LMFDB - Embedded newform 735.2.v.a.313.6

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			313.6
Character	$\chi$	$=$	735.313
Dual form			735.2.v.a.472.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.197706 + 0.737849i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.22672 - 0.708245i) q^{4} +(-2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.197706	+	0.737849i	0.139799	+	0.521738i	0.999932	+	0.0116677i	$0.00371404\pi$
$2$	0.197706	+	0.737849i	0.139799	+	0.521738i	−0.860133	+	0.510071i	$0.829619\pi$
$3$	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	0.995407	+	0.0957376i	$0.0305210\pi$
$11$	1.92568	+	3.33538i	0.580615	+	1.00565i	−0.414792	+	0.909916i	$0.636146\pi$
$12$	1.36822	−	0.366615i	0.394973	−	0.105833i
$13$	3.66816	−	3.66816i	1.01737	−	1.01737i	0.0175187	−	0.999847i	$-0.494423\pi$
$13$	3.66816	−	3.66816i	1.01737	−	1.01737i	0.999847	−	0.0175187i	$-0.00557667\pi$
$14$		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	$-0.998922\pi$
$17$	−0.545404	+	2.03548i	−0.132280	+	0.493675i	0.867714	+	0.497063i	$0.165588\pi$
$18$	−0.197706	+	0.737849i	−0.0465998	+	0.173913i
$19$	0.0348837	−	0.0604203i	0.00800286	−	0.0138614i	−0.861996	−	0.506915i	$-0.830786\pi$
$19$	0.0348837	−	0.0604203i	0.00800286	−	0.0138614i	0.869999	+	0.493053i	$0.164119\pi$
$20$	−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	−0.181939	−	0.983310i	$-0.558237\pi$
$23$	0.729698	−	0.195522i	0.152153	−	0.0407692i	0.334091	+	0.942541i	$0.391571\pi$
$24$	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	$-0.917171\pi$
$29$		−	2.77107i		−	0.514576i	0.966335	−	0.257288i	$-0.0828288\pi$
$30$	0.0710685	−	1.70660i	0.0129753	−	0.311582i
$31$	−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	$0.402385\pi$
$32$	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	0.857204	+	0.514976i	$0.172199\pi$
$37$	2.26481	+	8.45237i	0.372332	+	1.38956i	−0.484872	+	0.874585i	$0.661134\pi$
$38$	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	0.463508	−	0.886093i	$-0.346591\pi$
$43$	−2.77107	−	2.77107i	−0.422585	−	0.422585i	−0.886093	+	0.463508i	$0.846591\pi$
$44$	4.72453	+	2.72771i	0.712250	+	0.411218i
$45$	−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	$-0.391710\pi$
$47$	7.50006	−	2.00963i	1.09400	−	0.293135i	0.760317	+	0.649552i	$0.225043\pi$
$48$	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	−0.621174	−	0.783673i	$-0.713344\pi$
$53$	2.24675	−	8.38498i	0.308615	−	1.15177i	0.929789	−	0.368093i	$-0.119989\pi$
$54$	−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	$-0.316668\pi$
$59$	−3.48720	−	6.04001i	−0.453995	−	0.786342i	−0.998630	+	0.0523310i	$0.983335\pi$
$60$	−3.09090	+	0.691771i	−0.399034	+	0.0893072i
$61$	−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
$65$	−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	0.223898	−	0.974613i	$-0.428122\pi$
$67$	−0.568937	−	0.152446i	−0.0695067	−	0.0186243i	−0.293405	+	0.955988i	$0.594788\pi$
$68$	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	$-0.126468\pi$
$73$	13.0484	+	3.49631i	1.52720	+	0.409212i	0.605096	+	0.796152i	$0.293135\pi$
$74$	−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	−0.0645434	−	0.997915i	$-0.520559\pi$
$79$	−8.54186	−	4.93165i	−0.961035	−	0.554854i	−0.896491	+	0.443061i	$0.853892\pi$
$80$	−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	$-0.790520\pi$
$83$	−1.63570	+	1.63570i	−0.179541	+	0.179541i	0.611615	+	0.791156i	$0.290520\pi$
$84$		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	$-0.919635\pi$
$89$	−2.52657	+	4.37614i	−0.267815	+	0.463870i	0.700482	+	0.713670i	$0.252968\pi$
$90$	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	$-0.413885\pi$
$97$	−6.85851	−	6.85851i	−0.696376	−	0.696376i	−0.963627	+	0.267251i	$0.913885\pi$
$98$		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	−0.678752	+	0.734368i	$0.737479\pi$
$101$	−16.6236	+	9.59763i	−1.65411	+	0.955000i	−0.975357	+	0.220632i	$0.929188\pi$
$102$	−1.55485	−	0.416622i	−0.153954	−	0.0412517i
$103$	−0.855857	−	3.19410i	−0.0843301	−	0.314724i	0.910856	−	0.412723i	$-0.135422\pi$
$103$	−0.855857	−	3.19410i	−0.0843301	−	0.314724i	−0.995186	+	0.0979992i	$0.968756\pi$
$104$	13.5384			1.32755
$105$		0			0
$106$	6.63105			0.644064
$107$	−2.34164	−	8.73911i	−0.226375	−	0.844841i	−0.981849	−	0.189663i	$-0.939260\pi$
$107$	−2.34164	−	8.73911i	−0.226375	−	0.844841i	0.755475	−	0.655178i	$-0.227406\pi$
$108$	1.36822	+	0.366615i	0.131658	+	0.0352775i
$109$	1.87111	−	1.08029i	0.179220	−	0.103473i	−0.407706	−	0.913113i	$-0.633671\pi$
$109$	1.87111	−	1.08029i	0.179220	−	0.103473i	0.586926	+	0.809641i	$0.300338\pi$
$110$	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	0.485143	−	0.874435i	$-0.338768\pi$
$113$	−4.13823	−	4.13823i	−0.389292	−	0.389292i	−0.874435	+	0.485143i	$0.838768\pi$
$114$	0.0461537	+	0.0266469i	0.00432269	+	0.00249571i
$115$	−1.64843	+	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	−0.888239	−	0.459381i	$-0.848071\pi$
$127$	−4.83298	+	4.83298i	−0.428858	+	0.428858i	0.459381	+	0.888239i	$0.348071\pi$
$128$	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	$-0.342338\pi$
$131$	−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
$135$	−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	−0.393971	−	0.919123i	$-0.628899\pi$
$137$	−13.9839	−	3.74696i	−1.19472	−	0.320125i	−0.800751	+	0.598998i	$0.795566\pi$
$138$	0.149355	+	0.557400i	0.0127139	+	0.0474491i
$139$	22.1663			1.88012			0.940060	−	0.341009i	$-0.110769\pi$
$139$	22.1663			1.88012			0.940060	+	0.341009i	$0.110769\pi$
$140$		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	0.0539779	−	0.998542i	$-0.482810\pi$
$149$	−9.56745	−	5.52377i	−0.783796	−	0.452525i	−0.837774	+	0.546017i	$0.816143\pi$
$150$	−0.317553	+	3.80617i	−0.0259281	+	0.310772i
$151$	−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	$-0.435962\pi$
$152$	0.175873	−	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	$-0.897795\pi$
$157$	0.384306	−	1.43425i	0.0306709	−	0.114465i	0.979564	+	0.201132i	$0.0644619\pi$
$158$	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	−0.541020	−	0.841010i	$-0.681962\pi$
$163$	−7.52050	+	2.01511i	−0.589051	+	0.157836i	−0.0480317	+	0.998846i	$0.515295\pi$
$164$	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	$-0.282972\pi$
$167$	−1.88968	−	1.88968i	−0.146228	−	0.146228i	−0.776431	+	0.630203i	$0.782972\pi$
$168$		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	0.999987	+	0.00519041i	$0.00165217\pi$
$173$	1.79627	+	6.70378i	0.136568	+	0.509679i	−0.863419	+	0.504488i	$0.831681\pi$
$174$	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	−0.961231	−	0.275743i	$-0.911076\pi$
$179$	−16.0957	+	9.29284i	−1.20305	+	0.694579i	−0.241815	+	0.970322i	$0.577743\pi$
$180$	−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	−0.751813	−	0.659377i	$-0.770820\pi$
$191$	2.69676	−	4.67092i	0.195130	−	0.337976i	0.946943	+	0.321401i	$0.104154\pi$
$192$	−0.724193	+	2.70273i	−0.0522641	+	0.195052i
$193$	−1.75911	+	6.56510i	−0.126624	+	0.472566i	−0.999892	−	0.0146728i	$-0.995329\pi$
$193$	−1.75911	+	6.56510i	−0.126624	+	0.472566i	0.873269	+	0.487239i	$0.161996\pi$
$194$	3.70458	−	6.41652i	0.265973	−	0.460679i
$195$	−10.2783	+	5.37688i	−0.736044	+	0.385046i
$196$		0			0
$197$	12.6739	−	12.6739i	0.902981	−	0.902981i	−0.0927124	−	0.995693i	$-0.529554\pi$
$197$	12.6739	−	12.6739i	0.902981	−	0.902981i	0.995693	+	0.0927124i	$0.0295537\pi$
$198$	−2.84172	+	0.761438i	−0.201953	+	0.0541130i
$199$	−1.33556	−	2.31325i	−0.0946750	−	0.163982i	0.814798	−	0.579745i	$-0.196848\pi$
$199$	−1.33556	−	2.31325i	−0.0946750	−	0.163982i	−0.909473	+	0.415763i	$0.863515\pi$
$200$	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	$-0.563232\pi$
$223$	11.6925	−	11.6925i	0.782988	−	0.782988i	0.980334	+	0.197346i	$0.0632321\pi$
$224$		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	$-0.933184\pi$
$227$	−0.404524	+	1.50971i	−0.0268492	+	0.100203i	0.951201	+	0.308572i	$0.0998511\pi$
$228$	0.0255777	−	0.0954574i	0.00169393	−	0.00632182i
$229$	3.91654	−	6.78365i	0.258812	−	0.448276i	−0.707112	−	0.707102i	$-0.750002\pi$
$229$	3.91654	−	6.78365i	0.258812	−	0.448276i	0.965924	+	0.258826i	$0.0833355\pi$
$230$	−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	−0.303639	−	0.952787i	$-0.598202\pi$
$233$	−1.37692	+	0.368944i	−0.0902048	+	0.0241703i	0.213434	+	0.976957i	$0.431535\pi$
$234$	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	$0.227718\pi$
$239$			20.2805i			1.31183i	−0.754833	+	0.655917i	$0.772282\pi$
$240$	−1.38132	+	1.27088i	−0.0891641	+	0.0820349i
$241$	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	$0.304898\pi$
$242$	−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	$-0.611710\pi$
$257$	−2.75722	+	0.738795i	−0.171991	+	0.0460848i	0.171796	+	0.985133i	$0.445043\pi$
$258$	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	−0.469741	−	0.882804i	$-0.655653\pi$
$263$	6.13773	−	22.9063i	0.378469	−	1.41246i	0.848210	−	0.529660i	$-0.177681\pi$
$264$	−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	0.945838	+	0.324638i	$0.105242\pi$
$269$	12.3676	+	21.4213i	0.754064	+	1.30608i	−0.191774	+	0.981439i	$0.561424\pi$
$270$	0.914849	−	1.44243i	0.0556759	−	0.0877834i
$271$	−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
$275$	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	0.719003	−	0.695007i	$-0.244599\pi$
$277$	16.5463	+	4.43358i	0.994174	+	0.266388i	0.275171	+	0.961395i	$0.411266\pi$
$278$	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	$-0.438993\pi$
$283$	−2.27756	−	0.610271i	−0.135387	−	0.0362768i	−0.325876	+	0.945412i	$0.605659\pi$
$284$	−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	$-0.532972\pi$
$293$	15.2556	−	15.2556i	0.891240	−	0.891240i	0.994640	+	0.103400i	$0.0329722\pi$
$294$		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	$-0.0491256\pi$
$307$	14.6198	+	14.6198i	0.834394	+	0.834394i	−0.153721	+	0.988114i	$0.549126\pi$
$308$		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	$-0.640807\pi$
$311$	2.47872	−	1.43109i	0.140555	−	0.0811497i	0.568629	+	0.822594i	$0.307474\pi$
$312$	13.0771	+	3.50400i	0.740345	+	0.198375i
$313$	3.44732	+	12.8656i	0.194854	+	0.727204i	0.992305	+	0.123820i	$0.0395146\pi$
$313$	3.44732	+	12.8656i	0.194854	+	0.727204i	−0.797451	+	0.603384i	$0.793819\pi$
$314$	1.13424			0.0640088
$315$		0			0
$316$	−13.9713			−0.785945
$317$	2.70240	+	10.0855i	0.151782	+	0.566459i	0.999359	+	0.0357866i	$0.0113937\pi$
$317$	2.70240	+	10.0855i	0.151782	+	0.566459i	−0.847577	+	0.530672i	$0.821940\pi$
$318$	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	0.334193	+	0.942505i	$0.391536\pi$
$331$	−11.8100	+	20.4555i	−0.649136	+	1.12434i	−0.983330	+	0.181833i	$0.941797\pi$
$332$	−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	−0.828695	−	0.559700i	$-0.810916\pi$
$337$	−4.93809	+	4.93809i	−0.268995	+	0.268995i	0.559700	+	0.828695i	$0.310916\pi$
$338$	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	0.0383685	−	0.999264i	$-0.487784\pi$
$347$	−7.97341	−	2.13647i	−0.428035	−	0.114692i	−0.466404	+	0.884572i	$0.654451\pi$
$348$	−1.01592	−	3.79145i	−0.0544589	−	0.203243i
$349$	16.9121			0.905282			0.452641	−	0.891693i	$-0.350482\pi$
$349$	16.9121			0.905282			0.452641	+	0.891693i	$0.350482\pi$
$350$		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	$-0.554198\pi$
$353$	−15.1990	−	4.07257i	−0.808963	−	0.216761i	−0.639516	+	0.768778i	$0.720865\pi$
$354$	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	0.302078	−	0.953283i	$-0.402320\pi$
$359$	−7.05693	−	4.07432i	−0.372450	−	0.215034i	−0.674528	+	0.738249i	$0.735653\pi$
$360$	−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	0.669378	+	0.742922i	$0.266561\pi$
$367$	−5.39815	+	20.1462i	−0.281781	+	1.05162i	−0.951160	+	0.308700i	$0.900106\pi$
$368$	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	−0.311288	−	0.950316i	$-0.600760\pi$
$373$	−2.04168	+	0.547065i	−0.105714	+	0.0283260i	0.205574	+	0.978642i	$0.434094\pi$
$374$	−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	$0.159590\pi$
$379$			18.7135i			0.961248i	−0.876927	+	0.480624i	$0.840410\pi$
$380$	−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	−0.827569	−	0.561364i	$-0.810277\pi$
$383$	−7.66288	−	28.5983i	−0.391555	−	1.46130i	0.436014	−	0.899940i	$-0.356390\pi$
$384$	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	0.183641	−	0.982993i	$-0.441212\pi$
$389$	22.2232	−	12.8305i	1.12676	−	0.650535i	0.943118	+	0.332459i	$0.107878\pi$
$390$	−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	$-0.506498\pi$
$397$	9.20135	−	2.46549i	0.461802	−	0.123740i	0.482217	+	0.876052i	$0.339832\pi$
$398$	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	$0.286726\pi$
$402$	0.116450	−	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	$-0.0825848\pi$
$409$	5.28021	+	9.14560i	0.261090	+	0.452221i	−0.705442	+	0.708768i	$0.749251\pi$
$410$	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	$-0.623996\pi$
$419$	−15.5472			−0.759532			−0.379766	+	0.925083i	$0.623996\pi$
$420$		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	0.984315	−	0.176422i	$-0.0564523\pi$
$431$	7.04553	+	12.2032i	0.339371	+	0.587809i	−0.644943	+	0.764230i	$0.723119\pi$
$432$	0.810825	−	0.217260i	0.0390108	−	0.0104529i
$433$	1.72650	−	1.72650i	0.0829702	−	0.0829702i	−0.664404	−	0.747374i	$-0.731314\pi$
$433$	1.72650	−	1.72650i	0.0829702	−	0.0829702i	0.747374	+	0.664404i	$0.231314\pi$
$434$		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	0.336693	+	0.941615i	$0.390692\pi$
$439$	−13.5586	+	23.4841i	−0.647116	+	1.12084i	−0.983809	+	0.179223i	$0.942642\pi$
$440$	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	0.632396	−	0.774645i	$-0.282072\pi$
$443$	32.9897	−	8.83957i	1.56739	−	0.419981i	0.934994	+	0.354664i	$0.115405\pi$
$444$	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	$-0.925699\pi$
$449$		−	9.80267i		−	0.462617i	0.972881	−	0.231308i	$-0.0743006\pi$
$450$	−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	0.970475	−	0.241201i	$-0.0775415\pi$
$457$	0.201340	+	0.751411i	0.00941828	+	0.0351495i	−0.961057	+	0.276351i	$0.910875\pi$
$458$	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	0.822342	−	0.568994i	$-0.192667\pi$
$463$	5.45140	+	5.45140i	0.253348	+	0.253348i	−0.568994	+	0.822342i	$0.692667\pi$
$464$	−2.01448	−	1.16306i	−0.0935197	−	0.0539936i
$465$	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	$-0.859035\pi$
$467$	−31.8048	+	8.52208i	−1.47175	+	0.394355i	−0.568220	+	0.822876i	$0.692368\pi$
$468$	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	−0.793653	−	0.608371i	$-0.791823\pi$
$479$	−20.2160	−	35.0151i	−0.923691	−	1.59988i	−0.130038	−	0.991509i	$-0.541510\pi$
$480$	−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	0.475517	−	0.879706i	$-0.342261\pi$
$487$	9.87490	+	2.64597i	0.447474	+	0.119900i	−0.0280431	+	0.999607i	$0.508928\pi$
$488$	−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	0.170306	−	0.985391i	$-0.445525\pi$
$499$	−13.3564	−	7.71133i	−0.597916	−	0.345207i	−0.768221	+	0.640185i	$0.778858\pi$
$500$	−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	−0.174573	+	0.984644i	$0.555855\pi$
$503$	−25.9985	+	25.9985i	−1.15922	+	1.15922i	−0.984644	+	0.174573i	$0.944145\pi$
$504$		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	−0.0807619	−	0.996733i	$-0.525735\pi$
$509$	18.5636	−	32.1530i	0.822816	−	1.42516i	0.903577	−	0.428425i	$-0.140931\pi$
$510$	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	$-0.684745\pi$
$521$	−2.24415	+	1.29566i	−0.0983180	+	0.0567639i	0.450035	+	0.893011i	$0.351412\pi$
$522$	2.04464	+	0.547858i	0.0894913	+	0.0239791i
$523$	2.22856	+	8.31711i	0.0974482	+	0.363682i	0.997379	−	0.0723506i	$-0.0230500\pi$
$523$	2.22856	+	8.31711i	0.0974482	+	0.363682i	−0.899931	+	0.436032i	$0.856383\pi$
$524$	−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	−0.241894	−	0.970303i	$-0.577769\pi$
$541$	16.7319	−	28.9805i	0.719360	−	1.24597i	0.961254	−	0.275665i	$-0.0888980\pi$
$542$	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	−0.724594	−	0.689175i	$-0.757973\pi$
$547$	−0.828381	+	0.828381i	−0.0354190	+	0.0354190i	0.689175	+	0.724594i	$0.257973\pi$
$548$	−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	−0.193448	−	0.981111i	$-0.561967\pi$
$557$	−20.0969	−	5.38496i	−0.851534	−	0.228168i	−0.658086	+	0.752943i	$0.728634\pi$
$558$	−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	$-0.669926\pi$
$563$	−32.7427	−	8.77338i	−1.37994	−	0.369754i	−0.871100	+	0.491106i	$0.836593\pi$
$564$	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	0.187892	−	0.982190i	$-0.439835\pi$
$569$	−13.5671	−	7.83298i	−0.568763	−	0.328376i	−0.756655	+	0.653814i	$0.773168\pi$
$570$	−0.100634	−	0.0638266i	−0.00421511	−	0.00267340i
$571$	−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	$-0.448396\pi$
$572$	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	0.740119	+	0.672476i	$0.234769\pi$
$577$	−5.69488	+	21.2536i	−0.237081	+	0.884798i	−0.977200	+	0.212322i	$0.931897\pi$
$578$	−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	$-0.0983740\pi$
$587$	15.7111	+	15.7111i	0.648468	+	0.648468i	−0.304155	+	0.952623i	$0.598374\pi$
$588$		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	$-0.0662073\pi$
$593$	0.677877	+	2.52987i	0.0278371	+	0.103889i	−0.950610	+	0.310389i	$0.899541\pi$
$594$	−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	−0.709015	+	0.705193i	$0.750860\pi$
$599$	−40.9761	+	23.6576i	−1.67424	+	0.966622i	−0.965223	+	0.261429i	$0.915806\pi$
$600$	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	$-0.513840\pi$
$607$	10.3088	−	2.76222i	0.418419	−	0.112115i	0.461885	+	0.886940i	$0.347173\pi$
$608$	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	−0.982610	−	0.185679i	$-0.940551\pi$
$613$	−0.960769	+	3.58564i	−0.0388051	+	0.144823i	0.943805	+	0.330502i	$0.107218\pi$
$614$	−7.89676	+	13.6776i	−0.318687	+	0.551983i
$615$	5.79964	−	18.5241i	0.233864	−	0.746965i
$616$		0			0
$617$	11.3212	−	11.3212i	0.455774	−	0.455774i	−0.441491	−	0.897266i	$-0.645550\pi$
$617$	11.3212	−	11.3212i	0.455774	−	0.455774i	0.897266	+	0.441491i	$0.145550\pi$
$618$	2.43990	−	0.653770i	0.0981473	−	0.0262985i
$619$	−4.53385	−	7.85287i	−0.182231	−	0.315633i	0.760409	−	0.649445i	$-0.224999\pi$
$619$	−4.53385	−	7.85287i	−0.182231	−	0.315633i	−0.942640	+	0.333811i	$0.891665\pi$
$620$	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	0.918629	+	0.395122i	$0.129298\pi$
$641$	20.2924	+	35.1474i	0.801500	+	1.38824i	−0.117129	+	0.993117i	$0.537369\pi$
$642$	6.67561	−	1.78872i	0.263465	−	0.0705953i
$643$	−3.89544	+	3.89544i	−0.153621	+	0.153621i	−0.779733	−	0.626112i	$-0.784645\pi$
$643$	−3.89544	+	3.89544i	−0.153621	+	0.153621i	0.626112	+	0.779733i	$0.284645\pi$
$644$		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	0.732352	+	0.680927i	$0.238423\pi$
$647$	−6.16438	+	23.0058i	−0.242347	+	0.904450i	−0.974698	+	0.223524i	$0.928244\pi$
$648$	−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	0.414957	−	0.909841i	$-0.363797\pi$
$653$	31.4119	−	8.41678i	1.22924	−	0.329374i	0.814284	+	0.580467i	$0.197130\pi$
$654$	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	$-0.779777\pi$
$659$		−	32.7543i		−	1.27593i	0.770067	−	0.637963i	$-0.220223\pi$
$660$	−8.25941	−	8.97720i	−0.321497	−	0.349437i
$661$	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	$0.115407\pi$
$662$	−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	0.306179	−	0.951974i	$-0.400950\pi$
$673$	−16.7534	−	16.7534i	−0.645796	−	0.645796i	−0.951974	+	0.306179i	$0.900950\pi$
$674$	−4.61986	−	2.66728i	−0.177950	−	0.102740i
$675$	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	$-0.642987\pi$
$677$	−9.36503	+	2.50935i	−0.359927	+	0.0964422i	0.0743237	+	0.997234i	$0.476320\pi$
$678$	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	−0.588485	−	0.808508i	$-0.700275\pi$
$683$	8.50440	−	31.7389i	0.325412	−	1.21445i	0.913897	−	0.405946i	$-0.133058\pi$
$684$	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	$-0.632699\pi$
$691$	−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
$695$	−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	0.926179	−	0.377084i	$-0.123073\pi$
$709$	28.2967	+	16.3371i	1.06270	+	0.613552i	0.136525	+	0.990637i	$0.456407\pi$
$710$	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	$-0.950675\pi$
$719$	−9.66239	+	16.7357i	−0.360346	+	0.624138i	0.627671	+	0.778478i	$0.284008\pi$
$720$	−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	$-0.272708\pi$
$727$	−2.71795	−	2.71795i	−0.100803	−	0.100803i	−0.755710	+	0.654907i	$0.772708\pi$
$728$		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	$-0.0634981\pi$
$733$	0.872739	+	3.25711i	0.0322354	+	0.120304i	−0.947933	+	0.318469i	$0.896831\pi$
$734$	−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	−0.576873	−	0.816834i	$-0.695727\pi$
$739$	−4.29271	+	2.47840i	−0.157910	+	0.0911693i	0.418963	+	0.908003i	$0.362394\pi$
$740$	−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	0.933340	−	0.358993i	$-0.116880\pi$
$743$	15.6556	+	15.6556i	0.574347	+	0.574347i	−0.358993	+	0.933340i	$0.616880\pi$
$744$	−5.41695	−	3.12748i	−0.198595	−	0.114659i
$745$	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	−0.745691	−	0.666292i	$-0.767880\pi$
$751$	5.59544	−	9.69159i	0.204181	−	0.353651i	0.949871	+	0.312641i	$0.101214\pi$
$752$	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	0.0749214	−	0.997189i	$-0.476129\pi$
$757$	29.4977	−	29.4977i	1.07211	−	1.07211i	0.997189	−	0.0749214i	$-0.0238706\pi$
$758$	−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	$-0.503551\pi$
$761$	−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
$765$	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	$-0.538041\pi$
$769$	−6.61248			−0.238452			−0.119226	+	0.992867i	$0.538041\pi$
$770$		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	$-0.117838\pi$
$773$	43.3367	+	11.6120i	1.55871	+	0.417656i	0.626457	+	0.779456i	$0.284504\pi$
$774$	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	0.650011	+	0.759924i	$0.274764\pi$
$787$	−8.21624	+	30.6634i	−0.292877	+	1.09303i	−0.942889	+	0.333108i	$0.891903\pi$
$788$	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	$-0.291148\pi$
$797$	−5.14677	−	5.14677i	−0.182308	−	0.182308i	−0.792361	+	0.610053i	$0.791148\pi$
$798$		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	−0.802011	−	0.597309i	$-0.796237\pi$
$809$	−19.5042	+	11.2608i	−0.685732	+	0.395907i	0.116279	+	0.993217i	$0.462903\pi$
$810$	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	−0.930779	−	0.365582i	$-0.880870\pi$
$821$	−4.26320	+	7.38408i	−0.148787	+	0.257706i	0.781993	+	0.623288i	$0.214203\pi$
$822$	2.86222	−	10.6820i	0.0998315	−	0.372576i
$823$	−12.4099	+	46.3143i	−0.432581	+	1.61441i	0.314209	+	0.949354i	$0.398261\pi$
$823$	−12.4099	+	46.3143i	−0.432581	+	1.61441i	−0.746790	+	0.665060i	$0.768406\pi$
$824$	4.31498	−	7.47377i	0.150320	−	0.260361i
$825$	3.42027	+	18.9506i	0.119079	+	0.659776i
$826$		0			0
$827$	−37.8440	+	37.8440i	−1.31597	+	1.31597i	−0.399025	+	0.916940i	$0.630651\pi$
$827$	−37.8440	+	37.8440i	−1.31597	+	1.31597i	−0.916940	+	0.399025i	$0.869349\pi$
$828$	1.03361	−	0.276955i	0.0359205	−	0.00962486i
$829$	−16.8570	−	29.1972i	−0.585469	−	1.01406i	−0.994817	−	0.101683i	$-0.967577\pi$
$829$	−16.8570	−	29.1972i	−0.585469	−	1.01406i	0.409348	−	0.912378i	$-0.365756\pi$
$830$	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	$-0.410547\pi$
$839$	16.0665			0.554679			0.277339	+	0.960772i	$0.410547\pi$
$840$		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	$-0.789745\pi$
$853$	−5.14393	+	5.14393i	−0.176125	+	0.176125i	0.613539	+	0.789664i	$0.289745\pi$
$854$		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	$-0.873084\pi$
$857$	2.06832	−	7.71909i	0.0706526	−	0.263679i	0.992212	+	0.124557i	$0.0397511\pi$
$858$	−3.95001	+	14.7416i	−0.134851	+	0.503271i
$859$	21.0400	−	36.4424i	0.717877	−	1.24340i	−0.243963	−	0.969785i	$-0.578447\pi$
$859$	21.0400	−	36.4424i	0.717877	−	1.24340i	0.961839	−	0.273615i	$-0.0882193\pi$
$860$	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	0.0306516	−	0.999530i	$-0.490242\pi$
$863$	16.3618	−	4.38413i	0.556962	−	0.149237i	0.526310	+	0.850293i	$0.323575\pi$
$864$	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	−0.999831	−	0.0183902i	$-0.994146\pi$
$877$	−4.23918	−	15.8208i	−0.143147	−	0.534232i	0.856684	−	0.515842i	$-0.172521\pi$
$878$	−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	0.933534	−	0.358490i	$-0.116708\pi$
$883$	17.0876	+	17.0876i	0.575044	+	0.575044i	−0.358490	+	0.933534i	$0.616708\pi$
$884$	13.4100	+	7.74229i	0.451028	+	0.260401i
$885$	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	$-0.367675\pi$
$887$	36.0664	−	9.66396i	1.21099	−	0.324484i	0.807151	+	0.590346i	$0.201009\pi$
$888$	−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	0.751525	−	0.659705i	$-0.229319\pi$
$907$	32.3002	+	8.65482i	1.07251	+	0.287379i	0.320987	+	0.947084i	$0.395985\pi$
$908$	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	0.775447	−	0.631413i	$-0.217525\pi$
$919$	18.6847	+	10.7876i	0.616351	+	0.355850i	−0.159096	+	0.987263i	$0.550858\pi$
$920$	−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	−0.359467	−	0.933158i	$-0.617041\pi$
$929$	19.1535	−	33.1748i	0.628405	−	1.08843i	0.987872	−	0.155272i	$-0.0496253\pi$
$930$	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	$-0.348875\pi$
$937$	−13.2317	−	13.2317i	−0.432262	−	0.432262i	−0.889397	+	0.457135i	$0.848875\pi$
$938$		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	$-0.680061\pi$
$941$	−2.23517	+	1.29048i	−0.0728645	+	0.0420683i	0.463125	+	0.886293i	$0.346728\pi$
$942$	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	0.989069	−	0.147456i	$-0.0471086\pi$
$947$	1.80892	+	6.75097i	0.0587819	+	0.219377i	−0.930287	+	0.366833i	$0.880442\pi$
$948$	−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	0.390700	−	0.920518i	$-0.372233\pi$
$953$	−16.3558	−	16.3558i	−0.529818	−	0.529818i	−0.920518	+	0.390700i	$0.872233\pi$
$954$	5.74266	+	3.31552i	0.185925	+	0.107344i
$955$	−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	−0.553867	−	0.832605i	$-0.686848\pi$
$967$	8.66781	−	8.66781i	0.278738	−	0.278738i	0.832605	+	0.553867i	$0.186848\pi$
$968$	−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	$-0.265472\pi$
$971$	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
$975$	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	0.750657	−	0.660692i	$-0.229737\pi$
$977$	33.4574	+	8.96490i	1.07040	+	0.286812i	0.319742	+	0.947505i	$0.396404\pi$
$978$	−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	$-0.301181\pi$
$983$	21.4961	+	5.75986i	0.685618	+	0.183711i	0.100838	+	0.994903i	$0.467848\pi$
$984$	−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	0.999686	−	0.0250738i	$-0.00798206\pi$
$991$	15.0516	+	26.0701i	0.478128	+	0.828142i	−0.521557	+	0.853216i	$0.674649\pi$
$992$	−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	−0.697030	−	0.717042i	$-0.745496\pi$
$997$	8.37177	−	31.2439i	0.265137	−	0.989503i	0.962167	−	0.272461i	$-0.0878377\pi$
$998$	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.313.6		32
5.2	odd	4	inner	735.2.v.a.607.4		32
7.2	even	3		105.2.m.a.13.5	✓	16
7.3	odd	6	inner	735.2.v.a.178.4		32
7.4	even	3	inner	735.2.v.a.178.3		32
7.5	odd	6		105.2.m.a.13.6	yes	16
7.6	odd	2	inner	735.2.v.a.313.5		32
21.2	odd	6		315.2.p.e.118.3		16
21.5	even	6		315.2.p.e.118.4		16
28.19	even	6		1680.2.cz.d.433.2		16
28.23	odd	6		1680.2.cz.d.433.7		16
35.2	odd	12		105.2.m.a.97.6	yes	16
35.9	even	6		525.2.m.b.118.4		16
35.12	even	12		105.2.m.a.97.5	yes	16
35.17	even	12	inner	735.2.v.a.472.6		32
35.19	odd	6		525.2.m.b.118.3		16
35.23	odd	12		525.2.m.b.307.3		16
35.27	even	4	inner	735.2.v.a.607.3		32
35.32	odd	12	inner	735.2.v.a.472.5		32
35.33	even	12		525.2.m.b.307.4		16
105.2	even	12		315.2.p.e.307.4		16
105.47	odd	12		315.2.p.e.307.3		16
140.47	odd	12		1680.2.cz.d.97.7		16
140.107	even	12		1680.2.cz.d.97.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	7.2	even	3
105.2.m.a.13.6	yes	16	7.5	odd	6
105.2.m.a.97.5	yes	16	35.12	even	12
105.2.m.a.97.6	yes	16	35.2	odd	12
315.2.p.e.118.3		16	21.2	odd	6
315.2.p.e.118.4		16	21.5	even	6
315.2.p.e.307.3		16	105.47	odd	12
315.2.p.e.307.4		16	105.2	even	12
525.2.m.b.118.3		16	35.19	odd	6
525.2.m.b.118.4		16	35.9	even	6
525.2.m.b.307.3		16	35.23	odd	12
525.2.m.b.307.4		16	35.33	even	12
735.2.v.a.178.3		32	7.4	even	3	inner
735.2.v.a.178.4		32	7.3	odd	6	inner
735.2.v.a.313.5		32	7.6	odd	2	inner
735.2.v.a.313.6		32	1.1	even	1	trivial
735.2.v.a.472.5		32	35.32	odd	12	inner
735.2.v.a.472.6		32	35.17	even	12	inner
735.2.v.a.607.3		32	35.27	even	4	inner
735.2.v.a.607.4		32	5.2	odd	4	inner
1680.2.cz.d.97.2		16	140.107	even	12
1680.2.cz.d.97.7		16	140.47	odd	12
1680.2.cz.d.433.2		16	28.19	even	6
1680.2.cz.d.433.7		16	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.197706 + 0.737849i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.22672 - 0.708245i) q^{4} +(-2.23413 - 0.0930365i) q^{5} +0.763878i q^{6} +(1.84539 + 1.84539i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(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

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