LMFDB - Embedded newform 735.2.v.a.472.5

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			472.5
Character	$\chi$	$=$	735.472
Dual form			735.2.v.a.313.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.197706 - 0.737849i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.22672 + 0.708245i) q^{4} +(2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 - 1.84539i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.197706 - 0.737849i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.22672 + 0.708245i) q^{4} +(2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 - 1.84539i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.373055 - 1.66685i) q^{10} +(1.92568 - 3.33538i) q^{11} +(-1.36822 - 0.366615i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(-2.13393 + 0.668102i) q^{15} +(0.419714 + 0.726965i) q^{16} +(0.545404 + 2.03548i) q^{17} +(-0.197706 - 0.737849i) q^{18} +(-0.0348837 - 0.0604203i) q^{19} +(2.80654 + 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.729698 + 0.195522i) q^{23} +(-1.30489 + 2.26014i) q^{24} +(4.98269 - 0.415712i) q^{25} +(-3.43177 + 1.98133i) q^{26} +(-0.707107 + 0.707107i) q^{27} +2.77107i q^{29} +(0.0710685 + 1.70660i) q^{30} +(2.07564 + 1.19837i) q^{31} +(5.66108 - 1.51688i) q^{32} +(-0.996806 + 3.72013i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(2.26481 - 8.45237i) q^{37} +(-0.0514778 + 0.0137934i) q^{38} +(4.49256 + 2.59378i) q^{39} +(3.95116 - 4.29454i) q^{40} +8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} +(4.72453 - 2.72771i) q^{44} +(1.88830 - 1.19764i) q^{45} +(0.288532 - 0.499752i) q^{46} +(-7.50006 - 2.00963i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(0.678376 - 3.75866i) q^{50} +(-1.05364 - 1.82496i) q^{51} +(-1.90184 - 7.09776i) q^{52} +(2.24675 + 8.38498i) q^{53} +(0.381939 + 0.661538i) q^{54} +(3.99191 - 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} +(2.04464 + 0.547858i) q^{58} +(3.48720 - 6.04001i) q^{59} +(-3.09090 - 0.691771i) q^{60} +(12.3935 - 7.15536i) q^{61} +(1.29458 - 1.29458i) q^{62} -2.79807i q^{64} +(-8.53643 - 7.85389i) q^{65} +(2.54782 + 1.47098i) q^{66} +(-0.568937 + 0.152446i) q^{67} +(-0.772560 + 2.88323i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(0.675461 - 2.52086i) q^{72} +(-13.0484 + 3.49631i) q^{73} +(-5.78881 - 3.34217i) q^{74} +(-4.70531 + 1.69116i) q^{75} -0.0988248i q^{76} +(2.80203 - 2.80203i) q^{78} +(-8.54186 + 4.93165i) q^{79} +(1.00533 + 1.58509i) q^{80} +(0.500000 - 0.866025i) q^{81} +(6.40510 + 1.71624i) q^{82} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(1.49678 + 2.59249i) q^{86} +(-0.717207 - 2.67665i) q^{87} +(-2.60144 - 9.70872i) q^{88} +(2.52657 + 4.37614i) q^{89} +(-0.510348 - 1.63006i) q^{90} +(0.756656 + 0.756656i) q^{92} +(-2.31507 - 0.620321i) q^{93} +(-2.96561 + 5.13659i) q^{94} +(-0.0835560 - 0.131741i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.197706	−	0.737849i	0.139799	−	0.521738i	−0.860133	−	0.510071i	$-0.829619\pi$
$2$	0.197706	−	0.737849i	0.139799	−	0.521738i	0.999932	−	0.0116677i	$-0.00371404\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.22672	+	0.708245i	0.613358	+	0.354123i
$5$	2.23413	−	0.0930365i	0.999134	−	0.0416072i
$5$	2.23413	−	0.0930365i	0.999134	−	0.0416072i
$6$			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
$10$	0.373055	−	1.66685i	0.117970	−	0.527103i
$11$	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	$-0.0305210\pi$
$12$	−1.36822	−	0.366615i	−0.394973	−	0.105833i
$13$	−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
$17$	0.545404	+	2.03548i	0.132280	+	0.493675i	0.999994	−	0.00338789i	$-0.00107840\pi$
$17$	0.545404	+	2.03548i	0.132280	+	0.493675i	−0.867714	+	0.497063i	$0.834412\pi$
$18$	−0.197706	−	0.737849i	−0.0465998	−	0.173913i
$19$	−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
$23$	0.729698	+	0.195522i	0.152153	+	0.0407692i	0.334091	−	0.942541i	$-0.391571\pi$
$23$	0.729698	+	0.195522i	0.152153	+	0.0407692i	−0.181939	+	0.983310i	$0.558237\pi$
$24$	−1.30489	+	2.26014i	−0.266360	+	0.461349i
$25$	4.98269	−	0.415712i	0.996538	−	0.0831423i
$26$	−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	$0.917171\pi$
$30$	0.0710685	+	1.70660i	0.0129753	+	0.311582i
$31$	2.07564	+	1.19837i	0.372795	+	0.215233i	0.674679	−	0.738111i	$-0.264282\pi$
$31$	2.07564	+	1.19837i	0.372795	+	0.215233i	−0.301884	+	0.953345i	$0.597615\pi$
$32$	5.66108	−	1.51688i	1.00075	−	0.268149i
$33$	−0.996806	+	3.72013i	−0.173522	+	0.647591i
$34$	1.60970			0.276062
$35$		0			0
$36$	1.41649			0.236082
$37$	2.26481	−	8.45237i	0.372332	−	1.38956i	−0.484872	−	0.874585i	$-0.661134\pi$
$37$	2.26481	−	8.45237i	0.372332	−	1.38956i	0.857204	−	0.514976i	$-0.172199\pi$
$38$	−0.0514778	+	0.0137934i	−0.00835080	+	0.00223759i
$39$	4.49256	+	2.59378i	0.719386	+	0.415338i
$40$	3.95116	−	4.29454i	0.624734	−	0.679027i
$41$			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
$45$	1.88830	−	1.19764i	0.281491	−	0.178533i
$46$	0.288532	−	0.499752i	0.0425417	−	0.0736843i
$47$	−7.50006	−	2.00963i	−1.09400	−	0.293135i	−0.333678	−	0.942687i	$-0.608290\pi$
$47$	−7.50006	−	2.00963i	−1.09400	−	0.293135i	−0.760317	+	0.649552i	$0.774957\pi$
$48$	−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
$52$	−1.90184	−	7.09776i	−0.263737	−	0.984282i
$53$	2.24675	+	8.38498i	0.308615	+	1.15177i	0.929789	+	0.368093i	$0.119989\pi$
$53$	2.24675	+	8.38498i	0.308615	+	1.15177i	−0.621174	+	0.783673i	$0.713344\pi$
$54$	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
$58$	2.04464	+	0.547858i	0.268474	+	0.0719373i
$59$	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	$0.0166651\pi$
$60$	−3.09090	−	0.691771i	−0.399034	−	0.0893072i
$61$	12.3935	−	7.15536i	1.58682	−	0.916150i	0.592992	−	0.805208i	$-0.297946\pi$
$61$	12.3935	−	7.15536i	1.58682	−	0.916150i	0.993827	−	0.110942i	$-0.0353869\pi$
$62$	1.29458	−	1.29458i	0.164412	−	0.164412i
$63$		0			0
$64$		−	2.79807i		−	0.349758i
$65$	−8.53643	−	7.85389i	−1.05881	−	0.974155i
$66$	2.54782	+	1.47098i	0.313615	+	0.181066i
$67$	−0.568937	+	0.152446i	−0.0695067	+	0.0186243i	−0.293405	−	0.955988i	$-0.594788\pi$
$67$	−0.568937	+	0.152446i	−0.0695067	+	0.0186243i	0.223898	+	0.974613i	$0.428122\pi$
$68$	−0.772560	+	2.88323i	−0.0936866	+	0.349643i
$69$	−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	$0.660198\pi$
$72$	0.675461	−	2.52086i	0.0796039	−	0.297086i
$73$	−13.0484	+	3.49631i	−1.52720	+	0.409212i	−0.922105	−	0.386940i	$-0.873532\pi$
$73$	−13.0484	+	3.49631i	−1.52720	+	0.409212i	−0.605096	+	0.796152i	$0.706865\pi$
$74$	−5.78881	−	3.34217i	−0.672936	−	0.388520i
$75$	−4.70531	+	1.69116i	−0.543323	+	0.195278i
$76$		−	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	$-0.853892\pi$
$79$	−8.54186	+	4.93165i	−0.961035	+	0.554854i	−0.0645434	+	0.997915i	$0.520559\pi$
$80$	1.00533	+	1.58509i	0.112399	+	0.177218i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	6.40510	+	1.71624i	0.707325	+	0.189527i
$83$	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
$87$	−0.717207	−	2.67665i	−0.0768926	−	0.286967i
$88$	−2.60144	−	9.70872i	−0.277315	−	1.03495i
$89$	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
$93$	−2.31507	−	0.620321i	−0.240062	−	0.0643243i
$94$	−2.96561	+	5.13659i	−0.305880	+	0.529799i
$95$	−0.0835560	−	0.131741i	−0.00857267	−	0.0135164i
$96$	−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
$100$	6.40677	+	3.01901i	0.640677	+	0.301901i
$101$	16.6236	+	9.59763i	1.65411	+	0.955000i	0.975357	+	0.220632i	$0.0708121\pi$
$101$	16.6236	+	9.59763i	1.65411	+	0.955000i	0.678752	+	0.734368i	$0.262521\pi$
$102$	−1.55485	+	0.416622i	−0.153954	+	0.0412517i
$103$	0.855857	−	3.19410i	0.0843301	−	0.314724i	−0.910856	−	0.412723i	$-0.864578\pi$
$103$	0.855857	−	3.19410i	0.0843301	−	0.314724i	0.995186	+	0.0979992i	$0.0312443\pi$
$104$	−13.5384			−1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	−2.34164	+	8.73911i	−0.226375	+	0.844841i	0.755475	+	0.655178i	$0.227406\pi$
$107$	−2.34164	+	8.73911i	−0.226375	+	0.844841i	−0.981849	+	0.189663i	$0.939260\pi$
$108$	−1.36822	+	0.366615i	−0.131658	+	0.0352775i
$109$	1.87111	+	1.08029i	0.179220	+	0.103473i	0.586926	−	0.809641i	$-0.300338\pi$
$109$	1.87111	+	1.08029i	0.179220	+	0.103473i	−0.407706	+	0.913113i	$0.633671\pi$
$110$	−4.84118	−	4.45409i	−0.461588	−	0.424681i
$111$			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
$115$	1.64843	+	0.368934i	0.153717	+	0.0344032i
$116$	−1.96260	+	3.39932i	−0.182223	+	0.315619i
$117$	−5.01080	−	1.34264i	−0.463249	−	0.124127i
$118$	−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
$122$	−2.82932	−	10.5592i	−0.256154	−	0.955981i
$123$	−2.24675	−	8.38498i	−0.202583	−	0.756048i
$124$	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	$0.848071\pi$
$128$	9.25761	+	2.48057i	0.818265	+	0.219253i
$129$	1.95945	−	3.39386i	0.172520	−	0.298813i
$130$	−7.48269	+	4.74584i	−0.656275	+	0.416238i
$131$	0.560750	−	0.323749i	0.0489930	−	0.0282861i	−0.475303	−	0.879822i	$-0.657662\pi$
$131$	0.560750	−	0.323749i	0.0489930	−	0.0282861i	0.524296	+	0.851536i	$0.324328\pi$
$132$	−3.85756	+	3.85756i	−0.335758	+	0.335758i
$133$		0			0
$134$			0.449929i			0.0388680i
$135$	−1.51398	+	1.64556i	−0.130303	+	0.141627i
$136$	4.76274	+	2.74977i	0.408402	+	0.235791i
$137$	−13.9839	+	3.74696i	−1.19472	+	0.320125i	−0.800751	−	0.598998i	$-0.795566\pi$
$137$	−13.9839	+	3.74696i	−1.19472	+	0.320125i	−0.393971	+	0.919123i	$0.628899\pi$
$138$	−0.149355	+	0.557400i	−0.0127139	+	0.0474491i
$139$	−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
$142$	−1.60692	+	5.99711i	−0.134850	+	0.503266i
$143$	−19.2984	+	5.17099i	−1.61381	+	0.432420i
$144$	0.726965	+	0.419714i	0.0605804	+	0.0349761i
$145$	0.257811	+	6.19095i	0.0214100	+	0.514130i
$146$			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	$-0.816143\pi$
$149$	−9.56745	+	5.52377i	−0.783796	+	0.452525i	0.0539779	+	0.998542i	$0.482810\pi$
$150$	0.317553	+	3.80617i	0.0259281	+	0.310772i
$151$	−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	$0.897372\pi$
$152$	−0.175873	−	0.0471251i	−0.0142652	−	0.00382235i
$153$	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
$157$	−0.384306	−	1.43425i	−0.0306709	−	0.114465i	0.948893	−	0.315597i	$-0.102205\pi$
$157$	−0.384306	−	1.43425i	−0.0306709	−	0.114465i	−0.979564	+	0.201132i	$0.935538\pi$
$158$	1.95003	+	7.27763i	0.155136	+	0.578977i
$159$	−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
$163$	−7.52050	−	2.01511i	−0.589051	−	0.157836i	−0.0480317	−	0.998846i	$-0.515295\pi$
$163$	−7.52050	−	2.01511i	−0.589051	−	0.157836i	−0.541020	+	0.841010i	$0.681962\pi$
$164$	−6.14812	+	10.6488i	−0.480087	+	0.831535i
$165$	−1.88089	+	8.40400i	−0.146427	+	0.654250i
$166$	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
$170$	3.59629	−	0.149761i	0.275823	−	0.0114862i
$171$	−0.0604203	−	0.0348837i	−0.00462046	−	0.00266762i
$172$	−5.36192	+	1.43672i	−0.408843	+	0.109549i
$173$	−1.79627	+	6.70378i	−0.136568	+	0.509679i	0.863419	+	0.504488i	$0.168319\pi$
$173$	−1.79627	+	6.70378i	−0.136568	+	0.509679i	−0.999987	+	0.00519041i	$0.998348\pi$
$174$	−2.11676			−0.160471
$175$		0			0
$176$	3.23294			0.243692
$177$	−1.80511	+	6.73676i	−0.135680	+	0.506366i
$178$	3.72845	−	0.999035i	0.279459	−	0.0748808i
$179$	−16.0957	−	9.29284i	−1.20305	−	0.694579i	−0.241815	−	0.970322i	$-0.577743\pi$
$179$	−16.0957	−	9.29284i	−1.20305	−	0.694579i	−0.961231	+	0.275743i	$0.911076\pi$
$180$	3.16463	−	0.131785i	0.235877	−	0.00982270i
$181$			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
$185$	4.27350	−	19.0944i	0.314194	−	1.40385i
$186$	−0.915407	+	1.58553i	−0.0671209	+	0.116257i
$187$	7.83935	+	2.10055i	0.573270	+	0.153607i
$188$	−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	$0.770820\pi$
$192$	0.724193	+	2.70273i	0.0522641	+	0.195052i
$193$	−1.75911	−	6.56510i	−0.126624	−	0.472566i	0.873269	−	0.487239i	$-0.161996\pi$
$193$	−1.75911	−	6.56510i	−0.126624	−	0.472566i	−0.999892	+	0.0146728i	$0.995329\pi$
$194$	−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	$0.529554\pi$
$198$	−2.84172	−	0.761438i	−0.201953	−	0.0541130i
$199$	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	$0.136485\pi$
$200$	8.42787	−	9.96218i	0.595941	−	0.704432i
$201$	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
$205$	0.807629	+	19.3940i	0.0564072	+	1.35453i
$206$	−2.18756	−	1.26299i	−0.152414	−	0.0879965i
$207$	0.729698	−	0.195522i	0.0507175	−	0.0135897i
$208$	1.12705	−	4.20621i	0.0781468	−	0.291648i
$209$	−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	$0.635826\pi$
$212$	−3.18250	+	11.8772i	−0.218575	+	0.815733i
$213$	7.85088	−	2.10364i	0.537933	−	0.144139i
$214$	5.98519	+	3.45555i	0.409139	+	0.236217i
$215$	−5.93313	+	6.44876i	−0.404636	+	0.439802i
$216$			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
$220$	10.3014	−	6.53361i	0.694523	−	0.440496i
$221$	5.46582	−	9.46708i	0.367671	−	0.636825i
$222$	6.45658	+	1.73004i	0.433337	+	0.116112i
$223$	−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
$227$	0.404524	+	1.50971i	0.0268492	+	0.100203i	0.978050	−	0.208369i	$-0.0668156\pi$
$227$	0.404524	+	1.50971i	0.0268492	+	0.100203i	−0.951201	+	0.308572i	$0.900149\pi$
$228$	0.0255777	+	0.0954574i	0.00169393	+	0.00632182i
$229$	−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
$233$	−1.37692	−	0.368944i	−0.0902048	−	0.0241703i	0.213434	−	0.976957i	$-0.431535\pi$
$233$	−1.37692	−	0.368944i	−0.0902048	−	0.0241703i	−0.303639	+	0.952787i	$0.598202\pi$
$234$	−1.98133	+	3.43177i	−0.129524	+	0.224342i
$235$	−16.9431	−	3.79201i	−1.10524	−	0.247363i
$236$	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	$-0.227718\pi$
$240$	−1.38132	−	1.27088i	−0.0891641	−	0.0820349i
$241$	−2.39883	−	1.38497i	−0.154522	−	0.0892136i	0.420745	−	0.907179i	$-0.361769\pi$
$241$	−2.39883	−	1.38497i	−0.154522	−	0.0892136i	−0.575268	+	0.817965i	$0.695102\pi$
$242$	−2.82816	+	0.757804i	−0.181801	+	0.0487135i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	20.2710			1.29772
$245$		0			0
$246$	−6.63105			−0.422780
$247$	−0.0936725	+	0.349590i	−0.00596024	+	0.0222439i
$248$	6.04183	−	1.61890i	0.383656	−	0.102800i
$249$	−2.00331	−	1.15661i	−0.126955	−	0.0732973i
$250$	1.16589	−	8.46046i	0.0737372	−	0.535086i
$251$		−	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
$255$	−2.52376	−	3.97917i	−0.158044	−	0.249185i
$256$	6.45864	−	11.1867i	0.403665	−	0.699168i
$257$	2.75722	+	0.738795i	0.171991	+	0.0460848i	0.343787	−	0.939048i	$-0.388290\pi$
$257$	2.75722	+	0.738795i	0.171991	+	0.0460848i	−0.171796	+	0.985133i	$0.554957\pi$
$258$	−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
$262$	−0.128014	−	0.477756i	−0.00790876	−	0.0295159i
$263$	6.13773	+	22.9063i	0.378469	+	1.41246i	0.848210	+	0.529660i	$0.177681\pi$
$263$	6.13773	+	22.9063i	0.378469	+	1.41246i	−0.469741	+	0.882804i	$0.655653\pi$
$264$	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
$268$	−0.805894	−	0.215939i	−0.0492278	−	0.0131905i
$269$	−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	$0.894758\pi$
$270$	0.914849	+	1.44243i	0.0556759	+	0.0877834i
$271$	3.58076	−	2.06735i	0.217515	−	0.125583i	−0.387284	−	0.921961i	$-0.626587\pi$
$271$	3.58076	−	2.06735i	0.217515	−	0.125583i	0.604799	+	0.796378i	$0.293253\pi$
$272$	−1.25081	+	1.25081i	−0.0758413	+	0.0758413i
$273$		0			0
$274$			11.0588i			0.668085i
$275$	8.20851	−	17.4197i	0.494992	−	1.05045i
$276$	−0.926710	−	0.535036i	−0.0557814	−	0.0322054i
$277$	16.5463	−	4.43358i	0.994174	−	0.266388i	0.275171	−	0.961395i	$-0.411266\pi$
$277$	16.5463	−	4.43358i	0.994174	−	0.266388i	0.719003	+	0.695007i	$0.244599\pi$
$278$	−4.38241	+	16.3554i	−0.262840	+	0.980931i
$279$	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	$0.449922\pi$
$282$	1.53511	−	5.72913i	0.0914147	−	0.341164i
$283$	2.27756	−	0.610271i	0.135387	−	0.0362768i	−0.190489	−	0.981689i	$-0.561007\pi$
$283$	2.27756	−	0.610271i	0.135387	−	0.0362768i	0.325876	+	0.945412i	$0.394341\pi$
$284$	−9.97054	−	5.75649i	−0.591643	−	0.341585i
$285$	0.114806	+	0.105627i	0.00680053	+	0.00625678i
$286$			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
$290$	4.61896	+	1.03376i	0.271234	+	0.0607046i
$291$	−4.84970	+	8.39993i	−0.284294	+	0.492412i
$292$	−18.4830	−	4.95249i	−1.08163	−	0.289823i
$293$	−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
$297$	0.996806	+	3.72013i	0.0578405	+	0.215864i
$298$	2.18417	+	8.15142i	0.126525	+	0.472199i
$299$	−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
$303$	−18.5412	−	4.96810i	−1.06516	−	0.285410i
$304$	0.0292823	−	0.0507184i	0.00167946	−	0.00290890i
$305$	27.0229	−	17.1391i	1.54733	−	0.981380i
$306$	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
$310$	2.77182	−	3.01271i	0.157429	−	0.171110i
$311$	−2.47872	−	1.43109i	−0.140555	−	0.0811497i	0.428073	−	0.903744i	$-0.359193\pi$
$311$	−2.47872	−	1.43109i	−0.140555	−	0.0811497i	−0.568629	+	0.822594i	$0.692526\pi$
$312$	13.0771	−	3.50400i	0.740345	−	0.198375i
$313$	−3.44732	+	12.8656i	−0.194854	+	0.727204i	0.797451	+	0.603384i	$0.206181\pi$
$313$	−3.44732	+	12.8656i	−0.194854	+	0.727204i	−0.992305	+	0.123820i	$0.960485\pi$
$314$	−1.13424			−0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	2.70240	−	10.0855i	0.151782	−	0.566459i	−0.847577	−	0.530672i	$-0.821940\pi$
$317$	2.70240	−	10.0855i	0.151782	−	0.566459i	0.999359	−	0.0357866i	$-0.0113937\pi$
$318$	−6.40510	+	1.71624i	−0.359180	+	0.0962421i
$319$	9.24258	+	5.33620i	0.517485	+	0.298770i
$320$	−0.260322	−	6.25125i	−0.0145525	−	0.349456i
$321$		−	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
$325$	−19.8022	−	16.7524i	−1.09843	−	0.929257i
$326$	−2.97370	+	5.15060i	−0.164698	+	0.285265i
$327$	−2.08695	−	0.559197i	−0.115409	−	0.0309237i
$328$	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	$-0.391536\pi$
$332$	0.848062	+	3.16501i	0.0465435	+	0.173703i
$333$	−2.26481	−	8.45237i	−0.124111	−	0.463187i
$334$	−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	$0.810916\pi$
$338$	10.2641	+	2.75026i	0.558293	+	0.149594i
$339$	2.92617	−	5.06828i	0.158928	−	0.275271i
$340$	−1.45775	+	6.51340i	−0.0790578	+	0.353238i
$341$	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
$345$	−1.68775	+	0.0702834i	−0.0908655	+	0.00378393i
$346$	4.59124	+	2.65076i	0.246827	+	0.142505i
$347$	−7.97341	+	2.13647i	−0.428035	+	0.114692i	−0.466404	−	0.884572i	$-0.654451\pi$
$347$	−7.97341	+	2.13647i	−0.428035	+	0.114692i	0.0383685	+	0.999264i	$0.487784\pi$
$348$	1.01592	−	3.79145i	0.0544589	−	0.203243i
$349$	−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
$352$	5.84206	−	21.8029i	0.311383	−	1.16210i
$353$	15.1990	−	4.07257i	0.808963	−	0.216761i	0.169448	−	0.985539i	$-0.445802\pi$
$353$	15.1990	−	4.07257i	0.808963	−	0.216761i	0.639516	+	0.768778i	$0.279135\pi$
$354$	4.61383	+	2.66380i	0.245222	+	0.141579i
$355$	−18.1586	+	0.756184i	−0.963760	+	0.0401341i
$356$			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	$-0.735653\pi$
$359$	−7.05693	+	4.07432i	−0.372450	+	0.215034i	0.302078	+	0.953283i	$0.402320\pi$
$360$	1.27454	−	5.69477i	0.0671740	−	0.300140i
$361$	9.49757	−	16.4503i	0.499872	−	0.865804i
$362$	6.26086	+	1.67759i	0.329063	+	0.0881723i
$363$	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
$367$	5.39815	+	20.1462i	0.281781	+	1.05162i	0.951160	+	0.308700i	$0.0998938\pi$
$367$	5.39815	+	20.1462i	0.281781	+	1.05162i	−0.669378	+	0.742922i	$0.733439\pi$
$368$	0.164127	+	0.612529i	0.00855569	+	0.0319303i
$369$	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
$373$	−2.04168	−	0.547065i	−0.105714	−	0.0283260i	0.205574	−	0.978642i	$-0.434094\pi$
$373$	−2.04168	−	0.547065i	−0.105714	−	0.0283260i	−0.311288	+	0.950316i	$0.600760\pi$
$374$	3.09977	−	5.36897i	0.160286	−	0.277623i
$375$	−10.3549	+	4.21604i	−0.534727	+	0.217716i
$376$	−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	$-0.159590\pi$
$380$	−0.00919431	−	0.220788i	−0.000471658	−	0.0113262i
$381$	5.91917	+	3.41743i	0.303248	+	0.175080i
$382$	3.97960	−	1.06633i	0.203614	−	0.0545582i
$383$	7.66288	−	28.5983i	0.391555	−	1.46130i	−0.436014	−	0.899940i	$-0.643610\pi$
$383$	7.66288	−	28.5983i	0.391555	−	1.46130i	0.827569	−	0.561364i	$-0.189723\pi$
$384$	−9.58418			−0.489091
$385$		0			0
$386$	−5.19184			−0.264258
$387$	−1.01428	+	3.78536i	−0.0515589	+	0.192421i
$388$	13.2710	−	3.55594i	0.673731	−	0.180526i
$389$	22.2232	+	12.8305i	1.12676	+	0.650535i	0.943118	−	0.332459i	$-0.107878\pi$
$389$	22.2232	+	12.8305i	1.12676	+	0.650535i	0.183641	+	0.982993i	$0.441212\pi$
$390$	5.99941	−	6.52079i	0.303792	−	0.330193i
$391$			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
$395$	−18.6248	+	11.8127i	−0.937117	+	0.594359i
$396$	2.72771	−	4.72453i	0.137073	−	0.237417i
$397$	−9.20135	−	2.46549i	−0.461802	−	0.123740i	0.0204142	−	0.999792i	$-0.493502\pi$
$397$	−9.20135	−	2.46549i	−0.461802	−	0.123740i	−0.482217	+	0.876052i	$0.660168\pi$
$398$	−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	$0.953392\pi$
$402$	−0.116450	−	0.434598i	−0.00580801	−	0.0216758i
$403$	−3.21796	−	12.0096i	−0.160298	−	0.598240i
$404$	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
$408$	−5.31215	−	1.42339i	−0.262990	−	0.0704681i
$409$	−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	$0.250749\pi$
$410$	14.4695	+	3.23840i	0.714598	+	0.159933i
$411$	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
$415$	3.80654	+	3.50218i	0.186856	+	0.171915i
$416$	−26.3299	−	15.2016i	−1.29093	−	0.745320i
$417$	21.4110	−	5.73706i	1.04850	−	0.280945i
$418$	−0.0531235	+	0.198260i	−0.00259835	+	0.00969719i
$419$	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	$0.474384\pi$
$422$	−2.37719	+	8.87180i	−0.115720	+	0.431873i
$423$	−7.50006	+	2.00963i	−0.364665	+	0.0977117i
$424$	19.6197	+	11.3275i	0.952818	+	0.550110i
$425$	3.56375	+	9.91541i	0.172867	+	0.480968i
$426$		−	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
$430$	3.58519	+	5.65272i	0.172893	+	0.272598i
$431$	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	$0.0564523\pi$
$432$	−0.810825	−	0.217260i	−0.0390108	−	0.0104529i
$433$	−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
$437$	−0.0136411	−	0.0509091i	−0.000652540	−	0.00243531i
$438$	−2.67075	−	9.96739i	−0.127614	−	0.476260i
$439$	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
$443$	32.9897	+	8.83957i	1.56739	+	0.419981i	0.934994	−	0.354664i	$-0.115405\pi$
$443$	32.9897	+	8.83957i	1.56739	+	0.419981i	0.632396	+	0.774645i	$0.282072\pi$
$444$	−6.19753	+	10.7344i	−0.294122	+	0.509434i
$445$	6.05182	+	9.54181i	0.286884	+	0.452325i
$446$	−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	$0.925699\pi$
$450$	−1.29184	−	3.59428i	−0.0608979	−	0.169436i
$451$	28.9536	+	16.7164i	1.36337	+	0.787144i
$452$	−8.00732	+	2.14556i	−0.376633	+	0.100918i
$453$	4.76201	−	17.7721i	0.223739	−	0.835005i
$454$	1.19391			0.0560331
$455$		0			0
$456$	0.182078			0.00852656
$457$	0.201340	−	0.751411i	0.00941828	−	0.0351495i	−0.961057	−	0.276351i	$-0.910875\pi$
$457$	0.201340	−	0.751411i	0.00941828	−	0.0351495i	0.970475	+	0.241201i	$0.0775415\pi$
$458$	−5.77964	+	1.54865i	−0.270065	+	0.0723636i
$459$	−1.82496	−	1.05364i	−0.0851817	−	0.0491797i
$460$	1.76087	+	1.62007i	0.0821008	+	0.0755363i
$461$			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
$465$	−5.22988	−	1.17049i	−0.242530	−	0.0542803i
$466$	−0.544450	+	0.943015i	−0.0252211	+	0.0436843i
$467$	31.8048	+	8.52208i	1.47175	+	0.394355i	0.903531	−	0.428522i	$-0.140965\pi$
$467$	31.8048	+	8.52208i	1.47175	+	0.394355i	0.568220	+	0.822876i	$0.307632\pi$
$468$	−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
$472$	−4.71094	−	17.5815i	−0.216838	−	0.809252i
$473$	3.90637	+	14.5788i	0.179615	+	0.670333i
$474$	−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
$478$	−14.9639	−	4.00957i	−0.684434	−	0.183394i
$479$	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	$-0.208177\pi$
$480$	−11.0669	+	7.01909i	−0.505132	+	0.320376i
$481$	−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
$485$	14.6847	−	15.9609i	0.666799	−	0.724748i
$486$	0.661538	+	0.381939i	0.0300080	+	0.0173251i
$487$	9.87490	−	2.64597i	0.447474	−	0.119900i	−0.0280431	−	0.999607i	$-0.508928\pi$
$487$	9.87490	−	2.64597i	0.447474	−	0.119900i	0.475517	+	0.879706i	$0.342261\pi$
$488$	9.66634	−	36.0753i	0.437575	−	1.63305i
$489$	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	$0.350125\pi$
$492$	3.18250	−	11.8772i	0.143478	−	0.535468i
$493$	−5.64045	+	1.51135i	−0.254033	+	0.0680680i
$494$	0.239425	+	0.138232i	0.0107723	+	0.00621937i
$495$	−0.358317	−	8.60445i	−0.0161052	−	0.386741i
$496$			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	$-0.778858\pi$
$499$	−13.3564	+	7.71133i	−0.597916	+	0.345207i	0.170306	+	0.985391i	$0.445525\pi$
$500$	14.5945	+	6.14879i	0.652684	+	0.274982i
$501$	−1.33620	+	2.31437i	−0.0596972	+	0.103399i
$502$	−4.50075	−	1.20597i	−0.200878	−	0.0538252i
$503$	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
$507$	−3.60039	−	13.4368i	−0.159899	−	0.596751i
$508$	−2.50576	−	9.35164i	−0.111175	−	0.414912i
$509$	−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
$513$	0.0673901	+	0.0180571i	0.00297535	+	0.000797241i
$514$	1.09024	−	1.88835i	0.0480884	−	0.0832915i
$515$	1.61493	−	7.21567i	0.0711623	−	0.317960i
$516$	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
$520$	−30.2466	+	1.25957i	−1.32640	+	0.0552356i
$521$	2.24415	+	1.29566i	0.0983180	+	0.0567639i	0.548353	−	0.836247i	$-0.315255\pi$
$521$	2.24415	+	1.29566i	0.0983180	+	0.0567639i	−0.450035	+	0.893011i	$0.648588\pi$
$522$	2.04464	−	0.547858i	0.0894913	−	0.0239791i
$523$	−2.22856	+	8.31711i	−0.0974482	+	0.363682i	−0.997379	−	0.0723506i	$-0.976950\pi$
$523$	−2.22856	+	8.31711i	−0.0974482	+	0.363682i	0.899931	+	0.436032i	$0.143617\pi$
$524$	0.917176			0.0400670
$525$		0			0
$526$	18.1149			0.789846
$527$	−1.30719	+	4.87850i	−0.0569421	+	0.212511i
$528$	−3.12278	+	0.836746i	−0.135901	+	0.0364147i
$529$	−19.4244	−	11.2147i	−0.844537	−	0.487594i
$530$	14.8146	−	0.616930i	0.643507	−	0.0267977i
$531$		−	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
$535$	−4.41847	+	19.7422i	−0.191027	+	0.853529i
$536$	−0.768589	+	1.33124i	−0.0331980	+	0.0575006i
$537$	17.9524	+	4.81033i	0.774703	+	0.207581i
$538$	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	$0.577769\pi$
$542$	−0.817456	−	3.05079i	−0.0351127	−	0.131042i
$543$	−2.19615	−	8.19615i	−0.0942459	−	0.351731i
$544$	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	$0.757973\pi$
$548$	−19.8080	−	5.30754i	−0.846156	−	0.226727i
$549$	7.15536	−	12.3935i	0.305383	−	0.528940i
$550$	−11.2302	−	9.50062i	−0.478858	−	0.405108i
$551$	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
$555$	0.814119	+	19.5499i	0.0345574	+	0.829845i
$556$	−27.1918	−	15.6992i	−1.15319	−	0.665793i
$557$	−20.0969	+	5.38496i	−0.851534	+	0.228168i	−0.658086	−	0.752943i	$-0.728634\pi$
$557$	−20.0969	+	5.38496i	−0.851534	+	0.228168i	−0.193448	+	0.981111i	$0.561967\pi$
$558$	0.473850	−	1.76843i	0.0200597	−	0.0748636i
$559$	20.3295			0.859846
$560$		0			0
$561$	−8.11589			−0.342653
$562$	1.03851	−	3.87577i	0.0438069	−	0.163489i
$563$	32.7427	−	8.77338i	1.37994	−	0.369754i	0.508841	−	0.860860i	$-0.330074\pi$
$563$	32.7427	−	8.77338i	1.37994	−	0.369754i	0.871100	+	0.491106i	$0.163407\pi$
$564$	9.52500	+	5.49926i	0.401075	+	0.231561i
$565$	−8.86035	+	9.63036i	−0.372758	+	0.405152i
$566$		−	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	$-0.773168\pi$
$569$	−13.5671	+	7.83298i	−0.568763	+	0.328376i	0.187892	+	0.982190i	$0.439835\pi$
$570$	0.100634	−	0.0638266i	0.00421511	−	0.00267340i
$571$	−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	$0.884938\pi$
$572$	−27.3360	−	7.32466i	−1.14298	−	0.306260i
$573$	−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
$577$	5.69488	+	21.2536i	0.237081	+	0.884798i	0.977200	+	0.212322i	$0.0681025\pi$
$577$	5.69488	+	21.2536i	0.237081	+	0.884798i	−0.740119	+	0.672476i	$0.765231\pi$
$578$	−2.48307	−	9.26693i	−0.103282	−	0.385453i
$579$	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
$583$	32.2936	+	8.65304i	1.33746	+	0.358372i
$584$	−17.6274	+	30.5315i	−0.729427	+	1.26340i
$585$	−11.3197	−	2.53345i	−0.468012	−	0.104745i
$586$	−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
$590$	−8.76685	−	8.06588i	−0.360926	−	0.332067i
$591$	−15.5223	−	8.96183i	−0.638504	−	0.368640i
$592$	7.09515	−	1.90114i	0.291609	−	0.0781364i
$593$	−0.677877	+	2.52987i	−0.0278371	+	0.103889i	−0.978447	−	0.206500i	$-0.933793\pi$
$593$	−0.677877	+	2.52987i	−0.0278371	+	0.103889i	0.950610	+	0.310389i	$0.100459\pi$
$594$	2.94197			0.120710
$595$		0			0
$596$	−15.6487			−0.640997
$597$	−0.691334	+	2.58009i	−0.0282944	+	0.105596i
$598$	−2.89155	+	0.774789i	−0.118244	+	0.0316835i
$599$	−40.9761	−	23.6576i	−1.67424	−	0.966622i	−0.965223	−	0.261429i	$-0.915806\pi$
$599$	−40.9761	−	23.6576i	−1.67424	−	0.966622i	−0.709015	−	0.705193i	$-0.750860\pi$
$600$	−5.56230	+	11.8040i	−0.227080	+	0.481897i
$601$		−	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
$605$	−4.59052	−	7.23781i	−0.186631	−	0.294259i
$606$	−7.33142	+	12.6984i	−0.297819	+	0.515837i
$607$	−10.3088	−	2.76222i	−0.418419	−	0.112115i	0.0434656	−	0.999055i	$-0.486160\pi$
$607$	−10.3088	−	2.76222i	−0.418419	−	0.112115i	−0.461885	+	0.886940i	$0.652827\pi$
$608$	−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
$612$	0.772560	+	2.88323i	0.0312289	+	0.116548i
$613$	−0.960769	−	3.58564i	−0.0388051	−	0.144823i	0.943805	−	0.330502i	$-0.107218\pi$
$613$	−0.960769	−	3.58564i	−0.0388051	−	0.144823i	−0.982610	+	0.185679i	$0.940551\pi$
$614$	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	$0.645550\pi$
$618$	2.43990	+	0.653770i	0.0981473	+	0.0262985i
$619$	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	$0.108335\pi$
$620$	4.06593	+	6.41068i	0.163292	+	0.257459i
$621$	−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
$625$	24.6544	−	4.14272i	0.986175	−	0.165709i
$626$	8.81129	+	5.08720i	0.352170	+	0.203325i
$627$	0.259544	−	0.0695445i	0.0103652	−	0.00277734i
$628$	0.544366	−	2.03160i	0.0217225	−	0.0810697i
$629$	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	$0.561669\pi$
$632$	−6.66227	+	24.8639i	−0.265011	+	0.989034i
$633$	11.6142	−	3.11201i	0.461622	−	0.123691i
$634$	−6.90730	−	3.98793i	−0.274324	−	0.158381i
$635$	−11.2472	−	10.3479i	−0.446330	−	0.410643i
$636$		−	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
$640$	20.9135	+	4.68062i	0.826679	+	0.185018i
$641$	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	$-0.129298\pi$
$642$	−6.67561	−	1.78872i	−0.263465	−	0.0705953i
$643$	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
$647$	6.16438	+	23.0058i	0.242347	+	0.904450i	0.974698	+	0.223524i	$0.0717561\pi$
$647$	6.16438	+	23.0058i	0.242347	+	0.904450i	−0.732352	+	0.680927i	$0.761577\pi$
$648$	−0.675461	−	2.52086i	−0.0265346	−	0.0990285i
$649$	−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
$653$	31.4119	+	8.41678i	1.22924	+	0.329374i	0.814284	−	0.580467i	$-0.197130\pi$
$653$	31.4119	+	8.41678i	1.22924	+	0.329374i	0.414957	+	0.909841i	$0.363797\pi$
$654$	−0.825207	+	1.42930i	−0.0322681	+	0.0558901i
$655$	1.22267	−	0.775469i	0.0477737	−	0.0303001i
$656$	−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	$0.779777\pi$
$660$	−8.25941	+	8.97720i	−0.321497	+	0.349437i
$661$	−28.1609	−	16.2587i	−1.09533	−	0.632391i	−0.160341	−	0.987062i	$-0.551260\pi$
$661$	−28.1609	−	16.2587i	−1.09533	−	0.632391i	−0.934991	+	0.354671i	$0.884593\pi$
$662$	−17.4280	+	4.66982i	−0.677359	+	0.181498i
$663$	−2.82932	+	10.5592i	−0.109882	+	0.410084i
$664$	6.03701			0.234281
$665$		0			0
$666$	−6.68434			−0.259013
$667$	−0.541806	+	2.02205i	−0.0209788	+	0.0782940i
$668$	3.65646	−	0.979744i	0.141473	−	0.0379075i
$669$	14.3203	+	8.26785i	0.553656	+	0.319654i
$670$	0.0418598	+	1.00520i	0.00161719	+	0.0388343i
$671$		−	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
$675$	−3.22934	+	3.81725i	−0.124297	+	0.146926i
$676$	−9.85228	+	17.0647i	−0.378934	+	0.656333i
$677$	9.36503	+	2.50935i	0.359927	+	0.0964422i	0.434251	−	0.900792i	$-0.357013\pi$
$677$	9.36503	+	2.50935i	0.359927	+	0.0964422i	−0.0743237	+	0.997234i	$0.523680\pi$
$678$	−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
$682$	−1.82497	−	6.81087i	−0.0698816	−	0.260802i
$683$	8.50440	+	31.7389i	0.325412	+	1.21445i	0.913897	+	0.405946i	$0.133058\pi$
$683$	8.50440	+	31.7389i	0.325412	+	1.21445i	−0.588485	+	0.808508i	$0.700275\pi$
$684$	−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
$688$	−3.17753	−	0.851417i	−0.121142	−	0.0324600i
$689$	22.5160	−	38.9989i	0.857793	−	1.48574i
$690$	−0.281820	+	1.25920i	−0.0107287	+	0.0479370i
$691$	36.7813	−	21.2357i	1.39923	−	0.807845i	0.404916	−	0.914354i	$-0.367301\pi$
$691$	36.7813	−	21.2357i	1.39923	−	0.807845i	0.994312	+	0.106509i	$0.0339673\pi$
$692$	−6.95144	+	6.95144i	−0.264254	+	0.264254i
$693$		0			0
$694$			6.30557i			0.239356i
$695$	−49.5224	+	2.06227i	−1.87849	+	0.0782265i
$696$	−6.26301	−	3.61595i	−0.237399	−	0.137062i
$697$	−17.6695	+	4.73453i	−0.669280	+	0.179333i
$698$	−3.34362	+	12.4786i	−0.126558	+	0.472320i
$699$	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	$0.395464\pi$
$702$	1.02561	−	3.82764i	0.0387093	−	0.144465i
$703$	−0.589700	+	0.158010i	−0.0222409	+	0.00595944i
$704$	−9.33261	−	5.38818i	−0.351736	−	0.203075i
$705$	17.3472	−	0.722394i	0.653333	−	0.0272069i
$706$		−	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	$-0.456407\pi$
$709$	28.2967	−	16.3371i	1.06270	−	0.613552i	0.926179	+	0.377084i	$0.123073\pi$
$710$	−3.03212	+	13.5478i	−0.113794	+	0.508441i
$711$	−4.93165	+	8.54186i	−0.184951	+	0.320345i
$712$	12.7382	+	3.41319i	0.477385	+	0.127915i
$713$	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
$717$	5.24897	+	19.5894i	0.196027	+	0.731581i
$718$	1.61104	+	6.01247i	0.0601233	+	0.224383i
$719$	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
$723$	2.67555	+	0.716912i	0.0995048	+	0.0266622i
$724$	−6.00966	+	10.4090i	−0.223347	+	0.386849i
$725$	1.15197	+	13.8074i	0.0427830	+	0.512794i
$726$	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
$730$	0.960044	+	23.0540i	0.0355328	+	0.853267i
$731$	−7.15181	−	4.12910i	−0.264519	−	0.152720i
$732$	−19.5803	+	5.24652i	−0.723709	+	0.193917i
$733$	−0.872739	+	3.25711i	−0.0322354	+	0.120304i	−0.980169	−	0.198165i	$-0.936502\pi$
$733$	−0.872739	+	3.25711i	−0.0322354	+	0.120304i	0.947933	+	0.318469i	$0.103169\pi$
$734$	15.9321			0.588064
$735$		0			0
$736$	4.42747			0.163199
$737$	−0.587125	+	2.19118i	−0.0216270	+	0.0807132i
$738$	6.40510	−	1.71624i	0.235775	−	0.0631757i
$739$	−4.29271	−	2.47840i	−0.157910	−	0.0911693i	0.418963	−	0.908003i	$-0.362394\pi$
$739$	−4.29271	−	2.47840i	−0.157910	−	0.0911693i	−0.576873	+	0.816834i	$0.695727\pi$
$740$	18.7659	−	20.3968i	0.689848	−	0.749800i
$741$		−	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
$745$	−20.8610	+	13.2310i	−0.764289	+	0.484745i
$746$	−0.807303	+	1.39829i	−0.0295575	+	0.0511950i
$747$	2.23440	+	0.598706i	0.0817525	+	0.0219055i
$748$	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	$0.767880\pi$
$752$	−1.68694	−	6.29575i	−0.0615164	−	0.229582i
$753$	1.57875	+	5.89197i	0.0575328	+	0.214715i
$754$	−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	$0.476129\pi$
$758$	−13.8077	−	3.69977i	−0.501520	−	0.134382i
$759$	−1.45473	+	2.51967i	−0.0528035	+	0.0914584i
$760$	−0.397309	−	0.0889211i	−0.0144119	−	0.00322551i
$761$	24.3504	−	14.0587i	0.882703	−	0.509629i	0.0111541	−	0.999938i	$-0.496449\pi$
$761$	24.3504	−	14.0587i	0.882703	−	0.509629i	0.871549	+	0.490309i	$0.163116\pi$
$762$	3.69181	−	3.69181i	0.133740	−	0.133740i
$763$		0			0
$764$			7.63986i			0.276400i
$765$	3.46765	+	3.19038i	0.125373	+	0.115349i
$766$	−19.5862	−	11.3081i	−0.707679	−	0.408579i
$767$	−34.9474	+	9.36412i	−1.26188	+	0.338119i
$768$	−3.34324	+	12.4771i	−0.120639	+	0.450230i
$769$	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
$772$	2.49177	−	9.29941i	0.0896807	−	0.334693i
$773$	−43.3367	+	11.6120i	−1.55871	+	0.417656i	−0.932256	−	0.361800i	$-0.882162\pi$
$773$	−43.3367	+	11.6120i	−1.55871	+	0.417656i	−0.626457	+	0.779456i	$0.715496\pi$
$774$	2.59249	+	1.49678i	0.0931853	+	0.0538005i
$775$	10.8404	+	5.10823i	0.389399	+	0.183493i
$776$		−	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
$780$	8.80041	+	13.8755i	0.315105	+	0.496821i
$781$	−15.6516	+	27.1094i	−0.560058	+	0.970049i
$782$	1.17460	+	0.314733i	0.0420035	+	0.0112548i
$783$	−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
$787$	8.21624	+	30.6634i	0.292877	+	1.09303i	0.942889	+	0.333108i	$0.108097\pi$
$787$	8.21624	+	30.6634i	0.292877	+	1.09303i	−0.650011	+	0.759924i	$0.725236\pi$
$788$	6.57108	+	24.5236i	0.234085	+	0.873617i
$789$	−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
$793$	−71.7082	−	19.2142i	−2.54643	−	0.682315i
$794$	−3.63833	+	6.30177i	−0.129119	+	0.223641i
$795$	−10.3964	−	16.3919i	−0.368723	−	0.581360i
$796$	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
$800$	27.5768	−	9.91153i	0.974988	−	0.350425i
$801$	4.37614	+	2.52657i	0.154623	+	0.0892718i
$802$	−10.8835	+	2.91622i	−0.384309	+	0.102975i
$803$	−13.4656	+	50.2541i	−0.475189	+	1.77343i
$804$	0.834323			0.0294243
$805$		0			0
$806$	−9.49747			−0.334534
$807$	6.40192	−	23.8923i	0.225358	−	0.841049i
$808$	48.3885	−	12.9657i	1.70230	−	0.456130i
$809$	−19.5042	−	11.2608i	−0.685732	−	0.395907i	0.116279	−	0.993217i	$-0.462903\pi$
$809$	−19.5042	−	11.2608i	−0.685732	−	0.395907i	−0.802011	+	0.597309i	$0.796237\pi$
$810$	−1.25700	−	1.15650i	−0.0441666	−	0.0406352i
$811$		−	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
$815$	−16.9893	−	3.80235i	−0.595108	−	0.133190i
$816$	0.884454	−	1.53192i	0.0309621	−	0.0536279i
$817$	0.264094	+	0.0707639i	0.00923949	+	0.00247572i
$818$	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	$0.880870\pi$
$822$	−2.86222	−	10.6820i	−0.0998315	−	0.372576i
$823$	−12.4099	−	46.3143i	−0.432581	−	1.61441i	−0.746790	−	0.665060i	$-0.768406\pi$
$823$	−12.4099	−	46.3143i	−0.432581	−	1.61441i	0.314209	−	0.949354i	$-0.398261\pi$
$824$	−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	$-0.630651\pi$
$828$	1.03361	+	0.276955i	0.0359205	+	0.00962486i
$829$	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	$-0.0324228\pi$
$830$	3.33666	−	2.11625i	0.115817	−	0.0734561i
$831$	−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
$835$	4.04598	−	4.39760i	0.140017	−	0.152185i
$836$	−0.329618	−	0.190305i	−0.0114001	−	0.00658184i
$837$	−2.31507	+	0.620321i	−0.0800205	+	0.0214414i
$838$	3.07378	−	11.4715i	0.106182	−	0.396277i
$839$	−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
$842$	0.652204	−	2.43406i	0.0224764	−	0.0838832i
$843$	−5.07381	+	1.35952i	−0.174751	+	0.0468245i
$844$	−14.7499	−	8.51585i	−0.507712	−	0.293128i
$845$	1.29422	+	31.0786i	0.0445224	+	1.06914i
$846$			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
$850$	8.02065	−	0.669172i	0.275106	−	0.0229524i
$851$	3.30525	−	5.72486i	0.113303	−	0.196246i
$852$	11.1207	+	2.97978i	0.380989	+	0.102086i
$853$	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
$857$	−2.06832	−	7.71909i	−0.0706526	−	0.263679i	0.921560	−	0.388236i	$-0.126916\pi$
$857$	−2.06832	−	7.71909i	−0.0706526	−	0.263679i	−0.992212	+	0.124557i	$0.960249\pi$
$858$	−3.95001	−	14.7416i	−0.134851	−	0.503271i
$859$	−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
$863$	16.3618	+	4.38413i	0.556962	+	0.149237i	0.526310	−	0.850293i	$-0.323575\pi$
$863$	16.3618	+	4.38413i	0.556962	+	0.149237i	0.0306516	+	0.999530i	$0.490242\pi$
$864$	−2.93039	+	5.07559i	−0.0996939	+	0.172675i
$865$	−3.38941	+	15.1442i	−0.115243	+	0.514920i
$866$	−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
$870$	−4.72913	+	0.196936i	−0.160332	+	0.00667676i
$871$	2.64615	+	1.52776i	0.0896614	+	0.0517660i
$872$	5.44649	−	1.45938i	0.184441	−	0.0494209i
$873$	2.51039	−	9.36890i	0.0849638	−	0.317089i
$874$	−0.0402602			−0.00136182
$875$		0			0
$876$	19.1350			0.646510
$877$	−4.23918	+	15.8208i	−0.143147	+	0.534232i	0.856684	+	0.515842i	$0.172521\pi$
$877$	−4.23918	+	15.8208i	−0.143147	+	0.534232i	−0.999831	+	0.0183902i	$0.994146\pi$
$878$	20.0084	−	5.36123i	0.675250	−	0.180933i
$879$	18.6842	+	10.7873i	0.630202	+	0.363847i
$880$	7.22281	−	0.300781i	0.243481	−	0.0101393i
$881$			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
$885$	−3.40609	+	15.2187i	−0.114494	+	0.511572i
$886$	13.0445	−	22.5938i	0.438240	−	0.759054i
$887$	−36.0664	−	9.66396i	−1.21099	−	0.324484i	−0.403840	−	0.914830i	$-0.632325\pi$
$887$	−36.0664	−	9.66396i	−1.21099	−	0.324484i	−0.807151	+	0.590346i	$0.798991\pi$
$888$	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
$892$	−6.06223	−	22.6246i	−0.202979	−	0.757526i
$893$	0.140207	+	0.523259i	0.00469184	+	0.0175102i
$894$	−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
$898$	7.23289	+	1.93805i	0.241365	+	0.0646735i
$899$	−3.32077	+	5.75174i	−0.110754	+	0.191831i
$900$	7.05793	−	0.588852i	0.235264	−	0.0196284i
$901$	−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
$905$	0.789441	+	18.9572i	0.0262419	+	0.630160i
$906$	−12.1716	−	7.02729i	−0.404375	−	0.233466i
$907$	32.3002	−	8.65482i	1.07251	−	0.287379i	0.320987	−	0.947084i	$-0.395985\pi$
$907$	32.3002	−	8.65482i	1.07251	−	0.287379i	0.751525	+	0.659705i	$0.229319\pi$
$908$	−0.573005	+	2.13848i	−0.0190158	+	0.0709681i
$909$	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	$0.595401\pi$
$912$	−0.0151576	+	0.0565691i	−0.000501920	+	0.00187319i
$913$	8.60549	−	2.30583i	0.284800	−	0.0763120i
$914$	−0.514622	−	0.297117i	−0.0170222	−	0.00982776i
$915$	−21.6662	+	23.5491i	−0.716262	+	0.778510i
$916$		−	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	$-0.550858\pi$
$919$	18.6847	−	10.7876i	0.616351	−	0.355850i	0.775447	+	0.631413i	$0.217525\pi$
$920$	3.72284	−	2.36118i	0.122738	−	0.0778458i
$921$	10.3377	−	17.9055i	0.340640	−	0.590005i
$922$	0.613733	+	0.164449i	0.0202122	+	0.00541585i
$923$	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
$927$	−0.855857	−	3.19410i	−0.0281100	−	0.104908i
$928$	4.20339	+	15.6873i	0.137983	+	0.514960i
$929$	−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
$933$	2.76465	+	0.740787i	0.0905107	+	0.0242523i
$934$	12.5760	−	21.7823i	0.411500	−	0.712739i
$935$	17.7096	+	3.96355i	0.579165	+	0.129622i
$936$	−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
$940$	−18.0987	−	16.6516i	−0.590314	−	0.543115i
$941$	2.23517	+	1.29048i	0.0728645	+	0.0420683i	0.535990	−	0.844225i	$-0.319939\pi$
$941$	2.23517	+	1.29048i	0.0728645	+	0.0420683i	−0.463125	+	0.886293i	$0.653272\pi$
$942$	1.09559	−	0.293563i	0.0356963	−	0.00956479i
$943$	−1.69728	+	6.33435i	−0.0552711	+	0.206275i
$944$	5.85450			0.190548
$945$		0			0
$946$	11.5293			0.374848
$947$	1.80892	−	6.75097i	0.0587819	−	0.219377i	−0.930287	−	0.366833i	$-0.880442\pi$
$947$	1.80892	−	6.75097i	0.0587819	−	0.219377i	0.989069	+	0.147456i	$0.0471086\pi$
$948$	13.4952	−	3.61603i	0.438304	−	0.117443i
$949$	60.6887	+	35.0387i	1.97004	+	1.13740i
$950$	−0.250764	+	0.0901283i	−0.00813585	+	0.00292415i
$951$			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
$955$	6.45947	+	10.1845i	0.209024	+	0.329564i
$956$	14.3636	−	24.8784i	0.464551	−	0.804625i
$957$	−10.3088	−	2.76222i	−0.333235	−	0.0892900i
$958$	−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
$962$	8.97467	+	33.4939i	0.289355	+	1.07989i
$963$	2.34164	+	8.73911i	0.0754582	+	0.281614i
$964$	−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	$0.686848\pi$
$968$	−9.66239	−	2.58903i	−0.310561	−	0.0832146i
$969$	−0.0735096	+	0.127322i	−0.00236147	+	0.00409019i
$970$	−8.87349	−	13.9907i	−0.284910	−	0.449214i
$971$	−11.4195	+	6.59307i	−0.366470	+	0.211582i	−0.671915	−	0.740628i	$-0.734528\pi$
$971$	−11.4195	+	6.59307i	−0.366470	+	0.211582i	0.305445	+	0.952210i	$0.401195\pi$
$972$	−1.00161	+	1.00161i	−0.0321267	+	0.0321267i
$973$		0			0
$974$		−	7.80931i		−	0.250226i
$975$	23.4633	+	11.0564i	0.751427	+	0.354088i
$976$	10.4034	+	6.00641i	0.333005	+	0.192260i
$977$	33.4574	−	8.96490i	1.07040	−	0.286812i	0.319742	−	0.947505i	$-0.396404\pi$
$977$	33.4574	−	8.96490i	1.07040	−	0.286812i	0.750657	+	0.660692i	$0.229737\pi$
$978$	1.53930	−	5.74475i	0.0492214	−	0.183697i
$979$	19.4614			0.621990
$980$		0			0
$981$	2.16057			0.0689818
$982$	3.97468	−	14.8337i	0.126837	−	0.473362i
$983$	−21.4961	+	5.75986i	−0.685618	+	0.183711i	−0.584780	−	0.811192i	$-0.698819\pi$
$983$	−21.4961	+	5.75986i	−0.685618	+	0.183711i	−0.100838	+	0.994903i	$0.532152\pi$
$984$	−19.6197	−	11.3275i	−0.625454	−	0.361106i
$985$	29.4944	+	27.1361i	0.939769	+	0.864628i
$986$			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
$990$	−6.41963	−	1.43677i	−0.204029	−	0.0456635i
$991$	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	$0.00798206\pi$
$992$	13.5681	+	3.63557i	0.430788	+	0.115429i
$993$	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
$997$	−8.37177	−	31.2439i	−0.265137	−	0.989503i	−0.962167	−	0.272461i	$-0.912162\pi$
$997$	−8.37177	−	31.2439i	−0.265137	−	0.989503i	0.697030	−	0.717042i	$-0.254504\pi$
$998$	3.04916	+	11.3796i	0.0965194	+	0.360215i
$999$	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.472.5		32
5.3	odd	4	inner	735.2.v.a.178.3		32
7.2	even	3	inner	735.2.v.a.607.4		32
7.3	odd	6		105.2.m.a.97.5	yes	16
7.4	even	3		105.2.m.a.97.6	yes	16
7.5	odd	6	inner	735.2.v.a.607.3		32
7.6	odd	2	inner	735.2.v.a.472.6		32
21.11	odd	6		315.2.p.e.307.4		16
21.17	even	6		315.2.p.e.307.3		16
28.3	even	6		1680.2.cz.d.97.7		16
28.11	odd	6		1680.2.cz.d.97.2		16
35.3	even	12		105.2.m.a.13.6	yes	16
35.4	even	6		525.2.m.b.307.3		16
35.13	even	4	inner	735.2.v.a.178.4		32
35.17	even	12		525.2.m.b.118.3		16
35.18	odd	12		105.2.m.a.13.5	✓	16
35.23	odd	12	inner	735.2.v.a.313.6		32
35.24	odd	6		525.2.m.b.307.4		16
35.32	odd	12		525.2.m.b.118.4		16
35.33	even	12	inner	735.2.v.a.313.5		32
105.38	odd	12		315.2.p.e.118.4		16
105.53	even	12		315.2.p.e.118.3		16
140.3	odd	12		1680.2.cz.d.433.2		16
140.123	even	12		1680.2.cz.d.433.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	35.18	odd	12
105.2.m.a.13.6	yes	16	35.3	even	12
105.2.m.a.97.5	yes	16	7.3	odd	6
105.2.m.a.97.6	yes	16	7.4	even	3
315.2.p.e.118.3		16	105.53	even	12
315.2.p.e.118.4		16	105.38	odd	12
315.2.p.e.307.3		16	21.17	even	6
315.2.p.e.307.4		16	21.11	odd	6
525.2.m.b.118.3		16	35.17	even	12
525.2.m.b.118.4		16	35.32	odd	12
525.2.m.b.307.3		16	35.4	even	6
525.2.m.b.307.4		16	35.24	odd	6
735.2.v.a.178.3		32	5.3	odd	4	inner
735.2.v.a.178.4		32	35.13	even	4	inner
735.2.v.a.313.5		32	35.33	even	12	inner
735.2.v.a.313.6		32	35.23	odd	12	inner
735.2.v.a.472.5		32	1.1	even	1	trivial
735.2.v.a.472.6		32	7.6	odd	2	inner
735.2.v.a.607.3		32	7.5	odd	6	inner
735.2.v.a.607.4		32	7.2	even	3	inner
1680.2.cz.d.97.2		16	28.11	odd	6
1680.2.cz.d.97.7		16	28.3	even	6
1680.2.cz.d.433.2		16	140.3	odd	12
1680.2.cz.d.433.7		16	140.123	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)

\(f(q)\)	\(=\)	\(q+(0.197706 - 0.737849i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.22672 + 0.708245i) q^{4} +(2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 - 1.84539i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.197706 - 0.737849i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.22672 + 0.708245i) q^{4} +(2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 - 1.84539i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.373055 - 1.66685i) q^{10} +(1.92568 - 3.33538i) q^{11} +(-1.36822 - 0.366615i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(-2.13393 + 0.668102i) q^{15} +(0.419714 + 0.726965i) q^{16} +(0.545404 + 2.03548i) q^{17} +(-0.197706 - 0.737849i) q^{18} +(-0.0348837 - 0.0604203i) q^{19} +(2.80654 + 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.729698 + 0.195522i) q^{23} +(-1.30489 + 2.26014i) q^{24} +(4.98269 - 0.415712i) q^{25} +(-3.43177 + 1.98133i) q^{26} +(-0.707107 + 0.707107i) q^{27} +2.77107i q^{29} +(0.0710685 + 1.70660i) q^{30} +(2.07564 + 1.19837i) q^{31} +(5.66108 - 1.51688i) q^{32} +(-0.996806 + 3.72013i) q^{33} +1.60970 q^{34} +1.41649 q^{36} +(2.26481 - 8.45237i) q^{37} +(-0.0514778 + 0.0137934i) q^{38} +(4.49256 + 2.59378i) q^{39} +(3.95116 - 4.29454i) q^{40} +8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} +(4.72453 - 2.72771i) q^{44} +(1.88830 - 1.19764i) q^{45} +(0.288532 - 0.499752i) q^{46} +(-7.50006 - 2.00963i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(0.678376 - 3.75866i) q^{50} +(-1.05364 - 1.82496i) q^{51} +(-1.90184 - 7.09776i) q^{52} +(2.24675 + 8.38498i) q^{53} +(0.381939 + 0.661538i) q^{54} +(3.99191 - 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} +(2.04464 + 0.547858i) q^{58} +(3.48720 - 6.04001i) q^{59} +(-3.09090 - 0.691771i) q^{60} +(12.3935 - 7.15536i) q^{61} +(1.29458 - 1.29458i) q^{62} -2.79807i q^{64} +(-8.53643 - 7.85389i) q^{65} +(2.54782 + 1.47098i) q^{66} +(-0.568937 + 0.152446i) q^{67} +(-0.772560 + 2.88323i) q^{68} -0.755439 q^{69} -8.12783 q^{71} +(0.675461 - 2.52086i) q^{72} +(-13.0484 + 3.49631i) q^{73} +(-5.78881 - 3.34217i) q^{74} +(-4.70531 + 1.69116i) q^{75} -0.0988248i q^{76} +(2.80203 - 2.80203i) q^{78} +(-8.54186 + 4.93165i) q^{79} +(1.00533 + 1.58509i) q^{80} +(0.500000 - 0.866025i) q^{81} +(6.40510 + 1.71624i) q^{82} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(1.49678 + 2.59249i) q^{86} +(-0.717207 - 2.67665i) q^{87} +(-2.60144 - 9.70872i) q^{88} +(2.52657 + 4.37614i) q^{89} +(-0.510348 - 1.63006i) q^{90} +(0.756656 + 0.756656i) q^{92} +(-2.31507 - 0.620321i) q^{93} +(-2.96561 + 5.13659i) q^{94} +(-0.0835560 - 0.131741i) 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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