LMFDB - Embedded newform 735.2.v.a.178.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(178,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("735.178");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.v (of order $12$, degree $4$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			178.4
Character	$\chi$	$=$	735.178
Dual form			735.2.v.a.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.25700 - 1.15650i) q^{10} +(1.92568 - 3.33538i) q^{11} +(0.366615 - 1.36822i) q^{12} +(-3.66816 + 3.66816i) q^{13} +(-2.13393 - 0.668102i) q^{15} +(0.419714 + 0.726965i) q^{16} +(-2.03548 + 0.545404i) q^{17} +(0.737849 - 0.197706i) q^{18} +(-0.0348837 - 0.0604203i) q^{19} +(2.80654 - 1.46818i) q^{20} +(-2.08029 + 2.08029i) q^{22} +(-0.195522 + 0.729698i) q^{23} +(-1.30489 + 2.26014i) q^{24} +(-2.13133 - 4.52299i) q^{25} +(3.43177 - 1.98133i) q^{26} +(-0.707107 - 0.707107i) q^{27} -2.77107i q^{29} +(1.44243 + 0.914849i) q^{30} +(-2.07564 - 1.19837i) q^{31} +(-1.51688 - 5.66108i) q^{32} +(3.72013 + 0.996806i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(-8.45237 - 2.26481i) q^{37} +(0.0137934 + 0.0514778i) q^{38} +(-4.49256 - 2.59378i) q^{39} +(-5.69477 + 1.27454i) q^{40} -8.68077i q^{41} +(-2.77107 - 2.77107i) q^{43} +(-4.72453 + 2.72771i) q^{44} +(0.0930365 - 2.23413i) q^{45} +(0.288532 - 0.499752i) q^{46} +(2.00963 - 7.50006i) q^{47} +(-0.593565 + 0.593565i) q^{48} +(0.678376 + 3.75866i) q^{50} +(-1.05364 - 1.82496i) q^{51} +(7.09776 - 1.90184i) q^{52} +(-8.38498 + 2.24675i) q^{53} +(0.381939 + 0.661538i) q^{54} +(3.99191 + 7.63083i) q^{55} +(0.0493330 - 0.0493330i) q^{57} +(-0.547858 + 2.04464i) q^{58} +(3.48720 - 6.04001i) q^{59} +(2.14454 + 2.33092i) q^{60} +(-12.3935 + 7.15536i) q^{61} +(1.29458 + 1.29458i) q^{62} +2.79807i q^{64} +(-2.53345 - 11.3197i) q^{65} +(-2.54782 - 1.47098i) q^{66} +(0.152446 + 0.568937i) q^{67} +(2.88323 + 0.772560i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(-2.52086 - 0.675461i) q^{72} +(3.49631 + 13.0484i) q^{73} +(5.78881 + 3.34217i) q^{74} +(3.81725 - 3.22934i) q^{75} +0.0988248i q^{76} +(2.80203 + 2.80203i) q^{78} +(8.54186 - 4.93165i) q^{79} +(-1.87539 - 0.0780974i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.71624 + 6.40510i) q^{82} +(1.63570 - 1.63570i) q^{83} +(1.40788 - 4.49678i) q^{85} +(1.49678 + 2.59249i) q^{86} +(2.67665 - 0.717207i) q^{87} +(9.70872 - 2.60144i) q^{88} +(2.52657 + 4.37614i) q^{89} +(-0.510348 + 1.63006i) q^{90} +(0.756656 - 0.756656i) q^{92} +(0.620321 - 2.31507i) q^{93} +(-2.96561 + 5.13659i) q^{94} +(0.155869 + 0.00649091i) q^{95} +(5.07559 - 2.93039i) q^{96} +(6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 48 q^{8}+O(q^{10}) $ 32 * q + 48 * q^8	$ 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.737849	−	0.197706i	−0.521738	−	0.139799i	−0.0116677	−	0.999932i	$-0.503714\pi$
$2$	−0.737849	−	0.197706i	−0.521738	−	0.139799i	−0.510071	+	0.860133i	$0.670381\pi$
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	−1.22672	−	0.708245i	−0.613358	−	0.354123i
$5$	−1.19764	+	1.88830i	−0.535600	+	0.844472i
$5$	−1.19764	+	1.88830i	−0.535600	+	0.844472i
$6$		−	0.763878i		−	0.311852i
$7$		0			0
$7$		0			0
$8$	1.84539	+	1.84539i	0.652445	+	0.652445i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.25700	−	1.15650i	0.397500	−	0.365717i
$11$	1.92568	−	3.33538i	0.580615	−	1.00565i	−0.414792	−	0.909916i	$-0.636146\pi$
$11$	1.92568	−	3.33538i	0.580615	−	1.00565i	0.995407	−	0.0957376i	$-0.0305210\pi$
$12$	0.366615	−	1.36822i	0.105833	−	0.394973i
$13$	−3.66816	+	3.66816i	−1.01737	+	1.01737i	−0.0175187	+	0.999847i	$0.505577\pi$
$13$	−3.66816	+	3.66816i	−1.01737	+	1.01737i	−0.999847	+	0.0175187i	$0.994423\pi$
$14$		0			0
$15$	−2.13393	−	0.668102i	−0.550977	−	0.172503i
$16$	0.419714	+	0.726965i	0.104928	+	0.181741i
$17$	−2.03548	+	0.545404i	−0.493675	+	0.132280i	−0.497063	−	0.867714i	$-0.665588\pi$
$17$	−2.03548	+	0.545404i	−0.493675	+	0.132280i	0.00338789	+	0.999994i	$0.498922\pi$
$18$	0.737849	−	0.197706i	0.173913	−	0.0465998i
$19$	−0.0348837	−	0.0604203i	−0.00800286	−	0.0138614i	0.861996	−	0.506915i	$-0.169214\pi$
$19$	−0.0348837	−	0.0604203i	−0.00800286	−	0.0138614i	−0.869999	+	0.493053i	$0.835881\pi$
$20$	2.80654	−	1.46818i	0.627561	−	0.328296i
$21$		0			0
$22$	−2.08029	+	2.08029i	−0.443519	+	0.443519i
$23$	−0.195522	+	0.729698i	−0.0407692	+	0.152153i	−0.983310	−	0.181939i	$-0.941763\pi$
$23$	−0.195522	+	0.729698i	−0.0407692	+	0.152153i	0.942541	+	0.334091i	$0.108429\pi$
$24$	−1.30489	+	2.26014i	−0.266360	+	0.461349i
$25$	−2.13133	−	4.52299i	−0.426265	−	0.904598i
$26$	3.43177	−	1.98133i	0.673025	−	0.388571i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	2.77107i		−	0.514576i	−0.966335	−	0.257288i	$-0.917171\pi$
$29$		−	2.77107i		−	0.514576i	0.966335	−	0.257288i	$-0.0828288\pi$
$30$	1.44243	+	0.914849i	0.263350	+	0.167028i
$31$	−2.07564	−	1.19837i	−0.372795	−	0.215233i	0.301884	−	0.953345i	$-0.402385\pi$
$31$	−2.07564	−	1.19837i	−0.372795	−	0.215233i	−0.674679	+	0.738111i	$0.735718\pi$
$32$	−1.51688	−	5.66108i	−0.268149	−	1.00075i
$33$	3.72013	+	0.996806i	0.647591	+	0.173522i
$34$	1.60970			0.276062
$35$		0			0
$36$	1.41649			0.236082
$37$	−8.45237	−	2.26481i	−1.38956	−	0.372332i	−0.514976	−	0.857204i	$-0.672199\pi$
$37$	−8.45237	−	2.26481i	−1.38956	−	0.372332i	−0.874585	+	0.484872i	$0.838866\pi$
$38$	0.0137934	+	0.0514778i	0.00223759	+	0.00835080i
$39$	−4.49256	−	2.59378i	−0.719386	−	0.415338i
$40$	−5.69477	+	1.27454i	−0.900421	+	0.201522i
$41$		−	8.68077i		−	1.35571i	−0.735196	−	0.677854i	$-0.762910\pi$
$41$		−	8.68077i		−	1.35571i	0.735196	−	0.677854i	$-0.237090\pi$
$42$		0			0
$43$	−2.77107	−	2.77107i	−0.422585	−	0.422585i	0.463508	−	0.886093i	$-0.346591\pi$
$43$	−2.77107	−	2.77107i	−0.422585	−	0.422585i	−0.886093	+	0.463508i	$0.846591\pi$
$44$	−4.72453	+	2.72771i	−0.712250	+	0.411218i
$45$	0.0930365	−	2.23413i	0.0138691	−	0.333045i
$46$	0.288532	−	0.499752i	0.0425417	−	0.0736843i
$47$	2.00963	−	7.50006i	0.293135	−	1.09400i	−0.649552	−	0.760317i	$-0.725043\pi$
$47$	2.00963	−	7.50006i	0.293135	−	1.09400i	0.942687	−	0.333678i	$-0.108290\pi$
$48$	−0.593565	+	0.593565i	−0.0856737	+	0.0856737i
$49$		0			0
$50$	0.678376	+	3.75866i	0.0959368	+	0.531555i
$51$	−1.05364	−	1.82496i	−0.147539	−	0.255545i
$52$	7.09776	−	1.90184i	0.984282	−	0.263737i
$53$	−8.38498	+	2.24675i	−1.15177	+	0.308615i	−0.783673	−	0.621174i	$-0.786656\pi$
$53$	−8.38498	+	2.24675i	−1.15177	+	0.308615i	−0.368093	+	0.929789i	$0.619989\pi$
$54$	0.381939	+	0.661538i	0.0519753	+	0.0900239i
$55$	3.99191	+	7.63083i	0.538269	+	1.02894i
$56$		0			0
$57$	0.0493330	−	0.0493330i	0.00653431	−	0.00653431i
$58$	−0.547858	+	2.04464i	−0.0719373	+	0.268474i
$59$	3.48720	−	6.04001i	0.453995	−	0.786342i	−0.544635	−	0.838673i	$-0.683332\pi$
$59$	3.48720	−	6.04001i	0.453995	−	0.786342i	0.998630	+	0.0523310i	$0.0166651\pi$
$60$	2.14454	+	2.33092i	0.276859	+	0.300920i
$61$	−12.3935	+	7.15536i	−1.58682	+	0.916150i	−0.592992	+	0.805208i	$0.702054\pi$
$61$	−12.3935	+	7.15536i	−1.58682	+	0.916150i	−0.993827	+	0.110942i	$0.964613\pi$
$62$	1.29458	+	1.29458i	0.164412	+	0.164412i
$63$		0			0
$64$			2.79807i			0.349758i
$65$	−2.53345	−	11.3197i	−0.314236	−	1.40404i
$66$	−2.54782	−	1.47098i	−0.313615	−	0.181066i
$67$	0.152446	+	0.568937i	0.0186243	+	0.0695067i	0.974613	−	0.223898i	$-0.0718783\pi$
$67$	0.152446	+	0.568937i	0.0186243	+	0.0695067i	−0.955988	+	0.293405i	$0.905212\pi$
$68$	2.88323	+	0.772560i	0.349643	+	0.0936866i
$69$	−0.755439			−0.0909442
$70$		0			0
$71$	−8.12783			−0.964595			−0.482298	−	0.876007i	$-0.660198\pi$
$71$	−8.12783			−0.964595			−0.482298	+	0.876007i	$0.660198\pi$
$72$	−2.52086	−	0.675461i	−0.297086	−	0.0796039i
$73$	3.49631	+	13.0484i	0.409212	+	1.52720i	0.796152	+	0.605096i	$0.206865\pi$
$73$	3.49631	+	13.0484i	0.409212	+	1.52720i	−0.386940	+	0.922105i	$0.626468\pi$
$74$	5.78881	+	3.34217i	0.672936	+	0.388520i
$75$	3.81725	−	3.22934i	0.440778	−	0.372892i
$76$			0.0988248i			0.0113360i
$77$		0			0
$78$	2.80203	+	2.80203i	0.317267	+	0.317267i
$79$	8.54186	−	4.93165i	0.961035	−	0.554854i	0.0645434	−	0.997915i	$-0.479441\pi$
$79$	8.54186	−	4.93165i	0.961035	−	0.554854i	0.896491	+	0.443061i	$0.146108\pi$
$80$	−1.87539	−	0.0780974i	−0.209675	−	0.00873155i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.71624	+	6.40510i	−0.189527	+	0.707325i
$83$	1.63570	−	1.63570i	0.179541	−	0.179541i	−0.611615	−	0.791156i	$-0.709480\pi$
$83$	1.63570	−	1.63570i	0.179541	−	0.179541i	0.791156	+	0.611615i	$0.209480\pi$
$84$		0			0
$85$	1.40788	−	4.49678i	0.152706	−	0.487744i
$86$	1.49678	+	2.59249i	0.161402	+	0.279556i
$87$	2.67665	−	0.717207i	0.286967	−	0.0768926i
$88$	9.70872	−	2.60144i	1.03495	−	0.277315i
$89$	2.52657	+	4.37614i	0.267815	+	0.463870i	0.968297	−	0.249800i	$-0.0803649\pi$
$89$	2.52657	+	4.37614i	0.267815	+	0.463870i	−0.700482	+	0.713670i	$0.747032\pi$
$90$	−0.510348	+	1.63006i	−0.0537954	+	0.171823i
$91$		0			0
$92$	0.756656	−	0.756656i	0.0788868	−	0.0788868i
$93$	0.620321	−	2.31507i	0.0643243	−	0.240062i
$94$	−2.96561	+	5.13659i	−0.305880	+	0.529799i
$95$	0.155869	+	0.00649091i	0.0159919	+	0.000665953i
$96$	5.07559	−	2.93039i	0.518025	−	0.299082i
$97$	6.85851	+	6.85851i	0.696376	+	0.696376i	0.963627	−	0.267251i	$-0.0861152\pi$
$97$	6.85851	+	6.85851i	0.696376	+	0.696376i	−0.267251	+	0.963627i	$0.586115\pi$
$98$		0			0
$99$			3.85136i			0.387076i
$100$	−0.588852	+	7.05793i	−0.0588852	+	0.705793i
$101$	−16.6236	−	9.59763i	−1.65411	−	0.955000i	−0.975357	−	0.220632i	$-0.929188\pi$
$101$	−16.6236	−	9.59763i	−1.65411	−	0.955000i	−0.678752	−	0.734368i	$-0.737479\pi$
$102$	0.416622	+	1.55485i	0.0412517	+	0.153954i
$103$	−3.19410	−	0.855857i	−0.314724	−	0.0843301i	0.0979992	−	0.995186i	$-0.468756\pi$
$103$	−3.19410	−	0.855857i	−0.314724	−	0.0843301i	−0.412723	+	0.910856i	$0.635422\pi$
$104$	−13.5384			−1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	8.73911	+	2.34164i	0.844841	+	0.226375i	0.655178	−	0.755475i	$-0.272594\pi$
$107$	8.73911	+	2.34164i	0.844841	+	0.226375i	0.189663	+	0.981849i	$0.439260\pi$
$108$	0.366615	+	1.36822i	0.0352775	+	0.131658i
$109$	−1.87111	−	1.08029i	−0.179220	−	0.103473i	0.407706	−	0.913113i	$-0.366329\pi$
$109$	−1.87111	−	1.08029i	−0.179220	−	0.103473i	−0.586926	+	0.809641i	$0.699662\pi$
$110$	−1.43677	−	6.41963i	−0.136990	−	0.612087i
$111$		−	8.75054i		−	0.830564i
$112$		0			0
$113$	−4.13823	−	4.13823i	−0.389292	−	0.389292i	0.485143	−	0.874435i	$-0.338768\pi$
$113$	−4.13823	−	4.13823i	−0.389292	−	0.389292i	−0.874435	+	0.485143i	$0.838768\pi$
$114$	−0.0461537	+	0.0266469i	−0.00432269	+	0.00249571i
$115$	−1.14372	−	1.24312i	−0.106653	−	0.115921i
$116$	−1.96260	+	3.39932i	−0.182223	+	0.315619i
$117$	1.34264	−	5.01080i	0.124127	−	0.463249i
$118$	−3.76718	+	3.76718i	−0.346797	+	0.346797i
$119$		0			0
$120$	−2.70502	−	5.17085i	−0.246934	−	0.472032i
$121$	−1.91649	−	3.31946i	−0.174226	−	0.301769i
$122$	10.5592	−	2.82932i	0.955981	−	0.256154i
$123$	8.38498	−	2.24675i	0.756048	−	0.202583i
$124$	1.69748	+	2.94012i	0.152438	+	0.264030i
$125$	11.0933	+	1.39233i	0.992215	+	0.124533i
$126$		0			0
$127$	−4.83298	+	4.83298i	−0.428858	+	0.428858i	−0.888239	−	0.459381i	$-0.848071\pi$
$127$	−4.83298	+	4.83298i	−0.428858	+	0.428858i	0.459381	+	0.888239i	$0.348071\pi$
$128$	−2.48057	+	9.25761i	−0.219253	+	0.818265i
$129$	1.95945	−	3.39386i	0.172520	−	0.298813i
$130$	−0.368673	+	8.85312i	−0.0323347	+	0.776470i
$131$	−0.560750	+	0.323749i	−0.0489930	+	0.0282861i	−0.524296	−	0.851536i	$-0.675672\pi$
$131$	−0.560750	+	0.323749i	−0.0489930	+	0.0282861i	0.475303	+	0.879822i	$0.342338\pi$
$132$	−3.85756	−	3.85756i	−0.335758	−	0.335758i
$133$		0			0
$134$		−	0.449929i		−	0.0388680i
$135$	2.18209	−	0.488369i	0.187804	−	0.0420322i
$136$	−4.76274	−	2.74977i	−0.408402	−	0.235791i
$137$	3.74696	+	13.9839i	0.320125	+	1.19472i	0.919123	+	0.393971i	$0.128899\pi$
$137$	3.74696	+	13.9839i	0.320125	+	1.19472i	−0.598998	+	0.800751i	$0.704434\pi$
$138$	0.557400	+	0.149355i	0.0474491	+	0.0127139i
$139$	−22.1663			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$139$	−22.1663			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$140$		0			0
$141$	7.76463			0.653900
$142$	5.99711	+	1.60692i	0.503266	+	0.134850i
$143$	5.17099	+	19.2984i	0.432420	+	1.61381i
$144$	−0.726965	−	0.419714i	−0.0605804	−	0.0349761i
$145$	5.23261	+	3.31874i	0.434545	+	0.275607i
$146$		−	10.3190i		−	0.854007i
$147$		0			0
$148$	8.76463	+	8.76463i	0.720448	+	0.720448i
$149$	9.56745	−	5.52377i	0.783796	−	0.452525i	−0.0539779	−	0.998542i	$-0.517190\pi$
$149$	9.56745	−	5.52377i	0.783796	−	0.452525i	0.837774	+	0.546017i	$0.183857\pi$
$150$	−3.45501	+	1.62807i	−0.282101	+	0.132932i
$151$	−9.19950	+	15.9340i	−0.748645	+	1.29669i	0.199828	+	0.979831i	$0.435962\pi$
$151$	−9.19950	+	15.9340i	−0.748645	+	1.29669i	−0.948472	+	0.316859i	$0.897372\pi$
$152$	0.0471251	−	0.175873i	0.00382235	−	0.0142652i
$153$	1.49007	−	1.49007i	0.120465	−	0.120465i
$154$		0			0
$155$	4.74873	−	2.48420i	0.381428	−	0.199536i
$156$	3.67407	+	6.36367i	0.294161	+	0.509502i
$157$	1.43425	−	0.384306i	0.114465	−	0.0306709i	−0.201132	−	0.979564i	$-0.564462\pi$
$157$	1.43425	−	0.384306i	0.114465	−	0.0306709i	0.315597	+	0.948893i	$0.397795\pi$
$158$	−7.27763	+	1.95003i	−0.578977	+	0.155136i
$159$	−4.34039	−	7.51777i	−0.344215	−	0.596198i
$160$	12.5065	+	3.91560i	0.988724	+	0.309555i
$161$		0			0
$162$	−0.540143	+	0.540143i	−0.0424377	+	0.0424377i
$163$	2.01511	−	7.52050i	0.157836	−	0.589051i	−0.841010	−	0.541020i	$-0.818038\pi$
$163$	2.01511	−	7.52050i	0.157836	−	0.589051i	0.998846	−	0.0480317i	$-0.0152948\pi$
$164$	−6.14812	+	10.6488i	−0.480087	+	0.831535i
$165$	−6.33763	+	5.83089i	−0.493384	+	0.453935i
$166$	−1.53028	+	0.883510i	−0.118773	+	0.0685737i
$167$	1.88968	+	1.88968i	0.146228	+	0.146228i	0.776431	−	0.630203i	$-0.217028\pi$
$167$	1.88968	+	1.88968i	0.146228	+	0.146228i	−0.630203	+	0.776431i	$0.717028\pi$
$168$		0			0
$169$		−	13.9108i		−	1.07006i
$170$	−1.92784	+	3.03960i	−0.147859	+	0.233127i
$171$	0.0604203	+	0.0348837i	0.00462046	+	0.00266762i
$172$	1.43672	+	5.36192i	0.109549	+	0.408843i
$173$	6.70378	+	1.79627i	0.509679	+	0.136568i	0.504488	−	0.863419i	$-0.331681\pi$
$173$	6.70378	+	1.79627i	0.509679	+	0.136568i	0.00519041	+	0.999987i	$0.498348\pi$
$174$	−2.11676			−0.160471
$175$		0			0
$176$	3.23294			0.243692
$177$	6.73676	+	1.80511i	0.506366	+	0.135680i
$178$	−0.999035	−	3.72845i	−0.0748808	−	0.279459i
$179$	16.0957	+	9.29284i	1.20305	+	0.694579i	0.961231	−	0.275743i	$-0.0889239\pi$
$179$	16.0957	+	9.29284i	1.20305	+	0.694579i	0.241815	+	0.970322i	$0.422257\pi$
$180$	−1.69644	+	2.67475i	−0.126445	+	0.199364i
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	−10.1192	−	10.1192i	−0.748034	−	0.748034i
$184$	−1.70740	+	0.985766i	−0.125871	+	0.0726716i
$185$	14.3995	−	13.2482i	1.05867	−	0.974025i
$186$	−0.915407	+	1.58553i	−0.0671209	+	0.116257i
$187$	−2.10055	+	7.83935i	−0.153607	+	0.573270i
$188$	−7.77713	+	7.77713i	−0.567206	+	0.567206i
$189$		0			0
$190$	−0.113725	−	0.0356057i	−0.00825047	−	0.00258311i
$191$	2.69676	+	4.67092i	0.195130	+	0.337976i	0.946943	−	0.321401i	$-0.104154\pi$
$191$	2.69676	+	4.67092i	0.195130	+	0.337976i	−0.751813	+	0.659377i	$0.770820\pi$
$192$	−2.70273	+	0.724193i	−0.195052	+	0.0522641i
$193$	6.56510	−	1.75911i	0.472566	−	0.126624i	−0.0146728	−	0.999892i	$-0.504671\pi$
$193$	6.56510	−	1.75911i	0.472566	−	0.126624i	0.487239	+	0.873269i	$0.338004\pi$
$194$	−3.70458	−	6.41652i	−0.265973	−	0.460679i
$195$	10.2783	−	5.37688i	0.736044	−	0.385046i
$196$		0			0
$197$	12.6739	−	12.6739i	0.902981	−	0.902981i	−0.0927124	−	0.995693i	$-0.529554\pi$
$197$	12.6739	−	12.6739i	0.902981	−	0.902981i	0.995693	+	0.0927124i	$0.0295537\pi$
$198$	0.761438	−	2.84172i	0.0541130	−	0.201953i
$199$	1.33556	−	2.31325i	0.0946750	−	0.163982i	−0.814798	−	0.579745i	$-0.803152\pi$
$199$	1.33556	−	2.31325i	0.0946750	−	0.163982i	0.909473	+	0.415763i	$0.136485\pi$
$200$	4.41356	−	12.2798i	0.312086	−	0.868316i
$201$	−0.510095	+	0.294503i	−0.0359793	+	0.0207727i
$202$	10.3682	+	10.3682i	0.729503	+	0.729503i
$203$		0			0
$204$			2.98494i			0.208988i
$205$	16.3919	+	10.3964i	1.14486	+	0.726117i
$206$	2.18756	+	1.26299i	0.152414	+	0.0879965i
$207$	−0.195522	−	0.729698i	−0.0135897	−	0.0507175i
$208$	−4.20621	−	1.12705i	−0.291648	−	0.0781468i
$209$	−0.268699			−0.0185863
$210$		0			0
$211$	−12.0239			−0.827757			−0.413879	−	0.910332i	$-0.635826\pi$
$211$	−12.0239			−0.827757			−0.413879	+	0.910332i	$0.635826\pi$
$212$	11.8772	+	3.18250i	0.815733	+	0.218575i
$213$	−2.10364	−	7.85088i	−0.144139	−	0.537933i
$214$	−5.98519	−	3.45555i	−0.409139	−	0.236217i
$215$	8.55135	−	1.91387i	0.583198	−	0.130525i
$216$		−	2.60978i		−	0.177573i
$217$		0			0
$218$	1.16702	+	1.16702i	0.0790405	+	0.0790405i
$219$	−11.6989	+	6.75436i	−0.790538	+	0.456417i
$220$	0.507553	−	12.1881i	0.0342192	−	0.821723i
$221$	5.46582	−	9.46708i	0.367671	−	0.636825i
$222$	−1.73004	+	6.45658i	−0.116112	+	0.433337i
$223$	−11.6925	+	11.6925i	−0.782988	+	0.782988i	−0.980334	−	0.197346i	$-0.936768\pi$
$223$	−11.6925	+	11.6925i	−0.782988	+	0.782988i	0.197346	+	0.980334i	$0.436768\pi$
$224$		0			0
$225$	4.10728	+	2.85136i	0.273819	+	0.190091i
$226$	2.23524	+	3.87155i	0.148686	+	0.257531i
$227$	−1.50971	+	0.404524i	−0.100203	+	0.0268492i	−0.308572	−	0.951201i	$-0.599851\pi$
$227$	−1.50971	+	0.404524i	−0.100203	+	0.0268492i	0.208369	+	0.978050i	$0.433184\pi$
$228$	−0.0954574	+	0.0255777i	−0.00632182	+	0.00169393i
$229$	−3.91654	−	6.78365i	−0.258812	−	0.448276i	0.707112	−	0.707102i	$-0.249998\pi$
$229$	−3.91654	−	6.78365i	−0.258812	−	0.448276i	−0.965924	+	0.258826i	$0.916664\pi$
$230$	0.598123	+	1.14335i	0.0394390	+	0.0753906i
$231$		0			0
$232$	5.11372	−	5.11372i	0.335732	−	0.335732i
$233$	0.368944	−	1.37692i	0.0241703	−	0.0902048i	−0.952787	−	0.303639i	$-0.901798\pi$
$233$	0.368944	−	1.37692i	0.0241703	−	0.0902048i	0.976957	+	0.213434i	$0.0684649\pi$
$234$	−1.98133	+	3.43177i	−0.129524	+	0.224342i
$235$	11.7555	+	12.7771i	0.766845	+	0.833488i
$236$	−8.55562	+	4.93959i	−0.556923	+	0.321540i
$237$	6.97440	+	6.97440i	0.453036	+	0.453036i
$238$		0			0
$239$			20.2805i			1.31183i	0.754833	+	0.655917i	$0.227718\pi$
$239$			20.2805i			1.31183i	−0.754833	+	0.655917i	$0.772282\pi$
$240$	−0.409951	−	1.83170i	−0.0264622	−	0.118236i
$241$	2.39883	+	1.38497i	0.154522	+	0.0892136i	0.575268	−	0.817965i	$-0.304898\pi$
$241$	2.39883	+	1.38497i	0.154522	+	0.0892136i	−0.420745	+	0.907179i	$0.638231\pi$
$242$	0.757804	+	2.82816i	0.0487135	+	0.181801i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	20.2710			1.29772
$245$		0			0
$246$	−6.63105			−0.422780
$247$	0.349590	+	0.0936725i	0.0222439	+	0.00596024i
$248$	−1.61890	−	6.04183i	−0.102800	−	0.383656i
$249$	2.00331	+	1.15661i	0.126955	+	0.0732973i
$250$	−7.90992	−	3.22054i	−0.500267	−	0.203685i
$251$			6.09982i			0.385017i	0.981295	+	0.192509i	$0.0616623\pi$
$251$			6.09982i			0.385017i	−0.981295	+	0.192509i	$0.938338\pi$
$252$		0			0
$253$	2.05731	+	2.05731i	0.129342	+	0.129342i
$254$	4.52152	−	2.61050i	0.283706	−	0.163797i
$255$	4.70794	+	0.196054i	0.294823	+	0.0122774i
$256$	6.45864	−	11.1867i	0.403665	−	0.699168i
$257$	−0.738795	+	2.75722i	−0.0460848	+	0.171991i	−0.985133	−	0.171796i	$-0.945043\pi$
$257$	−0.738795	+	2.75722i	−0.0460848	+	0.171991i	0.939048	+	0.343787i	$0.111710\pi$
$258$	−2.11676	+	2.11676i	−0.131784	+	0.131784i
$259$		0			0
$260$	−4.90931	+	15.6804i	−0.304462	+	0.972456i
$261$	1.38554	+	2.39982i	0.0857626	+	0.148545i
$262$	0.477756	−	0.128014i	0.0295159	−	0.00790876i
$263$	−22.9063	+	6.13773i	−1.41246	+	0.378469i	−0.882804	−	0.469741i	$-0.844347\pi$
$263$	−22.9063	+	6.13773i	−1.41246	+	0.378469i	−0.529660	+	0.848210i	$0.677681\pi$
$264$	5.02561	+	8.70460i	0.309305	+	0.535731i
$265$	5.79964	−	18.5241i	0.356269	−	1.13793i
$266$		0			0
$267$	−3.57310	+	3.57310i	−0.218670	+	0.218670i
$268$	0.215939	−	0.805894i	0.0131905	−	0.0492278i
$269$	−12.3676	+	21.4213i	−0.754064	+	1.30608i	0.191774	+	0.981439i	$0.438576\pi$
$269$	−12.3676	+	21.4213i	−0.754064	+	1.30608i	−0.945838	+	0.324638i	$0.894758\pi$
$270$	−1.70660	−	0.0710685i	−0.103861	−	0.00432509i
$271$	−3.58076	+	2.06735i	−0.217515	+	0.125583i	−0.604799	−	0.796378i	$-0.706747\pi$
$271$	−3.58076	+	2.06735i	−0.217515	+	0.125583i	0.387284	+	0.921961i	$0.373413\pi$
$272$	−1.25081	−	1.25081i	−0.0758413	−	0.0758413i
$273$		0			0
$274$		−	11.0588i		−	0.668085i
$275$	−19.1901	−	1.60106i	−1.15721	−	0.0965473i
$276$	0.926710	+	0.535036i	0.0557814	+	0.0322054i
$277$	−4.43358	−	16.5463i	−0.266388	−	0.994174i	−0.961395	−	0.275171i	$-0.911266\pi$
$277$	−4.43358	−	16.5463i	−0.266388	−	0.994174i	0.695007	−	0.719003i	$-0.255401\pi$
$278$	16.3554	+	4.38241i	0.980931	+	0.262840i
$279$	2.39674			0.143489
$280$		0			0
$281$	5.25279			0.313355			0.156678	−	0.987650i	$-0.449922\pi$
$281$	5.25279			0.313355			0.156678	+	0.987650i	$0.449922\pi$
$282$	−5.72913	−	1.53511i	−0.341164	−	0.0914147i
$283$	−0.610271	−	2.27756i	−0.0362768	−	0.135387i	0.945412	−	0.325876i	$-0.105659\pi$
$283$	−0.610271	−	2.27756i	−0.0362768	−	0.135387i	−0.981689	+	0.190489i	$0.938993\pi$
$284$	9.97054	+	5.75649i	0.591643	+	0.341585i
$285$	0.0340722	+	0.152238i	0.00201827	+	0.00901782i
$286$		−	15.2617i		−	0.902441i
$287$		0			0
$288$	4.14420	+	4.14420i	0.244199	+	0.244199i
$289$	−10.8767	+	6.27969i	−0.639808	+	0.369393i
$290$	−3.20474	−	3.48325i	−0.188189	−	0.204544i
$291$	−4.84970	+	8.39993i	−0.284294	+	0.492412i
$292$	4.95249	−	18.4830i	0.289823	−	1.08163i
$293$	−15.2556	+	15.2556i	−0.891240	+	0.891240i	−0.994640	−	0.103400i	$-0.967028\pi$
$293$	−15.2556	+	15.2556i	−0.891240	+	0.891240i	0.103400	+	0.994640i	$0.467028\pi$
$294$		0			0
$295$	7.22893	+	13.8186i	0.420884	+	0.804551i
$296$	−11.4185	−	19.7774i	−0.663687	−	1.14954i
$297$	−3.72013	+	0.996806i	−0.215864	+	0.0578405i
$298$	−8.15142	+	2.18417i	−0.472199	+	0.126525i
$299$	−1.95945	−	3.39386i	−0.113318	−	0.196272i
$300$	−6.96984	+	1.25794i	−0.402404	+	0.0726272i
$301$		0			0
$302$	9.93809	−	9.93809i	0.571873	−	0.571873i
$303$	4.96810	−	18.5412i	0.285410	−	1.06516i
$304$	0.0292823	−	0.0507184i	0.00167946	−	0.00290890i
$305$	1.33142	−	31.9720i	0.0762369	−	1.83071i
$306$	−1.39404	+	0.804852i	−0.0796922	+	0.0460103i
$307$	−14.6198	−	14.6198i	−0.834394	−	0.834394i	0.153721	−	0.988114i	$-0.450874\pi$
$307$	−14.6198	−	14.6198i	−0.834394	−	0.834394i	−0.988114	+	0.153721i	$0.950874\pi$
$308$		0			0
$309$		−	3.30678i		−	0.188116i
$310$	−3.99499	+	0.894114i	−0.226900	+	0.0507823i
$311$	2.47872	+	1.43109i	0.140555	+	0.0811497i	0.568629	−	0.822594i	$-0.307474\pi$
$311$	2.47872	+	1.43109i	0.140555	+	0.0811497i	−0.428073	+	0.903744i	$0.640807\pi$
$312$	−3.50400	−	13.0771i	−0.198375	−	0.740345i
$313$	12.8656	+	3.44732i	0.727204	+	0.194854i	0.603384	−	0.797451i	$-0.293819\pi$
$313$	12.8656	+	3.44732i	0.727204	+	0.194854i	0.123820	+	0.992305i	$0.460485\pi$
$314$	−1.13424			−0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	−10.0855	−	2.70240i	−0.566459	−	0.151782i	−0.0357866	−	0.999359i	$-0.511394\pi$
$317$	−10.0855	−	2.70240i	−0.566459	−	0.151782i	−0.530672	+	0.847577i	$0.678060\pi$
$318$	1.71624	+	6.40510i	0.0962421	+	0.359180i
$319$	−9.24258	−	5.33620i	−0.517485	−	0.298770i
$320$	−5.28358	−	3.35107i	−0.295361	−	0.187331i
$321$			9.04739i			0.504976i
$322$		0			0
$323$	0.103958	+	0.103958i	0.00578440	+	0.00578440i
$324$	−1.22672	+	0.708245i	−0.0681509	+	0.0393470i
$325$	24.4091	+	8.77301i	1.35397	+	0.486639i
$326$	−2.97370	+	5.15060i	−0.164698	+	0.285265i
$327$	0.559197	−	2.08695i	0.0309237	−	0.115409i
$328$	16.0194	−	16.0194i	0.884526	−	0.884526i
$329$		0			0
$330$	5.82902	−	3.04933i	0.320877	−	0.167860i
$331$	−11.8100	−	20.4555i	−0.649136	−	1.12434i	−0.983330	−	0.181833i	$-0.941797\pi$
$331$	−11.8100	−	20.4555i	−0.649136	−	1.12434i	0.334193	−	0.942505i	$-0.391536\pi$
$332$	−3.16501	+	0.848062i	−0.173703	+	0.0465435i
$333$	8.45237	−	2.26481i	0.463187	−	0.124111i
$334$	−1.02070	−	1.76790i	−0.0558500	−	0.0967351i
$335$	−1.25690	−	0.393517i	−0.0686716	−	0.0215001i
$336$		0			0
$337$	−4.93809	+	4.93809i	−0.268995	+	0.268995i	−0.828695	−	0.559700i	$-0.810916\pi$
$337$	−4.93809	+	4.93809i	−0.268995	+	0.268995i	0.559700	+	0.828695i	$0.310916\pi$
$338$	−2.75026	+	10.2641i	−0.149594	+	0.558293i
$339$	2.92617	−	5.06828i	0.158928	−	0.275271i
$340$	−4.91189	+	4.51915i	−0.266385	+	0.245085i
$341$	−7.99402	+	4.61535i	−0.432900	+	0.249935i
$342$	−0.0376844	−	0.0376844i	−0.00203774	−	0.00203774i
$343$		0			0
$344$		−	10.2274i		−	0.551427i
$345$	0.904743	−	1.42649i	0.0487097	−	0.0767998i
$346$	−4.59124	−	2.65076i	−0.246827	−	0.142505i
$347$	2.13647	+	7.97341i	0.114692	+	0.428035i	0.999264	−	0.0383685i	$-0.0122161\pi$
$347$	2.13647	+	7.97341i	0.114692	+	0.428035i	−0.884572	+	0.466404i	$0.845549\pi$
$348$	−3.79145	−	1.01592i	−0.203243	−	0.0544589i
$349$	−16.9121			−0.905282			−0.452641	−	0.891693i	$-0.649518\pi$
$349$	−16.9121			−0.905282			−0.452641	+	0.891693i	$0.649518\pi$
$350$		0			0
$351$	5.18757			0.276892
$352$	−21.8029	−	5.84206i	−1.16210	−	0.311383i
$353$	−4.07257	−	15.1990i	−0.216761	−	0.808963i	−0.985539	−	0.169448i	$-0.945802\pi$
$353$	−4.07257	−	15.1990i	−0.216761	−	0.808963i	0.768778	−	0.639516i	$-0.220865\pi$
$354$	−4.61383	−	2.66380i	−0.245222	−	0.141579i
$355$	9.73419	−	15.3477i	0.516637	−	0.814574i
$356$		−	7.15771i		−	0.379358i
$357$		0			0
$358$	−10.0389	−	10.0389i	−0.530574	−	0.530574i
$359$	7.05693	−	4.07432i	0.372450	−	0.215034i	−0.302078	−	0.953283i	$-0.597680\pi$
$359$	7.05693	−	4.07432i	0.372450	−	0.215034i	0.674528	+	0.738249i	$0.264347\pi$
$360$	4.29454	−	3.95116i	0.226342	−	0.208245i
$361$	9.49757	−	16.4503i	0.499872	−	0.865804i
$362$	−1.67759	+	6.26086i	−0.0881723	+	0.329063i
$363$	2.71033	−	2.71033i	0.142255	−	0.142255i
$364$		0			0
$365$	−28.8266	−	9.02520i	−1.50885	−	0.472401i
$366$	5.46582	+	9.46708i	0.285703	+	0.494852i
$367$	−20.1462	+	5.39815i	−1.05162	+	0.281781i	−0.742922	−	0.669378i	$-0.766561\pi$
$367$	−20.1462	+	5.39815i	−1.05162	+	0.281781i	−0.308700	+	0.951160i	$0.599894\pi$
$368$	−0.612529	+	0.164127i	−0.0319303	+	0.00855569i
$369$	4.34039	+	7.51777i	0.225951	+	0.391359i
$370$	−13.2439	+	6.92828i	−0.688518	+	0.360184i
$371$		0			0
$372$	−2.40060	+	2.40060i	−0.124465	+	0.124465i
$373$	0.547065	−	2.04168i	0.0283260	−	0.105714i	−0.950316	−	0.311288i	$-0.899240\pi$
$373$	0.547065	−	2.04168i	0.0283260	−	0.105714i	0.978642	+	0.205574i	$0.0659062\pi$
$374$	3.09977	−	5.36897i	0.160286	−	0.277623i
$375$	1.52627	+	11.0757i	0.0788165	+	0.571945i
$376$	17.5491	−	10.1320i	0.905027	−	0.522518i
$377$	10.1648	+	10.1648i	0.523511	+	0.523511i
$378$		0			0
$379$			18.7135i			0.961248i	0.876927	+	0.480624i	$0.159590\pi$
$379$			18.7135i			0.961248i	−0.876927	+	0.480624i	$0.840410\pi$
$380$	−0.186611	−	0.118356i	−0.00957292	−	0.00607155i
$381$	−5.91917	−	3.41743i	−0.303248	−	0.175080i
$382$	−1.06633	−	3.97960i	−0.0545582	−	0.203614i
$383$	−28.5983	−	7.66288i	−1.46130	−	0.391555i	−0.561364	−	0.827569i	$-0.689723\pi$
$383$	−28.5983	−	7.66288i	−1.46130	−	0.391555i	−0.899940	+	0.436014i	$0.856390\pi$
$384$	−9.58418			−0.489091
$385$		0			0
$386$	−5.19184			−0.264258
$387$	3.78536	+	1.01428i	0.192421	+	0.0515589i
$388$	−3.55594	−	13.2710i	−0.180526	−	0.673731i
$389$	−22.2232	−	12.8305i	−1.12676	−	0.650535i	−0.183641	−	0.982993i	$-0.558788\pi$
$389$	−22.2232	−	12.8305i	−1.12676	−	0.650535i	−0.943118	+	0.332459i	$0.892122\pi$
$390$	−8.64687	+	1.93525i	−0.437852	+	0.0979949i
$391$		−	1.59192i		−	0.0805069i
$392$		0			0
$393$	−0.457851	−	0.457851i	−0.0230955	−	0.0230955i
$394$	−11.8572	+	6.84574i	−0.597356	+	0.344883i
$395$	−0.917646	+	22.0359i	−0.0461718	+	1.10875i
$396$	2.72771	−	4.72453i	0.137073	−	0.237417i
$397$	2.46549	−	9.20135i	0.123740	−	0.461802i	−0.876052	−	0.482217i	$-0.839832\pi$
$397$	2.46549	−	9.20135i	0.123740	−	0.461802i	0.999792	+	0.0204142i	$0.00649848\pi$
$398$	−1.44278	+	1.44278i	−0.0723201	+	0.0723201i
$399$		0			0
$400$	2.39351	−	3.44776i	0.119676	−	0.172388i
$401$	−7.37513	−	12.7741i	−0.368296	−	0.637908i	0.621003	−	0.783808i	$-0.286726\pi$
$401$	−7.37513	−	12.7741i	−0.368296	−	0.637908i	−0.989299	+	0.145900i	$0.953392\pi$
$402$	0.434598	−	0.116450i	0.0216758	−	0.00580801i
$403$	12.0096	−	3.21796i	0.598240	−	0.160298i
$404$	13.5950	+	23.5472i	0.676374	+	1.17151i
$405$	1.03649	+	1.98133i	0.0515038	+	0.0984532i
$406$		0			0
$407$	−23.8305	+	23.8305i	−1.18124	+	1.18124i
$408$	1.42339	−	5.31215i	0.0704681	−	0.262990i
$409$	−5.28021	+	9.14560i	−0.261090	+	0.452221i	−0.966532	−	0.256547i	$-0.917415\pi$
$409$	−5.28021	+	9.14560i	−0.261090	+	0.452221i	0.705442	+	0.708768i	$0.250749\pi$
$410$	−10.0393	−	10.9118i	−0.495805	−	0.538894i
$411$	−12.5376	+	7.23858i	−0.618434	+	0.357053i
$412$	3.31210	+	3.31210i	0.163176	+	0.163176i
$413$		0			0
$414$			0.577063i			0.0283611i
$415$	1.12971	+	5.04765i	0.0554552	+	0.247779i
$416$	26.3299	+	15.2016i	1.29093	+	0.745320i
$417$	−5.73706	−	21.4110i	−0.280945	−	1.04850i
$418$	0.198260	+	0.0531235i	0.00969719	+	0.00259835i
$419$	15.5472			0.759532			0.379766	−	0.925083i	$-0.376004\pi$
$419$	15.5472			0.759532			0.379766	+	0.925083i	$0.376004\pi$
$420$		0			0
$421$	3.29886			0.160776			0.0803882	−	0.996764i	$-0.474384\pi$
$421$	3.29886			0.160776			0.0803882	+	0.996764i	$0.474384\pi$
$422$	8.87180	+	2.37719i	0.431873	+	0.115720i
$423$	2.00963	+	7.50006i	0.0977117	+	0.364665i
$424$	−19.6197	−	11.3275i	−0.952818	−	0.550110i
$425$	6.80512	+	8.04400i	0.330097	+	0.390191i
$426$			6.20867i			0.300811i
$427$		0			0
$428$	−9.06196	−	9.06196i	−0.438026	−	0.438026i
$429$	−17.3025	+	9.98959i	−0.835372	+	0.482302i
$430$	−6.68799	−	0.278510i	−0.322524	−	0.0134309i
$431$	7.04553	−	12.2032i	0.339371	−	0.587809i	−0.644943	−	0.764230i	$-0.723119\pi$
$431$	7.04553	−	12.2032i	0.339371	−	0.587809i	0.984315	+	0.176422i	$0.0564523\pi$
$432$	0.217260	−	0.810825i	0.0104529	−	0.0390108i
$433$	−1.72650	+	1.72650i	−0.0829702	+	0.0829702i	−0.747374	−	0.664404i	$-0.768686\pi$
$433$	−1.72650	+	1.72650i	−0.0829702	+	0.0829702i	0.664404	+	0.747374i	$0.268686\pi$
$434$		0			0
$435$	−1.85136	+	5.91327i	−0.0887660	+	0.283519i
$436$	1.53022	+	2.65041i	0.0732840	+	0.126932i
$437$	0.0509091	−	0.0136411i	0.00243531	−	0.000652540i
$438$	9.96739	−	2.67075i	0.476260	−	0.127614i
$439$	13.5586	+	23.4841i	0.647116	+	1.12084i	0.983809	+	0.179223i	$0.0573582\pi$
$439$	13.5586	+	23.4841i	0.647116	+	1.12084i	−0.336693	+	0.941615i	$0.609308\pi$
$440$	−6.71524	+	21.4485i	−0.320136	+	1.02252i
$441$		0			0
$442$	−5.90465	+	5.90465i	−0.280856	+	0.280856i
$443$	−8.83957	+	32.9897i	−0.419981	+	1.56739i	0.354664	+	0.934994i	$0.384595\pi$
$443$	−8.83957	+	32.9897i	−0.419981	+	1.56739i	−0.774645	+	0.632396i	$0.782072\pi$
$444$	−6.19753	+	10.7344i	−0.294122	+	0.509434i
$445$	−11.2894	−	0.470126i	−0.535167	−	0.0222861i
$446$	10.9390	−	6.31563i	0.517976	−	0.299054i
$447$	7.81179	+	7.81179i	0.369485	+	0.369485i
$448$		0			0
$449$		−	9.80267i		−	0.462617i	−0.972881	−	0.231308i	$-0.925699\pi$
$449$		−	9.80267i		−	0.462617i	0.972881	−	0.231308i	$-0.0743006\pi$
$450$	−2.46682	−	2.91591i	−0.116287	−	0.137457i
$451$	−28.9536	−	16.7164i	−1.36337	−	0.787144i
$452$	2.14556	+	8.00732i	0.100918	+	0.376633i
$453$	−17.7721	−	4.76201i	−0.835005	−	0.223739i
$454$	1.19391			0.0560331
$455$		0			0
$456$	0.182078			0.00852656
$457$	−0.751411	−	0.201340i	−0.0351495	−	0.00941828i	0.241201	−	0.970475i	$-0.422459\pi$
$457$	−0.751411	−	0.201340i	−0.0351495	−	0.00941828i	−0.276351	+	0.961057i	$0.589125\pi$
$458$	1.54865	+	5.77964i	0.0723636	+	0.270065i
$459$	1.82496	+	1.05364i	0.0851817	+	0.0491797i
$460$	0.522591	+	2.33499i	0.0243659	+	0.108869i
$461$		−	0.831786i		−	0.0387401i	−0.999812	−	0.0193701i	$-0.993834\pi$
$461$		−	0.831786i		−	0.0387401i	0.999812	−	0.0193701i	$-0.00616607\pi$
$462$		0			0
$463$	5.45140	+	5.45140i	0.253348	+	0.253348i	0.822342	−	0.568994i	$-0.192667\pi$
$463$	5.45140	+	5.45140i	0.253348	+	0.253348i	−0.568994	+	0.822342i	$0.692667\pi$
$464$	2.01448	−	1.16306i	0.0935197	−	0.0539936i
$465$	3.62862	+	3.94397i	0.168273	+	0.182897i
$466$	−0.544450	+	0.943015i	−0.0252211	+	0.0436843i
$467$	−8.52208	+	31.8048i	−0.394355	+	1.47175i	0.428522	+	0.903531i	$0.359035\pi$
$467$	−8.52208	+	31.8048i	−0.394355	+	1.47175i	−0.822876	+	0.568220i	$0.807632\pi$
$468$	−5.19592	+	5.19592i	−0.240181	+	0.240181i
$469$		0			0
$470$	−6.14768	−	11.7517i	−0.283571	−	0.542067i
$471$	0.742422	+	1.28591i	0.0342090	+	0.0592517i
$472$	17.5815	−	4.71094i	0.809252	−	0.216838i
$473$	−14.5788	+	3.90637i	−0.670333	+	0.179615i
$474$	−3.76718	−	6.52494i	−0.173032	−	0.299700i
$475$	−0.198932	+	0.286554i	−0.00912762	+	0.0131480i
$476$		0			0
$477$	6.13823	−	6.13823i	0.281050	−	0.281050i
$478$	4.00957	−	14.9639i	0.183394	−	0.684434i
$479$	20.2160	−	35.0151i	0.923691	−	1.59988i	0.130038	−	0.991509i	$-0.458490\pi$
$479$	20.2160	−	35.0151i	0.923691	−	1.59988i	0.793653	−	0.608371i	$-0.208177\pi$
$480$	−0.545267	+	13.0938i	−0.0248879	+	0.597646i
$481$	39.3123	−	22.6970i	1.79249	−	1.03489i
$482$	−1.49616	−	1.49616i	−0.0681483	−	0.0681483i
$483$		0			0
$484$			5.42938i			0.246790i
$485$	−21.1649	+	4.73689i	−0.961049	+	0.215091i
$486$	−0.661538	−	0.381939i	−0.0300080	−	0.0173251i
$487$	−2.64597	−	9.87490i	−0.119900	−	0.447474i	0.879706	−	0.475517i	$-0.157739\pi$
$487$	−2.64597	−	9.87490i	−0.119900	−	0.447474i	−0.999607	+	0.0280431i	$0.991072\pi$
$488$	−36.0753	−	9.66634i	−1.63305	−	0.437575i
$489$	7.78580			0.352086
$490$		0			0
$491$	20.1040			0.907279			0.453639	−	0.891185i	$-0.350125\pi$
$491$	20.1040			0.907279			0.453639	+	0.891185i	$0.350125\pi$
$492$	−11.8772	−	3.18250i	−0.535468	−	0.143478i
$493$	1.51135	+	5.64045i	0.0680680	+	0.254033i
$494$	−0.239425	−	0.138232i	−0.0107723	−	0.00621937i
$495$	−7.27251	−	4.61254i	−0.326875	−	0.207318i
$496$		−	2.01189i		−	0.0903364i
$497$		0			0
$498$	−1.24947	−	1.24947i	−0.0559902	−	0.0559902i
$499$	13.3564	−	7.71133i	0.597916	−	0.345207i	−0.170306	−	0.985391i	$-0.554475\pi$
$499$	13.3564	−	7.71133i	0.597916	−	0.345207i	0.768221	+	0.640185i	$0.221142\pi$
$500$	−12.6222	−	9.56477i	−0.564484	−	0.427750i
$501$	−1.33620	+	2.31437i	−0.0596972	+	0.103399i
$502$	1.20597	−	4.50075i	0.0538252	−	0.200878i
$503$	25.9985	−	25.9985i	1.15922	−	1.15922i	0.174573	−	0.984644i	$-0.444145\pi$
$503$	25.9985	−	25.9985i	1.15922	−	1.15922i	0.984644	−	0.174573i	$-0.0558546\pi$
$504$		0			0
$505$	38.0322	−	19.8958i	1.69241	−	0.885350i
$506$	−1.11124	−	1.92472i	−0.0494006	−	0.0855644i
$507$	13.4368	−	3.60039i	0.596751	−	0.159899i
$508$	9.35164	−	2.50576i	0.414912	−	0.111175i
$509$	−18.5636	−	32.1530i	−0.822816	−	1.42516i	−0.903577	−	0.428425i	$-0.859069\pi$
$509$	−18.5636	−	32.1530i	−0.822816	−	1.42516i	0.0807619	−	0.996733i	$-0.474265\pi$
$510$	−3.43499	−	1.07545i	−0.152104	−	0.0476216i
$511$		0			0
$512$	6.57690	−	6.57690i	0.290661	−	0.290661i
$513$	−0.0180571	+	0.0673901i	−0.000797241	+	0.00297535i
$514$	1.09024	−	1.88835i	0.0480884	−	0.0832915i
$515$	5.44149	−	5.00641i	0.239781	−	0.220609i
$516$	−4.80737	+	2.77554i	−0.211633	+	0.122186i
$517$	−21.1456	−	21.1456i	−0.929982	−	0.929982i
$518$		0			0
$519$			6.94026i			0.304644i
$520$	16.2141	−	25.5645i	0.711036	−	1.12108i
$521$	−2.24415	−	1.29566i	−0.0983180	−	0.0567639i	0.450035	−	0.893011i	$-0.351412\pi$
$521$	−2.24415	−	1.29566i	−0.0983180	−	0.0567639i	−0.548353	+	0.836247i	$0.684745\pi$
$522$	−0.547858	−	2.04464i	−0.0239791	−	0.0894913i
$523$	8.31711	+	2.22856i	0.363682	+	0.0974482i	0.436032	−	0.899931i	$-0.356383\pi$
$523$	8.31711	+	2.22856i	0.363682	+	0.0974482i	−0.0723506	+	0.997379i	$0.523050\pi$
$524$	0.917176			0.0400670
$525$		0			0
$526$	18.1149			0.789846
$527$	4.87850	+	1.30719i	0.212511	+	0.0569421i
$528$	0.836746	+	3.12278i	0.0364147	+	0.135901i
$529$	19.4244	+	11.2147i	0.844537	+	0.487594i
$530$	−7.94159	+	12.5214i	−0.344961	+	0.543894i
$531$			6.97440i			0.302663i
$532$		0			0
$533$	31.8425	+	31.8425i	1.37925	+	1.37925i
$534$	3.34284	−	1.92999i	0.144659	−	0.0835187i
$535$	−14.8880	+	13.6976i	−0.643664	+	0.592199i
$536$	−0.768589	+	1.33124i	−0.0331980	+	0.0575006i
$537$	−4.81033	+	17.9524i	−0.207581	+	0.774703i
$538$	13.3605	−	13.3605i	0.576013	−	0.576013i
$539$		0			0
$540$	−3.02269	−	0.946361i	−0.130076	−	0.0407249i
$541$	16.7319	+	28.9805i	0.719360	+	1.24597i	0.961254	+	0.275665i	$0.0888980\pi$
$541$	16.7319	+	28.9805i	0.719360	+	1.24597i	−0.241894	+	0.970303i	$0.577769\pi$
$542$	3.05079	−	0.817456i	0.131042	−	0.0351127i
$543$	8.19615	−	2.19615i	0.351731	−	0.0942459i
$544$	6.17515	+	10.6957i	0.264757	+	0.458573i
$545$	4.28081	−	2.23942i	0.183370	−	0.0959262i
$546$		0			0
$547$	−0.828381	+	0.828381i	−0.0354190	+	0.0354190i	−0.724594	−	0.689175i	$-0.757973\pi$
$547$	−0.828381	+	0.828381i	−0.0354190	+	0.0354190i	0.689175	+	0.724594i	$0.257973\pi$
$548$	5.30754	−	19.8080i	0.226727	−	0.846156i
$549$	7.15536	−	12.3935i	0.305383	−	0.528940i
$550$	13.8429	+	4.97534i	0.590263	+	0.212149i
$551$	−0.167429	+	0.0966653i	−0.00713272	+	0.00411808i
$552$	−1.39408	−	1.39408i	−0.0593361	−	0.0593361i
$553$		0			0
$554$			13.0853i			0.555939i
$555$	16.5236	+	10.4800i	0.701388	+	0.444850i
$556$	27.1918	+	15.6992i	1.15319	+	0.665793i
$557$	5.38496	+	20.0969i	0.228168	+	0.851534i	0.981111	+	0.193448i	$0.0619671\pi$
$557$	5.38496	+	20.0969i	0.228168	+	0.851534i	−0.752943	+	0.658086i	$0.771366\pi$
$558$	−1.76843	−	0.473850i	−0.0748636	−	0.0200597i
$559$	20.3295			0.859846
$560$		0			0
$561$	−8.11589			−0.342653
$562$	−3.87577	−	1.03851i	−0.163489	−	0.0438069i
$563$	−8.77338	−	32.7427i	−0.369754	−	1.37994i	−0.860860	−	0.508841i	$-0.830074\pi$
$563$	−8.77338	−	32.7427i	−0.369754	−	1.37994i	0.491106	−	0.871100i	$-0.336593\pi$
$564$	−9.52500	−	5.49926i	−0.401075	−	0.231561i
$565$	12.7703	−	2.85811i	0.537251	−	0.120241i
$566$			1.80115i			0.0757080i
$567$		0			0
$568$	−14.9990	−	14.9990i	−0.629346	−	0.629346i
$569$	13.5671	−	7.83298i	0.568763	−	0.328376i	−0.187892	−	0.982190i	$-0.560165\pi$
$569$	13.5671	−	7.83298i	0.568763	−	0.328376i	0.756655	+	0.653814i	$0.226832\pi$
$570$	0.00495826	−	0.119065i	0.000207679	−	0.00498709i
$571$	−18.4943	+	32.0331i	−0.773964	+	1.34055i	0.161411	+	0.986887i	$0.448396\pi$
$571$	−18.4943	+	32.0331i	−0.773964	+	1.34055i	−0.935375	+	0.353658i	$0.884938\pi$
$572$	7.32466	−	27.3360i	0.306260	−	1.14298i
$573$	−3.81379	+	3.81379i	−0.159323	+	0.159323i
$574$		0			0
$575$	3.71714	−	0.670882i	0.155015	−	0.0279777i
$576$	−1.39903	−	2.42320i	−0.0582931	−	0.100967i
$577$	−21.2536	+	5.69488i	−0.884798	+	0.237081i	−0.672476	−	0.740119i	$-0.734769\pi$
$577$	−21.2536	+	5.69488i	−0.884798	+	0.237081i	−0.212322	+	0.977200i	$0.568103\pi$
$578$	9.26693	−	2.48307i	0.385453	−	0.103282i
$579$	3.39835	+	5.88611i	0.141230	+	0.244618i
$580$	−4.06845	−	7.77713i	−0.168933	−	0.322928i
$581$		0			0
$582$	5.23907	−	5.23907i	0.217166	−	0.217166i
$583$	−8.65304	+	32.2936i	−0.358372	+	1.33746i
$584$	−17.6274	+	30.5315i	−0.729427	+	1.26340i
$585$	7.85389	+	8.53643i	0.324718	+	0.352938i
$586$	14.2724	−	8.24019i	0.589589	−	0.340399i
$587$	−15.7111	−	15.7111i	−0.648468	−	0.648468i	0.304155	−	0.952623i	$-0.401626\pi$
$587$	−15.7111	−	15.7111i	−0.648468	−	0.648468i	−0.952623	+	0.304155i	$0.901626\pi$
$588$		0			0
$589$			0.167214i			0.00688993i
$590$	−2.60183	−	11.6253i	−0.107116	−	0.478604i
$591$	15.5223	+	8.96183i	0.638504	+	0.368640i
$592$	−1.90114	−	7.09515i	−0.0781364	−	0.291609i
$593$	2.52987	+	0.677877i	0.103889	+	0.0278371i	0.310389	−	0.950610i	$-0.399541\pi$
$593$	2.52987	+	0.677877i	0.103889	+	0.0278371i	−0.206500	+	0.978447i	$0.566207\pi$
$594$	2.94197			0.120710
$595$		0			0
$596$	−15.6487			−0.640997
$597$	2.58009	+	0.691334i	0.105596	+	0.0282944i
$598$	0.774789	+	2.89155i	0.0316835	+	0.118244i
$599$	40.9761	+	23.6576i	1.67424	+	0.966622i	0.965223	+	0.261429i	$0.0841936\pi$
$599$	40.9761	+	23.6576i	1.67424	+	0.966622i	0.709015	+	0.705193i	$0.249140\pi$
$600$	13.0037	+	1.08492i	0.530875	+	0.0442915i
$601$			11.0819i			0.452041i	0.974123	+	0.226021i	$0.0725717\pi$
$601$			11.0819i			0.452041i	−0.974123	+	0.226021i	$0.927428\pi$
$602$		0			0
$603$	−0.416491	−	0.416491i	−0.0169608	−	0.0169608i
$604$	22.5704	−	13.0310i	0.918375	−	0.530224i
$605$	8.56339	+	0.356607i	0.348151	+	0.0144981i
$606$	−7.33142	+	12.6984i	−0.297819	+	0.515837i
$607$	2.76222	−	10.3088i	0.112115	−	0.418419i	−0.886940	−	0.461885i	$-0.847173\pi$
$607$	2.76222	−	10.3088i	0.112115	−	0.418419i	0.999055	+	0.0434656i	$0.0138399\pi$
$608$	−0.289130	+	0.289130i	−0.0117258	+	0.0117258i
$609$		0			0
$610$	−7.30346	+	23.3273i	−0.295708	+	0.944496i
$611$	20.1398	+	34.8831i	0.814767	+	1.41122i
$612$	−2.88323	+	0.772560i	−0.116548	+	0.0312289i
$613$	3.58564	−	0.960769i	0.144823	−	0.0388051i	−0.185679	−	0.982610i	$-0.559449\pi$
$613$	3.58564	−	0.960769i	0.144823	−	0.0388051i	0.330502	+	0.943805i	$0.392782\pi$
$614$	7.89676	+	13.6776i	0.318687	+	0.551983i
$615$	−5.79964	+	18.5241i	−0.233864	+	0.746965i
$616$		0			0
$617$	11.3212	−	11.3212i	0.455774	−	0.455774i	−0.441491	−	0.897266i	$-0.645550\pi$
$617$	11.3212	−	11.3212i	0.455774	−	0.455774i	0.897266	+	0.441491i	$0.145550\pi$
$618$	−0.653770	+	2.43990i	−0.0262985	+	0.0981473i
$619$	4.53385	−	7.85287i	0.182231	−	0.315633i	−0.760409	−	0.649445i	$-0.775001\pi$
$619$	4.53385	−	7.85287i	0.182231	−	0.315633i	0.942640	+	0.333811i	$0.108335\pi$
$620$	−7.58478	−	0.315855i	−0.304612	−	0.0126850i
$621$	0.654230	−	0.377720i	0.0262533	−	0.0151574i
$622$	−1.54599	−	1.54599i	−0.0619884	−	0.0619884i
$623$		0			0
$624$		−	4.35458i		−	0.174323i
$625$	−15.9149	+	19.2799i	−0.636595	+	0.771198i
$626$	−8.81129	−	5.08720i	−0.352170	−	0.203325i
$627$	−0.0695445	−	0.259544i	−0.00277734	−	0.0103652i
$628$	−2.03160	−	0.544366i	−0.0810697	−	0.0217225i
$629$	18.4398			0.735244
$630$		0			0
$631$	−9.67260			−0.385060			−0.192530	−	0.981291i	$-0.561669\pi$
$631$	−9.67260			−0.385060			−0.192530	+	0.981291i	$0.561669\pi$
$632$	24.8639	+	6.66227i	0.989034	+	0.265011i
$633$	−3.11201	−	11.6142i	−0.123691	−	0.461622i
$634$	6.90730	+	3.98793i	0.274324	+	0.158381i
$635$	−3.33794	−	14.9143i	−0.132462	−	0.591854i
$636$			12.2962i			0.487577i
$637$		0			0
$638$	5.76463	+	5.76463i	0.228224	+	0.228224i
$639$	7.03890	−	4.06391i	0.278455	−	0.160766i
$640$	−14.5103	−	15.7713i	−0.573570	−	0.623416i
$641$	20.2924	−	35.1474i	0.801500	−	1.38824i	−0.117129	−	0.993117i	$-0.537369\pi$
$641$	20.2924	−	35.1474i	0.801500	−	1.38824i	0.918629	−	0.395122i	$-0.129298\pi$
$642$	1.78872	−	6.67561i	0.0705953	−	0.263465i
$643$	3.89544	−	3.89544i	0.153621	−	0.153621i	−0.626112	−	0.779733i	$-0.715355\pi$
$643$	3.89544	−	3.89544i	0.153621	−	0.153621i	0.779733	+	0.626112i	$0.215355\pi$
$644$		0			0
$645$	4.06191	+	7.76463i	0.159937	+	0.305732i
$646$	−0.0561524	−	0.0972588i	−0.00220929	−	0.00382660i
$647$	−23.0058	+	6.16438i	−0.904450	+	0.242347i	−0.680927	−	0.732352i	$-0.738423\pi$
$647$	−23.0058	+	6.16438i	−0.904450	+	0.242347i	−0.223524	+	0.974698i	$0.571756\pi$
$648$	2.52086	−	0.675461i	0.0990285	−	0.0265346i
$649$	−13.4305	−	23.2623i	−0.527192	−	0.913123i
$650$	−16.2758	−	11.2990i	−0.638388	−	0.443183i
$651$		0			0
$652$	−7.79833	+	7.79833i	−0.305406	+	0.305406i
$653$	−8.41678	+	31.4119i	−0.329374	+	1.22924i	0.580467	+	0.814284i	$0.302870\pi$
$653$	−8.41678	+	31.4119i	−0.329374	+	1.22924i	−0.909841	+	0.414957i	$0.863797\pi$
$654$	−0.825207	+	1.42930i	−0.0322681	+	0.0558901i
$655$	0.0602410	−	1.44660i	0.00235381	−	0.0565232i
$656$	6.31062	−	3.64344i	0.246388	−	0.142252i
$657$	−9.55210	−	9.55210i	−0.372663	−	0.372663i
$658$		0			0
$659$		−	32.7543i		−	1.27593i	−0.770067	−	0.637963i	$-0.779777\pi$
$659$		−	32.7543i		−	1.27593i	0.770067	−	0.637963i	$-0.220223\pi$
$660$	11.9042	−	2.66426i	0.463370	−	0.103706i
$661$	28.1609	+	16.2587i	1.09533	+	0.632391i	0.934991	−	0.354671i	$-0.115407\pi$
$661$	28.1609	+	16.2587i	1.09533	+	0.632391i	0.160341	+	0.987062i	$0.448740\pi$
$662$	4.66982	+	17.4280i	0.181498	+	0.677359i
$663$	10.5592	+	2.82932i	0.410084	+	0.109882i
$664$	6.03701			0.234281
$665$		0			0
$666$	−6.68434			−0.259013
$667$	2.02205	+	0.541806i	0.0782940	+	0.0209788i
$668$	−0.979744	−	3.65646i	−0.0379075	−	0.141473i
$669$	−14.3203	−	8.26785i	−0.553656	−	0.319654i
$670$	0.849600	+	0.538852i	0.0328229	+	0.0208177i
$671$			55.1158i			2.12772i
$672$		0			0
$673$	−16.7534	−	16.7534i	−0.645796	−	0.645796i	0.306179	−	0.951974i	$-0.400950\pi$
$673$	−16.7534	−	16.7534i	−0.645796	−	0.645796i	−0.951974	+	0.306179i	$0.900950\pi$
$674$	4.61986	−	2.66728i	0.177950	−	0.102740i
$675$	−1.69116	+	4.70531i	−0.0650928	+	0.181108i
$676$	−9.85228	+	17.0647i	−0.378934	+	0.656333i
$677$	−2.50935	+	9.36503i	−0.0964422	+	0.359927i	−0.997234	−	0.0743237i	$-0.976320\pi$
$677$	−2.50935	+	9.36503i	−0.0964422	+	0.359927i	0.900792	+	0.434251i	$0.142987\pi$
$678$	−3.16110	+	3.16110i	−0.121401	+	0.121401i
$679$		0			0
$680$	10.8964	−	5.70024i	0.417858	−	0.218594i
$681$	−0.781481	−	1.35357i	−0.0299464	−	0.0518687i
$682$	6.81087	−	1.82497i	0.260802	−	0.0698816i
$683$	−31.7389	+	8.50440i	−1.21445	+	0.325412i	−0.808508	−	0.588485i	$-0.799725\pi$
$683$	−31.7389	+	8.50440i	−1.21445	+	0.325412i	−0.405946	+	0.913897i	$0.633058\pi$
$684$	−0.0494124	−	0.0855848i	−0.00188933	−	0.00327242i
$685$	−30.8932	−	9.67222i	−1.18037	−	0.369557i
$686$		0			0
$687$	5.53883	−	5.53883i	0.211319	−	0.211319i
$688$	0.851417	−	3.17753i	0.0324600	−	0.121142i
$689$	22.5160	−	38.9989i	0.857793	−	1.48574i
$690$	−0.949590	+	0.873664i	−0.0361503	+	0.0332598i
$691$	−36.7813	+	21.2357i	−1.39923	+	0.807845i	−0.994312	−	0.106509i	$-0.966033\pi$
$691$	−36.7813	+	21.2357i	−1.39923	+	0.807845i	−0.404916	+	0.914354i	$0.632699\pi$
$692$	−6.95144	−	6.95144i	−0.264254	−	0.264254i
$693$		0			0
$694$		−	6.30557i		−	0.239356i
$695$	26.5472	−	41.8565i	1.00699	−	1.58771i
$696$	6.26301	+	3.61595i	0.237399	+	0.137062i
$697$	4.73453	+	17.6695i	0.179333	+	0.669280i
$698$	12.4786	+	3.34362i	0.472320	+	0.126558i
$699$	1.42549			0.0539169
$700$		0			0
$701$	17.0793			0.645077			0.322539	−	0.946556i	$-0.395464\pi$
$701$	17.0793			0.645077			0.322539	+	0.946556i	$0.395464\pi$
$702$	−3.82764	−	1.02561i	−0.144465	−	0.0387093i
$703$	0.158010	+	0.589700i	0.00595944	+	0.0222409i
$704$	9.33261	+	5.38818i	0.351736	+	0.203075i
$705$	−9.29921	+	14.6619i	−0.350229	+	0.552200i
$706$			12.0198i			0.452370i
$707$		0			0
$708$	−6.98563	−	6.98563i	−0.262536	−	0.262536i
$709$	−28.2967	+	16.3371i	−1.06270	+	0.613552i	−0.926179	−	0.377084i	$-0.876927\pi$
$709$	−28.2967	+	16.3371i	−1.06270	+	0.613552i	−0.136525	+	0.990637i	$0.543593\pi$
$710$	−10.2167	+	9.39981i	−0.383426	+	0.352769i
$711$	−4.93165	+	8.54186i	−0.184951	+	0.320345i
$712$	−3.41319	+	12.7382i	−0.127915	+	0.477385i
$713$	1.28028	−	1.28028i	0.0479469	−	0.0479469i
$714$		0			0
$715$	−42.6341	−	13.3481i	−1.59443	−	0.499192i
$716$	−13.1632	−	22.7994i	−0.491933	−	0.852052i
$717$	−19.5894	+	5.24897i	−0.731581	+	0.196027i
$718$	−6.01247	+	1.61104i	−0.224383	+	0.0601233i
$719$	9.66239	+	16.7357i	0.360346	+	0.624138i	0.988018	−	0.154340i	$-0.0493252\pi$
$719$	9.66239	+	16.7357i	0.360346	+	0.624138i	−0.627671	+	0.778478i	$0.715992\pi$
$720$	1.66319	−	0.870061i	0.0619832	−	0.0324253i
$721$		0			0
$722$	−10.2601	+	10.2601i	−0.381841	+	0.381841i
$723$	−0.716912	+	2.67555i	−0.0266622	+	0.0995048i
$724$	−6.00966	+	10.4090i	−0.223347	+	0.386849i
$725$	−12.5335	+	5.90607i	−0.465484	+	0.219346i
$726$	−2.53566	+	1.46396i	−0.0941072	+	0.0543328i
$727$	2.71795	+	2.71795i	0.100803	+	0.100803i	0.755710	−	0.654907i	$-0.227292\pi$
$727$	2.71795	+	2.71795i	0.100803	+	0.100803i	−0.654907	+	0.755710i	$0.727292\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	19.4853	+	12.3584i	0.721185	+	0.457406i
$731$	7.15181	+	4.12910i	0.264519	+	0.152720i
$732$	5.24652	+	19.5803i	0.193917	+	0.723709i
$733$	3.25711	+	0.872739i	0.120304	+	0.0322354i	0.318469	−	0.947933i	$-0.396831\pi$
$733$	3.25711	+	0.872739i	0.120304	+	0.0322354i	−0.198165	+	0.980169i	$0.563498\pi$
$734$	15.9321			0.588064
$735$		0			0
$736$	4.42747			0.163199
$737$	2.19118	+	0.587125i	0.0807132	+	0.0216270i
$738$	−1.71624	−	6.40510i	−0.0631757	−	0.235775i
$739$	4.29271	+	2.47840i	0.157910	+	0.0911693i	0.576873	−	0.816834i	$-0.304273\pi$
$739$	4.29271	+	2.47840i	0.157910	+	0.0911693i	−0.418963	+	0.908003i	$0.637606\pi$
$740$	−27.0471	+	6.05337i	−0.994270	+	0.222526i
$741$			0.361923i			0.0132956i
$742$		0			0
$743$	15.6556	+	15.6556i	0.574347	+	0.574347i	0.933340	−	0.358993i	$-0.116880\pi$
$743$	15.6556	+	15.6556i	0.574347	+	0.574347i	−0.358993	+	0.933340i	$0.616880\pi$
$744$	5.41695	−	3.12748i	0.198595	−	0.114659i
$745$	−1.02782	+	24.6817i	−0.0376566	+	0.904266i
$746$	−0.807303	+	1.39829i	−0.0295575	+	0.0511950i
$747$	−0.598706	+	2.23440i	−0.0219055	+	0.0817525i
$748$	8.12896	−	8.12896i	0.297224	−	0.297224i
$749$		0			0
$750$	1.06357	−	8.47393i	0.0388360	−	0.309424i
$751$	5.59544	+	9.69159i	0.204181	+	0.353651i	0.949871	−	0.312641i	$-0.101214\pi$
$751$	5.59544	+	9.69159i	0.204181	+	0.353651i	−0.745691	+	0.666292i	$0.767880\pi$
$752$	6.29575	−	1.68694i	0.229582	−	0.0615164i
$753$	−5.89197	+	1.57875i	−0.214715	+	0.0575328i
$754$	−5.49042	−	9.50969i	−0.199949	−	0.346322i
$755$	−19.0704	−	36.4545i	−0.694045	−	1.32672i
$756$		0			0
$757$	29.4977	−	29.4977i	1.07211	−	1.07211i	0.0749214	−	0.997189i	$-0.476129\pi$
$757$	29.4977	−	29.4977i	1.07211	−	1.07211i	0.997189	−	0.0749214i	$-0.0238706\pi$
$758$	3.69977	−	13.8077i	0.134382	−	0.501520i
$759$	−1.45473	+	2.51967i	−0.0528035	+	0.0914584i
$760$	0.275662	+	0.299619i	0.00999932	+	0.0108683i
$761$	−24.3504	+	14.0587i	−0.882703	+	0.509629i	−0.871549	−	0.490309i	$-0.836884\pi$
$761$	−24.3504	+	14.0587i	−0.882703	+	0.509629i	−0.0111541	+	0.999938i	$0.503551\pi$
$762$	3.69181	+	3.69181i	0.133740	+	0.133740i
$763$		0			0
$764$		−	7.63986i		−	0.276400i
$765$	1.02913	+	4.59826i	0.0372083	+	0.166251i
$766$	19.5862	+	11.3081i	0.707679	+	0.408579i
$767$	9.36412	+	34.9474i	0.338119	+	1.26188i
$768$	12.4771	+	3.34324i	0.450230	+	0.120639i
$769$	6.61248			0.238452			0.119226	−	0.992867i	$-0.461959\pi$
$769$	6.61248			0.238452			0.119226	+	0.992867i	$0.461959\pi$
$770$		0			0
$771$	−2.85449			−0.102802
$772$	−9.29941	−	2.49177i	−0.334693	−	0.0896807i
$773$	11.6120	+	43.3367i	0.417656	+	1.55871i	0.779456	+	0.626457i	$0.215496\pi$
$773$	11.6120	+	43.3367i	0.417656	+	1.55871i	−0.361800	+	0.932256i	$0.617838\pi$
$774$	−2.59249	−	1.49678i	−0.0931853	−	0.0538005i
$775$	−0.996351	+	11.9422i	−0.0357900	+	0.428976i
$776$			25.3133i			0.908695i
$777$		0			0
$778$	13.8607	+	13.8607i	0.496929	+	0.496929i
$779$	−0.524495	+	0.302817i	−0.0187920	+	0.0108496i
$780$	−16.4167	−	0.683645i	−0.587812	−	0.0244784i
$781$	−15.6516	+	27.1094i	−0.560058	+	0.970049i
$782$	−0.314733	+	1.17460i	−0.0112548	+	0.0420035i
$783$	−1.95945	+	1.95945i	−0.0700249	+	0.0700249i
$784$		0			0
$785$	−0.992027	+	3.16855i	−0.0354070	+	0.113090i
$786$	0.247305	+	0.428345i	0.00882108	+	0.0152786i
$787$	−30.6634	+	8.21624i	−1.09303	+	0.292877i	−0.759924	−	0.650011i	$-0.774764\pi$
$787$	−30.6634	+	8.21624i	−1.09303	+	0.292877i	−0.333108	+	0.942889i	$0.608097\pi$
$788$	−24.5236	+	6.57108i	−0.873617	+	0.234085i
$789$	−11.8572	−	20.5372i	−0.422127	−	0.731145i
$790$	5.03372	−	16.0777i	0.179092	−	0.572021i
$791$		0			0
$792$	−7.10728	+	7.10728i	−0.252546	+	0.252546i
$793$	19.2142	−	71.7082i	0.682315	−	2.54643i
$794$	−3.63833	+	6.30177i	−0.129119	+	0.223641i
$795$	19.3940	+	0.807629i	0.687834	+	0.0286436i
$796$	−3.27670	+	1.89180i	−0.116139	+	0.0670531i
$797$	5.14677	+	5.14677i	0.182308	+	0.182308i	0.792361	−	0.610053i	$-0.208852\pi$
$797$	5.14677	+	5.14677i	0.182308	+	0.182308i	−0.610053	+	0.792361i	$0.708852\pi$
$798$		0			0
$799$			16.3622i			0.578854i
$800$	−22.3720	+	18.9265i	−0.790971	+	0.669151i
$801$	−4.37614	−	2.52657i	−0.154623	−	0.0892718i
$802$	2.91622	+	10.8835i	0.102975	+	0.384309i
$803$	50.2541	+	13.4656i	1.77343	+	0.475189i
$804$	0.834323			0.0294243
$805$		0			0
$806$	−9.49747			−0.334534
$807$	−23.8923	−	6.40192i	−0.841049	−	0.225358i
$808$	−12.9657	−	48.3885i	−0.456130	−	1.70230i
$809$	19.5042	+	11.2608i	0.685732	+	0.395907i	0.802011	−	0.597309i	$-0.203763\pi$
$809$	19.5042	+	11.2608i	0.685732	+	0.395907i	−0.116279	+	0.993217i	$0.537097\pi$
$810$	−0.373055	−	1.66685i	−0.0131078	−	0.0585670i
$811$			34.9145i			1.22602i	0.790077	+	0.613008i	$0.210040\pi$
$811$			34.9145i			1.22602i	−0.790077	+	0.613008i	$0.789960\pi$
$812$		0			0
$813$	−2.92367	−	2.92367i	−0.102538	−	0.102538i
$814$	22.2948	−	12.8719i	0.781432	−	0.451160i
$815$	11.7876	+	12.8120i	0.412900	+	0.448784i
$816$	0.884454	−	1.53192i	0.0309621	−	0.0536279i
$817$	−0.0707639	+	0.264094i	−0.00247572	+	0.00923949i
$818$	5.70414	−	5.70414i	0.199441	−	0.199441i
$819$		0			0
$820$	−12.7450	−	24.3629i	−0.445074	−	0.850790i
$821$	−4.26320	−	7.38408i	−0.148787	−	0.257706i	0.781993	−	0.623288i	$-0.214203\pi$
$821$	−4.26320	−	7.38408i	−0.148787	−	0.257706i	−0.930779	+	0.365582i	$0.880870\pi$
$822$	10.6820	−	2.86222i	0.372576	−	0.0998315i
$823$	46.3143	−	12.4099i	1.61441	−	0.432581i	0.665060	−	0.746790i	$-0.268406\pi$
$823$	46.3143	−	12.4099i	1.61441	−	0.432581i	0.949354	+	0.314209i	$0.101739\pi$
$824$	−4.31498	−	7.47377i	−0.150320	−	0.260361i
$825$	−3.42027	−	18.9506i	−0.119079	−	0.659776i
$826$		0			0
$827$	−37.8440	+	37.8440i	−1.31597	+	1.31597i	−0.399025	+	0.916940i	$0.630651\pi$
$827$	−37.8440	+	37.8440i	−1.31597	+	1.31597i	−0.916940	+	0.399025i	$0.869349\pi$
$828$	−0.276955	+	1.03361i	−0.00962486	+	0.0359205i
$829$	16.8570	−	29.1972i	0.585469	−	1.01406i	−0.409348	−	0.912378i	$-0.634244\pi$
$829$	16.8570	−	29.1972i	0.585469	−	1.01406i	0.994817	−	0.101683i	$-0.0324228\pi$
$830$	0.164397	−	3.94776i	0.00570632	−	0.137029i
$831$	14.8350	−	8.56502i	0.514622	−	0.297117i
$832$	−10.2638	−	10.2638i	−0.355832	−	0.355832i
$833$		0			0
$834$			16.9323i			0.586319i
$835$	−5.83142	+	1.30512i	−0.201805	+	0.0451656i
$836$	0.329618	+	0.190305i	0.0114001	+	0.00658184i
$837$	0.620321	+	2.31507i	0.0214414	+	0.0800205i
$838$	−11.4715	−	3.07378i	−0.396277	−	0.106182i
$839$	−16.0665			−0.554679			−0.277339	−	0.960772i	$-0.589453\pi$
$839$	−16.0665			−0.554679			−0.277339	+	0.960772i	$0.589453\pi$
$840$		0			0
$841$	21.3211			0.735212
$842$	−2.43406	−	0.652204i	−0.0838832	−	0.0224764i
$843$	1.35952	+	5.07381i	0.0468245	+	0.174751i
$844$	14.7499	+	8.51585i	0.507712	+	0.293128i
$845$	26.2678	+	16.6601i	0.903639	+	0.573126i
$846$		−	5.93123i		−	0.203920i
$847$		0			0
$848$	−5.15260	−	5.15260i	−0.176941	−	0.176941i
$849$	2.04201	−	1.17895i	0.0700814	−	0.0404615i
$850$	−3.43081	−	7.28067i	−0.117676	−	0.249725i
$851$	3.30525	−	5.72486i	0.113303	−	0.196246i
$852$	−2.97978	+	11.1207i	−0.102086	+	0.380989i
$853$	5.14393	−	5.14393i	0.176125	−	0.176125i	−0.613539	−	0.789664i	$-0.710255\pi$
$853$	5.14393	−	5.14393i	0.176125	−	0.176125i	0.789664	+	0.613539i	$0.210255\pi$
$854$		0			0
$855$	−0.138232	+	0.0723134i	−0.00472745	+	0.00247307i
$856$	11.8059	+	20.4483i	0.403516	+	0.698910i
$857$	7.71909	−	2.06832i	0.263679	−	0.0706526i	−0.124557	−	0.992212i	$-0.539751\pi$
$857$	7.71909	−	2.06832i	0.263679	−	0.0706526i	0.388236	+	0.921560i	$0.373084\pi$
$858$	14.7416	−	3.95001i	0.503271	−	0.134851i
$859$	−21.0400	−	36.4424i	−0.717877	−	1.24340i	−0.961839	−	0.273615i	$-0.911781\pi$
$859$	−21.0400	−	36.4424i	−0.717877	−	1.24340i	0.243963	−	0.969785i	$-0.421553\pi$
$860$	−11.8456	−	3.70868i	−0.403931	−	0.126465i
$861$		0			0
$862$	−7.61119	+	7.61119i	−0.259238	+	0.259238i
$863$	−4.38413	+	16.3618i	−0.149237	+	0.556962i	0.850293	+	0.526310i	$0.176425\pi$
$863$	−4.38413	+	16.3618i	−0.149237	+	0.556962i	−0.999530	+	0.0306516i	$0.990242\pi$
$864$	−2.93039	+	5.07559i	−0.0996939	+	0.172675i
$865$	−11.4206	+	10.5074i	−0.388312	+	0.357264i
$866$	1.61524	−	0.932557i	0.0548879	−	0.0316896i
$867$	−8.88082	−	8.88082i	−0.301608	−	0.301608i
$868$		0			0
$869$		−	37.9871i		−	1.28862i
$870$	2.53511	−	3.99708i	0.0859484	−	0.135514i
$871$	−2.64615	−	1.52776i	−0.0896614	−	0.0517660i
$872$	−1.45938	−	5.44649i	−0.0494209	−	0.184441i
$873$	−9.36890	−	2.51039i	−0.317089	−	0.0849638i
$874$	−0.0402602			−0.00136182
$875$		0			0
$876$	19.1350			0.646510
$877$	15.8208	+	4.23918i	0.534232	+	0.143147i	0.515842	−	0.856684i	$-0.327479\pi$
$877$	15.8208	+	4.23918i	0.534232	+	0.143147i	0.0183902	+	0.999831i	$0.494146\pi$
$878$	−5.36123	−	20.0084i	−0.180933	−	0.675250i
$879$	−18.6842	−	10.7873i	−0.630202	−	0.363847i
$880$	−3.87189	+	6.10474i	−0.130521	+	0.205791i
$881$		−	8.72058i		−	0.293804i	−0.989151	−	0.146902i	$-0.953070\pi$
$881$		−	8.72058i		−	0.293804i	0.989151	−	0.146902i	$-0.0469301\pi$
$882$		0			0
$883$	17.0876	+	17.0876i	0.575044	+	0.575044i	0.933534	−	0.358490i	$-0.116708\pi$
$883$	17.0876	+	17.0876i	0.575044	+	0.575044i	−0.358490	+	0.933534i	$0.616708\pi$
$884$	−13.4100	+	7.74229i	−0.451028	+	0.260401i
$885$	−11.4768	+	10.5591i	−0.385787	+	0.354941i
$886$	13.0445	−	22.5938i	0.438240	−	0.759054i
$887$	9.66396	−	36.0664i	0.324484	−	1.21099i	−0.590346	−	0.807151i	$-0.701009\pi$
$887$	9.66396	−	36.0664i	0.324484	−	1.21099i	0.914830	−	0.403840i	$-0.132325\pi$
$888$	16.1482	−	16.1482i	0.541898	−	0.541898i
$889$		0			0
$890$	8.23690	+	2.57886i	0.276101	+	0.0864435i
$891$	−1.92568	−	3.33538i	−0.0645127	−	0.111739i
$892$	22.6246	−	6.06223i	0.757526	−	0.202979i
$893$	−0.523259	+	0.140207i	−0.0175102	+	0.00469184i
$894$	−4.21949	−	7.30836i	−0.141121	−	0.244428i
$895$	−36.8244	+	19.2639i	−1.23090	+	0.643922i
$896$		0			0
$897$	2.77107	−	2.77107i	0.0925235	−	0.0925235i
$898$	−1.93805	+	7.23289i	−0.0646735	+	0.241365i
$899$	−3.32077	+	5.75174i	−0.110754	+	0.191831i
$900$	−3.01901	−	6.40677i	−0.100634	−	0.213559i
$901$	15.8420	−	9.14640i	0.527775	−	0.304711i
$902$	18.0585	+	18.0585i	0.601282	+	0.601282i
$903$		0			0
$904$		−	15.2733i		−	0.507984i
$905$	16.0227	+	10.1623i	0.532613	+	0.337806i
$906$	12.1716	+	7.02729i	0.404375	+	0.233466i
$907$	−8.65482	−	32.3002i	−0.287379	−	1.07251i	−0.947084	−	0.320987i	$-0.895985\pi$
$907$	−8.65482	−	32.3002i	−0.287379	−	1.07251i	0.659705	−	0.751525i	$-0.270681\pi$
$908$	2.13848	+	0.573005i	0.0709681	+	0.0190158i
$909$	19.1953			0.636667
$910$		0			0
$911$	−17.8226			−0.590490			−0.295245	−	0.955422i	$-0.595401\pi$
$911$	−17.8226			−0.590490			−0.295245	+	0.955422i	$0.595401\pi$
$912$	0.0565691	+	0.0151576i	0.00187319	+	0.000501920i
$913$	−2.30583	−	8.60549i	−0.0763120	−	0.284800i
$914$	0.514622	+	0.297117i	0.0170222	+	0.00982776i
$915$	31.2272	−	6.98892i	1.03234	−	0.231047i
$916$			11.0955i			0.366605i
$917$		0			0
$918$	−1.13823	−	1.13823i	−0.0375673	−	0.0375673i
$919$	−18.6847	+	10.7876i	−0.616351	+	0.355850i	−0.775447	−	0.631413i	$-0.782475\pi$
$919$	−18.6847	+	10.7876i	−0.616351	+	0.355850i	0.159096	+	0.987263i	$0.449142\pi$
$920$	0.183424	−	4.40466i	0.00604732	−	0.145217i
$921$	10.3377	−	17.9055i	0.340640	−	0.590005i
$922$	−0.164449	+	0.613733i	−0.00541585	+	0.0202122i
$923$	29.8142	−	29.8142i	0.981346	−	0.981346i
$924$		0			0
$925$	7.77107	+	43.0570i	0.255511	+	1.41571i
$926$	−2.94454	−	5.10009i	−0.0967636	−	0.167599i
$927$	3.19410	−	0.855857i	0.104908	−	0.0281100i
$928$	−15.6873	+	4.20339i	−0.514960	+	0.137983i
$929$	−19.1535	−	33.1748i	−0.628405	−	1.08843i	−0.987872	−	0.155272i	$-0.950375\pi$
$929$	−19.1535	−	33.1748i	−0.628405	−	1.08843i	0.359467	−	0.933158i	$-0.382959\pi$
$930$	−1.89763	−	3.62745i	−0.0622257	−	0.118949i
$931$		0			0
$932$	−1.42778	+	1.42778i	−0.0467686	+	0.0467686i
$933$	−0.740787	+	2.76465i	−0.0242523	+	0.0905107i
$934$	12.5760	−	21.7823i	0.411500	−	0.712739i
$935$	−12.2873	−	13.3552i	−0.401838	−	0.436760i
$936$	11.7246	−	6.76921i	0.383231	−	0.221258i
$937$	13.2317	+	13.2317i	0.432262	+	0.432262i	0.889397	−	0.457135i	$-0.151125\pi$
$937$	13.2317	+	13.2317i	0.432262	+	0.432262i	−0.457135	+	0.889397i	$0.651125\pi$
$938$		0			0
$939$			13.3194i			0.434662i
$940$	−5.37134	−	23.9997i	−0.175194	−	0.782784i
$941$	−2.23517	−	1.29048i	−0.0728645	−	0.0420683i	0.463125	−	0.886293i	$-0.346728\pi$
$941$	−2.23517	−	1.29048i	−0.0728645	−	0.0420683i	−0.535990	+	0.844225i	$0.680061\pi$
$942$	−0.293563	−	1.09559i	−0.00956479	−	0.0356963i
$943$	6.33435	+	1.69728i	0.206275	+	0.0552711i
$944$	5.85450			0.190548
$945$		0			0
$946$	11.5293			0.374848
$947$	−6.75097	−	1.80892i	−0.219377	−	0.0587819i	0.147456	−	0.989069i	$-0.452891\pi$
$947$	−6.75097	−	1.80892i	−0.219377	−	0.0587819i	−0.366833	+	0.930287i	$0.619558\pi$
$948$	−3.61603	−	13.4952i	−0.117443	−	0.438304i
$949$	−60.6887	−	35.0387i	−1.97004	−	1.13740i
$950$	0.203435	−	0.172104i	0.00660031	−	0.00558378i
$951$		−	10.4413i		−	0.338582i
$952$		0			0
$953$	−16.3558	−	16.3558i	−0.529818	−	0.529818i	0.390700	−	0.920518i	$-0.372233\pi$
$953$	−16.3558	−	16.3558i	−0.529818	−	0.529818i	−0.920518	+	0.390700i	$0.872233\pi$
$954$	−5.74266	+	3.31552i	−0.185925	+	0.107344i
$955$	−12.0498	−	0.501793i	−0.389923	−	0.0162376i
$956$	14.3636	−	24.8784i	0.464551	−	0.804625i
$957$	2.76222	−	10.3088i	0.0892900	−	0.333235i
$958$	−21.8390	+	21.8390i	−0.705587	+	0.705587i
$959$		0			0
$960$	1.86939	−	5.97087i	0.0603345	−	0.192709i
$961$	−12.6278	−	21.8720i	−0.407349	−	0.705550i
$962$	−33.4939	+	8.97467i	−1.07989	+	0.289355i
$963$	−8.73911	+	2.34164i	−0.281614	+	0.0754582i
$964$	−1.96179	−	3.39793i	−0.0631851	−	0.109440i
$965$	−4.54089	+	14.5036i	−0.146176	+	0.466889i
$966$		0			0
$967$	8.66781	−	8.66781i	0.278738	−	0.278738i	−0.553867	−	0.832605i	$-0.686848\pi$
$967$	8.66781	−	8.66781i	0.278738	−	0.278738i	0.832605	+	0.553867i	$0.186848\pi$
$968$	2.58903	−	9.66239i	0.0832146	−	0.310561i
$969$	−0.0735096	+	0.127322i	−0.00236147	+	0.00409019i
$970$	16.5530	+	0.689322i	0.531486	+	0.0221328i
$971$	11.4195	−	6.59307i	0.366470	−	0.211582i	−0.305445	−	0.952210i	$-0.598805\pi$
$971$	11.4195	−	6.59307i	0.366470	−	0.211582i	0.671915	+	0.740628i	$0.265472\pi$
$972$	−1.00161	−	1.00161i	−0.0321267	−	0.0321267i
$973$		0			0
$974$			7.80931i			0.250226i
$975$	−2.15653	+	25.8480i	−0.0690643	+	0.827799i
$976$	−10.4034	−	6.00641i	−0.333005	−	0.192260i
$977$	−8.96490	−	33.4574i	−0.286812	−	1.07040i	−0.947505	−	0.319742i	$-0.896404\pi$
$977$	−8.96490	−	33.4574i	−0.286812	−	1.07040i	0.660692	−	0.750657i	$-0.270263\pi$
$978$	−5.74475	−	1.53930i	−0.183697	−	0.0492214i
$979$	19.4614			0.621990
$980$		0			0
$981$	2.16057			0.0689818
$982$	−14.8337	−	3.97468i	−0.473362	−	0.126837i
$983$	5.75986	+	21.4961i	0.183711	+	0.685618i	0.994903	+	0.100838i	$0.0321525\pi$
$983$	5.75986	+	21.4961i	0.183711	+	0.685618i	−0.811192	+	0.584780i	$0.801181\pi$
$984$	19.6197	+	11.3275i	0.625454	+	0.361106i
$985$	8.75336	+	39.1109i	0.278905	+	1.24618i
$986$		−	4.46061i		−	0.142055i
$987$		0			0
$988$	−0.362505	−	0.362505i	−0.0115328	−	0.0115328i
$989$	2.56386	−	1.48024i	0.0815259	−	0.0470690i
$990$	4.45409	+	4.84118i	0.141560	+	0.153863i
$991$	15.0516	−	26.0701i	0.478128	−	0.828142i	−0.521557	−	0.853216i	$-0.674649\pi$
$991$	15.0516	−	26.0701i	0.478128	−	0.828142i	0.999686	+	0.0250738i	$0.00798206\pi$
$992$	−3.63557	+	13.5681i	−0.115429	+	0.430788i
$993$	16.7019	−	16.7019i	0.530018	−	0.530018i
$994$		0			0
$995$	2.76859	+	5.29236i	0.0877702	+	0.167779i
$996$	−1.63833	−	2.83767i	−0.0519125	−	0.0899150i
$997$	31.2439	−	8.37177i	0.989503	−	0.265137i	0.272461	−	0.962167i	$-0.412162\pi$
$997$	31.2439	−	8.37177i	0.989503	−	0.265137i	0.717042	+	0.697030i	$0.245496\pi$
$998$	−11.3796	+	3.04916i	−0.360215	+	0.0965194i
$999$	4.37527	+	7.57819i	0.138427	+	0.239763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.v.a.178.4		32
5.2	odd	4	inner	735.2.v.a.472.6		32
7.2	even	3	inner	735.2.v.a.313.5		32
7.3	odd	6		105.2.m.a.13.5	✓	16
7.4	even	3		105.2.m.a.13.6	yes	16
7.5	odd	6	inner	735.2.v.a.313.6		32
7.6	odd	2	inner	735.2.v.a.178.3		32
21.11	odd	6		315.2.p.e.118.4		16
21.17	even	6		315.2.p.e.118.3		16
28.3	even	6		1680.2.cz.d.433.7		16
28.11	odd	6		1680.2.cz.d.433.2		16
35.2	odd	12	inner	735.2.v.a.607.3		32
35.3	even	12		525.2.m.b.307.3		16
35.4	even	6		525.2.m.b.118.3		16
35.12	even	12	inner	735.2.v.a.607.4		32
35.17	even	12		105.2.m.a.97.6	yes	16
35.18	odd	12		525.2.m.b.307.4		16
35.24	odd	6		525.2.m.b.118.4		16
35.27	even	4	inner	735.2.v.a.472.5		32
35.32	odd	12		105.2.m.a.97.5	yes	16
105.17	odd	12		315.2.p.e.307.4		16
105.32	even	12		315.2.p.e.307.3		16
140.67	even	12		1680.2.cz.d.97.7		16
140.87	odd	12		1680.2.cz.d.97.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	7.3	odd	6
105.2.m.a.13.6	yes	16	7.4	even	3
105.2.m.a.97.5	yes	16	35.32	odd	12
105.2.m.a.97.6	yes	16	35.17	even	12
315.2.p.e.118.3		16	21.17	even	6
315.2.p.e.118.4		16	21.11	odd	6
315.2.p.e.307.3		16	105.32	even	12
315.2.p.e.307.4		16	105.17	odd	12
525.2.m.b.118.3		16	35.4	even	6
525.2.m.b.118.4		16	35.24	odd	6
525.2.m.b.307.3		16	35.3	even	12
525.2.m.b.307.4		16	35.18	odd	12
735.2.v.a.178.3		32	7.6	odd	2	inner
735.2.v.a.178.4		32	1.1	even	1	trivial
735.2.v.a.313.5		32	7.2	even	3	inner
735.2.v.a.313.6		32	7.5	odd	6	inner
735.2.v.a.472.5		32	35.27	even	4	inner
735.2.v.a.472.6		32	5.2	odd	4	inner
735.2.v.a.607.3		32	35.2	odd	12	inner
735.2.v.a.607.4		32	35.12	even	12	inner
1680.2.cz.d.97.2		16	140.87	odd	12
1680.2.cz.d.97.7		16	140.67	even	12
1680.2.cz.d.433.2		16	28.11	odd	6
1680.2.cz.d.433.7		16	28.3	even	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.737849 - 0.197706i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.22672 - 0.708245i) q^{4} +(-1.19764 + 1.88830i) q^{5} -0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.25700 - 1.15650i) q^{10} +(1.92568 - 3.33538i) q^{11} +(0.366615 - 1.36822i) q^{12} +(-3.66816 + 3.66816i) q^{13} +(-2.13393 - 0.668102i) q^{15} +(0.419714 + 0.726965i) q^{16} +(-2.03548 + 0.545404i) q^{17} +(0.737849 - 0.197706i) q^{18} +(-0.0348837 - 0.0604203i) q^{19} +(2.80654 - 1.46818i) q^{20} +(-2.08029 + 2.08029i) q^{22} +(-0.195522 + 0.729698i) q^{23} +(-1.30489 + 2.26014i) q^{24} +(-2.13133 - 4.52299i) q^{25} +(3.43177 - 1.98133i) q^{26} +(-0.707107 - 0.707107i) q^{27} -2.77107i q^{29} +(1.44243 + 0.914849i) q^{30} +(-2.07564 - 1.19837i) q^{31} +(-1.51688 - 5.66108i) q^{32} +(3.72013 + 0.996806i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(-8.45237 - 2.26481i) q^{37} +(0.0137934 + 0.0514778i) q^{38} +(-4.49256 - 2.59378i) q^{39} +(-5.69477 + 1.27454i) q^{40} -8.68077i q^{41} +(-2.77107 - 2.77107i) q^{43} +(-4.72453 + 2.72771i) q^{44} +(0.0930365 - 2.23413i) q^{45} +(0.288532 - 0.499752i) q^{46} +(2.00963 - 7.50006i) q^{47} +(-0.593565 + 0.593565i) q^{48} +(0.678376 + 3.75866i) q^{50} +(-1.05364 - 1.82496i) q^{51} +(7.09776 - 1.90184i) q^{52} +(-8.38498 + 2.24675i) q^{53} +(0.381939 + 0.661538i) q^{54} +(3.99191 + 7.63083i) q^{55} +(0.0493330 - 0.0493330i) q^{57} +(-0.547858 + 2.04464i) q^{58} +(3.48720 - 6.04001i) q^{59} +(2.14454 + 2.33092i) q^{60} +(-12.3935 + 7.15536i) q^{61} +(1.29458 + 1.29458i) q^{62} +2.79807i q^{64} +(-2.53345 - 11.3197i) q^{65} +(-2.54782 - 1.47098i) q^{66} +(0.152446 + 0.568937i) q^{67} +(2.88323 + 0.772560i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(-2.52086 - 0.675461i) q^{72} +(3.49631 + 13.0484i) q^{73} +(5.78881 + 3.34217i) q^{74} +(3.81725 - 3.22934i) q^{75} +0.0988248i q^{76} +(2.80203 + 2.80203i) q^{78} +(8.54186 - 4.93165i) q^{79} +(-1.87539 - 0.0780974i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.71624 + 6.40510i) q^{82} +(1.63570 - 1.63570i) q^{83} +(1.40788 - 4.49678i) q^{85} +(1.49678 + 2.59249i) q^{86} +(2.67665 - 0.717207i) q^{87} +(9.70872 - 2.60144i) q^{88} +(2.52657 + 4.37614i) q^{89} +(-0.510348 + 1.63006i) q^{90} +(0.756656 - 0.756656i) q^{92} +(0.620321 - 2.31507i) q^{93} +(-2.96561 + 5.13659i) q^{94} +(0.155869 + 0.00649091i) q^{95} +(5.07559 - 2.93039i) q^{96} +(6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 48 q^{8}+O(q^{10}) \) 32 * q + 48 * q^8	\( 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

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