LMFDB - Embedded newform 875.2.bb.c.768.6

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			768.6
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.c.507.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10783 + 0.719435i) q^{2} +(-1.46183 + 0.561145i) q^{3} +(-0.103766 + 0.233063i) q^{4} +(1.21576 - 1.67335i) q^{6} +(2.58371 + 0.569615i) q^{7} +(-0.465999 - 2.94220i) q^{8} +(-0.407366 + 0.366794i) q^{9} +(-0.320535 + 0.355990i) q^{11} +(0.0209068 - 0.398926i) q^{12} +(0.0993879 + 0.195060i) q^{13} +(-3.27212 + 1.22777i) q^{14} +(2.29156 + 2.54503i) q^{16} +(3.73011 - 3.02058i) q^{17} +(0.187409 - 0.699421i) q^{18} +(4.90486 - 2.18378i) q^{19} +(-4.09658 + 0.617151i) q^{21} +(0.0989874 - 0.624982i) q^{22} +(0.290280 + 0.446992i) q^{23} +(2.33221 + 4.03951i) q^{24} +(-0.250438 - 0.144591i) q^{26} +(2.52230 - 4.95029i) q^{27} +(-0.400858 + 0.543059i) q^{28} +(-2.22883 - 3.06772i) q^{29} +(3.33026 + 0.350024i) q^{31} +(1.38510 + 0.371137i) q^{32} +(0.268806 - 0.700264i) q^{33} +(-1.95922 + 6.02987i) q^{34} +(-0.0432152 - 0.133003i) q^{36} +(7.61066 + 0.398858i) q^{37} +(-3.86267 + 5.94800i) q^{38} +(-0.254745 - 0.229374i) q^{39} +(2.67924 + 0.870538i) q^{41} +(4.09433 - 3.63092i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(-0.0497074 - 0.111645i) q^{44} +(-0.643164 - 0.286355i) q^{46} +(-4.70888 + 5.81498i) q^{47} +(-4.77800 - 2.43451i) q^{48} +(6.35108 + 2.94344i) q^{49} +(-3.75781 + 6.50871i) q^{51} +(-0.0557743 + 0.00292301i) q^{52} +(1.73588 + 4.52212i) q^{53} +(0.767126 + 7.29872i) q^{54} +(0.471919 - 7.86722i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(4.67619 + 1.79502i) q^{58} +(-5.23631 + 1.11301i) q^{59} +(-1.85075 + 8.70710i) q^{61} +(-3.94119 + 2.00814i) q^{62} +(-1.26145 + 0.715647i) q^{63} +(-8.31559 + 2.70190i) q^{64} +(0.206002 + 0.969164i) q^{66} +(8.17589 + 10.0964i) q^{67} +(0.316926 + 1.18278i) q^{68} +(-0.675168 - 0.490538i) q^{69} +(3.80548 - 2.76485i) q^{71} +(1.26902 + 1.02763i) q^{72} +(0.686467 + 13.0986i) q^{73} +(-8.71829 + 5.03351i) q^{74} +1.36974i q^{76} +(-1.03095 + 0.737192i) q^{77} +(0.447234 + 0.0708350i) q^{78} +(9.21497 - 0.968533i) q^{79} +(-0.737450 + 7.01637i) q^{81} +(-3.59445 + 0.963129i) q^{82} +(-9.38322 + 1.48616i) q^{83} +(0.281252 - 1.01880i) q^{84} +(11.0239 + 2.34320i) q^{86} +(4.97960 + 3.23379i) q^{87} +(1.19676 + 0.777187i) q^{88} +(-5.72901 - 1.21774i) q^{89} +(0.145680 + 0.560590i) q^{91} +(-0.134299 + 0.0212708i) q^{92} +(-5.06469 + 1.35708i) q^{93} +(1.03315 - 9.82977i) q^{94} +(-2.23304 + 0.234702i) q^{96} +(-9.51421 - 1.50690i) q^{97} +(-9.15355 + 1.30835i) q^{98} -0.262589i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.10783	+	0.719435i	−0.783356	+	0.508717i	−0.873273	−	0.487232i	$-0.838007\pi$
$2$	−1.10783	+	0.719435i	−0.783356	+	0.508717i	0.0899164	+	0.995949i	$0.471340\pi$
$3$	−1.46183	+	0.561145i	−0.843989	+	0.323977i	−0.741662	−	0.670774i	$-0.765962\pi$
$3$	−1.46183	+	0.561145i	−0.843989	+	0.323977i	−0.102327	+	0.994751i	$0.532629\pi$
$4$	−0.103766	+	0.233063i	−0.0518831	+	0.116531i
$5$		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
$8$	−0.465999	−	2.94220i	−0.164755	−	1.04023i
$9$	−0.407366	+	0.366794i	−0.135789	+	0.122265i
$10$		0			0
$11$	−0.320535	+	0.355990i	−0.0966449	+	0.107335i	−0.789527	−	0.613716i	$-0.789674\pi$
$11$	−0.320535	+	0.355990i	−0.0966449	+	0.107335i	0.692882	+	0.721051i	$0.256341\pi$
$12$	0.0209068	−	0.398926i	0.00603529	−	0.115160i
$13$	0.0993879	+	0.195060i	0.0275653	+	0.0540999i	0.904378	−	0.426731i	$-0.140335\pi$
$13$	0.0993879	+	0.195060i	0.0275653	+	0.0540999i	−0.876813	+	0.480831i	$0.840335\pi$
$14$	−3.27212	+	1.22777i	−0.874510	+	0.328135i
$15$		0			0
$16$	2.29156	+	2.54503i	0.572889	+	0.636258i
$17$	3.73011	−	3.02058i	0.904684	−	0.732599i	−0.0593890	−	0.998235i	$-0.518915\pi$
$17$	3.73011	−	3.02058i	0.904684	−	0.732599i	0.964073	+	0.265636i	$0.0855819\pi$
$18$	0.187409	−	0.699421i	0.0441728	−	0.164855i
$19$	4.90486	−	2.18378i	1.12525	−	0.500994i	0.242180	−	0.970231i	$-0.422138\pi$
$19$	4.90486	−	2.18378i	1.12525	−	0.500994i	0.883072	+	0.469237i	$0.155471\pi$
$20$		0			0
$21$	−4.09658	+	0.617151i	−0.893947	+	0.134673i
$22$	0.0989874	−	0.624982i	0.0211042	−	0.133247i
$23$	0.290280	+	0.446992i	0.0605276	+	0.0932044i	0.867639	−	0.497195i	$-0.165637\pi$
$23$	0.290280	+	0.446992i	0.0605276	+	0.0932044i	−0.807111	+	0.590400i	$0.798970\pi$
$24$	2.33221	+	4.03951i	0.476061	+	0.824561i
$25$		0			0
$26$	−0.250438	−	0.144591i	−0.0491150	−	0.0283565i
$27$	2.52230	−	4.95029i	0.485416	−	0.952683i
$28$	−0.400858	+	0.543059i	−0.0757550	+	0.102629i
$29$	−2.22883	−	3.06772i	−0.413883	−	0.569661i	0.550277	−	0.834982i	$-0.314522\pi$
$29$	−2.22883	−	3.06772i	−0.413883	−	0.569661i	−0.964160	+	0.265321i	$0.914522\pi$
$30$		0			0
$31$	3.33026	+	0.350024i	0.598132	+	0.0628662i	0.398756	−	0.917057i	$-0.369442\pi$
$31$	3.33026	+	0.350024i	0.598132	+	0.0628662i	0.199376	+	0.979923i	$0.436109\pi$
$32$	1.38510	+	0.371137i	0.244853	+	0.0656083i
$33$	0.268806	−	0.700264i	0.0467932	−	0.121900i
$34$	−1.95922	+	6.02987i	−0.336004	+	1.03411i
$35$		0			0
$36$	−0.0432152	−	0.133003i	−0.00720254	−	0.0221671i
$37$	7.61066	+	0.398858i	1.25118	+	0.0655718i	0.666386	−	0.745607i	$-0.267840\pi$
$37$	7.61066	+	0.398858i	1.25118	+	0.0655718i	0.584799	+	0.811179i	$0.301174\pi$
$38$	−3.86267	+	5.94800i	−0.626609	+	0.964893i
$39$	−0.254745	−	0.229374i	−0.0407919	−	0.0367292i
$40$		0			0
$41$	2.67924	+	0.870538i	0.418427	+	0.135955i	0.510661	−	0.859782i	$-0.329401\pi$
$41$	2.67924	+	0.870538i	0.418427	+	0.135955i	−0.0922339	+	0.995737i	$0.529401\pi$
$42$	4.09433	−	3.63092i	0.631768	−	0.560264i
$43$	−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	$0.975464\pi$
$44$	−0.0497074	−	0.111645i	−0.00749367	−	0.0168310i
$45$		0			0
$46$	−0.643164	−	0.286355i	−0.0948294	−	0.0422208i
$47$	−4.70888	+	5.81498i	−0.686861	+	0.848203i	−0.994655	−	0.103250i	$-0.967076\pi$
$47$	−4.70888	+	5.81498i	−0.686861	+	0.848203i	0.307795	+	0.951453i	$0.400409\pi$
$48$	−4.77800	−	2.43451i	−0.689645	−	0.351391i
$49$	6.35108	+	2.94344i	0.907297	+	0.420491i
$50$		0			0
$51$	−3.75781	+	6.50871i	−0.526198	+	0.911402i
$52$	−0.0557743	+	0.00292301i	−0.00773450	+	0.000405348i
$53$	1.73588	+	4.52212i	0.238442	+	0.621161i	0.999625	−	0.0273749i	$-0.00871478\pi$
$53$	1.73588	+	4.52212i	0.238442	+	0.621161i	−0.761184	+	0.648536i	$0.775381\pi$
$54$	0.767126	+	7.29872i	0.104393	+	0.993230i
$55$		0			0
$56$	0.471919	−	7.86722i	0.0630628	−	1.05130i
$57$	−5.94466	+	5.94466i	−0.787389	+	0.787389i
$58$	4.67619	+	1.79502i	0.614014	+	0.235698i
$59$	−5.23631	+	1.11301i	−0.681709	+	0.144902i	−0.535735	−	0.844386i	$-0.679965\pi$
$59$	−5.23631	+	1.11301i	−0.681709	+	0.144902i	−0.145975	+	0.989288i	$0.546632\pi$
$60$		0			0
$61$	−1.85075	+	8.70710i	−0.236964	+	1.11483i	0.685297	+	0.728263i	$0.259672\pi$
$61$	−1.85075	+	8.70710i	−0.236964	+	1.11483i	−0.922262	+	0.386566i	$0.873661\pi$
$62$	−3.94119	+	2.00814i	−0.500532	+	0.255034i
$63$	−1.26145	+	0.715647i	−0.158927	+	0.0901630i
$64$	−8.31559	+	2.70190i	−1.03945	+	0.337737i
$65$		0			0
$66$	0.206002	+	0.969164i	0.0253571	+	0.119296i
$67$	8.17589	+	10.0964i	0.998844	+	1.23347i	0.972279	+	0.233822i	$0.0751234\pi$
$67$	8.17589	+	10.0964i	0.998844	+	1.23347i	0.0265646	+	0.999647i	$0.491543\pi$
$68$	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	$0.209957\pi$
$72$	1.26902	+	1.02763i	0.149555	+	0.121107i
$73$	0.686467	+	13.0986i	0.0803449	+	1.53307i	0.680238	+	0.732991i	$0.261876\pi$
$73$	0.686467	+	13.0986i	0.0803449	+	1.53307i	−0.599893	+	0.800080i	$0.704790\pi$
$74$	−8.71829	+	5.03351i	−1.01348	+	0.585133i
$75$		0			0
$76$			1.36974i			0.157120i
$77$	−1.03095	+	0.737192i	−0.117487	+	0.0840109i
$78$	0.447234	+	0.0708350i	0.0506393	+	0.00802048i
$79$	9.21497	−	0.968533i	1.03677	−	0.108968i	0.429177	−	0.903220i	$-0.358804\pi$
$79$	9.21497	−	0.968533i	1.03677	−	0.108968i	0.607588	+	0.794252i	$0.292137\pi$
$80$		0			0
$81$	−0.737450	+	7.01637i	−0.0819389	+	0.779597i
$82$	−3.59445	+	0.963129i	−0.396940	+	0.106360i
$83$	−9.38322	+	1.48616i	−1.02994	+	0.163127i	−0.648459	−	0.761249i	$-0.724586\pi$
$83$	−9.38322	+	1.48616i	−1.02994	+	0.163127i	−0.381482	+	0.924376i	$0.624586\pi$
$84$	0.281252	−	1.01880i	0.0306871	−	0.111160i
$85$		0			0
$86$	11.0239	+	2.34320i	1.18874	+	0.252674i
$87$	4.97960	+	3.23379i	0.533869	+	0.346699i
$88$	1.19676	+	0.777187i	0.127575	+	0.0828484i
$89$	−5.72901	−	1.21774i	−0.607274	−	0.129080i	−0.105996	−	0.994367i	$-0.533803\pi$
$89$	−5.72901	−	1.21774i	−0.607274	−	0.129080i	−0.501278	+	0.865286i	$0.667136\pi$
$90$		0			0
$91$	0.145680	+	0.560590i	0.0152714	+	0.0587658i
$92$	−0.134299	+	0.0212708i	−0.0140016	+	0.00221764i
$93$	−5.06469	+	1.35708i	−0.525184	+	0.140723i
$94$	1.03315	−	9.82977i	0.106561	−	1.01386i
$95$		0			0
$96$	−2.23304	+	0.234702i	−0.227909	+	0.0239542i
$97$	−9.51421	−	1.50690i	−0.966022	−	0.153003i	−0.346558	−	0.938028i	$-0.612650\pi$
$97$	−9.51421	−	1.50690i	−0.966022	−	0.153003i	−0.619463	+	0.785026i	$0.712650\pi$
$98$	−9.15355	+	1.30835i	−0.924648	+	0.132163i
$99$		−	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	$0.00123422\pi$
$102$	−0.519574	−	9.91407i	−0.0514455	−	0.981639i
$103$	6.09966	+	4.93940i	0.601017	+	0.486694i	0.880876	−	0.473347i	$-0.156954\pi$
$103$	6.09966	+	4.93940i	0.601017	+	0.486694i	−0.279859	+	0.960041i	$0.590288\pi$
$104$	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	$0.883542\pi$
$108$	0.891998	+	1.10153i	0.0858326	+	0.105994i
$109$	−2.27297	−	10.6935i	−0.217711	−	1.02425i	−0.942223	−	0.334988i	$-0.891268\pi$
$109$	−2.27297	−	10.6935i	−0.217711	−	1.02425i	0.724511	−	0.689263i	$-0.242065\pi$
$110$		0			0
$111$	−11.3493	+	3.68762i	−1.07723	+	0.350013i
$112$	4.47102	+	7.88092i	0.422472	+	0.744677i
$113$	15.8409	−	8.07135i	1.49019	−	0.759289i	0.496142	−	0.868241i	$-0.334750\pi$
$113$	15.8409	−	8.07135i	1.49019	−	0.759289i	0.994047	+	0.108952i	$0.0347496\pi$
$114$	2.30889	−	10.8625i	0.216248	−	1.01737i
$115$		0			0
$116$	0.946248	−	0.201131i	0.0878569	−	0.0186746i
$117$	−0.112034	−	0.0430059i	−0.0103576	−	0.00397589i
$118$	5.00022	−	5.00022i	0.460307	−	0.460307i
$119$	11.3581	−	5.67957i	1.04119	−	0.520646i
$120$		0			0
$121$	1.12583	+	10.7115i	0.102348	+	0.973775i
$122$	−4.21387	−	10.9775i	−0.381506	−	0.993857i
$123$	−4.40510	+	0.230861i	−0.397194	+	0.0208161i
$124$	−0.427146	+	0.739839i	−0.0383589	+	0.0664395i
$125$		0			0
$126$	0.882611	−	1.70035i	0.0786293	−	0.151479i
$127$	−16.6373	−	8.47711i	−1.47632	−	0.752222i	−0.483899	−	0.875124i	$-0.660780\pi$
$127$	−16.6373	−	8.47711i	−1.47632	−	0.752222i	−0.992419	+	0.122902i	$0.960780\pi$
$128$	5.46360	−	6.74699i	0.482919	−	0.596355i
$129$	12.2046	+	5.43384i	1.07456	+	0.478423i
$130$		0			0
$131$	0.206928	+	0.464769i	0.0180794	+	0.0406070i	0.922360	−	0.386333i	$-0.126258\pi$
$131$	0.206928	+	0.464769i	0.0180794	+	0.0406070i	−0.904280	+	0.426940i	$0.859592\pi$
$132$	0.135313	+	0.135313i	0.0117774	+	0.0117774i
$133$	13.9166	−	2.84837i	1.20673	−	0.246985i
$134$	−16.3212	−	5.30308i	−1.40994	−	0.458117i
$135$		0			0
$136$	−10.6254	−	9.56714i	−0.911120	−	0.820376i
$137$	2.36953	−	3.64876i	0.202443	−	0.311734i	−0.722838	−	0.691018i	$-0.757163\pi$
$137$	2.36953	−	3.64876i	0.202443	−	0.311734i	0.925281	+	0.379283i	$0.123829\pi$
$138$	1.10088	+	0.0576949i	0.0937135	+	0.00491132i
$139$	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
$142$	−2.22671	+	5.80079i	−0.186862	+	0.486791i
$143$	−0.101297	−	0.0271424i	−0.00847085	−	0.00226976i
$144$	−1.86701	−	0.196230i	−0.155584	−	0.0163525i
$145$		0			0
$146$	−10.1841	−	14.0172i	−0.842839	−	1.16007i
$147$	−10.9359	−	0.738938i	−0.901978	−	0.0609466i
$148$	−0.882688	+	1.73237i	−0.0725565	+	0.142400i
$149$	−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	$0.604716\pi$
$152$	−8.71079	−	13.4134i	−0.706538	−	1.08797i
$153$	−0.411589	+	2.59867i	−0.0332750	+	0.210090i
$154$	0.611754	−	1.55838i	0.0492965	−	0.125578i
$155$		0			0
$156$	0.0798924	−	0.0355704i	0.00639651	−	0.00284791i
$157$	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	$0.0317785\pi$
$158$	−9.51185	+	7.70255i	−0.756723	+	0.612782i
$159$	−5.07513	−	5.63650i	−0.402484	−	0.447004i
$160$		0			0
$161$	0.495385	+	1.32025i	0.0390418	+	0.104050i
$162$	−4.23085	−	8.30351i	−0.332407	−	0.652386i
$163$	0.873876	−	16.6745i	0.0684472	−	1.30605i	−0.721302	−	0.692621i	$-0.756456\pi$
$163$	0.873876	−	16.6745i	0.0684472	−	1.30605i	0.789749	−	0.613430i	$-0.210211\pi$
$164$	−0.480905	+	0.534099i	−0.0375524	+	0.0417061i
$165$		0			0
$166$	9.32584	−	8.39703i	0.723826	−	0.651736i
$167$	3.73076	+	23.5551i	0.288695	+	1.82275i	0.525039	+	0.851078i	$0.324051\pi$
$167$	3.73076	+	23.5551i	0.288695	+	1.82275i	−0.236344	+	0.971669i	$0.575949\pi$
$168$	3.72478	+	11.7654i	0.287373	+	0.907718i
$169$	7.61304	−	10.4784i	0.585618	−	0.806034i
$170$		0			0
$171$	−1.19708	+	2.68868i	−0.0915427	+	0.205608i
$172$	2.03209	−	0.780046i	0.154945	−	0.0594780i
$173$	20.5286	−	13.3315i	1.56076	−	1.01357i	0.580883	−	0.813987i	$-0.302707\pi$
$173$	20.5286	−	13.3315i	1.56076	−	1.01357i	0.979881	−	0.199585i	$-0.0639593\pi$
$174$	−7.84307			−0.594581
$175$		0			0
$176$	−1.64053			−0.123660
$177$	7.03004	−	4.56536i	0.528410	−	0.343154i
$178$	7.22287	−	2.77260i	0.541377	−	0.207815i
$179$	−7.19967	+	16.1707i	−0.538129	+	1.20866i	0.416028	+	0.909352i	$0.363422\pi$
$179$	−7.19967	+	16.1707i	−0.538129	+	1.20866i	−0.954157	+	0.299306i	$0.903245\pi$
$180$		0			0
$181$	−0.557581	+	0.767444i	−0.0414447	+	0.0570437i	−0.829236	−	0.558898i	$-0.811224\pi$
$181$	−0.557581	+	0.767444i	−0.0414447	+	0.0570437i	0.787792	+	0.615942i	$0.211224\pi$
$182$	−0.564698	−	0.516233i	−0.0418582	−	0.0382657i
$183$	−2.18045	−	13.7668i	−0.161184	−	1.01767i
$184$	1.17987	−	1.06236i	0.0869813	−	0.0783183i
$185$		0			0
$186$	4.63450	−	5.14714i	0.339818	−	0.377406i
$187$	−0.120333	+	2.29609i	−0.00879960	+	0.167906i
$188$	−0.866634	−	1.70086i	−0.0632058	−	0.124048i
$189$	9.33663	−	11.3533i	0.679140	−	0.825835i
$190$		0			0
$191$	−7.00728	−	7.78237i	−0.507029	−	0.563112i	0.434229	−	0.900803i	$-0.357021\pi$
$191$	−7.00728	−	7.78237i	−0.507029	−	0.563112i	−0.941257	+	0.337690i	$0.890354\pi$
$192$	10.6398	−	8.61597i	0.767864	−	0.621804i
$193$	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	$-0.167387\pi$
$194$	11.6243	−	5.17546i	0.834574	−	0.371576i
$195$		0			0
$196$	−1.34503	+	1.17477i	−0.0960738	+	0.0839122i
$197$	2.23453	−	14.1083i	0.159204	−	1.00517i	−0.770654	−	0.637254i	$-0.780070\pi$
$197$	2.23453	−	14.1083i	0.159204	−	1.00517i	0.929858	−	0.367920i	$-0.119930\pi$
$198$	0.188916	+	0.290905i	0.0134257	+	0.0206737i
$199$	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
$202$	−10.4154	+	20.4413i	−0.732822	+	1.43824i
$203$	−4.01121	−	9.19565i	−0.281532	−	0.645408i
$204$	−1.12701	−	1.55119i	−0.0789062	−	0.108605i
$205$		0			0
$206$	−10.3110	−	1.08373i	−0.718400	−	0.0755069i
$207$	−0.282205	−	0.0756165i	−0.0196146	−	0.00525571i
$208$	−0.268680	+	0.699936i	−0.0186296	+	0.0485318i
$209$	−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	$0.941694\pi$
$212$	−1.23406	−	0.0646746i	−0.0847559	−	0.00444187i
$213$	−4.01150	+	6.17716i	−0.274863	+	0.423252i
$214$	−2.10958	−	1.89947i	−0.144208	−	0.129845i
$215$		0			0
$216$	−15.7401	−	5.11428i	−1.07098	−	0.347982i
$217$	8.40503	+	2.80133i	0.570571	+	0.190166i
$218$	10.2113	+	10.2113i	0.691600	+	0.691600i
$219$	−8.35369	−	18.7627i	−0.564490	−	1.26787i
$220$		0			0
$221$	0.959922	+	0.427385i	0.0645714	+	0.0287490i
$222$	9.92015	−	12.2504i	0.665797	−	0.822190i
$223$	−3.42142	−	1.74330i	−0.229115	−	0.116740i	0.335665	−	0.941981i	$-0.391039\pi$
$223$	−3.42142	−	1.74330i	−0.229115	−	0.116740i	−0.564780	+	0.825242i	$0.691039\pi$
$224$	3.36729	+	1.74788i	0.224986	+	0.116785i
$225$		0			0
$226$	−11.7423	+	20.3382i	−0.781085	+	1.35288i
$227$	−1.94977	+	0.102183i	−0.129411	+	0.00678213i	−0.116931	−	0.993140i	$-0.537306\pi$
$227$	−1.94977	+	0.102183i	−0.129411	+	0.00678213i	−0.0124794	+	0.999922i	$0.503972\pi$
$228$	−0.768624	−	2.00233i	−0.0509034	−	0.132608i
$229$	1.15255	+	10.9658i	0.0761626	+	0.724639i	0.964255	+	0.264975i	$0.0853636\pi$
$229$	1.15255	+	10.9658i	0.0761626	+	0.724639i	−0.888093	+	0.459664i	$0.847970\pi$
$230$		0			0
$231$	1.09340	−	1.65616i	0.0719403	−	0.108967i
$232$	−7.98721	+	7.98721i	−0.524386	+	0.524386i
$233$	18.2557	+	7.00772i	1.19597	+	0.459091i	0.873189	−	0.487382i	$-0.162048\pi$
$233$	18.2557	+	7.00772i	1.19597	+	0.459091i	0.322784	+	0.946473i	$0.395381\pi$
$234$	0.155055	−	0.0329580i	0.0101363	−	0.00215453i
$235$		0			0
$236$	0.283951	−	1.33588i	0.0184836	−	0.0869585i
$237$	−12.9273	+	6.58676i	−0.839715	+	0.427856i
$238$	−8.49677	+	14.4634i	−0.550764	+	0.937524i
$239$	9.20533	−	2.99099i	0.595443	−	0.193471i	0.00423616	−	0.999991i	$-0.498652\pi$
$239$	9.20533	−	2.99099i	0.595443	−	0.193471i	0.591207	+	0.806520i	$0.298652\pi$
$240$		0			0
$241$	2.60970	+	12.2777i	0.168106	+	0.790875i	0.978705	+	0.205274i	$0.0658084\pi$
$241$	2.60970	+	12.2777i	0.168106	+	0.790875i	−0.810599	+	0.585602i	$0.800858\pi$
$242$	−8.95348	−	11.0566i	−0.575551	−	0.710747i
$243$	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
$247$	0.913452	+	0.739699i	0.0581216	+	0.0470659i
$248$	−0.522055	−	9.96140i	−0.0331505	−	0.632550i
$249$	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	$-0.160650\pi$
$252$	−0.0358950	−	0.368256i	−0.00226117	−	0.0231980i
$253$	−0.252170	−	0.0399398i	−0.0158538	−	0.00251099i
$254$	24.5300	−	2.57821i	1.53915	−	0.161771i
$255$		0			0
$256$	0.629156	−	5.98602i	0.0393223	−	0.374126i
$257$	−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	$0.468813\pi$
$258$	−17.4300	+	2.76064i	−1.08514	+	0.171870i
$259$	19.4365	+	5.36568i	1.20773	+	0.333407i
$260$		0			0
$261$	2.03317	+	0.432164i	0.125850	+	0.0267503i
$262$	−0.563613	−	0.366015i	−0.0348201	−	0.0226125i
$263$	−9.76119	−	6.33899i	−0.601901	−	0.390879i	0.207415	−	0.978253i	$-0.433495\pi$
$263$	−9.76119	−	6.33899i	−0.601901	−	0.390879i	−0.809316	+	0.587374i	$0.800162\pi$
$264$	−2.18558	−	0.464560i	−0.134513	−	0.0285917i
$265$		0			0
$266$	−13.3681	+	13.1676i	−0.819650	+	0.807360i
$267$	9.05817	−	1.43467i	0.554351	−	0.0878006i
$268$	−3.20147	+	0.857832i	−0.195561	+	0.0524004i
$269$	1.26000	−	11.9881i	0.0768234	−	0.730926i	−0.886527	−	0.462678i	$-0.846889\pi$
$269$	1.26000	−	11.9881i	0.0768234	−	0.730926i	0.963350	−	0.268248i	$-0.0864446\pi$
$270$		0			0
$271$	14.5617	−	1.53049i	0.884558	−	0.0929708i	0.348656	−	0.937251i	$-0.386638\pi$
$271$	14.5617	−	1.53049i	0.884558	−	0.0929708i	0.535902	+	0.844280i	$0.319972\pi$
$272$	16.2352	+	2.57141i	0.984405	+	0.155915i
$273$	−0.527532	−	0.737741i	−0.0319277	−	0.0446501i
$274$			5.74694i			0.347185i
$275$		0			0
$276$	0.184386	−	0.106455i	0.0110987	−	0.00640785i
$277$	0.317200	+	6.05253i	0.0190587	+	0.363661i	0.991465	+	0.130370i	$0.0416164\pi$
$277$	0.317200	+	6.05253i	0.0190587	+	0.363661i	−0.972407	+	0.233292i	$0.925050\pi$
$278$	−22.3019	−	18.0597i	−1.33758	−	1.08315i
$279$	−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
$283$	2.43622	+	3.00848i	0.144818	+	0.178836i	0.844394	−	0.535723i	$-0.179961\pi$
$283$	2.43622	+	3.00848i	0.144818	+	0.178836i	−0.699575	+	0.714559i	$0.746628\pi$
$284$	0.249502	+	1.17381i	0.0148052	+	0.0696531i
$285$		0			0
$286$	0.131747	−	0.0428072i	0.00779036	−	0.00253124i
$287$	6.42650	+	3.77535i	0.379344	+	0.222852i
$288$	−0.700374	+	0.356858i	−0.0412699	+	0.0210281i
$289$	1.25530	−	5.90570i	0.0738410	−	0.347394i
$290$		0			0
$291$	14.7538	−	3.13601i	0.864881	−	0.183836i
$292$	−3.12402	−	1.19920i	−0.182820	−	0.0701778i
$293$	−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	$0.397545\pi$
$294$	12.6468	−	7.04905i	0.737574	−	0.411109i
$295$		0			0
$296$	−2.37304	−	22.5780i	−0.137930	−	1.31232i
$297$	0.953769	+	2.48465i	0.0553433	+	0.144174i
$298$	15.2468	−	0.799052i	0.883225	−	0.0462878i
$299$	−0.0583399	+	0.101048i	−0.00337388	+	0.00584374i
$300$		0			0
$301$	−12.1510	−	19.0240i	−0.700373	−	1.09652i
$302$	−19.0344	−	9.69850i	−1.09531	−	0.558086i
$303$	−17.1144	+	21.1345i	−0.983198	+	1.21415i
$304$	16.7976	+	7.47875i	0.963406	+	0.428936i
$305$		0			0
$306$	−1.41360	−	3.17500i	−0.0808102	−	0.181503i
$307$	−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	$0.801557\pi$
$308$	−0.0648348	−	0.316771i	−0.00369430	−	0.0180497i
$309$	−11.6884	−	3.79779i	−0.664929	−	0.216049i
$310$		0			0
$311$	−0.717211	−	0.645779i	−0.0406693	−	0.0366188i	0.648545	−	0.761176i	$-0.275378\pi$
$311$	−0.717211	−	0.645779i	−0.0406693	−	0.0366188i	−0.689215	+	0.724557i	$0.742044\pi$
$312$	−0.556152	+	0.856399i	−0.0314859	+	0.0484841i
$313$	−0.389843	−	0.0204308i	−0.0220352	−	0.00115482i	0.0413152	−	0.999146i	$-0.486845\pi$
$313$	−0.389843	−	0.0204308i	−0.0220352	−	0.00115482i	−0.0633504	+	0.997991i	$0.520179\pi$
$314$	1.64954	+	5.07677i	0.0930891	+	0.286499i
$315$		0			0
$316$	−0.730474	+	2.24817i	−0.0410924	+	0.126469i
$317$	10.7826	−	28.0896i	0.605611	−	1.57767i	−0.196505	−	0.980503i	$-0.562959\pi$
$317$	10.7826	−	28.0896i	0.605611	−	1.57767i	0.802116	−	0.597168i	$-0.203707\pi$
$318$	9.67749	+	2.59308i	0.542687	+	0.145413i
$319$	1.80649	+	0.189870i	0.101144	+	0.0106307i
$320$		0			0
$321$	−1.97789	−	2.72234i	−0.110395	−	0.151946i
$322$	−1.49864	−	1.10621i	−0.0835157	−	0.0616469i
$323$	11.6994	−	22.9613i	0.650970	−	1.27760i
$324$	−1.55873	−	0.899935i	−0.0865962	−	0.0499964i
$325$		0			0
$326$	11.0281	+	19.1013i	0.610792	+	1.05792i
$327$	9.32329	+	14.3566i	0.515579	+	0.793923i
$328$	1.31277	−	8.28853i	0.0724859	−	0.457658i
$329$	−15.4787	+	12.3420i	−0.853367	+	0.680434i
$330$		0			0
$331$	−8.09153	+	3.60258i	−0.444751	+	0.198016i	−0.616878	−	0.787059i	$-0.711603\pi$
$331$	−8.09153	+	3.60258i	−0.444751	+	0.198016i	0.172127	+	0.985075i	$0.444936\pi$
$332$	0.627294	−	2.34109i	0.0344272	−	0.128484i
$333$	−3.24663	+	2.62907i	−0.177914	+	0.144072i
$334$	−21.0794	−	23.4111i	−1.15341	−	1.28100i
$335$		0			0
$336$	−10.9582	−	9.01168i	−0.597819	−	0.491628i
$337$	9.00124	+	17.6659i	0.490329	+	0.962324i	0.995081	+	0.0990602i	$0.0315836\pi$
$337$	9.00124	+	17.6659i	0.490329	+	0.962324i	−0.504753	+	0.863264i	$0.668416\pi$
$338$	−0.895411	+	17.0855i	−0.0487039	+	0.929326i
$339$	−18.6276	+	20.6880i	−1.01171	+	1.12362i
$340$		0			0
$341$	−1.19207	+	1.07334i	−0.0645542	+	0.0581249i
$342$	−0.608168	−	3.83982i	−0.0328860	−	0.207634i
$343$	14.7327	+	11.2226i	0.795490	+	0.605966i
$344$	−14.9389	+	20.5617i	−0.805453	+	1.10861i
$345$		0			0
$346$	−13.1512	+	29.5381i	−0.707012	+	1.58798i
$347$	0.937932	−	0.360039i	0.0503509	−	0.0193279i	−0.333062	−	0.942905i	$-0.608082\pi$
$347$	0.937932	−	0.360039i	0.0503509	−	0.0193279i	0.383413	+	0.923577i	$0.374749\pi$
$348$	−1.27039	+	0.825001i	−0.0681001	+	0.0442247i
$349$	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
$352$	−0.576094	+	0.374120i	−0.0307059	+	0.0199407i
$353$	16.3857	−	6.28989i	0.872124	−	0.334777i	0.119189	−	0.992872i	$-0.461971\pi$
$353$	16.3857	−	6.28989i	0.872124	−	0.334777i	0.752935	+	0.658094i	$0.228637\pi$
$354$	−4.50363	+	10.1153i	−0.239365	+	0.537623i
$355$		0			0
$356$	0.878288	−	1.20886i	0.0465491	−	0.0640694i
$357$	−13.4165	+	14.6761i	−0.710078	+	0.776742i
$358$	−3.65776	−	23.0942i	−0.193318	−	1.22056i
$359$	−21.5239	+	19.3802i	−1.13599	+	1.02285i	−0.136506	+	0.990639i	$0.543587\pi$
$359$	−21.5239	+	19.3802i	−1.13599	+	1.02285i	−0.999481	+	0.0322078i	$0.989746\pi$
$360$		0			0
$361$	6.57525	−	7.30256i	0.346066	−	0.384345i
$362$	0.0655801	−	1.25134i	0.00344682	−	0.0657692i
$363$	−7.65648	−	15.0267i	−0.401861	−	0.788697i
$364$	−0.145769	−	0.0242177i	−0.00764039	−	0.00126935i
$365$		0			0
$366$	12.3199	+	13.6827i	0.643973	+	0.715205i
$367$	−12.8863	+	10.4351i	−0.672658	+	0.544708i	−0.903663	−	0.428245i	$-0.859132\pi$
$367$	−12.8863	+	10.4351i	−0.672658	+	0.544708i	0.231005	+	0.972953i	$0.425799\pi$
$368$	−0.472416	+	1.76308i	−0.0246264	+	0.0919069i
$369$	−1.41074	+	0.628103i	−0.0734403	+	0.0326977i
$370$		0			0
$371$	1.90913	+	12.6726i	0.0991173	+	0.657930i
$372$	0.209259	−	1.32121i	0.0108496	−	0.0685016i
$373$	15.9710	+	24.5932i	0.826946	+	1.27339i	0.959358	+	0.282191i	$0.0910612\pi$
$373$	15.9710	+	24.5932i	0.826946	+	1.27339i	−0.132412	+	0.991195i	$0.542272\pi$
$374$	−1.51858	−	2.63025i	−0.0785237	−	0.136007i
$375$		0			0
$376$	19.3032	+	11.1447i	0.995486	+	0.574744i
$377$	0.376870	−	0.739648i	0.0194098	−	0.0380938i
$378$	−2.17543	+	19.2947i	−0.111892	+	0.992413i
$379$	−10.6445	−	14.6509i	−0.546773	−	0.752568i	0.442797	−	0.896622i	$-0.353986\pi$
$379$	−10.6445	−	14.6509i	−0.546773	−	0.752568i	−0.989570	+	0.144054i	$0.953986\pi$
$380$		0			0
$381$	29.0778	+	3.05620i	1.48970	+	0.156574i
$382$	13.3618	+	3.58028i	0.683649	+	0.183183i
$383$	−10.6911	+	27.8513i	−0.546291	+	1.42314i	0.331209	+	0.943557i	$0.392544\pi$
$383$	−10.6911	+	27.8513i	−0.546291	+	1.42314i	−0.877499	+	0.479578i	$0.840790\pi$
$384$	−4.20083	+	12.9288i	−0.214373	+	0.659771i
$385$		0			0
$386$	8.03783	+	24.7379i	0.409115	+	1.25913i
$387$	4.67051	+	0.244771i	0.237415	+	0.0124424i
$388$	1.33846	−	2.06104i	0.0679499	−	0.104634i
$389$	−8.38594	−	7.55073i	−0.425184	−	0.382837i	0.428575	−	0.903506i	$-0.359016\pi$
$389$	−8.38594	−	7.55073i	−0.425184	−	0.382837i	−0.853759	+	0.520669i	$0.825683\pi$
$390$		0			0
$391$	2.43296	+	0.790515i	0.123040	+	0.0399781i
$392$	5.70059	−	20.0578i	0.287923	−	1.01307i
$393$	−0.563297	−	0.563297i	−0.0284146	−	0.0284146i
$394$	7.67451	+	17.2372i	0.386636	+	0.868399i
$395$		0			0
$396$	0.0611997	+	0.0272479i	0.00307540	+	0.00136926i
$397$	−3.12330	+	3.85695i	−0.156754	+	0.193575i	−0.849472	−	0.527633i	$-0.823080\pi$
$397$	−3.12330	+	3.85695i	−0.156754	+	0.193575i	0.692719	+	0.721208i	$0.256413\pi$
$398$	−8.44891	−	4.30493i	−0.423505	−	0.215787i
$399$	−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	$0.131617\pi$
$402$	26.8347	−	1.40634i	1.33839	−	0.0701421i
$403$	0.262712	+	0.684388i	0.0130866	+	0.0340918i
$404$	0.463150	+	4.40658i	0.0230426	+	0.219236i
$405$		0			0
$406$	11.0594	+	7.30144i	0.548870	+	0.362364i
$407$	−2.58147	+	2.58147i	−0.127959	+	0.127959i
$408$	20.9011	+	8.02317i	1.03476	+	0.397206i
$409$	0.210716	−	0.0447891i	0.0104192	−	0.00221468i	−0.202699	−	0.979241i	$-0.564971\pi$
$409$	0.210716	−	0.0447891i	0.0104192	−	0.00221468i	0.213118	+	0.977026i	$0.431638\pi$
$410$		0			0
$411$	−1.41637	+	6.66352i	−0.0698646	+	0.328687i
$412$	−1.78413	+	0.909060i	−0.0878978	+	0.0447862i
$413$	−14.1631	−	0.106986i	−0.696919	−	0.00526445i
$414$	0.367037	−	0.119258i	0.0180389	−	0.00586119i
$415$		0			0
$416$	0.0652684	+	0.307064i	0.00320005	+	0.0150550i
$417$	−21.4079	−	26.4365i	−1.04835	−	1.29460i
$418$	−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	$0.0384239\pi$
$422$	3.89531	+	3.15436i	0.189621	+	0.153552i
$423$	−0.214663	−	4.09602i	−0.0104373	−	0.199155i
$424$	12.4961	−	7.21461i	0.606863	−	0.350373i
$425$		0			0
$426$		−	9.72928i		−	0.471385i
$427$	−9.74149	+	21.4424i	−0.471424	+	1.03767i
$428$	−0.541504	−	0.0857658i	−0.0261746	−	0.00414565i
$429$	0.163309	−	0.0171645i	0.00788465	−	0.000828711i
$430$		0			0
$431$	−3.65977	+	34.8204i	−0.176285	+	1.67724i	0.446453	+	0.894807i	$0.352687\pi$
$431$	−3.65977	+	34.8204i	−0.176285	+	1.67724i	−0.622738	+	0.782431i	$0.713980\pi$
$432$	18.3786	−	4.92453i	0.884241	−	0.236932i
$433$	−5.71937	+	0.905859i	−0.274855	+	0.0435328i	−0.292340	−	0.956314i	$-0.594434\pi$
$433$	−5.71937	+	0.905859i	−0.274855	+	0.0435328i	0.0174852	+	0.999847i	$0.494434\pi$
$434$	−11.3267	+	2.94347i	−0.543701	+	0.141291i
$435$		0			0
$436$	2.72811	+	0.579878i	0.130653	+	0.0277711i
$437$	2.39992	+	1.55853i	0.114804	+	0.0745544i
$438$	22.7530	+	14.7760i	1.08718	+	0.706024i
$439$	−18.8155	−	3.99935i	−0.898013	−	0.190879i	−0.264294	−	0.964442i	$-0.585139\pi$
$439$	−18.8155	−	3.99935i	−0.898013	−	0.190879i	−0.633719	+	0.773563i	$0.718472\pi$
$440$		0			0
$441$	−3.66685	+	1.13048i	−0.174612	+	0.0538325i
$442$	−1.37091	+	0.217131i	−0.0652075	+	0.0103279i
$443$	−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	$0.536023\pi$
$444$	0.318230	−	3.02775i	0.0151025	−	0.143691i
$445$		0			0
$446$	5.04455	−	0.530203i	0.238866	−	0.0251059i
$447$	17.8755	+	2.83120i	0.845481	+	0.133911i
$448$	−23.0241	+	2.24423i	−1.08779	+	0.106030i
$449$			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
$452$	0.237379	+	4.52946i	0.0111654	+	0.213048i
$453$	−19.6799	−	15.9365i	−0.924643	−	0.748761i
$454$	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	$-0.320209\pi$
$458$	−9.16600	−	11.3191i	−0.428299	−	0.528905i
$459$	−5.54431	−	26.0839i	−0.258786	−	1.21749i
$460$		0			0
$461$	30.3418	−	9.85863i	1.41316	−	0.459162i	0.499735	−	0.866178i	$-0.333431\pi$
$461$	30.3418	−	9.85863i	1.41316	−	0.459162i	0.913421	+	0.407016i	$0.133431\pi$
$462$	−0.0198016	+	2.62138i	−0.000921254	+	0.121958i
$463$	−3.31433	+	1.68874i	−0.154030	+	0.0784822i	−0.529306	−	0.848431i	$-0.677548\pi$
$463$	−3.31433	+	1.68874i	−0.154030	+	0.0784822i	0.375276	+	0.926913i	$0.377548\pi$
$464$	2.69995	−	12.7023i	0.125342	−	0.589688i
$465$		0			0
$466$	−25.2659	+	5.37044i	−1.17042	+	0.248781i
$467$	−6.63789	−	2.54805i	−0.307165	−	0.117910i	0.199903	−	0.979816i	$-0.435937\pi$
$467$	−6.63789	−	2.54805i	−0.307165	−	0.117910i	−0.507068	+	0.861906i	$0.669271\pi$
$468$	0.0216484	−	0.0216484i	0.00100070	−	0.00100070i
$469$	15.3730	+	30.7432i	0.709861	+	1.41959i
$470$		0			0
$471$	0.661422	+	6.29301i	0.0304767	+	0.289966i
$472$	5.71482	+	14.8876i	0.263046	+	0.685258i
$473$	4.08148	−	0.213901i	0.187666	−	0.00983518i
$474$	9.58249	−	16.5974i	0.440138	−	0.762342i
$475$		0			0
$476$	0.145112	+	3.23649i	0.00665119	+	0.148344i
$477$	−2.36583	−	1.20545i	−0.108324	−	0.0551938i
$478$	−8.04614	+	9.93616i	−0.368022	+	0.454469i
$479$	−10.5264	−	4.68667i	−0.480965	−	0.214140i	0.151908	−	0.988395i	$-0.451458\pi$
$479$	−10.5264	−	4.68667i	−0.480965	−	0.214140i	−0.632874	+	0.774255i	$0.718125\pi$
$480$		0			0
$481$	0.678607	+	1.52418i	0.0309418	+	0.0694964i
$482$	−11.7241	−	11.7241i	−0.534019	−	0.534019i
$483$	−1.46502	−	1.65199i	−0.0666606	−	0.0751683i
$484$	−2.61328	−	0.849107i	−0.118786	−	0.0385958i
$485$		0			0
$486$	−5.51739	−	4.96788i	−0.250274	−	0.225347i
$487$	−2.38315	+	3.66973i	−0.107991	+	0.166291i	−0.888534	−	0.458810i	$-0.848276\pi$
$487$	−2.38315	+	3.66973i	−0.107991	+	0.166291i	0.780543	+	0.625102i	$0.214942\pi$
$488$	26.4805	+	1.38778i	1.19871	+	0.0628220i
$489$	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	$0.0300570\pi$
$492$	0.403295	−	1.05062i	0.0181819	−	0.0473656i
$493$	−17.5801	−	4.71056i	−0.791766	−	0.212153i
$494$	−1.54412	−	0.162293i	−0.0694732	−	0.00730192i
$495$		0			0
$496$	6.74065	+	9.27771i	0.302664	+	0.416582i
$497$	11.4071	−	4.97589i	0.511681	−	0.223199i
$498$	−8.92087	+	17.5082i	−0.399754	+	0.784561i
$499$	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
$502$	11.0228	+	16.9737i	0.491973	+	0.757573i
$503$	−0.623100	+	3.93410i	−0.0277826	+	0.175413i	−0.997678	−	0.0681101i	$-0.978303\pi$
$503$	−0.623100	+	3.93410i	−0.0277826	+	0.175413i	0.969895	+	0.243523i	$0.0783031\pi$
$504$	2.69341	+	3.37794i	0.119974	+	0.150465i
$505$		0			0
$506$	0.308096	−	0.137173i	0.0136965	−	0.00609810i
$507$	−5.24905	+	19.5897i	−0.233119	+	0.870011i
$508$	3.70209	−	2.99789i	0.164253	−	0.133010i
$509$	1.53153	+	1.70093i	0.0678838	+	0.0753926i	0.776130	−	0.630573i	$-0.217180\pi$
$509$	1.53153	+	1.70093i	0.0678838	+	0.0753926i	−0.708246	+	0.705965i	$0.750513\pi$
$510$		0			0
$511$	−5.68752	+	34.2339i	−0.251601	+	1.51442i
$512$	11.4924	+	22.5551i	0.507898	+	0.996806i
$513$	1.56116	−	29.7886i	0.0689267	−	1.31520i
$514$	4.62190	−	5.13314i	0.203863	−	0.226413i
$515$		0			0
$516$	−2.53285	+	2.28059i	−0.111503	+	0.100397i
$517$	−0.560716	−	3.54022i	−0.0246603	−	0.155699i
$518$	−25.3927	+	8.03903i	−1.11569	+	0.353215i
$519$	−22.5285	+	31.0079i	−0.988893	+	1.36109i
$520$		0			0
$521$	−5.48334	+	12.3158i	−0.240230	+	0.539565i	−0.992917	−	0.118814i	$-0.962091\pi$
$521$	−5.48334	+	12.3158i	−0.240230	+	0.539565i	0.752687	+	0.658379i	$0.228757\pi$
$522$	−2.56333	+	0.983969i	−0.112194	+	0.0430672i
$523$	−5.72408	+	3.71726i	−0.250297	+	0.162545i	−0.663689	−	0.748008i	$-0.731010\pi$
$523$	−5.72408	+	3.71726i	−0.250297	+	0.162545i	0.413393	+	0.910553i	$0.364344\pi$
$524$	−0.129793			−0.00567001
$525$		0			0
$526$	15.3743			0.670350
$527$	13.4795	−	8.75370i	0.587177	−	0.381317i
$528$	2.39818	−	0.920574i	0.104367	−	0.0400629i
$529$	9.23940	−	20.7520i	0.401713	−	0.902263i
$530$		0			0
$531$	1.72485	−	2.37405i	0.0748521	−	0.103025i
$532$	−0.780227	+	3.53902i	−0.0338271	+	0.153436i
$533$	0.0964772	+	0.609133i	0.00417889	+	0.0263845i
$534$	−9.00279	+	8.10615i	−0.389589	+	0.350787i
$535$		0			0
$536$	25.8956	−	28.7600i	1.11852	−	1.24224i
$537$	1.45059	−	27.6789i	0.0625977	−	1.19443i
$538$	7.22877	+	14.1873i	0.311655	+	0.611657i
$539$	−3.08358	+	1.31745i	−0.132819	+	0.0567464i
$540$		0			0
$541$	−5.10841	−	5.67347i	−0.219628	−	0.243921i	0.623255	−	0.782019i	$-0.285810\pi$
$541$	−5.10841	−	5.67347i	−0.219628	−	0.243921i	−0.842883	+	0.538097i	$0.819143\pi$
$542$	−15.0308	+	12.1717i	−0.645628	+	0.522819i
$543$	0.384442	−	1.43476i	0.0164980	−	0.0615714i
$544$	6.28762	−	2.79943i	0.269580	−	0.120025i
$545$		0			0
$546$	1.11517	+	0.437768i	0.0477250	+	0.0187348i
$547$	6.49848	−	41.0298i	0.277855	−	1.75431i	−0.315089	−	0.949062i	$-0.602034\pi$
$547$	6.49848	−	41.0298i	0.277855	−	1.75431i	0.592944	−	0.805244i	$-0.297966\pi$
$548$	0.604512	+	0.930867i	0.0258235	+	0.0397647i
$549$	−2.43978	−	4.22582i	−0.104127	−	0.180354i
$550$		0			0
$551$	−17.6313	−	10.1794i	−0.751119	−	0.433659i
$552$	−1.12863	+	2.21507i	−0.0480379	+	0.0942797i
$553$	24.3605	+	2.74659i	1.03591	+	0.116797i
$554$	−4.70581	−	6.47699i	−0.199931	−	0.275181i
$555$		0			0
$556$	−5.51206	−	0.579340i	−0.233763	−	0.0245695i
$557$	−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	$0.680544\pi$
$558$	0.868936	−	2.26365i	0.0367850	−	0.0958281i
$559$	0.577188	−	1.77640i	0.0244125	−	0.0751338i
$560$		0			0
$561$	−1.11253	−	3.42401i	−0.0469710	−	0.144562i
$562$	6.09130	+	0.319231i	0.256946	+	0.0134660i
$563$	−22.8733	+	35.2219i	−0.963997	+	1.48442i	−0.0914994	+	0.995805i	$0.529166\pi$
$563$	−22.8733	+	35.2219i	−0.963997	+	1.48442i	−0.872497	+	0.488619i	$0.837501\pi$
$564$	2.22130	+	2.00007i	0.0935337	+	0.0842181i
$565$		0			0
$566$	−4.86334	−	1.58019i	−0.204421	−	0.0664205i
$567$	−5.90199	+	17.7082i	−0.247860	+	0.743673i
$568$	−9.90808	−	9.90808i	−0.415734	−	0.415734i
$569$	9.54513	+	21.4387i	0.400153	+	0.898758i	0.995453	+	0.0952543i	$0.0303664\pi$
$569$	9.54513	+	21.4387i	0.400153	+	0.898758i	−0.595300	+	0.803503i	$0.702967\pi$
$570$		0			0
$571$	−8.83659	−	3.93430i	−0.369800	−	0.164645i	0.213419	−	0.976961i	$-0.431540\pi$
$571$	−8.83659	−	3.93430i	−0.369800	−	0.164645i	−0.583218	+	0.812315i	$0.698207\pi$
$572$	0.0168371	−	0.0207920i	0.000703993	−	0.000869358i
$573$	14.6105	+	7.44442i	0.610362	+	0.310995i
$574$	−9.83561	+	0.440991i	−0.410530	+	0.0184066i
$575$		0			0
$576$	2.39645	−	4.15077i	0.0998521	−	0.172949i
$577$	−1.66943	+	0.0874910i	−0.0694992	+	0.00364230i	−0.0870538	−	0.996204i	$-0.527745\pi$
$577$	−1.66943	+	0.0874910i	−0.0694992	+	0.00364230i	0.0175547	+	0.999846i	$0.494412\pi$
$578$	2.85811	+	7.44564i	0.118882	+	0.309698i
$579$	3.22295	+	30.6643i	0.133941	+	1.27437i
$580$		0			0
$581$	−25.0900	−	1.50503i	−1.04091	−	0.0624394i
$582$	−14.0886	+	14.0886i	−0.583989	+	0.583989i
$583$	−2.16624	−	0.831542i	−0.0897166	−	0.0344390i
$584$	38.2187	−	8.12364i	1.58150	−	0.336159i
$585$		0			0
$586$	4.20372	−	19.7770i	0.173654	−	0.816978i
$587$	0.544273	−	0.277321i	0.0224646	−	0.0114463i	−0.442722	−	0.896659i	$-0.645987\pi$
$587$	0.544273	−	0.277321i	0.0224646	−	0.0114463i	0.465187	+	0.885213i	$0.345987\pi$
$588$	1.30700	−	2.47207i	0.0538996	−	0.101947i
$589$	17.0988	−	5.55575i	0.704545	−	0.228921i
$590$		0			0
$591$	4.65028	+	21.8778i	0.191287	+	0.899934i
$592$	16.4251	+	20.2834i	0.675069	+	0.833641i
$593$	−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
$597$	−8.73544	−	7.07382i	−0.357518	−	0.289512i
$598$	−0.00806638	−	0.153916i	−0.000329859	−	0.00629408i
$599$	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	$0.984835\pi$
$602$	27.1478	+	12.3335i	1.10646	+	0.502678i
$603$	−7.03388	−	1.11406i	−0.286442	−	0.0453679i
$604$	−4.10329	+	0.431273i	−0.166960	+	0.0175482i
$605$		0			0
$606$	3.75498	−	35.7263i	0.152536	−	1.45128i
$607$	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	$0.288551\pi$
$608$	7.60420	−	1.20439i	0.308391	−	0.0488444i
$609$	11.0238	+	11.1916i	0.446707	+	0.453507i
$610$		0			0
$611$	−1.60228	−	0.340574i	−0.0648211	−	0.0137782i
$612$	−0.562944	−	0.365580i	−0.0227557	−	0.0147777i
$613$	−8.30505	−	5.39337i	−0.335438	−	0.217836i	0.365918	−	0.930647i	$-0.380755\pi$
$613$	−8.30505	−	5.39337i	−0.335438	−	0.217836i	−0.701356	+	0.712811i	$0.747422\pi$
$614$	7.30168	+	1.55202i	0.294672	+	0.0626345i
$615$		0			0
$616$	2.64939	+	2.68972i	0.106747	+	0.108372i
$617$	−5.48345	+	0.868493i	−0.220755	+	0.0349642i	−0.265832	−	0.964019i	$-0.585647\pi$
$617$	−5.48345	+	0.868493i	−0.220755	+	0.0349642i	0.0450769	+	0.998984i	$0.485647\pi$
$618$	15.6810	−	4.20172i	0.630784	−	0.169018i
$619$	3.98195	−	37.8857i	0.160048	−	1.52276i	−0.559802	−	0.828626i	$-0.689123\pi$
$619$	3.98195	−	37.8857i	0.160048	−	1.52276i	0.719850	−	0.694129i	$-0.244210\pi$
$620$		0			0
$621$	2.94491	−	0.309523i	0.118175	−	0.0124207i
$622$	1.25915	+	0.199429i	0.0504872	+	0.00799638i
$623$	−14.1084	−	6.40961i	−0.565243	−	0.256796i
$624$		−	1.17396i		−	0.0469959i
$625$		0			0
$626$	0.446579	−	0.257833i	0.0178489	−	0.0103051i
$627$	−0.210769	−	4.02171i	−0.00841730	−	0.160612i
$628$	0.801205	+	0.648803i	0.0319716	+	0.0258901i
$629$	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
$633$	3.73916	+	4.61748i	0.148618	+	0.183528i
$634$	8.26335	+	38.8760i	0.328180	+	1.54396i
$635$		0			0
$636$	1.84029	−	0.597945i	0.0729721	−	0.0237101i
$637$	0.0570740	+	1.53138i	0.00226136	+	0.0606756i
$638$	−2.13789	+	1.08931i	−0.0846400	+	0.0431262i
$639$	−0.536096	+	2.52213i	−0.0212076	+	0.0997741i
$640$		0			0
$641$	−7.58550	+	1.61235i	−0.299609	+	0.0636839i	−0.355263	−	0.934766i	$-0.615609\pi$
$641$	−7.58550	+	1.61235i	−0.299609	+	0.0636839i	0.0556544	+	0.998450i	$0.482276\pi$
$642$	4.14972	+	1.59293i	0.163777	+	0.0628679i
$643$	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	$0.0941251\pi$
$644$	−0.359104	−	0.0215410i	−0.0141507	−	0.000848835i
$645$		0			0
$646$	3.55822	+	33.8542i	0.139996	+	1.33198i
$647$	10.8463	+	28.2556i	0.426412	+	1.11084i	0.963593	+	0.267374i	$0.0861560\pi$
$647$	10.8463	+	28.2556i	0.426412	+	1.11084i	−0.537181	+	0.843467i	$0.680511\pi$
$648$	20.9872	−	1.09989i	0.824456	−	0.0432079i
$649$	1.28220	−	2.22083i	0.0503307	−	0.0871754i
$650$		0			0
$651$	−13.8587	+	0.621370i	−0.543165	+	0.0243534i
$652$	3.79554	+	1.93392i	0.148645	+	0.0757383i
$653$	−21.1279	+	26.0908i	−0.826800	+	1.02101i	0.172552	+	0.985000i	$0.444799\pi$
$653$	−21.1279	+	26.0908i	−0.826800	+	1.02101i	−0.999351	+	0.0360120i	$0.988535\pi$
$654$	−20.6573	−	9.19723i	−0.807765	−	0.359640i
$655$		0			0
$656$	3.92408	+	8.81364i	0.153210	+	0.344115i
$657$	−5.08413	−	5.08413i	−0.198351	−	0.198351i
$658$	8.26854	−	24.8087i	0.322341	−	0.967145i
$659$	45.9853	+	14.9415i	1.79133	+	0.582039i	0.999585	−	0.0288108i	$-0.00917203\pi$
$659$	45.9853	+	14.9415i	1.79133	+	0.582039i	0.791747	+	0.610850i	$0.209172\pi$
$660$		0			0
$661$	−5.08370	−	4.57738i	−0.197733	−	0.178040i	0.564316	−	0.825559i	$-0.309140\pi$
$661$	−5.08370	−	4.57738i	−0.197733	−	0.178040i	−0.762049	+	0.647519i	$0.775807\pi$
$662$	6.37224	−	9.81239i	0.247664	−	0.381369i
$663$	−1.64307	−	0.0861096i	−0.0638115	−	0.00334422i
$664$	8.74513	+	26.9148i	0.339377	+	1.04450i
$665$		0			0
$666$	1.70528	−	5.24830i	0.0660781	−	0.203368i
$667$	0.724262	−	1.88677i	0.0280435	−	0.0730559i
$668$	−5.87694	−	1.57472i	−0.227386	−	0.0609278i
$669$	5.97978	+	0.628500i	0.231192	+	0.0242992i
$670$		0			0
$671$	−2.50641	−	3.44978i	−0.0967589	−	0.133177i
$672$	−5.90322	−	0.665574i	−0.227722	−	0.0256751i
$673$	−12.8780	+	25.2746i	−0.496412	+	0.974263i	0.497847	+	0.867265i	$0.334124\pi$
$673$	−12.8780	+	25.2746i	−0.496412	+	0.974263i	−0.994259	+	0.106999i	$0.965876\pi$
$674$	−22.6814	−	13.0951i	−0.873653	−	0.504404i
$675$		0			0
$676$	1.65216	+	2.86163i	0.0635446	+	0.110063i
$677$	6.86510	+	10.5713i	0.263847	+	0.406289i	0.945619	−	0.325276i	$-0.105457\pi$
$677$	6.86510	+	10.5713i	0.263847	+	0.406289i	−0.681772	+	0.731565i	$0.738790\pi$
$678$	5.75255	−	36.3202i	0.220925	−	1.39487i
$679$	−23.7236	−	9.31284i	−0.910427	−	0.357394i
$680$		0			0
$681$	2.79289	−	1.24348i	0.107024	−	0.0476501i
$682$	0.548413	−	2.04670i	0.0209998	−	0.0783723i
$683$	3.95935	−	3.20622i	0.151500	−	0.122683i	−0.550574	−	0.834787i	$-0.685591\pi$
$683$	3.95935	−	3.20622i	0.151500	−	0.122683i	0.702074	+	0.712104i	$0.252258\pi$
$684$	−0.502414	−	0.557988i	−0.0192103	−	0.0213352i
$685$		0			0
$686$	−24.3953	−	1.83361i	−0.931418	−	0.0700074i
$687$	−7.83822	−	15.3834i	−0.299047	−	0.586912i
$688$	1.52921	−	29.1791i	0.0583007	−	1.11244i
$689$	−0.709559	+	0.788045i	−0.0270320	+	0.0300221i
$690$		0			0
$691$	−9.30768	+	8.38068i	−0.354081	+	0.318816i	−0.826906	−	0.562341i	$-0.809901\pi$
$691$	−9.30768	+	8.38068i	−0.354081	+	0.318816i	0.472825	+	0.881156i	$0.343234\pi$
$692$	0.976886	+	6.16782i	0.0371356	+	0.234465i
$693$	0.149575	−	0.678453i	0.00568187	−	0.0257723i
$694$	−0.780048	+	1.07364i	−0.0296102	+	0.0407550i
$695$		0			0
$696$	7.19397	−	16.1579i	0.272687	−	0.612465i
$697$	12.6234	−	4.84567i	0.478145	−	0.183543i
$698$	−25.3251	+	16.4463i	−0.958570	+	0.622503i
$699$	−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	$0.759361\pi$
$702$	−1.34744	+	0.875040i	−0.0508560	+	0.0330263i
$703$	38.2002	−	14.6637i	1.44075	−	0.553052i
$704$	1.70359	−	3.82632i	0.0642064	−	0.144210i
$705$		0			0
$706$	−13.6275	+	18.7566i	−0.512877	+	0.705915i
$707$	43.8079	−	13.8691i	1.64757	−	0.521601i
$708$	0.334535	+	2.11217i	0.0125726	+	0.0793803i
$709$	26.3654	−	23.7396i	0.990175	−	0.891558i	−0.00392835	−	0.999992i	$-0.501250\pi$
$709$	26.3654	−	23.7396i	0.990175	−	0.891558i	0.994104	+	0.108434i	$0.0345838\pi$
$710$		0			0
$711$	−3.39862	+	3.77455i	−0.127458	+	0.141557i
$712$	−0.913120	+	17.4234i	−0.0342206	+	0.652968i
$713$	0.810250	+	1.59021i	0.0303441	+	0.0595537i
$714$	4.30478	−	25.9110i	0.161102	−	0.969695i
$715$		0			0
$716$	−3.02171	−	3.35595i	−0.112927	−	0.125418i
$717$	−11.7783	+	9.53785i	−0.439867	+	0.356197i
$718$	9.90207	−	36.9550i	0.369542	−	1.37915i
$719$	−12.5161	+	5.57251i	−0.466771	+	0.207820i	−0.626625	−	0.779321i	$-0.715564\pi$
$719$	−12.5161	+	5.57251i	−0.466771	+	0.207820i	0.159854	+	0.987141i	$0.448898\pi$
$720$		0			0
$721$	12.9462	+	16.2364i	0.482140	+	0.604676i
$722$	−2.03057	+	12.8205i	−0.0755698	+	0.477129i
$723$	−10.7045	−	16.4835i	−0.398105	−	0.613027i
$724$	−0.121005	−	0.209586i	−0.00449710	−	0.00778921i
$725$		0			0
$726$	19.2928	+	11.1387i	0.716024	+	0.413397i
$727$	18.6979	−	36.6967i	0.693467	−	1.36101i	−0.228425	−	0.973561i	$-0.573358\pi$
$727$	18.6979	−	36.6967i	0.693467	−	1.36101i	0.921893	−	0.387445i	$-0.126642\pi$
$728$	1.58148	−	0.689855i	0.0586136	−	0.0255677i
$729$	−17.6135	−	24.2429i	−0.652352	−	0.897885i
$730$		0			0
$731$	−40.7269	−	4.28057i	−1.50634	−	0.158323i
$732$	3.43480	+	0.920351i	0.126954	+	0.0340172i
$733$	−10.3482	+	26.9579i	−0.382218	+	0.995713i	0.598645	+	0.801015i	$0.295706\pi$
$733$	−10.3482	+	26.9579i	−0.382218	+	0.995713i	−0.980863	+	0.194698i	$0.937627\pi$
$734$	6.76846	−	20.8312i	0.249829	−	0.768893i
$735$		0			0
$736$	0.236172	+	0.726863i	0.00870542	+	0.0267925i
$737$	−6.21487	−	0.325708i	−0.228928	−	0.0119976i
$738$	1.11099	−	1.71077i	0.0408960	−	0.0629743i
$739$	−13.5923	−	12.2385i	−0.499999	−	0.450202i	0.380132	−	0.924932i	$-0.375879\pi$
$739$	−13.5923	−	12.2385i	−0.499999	−	0.450202i	−0.880131	+	0.474731i	$0.842545\pi$
$740$		0			0
$741$	−1.75039	−	0.568737i	−0.0643022	−	0.0208931i
$742$	−11.2321	−	12.6657i	−0.412345	−	0.464971i
$743$	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	$0.588822\pi$
$744$	6.35294	+	14.2689i	0.232910	+	0.523125i
$745$		0			0
$746$	−35.3864	−	15.7550i	−1.29559	−	0.576833i
$747$	3.27729	−	4.04712i	0.119910	−	0.148076i
$748$	−0.522646	−	0.266301i	−0.0191098	−	0.00973694i
$749$	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	$-0.0131794\pi$
$752$	−25.5900	+	1.34111i	−0.933170	+	0.0489054i
$753$	8.59759	+	22.3975i	0.313313	+	0.816210i
$754$	0.114620	+	1.09054i	0.00417423	+	0.0397151i
$755$		0			0
$756$	1.67722	+	3.35412i	0.0609997	+	0.121988i
$757$	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	$0.0111650\pi$
$758$	22.3328	+	8.57275i	0.811163	+	0.311376i
$759$	0.391042	−	0.0831185i	0.0141939	−	0.00301701i
$760$		0			0
$761$	0.212683	−	1.00060i	0.00770976	−	0.0362716i	−0.974125	−	0.226012i	$-0.927431\pi$
$761$	0.212683	−	1.00060i	0.00770976	−	0.0362716i	0.981834	+	0.189740i	$0.0607646\pi$
$762$	−34.4120	+	17.5338i	−1.24662	+	0.635183i
$763$	0.218485	−	28.9236i	0.00790970	−	1.04710i
$764$	2.54090	−	0.825588i	0.0919265	−	0.0298687i
$765$		0			0
$766$	−8.19324	−	38.5462i	−0.296034	−	1.39273i
$767$	−0.737530	−	0.910774i	−0.0266307	−	0.0328861i
$768$	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
$772$	3.90408	+	3.16146i	0.140511	+	0.113784i
$773$	−1.36051	−	25.9601i	−0.0489342	−	0.933720i	−0.907248	−	0.420595i	$-0.861821\pi$
$773$	−1.36051	−	25.9601i	−0.0489342	−	0.933720i	0.858314	−	0.513124i	$-0.171512\pi$
$774$	−5.35024	+	3.08897i	−0.192311	+	0.111031i
$775$		0			0
$776$			28.6949i			1.03009i
$777$	−31.4238	+	3.06297i	−1.12732	+	0.109884i
$778$	14.7225	+	2.33181i	0.527827	+	0.0835995i
$779$	15.0424	−	1.58102i	0.538949	−	0.0566458i
$780$		0			0
$781$	−0.235533	+	2.24094i	−0.00842802	+	0.0801873i
$782$	−3.26403	+	0.874595i	−0.116722	+	0.0312754i
$783$	−20.8078	+	3.29564i	−0.743611	+	0.117776i
$784$	7.06271	+	22.9087i	0.252240	+	0.818169i
$785$		0			0
$786$	1.02929	+	0.218783i	0.0367137	+	0.00780374i
$787$	−40.7153	−	26.4408i	−1.45134	−	0.942514i	−0.998708	−	0.0508190i	$-0.983817\pi$
$787$	−40.7153	−	26.4408i	−1.45134	−	0.942514i	−0.452637	−	0.891695i	$-0.649517\pi$
$788$	3.05625	+	1.98475i	0.108874	+	0.0707038i
$789$	17.8263	+	3.78910i	0.634633	+	0.134895i
$790$		0			0
$791$	45.5259	−	11.8308i	1.61871	−	0.420654i
$792$	−0.772589	+	0.122366i	−0.0274528	+	0.00434809i
$793$	−1.88235	+	0.504373i	−0.0668441	+	0.0179108i
$794$	0.685265	−	6.51986i	0.0243192	−	0.231381i
$795$		0			0
$796$	−1.82135	+	0.191432i	−0.0645561	+	0.00678512i
$797$	−10.1052	−	1.60051i	−0.357945	−	0.0566929i	−0.0251277	−	0.999684i	$-0.507999\pi$
$797$	−10.1052	−	1.60051i	−0.357945	−	0.0566929i	−0.332817	+	0.942991i	$0.607999\pi$
$798$	12.1529	−	26.7503i	0.430209	−	0.946950i
$799$			35.9141i			1.27055i
$800$		0			0
$801$	2.78047	−	1.60530i	0.0982429	−	0.0567206i
$802$	0.304256	+	5.80555i	0.0107437	+	0.205001i
$803$	−4.88300	−	3.95417i	−0.172317	−	0.139540i
$804$	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
$808$	−32.5588	−	40.2068i	−1.14542	−	1.41447i
$809$	−8.76738	−	41.2473i	−0.308245	−	1.45018i	−0.810643	−	0.585540i	$-0.800882\pi$
$809$	−8.76738	−	41.2473i	−0.308245	−	1.45018i	0.502399	−	0.864636i	$-0.332451\pi$
$810$		0			0
$811$	−30.4344	+	9.88872i	−1.06869	+	0.347240i	−0.789979	−	0.613134i	$-0.789909\pi$
$811$	−30.4344	+	9.88872i	−1.06869	+	0.347240i	−0.278716	+	0.960374i	$0.589909\pi$
$812$	2.55939	+	0.0193334i	0.0898171	+	0.000678468i
$813$	−20.4279	+	10.4085i	−0.716436	+	0.365043i
$814$	1.00264	−	4.71704i	0.0351425	−	0.165332i
$815$		0			0
$816$	−25.1761	+	5.35135i	−0.881340	+	0.187335i
$817$	−42.7658	−	16.4162i	−1.49619	−	0.574332i
$818$	−0.201215	+	0.201215i	−0.00703533	+	0.00703533i
$819$	−0.264967	−	0.174931i	−0.00925868	−	0.00611258i
$820$		0			0
$821$	−5.08271	−	48.3588i	−0.177388	−	1.68773i	−0.614966	−	0.788553i	$-0.710830\pi$
$821$	−5.08271	−	48.3588i	−0.177388	−	1.68773i	0.437578	−	0.899180i	$-0.355836\pi$
$822$	−3.22486	−	8.40105i	−0.112480	−	0.293020i
$823$	1.79452	−	0.0940468i	0.0625531	−	0.00327827i	−0.0210338	−	0.999779i	$-0.506696\pi$
$823$	1.79452	−	0.0940468i	0.0625531	−	0.00327827i	0.0835868	+	0.996500i	$0.473362\pi$
$824$	11.6903	−	20.2482i	0.407250	−	0.705378i
$825$		0			0
$826$	15.7673	−	10.0709i	0.548614	−	0.350411i
$827$	15.8538	+	8.07790i	0.551290	+	0.280896i	0.707364	−	0.706849i	$-0.249884\pi$
$827$	15.8538	+	8.07790i	0.551290	+	0.280896i	−0.156075	+	0.987745i	$0.549884\pi$
$828$	0.0469067	−	0.0579250i	0.00163012	−	0.00201303i
$829$	−46.2932	−	20.6110i	−1.60783	−	0.715851i	−0.610719	−	0.791847i	$-0.709120\pi$
$829$	−46.2932	−	20.6110i	−1.60783	−	0.715851i	−0.997108	+	0.0759961i	$0.975786\pi$
$830$		0			0
$831$	−3.86004	−	8.66978i	−0.133903	−	0.300752i
$832$	−1.35350	−	1.35350i	−0.0469242	−	0.0469242i
$833$	32.5811	−	8.20461i	1.12887	−	0.284273i
$834$	42.7357	+	13.8857i	1.47982	+	0.480822i
$835$		0			0
$836$	−0.487615	−	0.439051i	−0.0168645	−	0.0151849i
$837$	10.1326	−	15.6029i	0.350235	−	0.539314i
$838$	45.7562	+	2.39798i	1.58062	+	0.0828368i
$839$	−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
$842$	−14.2266	+	37.0616i	−0.490281	+	1.27723i
$843$	6.98412	+	1.87139i	0.240546	+	0.0644541i
$844$	0.962751	+	0.101189i	0.0331393	+	0.00348308i
$845$		0			0
$846$	3.18463	+	4.38327i	0.109490	+	0.150700i
$847$	−3.19264	+	28.3167i	−0.109701	+	0.972974i
$848$	−7.53108	+	14.7806i	−0.258618	+	0.507567i
$849$	−5.24954	−	3.03082i	−0.180164	−	0.104018i
$850$		0			0
$851$	2.03094	+	3.51769i	0.0696197	+	0.120585i
$852$	−1.02341	−	1.57591i	−0.0350614	−	0.0539899i
$853$	−1.83983	+	11.6162i	−0.0629946	+	0.397732i	0.935964	+	0.352097i	$0.114531\pi$
$853$	−1.83983	+	11.6162i	−0.0629946	+	0.397732i	−0.998958	+	0.0456353i	$0.985469\pi$
$854$	−4.63445	−	30.7629i	−0.158587	−	1.05269i
$855$		0			0
$856$	5.84819	−	2.60378i	0.199887	−	0.0889954i
$857$	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	$0.0812618\pi$
$858$	−0.168571	+	0.136506i	−0.00575491	+	0.00466024i
$859$	6.46460	+	7.17966i	0.220569	+	0.244967i	0.843266	−	0.537496i	$-0.180630\pi$
$859$	6.46460	+	7.17966i	0.220569	+	0.244967i	−0.622697	+	0.782463i	$0.713963\pi$
$860$		0			0
$861$	−11.5130	−	1.91273i	−0.392361	−	0.0651858i
$862$	−20.9966	−	41.2081i	−0.715146	−	1.40355i
$863$	−0.263310	+	5.02426i	−0.00896318	+	0.171028i	0.990480	+	0.137658i	$0.0439573\pi$
$863$	−0.263310	+	5.02426i	−0.00896318	+	0.171028i	−0.999443	+	0.0333701i	$0.989376\pi$
$864$	5.33087	−	5.92053i	0.181360	−	0.201420i
$865$		0			0
$866$	5.68440	−	5.11825i	0.193164	−	0.173925i
$867$	1.47892	+	9.33755i	0.0502268	+	0.317120i
$868$	−1.52504	+	1.66822i	−0.0517634	+	0.0566230i
$869$	−2.60893	+	3.59089i	−0.0885020	+	0.121813i
$870$		0			0
$871$	−1.15681	+	2.59825i	−0.0391971	+	0.0880382i
$872$	−30.4032	+	11.6707i	−1.02958	+	0.395219i
$873$	4.42849	−	2.87590i	0.149882	−	0.0973344i
$874$	−3.77997			−0.127859
$875$		0			0
$876$	5.23972			0.177034
$877$	−18.1362	+	11.7778i	−0.612417	+	0.397708i	−0.813248	−	0.581918i	$-0.802303\pi$
$877$	−18.1362	+	11.7778i	−0.612417	+	0.397708i	0.200831	+	0.979626i	$0.435636\pi$
$878$	23.7217	−	9.10590i	0.800568	−	0.307309i
$879$	9.74835	−	21.8951i	0.328804	−	0.738505i
$880$		0			0
$881$	15.8503	−	21.8160i	0.534009	−	0.735001i	−0.453725	−	0.891142i	$-0.649905\pi$
$881$	15.8503	−	21.8160i	0.534009	−	0.735001i	0.987735	+	0.156141i	$0.0499053\pi$
$882$	3.24895	−	3.89045i	0.109398	−	0.130998i
$883$	−0.103976	−	0.656476i	−0.00349906	−	0.0220922i	0.985877	−	0.167471i	$-0.0535600\pi$
$883$	−0.103976	−	0.656476i	−0.00349906	−	0.0220922i	−0.989376	+	0.145379i	$0.953560\pi$
$884$	−0.199215	+	0.179374i	−0.00670033	+	0.00603300i
$885$		0			0
$886$	13.6268	−	15.1341i	0.457803	−	0.508441i
$887$	1.60164	−	30.5611i	0.0537778	−	1.02614i	−0.829860	−	0.557971i	$-0.811580\pi$
$887$	1.60164	−	30.5611i	0.0537778	−	1.02614i	0.883638	−	0.468170i	$-0.155087\pi$
$888$	16.1385	+	31.6735i	0.541572	+	1.06289i
$889$	−38.1571	−	31.3792i	−1.27975	−	1.05242i
$890$		0			0
$891$	−2.26138	−	2.51152i	−0.0757591	−	0.0841390i
$892$	0.761326	−	0.616509i	0.0254911	−	0.0206423i
$893$	−10.3977	+	38.8049i	−0.347947	+	1.29856i
$894$	−21.8399	+	9.72375i	−0.730436	+	0.325211i
$895$		0			0
$896$	17.9595	−	14.3201i	0.599986	−	0.478400i
$897$	0.0285808	−	0.180452i	0.000954284	−	0.00602511i
$898$	−10.1572	−	15.6407i	−0.338949	−	0.521935i
$899$	−6.34879	−	10.9964i	−0.211744	−	0.366752i
$900$		0			0
$901$	20.1345	+	11.6246i	0.670777	+	0.387273i
$902$	0.809282	−	1.58830i	0.0269461	−	0.0528848i
$903$	28.4379	+	20.9914i	0.946355	+	0.698550i
$904$	−31.1294	−	42.8459i	−1.03535	−	1.42503i
$905$		0			0
$906$	33.2673	+	3.49653i	1.10523	+	0.116165i
$907$	−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	$0.772961\pi$
$908$	0.178505	−	0.465022i	0.00592390	−	0.0154323i
$909$	−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	$0.790880\pi$
$912$	−28.7519	−	1.50682i	−0.952069	−	0.0498958i
$913$	2.47859	−	3.81670i	0.0820294	−	0.126314i
$914$	28.4292	+	25.5977i	0.940353	+	0.846697i
$915$		0			0
$916$	−2.67531	−	0.869261i	−0.0883948	−	0.0287212i
$917$	0.269903	+	1.31870i	0.00891298	+	0.0435472i
$918$	24.9079	+	24.9079i	0.822082	+	0.822082i
$919$	−13.0177	−	29.2383i	−0.429415	−	0.964481i	−0.990600	−	0.136791i	$-0.956321\pi$
$919$	−13.0177	−	29.2383i	−0.429415	−	0.964481i	0.561185	−	0.827690i	$-0.310346\pi$
$920$		0			0
$921$	8.08372	+	3.59911i	0.266368	+	0.118595i
$922$	−26.5210	+	32.7506i	−0.873421	+	1.07859i
$923$	0.917529	+	0.467504i	0.0302008	+	0.0153881i
$924$	0.272532	+	0.426684i	0.00896563	+	0.0140369i
$925$		0			0
$926$	2.45679	−	4.25528i	0.0807351	−	0.139837i
$927$	−4.29654	+	0.225172i	−0.141117	+	0.00739563i
$928$	−1.94861	−	5.07629i	−0.0639661	−	0.166637i
$929$	4.40135	+	41.8761i	0.144404	+	1.37391i	0.791345	+	0.611369i	$0.209381\pi$
$929$	4.40135	+	41.8761i	0.144404	+	1.37391i	−0.646942	+	0.762539i	$0.723952\pi$
$930$		0			0
$931$	37.5790	+	0.567767i	1.23160	+	0.0186078i
$932$	−3.52757	+	3.52757i	−0.115549	+	0.115549i
$933$	1.41082	+	0.541562i	0.0461881	+	0.0177299i
$934$	9.18683	−	1.95272i	0.300602	−	0.0638950i
$935$		0			0
$936$	−0.0743241	+	0.349668i	−0.00242936	+	0.0114292i
$937$	−14.8083	+	7.54518i	−0.483765	+	0.246490i	−0.678824	−	0.734301i	$-0.737510\pi$
$937$	−14.8083	+	7.54518i	−0.483765	+	0.246490i	0.195059	+	0.980791i	$0.437510\pi$
$938$	−39.1485	−	22.9984i	−1.27824	−	0.750925i
$939$	0.581349	−	0.188892i	0.0189716	−	0.00616425i
$940$		0			0
$941$	−2.27250	−	10.6913i	−0.0740814	−	0.348526i	0.925459	−	0.378848i	$-0.123680\pi$
$941$	−2.27250	−	10.6913i	−0.0740814	−	0.348526i	−0.999540	+	0.0303227i	$0.990347\pi$
$942$	−5.26016	−	6.49575i	−0.171385	−	0.211643i
$943$	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
$947$	25.4529	+	20.6113i	0.827107	+	0.669778i	0.946370	−	0.323084i	$-0.104720\pi$
$947$	25.4529	+	20.6113i	0.827107	+	0.669778i	−0.119263	+	0.992863i	$0.538053\pi$
$948$	−0.193717	−	3.69635i	−0.00629164	−	0.120052i
$949$	−2.48678	+	1.43574i	−0.0807242	+	0.0466062i
$950$		0			0
$951$			47.1129i			1.52774i
$952$	−22.0033	−	30.7711i	−0.713131	−	0.997296i
$953$	30.6299	+	4.85130i	0.992200	+	0.157149i	0.631369	−	0.775482i	$-0.282493\pi$
$953$	30.6299	+	4.85130i	0.992200	+	0.157149i	0.360831	+	0.932631i	$0.382493\pi$
$954$	3.48819	−	0.366623i	0.112934	−	0.0118699i
$955$		0			0
$956$	−0.258113	+	2.45578i	−0.00834798	+	0.0794257i
$957$	−2.74733	+	0.736146i	−0.0888087	+	0.0237962i
$958$	15.0333	−	2.38104i	0.485704	−	0.0769279i
$959$	8.20056	−	8.07759i	0.264810	−	0.260839i
$960$		0			0
$961$	−19.3545	−	4.11392i	−0.624338	−	0.132707i
$962$	−1.84833	−	1.20032i	−0.0595925	−	0.0386998i
$963$	−0.987966	−	0.641593i	−0.0318368	−	0.0206750i
$964$	−3.13227	−	0.665785i	−0.100884	−	0.0214435i
$965$		0			0
$966$	2.81150	+	0.776147i	0.0904585	+	0.0249721i
$967$	32.8149	−	5.19736i	1.05525	−	0.167136i	0.395385	−	0.918516i	$-0.370611\pi$
$967$	32.8149	−	5.19736i	1.05525	−	0.167136i	0.659870	+	0.751380i	$0.270611\pi$
$968$	30.9908	−	8.30397i	0.996083	−	0.266900i
$969$	−4.21789	+	40.1306i	−0.135498	+	1.28918i
$970$		0			0
$971$	−9.62205	+	1.01132i	−0.308786	+	0.0324547i	−0.257654	−	0.966237i	$-0.582950\pi$
$971$	−9.62205	+	1.01132i	−0.308786	+	0.0324547i	−0.0511320	+	0.998692i	$0.516283\pi$
$972$	−1.41625	−	0.224312i	−0.0454262	−	0.00719481i
$973$	5.57617	+	57.2074i	0.178764	+	1.83398i
$974$		−	5.77998i		−	0.185202i
$975$		0			0
$976$	−26.4009	+	15.2426i	−0.845073	+	0.487903i
$977$	0.219005	+	4.17887i	0.00700660	+	0.133694i	0.999893	+	0.0146284i	$0.00465653\pi$
$977$	0.219005	+	4.17887i	0.00700660	+	0.133694i	−0.992886	+	0.119066i	$0.962010\pi$
$978$	−26.8399	−	21.7345i	−0.858245	−	0.694993i
$979$	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
$983$	7.66884	+	9.47023i	0.244598	+	0.302053i	0.884629	−	0.466296i	$-0.154412\pi$
$983$	7.66884	+	9.47023i	0.244598	+	0.302053i	−0.640031	+	0.768349i	$0.721078\pi$
$984$	2.73201	+	12.8531i	0.0870933	+	0.409742i
$985$		0			0
$986$	22.8647	−	7.42920i	0.728161	−	0.236594i
$987$	15.7016	−	26.7276i	0.499787	−	0.850750i
$988$	−0.267182	+	0.136136i	−0.00850019	+	0.00433106i
$989$	0.945444	−	4.44797i	0.0300634	−	0.141437i
$990$		0			0
$991$	39.1306	−	8.31747i	1.24302	−	0.264213i	0.460966	−	0.887418i	$-0.347503\pi$
$991$	39.1306	−	8.31747i	1.24302	−	0.264213i	0.782059	+	0.623205i	$0.214170\pi$
$992$	4.48284	+	1.72080i	0.142330	+	0.0546354i
$993$	9.80688	−	9.80688i	0.311212	−	0.311212i
$994$	−9.05739	+	13.7192i	−0.287283	+	0.435145i
$995$		0			0
$996$	0.396693	+	3.77428i	0.0125697	+	0.119593i
$997$	−0.138605	−	0.361077i	−0.00438965	−	0.0114354i	0.931368	−	0.364079i	$-0.118616\pi$
$997$	−0.138605	−	0.361077i	−0.00438965	−	0.0114354i	−0.935758	+	0.352644i	$0.885283\pi$
$998$	−6.23160	+	0.326584i	−0.197258	+	0.0103378i
$999$	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.c.768.6		288
5.2	odd	4		875.2.bb.a.607.6		288
5.3	odd	4		875.2.bb.b.607.13		288
5.4	even	2		175.2.x.a.33.13	✓	288
7.3	odd	6	inner	875.2.bb.c.143.6		288
25.3	odd	20		175.2.x.a.47.13	yes	288
25.4	even	10		875.2.bb.b.243.6		288
25.21	even	5		875.2.bb.a.243.13		288
25.22	odd	20	inner	875.2.bb.c.257.6		288
35.3	even	12		875.2.bb.b.857.6		288
35.17	even	12		875.2.bb.a.857.13		288
35.24	odd	6		175.2.x.a.108.13	yes	288
175.3	even	60		175.2.x.a.122.13	yes	288
175.122	even	60	inner	875.2.bb.c.507.6		288
175.129	odd	30		875.2.bb.b.493.13		288
175.171	odd	30		875.2.bb.a.493.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	5.4	even	2
175.2.x.a.47.13	yes	288	25.3	odd	20
175.2.x.a.108.13	yes	288	35.24	odd	6
175.2.x.a.122.13	yes	288	175.3	even	60
875.2.bb.a.243.13		288	25.21	even	5
875.2.bb.a.493.6		288	175.171	odd	30
875.2.bb.a.607.6		288	5.2	odd	4
875.2.bb.a.857.13		288	35.17	even	12
875.2.bb.b.243.6		288	25.4	even	10
875.2.bb.b.493.13		288	175.129	odd	30
875.2.bb.b.607.13		288	5.3	odd	4
875.2.bb.b.857.6		288	35.3	even	12
875.2.bb.c.143.6		288	7.3	odd	6	inner
875.2.bb.c.257.6		288	25.22	odd	20	inner
875.2.bb.c.507.6		288	175.122	even	60	inner
875.2.bb.c.768.6		288	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.10783 + 0.719435i) q^{2} +(-1.46183 + 0.561145i) q^{3} +(-0.103766 + 0.233063i) q^{4} +(1.21576 - 1.67335i) q^{6} +(2.58371 + 0.569615i) q^{7} +(-0.465999 - 2.94220i) q^{8} +(-0.407366 + 0.366794i) q^{9} +(-0.320535 + 0.355990i) q^{11} +(0.0209068 - 0.398926i) q^{12} +(0.0993879 + 0.195060i) q^{13} +(-3.27212 + 1.22777i) q^{14} +(2.29156 + 2.54503i) q^{16} +(3.73011 - 3.02058i) q^{17} +(0.187409 - 0.699421i) q^{18} +(4.90486 - 2.18378i) q^{19} +(-4.09658 + 0.617151i) q^{21} +(0.0989874 - 0.624982i) q^{22} +(0.290280 + 0.446992i) q^{23} +(2.33221 + 4.03951i) q^{24} +(-0.250438 - 0.144591i) q^{26} +(2.52230 - 4.95029i) q^{27} +(-0.400858 + 0.543059i) q^{28} +(-2.22883 - 3.06772i) q^{29} +(3.33026 + 0.350024i) q^{31} +(1.38510 + 0.371137i) q^{32} +(0.268806 - 0.700264i) q^{33} +(-1.95922 + 6.02987i) q^{34} +(-0.0432152 - 0.133003i) q^{36} +(7.61066 + 0.398858i) q^{37} +(-3.86267 + 5.94800i) q^{38} +(-0.254745 - 0.229374i) q^{39} +(2.67924 + 0.870538i) q^{41} +(4.09433 - 3.63092i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(-0.0497074 - 0.111645i) q^{44} +(-0.643164 - 0.286355i) q^{46} +(-4.70888 + 5.81498i) q^{47} +(-4.77800 - 2.43451i) q^{48} +(6.35108 + 2.94344i) q^{49} +(-3.75781 + 6.50871i) q^{51} +(-0.0557743 + 0.00292301i) q^{52} +(1.73588 + 4.52212i) q^{53} +(0.767126 + 7.29872i) q^{54} +(0.471919 - 7.86722i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(4.67619 + 1.79502i) q^{58} +(-5.23631 + 1.11301i) q^{59} +(-1.85075 + 8.70710i) q^{61} +(-3.94119 + 2.00814i) q^{62} +(-1.26145 + 0.715647i) q^{63} +(-8.31559 + 2.70190i) q^{64} +(0.206002 + 0.969164i) q^{66} +(8.17589 + 10.0964i) q^{67} +(0.316926 + 1.18278i) q^{68} +(-0.675168 - 0.490538i) q^{69} +(3.80548 - 2.76485i) q^{71} +(1.26902 + 1.02763i) q^{72} +(0.686467 + 13.0986i) q^{73} +(-8.71829 + 5.03351i) q^{74} +1.36974i q^{76} +(-1.03095 + 0.737192i) q^{77} +(0.447234 + 0.0708350i) q^{78} +(9.21497 - 0.968533i) q^{79} +(-0.737450 + 7.01637i) q^{81} +(-3.59445 + 0.963129i) q^{82} +(-9.38322 + 1.48616i) q^{83} +(0.281252 - 1.01880i) q^{84} +(11.0239 + 2.34320i) q^{86} +(4.97960 + 3.23379i) q^{87} +(1.19676 + 0.777187i) q^{88} +(-5.72901 - 1.21774i) q^{89} +(0.145680 + 0.560590i) q^{91} +(-0.134299 + 0.0212708i) q^{92} +(-5.06469 + 1.35708i) q^{93} +(1.03315 - 9.82977i) q^{94} +(-2.23304 + 0.234702i) q^{96} +(-9.51421 - 1.50690i) q^{97} +(-9.15355 + 1.30835i) q^{98} -0.262589i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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