LMFDB - Embedded newform 735.2.v.a.607.4

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			607.4
Character	$\chi$	$=$	735.607
Dual form			735.2.v.a.178.4

$q$-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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.737849	+	0.197706i	−0.521738	+	0.139799i	−0.510071	−	0.860133i	$-0.670381\pi$
$2$	−0.737849	+	0.197706i	−0.521738	+	0.139799i	−0.0116677	+	0.999932i	$0.503714\pi$
$3$	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	0.995407	+	0.0957376i	$0.0305210\pi$
$11$	1.92568	+	3.33538i	0.580615	+	1.00565i	−0.414792	+	0.909916i	$0.636146\pi$
$12$	0.366615	+	1.36822i	0.105833	+	0.394973i
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.999847	−	0.0175187i	$-0.994423\pi$
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.0175187	−	0.999847i	$-0.505577\pi$
$14$		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	0.00338789	−	0.999994i	$-0.498922\pi$
$17$	−2.03548	−	0.545404i	−0.493675	−	0.132280i	−0.497063	+	0.867714i	$0.665588\pi$
$18$	0.737849	+	0.197706i	0.173913	+	0.0465998i
$19$	−0.0348837	+	0.0604203i	−0.00800286	+	0.0138614i	−0.869999	−	0.493053i	$-0.835881\pi$
$19$	−0.0348837	+	0.0604203i	−0.00800286	+	0.0138614i	0.861996	+	0.506915i	$0.169214\pi$
$20$	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	0.942541	−	0.334091i	$-0.108429\pi$
$23$	−0.195522	−	0.729698i	−0.0407692	−	0.152153i	−0.983310	+	0.181939i	$0.941763\pi$
$24$	−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	$0.0828288\pi$
$29$			2.77107i			0.514576i	−0.966335	+	0.257288i	$0.917171\pi$
$30$	1.44243	−	0.914849i	0.263350	−	0.167028i
$31$	−2.07564	+	1.19837i	−0.372795	+	0.215233i	−0.674679	−	0.738111i	$-0.735718\pi$
$31$	−2.07564	+	1.19837i	−0.372795	+	0.215233i	0.301884	+	0.953345i	$0.402385\pi$
$32$	−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	−0.874585	−	0.484872i	$-0.838866\pi$
$37$	−8.45237	+	2.26481i	−1.38956	+	0.372332i	−0.514976	+	0.857204i	$0.672199\pi$
$38$	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	$0.237090\pi$
$41$			8.68077i			1.35571i	−0.735196	+	0.677854i	$0.762910\pi$
$42$		0			0
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	−0.886093	−	0.463508i	$-0.846591\pi$
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	0.463508	+	0.886093i	$0.346591\pi$
$44$	−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	0.942687	+	0.333678i	$0.108290\pi$
$47$	2.00963	+	7.50006i	0.293135	+	1.09400i	−0.649552	+	0.760317i	$0.725043\pi$
$48$	−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	−0.368093	−	0.929789i	$-0.619989\pi$
$53$	−8.38498	−	2.24675i	−1.15177	−	0.308615i	−0.783673	+	0.621174i	$0.786656\pi$
$54$	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	0.998630	−	0.0523310i	$-0.0166651\pi$
$59$	3.48720	+	6.04001i	0.453995	+	0.786342i	−0.544635	+	0.838673i	$0.683332\pi$
$60$	2.14454	−	2.33092i	0.276859	−	0.300920i
$61$	−12.3935	−	7.15536i	−1.58682	−	0.916150i	−0.993827	−	0.110942i	$-0.964613\pi$
$61$	−12.3935	−	7.15536i	−1.58682	−	0.916150i	−0.592992	−	0.805208i	$-0.702054\pi$
$62$	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	−0.955988	−	0.293405i	$-0.905212\pi$
$67$	0.152446	−	0.568937i	0.0186243	−	0.0695067i	0.974613	+	0.223898i	$0.0718783\pi$
$68$	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	−0.386940	−	0.922105i	$-0.626468\pi$
$73$	3.49631	−	13.0484i	0.409212	−	1.52720i	0.796152	−	0.605096i	$-0.206865\pi$
$74$	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	0.896491	−	0.443061i	$-0.146108\pi$
$79$	8.54186	+	4.93165i	0.961035	+	0.554854i	0.0645434	+	0.997915i	$0.479441\pi$
$80$	−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	0.791156	−	0.611615i	$-0.209480\pi$
$83$	1.63570	+	1.63570i	0.179541	+	0.179541i	−0.611615	+	0.791156i	$0.709480\pi$
$84$		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	−0.700482	−	0.713670i	$-0.747032\pi$
$89$	2.52657	−	4.37614i	0.267815	−	0.463870i	0.968297	+	0.249800i	$0.0803649\pi$
$90$	−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	−0.267251	−	0.963627i	$-0.586115\pi$
$97$	6.85851	−	6.85851i	0.696376	−	0.696376i	0.963627	+	0.267251i	$0.0861152\pi$
$98$		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	−0.678752	+	0.734368i	$0.737479\pi$
$101$	−16.6236	+	9.59763i	−1.65411	+	0.955000i	−0.975357	+	0.220632i	$0.929188\pi$
$102$	0.416622	−	1.55485i	0.0412517	−	0.153954i
$103$	−3.19410	+	0.855857i	−0.314724	+	0.0843301i	−0.412723	−	0.910856i	$-0.635422\pi$
$103$	−3.19410	+	0.855857i	−0.314724	+	0.0843301i	0.0979992	+	0.995186i	$0.468756\pi$
$104$	−13.5384			−1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	8.73911	−	2.34164i	0.844841	−	0.226375i	0.189663	−	0.981849i	$-0.439260\pi$
$107$	8.73911	−	2.34164i	0.844841	−	0.226375i	0.655178	+	0.755475i	$0.272594\pi$
$108$	0.366615	−	1.36822i	0.0352775	−	0.131658i
$109$	−1.87111	+	1.08029i	−0.179220	+	0.103473i	−0.586926	−	0.809641i	$-0.699662\pi$
$109$	−1.87111	+	1.08029i	−0.179220	+	0.103473i	0.407706	+	0.913113i	$0.366329\pi$
$110$	−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	−0.874435	−	0.485143i	$-0.838768\pi$
$113$	−4.13823	+	4.13823i	−0.389292	+	0.389292i	0.485143	+	0.874435i	$0.338768\pi$
$114$	−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	0.459381	−	0.888239i	$-0.348071\pi$
$127$	−4.83298	−	4.83298i	−0.428858	−	0.428858i	−0.888239	+	0.459381i	$0.848071\pi$
$128$	−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	0.475303	−	0.879822i	$-0.342338\pi$
$131$	−0.560750	−	0.323749i	−0.0489930	−	0.0282861i	−0.524296	+	0.851536i	$0.675672\pi$
$132$	−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	−0.598998	−	0.800751i	$-0.704434\pi$
$137$	3.74696	−	13.9839i	0.320125	−	1.19472i	0.919123	−	0.393971i	$-0.128899\pi$
$138$	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	0.837774	−	0.546017i	$-0.183857\pi$
$149$	9.56745	+	5.52377i	0.783796	+	0.452525i	−0.0539779	+	0.998542i	$0.517190\pi$
$150$	−3.45501	−	1.62807i	−0.282101	−	0.132932i
$151$	−9.19950	−	15.9340i	−0.748645	−	1.29669i	−0.948472	−	0.316859i	$-0.897372\pi$
$151$	−9.19950	−	15.9340i	−0.748645	−	1.29669i	0.199828	−	0.979831i	$-0.435962\pi$
$152$	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	0.315597	−	0.948893i	$-0.397795\pi$
$157$	1.43425	+	0.384306i	0.114465	+	0.0306709i	−0.201132	+	0.979564i	$0.564462\pi$
$158$	−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	0.998846	+	0.0480317i	$0.0152948\pi$
$163$	2.01511	+	7.52050i	0.157836	+	0.589051i	−0.841010	+	0.541020i	$0.818038\pi$
$164$	−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	−0.630203	−	0.776431i	$-0.717028\pi$
$167$	1.88968	−	1.88968i	0.146228	−	0.146228i	0.776431	+	0.630203i	$0.217028\pi$
$168$		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	0.00519041	−	0.999987i	$-0.498348\pi$
$173$	6.70378	−	1.79627i	0.509679	−	0.136568i	0.504488	+	0.863419i	$0.331681\pi$
$174$	−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	0.241815	−	0.970322i	$-0.422257\pi$
$179$	16.0957	−	9.29284i	1.20305	−	0.694579i	0.961231	+	0.275743i	$0.0889239\pi$
$180$	−1.69644	−	2.67475i	−0.126445	−	0.199364i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		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	−0.751813	−	0.659377i	$-0.770820\pi$
$191$	2.69676	−	4.67092i	0.195130	−	0.337976i	0.946943	+	0.321401i	$0.104154\pi$
$192$	−2.70273	−	0.724193i	−0.195052	−	0.0522641i
$193$	6.56510	+	1.75911i	0.472566	+	0.126624i	0.487239	−	0.873269i	$-0.338004\pi$
$193$	6.56510	+	1.75911i	0.472566	+	0.126624i	−0.0146728	+	0.999892i	$0.504671\pi$
$194$	−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	0.995693	−	0.0927124i	$-0.0295537\pi$
$197$	12.6739	+	12.6739i	0.902981	+	0.902981i	−0.0927124	+	0.995693i	$0.529554\pi$
$198$	0.761438	+	2.84172i	0.0541130	+	0.201953i
$199$	1.33556	+	2.31325i	0.0946750	+	0.163982i	0.909473	−	0.415763i	$-0.136485\pi$
$199$	1.33556	+	2.31325i	0.0946750	+	0.163982i	−0.814798	+	0.579745i	$0.803152\pi$
$200$	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	0.197346	−	0.980334i	$-0.436768\pi$
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	−0.980334	+	0.197346i	$0.936768\pi$
$224$		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	0.208369	−	0.978050i	$-0.433184\pi$
$227$	−1.50971	−	0.404524i	−0.100203	−	0.0268492i	−0.308572	+	0.951201i	$0.599851\pi$
$228$	−0.0954574	−	0.0255777i	−0.00632182	−	0.00169393i
$229$	−3.91654	+	6.78365i	−0.258812	+	0.448276i	−0.965924	−	0.258826i	$-0.916664\pi$
$229$	−3.91654	+	6.78365i	−0.258812	+	0.448276i	0.707112	+	0.707102i	$0.249998\pi$
$230$	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	0.976957	−	0.213434i	$-0.0684649\pi$
$233$	0.368944	+	1.37692i	0.0241703	+	0.0902048i	−0.952787	+	0.303639i	$0.901798\pi$
$234$	−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	$-0.772282\pi$
$239$		−	20.2805i		−	1.31183i	0.754833	−	0.655917i	$-0.227718\pi$
$240$	−0.409951	+	1.83170i	−0.0264622	+	0.118236i
$241$	2.39883	−	1.38497i	0.154522	−	0.0892136i	−0.420745	−	0.907179i	$-0.638231\pi$
$241$	2.39883	−	1.38497i	0.154522	−	0.0892136i	0.575268	+	0.817965i	$0.304898\pi$
$242$	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	$-0.938338\pi$
$251$		−	6.09982i		−	0.385017i	0.981295	−	0.192509i	$-0.0616623\pi$
$252$		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	0.939048	−	0.343787i	$-0.111710\pi$
$257$	−0.738795	−	2.75722i	−0.0460848	−	0.171991i	−0.985133	+	0.171796i	$0.945043\pi$
$258$	−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	−0.529660	−	0.848210i	$-0.677681\pi$
$263$	−22.9063	−	6.13773i	−1.41246	−	0.378469i	−0.882804	+	0.469741i	$0.844347\pi$
$264$	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	−0.945838	−	0.324638i	$-0.894758\pi$
$269$	−12.3676	−	21.4213i	−0.754064	−	1.30608i	0.191774	−	0.981439i	$-0.438576\pi$
$270$	−1.70660	+	0.0710685i	−0.103861	+	0.00432509i
$271$	−3.58076	−	2.06735i	−0.217515	−	0.125583i	0.387284	−	0.921961i	$-0.373413\pi$
$271$	−3.58076	−	2.06735i	−0.217515	−	0.125583i	−0.604799	+	0.796378i	$0.706747\pi$
$272$	−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	0.695007	+	0.719003i	$0.255401\pi$
$277$	−4.43358	+	16.5463i	−0.266388	+	0.994174i	−0.961395	+	0.275171i	$0.911266\pi$
$278$	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	−0.981689	−	0.190489i	$-0.938993\pi$
$283$	−0.610271	+	2.27756i	−0.0362768	+	0.135387i	0.945412	+	0.325876i	$0.105659\pi$
$284$	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	0.103400	−	0.994640i	$-0.467028\pi$
$293$	−15.2556	−	15.2556i	−0.891240	−	0.891240i	−0.994640	+	0.103400i	$0.967028\pi$
$294$		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	−0.988114	−	0.153721i	$-0.950874\pi$
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	0.153721	+	0.988114i	$0.450874\pi$
$308$		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	−0.428073	−	0.903744i	$-0.640807\pi$
$311$	2.47872	−	1.43109i	0.140555	−	0.0811497i	0.568629	+	0.822594i	$0.307474\pi$
$312$	−3.50400	+	13.0771i	−0.198375	+	0.740345i
$313$	12.8656	−	3.44732i	0.727204	−	0.194854i	0.123820	−	0.992305i	$-0.460485\pi$
$313$	12.8656	−	3.44732i	0.727204	−	0.194854i	0.603384	+	0.797451i	$0.293819\pi$
$314$	−1.13424			−0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	−10.0855	+	2.70240i	−0.566459	+	0.151782i	−0.530672	−	0.847577i	$-0.678060\pi$
$317$	−10.0855	+	2.70240i	−0.566459	+	0.151782i	−0.0357866	+	0.999359i	$0.511394\pi$
$318$	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	0.334193	+	0.942505i	$0.391536\pi$
$331$	−11.8100	+	20.4555i	−0.649136	+	1.12434i	−0.983330	+	0.181833i	$0.941797\pi$
$332$	−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	0.559700	−	0.828695i	$-0.310916\pi$
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	−0.828695	+	0.559700i	$0.810916\pi$
$338$	−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	−0.884572	−	0.466404i	$-0.845549\pi$
$347$	2.13647	−	7.97341i	0.114692	−	0.428035i	0.999264	+	0.0383685i	$0.0122161\pi$
$348$	−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	0.768778	+	0.639516i	$0.220865\pi$
$353$	−4.07257	+	15.1990i	−0.216761	+	0.808963i	−0.985539	+	0.169448i	$0.945802\pi$
$354$	−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	0.674528	−	0.738249i	$-0.264347\pi$
$359$	7.05693	+	4.07432i	0.372450	+	0.215034i	−0.302078	+	0.953283i	$0.597680\pi$
$360$	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	−0.308700	−	0.951160i	$-0.599894\pi$
$367$	−20.1462	−	5.39815i	−1.05162	−	0.281781i	−0.742922	+	0.669378i	$0.766561\pi$
$368$	−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	0.978642	−	0.205574i	$-0.0659062\pi$
$373$	0.547065	+	2.04168i	0.0283260	+	0.105714i	−0.950316	+	0.311288i	$0.899240\pi$
$374$	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	$-0.840410\pi$
$379$		−	18.7135i		−	0.961248i	0.876927	−	0.480624i	$-0.159590\pi$
$380$	−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	−0.899940	−	0.436014i	$-0.856390\pi$
$383$	−28.5983	+	7.66288i	−1.46130	+	0.391555i	−0.561364	+	0.827569i	$0.689723\pi$
$384$	−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	−0.943118	−	0.332459i	$-0.892122\pi$
$389$	−22.2232	+	12.8305i	−1.12676	+	0.650535i	−0.183641	+	0.982993i	$0.558788\pi$
$390$	−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	0.999792	−	0.0204142i	$-0.00649848\pi$
$397$	2.46549	+	9.20135i	0.123740	+	0.461802i	−0.876052	+	0.482217i	$0.839832\pi$
$398$	−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	−0.989299	−	0.145900i	$-0.953392\pi$
$401$	−7.37513	+	12.7741i	−0.368296	+	0.637908i	0.621003	+	0.783808i	$0.286726\pi$
$402$	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	0.705442	−	0.708768i	$-0.250749\pi$
$409$	−5.28021	−	9.14560i	−0.261090	−	0.452221i	−0.966532	+	0.256547i	$0.917415\pi$
$410$	−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	0.984315	−	0.176422i	$-0.0564523\pi$
$431$	7.04553	+	12.2032i	0.339371	+	0.587809i	−0.644943	+	0.764230i	$0.723119\pi$
$432$	0.217260	+	0.810825i	0.0104529	+	0.0390108i
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	0.664404	−	0.747374i	$-0.268686\pi$
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	−0.747374	+	0.664404i	$0.768686\pi$
$434$		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	−0.336693	−	0.941615i	$-0.609308\pi$
$439$	13.5586	−	23.4841i	0.647116	−	1.12084i	0.983809	−	0.179223i	$-0.0573582\pi$
$440$	−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	−0.774645	−	0.632396i	$-0.782072\pi$
$443$	−8.83957	−	32.9897i	−0.419981	−	1.56739i	0.354664	−	0.934994i	$-0.384595\pi$
$444$	−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	$0.0743006\pi$
$449$			9.80267i			0.462617i	−0.972881	+	0.231308i	$0.925699\pi$
$450$	−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	−0.276351	−	0.961057i	$-0.589125\pi$
$457$	−0.751411	+	0.201340i	−0.0351495	+	0.00941828i	0.241201	+	0.970475i	$0.422459\pi$
$458$	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	$0.00616607\pi$
$461$			0.831786i			0.0387401i	−0.999812	+	0.0193701i	$0.993834\pi$
$462$		0			0
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	−0.568994	−	0.822342i	$-0.692667\pi$
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	0.822342	+	0.568994i	$0.192667\pi$
$464$	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	−0.822876	−	0.568220i	$-0.807632\pi$
$467$	−8.52208	−	31.8048i	−0.394355	−	1.47175i	0.428522	−	0.903531i	$-0.359035\pi$
$468$	−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	0.793653	+	0.608371i	$0.208177\pi$
$479$	20.2160	+	35.0151i	0.923691	+	1.59988i	0.130038	+	0.991509i	$0.458490\pi$
$480$	−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	−0.999607	−	0.0280431i	$-0.991072\pi$
$487$	−2.64597	+	9.87490i	−0.119900	+	0.447474i	0.879706	+	0.475517i	$0.157739\pi$
$488$	−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	0.768221	−	0.640185i	$-0.221142\pi$
$499$	13.3564	+	7.71133i	0.597916	+	0.345207i	−0.170306	+	0.985391i	$0.554475\pi$
$500$	−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	0.984644	+	0.174573i	$0.0558546\pi$
$503$	25.9985	+	25.9985i	1.15922	+	1.15922i	0.174573	+	0.984644i	$0.444145\pi$
$504$		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	0.0807619	+	0.996733i	$0.474265\pi$
$509$	−18.5636	+	32.1530i	−0.822816	+	1.42516i	−0.903577	+	0.428425i	$0.859069\pi$
$510$	−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	−0.548353	−	0.836247i	$-0.684745\pi$
$521$	−2.24415	+	1.29566i	−0.0983180	+	0.0567639i	0.450035	+	0.893011i	$0.351412\pi$
$522$	−0.547858	+	2.04464i	−0.0239791	+	0.0894913i
$523$	8.31711	−	2.22856i	0.363682	−	0.0974482i	−0.0723506	−	0.997379i	$-0.523050\pi$
$523$	8.31711	−	2.22856i	0.363682	−	0.0974482i	0.436032	+	0.899931i	$0.356383\pi$
$524$	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	−0.241894	−	0.970303i	$-0.577769\pi$
$541$	16.7319	−	28.9805i	0.719360	−	1.24597i	0.961254	−	0.275665i	$-0.0888980\pi$
$542$	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	0.689175	−	0.724594i	$-0.257973\pi$
$547$	−0.828381	−	0.828381i	−0.0354190	−	0.0354190i	−0.724594	+	0.689175i	$0.757973\pi$
$548$	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	−0.752943	−	0.658086i	$-0.771366\pi$
$557$	5.38496	−	20.0969i	0.228168	−	0.851534i	0.981111	−	0.193448i	$-0.0619671\pi$
$558$	−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	0.491106	+	0.871100i	$0.336593\pi$
$563$	−8.77338	+	32.7427i	−0.369754	+	1.37994i	−0.860860	+	0.508841i	$0.830074\pi$
$564$	−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	0.756655	−	0.653814i	$-0.226832\pi$
$569$	13.5671	+	7.83298i	0.568763	+	0.328376i	−0.187892	+	0.982190i	$0.560165\pi$
$570$	0.00495826	+	0.119065i	0.000207679	+	0.00498709i
$571$	−18.4943	−	32.0331i	−0.773964	−	1.34055i	−0.935375	−	0.353658i	$-0.884938\pi$
$571$	−18.4943	−	32.0331i	−0.773964	−	1.34055i	0.161411	−	0.986887i	$-0.448396\pi$
$572$	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	−0.212322	−	0.977200i	$-0.568103\pi$
$577$	−21.2536	−	5.69488i	−0.884798	−	0.237081i	−0.672476	+	0.740119i	$0.734769\pi$
$578$	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	−0.952623	−	0.304155i	$-0.901626\pi$
$587$	−15.7111	+	15.7111i	−0.648468	+	0.648468i	0.304155	+	0.952623i	$0.401626\pi$
$588$		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	−0.206500	−	0.978447i	$-0.566207\pi$
$593$	2.52987	−	0.677877i	0.103889	−	0.0278371i	0.310389	+	0.950610i	$0.399541\pi$
$594$	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	0.709015	−	0.705193i	$-0.249140\pi$
$599$	40.9761	−	23.6576i	1.67424	−	0.966622i	0.965223	−	0.261429i	$-0.0841936\pi$
$600$	13.0037	−	1.08492i	0.530875	−	0.0442915i
$601$		−	11.0819i		−	0.452041i	−0.974123	−	0.226021i	$-0.927428\pi$
$601$		−	11.0819i		−	0.452041i	0.974123	−	0.226021i	$-0.0725717\pi$
$602$		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	0.999055	−	0.0434656i	$-0.0138399\pi$
$607$	2.76222	+	10.3088i	0.112115	+	0.418419i	−0.886940	+	0.461885i	$0.847173\pi$
$608$	−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	0.330502	−	0.943805i	$-0.392782\pi$
$613$	3.58564	+	0.960769i	0.144823	+	0.0388051i	−0.185679	+	0.982610i	$0.559449\pi$
$614$	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	0.897266	−	0.441491i	$-0.145550\pi$
$617$	11.3212	+	11.3212i	0.455774	+	0.455774i	−0.441491	+	0.897266i	$0.645550\pi$
$618$	−0.653770	−	2.43990i	−0.0262985	−	0.0981473i
$619$	4.53385	+	7.85287i	0.182231	+	0.315633i	0.942640	−	0.333811i	$-0.108335\pi$
$619$	4.53385	+	7.85287i	0.182231	+	0.315633i	−0.760409	+	0.649445i	$0.775001\pi$
$620$	−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	0.918629	+	0.395122i	$0.129298\pi$
$641$	20.2924	+	35.1474i	0.801500	+	1.38824i	−0.117129	+	0.993117i	$0.537369\pi$
$642$	1.78872	+	6.67561i	0.0705953	+	0.263465i
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	0.779733	−	0.626112i	$-0.215355\pi$
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	−0.626112	+	0.779733i	$0.715355\pi$
$644$		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	−0.223524	−	0.974698i	$-0.571756\pi$
$647$	−23.0058	−	6.16438i	−0.904450	−	0.242347i	−0.680927	+	0.732352i	$0.738423\pi$
$648$	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	−0.909841	−	0.414957i	$-0.863797\pi$
$653$	−8.41678	−	31.4119i	−0.329374	−	1.22924i	0.580467	−	0.814284i	$-0.302870\pi$
$654$	−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	$0.220223\pi$
$659$			32.7543i			1.27593i	−0.770067	+	0.637963i	$0.779777\pi$
$660$	11.9042	+	2.66426i	0.463370	+	0.103706i
$661$	28.1609	−	16.2587i	1.09533	−	0.632391i	0.160341	−	0.987062i	$-0.448740\pi$
$661$	28.1609	−	16.2587i	1.09533	−	0.632391i	0.934991	+	0.354671i	$0.115407\pi$
$662$	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	−0.951974	−	0.306179i	$-0.900950\pi$
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	0.306179	+	0.951974i	$0.400950\pi$
$674$	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	0.900792	−	0.434251i	$-0.142987\pi$
$677$	−2.50935	−	9.36503i	−0.0964422	−	0.359927i	−0.997234	+	0.0743237i	$0.976320\pi$
$678$	−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	−0.405946	−	0.913897i	$-0.633058\pi$
$683$	−31.7389	−	8.50440i	−1.21445	−	0.325412i	−0.808508	+	0.588485i	$0.799725\pi$
$684$	−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	−0.404916	−	0.914354i	$-0.632699\pi$
$691$	−36.7813	−	21.2357i	−1.39923	−	0.807845i	−0.994312	+	0.106509i	$0.966033\pi$
$692$	−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	−0.136525	−	0.990637i	$-0.543593\pi$
$709$	−28.2967	−	16.3371i	−1.06270	−	0.613552i	−0.926179	+	0.377084i	$0.876927\pi$
$710$	−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	−0.627671	−	0.778478i	$-0.715992\pi$
$719$	9.66239	−	16.7357i	0.360346	−	0.624138i	0.988018	+	0.154340i	$0.0493252\pi$
$720$	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	−0.654907	−	0.755710i	$-0.727292\pi$
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	0.755710	+	0.654907i	$0.227292\pi$
$728$		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	−0.198165	−	0.980169i	$-0.563498\pi$
$733$	3.25711	−	0.872739i	0.120304	−	0.0322354i	0.318469	+	0.947933i	$0.396831\pi$
$734$	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	−0.418963	−	0.908003i	$-0.637606\pi$
$739$	4.29271	−	2.47840i	0.157910	−	0.0911693i	0.576873	+	0.816834i	$0.304273\pi$
$740$	−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	−0.358993	−	0.933340i	$-0.616880\pi$
$743$	15.6556	−	15.6556i	0.574347	−	0.574347i	0.933340	+	0.358993i	$0.116880\pi$
$744$	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	−0.745691	−	0.666292i	$-0.767880\pi$
$751$	5.59544	−	9.69159i	0.204181	−	0.353651i	0.949871	+	0.312641i	$0.101214\pi$
$752$	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	0.997189	+	0.0749214i	$0.0238706\pi$
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.0749214	+	0.997189i	$0.476129\pi$
$758$	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	−0.0111541	−	0.999938i	$-0.503551\pi$
$761$	−24.3504	−	14.0587i	−0.882703	−	0.509629i	−0.871549	+	0.490309i	$0.836884\pi$
$762$	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	−0.361800	−	0.932256i	$-0.617838\pi$
$773$	11.6120	−	43.3367i	0.417656	−	1.55871i	0.779456	−	0.626457i	$-0.215496\pi$
$774$	−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	−0.333108	−	0.942889i	$-0.608097\pi$
$787$	−30.6634	−	8.21624i	−1.09303	−	0.292877i	−0.759924	+	0.650011i	$0.774764\pi$
$788$	−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	−0.610053	−	0.792361i	$-0.708852\pi$
$797$	5.14677	−	5.14677i	0.182308	−	0.182308i	0.792361	+	0.610053i	$0.208852\pi$
$798$		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	−0.116279	−	0.993217i	$-0.537097\pi$
$809$	19.5042	−	11.2608i	0.685732	−	0.395907i	0.802011	+	0.597309i	$0.203763\pi$
$810$	−0.373055	+	1.66685i	−0.0131078	+	0.0585670i
$811$		−	34.9145i		−	1.22602i	−0.790077	−	0.613008i	$-0.789960\pi$
$811$		−	34.9145i		−	1.22602i	0.790077	−	0.613008i	$-0.210040\pi$
$812$		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	−0.930779	−	0.365582i	$-0.880870\pi$
$821$	−4.26320	+	7.38408i	−0.148787	+	0.257706i	0.781993	+	0.623288i	$0.214203\pi$
$822$	10.6820	+	2.86222i	0.372576	+	0.0998315i
$823$	46.3143	+	12.4099i	1.61441	+	0.432581i	0.949354	−	0.314209i	$-0.101739\pi$
$823$	46.3143	+	12.4099i	1.61441	+	0.432581i	0.665060	+	0.746790i	$0.268406\pi$
$824$	−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	−0.916940	−	0.399025i	$-0.869349\pi$
$827$	−37.8440	−	37.8440i	−1.31597	−	1.31597i	−0.399025	−	0.916940i	$-0.630651\pi$
$828$	−0.276955	−	1.03361i	−0.00962486	−	0.0359205i
$829$	16.8570	+	29.1972i	0.585469	+	1.01406i	0.994817	+	0.101683i	$0.0324228\pi$
$829$	16.8570	+	29.1972i	0.585469	+	1.01406i	−0.409348	+	0.912378i	$0.634244\pi$
$830$	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	0.789664	−	0.613539i	$-0.210255\pi$
$853$	5.14393	+	5.14393i	0.176125	+	0.176125i	−0.613539	+	0.789664i	$0.710255\pi$
$854$		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	0.388236	−	0.921560i	$-0.373084\pi$
$857$	7.71909	+	2.06832i	0.263679	+	0.0706526i	−0.124557	+	0.992212i	$0.539751\pi$
$858$	14.7416	+	3.95001i	0.503271	+	0.134851i
$859$	−21.0400	+	36.4424i	−0.717877	+	1.24340i	0.243963	+	0.969785i	$0.421553\pi$
$859$	−21.0400	+	36.4424i	−0.717877	+	1.24340i	−0.961839	+	0.273615i	$0.911781\pi$
$860$	−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	−0.999530	−	0.0306516i	$-0.990242\pi$
$863$	−4.38413	−	16.3618i	−0.149237	−	0.556962i	0.850293	−	0.526310i	$-0.176425\pi$
$864$	−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	0.0183902	−	0.999831i	$-0.494146\pi$
$877$	15.8208	−	4.23918i	0.534232	−	0.143147i	0.515842	+	0.856684i	$0.327479\pi$
$878$	−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	$0.0469301\pi$
$881$			8.72058i			0.293804i	−0.989151	+	0.146902i	$0.953070\pi$
$882$		0			0
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	−0.358490	−	0.933534i	$-0.616708\pi$
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	0.933534	+	0.358490i	$0.116708\pi$
$884$	−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	0.914830	+	0.403840i	$0.132325\pi$
$887$	9.66396	+	36.0664i	0.324484	+	1.21099i	−0.590346	+	0.807151i	$0.701009\pi$
$888$	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	0.659705	+	0.751525i	$0.270681\pi$
$907$	−8.65482	+	32.3002i	−0.287379	+	1.07251i	−0.947084	+	0.320987i	$0.895985\pi$
$908$	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	0.159096	−	0.987263i	$-0.449142\pi$
$919$	−18.6847	−	10.7876i	−0.616351	−	0.355850i	−0.775447	+	0.631413i	$0.782475\pi$
$920$	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	0.359467	+	0.933158i	$0.382959\pi$
$929$	−19.1535	+	33.1748i	−0.628405	+	1.08843i	−0.987872	+	0.155272i	$0.950375\pi$
$930$	−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	−0.457135	−	0.889397i	$-0.651125\pi$
$937$	13.2317	−	13.2317i	0.432262	−	0.432262i	0.889397	+	0.457135i	$0.151125\pi$
$938$		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	−0.535990	−	0.844225i	$-0.680061\pi$
$941$	−2.23517	+	1.29048i	−0.0728645	+	0.0420683i	0.463125	+	0.886293i	$0.346728\pi$
$942$	−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	−0.366833	−	0.930287i	$-0.619558\pi$
$947$	−6.75097	+	1.80892i	−0.219377	+	0.0587819i	0.147456	+	0.989069i	$0.452891\pi$
$948$	−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	−0.920518	−	0.390700i	$-0.872233\pi$
$953$	−16.3558	+	16.3558i	−0.529818	+	0.529818i	0.390700	+	0.920518i	$0.372233\pi$
$954$	−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	0.832605	−	0.553867i	$-0.186848\pi$
$967$	8.66781	+	8.66781i	0.278738	+	0.278738i	−0.553867	+	0.832605i	$0.686848\pi$
$968$	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	0.671915	−	0.740628i	$-0.265472\pi$
$971$	11.4195	+	6.59307i	0.366470	+	0.211582i	−0.305445	+	0.952210i	$0.598805\pi$
$972$	−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	0.660692	+	0.750657i	$0.270263\pi$
$977$	−8.96490	+	33.4574i	−0.286812	+	1.07040i	−0.947505	+	0.319742i	$0.896404\pi$
$978$	−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	−0.811192	−	0.584780i	$-0.801181\pi$
$983$	5.75986	−	21.4961i	0.183711	−	0.685618i	0.994903	−	0.100838i	$-0.0321525\pi$
$984$	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	0.999686	−	0.0250738i	$-0.00798206\pi$
$991$	15.0516	+	26.0701i	0.478128	+	0.828142i	−0.521557	+	0.853216i	$0.674649\pi$
$992$	−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	0.717042	−	0.697030i	$-0.245496\pi$
$997$	31.2439	+	8.37177i	0.989503	+	0.265137i	0.272461	+	0.962167i	$0.412162\pi$
$998$	−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.607.4		32
5.3	odd	4	inner	735.2.v.a.313.6		32
7.2	even	3		105.2.m.a.97.6	yes	16
7.3	odd	6	inner	735.2.v.a.472.6		32
7.4	even	3	inner	735.2.v.a.472.5		32
7.5	odd	6		105.2.m.a.97.5	yes	16
7.6	odd	2	inner	735.2.v.a.607.3		32
21.2	odd	6		315.2.p.e.307.4		16
21.5	even	6		315.2.p.e.307.3		16
28.19	even	6		1680.2.cz.d.97.7		16
28.23	odd	6		1680.2.cz.d.97.2		16
35.2	odd	12		525.2.m.b.118.4		16
35.3	even	12	inner	735.2.v.a.178.4		32
35.9	even	6		525.2.m.b.307.3		16
35.12	even	12		525.2.m.b.118.3		16
35.13	even	4	inner	735.2.v.a.313.5		32
35.18	odd	12	inner	735.2.v.a.178.3		32
35.19	odd	6		525.2.m.b.307.4		16
35.23	odd	12		105.2.m.a.13.5	✓	16
35.33	even	12		105.2.m.a.13.6	yes	16
105.23	even	12		315.2.p.e.118.3		16
105.68	odd	12		315.2.p.e.118.4		16
140.23	even	12		1680.2.cz.d.433.7		16
140.103	odd	12		1680.2.cz.d.433.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	35.23	odd	12
105.2.m.a.13.6	yes	16	35.33	even	12
105.2.m.a.97.5	yes	16	7.5	odd	6
105.2.m.a.97.6	yes	16	7.2	even	3
315.2.p.e.118.3		16	105.23	even	12
315.2.p.e.118.4		16	105.68	odd	12
315.2.p.e.307.3		16	21.5	even	6
315.2.p.e.307.4		16	21.2	odd	6
525.2.m.b.118.3		16	35.12	even	12
525.2.m.b.118.4		16	35.2	odd	12
525.2.m.b.307.3		16	35.9	even	6
525.2.m.b.307.4		16	35.19	odd	6
735.2.v.a.178.3		32	35.18	odd	12	inner
735.2.v.a.178.4		32	35.3	even	12	inner
735.2.v.a.313.5		32	35.13	even	4	inner
735.2.v.a.313.6		32	5.3	odd	4	inner
735.2.v.a.472.5		32	7.4	even	3	inner
735.2.v.a.472.6		32	7.3	odd	6	inner
735.2.v.a.607.3		32	7.6	odd	2	inner
735.2.v.a.607.4		32	1.1	even	1	trivial
1680.2.cz.d.97.2		16	28.23	odd	6
1680.2.cz.d.97.7		16	28.19	even	6
1680.2.cz.d.433.2		16	140.103	odd	12
1680.2.cz.d.433.7		16	140.23	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
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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