LMFDB - Embedded newform 383.2.a.c.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [383,2,Mod(1,383)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(383, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("383.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	383.a (trivial)

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:	yes
Analytic conductor:	$3.05827039742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.58110 q^{2} +2.57388 q^{3} +4.66207 q^{4} -4.25360 q^{5} +6.64345 q^{6} -1.55327 q^{7} +6.87105 q^{8} +3.62488 q^{9} -10.9790 q^{10} -1.50526 q^{11} +11.9996 q^{12} -0.166872 q^{13} -4.00915 q^{14} -10.9483 q^{15} +8.41073 q^{16} -7.68231 q^{17} +9.35616 q^{18} +7.82416 q^{19} -19.8306 q^{20} -3.99795 q^{21} -3.88523 q^{22} +1.82098 q^{23} +17.6853 q^{24} +13.0931 q^{25} -0.430713 q^{26} +1.60836 q^{27} -7.24147 q^{28} +2.12508 q^{29} -28.2586 q^{30} -5.38423 q^{31} +7.96681 q^{32} -3.87438 q^{33} -19.8288 q^{34} +6.60701 q^{35} +16.8994 q^{36} +3.94801 q^{37} +20.1949 q^{38} -0.429510 q^{39} -29.2267 q^{40} -0.332492 q^{41} -10.3191 q^{42} +4.68328 q^{43} -7.01764 q^{44} -15.4188 q^{45} +4.70013 q^{46} -1.24434 q^{47} +21.6482 q^{48} -4.58734 q^{49} +33.7947 q^{50} -19.7734 q^{51} -0.777969 q^{52} -9.61215 q^{53} +4.15133 q^{54} +6.40280 q^{55} -10.6726 q^{56} +20.1385 q^{57} +5.48504 q^{58} +15.2225 q^{59} -51.0416 q^{60} -4.86732 q^{61} -13.8972 q^{62} -5.63043 q^{63} +3.74166 q^{64} +0.709808 q^{65} -10.0001 q^{66} +9.31251 q^{67} -35.8154 q^{68} +4.68699 q^{69} +17.0533 q^{70} +7.05460 q^{71} +24.9067 q^{72} +8.88768 q^{73} +10.1902 q^{74} +33.7002 q^{75} +36.4767 q^{76} +2.33809 q^{77} -1.10861 q^{78} -0.129066 q^{79} -35.7759 q^{80} -6.73490 q^{81} -0.858194 q^{82} +3.08459 q^{83} -18.6387 q^{84} +32.6775 q^{85} +12.0880 q^{86} +5.46971 q^{87} -10.3428 q^{88} -9.24888 q^{89} -39.7974 q^{90} +0.259198 q^{91} +8.48953 q^{92} -13.8584 q^{93} -3.21177 q^{94} -33.2808 q^{95} +20.5056 q^{96} -10.1487 q^{97} -11.8404 q^{98} -5.45640 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) $ 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * q^99

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 $

$2$	2.58110	1.82511	0.912556	−	0.408952i	$-0.134106\pi$
$2$	2.58110	1.82511	0.912556	+	0.408952i	$0.134106\pi$
$3$	2.57388	1.48603	0.743016	−	0.669274i	$-0.233395\pi$
$3$	2.57388	1.48603	0.743016	+	0.669274i	$0.233395\pi$
$4$	4.66207	2.33103
$5$	−4.25360	−1.90227	−0.951134	−	0.308777i	$-0.900080\pi$
$5$	−4.25360	−1.90227	−0.951134	+	0.308777i	$0.900080\pi$
$6$	6.64345	2.71218
$7$	−1.55327	−0.587083	−0.293541	−	0.955946i	$-0.594834\pi$
$7$	−1.55327	−0.587083	−0.293541	+	0.955946i	$0.594834\pi$
$8$	6.87105	2.42928
$9$	3.62488	1.20829
$10$	−10.9790	−3.47185
$11$	−1.50526	−0.453854	−0.226927	−	0.973912i	$-0.572868\pi$
$11$	−1.50526	−0.453854	−0.226927	+	0.973912i	$0.572868\pi$
$12$	11.9996	3.46399
$13$	−0.166872	−0.0462820	−0.0231410	−	0.999732i	$-0.507367\pi$
$13$	−0.166872	−0.0462820	−0.0231410	+	0.999732i	$0.507367\pi$
$14$	−4.00915	−1.07149
$15$	−10.9483	−2.82683
$16$	8.41073	2.10268
$17$	−7.68231	−1.86323	−0.931617	−	0.363442i	$-0.881601\pi$
$17$	−7.68231	−1.86323	−0.931617	+	0.363442i	$0.881601\pi$
$18$	9.35616	2.20527
$19$	7.82416	1.79498	0.897492	−	0.441030i	$-0.145387\pi$
$19$	7.82416	1.79498	0.897492	+	0.441030i	$0.145387\pi$
$20$	−19.8306	−4.43425
$21$	−3.99795	−0.872424
$22$	−3.88523	−0.828335
$23$	1.82098	0.379701	0.189850	−	0.981813i	$-0.439200\pi$
$23$	1.82098	0.379701	0.189850	+	0.981813i	$0.439200\pi$
$24$	17.6853	3.61000
$25$	13.0931	2.61863
$26$	−0.430713	−0.0844698
$27$	1.60836	0.309529
$28$	−7.24147	−1.36851
$29$	2.12508	0.394618	0.197309	−	0.980341i	$-0.436780\pi$
$29$	2.12508	0.394618	0.197309	+	0.980341i	$0.436780\pi$
$30$	−28.2586	−5.15929
$31$	−5.38423	−0.967037	−0.483518	−	0.875334i	$-0.660641\pi$
$31$	−5.38423	−0.967037	−0.483518	+	0.875334i	$0.660641\pi$
$32$	7.96681	1.40835
$33$	−3.87438	−0.674442
$34$	−19.8288	−3.40061
$35$	6.60701	1.11679
$36$	16.8994	2.81657
$37$	3.94801	0.649049	0.324525	−	0.945877i	$-0.394796\pi$
$37$	3.94801	0.649049	0.324525	+	0.945877i	$0.394796\pi$
$38$	20.1949	3.27605
$39$	−0.429510	−0.0687766
$40$	−29.2267	−4.62115
$41$	−0.332492	−0.0519265	−0.0259632	−	0.999663i	$-0.508265\pi$
$41$	−0.332492	−0.0519265	−0.0259632	+	0.999663i	$0.508265\pi$
$42$	−10.3191	−1.59227
$43$	4.68328	0.714194	0.357097	−	0.934067i	$-0.383767\pi$
$43$	4.68328	0.714194	0.357097	+	0.934067i	$0.383767\pi$
$44$	−7.01764	−1.05795
$45$	−15.4188	−2.29850
$46$	4.70013	0.692996
$47$	−1.24434	−0.181506	−0.0907531	−	0.995873i	$-0.528927\pi$
$47$	−1.24434	−0.181506	−0.0907531	+	0.995873i	$0.528927\pi$
$48$	21.6482	3.12465
$49$	−4.58734	−0.655334
$50$	33.7947	4.77929
$51$	−19.7734	−2.76882
$52$	−0.777969	−0.107885
$53$	−9.61215	−1.32033	−0.660165	−	0.751120i	$-0.729514\pi$
$53$	−9.61215	−1.32033	−0.660165	+	0.751120i	$0.729514\pi$
$54$	4.15133	0.564924
$55$	6.40280	0.863353
$56$	−10.6726	−1.42619
$57$	20.1385	2.66740
$58$	5.48504	0.720222
$59$	15.2225	1.98181	0.990903	−	0.134580i	$-0.0429685\pi$
$59$	15.2225	1.98181	0.990903	+	0.134580i	$0.0429685\pi$
$60$	−51.0416	−6.58944
$61$	−4.86732	−0.623197	−0.311599	−	0.950214i	$-0.600864\pi$
$61$	−4.86732	−0.623197	−0.311599	+	0.950214i	$0.600864\pi$
$62$	−13.8972	−1.76495
$63$	−5.63043	−0.709367
$64$	3.74166	0.467708
$65$	0.709808	0.0880408
$66$	−10.0001	−1.23093
$67$	9.31251	1.13770	0.568852	−	0.822440i	$-0.307388\pi$
$67$	9.31251	1.13770	0.568852	+	0.822440i	$0.307388\pi$
$68$	−35.8154	−4.34326
$69$	4.68699	0.564248
$70$	17.0533	2.03826
$71$	7.05460	0.837227	0.418614	−	0.908164i	$-0.362516\pi$
$71$	7.05460	0.837227	0.418614	+	0.908164i	$0.362516\pi$
$72$	24.9067	2.93529
$73$	8.88768	1.04022	0.520112	−	0.854098i	$-0.325890\pi$
$73$	8.88768	1.04022	0.520112	+	0.854098i	$0.325890\pi$
$74$	10.1902	1.18459
$75$	33.7002	3.89136
$76$	36.4767	4.18417
$77$	2.33809	0.266450
$78$	−1.10861	−0.125525
$79$	−0.129066	−0.0145211	−0.00726053	−	0.999974i	$-0.502311\pi$
$79$	−0.129066	−0.0145211	−0.00726053	+	0.999974i	$0.502311\pi$
$80$	−35.7759	−3.99987
$81$	−6.73490	−0.748323
$82$	−0.858194	−0.0947716
$83$	3.08459	0.338577	0.169289	−	0.985567i	$-0.445853\pi$
$83$	3.08459	0.338577	0.169289	+	0.985567i	$0.445853\pi$
$84$	−18.6387	−2.03365
$85$	32.6775	3.54437
$86$	12.0880	1.30348
$87$	5.46971	0.586415
$88$	−10.3428	−1.10254
$89$	−9.24888	−0.980379	−0.490189	−	0.871616i	$-0.663072\pi$
$89$	−9.24888	−0.980379	−0.490189	+	0.871616i	$0.663072\pi$
$90$	−39.7974	−4.19501
$91$	0.259198	0.0271714
$92$	8.48953	0.885095
$93$	−13.8584	−1.43705
$94$	−3.21177	−0.331269
$95$	−33.2808	−3.41454
$96$	20.5056	2.09285
$97$	−10.1487	−1.03044	−0.515222	−	0.857057i	$-0.672291\pi$
$97$	−10.1487	−1.03044	−0.515222	+	0.857057i	$0.672291\pi$
$98$	−11.8404	−1.19606
$99$	−5.45640	−0.548388
$100$	61.0411	6.10411
$101$	−6.98437	−0.694971	−0.347485	−	0.937685i	$-0.612964\pi$
$101$	−6.98437	−0.694971	−0.347485	+	0.937685i	$0.612964\pi$
$102$	−51.0370	−5.05341
$103$	10.6733	1.05167	0.525837	−	0.850586i	$-0.323752\pi$
$103$	10.6733	1.05167	0.525837	+	0.850586i	$0.323752\pi$
$104$	−1.14659	−0.112432
$105$	17.0057	1.65958
$106$	−24.8099	−2.40975
$107$	6.46852	0.625336	0.312668	−	0.949862i	$-0.398777\pi$
$107$	6.46852	0.625336	0.312668	+	0.949862i	$0.398777\pi$
$108$	7.49827	0.721521
$109$	−5.24266	−0.502156	−0.251078	−	0.967967i	$-0.580785\pi$
$109$	−5.24266	−0.502156	−0.251078	+	0.967967i	$0.580785\pi$
$110$	16.5262	1.57572
$111$	10.1617	0.964508
$112$	−13.0642	−1.23445
$113$	4.72006	0.444026	0.222013	−	0.975044i	$-0.428737\pi$
$113$	4.72006	0.444026	0.222013	+	0.975044i	$0.428737\pi$
$114$	51.9793	4.86831
$115$	−7.74573	−0.722293
$116$	9.90727	0.919867
$117$	−0.604891	−0.0559222
$118$	39.2909	3.61702
$119$	11.9327	1.09387
$120$	−75.2262	−6.86718
$121$	−8.73418	−0.794016
$122$	−12.5630	−1.13740
$123$	−0.855795	−0.0771644
$124$	−25.1017	−2.25420
$125$	−34.4250	−3.07906
$126$	−14.5327	−1.29467
$127$	−10.1154	−0.897599	−0.448800	−	0.893632i	$-0.648148\pi$
$127$	−10.1154	−0.897599	−0.448800	+	0.893632i	$0.648148\pi$
$128$	−6.27603	−0.554728
$129$	12.0542	1.06132
$130$	1.83208	0.160684
$131$	−3.14047	−0.274385	−0.137192	−	0.990544i	$-0.543808\pi$
$131$	−3.14047	−0.274385	−0.137192	+	0.990544i	$0.543808\pi$
$132$	−18.0626	−1.57215
$133$	−12.1531	−1.05380
$134$	24.0365	2.07644
$135$	−6.84131	−0.588806
$136$	−52.7856	−4.52632
$137$	8.77278	0.749509	0.374755	−	0.927124i	$-0.377727\pi$
$137$	8.77278	0.749509	0.374755	+	0.927124i	$0.377727\pi$
$138$	12.0976	1.02982
$139$	−13.3382	−1.13133	−0.565667	−	0.824634i	$-0.691381\pi$
$139$	−13.3382	−1.13133	−0.565667	+	0.824634i	$0.691381\pi$
$140$	30.8023	2.60327
$141$	−3.20279	−0.269724
$142$	18.2086	1.52803
$143$	0.251187	0.0210053
$144$	30.4879	2.54065
$145$	−9.03925	−0.750669
$146$	22.9400	1.89852
$147$	−11.8073	−0.973848
$148$	18.4059	1.51296
$149$	−5.16087	−0.422795	−0.211397	−	0.977400i	$-0.567801\pi$
$149$	−5.16087	−0.422795	−0.211397	+	0.977400i	$0.567801\pi$
$150$	86.9835	7.10217
$151$	7.15492	0.582259	0.291130	−	0.956684i	$-0.405969\pi$
$151$	7.15492	0.582259	0.291130	+	0.956684i	$0.405969\pi$
$152$	53.7602	4.36053
$153$	−27.8474	−2.25133
$154$	6.03484	0.486301
$155$	22.9024	1.83956
$156$	−2.00240	−0.160320
$157$	18.9675	1.51377	0.756887	−	0.653546i	$-0.226719\pi$
$157$	18.9675	1.51377	0.756887	+	0.653546i	$0.226719\pi$
$158$	−0.333132	−0.0265025
$159$	−24.7406	−1.96205
$160$	−33.8877	−2.67905
$161$	−2.82848	−0.222916
$162$	−17.3834	−1.36577
$163$	−2.08285	−0.163142	−0.0815708	−	0.996668i	$-0.525994\pi$
$163$	−2.08285	−0.163142	−0.0815708	+	0.996668i	$0.525994\pi$
$164$	−1.55010	−0.121042
$165$	16.4801	1.28297
$166$	7.96162	0.617941
$167$	8.65764	0.669948	0.334974	−	0.942227i	$-0.391272\pi$
$167$	8.65764	0.669948	0.334974	+	0.942227i	$0.391272\pi$
$168$	−27.4701	−2.11937
$169$	−12.9722	−0.997858
$170$	84.3438	6.46887
$171$	28.3616	2.16887
$172$	21.8338	1.66481
$173$	−0.0384860	−0.00292603	−0.00146302	−	0.999999i	$-0.500466\pi$
$173$	−0.0384860	−0.00292603	−0.00146302	+	0.999999i	$0.500466\pi$
$174$	14.1179	1.07027
$175$	−20.3372	−1.53735
$176$	−12.6604	−0.954312
$177$	39.1810	2.94503
$178$	−23.8723	−1.78930
$179$	−11.9385	−0.892327	−0.446163	−	0.894951i	$-0.647210\pi$
$179$	−11.9385	−0.892327	−0.446163	+	0.894951i	$0.647210\pi$
$180$	−71.8834	−5.35787
$181$	−23.4257	−1.74122	−0.870611	−	0.491972i	$-0.836276\pi$
$181$	−23.4257	−1.74122	−0.870611	+	0.491972i	$0.836276\pi$
$182$	0.669016	0.0495908
$183$	−12.5279	−0.926091
$184$	12.5121	0.922401
$185$	−16.7933	−1.23467
$186$	−35.7699	−2.62277
$187$	11.5639	0.845636
$188$	−5.80121	−0.423097
$189$	−2.49822	−0.181719
$190$	−85.9011	−6.23192
$191$	13.4857	0.975794	0.487897	−	0.872901i	$-0.337764\pi$
$191$	13.4857	0.975794	0.487897	+	0.872901i	$0.337764\pi$
$192$	9.63060	0.695029
$193$	25.9852	1.87045	0.935226	−	0.354051i	$-0.115196\pi$
$193$	25.9852	1.87045	0.935226	+	0.354051i	$0.115196\pi$
$194$	−26.1948	−1.88068
$195$	1.82696	0.130832
$196$	−21.3865	−1.52761
$197$	−11.3574	−0.809183	−0.404592	−	0.914497i	$-0.632586\pi$
$197$	−11.3574	−0.809183	−0.404592	+	0.914497i	$0.632586\pi$
$198$	−14.0835	−1.00087
$199$	−16.7821	−1.18965	−0.594827	−	0.803853i	$-0.702780\pi$
$199$	−16.7821	−1.18965	−0.594827	+	0.803853i	$0.702780\pi$
$200$	89.9636	6.36139
$201$	23.9693	1.69067
$202$	−18.0273	−1.26840
$203$	−3.30084	−0.231673
$204$	−92.1847	−6.45422
$205$	1.41429	0.0987781
$206$	27.5489	1.91942
$207$	6.60083	0.458789
$208$	−1.40352	−0.0973164
$209$	−11.7774	−0.814661
$210$	43.8933	3.02893
$211$	7.33286	0.504815	0.252407	−	0.967621i	$-0.418778\pi$
$211$	7.33286	0.504815	0.252407	+	0.967621i	$0.418778\pi$
$212$	−44.8125	−3.07774
$213$	18.1577	1.24415
$214$	16.6959	1.14131
$215$	−19.9208	−1.35859
$216$	11.0511	0.751933
$217$	8.36319	0.567731
$218$	−13.5318	−0.916491
$219$	22.8758	1.54581
$220$	29.8503	2.01250
$221$	1.28196	0.0862342
$222$	26.2284	1.76034
$223$	3.77173	0.252574	0.126287	−	0.991994i	$-0.459694\pi$
$223$	3.77173	0.252574	0.126287	+	0.991994i	$0.459694\pi$
$224$	−12.3746	−0.826816
$225$	47.4610	3.16407
$226$	12.1829	0.810397
$227$	2.68713	0.178351	0.0891757	−	0.996016i	$-0.471577\pi$
$227$	2.68713	0.178351	0.0891757	+	0.996016i	$0.471577\pi$
$228$	93.8869	6.21781
$229$	−5.12320	−0.338550	−0.169275	−	0.985569i	$-0.554143\pi$
$229$	−5.12320	−0.338550	−0.169275	+	0.985569i	$0.554143\pi$
$230$	−19.9925	−1.31827
$231$	6.01797	0.395953
$232$	14.6016	0.958639
$233$	−16.4945	−1.08059	−0.540295	−	0.841476i	$-0.681687\pi$
$233$	−16.4945	−1.08059	−0.540295	+	0.841476i	$0.681687\pi$
$234$	−1.56128	−0.102064
$235$	5.29294	0.345273
$236$	70.9685	4.61965
$237$	−0.332201	−0.0215788
$238$	30.7996	1.99644
$239$	−6.38220	−0.412830	−0.206415	−	0.978465i	$-0.566180\pi$
$239$	−6.38220	−0.412830	−0.206415	+	0.978465i	$0.566180\pi$
$240$	−92.0830	−5.94393
$241$	4.11739	0.265225	0.132612	−	0.991168i	$-0.457663\pi$
$241$	4.11739	0.265225	0.132612	+	0.991168i	$0.457663\pi$
$242$	−22.5438	−1.44917
$243$	−22.1599	−1.42156
$244$	−22.6918	−1.45269
$245$	19.5127	1.24662
$246$	−2.20889	−0.140834
$247$	−1.30563	−0.0830755
$248$	−36.9954	−2.34921
$249$	7.93936	0.503137
$250$	−88.8542	−5.61963
$251$	−19.6004	−1.23717	−0.618583	−	0.785719i	$-0.712293\pi$
$251$	−19.6004	−1.23717	−0.618583	+	0.785719i	$0.712293\pi$
$252$	−26.2494	−1.65356
$253$	−2.74106	−0.172329
$254$	−26.1089	−1.63822
$255$	84.1080	5.26705
$256$	−23.6824	−1.48015
$257$	19.4944	1.21603	0.608014	−	0.793926i	$-0.291966\pi$
$257$	19.4944	1.21603	0.608014	+	0.793926i	$0.291966\pi$
$258$	31.1131	1.93702
$259$	−6.13235	−0.381045
$260$	3.30917	0.205226
$261$	7.70316	0.476814
$262$	−8.10587	−0.500782
$263$	8.00691	0.493727	0.246864	−	0.969050i	$-0.420600\pi$
$263$	8.00691	0.493727	0.246864	+	0.969050i	$0.420600\pi$
$264$	−26.6210	−1.63841
$265$	40.8863	2.51162
$266$	−31.3682	−1.92331
$267$	−23.8055	−1.45687
$268$	43.4155	2.65203
$269$	6.64635	0.405235	0.202617	−	0.979258i	$-0.435055\pi$
$269$	6.64635	0.405235	0.202617	+	0.979258i	$0.435055\pi$
$270$	−17.6581	−1.07464
$271$	16.7286	1.01619	0.508095	−	0.861301i	$-0.330350\pi$
$271$	16.7286	1.01619	0.508095	+	0.861301i	$0.330350\pi$
$272$	−64.6138	−3.91779
$273$	0.667146	0.0403775
$274$	22.6434	1.36794
$275$	−19.7086	−1.18847
$276$	21.8511	1.31528
$277$	13.7869	0.828373	0.414186	−	0.910192i	$-0.364066\pi$
$277$	13.7869	0.828373	0.414186	+	0.910192i	$0.364066\pi$
$278$	−34.4273	−2.06481
$279$	−19.5172	−1.16846
$280$	45.3971	2.71300
$281$	24.5323	1.46347	0.731737	−	0.681587i	$-0.238710\pi$
$281$	24.5323	1.46347	0.731737	+	0.681587i	$0.238710\pi$
$282$	−8.26673	−0.492276
$283$	−22.6649	−1.34729	−0.673644	−	0.739056i	$-0.735272\pi$
$283$	−22.6649	−1.34729	−0.673644	+	0.739056i	$0.735272\pi$
$284$	32.8890	1.95160
$285$	−85.6610	−5.07412
$286$	0.648338	0.0383370
$287$	0.516451	0.0304851
$288$	28.8787	1.70169
$289$	42.0179	2.47164
$290$	−23.3312	−1.37006
$291$	−26.1216	−1.53127
$292$	41.4349	2.42480
$293$	2.60088	0.151945	0.0759725	−	0.997110i	$-0.475794\pi$
$293$	2.60088	0.151945	0.0759725	+	0.997110i	$0.475794\pi$
$294$	−30.4757	−1.77738
$295$	−64.7506	−3.76993
$296$	27.1270	1.57673
$297$	−2.42100	−0.140481
$298$	−13.3207	−0.771647
$299$	−0.303871	−0.0175733
$300$	157.113	9.07090
$301$	−7.27443	−0.419291
$302$	18.4676	1.06269
$303$	−17.9770	−1.03275
$304$	65.8069	3.77428
$305$	20.7037	1.18549
$306$	−71.8769	−4.10893
$307$	−18.3612	−1.04793	−0.523964	−	0.851741i	$-0.675547\pi$
$307$	−18.3612	−1.04793	−0.523964	+	0.851741i	$0.675547\pi$
$308$	10.9003	0.621104
$309$	27.4719	1.56282
$310$	59.1133	3.35741
$311$	9.92640	0.562874	0.281437	−	0.959580i	$-0.409189\pi$
$311$	9.92640	0.562874	0.281437	+	0.959580i	$0.409189\pi$
$312$	−2.95118	−0.167078
$313$	−2.26752	−0.128168	−0.0640838	−	0.997945i	$-0.520412\pi$
$313$	−2.26752	−0.128168	−0.0640838	+	0.997945i	$0.520412\pi$
$314$	48.9571	2.76281
$315$	23.9496	1.34941
$316$	−0.601714	−0.0338491
$317$	23.9947	1.34767	0.673837	−	0.738880i	$-0.264645\pi$
$317$	23.9947	1.34767	0.673837	+	0.738880i	$0.264645\pi$
$318$	−63.8578	−3.58097
$319$	−3.19881	−0.179099
$320$	−15.9155	−0.889706
$321$	16.6492	0.929269
$322$	−7.30059	−0.406846
$323$	−60.1076	−3.34447
$324$	−31.3986	−1.74436
$325$	−2.18488	−0.121195
$326$	−5.37604	−0.297752
$327$	−13.4940	−0.746220
$328$	−2.28457	−0.126144
$329$	1.93281	0.106559
$330$	42.5366	2.34156
$331$	−2.07464	−0.114032	−0.0570162	−	0.998373i	$-0.518159\pi$
$331$	−2.07464	−0.114032	−0.0570162	+	0.998373i	$0.518159\pi$
$332$	14.3805	0.789235
$333$	14.3111	0.784241
$334$	22.3462	1.22273
$335$	−39.6117	−2.16422
$336$	−33.6257	−1.83443
$337$	1.88017	0.102419	0.0512097	−	0.998688i	$-0.483692\pi$
$337$	1.88017	0.102419	0.0512097	+	0.998688i	$0.483692\pi$
$338$	−33.4824	−1.82120
$339$	12.1489	0.659837
$340$	152.345	8.26205
$341$	8.10470	0.438894
$342$	73.2040	3.95842
$343$	17.9983	0.971818
$344$	32.1791	1.73498
$345$	−19.9366	−1.07335
$346$	−0.0993360	−0.00534034
$347$	−28.8389	−1.54815	−0.774076	−	0.633093i	$-0.781785\pi$
$347$	−28.8389	−1.54815	−0.774076	+	0.633093i	$0.781785\pi$
$348$	25.5002	1.36695
$349$	0.147924	0.00791819	0.00395910	−	0.999992i	$-0.498740\pi$
$349$	0.147924	0.00791819	0.00395910	+	0.999992i	$0.498740\pi$
$350$	−52.4924	−2.80584
$351$	−0.268390	−0.0143256
$352$	−11.9922	−0.639184
$353$	−2.49447	−0.132767	−0.0663836	−	0.997794i	$-0.521146\pi$
$353$	−2.49447	−0.132767	−0.0663836	+	0.997794i	$0.521146\pi$
$354$	101.130	5.37500
$355$	−30.0075	−1.59263
$356$	−43.1189	−2.28530
$357$	30.7135	1.62553
$358$	−30.8145	−1.62860
$359$	13.3856	0.706467	0.353234	−	0.935535i	$-0.385082\pi$
$359$	13.3856	0.706467	0.353234	+	0.935535i	$0.385082\pi$
$360$	−105.943	−5.58370
$361$	42.2174	2.22197
$362$	−60.4641	−3.17792
$363$	−22.4808	−1.17993
$364$	1.20840	0.0633374
$365$	−37.8046	−1.97879
$366$	−32.3358	−1.69022
$367$	21.8109	1.13852	0.569260	−	0.822158i	$-0.307230\pi$
$367$	21.8109	1.13852	0.569260	+	0.822158i	$0.307230\pi$
$368$	15.3158	0.798390
$369$	−1.20524	−0.0627424
$370$	−43.3451	−2.25340
$371$	14.9303	0.775143
$372$	−64.6087	−3.34981
$373$	−13.9236	−0.720935	−0.360467	−	0.932772i	$-0.617383\pi$
$373$	−13.9236	−0.720935	−0.360467	+	0.932772i	$0.617383\pi$
$374$	29.8476	1.54338
$375$	−88.6058	−4.57559
$376$	−8.54995	−0.440930
$377$	−0.354617	−0.0182637
$378$	−6.44815	−0.331657
$379$	11.6065	0.596187	0.298094	−	0.954537i	$-0.403649\pi$
$379$	11.6065	0.596187	0.298094	+	0.954537i	$0.403649\pi$
$380$	−155.158	−7.95941
$381$	−26.0359	−1.33386
$382$	34.8080	1.78093
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−16.1538	−0.824344
$385$	−9.94530	−0.506859
$386$	67.0702	3.41378
$387$	16.9763	0.862955
$388$	−47.3139	−2.40200
$389$	−11.0407	−0.559786	−0.279893	−	0.960031i	$-0.590299\pi$
$389$	−11.0407	−0.559786	−0.279893	+	0.960031i	$0.590299\pi$
$390$	4.71557	0.238782
$391$	−13.9893	−0.707471
$392$	−31.5199	−1.59199
$393$	−8.08322	−0.407744
$394$	−29.3146	−1.47685
$395$	0.548995	0.0276229
$396$	−25.4381	−1.27831
$397$	−11.4621	−0.575265	−0.287633	−	0.957741i	$-0.592868\pi$
$397$	−11.4621	−0.575265	−0.287633	+	0.957741i	$0.592868\pi$
$398$	−43.3164	−2.17125
$399$	−31.2806	−1.56599
$400$	110.123	5.50614
$401$	−17.0940	−0.853635	−0.426817	−	0.904338i	$-0.640365\pi$
$401$	−17.0940	−0.853635	−0.426817	+	0.904338i	$0.640365\pi$
$402$	61.8672	3.08565
$403$	0.898479	0.0447564
$404$	−32.5616	−1.62000
$405$	28.6476	1.42351
$406$	−8.51978	−0.422830
$407$	−5.94280	−0.294574
$408$	−135.864	−6.72626
$409$	15.8540	0.783929	0.391965	−	0.919980i	$-0.371796\pi$
$409$	15.8540	0.783929	0.391965	+	0.919980i	$0.371796\pi$
$410$	3.65041	0.180281
$411$	22.5801	1.11379
$412$	49.7597	2.45149
$413$	−23.6448	−1.16348
$414$	17.0374	0.837342
$415$	−13.1206	−0.644065
$416$	−1.32944	−0.0651811
$417$	−34.3311	−1.68120
$418$	−30.3987	−1.48685
$419$	13.9445	0.681234	0.340617	−	0.940202i	$-0.389364\pi$
$419$	13.9445	0.681234	0.340617	+	0.940202i	$0.389364\pi$
$420$	79.2816	3.86855
$421$	−22.0016	−1.07229	−0.536147	−	0.844125i	$-0.680121\pi$
$421$	−22.0016	−1.07229	−0.536147	+	0.844125i	$0.680121\pi$
$422$	18.9268	0.921343
$423$	−4.51059	−0.219312
$424$	−66.0456	−3.20746
$425$	−100.585	−4.87911
$426$	46.8669	2.27071
$427$	7.56029	0.365868
$428$	30.1567	1.45768
$429$	0.646525	0.0312145
$430$	−51.4176	−2.47958
$431$	−33.5644	−1.61674	−0.808370	−	0.588675i	$-0.799650\pi$
$431$	−33.5644	−1.61674	−0.808370	+	0.588675i	$0.799650\pi$
$432$	13.5275	0.650840
$433$	−24.2287	−1.16436	−0.582178	−	0.813061i	$-0.697799\pi$
$433$	−24.2287	−1.16436	−0.582178	+	0.813061i	$0.697799\pi$
$434$	21.5862	1.03617
$435$	−23.2660	−1.11552
$436$	−24.4416	−1.17054
$437$	14.2476	0.681557
$438$	59.0448	2.82127
$439$	9.16240	0.437297	0.218649	−	0.975804i	$-0.429835\pi$
$439$	9.16240	0.437297	0.218649	+	0.975804i	$0.429835\pi$
$440$	43.9940	2.09733
$441$	−16.6285	−0.791835
$442$	3.30887	0.157387
$443$	1.91989	0.0912170	0.0456085	−	0.998959i	$-0.485477\pi$
$443$	1.91989	0.0912170	0.0456085	+	0.998959i	$0.485477\pi$
$444$	47.3746	2.24830
$445$	39.3410	1.86494
$446$	9.73521	0.460976
$447$	−13.2835	−0.628286
$448$	−5.81183	−0.274583
$449$	−17.4866	−0.825243	−0.412621	−	0.910903i	$-0.635387\pi$
$449$	−17.4866	−0.825243	−0.412621	+	0.910903i	$0.635387\pi$
$450$	122.501	5.77477
$451$	0.500488	0.0235671
$452$	22.0052	1.03504
$453$	18.4159	0.865256
$454$	6.93576	0.325511
$455$	−1.10253	−0.0516872
$456$	138.372	6.47989
$457$	24.5140	1.14672	0.573359	−	0.819304i	$-0.305640\pi$
$457$	24.5140	1.14672	0.573359	+	0.819304i	$0.305640\pi$
$458$	−13.2235	−0.617892
$459$	−12.3559	−0.576724
$460$	−36.1111	−1.68369
$461$	11.9651	0.557268	0.278634	−	0.960397i	$-0.410118\pi$
$461$	11.9651	0.557268	0.278634	+	0.960397i	$0.410118\pi$
$462$	15.5330	0.722659
$463$	−12.5200	−0.581852	−0.290926	−	0.956745i	$-0.593963\pi$
$463$	−12.5200	−0.581852	−0.290926	+	0.956745i	$0.593963\pi$
$464$	17.8735	0.829756
$465$	58.9481	2.73365
$466$	−42.5739	−1.97220
$467$	33.4951	1.54997	0.774985	−	0.631980i	$-0.217758\pi$
$467$	33.4951	1.54997	0.774985	+	0.631980i	$0.217758\pi$
$468$	−2.82004	−0.130356
$469$	−14.4649	−0.667926
$470$	13.6616	0.630163
$471$	48.8202	2.24952
$472$	104.595	4.81437
$473$	−7.04958	−0.324140
$474$	−0.857442	−0.0393836
$475$	102.443	4.70039
$476$	55.6312	2.54985
$477$	−34.8429	−1.59535
$478$	−16.4731	−0.753461
$479$	26.2231	1.19816	0.599082	−	0.800687i	$-0.295532\pi$
$479$	26.2231	1.19816	0.599082	+	0.800687i	$0.295532\pi$
$480$	−87.2229	−3.98116
$481$	−0.658813	−0.0300393
$482$	10.6274	0.484065
$483$	−7.28019	−0.331260
$484$	−40.7193	−1.85088
$485$	43.1685	1.96018
$486$	−57.1969	−2.59451
$487$	−32.4390	−1.46995	−0.734976	−	0.678093i	$-0.762807\pi$
$487$	−32.4390	−1.46995	−0.734976	+	0.678093i	$0.762807\pi$
$488$	−33.4437	−1.51392
$489$	−5.36102	−0.242434
$490$	50.3642	2.27522
$491$	−37.1110	−1.67479	−0.837397	−	0.546595i	$-0.815924\pi$
$491$	−37.1110	−1.67479	−0.837397	+	0.546595i	$0.815924\pi$
$492$	−3.98977	−0.179873
$493$	−16.3255	−0.735265
$494$	−3.36997	−0.151622
$495$	23.2093	1.04318
$496$	−45.2853	−2.03337
$497$	−10.9577	−0.491521
$498$	20.4923	0.918281
$499$	5.79833	0.259569	0.129784	−	0.991542i	$-0.458571\pi$
$499$	5.79833	0.259569	0.129784	+	0.991542i	$0.458571\pi$
$500$	−160.491	−7.17740
$501$	22.2838	0.995565
$502$	−50.5906	−2.25797
$503$	10.9238	0.487067	0.243533	−	0.969893i	$-0.421693\pi$
$503$	10.9238	0.487067	0.243533	+	0.969893i	$0.421693\pi$
$504$	−38.6870	−1.72325
$505$	29.7087	1.32202
$506$	−7.07494	−0.314519
$507$	−33.3888	−1.48285
$508$	−47.1588	−2.09233
$509$	−7.86855	−0.348767	−0.174384	−	0.984678i	$-0.555793\pi$
$509$	−7.86855	−0.348767	−0.174384	+	0.984678i	$0.555793\pi$
$510$	217.091	9.61295
$511$	−13.8050	−0.610697
$512$	−48.5745	−2.14671
$513$	12.5840	0.555599
$514$	50.3170	2.21939
$515$	−45.4001	−2.00057
$516$	56.1976	2.47396
$517$	1.87307	0.0823773
$518$	−15.8282	−0.695451
$519$	−0.0990584	−0.00434818
$520$	4.87713	0.213876
$521$	−14.6913	−0.643637	−0.321818	−	0.946801i	$-0.604294\pi$
$521$	−14.6913	−0.643637	−0.321818	+	0.946801i	$0.604294\pi$
$522$	19.8826	0.870238
$523$	8.37124	0.366049	0.183024	−	0.983108i	$-0.441411\pi$
$523$	8.37124	0.366049	0.183024	+	0.983108i	$0.441411\pi$
$524$	−14.6411	−0.639600
$525$	−52.3457	−2.28455
$526$	20.6666	0.901107
$527$	41.3633	1.80182
$528$	−32.5863	−1.41814
$529$	−19.6840	−0.855827
$530$	105.531	4.58400
$531$	55.1798	2.39460
$532$	−56.6584	−2.45645
$533$	0.0554836	0.00240326
$534$	−61.4444	−2.65896
$535$	−27.5145	−1.18956
$536$	63.9868	2.76381
$537$	−30.7284	−1.32603
$538$	17.1549	0.739599
$539$	6.90516	0.297426
$540$	−31.8947	−1.37253
$541$	45.2764	1.94658	0.973292	−	0.229573i	$-0.0737328\pi$
$541$	45.2764	1.94658	0.973292	+	0.229573i	$0.0737328\pi$
$542$	43.1782	1.85466
$543$	−60.2951	−2.58751
$544$	−61.2035	−2.62408
$545$	22.3002	0.955236
$546$	1.72197	0.0736935
$547$	33.4144	1.42870	0.714348	−	0.699790i	$-0.246723\pi$
$547$	33.4144	1.42870	0.714348	+	0.699790i	$0.246723\pi$
$548$	40.8993	1.74713
$549$	−17.6434	−0.753004
$550$	−50.8699	−2.16910
$551$	16.6270	0.708333
$552$	32.2046	1.37072
$553$	0.200475	0.00852506
$554$	35.5853	1.51187
$555$	−43.2239	−1.83475
$556$	−62.1838	−2.63718
$557$	−19.5238	−0.827252	−0.413626	−	0.910447i	$-0.635738\pi$
$557$	−19.5238	−0.827252	−0.413626	+	0.910447i	$0.635738\pi$
$558$	−50.3757	−2.13258
$559$	−0.781510	−0.0330543
$560$	55.5698	2.34825
$561$	29.7641	1.25664
$562$	63.3202	2.67100
$563$	6.70777	0.282699	0.141349	−	0.989960i	$-0.454856\pi$
$563$	6.70777	0.282699	0.141349	+	0.989960i	$0.454856\pi$
$564$	−14.9316	−0.628735
$565$	−20.0773	−0.844657
$566$	−58.5003	−2.45895
$567$	10.4612	0.439327
$568$	48.4725	2.03386
$569$	1.49454	0.0626543	0.0313271	−	0.999509i	$-0.490027\pi$
$569$	1.49454	0.0626543	0.0313271	+	0.999509i	$0.490027\pi$
$570$	−221.099	−9.26084
$571$	30.9339	1.29454	0.647271	−	0.762260i	$-0.275910\pi$
$571$	30.9339	1.29454	0.647271	+	0.762260i	$0.275910\pi$
$572$	1.17105	0.0489640
$573$	34.7107	1.45006
$574$	1.33301	0.0556388
$575$	23.8423	0.994294
$576$	13.5631	0.565128
$577$	27.8334	1.15872	0.579359	−	0.815072i	$-0.303303\pi$
$577$	27.8334	1.15872	0.579359	+	0.815072i	$0.303303\pi$
$578$	108.452	4.51102
$579$	66.8828	2.77955
$580$	−42.1416	−1.74983
$581$	−4.79121	−0.198773
$582$	−67.4223	−2.79475
$583$	14.4688	0.599238
$584$	61.0677	2.52700
$585$	2.57297	0.106379
$586$	6.71313	0.277317
$587$	−16.6001	−0.685159	−0.342580	−	0.939489i	$-0.611301\pi$
$587$	−16.6001	−0.685159	−0.342580	+	0.939489i	$0.611301\pi$
$588$	−55.0463	−2.27007
$589$	−42.1271	−1.73582
$590$	−167.128	−6.88054
$591$	−29.2327	−1.20247
$592$	33.2057	1.36474
$593$	−8.39100	−0.344577	−0.172288	−	0.985047i	$-0.555116\pi$
$593$	−8.39100	−0.344577	−0.172288	+	0.985047i	$0.555116\pi$
$594$	−6.24885	−0.256393
$595$	−50.7571	−2.08084
$596$	−24.0603	−0.985548
$597$	−43.1953	−1.76787
$598$	−0.784321	−0.0320733
$599$	−9.91342	−0.405051	−0.202526	−	0.979277i	$-0.564915\pi$
$599$	−9.91342	−0.405051	−0.202526	+	0.979277i	$0.564915\pi$
$600$	231.556	9.45323
$601$	9.98252	0.407195	0.203598	−	0.979055i	$-0.434737\pi$
$601$	9.98252	0.407195	0.203598	+	0.979055i	$0.434737\pi$
$602$	−18.7760	−0.765253
$603$	33.7567	1.37468
$604$	33.3567	1.35727
$605$	37.1517	1.51043
$606$	−46.4003	−1.88488
$607$	−13.6457	−0.553860	−0.276930	−	0.960890i	$-0.589317\pi$
$607$	−13.6457	−0.553860	−0.276930	+	0.960890i	$0.589317\pi$
$608$	62.3336	2.52796
$609$	−8.49597	−0.344274
$610$	53.4382	2.16365
$611$	0.207646	0.00840047
$612$	−129.826	−5.24792
$613$	−4.77723	−0.192951	−0.0964753	−	0.995335i	$-0.530757\pi$
$613$	−4.77723	−0.192951	−0.0964753	+	0.995335i	$0.530757\pi$
$614$	−47.3920	−1.91258
$615$	3.64021	0.146787
$616$	16.0651	0.647283
$617$	41.7811	1.68204	0.841021	−	0.541002i	$-0.181955\pi$
$617$	41.7811	1.68204	0.841021	+	0.541002i	$0.181955\pi$
$618$	70.9076	2.85232
$619$	2.02804	0.0815138	0.0407569	−	0.999169i	$-0.487023\pi$
$619$	2.02804	0.0815138	0.0407569	+	0.999169i	$0.487023\pi$
$620$	106.772	4.28809
$621$	2.92879	0.117528
$622$	25.6210	1.02731
$623$	14.3660	0.575563
$624$	−3.61249	−0.144615
$625$	80.9644	3.23858
$626$	−5.85268	−0.233920
$627$	−30.3137	−1.21061
$628$	88.4279	3.52866
$629$	−30.3298	−1.20933
$630$	61.8163	2.46282
$631$	−34.8608	−1.38779	−0.693893	−	0.720079i	$-0.744106\pi$
$631$	−34.8608	−1.38779	−0.693893	+	0.720079i	$0.744106\pi$
$632$	−0.886819	−0.0352758
$633$	18.8739	0.750171
$634$	61.9326	2.45966
$635$	43.0270	1.70747
$636$	−115.342	−4.57361
$637$	0.765499	0.0303302
$638$	−8.25644	−0.326876
$639$	25.5721	1.01161
$640$	26.6957	1.05524
$641$	13.2080	0.521683	0.260842	−	0.965382i	$-0.416000\pi$
$641$	13.2080	0.521683	0.260842	+	0.965382i	$0.416000\pi$
$642$	42.9733	1.69602
$643$	−25.7071	−1.01379	−0.506894	−	0.862008i	$-0.669207\pi$
$643$	−25.7071	−1.01379	−0.506894	+	0.862008i	$0.669207\pi$
$644$	−13.1866	−0.519624
$645$	−51.2739	−2.01891
$646$	−155.144	−6.10404
$647$	5.44019	0.213876	0.106938	−	0.994266i	$-0.465895\pi$
$647$	5.44019	0.213876	0.106938	+	0.994266i	$0.465895\pi$
$648$	−46.2759	−1.81789
$649$	−22.9139	−0.899451
$650$	−5.63939	−0.221195
$651$	21.5259	0.843666
$652$	−9.71039	−0.380288
$653$	−16.6654	−0.652167	−0.326084	−	0.945341i	$-0.605729\pi$
$653$	−16.6654	−0.652167	−0.326084	+	0.945341i	$0.605729\pi$
$654$	−34.8293	−1.36194
$655$	13.3583	0.521953
$656$	−2.79650	−0.109185
$657$	32.2167	1.25689
$658$	4.98876	0.194482
$659$	8.50057	0.331135	0.165568	−	0.986198i	$-0.447054\pi$
$659$	8.50057	0.331135	0.165568	+	0.986198i	$0.447054\pi$
$660$	76.8311	2.99065
$661$	−7.81643	−0.304024	−0.152012	−	0.988379i	$-0.548575\pi$
$661$	−7.81643	−0.304024	−0.152012	+	0.988379i	$0.548575\pi$
$662$	−5.35484	−0.208122
$663$	3.29962	0.128147
$664$	21.1944	0.822500
$665$	51.6943	2.00462
$666$	36.9382	1.43133
$667$	3.86973	0.149837
$668$	40.3625	1.56167
$669$	9.70800	0.375333
$670$	−102.242	−3.94994
$671$	7.32661	0.282841
$672$	−31.8509	−1.22868
$673$	0.334170	0.0128813	0.00644065	−	0.999979i	$-0.497950\pi$
$673$	0.334170	0.0128813	0.00644065	+	0.999979i	$0.497950\pi$
$674$	4.85290	0.186927
$675$	21.0584	0.810540
$676$	−60.4770	−2.32604
$677$	9.17504	0.352625	0.176313	−	0.984334i	$-0.443583\pi$
$677$	9.17504	0.352625	0.176313	+	0.984334i	$0.443583\pi$
$678$	31.3575	1.20428
$679$	15.7637	0.604956
$680$	224.529	8.61028
$681$	6.91637	0.265036
$682$	20.9190	0.801030
$683$	−20.6041	−0.788392	−0.394196	−	0.919026i	$-0.628977\pi$
$683$	−20.6041	−0.788392	−0.394196	+	0.919026i	$0.628977\pi$
$684$	132.224	5.05570
$685$	−37.3159	−1.42577
$686$	46.4554	1.77368
$687$	−13.1865	−0.503097
$688$	39.3899	1.50172
$689$	1.60400	0.0611076
$690$	−51.4583	−1.95898
$691$	−31.4224	−1.19537	−0.597683	−	0.801733i	$-0.703912\pi$
$691$	−31.4224	−1.19537	−0.597683	+	0.801733i	$0.703912\pi$
$692$	−0.179424	−0.00682068
$693$	8.47528	0.321949
$694$	−74.4360	−2.82555
$695$	56.7356	2.15210
$696$	37.5827	1.42457
$697$	2.55430	0.0967512
$698$	0.381807	0.0144516
$699$	−42.4549	−1.60579
$700$	−94.8135	−3.58361
$701$	−17.3859	−0.656655	−0.328328	−	0.944564i	$-0.606485\pi$
$701$	−17.3859	−0.656655	−0.328328	+	0.944564i	$0.606485\pi$
$702$	−0.692741	−0.0261458
$703$	30.8899	1.16503
$704$	−5.63219	−0.212271
$705$	13.6234	0.513087
$706$	−6.43847	−0.242315
$707$	10.8486	0.408005
$708$	182.665	6.86496
$709$	38.2186	1.43533	0.717665	−	0.696389i	$-0.245211\pi$
$709$	38.2186	1.43533	0.717665	+	0.696389i	$0.245211\pi$
$710$	−77.4522	−2.90673
$711$	−0.467848	−0.0175457
$712$	−63.5495	−2.38162
$713$	−9.80459	−0.367185
$714$	79.2745	2.96677
$715$	−1.06845	−0.0399577
$716$	−55.6582	−2.08004
$717$	−16.4270	−0.613479
$718$	34.5497	1.28938
$719$	−19.7424	−0.736268	−0.368134	−	0.929773i	$-0.620003\pi$
$719$	−19.7424	−0.736268	−0.368134	+	0.929773i	$0.620003\pi$
$720$	−129.683	−4.83301
$721$	−16.5786	−0.617419
$722$	108.967	4.05534
$723$	10.5977	0.394132
$724$	−109.212	−4.05885
$725$	27.8240	1.03336
$726$	−58.0250	−2.15351
$727$	−22.2866	−0.826564	−0.413282	−	0.910603i	$-0.635618\pi$
$727$	−22.2866	−0.826564	−0.413282	+	0.910603i	$0.635618\pi$
$728$	1.78097	0.0660070
$729$	−36.8324	−1.36416
$730$	−97.5775	−3.61150
$731$	−35.9784	−1.33071
$732$	−58.4060	−2.15875
$733$	26.6840	0.985596	0.492798	−	0.870144i	$-0.335974\pi$
$733$	26.6840	0.985596	0.492798	+	0.870144i	$0.335974\pi$
$734$	56.2960	2.07792
$735$	50.2234	1.85252
$736$	14.5074	0.534750
$737$	−14.0178	−0.516352
$738$	−3.11085	−0.114512
$739$	26.9464	0.991240	0.495620	−	0.868540i	$-0.334941\pi$
$739$	26.9464	0.991240	0.495620	+	0.868540i	$0.334941\pi$
$740$	−78.2914	−2.87805
$741$	−3.36055	−0.123453
$742$	38.5366	1.41472
$743$	10.8798	0.399140	0.199570	−	0.979884i	$-0.436046\pi$
$743$	10.8798	0.399140	0.199570	+	0.979884i	$0.436046\pi$
$744$	−95.2218	−3.49100
$745$	21.9523	0.804269
$746$	−35.9381	−1.31579
$747$	11.1812	0.409100
$748$	53.9117	1.97121
$749$	−10.0474	−0.367124
$750$	−228.700	−8.35096
$751$	46.3601	1.69170	0.845852	−	0.533417i	$-0.179092\pi$
$751$	46.3601	1.69170	0.845852	+	0.533417i	$0.179092\pi$
$752$	−10.4658	−0.381650
$753$	−50.4492	−1.83847
$754$	−0.915301	−0.0333333
$755$	−30.4342	−1.10761
$756$	−11.6469	−0.423593
$757$	41.1991	1.49741	0.748704	−	0.662905i	$-0.230676\pi$
$757$	41.1991	1.49741	0.748704	+	0.662905i	$0.230676\pi$
$758$	29.9576	1.08811
$759$	−7.05516	−0.256086
$760$	−228.675	−8.29490
$761$	−9.29105	−0.336800	−0.168400	−	0.985719i	$-0.553860\pi$
$761$	−9.29105	−0.336800	−0.168400	+	0.985719i	$0.553860\pi$
$762$	−67.2013	−2.43445
$763$	8.14330	0.294807
$764$	62.8714	2.27461
$765$	118.452	4.28263
$766$	2.58110	0.0932589
$767$	−2.54022	−0.0917219
$768$	−60.9557	−2.19955
$769$	−26.4255	−0.952928	−0.476464	−	0.879194i	$-0.658082\pi$
$769$	−26.4255	−0.952928	−0.476464	+	0.879194i	$0.658082\pi$
$770$	−25.6698	−0.925075
$771$	50.1764	1.80706
$772$	121.145	4.36009
$773$	28.5566	1.02711	0.513554	−	0.858057i	$-0.328329\pi$
$773$	28.5566	1.02711	0.513554	+	0.858057i	$0.328329\pi$
$774$	43.8176	1.57499
$775$	−70.4965	−2.53231
$776$	−69.7323	−2.50324
$777$	−15.7839	−0.566246
$778$	−28.4971	−1.02167
$779$	−2.60147	−0.0932072
$780$	8.51742	0.304973
$781$	−10.6190	−0.379979
$782$	−36.1078	−1.29121
$783$	3.41789	0.122145
$784$	−38.5829	−1.37796
$785$	−80.6804	−2.87961
$786$	−20.8636	−0.744179
$787$	31.1708	1.11112	0.555559	−	0.831477i	$-0.312504\pi$
$787$	31.1708	1.11112	0.555559	+	0.831477i	$0.312504\pi$
$788$	−52.9491	−1.88623
$789$	20.6088	0.733694
$790$	1.41701	0.0504150
$791$	−7.33155	−0.260680
$792$	−37.4912	−1.33219
$793$	0.812221	0.0288428
$794$	−29.5848	−1.04992
$795$	105.237	3.73235
$796$	−78.2395	−2.77313
$797$	23.3338	0.826524	0.413262	−	0.910612i	$-0.364389\pi$
$797$	23.3338	0.826524	0.413262	+	0.910612i	$0.364389\pi$
$798$	−80.7382	−2.85810
$799$	9.55943	0.338188
$800$	104.311	3.68793
$801$	−33.5260	−1.18458
$802$	−44.1214	−1.55798
$803$	−13.3783	−0.472110
$804$	111.747	3.94100
$805$	12.0312	0.424046
$806$	2.31906	0.0816855
$807$	17.1069	0.602192
$808$	−47.9900	−1.68828
$809$	29.6986	1.04415	0.522074	−	0.852900i	$-0.325159\pi$
$809$	29.6986	1.04415	0.522074	+	0.852900i	$0.325159\pi$
$810$	73.9423	2.59807
$811$	−26.5649	−0.932820	−0.466410	−	0.884569i	$-0.654453\pi$
$811$	−26.5649	−0.932820	−0.466410	+	0.884569i	$0.654453\pi$
$812$	−15.3887	−0.540038
$813$	43.0575	1.51009
$814$	−15.3390	−0.537630
$815$	8.85962	0.310339
$816$	−166.308	−5.82196
$817$	36.6427	1.28197
$818$	40.9207	1.43076
$819$	0.939562	0.0328309
$820$	6.59350	0.230255
$821$	−35.1382	−1.22633	−0.613165	−	0.789955i	$-0.710104\pi$
$821$	−35.1382	−1.22633	−0.613165	+	0.789955i	$0.710104\pi$
$822$	58.2815	2.03280
$823$	−3.41873	−0.119169	−0.0595847	−	0.998223i	$-0.518978\pi$
$823$	−3.41873	−0.119169	−0.0595847	+	0.998223i	$0.518978\pi$
$824$	73.3370	2.55481
$825$	−50.7277	−1.76611
$826$	−61.0295	−2.12349
$827$	−23.0916	−0.802974	−0.401487	−	0.915865i	$-0.631506\pi$
$827$	−23.0916	−0.802974	−0.401487	+	0.915865i	$0.631506\pi$
$828$	30.7735	1.06945
$829$	49.9112	1.73349	0.866743	−	0.498754i	$-0.166209\pi$
$829$	49.9112	1.73349	0.866743	+	0.498754i	$0.166209\pi$
$830$	−33.8655	−1.17549
$831$	35.4858	1.23099
$832$	−0.624379	−0.0216465
$833$	35.2413	1.22104
$834$	−88.6119	−3.06838
$835$	−36.8262	−1.27442
$836$	−54.9071	−1.89900
$837$	−8.65977	−0.299326
$838$	35.9922	1.24333
$839$	−5.90244	−0.203775	−0.101887	−	0.994796i	$-0.532488\pi$
$839$	−5.90244	−0.203775	−0.101887	+	0.994796i	$0.532488\pi$
$840$	116.847	4.03160
$841$	−24.4840	−0.844277
$842$	−56.7884	−1.95706
$843$	63.1433	2.17477
$844$	34.1863	1.17674
$845$	55.1784	1.89819
$846$	−11.6423	−0.400270
$847$	13.5666	0.466153
$848$	−80.8453	−2.77624
$849$	−58.3368	−2.00211
$850$	−259.621	−8.90492
$851$	7.18926	0.246444
$852$	84.6525	2.90015
$853$	−25.5062	−0.873315	−0.436657	−	0.899628i	$-0.643838\pi$
$853$	−25.5062	−0.873315	−0.436657	+	0.899628i	$0.643838\pi$
$854$	19.5139	0.667750
$855$	−120.639	−4.12576
$856$	44.4456	1.51912
$857$	−29.6954	−1.01437	−0.507187	−	0.861836i	$-0.669315\pi$
$857$	−29.6954	−1.01437	−0.507187	+	0.861836i	$0.669315\pi$
$858$	1.66875	0.0569700
$859$	45.1715	1.54123	0.770616	−	0.637300i	$-0.219949\pi$
$859$	45.1715	1.54123	0.770616	+	0.637300i	$0.219949\pi$
$860$	−92.8722	−3.16692
$861$	1.32928	0.0453019
$862$	−86.6330	−2.95073
$863$	9.41843	0.320607	0.160303	−	0.987068i	$-0.448753\pi$
$863$	9.41843	0.320607	0.160303	+	0.987068i	$0.448753\pi$
$864$	12.8135	0.435924
$865$	0.163704	0.00556610
$866$	−62.5366	−2.12508
$867$	108.149	3.67293
$868$	38.9898	1.32340
$869$	0.194278	0.00659044
$870$	−60.0518	−2.03595
$871$	−1.55400	−0.0526552
$872$	−36.0226	−1.21988
$873$	−36.7878	−1.24508
$874$	36.7746	1.24392
$875$	53.4714	1.80766
$876$	106.649	3.60333
$877$	−50.5960	−1.70851	−0.854253	−	0.519857i	$-0.825985\pi$
$877$	−50.5960	−1.70851	−0.854253	+	0.519857i	$0.825985\pi$
$878$	23.6490	0.798117
$879$	6.69436	0.225795
$880$	53.8522	1.81536
$881$	−2.72131	−0.0916833	−0.0458416	−	0.998949i	$-0.514597\pi$
$881$	−2.72131	−0.0916833	−0.0458416	+	0.998949i	$0.514597\pi$
$882$	−42.9199	−1.44519
$883$	−38.9747	−1.31160	−0.655801	−	0.754934i	$-0.727669\pi$
$883$	−38.9747	−1.31160	−0.655801	+	0.754934i	$0.727669\pi$
$884$	5.97660	0.201015
$885$	−166.661	−5.60223
$886$	4.95544	0.166481
$887$	43.2030	1.45061	0.725307	−	0.688426i	$-0.241698\pi$
$887$	43.2030	1.45061	0.725307	+	0.688426i	$0.241698\pi$
$888$	69.8218	2.34306
$889$	15.7120	0.526965
$890$	101.543	3.40373
$891$	10.1378	0.339629
$892$	17.5841	0.588758
$893$	−9.73593	−0.325801
$894$	−34.2859	−1.14669
$895$	50.7817	1.69745
$896$	9.74840	0.325671
$897$	−0.782129	−0.0261145
$898$	−45.1346	−1.50616
$899$	−11.4419	−0.381610
$900$	221.266	7.37554
$901$	73.8435	2.46008
$902$	1.29181	0.0430125
$903$	−18.7235	−0.623080
$904$	32.4318	1.07867
$905$	99.6438	3.31227
$906$	47.5333	1.57919
$907$	−6.38275	−0.211936	−0.105968	−	0.994370i	$-0.533794\pi$
$907$	−6.38275	−0.211936	−0.105968	+	0.994370i	$0.533794\pi$
$908$	12.5276	0.415743
$909$	−25.3175	−0.839728
$910$	−2.84573	−0.0943350
$911$	48.1594	1.59559	0.797797	−	0.602927i	$-0.205999\pi$
$911$	48.1594	1.59559	0.797797	+	0.602927i	$0.205999\pi$
$912$	169.379	5.60871
$913$	−4.64312	−0.153665
$914$	63.2731	2.09289
$915$	53.2888	1.76167
$916$	−23.8847	−0.789172
$917$	4.87802	0.161086
$918$	−31.8918	−1.05259
$919$	−32.2668	−1.06439	−0.532193	−	0.846623i	$-0.678632\pi$
$919$	−32.2668	−1.06439	−0.532193	+	0.846623i	$0.678632\pi$
$920$	−53.2213	−1.75466
$921$	−47.2595	−1.55725
$922$	30.8830	1.01708
$923$	−1.17722	−0.0387486
$924$	28.0562	0.922980
$925$	51.6918	1.69962
$926$	−32.3153	−1.06195
$927$	38.6895	1.27073
$928$	16.9301	0.555759
$929$	−46.6399	−1.53020	−0.765102	−	0.643909i	$-0.777312\pi$
$929$	−46.6399	−1.53020	−0.765102	+	0.643909i	$0.777312\pi$
$930$	152.151	4.98922
$931$	−35.8921	−1.17631
$932$	−76.8984	−2.51889
$933$	25.5494	0.836450
$934$	86.4542	2.82887
$935$	−49.1883	−1.60863
$936$	−4.15624	−0.135851
$937$	−8.11948	−0.265252	−0.132626	−	0.991166i	$-0.542341\pi$
$937$	−8.11948	−0.265252	−0.132626	+	0.991166i	$0.542341\pi$
$938$	−37.3353	−1.21904
$939$	−5.83632	−0.190461
$940$	24.6760	0.804844
$941$	−36.2879	−1.18295	−0.591476	−	0.806322i	$-0.701455\pi$
$941$	−36.2879	−1.18295	−0.591476	+	0.806322i	$0.701455\pi$
$942$	126.010	4.10562
$943$	−0.605461	−0.0197165
$944$	128.033	4.16711
$945$	10.6264	0.345678
$946$	−18.1957	−0.591592
$947$	−27.6412	−0.898217	−0.449109	−	0.893477i	$-0.648258\pi$
$947$	−27.6412	−0.898217	−0.449109	+	0.893477i	$0.648258\pi$
$948$	−1.54874	−0.0503008
$949$	−1.48311	−0.0481437
$950$	264.415	8.57874
$951$	61.7595	2.00269
$952$	81.9905	2.65733
$953$	9.40326	0.304602	0.152301	−	0.988334i	$-0.451332\pi$
$953$	9.40326	0.304602	0.152301	+	0.988334i	$0.451332\pi$
$954$	−89.9328	−2.91168
$955$	−57.3630	−1.85622
$956$	−29.7542	−0.962320
$957$	−8.23336	−0.266147
$958$	67.6844	2.18678
$959$	−13.6265	−0.440024
$960$	−40.9648	−1.32213
$961$	−2.01003	−0.0648396
$962$	−1.70046	−0.0548251
$963$	23.4476	0.755588
$964$	19.1956	0.618248
$965$	−110.531	−3.55810
$966$	−18.7909	−0.604586
$967$	11.7730	0.378595	0.189297	−	0.981920i	$-0.439379\pi$
$967$	11.7730	0.378595	0.189297	+	0.981920i	$0.439379\pi$
$968$	−60.0130	−1.92889
$969$	−154.710	−4.97000
$970$	111.422	3.57755
$971$	−18.4018	−0.590542	−0.295271	−	0.955414i	$-0.595410\pi$
$971$	−18.4018	−0.590542	−0.295271	+	0.955414i	$0.595410\pi$
$972$	−103.311	−3.31370
$973$	20.7179	0.664187
$974$	−83.7283	−2.68283
$975$	−5.62362	−0.180100
$976$	−40.9378	−1.31039
$977$	23.1625	0.741035	0.370517	−	0.928826i	$-0.379180\pi$
$977$	23.1625	0.741035	0.370517	+	0.928826i	$0.379180\pi$
$978$	−13.8373	−0.442468
$979$	13.9220	0.444949
$980$	90.9696	2.90592
$981$	−19.0040	−0.606751
$982$	−95.7870	−3.05669
$983$	33.3799	1.06465	0.532327	−	0.846539i	$-0.321318\pi$
$983$	33.3799	1.06465	0.532327	+	0.846539i	$0.321318\pi$
$984$	−5.88021	−0.187454
$985$	48.3100	1.53928
$986$	−42.1378	−1.34194
$987$	4.97482	0.158350
$988$	−6.08695	−0.193652
$989$	8.52817	0.271180
$990$	59.9056	1.90392
$991$	−13.1016	−0.416185	−0.208093	−	0.978109i	$-0.566726\pi$
$991$	−13.1016	−0.416185	−0.208093	+	0.978109i	$0.566726\pi$
$992$	−42.8952	−1.36192
$993$	−5.33988	−0.169456
$994$	−28.2830	−0.897082
$995$	71.3846	2.26304
$996$	37.0138	1.17283
$997$	31.4260	0.995272	0.497636	−	0.867386i	$-0.334202\pi$
$997$	31.4260	0.995272	0.497636	+	0.867386i	$0.334202\pi$
$998$	14.9660	0.473742
$999$	6.34981	0.200899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	383.2.a.c.1.23	✓	24
3.2	odd	2		3447.2.a.j.1.2		24
4.3	odd	2		6128.2.a.p.1.4		24
5.4	even	2		9575.2.a.e.1.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
383.2.a.c.1.23	✓	24	1.1	even	1	trivial
3447.2.a.j.1.2		24	3.2	odd	2
6128.2.a.p.1.4		24	4.3	odd	2
9575.2.a.e.1.2		24	5.4	even	2

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:	\( N \)	\(=\)	\( 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	383.a (trivial)

\(f(q)\)	\(=\)	\(q+2.58110 q^{2} +2.57388 q^{3} +4.66207 q^{4} -4.25360 q^{5} +6.64345 q^{6} -1.55327 q^{7} +6.87105 q^{8} +3.62488 q^{9} -10.9790 q^{10} -1.50526 q^{11} +11.9996 q^{12} -0.166872 q^{13} -4.00915 q^{14} -10.9483 q^{15} +8.41073 q^{16} -7.68231 q^{17} +9.35616 q^{18} +7.82416 q^{19} -19.8306 q^{20} -3.99795 q^{21} -3.88523 q^{22} +1.82098 q^{23} +17.6853 q^{24} +13.0931 q^{25} -0.430713 q^{26} +1.60836 q^{27} -7.24147 q^{28} +2.12508 q^{29} -28.2586 q^{30} -5.38423 q^{31} +7.96681 q^{32} -3.87438 q^{33} -19.8288 q^{34} +6.60701 q^{35} +16.8994 q^{36} +3.94801 q^{37} +20.1949 q^{38} -0.429510 q^{39} -29.2267 q^{40} -0.332492 q^{41} -10.3191 q^{42} +4.68328 q^{43} -7.01764 q^{44} -15.4188 q^{45} +4.70013 q^{46} -1.24434 q^{47} +21.6482 q^{48} -4.58734 q^{49} +33.7947 q^{50} -19.7734 q^{51} -0.777969 q^{52} -9.61215 q^{53} +4.15133 q^{54} +6.40280 q^{55} -10.6726 q^{56} +20.1385 q^{57} +5.48504 q^{58} +15.2225 q^{59} -51.0416 q^{60} -4.86732 q^{61} -13.8972 q^{62} -5.63043 q^{63} +3.74166 q^{64} +0.709808 q^{65} -10.0001 q^{66} +9.31251 q^{67} -35.8154 q^{68} +4.68699 q^{69} +17.0533 q^{70} +7.05460 q^{71} +24.9067 q^{72} +8.88768 q^{73} +10.1902 q^{74} +33.7002 q^{75} +36.4767 q^{76} +2.33809 q^{77} -1.10861 q^{78} -0.129066 q^{79} -35.7759 q^{80} -6.73490 q^{81} -0.858194 q^{82} +3.08459 q^{83} -18.6387 q^{84} +32.6775 q^{85} +12.0880 q^{86} +5.46971 q^{87} -10.3428 q^{88} -9.24888 q^{89} -39.7974 q^{90} +0.259198 q^{91} +8.48953 q^{92} -13.8584 q^{93} -3.21177 q^{94} -33.2808 q^{95} +20.5056 q^{96} -10.1487 q^{97} -11.8404 q^{98} -5.45640 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} + 2 q^{3} + 29 q^{4} + 3 q^{5} + q^{6} + 17 q^{7} + 15 q^{8} + 34 q^{9} + q^{10} - 7 q^{12} + 28 q^{13} - 8 q^{14} - 2 q^{15} + 35 q^{16} + 16 q^{17} + 19 q^{18} + 13 q^{19} - 4 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 24 * q + 5 * q^2 + 2 * q^3 + 29 * q^4 + 3 * q^5 + q^6 + 17 * q^7 + 15 * q^8 + 34 * q^9 + q^10 - 7 * q^12 + 28 * q^13 - 8 * q^14 - 2 * q^15 + 35 * q^16 + 16 * q^17 + 19 * q^18 + 13 * q^19 - 4 * q^20 - 4 * q^21 + 12 * q^22 + 7 * q^23 - 11 * q^24 + 67 * q^25 - 14 * q^26 - 10 * q^27 + 39 * q^28 - 2 * q^29 - 17 * q^30 + 20 * q^32 + 24 * q^33 - 18 * q^34 - 10 * q^35 + 20 * q^36 + 35 * q^37 - 5 * q^38 - 12 * q^39 - 36 * q^40 - 36 * q^42 + 34 * q^43 - 36 * q^44 - 27 * q^45 - 17 * q^46 - 3 * q^47 - 56 * q^48 + 49 * q^49 - 20 * q^50 - 28 * q^51 + 29 * q^52 - 9 * q^53 - 53 * q^54 + 10 * q^55 - 47 * q^56 + 47 * q^57 + 12 * q^58 - 6 * q^59 - 83 * q^60 + 3 * q^61 - 58 * q^62 + 13 * q^63 + 15 * q^64 + 8 * q^65 - 71 * q^66 + 42 * q^67 - 23 * q^68 - 30 * q^69 - 59 * q^70 - 13 * q^71 + 16 * q^72 + 83 * q^73 - 45 * q^74 - 65 * q^75 + 4 * q^76 - 21 * q^77 - 60 * q^78 - 3 * q^79 - 93 * q^80 + 28 * q^81 - 13 * q^82 - 23 * q^83 - 148 * q^84 + 52 * q^85 - 43 * q^86 - 5 * q^87 - 25 * q^88 - 38 * q^89 - 142 * q^90 - 17 * q^91 - 61 * q^92 + 17 * q^93 - 71 * q^94 - 66 * q^95 - 101 * q^96 + 63 * q^97 - 29 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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