LMFDB - Embedded newform 1035.2.j.b.737.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, degree $2$, 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:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.18
Character	$\chi$	$=$	1035.737
Dual form			1035.2.j.b.323.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47325 - 1.47325i) q^{2} -2.34094i q^{4} +(0.834294 + 2.07460i) q^{5} +(0.188870 + 0.188870i) q^{7} +(-0.502291 - 0.502291i) q^{8} +O(q^{10})$	\(q+(1.47325 - 1.47325i) q^{2} -2.34094i q^{4} +(0.834294 + 2.07460i) q^{5} +(0.188870 + 0.188870i) q^{7} +(-0.502291 - 0.502291i) q^{8} +(4.28553 + 1.82728i) q^{10} +2.92106i q^{11} +(0.0612095 - 0.0612095i) q^{13} +0.556506 q^{14} +3.20188 q^{16} +(1.41414 - 1.41414i) q^{17} +1.33783i q^{19} +(4.85651 - 1.95303i) q^{20} +(4.30345 + 4.30345i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-3.60791 + 3.46165i) q^{25} -0.180354i q^{26} +(0.442133 - 0.442133i) q^{28} +4.81044 q^{29} +4.71665 q^{31} +(5.72176 - 5.72176i) q^{32} -4.16676i q^{34} +(-0.234256 + 0.549402i) q^{35} +(-1.78845 - 1.78845i) q^{37} +(1.97097 + 1.97097i) q^{38} +(0.622993 - 1.46111i) q^{40} +2.01769i q^{41} +(-5.51037 + 5.51037i) q^{43} +6.83802 q^{44} +2.08349 q^{46} +(7.37831 - 7.37831i) q^{47} -6.92866i q^{49} +(-0.215479 + 10.4152i) q^{50} +(-0.143288 - 0.143288i) q^{52} +(-3.62571 - 3.62571i) q^{53} +(-6.06001 + 2.43702i) q^{55} -0.189735i q^{56} +(7.08699 - 7.08699i) q^{58} +5.14710 q^{59} -13.3295 q^{61} +(6.94882 - 6.94882i) q^{62} -10.4554i q^{64} +(0.178052 + 0.0759183i) q^{65} +(-4.95769 - 4.95769i) q^{67} +(-3.31041 - 3.31041i) q^{68} +(0.464289 + 1.15453i) q^{70} -7.80103i q^{71} +(-8.46606 + 8.46606i) q^{73} -5.26967 q^{74} +3.13179 q^{76} +(-0.551700 + 0.551700i) q^{77} -5.81384i q^{79} +(2.67131 + 6.64261i) q^{80} +(2.97257 + 2.97257i) q^{82} +(0.630813 + 0.630813i) q^{83} +(4.11358 + 1.75396i) q^{85} +16.2363i q^{86} +(1.46722 - 1.46722i) q^{88} -2.89558 q^{89} +0.0231213 q^{91} +(1.65529 - 1.65529i) q^{92} -21.7402i q^{94} +(-2.77547 + 1.11615i) q^{95} +(-1.69043 - 1.69043i) q^{97} +(-10.2077 - 10.2077i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.47325	−	1.47325i	1.04175	−	1.04175i	0.0426564	−	0.999090i	$-0.486418\pi$
$2$	1.47325	−	1.47325i	1.04175	−	1.04175i	0.999090	−	0.0426564i	$-0.0135821\pi$
$3$		0			0
$3$		0			0
$4$		−	2.34094i		−	1.17047i
$5$	0.834294	+	2.07460i	0.373108	+	0.927788i
$5$	0.834294	+	2.07460i	0.373108	+	0.927788i
$6$		0			0
$7$	0.188870	+	0.188870i	0.0713861	+	0.0713861i	0.741898	−	0.670512i	$-0.233926\pi$
$7$	0.188870	+	0.188870i	0.0713861	+	0.0713861i	−0.670512	+	0.741898i	$0.733926\pi$
$8$	−0.502291	−	0.502291i	−0.177587	−	0.177587i
$9$		0			0
$10$	4.28553	+	1.82728i	1.35520	+	0.577836i
$11$			2.92106i			0.880731i	0.897818	+	0.440366i	$0.145151\pi$
$11$			2.92106i			0.880731i	−0.897818	+	0.440366i	$0.854849\pi$
$12$		0			0
$13$	0.0612095	−	0.0612095i	0.0169764	−	0.0169764i	−0.698568	−	0.715544i	$-0.746179\pi$
$13$	0.0612095	−	0.0612095i	0.0169764	−	0.0169764i	0.715544	+	0.698568i	$0.246179\pi$
$14$	0.556506			0.148732
$15$		0			0
$16$	3.20188			0.800470
$17$	1.41414	−	1.41414i	0.342979	−	0.342979i	−0.514507	−	0.857486i	$-0.672025\pi$
$17$	1.41414	−	1.41414i	0.342979	−	0.342979i	0.857486	+	0.514507i	$0.172025\pi$
$18$		0			0
$19$			1.33783i			0.306920i	0.988155	+	0.153460i	$0.0490417\pi$
$19$			1.33783i			0.306920i	−0.988155	+	0.153460i	$0.950958\pi$
$20$	4.85651	−	1.95303i	1.08595	−	0.436711i
$21$		0			0
$22$	4.30345	+	4.30345i	0.917499	+	0.917499i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−3.60791	+	3.46165i	−0.721582	+	0.692329i
$26$		−	0.180354i		−	0.0353703i
$27$		0			0
$28$	0.442133	−	0.442133i	0.0835553	−	0.0835553i
$29$	4.81044			0.893277			0.446638	−	0.894715i	$-0.352621\pi$
$29$	4.81044			0.893277			0.446638	+	0.894715i	$0.352621\pi$
$30$		0			0
$31$	4.71665			0.847136			0.423568	−	0.905864i	$-0.360777\pi$
$31$	4.71665			0.847136			0.423568	+	0.905864i	$0.360777\pi$
$32$	5.72176	−	5.72176i	1.01147	−	1.01147i
$33$		0			0
$34$		−	4.16676i		−	0.714594i
$35$	−0.234256	+	0.549402i	−0.0395965	+	0.0928659i
$36$		0			0
$37$	−1.78845	−	1.78845i	−0.294019	−	0.294019i	0.544646	−	0.838666i	$-0.316664\pi$
$37$	−1.78845	−	1.78845i	−0.294019	−	0.294019i	−0.838666	+	0.544646i	$0.816664\pi$
$38$	1.97097	+	1.97097i	0.319733	+	0.319733i
$39$		0			0
$40$	0.622993	−	1.46111i	0.0985038	−	0.231022i
$41$			2.01769i			0.315111i	0.987510	+	0.157555i	$0.0503613\pi$
$41$			2.01769i			0.315111i	−0.987510	+	0.157555i	$0.949639\pi$
$42$		0			0
$43$	−5.51037	+	5.51037i	−0.840324	+	0.840324i	−0.988901	−	0.148577i	$-0.952531\pi$
$43$	−5.51037	+	5.51037i	−0.840324	+	0.840324i	0.148577	+	0.988901i	$0.452531\pi$
$44$	6.83802			1.03087
$45$		0			0
$46$	2.08349			0.307194
$47$	7.37831	−	7.37831i	1.07624	−	1.07624i	0.0793931	−	0.996843i	$-0.474702\pi$
$47$	7.37831	−	7.37831i	1.07624	−	1.07624i	0.996843	−	0.0793931i	$-0.0252982\pi$
$48$		0			0
$49$		−	6.92866i		−	0.989808i
$50$	−0.215479	+	10.4152i	−0.0304733	+	1.47294i
$51$		0			0
$52$	−0.143288	−	0.143288i	−0.0198704	−	0.0198704i
$53$	−3.62571	−	3.62571i	−0.498029	−	0.498029i	0.412795	−	0.910824i	$-0.364553\pi$
$53$	−3.62571	−	3.62571i	−0.498029	−	0.498029i	−0.910824	+	0.412795i	$0.864553\pi$
$54$		0			0
$55$	−6.06001	+	2.43702i	−0.817132	+	0.328608i
$56$		−	0.189735i		−	0.0253544i
$57$		0			0
$58$	7.08699	−	7.08699i	0.930567	−	0.930567i
$59$	5.14710			0.670095			0.335048	−	0.942201i	$-0.391248\pi$
$59$	5.14710			0.670095			0.335048	+	0.942201i	$0.391248\pi$
$60$		0			0
$61$	−13.3295			−1.70667			−0.853333	−	0.521366i	$-0.825423\pi$
$61$	−13.3295			−1.70667			−0.853333	+	0.521366i	$0.825423\pi$
$62$	6.94882	−	6.94882i	0.882501	−	0.882501i
$63$		0			0
$64$		−	10.4554i		−	1.30693i
$65$	0.178052	+	0.0759183i	0.0220846	+	0.00941651i
$66$		0			0
$67$	−4.95769	−	4.95769i	−0.605678	−	0.605678i	0.336136	−	0.941814i	$-0.390880\pi$
$67$	−4.95769	−	4.95769i	−0.605678	−	0.605678i	−0.941814	+	0.336136i	$0.890880\pi$
$68$	−3.31041	−	3.31041i	−0.401447	−	0.401447i
$69$		0			0
$70$	0.464289	+	1.15453i	0.0554932	+	0.137992i
$71$		−	7.80103i		−	0.925811i	−0.886408	−	0.462906i	$-0.846807\pi$
$71$		−	7.80103i		−	0.925811i	0.886408	−	0.462906i	$-0.153193\pi$
$72$		0			0
$73$	−8.46606	+	8.46606i	−0.990877	+	0.990877i	−0.999959	−	0.00908142i	$-0.997109\pi$
$73$	−8.46606	+	8.46606i	−0.990877	+	0.990877i	0.00908142	+	0.999959i	$0.497109\pi$
$74$	−5.26967			−0.612587
$75$		0			0
$76$	3.13179			0.359241
$77$	−0.551700	+	0.551700i	−0.0628720	+	0.0628720i
$78$		0			0
$79$		−	5.81384i		−	0.654108i	−0.945006	−	0.327054i	$-0.893944\pi$
$79$		−	5.81384i		−	0.654108i	0.945006	−	0.327054i	$-0.106056\pi$
$80$	2.67131	+	6.64261i	0.298661	+	0.742666i
$81$		0			0
$82$	2.97257	+	2.97257i	0.328266	+	0.328266i
$83$	0.630813	+	0.630813i	0.0692407	+	0.0692407i	0.740879	−	0.671638i	$-0.234409\pi$
$83$	0.630813	+	0.630813i	0.0692407	+	0.0692407i	−0.671638	+	0.740879i	$0.734409\pi$
$84$		0			0
$85$	4.11358	+	1.75396i	0.446180	+	0.190244i
$86$			16.2363i			1.75081i
$87$		0			0
$88$	1.46722	−	1.46722i	0.156406	−	0.156406i
$89$	−2.89558			−0.306931			−0.153466	−	0.988154i	$-0.549043\pi$
$89$	−2.89558			−0.306931			−0.153466	+	0.988154i	$0.549043\pi$
$90$		0			0
$91$	0.0231213			0.00242377
$92$	1.65529	−	1.65529i	0.172576	−	0.172576i
$93$		0			0
$94$		−	21.7402i		−	2.24233i
$95$	−2.77547	+	1.11615i	−0.284757	+	0.114514i
$96$		0			0
$97$	−1.69043	−	1.69043i	−0.171637	−	0.171637i	0.616061	−	0.787698i	$-0.288727\pi$
$97$	−1.69043	−	1.69043i	−0.171637	−	0.171637i	−0.787698	+	0.616061i	$0.788727\pi$
$98$	−10.2077	−	10.2077i	−1.03113	−	1.03113i
$99$		0			0
$100$	8.10351	+	8.44590i	0.810351	+	0.844590i
$101$			11.9550i			1.18957i	0.803884	+	0.594786i	$0.202763\pi$
$101$			11.9550i			1.18957i	−0.803884	+	0.594786i	$0.797237\pi$
$102$		0			0
$103$	1.40640	−	1.40640i	0.138577	−	0.138577i	−0.634415	−	0.772992i	$-0.718759\pi$
$103$	1.40640	−	1.40640i	0.138577	−	0.138577i	0.772992	+	0.634415i	$0.218759\pi$
$104$	−0.0614899			−0.00602958
$105$		0			0
$106$	−10.6832			−1.03764
$107$	−4.60023	+	4.60023i	−0.444721	+	0.444721i	−0.893595	−	0.448874i	$-0.851825\pi$
$107$	−4.60023	+	4.60023i	−0.444721	+	0.444721i	0.448874	+	0.893595i	$0.351825\pi$
$108$		0			0
$109$		−	0.218603i		−	0.0209384i	−0.999945	−	0.0104692i	$-0.996667\pi$
$109$		−	0.218603i		−	0.0209384i	0.999945	−	0.0104692i	$-0.00333251\pi$
$110$	−5.33758	+	12.5183i	−0.508919	+	1.19357i
$111$		0			0
$112$	0.604739	+	0.604739i	0.0571424	+	0.0571424i
$113$	−1.46395	−	1.46395i	−0.137717	−	0.137717i	0.634887	−	0.772605i	$-0.281046\pi$
$113$	−1.46395	−	1.46395i	−0.137717	−	0.137717i	−0.772605	+	0.634887i	$0.781046\pi$
$114$		0			0
$115$	−0.877027	+	2.05690i	−0.0817832	+	0.191807i
$116$		−	11.2610i		−	1.04555i
$117$		0			0
$118$	7.58297	−	7.58297i	0.698069	−	0.698069i
$119$	0.534177			0.0489679
$120$		0			0
$121$	2.46743			0.224312
$122$	−19.6377	+	19.6377i	−1.77791	+	1.77791i
$123$		0			0
$124$		−	11.0414i		−	0.991548i
$125$	−10.1916	−	4.59693i	−0.911563	−	0.411161i
$126$		0			0
$127$	−7.40580	−	7.40580i	−0.657158	−	0.657158i	0.297549	−	0.954707i	$-0.403831\pi$
$127$	−7.40580	−	7.40580i	−0.657158	−	0.657158i	−0.954707	+	0.297549i	$0.903831\pi$
$128$	−3.95994	−	3.95994i	−0.350012	−	0.350012i
$129$		0			0
$130$	0.374162	−	0.150468i	0.0328161	−	0.0131969i
$131$		−	1.42633i		−	0.124619i	−0.998057	−	0.0623096i	$-0.980153\pi$
$131$		−	1.42633i		−	0.124619i	0.998057	−	0.0623096i	$-0.0198466\pi$
$132$		0			0
$133$	−0.252677	+	0.252677i	−0.0219099	+	0.0219099i
$134$	−14.6078			−1.26192
$135$		0			0
$136$	−1.42062			−0.121817
$137$	7.40914	−	7.40914i	0.633006	−	0.633006i	−0.315815	−	0.948821i	$-0.602278\pi$
$137$	7.40914	−	7.40914i	0.633006	−	0.633006i	0.948821	+	0.315815i	$0.102278\pi$
$138$		0			0
$139$		−	9.70275i		−	0.822976i	−0.911415	−	0.411488i	$-0.865009\pi$
$139$		−	9.70275i		−	0.822976i	0.911415	−	0.411488i	$-0.134991\pi$
$140$	1.28612	+	0.548379i	0.108697	+	0.0463465i
$141$		0			0
$142$	−11.4929	−	11.4929i	−0.964461	−	0.964461i
$143$	0.178796	+	0.178796i	0.0149517	+	0.0149517i
$144$		0			0
$145$	4.01332	+	9.97973i	0.333288	+	0.828771i
$146$			24.9453i			2.06449i
$147$		0			0
$148$	−4.18665	+	4.18665i	−0.344141	+	0.344141i
$149$	5.82432			0.477147			0.238573	−	0.971124i	$-0.423320\pi$
$149$	5.82432			0.477147			0.238573	+	0.971124i	$0.423320\pi$
$150$		0			0
$151$	−3.47641			−0.282906			−0.141453	−	0.989945i	$-0.545177\pi$
$151$	−3.47641			−0.282906			−0.141453	+	0.989945i	$0.545177\pi$
$152$	0.671982	−	0.671982i	0.0545049	−	0.0545049i
$153$		0			0
$154$			1.62558i			0.130993i
$155$	3.93508	+	9.78516i	0.316073	+	0.785963i
$156$		0			0
$157$	1.21296	+	1.21296i	0.0968045	+	0.0968045i	0.753850	−	0.657046i	$-0.228194\pi$
$157$	1.21296	+	1.21296i	0.0968045	+	0.0968045i	−0.657046	+	0.753850i	$0.728194\pi$
$158$	−8.56525	−	8.56525i	−0.681415	−	0.681415i
$159$		0			0
$160$	16.6440	+	7.09671i	1.31582	+	0.561044i
$161$			0.267102i			0.0210506i
$162$		0			0
$163$	4.86564	−	4.86564i	0.381106	−	0.381106i	−0.490394	−	0.871501i	$-0.663147\pi$
$163$	4.86564	−	4.86564i	0.381106	−	0.381106i	0.871501	+	0.490394i	$0.163147\pi$
$164$	4.72330			0.368828
$165$		0			0
$166$	1.85869			0.144262
$167$	11.3927	−	11.3927i	0.881596	−	0.881596i	−0.112101	−	0.993697i	$-0.535758\pi$
$167$	11.3927	−	11.3927i	0.881596	−	0.881596i	0.993697	+	0.112101i	$0.0357581\pi$
$168$		0			0
$169$			12.9925i			0.999424i
$170$	8.64436	−	3.47631i	0.662992	−	0.266621i
$171$		0			0
$172$	12.8994	+	12.8994i	0.983574	+	0.983574i
$173$	−6.65676	−	6.65676i	−0.506104	−	0.506104i	0.407224	−	0.913328i	$-0.366497\pi$
$173$	−6.65676	−	6.65676i	−0.506104	−	0.506104i	−0.913328	+	0.407224i	$0.866497\pi$
$174$		0			0
$175$	−1.33523	−	0.0276242i	−0.100934	−	0.00208820i
$176$			9.35287i			0.704999i
$177$		0			0
$178$	−4.26592	+	4.26592i	−0.319745	+	0.319745i
$179$	−1.91558			−0.143177			−0.0715885	−	0.997434i	$-0.522807\pi$
$179$	−1.91558			−0.143177			−0.0715885	+	0.997434i	$0.522807\pi$
$180$		0			0
$181$	−14.8105			−1.10086			−0.550428	−	0.834883i	$-0.685535\pi$
$181$	−14.8105			−1.10086			−0.550428	+	0.834883i	$0.685535\pi$
$182$	0.0340634	−	0.0340634i	0.00252495	−	0.00252495i
$183$		0			0
$184$		−	0.710346i		−	0.0523674i
$185$	2.21822	−	5.20241i	0.163087	−	0.382488i
$186$		0			0
$187$	4.13078	+	4.13078i	0.302072	+	0.302072i
$188$	−17.2722	−	17.2722i	−1.25970	−	1.25970i
$189$		0			0
$190$	−2.44460	+	5.73333i	−0.177350	+	0.415939i
$191$			24.4073i			1.76605i	0.469326	+	0.883025i	$0.344497\pi$
$191$			24.4073i			1.76605i	−0.469326	+	0.883025i	$0.655503\pi$
$192$		0			0
$193$	−17.0229	+	17.0229i	−1.22533	+	1.22533i	−0.259625	+	0.965709i	$0.583599\pi$
$193$	−17.0229	+	17.0229i	−1.22533	+	1.22533i	−0.965709	+	0.259625i	$0.916401\pi$
$194$	−4.98085			−0.357604
$195$		0			0
$196$	−16.2196			−1.15854
$197$	3.26436	−	3.26436i	0.232576	−	0.232576i	−0.581191	−	0.813767i	$-0.697413\pi$
$197$	3.26436	−	3.26436i	0.232576	−	0.232576i	0.813767	+	0.581191i	$0.197413\pi$
$198$		0			0
$199$		−	0.627606i		−	0.0444898i	−0.999753	−	0.0222449i	$-0.992919\pi$
$199$		−	0.627606i		−	0.0444898i	0.999753	−	0.0222449i	$-0.00708136\pi$
$200$	3.55097	+	0.0734653i	0.251092	+	0.00519478i
$201$		0			0
$202$	17.6128	+	17.6128i	1.23923	+	1.23923i
$203$	0.908548	+	0.908548i	0.0637676	+	0.0637676i
$204$		0			0
$205$	−4.18590	+	1.68335i	−0.292356	+	0.117570i
$206$		−	4.14397i		−	0.288724i
$207$		0			0
$208$	0.195985	−	0.195985i	0.0135891	−	0.0135891i
$209$	−3.90789			−0.270314
$210$		0			0
$211$	−26.0811			−1.79550			−0.897748	−	0.440508i	$-0.854798\pi$
$211$	−26.0811			−1.79550			−0.897748	+	0.440508i	$0.854798\pi$
$212$	−8.48757	+	8.48757i	−0.582928	+	0.582928i
$213$		0			0
$214$			13.5546i			0.926573i
$215$	−16.0291	−	6.83453i	−1.09317	−	0.466111i
$216$		0			0
$217$	0.890834	+	0.890834i	0.0604738	+	0.0604738i
$218$	−0.322058	−	0.322058i	−0.0218125	−	0.0218125i
$219$		0			0
$220$	5.70492	+	14.1861i	0.384625	+	0.956429i
$221$		−	0.173117i		−	0.0116451i
$222$		0			0
$223$	15.0896	−	15.0896i	1.01048	−	1.01048i	0.0105327	−	0.999945i	$-0.496647\pi$
$223$	15.0896	−	15.0896i	1.01048	−	1.01048i	0.999945	−	0.0105327i	$-0.00335273\pi$
$224$	2.16134			0.144410
$225$		0			0
$226$	−4.31355			−0.286933
$227$	9.61081	−	9.61081i	0.637892	−	0.637892i	−0.312143	−	0.950035i	$-0.601047\pi$
$227$	9.61081	−	9.61081i	0.637892	−	0.637892i	0.950035	+	0.312143i	$0.101047\pi$
$228$		0			0
$229$			21.7615i			1.43804i	0.694988	+	0.719022i	$0.255410\pi$
$229$			21.7615i			1.43804i	−0.694988	+	0.719022i	$0.744590\pi$
$230$	1.73824	+	4.32241i	0.114616	+	0.285011i
$231$		0			0
$232$	−2.41624	−	2.41624i	−0.158634	−	0.158634i
$233$	−17.5894	−	17.5894i	−1.15232	−	1.15232i	−0.986087	−	0.166231i	$-0.946840\pi$
$233$	−17.5894	−	17.5894i	−1.15232	−	1.15232i	−0.166231	−	0.986087i	$-0.553160\pi$
$234$		0			0
$235$	21.4627	+	9.15134i	1.40007	+	0.596967i
$236$		−	12.0491i		−	0.784327i
$237$		0			0
$238$	0.786977	−	0.786977i	0.0510121	−	0.0510121i
$239$	22.5813			1.46066			0.730330	−	0.683094i	$-0.239366\pi$
$239$	22.5813			1.46066			0.730330	+	0.683094i	$0.239366\pi$
$240$		0			0
$241$	18.1339			1.16811			0.584054	−	0.811715i	$-0.301466\pi$
$241$	18.1339			1.16811			0.584054	+	0.811715i	$0.301466\pi$
$242$	3.63515	−	3.63515i	0.233676	−	0.233676i
$243$		0			0
$244$			31.2035i			1.99760i
$245$	14.3742	−	5.78053i	0.918332	−	0.369305i
$246$		0			0
$247$	0.0818882	+	0.0818882i	0.00521042	+	0.00521042i
$248$	−2.36913	−	2.36913i	−0.150440	−	0.150440i
$249$		0			0
$250$	−21.7872	+	8.24233i	−1.37794	+	0.521291i
$251$		−	14.8610i		−	0.938016i	−0.883194	−	0.469008i	$-0.844611\pi$
$251$		−	14.8610i		−	0.938016i	0.883194	−	0.469008i	$-0.155389\pi$
$252$		0			0
$253$	−2.06550	+	2.06550i	−0.129857	+	0.129857i
$254$	−21.8212			−1.36918
$255$		0			0
$256$	9.24285			0.577678
$257$	8.92969	−	8.92969i	0.557019	−	0.557019i	−0.371439	−	0.928457i	$-0.621135\pi$
$257$	8.92969	−	8.92969i	0.557019	−	0.557019i	0.928457	+	0.371439i	$0.121135\pi$
$258$		0			0
$259$		−	0.675569i		−	0.0419778i
$260$	0.177720	−	0.416808i	0.0110217	−	0.0258493i
$261$		0			0
$262$	−2.10134	−	2.10134i	−0.129821	−	0.129821i
$263$	−13.6043	−	13.6043i	−0.838879	−	0.838879i	0.149832	−	0.988711i	$-0.452127\pi$
$263$	−13.6043	−	13.6043i	−0.838879	−	0.838879i	−0.988711	+	0.149832i	$0.952127\pi$
$264$		0			0
$265$	4.49698	−	10.5468i	0.276247	−	0.647884i
$266$			0.744513i			0.0456490i
$267$		0			0
$268$	−11.6056	+	11.6056i	−0.708928	+	0.708928i
$269$	−0.539928			−0.0329200			−0.0164600	−	0.999865i	$-0.505240\pi$
$269$	−0.539928			−0.0329200			−0.0164600	+	0.999865i	$0.505240\pi$
$270$		0			0
$271$	11.3817			0.691389			0.345695	−	0.938347i	$-0.387643\pi$
$271$	11.3817			0.691389			0.345695	+	0.938347i	$0.387643\pi$
$272$	4.52790	−	4.52790i	0.274544	−	0.274544i
$273$		0			0
$274$		−	21.8311i		−	1.31886i
$275$	−10.1117	−	10.5389i	−0.609756	−	0.635520i
$276$		0			0
$277$	−9.82324	−	9.82324i	−0.590221	−	0.590221i	0.347470	−	0.937691i	$-0.387041\pi$
$277$	−9.82324	−	9.82324i	−0.590221	−	0.590221i	−0.937691	+	0.347470i	$0.887041\pi$
$278$	−14.2946	−	14.2946i	−0.857333	−	0.857333i
$279$		0			0
$280$	0.393624	−	0.158295i	0.0235235	−	0.00945993i
$281$			20.3332i			1.21298i	0.795093	+	0.606488i	$0.207422\pi$
$281$			20.3332i			1.21298i	−0.795093	+	0.606488i	$0.792578\pi$
$282$		0			0
$283$	14.8734	−	14.8734i	0.884132	−	0.884132i	−0.109820	−	0.993952i	$-0.535027\pi$
$283$	14.8734	−	14.8734i	0.884132	−	0.884132i	0.993952	+	0.109820i	$0.0350274\pi$
$284$	−18.2617			−1.08363
$285$		0			0
$286$	0.526824			0.0311517
$287$	−0.381082	+	0.381082i	−0.0224946	+	0.0224946i
$288$		0			0
$289$			13.0004i			0.764731i
$290$	20.6153	+	8.79002i	1.21057	+	0.516168i
$291$		0			0
$292$	19.8185	+	19.8185i	1.15979	+	1.15979i
$293$	16.0603	+	16.0603i	0.938252	+	0.938252i	0.998201	−	0.0599491i	$-0.0190938\pi$
$293$	16.0603	+	16.0603i	0.938252	+	0.938252i	−0.0599491	+	0.998201i	$0.519094\pi$
$294$		0			0
$295$	4.29419	+	10.6782i	0.250018	+	0.621707i
$296$			1.79664i			0.104428i
$297$		0			0
$298$	8.58068	−	8.58068i	0.497066	−	0.497066i
$299$	0.0865632			0.00500608
$300$		0			0
$301$	−2.08149			−0.119975
$302$	−5.12163	+	5.12163i	−0.294717	+	0.294717i
$303$		0			0
$304$			4.28359i			0.245681i
$305$	−11.1207	−	27.6533i	−0.636770	−	1.58343i
$306$		0			0
$307$	−18.7535	−	18.7535i	−1.07032	−	1.07032i	−0.997333	−	0.0729828i	$-0.976748\pi$
$307$	−18.7535	−	18.7535i	−1.07032	−	1.07032i	−0.0729828	−	0.997333i	$-0.523252\pi$
$308$	1.29150	+	1.29150i	0.0735898	+	0.0735898i
$309$		0			0
$310$	20.2134	+	8.61864i	1.14804	+	0.489506i
$311$		−	12.9045i		−	0.731745i	−0.930665	−	0.365873i	$-0.880771\pi$
$311$		−	12.9045i		−	0.731745i	0.930665	−	0.365873i	$-0.119229\pi$
$312$		0			0
$313$	7.71007	−	7.71007i	0.435799	−	0.435799i	−0.454797	−	0.890595i	$-0.650288\pi$
$313$	7.71007	−	7.71007i	0.435799	−	0.435799i	0.890595	+	0.454797i	$0.150288\pi$
$314$	3.57398			0.201691
$315$		0			0
$316$	−13.6099			−0.765614
$317$	−15.6804	+	15.6804i	−0.880698	+	0.880698i	−0.993606	−	0.112907i	$-0.963984\pi$
$317$	−15.6804	+	15.6804i	−0.880698	+	0.880698i	0.112907	+	0.993606i	$0.463984\pi$
$318$		0			0
$319$			14.0516i			0.786737i
$320$	21.6908	−	8.72288i	1.21255	−	0.487624i
$321$		0			0
$322$	0.393509	+	0.393509i	0.0219294	+	0.0219294i
$323$	1.89188	+	1.89188i	0.105267	+	0.105267i
$324$		0			0
$325$	−0.00895253	+	0.432724i	−0.000496597	+	0.0240032i
$326$		−	14.3366i		−	0.794032i
$327$		0			0
$328$	1.01347	−	1.01347i	0.0559595	−	0.0559595i
$329$	2.78708			0.153657
$330$		0			0
$331$	−15.3489			−0.843650			−0.421825	−	0.906677i	$-0.638610\pi$
$331$	−15.3489			−0.843650			−0.421825	+	0.906677i	$0.638610\pi$
$332$	1.47669	−	1.47669i	0.0810441	−	0.0810441i
$333$		0			0
$334$		−	33.5687i		−	1.83680i
$335$	6.14904	−	14.4214i	0.335958	−	0.787924i
$336$		0			0
$337$	6.29899	+	6.29899i	0.343128	+	0.343128i	0.857542	−	0.514414i	$-0.171991\pi$
$337$	6.29899	+	6.29899i	0.343128	+	0.343128i	−0.514414	+	0.857542i	$0.671991\pi$
$338$	19.1412	+	19.1412i	1.04115	+	1.04115i
$339$		0			0
$340$	4.10592	−	9.62964i	0.222675	−	0.522240i
$341$			13.7776i			0.746100i
$342$		0			0
$343$	2.63070	−	2.63070i	0.142045	−	0.142045i
$344$	5.53561			0.298460
$345$		0			0
$346$	−19.6142			−1.05446
$347$	10.6967	−	10.6967i	0.574227	−	0.574227i	−0.359080	−	0.933307i	$-0.616909\pi$
$347$	10.6967	−	10.6967i	0.574227	−	0.574227i	0.933307	+	0.359080i	$0.116909\pi$
$348$		0			0
$349$			16.3040i			0.872731i	0.899770	+	0.436365i	$0.143734\pi$
$349$			16.3040i			0.872731i	−0.899770	+	0.436365i	$0.856266\pi$
$350$	−2.00782	+	1.92643i	−0.107323	+	0.102972i
$351$		0			0
$352$	16.7136	+	16.7136i	0.890836	+	0.890836i
$353$	18.4718	+	18.4718i	0.983152	+	0.983152i	0.999860	−	0.0167083i	$-0.00531865\pi$
$353$	18.4718	+	18.4718i	0.983152	+	0.983152i	−0.0167083	+	0.999860i	$0.505319\pi$
$354$		0			0
$355$	16.1840	−	6.50835i	0.858957	−	0.345427i
$356$			6.77839i			0.359254i
$357$		0			0
$358$	−2.82213	+	2.82213i	−0.149154	+	0.149154i
$359$	−8.96639			−0.473228			−0.236614	−	0.971604i	$-0.576038\pi$
$359$	−8.96639			−0.473228			−0.236614	+	0.971604i	$0.576038\pi$
$360$		0			0
$361$	17.2102			0.905800
$362$	−21.8196	+	21.8196i	−1.14681	+	1.14681i
$363$		0			0
$364$		−	0.0541255i		−	0.00283695i
$365$	−24.6268	−	10.5005i	−1.28903	−	0.549620i
$366$		0			0
$367$	−11.3199	−	11.3199i	−0.590893	−	0.590893i	0.346980	−	0.937873i	$-0.387207\pi$
$367$	−11.3199	−	11.3199i	−0.590893	−	0.590893i	−0.937873	+	0.346980i	$0.887207\pi$
$368$	2.26407	+	2.26407i	0.118023	+	0.118023i
$369$		0			0
$370$	−4.39646	−	10.9324i	−0.228561	−	0.568351i
$371$		−	1.36957i		−	0.0711048i
$372$		0			0
$373$	12.6377	−	12.6377i	0.654355	−	0.654355i	−0.299684	−	0.954039i	$-0.596881\pi$
$373$	12.6377	−	12.6377i	0.654355	−	0.654355i	0.954039	+	0.299684i	$0.0968811\pi$
$374$	12.1714			0.629366
$375$		0			0
$376$	−7.41211			−0.382250
$377$	0.294444	−	0.294444i	0.0151647	−	0.0151647i
$378$		0			0
$379$			6.08513i			0.312572i	0.987712	+	0.156286i	$0.0499522\pi$
$379$			6.08513i			0.312572i	−0.987712	+	0.156286i	$0.950048\pi$
$380$	2.61283	+	6.49721i	0.134036	+	0.333300i
$381$		0			0
$382$	35.9581	+	35.9581i	1.83978	+	1.83978i
$383$	−0.380186	−	0.380186i	−0.0194266	−	0.0194266i	0.697327	−	0.716753i	$-0.254373\pi$
$383$	−0.380186	−	0.380186i	−0.0194266	−	0.0194266i	−0.716753	+	0.697327i	$0.754373\pi$
$384$		0			0
$385$	−1.60483	−	0.684275i	−0.0817899	−	0.0348739i
$386$			50.1580i			2.55298i
$387$		0			0
$388$	−3.95719	+	3.95719i	−0.200896	+	0.200896i
$389$	−35.4964			−1.79974			−0.899870	−	0.436158i	$-0.856339\pi$
$389$	−35.4964			−1.79974			−0.899870	+	0.436158i	$0.856339\pi$
$390$		0			0
$391$	1.99989			0.101139
$392$	−3.48020	+	3.48020i	−0.175777	+	0.175777i
$393$		0			0
$394$		−	9.61845i		−	0.484570i
$395$	12.0614	−	4.85045i	0.606874	−	0.244053i
$396$		0			0
$397$	−17.9224	−	17.9224i	−0.899501	−	0.899501i	0.0958906	−	0.995392i	$-0.469430\pi$
$397$	−17.9224	−	17.9224i	−0.899501	−	0.899501i	−0.995392	+	0.0958906i	$0.969430\pi$
$398$	−0.924622	−	0.924622i	−0.0463471	−	0.0463471i
$399$		0			0
$400$	−11.5521	+	11.0838i	−0.577604	+	0.554189i
$401$		−	32.9562i		−	1.64575i	−0.568221	−	0.822876i	$-0.692368\pi$
$401$		−	32.9562i		−	1.64575i	0.568221	−	0.822876i	$-0.307632\pi$
$402$		0			0
$403$	0.288704	−	0.288704i	0.0143814	−	0.0143814i
$404$	27.9861			1.39236
$405$		0			0
$406$	2.67704			0.132859
$407$	5.22416	−	5.22416i	0.258952	−	0.258952i
$408$		0			0
$409$			22.8650i			1.13060i	0.824886	+	0.565300i	$0.191239\pi$
$409$			22.8650i			1.13060i	−0.824886	+	0.565300i	$0.808761\pi$
$410$	−3.68689	+	8.64689i	−0.182083	+	0.427039i
$411$		0			0
$412$	−3.29231	−	3.29231i	−0.162200	−	0.162200i
$413$	0.972133	+	0.972133i	0.0478355	+	0.0478355i
$414$		0			0
$415$	−0.782399	+	1.83497i	−0.0384065	+	0.0900749i
$416$		−	0.700451i		−	0.0343424i
$417$		0			0
$418$	−5.75731	+	5.75731i	−0.281599	+	0.281599i
$419$	−17.8439			−0.871731			−0.435865	−	0.900012i	$-0.643558\pi$
$419$	−17.8439			−0.871731			−0.435865	+	0.900012i	$0.643558\pi$
$420$		0			0
$421$	−4.21281			−0.205320			−0.102660	−	0.994717i	$-0.532735\pi$
$421$	−4.21281			−0.205320			−0.102660	+	0.994717i	$0.532735\pi$
$422$	−38.4240	+	38.4240i	−1.87045	+	1.87045i
$423$		0			0
$424$			3.64232i			0.176887i
$425$	−0.206833	+	9.99733i	−0.0100329	+	0.484942i
$426$		0			0
$427$	−2.51754	−	2.51754i	−0.121832	−	0.121832i
$428$	10.7689	+	10.7689i	0.520533	+	0.520533i
$429$		0			0
$430$	−33.6838	+	13.5459i	−1.62438	+	0.653239i
$431$			35.1309i			1.69220i	0.533026	+	0.846099i	$0.321055\pi$
$431$			35.1309i			1.69220i	−0.533026	+	0.846099i	$0.678945\pi$
$432$		0			0
$433$	19.7831	−	19.7831i	0.950716	−	0.950716i	−0.0481255	−	0.998841i	$-0.515325\pi$
$433$	19.7831	−	19.7831i	0.950716	−	0.950716i	0.998841	+	0.0481255i	$0.0153247\pi$
$434$	2.62485			0.125997
$435$		0			0
$436$	−0.511737			−0.0245078
$437$	−0.945992	+	0.945992i	−0.0452529	+	0.0452529i
$438$		0			0
$439$		−	21.6241i		−	1.03206i	−0.856570	−	0.516030i	$-0.827409\pi$
$439$		−	21.6241i		−	1.03206i	0.856570	−	0.516030i	$-0.172591\pi$
$440$	4.26798	+	1.81980i	0.203468	+	0.0867554i
$441$		0			0
$442$	−0.255045	−	0.255045i	−0.0121313	−	0.0121313i
$443$	−1.63706	−	1.63706i	−0.0777792	−	0.0777792i	0.667147	−	0.744926i	$-0.267515\pi$
$443$	−1.63706	−	1.63706i	−0.0777792	−	0.0777792i	−0.744926	+	0.667147i	$0.767515\pi$
$444$		0			0
$445$	−2.41577	−	6.00717i	−0.114518	−	0.284767i
$446$		−	44.4617i		−	2.10532i
$447$		0			0
$448$	1.97471	−	1.97471i	0.0932964	−	0.0932964i
$449$	−17.1545			−0.809571			−0.404786	−	0.914412i	$-0.632654\pi$
$449$	−17.1545			−0.809571			−0.404786	+	0.914412i	$0.632654\pi$
$450$		0			0
$451$	−5.89380			−0.277528
$452$	−3.42703	+	3.42703i	−0.161194	+	0.161194i
$453$		0			0
$454$		−	28.3183i		−	1.32904i
$455$	0.0192899	+	0.0479673i	0.000904325	+	0.00224874i
$456$		0			0
$457$	−23.7976	−	23.7976i	−1.11321	−	1.11321i	−0.992714	−	0.120492i	$-0.961553\pi$
$457$	−23.7976	−	23.7976i	−1.11321	−	1.11321i	−0.120492	−	0.992714i	$-0.538447\pi$
$458$	32.0602	+	32.0602i	1.49808	+	1.49808i
$459$		0			0
$460$	4.81507	+	2.05307i	0.224504	+	0.0957248i
$461$			0.170482i			0.00794016i	0.999992	+	0.00397008i	$0.00126372\pi$
$461$			0.170482i			0.00794016i	−0.999992	+	0.00397008i	$0.998736\pi$
$462$		0			0
$463$	10.1996	−	10.1996i	0.474014	−	0.474014i	−0.429197	−	0.903211i	$-0.641203\pi$
$463$	10.1996	−	10.1996i	0.474014	−	0.474014i	0.903211	+	0.429197i	$0.141203\pi$
$464$	15.4025			0.715041
$465$		0			0
$466$	−51.8271			−2.40085
$467$	−11.5461	+	11.5461i	−0.534289	+	0.534289i	−0.921846	−	0.387557i	$-0.873319\pi$
$467$	−11.5461	+	11.5461i	−0.534289	+	0.534289i	0.387557	+	0.921846i	$0.373319\pi$
$468$		0			0
$469$		−	1.87272i		−	0.0864740i
$470$	45.1022	−	18.1377i	2.08041	−	0.836630i
$471$		0			0
$472$	−2.58534	−	2.58534i	−0.119000	−	0.119000i
$473$	−16.0961	−	16.0961i	−0.740099	−	0.740099i
$474$		0			0
$475$	−4.63111	−	4.82679i	−0.212490	−	0.221468i
$476$		−	1.25048i		−	0.0573155i
$477$		0			0
$478$	33.2679	−	33.2679i	1.52164	−	1.52164i
$479$	19.5499			0.893258			0.446629	−	0.894719i	$-0.352624\pi$
$479$	19.5499			0.893258			0.446629	+	0.894719i	$0.352624\pi$
$480$		0			0
$481$	−0.218940			−0.00998281
$482$	26.7158	−	26.7158i	1.21687	−	1.21687i
$483$		0			0
$484$		−	5.77611i		−	0.262551i
$485$	2.09664	−	4.91727i	0.0952037	−	0.223282i
$486$		0			0
$487$	−1.43485	−	1.43485i	−0.0650194	−	0.0650194i	0.673849	−	0.738869i	$-0.264640\pi$
$487$	−1.43485	−	1.43485i	−0.0650194	−	0.0650194i	−0.738869	+	0.673849i	$0.764640\pi$
$488$	6.69528	+	6.69528i	0.303081	+	0.303081i
$489$		0			0
$490$	12.6606	−	29.6930i	0.571947	−	1.34139i
$491$			32.8907i			1.48434i	0.670213	+	0.742169i	$0.266203\pi$
$491$			32.8907i			1.48434i	−0.670213	+	0.742169i	$0.733797\pi$
$492$		0			0
$493$	6.80263	−	6.80263i	0.306375	−	0.306375i
$494$	0.241284			0.0108559
$495$		0			0
$496$	15.1022			0.678107
$497$	1.47338	−	1.47338i	0.0660901	−	0.0660901i
$498$		0			0
$499$		−	29.1376i		−	1.30438i	−0.758056	−	0.652189i	$-0.773851\pi$
$499$		−	29.1376i		−	1.30438i	0.758056	−	0.652189i	$-0.226149\pi$
$500$	−10.7611	+	23.8579i	−0.481252	+	1.06696i
$501$		0			0
$502$	−21.8940	−	21.8940i	−0.977175	−	0.977175i
$503$	19.5279	+	19.5279i	0.870708	+	0.870708i	0.992550	−	0.121842i	$-0.0388800\pi$
$503$	19.5279	+	19.5279i	0.870708	+	0.870708i	−0.121842	+	0.992550i	$0.538880\pi$
$504$		0			0
$505$	−24.8019	+	9.97402i	−1.10367	+	0.443838i
$506$			6.08600i			0.270556i
$507$		0			0
$508$	−17.3365	+	17.3365i	−0.769184	+	0.769184i
$509$	−11.7734			−0.521845			−0.260922	−	0.965360i	$-0.584027\pi$
$509$	−11.7734			−0.521845			−0.260922	+	0.965360i	$0.584027\pi$
$510$		0			0
$511$	−3.19797			−0.141470
$512$	21.5369	−	21.5369i	0.951806	−	0.951806i
$513$		0			0
$514$		−	26.3114i		−	1.16054i
$515$	4.09108	+	1.74437i	0.180274	+	0.0768660i
$516$		0			0
$517$	21.5524	+	21.5524i	0.947875	+	0.947875i
$518$	−0.995283	−	0.995283i	−0.0437302	−	0.0437302i
$519$		0			0
$520$	−0.0513006	−	0.127567i	−0.00224968	−	0.00559417i
$521$		−	33.9777i		−	1.48859i	−0.667852	−	0.744294i	$-0.732786\pi$
$521$		−	33.9777i		−	1.48859i	0.667852	−	0.744294i	$-0.267214\pi$
$522$		0			0
$523$	23.3124	−	23.3124i	1.01938	−	1.01938i	0.0195736	−	0.999808i	$-0.493769\pi$
$523$	23.3124	−	23.3124i	1.01938	−	1.01938i	0.999808	−	0.0195736i	$-0.00623086\pi$
$524$	−3.33896			−0.145863
$525$		0			0
$526$	−40.0852			−1.74780
$527$	6.67001	−	6.67001i	0.290550	−	0.290550i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−8.91289	−	22.1633i	−0.387151	−	0.962710i
$531$		0			0
$532$	0.591501	+	0.591501i	0.0256448	+	0.0256448i
$533$	0.123502	+	0.123502i	0.00534947	+	0.00534947i
$534$		0			0
$535$	−13.3816	−	5.70568i	−0.578536	−	0.246678i
$536$			4.98040i			0.215120i
$537$		0			0
$538$	−0.795449	+	0.795449i	−0.0342943	+	0.0342943i
$539$	20.2390			0.871755
$540$		0			0
$541$	6.88074			0.295826			0.147913	−	0.989000i	$-0.452744\pi$
$541$	6.88074			0.295826			0.147913	+	0.989000i	$0.452744\pi$
$542$	16.7681	−	16.7681i	0.720252	−	0.720252i
$543$		0			0
$544$		−	16.1827i		−	0.693828i
$545$	0.453514	−	0.182379i	0.0194264	−	0.00781227i
$546$		0			0
$547$	−6.49052	−	6.49052i	−0.277515	−	0.277515i	0.554601	−	0.832116i	$-0.312871\pi$
$547$	−6.49052	−	6.49052i	−0.277515	−	0.277515i	−0.832116	+	0.554601i	$0.812871\pi$
$548$	−17.3444	−	17.3444i	−0.740914	−	0.740914i
$549$		0			0
$550$	−30.4235	−	0.629425i	−1.29726	−	0.0268388i
$551$			6.43558i			0.274165i
$552$		0			0
$553$	1.09806	−	1.09806i	0.0466943	−	0.0466943i
$554$	−28.9442			−1.22972
$555$		0			0
$556$	−22.7136			−0.963269
$557$	−24.3041	+	24.3041i	−1.02980	+	1.02980i	−0.0302537	+	0.999542i	$0.509632\pi$
$557$	−24.3041	+	24.3041i	−1.02980	+	1.02980i	−0.999542	+	0.0302537i	$0.990368\pi$
$558$		0			0
$559$			0.674573i			0.0285314i
$560$	−0.750060	+	1.75912i	−0.0316958	+	0.0743364i
$561$		0			0
$562$	29.9559	+	29.9559i	1.26361	+	1.26361i
$563$	28.5997	+	28.5997i	1.20533	+	1.20533i	0.972522	+	0.232809i	$0.0747918\pi$
$563$	28.5997	+	28.5997i	1.20533	+	1.20533i	0.232809	+	0.972522i	$0.425208\pi$
$564$		0			0
$565$	1.81575	−	4.25849i	0.0763891	−	0.179156i
$566$		−	43.8245i		−	1.84208i
$567$		0			0
$568$	−3.91838	+	3.91838i	−0.164412	+	0.164412i
$569$	−37.3166			−1.56439			−0.782196	−	0.623033i	$-0.785900\pi$
$569$	−37.3166			−1.56439			−0.782196	+	0.623033i	$0.785900\pi$
$570$		0			0
$571$	−24.2092			−1.01313			−0.506563	−	0.862203i	$-0.669084\pi$
$571$	−24.2092			−1.01313			−0.506563	+	0.862203i	$0.669084\pi$
$572$	0.418551	−	0.418551i	0.0175005	−	0.0175005i
$573$		0			0
$574$			1.12286i			0.0468672i
$575$	−4.99893	−	0.103422i	−0.208470	−	0.00431299i
$576$		0			0
$577$	−11.5086	−	11.5086i	−0.479108	−	0.479108i	0.425738	−	0.904846i	$-0.360015\pi$
$577$	−11.5086	−	11.5086i	−0.479108	−	0.479108i	−0.904846	+	0.425738i	$0.860015\pi$
$578$	19.1529	+	19.1529i	0.796655	+	0.796655i
$579$		0			0
$580$	23.3619	−	9.39495i	0.970052	−	0.390104i
$581$			0.238283i			0.00988565i
$582$		0			0
$583$	10.5909	−	10.5909i	0.438630	−	0.438630i
$584$	8.50485			0.351933
$585$		0			0
$586$	47.3217			1.95484
$587$	16.4387	−	16.4387i	0.678499	−	0.678499i	−0.281161	−	0.959661i	$-0.590720\pi$
$587$	16.4387	−	16.4387i	0.678499	−	0.678499i	0.959661	+	0.281161i	$0.0907196\pi$
$588$		0			0
$589$			6.31011i			0.260003i
$590$	22.0580	+	9.40519i	0.908115	+	0.387206i
$591$		0			0
$592$	−5.72640	−	5.72640i	−0.235354	−	0.235354i
$593$	−2.38142	−	2.38142i	−0.0977932	−	0.0977932i	0.656518	−	0.754311i	$-0.272029\pi$
$593$	−2.38142	−	2.38142i	−0.0977932	−	0.0977932i	−0.754311	+	0.656518i	$0.772029\pi$
$594$		0			0
$595$	0.445660	+	1.10820i	0.0182703	+	0.0454318i
$596$		−	13.6344i		−	0.558486i
$597$		0			0
$598$	0.127529	−	0.127529i	0.00521507	−	0.00521507i
$599$	14.3231			0.585225			0.292613	−	0.956231i	$-0.405475\pi$
$599$	14.3231			0.585225			0.292613	+	0.956231i	$0.405475\pi$
$600$		0			0
$601$	16.4160			0.669625			0.334812	−	0.942285i	$-0.391327\pi$
$601$	16.4160			0.669625			0.334812	+	0.942285i	$0.391327\pi$
$602$	−3.06655	+	3.06655i	−0.124983	+	0.124983i
$603$		0			0
$604$			8.13807i			0.331133i
$605$	2.05856	+	5.11893i	0.0836925	+	0.208114i
$606$		0			0
$607$	27.5220	+	27.5220i	1.11708	+	1.11708i	0.992167	+	0.124917i	$0.0398666\pi$
$607$	27.5220	+	27.5220i	1.11708	+	1.11708i	0.124917	+	0.992167i	$0.460133\pi$
$608$	7.65476	+	7.65476i	0.310442	+	0.310442i
$609$		0			0
$610$	−57.1239	−	24.3567i	−2.31288	−	0.986174i
$611$		−	0.903244i		−	0.0365413i
$612$		0			0
$613$	−13.2102	+	13.2102i	−0.533555	+	0.533555i	−0.921629	−	0.388073i	$-0.873141\pi$
$613$	−13.2102	+	13.2102i	−0.533555	+	0.533555i	0.388073	+	0.921629i	$0.373141\pi$
$614$	−55.2571			−2.23000
$615$		0			0
$616$	0.554227			0.0223304
$617$	1.54927	−	1.54927i	0.0623711	−	0.0623711i	−0.675233	−	0.737604i	$-0.735957\pi$
$617$	1.54927	−	1.54927i	0.0623711	−	0.0623711i	0.737604	+	0.675233i	$0.235957\pi$
$618$		0			0
$619$		−	10.7942i		−	0.433854i	−0.976188	−	0.216927i	$-0.930397\pi$
$619$		−	10.7942i		−	0.433854i	0.976188	−	0.216927i	$-0.0696034\pi$
$620$	22.9065	−	9.21178i	0.919946	−	0.369954i
$621$		0			0
$622$	−19.0115	−	19.0115i	−0.762293	−	0.762293i
$623$	−0.546889	−	0.546889i	−0.0219106	−	0.0219106i
$624$		0			0
$625$	1.03400	−	24.9786i	0.0413599	−	0.999144i
$626$		−	22.7177i		−	0.907983i
$627$		0			0
$628$	2.83946	−	2.83946i	0.113307	−	0.113307i
$629$	−5.05823			−0.201685
$630$		0			0
$631$	22.8709			0.910475			0.455237	−	0.890370i	$-0.349554\pi$
$631$	22.8709			0.910475			0.455237	+	0.890370i	$0.349554\pi$
$632$	−2.92024	+	2.92024i	−0.116161	+	0.116161i
$633$		0			0
$634$			46.2023i			1.83493i
$635$	9.18544	−	21.5427i	0.364513	−	0.854894i
$636$		0			0
$637$	−0.424099	−	0.424099i	−0.0168034	−	0.0168034i
$638$	20.7015	+	20.7015i	0.819580	+	0.819580i
$639$		0			0
$640$	4.91153	−	11.5190i	0.194145	−	0.455330i
$641$		−	16.7908i		−	0.663196i	−0.943421	−	0.331598i	$-0.892412\pi$
$641$		−	16.7908i		−	0.663196i	0.943421	−	0.331598i	$-0.107588\pi$
$642$		0			0
$643$	−6.12835	+	6.12835i	−0.241678	+	0.241678i	−0.817544	−	0.575866i	$-0.804665\pi$
$643$	−6.12835	+	6.12835i	−0.241678	+	0.241678i	0.575866	+	0.817544i	$0.304665\pi$
$644$	0.625271			0.0246391
$645$		0			0
$646$	5.57444			0.219324
$647$	−24.6271	+	24.6271i	−0.968192	+	0.968192i	−0.999510	−	0.0313171i	$-0.990030\pi$
$647$	−24.6271	+	24.6271i	−0.968192	+	0.968192i	0.0313171	+	0.999510i	$0.490030\pi$
$648$		0			0
$649$			15.0350i			0.590174i
$650$	0.624321	+	0.650700i	0.0244879	+	0.0255226i
$651$		0			0
$652$	−11.3902	−	11.3902i	−0.446074	−	0.446074i
$653$	−1.18319	−	1.18319i	−0.0463018	−	0.0463018i	0.683577	−	0.729879i	$-0.260423\pi$
$653$	−1.18319	−	1.18319i	−0.0463018	−	0.0463018i	−0.729879	+	0.683577i	$0.760423\pi$
$654$		0			0
$655$	2.95906	−	1.18998i	0.115620	−	0.0464963i
$656$			6.46042i			0.252237i
$657$		0			0
$658$	4.10607	−	4.10607i	0.160071	−	0.160071i
$659$	14.1965			0.553018			0.276509	−	0.961011i	$-0.410823\pi$
$659$	14.1965			0.553018			0.276509	+	0.961011i	$0.410823\pi$
$660$		0			0
$661$	21.2009			0.824618			0.412309	−	0.911044i	$-0.364722\pi$
$661$	21.2009			0.824618			0.412309	+	0.911044i	$0.364722\pi$
$662$	−22.6127	+	22.6127i	−0.878869	+	0.878869i
$663$		0			0
$664$		−	0.633703i		−	0.0245924i
$665$	−0.735009	−	0.313396i	−0.0285024	−	0.0121530i
$666$		0			0
$667$	3.40150	+	3.40150i	0.131706	+	0.131706i
$668$	−26.6697	−	26.6697i	−1.03188	−	1.03188i
$669$		0			0
$670$	−12.1872	−	30.3054i	−0.470834	−	1.17080i
$671$		−	38.9362i		−	1.50312i
$672$		0			0
$673$	−0.820003	+	0.820003i	−0.0316088	+	0.0316088i	−0.722735	−	0.691126i	$-0.757115\pi$
$673$	−0.820003	+	0.820003i	−0.0316088	+	0.0316088i	0.691126	+	0.722735i	$0.257115\pi$
$674$	18.5600			0.714904
$675$		0			0
$676$	30.4147			1.16980
$677$	−11.0786	+	11.0786i	−0.425784	+	0.425784i	−0.887189	−	0.461405i	$-0.847345\pi$
$677$	−11.0786	+	11.0786i	−0.425784	+	0.425784i	0.461405	+	0.887189i	$0.347345\pi$
$678$		0			0
$679$		−	0.638542i		−	0.0245050i
$680$	−1.18521	−	2.94721i	−0.0454508	−	0.113020i
$681$		0			0
$682$	20.2979	+	20.2979i	0.777246	+	0.777246i
$683$	35.8041	+	35.8041i	1.37000	+	1.37000i	0.860422	+	0.509582i	$0.170200\pi$
$683$	35.8041	+	35.8041i	1.37000	+	1.37000i	0.509582	+	0.860422i	$0.329800\pi$
$684$		0			0
$685$	21.5524	+	9.18958i	0.823474	+	0.351116i
$686$		−	7.75138i		−	0.295949i
$687$		0			0
$688$	−17.6435	+	17.6435i	−0.672654	+	0.672654i
$689$	−0.443855			−0.0169095
$690$		0			0
$691$	−3.38893			−0.128921			−0.0644605	−	0.997920i	$-0.520533\pi$
$691$	−3.38893			−0.128921			−0.0644605	+	0.997920i	$0.520533\pi$
$692$	−15.5831	+	15.5831i	−0.592380	+	0.592380i
$693$		0			0
$694$		−	31.5178i		−	1.19640i
$695$	20.1293	−	8.09494i	0.763548	−	0.307059i
$696$		0			0
$697$	2.85330	+	2.85330i	0.108076	+	0.108076i
$698$	24.0198	+	24.0198i	0.909164	+	0.909164i
$699$		0			0
$700$	−0.0646667	+	3.12569i	−0.00244417	+	0.118140i
$701$			29.7827i			1.12488i	0.826839	+	0.562438i	$0.190137\pi$
$701$			29.7827i			1.12488i	−0.826839	+	0.562438i	$0.809863\pi$
$702$		0			0
$703$	2.39265	−	2.39265i	0.0902405	−	0.0902405i
$704$	30.5408			1.15105
$705$		0			0
$706$	54.4271			2.04839
$707$	−2.25795	+	2.25795i	−0.0849189	+	0.0849189i
$708$		0			0
$709$		−	20.2200i		−	0.759376i	−0.925115	−	0.379688i	$-0.876031\pi$
$709$		−	20.2200i		−	0.759376i	0.925115	−	0.379688i	$-0.123969\pi$
$710$	14.2547	−	33.4315i	0.534968	−	1.25466i
$711$		0			0
$712$	1.45443	+	1.45443i	0.0545069	+	0.0545069i
$713$	3.33518	+	3.33518i	0.124903	+	0.124903i
$714$		0			0
$715$	−0.221762	+	0.520099i	−0.00829341	+	0.0194506i
$716$			4.48425i			0.167584i
$717$		0			0
$718$	−13.2098	+	13.2098i	−0.492984	+	0.492984i
$719$	−27.9665			−1.04298			−0.521488	−	0.853259i	$-0.674623\pi$
$719$	−27.9665			−1.04298			−0.521488	+	0.853259i	$0.674623\pi$
$720$		0			0
$721$	0.531255			0.0197850
$722$	25.3550	−	25.3550i	0.943614	−	0.943614i
$723$		0			0
$724$			34.6705i			1.28852i
$725$	−17.3556	+	16.6521i	−0.644572	+	0.618442i
$726$		0			0
$727$	20.4001	+	20.4001i	0.756596	+	0.756596i	0.975701	−	0.219105i	$-0.0703137\pi$
$727$	20.4001	+	20.4001i	0.756596	+	0.756596i	−0.219105	+	0.975701i	$0.570314\pi$
$728$	−0.0116136	−	0.0116136i	−0.000430428	−	0.000430428i
$729$		0			0
$730$	−51.7514	+	20.8117i	−1.91540	+	0.770275i
$731$			15.5849i			0.576427i
$732$		0			0
$733$	20.7367	−	20.7367i	0.765929	−	0.765929i	−0.211458	−	0.977387i	$-0.567821\pi$
$733$	20.7367	−	20.7367i	0.765929	−	0.765929i	0.977387	+	0.211458i	$0.0678212\pi$
$734$	−33.3541			−1.23112
$735$		0			0
$736$	8.09178			0.298267
$737$	14.4817	−	14.4817i	0.533439	−	0.533439i
$738$		0			0
$739$			49.7152i			1.82880i	0.404808	+	0.914402i	$0.367339\pi$
$739$			49.7152i			1.82880i	−0.404808	+	0.914402i	$0.632661\pi$
$740$	−12.1785	−	5.19272i	−0.447691	−	0.190888i
$741$		0			0
$742$	−2.01773	−	2.01773i	−0.0740731	−	0.0740731i
$743$	21.4078	+	21.4078i	0.785375	+	0.785375i	0.980732	−	0.195357i	$-0.0625865\pi$
$743$	21.4078	+	21.4078i	0.785375	+	0.785375i	−0.195357	+	0.980732i	$0.562586\pi$
$744$		0			0
$745$	4.85919	+	12.0831i	0.178027	+	0.442691i
$746$		−	37.2370i		−	1.36334i
$747$		0			0
$748$	9.66991	−	9.66991i	0.353567	−	0.353567i
$749$	−1.73769			−0.0634938
$750$		0			0
$751$	−1.60826			−0.0586863			−0.0293431	−	0.999569i	$-0.509342\pi$
$751$	−1.60826			−0.0586863			−0.0293431	+	0.999569i	$0.509342\pi$
$752$	23.6244	−	23.6244i	0.861495	−	0.861495i
$753$		0			0
$754$		−	0.867582i		−	0.0315955i
$755$	−2.90035	−	7.21215i	−0.105554	−	0.262477i
$756$		0			0
$757$	31.7932	+	31.7932i	1.15554	+	1.15554i	0.985423	+	0.170121i	$0.0544158\pi$
$757$	31.7932	+	31.7932i	1.15554	+	1.15554i	0.170121	+	0.985423i	$0.445584\pi$
$758$	8.96493	+	8.96493i	0.325621	+	0.325621i
$759$		0			0
$760$	1.95472	+	0.833462i	0.0709052	+	0.0302328i
$761$		−	5.69377i		−	0.206399i	−0.994661	−	0.103200i	$-0.967092\pi$
$761$		−	5.69377i		−	0.206399i	0.994661	−	0.103200i	$-0.0329080\pi$
$762$		0			0
$763$	0.0412876	−	0.0412876i	0.00149471	−	0.00149471i
$764$	57.1360			2.06711
$765$		0			0
$766$	−1.12022			−0.0404752
$767$	0.315051	−	0.315051i	0.0113758	−	0.0113758i
$768$		0			0
$769$			8.46275i			0.305174i	0.988290	+	0.152587i	$0.0487605\pi$
$769$			8.46275i			0.305174i	−0.988290	+	0.152587i	$0.951240\pi$
$770$	−3.37243	+	1.35622i	−0.121534	+	0.0488746i
$771$		0			0
$772$	39.8496	+	39.8496i	1.43422	+	1.43422i
$773$	−14.7038	−	14.7038i	−0.528858	−	0.528858i	0.391374	−	0.920232i	$-0.372000\pi$
$773$	−14.7038	−	14.7038i	−0.528858	−	0.528858i	−0.920232	+	0.391374i	$0.872000\pi$
$774$		0			0
$775$	−17.0173	+	16.3274i	−0.611278	+	0.586497i
$776$			1.69817i			0.0609608i
$777$		0			0
$778$	−52.2952	+	52.2952i	−1.87487	+	1.87487i
$779$	−2.69934			−0.0967140
$780$		0			0
$781$	22.7872			0.815391
$782$	2.94635	−	2.94635i	0.105361	−	0.105361i
$783$		0			0
$784$		−	22.1847i		−	0.792311i
$785$	−1.50443	+	3.52836i	−0.0536956	+	0.125932i
$786$		0			0
$787$	15.5182	+	15.5182i	0.553165	+	0.553165i	0.927353	−	0.374188i	$-0.122078\pi$
$787$	15.5182	+	15.5182i	0.553165	+	0.553165i	−0.374188	+	0.927353i	$0.622078\pi$
$788$	−7.64167	−	7.64167i	−0.272223	−	0.272223i
$789$		0			0
$790$	10.6235	−	24.9154i	0.377968	−	0.886450i
$791$		−	0.552994i		−	0.0196622i
$792$		0			0
$793$	−0.815891	+	0.815891i	−0.0289731	+	0.0289731i
$794$	−52.8085			−1.87410
$795$		0			0
$796$	−1.46919			−0.0520740
$797$	−23.2479	+	23.2479i	−0.823482	+	0.823482i	−0.986606	−	0.163123i	$-0.947843\pi$
$797$	−23.2479	+	23.2479i	−0.823482	+	0.823482i	0.163123	+	0.986606i	$0.447843\pi$
$798$		0			0
$799$		−	20.8679i		−	0.738253i
$800$	−0.836867	+	40.4503i	−0.0295877	+	1.43013i
$801$		0			0
$802$	−48.5527	−	48.5527i	−1.71446	−	1.71446i
$803$	−24.7298	−	24.7298i	−0.872697	−	0.872697i
$804$		0			0
$805$	−0.554130	+	0.222842i	−0.0195305	+	0.00785414i
$806$		−	0.850667i		−	0.0299635i
$807$		0			0
$808$	6.00491	−	6.00491i	0.211252	−	0.211252i
$809$	39.3349			1.38294			0.691471	−	0.722404i	$-0.256963\pi$
$809$	39.3349			1.38294			0.691471	+	0.722404i	$0.256963\pi$
$810$		0			0
$811$	37.4972			1.31671			0.658353	−	0.752709i	$-0.271253\pi$
$811$	37.4972			1.31671			0.658353	+	0.752709i	$0.271253\pi$
$812$	2.12686	−	2.12686i	0.0746380	−	0.0746380i
$813$		0			0
$814$		−	15.3930i		−	0.539525i
$815$	14.1536	+	6.03487i	0.495780	+	0.211392i
$816$		0			0
$817$	−7.37197	−	7.37197i	−0.257912	−	0.257912i
$818$	33.6858	+	33.6858i	1.17780	+	1.17780i
$819$		0			0
$820$	3.94062	+	9.79895i	0.137612	+	0.342194i
$821$			31.7616i			1.10849i	0.832355	+	0.554243i	$0.186992\pi$
$821$			31.7616i			1.10849i	−0.832355	+	0.554243i	$0.813008\pi$
$822$		0			0
$823$	−4.75128	+	4.75128i	−0.165619	+	0.165619i	−0.785051	−	0.619432i	$-0.787363\pi$
$823$	−4.75128	+	4.75128i	−0.165619	+	0.165619i	0.619432	+	0.785051i	$0.287363\pi$
$824$	−1.41285			−0.0492189
$825$		0			0
$826$	2.86439			0.0996649
$827$	14.8925	−	14.8925i	0.517862	−	0.517862i	−0.399062	−	0.916924i	$-0.630664\pi$
$827$	14.8925	−	14.8925i	0.517862	−	0.517862i	0.916924	+	0.399062i	$0.130664\pi$
$828$		0			0
$829$			30.9745i			1.07579i	0.843012	+	0.537895i	$0.180780\pi$
$829$			30.9745i			1.07579i	−0.843012	+	0.537895i	$0.819220\pi$
$830$	1.55069	+	3.85604i	0.0538254	+	0.133845i
$831$		0			0
$832$	−0.639970	−	0.639970i	−0.0221870	−	0.0221870i
$833$	−9.79808	−	9.79808i	−0.339483	−	0.339483i
$834$		0			0
$835$	33.1402	+	14.1304i	1.14686	+	0.489004i
$836$			9.14814i			0.316395i
$837$		0			0
$838$	−26.2885	+	26.2885i	−0.908122	+	0.908122i
$839$	35.9161			1.23996			0.619981	−	0.784617i	$-0.287140\pi$
$839$	35.9161			1.23996			0.619981	+	0.784617i	$0.287140\pi$
$840$		0			0
$841$	−5.85965			−0.202057
$842$	−6.20652	+	6.20652i	−0.213891	+	0.213891i
$843$		0			0
$844$			61.0543i			2.10158i
$845$	−26.9542	+	10.8396i	−0.927253	+	0.372892i
$846$		0			0
$847$	0.466024	+	0.466024i	0.0160128	+	0.0160128i
$848$	−11.6091	−	11.6091i	−0.398657	−	0.398657i
$849$		0			0
$850$	14.4239	+	15.0333i	0.494735	+	0.515638i
$851$		−	2.52925i		−	0.0867016i
$852$		0			0
$853$	−17.7067	+	17.7067i	−0.606266	+	0.606266i	−0.941968	−	0.335702i	$-0.891026\pi$
$853$	−17.7067	+	17.7067i	−0.606266	+	0.606266i	0.335702	+	0.941968i	$0.391026\pi$
$854$	−7.41794			−0.253837
$855$		0			0
$856$	4.62131			0.157953
$857$	25.9630	−	25.9630i	0.886878	−	0.886878i	−0.107344	−	0.994222i	$-0.534235\pi$
$857$	25.9630	−	25.9630i	0.886878	−	0.886878i	0.994222	+	0.107344i	$0.0342346\pi$
$858$		0			0
$859$			42.8789i			1.46301i	0.681837	+	0.731504i	$0.261181\pi$
$859$			42.8789i			1.46301i	−0.681837	+	0.731504i	$0.738819\pi$
$860$	−15.9992	+	37.5231i	−0.545569	+	1.27953i
$861$		0			0
$862$	51.7567	+	51.7567i	1.76284	+	1.76284i
$863$	11.5306	+	11.5306i	0.392506	+	0.392506i	0.875580	−	0.483074i	$-0.160480\pi$
$863$	11.5306	+	11.5306i	0.392506	+	0.392506i	−0.483074	+	0.875580i	$0.660480\pi$
$864$		0			0
$865$	8.25640	−	19.3638i	0.280726	−	0.658389i
$866$		−	58.2910i		−	1.98081i
$867$		0			0
$868$	2.08539	−	2.08539i	0.0707827	−	0.0707827i
$869$	16.9826			0.576094
$870$		0			0
$871$	−0.606915			−0.0205645
$872$	−0.109802	+	0.109802i	−0.00371838	+	0.00371838i
$873$		0			0
$874$			2.78737i			0.0942842i
$875$	−1.05666	−	2.79310i	−0.0357217	−	0.0944241i
$876$		0			0
$877$	−9.18798	−	9.18798i	−0.310256	−	0.310256i	0.534753	−	0.845009i	$-0.320405\pi$
$877$	−9.18798	−	9.18798i	−0.310256	−	0.310256i	−0.845009	+	0.534753i	$0.820405\pi$
$878$	−31.8577	−	31.8577i	−1.07515	−	1.07515i
$879$		0			0
$880$	−19.4034	+	7.80304i	−0.654090	+	0.263040i
$881$			32.6025i			1.09841i	0.835689	+	0.549203i	$0.185069\pi$
$881$			32.6025i			1.09841i	−0.835689	+	0.549203i	$0.814931\pi$
$882$		0			0
$883$	−7.22715	+	7.22715i	−0.243213	+	0.243213i	−0.818178	−	0.574965i	$-0.805016\pi$
$883$	−7.22715	+	7.22715i	−0.243213	+	0.243213i	0.574965	+	0.818178i	$0.305016\pi$
$884$	−0.405257			−0.0136303
$885$		0			0
$886$	−4.82361			−0.162052
$887$	21.3979	−	21.3979i	0.718472	−	0.718472i	−0.249820	−	0.968292i	$-0.580372\pi$
$887$	21.3979	−	21.3979i	0.718472	−	0.718472i	0.968292	+	0.249820i	$0.0803715\pi$
$888$		0			0
$889$		−	2.79746i		−	0.0938240i
$890$	−12.4091	−	5.29104i	−0.415954	−	0.177356i
$891$		0			0
$892$	−35.3240	−	35.3240i	−1.18273	−	1.18273i
$893$	9.87096	+	9.87096i	0.330319	+	0.330319i
$894$		0			0
$895$	−1.59815	−	3.97405i	−0.0534204	−	0.132838i
$896$		−	1.49583i		−	0.0499721i
$897$		0			0
$898$	−25.2729	+	25.2729i	−0.843368	+	0.843368i
$899$	22.6892			0.756727
$900$		0			0
$901$	−10.2545			−0.341627
$902$	−8.68305	+	8.68305i	−0.289114	+	0.289114i
$903$		0			0
$904$			1.47066i			0.0489135i
$905$	−12.3563	−	30.7258i	−0.410738	−	1.02136i
$906$		0			0
$907$	−17.8353	−	17.8353i	−0.592212	−	0.592212i	0.346016	−	0.938228i	$-0.387534\pi$
$907$	−17.8353	−	17.8353i	−0.592212	−	0.592212i	−0.938228	+	0.346016i	$0.887534\pi$
$908$	−22.4983	−	22.4983i	−0.746634	−	0.746634i
$909$		0			0
$910$	0.0990868	+	0.0422490i	0.00328469	+	0.00140054i
$911$			20.9309i			0.693471i	0.937963	+	0.346735i	$0.112710\pi$
$911$			20.9309i			0.693471i	−0.937963	+	0.346735i	$0.887290\pi$
$912$		0			0
$913$	−1.84264	+	1.84264i	−0.0609824	+	0.0609824i
$914$	−70.1198			−2.31936
$915$		0			0
$916$	50.9425			1.68319
$917$	0.269391	−	0.269391i	0.00889608	−	0.00889608i
$918$		0			0
$919$			55.1108i			1.81794i	0.416863	+	0.908969i	$0.363130\pi$
$919$			55.1108i			1.81794i	−0.416863	+	0.908969i	$0.636870\pi$
$920$	1.47368	−	0.592637i	0.0485859	−	0.0195387i
$921$		0			0
$922$	0.251163	+	0.251163i	0.00827163	+	0.00827163i
$923$	−0.477497	−	0.477497i	−0.0157170	−	0.0157170i
$924$		0			0
$925$	12.6435	+	0.261580i	0.415717	+	0.00860069i
$926$		−	30.0531i		−	0.987605i
$927$		0			0
$928$	27.5242	−	27.5242i	0.903525	−	0.903525i
$929$	−59.2833			−1.94502			−0.972511	−	0.232857i	$-0.925193\pi$
$929$	−59.2833			−1.94502			−0.972511	+	0.232857i	$0.925193\pi$
$930$		0			0
$931$	9.26940			0.303792
$932$	−41.1757	+	41.1757i	−1.34875	+	1.34875i
$933$		0			0
$934$			34.0206i			1.11319i
$935$	−5.12342	+	12.0160i	−0.167554	+	0.392965i
$936$		0			0
$937$	20.1704	+	20.1704i	0.658937	+	0.658937i	0.955129	−	0.296191i	$-0.0957166\pi$
$937$	20.1704	+	20.1704i	0.658937	+	0.658937i	−0.296191	+	0.955129i	$0.595717\pi$
$938$	−2.75898	−	2.75898i	−0.0900839	−	0.0900839i
$939$		0			0
$940$	21.4227	−	50.2429i	0.698733	−	1.63874i
$941$		−	38.5667i		−	1.25724i	−0.777713	−	0.628619i	$-0.783620\pi$
$941$		−	38.5667i		−	1.25724i	0.777713	−	0.628619i	$-0.216380\pi$
$942$		0			0
$943$	−1.42673	+	1.42673i	−0.0464606	+	0.0464606i
$944$	16.4804			0.536391
$945$		0			0
$946$	−47.4272			−1.54199
$947$	−36.6686	+	36.6686i	−1.19157	+	1.19157i	−0.214941	+	0.976627i	$0.568956\pi$
$947$	−36.6686	+	36.6686i	−1.19157	+	1.19157i	−0.976627	+	0.214941i	$0.931044\pi$
$948$		0			0
$949$			1.03641i			0.0336432i
$950$	−13.9339	−	0.288275i	−0.452074	−	0.00935287i
$951$		0			0
$952$	−0.268312	−	0.268312i	−0.00869604	−	0.00869604i
$953$	11.8116	+	11.8116i	0.382617	+	0.382617i	0.872044	−	0.489427i	$-0.162794\pi$
$953$	11.8116	+	11.8116i	0.382617	+	0.382617i	−0.489427	+	0.872044i	$0.662794\pi$
$954$		0			0
$955$	−50.6353	+	20.3629i	−1.63852	+	0.658927i
$956$		−	52.8614i		−	1.70966i
$957$		0			0
$958$	28.8019	−	28.8019i	0.930548	−	0.930548i
$959$	2.79873			0.0903756
$960$		0			0
$961$	−8.75317			−0.282360
$962$	−0.322554	+	0.322554i	−0.0103996	+	0.0103996i
$963$		0			0
$964$		−	42.4504i		−	1.36723i
$965$	−49.5177	−	21.1136i	−1.59403	−	0.679669i
$966$		0			0
$967$	−41.9936	−	41.9936i	−1.35042	−	1.35042i	−0.885188	−	0.465234i	$-0.845970\pi$
$967$	−41.9936	−	41.9936i	−1.35042	−	1.35042i	−0.465234	−	0.885188i	$-0.654030\pi$
$968$	−1.23937	−	1.23937i	−0.0398348	−	0.0398348i
$969$		0			0
$970$	−4.15549	−	10.3333i	−0.133425	−	0.331781i
$971$			44.7907i			1.43740i	0.695320	+	0.718700i	$0.255263\pi$
$971$			44.7907i			1.43740i	−0.695320	+	0.718700i	$0.744737\pi$
$972$		0			0
$973$	1.83256	−	1.83256i	0.0587491	−	0.0587491i
$974$	−4.22780			−0.135467
$975$		0			0
$976$	−42.6794			−1.36614
$977$	−18.4976	+	18.4976i	−0.591790	+	0.591790i	−0.938115	−	0.346324i	$-0.887430\pi$
$977$	−18.4976	+	18.4976i	−0.591790	+	0.591790i	0.346324	+	0.938115i	$0.387430\pi$
$978$		0			0
$979$		−	8.45816i		−	0.270324i
$980$	−13.5319	−	33.6491i	−0.432260	−	1.07488i
$981$		0			0
$982$	48.4563	+	48.4563i	1.54630	+	1.54630i
$983$	−1.21333	−	1.21333i	−0.0386993	−	0.0386993i	0.687492	−	0.726192i	$-0.258711\pi$
$983$	−1.21333	−	1.21333i	−0.0386993	−	0.0386993i	−0.726192	+	0.687492i	$0.758711\pi$
$984$		0			0
$985$	9.49567	+	4.04880i	0.302557	+	0.129005i
$986$		−	20.0440i		−	0.638330i
$987$		0			0
$988$	0.191695	−	0.191695i	0.00609864	−	0.00609864i
$989$	−7.79284			−0.247798
$990$		0			0
$991$	−60.8775			−1.93384			−0.966918	−	0.255086i	$-0.917896\pi$
$991$	−60.8775			−1.93384			−0.966918	+	0.255086i	$0.917896\pi$
$992$	26.9875	−	26.9875i	0.856855	−	0.856855i
$993$		0			0
$994$		−	4.34132i		−	0.137698i
$995$	1.30203	−	0.523608i	0.0412771	−	0.0165995i
$996$		0			0
$997$	−42.2177	−	42.2177i	−1.33705	−	1.33705i	−0.898906	−	0.438142i	$-0.855637\pi$
$997$	−42.2177	−	42.2177i	−1.33705	−	1.33705i	−0.438142	−	0.898906i	$-0.644363\pi$
$998$	−42.9270	−	42.9270i	−1.35883	−	1.35883i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.737.18	yes	44
3.2	odd	2	inner	1035.2.j.b.737.5	yes	44
5.3	odd	4	inner	1035.2.j.b.323.5	✓	44
15.8	even	4	inner	1035.2.j.b.323.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.5	✓	44	5.3	odd	4	inner
1035.2.j.b.323.18	yes	44	15.8	even	4	inner
1035.2.j.b.737.5	yes	44	3.2	odd	2	inner
1035.2.j.b.737.18	yes	44	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:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47325 - 1.47325i) q^{2} -2.34094i q^{4} +(0.834294 + 2.07460i) q^{5} +(0.188870 + 0.188870i) q^{7} +(-0.502291 - 0.502291i) q^{8} +O(q^{10})\)	\(q+(1.47325 - 1.47325i) q^{2} -2.34094i q^{4} +(0.834294 + 2.07460i) q^{5} +(0.188870 + 0.188870i) q^{7} +(-0.502291 - 0.502291i) q^{8} +(4.28553 + 1.82728i) q^{10} +2.92106i q^{11} +(0.0612095 - 0.0612095i) q^{13} +0.556506 q^{14} +3.20188 q^{16} +(1.41414 - 1.41414i) q^{17} +1.33783i q^{19} +(4.85651 - 1.95303i) q^{20} +(4.30345 + 4.30345i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-3.60791 + 3.46165i) q^{25} -0.180354i q^{26} +(0.442133 - 0.442133i) q^{28} +4.81044 q^{29} +4.71665 q^{31} +(5.72176 - 5.72176i) q^{32} -4.16676i q^{34} +(-0.234256 + 0.549402i) q^{35} +(-1.78845 - 1.78845i) q^{37} +(1.97097 + 1.97097i) q^{38} +(0.622993 - 1.46111i) q^{40} +2.01769i q^{41} +(-5.51037 + 5.51037i) q^{43} +6.83802 q^{44} +2.08349 q^{46} +(7.37831 - 7.37831i) q^{47} -6.92866i q^{49} +(-0.215479 + 10.4152i) q^{50} +(-0.143288 - 0.143288i) q^{52} +(-3.62571 - 3.62571i) q^{53} +(-6.06001 + 2.43702i) q^{55} -0.189735i q^{56} +(7.08699 - 7.08699i) q^{58} +5.14710 q^{59} -13.3295 q^{61} +(6.94882 - 6.94882i) q^{62} -10.4554i q^{64} +(0.178052 + 0.0759183i) q^{65} +(-4.95769 - 4.95769i) q^{67} +(-3.31041 - 3.31041i) q^{68} +(0.464289 + 1.15453i) q^{70} -7.80103i q^{71} +(-8.46606 + 8.46606i) q^{73} -5.26967 q^{74} +3.13179 q^{76} +(-0.551700 + 0.551700i) q^{77} -5.81384i q^{79} +(2.67131 + 6.64261i) q^{80} +(2.97257 + 2.97257i) q^{82} +(0.630813 + 0.630813i) q^{83} +(4.11358 + 1.75396i) q^{85} +16.2363i q^{86} +(1.46722 - 1.46722i) q^{88} -2.89558 q^{89} +0.0231213 q^{91} +(1.65529 - 1.65529i) q^{92} -21.7402i q^{94} +(-2.77547 + 1.11615i) q^{95} +(-1.69043 - 1.69043i) q^{97} +(-10.2077 - 10.2077i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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