LMFDB - Embedded newform 6031.2.a.c.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6031,2,Mod(1,6031)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6031.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6031, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment:select newform

sage:traces = [110] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6031.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.55998 q^{2} +2.69028 q^{3} +4.55348 q^{4} -2.87781 q^{5} -6.88705 q^{6} +3.57411 q^{7} -6.53686 q^{8} +4.23759 q^{9} +7.36714 q^{10} -0.204869 q^{11} +12.2501 q^{12} +5.75028 q^{13} -9.14963 q^{14} -7.74212 q^{15} +7.62724 q^{16} -3.17544 q^{17} -10.8481 q^{18} -3.84688 q^{19} -13.1041 q^{20} +9.61533 q^{21} +0.524459 q^{22} -3.73306 q^{23} -17.5860 q^{24} +3.28181 q^{25} -14.7206 q^{26} +3.32947 q^{27} +16.2746 q^{28} -2.82267 q^{29} +19.8196 q^{30} -7.84664 q^{31} -6.45184 q^{32} -0.551153 q^{33} +8.12905 q^{34} -10.2856 q^{35} +19.2958 q^{36} -1.00000 q^{37} +9.84792 q^{38} +15.4698 q^{39} +18.8119 q^{40} +8.71866 q^{41} -24.6150 q^{42} -4.96651 q^{43} -0.932866 q^{44} -12.1950 q^{45} +9.55655 q^{46} -3.50372 q^{47} +20.5194 q^{48} +5.77423 q^{49} -8.40136 q^{50} -8.54281 q^{51} +26.1838 q^{52} -4.86068 q^{53} -8.52336 q^{54} +0.589574 q^{55} -23.3634 q^{56} -10.3492 q^{57} +7.22596 q^{58} -9.91272 q^{59} -35.2536 q^{60} +4.09925 q^{61} +20.0872 q^{62} +15.1456 q^{63} +1.26209 q^{64} -16.5482 q^{65} +1.41094 q^{66} -10.6575 q^{67} -14.4593 q^{68} -10.0430 q^{69} +26.3309 q^{70} -13.1054 q^{71} -27.7005 q^{72} -0.381188 q^{73} +2.55998 q^{74} +8.82898 q^{75} -17.5167 q^{76} -0.732222 q^{77} -39.6025 q^{78} -7.53620 q^{79} -21.9498 q^{80} -3.75559 q^{81} -22.3196 q^{82} +2.12360 q^{83} +43.7833 q^{84} +9.13832 q^{85} +12.7142 q^{86} -7.59376 q^{87} +1.33920 q^{88} +7.68868 q^{89} +31.2189 q^{90} +20.5521 q^{91} -16.9984 q^{92} -21.1096 q^{93} +8.96945 q^{94} +11.0706 q^{95} -17.3572 q^{96} -3.46757 q^{97} -14.7819 q^{98} -0.868150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.55998	−1.81018	−0.905089	−	0.425223i	$-0.860196\pi$
$2$	−2.55998	−1.81018	−0.905089	+	0.425223i	$0.860196\pi$
$3$	2.69028	1.55323	0.776616	−	0.629974i	$-0.216934\pi$
$3$	2.69028	1.55323	0.776616	+	0.629974i	$0.216934\pi$
$4$	4.55348	2.27674
$5$	−2.87781	−1.28700	−0.643499	−	0.765447i	$-0.722518\pi$
$5$	−2.87781	−1.28700	−0.643499	+	0.765447i	$0.722518\pi$
$6$	−6.88705	−2.81163
$7$	3.57411	1.35088	0.675442	−	0.737413i	$-0.263953\pi$
$7$	3.57411	1.35088	0.675442	+	0.737413i	$0.263953\pi$
$8$	−6.53686	−2.31113
$9$	4.23759	1.41253
$10$	7.36714	2.32969
$11$	−0.204869	−0.0617702	−0.0308851	−	0.999523i	$-0.509833\pi$
$11$	−0.204869	−0.0617702	−0.0308851	+	0.999523i	$0.509833\pi$
$12$	12.2501	3.53631
$13$	5.75028	1.59484	0.797420	−	0.603424i	$-0.206197\pi$
$13$	5.75028	1.59484	0.797420	+	0.603424i	$0.206197\pi$
$14$	−9.14963	−2.44534
$15$	−7.74212	−1.99901
$16$	7.62724	1.90681
$17$	−3.17544	−0.770157	−0.385078	−	0.922884i	$-0.625826\pi$
$17$	−3.17544	−0.770157	−0.385078	+	0.922884i	$0.625826\pi$
$18$	−10.8481	−2.55693
$19$	−3.84688	−0.882534	−0.441267	−	0.897376i	$-0.645471\pi$
$19$	−3.84688	−0.882534	−0.441267	+	0.897376i	$0.645471\pi$
$20$	−13.1041	−2.93016
$21$	9.61533	2.09824
$22$	0.524459	0.111815
$23$	−3.73306	−0.778397	−0.389199	−	0.921154i	$-0.627248\pi$
$23$	−3.73306	−0.778397	−0.389199	+	0.921154i	$0.627248\pi$
$24$	−17.5860	−3.58972
$25$	3.28181	0.656362
$26$	−14.7206	−2.88694
$27$	3.32947	0.640756
$28$	16.2746	3.07562
$29$	−2.82267	−0.524156	−0.262078	−	0.965047i	$-0.584408\pi$
$29$	−2.82267	−0.524156	−0.262078	+	0.965047i	$0.584408\pi$
$30$	19.8196	3.61855
$31$	−7.84664	−1.40930	−0.704649	−	0.709556i	$-0.748895\pi$
$31$	−7.84664	−1.40930	−0.704649	+	0.709556i	$0.748895\pi$
$32$	−6.45184	−1.14054
$33$	−0.551153	−0.0959435
$34$	8.12905	1.39412
$35$	−10.2856	−1.73859
$36$	19.2958	3.21597
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	9.84792	1.59754
$39$	15.4698	2.47716
$40$	18.8119	2.97442
$41$	8.71866	1.36163	0.680813	−	0.732457i	$-0.261627\pi$
$41$	8.71866	1.36163	0.680813	+	0.732457i	$0.261627\pi$
$42$	−24.6150	−3.79818
$43$	−4.96651	−0.757386	−0.378693	−	0.925522i	$-0.623626\pi$
$43$	−4.96651	−0.757386	−0.378693	+	0.925522i	$0.623626\pi$
$44$	−0.932866	−0.140635
$45$	−12.1950	−1.81792
$46$	9.55655	1.40904
$47$	−3.50372	−0.511071	−0.255535	−	0.966800i	$-0.582252\pi$
$47$	−3.50372	−0.511071	−0.255535	+	0.966800i	$0.582252\pi$
$48$	20.5194	2.96172
$49$	5.77423	0.824890
$50$	−8.40136	−1.18813
$51$	−8.54281	−1.19623
$52$	26.1838	3.63104
$53$	−4.86068	−0.667666	−0.333833	−	0.942632i	$-0.608342\pi$
$53$	−4.86068	−0.667666	−0.333833	+	0.942632i	$0.608342\pi$
$54$	−8.52336	−1.15988
$55$	0.589574	0.0794981
$56$	−23.3634	−3.12207
$57$	−10.3492	−1.37078
$58$	7.22596	0.948815
$59$	−9.91272	−1.29053	−0.645263	−	0.763961i	$-0.723252\pi$
$59$	−9.91272	−1.29053	−0.645263	+	0.763961i	$0.723252\pi$
$60$	−35.2536	−4.55122
$61$	4.09925	0.524855	0.262427	−	0.964952i	$-0.415477\pi$
$61$	4.09925	0.524855	0.262427	+	0.964952i	$0.415477\pi$
$62$	20.0872	2.55108
$63$	15.1456	1.90817
$64$	1.26209	0.157761
$65$	−16.5482	−2.05256
$66$	1.41094	0.173675
$67$	−10.6575	−1.30202	−0.651010	−	0.759069i	$-0.725654\pi$
$67$	−10.6575	−1.30202	−0.651010	+	0.759069i	$0.725654\pi$
$68$	−14.4593	−1.75345
$69$	−10.0430	−1.20903
$70$	26.3309	3.14715
$71$	−13.1054	−1.55532	−0.777660	−	0.628685i	$-0.783593\pi$
$71$	−13.1054	−1.55532	−0.777660	+	0.628685i	$0.783593\pi$
$72$	−27.7005	−3.26454
$73$	−0.381188	−0.0446147	−0.0223074	−	0.999751i	$-0.507101\pi$
$73$	−0.381188	−0.0446147	−0.0223074	+	0.999751i	$0.507101\pi$
$74$	2.55998	0.297591
$75$	8.82898	1.01948
$76$	−17.5167	−2.00930
$77$	−0.732222	−0.0834444
$78$	−39.6025	−4.48410
$79$	−7.53620	−0.847888	−0.423944	−	0.905688i	$-0.639355\pi$
$79$	−7.53620	−0.847888	−0.423944	+	0.905688i	$0.639355\pi$
$80$	−21.9498	−2.45406
$81$	−3.75559	−0.417287
$82$	−22.3196	−2.46478
$83$	2.12360	0.233095	0.116547	−	0.993185i	$-0.462817\pi$
$83$	2.12360	0.233095	0.116547	+	0.993185i	$0.462817\pi$
$84$	43.7833	4.77715
$85$	9.13832	0.991190
$86$	12.7142	1.37100
$87$	−7.59376	−0.814136
$88$	1.33920	0.142759
$89$	7.68868	0.814999	0.407499	−	0.913205i	$-0.366401\pi$
$89$	7.68868	0.814999	0.407499	+	0.913205i	$0.366401\pi$
$90$	31.2189	3.29076
$91$	20.5521	2.15445
$92$	−16.9984	−1.77221
$93$	−21.1096	−2.18897
$94$	8.96945	0.925128
$95$	11.0706	1.13582
$96$	−17.3572	−1.77152
$97$	−3.46757	−0.352078	−0.176039	−	0.984383i	$-0.556328\pi$
$97$	−3.46757	−0.352078	−0.176039	+	0.984383i	$0.556328\pi$
$98$	−14.7819	−1.49320
$99$	−0.868150	−0.0872523
$100$	14.9437	1.49437
$101$	−14.2028	−1.41323	−0.706617	−	0.707596i	$-0.749780\pi$
$101$	−14.2028	−1.41323	−0.706617	+	0.707596i	$0.749780\pi$
$102$	21.8694	2.16539
$103$	1.96968	0.194078	0.0970389	−	0.995281i	$-0.469063\pi$
$103$	1.96968	0.194078	0.0970389	+	0.995281i	$0.469063\pi$
$104$	−37.5888	−3.68588
$105$	−27.6711	−2.70043
$106$	12.4432	1.20859
$107$	0.131515	0.0127141	0.00635703	−	0.999980i	$-0.497976\pi$
$107$	0.131515	0.0127141	0.00635703	+	0.999980i	$0.497976\pi$
$108$	15.1607	1.45884
$109$	−0.964558	−0.0923879	−0.0461939	−	0.998932i	$-0.514709\pi$
$109$	−0.964558	−0.0923879	−0.0461939	+	0.998932i	$0.514709\pi$
$110$	−1.50929	−0.143906
$111$	−2.69028	−0.255350
$112$	27.2606	2.57588
$113$	−12.5856	−1.18395	−0.591975	−	0.805957i	$-0.701651\pi$
$113$	−12.5856	−1.18395	−0.591975	+	0.805957i	$0.701651\pi$
$114$	26.4936	2.48136
$115$	10.7431	1.00179
$116$	−12.8530	−1.19337
$117$	24.3673	2.25276
$118$	25.3763	2.33608
$119$	−11.3494	−1.04039
$120$	50.6091	4.61996
$121$	−10.9580	−0.996184
$122$	−10.4940	−0.950080
$123$	23.4556	2.11492
$124$	−35.7295	−3.20861
$125$	4.94463	0.442261
$126$	−38.7724	−3.45412
$127$	−7.66437	−0.680103	−0.340051	−	0.940407i	$-0.610444\pi$
$127$	−7.66437	−0.680103	−0.340051	+	0.940407i	$0.610444\pi$
$128$	9.67276	0.854959
$129$	−13.3613	−1.17640
$130$	42.3631	3.71549
$131$	4.16026	0.363483	0.181742	−	0.983346i	$-0.441827\pi$
$131$	4.16026	0.363483	0.181742	+	0.983346i	$0.441827\pi$
$132$	−2.50967	−0.218439
$133$	−13.7491	−1.19220
$134$	27.2829	2.35689
$135$	−9.58159	−0.824652
$136$	20.7574	1.77993
$137$	5.70912	0.487763	0.243882	−	0.969805i	$-0.421579\pi$
$137$	5.70912	0.487763	0.243882	+	0.969805i	$0.421579\pi$
$138$	25.7098	2.18856
$139$	−9.59756	−0.814054	−0.407027	−	0.913416i	$-0.633435\pi$
$139$	−9.59756	−0.814054	−0.407027	+	0.913416i	$0.633435\pi$
$140$	−46.8353	−3.95831
$141$	−9.42599	−0.793812
$142$	33.5494	2.81540
$143$	−1.17805	−0.0985136
$144$	32.3211	2.69343
$145$	8.12311	0.674588
$146$	0.975833	0.0807605
$147$	15.5343	1.28125
$148$	−4.55348	−0.374294
$149$	20.5419	1.68286	0.841428	−	0.540369i	$-0.181715\pi$
$149$	20.5419	1.68286	0.841428	+	0.540369i	$0.181715\pi$
$150$	−22.6020	−1.84544
$151$	18.2707	1.48685	0.743424	−	0.668821i	$-0.233201\pi$
$151$	18.2707	1.48685	0.743424	+	0.668821i	$0.233201\pi$
$152$	25.1465	2.03965
$153$	−13.4562	−1.08787
$154$	1.87447	0.151049
$155$	22.5812	1.81376
$156$	70.4417	5.63985
$157$	3.30675	0.263907	0.131954	−	0.991256i	$-0.457875\pi$
$157$	3.30675	0.263907	0.131954	+	0.991256i	$0.457875\pi$
$158$	19.2925	1.53483
$159$	−13.0766	−1.03704
$160$	18.5672	1.46787
$161$	−13.3424	−1.05152
$162$	9.61421	0.755364
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	39.7003	3.10007
$165$	1.58612	0.123479
$166$	−5.43636	−0.421943
$167$	5.27157	0.407926	0.203963	−	0.978979i	$-0.434618\pi$
$167$	5.27157	0.407926	0.203963	+	0.978979i	$0.434618\pi$
$168$	−62.8541	−4.84930
$169$	20.0657	1.54352
$170$	−23.3939	−1.79423
$171$	−16.3015	−1.24661
$172$	−22.6149	−1.72437
$173$	−19.3970	−1.47472	−0.737361	−	0.675498i	$-0.763929\pi$
$173$	−19.3970	−1.47472	−0.737361	+	0.675498i	$0.763929\pi$
$174$	19.4398	1.47373
$175$	11.7295	0.886670
$176$	−1.56258	−0.117784
$177$	−26.6680	−2.00449
$178$	−19.6829	−1.47529
$179$	7.43315	0.555580	0.277790	−	0.960642i	$-0.410398\pi$
$179$	7.43315	0.555580	0.277790	+	0.960642i	$0.410398\pi$
$180$	−55.5297	−4.13894
$181$	4.63465	0.344491	0.172245	−	0.985054i	$-0.444898\pi$
$181$	4.63465	0.344491	0.172245	+	0.985054i	$0.444898\pi$
$182$	−52.6129	−3.89993
$183$	11.0281	0.815221
$184$	24.4025	1.79898
$185$	2.87781	0.211581
$186$	54.0402	3.96242
$187$	0.650548	0.0475728
$188$	−15.9541	−1.16358
$189$	11.8999	0.865588
$190$	−28.3405	−2.05603
$191$	16.5032	1.19413	0.597066	−	0.802192i	$-0.296333\pi$
$191$	16.5032	1.19413	0.597066	+	0.802192i	$0.296333\pi$
$192$	3.39537	0.245040
$193$	16.7264	1.20400	0.601998	−	0.798498i	$-0.294372\pi$
$193$	16.7264	1.20400	0.601998	+	0.798498i	$0.294372\pi$
$194$	8.87689	0.637324
$195$	−44.5193	−3.18810
$196$	26.2928	1.87806
$197$	−3.69640	−0.263357	−0.131679	−	0.991292i	$-0.542037\pi$
$197$	−3.69640	−0.263357	−0.131679	+	0.991292i	$0.542037\pi$
$198$	2.22244	0.157942
$199$	−4.99901	−0.354371	−0.177185	−	0.984178i	$-0.556699\pi$
$199$	−4.99901	−0.354371	−0.177185	+	0.984178i	$0.556699\pi$
$200$	−21.4527	−1.51694
$201$	−28.6716	−2.02234
$202$	36.3589	2.55821
$203$	−10.0885	−0.708075
$204$	−38.8995	−2.72351
$205$	−25.0907	−1.75241
$206$	−5.04232	−0.351315
$207$	−15.8192	−1.09951
$208$	43.8588	3.04106
$209$	0.788105	0.0545143
$210$	70.8375	4.88825
$211$	18.8927	1.30063	0.650313	−	0.759667i	$-0.274638\pi$
$211$	18.8927	1.30063	0.650313	+	0.759667i	$0.274638\pi$
$212$	−22.1330	−1.52010
$213$	−35.2570	−2.41577
$214$	−0.336676	−0.0230147
$215$	14.2927	0.974753
$216$	−21.7643	−1.48087
$217$	−28.0447	−1.90380
$218$	2.46925	0.167238
$219$	−1.02550	−0.0692970
$220$	2.68461	0.180997
$221$	−18.2597	−1.22828
$222$	6.88705	0.462228
$223$	−1.02005	−0.0683073	−0.0341537	−	0.999417i	$-0.510874\pi$
$223$	−1.02005	−0.0683073	−0.0341537	+	0.999417i	$0.510874\pi$
$224$	−23.0596	−1.54073
$225$	13.9070	0.927132
$226$	32.2187	2.14316
$227$	−8.59594	−0.570532	−0.285266	−	0.958448i	$-0.592082\pi$
$227$	−8.59594	−0.570532	−0.285266	+	0.958448i	$0.592082\pi$
$228$	−47.1248	−3.12091
$229$	−27.8544	−1.84067	−0.920337	−	0.391127i	$-0.872085\pi$
$229$	−27.8544	−1.84067	−0.920337	+	0.391127i	$0.872085\pi$
$230$	−27.5020	−1.81343
$231$	−1.96988	−0.129609
$232$	18.4514	1.21139
$233$	−17.2900	−1.13271	−0.566354	−	0.824162i	$-0.691646\pi$
$233$	−17.2900	−1.13271	−0.566354	+	0.824162i	$0.691646\pi$
$234$	−62.3798	−4.07790
$235$	10.0831	0.657747
$236$	−45.1374	−2.93819
$237$	−20.2745	−1.31697
$238$	29.0541	1.88330
$239$	29.5309	1.91020	0.955099	−	0.296287i	$-0.0957485\pi$
$239$	29.5309	1.91020	0.955099	+	0.296287i	$0.0957485\pi$
$240$	−59.0510	−3.81172
$241$	4.10618	0.264502	0.132251	−	0.991216i	$-0.457779\pi$
$241$	4.10618	0.264502	0.132251	+	0.991216i	$0.457779\pi$
$242$	28.0523	1.80327
$243$	−20.0920	−1.28890
$244$	18.6658	1.19496
$245$	−16.6172	−1.06163
$246$	−60.0459	−3.82838
$247$	−22.1206	−1.40750
$248$	51.2923	3.25707
$249$	5.71306	0.362051
$250$	−12.6581	−0.800571
$251$	5.67381	0.358128	0.179064	−	0.983837i	$-0.442693\pi$
$251$	5.67381	0.358128	0.179064	+	0.983837i	$0.442693\pi$
$252$	68.9652	4.34440
$253$	0.764787	0.0480817
$254$	19.6206	1.23111
$255$	24.5846	1.53955
$256$	−27.2862	−1.70539
$257$	9.86323	0.615251	0.307626	−	0.951507i	$-0.400466\pi$
$257$	9.86323	0.615251	0.307626	+	0.951507i	$0.400466\pi$
$258$	34.2046	2.12949
$259$	−3.57411	−0.222084
$260$	−75.3521	−4.67314
$261$	−11.9613	−0.740387
$262$	−10.6502	−0.657969
$263$	−6.25586	−0.385753	−0.192876	−	0.981223i	$-0.561782\pi$
$263$	−6.25586	−0.385753	−0.192876	+	0.981223i	$0.561782\pi$
$264$	3.60281	0.221738
$265$	13.9881	0.859284
$266$	35.1975	2.15810
$267$	20.6847	1.26588
$268$	−48.5287	−2.96436
$269$	−24.6631	−1.50374	−0.751869	−	0.659313i	$-0.770847\pi$
$269$	−24.6631	−1.50374	−0.751869	+	0.659313i	$0.770847\pi$
$270$	24.5286	1.49277
$271$	−3.81417	−0.231695	−0.115847	−	0.993267i	$-0.536958\pi$
$271$	−3.81417	−0.231695	−0.115847	+	0.993267i	$0.536958\pi$
$272$	−24.2198	−1.46854
$273$	55.2909	3.34636
$274$	−14.6152	−0.882938
$275$	−0.672340	−0.0405436
$276$	−45.7305	−2.75265
$277$	24.3163	1.46103	0.730514	−	0.682898i	$-0.239281\pi$
$277$	24.3163	1.46103	0.730514	+	0.682898i	$0.239281\pi$
$278$	24.5695	1.47358
$279$	−33.2508	−1.99068
$280$	67.2355	4.01809
$281$	−21.9076	−1.30690	−0.653448	−	0.756971i	$-0.726678\pi$
$281$	−21.9076	−1.30690	−0.653448	+	0.756971i	$0.726678\pi$
$282$	24.1303	1.43694
$283$	−22.1400	−1.31608	−0.658042	−	0.752981i	$-0.728615\pi$
$283$	−22.1400	−1.31608	−0.658042	+	0.752981i	$0.728615\pi$
$284$	−59.6750	−3.54106
$285$	29.7830	1.76419
$286$	3.01579	0.178327
$287$	31.1614	1.83940
$288$	−27.3403	−1.61104
$289$	−6.91659	−0.406858
$290$	−20.7950	−1.22112
$291$	−9.32871	−0.546859
$292$	−1.73573	−0.101576
$293$	8.43267	0.492642	0.246321	−	0.969188i	$-0.420778\pi$
$293$	8.43267	0.492642	0.246321	+	0.969188i	$0.420778\pi$
$294$	−39.7674	−2.31928
$295$	28.5269	1.66090
$296$	6.53686	0.379947
$297$	−0.682104	−0.0395797
$298$	−52.5867	−3.04627
$299$	−21.4661	−1.24142
$300$	40.2026	2.32110
$301$	−17.7508	−1.02314
$302$	−46.7725	−2.69146
$303$	−38.2096	−2.19508
$304$	−29.3411	−1.68283
$305$	−11.7969	−0.675487
$306$	34.4476	1.96924
$307$	26.6638	1.52179	0.760893	−	0.648878i	$-0.224761\pi$
$307$	26.6638	1.52179	0.760893	+	0.648878i	$0.224761\pi$
$308$	−3.33416	−0.189981
$309$	5.29897	0.301448
$310$	−57.8072	−3.28323
$311$	−1.41062	−0.0799890	−0.0399945	−	0.999200i	$-0.512734\pi$
$311$	−1.41062	−0.0799890	−0.0399945	+	0.999200i	$0.512734\pi$
$312$	−101.124	−5.72503
$313$	25.9496	1.46676	0.733378	−	0.679821i	$-0.237943\pi$
$313$	25.9496	1.46676	0.733378	+	0.679821i	$0.237943\pi$
$314$	−8.46519	−0.477719
$315$	−43.5862	−2.45581
$316$	−34.3159	−1.93042
$317$	5.31669	0.298615	0.149308	−	0.988791i	$-0.452296\pi$
$317$	5.31669	0.298615	0.149308	+	0.988791i	$0.452296\pi$
$318$	33.4758	1.87723
$319$	0.578276	0.0323772
$320$	−3.63206	−0.203038
$321$	0.353812	0.0197479
$322$	34.1561	1.90345
$323$	12.2155	0.679690
$324$	−17.1010	−0.950055
$325$	18.8713	1.04679
$326$	2.55998	0.141784
$327$	−2.59493	−0.143500
$328$	−56.9926	−3.14689
$329$	−12.5227	−0.690398
$330$	−4.06042	−0.223519
$331$	34.2845	1.88444	0.942222	−	0.334988i	$-0.108732\pi$
$331$	34.2845	1.88444	0.942222	+	0.334988i	$0.108732\pi$
$332$	9.66976	0.530697
$333$	−4.23759	−0.232219
$334$	−13.4951	−0.738418
$335$	30.6703	1.67570
$336$	73.3385	4.00094
$337$	7.76271	0.422862	0.211431	−	0.977393i	$-0.432188\pi$
$337$	7.76271	0.422862	0.211431	+	0.977393i	$0.432188\pi$
$338$	−51.3678	−2.79404
$339$	−33.8586	−1.83895
$340$	41.6112	2.25668
$341$	1.60753	0.0870526
$342$	41.7315	2.25658
$343$	−4.38104	−0.236554
$344$	32.4654	1.75042
$345$	28.9018	1.55602
$346$	49.6557	2.66951
$347$	−2.80873	−0.150781	−0.0753903	−	0.997154i	$-0.524020\pi$
$347$	−2.80873	−0.150781	−0.0753903	+	0.997154i	$0.524020\pi$
$348$	−34.5780	−1.85358
$349$	24.6298	1.31840	0.659201	−	0.751967i	$-0.270895\pi$
$349$	24.6298	1.31840	0.659201	+	0.751967i	$0.270895\pi$
$350$	−30.0273	−1.60503
$351$	19.1454	1.02190
$352$	1.32178	0.0704511
$353$	13.3863	0.712483	0.356241	−	0.934394i	$-0.384058\pi$
$353$	13.3863	0.712483	0.356241	+	0.934394i	$0.384058\pi$
$354$	68.2694	3.62848
$355$	37.7148	2.00169
$356$	35.0103	1.85554
$357$	−30.5329	−1.61597
$358$	−19.0287	−1.00570
$359$	4.28309	0.226053	0.113026	−	0.993592i	$-0.463946\pi$
$359$	4.28309	0.226053	0.113026	+	0.993592i	$0.463946\pi$
$360$	79.7170	4.20145
$361$	−4.20153	−0.221133
$362$	−11.8646	−0.623589
$363$	−29.4801	−1.54731
$364$	93.5837	4.90512
$365$	1.09699	0.0574190
$366$	−28.2317	−1.47570
$367$	−23.4771	−1.22550	−0.612748	−	0.790279i	$-0.709936\pi$
$367$	−23.4771	−1.22550	−0.612748	+	0.790279i	$0.709936\pi$
$368$	−28.4729	−1.48425
$369$	36.9461	1.92334
$370$	−7.36714	−0.382999
$371$	−17.3726	−0.901940
$372$	−96.1223	−4.98371
$373$	−0.766183	−0.0396715	−0.0198357	−	0.999803i	$-0.506314\pi$
$373$	−0.766183	−0.0396715	−0.0198357	+	0.999803i	$0.506314\pi$
$374$	−1.66539	−0.0861151
$375$	13.3024	0.686934
$376$	22.9033	1.18115
$377$	−16.2311	−0.835946
$378$	−30.4634	−1.56687
$379$	33.3169	1.71138	0.855688	−	0.517492i	$-0.173134\pi$
$379$	33.3169	1.71138	0.855688	+	0.517492i	$0.173134\pi$
$380$	50.4098	2.58597
$381$	−20.6193	−1.05636
$382$	−42.2479	−2.16159
$383$	−2.37791	−0.121506	−0.0607528	−	0.998153i	$-0.519350\pi$
$383$	−2.37791	−0.121506	−0.0607528	+	0.998153i	$0.519350\pi$
$384$	26.0224	1.32795
$385$	2.10720	0.107393
$386$	−42.8193	−2.17944
$387$	−21.0460	−1.06983
$388$	−15.7895	−0.801591
$389$	−6.97059	−0.353423	−0.176712	−	0.984263i	$-0.556546\pi$
$389$	−6.97059	−0.353423	−0.176712	+	0.984263i	$0.556546\pi$
$390$	113.968	5.77102
$391$	11.8541	0.599488
$392$	−37.7453	−1.90643
$393$	11.1922	0.564574
$394$	9.46269	0.476723
$395$	21.6878	1.09123
$396$	−3.95310	−0.198651
$397$	−23.9099	−1.20001	−0.600003	−	0.799998i	$-0.704834\pi$
$397$	−23.9099	−1.20001	−0.600003	+	0.799998i	$0.704834\pi$
$398$	12.7974	0.641473
$399$	−36.9890	−1.85177
$400$	25.0311	1.25156
$401$	4.94681	0.247032	0.123516	−	0.992343i	$-0.460583\pi$
$401$	4.94681	0.247032	0.123516	+	0.992343i	$0.460583\pi$
$402$	73.3987	3.66079
$403$	−45.1204	−2.24760
$404$	−64.6724	−3.21757
$405$	10.8079	0.537048
$406$	25.8264	1.28174
$407$	0.204869	0.0101550
$408$	55.8431	2.76465
$409$	−36.7187	−1.81563	−0.907813	−	0.419376i	$-0.862249\pi$
$409$	−36.7187	−1.81563	−0.907813	+	0.419376i	$0.862249\pi$
$410$	64.2316	3.17217
$411$	15.3591	0.757609
$412$	8.96888	0.441865
$413$	−35.4291	−1.74335
$414$	40.4968	1.99031
$415$	−6.11131	−0.299993
$416$	−37.0999	−1.81897
$417$	−25.8201	−1.26442
$418$	−2.01753	−0.0986806
$419$	29.8167	1.45664	0.728320	−	0.685237i	$-0.240301\pi$
$419$	29.8167	1.45664	0.728320	+	0.685237i	$0.240301\pi$
$420$	−126.000	−6.14817
$421$	13.9722	0.680962	0.340481	−	0.940251i	$-0.389410\pi$
$421$	13.9722	0.680962	0.340481	+	0.940251i	$0.389410\pi$
$422$	−48.3648	−2.35436
$423$	−14.8474	−0.721903
$424$	31.7736	1.54306
$425$	−10.4212	−0.505502
$426$	90.2572	4.37298
$427$	14.6511	0.709018
$428$	0.598852	0.0289466
$429$	−3.16929	−0.153015
$430$	−36.5890	−1.76448
$431$	22.3910	1.07854	0.539268	−	0.842135i	$-0.318701\pi$
$431$	22.3910	1.07854	0.539268	+	0.842135i	$0.318701\pi$
$432$	25.3946	1.22180
$433$	5.48101	0.263400	0.131700	−	0.991290i	$-0.457956\pi$
$433$	5.48101	0.263400	0.131700	+	0.991290i	$0.457956\pi$
$434$	71.7938	3.44621
$435$	21.8534	1.04779
$436$	−4.39210	−0.210343
$437$	14.3606	0.686962
$438$	2.62526	0.125440
$439$	34.7387	1.65799	0.828995	−	0.559256i	$-0.188913\pi$
$439$	34.7387	1.65799	0.828995	+	0.559256i	$0.188913\pi$
$440$	−3.85396	−0.183730
$441$	24.4688	1.16518
$442$	46.7443	2.22340
$443$	13.6472	0.648399	0.324200	−	0.945989i	$-0.394905\pi$
$443$	13.6472	0.648399	0.324200	+	0.945989i	$0.394905\pi$
$444$	−12.2501	−0.581366
$445$	−22.1266	−1.04890
$446$	2.61129	0.123648
$447$	55.2634	2.61387
$448$	4.51084	0.213117
$449$	−14.5628	−0.687262	−0.343631	−	0.939105i	$-0.611657\pi$
$449$	−14.5628	−0.687262	−0.343631	+	0.939105i	$0.611657\pi$
$450$	−35.6015	−1.67827
$451$	−1.78618	−0.0841079
$452$	−57.3081	−2.69555
$453$	49.1532	2.30942
$454$	22.0054	1.03276
$455$	−59.1451	−2.77277
$456$	67.6510	3.16805
$457$	−35.4179	−1.65678	−0.828390	−	0.560152i	$-0.810743\pi$
$457$	−35.4179	−1.65678	−0.828390	+	0.560152i	$0.810743\pi$
$458$	71.3067	3.33194
$459$	−10.5725	−0.493483
$460$	48.9183	2.28083
$461$	17.2745	0.804555	0.402278	−	0.915518i	$-0.368219\pi$
$461$	17.2745	0.804555	0.402278	+	0.915518i	$0.368219\pi$
$462$	5.04285	0.234615
$463$	−11.1523	−0.518293	−0.259146	−	0.965838i	$-0.583441\pi$
$463$	−11.1523	−0.518293	−0.259146	+	0.965838i	$0.583441\pi$
$464$	−21.5292	−0.999466
$465$	60.7496	2.81719
$466$	44.2621	2.05040
$467$	13.8787	0.642231	0.321116	−	0.947040i	$-0.395942\pi$
$467$	13.8787	0.642231	0.321116	+	0.947040i	$0.395942\pi$
$468$	110.956	5.12896
$469$	−38.0910	−1.75888
$470$	−25.8124	−1.19064
$471$	8.89606	0.409909
$472$	64.7980	2.98257
$473$	1.01748	0.0467839
$474$	51.9021	2.38394
$475$	−12.6247	−0.579262
$476$	−51.6791	−2.36871
$477$	−20.5976	−0.943099
$478$	−75.5985	−3.45780
$479$	−30.3838	−1.38827	−0.694135	−	0.719845i	$-0.744213\pi$
$479$	−30.3838	−1.38827	−0.694135	+	0.719845i	$0.744213\pi$
$480$	49.9509	2.27994
$481$	−5.75028	−0.262190
$482$	−10.5117	−0.478796
$483$	−35.8946	−1.63326
$484$	−49.8972	−2.26805
$485$	9.97901	0.453123
$486$	51.4350	2.33314
$487$	−35.1251	−1.59167	−0.795834	−	0.605515i	$-0.792967\pi$
$487$	−35.1251	−1.59167	−0.795834	+	0.605515i	$0.792967\pi$
$488$	−26.7962	−1.21301
$489$	−2.69028	−0.121659
$490$	42.5395	1.92174
$491$	12.2032	0.550722	0.275361	−	0.961341i	$-0.411203\pi$
$491$	12.2032	0.550722	0.275361	+	0.961341i	$0.411203\pi$
$492$	106.805	4.81513
$493$	8.96321	0.403682
$494$	56.6283	2.54783
$495$	2.49837	0.112294
$496$	−59.8482	−2.68726
$497$	−46.8399	−2.10106
$498$	−14.6253	−0.655376
$499$	−31.7769	−1.42253	−0.711265	−	0.702924i	$-0.751878\pi$
$499$	−31.7769	−1.42253	−0.711265	+	0.702924i	$0.751878\pi$
$500$	22.5153	1.00691
$501$	14.1820	0.633604
$502$	−14.5248	−0.648274
$503$	11.1447	0.496918	0.248459	−	0.968642i	$-0.420076\pi$
$503$	11.1447	0.496918	0.248459	+	0.968642i	$0.420076\pi$
$504$	−99.0046	−4.41002
$505$	40.8731	1.81883
$506$	−1.95784	−0.0870365
$507$	53.9824	2.39744
$508$	−34.8996	−1.54842
$509$	10.4416	0.462814	0.231407	−	0.972857i	$-0.425667\pi$
$509$	10.4416	0.462814	0.231407	+	0.972857i	$0.425667\pi$
$510$	−62.9360	−2.78685
$511$	−1.36241	−0.0602693
$512$	50.5066	2.23210
$513$	−12.8081	−0.565490
$514$	−25.2496	−1.11371
$515$	−5.66836	−0.249778
$516$	−60.8404	−2.67835
$517$	0.717803	0.0315689
$518$	9.14963	0.402012
$519$	−52.1832	−2.29059
$520$	108.173	4.74372
$521$	−36.0100	−1.57763	−0.788813	−	0.614633i	$-0.789304\pi$
$521$	−36.0100	−1.57763	−0.788813	+	0.614633i	$0.789304\pi$
$522$	30.6207	1.34023
$523$	−11.1885	−0.489241	−0.244620	−	0.969619i	$-0.578663\pi$
$523$	−11.1885	−0.489241	−0.244620	+	0.969619i	$0.578663\pi$
$524$	18.9437	0.827557
$525$	31.5557	1.37720
$526$	16.0149	0.698281
$527$	24.9165	1.08538
$528$	−4.20378	−0.182946
$529$	−9.06425	−0.394098
$530$	−35.8093	−1.55546
$531$	−42.0061	−1.82291
$532$	−62.6065	−2.71434
$533$	50.1348	2.17158
$534$	−52.9523	−2.29147
$535$	−0.378476	−0.0163630
$536$	69.6665	3.00914
$537$	19.9972	0.862944
$538$	63.1370	2.72203
$539$	−1.18296	−0.0509536
$540$	−43.6296	−1.87752
$541$	−13.1443	−0.565116	−0.282558	−	0.959250i	$-0.591183\pi$
$541$	−13.1443	−0.565116	−0.282558	+	0.959250i	$0.591183\pi$
$542$	9.76420	0.419408
$543$	12.4685	0.535074
$544$	20.4874	0.878391
$545$	2.77582	0.118903
$546$	−141.543	−6.05750
$547$	−9.10867	−0.389459	−0.194729	−	0.980857i	$-0.562383\pi$
$547$	−9.10867	−0.389459	−0.194729	+	0.980857i	$0.562383\pi$
$548$	25.9964	1.11051
$549$	17.3709	0.741374
$550$	1.72117	0.0733911
$551$	10.8585	0.462586
$552$	65.6495	2.79423
$553$	−26.9352	−1.14540
$554$	−62.2493	−2.64472
$555$	7.74212	0.328635
$556$	−43.7023	−1.85339
$557$	−29.6172	−1.25492	−0.627460	−	0.778649i	$-0.715905\pi$
$557$	−29.6172	−1.25492	−0.627460	+	0.778649i	$0.715905\pi$
$558$	85.1214	3.60348
$559$	−28.5588	−1.20791
$560$	−78.4508	−3.31515
$561$	1.75015	0.0738915
$562$	56.0829	2.36571
$563$	27.2132	1.14690	0.573450	−	0.819241i	$-0.305605\pi$
$563$	27.2132	1.14690	0.573450	+	0.819241i	$0.305605\pi$
$564$	−42.9211	−1.80730
$565$	36.2189	1.52374
$566$	56.6778	2.38235
$567$	−13.4229	−0.563707
$568$	85.6678	3.59454
$569$	−0.872217	−0.0365653	−0.0182826	−	0.999833i	$-0.505820\pi$
$569$	−0.872217	−0.0365653	−0.0182826	+	0.999833i	$0.505820\pi$
$570$	−76.2437	−3.19350
$571$	5.35864	0.224252	0.112126	−	0.993694i	$-0.464234\pi$
$571$	5.35864	0.224252	0.112126	+	0.993694i	$0.464234\pi$
$572$	−5.36424	−0.224290
$573$	44.3982	1.85476
$574$	−79.7725	−3.32964
$575$	−12.2512	−0.510910
$576$	5.34822	0.222843
$577$	−20.6328	−0.858954	−0.429477	−	0.903078i	$-0.641302\pi$
$577$	−20.6328	−0.858954	−0.429477	+	0.903078i	$0.641302\pi$
$578$	17.7063	0.736486
$579$	44.9987	1.87008
$580$	36.9884	1.53586
$581$	7.58996	0.314884
$582$	23.8813	0.989912
$583$	0.995801	0.0412419
$584$	2.49177	0.103110
$585$	−70.1247	−2.89930
$586$	−21.5874	−0.891769
$587$	−11.4717	−0.473486	−0.236743	−	0.971572i	$-0.576080\pi$
$587$	−11.4717	−0.473486	−0.236743	+	0.971572i	$0.576080\pi$
$588$	70.7351	2.91706
$589$	30.1851	1.24375
$590$	−73.0283	−3.00653
$591$	−9.94433	−0.409055
$592$	−7.62724	−0.313478
$593$	11.7223	0.481378	0.240689	−	0.970602i	$-0.422627\pi$
$593$	11.7223	0.481378	0.240689	+	0.970602i	$0.422627\pi$
$594$	1.74617	0.0716462
$595$	32.6613	1.33898
$596$	93.5371	3.83143
$597$	−13.4487	−0.550420
$598$	54.9528	2.24719
$599$	6.84998	0.279882	0.139941	−	0.990160i	$-0.455309\pi$
$599$	6.84998	0.279882	0.139941	+	0.990160i	$0.455309\pi$
$600$	−57.7138	−2.35616
$601$	−10.2934	−0.419875	−0.209937	−	0.977715i	$-0.567326\pi$
$601$	−10.2934	−0.419875	−0.209937	+	0.977715i	$0.567326\pi$
$602$	45.4417	1.85207
$603$	−45.1621	−1.83914
$604$	83.1952	3.38517
$605$	31.5352	1.28209
$606$	97.8156	3.97349
$607$	−31.7744	−1.28968	−0.644841	−	0.764317i	$-0.723076\pi$
$607$	−31.7744	−1.28968	−0.644841	+	0.764317i	$0.723076\pi$
$608$	24.8194	1.00656
$609$	−27.1409	−1.09980
$610$	30.1997	1.22275
$611$	−20.1474	−0.815076
$612$	−61.2726	−2.47680
$613$	−9.09383	−0.367296	−0.183648	−	0.982992i	$-0.558791\pi$
$613$	−9.09383	−0.367296	−0.183648	+	0.982992i	$0.558791\pi$
$614$	−68.2588	−2.75470
$615$	−67.5009	−2.72190
$616$	4.78643	0.192851
$617$	22.8815	0.921174	0.460587	−	0.887614i	$-0.347639\pi$
$617$	22.8815	0.921174	0.460587	+	0.887614i	$0.347639\pi$
$618$	−13.5652	−0.545674
$619$	3.50894	0.141036	0.0705181	−	0.997510i	$-0.477535\pi$
$619$	3.50894	0.141036	0.0705181	+	0.997510i	$0.477535\pi$
$620$	102.823	4.12947
$621$	−12.4291	−0.498763
$622$	3.61116	0.144794
$623$	27.4802	1.10097
$624$	117.992	4.72347
$625$	−30.6388	−1.22555
$626$	−66.4303	−2.65509
$627$	2.12022	0.0846734
$628$	15.0572	0.600848
$629$	3.17544	0.126613
$630$	111.580	4.44544
$631$	27.6391	1.10030	0.550148	−	0.835067i	$-0.314571\pi$
$631$	27.6391	1.10030	0.550148	+	0.835067i	$0.314571\pi$
$632$	49.2630	1.95958
$633$	50.8265	2.02017
$634$	−13.6106	−0.540546
$635$	22.0566	0.875290
$636$	−59.5440	−2.36107
$637$	33.2034	1.31557
$638$	−1.48037	−0.0586085
$639$	−55.5352	−2.19694
$640$	−27.8364	−1.10033
$641$	17.7256	0.700120	0.350060	−	0.936727i	$-0.386161\pi$
$641$	17.7256	0.700120	0.350060	+	0.936727i	$0.386161\pi$
$642$	−0.905752	−0.0357472
$643$	26.4083	1.04144	0.520720	−	0.853727i	$-0.325663\pi$
$643$	26.4083	1.04144	0.520720	+	0.853727i	$0.325663\pi$
$644$	−60.7542	−2.39405
$645$	38.4513	1.51402
$646$	−31.2715	−1.23036
$647$	−44.2511	−1.73969	−0.869846	−	0.493324i	$-0.835782\pi$
$647$	−44.2511	−1.73969	−0.869846	+	0.493324i	$0.835782\pi$
$648$	24.5497	0.964404
$649$	2.03080	0.0797160
$650$	−48.3102	−1.89488
$651$	−75.4480	−2.95704
$652$	−4.55348	−0.178328
$653$	−16.1709	−0.632815	−0.316408	−	0.948623i	$-0.602477\pi$
$653$	−16.1709	−0.632815	−0.316408	+	0.948623i	$0.602477\pi$
$654$	6.64296	0.259760
$655$	−11.9724	−0.467802
$656$	66.4993	2.59636
$657$	−1.61532	−0.0630196
$658$	32.0578	1.24974
$659$	−24.6948	−0.961973	−0.480986	−	0.876728i	$-0.659721\pi$
$659$	−24.6948	−0.961973	−0.480986	+	0.876728i	$0.659721\pi$
$660$	7.22235	0.281130
$661$	−10.3370	−0.402062	−0.201031	−	0.979585i	$-0.564429\pi$
$661$	−10.3370	−0.402062	−0.201031	+	0.979585i	$0.564429\pi$
$662$	−87.7674	−3.41118
$663$	−49.1235	−1.90780
$664$	−13.8816	−0.538712
$665$	39.5675	1.53436
$666$	10.8481	0.420357
$667$	10.5372	0.408002
$668$	24.0040	0.928742
$669$	−2.74421	−0.106097
$670$	−78.5152	−3.03331
$671$	−0.839807	−0.0324204
$672$	−62.0366	−2.39311
$673$	−38.2385	−1.47399	−0.736993	−	0.675900i	$-0.763755\pi$
$673$	−38.2385	−1.47399	−0.736993	+	0.675900i	$0.763755\pi$
$674$	−19.8724	−0.765455
$675$	10.9267	0.420568
$676$	91.3689	3.51419
$677$	−17.5899	−0.676035	−0.338017	−	0.941140i	$-0.609756\pi$
$677$	−17.5899	−0.676035	−0.338017	+	0.941140i	$0.609756\pi$
$678$	86.6773	3.32882
$679$	−12.3934	−0.475617
$680$	−59.7359	−2.29077
$681$	−23.1255	−0.886169
$682$	−4.11524	−0.157581
$683$	−24.8432	−0.950599	−0.475299	−	0.879824i	$-0.657660\pi$
$683$	−24.8432	−0.950599	−0.475299	+	0.879824i	$0.657660\pi$
$684$	−74.2286	−2.83820
$685$	−16.4298	−0.627750
$686$	11.2154	0.428204
$687$	−74.9362	−2.85899
$688$	−37.8808	−1.44419
$689$	−27.9503	−1.06482
$690$	−73.9879	−2.81667
$691$	22.6148	0.860308	0.430154	−	0.902756i	$-0.358459\pi$
$691$	22.6148	0.860308	0.430154	+	0.902756i	$0.358459\pi$
$692$	−88.3237	−3.35756
$693$	−3.10286	−0.117868
$694$	7.19028	0.272939
$695$	27.6200	1.04769
$696$	49.6393	1.88157
$697$	−27.6856	−1.04867
$698$	−63.0517	−2.38654
$699$	−46.5150	−1.75936
$700$	53.4102	2.01872
$701$	37.4143	1.41312	0.706559	−	0.707654i	$-0.250247\pi$
$701$	37.4143	1.41312	0.706559	+	0.707654i	$0.250247\pi$
$702$	−49.0117	−1.84983
$703$	3.84688	0.145088
$704$	−0.258563	−0.00974495
$705$	27.1262	1.02163
$706$	−34.2687	−1.28972
$707$	−50.7624	−1.90912
$708$	−121.432	−4.56370
$709$	−31.9959	−1.20163	−0.600816	−	0.799388i	$-0.705157\pi$
$709$	−31.9959	−1.20163	−0.600816	+	0.799388i	$0.705157\pi$
$710$	−96.5489	−3.62342
$711$	−31.9353	−1.19767
$712$	−50.2598	−1.88357
$713$	29.2920	1.09699
$714$	78.1635	2.92520
$715$	3.39021	0.126787
$716$	33.8467	1.26491
$717$	79.4464	2.96698
$718$	−10.9646	−0.409196
$719$	11.1089	0.414294	0.207147	−	0.978310i	$-0.433582\pi$
$719$	11.1089	0.414294	0.207147	+	0.978310i	$0.433582\pi$
$720$	−93.0142	−3.46643
$721$	7.03983	0.262177
$722$	10.7558	0.400290
$723$	11.0468	0.410834
$724$	21.1038	0.784316
$725$	−9.26346	−0.344036
$726$	75.4685	2.80090
$727$	42.6822	1.58300	0.791498	−	0.611171i	$-0.209301\pi$
$727$	42.6822	1.58300	0.791498	+	0.611171i	$0.209301\pi$
$728$	−134.346	−4.97920
$729$	−42.7862	−1.58467
$730$	−2.80827	−0.103939
$731$	15.7708	0.583306
$732$	50.2163	1.85605
$733$	3.25903	0.120375	0.0601876	−	0.998187i	$-0.480830\pi$
$733$	3.25903	0.120375	0.0601876	+	0.998187i	$0.480830\pi$
$734$	60.1009	2.21836
$735$	−44.7048	−1.64896
$736$	24.0851	0.887789
$737$	2.18339	0.0804261
$738$	−94.5813	−3.48159
$739$	−45.9728	−1.69114	−0.845569	−	0.533866i	$-0.820739\pi$
$739$	−45.9728	−1.69114	−0.845569	+	0.533866i	$0.820739\pi$
$740$	13.1041	0.481715
$741$	−59.5106	−2.18618
$742$	44.4734	1.63267
$743$	−8.39433	−0.307958	−0.153979	−	0.988074i	$-0.549209\pi$
$743$	−8.39433	−0.307958	−0.153979	+	0.988074i	$0.549209\pi$
$744$	137.991	5.05898
$745$	−59.1157	−2.16583
$746$	1.96141	0.0718124
$747$	8.99894	0.329254
$748$	2.96226	0.108311
$749$	0.470049	0.0171752
$750$	−34.0539	−1.24347
$751$	−5.30718	−0.193662	−0.0968308	−	0.995301i	$-0.530871\pi$
$751$	−5.30718	−0.193662	−0.0968308	+	0.995301i	$0.530871\pi$
$752$	−26.7237	−0.974514
$753$	15.2641	0.556255
$754$	41.5513	1.51321
$755$	−52.5796	−1.91357
$756$	54.1859	1.97072
$757$	−22.6551	−0.823413	−0.411706	−	0.911317i	$-0.635067\pi$
$757$	−22.6551	−0.823413	−0.411706	+	0.911317i	$0.635067\pi$
$758$	−85.2906	−3.09789
$759$	2.05749	0.0746821
$760$	−72.3669	−2.62502
$761$	−10.9112	−0.395531	−0.197765	−	0.980249i	$-0.563368\pi$
$761$	−10.9112	−0.395531	−0.197765	+	0.980249i	$0.563368\pi$
$762$	52.7849	1.91219
$763$	−3.44743	−0.124805
$764$	75.1471	2.71873
$765$	38.7245	1.40009
$766$	6.08740	0.219947
$767$	−57.0009	−2.05818
$768$	−73.4075	−2.64887
$769$	10.5578	0.380725	0.190362	−	0.981714i	$-0.439034\pi$
$769$	10.5578	0.380725	0.190362	+	0.981714i	$0.439034\pi$
$770$	−5.39438	−0.194400
$771$	26.5348	0.955628
$772$	76.1635	2.74119
$773$	54.1034	1.94596	0.972981	−	0.230884i	$-0.0741619\pi$
$773$	54.1034	1.94596	0.972981	+	0.230884i	$0.0741619\pi$
$774$	53.8774	1.93658
$775$	−25.7512	−0.925009
$776$	22.6670	0.813697
$777$	−9.61533	−0.344948
$778$	17.8446	0.639759
$779$	−33.5396	−1.20168
$780$	−202.718	−7.25847
$781$	2.68488	0.0960724
$782$	−30.3462	−1.08518
$783$	−9.39798	−0.335856
$784$	44.0414	1.57291
$785$	−9.51620	−0.339648
$786$	−28.6519	−1.02198
$787$	7.89819	0.281540	0.140770	−	0.990042i	$-0.455042\pi$
$787$	7.89819	0.281540	0.140770	+	0.990042i	$0.455042\pi$
$788$	−16.8315	−0.599596
$789$	−16.8300	−0.599164
$790$	−55.5202	−1.97532
$791$	−44.9821	−1.59938
$792$	5.67497	0.201651
$793$	23.5718	0.837060
$794$	61.2089	2.17222
$795$	37.6320	1.33467
$796$	−22.7629	−0.806810
$797$	−33.0078	−1.16920	−0.584598	−	0.811323i	$-0.698748\pi$
$797$	−33.0078	−1.16920	−0.584598	+	0.811323i	$0.698748\pi$
$798$	94.6910	3.35203
$799$	11.1259	0.393605
$800$	−21.1737	−0.748604
$801$	32.5815	1.15121
$802$	−12.6637	−0.447171
$803$	0.0780935	0.00275586
$804$	−130.556	−4.60435
$805$	38.3968	1.35331
$806$	115.507	4.06856
$807$	−66.3507	−2.33565
$808$	92.8419	3.26617
$809$	−7.74180	−0.272187	−0.136094	−	0.990696i	$-0.543455\pi$
$809$	−7.74180	−0.272187	−0.136094	+	0.990696i	$0.543455\pi$
$810$	−27.6679	−0.972151
$811$	9.19158	0.322760	0.161380	−	0.986892i	$-0.448405\pi$
$811$	9.19158	0.322760	0.161380	+	0.986892i	$0.448405\pi$
$812$	−45.9379	−1.61210
$813$	−10.2612	−0.359875
$814$	−0.524459	−0.0183823
$815$	2.87781	0.100805
$816$	−65.1580	−2.28099
$817$	19.1056	0.668419
$818$	93.9992	3.28660
$819$	87.0915	3.04322
$820$	−114.250	−3.98978
$821$	−49.3878	−1.72365	−0.861824	−	0.507208i	$-0.830678\pi$
$821$	−49.3878	−1.72365	−0.861824	+	0.507208i	$0.830678\pi$
$822$	−39.3190	−1.37141
$823$	44.1675	1.53958	0.769791	−	0.638295i	$-0.220360\pi$
$823$	44.1675	1.53958	0.769791	+	0.638295i	$0.220360\pi$
$824$	−12.8755	−0.448539
$825$	−1.80878	−0.0629737
$826$	90.6977	3.15578
$827$	46.9585	1.63291	0.816453	−	0.577412i	$-0.195937\pi$
$827$	46.9585	1.63291	0.816453	+	0.577412i	$0.195937\pi$
$828$	−72.0324	−2.50330
$829$	−13.0794	−0.454267	−0.227133	−	0.973864i	$-0.572935\pi$
$829$	−13.0794	−0.454267	−0.227133	+	0.973864i	$0.572935\pi$
$830$	15.6448	0.543040
$831$	65.4177	2.26931
$832$	7.25737	0.251604
$833$	−18.3357	−0.635295
$834$	66.0989	2.28882
$835$	−15.1706	−0.525000
$836$	3.58862	0.124115
$837$	−26.1251	−0.903016
$838$	−76.3300	−2.63678
$839$	32.0085	1.10506	0.552528	−	0.833494i	$-0.313663\pi$
$839$	32.0085	1.10506	0.552528	+	0.833494i	$0.313663\pi$
$840$	180.882	6.24103
$841$	−21.0325	−0.725260
$842$	−35.7685	−1.23266
$843$	−58.9375	−2.02991
$844$	86.0275	2.96119
$845$	−57.7454	−1.98650
$846$	38.0089	1.30677
$847$	−39.1651	−1.34573
$848$	−37.0736	−1.27311
$849$	−59.5626	−2.04418
$850$	26.6780	0.915048
$851$	3.73306	0.127968
$852$	−160.542	−5.50009
$853$	13.2940	0.455176	0.227588	−	0.973757i	$-0.426916\pi$
$853$	13.2940	0.455176	0.227588	+	0.973757i	$0.426916\pi$
$854$	−37.5066	−1.28345
$855$	46.9127	1.60438
$856$	−0.859696	−0.0293838
$857$	25.6114	0.874869	0.437434	−	0.899250i	$-0.355887\pi$
$857$	25.6114	0.874869	0.437434	+	0.899250i	$0.355887\pi$
$858$	8.11330	0.276983
$859$	−6.10213	−0.208202	−0.104101	−	0.994567i	$-0.533197\pi$
$859$	−6.10213	−0.208202	−0.104101	+	0.994567i	$0.533197\pi$
$860$	65.0815	2.21926
$861$	83.8329	2.85702
$862$	−57.3204	−1.95234
$863$	43.4642	1.47954	0.739768	−	0.672862i	$-0.234935\pi$
$863$	43.4642	1.47954	0.739768	+	0.672862i	$0.234935\pi$
$864$	−21.4812	−0.730805
$865$	55.8208	1.89796
$866$	−14.0313	−0.476801
$867$	−18.6076	−0.631946
$868$	−127.701	−4.33446
$869$	1.54393	0.0523742
$870$	−55.9443	−1.89669
$871$	−61.2836	−2.07651
$872$	6.30518	0.213520
$873$	−14.6941	−0.497321
$874$	−36.7629	−1.24352
$875$	17.6726	0.597444
$876$	−4.66961	−0.157771
$877$	8.00816	0.270416	0.135208	−	0.990817i	$-0.456830\pi$
$877$	8.00816	0.270416	0.135208	+	0.990817i	$0.456830\pi$
$878$	−88.9304	−3.00126
$879$	22.6862	0.765188
$880$	4.49682	0.151588
$881$	−15.5627	−0.524320	−0.262160	−	0.965024i	$-0.584435\pi$
$881$	−15.5627	−0.524320	−0.262160	+	0.965024i	$0.584435\pi$
$882$	−62.6396	−2.10919
$883$	9.72155	0.327156	0.163578	−	0.986530i	$-0.447696\pi$
$883$	9.72155	0.327156	0.163578	+	0.986530i	$0.447696\pi$
$884$	−83.1450	−2.79647
$885$	76.7454	2.57977
$886$	−34.9366	−1.17372
$887$	32.3072	1.08477	0.542385	−	0.840130i	$-0.317521\pi$
$887$	32.3072	1.08477	0.542385	+	0.840130i	$0.317521\pi$
$888$	17.5860	0.590146
$889$	−27.3933	−0.918741
$890$	56.6436	1.89870
$891$	0.769401	0.0257759
$892$	−4.64476	−0.155518
$893$	13.4784	0.451037
$894$	−141.473	−4.73156
$895$	−21.3912	−0.715030
$896$	34.5715	1.15495
$897$	−57.7499	−1.92821
$898$	37.2805	1.24407
$899$	22.1484	0.738692
$900$	63.3252	2.11084
$901$	15.4348	0.514208
$902$	4.57258	0.152250
$903$	−47.7547	−1.58918
$904$	82.2700	2.73626
$905$	−13.3377	−0.443359
$906$	−125.831	−4.18046
$907$	−35.3616	−1.17416	−0.587081	−	0.809528i	$-0.699723\pi$
$907$	−35.3616	−1.17416	−0.587081	+	0.809528i	$0.699723\pi$
$908$	−39.1414	−1.29895
$909$	−60.1858	−1.99624
$910$	151.410	5.01920
$911$	−35.1681	−1.16517	−0.582585	−	0.812770i	$-0.697959\pi$
$911$	−35.1681	−1.16517	−0.582585	+	0.812770i	$0.697959\pi$
$912$	−78.9356	−2.61382
$913$	−0.435058	−0.0143983
$914$	90.6690	2.99906
$915$	−31.7368	−1.04919
$916$	−126.835	−4.19074
$917$	14.8692	0.491024
$918$	27.0654	0.893292
$919$	−48.8594	−1.61172	−0.805861	−	0.592105i	$-0.798297\pi$
$919$	−48.8594	−1.61172	−0.805861	+	0.592105i	$0.798297\pi$
$920$	−70.2258	−2.31528
$921$	71.7331	2.36369
$922$	−44.2224	−1.45639
$923$	−75.3595	−2.48049
$924$	−8.96982	−0.295085
$925$	−3.28181	−0.107905
$926$	28.5497	0.938202
$927$	8.34668	0.274141
$928$	18.2114	0.597819
$929$	−10.5676	−0.346713	−0.173356	−	0.984859i	$-0.555461\pi$
$929$	−10.5676	−0.346713	−0.173356	+	0.984859i	$0.555461\pi$
$930$	−155.518	−5.09962
$931$	−22.2128	−0.727994
$932$	−78.7298	−2.57888
$933$	−3.79496	−0.124242
$934$	−35.5292	−1.16255
$935$	−1.87215	−0.0612260
$936$	−159.286	−5.20642
$937$	−45.9703	−1.50178	−0.750891	−	0.660426i	$-0.770376\pi$
$937$	−45.9703	−1.50178	−0.750891	+	0.660426i	$0.770376\pi$
$938$	97.5121	3.18388
$939$	69.8115	2.27821
$940$	45.9131	1.49752
$941$	6.55584	0.213714	0.106857	−	0.994274i	$-0.465921\pi$
$941$	6.55584	0.213714	0.106857	+	0.994274i	$0.465921\pi$
$942$	−22.7737	−0.742008
$943$	−32.5473	−1.05989
$944$	−75.6067	−2.46079
$945$	−34.2456	−1.11401
$946$	−2.60473	−0.0846871
$947$	−26.9920	−0.877122	−0.438561	−	0.898701i	$-0.644512\pi$
$947$	−26.9920	−0.877122	−0.438561	+	0.898701i	$0.644512\pi$
$948$	−92.3194	−2.99839
$949$	−2.19194	−0.0711533
$950$	32.3190	1.04857
$951$	14.3034	0.463819
$952$	74.1891	2.40448
$953$	10.2369	0.331605	0.165802	−	0.986159i	$-0.446979\pi$
$953$	10.2369	0.331605	0.165802	+	0.986159i	$0.446979\pi$
$954$	52.7294	1.70718
$955$	−47.4932	−1.53684
$956$	134.469	4.34903
$957$	1.55572	0.0502894
$958$	77.7817	2.51301
$959$	20.4050	0.658912
$960$	−9.77125	−0.315366
$961$	30.5697	0.986119
$962$	14.7206	0.474611
$963$	0.557308	0.0179590
$964$	18.6974	0.602203
$965$	−48.1356	−1.54954
$966$	91.8894	2.95649
$967$	2.28732	0.0735554	0.0367777	−	0.999323i	$-0.488291\pi$
$967$	2.28732	0.0735554	0.0367777	+	0.999323i	$0.488291\pi$
$968$	71.6311	2.30231
$969$	32.8631	1.05572
$970$	−25.5460	−0.820234
$971$	−33.2332	−1.06650	−0.533252	−	0.845956i	$-0.679030\pi$
$971$	−33.2332	−1.06650	−0.533252	+	0.845956i	$0.679030\pi$
$972$	−91.4884	−2.93449
$973$	−34.3027	−1.09969
$974$	89.9193	2.88120
$975$	50.7691	1.62591
$976$	31.2659	1.00080
$977$	−26.3375	−0.842612	−0.421306	−	0.906919i	$-0.638428\pi$
$977$	−26.3375	−0.842612	−0.421306	+	0.906919i	$0.638428\pi$
$978$	6.88705	0.220224
$979$	−1.57517	−0.0503427
$980$	−75.6659	−2.41706
$981$	−4.08740	−0.130501
$982$	−31.2399	−0.996905
$983$	4.22621	0.134795	0.0673976	−	0.997726i	$-0.478530\pi$
$983$	4.22621	0.134795	0.0673976	+	0.997726i	$0.478530\pi$
$984$	−153.326	−4.88786
$985$	10.6375	0.338940
$986$	−22.9456	−0.730737
$987$	−33.6895	−1.07235
$988$	−100.726	−3.20452
$989$	18.5403	0.589547
$990$	−6.39578	−0.203271
$991$	−36.6227	−1.16336	−0.581679	−	0.813418i	$-0.697604\pi$
$991$	−36.6227	−1.16336	−0.581679	+	0.813418i	$0.697604\pi$
$992$	50.6253	1.60735
$993$	92.2347	2.92698
$994$	119.909	3.80329
$995$	14.3862	0.456074
$996$	26.0143	0.824296
$997$	−51.0880	−1.61797	−0.808987	−	0.587827i	$-0.799984\pi$
$997$	−51.0880	−1.61797	−0.808987	+	0.587827i	$0.799984\pi$
$998$	81.3482	2.57503
$999$	−3.32947	−0.105340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.7	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.7	✓	110	1.1	even	1	trivial

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55998 q^{2} +2.69028 q^{3} +4.55348 q^{4} -2.87781 q^{5} -6.88705 q^{6} +3.57411 q^{7} -6.53686 q^{8} +4.23759 q^{9} +7.36714 q^{10} -0.204869 q^{11} +12.2501 q^{12} +5.75028 q^{13} -9.14963 q^{14} -7.74212 q^{15} +7.62724 q^{16} -3.17544 q^{17} -10.8481 q^{18} -3.84688 q^{19} -13.1041 q^{20} +9.61533 q^{21} +0.524459 q^{22} -3.73306 q^{23} -17.5860 q^{24} +3.28181 q^{25} -14.7206 q^{26} +3.32947 q^{27} +16.2746 q^{28} -2.82267 q^{29} +19.8196 q^{30} -7.84664 q^{31} -6.45184 q^{32} -0.551153 q^{33} +8.12905 q^{34} -10.2856 q^{35} +19.2958 q^{36} -1.00000 q^{37} +9.84792 q^{38} +15.4698 q^{39} +18.8119 q^{40} +8.71866 q^{41} -24.6150 q^{42} -4.96651 q^{43} -0.932866 q^{44} -12.1950 q^{45} +9.55655 q^{46} -3.50372 q^{47} +20.5194 q^{48} +5.77423 q^{49} -8.40136 q^{50} -8.54281 q^{51} +26.1838 q^{52} -4.86068 q^{53} -8.52336 q^{54} +0.589574 q^{55} -23.3634 q^{56} -10.3492 q^{57} +7.22596 q^{58} -9.91272 q^{59} -35.2536 q^{60} +4.09925 q^{61} +20.0872 q^{62} +15.1456 q^{63} +1.26209 q^{64} -16.5482 q^{65} +1.41094 q^{66} -10.6575 q^{67} -14.4593 q^{68} -10.0430 q^{69} +26.3309 q^{70} -13.1054 q^{71} -27.7005 q^{72} -0.381188 q^{73} +2.55998 q^{74} +8.82898 q^{75} -17.5167 q^{76} -0.732222 q^{77} -39.6025 q^{78} -7.53620 q^{79} -21.9498 q^{80} -3.75559 q^{81} -22.3196 q^{82} +2.12360 q^{83} +43.7833 q^{84} +9.13832 q^{85} +12.7142 q^{86} -7.59376 q^{87} +1.33920 q^{88} +7.68868 q^{89} +31.2189 q^{90} +20.5521 q^{91} -16.9984 q^{92} -21.1096 q^{93} +8.96945 q^{94} +11.0706 q^{95} -17.3572 q^{96} -3.46757 q^{97} -14.7819 q^{98} -0.868150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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