LMFDB - Embedded newform 637.2.r.f.116.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.8
Root			$-1.97871 - 1.14241i$ of defining polynomial
Character	$\chi$	$=$	637.116
Dual form			637.2.r.f.324.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97871 - 1.14241i) q^{2} +(1.57521 - 2.72835i) q^{3} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} -7.19813i q^{6} -2.78832i q^{8} +(-3.46258 - 5.99736i) q^{9} +O(q^{10})$	\(q+(1.97871 - 1.14241i) q^{2} +(1.57521 - 2.72835i) q^{3} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} -7.19813i q^{6} -2.78832i q^{8} +(-3.46258 - 5.99736i) q^{9} +(-2.42760 + 4.20473i) q^{10} +(0.267139 + 0.154233i) q^{11} +(-5.07276 - 8.78629i) q^{12} +(3.22037 + 1.62148i) q^{13} +6.69462i q^{15} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(-13.7029 - 7.91135i) q^{18} +(-1.54266 + 0.890653i) q^{19} +6.84326i q^{20} +0.704786 q^{22} +(0.575211 + 0.996294i) q^{23} +(-7.60750 - 4.39219i) q^{24} +(-0.242207 + 0.419515i) q^{25} +(8.22456 - 0.470536i) q^{26} -12.3659 q^{27} +2.01052 q^{29} +(7.64798 + 13.2467i) q^{30} +(-3.98791 - 2.30242i) q^{31} +(4.96792 + 2.86823i) q^{32} +(0.841600 - 0.485898i) q^{33} -4.05494i q^{34} -22.3016 q^{36} +(4.79901 - 2.77071i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(9.49673 - 6.23211i) q^{39} +(2.96258 + 5.13134i) q^{40} +6.72984i q^{41} -1.52611 q^{43} +(0.860286 - 0.496686i) q^{44} +(12.7443 + 7.35795i) q^{45} +(2.27635 + 1.31425i) q^{46} +(8.24297 - 4.75908i) q^{47} +0.220372 q^{48} +1.10680i q^{50} +(-2.79558 - 4.84209i) q^{51} +(9.70759 - 6.37048i) q^{52} +(-3.72037 + 6.44387i) q^{53} +(-24.4685 + 14.1269i) q^{54} -0.655486 q^{55} +5.61186i q^{57} +(3.97823 - 2.29683i) q^{58} +(7.03304 + 4.06053i) q^{59} +(18.6708 + 10.7796i) q^{60} +(-1.72037 - 2.97977i) q^{61} -10.5212 q^{62} +12.9669 q^{64} +(-7.64926 + 0.437622i) q^{65} +(1.11019 - 1.92290i) q^{66} +(-10.9249 - 6.30747i) q^{67} +(-2.85765 - 4.94960i) q^{68} +3.62431 q^{69} -1.35070i q^{71} +(-16.7226 + 9.65478i) q^{72} +(-10.2894 - 5.94059i) q^{73} +(6.33056 - 10.9648i) q^{74} +(0.763054 + 1.32165i) q^{75} +5.73646i q^{76} +(11.6716 - 23.1806i) q^{78} +(3.96258 + 6.86339i) q^{79} +(-0.128728 - 0.0743214i) q^{80} +(-9.09116 + 15.7464i) q^{81} +(7.68821 + 13.3164i) q^{82} +11.2290i q^{83} +3.77130i q^{85} +(-3.01972 + 1.74344i) q^{86} +(3.16700 - 5.48540i) q^{87} +(0.430050 - 0.744869i) q^{88} +(-1.43688 + 0.829583i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(-12.5636 + 7.25360i) q^{93} +(10.8736 - 18.8336i) q^{94} +(1.89263 - 3.27813i) q^{95} +(15.6511 - 9.03614i) q^{96} +7.66641i q^{97} -2.13617i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.97871	−	1.14241i	1.39916	−	0.807803i	0.404852	−	0.914382i	$-0.367323\pi$
$2$	1.97871	−	1.14241i	1.39916	−	0.807803i	0.994304	+	0.106579i	$0.0339896\pi$
$3$	1.57521	−	2.72835i	0.909448	−	1.57521i	0.0946163	−	0.995514i	$-0.469838\pi$
$3$	1.57521	−	2.72835i	0.909448	−	1.57521i	0.814832	−	0.579697i	$-0.196829\pi$
$4$	1.61019	−	2.78892i	0.805093	−	1.39446i
$5$	−1.84030	+	1.06250i	−0.823005	+	0.475162i	−0.851452	−	0.524433i	$-0.824277\pi$
$5$	−1.84030	+	1.06250i	−0.823005	+	0.475162i	0.0284464	+	0.999595i	$0.490944\pi$
$6$		−	7.19813i		−	2.93862i
$7$		0			0
$7$		0			0
$8$		−	2.78832i		−	0.985820i
$9$	−3.46258	−	5.99736i	−1.15419	−	1.99912i
$10$	−2.42760	+	4.20473i	−0.767676	+	1.32965i
$11$	0.267139	+	0.154233i	0.0805454	+	0.0465029i	0.539732	−	0.841837i	$-0.318526\pi$
$11$	0.267139	+	0.154233i	0.0805454	+	0.0465029i	−0.459186	+	0.888340i	$0.651859\pi$
$12$	−5.07276	−	8.78629i	−1.46438	−	2.53638i
$13$	3.22037	+	1.62148i	0.893170	+	0.449718i
$13$	3.22037	+	1.62148i	0.893170	+	0.449718i
$14$		0			0
$15$			6.69462i			1.72854i
$16$	0.0349749	+	0.0605784i	0.00874373	+	0.0151446i
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	−0.738122	−	0.674667i	$-0.764287\pi$
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	0.953340	+	0.301898i	$0.0976204\pi$
$18$	−13.7029	−	7.91135i	−3.22979	−	1.86472i
$19$	−1.54266	+	0.890653i	−0.353909	+	0.204330i	−0.666406	−	0.745589i	$-0.732168\pi$
$19$	−1.54266	+	0.890653i	−0.353909	+	0.204330i	0.312496	+	0.949919i	$0.398835\pi$
$20$			6.84326i			1.53020i
$21$		0			0
$22$	0.704786			0.150261
$23$	0.575211	+	0.996294i	0.119940	+	0.207742i	0.919744	−	0.392520i	$-0.128397\pi$
$23$	0.575211	+	0.996294i	0.119940	+	0.207742i	−0.799804	+	0.600261i	$0.795063\pi$
$24$	−7.60750	−	4.39219i	−1.55288	−	0.896553i
$25$	−0.242207	+	0.419515i	−0.0484414	+	0.0839029i
$26$	8.22456	−	0.470536i	1.61297	−	0.0922796i
$27$	−12.3659			−2.37982
$28$		0			0
$29$	2.01052			0.373345			0.186672	−	0.982422i	$-0.440230\pi$
$29$	2.01052			0.373345			0.186672	+	0.982422i	$0.440230\pi$
$30$	7.64798	+	13.2467i	1.39632	+	2.41850i
$31$	−3.98791	−	2.30242i	−0.716251	−	0.413527i	0.0971205	−	0.995273i	$-0.469037\pi$
$31$	−3.98791	−	2.30242i	−0.716251	−	0.413527i	−0.813371	+	0.581745i	$0.802370\pi$
$32$	4.96792	+	2.86823i	0.878213	+	0.507037i
$33$	0.841600	−	0.485898i	0.146504	−	0.0845840i
$34$		−	4.05494i		−	0.695416i
$35$		0			0
$36$	−22.3016			−3.71693
$37$	4.79901	−	2.77071i	0.788953	−	0.455502i	−0.0506410	−	0.998717i	$-0.516126\pi$
$37$	4.79901	−	2.77071i	0.788953	−	0.455502i	0.839594	+	0.543215i	$0.182793\pi$
$38$	−2.03497	+	3.52468i	−0.330117	+	0.571779i
$39$	9.49673	−	6.23211i	1.52069	−	0.997936i
$40$	2.96258	+	5.13134i	0.468425	+	0.811336i
$41$			6.72984i			1.05102i	0.850786	+	0.525512i	$0.176126\pi$
$41$			6.72984i			1.05102i	−0.850786	+	0.525512i	$0.823874\pi$
$42$		0			0
$43$	−1.52611			−0.232729			−0.116365	−	0.993207i	$-0.537124\pi$
$43$	−1.52611			−0.232729			−0.116365	+	0.993207i	$0.537124\pi$
$44$	0.860286	−	0.496686i	0.129693	−	0.0748783i
$45$	12.7443	+	7.35795i	1.89981	+	1.09686i
$46$	2.27635	+	1.31425i	0.335629	+	0.193776i
$47$	8.24297	−	4.75908i	1.20236	−	0.694183i	0.241281	−	0.970455i	$-0.422432\pi$
$47$	8.24297	−	4.75908i	1.20236	−	0.694183i	0.961079	+	0.276272i	$0.0890991\pi$
$48$	0.220372			0.0318079
$49$		0			0
$50$			1.10680i			0.156524i
$51$	−2.79558	−	4.84209i	−0.391460	−	0.678028i
$52$	9.70759	−	6.37048i	1.34620	−	0.883427i
$53$	−3.72037	+	6.44387i	−0.511032	+	0.885134i	0.488886	+	0.872348i	$0.337403\pi$
$53$	−3.72037	+	6.44387i	−0.511032	+	0.885134i	−0.999918	+	0.0127862i	$0.995930\pi$
$54$	−24.4685	+	14.1269i	−3.32974	+	1.92243i
$55$	−0.655486			−0.0883857
$56$		0			0
$57$			5.61186i			0.743309i
$58$	3.97823	−	2.29683i	0.522368	−	0.301589i
$59$	7.03304	+	4.06053i	0.915624	+	0.528636i	0.882236	−	0.470807i	$-0.156037\pi$
$59$	7.03304	+	4.06053i	0.915624	+	0.528636i	0.0333877	+	0.999442i	$0.489370\pi$
$60$	18.6708	+	10.7796i	2.41039	+	1.39164i
$61$	−1.72037	−	2.97977i	−0.220271	−	0.381521i	0.734619	−	0.678480i	$-0.237361\pi$
$61$	−1.72037	−	2.97977i	−0.220271	−	0.381521i	−0.954890	+	0.296959i	$0.904028\pi$
$62$	−10.5212			−1.33620
$63$		0			0
$64$	12.9669			1.62086
$65$	−7.64926	+	0.437622i	−0.948773	+	0.0542803i
$66$	1.11019	−	1.92290i	0.136654	−	0.236692i
$67$	−10.9249	−	6.30747i	−1.33468	−	0.770580i	−0.348671	−	0.937245i	$-0.613367\pi$
$67$	−10.9249	−	6.30747i	−1.33468	−	0.770580i	−0.986014	+	0.166665i	$0.946700\pi$
$68$	−2.85765	−	4.94960i	−0.346541	−	0.600227i
$69$	3.62431			0.436316
$70$		0			0
$71$		−	1.35070i		−	0.160299i	−0.996783	−	0.0801494i	$-0.974460\pi$
$71$		−	1.35070i		−	0.160299i	0.996783	−	0.0801494i	$-0.0255397\pi$
$72$	−16.7226	+	9.65478i	−1.97077	+	1.13783i
$73$	−10.2894	−	5.94059i	−1.20428	−	0.695293i	−0.242778	−	0.970082i	$-0.578059\pi$
$73$	−10.2894	−	5.94059i	−1.20428	−	0.695293i	−0.961505	+	0.274789i	$0.911392\pi$
$74$	6.33056	−	10.9648i	0.735912	−	1.27464i
$75$	0.763054	+	1.32165i	0.0881099	+	0.152611i
$76$			5.73646i			0.658018i
$77$		0			0
$78$	11.6716	−	23.1806i	1.32155	−	2.62469i
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	0.998109	−	0.0614644i	$-0.0195771\pi$
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	−0.552284	+	0.833656i	$0.686244\pi$
$80$	−0.128728	−	0.0743214i	−0.0143923	−	0.00830939i
$81$	−9.09116	+	15.7464i	−1.01013	+	1.74960i
$82$	7.68821	+	13.3164i	0.849021	+	1.47055i
$83$			11.2290i			1.23255i	0.787533	+	0.616273i	$0.211358\pi$
$83$			11.2290i			1.23255i	−0.787533	+	0.616273i	$0.788642\pi$
$84$		0			0
$85$			3.77130i			0.409055i
$86$	−3.01972	+	1.74344i	−0.325625	+	0.188000i
$87$	3.16700	−	5.48540i	0.339538	−	0.588096i
$88$	0.430050	−	0.744869i	0.0458435	−	0.0794033i
$89$	−1.43688	+	0.829583i	−0.152309	+	0.0879357i	−0.574218	−	0.818703i	$-0.694694\pi$
$89$	−1.43688	+	0.829583i	−0.152309	+	0.0879357i	0.421909	+	0.906638i	$0.361360\pi$
$90$	33.6231			3.54418
$91$		0			0
$92$	3.70479			0.386251
$93$	−12.5636	+	7.25360i	−1.30279	+	0.752164i
$94$	10.8736	−	18.8336i	1.12153	−	1.94254i
$95$	1.89263	−	3.27813i	0.194180	−	0.336329i
$96$	15.6511	−	9.03614i	1.59738	−	0.922247i
$97$			7.66641i			0.778406i	0.921152	+	0.389203i	$0.127250\pi$
$97$			7.66641i			0.778406i	−0.921152	+	0.389203i	$0.872750\pi$
$98$		0			0
$99$		−	2.13617i		−	0.214693i
$100$	0.779996	+	1.35099i	0.0779996	+	0.135099i
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	−0.998607	−	0.0527721i	$-0.983194\pi$
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	0.545005	+	0.838433i	$0.316528\pi$
$102$	−11.0633	−	6.38738i	−1.09543	−	0.632445i
$103$	−3.02085	−	5.23226i	−0.297653	−	0.515550i	0.677946	−	0.735112i	$-0.262870\pi$
$103$	−3.02085	−	5.23226i	−0.297653	−	0.515550i	−0.975599	+	0.219562i	$0.929537\pi$
$104$	4.52122	−	8.97943i	0.443342	−	0.880506i
$105$		0			0
$106$			17.0007i			1.65125i
$107$	−6.04305	−	10.4669i	−0.584204	−	1.01187i	−0.994974	−	0.100132i	$-0.968074\pi$
$107$	−6.04305	−	10.4669i	−0.584204	−	1.01187i	0.410770	−	0.911739i	$-0.365260\pi$
$108$	−19.9114	+	34.4876i	−1.91598	+	3.31857i
$109$	−1.17942	−	0.680941i	−0.112968	−	0.0652223i	0.442451	−	0.896793i	$-0.354109\pi$
$109$	−1.17942	−	0.680941i	−0.112968	−	0.0652223i	−0.555420	+	0.831570i	$0.687442\pi$
$110$	−1.29701	+	0.748831i	−0.123665	+	0.0713983i
$111$		−	17.4578i		−	1.65702i
$112$		0			0
$113$	−9.42009			−0.886168			−0.443084	−	0.896480i	$-0.646116\pi$
$113$	−9.42009			−0.886168			−0.443084	+	0.896480i	$0.646116\pi$
$114$	6.41103	+	11.1042i	0.600448	+	1.04001i
$115$	−2.11712	−	1.22232i	−0.197422	−	0.113982i
$116$	3.23731	−	5.60719i	0.300577	−	0.520615i
$117$	−1.42617	−	24.9282i	−0.131849	−	2.30462i
$118$	18.5551			1.70814
$119$		0			0
$120$	18.6667			1.70403
$121$	−5.45242	−	9.44388i	−0.495675	−	0.858534i
$122$	−6.80822	−	3.93073i	−0.616387	−	0.355871i
$123$	18.3613	+	10.6009i	1.65558	+	0.955852i
$124$	−12.8426	+	7.41466i	−1.15330	+	0.665856i
$125$		−	11.6543i		−	1.04239i
$126$		0			0
$127$	13.3998			1.18904			0.594519	−	0.804081i	$-0.297342\pi$
$127$	13.3998			1.18904			0.594519	+	0.804081i	$0.297342\pi$
$128$	15.7217	−	9.07695i	1.38962	−	0.802297i
$129$	−2.40394	+	4.16375i	−0.211655	+	0.366598i
$130$	−14.6357	+	9.60448i	−1.28363	+	0.842369i
$131$	6.69854	+	11.6022i	0.585254	+	1.01369i	0.994844	+	0.101420i	$0.0323385\pi$
$131$	6.69854	+	11.6022i	0.585254	+	1.01369i	−0.409590	+	0.912270i	$0.634328\pi$
$132$		−	3.12954i		−	0.272392i
$133$		0			0
$134$	−28.8228			−2.48991
$135$	22.7569	−	13.1387i	1.95860	−	1.13080i
$136$	−4.28555	−	2.47427i	−0.367483	−	0.212167i
$137$	0.433917	+	0.250522i	0.0370720	+	0.0214036i	0.518421	−	0.855125i	$-0.326520\pi$
$137$	0.433917	+	0.250522i	0.0370720	+	0.0214036i	−0.481349	+	0.876529i	$0.659853\pi$
$138$	7.17145	−	4.14044i	0.610475	−	0.352458i
$139$	−1.41936			−0.120388			−0.0601941	−	0.998187i	$-0.519172\pi$
$139$	−1.41936			−0.120388			−0.0601941	+	0.998187i	$0.519172\pi$
$140$		0			0
$141$		−	29.9862i		−	2.52529i
$142$	−1.54305	−	2.67264i	−0.129490	−	0.224283i
$143$	0.610200	+	0.929847i	0.0510275	+	0.0777577i
$144$	0.242207	−	0.419515i	0.0201839	−	0.0349596i
$145$	−3.69996	+	2.13617i	−0.307265	+	0.177399i
$146$	−27.1463			−2.24664
$147$		0			0
$148$		−	17.8454i		−	1.46689i
$149$	−18.2652	+	10.5454i	−1.49635	+	0.863916i	−0.999991	−	0.00420426i	$-0.998662\pi$
$149$	−18.2652	+	10.5454i	−1.49635	+	0.863916i	−0.496355	+	0.868120i	$0.665328\pi$
$150$	3.01972	+	1.74344i	0.246559	+	0.142351i
$151$	−15.1591	−	8.75211i	−1.23363	−	0.712236i	−0.265845	−	0.964016i	$-0.585651\pi$
$151$	−15.1591	−	8.75211i	−1.23363	−	0.712236i	−0.967785	+	0.251779i	$0.918984\pi$
$152$	2.48343	+	4.30142i	0.201432	+	0.348891i
$153$	−12.2903			−0.993614
$154$		0			0
$155$	9.78526			0.785971
$156$	−2.08937	−	36.5205i	−0.167284	−	2.92398i
$157$	0.0377894	−	0.0654532i	0.00301593	−	0.00522374i	−0.864514	−	0.502610i	$-0.832373\pi$
$157$	0.0377894	−	0.0654532i	0.00301593	−	0.00522374i	0.867529	+	0.497386i	$0.165707\pi$
$158$	15.6816	+	9.05375i	1.24756	+	0.720278i
$159$	11.7207	+	20.3009i	0.929515	+	1.60997i
$160$	−12.1899			−0.963699
$161$		0			0
$162$			41.5432i			3.26394i
$163$	8.73102	−	5.04086i	0.683866	−	0.394830i	−0.117444	−	0.993080i	$-0.537470\pi$
$163$	8.73102	−	5.04086i	0.683866	−	0.394830i	0.801310	+	0.598249i	$0.204137\pi$
$164$	18.7690	+	10.8363i	1.46561	+	0.846172i
$165$	−1.03253	+	1.78839i	−0.0803822	+	0.139226i
$166$	12.8281	+	22.2189i	0.995655	+	1.72452i
$167$		−	5.84989i		−	0.452678i	−0.974049	−	0.226339i	$-0.927324\pi$
$167$		−	5.84989i		−	0.452678i	0.974049	−	0.226339i	$-0.0726757\pi$
$168$		0			0
$169$	7.74159	+	10.4436i	0.595507	+	0.803350i
$170$	4.30835	+	7.46229i	0.330436	+	0.572331i
$171$	10.6831	+	6.16791i	0.816960	+	0.471672i
$172$	−2.45732	+	4.25620i	−0.187369	+	0.324532i
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	−0.984100	−	0.177617i	$-0.943161\pi$
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	0.338229	−	0.941064i	$-0.390172\pi$
$174$		−	14.4720i		−	1.09712i
$175$		0			0
$176$			0.0215771i			0.00162644i
$177$	22.1570	−	12.7924i	1.66543	−	0.961534i
$178$	−1.89544	+	3.28300i	−0.142069	+	0.246072i
$179$	−7.65079	+	13.2516i	−0.571847	+	0.990468i	0.424529	+	0.905414i	$0.360440\pi$
$179$	−7.65079	+	13.2516i	−0.571847	+	0.990468i	−0.996376	+	0.0850537i	$0.972894\pi$
$180$	41.0415	−	23.6953i	3.05905	−	1.76615i
$181$	5.84958			0.434796			0.217398	−	0.976083i	$-0.430243\pi$
$181$	5.84958			0.434796			0.217398	+	0.976083i	$0.430243\pi$
$182$		0			0
$183$	−10.8398			−0.801301
$184$	2.77799	−	1.60387i	0.204796	−	0.118239i
$185$	−5.88774	+	10.1979i	−0.432875	+	0.749761i
$186$	−16.5731	+	28.7055i	−1.21520	+	2.10479i
$187$	0.474101	−	0.273722i	0.0346697	−	0.0200165i
$188$		−	30.6520i		−	2.23553i
$189$		0			0
$190$		−	8.64861i		−	0.627436i
$191$	13.4090	+	23.2250i	0.970238	+	1.68050i	0.694831	+	0.719173i	$0.255479\pi$
$191$	13.4090	+	23.2250i	0.970238	+	1.68050i	0.275407	+	0.961328i	$0.411188\pi$
$192$	20.4255	−	35.3780i	1.47409	−	2.55319i
$193$	−0.185315	−	0.106992i	−0.0133393	−	0.00770145i	0.493316	−	0.869850i	$-0.335785\pi$
$193$	−0.185315	−	0.106992i	−0.0133393	−	0.00770145i	−0.506655	+	0.862149i	$0.669118\pi$
$194$	8.75816	+	15.1696i	0.628799	+	1.08911i
$195$	−10.8552	+	21.5592i	−0.777358	+	1.54388i
$196$		0			0
$197$			11.2290i			0.800035i	0.916508	+	0.400017i	$0.130996\pi$
$197$			11.2290i			0.800035i	−0.916508	+	0.400017i	$0.869004\pi$
$198$	−2.44038	−	4.22685i	−0.173430	−	0.300389i
$199$	−10.2100	+	17.6843i	−0.723771	+	1.25361i	0.235707	+	0.971824i	$0.424259\pi$
$199$	−10.2100	+	17.6843i	−0.723771	+	1.25361i	−0.959478	+	0.281784i	$0.909074\pi$
$200$	1.16974	+	0.675351i	0.0827132	+	0.0477545i
$201$	−34.4179	+	19.8712i	−2.42765	+	1.40161i
$202$			20.8313i			1.46568i
$203$		0			0
$204$	−18.0056			−1.26065
$205$	−7.15042	−	12.3849i	−0.499407	−	0.864999i
$206$	−11.9547	−	6.90207i	−0.832926	−	0.480890i
$207$	3.98343	−	6.89950i	0.276867	−	0.479548i
$208$	0.0144055	+	0.251796i	0.000998842	+	0.0174589i
$209$	−0.549471			−0.0380077
$210$		0			0
$211$	8.41738			0.579476			0.289738	−	0.957106i	$-0.406432\pi$
$211$	8.41738			0.579476			0.289738	+	0.957106i	$0.406432\pi$
$212$	11.9810	+	20.7517i	0.822857	+	1.42523i
$213$	−3.68518	−	2.12764i	−0.252504	−	0.145783i
$214$	−23.9148	−	13.8072i	−1.63479	−	0.943844i
$215$	2.80849	−	1.62148i	0.191537	−	0.110584i
$216$			34.4801i			2.34607i
$217$		0			0
$218$	−3.11164			−0.210747
$219$	−32.4159	+	18.7154i	−2.19047	+	1.26467i
$220$	−1.05545	+	1.82810i	−0.0711587	+	0.123250i
$221$	5.34982	−	3.51075i	0.359868	−	0.236159i
$222$	−19.9439	−	34.5439i	−1.33855	−	2.31843i
$223$		−	13.6091i		−	0.911333i	−0.890151	−	0.455666i	$-0.849401\pi$
$223$		−	13.6091i		−	0.911333i	0.890151	−	0.455666i	$-0.150599\pi$
$224$		0			0
$225$	3.35464			0.223643
$226$	−18.6396	+	10.7616i	−1.23989	+	0.715849i
$227$	−3.12008	−	1.80138i	−0.207087	−	0.119562i	0.392870	−	0.919594i	$-0.371482\pi$
$227$	−3.12008	−	1.80138i	−0.207087	−	0.119562i	−0.599957	+	0.800032i	$0.704816\pi$
$228$	15.6511	+	9.03614i	1.03652	+	0.598433i
$229$	−15.9212	+	9.19208i	−1.05210	+	0.607430i	−0.923236	−	0.384232i	$-0.874466\pi$
$229$	−15.9212	+	9.19208i	−1.05210	+	0.607430i	−0.128863	+	0.991662i	$0.541133\pi$
$230$	−5.58554			−0.368299
$231$		0			0
$232$		−	5.60598i		−	0.368051i
$233$	10.1348	+	17.5541i	0.663955	+	1.15000i	0.979567	+	0.201116i	$0.0644568\pi$
$233$	10.1348	+	17.5541i	0.663955	+	1.15000i	−0.315612	+	0.948888i	$0.602210\pi$
$234$	−31.3002	−	47.6964i	−2.04616	−	3.11801i
$235$	−10.1130	+	17.5162i	−0.659699	+	1.14263i
$236$	22.6490	−	13.0764i	1.47432	−	0.851202i
$237$	24.9676			1.62182
$238$		0			0
$239$		−	20.8097i		−	1.34607i	−0.739612	−	0.673033i	$-0.764991\pi$
$239$		−	20.8097i		−	1.34607i	0.739612	−	0.673033i	$-0.235009\pi$
$240$	−0.405549	+	0.234144i	−0.0261781	+	0.0151139i
$241$	−11.0113	−	6.35736i	−0.709299	−	0.409514i	0.101503	−	0.994835i	$-0.467635\pi$
$241$	−11.0113	−	6.35736i	−0.709299	−	0.409514i	−0.810801	+	0.585322i	$0.800968\pi$
$242$	−21.5775	−	12.4578i	−1.38705	−	0.800816i
$243$	10.0922	+	17.4801i	0.647412	+	1.12135i
$244$	−11.0805			−0.709355
$245$		0			0
$246$	48.4422			3.08856
$247$	−6.41210	+	0.366843i	−0.407992	+	0.0233417i
$248$	−6.41990	+	11.1196i	−0.407664	+	0.706094i
$249$	30.6367	+	17.6881i	1.94152	+	1.12094i
$250$	−13.3140	−	23.0605i	−0.842050	−	1.45847i
$251$	13.7436			0.867486			0.433743	−	0.901037i	$-0.357193\pi$
$251$	13.7436			0.867486			0.433743	+	0.901037i	$0.357193\pi$
$252$		0			0
$253$			0.354865i			0.0223102i
$254$	26.5142	−	15.3080i	1.66365	−	0.960510i
$255$	10.2894	+	5.94059i	0.644347	+	0.372014i
$256$	7.77229	−	13.4620i	0.485768	−	0.841375i
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	0.957442	−	0.288626i	$-0.0931983\pi$
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	−0.728678	+	0.684856i	$0.759865\pi$
$258$			10.9851i			0.683904i
$259$		0			0
$260$	−11.0962	+	22.0378i	−0.688159	+	1.36673i
$261$	−6.96159	−	12.0578i	−0.430912	−	0.746361i
$262$	26.5089	+	15.3049i	1.63772	+	0.945540i
$263$	3.33942	−	5.78405i	0.205918	−	0.356660i	−0.744507	−	0.667615i	$-0.767315\pi$
$263$	3.33942	−	5.78405i	0.205918	−	0.356660i	0.950425	+	0.310955i	$0.100649\pi$
$264$	−1.35484	−	2.34665i	−0.0833846	−	0.144426i
$265$		−	15.8115i		−	0.971293i
$266$		0			0
$267$			5.22708i			0.319892i
$268$	−35.1821	+	20.3124i	−2.14909	+	1.24078i
$269$	8.11263	−	14.0515i	0.494636	−	0.856735i	−0.505345	−	0.862917i	$-0.668635\pi$
$269$	8.11263	−	14.0515i	0.494636	−	0.856735i	0.999981	+	0.00618287i	$0.00196808\pi$
$270$	30.0195	−	51.9953i	1.82693	−	3.16433i
$271$	16.2277	−	9.36904i	0.985760	−	0.569129i	0.0817555	−	0.996652i	$-0.473947\pi$
$271$	16.2277	−	9.36904i	0.985760	−	0.569129i	0.904004	+	0.427524i	$0.140614\pi$
$272$	0.124143			0.00752725
$273$		0			0
$274$	1.14479			0.0691595
$275$	−0.129406	+	0.0747124i	−0.00780346	+	0.00450533i
$276$	5.83582	−	10.1079i	0.351275	−	0.608426i
$277$	15.0163	−	26.0090i	0.902243	−	1.56273i	0.0776679	−	0.996979i	$-0.475253\pi$
$277$	15.0163	−	26.0090i	0.902243	−	1.56273i	0.824575	−	0.565752i	$-0.191414\pi$
$278$	−2.80849	+	1.62148i	−0.168442	+	0.0972501i
$279$			31.8893i			1.90916i
$280$		0			0
$281$			2.23065i			0.133070i	0.997784	+	0.0665348i	$0.0211943\pi$
$281$			2.23065i			0.133070i	−0.997784	+	0.0665348i	$0.978806\pi$
$282$	−34.2565	−	59.3339i	−2.03994	−	3.53328i
$283$	−6.88774	+	11.9299i	−0.409433	+	0.709159i	−0.994826	−	0.101590i	$-0.967607\pi$
$283$	−6.88774	+	11.9299i	−0.409433	+	0.709159i	0.585393	+	0.810750i	$0.300940\pi$
$284$	−3.76700	−	2.17488i	−0.223531	−	0.129055i
$285$	−5.96258	−	10.3275i	−0.353193	−	0.611748i
$286$	2.26967	+	1.14280i	0.134208	+	0.0675750i
$287$		0			0
$288$		−	39.7259i		−	2.34087i
$289$	6.92516	+	11.9947i	0.407362	+	0.705572i
$290$	−4.88075	+	8.45371i	−0.286608	+	0.496419i
$291$	20.9166	+	12.0762i	1.22615	+	0.707920i
$292$	−33.1357	+	19.1309i	−1.93912	+	1.11955i
$293$			1.01231i			0.0591400i	0.999563	+	0.0295700i	$0.00941380\pi$
$293$			1.01231i			0.0591400i	−0.999563	+	0.0295700i	$0.990586\pi$
$294$		0			0
$295$	−17.2572			−1.00475
$296$	−7.72563	−	13.3812i	−0.449043	−	0.777766i
$297$	−3.30341	−	1.90723i	−0.191683	−	0.110668i
$298$	−24.0943	+	41.7326i	−1.39575	+	2.41751i
$299$	0.236918	+	4.14113i	0.0137013	+	0.239488i
$300$	4.91464			0.283747
$301$		0			0
$302$	−39.9939			−2.30139
$303$	14.3616	+	24.8751i	0.825054	+	1.42904i
$304$	−0.107909	−	0.0623010i	−0.00618898	−	0.00357321i
$305$	6.33199	+	3.65577i	0.362568	+	0.209329i
$306$	−24.3189	+	14.0405i	−1.39022	+	0.802645i
$307$		−	24.0527i		−	1.37276i	−0.727244	−	0.686379i	$-0.759199\pi$
$307$		−	24.0527i		−	1.37276i	0.727244	−	0.686379i	$-0.240801\pi$
$308$		0			0
$309$	−19.0339			−1.08280
$310$	19.3622	−	11.1787i	1.09970	−	0.634910i
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	−0.709957	−	0.704245i	$-0.751286\pi$
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	0.964872	+	0.262719i	$0.0846192\pi$
$312$	−17.3771	−	26.4799i	−0.983786	−	1.49913i
$313$	−7.61806	−	13.1949i	−0.430598	−	0.745818i	0.566326	−	0.824181i	$-0.308364\pi$
$313$	−7.61806	−	13.1949i	−0.430598	−	0.745818i	−0.996925	+	0.0783626i	$0.975031\pi$
$314$		−	0.172684i		−	0.00974510i
$315$		0			0
$316$	25.5220			1.43572
$317$	−5.91972	+	3.41775i	−0.332484	+	0.191960i	−0.656944	−	0.753940i	$-0.728151\pi$
$317$	−5.91972	+	3.41775i	−0.332484	+	0.191960i	0.324459	+	0.945900i	$0.394818\pi$
$318$	46.3838	+	26.7797i	2.60107	+	1.50173i
$319$	0.537088	+	0.310088i	0.0300712	+	0.0173616i
$320$	−23.8628	+	13.7772i	−1.33397	+	0.770170i
$321$	−38.0763			−2.12521
$322$		0			0
$323$			3.16135i			0.175902i
$324$	29.2769	+	50.7091i	1.62650	+	2.81717i
$325$	−1.46023	+	0.958259i	−0.0809991	+	0.0531546i
$326$	11.5174	−	19.9487i	0.637890	−	1.10486i
$327$	−3.71568	+	2.14525i	−0.205478	+	0.118633i
$328$	18.7649			1.03612
$329$		0			0
$330$			4.71827i			0.259732i
$331$	−11.9637	+	6.90727i	−0.657587	+	0.379658i	−0.791357	−	0.611354i	$-0.790625\pi$
$331$	−11.9637	+	6.90727i	−0.657587	+	0.379658i	0.133770	+	0.991012i	$0.457292\pi$
$332$	31.3169	+	18.0808i	1.71874	+	0.992314i
$333$	−33.2339	−	19.1876i	−1.82121	−	1.05147i
$334$	−6.68295	−	11.5752i	−0.365675	−	0.633367i
$335$	26.8066			1.46460
$336$		0			0
$337$	−27.0432			−1.47314			−0.736568	−	0.676364i	$-0.763555\pi$
$337$	−27.0432			−1.47314			−0.736568	+	0.676364i	$0.763555\pi$
$338$	27.2491	+	11.8207i	1.48216	+	0.642961i
$339$	−14.8386	+	25.7013i	−0.805924	+	1.39590i
$340$	10.5179	+	6.07249i	0.570411	+	0.329327i
$341$	−0.710218	−	1.23013i	−0.0384604	−	0.0666154i
$342$	28.1850			1.52407
$343$		0			0
$344$			4.25528i			0.229429i
$345$	−6.66981	+	3.85082i	−0.359091	+	0.207321i
$346$	−33.6186	−	19.4097i	−1.80735	−	1.04347i
$347$	9.65568	−	16.7241i	0.518344	−	0.897799i	−0.481429	−	0.876485i	$-0.659882\pi$
$347$	9.65568	−	16.7241i	0.518344	−	0.897799i	0.999773	−	0.0213132i	$-0.00678472\pi$
$348$	−10.1989	−	17.6650i	−0.546719	−	0.946944i
$349$			14.1573i			0.757821i	0.925433	+	0.378911i	$0.123701\pi$
$349$			14.1573i			0.757821i	−0.925433	+	0.378911i	$0.876299\pi$
$350$		0			0
$351$	−39.8228	−	20.0511i	−2.12558	−	1.07025i
$352$	0.884750	+	1.53243i	0.0471573	+	0.0816789i
$353$	14.6919	+	8.48235i	0.781969	+	0.451470i	0.837128	−	0.547008i	$-0.184233\pi$
$353$	14.6919	+	8.48235i	0.781969	+	0.451470i	−0.0551585	+	0.998478i	$0.517566\pi$
$354$	29.2282	−	50.6247i	1.55346	−	2.69067i
$355$	1.43511	+	2.48569i	0.0761680	+	0.131927i
$356$			5.34313i			0.283186i
$357$		0			0
$358$			34.9613i			1.84776i
$359$	19.7136	−	11.3816i	1.04044	−	0.600700i	0.120484	−	0.992715i	$-0.461555\pi$
$359$	19.7136	−	11.3816i	1.04044	−	0.600700i	0.919959	+	0.392016i	$0.128222\pi$
$360$	20.5163	−	35.5353i	1.08131	−	1.87288i
$361$	−7.91348	+	13.7065i	−0.416499	+	0.721397i
$362$	11.5746	−	6.68260i	0.608347	−	0.351229i
$363$	−34.3549			−1.80316
$364$		0			0
$365$	25.2474			1.32151
$366$	−21.4488	+	12.3835i	−1.12114	+	0.647293i
$367$	8.29168	−	14.3616i	0.432822	−	0.749670i	−0.564293	−	0.825575i	$-0.690851\pi$
$367$	8.29168	−	14.3616i	0.432822	−	0.749670i	0.997115	+	0.0759048i	$0.0241845\pi$
$368$	−0.0402359	+	0.0696907i	−0.00209744	+	0.00363288i
$369$	40.3613	−	23.3026i	2.10112	−	1.21308i
$370$			26.9048i			1.39871i
$371$		0			0
$372$			46.7186i			2.42225i
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	−0.962677	−	0.270652i	$-0.912761\pi$
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	0.246947	−	0.969029i	$-0.420573\pi$
$374$	0.625404	−	1.08323i	0.0323389	−	0.0560126i
$375$	−31.7970	−	18.3580i	−1.64199	−	0.948004i
$376$	−13.2698	−	22.9840i	−0.684340	−	1.18531i
$377$	6.47463	+	3.26003i	0.333460	+	0.167900i
$378$		0			0
$379$		−	9.24228i		−	0.474744i	−0.971419	−	0.237372i	$-0.923714\pi$
$379$		−	9.24228i		−	0.474744i	0.971419	−	0.237372i	$-0.0762860\pi$
$380$	−6.09497	−	10.5568i	−0.312665	−	0.541552i
$381$	21.1075	−	36.5592i	1.08137	−	1.87299i
$382$	53.0648	+	30.6369i	2.71503	+	1.56752i
$383$	−6.62358	+	3.82413i	−0.338449	+	0.195404i	−0.659586	−	0.751629i	$-0.729268\pi$
$383$	−6.62358	+	3.82413i	−0.338449	+	0.195404i	0.321137	+	0.947033i	$0.395935\pi$
$384$		−	57.1925i		−	2.91859i
$385$		0			0
$386$	−0.488913			−0.0248850
$387$	5.28427	+	9.15262i	0.268614	+	0.465254i
$388$	21.3810	+	12.3443i	1.08546	+	0.626689i
$389$	3.26868	−	5.66153i	0.165729	−	0.287051i	−0.771185	−	0.636611i	$-0.780336\pi$
$389$	3.26868	−	5.66153i	0.165729	−	0.287051i	0.936914	+	0.349560i	$0.113669\pi$
$390$	3.15006	+	55.0603i	0.159509	+	2.78809i
$391$	2.04169			0.103253
$392$		0			0
$393$	42.2064			2.12903
$394$	12.8281	+	22.2189i	0.646271	+	1.11937i
$395$	−14.5846	−	8.42044i	−0.733833	−	0.423678i
$396$	−5.95762	−	3.43963i	−0.299381	−	0.172848i
$397$	25.0548	−	14.4654i	1.25746	−	0.725996i	0.284882	−	0.958563i	$-0.408046\pi$
$397$	25.0548	−	14.4654i	1.25746	−	0.725996i	0.972581	+	0.232566i	$0.0747123\pi$
$398$			46.6561i			2.33866i
$399$		0			0
$400$	−0.0338847			−0.00169423
$401$	−23.1603	+	13.3716i	−1.15657	+	0.667747i	−0.950480	−	0.310786i	$-0.899408\pi$
$401$	−23.1603	+	13.3716i	−1.15657	+	0.667747i	−0.206092	+	0.978533i	$0.566075\pi$
$402$	−45.4020	+	78.6385i	−2.26444	+	3.92213i
$403$	−9.10923	−	13.8810i	−0.453763	−	0.691462i
$404$	14.6805	+	25.4274i	0.730382	+	1.26506i
$405$		−	38.6373i		−	1.91990i
$406$		0			0
$407$	1.70934			0.0847287
$408$	−13.5013	+	7.79498i	−0.668414	+	0.385909i
$409$	−30.1138	−	17.3862i	−1.48903	−	0.859694i	−0.489112	−	0.872221i	$-0.662679\pi$
$409$	−30.1138	−	17.3862i	−1.48903	−	0.859694i	−0.999922	+	0.0125273i	$0.996012\pi$
$410$	−28.2972	−	16.3374i	−1.39750	−	0.806846i
$411$	1.36702	−	0.789250i	0.0674302	−	0.0389309i
$412$	−19.4565			−0.958553
$413$		0			0
$414$		−	18.2028i		−	0.894617i
$415$	−11.9308	−	20.6647i	−0.585659	−	1.01439i
$416$	11.3478	+	17.2922i	0.556370	+	0.847819i
$417$	−2.23579	+	3.87250i	−0.109487	+	0.189637i
$418$	−1.08724	+	0.627719i	−0.0531787	+	0.0307027i
$419$	4.19246			0.204815			0.102407	−	0.994743i	$-0.467345\pi$
$419$	4.19246			0.204815			0.102407	+	0.994743i	$0.467345\pi$
$420$		0			0
$421$		−	20.9526i		−	1.02117i	−0.859828	−	0.510584i	$-0.829429\pi$
$421$		−	20.9526i		−	1.02117i	0.859828	−	0.510584i	$-0.170571\pi$
$422$	16.6555	−	9.61607i	0.810778	−	0.468103i
$423$	−57.0838	−	32.9574i	−2.77551	−	1.60244i
$424$	17.9676	+	10.3736i	0.872583	+	0.503786i
$425$	0.429853	+	0.744528i	0.0208509	+	0.0361149i
$426$	−9.72252			−0.471058
$427$		0			0
$428$	−38.9217			−1.88135
$429$	3.49814	−	0.200132i	0.168892	−	0.00966247i
$430$	3.70479	−	6.41688i	0.178661	−	0.309449i
$431$	−14.6309	−	8.44713i	−0.704744	−	0.406884i	0.104368	−	0.994539i	$-0.466718\pi$
$431$	−14.6309	−	8.44713i	−0.704744	−	0.406884i	−0.809112	+	0.587655i	$0.800051\pi$
$432$	−0.432497	−	0.749106i	−0.0208085	−	0.0360414i
$433$	−3.42241			−0.164471			−0.0822353	−	0.996613i	$-0.526206\pi$
$433$	−3.42241			−0.164471			−0.0822353	+	0.996613i	$0.526206\pi$
$434$		0			0
$435$			13.4597i			0.645342i
$436$	−3.79818	+	2.19288i	−0.181900	+	0.105020i
$437$	−1.77470	−	1.02463i	−0.0848956	−	0.0490145i
$438$	−42.7611	+	74.0644i	−2.04320	+	3.53893i
$439$	−9.03253	−	15.6448i	−0.431099	−	0.746685i	0.565869	−	0.824495i	$-0.308541\pi$
$439$	−9.03253	−	15.6448i	−0.431099	−	0.746685i	−0.996968	+	0.0778096i	$0.975207\pi$
$440$			1.82771i			0.0871324i
$441$		0			0
$442$	6.57501	−	13.0584i	0.312742	−	0.621125i
$443$	−3.22173	−	5.58020i	−0.153069	−	0.265123i	0.779285	−	0.626669i	$-0.215582\pi$
$443$	−3.22173	−	5.58020i	−0.153069	−	0.265123i	−0.932354	+	0.361546i	$0.882249\pi$
$444$	−48.6885	−	28.1103i	−2.31065	−	1.33406i
$445$	1.76286	−	3.05336i	0.0835674	−	0.144743i
$446$	−15.5471	−	26.9284i	−0.736178	−	1.27510i
$447$			66.4451i			3.14275i
$448$		0			0
$449$		−	1.75306i		−	0.0827322i	−0.999144	−	0.0413661i	$-0.986829\pi$
$449$		−	1.75306i		−	0.0827322i	0.999144	−	0.0413661i	$-0.0131710\pi$
$450$	6.63785	−	3.83237i	0.312911	−	0.180659i
$451$	−1.03796	+	1.79780i	−0.0488757	+	0.0846551i
$452$	−15.1681	+	26.2719i	−0.713447	+	1.23573i
$453$	−47.7575	+	27.5728i	−2.24385	+	1.29548i
$454$	−8.23163			−0.386330
$455$		0			0
$456$	15.6477			0.732770
$457$	28.3277	−	16.3550i	1.32511	−	0.765054i	0.340573	−	0.940218i	$-0.389379\pi$
$457$	28.3277	−	16.3550i	1.32511	−	0.765054i	0.984539	+	0.175164i	$0.0560455\pi$
$458$	−21.0022	+	36.3769i	−0.981368	+	1.69978i
$459$	−10.9731	+	19.0060i	−0.512180	+	0.887123i
$460$	−6.81790	+	3.93632i	−0.317886	+	0.183532i
$461$		−	7.66641i		−	0.357060i	−0.983934	−	0.178530i	$-0.942866\pi$
$461$		−	7.66641i		−	0.357060i	0.983934	−	0.178530i	$-0.0571342\pi$
$462$		0			0
$463$			14.4720i			0.672570i	0.941760	+	0.336285i	$0.109171\pi$
$463$			14.4720i			0.672570i	−0.941760	+	0.336285i	$0.890829\pi$
$464$	0.0703179	+	0.121794i	0.00326443	+	0.00565415i
$465$	15.4138	−	26.6976i	0.714800	−	1.23807i
$466$	40.1077	+	23.1562i	1.85795	+	1.07269i
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	0.902435	−	0.430825i	$-0.141777\pi$
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	−0.824323	+	0.566119i	$0.808444\pi$
$468$	−71.8194	−	36.1616i	−3.31985	−	1.67157i
$469$		0			0
$470$			46.2126i			2.13163i
$471$	−0.119053	−	0.206205i	−0.00548566	−	0.00950144i
$472$	11.3221	−	19.6104i	0.521140	−	0.902641i
$473$	−0.407683	−	0.235376i	−0.0187453	−	0.0108226i
$474$	49.4035	−	28.5231i	2.26918	−	1.31011i
$475$		−	0.862889i		−	0.0395921i
$476$		0			0
$477$	51.5283			2.35932
$478$	−23.7731	−	41.1763i	−1.08736	−	1.88336i
$479$	−0.125768	−	0.0726124i	−0.00574651	−	0.00331775i	0.497124	−	0.867680i	$-0.334389\pi$
$479$	−0.125768	−	0.0726124i	−0.00574651	−	0.00331775i	−0.502871	+	0.864362i	$0.667723\pi$
$480$	−19.2017	+	33.2584i	−0.876435	+	1.51803i
$481$	19.9473	−	1.14120i	0.909517	−	0.0520344i
$482$	−29.0508			−1.32323
$483$		0			0
$484$	−35.1177			−1.59626
$485$	−8.14553	−	14.1085i	−0.369869	−	0.640633i
$486$	39.9388	+	23.0587i	1.81166	+	1.04596i
$487$	14.2214	+	8.21073i	0.644433	+	0.372064i	0.786320	−	0.617819i	$-0.211984\pi$
$487$	14.2214	+	8.21073i	0.644433	+	0.372064i	−0.141887	+	0.989883i	$0.545317\pi$
$488$	−8.30856	+	4.79695i	−0.376111	+	0.217148i
$489$		−	31.7616i		−	1.43631i
$490$		0			0
$491$	−18.2077			−0.821701			−0.410850	−	0.911703i	$-0.634768\pi$
$491$	−18.2077			−0.821701			−0.410850	+	0.911703i	$0.634768\pi$
$492$	59.1303	−	34.1389i	2.66580	−	1.53910i
$493$	1.78407	−	3.09010i	0.0803506	−	0.139171i
$494$	−12.2686	+	8.05110i	−0.551990	+	0.362236i
$495$	2.26967	+	3.93119i	0.102014	+	0.176694i
$496$		−	0.322108i		−	0.0144631i
$497$		0			0
$498$	80.8279			3.62199
$499$	32.5383	−	18.7860i	1.45661	−	0.840976i	0.457770	−	0.889070i	$-0.348648\pi$
$499$	32.5383	−	18.7860i	1.45661	−	0.840976i	0.998843	+	0.0480945i	$0.0153148\pi$
$500$	−32.5030	−	18.7656i	−1.45358	−	0.839225i
$501$	−15.9605	−	9.21481i	−0.713063	−	0.411687i
$502$	27.1945	−	15.7007i	1.21375	−	0.700758i
$503$	4.20535			0.187507			0.0937537	−	0.995595i	$-0.470113\pi$
$503$	4.20535			0.187507			0.0937537	+	0.995595i	$0.470113\pi$
$504$		0			0
$505$		−	19.3741i		−	0.862137i
$506$	0.405400	+	0.702174i	0.0180222	+	0.0312154i
$507$	40.6883	−	4.67092i	1.80703	−	0.207443i
$508$	21.5761	−	37.3710i	0.957287	−	1.65807i
$509$	7.30705	−	4.21873i	0.323879	−	0.186992i	−0.329241	−	0.944246i	$-0.606793\pi$
$509$	7.30705	−	4.21873i	0.323879	−	0.186992i	0.653120	+	0.757254i	$0.273460\pi$
$510$	27.1463			1.20206
$511$		0			0
$512$			0.791350i			0.0349731i
$513$	19.0763	−	11.0137i	0.842240	−	0.486268i
$514$	14.5133	+	8.37924i	0.640153	+	0.369593i
$515$	11.1185	+	6.41927i	0.489940	+	0.282867i
$516$	7.74159	+	13.4088i	0.340804	+	0.590290i
$517$	2.93602			0.129126
$518$		0			0
$519$	−53.5263			−2.34955
$520$	1.22023	+	21.3286i	0.0535106	+	0.935320i
$521$	12.9140	−	22.3677i	0.565773	−	0.979948i	−0.431204	−	0.902254i	$-0.641911\pi$
$521$	12.9140	−	22.3677i	0.565773	−	0.979948i	0.996977	−	0.0776936i	$-0.0247556\pi$
$522$	−27.5499	−	15.9059i	−1.20583	−	0.696184i
$523$	−0.378202	−	0.655065i	−0.0165376	−	0.0286440i	0.857638	−	0.514254i	$-0.171931\pi$
$523$	−0.378202	−	0.655065i	−0.0165376	−	0.0286440i	−0.874176	+	0.485610i	$0.838598\pi$
$524$	43.1436			1.88473
$525$		0			0
$526$		−	15.2599i		−	0.665364i
$527$	−7.07749	+	4.08619i	−0.308300	+	0.177997i
$528$	0.0588698	+	0.0339885i	0.00256198	+	0.00147916i
$529$	10.8383	−	18.7724i	0.471229	−	0.816192i
$530$	−18.0632	−	31.2863i	−0.784614	−	1.35899i
$531$		−	56.2396i		−	2.44059i
$532$		0			0
$533$	−10.9123	+	21.6726i	−0.472665	+	0.938744i
$534$	5.97145	+	10.3428i	0.258410	+	0.447579i
$535$	22.2420	+	12.8414i	0.961606	+	0.555183i
$536$	−17.5873	+	30.4620i	−0.759654	+	1.31576i
$537$	24.1032	+	41.7480i	1.04013	+	1.80156i
$538$		−	37.0717i		−	1.59827i
$539$		0			0
$540$		−	84.6231i		−	3.64160i
$541$	−19.4099	+	11.2063i	−0.834496	+	0.481797i	−0.855390	−	0.517985i	$-0.826682\pi$
$541$	−19.4099	+	11.2063i	−0.834496	+	0.481797i	0.0208936	+	0.999782i	$0.493349\pi$
$542$	21.4065	−	37.0772i	0.919488	−	1.59260i
$543$	9.21432	−	15.9597i	0.395424	−	0.684895i
$544$	8.81675	−	5.09035i	0.378015	−	0.218247i
$545$	2.89398			0.123965
$546$		0			0
$547$	−11.8059			−0.504784			−0.252392	−	0.967625i	$-0.581217\pi$
$547$	−11.8059			−0.504784			−0.252392	+	0.967625i	$0.581217\pi$
$548$	1.39737	−	0.806774i	0.0596929	−	0.0344637i
$549$	−11.9138	+	20.6354i	−0.508470	+	0.880697i
$550$	−0.170704	+	0.295668i	−0.00727884	+	0.0126073i
$551$	−3.10154	+	1.79068i	−0.132130	+	0.0762854i
$552$		−	10.1058i		−	0.430129i
$553$		0			0
$554$		−	68.6190i		−	2.91534i
$555$	18.5489	+	32.1276i	0.787355	+	1.36374i
$556$	−2.28543	+	3.95848i	−0.0969238	+	0.167877i
$557$	7.59273	+	4.38366i	0.321714	+	0.185742i	0.652156	−	0.758084i	$-0.273865\pi$
$557$	7.59273	+	4.38366i	0.321714	+	0.185742i	−0.330442	+	0.943826i	$0.607198\pi$
$558$	36.4305	+	63.0995i	1.54223	+	2.67122i
$559$	−4.91464	−	2.47456i	−0.207867	−	0.104663i
$560$		0			0
$561$		−	1.72468i		−	0.0728161i
$562$	2.54831	+	4.41380i	0.107494	+	0.186185i
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	0.159860	+	0.987140i	$0.448896\pi$
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	−0.934818	+	0.355127i	$0.884438\pi$
$564$	−83.6293	−	48.2834i	−3.52143	−	2.03310i
$565$	17.3358	−	10.0088i	0.729321	−	0.421074i
$566$			31.4744i			1.32297i
$567$		0			0
$568$	−3.76619			−0.158026
$569$	−17.8918	−	30.9896i	−0.750065	−	1.29915i	−0.947791	−	0.318893i	$-0.896689\pi$
$569$	−17.8918	−	30.9896i	−0.750065	−	1.29915i	0.197726	−	0.980257i	$-0.436644\pi$
$570$	−23.5964	−	13.6234i	−0.988344	−	0.570621i
$571$	7.46920	−	12.9370i	0.312576	−	0.541398i	−0.666343	−	0.745645i	$-0.732141\pi$
$571$	7.46920	−	12.9370i	0.312576	−	0.541398i	0.978919	+	0.204248i	$0.0654747\pi$
$572$	3.57581	−	0.204576i	0.149512	−	0.00855374i
$573$	84.4877			3.52952
$574$		0			0
$575$	−0.557280			−0.0232402
$576$	−44.8987	−	77.7669i	−1.87078	−	3.24029i
$577$	14.5892	+	8.42309i	0.607357	+	0.350658i	0.771930	−	0.635707i	$-0.219291\pi$
$577$	14.5892	+	8.42309i	0.607357	+	0.350658i	−0.164573	+	0.986365i	$0.552625\pi$
$578$	27.4057	+	15.8227i	1.13993	+	0.658137i
$579$	−0.583822	+	0.337070i	−0.0242628	+	0.0140081i
$580$			13.7585i			0.571292i
$581$		0			0
$582$	55.1838			2.28744
$583$	−1.98771	+	1.14761i	−0.0823226	+	0.0475290i
$584$	−16.5643	+	28.6901i	−0.685434	+	1.18721i
$585$	29.1107	+	44.3601i	1.20358	+	1.83406i
$586$	1.15647	+	2.00307i	0.0477735	+	0.0827461i
$587$			36.8833i			1.52234i	0.648555	+	0.761168i	$0.275374\pi$
$587$			36.8833i			1.52234i	−0.648555	+	0.761168i	$0.724626\pi$
$588$		0			0
$589$	8.20264			0.337984
$590$	−34.1469	+	19.7147i	−1.40580	+	0.811642i
$591$	30.6367	+	17.6881i	1.26022	+	0.727590i
$592$	0.335690	+	0.193811i	0.0137968	+	0.00796558i
$593$	−13.9894	+	8.07676i	−0.574474	+	0.331673i	−0.758934	−	0.651167i	$-0.774280\pi$
$593$	−13.9894	+	8.07676i	−0.574474	+	0.331673i	0.184460	+	0.982840i	$0.440946\pi$
$594$	−8.71531			−0.357593
$595$		0			0
$596$			67.9204i			2.78213i
$597$	32.1660	+	55.7131i	1.31646	+	2.28018i
$598$	5.19965	+	7.92343i	0.212629	+	0.324013i
$599$	1.24238	−	2.15186i	0.0507622	−	0.0879227i	−0.839528	−	0.543317i	$-0.817168\pi$
$599$	1.24238	−	2.15186i	0.0507622	−	0.0879227i	0.890290	+	0.455394i	$0.150502\pi$
$600$	3.68518	−	2.12764i	0.150447	−	0.0868605i
$601$	−9.55999			−0.389960			−0.194980	−	0.980807i	$-0.562464\pi$
$601$	−9.55999			−0.389960			−0.194980	+	0.980807i	$0.562464\pi$
$602$		0			0
$603$			87.3605i			3.55759i
$604$	−48.8179	+	28.1850i	−1.98637	+	1.14683i
$605$	20.0682	+	11.5864i	0.815886	+	0.471052i
$606$	56.8349	+	32.8136i	2.30876	+	1.33296i
$607$	−9.74294	−	16.8753i	−0.395454	−	0.684946i	0.597705	−	0.801716i	$-0.296079\pi$
$607$	−9.74294	−	16.8753i	−0.395454	−	0.684946i	−0.993159	+	0.116770i	$0.962746\pi$
$608$	−10.2184			−0.414411
$609$		0			0
$610$	16.7055			0.676387
$611$	34.2622	−	1.96017i	1.38610	−	0.0793002i
$612$	−19.7897	+	34.2768i	−0.799951	+	1.38556i
$613$	−12.7896	−	7.38409i	−0.516568	−	0.298241i	0.218962	−	0.975733i	$-0.429733\pi$
$613$	−12.7896	−	7.38409i	−0.516568	−	0.298241i	−0.735529	+	0.677493i	$0.763066\pi$
$614$	−27.4779	−	47.5931i	−1.10892	−	1.92070i
$615$	−45.0537			−1.81674
$616$		0			0
$617$		−	30.9478i		−	1.24591i	−0.782257	−	0.622955i	$-0.785932\pi$
$617$		−	30.9478i		−	1.24591i	0.782257	−	0.622955i	$-0.214068\pi$
$618$	−37.6625	+	21.7444i	−1.51501	+	0.874689i
$619$	11.3297	+	6.54123i	0.455380	+	0.262914i	0.710100	−	0.704101i	$-0.248650\pi$
$619$	11.3297	+	6.54123i	0.455380	+	0.262914i	−0.254719	+	0.967015i	$0.581983\pi$
$620$	15.7561	−	27.2903i	0.632780	−	1.09601i
$621$	−7.11300	−	12.3201i	−0.285435	−	0.494388i
$622$		−	20.5426i		−	0.823685i
$623$		0			0
$624$	0.709679	+	0.357329i	0.0284099	+	0.0143046i
$625$	11.1716	+	19.3498i	0.446865	+	0.773994i
$626$	−30.1478	−	17.4059i	−1.20495	−	0.695678i
$627$	−0.865532	+	1.49915i	−0.0345660	+	0.0598701i
$628$	−0.121696	−	0.210784i	−0.00485620	−	0.00841119i
$629$		−	9.83456i		−	0.392130i
$630$		0			0
$631$			35.3591i			1.40762i	0.710387	+	0.703812i	$0.248520\pi$
$631$			35.3591i			1.40762i	−0.710387	+	0.703812i	$0.751480\pi$
$632$	19.1373	−	11.0489i	0.761242	−	0.439503i
$633$	13.2591	−	22.9655i	0.527004	−	0.912797i
$634$	−7.80892	+	13.5254i	−0.310132	+	0.537164i
$635$	−24.6596	+	14.2372i	−0.978585	+	0.564986i
$636$	75.4903			2.99338
$637$		0			0
$638$	1.41699			0.0560990
$639$	−8.10065	+	4.67691i	−0.320457	+	0.185016i
$640$	−19.2884	+	33.4086i	−0.762443	+	1.32059i
$641$	−10.6188	+	18.3923i	−0.419417	+	0.726452i	−0.995881	−	0.0906706i	$-0.971099\pi$
$641$	−10.6188	+	18.3923i	−0.419417	+	0.726452i	0.576464	+	0.817123i	$0.304432\pi$
$642$	−75.3418	+	43.4986i	−2.97351	+	1.71675i
$643$		−	25.4808i		−	1.00486i	−0.864617	−	0.502432i	$-0.832439\pi$
$643$		−	25.4808i		−	1.00486i	0.864617	−	0.502432i	$-0.167561\pi$
$644$		0			0
$645$		−	10.2167i		−	0.402283i
$646$	3.61154	+	6.25537i	0.142094	+	0.246114i
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	−0.998249	−	0.0591522i	$-0.981160\pi$
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	0.550352	+	0.834933i	$0.314494\pi$
$648$	43.9059	+	25.3491i	1.72479	+	0.995806i
$649$	1.25253	+	2.16945i	0.0491662	+	0.0851583i
$650$	−1.79465	+	3.56429i	−0.0703919	+	0.139803i
$651$		0			0
$652$		−	32.4669i		−	1.27150i
$653$	−8.13928	−	14.0976i	−0.318515	−	0.551684i	0.661664	−	0.749801i	$-0.269851\pi$
$653$	−8.13928	−	14.0976i	−0.318515	−	0.551684i	−0.980178	+	0.198117i	$0.936517\pi$
$654$	−4.90150	+	8.48964i	−0.191664	+	0.331971i
$655$	−24.6546	−	14.2343i	−0.963334	−	0.556181i
$656$	−0.407683	+	0.235376i	−0.0159173	+	0.00918988i
$657$			82.2790i			3.21001i
$658$		0			0
$659$	20.5596			0.800888			0.400444	−	0.916321i	$-0.368856\pi$
$659$	20.5596			0.800888			0.400444	+	0.916321i	$0.368856\pi$
$660$	3.32513	+	5.75929i	0.129430	+	0.224180i
$661$	24.0518	+	13.8863i	0.935507	+	0.540115i	0.888549	−	0.458782i	$-0.151714\pi$
$661$	24.0518	+	13.8863i	0.935507	+	0.540115i	0.0469576	+	0.998897i	$0.485047\pi$
$662$	−15.7818	+	27.3349i	−0.613378	+	1.06240i
$663$	−1.15145	−	20.1263i	−0.0447185	−	0.781642i
$664$	31.3101			1.21507
$665$		0			0
$666$	−87.6802			−3.39754
$667$	1.15647	+	2.00307i	0.0447789	+	0.0775593i
$668$	−16.3149	−	9.41941i	−0.631242	−	0.364448i
$669$	−37.1303	−	21.4372i	−1.43554	−	0.828810i
$670$	53.0425	−	30.6241i	2.04921	−	1.18311i
$671$		−	1.06135i		−	0.0409730i
$672$		0			0
$673$	5.20337			0.200575			0.100288	−	0.994958i	$-0.468024\pi$
$673$	5.20337			0.200575			0.100288	+	0.994958i	$0.468024\pi$
$674$	−53.5105	+	30.8943i	−2.06115	+	1.19000i
$675$	2.99511	−	5.18768i	0.115282	−	0.199674i
$676$	41.5917	−	4.77463i	1.59968	−	0.183640i
$677$	22.4239	+	38.8394i	0.861821	+	1.49272i	0.870169	+	0.492753i	$0.164009\pi$
$677$	22.4239	+	38.8394i	0.861821	+	1.49272i	−0.00834820	+	0.999965i	$0.502657\pi$
$678$			67.8070i			2.60411i
$679$		0			0
$680$	10.5156			0.403254
$681$	−9.82957	+	5.67510i	−0.376670	+	0.217470i
$682$	−2.81062	−	1.62271i	−0.107624	−	0.0621370i
$683$	16.4318	+	9.48691i	0.628745	+	0.363006i	0.780266	−	0.625448i	$-0.215084\pi$
$683$	16.4318	+	9.48691i	0.628745	+	0.363006i	−0.151521	+	0.988454i	$0.548417\pi$
$684$	34.4037	−	19.8630i	1.31546	−	0.759479i
$685$	−1.06471			−0.0406807
$686$		0			0
$687$			57.9179i			2.20970i
$688$	−0.0533755	−	0.0924491i	−0.00203492	−	0.00352459i
$689$	−22.4296	+	14.7191i	−0.854500	+	0.560755i
$690$	−8.79840	+	15.2393i	−0.334949	+	0.580149i
$691$	−32.4085	+	18.7111i	−1.23288	+	0.711803i	−0.967629	−	0.252376i	$-0.918788\pi$
$691$	−32.4085	+	18.7111i	−1.23288	+	0.711803i	−0.265250	+	0.964180i	$0.585455\pi$
$692$	−54.7148			−2.07994
$693$		0			0
$694$		−	44.1229i		−	1.67488i
$695$	2.61204	−	1.50806i	0.0990802	−	0.0572040i
$696$	−15.2951	−	8.83060i	−0.579757	−	0.334723i
$697$	10.3435	+	5.97184i	0.391789	+	0.226200i
$698$	16.1734	+	28.0131i	0.612171	+	1.06031i
$699$	63.8580			2.41533
$700$		0			0
$701$	42.5513			1.60714			0.803570	−	0.595210i	$-0.202931\pi$
$701$	42.5513			1.60714			0.803570	+	0.595210i	$0.202931\pi$
$702$	−101.704	+	5.81860i	−3.83857	+	0.219609i
$703$	−4.93548	+	8.54851i	−0.186145	+	0.322413i
$704$	3.46395	+	1.99991i	0.130552	+	0.0753745i
$705$	31.8602	+	55.1835i	1.19993	+	2.07833i
$706$	38.7612			1.45880
$707$		0			0
$708$		−	82.3924i		−	3.09650i
$709$	43.5889	−	25.1661i	1.63702	−	0.945131i	0.655163	−	0.755488i	$-0.272600\pi$
$709$	43.5889	−	25.1661i	1.63702	−	0.945131i	0.981853	−	0.189644i	$-0.0607333\pi$
$710$	5.67934	+	3.27897i	0.213142	+	0.123057i
$711$	27.4415	−	47.5300i	1.02914	−	1.78252i
$712$	2.31315	+	4.00648i	0.0866888	+	0.150149i
$713$		−	5.29752i		−	0.198394i
$714$		0			0
$715$	−2.11091	−	1.06286i	−0.0789435	−	0.0397487i
$716$	24.6384	+	42.6749i	0.920780	+	1.59484i
$717$	−56.7760	−	32.7796i	−2.12034	−	1.22418i
$718$	26.0049	−	45.0418i	0.970495	−	1.68095i
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	−0.998940	−	0.0460219i	$-0.985346\pi$
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	0.459614	−	0.888119i	$-0.347988\pi$
$720$			1.02938i			0.0383625i
$721$		0			0
$722$			36.1616i			1.34580i
$723$	−34.6902	+	20.0284i	−1.29014	+	0.744863i
$724$	9.41891	−	16.3140i	0.350051	−	0.606306i
$725$	−0.486962	+	0.843444i	−0.0180853	+	0.0313247i
$726$	−67.9782	+	39.2472i	−2.52291	+	1.45660i
$727$	−19.8593			−0.736539			−0.368269	−	0.929719i	$-0.620050\pi$
$727$	−19.8593			−0.736539			−0.368269	+	0.929719i	$0.620050\pi$
$728$		0			0
$729$	9.04209			0.334892
$730$	49.9572	−	28.8428i	1.84900	−	1.06752i
$731$	−1.35422	+	2.34558i	−0.0500876	+	0.0867543i
$732$	−17.4541	+	30.2314i	−0.645121	+	1.11738i
$733$	−17.6237	+	10.1751i	−0.650947	+	0.375824i	−0.788819	−	0.614626i	$-0.789307\pi$
$733$	−17.6237	+	10.1751i	−0.650947	+	0.375824i	0.137872	+	0.990450i	$0.455974\pi$
$734$		−	37.8899i		−	1.39854i
$735$		0			0
$736$			6.59935i			0.243255i
$737$	−1.94564	−	3.36994i	−0.0716684	−	0.124133i
$738$	53.2421	−	92.2180i	1.95987	−	3.39459i
$739$	16.4554	+	9.50055i	0.605323	+	0.349483i	0.771133	−	0.636674i	$-0.219690\pi$
$739$	16.4554	+	9.50055i	0.605323	+	0.349483i	−0.165810	+	0.986158i	$0.553024\pi$
$740$	18.9607	+	32.8409i	0.697009	+	1.20726i
$741$	−9.09954	+	18.0723i	−0.334280	+	0.663902i
$742$		0			0
$743$			8.15098i			0.299030i	0.988759	+	0.149515i	$0.0477713\pi$
$743$			8.15098i			0.299030i	−0.988759	+	0.149515i	$0.952229\pi$
$744$	20.2254	+	35.0314i	0.741498	+	1.28431i
$745$	22.4090	−	38.8134i	0.821000	−	1.42201i
$746$	−54.7035	−	31.5831i	−2.00284	−	1.15634i
$747$	67.3445	−	38.8814i	2.46401	−	1.42260i
$748$		−	1.76297i		−	0.0644607i
$749$		0			0
$750$	−83.8893			−3.06320
$751$	18.3713	+	31.8201i	0.670379	+	1.16113i	0.977797	+	0.209556i	$0.0672020\pi$
$751$	18.3713	+	31.8201i	0.670379	+	1.16113i	−0.307417	+	0.951575i	$0.599465\pi$
$752$	0.576595	+	0.332897i	0.0210262	+	0.0121395i
$753$	21.6490	−	37.4972i	0.788934	−	1.36647i
$754$	16.5357	−	0.946022i	0.602193	−	0.0344521i
$755$	37.1963			1.35371
$756$		0			0
$757$	38.3971			1.39557			0.697783	−	0.716310i	$-0.254170\pi$
$757$	38.3971			1.39557			0.697783	+	0.716310i	$0.254170\pi$
$758$	−10.5584	−	18.2878i	−0.383500	−	0.664241i
$759$	0.968195	+	0.558987i	0.0351432	+	0.0202900i
$760$	−9.14048	−	5.27726i	−0.331560	−	0.191426i
$761$	10.7922	−	6.23089i	0.391218	−	0.225870i	−0.291470	−	0.956580i	$-0.594144\pi$
$761$	10.7922	−	6.23089i	0.391218	−	0.225870i	0.682688	+	0.730710i	$0.260811\pi$
$762$		−	96.4533i		−	3.49414i
$763$		0			0
$764$	86.3636			3.12453
$765$	22.6178	−	13.0584i	0.817749	−	0.472128i
$766$	−8.73742	+	15.1336i	−0.315696	+	0.546801i
$767$	16.0649	+	24.4804i	0.580071	+	0.883935i
$768$	−24.4860	−	42.4110i	−0.883562	−	1.53037i
$769$		−	4.81390i		−	0.173594i	−0.996226	−	0.0867969i	$-0.972337\pi$
$769$		−	4.81390i		−	0.173594i	0.996226	−	0.0867969i	$-0.0276631\pi$
$770$		0			0
$771$	23.1075			0.832196
$772$	−0.596785	+	0.344554i	−0.0214787	+	0.0124008i
$773$	24.4863	+	14.1372i	0.880713	+	0.508480i	0.870893	−	0.491472i	$-0.163541\pi$
$773$	24.4863	+	14.1372i	0.880713	+	0.508480i	0.00981931	+	0.999952i	$0.496874\pi$
$774$	20.9120	+	12.0736i	0.751668	+	0.433975i
$775$	1.93180	−	1.11533i	0.0693923	−	0.0400637i
$776$	21.3764			0.767369
$777$		0			0
$778$		−	14.9367i		−	0.535505i
$779$	−5.99395	−	10.3818i	−0.214755	−	0.371967i
$780$	42.6479	+	64.9886i	1.52704	+	2.32696i
$781$	0.208322	−	0.360825i	0.00745436	−	0.0129113i
$782$	4.03991	−	2.33244i	0.144467	−	0.0834081i
$783$	−24.8619			−0.888492
$784$		0			0
$785$			0.160604i			0.00573222i
$786$	83.5141	−	48.2169i	2.97885	−	1.71984i
$787$	43.0053	+	24.8291i	1.53297	+	0.885062i	0.999223	+	0.0394193i	$0.0125508\pi$
$787$	43.0053	+	24.8291i	1.53297	+	0.885062i	0.533749	+	0.845643i	$0.320783\pi$
$788$	31.3169	+	18.0808i	1.11562	+	0.644102i
$789$	−10.5206	−	18.2222i	−0.374543	−	0.648728i
$790$	−38.4783			−1.36900
$791$		0			0
$792$	−5.95633			−0.211649
$793$	−0.708588	−	12.3855i	−0.0251627	−	0.439823i
$794$	33.0507	−	57.2455i	1.17292	−	2.03157i
$795$	−43.1393	−	24.9065i	−1.52999	−	0.883341i
$796$	32.8801	+	56.9501i	1.16541	+	2.01854i
$797$	5.37263			0.190308			0.0951542	−	0.995463i	$-0.469666\pi$
$797$	5.37263			0.190308			0.0951542	+	0.995463i	$0.469666\pi$
$798$		0			0
$799$		−	16.8922i		−	0.597604i
$800$	−2.40653	+	1.38941i	−0.0850837	+	0.0491231i
$801$	9.95062	+	5.74500i	0.351588	+	0.202989i
$802$	−30.5517	+	52.9170i	−1.07882	+	1.86857i
$803$	−1.83246	−	3.17392i	−0.0646663	−	0.112005i
$804$			127.985i			4.51369i
$805$		0			0
$806$	−33.8822	−	17.0600i	−1.19345	−	0.600912i
$807$	−25.5582	−	44.2681i	−0.899692	−	1.55831i
$808$	22.0160	+	12.7109i	0.774520	+	0.447169i
$809$	−20.6184	+	35.7122i	−0.724905	+	1.25557i	0.234107	+	0.972211i	$0.424783\pi$
$809$	−20.6184	+	35.7122i	−0.724905	+	1.25557i	−0.959013	+	0.283362i	$0.908550\pi$
$810$	−44.1395	−	76.4518i	−1.55090	−	2.68624i
$811$		−	19.4366i		−	0.682512i	−0.939970	−	0.341256i	$-0.889148\pi$
$811$		−	19.4366i		−	0.682512i	0.939970	−	0.341256i	$-0.110852\pi$
$812$		0			0
$813$		−	59.0328i		−	2.07037i
$814$	3.38227	−	1.95276i	0.118549	−	0.0684441i
$815$	−10.7118	+	18.5533i	−0.375217	+	0.649895i
$816$	0.195551	−	0.338704i	0.00684564	−	0.0118570i
$817$	2.35426	−	1.35923i	0.0823651	−	0.0475535i
$818$	−79.4486			−2.77785
$819$		0			0
$820$	−46.0540			−1.60828
$821$	−17.4856	+	10.0953i	−0.610251	+	0.352329i	−0.773064	−	0.634328i	$-0.781277\pi$
$821$	−17.4856	+	10.0953i	−0.610251	+	0.352329i	0.162813	+	0.986657i	$0.447943\pi$
$822$	1.80329	−	3.12339i	0.0628970	−	0.108941i
$823$	−21.4049	+	37.0743i	−0.746127	+	1.29233i	0.203539	+	0.979067i	$0.434756\pi$
$823$	−21.4049	+	37.0743i	−0.746127	+	1.29233i	−0.949666	+	0.313263i	$0.898578\pi$
$824$	−14.5892	+	8.42309i	−0.508240	+	0.293432i
$825$			0.470751i			0.0163895i
$826$		0			0
$827$		−	33.5376i		−	1.16622i	−0.812394	−	0.583109i	$-0.801836\pi$
$827$		−	33.5376i		−	1.16622i	0.812394	−	0.583109i	$-0.198164\pi$
$828$	−12.8281	−	22.2189i	−0.445808	−	0.772162i
$829$	19.8949	−	34.4590i	0.690978	−	1.19681i	−0.280540	−	0.959842i	$-0.590513\pi$
$829$	19.8949	−	34.4590i	0.690978	−	1.19681i	0.971518	−	0.236967i	$-0.0761533\pi$
$830$	−47.2150	−	27.2596i	−1.63886	−	0.946195i
$831$	−47.3077	−	81.9394i	−1.64109	−	2.84245i
$832$	41.7581	+	21.0255i	1.44770	+	0.728929i
$833$		0			0
$834$			10.2167i			0.353776i
$835$	6.21548	+	10.7655i	0.215096	+	0.372556i
$836$	−0.884750	+	1.53243i	−0.0305997	+	0.0530003i
$837$	49.3142	+	28.4715i	1.70455	+	0.984120i
$838$	8.29564	−	4.78949i	0.286568	−	0.165450i
$839$		−	36.7098i		−	1.26736i	−0.773594	−	0.633682i	$-0.781543\pi$
$839$		−	36.7098i		−	1.26736i	0.773594	−	0.633682i	$-0.218457\pi$
$840$		0			0
$841$	−24.9578			−0.860614
$842$	−23.9364	−	41.4591i	−0.824903	−	1.42877i
$843$	6.08599	+	3.51375i	0.209613	+	0.121020i
$844$	13.5535	−	23.4754i	0.466532	−	0.808058i
$845$	−25.3430	−	10.9938i	−0.871827	−	0.378199i
$846$	−150.603			−5.17783
$847$		0			0
$848$	−0.520479			−0.0178733
$849$	21.6993	+	37.5842i	0.744717	+	1.28989i
$850$	1.70111	+	0.982134i	0.0583475	+	0.0336869i
$851$	5.52089	+	3.18749i	0.189254	+	0.109266i
$852$	−11.8676	+	6.85179i	−0.406579	+	0.234738i
$853$			11.7156i			0.401136i	0.979680	+	0.200568i	$0.0642788\pi$
$853$			11.7156i			0.401136i	−0.979680	+	0.200568i	$0.935721\pi$
$854$		0			0
$855$	−26.2135			−0.896483
$856$	−29.1850	+	16.8500i	−0.997523	+	0.575920i
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	−0.526576	−	0.850128i	$-0.676524\pi$
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	0.999521	+	0.0309639i	$0.00985769\pi$
$858$	6.69316	−	4.39230i	0.228501	−	0.149951i
$859$	−19.2819	−	33.3972i	−0.657890	−	1.13950i	−0.981161	−	0.193192i	$-0.938116\pi$
$859$	−19.2819	−	33.3972i	−0.657890	−	1.13950i	0.323271	−	0.946306i	$-0.395217\pi$
$860$		−	10.4436i		−	0.356122i
$861$		0			0
$862$	−38.6002			−1.31473
$863$	−15.4613	+	8.92660i	−0.526310	+	0.303865i	−0.739512	−	0.673143i	$-0.764944\pi$
$863$	−15.4613	+	8.92660i	−0.526310	+	0.303865i	0.213203	+	0.977008i	$0.431611\pi$
$864$	−61.4329	−	35.4683i	−2.08999	−	1.20666i
$865$	31.2670	+	18.0520i	1.06311	+	0.613787i
$866$	−6.77195	+	3.90979i	−0.230120	+	0.132860i
$867$	43.6343			1.48190
$868$		0			0
$869$			2.44464i			0.0829286i
$870$	15.3764	+	26.6327i	0.521310	+	0.902935i
$871$	−24.9547	−	38.0269i	−0.845556	−	1.28849i
$872$	−1.89868	+	3.28861i	−0.0642975	+	0.111366i
$873$	45.9783	−	26.5456i	1.55613	−	0.898431i
$874$	−4.68216			−0.158376
$875$		0			0
$876$			120.541i			4.07270i
$877$	7.72524	−	4.46017i	0.260863	−	0.150609i	−0.363865	−	0.931452i	$-0.618543\pi$
$877$	7.72524	−	4.46017i	0.260863	−	0.150609i	0.624728	+	0.780842i	$0.285210\pi$
$878$	−35.7454	−	20.6376i	−1.20635	−	0.696487i
$879$	2.76194	+	1.59461i	0.0931580	+	0.0537848i
$880$	−0.0229256	−	0.0397083i	−0.000772821	−	0.00133857i
$881$	−54.6144			−1.84001			−0.920003	−	0.391911i	$-0.871814\pi$
$881$	−54.6144			−1.84001			−0.920003	+	0.391911i	$0.871814\pi$
$882$		0			0
$883$	−7.51632			−0.252944			−0.126472	−	0.991970i	$-0.540365\pi$
$883$	−7.51632			−0.252944			−0.126472	+	0.991970i	$0.540365\pi$
$884$	−1.17701	−	20.5732i	−0.0395872	−	0.691951i
$885$	−27.1837	+	47.0835i	−0.913770	+	1.58270i
$886$	−12.7497	−	7.36105i	−0.428335	−	0.247299i
$887$	22.5391	+	39.0389i	0.756790	+	1.31080i	0.944479	+	0.328571i	$0.106567\pi$
$887$	22.5391	+	39.0389i	0.756790	+	1.31080i	−0.187689	+	0.982229i	$0.560100\pi$
$888$	−48.6780			−1.63353
$889$		0			0
$890$		−	8.05560i		−	0.270024i
$891$	−4.85720	+	2.80431i	−0.162722	+	0.0939479i
$892$	−37.9547	−	21.9132i	−1.27082	−	0.733708i
$893$	−8.47737	+	14.6832i	−0.283684	+	0.491356i
$894$	75.9074	+	131.475i	2.53872	+	4.39720i
$895$		−	32.5157i		−	1.08688i
$896$		0			0
$897$	11.6716	+	5.87676i	0.389705	+	0.196219i
$898$	−2.00271	−	3.46880i	−0.0668314	−	0.115755i
$899$	−8.01779	−	4.62907i	−0.267408	−	0.154388i
$900$	5.40160	−	9.35584i	0.180053	−	0.311861i
$901$	6.60268	+	11.4362i	0.219967	+	0.380994i
$902$			4.74309i			0.157928i
$903$		0			0
$904$			26.2662i			0.873602i
$905$	−10.7650	+	6.21515i	−0.357839	+	0.206599i
$906$	−62.9988	+	109.117i	−2.09299	+	3.62517i
$907$	3.18295	−	5.51303i	0.105688	−	0.183057i	−0.808331	−	0.588728i	$-0.799629\pi$
$907$	3.18295	−	5.51303i	0.105688	−	0.183057i	0.914019	+	0.405671i	$0.132962\pi$
$908$	−10.0478	+	5.80111i	−0.333449	+	0.192517i
$909$	63.1385			2.09417
$910$		0			0
$911$	20.9161			0.692982			0.346491	−	0.938053i	$-0.387373\pi$
$911$	20.9161			0.692982			0.346491	+	0.938053i	$0.387373\pi$
$912$	−0.339958	+	0.196275i	−0.0112571	+	0.00649930i
$913$	−1.73188	+	2.99971i	−0.0573169	+	0.0992758i
$914$	37.3681	−	64.7234i	1.23603	−	2.14086i
$915$	19.9484	−	11.5172i	0.659475	−	0.380748i
$916$			59.2038i			1.95615i
$917$		0			0
$918$			50.1430i			1.65496i
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	0.822910	−	0.568171i	$-0.192349\pi$
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	−0.903506	+	0.428576i	$0.859016\pi$
$920$	−3.40821	+	5.90320i	−0.112366	+	0.194623i
$921$	−65.6239	−	37.8880i	−2.16238	−	1.24845i
$922$	−8.75816	−	15.1696i	−0.288435	−	0.499584i
$923$	2.19014	−	4.34976i	0.0720893	−	0.143174i
$924$		0			0
$925$			2.68434i			0.0882606i
$926$	16.5329	+	28.6358i	0.543305	+	0.941031i
$927$	−20.9198	+	36.2342i	−0.687098	+	1.19009i
$928$	9.98812	+	5.76664i	0.327876	+	0.189299i
$929$	44.6306	−	25.7675i	1.46428	−	0.845404i	0.465077	−	0.885270i	$-0.346027\pi$
$929$	44.6306	−	25.7675i	1.46428	−	0.845404i	0.999205	+	0.0398663i	$0.0126932\pi$
$930$		−	70.4355i		−	2.30967i
$931$		0			0
$932$	65.2759			2.13818
$933$	−14.1626	−	24.5304i	−0.463664	−	0.803090i
$934$	6.68017	+	3.85680i	0.218582	+	0.126198i
$935$	−0.581657	+	1.00746i	−0.0190222	+	0.0329474i
$936$	−69.5080	+	3.97662i	−2.27194	+	0.129980i
$937$	−20.3565			−0.665016			−0.332508	−	0.943100i	$-0.607895\pi$
$937$	−20.3565			−0.665016			−0.332508	+	0.943100i	$0.607895\pi$
$938$		0			0
$939$	−48.0002			−1.56643
$940$	32.5676	+	56.4088i	1.06224	+	1.83985i
$941$	−29.6730	−	17.1317i	−0.967314	−	0.558479i	−0.0688974	−	0.997624i	$-0.521948\pi$
$941$	−29.6730	−	17.1317i	−0.967314	−	0.558479i	−0.898416	+	0.439145i	$0.855281\pi$
$942$	−0.471141	−	0.272013i	−0.0153506	−	0.00886267i
$943$	−6.70490	+	3.87108i	−0.218342	+	0.126060i
$944$			0.568067i			0.0184890i
$945$		0			0
$946$	−1.07558			−0.0349701
$947$	47.9046	−	27.6578i	1.55669	−	0.898756i	0.559122	−	0.829086i	$-0.311138\pi$
$947$	47.9046	−	27.6578i	1.55669	−	0.898756i	0.997570	−	0.0696707i	$-0.0221949\pi$
$948$	40.2025	−	69.6327i	1.30572	−	2.26156i
$949$	−23.5031	−	35.8150i	−0.762944	−	1.16260i
$950$	−0.985770	−	1.70740i	−0.0319826	−	0.0553955i
$951$			21.5347i			0.698311i
$952$		0			0
$953$	−14.8378			−0.480644			−0.240322	−	0.970693i	$-0.577253\pi$
$953$	−14.8378			−0.480644			−0.240322	+	0.970693i	$0.577253\pi$
$954$	101.959	−	58.8663i	3.30106	−	1.90587i
$955$	−49.3529	−	28.4939i	−1.59702	−	0.922041i
$956$	−58.0366	−	33.5075i	−1.87704	−	1.08371i
$957$	1.69205	−	0.976908i	0.0546964	−	0.0315790i
$958$	−0.331812			−0.0107203
$959$		0			0
$960$			86.8081i			2.80172i
$961$	−4.89769	−	8.48305i	−0.157990	−	0.273647i
$962$	38.1661	−	25.0460i	1.23052	−	0.807515i
$963$	−41.8491	+	72.4847i	−1.34857	+	2.33579i
$964$	−35.4604	+	20.4731i	−1.14210	+	0.659393i
$965$	0.454714			0.0146378
$966$		0			0
$967$		−	3.09473i		−	0.0995199i	−0.998761	−	0.0497600i	$-0.984154\pi$
$967$		−	3.09473i		−	0.0995199i	0.998761	−	0.0497600i	$-0.0158456\pi$
$968$	−26.3326	+	15.2031i	−0.846361	+	0.488647i
$969$	8.62524	+	4.97979i	0.277083	+	0.159974i
$970$	−32.2352	−	18.6110i	−1.03501	−	0.597564i
$971$	27.4506	+	47.5459i	0.880933	+	1.52582i	0.850305	+	0.526290i	$0.176417\pi$
$971$	27.4506	+	47.5459i	0.880933	+	1.52582i	0.0306280	+	0.999531i	$0.490249\pi$
$972$	65.0010			2.08491
$973$		0			0
$974$	37.5200			1.20222
$975$	0.314287	+	5.49348i	0.0100653	+	0.175932i
$976$	0.120340	−	0.208435i	0.00385198	−	0.00667183i
$977$	−37.4196	−	21.6042i	−1.19716	−	0.691181i	−0.237239	−	0.971451i	$-0.576243\pi$
$977$	−37.4196	−	21.6042i	−1.19716	−	0.691181i	−0.959921	+	0.280270i	$0.909576\pi$
$978$	−36.2847	−	62.8470i	−1.16026	−	2.00962i
$979$	−0.511795			−0.0163570
$980$		0			0
$981$			9.43124i			0.301116i
$982$	−36.0276	+	20.8006i	−1.14969	+	0.663773i
$983$	21.5498	+	12.4418i	0.687332	+	0.396831i	0.802612	−	0.596502i	$-0.203443\pi$
$983$	21.5498	+	12.4418i	0.687332	+	0.396831i	−0.115280	+	0.993333i	$0.536776\pi$
$984$	29.5588	−	51.1973i	0.942299	−	1.63211i
$985$	−11.9308	−	20.6647i	−0.380146	−	0.658433i
$986$		−	8.15254i		−	0.259630i
$987$		0			0
$988$	−9.30158	+	18.4735i	−0.295923	+	0.587722i
$989$	−0.877834	−	1.52045i	−0.0279135	−	0.0483476i
$990$	8.98203	+	5.18578i	0.285468	+	0.164815i
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	−0.901509	−	0.432760i	$-0.857540\pi$
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	0.825536	+	0.564349i	$0.190873\pi$
$992$	−13.2078	−	22.8765i	−0.419347	−	0.726331i
$993$			43.5216i			1.38112i
$994$		0			0
$995$		−	43.3925i		−	1.37564i
$996$	98.6614	−	56.9622i	3.12621	−	1.80492i
$997$	1.72037	−	2.97977i	0.0544847	−	0.0943703i	−0.837497	−	0.546442i	$-0.815982\pi$
$997$	1.72037	−	2.97977i	0.0544847	−	0.0943703i	0.891981	+	0.452072i	$0.149315\pi$
$998$	42.9225	−	74.3439i	1.35869	−	2.35331i
$999$	−59.3441	+	34.2623i	−1.87756	+	1.08401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.f.116.8		16
7.2	even	3	inner	637.2.r.f.324.1		16
7.3	odd	6		637.2.c.f.246.8		8
7.4	even	3		637.2.c.e.246.8		8
7.5	odd	6		91.2.r.a.51.1	yes	16
7.6	odd	2		91.2.r.a.25.8	yes	16
13.12	even	2	inner	637.2.r.f.116.1		16
21.5	even	6		819.2.dl.e.415.8		16
21.20	even	2		819.2.dl.e.298.1		16
91.5	even	12		1183.2.e.i.170.1		16
91.12	odd	6		91.2.r.a.51.8	yes	16
91.18	odd	12		8281.2.a.cj.1.8		8
91.25	even	6		637.2.c.e.246.1		8
91.31	even	12		8281.2.a.ck.1.8		8
91.34	even	4		1183.2.e.i.508.8		16
91.38	odd	6		637.2.c.f.246.1		8
91.47	even	12		1183.2.e.i.170.8		16
91.51	even	6	inner	637.2.r.f.324.8		16
91.60	odd	12		8281.2.a.cj.1.1		8
91.73	even	12		8281.2.a.ck.1.1		8
91.83	even	4		1183.2.e.i.508.1		16
91.90	odd	2		91.2.r.a.25.1	✓	16
273.194	even	6		819.2.dl.e.415.1		16
273.272	even	2		819.2.dl.e.298.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.1	✓	16	91.90	odd	2
91.2.r.a.25.8	yes	16	7.6	odd	2
91.2.r.a.51.1	yes	16	7.5	odd	6
91.2.r.a.51.8	yes	16	91.12	odd	6
637.2.c.e.246.1		8	91.25	even	6
637.2.c.e.246.8		8	7.4	even	3
637.2.c.f.246.1		8	91.38	odd	6
637.2.c.f.246.8		8	7.3	odd	6
637.2.r.f.116.1		16	13.12	even	2	inner
637.2.r.f.116.8		16	1.1	even	1	trivial
637.2.r.f.324.1		16	7.2	even	3	inner
637.2.r.f.324.8		16	91.51	even	6	inner
819.2.dl.e.298.1		16	21.20	even	2
819.2.dl.e.298.8		16	273.272	even	2
819.2.dl.e.415.1		16	273.194	even	6
819.2.dl.e.415.8		16	21.5	even	6
1183.2.e.i.170.1		16	91.5	even	12
1183.2.e.i.170.8		16	91.47	even	12
1183.2.e.i.508.1		16	91.83	even	4
1183.2.e.i.508.8		16	91.34	even	4
8281.2.a.cj.1.1		8	91.60	odd	12
8281.2.a.cj.1.8		8	91.18	odd	12
8281.2.a.ck.1.1		8	91.73	even	12
8281.2.a.ck.1.8		8	91.31	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.97871 - 1.14241i) q^{2} +(1.57521 - 2.72835i) q^{3} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} -7.19813i q^{6} -2.78832i q^{8} +(-3.46258 - 5.99736i) q^{9} +O(q^{10})\)	\(q+(1.97871 - 1.14241i) q^{2} +(1.57521 - 2.72835i) q^{3} +(1.61019 - 2.78892i) q^{4} +(-1.84030 + 1.06250i) q^{5} -7.19813i q^{6} -2.78832i q^{8} +(-3.46258 - 5.99736i) q^{9} +(-2.42760 + 4.20473i) q^{10} +(0.267139 + 0.154233i) q^{11} +(-5.07276 - 8.78629i) q^{12} +(3.22037 + 1.62148i) q^{13} +6.69462i q^{15} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(-13.7029 - 7.91135i) q^{18} +(-1.54266 + 0.890653i) q^{19} +6.84326i q^{20} +0.704786 q^{22} +(0.575211 + 0.996294i) q^{23} +(-7.60750 - 4.39219i) q^{24} +(-0.242207 + 0.419515i) q^{25} +(8.22456 - 0.470536i) q^{26} -12.3659 q^{27} +2.01052 q^{29} +(7.64798 + 13.2467i) q^{30} +(-3.98791 - 2.30242i) q^{31} +(4.96792 + 2.86823i) q^{32} +(0.841600 - 0.485898i) q^{33} -4.05494i q^{34} -22.3016 q^{36} +(4.79901 - 2.77071i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(9.49673 - 6.23211i) q^{39} +(2.96258 + 5.13134i) q^{40} +6.72984i q^{41} -1.52611 q^{43} +(0.860286 - 0.496686i) q^{44} +(12.7443 + 7.35795i) q^{45} +(2.27635 + 1.31425i) q^{46} +(8.24297 - 4.75908i) q^{47} +0.220372 q^{48} +1.10680i q^{50} +(-2.79558 - 4.84209i) q^{51} +(9.70759 - 6.37048i) q^{52} +(-3.72037 + 6.44387i) q^{53} +(-24.4685 + 14.1269i) q^{54} -0.655486 q^{55} +5.61186i q^{57} +(3.97823 - 2.29683i) q^{58} +(7.03304 + 4.06053i) q^{59} +(18.6708 + 10.7796i) q^{60} +(-1.72037 - 2.97977i) q^{61} -10.5212 q^{62} +12.9669 q^{64} +(-7.64926 + 0.437622i) q^{65} +(1.11019 - 1.92290i) q^{66} +(-10.9249 - 6.30747i) q^{67} +(-2.85765 - 4.94960i) q^{68} +3.62431 q^{69} -1.35070i q^{71} +(-16.7226 + 9.65478i) q^{72} +(-10.2894 - 5.94059i) q^{73} +(6.33056 - 10.9648i) q^{74} +(0.763054 + 1.32165i) q^{75} +5.73646i q^{76} +(11.6716 - 23.1806i) q^{78} +(3.96258 + 6.86339i) q^{79} +(-0.128728 - 0.0743214i) q^{80} +(-9.09116 + 15.7464i) q^{81} +(7.68821 + 13.3164i) q^{82} +11.2290i q^{83} +3.77130i q^{85} +(-3.01972 + 1.74344i) q^{86} +(3.16700 - 5.48540i) q^{87} +(0.430050 - 0.744869i) q^{88} +(-1.43688 + 0.829583i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(-12.5636 + 7.25360i) q^{93} +(10.8736 - 18.8336i) q^{94} +(1.89263 - 3.27813i) q^{95} +(15.6511 - 9.03614i) q^{96} +7.66641i q^{97} -2.13617i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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