LMFDB - Embedded newform 875.2.bb.a.493.6

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			493.6
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.a.607.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.719435 + 1.10783i) q^{2} +(0.561145 - 1.46183i) q^{3} +(0.103766 + 0.233063i) q^{4} +(1.21576 + 1.67335i) q^{6} +(-0.569615 - 2.58371i) q^{7} +(-2.94220 - 0.465999i) q^{8} +(0.407366 + 0.366794i) q^{9} +(-0.320535 - 0.355990i) q^{11} +(0.398926 - 0.0209068i) q^{12} +(0.195060 + 0.0993879i) q^{13} +(3.27212 + 1.22777i) q^{14} +(2.29156 - 2.54503i) q^{16} +(3.02058 - 3.73011i) q^{17} +(-0.699421 + 0.187409i) q^{18} +(-4.90486 - 2.18378i) q^{19} +(-4.09658 - 0.617151i) q^{21} +(0.624982 - 0.0989874i) q^{22} +(0.446992 + 0.290280i) q^{23} +(-2.33221 + 4.03951i) q^{24} +(-0.250438 + 0.144591i) q^{26} +(4.95029 - 2.52230i) q^{27} +(0.543059 - 0.400858i) q^{28} +(2.22883 - 3.06772i) q^{29} +(3.33026 - 0.350024i) q^{31} +(-0.371137 - 1.38510i) q^{32} +(-0.700264 + 0.268806i) q^{33} +(1.95922 + 6.02987i) q^{34} +(-0.0432152 + 0.133003i) q^{36} +(-0.398858 - 7.61066i) q^{37} +(5.94800 - 3.86267i) q^{38} +(0.254745 - 0.229374i) q^{39} +(2.67924 - 0.870538i) q^{41} +(3.63092 - 4.09433i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(0.0497074 - 0.111645i) q^{44} +(-0.643164 + 0.286355i) q^{46} +(-5.81498 + 4.70888i) q^{47} +(-2.43451 - 4.77800i) q^{48} +(-6.35108 + 2.94344i) q^{49} +(-3.75781 - 6.50871i) q^{51} +(-0.00292301 + 0.0557743i) q^{52} +(4.52212 + 1.73588i) q^{53} +(-0.767126 + 7.29872i) q^{54} +(0.471919 + 7.86722i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(1.79502 + 4.67619i) q^{58} +(5.23631 + 1.11301i) q^{59} +(-1.85075 - 8.70710i) q^{61} +(-2.00814 + 3.94119i) q^{62} +(0.715647 - 1.26145i) q^{63} +(8.31559 + 2.70190i) q^{64} +(0.206002 - 0.969164i) q^{66} +(-10.0964 - 8.17589i) q^{67} +(1.18278 + 0.316926i) q^{68} +(0.675168 - 0.490538i) q^{69} +(3.80548 + 2.76485i) q^{71} +(-1.02763 - 1.26902i) q^{72} +(13.0986 + 0.686467i) q^{73} +(8.71829 + 5.03351i) q^{74} -1.36974i q^{76} +(-0.737192 + 1.03095i) q^{77} +(0.0708350 + 0.447234i) q^{78} +(-9.21497 - 0.968533i) q^{79} +(-0.737450 - 7.01637i) q^{81} +(-0.963129 + 3.59445i) q^{82} +(1.48616 - 9.38322i) q^{83} +(-0.281252 - 1.01880i) q^{84} +(11.0239 - 2.34320i) q^{86} +(-3.23379 - 4.97960i) q^{87} +(0.777187 + 1.19676i) q^{88} +(5.72901 - 1.21774i) q^{89} +(0.145680 - 0.560590i) q^{91} +(-0.0212708 + 0.134299i) q^{92} +(1.35708 - 5.06469i) q^{93} +(-1.03315 - 9.82977i) q^{94} +(-2.23304 - 0.234702i) q^{96} +(1.50690 + 9.51421i) q^{97} +(1.30835 - 9.15355i) q^{98} -0.262589i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.719435	+	1.10783i	−0.508717	+	0.783356i	−0.995949	−	0.0899164i	$-0.971340\pi$
$2$	−0.719435	+	1.10783i	−0.508717	+	0.783356i	0.487232	+	0.873273i	$0.338007\pi$
$3$	0.561145	−	1.46183i	0.323977	−	0.843989i	−0.670774	−	0.741662i	$-0.734038\pi$
$3$	0.561145	−	1.46183i	0.323977	−	0.843989i	0.994751	−	0.102327i	$-0.0326288\pi$
$4$	0.103766	+	0.233063i	0.0518831	+	0.116531i
$5$		0			0
$5$		0			0
$6$	1.21576	+	1.67335i	0.496331	+	0.683141i
$7$	−0.569615	−	2.58371i	−0.215294	−	0.976549i
$7$	−0.569615	−	2.58371i	−0.215294	−	0.976549i
$8$	−2.94220	−	0.465999i	−1.04023	−	0.164755i
$9$	0.407366	+	0.366794i	0.135789	+	0.122265i
$10$		0			0
$11$	−0.320535	−	0.355990i	−0.0966449	−	0.107335i	0.692882	−	0.721051i	$-0.256341\pi$
$11$	−0.320535	−	0.355990i	−0.0966449	−	0.107335i	−0.789527	+	0.613716i	$0.789674\pi$
$12$	0.398926	−	0.0209068i	0.115160	−	0.00603529i
$13$	0.195060	+	0.0993879i	0.0540999	+	0.0275653i	0.480831	−	0.876813i	$-0.340335\pi$
$13$	0.195060	+	0.0993879i	0.0540999	+	0.0275653i	−0.426731	+	0.904378i	$0.640335\pi$
$14$	3.27212	+	1.22777i	0.874510	+	0.328135i
$15$		0			0
$16$	2.29156	−	2.54503i	0.572889	−	0.636258i
$17$	3.02058	−	3.73011i	0.732599	−	0.904684i	−0.265636	−	0.964073i	$-0.585582\pi$
$17$	3.02058	−	3.73011i	0.732599	−	0.904684i	0.998235	+	0.0593890i	$0.0189152\pi$
$18$	−0.699421	+	0.187409i	−0.164855	+	0.0441728i
$19$	−4.90486	−	2.18378i	−1.12525	−	0.500994i	−0.242180	−	0.970231i	$-0.577862\pi$
$19$	−4.90486	−	2.18378i	−1.12525	−	0.500994i	−0.883072	+	0.469237i	$0.844529\pi$
$20$		0			0
$21$	−4.09658	−	0.617151i	−0.893947	−	0.134673i
$22$	0.624982	−	0.0989874i	0.133247	−	0.0211042i
$23$	0.446992	+	0.290280i	0.0932044	+	0.0605276i	0.590400	−	0.807111i	$-0.298970\pi$
$23$	0.446992	+	0.290280i	0.0932044	+	0.0605276i	−0.497195	+	0.867639i	$0.665637\pi$
$24$	−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
$28$	0.543059	−	0.400858i	0.102629	−	0.0757550i
$29$	2.22883	−	3.06772i	0.413883	−	0.569661i	−0.550277	−	0.834982i	$-0.685478\pi$
$29$	2.22883	−	3.06772i	0.413883	−	0.569661i	0.964160	+	0.265321i	$0.0854780\pi$
$30$		0			0
$31$	3.33026	−	0.350024i	0.598132	−	0.0628662i	0.199376	−	0.979923i	$-0.436109\pi$
$31$	3.33026	−	0.350024i	0.598132	−	0.0628662i	0.398756	+	0.917057i	$0.369442\pi$
$32$	−0.371137	−	1.38510i	−0.0656083	−	0.244853i
$33$	−0.700264	+	0.268806i	−0.121900	+	0.0467932i
$34$	1.95922	+	6.02987i	0.336004	+	1.03411i
$35$		0			0
$36$	−0.0432152	+	0.133003i	−0.00720254	+	0.0221671i
$37$	−0.398858	−	7.61066i	−0.0655718	−	1.25118i	−0.811179	−	0.584799i	$-0.801174\pi$
$37$	−0.398858	−	7.61066i	−0.0655718	−	1.25118i	0.745607	−	0.666386i	$-0.232160\pi$
$38$	5.94800	−	3.86267i	0.964893	−	0.626609i
$39$	0.254745	−	0.229374i	0.0407919	−	0.0367292i
$40$		0			0
$41$	2.67924	−	0.870538i	0.418427	−	0.135955i	−0.0922339	−	0.995737i	$-0.529401\pi$
$41$	2.67924	−	0.870538i	0.418427	−	0.135955i	0.510661	+	0.859782i	$0.329401\pi$
$42$	3.63092	−	4.09433i	0.560264	−	0.631768i
$43$	−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
$47$	−5.81498	+	4.70888i	−0.848203	+	0.686861i	−0.951453	−	0.307795i	$-0.900409\pi$
$47$	−5.81498	+	4.70888i	−0.848203	+	0.686861i	0.103250	+	0.994655i	$0.467076\pi$
$48$	−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
$52$	−0.00292301	+	0.0557743i	−0.000405348	+	0.00773450i
$53$	4.52212	+	1.73588i	0.621161	+	0.238442i	0.648536	−	0.761184i	$-0.275381\pi$
$53$	4.52212	+	1.73588i	0.621161	+	0.238442i	−0.0273749	+	0.999625i	$0.508715\pi$
$54$	−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
$58$	1.79502	+	4.67619i	0.235698	+	0.614014i
$59$	5.23631	+	1.11301i	0.681709	+	0.144902i	0.535735	−	0.844386i	$-0.320035\pi$
$59$	5.23631	+	1.11301i	0.681709	+	0.144902i	0.145975	+	0.989288i	$0.453368\pi$
$60$		0			0
$61$	−1.85075	−	8.70710i	−0.236964	−	1.11483i	−0.922262	−	0.386566i	$-0.873661\pi$
$61$	−1.85075	−	8.70710i	−0.236964	−	1.11483i	0.685297	−	0.728263i	$-0.259672\pi$
$62$	−2.00814	+	3.94119i	−0.255034	+	0.500532i
$63$	0.715647	−	1.26145i	0.0901630	−	0.158927i
$64$	8.31559	+	2.70190i	1.03945	+	0.337737i
$65$		0			0
$66$	0.206002	−	0.969164i	0.0253571	−	0.119296i
$67$	−10.0964	−	8.17589i	−1.23347	−	0.998844i	−0.999647	−	0.0265646i	$-0.991543\pi$
$67$	−10.0964	−	8.17589i	−1.23347	−	0.998844i	−0.233822	−	0.972279i	$-0.575123\pi$
$68$	1.18278	+	0.316926i	0.143434	+	0.0384329i
$69$	0.675168	−	0.490538i	0.0812807	−	0.0590539i
$70$		0			0
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	0.790238	−	0.612800i	$-0.209957\pi$
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	−0.338610	+	0.940927i	$0.609957\pi$
$72$	−1.02763	−	1.26902i	−0.121107	−	0.149555i
$73$	13.0986	+	0.686467i	1.53307	+	0.0803449i	0.800080	−	0.599893i	$-0.204790\pi$
$73$	13.0986	+	0.686467i	1.53307	+	0.0803449i	0.732991	+	0.680238i	$0.238124\pi$
$74$	8.71829	+	5.03351i	1.01348	+	0.585133i
$75$		0			0
$76$		−	1.36974i		−	0.157120i
$77$	−0.737192	+	1.03095i	−0.0840109	+	0.117487i
$78$	0.0708350	+	0.447234i	0.00802048	+	0.0506393i
$79$	−9.21497	−	0.968533i	−1.03677	−	0.108968i	−0.429177	−	0.903220i	$-0.641196\pi$
$79$	−9.21497	−	0.968533i	−1.03677	−	0.108968i	−0.607588	+	0.794252i	$0.707863\pi$
$80$		0			0
$81$	−0.737450	−	7.01637i	−0.0819389	−	0.779597i
$82$	−0.963129	+	3.59445i	−0.106360	+	0.396940i
$83$	1.48616	−	9.38322i	0.163127	−	1.02994i	−0.761249	−	0.648459i	$-0.775414\pi$
$83$	1.48616	−	9.38322i	0.163127	−	1.02994i	0.924376	−	0.381482i	$-0.124586\pi$
$84$	−0.281252	−	1.01880i	−0.0306871	−	0.111160i
$85$		0			0
$86$	11.0239	−	2.34320i	1.18874	−	0.252674i
$87$	−3.23379	−	4.97960i	−0.346699	−	0.533869i
$88$	0.777187	+	1.19676i	0.0828484	+	0.127575i
$89$	5.72901	−	1.21774i	0.607274	−	0.129080i	0.105996	−	0.994367i	$-0.466197\pi$
$89$	5.72901	−	1.21774i	0.607274	−	0.129080i	0.501278	+	0.865286i	$0.332864\pi$
$90$		0			0
$91$	0.145680	−	0.560590i	0.0152714	−	0.0587658i
$92$	−0.0212708	+	0.134299i	−0.00221764	+	0.0140016i
$93$	1.35708	−	5.06469i	0.140723	−	0.525184i
$94$	−1.03315	−	9.82977i	−0.106561	−	1.01386i
$95$		0			0
$96$	−2.23304	−	0.234702i	−0.227909	−	0.0239542i
$97$	1.50690	+	9.51421i	0.153003	+	0.966022i	0.938028	+	0.346558i	$0.112650\pi$
$97$	1.50690	+	9.51421i	0.153003	+	0.966022i	−0.785026	+	0.619463i	$0.787350\pi$
$98$	1.30835	−	9.15355i	0.132163	−	0.924648i
$99$		−	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	$0.334568\pi$
$102$	9.91407	+	0.519574i	0.981639	+	0.0514455i
$103$	4.93940	+	6.09966i	0.486694	+	0.601017i	0.960041	−	0.279859i	$-0.0902877\pi$
$103$	4.93940	+	6.09966i	0.486694	+	0.601017i	−0.473347	+	0.880876i	$0.656954\pi$
$104$	−0.527590	−	0.383317i	−0.0517345	−	0.0375873i
$105$		0			0
$106$	−5.17644	+	3.76090i	−0.502780	+	0.365291i
$107$	−2.07579	−	0.556205i	−0.200674	−	0.0537704i	0.157082	−	0.987586i	$-0.449791\pi$
$107$	−2.07579	−	0.556205i	−0.200674	−	0.0537704i	−0.357756	+	0.933815i	$0.616458\pi$
$108$	1.10153	+	0.891998i	0.105994	+	0.0858326i
$109$	2.27297	−	10.6935i	0.217711	−	1.02425i	−0.724511	−	0.689263i	$-0.757935\pi$
$109$	2.27297	−	10.6935i	0.217711	−	1.02425i	0.942223	−	0.334988i	$-0.108732\pi$
$110$		0			0
$111$	−11.3493	−	3.68762i	−1.07723	−	0.350013i
$112$	−7.88092	−	4.47102i	−0.744677	−	0.422472i
$113$	−8.07135	+	15.8409i	−0.759289	+	1.49019i	0.108952	+	0.994047i	$0.465250\pi$
$113$	−8.07135	+	15.8409i	−0.759289	+	1.49019i	−0.868241	+	0.496142i	$0.834750\pi$
$114$	−2.30889	−	10.8625i	−0.216248	−	1.01737i
$115$		0			0
$116$	0.946248	+	0.201131i	0.0878569	+	0.0186746i
$117$	0.0430059	+	0.112034i	0.00397589	+	0.0103576i
$118$	−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
$122$	10.9775	+	4.21387i	0.993857	+	0.381506i
$123$	0.230861	−	4.40510i	0.0208161	−	0.397194i
$124$	0.427146	+	0.739839i	0.0383589	+	0.0664395i
$125$		0			0
$126$	0.882611	+	1.70035i	0.0786293	+	0.151479i
$127$	8.47711	+	16.6373i	0.752222	+	1.47632i	0.875124	+	0.483899i	$0.160780\pi$
$127$	8.47711	+	16.6373i	0.752222	+	1.47632i	−0.122902	+	0.992419i	$0.539220\pi$
$128$	−6.74699	+	5.46360i	−0.596355	+	0.482919i
$129$	−12.2046	+	5.43384i	−1.07456	+	0.478423i
$130$		0			0
$131$	0.206928	−	0.464769i	0.0180794	−	0.0406070i	−0.904280	−	0.426940i	$-0.859592\pi$
$131$	0.206928	−	0.464769i	0.0180794	−	0.0406070i	0.922360	+	0.386333i	$0.126258\pi$
$132$	−0.135313	−	0.135313i	−0.0117774	−	0.0117774i
$133$	−2.84837	+	13.9166i	−0.246985	+	1.20673i
$134$	16.3212	−	5.30308i	1.40994	−	0.458117i
$135$		0			0
$136$	−10.6254	+	9.56714i	−0.911120	+	0.820376i
$137$	3.64876	−	2.36953i	0.311734	−	0.202443i	−0.379283	−	0.925281i	$-0.623829\pi$
$137$	3.64876	−	2.36953i	0.311734	−	0.202443i	0.691018	+	0.722838i	$0.257163\pi$
$138$	0.0576949	+	1.10088i	0.00491132	+	0.0937135i
$139$	−6.71334	+	20.6615i	−0.569418	+	1.75249i	0.0850255	+	0.996379i	$0.472903\pi$
$139$	−6.71334	+	20.6615i	−0.569418	+	1.75249i	−0.654444	+	0.756111i	$0.727097\pi$
$140$		0			0
$141$	3.62054	+	11.1429i	0.304905	+	0.938401i
$142$	−5.80079	+	2.22671i	−0.486791	+	0.186862i
$143$	−0.0271424	−	0.101297i	−0.00226976	−	0.00847085i
$144$	1.86701	−	0.196230i	0.155584	−	0.0163525i
$145$		0			0
$146$	−10.1841	+	14.0172i	−0.842839	+	1.16007i
$147$	0.738938	+	10.9359i	0.0609466	+	0.901978i
$148$	1.73237	−	0.882688i	0.142400	−	0.0725565i
$149$	10.0097	−	5.77912i	0.820030	−	0.473444i	−0.0303970	−	0.999538i	$-0.509677\pi$
$149$	10.0097	−	5.77912i	0.820030	−	0.473444i	0.850427	+	0.526094i	$0.176344\pi$
$150$		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	$-0.0619502\pi$
$152$	13.4134	+	8.71079i	1.08797	+	0.706538i
$153$	2.59867	−	0.411589i	0.210090	−	0.0332750i
$154$	−0.611754	−	1.55838i	−0.0492965	−	0.125578i
$155$		0			0
$156$	0.0798924	+	0.0355704i	0.00639651	+	0.00284791i
$157$	3.90339	−	1.04591i	0.311525	−	0.0834728i	−0.0996695	−	0.995021i	$-0.531779\pi$
$157$	3.90339	−	1.04591i	0.311525	−	0.0834728i	0.411194	+	0.911548i	$0.365112\pi$
$158$	7.70255	−	9.51185i	0.612782	−	0.756723i
$159$	5.07513	−	5.63650i	0.402484	−	0.447004i
$160$		0			0
$161$	0.495385	−	1.32025i	0.0390418	−	0.104050i
$162$	8.30351	+	4.23085i	0.652386	+	0.332407i
$163$	−16.6745	+	0.873876i	−1.30605	+	0.0684472i	−0.692621	−	0.721302i	$-0.743544\pi$
$163$	−16.6745	+	0.873876i	−1.30605	+	0.0684472i	−0.613430	+	0.789749i	$0.710211\pi$
$164$	0.480905	+	0.534099i	0.0375524	+	0.0417061i
$165$		0			0
$166$	9.32584	+	8.39703i	0.723826	+	0.651736i
$167$	−23.5551	−	3.73076i	−1.82275	−	0.288695i	−0.851078	−	0.525039i	$-0.824051\pi$
$167$	−23.5551	−	3.73076i	−1.82275	−	0.288695i	−0.971669	+	0.236344i	$0.924051\pi$
$168$	11.7654	+	3.72478i	0.907718	+	0.287373i
$169$	−7.61304	−	10.4784i	−0.585618	−	0.806034i
$170$		0			0
$171$	−1.19708	−	2.68868i	−0.0915427	−	0.205608i
$172$	0.780046	−	2.03209i	0.0594780	−	0.154945i
$173$	−13.3315	+	20.5286i	−1.01357	+	1.56076i	−0.199585	+	0.979881i	$0.563959\pi$
$173$	−13.3315	+	20.5286i	−1.01357	+	1.56076i	−0.813987	+	0.580883i	$0.802707\pi$
$174$	7.84307			0.594581
$175$		0			0
$176$	−1.64053			−0.123660
$177$	4.56536	−	7.03004i	0.343154	−	0.528410i
$178$	−2.77260	+	7.22287i	−0.207815	+	0.541377i
$179$	7.19967	+	16.1707i	0.538129	+	1.20866i	0.954157	+	0.299306i	$0.0967550\pi$
$179$	7.19967	+	16.1707i	0.538129	+	1.20866i	−0.416028	+	0.909352i	$0.636578\pi$
$180$		0			0
$181$	−0.557581	−	0.767444i	−0.0414447	−	0.0570437i	0.787792	−	0.615942i	$-0.211224\pi$
$181$	−0.557581	−	0.767444i	−0.0414447	−	0.0570437i	−0.829236	+	0.558898i	$0.811224\pi$
$182$	0.516233	+	0.564698i	0.0382657	+	0.0418582i
$183$	−13.7668	−	2.18045i	−1.01767	−	0.161184i
$184$	−1.17987	−	1.06236i	−0.0869813	−	0.0783183i
$185$		0			0
$186$	4.63450	+	5.14714i	0.339818	+	0.377406i
$187$	−2.29609	+	0.120333i	−0.167906	+	0.00879960i
$188$	−1.70086	−	0.866634i	−0.124048	−	0.0632058i
$189$	−9.33663	−	11.3533i	−0.679140	−	0.825835i
$190$		0			0
$191$	−7.00728	+	7.78237i	−0.507029	+	0.563112i	−0.941257	−	0.337690i	$-0.890354\pi$
$191$	−7.00728	+	7.78237i	−0.507029	+	0.563112i	0.434229	+	0.900803i	$0.357021\pi$
$192$	8.61597	−	10.6398i	0.621804	−	0.767864i
$193$	−19.0203	+	5.09648i	−1.36911	+	0.366852i	−0.867154	−	0.498040i	$-0.834053\pi$
$193$	−19.0203	+	5.09648i	−1.36911	+	0.366852i	−0.501957	+	0.864892i	$0.667387\pi$
$194$	−11.6243	−	5.17546i	−0.834574	−	0.371576i
$195$		0			0
$196$	−1.34503	−	1.17477i	−0.0960738	−	0.0839122i
$197$	14.1083	−	2.23453i	1.00517	−	0.159204i	0.367920	−	0.929858i	$-0.380070\pi$
$197$	14.1083	−	2.23453i	1.00517	−	0.159204i	0.637254	+	0.770654i	$0.280070\pi$
$198$	0.290905	+	0.188916i	0.0206737	+	0.0134257i
$199$	−3.58928	+	6.21681i	−0.254437	+	0.440698i	−0.964742	−	0.263196i	$-0.915223\pi$
$199$	−3.58928	+	6.21681i	−0.254437	+	0.440698i	0.710305	+	0.703894i	$0.248557\pi$
$200$		0			0
$201$	−17.6173	+	10.1714i	−1.24263	+	0.717432i
$202$	−20.4413	+	10.4154i	−1.43824	+	0.732822i
$203$	−9.19565	−	4.01121i	−0.645408	−	0.281532i
$204$	1.12701	−	1.55119i	0.0789062	−	0.108605i
$205$		0			0
$206$	−10.3110	+	1.08373i	−0.718400	+	0.0755069i
$207$	0.0756165	+	0.282205i	0.00525571	+	0.0196146i
$208$	0.699936	−	0.268680i	0.0485318	−	0.0186296i
$209$	0.794773	+	2.44606i	0.0549756	+	0.169198i
$210$		0			0
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	−0.983271	−	0.182150i	$-0.941694\pi$
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	0.902548	+	0.430590i	$0.141694\pi$
$212$	0.0646746	+	1.23406i	0.00444187	+	0.0847559i
$213$	6.17716	−	4.01150i	0.423252	−	0.274863i
$214$	2.10958	−	1.89947i	0.144208	−	0.129845i
$215$		0			0
$216$	−15.7401	+	5.11428i	−1.07098	+	0.347982i
$217$	−2.80133	−	8.40503i	−0.190166	−	0.570571i
$218$	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
$222$	12.2504	−	9.92015i	0.822190	−	0.665797i
$223$	−1.74330	−	3.42142i	−0.116740	−	0.229115i	0.825242	−	0.564780i	$-0.191039\pi$
$223$	−1.74330	−	3.42142i	−0.116740	−	0.229115i	−0.941981	+	0.335665i	$0.891039\pi$
$224$	−3.36729	+	1.74788i	−0.224986	+	0.116785i
$225$		0			0
$226$	−11.7423	−	20.3382i	−0.781085	−	1.35288i
$227$	−0.102183	+	1.94977i	−0.00678213	+	0.129411i	0.993140	+	0.116931i	$0.0373057\pi$
$227$	−0.102183	+	1.94977i	−0.00678213	+	0.129411i	−0.999922	+	0.0124794i	$0.996028\pi$
$228$	−2.00233	−	0.768624i	−0.132608	−	0.0509034i
$229$	−1.15255	+	10.9658i	−0.0761626	+	0.724639i	0.888093	+	0.459664i	$0.152030\pi$
$229$	−1.15255	+	10.9658i	−0.0761626	+	0.724639i	−0.964255	+	0.264975i	$0.914636\pi$
$230$		0			0
$231$	1.09340	+	1.65616i	0.0719403	+	0.108967i
$232$	−7.98721	+	7.98721i	−0.524386	+	0.524386i
$233$	7.00772	+	18.2557i	0.459091	+	1.19597i	0.946473	+	0.322784i	$0.104619\pi$
$233$	7.00772	+	18.2557i	0.459091	+	1.19597i	−0.487382	+	0.873189i	$0.662048\pi$
$234$	−0.155055	−	0.0329580i	−0.0101363	−	0.00215453i
$235$		0			0
$236$	0.283951	+	1.33588i	0.0184836	+	0.0869585i
$237$	−6.58676	+	12.9273i	−0.427856	+	0.839715i
$238$	14.4634	−	8.49677i	0.937524	−	0.550764i
$239$	−9.20533	−	2.99099i	−0.595443	−	0.193471i	−0.00423616	−	0.999991i	$-0.501348\pi$
$239$	−9.20533	−	2.99099i	−0.595443	−	0.193471i	−0.591207	+	0.806520i	$0.701348\pi$
$240$		0			0
$241$	2.60970	−	12.2777i	0.168106	−	0.790875i	−0.810599	−	0.585602i	$-0.800858\pi$
$241$	2.60970	−	12.2777i	0.168106	−	0.790875i	0.978705	−	0.205274i	$-0.0658084\pi$
$242$	11.0566	+	8.95348i	0.710747	+	0.575551i
$243$	5.42901	+	1.45470i	0.348271	+	0.0933190i
$244$	1.83726	−	1.33484i	0.117618	−	0.0854546i
$245$		0			0
$246$	4.71402	+	3.42494i	0.300555	+	0.218366i
$247$	−0.739699	−	0.913452i	−0.0470659	−	0.0581216i
$248$	−9.96140	−	0.522055i	−0.632550	−	0.0331505i
$249$	−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	$0.839350\pi$
$252$	0.368256	+	0.0358950i	0.0231980	+	0.00226117i
$253$	−0.0399398	−	0.252170i	−0.00251099	−	0.0158538i
$254$	−24.5300	−	2.57821i	−1.53915	−	0.161771i
$255$		0			0
$256$	0.629156	+	5.98602i	0.0393223	+	0.374126i
$257$	−1.35339	+	5.05092i	−0.0844221	+	0.315068i	−0.995204	−	0.0978199i	$-0.968813\pi$
$257$	−1.35339	+	5.05092i	−0.0844221	+	0.315068i	0.910782	+	0.412888i	$0.135480\pi$
$258$	2.76064	−	17.4300i	0.171870	−	1.08514i
$259$	−19.4365	+	5.36568i	−1.20773	+	0.333407i
$260$		0			0
$261$	2.03317	−	0.432164i	0.125850	−	0.0267503i
$262$	0.366015	+	0.563613i	0.0226125	+	0.0348201i
$263$	−6.33899	−	9.76119i	−0.390879	−	0.601901i	0.587374	−	0.809316i	$-0.300162\pi$
$263$	−6.33899	−	9.76119i	−0.390879	−	0.601901i	−0.978253	+	0.207415i	$0.933495\pi$
$264$	2.18558	−	0.464560i	0.134513	−	0.0285917i
$265$		0			0
$266$	−13.3681	−	13.1676i	−0.819650	−	0.807360i
$267$	1.43467	−	9.05817i	0.0878006	−	0.554351i
$268$	0.857832	−	3.20147i	0.0524004	−	0.195561i
$269$	−1.26000	−	11.9881i	−0.0768234	−	0.730926i	−0.963350	−	0.268248i	$-0.913555\pi$
$269$	−1.26000	−	11.9881i	−0.0768234	−	0.730926i	0.886527	−	0.462678i	$-0.153111\pi$
$270$		0			0
$271$	14.5617	+	1.53049i	0.884558	+	0.0929708i	0.535902	−	0.844280i	$-0.319972\pi$
$271$	14.5617	+	1.53049i	0.884558	+	0.0929708i	0.348656	+	0.937251i	$0.386638\pi$
$272$	−2.57141	−	16.2352i	−0.155915	−	0.984405i
$273$	−0.737741	−	0.527532i	−0.0446501	−	0.0319277i
$274$			5.74694i			0.347185i
$275$		0			0
$276$	0.184386	+	0.106455i	0.0110987	+	0.00640785i
$277$	−6.05253	−	0.317200i	−0.363661	−	0.0190587i	−0.130370	−	0.991465i	$-0.541616\pi$
$277$	−6.05253	−	0.317200i	−0.363661	−	0.0190587i	−0.233292	+	0.972407i	$0.574950\pi$
$278$	−18.0597	−	22.3019i	−1.08315	−	1.33758i
$279$	1.48502	+	1.07893i	0.0889060	+	0.0645940i
$280$		0			0
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	−0.693612	−	0.720349i	$-0.743982\pi$
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	0.470755	+	0.882264i	$0.343982\pi$
$282$	−14.9492	−	4.00563i	−0.890212	−	0.238532i
$283$	3.00848	+	2.43622i	0.178836	+	0.144818i	0.714559	−	0.699575i	$-0.246628\pi$
$283$	3.00848	+	2.43622i	0.178836	+	0.144818i	−0.535723	+	0.844394i	$0.679961\pi$
$284$	−0.249502	+	1.17381i	−0.0148052	+	0.0696531i
$285$		0			0
$286$	0.131747	+	0.0428072i	0.00779036	+	0.00253124i
$287$	−3.77535	−	6.42650i	−0.222852	−	0.379344i
$288$	0.356858	−	0.700374i	0.0210281	−	0.0412699i
$289$	−1.25530	−	5.90570i	−0.0738410	−	0.347394i
$290$		0			0
$291$	14.7538	+	3.13601i	0.864881	+	0.183836i
$292$	1.19920	+	3.12402i	0.0701778	+	0.182820i
$293$	10.8232	−	10.8232i	0.632300	−	0.632300i	−0.316344	−	0.948644i	$-0.602455\pi$
$293$	10.8232	−	10.8232i	0.632300	−	0.632300i	0.948644	+	0.316344i	$0.102455\pi$
$294$	−12.6468	−	7.04905i	−0.737574	−	0.411109i
$295$		0			0
$296$	−2.37304	+	22.5780i	−0.137930	+	1.31232i
$297$	−2.48465	−	0.953769i	−0.144174	−	0.0553433i
$298$	−0.799052	+	15.2468i	−0.0462878	+	0.883225i
$299$	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
$303$	21.1345	−	17.1144i	1.21415	−	0.983198i
$304$	−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	0.811882	−	0.583821i	$-0.198443\pi$
$307$	3.99596	+	3.99596i	0.228061	+	0.228061i	−0.583821	+	0.811882i	$0.698443\pi$
$308$	−0.316771	−	0.0648348i	−0.0180497	−	0.00369430i
$309$	11.6884	−	3.79779i	0.664929	−	0.216049i
$310$		0			0
$311$	−0.717211	+	0.645779i	−0.0406693	+	0.0366188i	−0.689215	−	0.724557i	$-0.742044\pi$
$311$	−0.717211	+	0.645779i	−0.0406693	+	0.0366188i	0.648545	+	0.761176i	$0.275378\pi$
$312$	−0.856399	+	0.556152i	−0.0484841	+	0.0314859i
$313$	−0.0204308	−	0.389843i	−0.00115482	−	0.0220352i	0.997991	−	0.0633504i	$-0.0201786\pi$
$313$	−0.0204308	−	0.389843i	−0.00115482	−	0.0220352i	−0.999146	+	0.0413152i	$0.986845\pi$
$314$	−1.64954	+	5.07677i	−0.0930891	+	0.286499i
$315$		0			0
$316$	−0.730474	−	2.24817i	−0.0410924	−	0.126469i
$317$	28.0896	−	10.7826i	1.57767	−	0.605611i	0.597168	−	0.802116i	$-0.296293\pi$
$317$	28.0896	−	10.7826i	1.57767	−	0.605611i	0.980503	+	0.196505i	$0.0629592\pi$
$318$	2.59308	+	9.67749i	0.145413	+	0.542687i
$319$	−1.80649	+	0.189870i	−0.101144	+	0.0106307i
$320$		0			0
$321$	−1.97789	+	2.72234i	−0.110395	+	0.151946i
$322$	1.10621	+	1.49864i	0.0616469	+	0.0835157i
$323$	−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
$327$	−14.3566	−	9.32329i	−0.793923	−	0.515579i
$328$	−8.28853	+	1.31277i	−0.457658	+	0.0724859i
$329$	15.4787	+	12.3420i	0.853367	+	0.680434i
$330$		0			0
$331$	−8.09153	−	3.60258i	−0.444751	−	0.198016i	0.172127	−	0.985075i	$-0.444936\pi$
$331$	−8.09153	−	3.60258i	−0.444751	−	0.198016i	−0.616878	+	0.787059i	$0.711603\pi$
$332$	2.34109	−	0.627294i	0.128484	−	0.0344272i
$333$	2.62907	−	3.24663i	0.144072	−	0.177914i
$334$	21.0794	−	23.4111i	1.15341	−	1.28100i
$335$		0			0
$336$	−10.9582	+	9.01168i	−0.597819	+	0.491628i
$337$	−17.6659	−	9.00124i	−0.962324	−	0.490329i	−0.0990602	−	0.995081i	$-0.531584\pi$
$337$	−17.6659	−	9.00124i	−0.962324	−	0.490329i	−0.863264	+	0.504753i	$0.831584\pi$
$338$	17.0855	−	0.895411i	0.929326	−	0.0487039i
$339$	18.6276	+	20.6880i	1.01171	+	1.12362i
$340$		0			0
$341$	−1.19207	−	1.07334i	−0.0645542	−	0.0581249i
$342$	3.83982	+	0.608168i	0.207634	+	0.0328860i
$343$	11.2226	+	14.7327i	0.605966	+	0.795490i
$344$	14.9389	+	20.5617i	0.805453	+	1.10861i
$345$		0			0
$346$	−13.1512	−	29.5381i	−0.707012	−	1.58798i
$347$	0.360039	−	0.937932i	0.0193279	−	0.0503509i	−0.923577	−	0.383413i	$-0.874749\pi$
$347$	0.360039	−	0.937932i	0.0193279	−	0.0503509i	0.942905	+	0.333062i	$0.108082\pi$
$348$	0.825001	−	1.27039i	0.0442247	−	0.0681001i
$349$	−22.8601			−1.22367			−0.611835	−	0.790985i	$-0.709569\pi$
$349$	−22.8601			−1.22367			−0.611835	+	0.790985i	$0.709569\pi$
$350$		0			0
$351$	1.21629			0.0649206
$352$	−0.374120	+	0.576094i	−0.0199407	+	0.0307059i
$353$	−6.28989	+	16.3857i	−0.334777	+	0.872124i	0.658094	+	0.752935i	$0.271363\pi$
$353$	−6.28989	+	16.3857i	−0.334777	+	0.872124i	−0.992872	+	0.119189i	$0.961971\pi$
$354$	4.50363	+	10.1153i	0.239365	+	0.537623i
$355$		0			0
$356$	0.878288	+	1.20886i	0.0465491	+	0.0640694i
$357$	−14.6761	+	13.4165i	−0.776742	+	0.710078i
$358$	−23.0942	−	3.65776i	−1.22056	−	0.193318i
$359$	21.5239	+	19.3802i	1.13599	+	1.02285i	0.999481	+	0.0322078i	$0.0102538\pi$
$359$	21.5239	+	19.3802i	1.13599	+	1.02285i	0.136506	+	0.990639i	$0.456413\pi$
$360$		0			0
$361$	6.57525	+	7.30256i	0.346066	+	0.384345i
$362$	1.25134	−	0.0655801i	0.0657692	−	0.00344682i
$363$	−15.0267	−	7.65648i	−0.788697	−	0.401861i
$364$	0.145769	−	0.0242177i	0.00764039	−	0.00126935i
$365$		0			0
$366$	12.3199	−	13.6827i	0.643973	−	0.715205i
$367$	−10.4351	+	12.8863i	−0.544708	+	0.672658i	−0.972953	−	0.231005i	$-0.925799\pi$
$367$	−10.4351	+	12.8863i	−0.544708	+	0.672658i	0.428245	+	0.903663i	$0.359132\pi$
$368$	1.76308	−	0.472416i	0.0919069	−	0.0246264i
$369$	1.41074	+	0.628103i	0.0734403	+	0.0326977i
$370$		0			0
$371$	1.90913	−	12.6726i	0.0991173	−	0.657930i
$372$	1.32121	−	0.209259i	0.0685016	−	0.0108496i
$373$	24.5932	+	15.9710i	1.27339	+	0.826946i	0.991195	−	0.132412i	$-0.0422722\pi$
$373$	24.5932	+	15.9710i	1.27339	+	0.826946i	0.282191	+	0.959358i	$0.408939\pi$
$374$	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
$378$	19.2947	−	2.17543i	0.992413	−	0.111892i
$379$	10.6445	−	14.6509i	0.546773	−	0.752568i	−0.442797	−	0.896622i	$-0.646014\pi$
$379$	10.6445	−	14.6509i	0.546773	−	0.752568i	0.989570	+	0.144054i	$0.0460137\pi$
$380$		0			0
$381$	29.0778	−	3.05620i	1.48970	−	0.156574i
$382$	−3.58028	−	13.3618i	−0.183183	−	0.683649i
$383$	27.8513	−	10.6911i	1.42314	−	0.546291i	0.479578	−	0.877499i	$-0.340790\pi$
$383$	27.8513	−	10.6911i	1.42314	−	0.546291i	0.943557	+	0.331209i	$0.107456\pi$
$384$	4.20083	+	12.9288i	0.214373	+	0.659771i
$385$		0			0
$386$	8.03783	−	24.7379i	0.409115	−	1.25913i
$387$	−0.244771	−	4.67051i	−0.0124424	−	0.237415i
$388$	−2.06104	+	1.33846i	−0.104634	+	0.0679499i
$389$	8.38594	−	7.55073i	0.425184	−	0.382837i	−0.428575	−	0.903506i	$-0.640984\pi$
$389$	8.38594	−	7.55073i	0.425184	−	0.382837i	0.853759	+	0.520669i	$0.174317\pi$
$390$		0			0
$391$	2.43296	−	0.790515i	0.123040	−	0.0399781i
$392$	20.0578	−	5.70059i	1.01307	−	0.287923i
$393$	−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
$397$	−3.85695	+	3.12330i	−0.193575	+	0.156754i	−0.721208	−	0.692719i	$-0.756413\pi$
$397$	−3.85695	+	3.12330i	−0.193575	+	0.156754i	0.527633	+	0.849472i	$0.323080\pi$
$398$	−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	$0.798284\pi$
$402$	1.40634	−	26.8347i	0.0701421	−	1.33839i
$403$	0.684388	+	0.262712i	0.0340918	+	0.0130866i
$404$	−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
$408$	8.02317	+	20.9011i	0.397206	+	1.03476i
$409$	−0.210716	−	0.0447891i	−0.0104192	−	0.00221468i	0.202699	−	0.979241i	$-0.435029\pi$
$409$	−0.210716	−	0.0447891i	−0.0104192	−	0.00221468i	−0.213118	+	0.977026i	$0.568362\pi$
$410$		0			0
$411$	−1.41637	−	6.66352i	−0.0698646	−	0.328687i
$412$	−0.909060	+	1.78413i	−0.0447862	+	0.0878978i
$413$	−0.106986	−	14.1631i	−0.00526445	−	0.696919i
$414$	−0.367037	−	0.119258i	−0.0180389	−	0.00586119i
$415$		0			0
$416$	0.0652684	−	0.307064i	0.00320005	−	0.0150550i
$417$	26.4365	+	21.4079i	1.29460	+	1.04835i
$418$	−3.28162	−	0.879306i	−0.160509	−	0.0430083i
$419$	28.0621	−	20.3883i	1.37092	−	0.996034i	0.373259	−	0.927727i	$-0.378240\pi$
$419$	28.0621	−	20.3883i	1.37092	−	0.996034i	0.997664	−	0.0683067i	$-0.0217596\pi$
$420$		0			0
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.992723	−	0.120419i	$-0.0384239\pi$
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.192243	+	0.981347i	$0.438424\pi$
$422$	−3.15436	−	3.89531i	−0.153552	−	0.189621i
$423$	−4.09602	−	0.214663i	−0.199155	−	0.0104373i
$424$	−12.4961	−	7.21461i	−0.606863	−	0.350373i
$425$		0			0
$426$			9.72928i			0.471385i
$427$	−21.4424	+	9.74149i	−1.03767	+	0.471424i
$428$	−0.0857658	−	0.541504i	−0.00414565	−	0.0261746i
$429$	−0.163309	−	0.0171645i	−0.00788465	−	0.000828711i
$430$		0			0
$431$	−3.65977	−	34.8204i	−0.176285	−	1.67724i	−0.622738	−	0.782431i	$-0.713980\pi$
$431$	−3.65977	−	34.8204i	−0.176285	−	1.67724i	0.446453	−	0.894807i	$-0.352687\pi$
$432$	4.92453	−	18.3786i	0.236932	−	0.884241i
$433$	0.905859	−	5.71937i	0.0435328	−	0.274855i	−0.956314	−	0.292340i	$-0.905566\pi$
$433$	0.905859	−	5.71937i	0.0435328	−	0.274855i	0.999847	+	0.0174852i	$0.00556599\pi$
$434$	11.3267	+	2.94347i	0.543701	+	0.141291i
$435$		0			0
$436$	2.72811	−	0.579878i	0.130653	−	0.0277711i
$437$	−1.55853	−	2.39992i	−0.0745544	−	0.114804i
$438$	14.7760	+	22.7530i	0.706024	+	1.08718i
$439$	18.8155	−	3.99935i	0.898013	−	0.190879i	0.264294	−	0.964442i	$-0.414861\pi$
$439$	18.8155	−	3.99935i	0.898013	−	0.190879i	0.633719	+	0.773563i	$0.281528\pi$
$440$		0			0
$441$	−3.66685	−	1.13048i	−0.174612	−	0.0538325i
$442$	−0.217131	+	1.37091i	−0.0103279	+	0.0652075i
$443$	3.99023	−	14.8917i	0.189581	−	0.707527i	−0.804022	−	0.594600i	$-0.797311\pi$
$443$	3.99023	−	14.8917i	0.189581	−	0.707527i	0.993603	−	0.112928i	$-0.0360228\pi$
$444$	−0.318230	−	3.02775i	−0.0151025	−	0.143691i
$445$		0			0
$446$	5.04455	+	0.530203i	0.238866	+	0.0251059i
$447$	−2.83120	−	17.8755i	−0.133911	−	0.845481i
$448$	2.24423	−	23.0241i	0.106030	−	1.08779i
$449$			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
$452$	−4.52946	−	0.237379i	−0.213048	−	0.0111654i
$453$	−15.9365	−	19.6799i	−0.748761	−	0.924643i
$454$	−2.08650	−	1.51593i	−0.0979245	−	0.0711463i
$455$		0			0
$456$	20.2606	−	14.7202i	0.948789	−	0.689335i
$457$	27.9738	+	7.49556i	1.30856	+	0.350627i	0.844680	−	0.535271i	$-0.179791\pi$
$457$	27.9738	+	7.49556i	1.30856	+	0.350627i	0.463879	+	0.885899i	$0.346457\pi$
$458$	−11.3191	−	9.16600i	−0.528905	−	0.428299i
$459$	5.54431	−	26.0839i	0.258786	−	1.21749i
$460$		0			0
$461$	30.3418	+	9.85863i	1.41316	+	0.459162i	0.913421	−	0.407016i	$-0.133431\pi$
$461$	30.3418	+	9.85863i	1.41316	+	0.459162i	0.499735	+	0.866178i	$0.333431\pi$
$462$	−2.62138	+	0.0198016i	−0.121958	+	0.000921254i
$463$	1.68874	−	3.31433i	0.0784822	−	0.154030i	−0.848431	−	0.529306i	$-0.822452\pi$
$463$	1.68874	−	3.31433i	0.0784822	−	0.154030i	0.926913	+	0.375276i	$0.122452\pi$
$464$	−2.69995	−	12.7023i	−0.125342	−	0.589688i
$465$		0			0
$466$	−25.2659	−	5.37044i	−1.17042	−	0.248781i
$467$	2.54805	+	6.63789i	0.117910	+	0.307165i	0.979816	−	0.199903i	$-0.0640627\pi$
$467$	2.54805	+	6.63789i	0.117910	+	0.307165i	−0.861906	+	0.507068i	$0.830729\pi$
$468$	−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
$472$	−14.8876	−	5.71482i	−0.685258	−	0.263046i
$473$	−0.213901	+	4.08148i	−0.00983518	+	0.187666i
$474$	−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
$478$	9.93616	−	8.04614i	0.454469	−	0.368022i
$479$	10.5264	−	4.68667i	0.480965	−	0.214140i	−0.151908	−	0.988395i	$-0.548542\pi$
$479$	10.5264	−	4.68667i	0.480965	−	0.214140i	0.632874	+	0.774255i	$0.281875\pi$
$480$		0			0
$481$	0.678607	−	1.52418i	0.0309418	−	0.0694964i
$482$	11.7241	+	11.7241i	0.534019	+	0.534019i
$483$	−1.65199	−	1.46502i	−0.0751683	−	0.0666606i
$484$	2.61328	−	0.849107i	0.118786	−	0.0385958i
$485$		0			0
$486$	−5.51739	+	4.96788i	−0.250274	+	0.225347i
$487$	−3.66973	+	2.38315i	−0.166291	+	0.107991i	−0.625102	−	0.780543i	$-0.714942\pi$
$487$	−3.66973	+	2.38315i	−0.166291	+	0.107991i	0.458810	+	0.888534i	$0.348276\pi$
$488$	1.38778	+	26.4805i	0.0628220	+	1.19871i
$489$	−8.07937	+	24.8657i	−0.365362	+	1.12447i
$490$		0			0
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	0.995545	−	0.0942867i	$-0.0300570\pi$
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	−0.860833	+	0.508887i	$0.830057\pi$
$492$	1.05062	−	0.403295i	0.0473656	−	0.0181819i
$493$	−4.71056	−	17.5801i	−0.212153	−	0.791766i
$494$	1.54412	−	0.162293i	0.0694732	−	0.00730192i
$495$		0			0
$496$	6.74065	−	9.27771i	0.302664	−	0.416582i
$497$	4.97589	−	11.4071i	0.223199	−	0.511681i
$498$	17.5082	−	8.92087i	0.784561	−	0.399754i
$499$	−4.09112	+	2.36201i	−0.183144	+	0.105738i	−0.588769	−	0.808301i	$-0.700387\pi$
$499$	−4.09112	+	2.36201i	−0.183144	+	0.105738i	0.405625	+	0.914040i	$0.367054\pi$
$500$		0			0
$501$	−18.6716	+	32.3401i	−0.834184	+	1.44485i
$502$	−16.9737	−	11.0228i	−0.757573	−	0.491973i
$503$	3.93410	−	0.623100i	0.175413	−	0.0277826i	−0.0681101	−	0.997678i	$-0.521697\pi$
$503$	3.93410	−	0.623100i	0.175413	−	0.0277826i	0.243523	+	0.969895i	$0.421697\pi$
$504$	−2.69341	+	3.37794i	−0.119974	+	0.150465i
$505$		0			0
$506$	0.308096	+	0.137173i	0.0136965	+	0.00609810i
$507$	−19.5897	+	5.24905i	−0.870011	+	0.233119i
$508$	−2.99789	+	3.70209i	−0.133010	+	0.164253i
$509$	−1.53153	+	1.70093i	−0.0678838	+	0.0753926i	−0.776130	−	0.630573i	$-0.782820\pi$
$509$	−1.53153	+	1.70093i	−0.0678838	+	0.0753926i	0.708246	+	0.705965i	$0.249487\pi$
$510$		0			0
$511$	−5.68752	−	34.2339i	−0.251601	−	1.51442i
$512$	−22.5551	−	11.4924i	−0.996806	−	0.507898i
$513$	−29.7886	+	1.56116i	−1.31520	+	0.0689267i
$514$	−4.62190	−	5.13314i	−0.203863	−	0.226413i
$515$		0			0
$516$	−2.53285	−	2.28059i	−0.111503	−	0.100397i
$517$	3.54022	+	0.560716i	0.155699	+	0.0246603i
$518$	8.03903	−	25.3927i	0.353215	−	1.11569i
$519$	22.5285	+	31.0079i	0.988893	+	1.36109i
$520$		0			0
$521$	−5.48334	−	12.3158i	−0.240230	−	0.539565i	0.752687	−	0.658379i	$-0.228757\pi$
$521$	−5.48334	−	12.3158i	−0.240230	−	0.539565i	−0.992917	+	0.118814i	$0.962091\pi$
$522$	−0.983969	+	2.56333i	−0.0430672	+	0.112194i
$523$	3.71726	−	5.72408i	0.162545	−	0.250297i	−0.748008	−	0.663689i	$-0.768990\pi$
$523$	3.71726	−	5.72408i	0.162545	−	0.250297i	0.910553	+	0.413393i	$0.135656\pi$
$524$	0.129793			0.00567001
$525$		0			0
$526$	15.3743			0.670350
$527$	8.75370	−	13.4795i	0.381317	−	0.587177i
$528$	−0.920574	+	2.39818i	−0.0400629	+	0.104367i
$529$	−9.23940	−	20.7520i	−0.401713	−	0.902263i
$530$		0			0
$531$	1.72485	+	2.37405i	0.0748521	+	0.103025i
$532$	−3.53902	+	0.780227i	−0.153436	+	0.0338271i
$533$	0.609133	+	0.0964772i	0.0263845	+	0.00417889i
$534$	9.00279	+	8.10615i	0.389589	+	0.350787i
$535$		0			0
$536$	25.8956	+	28.7600i	1.11852	+	1.24224i
$537$	27.6789	−	1.45059i	1.19443	−	0.0625977i
$538$	14.1873	+	7.22877i	0.611657	+	0.311655i
$539$	3.08358	+	1.31745i	0.132819	+	0.0567464i
$540$		0			0
$541$	−5.10841	+	5.67347i	−0.219628	+	0.243921i	−0.842883	−	0.538097i	$-0.819143\pi$
$541$	−5.10841	+	5.67347i	−0.219628	+	0.243921i	0.623255	+	0.782019i	$0.285810\pi$
$542$	−12.1717	+	15.0308i	−0.522819	+	0.645628i
$543$	−1.43476	+	0.384442i	−0.0615714	+	0.0164980i
$544$	−6.28762	−	2.79943i	−0.269580	−	0.120025i
$545$		0			0
$546$	1.11517	−	0.437768i	0.0477250	−	0.0187348i
$547$	41.0298	−	6.49848i	1.75431	−	0.277855i	0.805244	−	0.592944i	$-0.202034\pi$
$547$	41.0298	−	6.49848i	1.75431	−	0.277855i	0.949062	+	0.315089i	$0.102034\pi$
$548$	0.930867	+	0.604512i	0.0397647	+	0.0258235i
$549$	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
$553$	2.74659	+	24.3605i	0.116797	+	1.03591i
$554$	4.70581	−	6.47699i	0.199931	−	0.275181i
$555$		0			0
$556$	−5.51206	+	0.579340i	−0.233763	+	0.0245695i
$557$	3.67322	+	13.7087i	0.155640	+	0.580855i	0.999050	+	0.0435845i	$0.0138778\pi$
$557$	3.67322	+	13.7087i	0.155640	+	0.580855i	−0.843410	+	0.537270i	$0.819456\pi$
$558$	−2.26365	+	0.868936i	−0.0958281	+	0.0367850i
$559$	−0.577188	−	1.77640i	−0.0244125	−	0.0751338i
$560$		0			0
$561$	−1.11253	+	3.42401i	−0.0469710	+	0.144562i
$562$	−0.319231	−	6.09130i	−0.0134660	−	0.256946i
$563$	35.2219	−	22.8733i	1.48442	−	0.963997i	0.488619	−	0.872497i	$-0.337501\pi$
$563$	35.2219	−	22.8733i	1.48442	−	0.963997i	0.995805	−	0.0914994i	$-0.0291660\pi$
$564$	−2.22130	+	2.00007i	−0.0935337	+	0.0842181i
$565$		0			0
$566$	−4.86334	+	1.58019i	−0.204421	+	0.0664205i
$567$	−17.7082	+	5.90199i	−0.743673	+	0.247860i
$568$	−9.90808	−	9.90808i	−0.415734	−	0.415734i
$569$	−9.54513	+	21.4387i	−0.400153	+	0.898758i	0.595300	+	0.803503i	$0.297033\pi$
$569$	−9.54513	+	21.4387i	−0.400153	+	0.898758i	−0.995453	+	0.0952543i	$0.969634\pi$
$570$		0			0
$571$	−8.83659	+	3.93430i	−0.369800	+	0.164645i	−0.583218	−	0.812315i	$-0.698207\pi$
$571$	−8.83659	+	3.93430i	−0.369800	+	0.164645i	0.213419	+	0.976961i	$0.431540\pi$
$572$	0.0207920	−	0.0168371i	0.000869358	−	0.000703993i
$573$	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
$577$	−0.0874910	+	1.66943i	−0.00364230	+	0.0694992i	−0.999846	−	0.0175547i	$-0.994412\pi$
$577$	−0.0874910	+	1.66943i	−0.00364230	+	0.0694992i	0.996204	+	0.0870538i	$0.0277452\pi$
$578$	7.44564	+	2.85811i	0.309698	+	0.118882i
$579$	−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
$583$	−0.831542	−	2.16624i	−0.0344390	−	0.0897166i
$584$	−38.2187	−	8.12364i	−1.58150	−	0.336159i
$585$		0			0
$586$	4.20372	+	19.7770i	0.173654	+	0.816978i
$587$	0.277321	−	0.544273i	0.0114463	−	0.0224646i	−0.885213	−	0.465187i	$-0.845987\pi$
$587$	0.277321	−	0.544273i	0.0114463	−	0.0224646i	0.896659	+	0.442722i	$0.145987\pi$
$588$	−2.47207	+	1.30700i	−0.101947	+	0.0538996i
$589$	−17.0988	−	5.55575i	−0.704545	−	0.228921i
$590$		0			0
$591$	4.65028	−	21.8778i	0.191287	−	0.899934i
$592$	−20.2834	−	16.4251i	−0.833641	−	0.675069i
$593$	−24.4672	−	6.55597i	−1.00475	−	0.269221i	−0.281314	−	0.959616i	$-0.590770\pi$
$593$	−24.4672	−	6.55597i	−1.00475	−	0.269221i	−0.723433	+	0.690394i	$0.757437\pi$
$594$	2.84416	−	2.06641i	0.116697	−	0.0847857i
$595$		0			0
$596$	2.38557	+	1.73322i	0.0977168	+	0.0709954i
$597$	7.07382	+	8.73544i	0.289512	+	0.357518i
$598$	−0.153916	−	0.00806638i	−0.00629408	−	0.000329859i
$599$	−2.55964	−	1.47781i	−0.104584	−	0.0603816i	0.446796	−	0.894636i	$-0.352565\pi$
$599$	−2.55964	−	1.47781i	−0.104584	−	0.0603816i	−0.551380	+	0.834254i	$0.685898\pi$
$600$		0			0
$601$		−	2.33505i		−	0.0952489i	−0.998865	−	0.0476244i	$-0.984835\pi$
$601$		−	2.33505i		−	0.0952489i	0.998865	−	0.0476244i	$-0.0151651\pi$
$602$	−12.3335	−	27.1478i	−0.502678	−	1.10646i
$603$	−1.11406	−	7.03388i	−0.0453679	−	0.286442i
$604$	4.10329	+	0.431273i	0.166960	+	0.0175482i
$605$		0			0
$606$	3.75498	+	35.7263i	0.152536	+	1.45128i
$607$	4.99555	−	18.6437i	0.202763	−	0.756723i	−0.787356	−	0.616498i	$-0.788551\pi$
$607$	4.99555	−	18.6437i	0.202763	−	0.756723i	0.990120	−	0.140225i	$-0.0447825\pi$
$608$	−1.20439	+	7.60420i	−0.0488444	+	0.308391i
$609$	−11.0238	+	11.1916i	−0.446707	+	0.453507i
$610$		0			0
$611$	−1.60228	+	0.340574i	−0.0648211	+	0.0137782i
$612$	0.365580	+	0.562944i	0.0147777	+	0.0227557i
$613$	−5.39337	−	8.30505i	−0.217836	−	0.335438i	0.712811	−	0.701356i	$-0.247422\pi$
$613$	−5.39337	−	8.30505i	−0.217836	−	0.335438i	−0.930647	+	0.365918i	$0.880755\pi$
$614$	−7.30168	+	1.55202i	−0.294672	+	0.0626345i
$615$		0			0
$616$	2.64939	−	2.68972i	0.106747	−	0.108372i
$617$	−0.868493	+	5.48345i	−0.0349642	+	0.220755i	−0.998984	−	0.0450769i	$-0.985647\pi$
$617$	−0.868493	+	5.48345i	−0.0349642	+	0.220755i	0.964019	+	0.265832i	$0.0856467\pi$
$618$	−4.20172	+	15.6810i	−0.169018	+	0.630784i
$619$	−3.98195	−	37.8857i	−0.160048	−	1.52276i	−0.719850	−	0.694129i	$-0.755790\pi$
$619$	−3.98195	−	37.8857i	−0.160048	−	1.52276i	0.559802	−	0.828626i	$-0.310877\pi$
$620$		0			0
$621$	2.94491	+	0.309523i	0.118175	+	0.0124207i
$622$	−0.199429	−	1.25915i	−0.00799638	−	0.0504872i
$623$	−6.40961	−	14.1084i	−0.256796	−	0.565243i
$624$		−	1.17396i		−	0.0469959i
$625$		0			0
$626$	0.446579	+	0.257833i	0.0178489	+	0.0103051i
$627$	4.02171	+	0.210769i	0.160612	+	0.00841730i
$628$	0.648803	+	0.801205i	0.0258901	+	0.0319716i
$629$	−29.5934	−	21.5008i	−1.17997	−	0.857295i
$630$		0			0
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	−0.791623	−	0.611010i	$-0.790764\pi$
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	0.336480	+	0.941691i	$0.390764\pi$
$632$	26.6610	+	7.14378i	1.06052	+	0.284164i
$633$	4.61748	+	3.73916i	0.183528	+	0.148618i
$634$	−8.26335	+	38.8760i	−0.328180	+	1.54396i
$635$		0			0
$636$	1.84029	+	0.597945i	0.0729721	+	0.0237101i
$637$	−1.53138	−	0.0570740i	−0.0606756	−	0.00226136i
$638$	1.08931	−	2.13789i	0.0431262	−	0.0846400i
$639$	0.536096	+	2.52213i	0.0212076	+	0.0997741i
$640$		0			0
$641$	−7.58550	−	1.61235i	−0.299609	−	0.0636839i	0.0556544	−	0.998450i	$-0.482276\pi$
$641$	−7.58550	−	1.61235i	−0.299609	−	0.0636839i	−0.355263	+	0.934766i	$0.615609\pi$
$642$	−1.59293	−	4.14972i	−0.0628679	−	0.163777i
$643$	−16.8674	+	16.8674i	−0.665185	+	0.665185i	−0.956598	−	0.291412i	$-0.905875\pi$
$643$	−16.8674	+	16.8674i	−0.665185	+	0.665185i	0.291412	+	0.956598i	$0.405875\pi$
$644$	0.359104	−	0.0215410i	0.0141507	−	0.000848835i
$645$		0			0
$646$	3.55822	−	33.8542i	0.139996	−	1.33198i
$647$	−28.2556	−	10.8463i	−1.11084	−	0.426412i	−0.267374	−	0.963593i	$-0.586156\pi$
$647$	−28.2556	−	10.8463i	−1.11084	−	0.426412i	−0.843467	+	0.537181i	$0.819489\pi$
$648$	−1.09989	+	20.9872i	−0.0432079	+	0.824456i
$649$	−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
$653$	26.0908	−	21.1279i	1.02101	−	0.826800i	0.0360120	−	0.999351i	$-0.488535\pi$
$653$	26.0908	−	21.1279i	1.02101	−	0.826800i	0.985000	+	0.172552i	$0.0552012\pi$
$654$	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
$658$	−24.8087	+	8.26854i	−0.967145	+	0.322341i
$659$	−45.9853	+	14.9415i	−1.79133	+	0.582039i	−0.999585	−	0.0288108i	$-0.990828\pi$
$659$	−45.9853	+	14.9415i	−1.79133	+	0.582039i	−0.791747	+	0.610850i	$0.790828\pi$
$660$		0			0
$661$	−5.08370	+	4.57738i	−0.197733	+	0.178040i	−0.762049	−	0.647519i	$-0.775807\pi$
$661$	−5.08370	+	4.57738i	−0.197733	+	0.178040i	0.564316	+	0.825559i	$0.309140\pi$
$662$	9.81239	−	6.37224i	0.381369	−	0.247664i
$663$	−0.0861096	−	1.64307i	−0.00334422	−	0.0638115i
$664$	−8.74513	+	26.9148i	−0.339377	+	1.04450i
$665$		0			0
$666$	1.70528	+	5.24830i	0.0660781	+	0.203368i
$667$	1.88677	−	0.724262i	0.0730559	−	0.0280435i
$668$	−1.57472	−	5.87694i	−0.0609278	−	0.227386i
$669$	−5.97978	+	0.628500i	−0.231192	+	0.0242992i
$670$		0			0
$671$	−2.50641	+	3.44978i	−0.0967589	+	0.133177i
$672$	0.665574	+	5.90322i	0.0256751	+	0.227722i
$673$	25.2746	−	12.8780i	0.974263	−	0.496412i	0.106999	−	0.994259i	$-0.465876\pi$
$673$	25.2746	−	12.8780i	0.974263	−	0.496412i	0.867265	+	0.497847i	$0.165876\pi$
$674$	22.6814	−	13.0951i	0.873653	−	0.504404i
$675$		0			0
$676$	1.65216	−	2.86163i	0.0635446	−	0.110063i
$677$	−10.5713	−	6.86510i	−0.406289	−	0.263847i	0.325276	−	0.945619i	$-0.394543\pi$
$677$	−10.5713	−	6.86510i	−0.406289	−	0.263847i	−0.731565	+	0.681772i	$0.761210\pi$
$678$	−36.3202	+	5.75255i	−1.39487	+	0.220925i
$679$	23.7236	−	9.31284i	0.910427	−	0.357394i
$680$		0			0
$681$	2.79289	+	1.24348i	0.107024	+	0.0476501i
$682$	2.04670	−	0.548413i	0.0783723	−	0.0209998i
$683$	−3.20622	+	3.95935i	−0.122683	+	0.151500i	−0.834787	−	0.550574i	$-0.814409\pi$
$683$	−3.20622	+	3.95935i	−0.122683	+	0.151500i	0.712104	+	0.702074i	$0.247742\pi$
$684$	0.502414	−	0.557988i	0.0192103	−	0.0213352i
$685$		0			0
$686$	−24.3953	+	1.83361i	−0.931418	+	0.0700074i
$687$	15.3834	+	7.83822i	0.586912	+	0.299047i
$688$	−29.1791	+	1.52921i	−1.11244	+	0.0583007i
$689$	0.709559	+	0.788045i	0.0270320	+	0.0300221i
$690$		0			0
$691$	−9.30768	−	8.38068i	−0.354081	−	0.318816i	0.472825	−	0.881156i	$-0.343234\pi$
$691$	−9.30768	−	8.38068i	−0.354081	−	0.318816i	−0.826906	+	0.562341i	$0.809901\pi$
$692$	−6.16782	−	0.976886i	−0.234465	−	0.0371356i
$693$	−0.678453	+	0.149575i	−0.0257723	+	0.00568187i
$694$	0.780048	+	1.07364i	0.0296102	+	0.0407550i
$695$		0			0
$696$	7.19397	+	16.1579i	0.272687	+	0.612465i
$697$	4.84567	−	12.6234i	0.183543	−	0.478145i
$698$	16.4463	−	25.3251i	0.622503	−	0.958570i
$699$	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	$0.759361\pi$
$702$	−0.875040	+	1.34744i	−0.0330263	+	0.0508560i
$703$	−14.6637	+	38.2002i	−0.553052	+	1.44075i
$704$	−1.70359	−	3.82632i	−0.0642064	−	0.144210i
$705$		0			0
$706$	−13.6275	−	18.7566i	−0.512877	−	0.705915i
$707$	13.8691	−	43.8079i	0.521601	−	1.64757i
$708$	2.11217	+	0.334535i	0.0793803	+	0.0125726i
$709$	−26.3654	−	23.7396i	−0.990175	−	0.891558i	0.00392835	−	0.999992i	$-0.498750\pi$
$709$	−26.3654	−	23.7396i	−0.990175	−	0.891558i	−0.994104	+	0.108434i	$0.965416\pi$
$710$		0			0
$711$	−3.39862	−	3.77455i	−0.127458	−	0.141557i
$712$	−17.4234	+	0.913120i	−0.652968	+	0.0342206i
$713$	1.59021	+	0.810250i	0.0595537	+	0.0303441i
$714$	−4.30478	−	25.9110i	−0.161102	−	0.969695i
$715$		0			0
$716$	−3.02171	+	3.35595i	−0.112927	+	0.125418i
$717$	−9.53785	+	11.7783i	−0.356197	+	0.439867i
$718$	−36.9550	+	9.90207i	−1.37915	+	0.369542i
$719$	12.5161	+	5.57251i	0.466771	+	0.207820i	0.626625	−	0.779321i	$-0.284436\pi$
$719$	12.5161	+	5.57251i	0.466771	+	0.207820i	−0.159854	+	0.987141i	$0.551102\pi$
$720$		0			0
$721$	12.9462	−	16.2364i	0.482140	−	0.604676i
$722$	−12.8205	+	2.03057i	−0.477129	+	0.0755698i
$723$	−16.4835	−	10.7045i	−0.613027	−	0.398105i
$724$	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	$-0.373358\pi$
$727$	36.6967	−	18.6979i	1.36101	−	0.693467i	0.973561	+	0.228425i	$0.0733577\pi$
$728$	−0.689855	+	1.58148i	−0.0255677	+	0.0586136i
$729$	17.6135	−	24.2429i	0.652352	−	0.897885i
$730$		0			0
$731$	−40.7269	+	4.28057i	−1.50634	+	0.158323i
$732$	−0.920351	−	3.43480i	−0.0340172	−	0.126954i
$733$	26.9579	−	10.3482i	0.995713	−	0.382218i	0.194698	−	0.980863i	$-0.437627\pi$
$733$	26.9579	−	10.3482i	0.995713	−	0.382218i	0.801015	+	0.598645i	$0.204294\pi$
$734$	−6.76846	−	20.8312i	−0.249829	−	0.768893i
$735$		0			0
$736$	0.236172	−	0.726863i	0.00870542	−	0.0267925i
$737$	0.325708	+	6.21487i	0.0119976	+	0.228928i
$738$	−1.71077	+	1.11099i	−0.0629743	+	0.0408960i
$739$	13.5923	−	12.2385i	0.499999	−	0.450202i	−0.380132	−	0.924932i	$-0.624121\pi$
$739$	13.5923	−	12.2385i	0.499999	−	0.450202i	0.880131	+	0.474731i	$0.157455\pi$
$740$		0			0
$741$	−1.75039	+	0.568737i	−0.0643022	+	0.0208931i
$742$	12.6657	+	11.2321i	0.464971	+	0.412345i
$743$	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
$747$	4.04712	−	3.27729i	0.148076	−	0.119910i
$748$	−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	$0.653487\pi$
$752$	−1.34111	+	25.5900i	−0.0489054	+	0.933170i
$753$	22.3975	+	8.59759i	0.816210	+	0.313313i
$754$	−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	$0.0111650\pi$
$758$	8.57275	+	22.3328i	0.311376	+	0.811163i
$759$	−0.391042	−	0.0831185i	−0.0141939	−	0.00301701i
$760$		0			0
$761$	0.212683	+	1.00060i	0.00770976	+	0.0362716i	0.981834	−	0.189740i	$-0.0607646\pi$
$761$	0.212683	+	1.00060i	0.00770976	+	0.0362716i	−0.974125	+	0.226012i	$0.927431\pi$
$762$	−17.5338	+	34.4120i	−0.635183	+	1.24662i
$763$	−28.9236	+	0.218485i	−1.04710	+	0.00790970i
$764$	−2.54090	−	0.825588i	−0.0919265	−	0.0298687i
$765$		0			0
$766$	−8.19324	+	38.5462i	−0.296034	+	1.39273i
$767$	0.910774	+	0.737530i	0.0328861	+	0.0266307i
$768$	9.10360	+	2.43930i	0.328498	+	0.0880207i
$769$	−16.8522	+	12.2439i	−0.607708	+	0.441525i	−0.848606	−	0.529025i	$-0.822558\pi$
$769$	−16.8522	+	12.2439i	−0.607708	+	0.441525i	0.240899	+	0.970550i	$0.422558\pi$
$770$		0			0
$771$	6.62415	+	4.81272i	0.238563	+	0.173326i
$772$	−3.16146	−	3.90408i	−0.113784	−	0.140511i
$773$	−25.9601	−	1.36051i	−0.933720	−	0.0489342i	−0.420595	−	0.907248i	$-0.638179\pi$
$773$	−25.9601	−	1.36051i	−0.933720	−	0.0489342i	−0.513124	+	0.858314i	$0.671512\pi$
$774$	5.35024	+	3.08897i	0.192311	+	0.111031i
$775$		0			0
$776$		−	28.6949i		−	1.03009i
$777$	−3.06297	+	31.4238i	−0.109884	+	1.12732i
$778$	2.33181	+	14.7225i	0.0835995	+	0.527827i
$779$	−15.0424	−	1.58102i	−0.538949	−	0.0566458i
$780$		0			0
$781$	−0.235533	−	2.24094i	−0.00842802	−	0.0801873i
$782$	−0.874595	+	3.26403i	−0.0312754	+	0.116722i
$783$	3.29564	−	20.8078i	0.117776	−	0.743611i
$784$	−7.06271	+	22.9087i	−0.252240	+	0.818169i
$785$		0			0
$786$	1.02929	−	0.218783i	0.0367137	−	0.00780374i
$787$	26.4408	+	40.7153i	0.942514	+	1.45134i	0.891695	+	0.452637i	$0.149517\pi$
$787$	26.4408	+	40.7153i	0.942514	+	1.45134i	0.0508190	+	0.998708i	$0.483817\pi$
$788$	1.98475	+	3.05625i	0.0707038	+	0.108874i
$789$	−17.8263	+	3.78910i	−0.634633	+	0.134895i
$790$		0			0
$791$	45.5259	+	11.8308i	1.61871	+	0.420654i
$792$	−0.122366	+	0.772589i	−0.00434809	+	0.0274528i
$793$	0.504373	−	1.88235i	0.0179108	−	0.0668441i
$794$	−0.685265	−	6.51986i	−0.0243192	−	0.231381i
$795$		0			0
$796$	−1.82135	−	0.191432i	−0.0645561	−	0.00678512i
$797$	1.60051	+	10.1052i	0.0566929	+	0.357945i	0.999684	+	0.0251277i	$0.00799924\pi$
$797$	1.60051	+	10.1052i	0.0566929	+	0.357945i	−0.942991	+	0.332817i	$0.892001\pi$
$798$	−26.7503	+	12.1529i	−0.946950	+	0.430209i
$799$			35.9141i			1.27055i
$800$		0			0
$801$	2.78047	+	1.60530i	0.0982429	+	0.0567206i
$802$	−5.80555	−	0.304256i	−0.205001	−	0.0107437i
$803$	−3.95417	−	4.88300i	−0.139540	−	0.172317i
$804$	−4.19865	−	3.05049i	−0.148075	−	0.107583i
$805$		0			0
$806$	−0.783414	+	0.569183i	−0.0275946	+	0.0200486i
$807$	−18.2316	−	4.88514i	−0.641782	−	0.171965i
$808$	−40.2068	−	32.5588i	−1.41447	−	1.14542i
$809$	8.76738	−	41.2473i	0.308245	−	1.45018i	−0.502399	−	0.864636i	$-0.667549\pi$
$809$	8.76738	−	41.2473i	0.308245	−	1.45018i	0.810643	−	0.585540i	$-0.199118\pi$
$810$		0			0
$811$	−30.4344	−	9.88872i	−1.06869	−	0.347240i	−0.278716	−	0.960374i	$-0.589909\pi$
$811$	−30.4344	−	9.88872i	−1.06869	−	0.347240i	−0.789979	+	0.613134i	$0.789909\pi$
$812$	−0.0193334	−	2.55939i	−0.000678468	−	0.0898171i
$813$	10.4085	−	20.4279i	0.365043	−	0.716436i
$814$	−1.00264	−	4.71704i	−0.0351425	−	0.165332i
$815$		0			0
$816$	−25.1761	−	5.35135i	−0.881340	−	0.187335i
$817$	16.4162	+	42.7658i	0.574332	+	1.49619i
$818$	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	0.437578	+	0.899180i	$0.355836\pi$
$821$	−5.08271	+	48.3588i	−0.177388	+	1.68773i	−0.614966	+	0.788553i	$0.710830\pi$
$822$	8.40105	+	3.22486i	0.293020	+	0.112480i
$823$	−0.0940468	+	1.79452i	−0.00327827	+	0.0625531i	−0.999779	−	0.0210338i	$-0.993304\pi$
$823$	−0.0940468	+	1.79452i	−0.00327827	+	0.0625531i	0.996500	+	0.0835868i	$0.0266376\pi$
$824$	−11.6903	−	20.2482i	−0.407250	−	0.705378i
$825$		0			0
$826$	15.7673	+	10.0709i	0.548614	+	0.350411i
$827$	−8.07790	−	15.8538i	−0.280896	−	0.551290i	0.706849	−	0.707364i	$-0.250116\pi$
$827$	−8.07790	−	15.8538i	−0.280896	−	0.551290i	−0.987745	+	0.156075i	$0.950116\pi$
$828$	−0.0579250	+	0.0469067i	−0.00201303	+	0.00163012i
$829$	46.2932	−	20.6110i	1.60783	−	0.715851i	0.610719	−	0.791847i	$-0.290880\pi$
$829$	46.2932	−	20.6110i	1.60783	−	0.715851i	0.997108	+	0.0759961i	$0.0242136\pi$
$830$		0			0
$831$	−3.86004	+	8.66978i	−0.133903	+	0.300752i
$832$	1.35350	+	1.35350i	0.0469242	+	0.0469242i
$833$	−8.20461	+	32.5811i	−0.284273	+	1.12887i
$834$	−42.7357	+	13.8857i	−1.47982	+	0.480822i
$835$		0			0
$836$	−0.487615	+	0.439051i	−0.0168645	+	0.0151849i
$837$	15.6029	−	10.1326i	0.539314	−	0.350235i
$838$	2.39798	+	45.7562i	0.0828368	+	1.58062i
$839$	2.38981	−	7.35507i	0.0825053	−	0.253925i	−0.901291	−	0.433214i	$-0.857380\pi$
$839$	2.38981	−	7.35507i	0.0825053	−	0.253925i	0.983797	+	0.179288i	$0.0573795\pi$
$840$		0			0
$841$	4.51828	+	13.9058i	0.155803	+	0.479511i
$842$	−37.0616	+	14.2266i	−1.27723	+	0.490281i
$843$	1.87139	+	6.98412i	0.0644541	+	0.240546i
$844$	−0.962751	+	0.101189i	−0.0331393	+	0.00348308i
$845$		0			0
$846$	3.18463	−	4.38327i	0.109490	−	0.150700i
$847$	−28.3167	+	3.19264i	−0.972974	+	0.109701i
$848$	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
$852$	1.57591	+	1.02341i	0.0539899	+	0.0350614i
$853$	11.6162	−	1.83983i	0.397732	−	0.0629946i	0.0456353	−	0.998958i	$-0.485469\pi$
$853$	11.6162	−	1.83983i	0.397732	−	0.0629946i	0.352097	+	0.935964i	$0.385469\pi$
$854$	4.63445	−	30.7629i	0.158587	−	1.05269i
$855$		0			0
$856$	5.84819	+	2.60378i	0.199887	+	0.0889954i
$857$	0.368054	−	0.0986197i	0.0125725	−	0.00336878i	−0.252527	−	0.967590i	$-0.581262\pi$
$857$	0.368054	−	0.0986197i	0.0125725	−	0.00336878i	0.265100	+	0.964221i	$0.414595\pi$
$858$	0.136506	−	0.168571i	0.00466024	−	0.00575491i
$859$	−6.46460	+	7.17966i	−0.220569	+	0.244967i	−0.843266	−	0.537496i	$-0.819370\pi$
$859$	−6.46460	+	7.17966i	−0.220569	+	0.244967i	0.622697	+	0.782463i	$0.286037\pi$
$860$		0			0
$861$	−11.5130	+	1.91273i	−0.392361	+	0.0651858i
$862$	41.2081	+	20.9966i	1.40355	+	0.715146i
$863$	5.02426	−	0.263310i	0.171028	−	0.00896318i	0.0333701	−	0.999443i	$-0.489376\pi$
$863$	5.02426	−	0.263310i	0.171028	−	0.00896318i	0.137658	+	0.990480i	$0.456043\pi$
$864$	−5.33087	−	5.92053i	−0.181360	−	0.201420i
$865$		0			0
$866$	5.68440	+	5.11825i	0.193164	+	0.173925i
$867$	−9.33755	−	1.47892i	−0.317120	−	0.0502268i
$868$	1.66822	−	1.52504i	0.0566230	−	0.0517634i
$869$	2.60893	+	3.59089i	0.0885020	+	0.121813i
$870$		0			0
$871$	−1.15681	−	2.59825i	−0.0391971	−	0.0880382i
$872$	−11.6707	+	30.4032i	−0.395219	+	1.02958i
$873$	−2.87590	+	4.42849i	−0.0973344	+	0.149882i
$874$	3.77997			0.127859
$875$		0			0
$876$	5.23972			0.177034
$877$	−11.7778	+	18.1362i	−0.397708	+	0.612417i	−0.979626	−	0.200831i	$-0.935636\pi$
$877$	−11.7778	+	18.1362i	−0.397708	+	0.612417i	0.581918	+	0.813248i	$0.302303\pi$
$878$	−9.10590	+	23.7217i	−0.307309	+	0.800568i
$879$	−9.74835	−	21.8951i	−0.328804	−	0.738505i
$880$		0			0
$881$	15.8503	+	21.8160i	0.534009	+	0.735001i	0.987735	−	0.156141i	$-0.0499053\pi$
$881$	15.8503	+	21.8160i	0.534009	+	0.735001i	−0.453725	+	0.891142i	$0.649905\pi$
$882$	3.89045	−	3.24895i	0.130998	−	0.109398i
$883$	−0.656476	−	0.103976i	−0.0220922	−	0.00349906i	0.145379	−	0.989376i	$-0.453560\pi$
$883$	−0.656476	−	0.103976i	−0.0220922	−	0.00349906i	−0.167471	+	0.985877i	$0.553560\pi$
$884$	0.199215	+	0.179374i	0.00670033	+	0.00603300i
$885$		0			0
$886$	13.6268	+	15.1341i	0.457803	+	0.508441i
$887$	30.5611	−	1.60164i	1.02614	−	0.0537778i	0.468170	−	0.883638i	$-0.344913\pi$
$887$	30.5611	−	1.60164i	1.02614	−	0.0537778i	0.557971	+	0.829860i	$0.311580\pi$
$888$	31.6735	+	16.1385i	1.06289	+	0.541572i
$889$	38.1571	−	31.3792i	1.27975	−	1.05242i
$890$		0			0
$891$	−2.26138	+	2.51152i	−0.0757591	+	0.0841390i
$892$	0.616509	−	0.761326i	0.0206423	−	0.0254911i
$893$	38.8049	−	10.3977i	1.29856	−	0.347947i
$894$	21.8399	+	9.72375i	0.730436	+	0.325211i
$895$		0			0
$896$	17.9595	+	14.3201i	0.599986	+	0.478400i
$897$	0.180452	−	0.0285808i	0.00602511	−	0.000954284i
$898$	−15.6407	−	10.1572i	−0.521935	−	0.338949i
$899$	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
$903$	20.9914	+	28.4379i	0.698550	+	0.946355i
$904$	31.1294	−	42.8459i	1.03535	−	1.42503i
$905$		0			0
$906$	33.2673	−	3.49653i	1.10523	−	0.116165i
$907$	8.74745	+	32.6459i	0.290454	+	1.08399i	0.944761	+	0.327760i	$0.106294\pi$
$907$	8.74745	+	32.6459i	0.290454	+	1.08399i	−0.654307	+	0.756229i	$0.727039\pi$
$908$	−0.465022	+	0.178505i	−0.0154323	+	0.00592390i
$909$	2.94197	+	9.05447i	0.0975791	+	0.300318i
$910$		0			0
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	−0.791847	−	0.610719i	$-0.790880\pi$
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	0.999590	−	0.0286459i	$-0.00911953\pi$
$912$	1.50682	+	28.7519i	0.0498958	+	0.952069i
$913$	−3.81670	+	2.47859i	−0.126314	+	0.0820294i
$914$	−28.4292	+	25.5977i	−0.940353	+	0.846697i
$915$		0			0
$916$	−2.67531	+	0.869261i	−0.0883948	+	0.0287212i
$917$	−1.31870	−	0.269903i	−0.0435472	−	0.00891298i
$918$	24.9079	+	24.9079i	0.822082	+	0.822082i
$919$	13.0177	−	29.2383i	0.429415	−	0.964481i	−0.561185	−	0.827690i	$-0.689654\pi$
$919$	13.0177	−	29.2383i	0.429415	−	0.964481i	0.990600	−	0.136791i	$-0.0436789\pi$
$920$		0			0
$921$	8.08372	−	3.59911i	0.266368	−	0.118595i
$922$	−32.7506	+	26.5210i	−1.07859	+	0.873421i
$923$	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
$927$	−0.225172	+	4.29654i	−0.00739563	+	0.141117i
$928$	−5.07629	−	1.94861i	−0.166637	−	0.0639661i
$929$	−4.40135	+	41.8761i	−0.144404	+	1.37391i	0.646942	+	0.762539i	$0.276048\pi$
$929$	−4.40135	+	41.8761i	−0.144404	+	1.37391i	−0.791345	+	0.611369i	$0.790619\pi$
$930$		0			0
$931$	37.5790	−	0.567767i	1.23160	−	0.0186078i
$932$	−3.52757	+	3.52757i	−0.115549	+	0.115549i
$933$	0.541562	+	1.41082i	0.0177299	+	0.0461881i
$934$	−9.18683	−	1.95272i	−0.300602	−	0.0638950i
$935$		0			0
$936$	−0.0743241	−	0.349668i	−0.00242936	−	0.0114292i
$937$	−7.54518	+	14.8083i	−0.246490	+	0.483765i	−0.980791	−	0.195059i	$-0.937510\pi$
$937$	−7.54518	+	14.8083i	−0.246490	+	0.483765i	0.734301	+	0.678824i	$0.237510\pi$
$938$	−22.9984	−	39.1485i	−0.750925	−	1.27824i
$939$	−0.581349	−	0.188892i	−0.0189716	−	0.00616425i
$940$		0			0
$941$	−2.27250	+	10.6913i	−0.0740814	+	0.348526i	−0.999540	−	0.0303227i	$-0.990347\pi$
$941$	−2.27250	+	10.6913i	−0.0740814	+	0.348526i	0.925459	+	0.378848i	$0.123680\pi$
$942$	6.49575	+	5.26016i	0.211643	+	0.171385i
$943$	1.45030	+	0.388607i	0.0472283	+	0.0126548i
$944$	14.8319	−	10.7760i	0.482739	−	0.350730i
$945$		0			0
$946$	−4.36771	−	3.17332i	−0.142006	−	0.103174i
$947$	−20.6113	−	25.4529i	−0.669778	−	0.827107i	0.323084	−	0.946370i	$-0.395280\pi$
$947$	−20.6113	−	25.4529i	−0.669778	−	0.827107i	−0.992863	+	0.119263i	$0.961947\pi$
$948$	−3.69635	−	0.193717i	−0.120052	−	0.00629164i
$949$	2.48678	+	1.43574i	0.0807242	+	0.0466062i
$950$		0			0
$951$		−	47.1129i		−	1.52774i
$952$	30.7711	+	22.0033i	0.997296	+	0.713131i
$953$	4.85130	+	30.6299i	0.157149	+	0.992200i	0.932631	+	0.360831i	$0.117507\pi$
$953$	4.85130	+	30.6299i	0.157149	+	0.992200i	−0.775482	+	0.631369i	$0.782493\pi$
$954$	−3.48819	−	0.366623i	−0.112934	−	0.0118699i
$955$		0			0
$956$	−0.258113	−	2.45578i	−0.00834798	−	0.0794257i
$957$	−0.736146	+	2.74733i	−0.0237962	+	0.0888087i
$958$	−2.38104	+	15.0333i	−0.0769279	+	0.485704i
$959$	−8.20056	−	8.07759i	−0.264810	−	0.260839i
$960$		0			0
$961$	−19.3545	+	4.11392i	−0.624338	+	0.132707i
$962$	1.20032	+	1.84833i	0.0386998	+	0.0595925i
$963$	−0.641593	−	0.987966i	−0.0206750	−	0.0318368i
$964$	3.13227	−	0.665785i	0.100884	−	0.0214435i
$965$		0			0
$966$	2.81150	−	0.776147i	0.0904585	−	0.0249721i
$967$	5.19736	−	32.8149i	0.167136	−	1.05525i	−0.751380	−	0.659870i	$-0.770611\pi$
$967$	5.19736	−	32.8149i	0.167136	−	1.05525i	0.918516	−	0.395385i	$-0.129389\pi$
$968$	−8.30397	+	30.9908i	−0.266900	+	0.996083i
$969$	4.21789	+	40.1306i	0.135498	+	1.28918i
$970$		0			0
$971$	−9.62205	−	1.01132i	−0.308786	−	0.0324547i	−0.0511320	−	0.998692i	$-0.516283\pi$
$971$	−9.62205	−	1.01132i	−0.308786	−	0.0324547i	−0.257654	+	0.966237i	$0.582950\pi$
$972$	0.224312	+	1.41625i	0.00719481	+	0.0454262i
$973$	57.2074	+	5.57617i	1.83398	+	0.178764i
$974$		−	5.77998i		−	0.185202i
$975$		0			0
$976$	−26.4009	−	15.2426i	−0.845073	−	0.487903i
$977$	−4.17887	−	0.219005i	−0.133694	−	0.00700660i	−0.0146284	−	0.999893i	$-0.504657\pi$
$977$	−4.17887	−	0.219005i	−0.133694	−	0.00700660i	−0.119066	+	0.992886i	$0.537990\pi$
$978$	−21.7345	−	26.8399i	−0.694993	−	0.858245i
$979$	−2.26985	−	1.64914i	−0.0725448	−	0.0527069i
$980$		0			0
$981$	4.84824	−	3.52246i	0.154793	−	0.112463i
$982$	−12.3251	−	3.30250i	−0.393310	−	0.105387i
$983$	9.47023	+	7.66884i	0.302053	+	0.244598i	0.768349	−	0.640031i	$-0.221078\pi$
$983$	9.47023	+	7.66884i	0.302053	+	0.244598i	−0.466296	+	0.884629i	$0.654412\pi$
$984$	−2.73201	+	12.8531i	−0.0870933	+	0.409742i
$985$		0			0
$986$	22.8647	+	7.42920i	0.728161	+	0.236594i
$987$	26.7276	−	15.7016i	0.850750	−	0.499787i
$988$	0.136136	−	0.267182i	0.00433106	−	0.00850019i
$989$	−0.945444	−	4.44797i	−0.0300634	−	0.141437i
$990$		0			0
$991$	39.1306	+	8.31747i	1.24302	+	0.264213i	0.782059	−	0.623205i	$-0.214170\pi$
$991$	39.1306	+	8.31747i	1.24302	+	0.264213i	0.460966	+	0.887418i	$0.347503\pi$
$992$	−1.72080	−	4.48284i	−0.0546354	−	0.142330i
$993$	−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
$997$	0.361077	+	0.138605i	0.0114354	+	0.00438965i	0.364079	−	0.931368i	$-0.381384\pi$
$997$	0.361077	+	0.138605i	0.0114354	+	0.00438965i	−0.352644	+	0.935758i	$0.614717\pi$
$998$	0.326584	−	6.23160i	0.0103378	−	0.197258i
$999$	−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.493.6		288
5.2	odd	4		875.2.bb.c.507.6		288
5.3	odd	4		175.2.x.a.122.13	yes	288
5.4	even	2		875.2.bb.b.493.13		288
7.5	odd	6	inner	875.2.bb.a.243.13		288
25.6	even	5		875.2.bb.c.143.6		288
25.8	odd	20		875.2.bb.b.857.6		288
25.17	odd	20	inner	875.2.bb.a.857.13		288
25.19	even	10		175.2.x.a.108.13	yes	288
35.12	even	12		875.2.bb.c.257.6		288
35.19	odd	6		875.2.bb.b.243.6		288
35.33	even	12		175.2.x.a.47.13	yes	288
175.19	odd	30		175.2.x.a.33.13	✓	288
175.33	even	60		875.2.bb.b.607.13		288
175.117	even	60	inner	875.2.bb.a.607.6		288
175.131	odd	30		875.2.bb.c.768.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	175.19	odd	30
175.2.x.a.47.13	yes	288	35.33	even	12
175.2.x.a.108.13	yes	288	25.19	even	10
175.2.x.a.122.13	yes	288	5.3	odd	4
875.2.bb.a.243.13		288	7.5	odd	6	inner
875.2.bb.a.493.6		288	1.1	even	1	trivial
875.2.bb.a.607.6		288	175.117	even	60	inner
875.2.bb.a.857.13		288	25.17	odd	20	inner
875.2.bb.b.243.6		288	35.19	odd	6
875.2.bb.b.493.13		288	5.4	even	2
875.2.bb.b.607.13		288	175.33	even	60
875.2.bb.b.857.6		288	25.8	odd	20
875.2.bb.c.143.6		288	25.6	even	5
875.2.bb.c.257.6		288	35.12	even	12
875.2.bb.c.507.6		288	5.2	odd	4
875.2.bb.c.768.6		288	175.131	odd	30

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+(-0.719435 + 1.10783i) q^{2} +(0.561145 - 1.46183i) q^{3} +(0.103766 + 0.233063i) q^{4} +(1.21576 + 1.67335i) q^{6} +(-0.569615 - 2.58371i) q^{7} +(-2.94220 - 0.465999i) q^{8} +(0.407366 + 0.366794i) q^{9} +(-0.320535 - 0.355990i) q^{11} +(0.398926 - 0.0209068i) q^{12} +(0.195060 + 0.0993879i) q^{13} +(3.27212 + 1.22777i) q^{14} +(2.29156 - 2.54503i) q^{16} +(3.02058 - 3.73011i) q^{17} +(-0.699421 + 0.187409i) q^{18} +(-4.90486 - 2.18378i) q^{19} +(-4.09658 - 0.617151i) q^{21} +(0.624982 - 0.0989874i) q^{22} +(0.446992 + 0.290280i) q^{23} +(-2.33221 + 4.03951i) q^{24} +(-0.250438 + 0.144591i) q^{26} +(4.95029 - 2.52230i) q^{27} +(0.543059 - 0.400858i) q^{28} +(2.22883 - 3.06772i) q^{29} +(3.33026 - 0.350024i) q^{31} +(-0.371137 - 1.38510i) q^{32} +(-0.700264 + 0.268806i) q^{33} +(1.95922 + 6.02987i) q^{34} +(-0.0432152 + 0.133003i) q^{36} +(-0.398858 - 7.61066i) q^{37} +(5.94800 - 3.86267i) q^{38} +(0.254745 - 0.229374i) q^{39} +(2.67924 - 0.870538i) q^{41} +(3.63092 - 4.09433i) q^{42} +(-6.03300 - 6.03300i) q^{43} +(0.0497074 - 0.111645i) q^{44} +(-0.643164 + 0.286355i) q^{46} +(-5.81498 + 4.70888i) q^{47} +(-2.43451 - 4.77800i) q^{48} +(-6.35108 + 2.94344i) q^{49} +(-3.75781 - 6.50871i) q^{51} +(-0.00292301 + 0.0557743i) q^{52} +(4.52212 + 1.73588i) q^{53} +(-0.767126 + 7.29872i) q^{54} +(0.471919 + 7.86722i) q^{56} +(-5.94466 + 5.94466i) q^{57} +(1.79502 + 4.67619i) q^{58} +(5.23631 + 1.11301i) q^{59} +(-1.85075 - 8.70710i) q^{61} +(-2.00814 + 3.94119i) q^{62} +(0.715647 - 1.26145i) q^{63} +(8.31559 + 2.70190i) q^{64} +(0.206002 - 0.969164i) q^{66} +(-10.0964 - 8.17589i) q^{67} +(1.18278 + 0.316926i) q^{68} +(0.675168 - 0.490538i) q^{69} +(3.80548 + 2.76485i) q^{71} +(-1.02763 - 1.26902i) q^{72} +(13.0986 + 0.686467i) q^{73} +(8.71829 + 5.03351i) q^{74} -1.36974i q^{76} +(-0.737192 + 1.03095i) q^{77} +(0.0708350 + 0.447234i) q^{78} +(-9.21497 - 0.968533i) q^{79} +(-0.737450 - 7.01637i) q^{81} +(-0.963129 + 3.59445i) q^{82} +(1.48616 - 9.38322i) q^{83} +(-0.281252 - 1.01880i) q^{84} +(11.0239 - 2.34320i) q^{86} +(-3.23379 - 4.97960i) q^{87} +(0.777187 + 1.19676i) q^{88} +(5.72901 - 1.21774i) q^{89} +(0.145680 - 0.560590i) q^{91} +(-0.0212708 + 0.134299i) q^{92} +(1.35708 - 5.06469i) q^{93} +(-1.03315 - 9.82977i) q^{94} +(-2.23304 - 0.234702i) q^{96} +(1.50690 + 9.51421i) q^{97} +(1.30835 - 9.15355i) q^{98} -0.262589i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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