LMFDB - Embedded newform 529.4.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.07272 q^{2} -8.78974 q^{3} +17.7325 q^{4} +5.97134 q^{5} +44.5879 q^{6} +21.9327 q^{7} -49.3704 q^{8} +50.2595 q^{9} -30.2909 q^{10} -9.86490 q^{11} -155.864 q^{12} -17.9602 q^{13} -111.259 q^{14} -52.4865 q^{15} +108.582 q^{16} +26.7743 q^{17} -254.952 q^{18} -69.4348 q^{19} +105.887 q^{20} -192.783 q^{21} +50.0419 q^{22} +433.953 q^{24} -89.3431 q^{25} +91.1069 q^{26} -204.445 q^{27} +388.923 q^{28} -40.9508 q^{29} +266.249 q^{30} -89.6126 q^{31} -155.844 q^{32} +86.7099 q^{33} -135.819 q^{34} +130.968 q^{35} +891.227 q^{36} +443.254 q^{37} +352.224 q^{38} +157.865 q^{39} -294.807 q^{40} -283.837 q^{41} +977.935 q^{42} +532.210 q^{43} -174.929 q^{44} +300.116 q^{45} -228.723 q^{47} -954.408 q^{48} +138.045 q^{49} +453.213 q^{50} -235.339 q^{51} -318.479 q^{52} -372.354 q^{53} +1037.09 q^{54} -58.9066 q^{55} -1082.83 q^{56} +610.314 q^{57} +207.732 q^{58} -741.502 q^{59} -930.718 q^{60} +525.402 q^{61} +454.580 q^{62} +1102.33 q^{63} -78.1043 q^{64} -107.246 q^{65} -439.855 q^{66} +45.2081 q^{67} +474.777 q^{68} -664.364 q^{70} +178.587 q^{71} -2481.33 q^{72} +224.659 q^{73} -2248.50 q^{74} +785.302 q^{75} -1231.25 q^{76} -216.364 q^{77} -800.806 q^{78} +60.2745 q^{79} +648.380 q^{80} +440.008 q^{81} +1439.82 q^{82} -461.150 q^{83} -3418.53 q^{84} +159.879 q^{85} -2699.75 q^{86} +359.947 q^{87} +487.034 q^{88} -86.3813 q^{89} -1522.41 q^{90} -393.916 q^{91} +787.671 q^{93} +1160.25 q^{94} -414.619 q^{95} +1369.83 q^{96} +621.689 q^{97} -700.265 q^{98} -495.804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * 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 $

$2$	−5.07272	−1.79348	−0.896739	−	0.442559i	$-0.854071\pi$
$2$	−5.07272	−1.79348	−0.896739	+	0.442559i	$0.854071\pi$
$3$	−8.78974	−1.69159	−0.845793	−	0.533512i	$-0.820872\pi$
$3$	−8.78974	−1.69159	−0.845793	+	0.533512i	$0.820872\pi$
$4$	17.7325	2.21656
$5$	5.97134	0.534093	0.267046	−	0.963684i	$-0.413952\pi$
$5$	5.97134	0.534093	0.267046	+	0.963684i	$0.413952\pi$
$6$	44.5879	3.03382
$7$	21.9327	1.18426	0.592128	−	0.805844i	$-0.298288\pi$
$7$	21.9327	1.18426	0.592128	+	0.805844i	$0.298288\pi$
$8$	−49.3704	−2.18188
$9$	50.2595	1.86146
$10$	−30.2909	−0.957884
$11$	−9.86490	−0.270398	−0.135199	−	0.990818i	$-0.543167\pi$
$11$	−9.86490	−0.270398	−0.135199	+	0.990818i	$0.543167\pi$
$12$	−155.864	−3.74951
$13$	−17.9602	−0.383173	−0.191587	−	0.981476i	$-0.561363\pi$
$13$	−17.9602	−0.383173	−0.191587	+	0.981476i	$0.561363\pi$
$14$	−111.259	−2.12394
$15$	−52.4865	−0.903464
$16$	108.582	1.69659
$17$	26.7743	0.381984	0.190992	−	0.981592i	$-0.438829\pi$
$17$	26.7743	0.381984	0.190992	+	0.981592i	$0.438829\pi$
$18$	−254.952	−3.33849
$19$	−69.4348	−0.838392	−0.419196	−	0.907896i	$-0.637688\pi$
$19$	−69.4348	−0.838392	−0.419196	+	0.907896i	$0.637688\pi$
$20$	105.887	1.18385
$21$	−192.783	−2.00327
$22$	50.0419	0.484953
$23$	0	0
$23$	0	0
$24$	433.953	3.69084
$25$	−89.3431	−0.714745
$26$	91.1069	0.687213
$27$	−204.445	−1.45724
$28$	388.923	2.62498
$29$	−40.9508	−0.262220	−0.131110	−	0.991368i	$-0.541854\pi$
$29$	−40.9508	−0.262220	−0.131110	+	0.991368i	$0.541854\pi$
$30$	266.249	1.62034
$31$	−89.6126	−0.519190	−0.259595	−	0.965718i	$-0.583589\pi$
$31$	−89.6126	−0.519190	−0.259595	+	0.965718i	$0.583589\pi$
$32$	−155.844	−0.860923
$33$	86.7099	0.457401
$34$	−135.819	−0.685081
$35$	130.968	0.632503
$36$	891.227	4.12605
$37$	443.254	1.96947	0.984736	−	0.174052i	$-0.0556861\pi$
$37$	443.254	1.96947	0.984736	+	0.174052i	$0.0556861\pi$
$38$	352.224	1.50364
$39$	157.865	0.648170
$40$	−294.807	−1.16533
$41$	−283.837	−1.08117	−0.540583	−	0.841291i	$-0.681796\pi$
$41$	−283.837	−1.08117	−0.540583	+	0.841291i	$0.681796\pi$
$42$	977.935	3.59282
$43$	532.210	1.88747	0.943735	−	0.330702i	$-0.107285\pi$
$43$	532.210	1.88747	0.943735	+	0.330702i	$0.107285\pi$
$44$	−174.929	−0.599355
$45$	300.116	0.994193
$46$	0	0
$47$	−228.723	−0.709845	−0.354922	−	0.934896i	$-0.615493\pi$
$47$	−228.723	−0.709845	−0.354922	+	0.934896i	$0.615493\pi$
$48$	−954.408	−2.86993
$49$	138.045	0.402464
$50$	453.213	1.28188
$51$	−235.339	−0.646159
$52$	−318.479	−0.849328
$53$	−372.354	−0.965032	−0.482516	−	0.875887i	$-0.660277\pi$
$53$	−372.354	−0.965032	−0.482516	+	0.875887i	$0.660277\pi$
$54$	1037.09	2.61352
$55$	−58.9066	−0.144418
$56$	−1082.83	−2.58391
$57$	610.314	1.41821
$58$	207.732	0.470286
$59$	−741.502	−1.63619	−0.818096	−	0.575081i	$-0.804970\pi$
$59$	−741.502	−1.63619	−0.818096	+	0.575081i	$0.804970\pi$
$60$	−930.718	−2.00259
$61$	525.402	1.10280	0.551400	−	0.834241i	$-0.314094\pi$
$61$	525.402	1.10280	0.551400	+	0.834241i	$0.314094\pi$
$62$	454.580	0.931156
$63$	1102.33	2.20445
$64$	−78.1043	−0.152548
$65$	−107.246	−0.204650
$66$	−439.855	−0.820340
$67$	45.2081	0.0824335	0.0412168	−	0.999150i	$-0.486877\pi$
$67$	45.2081	0.0824335	0.0412168	+	0.999150i	$0.486877\pi$
$68$	474.777	0.846693
$69$	0	0
$70$	−664.364	−1.13438
$71$	178.587	0.298513	0.149257	−	0.988799i	$-0.452312\pi$
$71$	178.587	0.298513	0.149257	+	0.988799i	$0.452312\pi$
$72$	−2481.33	−4.06149
$73$	224.659	0.360197	0.180098	−	0.983649i	$-0.442358\pi$
$73$	224.659	0.360197	0.180098	+	0.983649i	$0.442358\pi$
$74$	−2248.50	−3.53221
$75$	785.302	1.20905
$76$	−1231.25	−1.85835
$77$	−216.364	−0.320221
$78$	−800.806	−1.16248
$79$	60.2745	0.0858406	0.0429203	−	0.999078i	$-0.486334\pi$
$79$	60.2745	0.0858406	0.0429203	+	0.999078i	$0.486334\pi$
$80$	648.380	0.906139
$81$	440.008	0.603577
$82$	1439.82	1.93905
$83$	−461.150	−0.609853	−0.304927	−	0.952376i	$-0.598632\pi$
$83$	−461.150	−0.609853	−0.304927	+	0.952376i	$0.598632\pi$
$84$	−3418.53	−4.44038
$85$	159.879	0.204015
$86$	−2699.75	−3.38514
$87$	359.947	0.443567
$88$	487.034	0.589977
$89$	−86.3813	−0.102881	−0.0514405	−	0.998676i	$-0.516381\pi$
$89$	−86.3813	−0.102881	−0.0514405	+	0.998676i	$0.516381\pi$
$90$	−1522.41	−1.78306
$91$	−393.916	−0.453776
$92$	0	0
$93$	787.671	0.878254
$94$	1160.25	1.27309
$95$	−414.619	−0.447779
$96$	1369.83	1.45633
$97$	621.689	0.650752	0.325376	−	0.945585i	$-0.394509\pi$
$97$	621.689	0.650752	0.325376	+	0.945585i	$0.394509\pi$
$98$	−700.265	−0.721811
$99$	−495.804	−0.503336
$100$	−1584.28	−1.58428
$101$	666.228	0.656358	0.328179	−	0.944616i	$-0.393565\pi$
$101$	666.228	0.656358	0.328179	+	0.944616i	$0.393565\pi$
$102$	1193.81	1.15887
$103$	−828.548	−0.792614	−0.396307	−	0.918118i	$-0.629708\pi$
$103$	−828.548	−0.792614	−0.396307	+	0.918118i	$0.629708\pi$
$104$	886.700	0.836039
$105$	−1151.17	−1.06993
$106$	1888.85	1.73076
$107$	−805.788	−0.728023	−0.364012	−	0.931394i	$-0.618593\pi$
$107$	−805.788	−0.728023	−0.364012	+	0.931394i	$0.618593\pi$
$108$	−3625.32	−3.23006
$109$	1399.41	1.22972	0.614861	−	0.788636i	$-0.289212\pi$
$109$	1399.41	1.22972	0.614861	+	0.788636i	$0.289212\pi$
$110$	298.817	0.259010
$111$	−3896.09	−3.33153
$112$	2381.50	2.00920
$113$	92.0086	0.0765968	0.0382984	−	0.999266i	$-0.487806\pi$
$113$	92.0086	0.0765968	0.0382984	+	0.999266i	$0.487806\pi$
$114$	−3095.95	−2.54353
$115$	0	0
$116$	−726.161	−0.581227
$117$	−902.668	−0.713262
$118$	3761.43	2.93448
$119$	587.235	0.452368
$120$	2591.28	1.97125
$121$	−1233.68	−0.926885
$122$	−2665.22	−1.97785
$123$	2494.85	1.82889
$124$	−1589.06	−1.15082
$125$	−1279.92	−0.915833
$126$	−5591.80	−3.95363
$127$	289.712	0.202424	0.101212	−	0.994865i	$-0.467728\pi$
$127$	289.712	0.202424	0.101212	+	0.994865i	$0.467728\pi$
$128$	1642.95	1.13451
$129$	−4677.98	−3.19282
$130$	544.030	0.367035
$131$	−1628.42	−1.08607	−0.543036	−	0.839710i	$-0.682725\pi$
$131$	−1628.42	−1.08607	−0.543036	+	0.839710i	$0.682725\pi$
$132$	1537.58	1.01386
$133$	−1522.90	−0.992871
$134$	−229.328	−0.147843
$135$	−1220.81	−0.778299
$136$	−1321.86	−0.833445
$137$	1600.56	0.998138	0.499069	−	0.866562i	$-0.333675\pi$
$137$	1600.56	0.998138	0.499069	+	0.866562i	$0.333675\pi$
$138$	0	0
$139$	1117.61	0.681976	0.340988	−	0.940068i	$-0.389238\pi$
$139$	1117.61	0.681976	0.340988	+	0.940068i	$0.389238\pi$
$140$	2322.39	1.40198
$141$	2010.42	1.20076
$142$	−905.924	−0.535377
$143$	177.175	0.103609
$144$	5457.28	3.15815
$145$	−244.531	−0.140050
$146$	−1139.63	−0.646005
$147$	−1213.38	−0.680803
$148$	7860.01	4.36546
$149$	2612.21	1.43624	0.718122	−	0.695918i	$-0.245002\pi$
$149$	2612.21	1.43624	0.718122	+	0.695918i	$0.245002\pi$
$150$	−3983.62	−2.16841
$151$	−2150.78	−1.15913	−0.579563	−	0.814927i	$-0.696777\pi$
$151$	−2150.78	−1.15913	−0.579563	+	0.814927i	$0.696777\pi$
$152$	3428.02	1.82927
$153$	1345.66	0.711049
$154$	1097.56	0.574309
$155$	−535.107	−0.277296
$156$	2799.35	1.43671
$157$	73.8242	0.0375275	0.0187637	−	0.999824i	$-0.494027\pi$
$157$	73.8242	0.0375275	0.0187637	+	0.999824i	$0.494027\pi$
$158$	−305.756	−0.153953
$159$	3272.89	1.63243
$160$	−930.596	−0.459813
$161$	0	0
$162$	−2232.04	−1.08250
$163$	371.145	0.178346	0.0891728	−	0.996016i	$-0.471578\pi$
$163$	371.145	0.178346	0.0891728	+	0.996016i	$0.471578\pi$
$164$	−5033.14	−2.39648
$165$	517.774	0.244295
$166$	2339.29	1.09376
$167$	−2677.42	−1.24063	−0.620314	−	0.784353i	$-0.712995\pi$
$167$	−2677.42	−1.24063	−0.620314	+	0.784353i	$0.712995\pi$
$168$	9517.77	4.37090
$169$	−1874.43	−0.853178
$170$	−811.020	−0.365897
$171$	−3489.76	−1.56063
$172$	9437.42	4.18370
$173$	−235.491	−0.103491	−0.0517457	−	0.998660i	$-0.516479\pi$
$173$	−235.491	−0.103491	−0.0517457	+	0.998660i	$0.516479\pi$
$174$	−1825.91	−0.795528
$175$	−1959.54	−0.846442
$176$	−1071.15	−0.458756
$177$	6517.61	2.76776
$178$	438.189	0.184515
$179$	2866.65	1.19700	0.598501	−	0.801122i	$-0.295763\pi$
$179$	2866.65	1.19700	0.598501	+	0.801122i	$0.295763\pi$
$180$	5321.82	2.20369
$181$	1398.87	0.574459	0.287229	−	0.957862i	$-0.407266\pi$
$181$	1398.87	0.574459	0.287229	+	0.957862i	$0.407266\pi$
$182$	1998.22	0.813837
$183$	−4618.14	−1.86548
$184$	0	0
$185$	2646.82	1.05188
$186$	−3995.64	−1.57513
$187$	−264.126	−0.103288
$188$	−4055.84	−1.57342
$189$	−4484.03	−1.72574
$190$	2103.25	0.803082
$191$	−2944.71	−1.11556	−0.557779	−	0.829989i	$-0.688346\pi$
$191$	−2944.71	−1.11556	−0.557779	+	0.829989i	$0.688346\pi$
$192$	686.516	0.258047
$193$	−2262.19	−0.843711	−0.421855	−	0.906663i	$-0.638621\pi$
$193$	−2262.19	−0.843711	−0.421855	+	0.906663i	$0.638621\pi$
$194$	−3153.66	−1.16711
$195$	942.666	0.346183
$196$	2447.89	0.892088
$197$	−548.702	−0.198444	−0.0992218	−	0.995065i	$-0.531635\pi$
$197$	−548.702	−0.198444	−0.0992218	+	0.995065i	$0.531635\pi$
$198$	2515.08	0.902722
$199$	−3534.06	−1.25891	−0.629455	−	0.777037i	$-0.716722\pi$
$199$	−3534.06	−1.25891	−0.629455	+	0.777037i	$0.716722\pi$
$200$	4410.90	1.55949
$201$	−397.367	−0.139443
$202$	−3379.59	−1.17716
$203$	−898.164	−0.310536
$204$	−4173.16	−1.43225
$205$	−1694.88	−0.577443
$206$	4202.99	1.42154
$207$	0	0
$208$	−1950.15	−0.650090
$209$	684.968	0.226700
$210$	5839.58	1.91890
$211$	−3665.91	−1.19607	−0.598037	−	0.801469i	$-0.704052\pi$
$211$	−3665.91	−1.19607	−0.598037	+	0.801469i	$0.704052\pi$
$212$	−6602.77	−2.13906
$213$	−1569.74	−0.504960
$214$	4087.54	1.30569
$215$	3178.00	1.00808
$216$	10093.5	3.17952
$217$	−1965.45	−0.614854
$218$	−7098.84	−2.20548
$219$	−1974.69	−0.609303
$220$	−1044.56	−0.320111
$221$	−480.872	−0.146366
$222$	19763.8	5.97503
$223$	1945.04	0.584078	0.292039	−	0.956406i	$-0.405666\pi$
$223$	1945.04	0.584078	0.292039	+	0.956406i	$0.405666\pi$
$224$	−3418.08	−1.01955
$225$	−4490.34	−1.33047
$226$	−466.734	−0.137375
$227$	−5598.62	−1.63698	−0.818488	−	0.574524i	$-0.805187\pi$
$227$	−5598.62	−1.63698	−0.818488	+	0.574524i	$0.805187\pi$
$228$	10822.4	3.14356
$229$	2059.72	0.594367	0.297183	−	0.954820i	$-0.403953\pi$
$229$	2059.72	0.594367	0.297183	+	0.954820i	$0.403953\pi$
$230$	0	0
$231$	1901.78	0.541681
$232$	2021.76	0.572133
$233$	2585.00	0.726820	0.363410	−	0.931629i	$-0.381612\pi$
$233$	2585.00	0.726820	0.363410	+	0.931629i	$0.381612\pi$
$234$	4578.98	1.27922
$235$	−1365.78	−0.379123
$236$	−13148.7	−3.62673
$237$	−529.797	−0.145207
$238$	−2978.88	−0.811311
$239$	3668.76	0.992939	0.496469	−	0.868054i	$-0.334630\pi$
$239$	3668.76	0.992939	0.496469	+	0.868054i	$0.334630\pi$
$240$	−5699.09	−1.53281
$241$	−2676.73	−0.715449	−0.357724	−	0.933827i	$-0.616447\pi$
$241$	−2676.73	−0.715449	−0.357724	+	0.933827i	$0.616447\pi$
$242$	6258.14	1.66235
$243$	1652.45	0.436233
$244$	9316.69	2.44443
$245$	824.315	0.214953
$246$	−12655.7	−3.28007
$247$	1247.06	0.321249
$248$	4424.21	1.13281
$249$	4053.39	1.03162
$250$	6492.66	1.64253
$251$	−5487.38	−1.37992	−0.689961	−	0.723847i	$-0.742372\pi$
$251$	−5487.38	−1.37992	−0.689961	+	0.723847i	$0.742372\pi$
$252$	19547.0	4.88630
$253$	0	0
$254$	−1469.63	−0.363042
$255$	−1405.29	−0.345109
$256$	−7709.40	−1.88218
$257$	−506.268	−0.122880	−0.0614400	−	0.998111i	$-0.519569\pi$
$257$	−506.268	−0.122880	−0.0614400	+	0.998111i	$0.519569\pi$
$258$	23730.1	5.72625
$259$	9721.77	2.33236
$260$	−1901.74	−0.453620
$261$	−2058.17	−0.488112
$262$	8260.50	1.94785
$263$	1667.24	0.390900	0.195450	−	0.980714i	$-0.437383\pi$
$263$	1667.24	0.390900	0.195450	+	0.980714i	$0.437383\pi$
$264$	−4280.90	−0.997996
$265$	−2223.45	−0.515417
$266$	7725.23	1.78069
$267$	759.269	0.174032
$268$	801.653	0.182719
$269$	−5139.36	−1.16488	−0.582440	−	0.812874i	$-0.697902\pi$
$269$	−5139.36	−1.16488	−0.582440	+	0.812874i	$0.697902\pi$
$270$	6192.82	1.39586
$271$	−4468.71	−1.00168	−0.500839	−	0.865541i	$-0.666975\pi$
$271$	−4468.71	−1.00168	−0.500839	+	0.865541i	$0.666975\pi$
$272$	2907.21	0.648073
$273$	3462.41	0.767600
$274$	−8119.19	−1.79014
$275$	881.361	0.193266
$276$	0	0
$277$	−6185.57	−1.34172	−0.670858	−	0.741586i	$-0.734074\pi$
$277$	−6185.57	−1.34172	−0.670858	+	0.741586i	$0.734074\pi$
$278$	−5669.34	−1.22311
$279$	−4503.88	−0.966452
$280$	−6465.93	−1.38005
$281$	−3127.99	−0.664059	−0.332029	−	0.943269i	$-0.607733\pi$
$281$	−3127.99	−0.664059	−0.332029	+	0.943269i	$0.607733\pi$
$282$	−10198.3	−2.15354
$283$	6610.70	1.38857	0.694285	−	0.719700i	$-0.255721\pi$
$283$	6610.70	1.38857	0.694285	+	0.719700i	$0.255721\pi$
$284$	3166.80	0.661673
$285$	3644.39	0.757456
$286$	−898.760	−0.185821
$287$	−6225.32	−1.28038
$288$	−7832.62	−1.60258
$289$	−4196.13	−0.854088
$290$	1240.44	0.251176
$291$	−5464.48	−1.10080
$292$	3983.77	0.798399
$293$	−3551.25	−0.708075	−0.354038	−	0.935231i	$-0.615191\pi$
$293$	−3551.25	−0.708075	−0.354038	+	0.935231i	$0.615191\pi$
$294$	6155.15	1.22100
$295$	−4427.76	−0.873879
$296$	−21883.6	−4.29716
$297$	2016.82	0.394034
$298$	−13251.0	−2.57587
$299$	0	0
$300$	13925.4	2.67994
$301$	11672.8	2.23525
$302$	10910.3	2.07887
$303$	−5855.97	−1.11029
$304$	−7539.38	−1.42241
$305$	3137.35	0.588997
$306$	−6826.18	−1.27525
$307$	−5575.87	−1.03659	−0.518293	−	0.855203i	$-0.673432\pi$
$307$	−5575.87	−1.03659	−0.518293	+	0.855203i	$0.673432\pi$
$308$	−3836.68	−0.709790
$309$	7282.72	1.34077
$310$	2714.45	0.497324
$311$	−3627.73	−0.661447	−0.330723	−	0.943728i	$-0.607293\pi$
$311$	−3627.73	−0.661447	−0.330723	+	0.943728i	$0.607293\pi$
$312$	−7793.86	−1.41423
$313$	2818.02	0.508894	0.254447	−	0.967087i	$-0.418107\pi$
$313$	2818.02	0.508894	0.254447	+	0.967087i	$0.418107\pi$
$314$	−374.490	−0.0673047
$315$	6582.37	1.17738
$316$	1068.82	0.190271
$317$	−6095.86	−1.08006	−0.540028	−	0.841647i	$-0.681586\pi$
$317$	−6095.86	−1.08006	−0.540028	+	0.841647i	$0.681586\pi$
$318$	−16602.5	−2.92774
$319$	403.976	0.0709037
$320$	−466.387	−0.0814745
$321$	7082.67	1.23151
$322$	0	0
$323$	−1859.07	−0.320253
$324$	7802.45	1.33787
$325$	1604.62	0.273871
$326$	−1882.72	−0.319859
$327$	−12300.5	−2.08018
$328$	14013.1	2.35898
$329$	−5016.53	−0.840639
$330$	−2626.52	−0.438137
$331$	7093.62	1.17795	0.588973	−	0.808152i	$-0.299532\pi$
$331$	7093.62	1.17795	0.588973	+	0.808152i	$0.299532\pi$
$332$	−8177.36	−1.35178
$333$	22277.7	3.66610
$334$	13581.8	2.22504
$335$	269.953	0.0440271
$336$	−20932.8	−3.39874
$337$	−5475.78	−0.885119	−0.442559	−	0.896739i	$-0.645929\pi$
$337$	−5475.78	−0.885119	−0.442559	+	0.896739i	$0.645929\pi$
$338$	9508.48	1.53016
$339$	−808.731	−0.129570
$340$	2835.05	0.452213
$341$	884.019	0.140388
$342$	17702.6	2.79896
$343$	−4495.22	−0.707636
$344$	−26275.4	−4.11824
$345$	0	0
$346$	1194.58	0.185610
$347$	−4019.09	−0.621776	−0.310888	−	0.950447i	$-0.600626\pi$
$347$	−4019.09	−0.621776	−0.310888	+	0.950447i	$0.600626\pi$
$348$	6382.76	0.983195
$349$	11190.2	1.71633	0.858166	−	0.513373i	$-0.171604\pi$
$349$	11190.2	1.71633	0.858166	+	0.513373i	$0.171604\pi$
$350$	9940.20	1.51807
$351$	3671.86	0.558374
$352$	1537.38	0.232792
$353$	−10611.8	−1.60003	−0.800014	−	0.599981i	$-0.795175\pi$
$353$	−10611.8	−1.60003	−0.800014	+	0.599981i	$0.795175\pi$
$354$	−33062.0	−4.96392
$355$	1066.41	0.159434
$356$	−1531.76	−0.228042
$357$	−5161.64	−0.765218
$358$	−14541.7	−2.14680
$359$	−7061.44	−1.03813	−0.519065	−	0.854735i	$-0.673720\pi$
$359$	−7061.44	−1.03813	−0.519065	+	0.854735i	$0.673720\pi$
$360$	−14816.8	−2.16921
$361$	−2037.80	−0.297099
$362$	−7096.07	−1.03028
$363$	10843.8	1.56791
$364$	−6985.12	−1.00582
$365$	1341.52	0.192378
$366$	23426.5	3.34570
$367$	−3185.45	−0.453077	−0.226538	−	0.974002i	$-0.572741\pi$
$367$	−3185.45	−0.453077	−0.226538	+	0.974002i	$0.572741\pi$
$368$	0	0
$369$	−14265.5	−2.01255
$370$	−13426.6	−1.88653
$371$	−8166.74	−1.14285
$372$	13967.4	1.94671
$373$	−3217.73	−0.446670	−0.223335	−	0.974742i	$-0.571694\pi$
$373$	−3217.73	−0.446670	−0.223335	+	0.974742i	$0.571694\pi$
$374$	1339.84	0.185244
$375$	11250.1	1.54921
$376$	11292.1	1.54880
$377$	735.483	0.100476
$378$	22746.2	3.09508
$379$	−8097.47	−1.09746	−0.548732	−	0.835998i	$-0.684889\pi$
$379$	−8097.47	−1.09746	−0.548732	+	0.835998i	$0.684889\pi$
$380$	−7352.24	−0.992531
$381$	−2546.49	−0.342417
$382$	14937.7	2.00073
$383$	−19.9691	−0.00266416	−0.00133208	−	0.999999i	$-0.500424\pi$
$383$	−19.9691	−0.00266416	−0.00133208	+	0.999999i	$0.500424\pi$
$384$	−14441.1	−1.91913
$385$	−1291.98	−0.171028
$386$	11475.5	1.51318
$387$	26748.6	3.51345
$388$	11024.1	1.44243
$389$	7857.59	1.02415	0.512077	−	0.858940i	$-0.328876\pi$
$389$	7857.59	1.02415	0.512077	+	0.858940i	$0.328876\pi$
$390$	−4781.88	−0.620872
$391$	0	0
$392$	−6815.34	−0.878130
$393$	14313.3	1.83718
$394$	2783.41	0.355904
$395$	359.919	0.0458468
$396$	−8791.86	−1.11568
$397$	6626.11	0.837670	0.418835	−	0.908062i	$-0.362439\pi$
$397$	6626.11	0.837670	0.418835	+	0.908062i	$0.362439\pi$
$398$	17927.3	2.25783
$399$	13385.9	1.67953
$400$	−9701.06	−1.21263
$401$	6126.94	0.763005	0.381502	−	0.924368i	$-0.375407\pi$
$401$	6126.94	0.763005	0.381502	+	0.924368i	$0.375407\pi$
$402$	2015.73	0.250089
$403$	1609.46	0.198940
$404$	11813.9	1.45486
$405$	2627.44	0.322366
$406$	4556.14	0.556939
$407$	−4372.66	−0.532542
$408$	11618.8	1.40984
$409$	4057.92	0.490590	0.245295	−	0.969448i	$-0.421115\pi$
$409$	4057.92	0.490590	0.245295	+	0.969448i	$0.421115\pi$
$410$	8597.68	1.03563
$411$	−14068.5	−1.68844
$412$	−14692.2	−1.75688
$413$	−16263.2	−1.93767
$414$	0	0
$415$	−2753.69	−0.325718
$416$	2798.98	0.329883
$417$	−9823.52	−1.15362
$418$	−3474.65	−0.406581
$419$	13990.6	1.63123	0.815615	−	0.578595i	$-0.196399\pi$
$419$	13990.6	1.63123	0.815615	+	0.578595i	$0.196399\pi$
$420$	−20413.2	−2.37158
$421$	−9345.16	−1.08184	−0.540921	−	0.841074i	$-0.681924\pi$
$421$	−9345.16	−1.08184	−0.540921	+	0.841074i	$0.681924\pi$
$422$	18596.1	2.14513
$423$	−11495.5	−1.32135
$424$	18383.2	2.10559
$425$	−2392.10	−0.273021
$426$	7962.84	0.905635
$427$	11523.5	1.30600
$428$	−14288.7	−1.61371
$429$	−1557.32	−0.175264
$430$	−16121.1	−1.80798
$431$	−1039.90	−0.116219	−0.0581095	−	0.998310i	$-0.518507\pi$
$431$	−1039.90	−0.116219	−0.0581095	+	0.998310i	$0.518507\pi$
$432$	−22199.0	−2.47234
$433$	−10363.9	−1.15024	−0.575122	−	0.818068i	$-0.695045\pi$
$433$	−10363.9	−1.15024	−0.575122	+	0.818068i	$0.695045\pi$
$434$	9970.18	1.10273
$435$	2149.36	0.236906
$436$	24815.1	2.72576
$437$	0	0
$438$	10017.1	1.09277
$439$	−11713.7	−1.27349	−0.636745	−	0.771074i	$-0.719720\pi$
$439$	−11713.7	−1.27349	−0.636745	+	0.771074i	$0.719720\pi$
$440$	2908.24	0.315102
$441$	6938.08	0.749172
$442$	2439.33	0.262505
$443$	4658.33	0.499603	0.249801	−	0.968297i	$-0.419635\pi$
$443$	4658.33	0.499603	0.249801	+	0.968297i	$0.419635\pi$
$444$	−69087.4	−7.38456
$445$	−515.812	−0.0549479
$446$	−9866.65	−1.04753
$447$	−22960.6	−2.42953
$448$	−1713.04	−0.180655
$449$	−3186.23	−0.334895	−0.167447	−	0.985881i	$-0.553552\pi$
$449$	−3186.23	−0.334895	−0.167447	+	0.985881i	$0.553552\pi$
$450$	22778.2	2.38617
$451$	2800.02	0.292345
$452$	1631.54	0.169782
$453$	18904.8	1.96076
$454$	28400.2	2.93588
$455$	−2352.20	−0.242358
$456$	−30131.4	−3.09437
$457$	6547.13	0.670157	0.335079	−	0.942190i	$-0.391237\pi$
$457$	6547.13	0.670157	0.335079	+	0.942190i	$0.391237\pi$
$458$	−10448.4	−1.06598
$459$	−5473.87	−0.556641
$460$	0	0
$461$	16345.4	1.65137	0.825684	−	0.564132i	$-0.190789\pi$
$461$	16345.4	1.65137	0.825684	+	0.564132i	$0.190789\pi$
$462$	−9647.23	−0.971493
$463$	3614.21	0.362778	0.181389	−	0.983411i	$-0.441941\pi$
$463$	3614.21	0.362778	0.181389	+	0.983411i	$0.441941\pi$
$464$	−4446.52	−0.444881
$465$	4703.45	0.469069
$466$	−13113.0	−1.30354
$467$	19296.2	1.91204	0.956020	−	0.293302i	$-0.0947542\pi$
$467$	19296.2	1.91204	0.956020	+	0.293302i	$0.0947542\pi$
$468$	−16006.6	−1.58099
$469$	991.537	0.0976225
$470$	6928.24	0.679949
$471$	−648.895	−0.0634809
$472$	36608.2	3.56998
$473$	−5250.20	−0.510368
$474$	2687.51	0.260425
$475$	6203.53	0.599236
$476$	10413.2	1.00270
$477$	−18714.3	−1.79637
$478$	−18610.6	−1.78081
$479$	−12947.0	−1.23500	−0.617500	−	0.786571i	$-0.711854\pi$
$479$	−12947.0	−1.23500	−0.617500	+	0.786571i	$0.711854\pi$
$480$	8179.69	0.777813
$481$	−7960.91	−0.754649
$482$	13578.3	1.28314
$483$	0	0
$484$	−21876.3	−2.05450
$485$	3712.32	0.347562
$486$	−8382.41	−0.782375
$487$	−6878.46	−0.640026	−0.320013	−	0.947413i	$-0.603687\pi$
$487$	−6878.46	−0.640026	−0.320013	+	0.947413i	$0.603687\pi$
$488$	−25939.3	−2.40618
$489$	−3262.27	−0.301687
$490$	−4181.52	−0.385514
$491$	−11985.7	−1.10164	−0.550820	−	0.834624i	$-0.685685\pi$
$491$	−11985.7	−1.10164	−0.550820	+	0.834624i	$0.685685\pi$
$492$	44240.0	4.05384
$493$	−1096.43	−0.100164
$494$	−6325.99	−0.576154
$495$	−2960.62	−0.268828
$496$	−9730.32	−0.880855
$497$	3916.91	0.353516
$498$	−20561.7	−1.85019
$499$	−18723.3	−1.67970	−0.839851	−	0.542817i	$-0.817358\pi$
$499$	−18723.3	−1.67970	−0.839851	+	0.542817i	$0.817358\pi$
$500$	−22696.1	−2.03000
$501$	23533.8	2.09863
$502$	27836.0	2.47486
$503$	−18125.4	−1.60670	−0.803350	−	0.595507i	$-0.796951\pi$
$503$	−18125.4	−1.60670	−0.803350	+	0.595507i	$0.796951\pi$
$504$	−54422.3	−4.80985
$505$	3978.27	0.350556
$506$	0	0
$507$	16475.8	1.44322
$508$	5137.33	0.448685
$509$	−2750.25	−0.239495	−0.119747	−	0.992804i	$-0.538208\pi$
$509$	−2750.25	−0.239495	−0.119747	+	0.992804i	$0.538208\pi$
$510$	7128.65	0.618945
$511$	4927.39	0.426565
$512$	25964.1	2.24113
$513$	14195.6	1.22173
$514$	2568.16	0.220383
$515$	−4947.54	−0.423330
$516$	−82952.4	−7.07709
$517$	2256.33	0.191941
$518$	−49315.9	−4.18304
$519$	2069.90	0.175065
$520$	5294.78	0.446522
$521$	−21534.4	−1.81082	−0.905412	−	0.424533i	$-0.860438\pi$
$521$	−21534.4	−1.81082	−0.905412	+	0.424533i	$0.860438\pi$
$522$	10440.5	0.875418
$523$	−22861.7	−1.91142	−0.955710	−	0.294309i	$-0.904911\pi$
$523$	−22861.7	−1.91142	−0.955710	+	0.294309i	$0.904911\pi$
$524$	−28875.9	−2.40735
$525$	17223.8	1.43183
$526$	−8457.47	−0.701071
$527$	−2399.32	−0.198322
$528$	9415.13	0.776025
$529$	0	0
$530$	11278.9	0.924389
$531$	−37267.5	−3.04571
$532$	−27004.8	−2.20076
$533$	5097.75	0.414274
$534$	−3851.56	−0.312122
$535$	−4811.63	−0.388832
$536$	−2231.94	−0.179860
$537$	−25197.1	−2.02483
$538$	26070.6	2.08919
$539$	−1361.80	−0.108826
$540$	−21648.0	−1.72515
$541$	−1434.30	−0.113984	−0.0569922	−	0.998375i	$-0.518151\pi$
$541$	−1434.30	−0.113984	−0.0569922	+	0.998375i	$0.518151\pi$
$542$	22668.5	1.79649
$543$	−12295.7	−0.971746
$544$	−4172.61	−0.328859
$545$	8356.38	0.656785
$546$	−17563.9	−1.37667
$547$	3469.68	0.271212	0.135606	−	0.990763i	$-0.456702\pi$
$547$	3469.68	0.271212	0.135606	+	0.990763i	$0.456702\pi$
$548$	28381.9	2.21244
$549$	26406.4	2.05282
$550$	−4470.90	−0.346618
$551$	2843.41	0.219843
$552$	0	0
$553$	1321.98	0.101657
$554$	31377.7	2.40634
$555$	−23264.8	−1.77935
$556$	19818.1	1.51164
$557$	8589.05	0.653375	0.326687	−	0.945132i	$-0.394068\pi$
$557$	8589.05	0.653375	0.326687	+	0.945132i	$0.394068\pi$
$558$	22846.9	1.73331
$559$	−9558.57	−0.723228
$560$	14220.8	1.07310
$561$	2321.60	0.174720
$562$	15867.4	1.19097
$563$	16237.2	1.21548	0.607739	−	0.794137i	$-0.292077\pi$
$563$	16237.2	1.21548	0.607739	+	0.794137i	$0.292077\pi$
$564$	35649.7	2.66157
$565$	549.415	0.0409098
$566$	−33534.2	−2.49037
$567$	9650.58	0.714791
$568$	−8816.93	−0.651320
$569$	16517.9	1.21699	0.608496	−	0.793557i	$-0.291773\pi$
$569$	16517.9	1.21699	0.608496	+	0.793557i	$0.291773\pi$
$570$	−18487.0	−1.35848
$571$	−1811.50	−0.132766	−0.0663828	−	0.997794i	$-0.521146\pi$
$571$	−1811.50	−0.132766	−0.0663828	+	0.997794i	$0.521146\pi$
$572$	3141.76	0.229657
$573$	25883.2	1.88706
$574$	31579.3	2.29633
$575$	0	0
$576$	−3925.48	−0.283961
$577$	10058.8	0.725743	0.362871	−	0.931839i	$-0.381796\pi$
$577$	10058.8	0.725743	0.362871	+	0.931839i	$0.381796\pi$
$578$	21285.8	1.53179
$579$	19884.1	1.42721
$580$	−4336.15	−0.310429
$581$	−10114.3	−0.722223
$582$	27719.8	1.97427
$583$	3673.23	0.260943
$584$	−11091.5	−0.785907
$585$	−5390.14	−0.380948
$586$	18014.5	1.26992
$587$	−8786.09	−0.617787	−0.308893	−	0.951097i	$-0.599959\pi$
$587$	−8786.09	−0.617787	−0.308893	+	0.951097i	$0.599959\pi$
$588$	−21516.3	−1.50904
$589$	6222.23	0.435285
$590$	22460.8	1.56728
$591$	4822.95	0.335684
$592$	48129.4	3.34140
$593$	−6423.07	−0.444795	−0.222398	−	0.974956i	$-0.571388\pi$
$593$	−6423.07	−0.444795	−0.222398	+	0.974956i	$0.571388\pi$
$594$	−10230.8	−0.706691
$595$	3506.58	0.241606
$596$	46321.0	3.18353
$597$	31063.5	2.12955
$598$	0	0
$599$	18413.1	1.25599	0.627995	−	0.778217i	$-0.283876\pi$
$599$	18413.1	1.25599	0.627995	+	0.778217i	$0.283876\pi$
$600$	−38770.7	−2.63801
$601$	12919.9	0.876898	0.438449	−	0.898756i	$-0.355528\pi$
$601$	12919.9	0.876898	0.438449	+	0.898756i	$0.355528\pi$
$602$	−59213.0	−4.00887
$603$	2272.13	0.153447
$604$	−38138.8	−2.56928
$605$	−7366.74	−0.495042
$606$	29705.7	1.99127
$607$	12746.6	0.852339	0.426170	−	0.904643i	$-0.359863\pi$
$607$	12746.6	0.852339	0.426170	+	0.904643i	$0.359863\pi$
$608$	10821.0	0.721791
$609$	7894.62	0.525298
$610$	−15914.9	−1.05635
$611$	4107.91	0.271994
$612$	23862.0	1.57609
$613$	15045.4	0.991318	0.495659	−	0.868517i	$-0.334927\pi$
$613$	15045.4	0.991318	0.495659	+	0.868517i	$0.334927\pi$
$614$	28284.9	1.85909
$615$	14897.6	0.976795
$616$	10682.0	0.698684
$617$	−4013.47	−0.261874	−0.130937	−	0.991391i	$-0.541799\pi$
$617$	−4013.47	−0.261874	−0.130937	+	0.991391i	$0.541799\pi$
$618$	−36943.2	−2.40465
$619$	8639.85	0.561009	0.280505	−	0.959853i	$-0.409498\pi$
$619$	8639.85	0.561009	0.280505	+	0.959853i	$0.409498\pi$
$620$	−9488.79	−0.614644
$621$	0	0
$622$	18402.5	1.18629
$623$	−1894.58	−0.121837
$624$	17141.3	1.09968
$625$	3525.08	0.225605
$626$	−14295.0	−0.912690
$627$	−6020.69	−0.383482
$628$	1309.09	0.0831821
$629$	11867.8	0.752308
$630$	−33390.6	−2.11161
$631$	4277.53	0.269866	0.134933	−	0.990855i	$-0.456918\pi$
$631$	4277.53	0.269866	0.134933	+	0.990855i	$0.456918\pi$
$632$	−2975.77	−0.187294
$633$	32222.4	2.02326
$634$	30922.6	1.93706
$635$	1729.97	0.108113
$636$	58036.6	3.61840
$637$	−2479.31	−0.154214
$638$	−2049.26	−0.127164
$639$	8975.71	0.555670
$640$	9810.62	0.605936
$641$	16785.9	1.03433	0.517163	−	0.855887i	$-0.326988\pi$
$641$	16785.9	1.03433	0.517163	+	0.855887i	$0.326988\pi$
$642$	−35928.4	−2.20869
$643$	−9599.04	−0.588723	−0.294362	−	0.955694i	$-0.595107\pi$
$643$	−9599.04	−0.588723	−0.294362	+	0.955694i	$0.595107\pi$
$644$	0	0
$645$	−27933.8	−1.70526
$646$	9430.56	0.574366
$647$	7758.84	0.471455	0.235728	−	0.971819i	$-0.424253\pi$
$647$	7758.84	0.471455	0.235728	+	0.971819i	$0.424253\pi$
$648$	−21723.4	−1.31693
$649$	7314.84	0.442423
$650$	−8139.78	−0.491182
$651$	17275.8	1.04008
$652$	6581.34	0.395314
$653$	−4874.07	−0.292094	−0.146047	−	0.989278i	$-0.546655\pi$
$653$	−4874.07	−0.292094	−0.146047	+	0.989278i	$0.546655\pi$
$654$	62397.0	3.73076
$655$	−9723.82	−0.580063
$656$	−30819.6	−1.83430
$657$	11291.2	0.670492
$658$	25447.5	1.50767
$659$	−17267.0	−1.02068	−0.510339	−	0.859973i	$-0.670480\pi$
$659$	−17267.0	−1.02068	−0.510339	+	0.859973i	$0.670480\pi$
$660$	9181.43	0.541495
$661$	4230.17	0.248918	0.124459	−	0.992225i	$-0.460281\pi$
$661$	4230.17	0.248918	0.124459	+	0.992225i	$0.460281\pi$
$662$	−35983.9	−2.11262
$663$	4226.73	0.247591
$664$	22767.2	1.33063
$665$	−9093.73	−0.530285
$666$	−113009.	−6.57507
$667$	0	0
$668$	−47477.4	−2.74993
$669$	−17096.4	−0.988019
$670$	−1369.40	−0.0789617
$671$	−5183.03	−0.298195
$672$	30044.0	1.72466
$673$	19067.5	1.09212	0.546061	−	0.837745i	$-0.316127\pi$
$673$	19067.5	1.09212	0.546061	+	0.837745i	$0.316127\pi$
$674$	27777.1	1.58744
$675$	18265.7	1.04155
$676$	−33238.4	−1.89112
$677$	16952.8	0.962405	0.481203	−	0.876609i	$-0.340200\pi$
$677$	16952.8	0.962405	0.481203	+	0.876609i	$0.340200\pi$
$678$	4102.47	0.232381
$679$	13635.4	0.770658
$680$	−7893.27	−0.445137
$681$	49210.4	2.76908
$682$	−4484.38	−0.251783
$683$	−30621.7	−1.71553	−0.857764	−	0.514043i	$-0.828147\pi$
$683$	−30621.7	−1.71553	−0.857764	+	0.514043i	$0.828147\pi$
$684$	−61882.2	−3.45925
$685$	9557.47	0.533098
$686$	22803.0	1.26913
$687$	−18104.4	−1.00542
$688$	57788.4	3.20227
$689$	6687.53	0.369775
$690$	0	0
$691$	−11836.4	−0.651631	−0.325816	−	0.945433i	$-0.605639\pi$
$691$	−11836.4	−0.651631	−0.325816	+	0.945433i	$0.605639\pi$
$692$	−4175.84	−0.229395
$693$	−10874.4	−0.596079
$694$	20387.7	1.11514
$695$	6673.65	0.364239
$696$	−17770.7	−0.967812
$697$	−7599.54	−0.412989
$698$	−56765.0	−3.07820
$699$	−22721.5	−1.22948
$700$	−34747.6	−1.87619
$701$	−4320.64	−0.232793	−0.116397	−	0.993203i	$-0.537134\pi$
$701$	−4320.64	−0.232793	−0.116397	+	0.993203i	$0.537134\pi$
$702$	−18626.3	−1.00143
$703$	−30777.3	−1.65119
$704$	770.491	0.0412486
$705$	12004.9	0.641319
$706$	53830.8	2.86962
$707$	14612.2	0.777296
$708$	115574.	6.13492
$709$	−5277.45	−0.279547	−0.139774	−	0.990183i	$-0.544637\pi$
$709$	−5277.45	−0.279547	−0.139774	+	0.990183i	$0.544637\pi$
$710$	−5409.58	−0.285941
$711$	3029.36	0.159789
$712$	4264.68	0.224474
$713$	0	0
$714$	26183.6	1.37240
$715$	1057.97	0.0553370
$716$	50832.9	2.65323
$717$	−32247.4	−1.67964
$718$	35820.7	1.86186
$719$	26356.5	1.36708	0.683539	−	0.729914i	$-0.260440\pi$
$719$	26356.5	1.36708	0.683539	+	0.729914i	$0.260440\pi$
$720$	32587.2	1.68674
$721$	−18172.3	−0.938659
$722$	10337.2	0.532841
$723$	23527.7	1.21024
$724$	24805.5	1.27333
$725$	3658.67	0.187420
$726$	−55007.4	−2.81200
$727$	−26836.5	−1.36906	−0.684532	−	0.728983i	$-0.739994\pi$
$727$	−26836.5	−1.36906	−0.684532	+	0.728983i	$0.739994\pi$
$728$	19447.8	0.990085
$729$	−26404.8	−1.34150
$730$	−6805.13	−0.345026
$731$	14249.6	0.720984
$732$	−81891.3	−4.13496
$733$	30290.7	1.52635	0.763174	−	0.646194i	$-0.223640\pi$
$733$	30290.7	1.52635	0.763174	+	0.646194i	$0.223640\pi$
$734$	16158.9	0.812583
$735$	−7245.51	−0.363612
$736$	0	0
$737$	−445.973	−0.0222899
$738$	72364.8	3.60946
$739$	−3077.59	−0.153195	−0.0765975	−	0.997062i	$-0.524406\pi$
$739$	−3077.59	−0.153195	−0.0765975	+	0.997062i	$0.524406\pi$
$740$	46934.8	2.33156
$741$	−10961.3	−0.543421
$742$	41427.6	2.04967
$743$	−21917.7	−1.08221	−0.541106	−	0.840954i	$-0.681994\pi$
$743$	−21917.7	−1.08221	−0.541106	+	0.840954i	$0.681994\pi$
$744$	−38887.6	−1.91625
$745$	15598.4	0.767087
$746$	16322.7	0.801093
$747$	−23177.2	−1.13522
$748$	−4683.62	−0.228944
$749$	−17673.1	−0.862167
$750$	−57068.7	−2.77847
$751$	448.256	0.0217804	0.0108902	−	0.999941i	$-0.496533\pi$
$751$	448.256	0.0217804	0.0108902	+	0.999941i	$0.496533\pi$
$752$	−24835.2	−1.20432
$753$	48232.6	2.33426
$754$	−3730.90	−0.180201
$755$	−12843.0	−0.619081
$756$	−79513.1	−3.82522
$757$	−26761.0	−1.28487	−0.642434	−	0.766341i	$-0.722075\pi$
$757$	−26761.0	−1.28487	−0.642434	+	0.766341i	$0.722075\pi$
$758$	41076.2	1.96828
$759$	0	0
$760$	20469.9	0.977001
$761$	23044.3	1.09771	0.548854	−	0.835919i	$-0.315064\pi$
$761$	23044.3	1.09771	0.548854	+	0.835919i	$0.315064\pi$
$762$	12917.7	0.614117
$763$	30693.0	1.45631
$764$	−52217.1	−2.47271
$765$	8035.42	0.379766
$766$	101.298	0.00477812
$767$	13317.5	0.626945
$768$	67763.6	3.18387
$769$	−27535.6	−1.29123	−0.645617	−	0.763661i	$-0.723400\pi$
$769$	−27535.6	−1.29123	−0.645617	+	0.763661i	$0.723400\pi$
$770$	6553.88	0.306734
$771$	4449.97	0.207862
$772$	−40114.4	−1.87014
$773$	13662.9	0.635731	0.317865	−	0.948136i	$-0.397034\pi$
$773$	13662.9	0.635731	0.317865	+	0.948136i	$0.397034\pi$
$774$	−135688.	−6.30130
$775$	8006.27	0.371088
$776$	−30693.0	−1.41987
$777$	−85451.8	−3.94539
$778$	−39859.4	−1.83680
$779$	19708.1	0.906441
$780$	16715.8	0.767337
$781$	−1761.75	−0.0807173
$782$	0	0
$783$	8372.17	0.382116
$784$	14989.2	0.682819
$785$	440.829	0.0200431
$786$	−72607.6	−3.29495
$787$	−10422.7	−0.472082	−0.236041	−	0.971743i	$-0.575850\pi$
$787$	−10422.7	−0.472082	−0.236041	+	0.971743i	$0.575850\pi$
$788$	−9729.87	−0.439863
$789$	−14654.6	−0.661241
$790$	−1825.77	−0.0822253
$791$	2018.00	0.0907103
$792$	24478.0	1.09822
$793$	−9436.30	−0.422563
$794$	−33612.4	−1.50234
$795$	19543.5	0.871872
$796$	−62667.8	−2.79045
$797$	499.417	0.0221961	0.0110980	−	0.999938i	$-0.496467\pi$
$797$	499.417	0.0221961	0.0110980	+	0.999938i	$0.496467\pi$
$798$	−67902.8	−3.01219
$799$	−6123.91	−0.271150
$800$	13923.6	0.615340
$801$	−4341.48	−0.191509
$802$	−31080.3	−1.36843
$803$	−2216.24	−0.0973965
$804$	−7046.32	−0.309085
$805$	0	0
$806$	−8164.32	−0.356794
$807$	45173.7	1.97049
$808$	−32891.9	−1.43210
$809$	4401.92	0.191302	0.0956510	−	0.995415i	$-0.469507\pi$
$809$	4401.92	0.191302	0.0956510	+	0.995415i	$0.469507\pi$
$810$	−13328.3	−0.578157
$811$	−22761.6	−0.985535	−0.492767	−	0.870161i	$-0.664015\pi$
$811$	−22761.6	−0.985535	−0.492767	+	0.870161i	$0.664015\pi$
$812$	−15926.7	−0.688322
$813$	39278.7	1.69442
$814$	22181.3	0.955102
$815$	2216.23	0.0952531
$816$	−25553.6	−1.09627
$817$	−36953.9	−1.58244
$818$	−20584.7	−0.879863
$819$	−19798.0	−0.844686
$820$	−30054.6	−1.27994
$821$	−1327.81	−0.0564446	−0.0282223	−	0.999602i	$-0.508985\pi$
$821$	−1327.81	−0.0564446	−0.0282223	+	0.999602i	$0.508985\pi$
$822$	71365.5	3.02817
$823$	17466.7	0.739794	0.369897	−	0.929073i	$-0.379393\pi$
$823$	17466.7	0.739794	0.369897	+	0.929073i	$0.379393\pi$
$824$	40905.7	1.72939
$825$	−7746.93	−0.326925
$826$	82498.6	3.47517
$827$	−22186.9	−0.932907	−0.466454	−	0.884546i	$-0.654469\pi$
$827$	−22186.9	−0.932907	−0.466454	+	0.884546i	$0.654469\pi$
$828$	0	0
$829$	−15342.3	−0.642776	−0.321388	−	0.946948i	$-0.604149\pi$
$829$	−15342.3	−0.642776	−0.321388	+	0.946948i	$0.604149\pi$
$830$	13968.7	0.584169
$831$	54369.6	2.26963
$832$	1402.77	0.0584521
$833$	3696.07	0.153735
$834$	49832.0	2.06899
$835$	−15987.8	−0.662611
$836$	12146.2	0.502494
$837$	18320.8	0.756582
$838$	−70970.4	−2.92558
$839$	−4921.91	−0.202531	−0.101265	−	0.994859i	$-0.532289\pi$
$839$	−4921.91	−0.202531	−0.101265	+	0.994859i	$0.532289\pi$
$840$	56833.8	2.33447
$841$	−22712.0	−0.931241
$842$	47405.4	1.94026
$843$	27494.2	1.12331
$844$	−65005.8	−2.65118
$845$	−11192.9	−0.455676
$846$	58313.5	2.36981
$847$	−27058.1	−1.09767
$848$	−40430.9	−1.63727
$849$	−58106.3	−2.34888
$850$	12134.5	0.489658
$851$	0	0
$852$	−27835.4	−1.11928
$853$	−16030.9	−0.643478	−0.321739	−	0.946828i	$-0.604267\pi$
$853$	−16030.9	−0.643478	−0.321739	+	0.946828i	$0.604267\pi$
$854$	−58455.5	−2.34228
$855$	−20838.5	−0.833523
$856$	39782.1	1.58846
$857$	−20059.2	−0.799544	−0.399772	−	0.916615i	$-0.630911\pi$
$857$	−20059.2	−0.799544	−0.399772	+	0.916615i	$0.630911\pi$
$858$	7899.87	0.314332
$859$	−37544.3	−1.49126	−0.745631	−	0.666359i	$-0.767852\pi$
$859$	−37544.3	−1.49126	−0.745631	+	0.666359i	$0.767852\pi$
$860$	56354.0	2.23448
$861$	54718.9	2.16587
$862$	5275.14	0.208436
$863$	41927.6	1.65380	0.826901	−	0.562347i	$-0.190101\pi$
$863$	41927.6	1.65380	0.826901	+	0.562347i	$0.190101\pi$
$864$	31861.4	1.25457
$865$	−1406.19	−0.0552740
$866$	52573.0	2.06294
$867$	36882.9	1.44476
$868$	−34852.4	−1.36286
$869$	−594.601	−0.0232111
$870$	−10903.1	−0.424886
$871$	−811.944	−0.0315863
$872$	−69089.6	−2.68311
$873$	31245.8	1.21135
$874$	0	0
$875$	−28072.1	−1.08458
$876$	−35016.3	−1.35056
$877$	40008.5	1.54047	0.770235	−	0.637760i	$-0.220139\pi$
$877$	40008.5	1.54047	0.770235	+	0.637760i	$0.220139\pi$
$878$	59420.1	2.28398
$879$	31214.5	1.19777
$880$	−6396.20	−0.245018
$881$	7729.05	0.295571	0.147786	−	0.989019i	$-0.452785\pi$
$881$	7729.05	0.295571	0.147786	+	0.989019i	$0.452785\pi$
$882$	−35195.0	−1.34362
$883$	−28093.5	−1.07069	−0.535346	−	0.844633i	$-0.679819\pi$
$883$	−28093.5	−1.07069	−0.535346	+	0.844633i	$0.679819\pi$
$884$	−8527.06	−0.324430
$885$	38918.8	1.47824
$886$	−23630.4	−0.896026
$887$	28627.9	1.08369	0.541843	−	0.840480i	$-0.317727\pi$
$887$	28627.9	1.08369	0.541843	+	0.840480i	$0.317727\pi$
$888$	192351.	7.26901
$889$	6354.18	0.239722
$890$	2616.57	0.0985480
$891$	−4340.63	−0.163206
$892$	34490.5	1.29465
$893$	15881.4	0.595128
$894$	116473.	4.35731
$895$	17117.7	0.639310
$896$	36034.4	1.34356
$897$	0	0
$898$	16162.9	0.600626
$899$	3669.71	0.136142
$900$	−79625.0	−2.94907
$901$	−9969.53	−0.368627
$902$	−14203.7	−0.524315
$903$	−102601.	−3.78112
$904$	−4542.50	−0.167125
$905$	8353.12	0.306814
$906$	−95898.8	−3.51658
$907$	−304.419	−0.0111445	−0.00557225	−	0.999984i	$-0.501774\pi$
$907$	−304.419	−0.0111445	−0.00557225	+	0.999984i	$0.501774\pi$
$908$	−99277.6	−3.62846
$909$	33484.3	1.22179
$910$	11932.1	0.434664
$911$	8806.61	0.320281	0.160141	−	0.987094i	$-0.448805\pi$
$911$	8806.61	0.320281	0.160141	+	0.987094i	$0.448805\pi$
$912$	66269.1	2.40613
$913$	4549.20	0.164903
$914$	−33211.8	−1.20191
$915$	−27576.5	−0.996339
$916$	36524.0	1.31745
$917$	−35715.6	−1.28619
$918$	27767.4	0.998324
$919$	−35206.4	−1.26371	−0.631856	−	0.775086i	$-0.717706\pi$
$919$	−35206.4	−1.26371	−0.631856	+	0.775086i	$0.717706\pi$
$920$	0	0
$921$	49010.5	1.75347
$922$	−82915.7	−2.96169
$923$	−3207.46	−0.114382
$924$	33723.4	1.20067
$925$	−39601.7	−1.40767
$926$	−18333.9	−0.650635
$927$	−41642.4	−1.47542
$928$	6381.93	0.225751
$929$	4935.90	0.174318	0.0871591	−	0.996194i	$-0.472221\pi$
$929$	4935.90	0.174318	0.0871591	+	0.996194i	$0.472221\pi$
$930$	−23859.3	−0.841266
$931$	−9585.15	−0.337423
$932$	45838.6	1.61104
$933$	31886.8	1.11889
$934$	−97884.4	−3.42920
$935$	−1577.19	−0.0551653
$936$	44565.0	1.55625
$937$	−39880.3	−1.39043	−0.695214	−	0.718803i	$-0.744691\pi$
$937$	−39880.3	−1.39043	−0.695214	+	0.718803i	$0.744691\pi$
$938$	−5029.79	−0.175084
$939$	−24769.6	−0.860838
$940$	−24218.8	−0.840351
$941$	11194.0	0.387794	0.193897	−	0.981022i	$-0.437887\pi$
$941$	11194.0	0.387794	0.193897	+	0.981022i	$0.437887\pi$
$942$	3291.67	0.113852
$943$	0	0
$944$	−80513.8	−2.77596
$945$	−26775.7	−0.921706
$946$	26632.8	0.915335
$947$	−45511.6	−1.56170	−0.780849	−	0.624720i	$-0.785213\pi$
$947$	−45511.6	−1.56170	−0.780849	+	0.624720i	$0.785213\pi$
$948$	−9394.63	−0.321860
$949$	−4034.91	−0.138018
$950$	−31468.8	−1.07472
$951$	53581.0	1.82701
$952$	−28992.0	−0.987013
$953$	−1929.88	−0.0655982	−0.0327991	−	0.999462i	$-0.510442\pi$
$953$	−1929.88	−0.0655982	−0.0327991	+	0.999462i	$0.510442\pi$
$954$	94932.4	3.22175
$955$	−17583.9	−0.595812
$956$	65056.3	2.20091
$957$	−3550.84	−0.119940
$958$	65676.7	2.21494
$959$	35104.6	1.18205
$960$	4099.42	0.137821
$961$	−21760.6	−0.730442
$962$	40383.5	1.35345
$963$	−40498.5	−1.35519
$964$	−47465.1	−1.58584
$965$	−13508.3	−0.450620
$966$	0	0
$967$	−12637.5	−0.420264	−0.210132	−	0.977673i	$-0.567389\pi$
$967$	−12637.5	−0.420264	−0.210132	+	0.977673i	$0.567389\pi$
$968$	60907.4	2.02235
$969$	16340.8	0.541735
$970$	−18831.6	−0.623345
$971$	−938.353	−0.0310126	−0.0155063	−	0.999880i	$-0.504936\pi$
$971$	−938.353	−0.0310126	−0.0155063	+	0.999880i	$0.504936\pi$
$972$	29302.1	0.966939
$973$	24512.3	0.807635
$974$	34892.5	1.14787
$975$	−14104.2	−0.463276
$976$	57049.2	1.87100
$977$	−50467.6	−1.65261	−0.826306	−	0.563221i	$-0.809562\pi$
$977$	−50467.6	−1.65261	−0.826306	+	0.563221i	$0.809562\pi$
$978$	16548.6	0.541069
$979$	852.143	0.0278188
$980$	14617.2	0.476458
$981$	70333.8	2.28908
$982$	60800.0	1.97577
$983$	6973.78	0.226276	0.113138	−	0.993579i	$-0.463910\pi$
$983$	6973.78	0.226276	0.113138	+	0.993579i	$0.463910\pi$
$984$	−123172.	−3.99041
$985$	−3276.49	−0.105987
$986$	5561.89	0.179642
$987$	44094.0	1.42201
$988$	22113.5	0.712070
$989$	0	0
$990$	15018.4	0.482137
$991$	−13400.3	−0.429541	−0.214770	−	0.976665i	$-0.568900\pi$
$991$	−13400.3	−0.429541	−0.214770	+	0.976665i	$0.568900\pi$
$992$	13965.6	0.446983
$993$	−62351.0	−1.99260
$994$	−19869.4	−0.634023
$995$	−21103.1	−0.672374
$996$	71876.8	2.28665
$997$	37713.3	1.19799	0.598993	−	0.800754i	$-0.295568\pi$
$997$	37713.3	1.19799	0.598993	+	0.800754i	$0.295568\pi$
$998$	94978.3	3.01251
$999$	−90620.8	−2.86999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.2		25
23.11	odd	22		23.4.c.a.6.1	yes	50
23.21	odd	22		23.4.c.a.4.1	✓	50
23.22	odd	2		529.4.a.n.1.2		25
69.11	even	22		207.4.i.a.190.5		50
69.44	even	22		207.4.i.a.73.5		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.4.1	✓	50	23.21	odd	22
23.4.c.a.6.1	yes	50	23.11	odd	22
207.4.i.a.73.5		50	69.44	even	22
207.4.i.a.190.5		50	69.11	even	22
529.4.a.m.1.2		25	1.1	even	1	trivial
529.4.a.n.1.2		25	23.22	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-5.07272 q^{2} -8.78974 q^{3} +17.7325 q^{4} +5.97134 q^{5} +44.5879 q^{6} +21.9327 q^{7} -49.3704 q^{8} +50.2595 q^{9} -30.2909 q^{10} -9.86490 q^{11} -155.864 q^{12} -17.9602 q^{13} -111.259 q^{14} -52.4865 q^{15} +108.582 q^{16} +26.7743 q^{17} -254.952 q^{18} -69.4348 q^{19} +105.887 q^{20} -192.783 q^{21} +50.0419 q^{22} +433.953 q^{24} -89.3431 q^{25} +91.1069 q^{26} -204.445 q^{27} +388.923 q^{28} -40.9508 q^{29} +266.249 q^{30} -89.6126 q^{31} -155.844 q^{32} +86.7099 q^{33} -135.819 q^{34} +130.968 q^{35} +891.227 q^{36} +443.254 q^{37} +352.224 q^{38} +157.865 q^{39} -294.807 q^{40} -283.837 q^{41} +977.935 q^{42} +532.210 q^{43} -174.929 q^{44} +300.116 q^{45} -228.723 q^{47} -954.408 q^{48} +138.045 q^{49} +453.213 q^{50} -235.339 q^{51} -318.479 q^{52} -372.354 q^{53} +1037.09 q^{54} -58.9066 q^{55} -1082.83 q^{56} +610.314 q^{57} +207.732 q^{58} -741.502 q^{59} -930.718 q^{60} +525.402 q^{61} +454.580 q^{62} +1102.33 q^{63} -78.1043 q^{64} -107.246 q^{65} -439.855 q^{66} +45.2081 q^{67} +474.777 q^{68} -664.364 q^{70} +178.587 q^{71} -2481.33 q^{72} +224.659 q^{73} -2248.50 q^{74} +785.302 q^{75} -1231.25 q^{76} -216.364 q^{77} -800.806 q^{78} +60.2745 q^{79} +648.380 q^{80} +440.008 q^{81} +1439.82 q^{82} -461.150 q^{83} -3418.53 q^{84} +159.879 q^{85} -2699.75 q^{86} +359.947 q^{87} +487.034 q^{88} -86.3813 q^{89} -1522.41 q^{90} -393.916 q^{91} +787.671 q^{93} +1160.25 q^{94} -414.619 q^{95} +1369.83 q^{96} +621.689 q^{97} -700.265 q^{98} -495.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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