0.791847	+	0.610719i	$0.790880\pi$
$912$	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	−0.436208	−	0.899846i	$-0.643679\pi$
$919$	−31.8299	−	3.34546i	−1.04997	−	0.110357i	−0.613764	+	0.789489i	$0.710346\pi$
$920$		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	−0.336908	−	0.941538i	$-0.609381\pi$
$929$	−38.4664	−	17.1263i	−1.26204	−	0.561897i	−0.925134	+	0.379641i	$0.876048\pi$
$930$		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	0.980791	−	0.195059i	$-0.0624900\pi$
$937$	7.54518	+	14.8083i	0.246490	+	0.483765i	−0.734301	+	0.678824i	$0.762490\pi$
$938$	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	−0.526030	−	0.850466i	$-0.676320\pi$
$941$	8.12267	−	7.31369i	0.264791	−	0.238419i	0.790822	+	0.612047i	$0.209653\pi$
$942$	−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	−0.981123	−	0.193386i	$-0.938053\pi$
$947$	−11.7372	−	30.5764i	−0.381407	−	0.993599i	0.599716	−	0.800213i	$-0.295280\pi$
$948$	−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	−0.775482	−	0.631369i	$-0.782493\pi$
$953$	4.85130	−	30.6299i	0.157149	−	0.992200i	0.932631	−	0.360831i	$-0.117507\pi$
$954$	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	0.918516	+	0.395385i	$0.129389\pi$
$967$	5.19736	+	32.8149i	0.167136	+	1.05525i	−0.751380	+	0.659870i	$0.770611\pi$
$968$	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	−0.965613	−	0.259983i	$-0.916283\pi$
$971$	−3.93520	+	8.83860i	−0.126287	+	0.283644i	0.839327	+	0.543628i	$0.182950\pi$
$972$	−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	0.873247	−	0.487278i	$-0.162010\pi$
$977$	2.27910	+	3.50951i	0.0729149	+	0.112279i	−0.800332	+	0.599557i	$0.795343\pi$
$978$	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	0.532963	−	0.846138i	$-0.321078\pi$
$983$	11.3765	+	4.36704i	0.362855	+	0.139287i	−0.170108	+	0.985425i	$0.554412\pi$
$984$	−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	0.148682	−	0.988885i	$-0.452497\pi$
$991$	−26.7684	−	29.7294i	−0.850327	−	0.944384i	−0.999009	+	0.0445008i	$0.985830\pi$
$992$	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	0.634068	−	0.773277i	$-0.281384\pi$
$997$	0.300574	+	0.243400i	0.00951926	+	0.00770855i	−0.624549	+	0.780986i	$0.714717\pi$
$998$	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.857.13		288
5.2	odd	4		175.2.x.a.108.13	yes	288
5.3	odd	4		875.2.bb.c.143.6		288
5.4	even	2		875.2.bb.b.857.6		288
7.5	odd	6	inner	875.2.bb.a.607.6		288
25.3	odd	20	inner	875.2.bb.a.493.6		288
25.4	even	10		175.2.x.a.122.13	yes	288
25.21	even	5		875.2.bb.c.507.6		288
25.22	odd	20		875.2.bb.b.493.13		288
35.12	even	12		175.2.x.a.33.13	✓	288
35.19	odd	6		875.2.bb.b.607.13		288
35.33	even	12		875.2.bb.c.768.6		288
175.47	even	60		875.2.bb.b.243.6		288
175.54	odd	30		175.2.x.a.47.13	yes	288
175.96	odd	30		875.2.bb.c.257.6		288
175.103	even	60	inner	875.2.bb.a.243.13		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	35.12	even	12
175.2.x.a.47.13	yes	288	175.54	odd	30
175.2.x.a.108.13	yes	288	5.2	odd	4
175.2.x.a.122.13	yes	288	25.4	even	10
875.2.bb.a.243.13		288	175.103	even	60	inner
875.2.bb.a.493.6		288	25.3	odd	20	inner
875.2.bb.a.607.6		288	7.5	odd	6	inner
875.2.bb.a.857.13		288	1.1	even	1	trivial
875.2.bb.b.243.6		288	175.47	even	60
875.2.bb.b.493.13		288	25.22	odd	20
875.2.bb.b.607.13		288	35.19	odd	6
875.2.bb.b.857.6		288	5.4	even	2
875.2.bb.c.143.6		288	5.3	odd	4
875.2.bb.c.257.6		288	175.96	odd	30
875.2.bb.c.507.6		288	25.21	even	5
875.2.bb.c.768.6		288	35.33	even	12

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

Related objects

Downloads

Learn more