LMFDB - Embedded newform 2445.4.a.g.1.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2445,4,Mod(1,2445)] 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("2445.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 2445 = 3 \cdot 5 \cdot 163 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [42,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$144.259669964$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	2445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.45575 q^{2} +3.00000 q^{3} +3.94219 q^{4} -5.00000 q^{5} +10.3672 q^{6} +5.05754 q^{7} -14.0228 q^{8} +9.00000 q^{9} -17.2787 q^{10} -39.7102 q^{11} +11.8266 q^{12} -4.79738 q^{13} +17.4776 q^{14} -15.0000 q^{15} -79.9967 q^{16} -1.66569 q^{17} +31.1017 q^{18} +93.2413 q^{19} -19.7109 q^{20} +15.1726 q^{21} -137.228 q^{22} +103.349 q^{23} -42.0683 q^{24} +25.0000 q^{25} -16.5785 q^{26} +27.0000 q^{27} +19.9378 q^{28} -64.4981 q^{29} -51.8362 q^{30} +21.1089 q^{31} -164.266 q^{32} -119.131 q^{33} -5.75620 q^{34} -25.2877 q^{35} +35.4797 q^{36} +157.112 q^{37} +322.218 q^{38} -14.3921 q^{39} +70.1139 q^{40} -167.680 q^{41} +52.4328 q^{42} +171.593 q^{43} -156.545 q^{44} -45.0000 q^{45} +357.147 q^{46} +426.717 q^{47} -239.990 q^{48} -317.421 q^{49} +86.3937 q^{50} -4.99707 q^{51} -18.9122 q^{52} +194.321 q^{53} +93.3052 q^{54} +198.551 q^{55} -70.9208 q^{56} +279.724 q^{57} -222.889 q^{58} +546.642 q^{59} -59.1328 q^{60} -525.698 q^{61} +72.9470 q^{62} +45.5179 q^{63} +72.3114 q^{64} +23.9869 q^{65} -411.685 q^{66} +329.339 q^{67} -6.56646 q^{68} +310.046 q^{69} -87.3880 q^{70} +54.5730 q^{71} -126.205 q^{72} +610.512 q^{73} +542.939 q^{74} +75.0000 q^{75} +367.575 q^{76} -200.836 q^{77} -49.7356 q^{78} -363.319 q^{79} +399.983 q^{80} +81.0000 q^{81} -579.459 q^{82} +70.0298 q^{83} +59.8134 q^{84} +8.32845 q^{85} +592.981 q^{86} -193.494 q^{87} +556.847 q^{88} +805.758 q^{89} -155.509 q^{90} -24.2629 q^{91} +407.419 q^{92} +63.3267 q^{93} +1474.62 q^{94} -466.206 q^{95} -492.798 q^{96} +1626.55 q^{97} -1096.93 q^{98} -357.392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 5 q^{2} + 126 q^{3} + 171 q^{4} - 210 q^{5} + 15 q^{6} - 25 q^{7} + 60 q^{8} + 378 q^{9} - 25 q^{10} + 181 q^{11} + 513 q^{12} + 40 q^{13} + 140 q^{14} - 630 q^{15} + 795 q^{16} + 313 q^{17} + 45 q^{18}+ \cdots + 1629 q^{99}+O(q^{100}) $ 42 * q + 5 * q^2 + 126 * q^3 + 171 * q^4 - 210 * q^5 + 15 * q^6 - 25 * q^7 + 60 * q^8 + 378 * q^9 - 25 * q^10 + 181 * q^11 + 513 * q^12 + 40 * q^13 + 140 * q^14 - 630 * q^15 + 795 * q^16 + 313 * q^17 + 45 * q^18 + 149 * q^19 - 855 * q^20 - 75 * q^21 - 137 * q^22 + 165 * q^23 + 180 * q^24 + 1050 * q^25 + 556 * q^26 + 1134 * q^27 - 31 * q^28 + 691 * q^29 - 75 * q^30 - 114 * q^31 + 710 * q^32 + 543 * q^33 + 69 * q^34 + 125 * q^35 + 1539 * q^36 - 136 * q^37 + 694 * q^38 + 120 * q^39 - 300 * q^40 + 1899 * q^41 + 420 * q^42 + 249 * q^43 + 1850 * q^44 - 1890 * q^45 + 1071 * q^46 + 534 * q^47 + 2385 * q^48 + 2569 * q^49 + 125 * q^50 + 939 * q^51 + 332 * q^52 + 1579 * q^53 + 135 * q^54 - 905 * q^55 + 5138 * q^56 + 447 * q^57 + 478 * q^58 + 2855 * q^59 - 2565 * q^60 - 576 * q^61 + 1851 * q^62 - 225 * q^63 + 3396 * q^64 - 200 * q^65 - 411 * q^66 + 844 * q^67 + 5024 * q^68 + 495 * q^69 - 700 * q^70 + 3751 * q^71 + 540 * q^72 + 1649 * q^73 + 2702 * q^74 + 3150 * q^75 + 724 * q^76 + 3538 * q^77 + 1668 * q^78 + 766 * q^79 - 3975 * q^80 + 3402 * q^81 + 1416 * q^82 + 3283 * q^83 - 93 * q^84 - 1565 * q^85 + 6489 * q^86 + 2073 * q^87 - 2239 * q^88 + 2584 * q^89 - 225 * q^90 + 1564 * q^91 + 3940 * q^92 - 342 * q^93 + 1579 * q^94 - 745 * q^95 + 2130 * q^96 + 1040 * q^97 + 5971 * q^98 + 1629 * 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 $

$2$	3.45575	1.22179	0.610896	−	0.791711i	$-0.290810\pi$
$2$	3.45575	1.22179	0.610896	+	0.791711i	$0.290810\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	3.94219	0.492773
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	10.3672	0.705401
$7$	5.05754	0.273082	0.136541	−	0.990634i	$-0.456402\pi$
$7$	5.05754	0.273082	0.136541	+	0.990634i	$0.456402\pi$
$8$	−14.0228	−0.619725
$9$	9.00000	0.333333
$10$	−17.2787	−0.546402
$11$	−39.7102	−1.08846	−0.544231	−	0.838935i	$-0.683178\pi$
$11$	−39.7102	−1.08846	−0.544231	+	0.838935i	$0.683178\pi$
$12$	11.8266	0.284503
$13$	−4.79738	−0.102350	−0.0511751	−	0.998690i	$-0.516297\pi$
$13$	−4.79738	−0.102350	−0.0511751	+	0.998690i	$0.516297\pi$
$14$	17.4776	0.333649
$15$	−15.0000	−0.258199
$16$	−79.9967	−1.24995
$17$	−1.66569	−0.0237641	−0.0118820	−	0.999929i	$-0.503782\pi$
$17$	−1.66569	−0.0237641	−0.0118820	+	0.999929i	$0.503782\pi$
$18$	31.1017	0.407264
$19$	93.2413	1.12584	0.562921	−	0.826510i	$-0.309677\pi$
$19$	93.2413	1.12584	0.562921	+	0.826510i	$0.309677\pi$
$20$	−19.7109	−0.220375
$21$	15.1726	0.157664
$22$	−137.228	−1.32987
$23$	103.349	0.936942	0.468471	−	0.883479i	$-0.344805\pi$
$23$	103.349	0.936942	0.468471	+	0.883479i	$0.344805\pi$
$24$	−42.0683	−0.357798
$25$	25.0000	0.200000
$26$	−16.5785	−0.125051
$27$	27.0000	0.192450
$28$	19.9378	0.134567
$29$	−64.4981	−0.413000	−0.206500	−	0.978447i	$-0.566207\pi$
$29$	−64.4981	−0.413000	−0.206500	+	0.978447i	$0.566207\pi$
$30$	−51.8362	−0.315465
$31$	21.1089	0.122299	0.0611495	−	0.998129i	$-0.480523\pi$
$31$	21.1089	0.122299	0.0611495	+	0.998129i	$0.480523\pi$
$32$	−164.266	−0.907450
$33$	−119.131	−0.628424
$34$	−5.75620	−0.0290347
$35$	−25.2877	−0.122126
$36$	35.4797	0.164258
$37$	157.112	0.698082	0.349041	−	0.937108i	$-0.386507\pi$
$37$	157.112	0.698082	0.349041	+	0.937108i	$0.386507\pi$
$38$	322.218	1.37554
$39$	−14.3921	−0.0590919
$40$	70.1139	0.277149
$41$	−167.680	−0.638712	−0.319356	−	0.947635i	$-0.603467\pi$
$41$	−167.680	−0.638712	−0.319356	+	0.947635i	$0.603467\pi$
$42$	52.4328	0.192632
$43$	171.593	0.608550	0.304275	−	0.952584i	$-0.401586\pi$
$43$	171.593	0.608550	0.304275	+	0.952584i	$0.401586\pi$
$44$	−156.545	−0.536365
$45$	−45.0000	−0.149071
$46$	357.147	1.14475
$47$	426.717	1.32432	0.662160	−	0.749363i	$-0.269640\pi$
$47$	426.717	1.32432	0.662160	+	0.749363i	$0.269640\pi$
$48$	−239.990	−0.721658
$49$	−317.421	−0.925426
$50$	86.3937	0.244358
$51$	−4.99707	−0.0137202
$52$	−18.9122	−0.0504355
$53$	194.321	0.503622	0.251811	−	0.967776i	$-0.418974\pi$
$53$	194.321	0.503622	0.251811	+	0.967776i	$0.418974\pi$
$54$	93.3052	0.235134
$55$	198.551	0.486775
$56$	−70.9208	−0.169236
$57$	279.724	0.650006
$58$	−222.889	−0.504600
$59$	546.642	1.20622	0.603108	−	0.797659i	$-0.293929\pi$
$59$	546.642	1.20622	0.603108	+	0.797659i	$0.293929\pi$
$60$	−59.1328	−0.127234
$61$	−525.698	−1.10342	−0.551711	−	0.834035i	$-0.686025\pi$
$61$	−525.698	−1.10342	−0.551711	+	0.834035i	$0.686025\pi$
$62$	72.9470	0.149424
$63$	45.5179	0.0910272
$64$	72.3114	0.141233
$65$	23.9869	0.0457724
$66$	−411.685	−0.767803
$67$	329.339	0.600525	0.300262	−	0.953857i	$-0.402926\pi$
$67$	329.339	0.600525	0.300262	+	0.953857i	$0.402926\pi$
$68$	−6.56646	−0.0117103
$69$	310.046	0.540944
$70$	−87.3880	−0.149212
$71$	54.5730	0.0912200	0.0456100	−	0.998959i	$-0.485477\pi$
$71$	54.5730	0.0912200	0.0456100	+	0.998959i	$0.485477\pi$
$72$	−126.205	−0.206575
$73$	610.512	0.978836	0.489418	−	0.872049i	$-0.337209\pi$
$73$	610.512	0.978836	0.489418	+	0.872049i	$0.337209\pi$
$74$	542.939	0.852910
$75$	75.0000	0.115470
$76$	367.575	0.554786
$77$	−200.836	−0.297239
$78$	−49.7356	−0.0721980
$79$	−363.319	−0.517425	−0.258713	−	0.965954i	$-0.583298\pi$
$79$	−363.319	−0.517425	−0.258713	+	0.965954i	$0.583298\pi$
$80$	399.983	0.558994
$81$	81.0000	0.111111
$82$	−579.459	−0.780373
$83$	70.0298	0.0926117	0.0463058	−	0.998927i	$-0.485255\pi$
$83$	70.0298	0.0926117	0.0463058	+	0.998927i	$0.485255\pi$
$84$	59.8134	0.0776925
$85$	8.32845	0.0106276
$86$	592.981	0.743521
$87$	−193.494	−0.238446
$88$	556.847	0.674547
$89$	805.758	0.959665	0.479833	−	0.877360i	$-0.340697\pi$
$89$	805.758	0.959665	0.479833	+	0.877360i	$0.340697\pi$
$90$	−155.509	−0.182134
$91$	−24.2629	−0.0279500
$92$	407.419	0.461700
$93$	63.3267	0.0706094
$94$	1474.62	1.61804
$95$	−466.206	−0.503492
$96$	−492.798	−0.523917
$97$	1626.55	1.70259	0.851293	−	0.524691i	$-0.175819\pi$
$97$	1626.55	1.70259	0.851293	+	0.524691i	$0.175819\pi$
$98$	−1096.93	−1.13068
$99$	−357.392	−0.362821
$100$	98.5547	0.0985547
$101$	−424.421	−0.418133	−0.209067	−	0.977901i	$-0.567043\pi$
$101$	−424.421	−0.418133	−0.209067	+	0.977901i	$0.567043\pi$
$102$	−17.2686	−0.0167632
$103$	650.504	0.622292	0.311146	−	0.950362i	$-0.399287\pi$
$103$	650.504	0.622292	0.311146	+	0.950362i	$0.399287\pi$
$104$	67.2725	0.0634290
$105$	−75.8632	−0.0705094
$106$	671.523	0.615321
$107$	524.747	0.474105	0.237052	−	0.971497i	$-0.423819\pi$
$107$	524.747	0.474105	0.237052	+	0.971497i	$0.423819\pi$
$108$	106.439	0.0948343
$109$	1807.19	1.58805	0.794025	−	0.607885i	$-0.207982\pi$
$109$	1807.19	1.58805	0.794025	+	0.607885i	$0.207982\pi$
$110$	686.142	0.594737
$111$	471.335	0.403038
$112$	−404.587	−0.341338
$113$	1832.50	1.52555	0.762774	−	0.646665i	$-0.223837\pi$
$113$	1832.50	1.52555	0.762774	+	0.646665i	$0.223837\pi$
$114$	966.655	0.794171
$115$	−516.743	−0.419013
$116$	−254.264	−0.203515
$117$	−43.1764	−0.0341167
$118$	1889.06	1.47374
$119$	−8.42430	−0.00648953
$120$	210.342	0.160012
$121$	245.902	0.184750
$122$	−1816.68	−1.34815
$123$	−503.040	−0.368761
$124$	83.2152	0.0602657
$125$	−125.000	−0.0894427
$126$	157.298	0.111216
$127$	−1747.84	−1.22123	−0.610613	−	0.791929i	$-0.709077\pi$
$127$	−1747.84	−1.22123	−0.610613	+	0.791929i	$0.709077\pi$
$128$	1564.02	1.08001
$129$	514.778	0.351347
$130$	82.8926	0.0559243
$131$	876.555	0.584618	0.292309	−	0.956324i	$-0.405576\pi$
$131$	876.555	0.584618	0.292309	+	0.956324i	$0.405576\pi$
$132$	−469.635	−0.309671
$133$	471.572	0.307447
$134$	1138.11	0.733716
$135$	−135.000	−0.0860663
$136$	23.3576	0.0147272
$137$	2788.06	1.73869	0.869343	−	0.494209i	$-0.164542\pi$
$137$	2788.06	1.73869	0.869343	+	0.494209i	$0.164542\pi$
$138$	1071.44	0.660920
$139$	−1329.64	−0.811358	−0.405679	−	0.914016i	$-0.632965\pi$
$139$	−1329.64	−0.811358	−0.405679	+	0.914016i	$0.632965\pi$
$140$	−99.6889	−0.0601804
$141$	1280.15	0.764596
$142$	188.590	0.111452
$143$	190.505	0.111404
$144$	−719.970	−0.416649
$145$	322.491	0.184699
$146$	2109.78	1.19593
$147$	−952.264	−0.534295
$148$	619.364	0.343996
$149$	3550.10	1.95191	0.975957	−	0.217963i	$-0.0699413\pi$
$149$	3550.10	1.95191	0.975957	+	0.217963i	$0.0699413\pi$
$150$	259.181	0.141080
$151$	−3610.91	−1.94604	−0.973019	−	0.230723i	$-0.925891\pi$
$151$	−3610.91	−1.94604	−0.973019	+	0.230723i	$0.925891\pi$
$152$	−1307.50	−0.697713
$153$	−14.9912	−0.00792136
$154$	−694.039	−0.363164
$155$	−105.544	−0.0546938
$156$	−56.7365	−0.0291189
$157$	−1879.17	−0.955247	−0.477623	−	0.878565i	$-0.658502\pi$
$157$	−1879.17	−0.955247	−0.477623	+	0.878565i	$0.658502\pi$
$158$	−1255.54	−0.632186
$159$	582.962	0.290766
$160$	821.330	0.405824
$161$	522.690	0.255862
$162$	279.916	0.135755
$163$	163.000	0.0783260
$163$	163.000	0.0783260
$164$	−661.025	−0.314740
$165$	595.653	0.281040
$166$	242.005	0.113152
$167$	−1252.77	−0.580494	−0.290247	−	0.956952i	$-0.593737\pi$
$167$	−1252.77	−0.580494	−0.290247	+	0.956952i	$0.593737\pi$
$168$	−212.762	−0.0977082
$169$	−2173.99	−0.989524
$170$	28.7810	0.0129847
$171$	839.172	0.375281
$172$	676.451	0.299877
$173$	2664.50	1.17097	0.585486	−	0.810682i	$-0.300904\pi$
$173$	2664.50	1.17097	0.585486	+	0.810682i	$0.300904\pi$
$174$	−668.668	−0.291331
$175$	126.439	0.0546163
$176$	3176.68	1.36052
$177$	1639.93	0.696409
$178$	2784.50	1.17251
$179$	−2516.43	−1.05076	−0.525382	−	0.850867i	$-0.676077\pi$
$179$	−2516.43	−1.05076	−0.525382	+	0.850867i	$0.676077\pi$
$180$	−177.398	−0.0734583
$181$	−203.418	−0.0835355	−0.0417678	−	0.999127i	$-0.513299\pi$
$181$	−203.418	−0.0835355	−0.0417678	+	0.999127i	$0.513299\pi$
$182$	−83.8466	−0.0341490
$183$	−1577.09	−0.637061
$184$	−1449.23	−0.580646
$185$	−785.559	−0.312192
$186$	218.841	0.0862699
$187$	66.1449	0.0258663
$188$	1682.20	0.652589
$189$	136.554	0.0525546
$190$	−1611.09	−0.615162
$191$	−1873.39	−0.709706	−0.354853	−	0.934922i	$-0.615469\pi$
$191$	−1873.39	−0.709706	−0.354853	+	0.934922i	$0.615469\pi$
$192$	216.934	0.0815411
$193$	−28.4368	−0.0106058	−0.00530291	−	0.999986i	$-0.501688\pi$
$193$	−28.4368	−0.0106058	−0.00530291	+	0.999986i	$0.501688\pi$
$194$	5620.93	2.08020
$195$	71.9606	0.0264267
$196$	−1251.33	−0.456026
$197$	−964.825	−0.348939	−0.174469	−	0.984663i	$-0.555821\pi$
$197$	−964.825	−0.348939	−0.174469	+	0.984663i	$0.555821\pi$
$198$	−1235.06	−0.443291
$199$	2049.39	0.730039	0.365019	−	0.931000i	$-0.381062\pi$
$199$	2049.39	0.730039	0.365019	+	0.931000i	$0.381062\pi$
$200$	−350.569	−0.123945
$201$	988.017	0.346713
$202$	−1466.69	−0.510871
$203$	−326.202	−0.112783
$204$	−19.6994	−0.00676095
$205$	838.399	0.285641
$206$	2247.98	0.760311
$207$	930.137	0.312314
$208$	383.774	0.127932
$209$	−3702.63	−1.22544
$210$	−262.164	−0.0861477
$211$	80.2293	0.0261763	0.0130882	−	0.999914i	$-0.495834\pi$
$211$	80.2293	0.0261763	0.0130882	+	0.999914i	$0.495834\pi$
$212$	766.048	0.248172
$213$	163.719	0.0526659
$214$	1813.39	0.579257
$215$	−857.964	−0.272152
$216$	−378.615	−0.119266
$217$	106.759	0.0333976
$218$	6245.19	1.94027
$219$	1831.54	0.565131
$220$	782.726	0.239870
$221$	7.99094	0.00243226
$222$	1628.82	0.492428
$223$	5273.84	1.58369	0.791844	−	0.610723i	$-0.209121\pi$
$223$	5273.84	1.58369	0.791844	+	0.610723i	$0.209121\pi$
$224$	−830.783	−0.247808
$225$	225.000	0.0666667
$226$	6332.65	1.86390
$227$	2002.93	0.585635	0.292817	−	0.956168i	$-0.405407\pi$
$227$	2002.93	0.585635	0.292817	+	0.956168i	$0.405407\pi$
$228$	1102.72	0.320306
$229$	−5030.13	−1.45153	−0.725765	−	0.687942i	$-0.758514\pi$
$229$	−5030.13	−1.45153	−0.725765	+	0.687942i	$0.758514\pi$
$230$	−1785.73	−0.511947
$231$	−602.509	−0.171611
$232$	904.443	0.255946
$233$	−2903.99	−0.816510	−0.408255	−	0.912868i	$-0.633863\pi$
$233$	−2903.99	−0.816510	−0.408255	+	0.912868i	$0.633863\pi$
$234$	−149.207	−0.0416835
$235$	−2133.58	−0.592254
$236$	2154.97	0.594391
$237$	−1089.96	−0.298736
$238$	−29.1122	−0.00792885
$239$	−3077.16	−0.832824	−0.416412	−	0.909176i	$-0.636713\pi$
$239$	−3077.16	−0.832824	−0.416412	+	0.909176i	$0.636713\pi$
$240$	1199.95	0.322735
$241$	−831.606	−0.222276	−0.111138	−	0.993805i	$-0.535450\pi$
$241$	−831.606	−0.222276	−0.111138	+	0.993805i	$0.535450\pi$
$242$	849.774	0.225725
$243$	243.000	0.0641500
$244$	−2072.40	−0.543737
$245$	1587.11	0.413863
$246$	−1738.38	−0.450548
$247$	−447.314	−0.115230
$248$	−296.005	−0.0757917
$249$	210.089	0.0534694
$250$	−431.968	−0.109280
$251$	5220.97	1.31293	0.656464	−	0.754357i	$-0.272051\pi$
$251$	5220.97	1.31293	0.656464	+	0.754357i	$0.272051\pi$
$252$	179.440	0.0448558
$253$	−4103.99	−1.01983
$254$	−6040.09	−1.49208
$255$	24.9854	0.00613586
$256$	4826.36	1.17831
$257$	554.869	0.134676	0.0673381	−	0.997730i	$-0.478549\pi$
$257$	554.869	0.134676	0.0673381	+	0.997730i	$0.478549\pi$
$258$	1778.94	0.429272
$259$	794.600	0.190633
$260$	94.5608	0.0225554
$261$	−580.483	−0.137667
$262$	3029.15	0.714281
$263$	7740.74	1.81488	0.907442	−	0.420177i	$-0.138032\pi$
$263$	7740.74	1.81488	0.907442	+	0.420177i	$0.138032\pi$
$264$	1670.54	0.389450
$265$	−971.603	−0.225227
$266$	1629.63	0.375636
$267$	2417.27	0.554063
$268$	1298.32	0.295923
$269$	2732.03	0.619237	0.309618	−	0.950861i	$-0.399799\pi$
$269$	2732.03	0.619237	0.309618	+	0.950861i	$0.399799\pi$
$270$	−466.526	−0.105155
$271$	−4065.61	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$271$	−4065.61	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$272$	133.250	0.0297038
$273$	−72.7888	−0.0161369
$274$	9634.83	2.12431
$275$	−992.756	−0.217692
$276$	1222.26	0.266563
$277$	625.777	0.135738	0.0678688	−	0.997694i	$-0.478380\pi$
$277$	625.777	0.135738	0.0678688	+	0.997694i	$0.478380\pi$
$278$	−4594.90	−0.991309
$279$	189.980	0.0407663
$280$	354.604	0.0756844
$281$	8366.41	1.77615	0.888075	−	0.459698i	$-0.152042\pi$
$281$	8366.41	1.77615	0.888075	+	0.459698i	$0.152042\pi$
$282$	4423.87	0.934177
$283$	−4506.46	−0.946578	−0.473289	−	0.880907i	$-0.656933\pi$
$283$	−4506.46	−0.946578	−0.473289	+	0.880907i	$0.656933\pi$
$284$	215.137	0.0449508
$285$	−1398.62	−0.290691
$286$	658.337	0.136113
$287$	−848.048	−0.174421
$288$	−1478.39	−0.302483
$289$	−4910.23	−0.999435
$290$	1114.45	0.225664
$291$	4879.64	0.982988
$292$	2406.75	0.482344
$293$	−6252.94	−1.24676	−0.623380	−	0.781919i	$-0.714241\pi$
$293$	−6252.94	−1.24676	−0.623380	+	0.781919i	$0.714241\pi$
$294$	−3290.78	−0.652797
$295$	−2733.21	−0.539436
$296$	−2203.14	−0.432619
$297$	−1072.18	−0.209475
$298$	12268.2	2.38483
$299$	−495.802	−0.0958962
$300$	295.664	0.0569006
$301$	867.838	0.166184
$302$	−12478.4	−2.37765
$303$	−1273.26	−0.241409
$304$	−7458.99	−1.40724
$305$	2628.49	0.493465
$306$	−51.8058	−0.00967824
$307$	5355.15	0.995553	0.497777	−	0.867305i	$-0.334150\pi$
$307$	5355.15	0.995553	0.497777	+	0.867305i	$0.334150\pi$
$308$	−791.734	−0.146471
$309$	1951.51	0.359281
$310$	−364.735	−0.0668244
$311$	1464.15	0.266960	0.133480	−	0.991052i	$-0.457385\pi$
$311$	1464.15	0.266960	0.133480	+	0.991052i	$0.457385\pi$
$312$	201.818	0.0366207
$313$	−7485.47	−1.35177	−0.675885	−	0.737007i	$-0.736238\pi$
$313$	−7485.47	−1.35177	−0.675885	+	0.737007i	$0.736238\pi$
$314$	−6493.92	−1.16711
$315$	−227.589	−0.0407086
$316$	−1432.27	−0.254974
$317$	1791.50	0.317415	0.158707	−	0.987326i	$-0.449267\pi$
$317$	1791.50	0.317415	0.158707	+	0.987326i	$0.449267\pi$
$318$	2014.57	0.355256
$319$	2561.23	0.449535
$320$	−361.557	−0.0631614
$321$	1574.24	0.273725
$322$	1806.28	0.312610
$323$	−155.311	−0.0267546
$324$	319.317	0.0547526
$325$	−119.934	−0.0204700
$326$	563.287	0.0956981
$327$	5421.57	0.916861
$328$	2351.34	0.395826
$329$	2158.14	0.361647
$330$	2058.43	0.343372
$331$	−566.536	−0.0940775	−0.0470387	−	0.998893i	$-0.514978\pi$
$331$	−566.536	−0.0940775	−0.0470387	+	0.998893i	$0.514978\pi$
$332$	276.071	0.0456366
$333$	1414.01	0.232694
$334$	−4329.27	−0.709242
$335$	−1646.69	−0.268563
$336$	−1213.76	−0.197071
$337$	8347.20	1.34926	0.674631	−	0.738155i	$-0.264303\pi$
$337$	8347.20	1.34926	0.674631	+	0.738155i	$0.264303\pi$
$338$	−7512.74	−1.20899
$339$	5497.50	0.880776
$340$	32.8323	0.00523701
$341$	−838.239	−0.133118
$342$	2899.96	0.458515
$343$	−3340.11	−0.525799
$344$	−2406.21	−0.377134
$345$	−1550.23	−0.241917
$346$	9207.84	1.43068
$347$	−3482.93	−0.538828	−0.269414	−	0.963024i	$-0.586830\pi$
$347$	−3482.93	−0.538828	−0.269414	+	0.963024i	$0.586830\pi$
$348$	−762.791	−0.117500
$349$	9899.32	1.51833	0.759167	−	0.650896i	$-0.225607\pi$
$349$	9899.32	1.51833	0.759167	+	0.650896i	$0.225607\pi$
$350$	436.940	0.0667298
$351$	−129.529	−0.0196973
$352$	6523.04	0.987725
$353$	4750.85	0.716323	0.358162	−	0.933660i	$-0.383404\pi$
$353$	4750.85	0.716323	0.358162	+	0.933660i	$0.383404\pi$
$354$	5667.17	0.850867
$355$	−272.865	−0.0407948
$356$	3176.45	0.472897
$357$	−25.2729	−0.00374673
$358$	−8696.14	−1.28381
$359$	5469.75	0.804129	0.402065	−	0.915611i	$-0.368293\pi$
$359$	5469.75	0.804129	0.402065	+	0.915611i	$0.368293\pi$
$360$	631.025	0.0923831
$361$	1834.94	0.267522
$362$	−702.961	−0.102063
$363$	737.705	0.106665
$364$	−95.6491	−0.0137730
$365$	−3052.56	−0.437749
$366$	−5450.04	−0.778356
$367$	24.7226	0.00351637	0.00175819	−	0.999998i	$-0.499440\pi$
$367$	24.7226	0.00351637	0.00175819	+	0.999998i	$0.499440\pi$
$368$	−8267.54	−1.17113
$369$	−1509.12	−0.212904
$370$	−2714.69	−0.381433
$371$	982.785	0.137530
$372$	249.646	0.0347944
$373$	−3215.88	−0.446413	−0.223206	−	0.974771i	$-0.571652\pi$
$373$	−3215.88	−0.446413	−0.223206	+	0.974771i	$0.571652\pi$
$374$	228.580	0.0316032
$375$	−375.000	−0.0516398
$376$	−5983.75	−0.820714
$377$	309.422	0.0422706
$378$	471.895	0.0642107
$379$	6941.00	0.940727	0.470363	−	0.882473i	$-0.344123\pi$
$379$	6941.00	0.940727	0.470363	+	0.882473i	$0.344123\pi$
$380$	−1837.87	−0.248108
$381$	−5243.52	−0.705075
$382$	−6473.97	−0.867113
$383$	2663.53	0.355353	0.177676	−	0.984089i	$-0.443142\pi$
$383$	2663.53	0.355353	0.177676	+	0.984089i	$0.443142\pi$
$384$	4692.05	0.623543
$385$	1004.18	0.132929
$386$	−98.2702	−0.0129581
$387$	1544.34	0.202850
$388$	6412.15	0.838989
$389$	8971.22	1.16930	0.584652	−	0.811284i	$-0.301231\pi$
$389$	8971.22	1.16930	0.584652	+	0.811284i	$0.301231\pi$
$390$	248.678	0.0322879
$391$	−172.147	−0.0222656
$392$	4451.13	0.573510
$393$	2629.66	0.337529
$394$	−3334.19	−0.426330
$395$	1816.60	0.231400
$396$	−1408.91	−0.178788
$397$	−8043.32	−1.01683	−0.508417	−	0.861111i	$-0.669769\pi$
$397$	−8043.32	−1.01683	−0.508417	+	0.861111i	$0.669769\pi$
$398$	7082.19	0.891955
$399$	1414.72	0.177505
$400$	−1999.92	−0.249990
$401$	−3678.78	−0.458129	−0.229065	−	0.973411i	$-0.573567\pi$
$401$	−3678.78	−0.458129	−0.229065	+	0.973411i	$0.573567\pi$
$402$	3414.34	0.423611
$403$	−101.267	−0.0125173
$404$	−1673.15	−0.206045
$405$	−405.000	−0.0496904
$406$	−1127.27	−0.137797
$407$	−6238.94	−0.759835
$408$	70.0728	0.00850274
$409$	313.742	0.0379304	0.0189652	−	0.999820i	$-0.493963\pi$
$409$	313.742	0.0379304	0.0189652	+	0.999820i	$0.493963\pi$
$410$	2897.30	0.348993
$411$	8364.18	1.00383
$412$	2564.41	0.306649
$413$	2764.67	0.329396
$414$	3214.32	0.381582
$415$	−350.149	−0.0414172
$416$	788.046	0.0928777
$417$	−3988.92	−0.468437
$418$	−12795.4	−1.49723
$419$	−10405.4	−1.21322	−0.606609	−	0.795000i	$-0.707471\pi$
$419$	−10405.4	−1.21322	−0.606609	+	0.795000i	$0.707471\pi$
$420$	−299.067	−0.0347452
$421$	15510.0	1.79552	0.897760	−	0.440486i	$-0.145194\pi$
$421$	15510.0	1.79552	0.897760	+	0.440486i	$0.145194\pi$
$422$	277.252	0.0319820
$423$	3840.45	0.441440
$424$	−2724.91	−0.312107
$425$	−41.6423	−0.00475281
$426$	565.771	0.0643467
$427$	−2658.74	−0.301324
$428$	2068.65	0.233626
$429$	571.515	0.0643193
$430$	−2964.91	−0.332513
$431$	−8029.63	−0.897387	−0.448693	−	0.893686i	$-0.648110\pi$
$431$	−8029.63	−0.897387	−0.448693	+	0.893686i	$0.648110\pi$
$432$	−2159.91	−0.240553
$433$	4074.15	0.452173	0.226087	−	0.974107i	$-0.427407\pi$
$433$	4074.15	0.452173	0.226087	+	0.974107i	$0.427407\pi$
$434$	368.933	0.0408049
$435$	967.472	0.106636
$436$	7124.28	0.782549
$437$	9636.35	1.05485
$438$	6329.33	0.690472
$439$	−7805.44	−0.848595	−0.424298	−	0.905523i	$-0.639479\pi$
$439$	−7805.44	−0.848595	−0.424298	+	0.905523i	$0.639479\pi$
$440$	−2784.24	−0.301667
$441$	−2856.79	−0.308475
$442$	27.6147	0.00297171
$443$	4826.55	0.517644	0.258822	−	0.965925i	$-0.416666\pi$
$443$	4826.55	0.517644	0.258822	+	0.965925i	$0.416666\pi$
$444$	1858.09	0.198606
$445$	−4028.79	−0.429175
$446$	18225.1	1.93494
$447$	10650.3	1.12694
$448$	365.718	0.0385682
$449$	−16195.5	−1.70226	−0.851129	−	0.524957i	$-0.824081\pi$
$449$	−16195.5	−1.70226	−0.851129	+	0.524957i	$0.824081\pi$
$450$	777.543	0.0814527
$451$	6658.60	0.695214
$452$	7224.05	0.751750
$453$	−10832.7	−1.12355
$454$	6921.62	0.715523
$455$	121.315	0.0124996
$456$	−3922.50	−0.402825
$457$	3743.79	0.383210	0.191605	−	0.981472i	$-0.438631\pi$
$457$	3743.79	0.383210	0.191605	+	0.981472i	$0.438631\pi$
$458$	−17382.9	−1.77347
$459$	−44.9736	−0.00457340
$460$	−2037.10	−0.206479
$461$	−14767.4	−1.49195	−0.745973	−	0.665977i	$-0.768015\pi$
$461$	−14767.4	−1.49195	−0.745973	+	0.665977i	$0.768015\pi$
$462$	−2082.12	−0.209673
$463$	−485.082	−0.0486904	−0.0243452	−	0.999704i	$-0.507750\pi$
$463$	−485.082	−0.0486904	−0.0243452	+	0.999704i	$0.507750\pi$
$464$	5159.63	0.516229
$465$	−316.633	−0.0315775
$466$	−10035.5	−0.997605
$467$	−6613.96	−0.655370	−0.327685	−	0.944787i	$-0.606268\pi$
$467$	−6613.96	−0.655370	−0.327685	+	0.944787i	$0.606268\pi$
$468$	−170.209	−0.0168118
$469$	1665.65	0.163992
$470$	−7373.12	−0.723610
$471$	−5637.50	−0.551512
$472$	−7665.44	−0.747522
$473$	−6813.99	−0.662384
$474$	−3766.62	−0.364993
$475$	2331.03	0.225169
$476$	−33.2102	−0.00319787
$477$	1748.88	0.167874
$478$	−10633.9	−1.01754
$479$	−7863.36	−0.750075	−0.375038	−	0.927010i	$-0.622370\pi$
$479$	−7863.36	−0.750075	−0.375038	+	0.927010i	$0.622370\pi$
$480$	2463.99	0.234303
$481$	−753.724	−0.0714488
$482$	−2873.82	−0.271574
$483$	1568.07	0.147722
$484$	969.390	0.0910397
$485$	−8132.73	−0.761419
$486$	839.747	0.0783779
$487$	−3682.51	−0.342650	−0.171325	−	0.985215i	$-0.554805\pi$
$487$	−3682.51	−0.342650	−0.171325	+	0.985215i	$0.554805\pi$
$488$	7371.75	0.683818
$489$	489.000	0.0452216
$490$	5484.64	0.505654
$491$	−3128.47	−0.287548	−0.143774	−	0.989611i	$-0.545924\pi$
$491$	−3128.47	−0.287548	−0.143774	+	0.989611i	$0.545924\pi$
$492$	−1983.08	−0.181715
$493$	107.434	0.00981456
$494$	−1545.80	−0.140787
$495$	1786.96	0.162258
$496$	−1688.64	−0.152867
$497$	276.005	0.0249105
$498$	726.016	0.0653284
$499$	−6895.54	−0.618611	−0.309305	−	0.950963i	$-0.600096\pi$
$499$	−6895.54	−0.618611	−0.309305	+	0.950963i	$0.600096\pi$
$500$	−492.773	−0.0440750
$501$	−3758.32	−0.335148
$502$	18042.4	1.60412
$503$	19522.3	1.73053	0.865264	−	0.501317i	$-0.167151\pi$
$503$	19522.3	1.73053	0.865264	+	0.501317i	$0.167151\pi$
$504$	−638.287	−0.0564118
$505$	2122.10	0.186995
$506$	−14182.4	−1.24601
$507$	−6521.96	−0.571302
$508$	−6890.31	−0.601787
$509$	−10882.9	−0.947689	−0.473845	−	0.880608i	$-0.657134\pi$
$509$	−10882.9	−0.947689	−0.473845	+	0.880608i	$0.657134\pi$
$510$	86.3431	0.00749673
$511$	3087.69	0.267302
$512$	4166.53	0.359642
$513$	2517.51	0.216669
$514$	1917.49	0.164546
$515$	−3252.52	−0.278297
$516$	2029.35	0.173134
$517$	−16945.0	−1.44147
$518$	2745.94	0.232914
$519$	7993.50	0.676061
$520$	−336.363	−0.0283663
$521$	21739.2	1.82804	0.914021	−	0.405668i	$-0.132961\pi$
$521$	21739.2	1.82804	0.914021	+	0.405668i	$0.132961\pi$
$522$	−2006.00	−0.168200
$523$	−12176.1	−1.01802	−0.509011	−	0.860760i	$-0.669989\pi$
$523$	−12176.1	−1.01802	−0.509011	+	0.860760i	$0.669989\pi$
$524$	3455.54	0.288084
$525$	379.316	0.0315328
$526$	26750.0	2.21741
$527$	−35.1609	−0.00290632
$528$	9530.05	0.785497
$529$	−1486.07	−0.122140
$530$	−3357.61	−0.275180
$531$	4919.78	0.402072
$532$	1859.02	0.151502
$533$	804.423	0.0653723
$534$	8353.49	0.676949
$535$	−2623.74	−0.212026
$536$	−4618.25	−0.372160
$537$	−7549.28	−0.606658
$538$	9441.20	0.756578
$539$	12604.9	1.00729
$540$	−532.195	−0.0424112
$541$	19534.8	1.55243	0.776217	−	0.630465i	$-0.217136\pi$
$541$	19534.8	1.55243	0.776217	+	0.630465i	$0.217136\pi$
$542$	−14049.7	−1.11345
$543$	−610.254	−0.0482293
$544$	273.616	0.0215647
$545$	−9035.95	−0.710198
$546$	−251.540	−0.0197159
$547$	5564.31	0.434941	0.217470	−	0.976067i	$-0.430219\pi$
$547$	5564.31	0.434941	0.217470	+	0.976067i	$0.430219\pi$
$548$	10991.1	0.856778
$549$	−4731.28	−0.367807
$550$	−3430.71	−0.265975
$551$	−6013.89	−0.464973
$552$	−4347.70	−0.335236
$553$	−1837.50	−0.141299
$554$	2162.53	0.165843
$555$	−2356.68	−0.180244
$556$	−5241.70	−0.399815
$557$	14105.7	1.07303	0.536513	−	0.843892i	$-0.319741\pi$
$557$	14105.7	1.07303	0.536513	+	0.843892i	$0.319741\pi$
$558$	656.523	0.0498079
$559$	−823.195	−0.0622852
$560$	2022.93	0.152651
$561$	198.435	0.0149339
$562$	28912.2	2.17008
$563$	−12521.7	−0.937347	−0.468674	−	0.883371i	$-0.655268\pi$
$563$	−12521.7	−0.937347	−0.468674	+	0.883371i	$0.655268\pi$
$564$	5046.59	0.376773
$565$	−9162.49	−0.682246
$566$	−15573.2	−1.15652
$567$	409.661	0.0303424
$568$	−765.265	−0.0565313
$569$	3465.04	0.255294	0.127647	−	0.991820i	$-0.459258\pi$
$569$	3465.04	0.255294	0.127647	+	0.991820i	$0.459258\pi$
$570$	−4833.27	−0.355164
$571$	1268.82	0.0929920	0.0464960	−	0.998918i	$-0.485195\pi$
$571$	1268.82	0.0929920	0.0464960	+	0.998918i	$0.485195\pi$
$572$	751.006	0.0548971
$573$	−5620.18	−0.409749
$574$	−2930.64	−0.213105
$575$	2583.71	0.187388
$576$	650.803	0.0470778
$577$	−1991.07	−0.143656	−0.0718279	−	0.997417i	$-0.522883\pi$
$577$	−1991.07	−0.143656	−0.0718279	+	0.997417i	$0.522883\pi$
$578$	−16968.5	−1.22110
$579$	−85.3103	−0.00612327
$580$	1271.32	0.0910149
$581$	354.179	0.0252906
$582$	16862.8	1.20101
$583$	−7716.51	−0.548174
$584$	−8561.07	−0.606609
$585$	215.882	0.0152575
$586$	−21608.6	−1.52328
$587$	4204.42	0.295630	0.147815	−	0.989015i	$-0.452776\pi$
$587$	4204.42	0.295630	0.147815	+	0.989015i	$0.452776\pi$
$588$	−3754.00	−0.263286
$589$	1968.22	0.137689
$590$	−9445.29	−0.659078
$591$	−2894.48	−0.201460
$592$	−12568.4	−0.872566
$593$	−24996.6	−1.73101	−0.865504	−	0.500902i	$-0.833002\pi$
$593$	−24996.6	−1.73101	−0.865504	+	0.500902i	$0.833002\pi$
$594$	−3705.17	−0.255934
$595$	42.1215	0.00290221
$596$	13995.1	0.961851
$597$	6148.18	0.421488
$598$	−1713.37	−0.117165
$599$	−2100.97	−0.143311	−0.0716553	−	0.997429i	$-0.522828\pi$
$599$	−2100.97	−0.143311	−0.0716553	+	0.997429i	$0.522828\pi$
$600$	−1051.71	−0.0715597
$601$	−18958.3	−1.28673	−0.643366	−	0.765559i	$-0.722463\pi$
$601$	−18958.3	−1.28673	−0.643366	+	0.765559i	$0.722463\pi$
$602$	2999.03	0.203042
$603$	2964.05	0.200175
$604$	−14234.9	−0.958956
$605$	−1229.51	−0.0826225
$606$	−4400.07	−0.294952
$607$	28550.6	1.90911	0.954556	−	0.298030i	$-0.0963296\pi$
$607$	28550.6	1.90911	0.954556	+	0.298030i	$0.0963296\pi$
$608$	−15316.4	−1.02165
$609$	−978.606	−0.0651152
$610$	9083.40	0.602912
$611$	−2047.12	−0.135544
$612$	−59.0982	−0.00390343
$613$	28511.3	1.87856	0.939282	−	0.343146i	$-0.111492\pi$
$613$	28511.3	1.87856	0.939282	+	0.343146i	$0.111492\pi$
$614$	18506.1	1.21636
$615$	2515.20	0.164915
$616$	2816.28	0.184206
$617$	9761.70	0.636939	0.318469	−	0.947933i	$-0.396831\pi$
$617$	9761.70	0.636939	0.318469	+	0.947933i	$0.396831\pi$
$618$	6743.93	0.438966
$619$	−24419.0	−1.58560	−0.792798	−	0.609485i	$-0.791376\pi$
$619$	−24419.0	−1.58560	−0.792798	+	0.609485i	$0.791376\pi$
$620$	−416.076	−0.0269516
$621$	2790.41	0.180315
$622$	5059.74	0.326169
$623$	4075.16	0.262067
$624$	1151.32	0.0738618
$625$	625.000	0.0400000
$626$	−25867.9	−1.65158
$627$	−11107.9	−0.707507
$628$	−7408.02	−0.470720
$629$	−261.700	−0.0165893
$630$	−786.492	−0.0497374
$631$	−19549.2	−1.23335	−0.616673	−	0.787219i	$-0.711520\pi$
$631$	−19549.2	−1.23335	−0.616673	+	0.787219i	$0.711520\pi$
$632$	5094.74	0.320661
$633$	240.688	0.0151129
$634$	6190.96	0.387815
$635$	8739.19	0.546148
$636$	2298.14	0.143282
$637$	1522.79	0.0947176
$638$	8850.98	0.549238
$639$	491.157	0.0304067
$640$	−7820.09	−0.482994
$641$	−17044.3	−1.05025	−0.525125	−	0.851025i	$-0.675981\pi$
$641$	−17044.3	−1.05025	−0.525125	+	0.851025i	$0.675981\pi$
$642$	5440.18	0.334434
$643$	−21963.1	−1.34703	−0.673516	−	0.739173i	$-0.735217\pi$
$643$	−21963.1	−1.34703	−0.673516	+	0.739173i	$0.735217\pi$
$644$	2060.54	0.126082
$645$	−2573.89	−0.157127
$646$	−536.716	−0.0326885
$647$	−3713.44	−0.225642	−0.112821	−	0.993615i	$-0.535989\pi$
$647$	−3713.44	−0.225642	−0.112821	+	0.993615i	$0.535989\pi$
$648$	−1135.84	−0.0688583
$649$	−21707.3	−1.31292
$650$	−414.463	−0.0250101
$651$	320.277	0.0192821
$652$	642.577	0.0385970
$653$	11938.5	0.715450	0.357725	−	0.933827i	$-0.383553\pi$
$653$	11938.5	0.715450	0.357725	+	0.933827i	$0.383553\pi$
$654$	18735.6	1.12021
$655$	−4382.77	−0.261449
$656$	13413.8	0.798357
$657$	5494.61	0.326279
$658$	7457.98	0.441858
$659$	−7990.44	−0.472327	−0.236163	−	0.971713i	$-0.575890\pi$
$659$	−7990.44	−0.472327	−0.236163	+	0.971713i	$0.575890\pi$
$660$	2348.18	0.138489
$661$	−6833.44	−0.402103	−0.201051	−	0.979581i	$-0.564436\pi$
$661$	−6833.44	−0.402103	−0.201051	+	0.979581i	$0.564436\pi$
$662$	−1957.81	−0.114943
$663$	23.9728	0.00140426
$664$	−982.012	−0.0573938
$665$	−2357.86	−0.137495
$666$	4886.45	0.284303
$667$	−6665.79	−0.386957
$668$	−4938.66	−0.286052
$669$	15821.5	0.914343
$670$	−5690.56	−0.328128
$671$	20875.6	1.20103
$672$	−2492.35	−0.143072
$673$	31978.2	1.83161	0.915803	−	0.401628i	$-0.131556\pi$
$673$	31978.2	1.83161	0.915803	+	0.401628i	$0.131556\pi$
$674$	28845.8	1.64852
$675$	675.000	0.0384900
$676$	−8570.26	−0.487611
$677$	−15434.6	−0.876221	−0.438111	−	0.898921i	$-0.644352\pi$
$677$	−15434.6	−0.876221	−0.438111	+	0.898921i	$0.644352\pi$
$678$	18998.0	1.07612
$679$	8226.33	0.464945
$680$	−116.788	−0.00658620
$681$	6008.79	0.338116
$682$	−2896.74	−0.162642
$683$	−21124.4	−1.18346	−0.591729	−	0.806137i	$-0.701555\pi$
$683$	−21124.4	−1.18346	−0.591729	+	0.806137i	$0.701555\pi$
$684$	3308.17	0.184929
$685$	−13940.3	−0.777564
$686$	−11542.6	−0.642416
$687$	−15090.4	−0.838042
$688$	−13726.9	−0.760656
$689$	−932.229	−0.0515459
$690$	−5357.20	−0.295573
$691$	20242.8	1.11443	0.557217	−	0.830367i	$-0.311869\pi$
$691$	20242.8	1.11443	0.557217	+	0.830367i	$0.311869\pi$
$692$	10504.0	0.577024
$693$	−1807.53	−0.0990797
$694$	−12036.1	−0.658336
$695$	6648.21	0.362850
$696$	2713.33	0.147771
$697$	279.303	0.0151784
$698$	34209.5	1.85509
$699$	−8711.98	−0.471412
$700$	498.445	0.0269135
$701$	−16771.2	−0.903623	−0.451812	−	0.892113i	$-0.649222\pi$
$701$	−16771.2	−0.903623	−0.451812	+	0.892113i	$0.649222\pi$
$702$	−447.620	−0.0240660
$703$	14649.3	0.785930
$704$	−2871.50	−0.153727
$705$	−6400.75	−0.341938
$706$	16417.7	0.875197
$707$	−2146.53	−0.114184
$708$	6464.90	0.343172
$709$	2488.65	0.131824	0.0659119	−	0.997825i	$-0.479004\pi$
$709$	2488.65	0.131824	0.0659119	+	0.997825i	$0.479004\pi$
$710$	−942.952	−0.0498428
$711$	−3269.87	−0.172475
$712$	−11299.0	−0.594728
$713$	2181.57	0.114587
$714$	−87.3367	−0.00457772
$715$	−952.524	−0.0498215
$716$	−9920.23	−0.517788
$717$	−9231.48	−0.480831
$718$	18902.1	0.982478
$719$	−24156.8	−1.25299	−0.626493	−	0.779427i	$-0.715510\pi$
$719$	−24156.8	−1.25299	−0.626493	+	0.779427i	$0.715510\pi$
$720$	3599.85	0.186331
$721$	3289.95	0.169937
$722$	6341.08	0.326856
$723$	−2494.82	−0.128331
$724$	−801.911	−0.0411641
$725$	−1612.45	−0.0826000
$726$	2549.32	0.130323
$727$	455.105	0.0232172	0.0116086	−	0.999933i	$-0.496305\pi$
$727$	455.105	0.0232172	0.0116086	+	0.999933i	$0.496305\pi$
$728$	340.234	0.0173213
$729$	729.000	0.0370370
$730$	−10548.9	−0.534838
$731$	−285.820	−0.0144616
$732$	−6217.20	−0.313927
$733$	24282.9	1.22362	0.611808	−	0.791006i	$-0.290443\pi$
$733$	24282.9	1.22362	0.611808	+	0.791006i	$0.290443\pi$
$734$	85.4350	0.00429627
$735$	4761.32	0.238944
$736$	−16976.7	−0.850228
$737$	−13078.1	−0.653648
$738$	−5215.13	−0.260124
$739$	−26817.9	−1.33493	−0.667465	−	0.744641i	$-0.732621\pi$
$739$	−26817.9	−1.33493	−0.667465	+	0.744641i	$0.732621\pi$
$740$	−3096.82	−0.153840
$741$	−1341.94	−0.0665282
$742$	3396.26	0.168033
$743$	20051.7	0.990073	0.495036	−	0.868872i	$-0.335155\pi$
$743$	20051.7	0.990073	0.495036	+	0.868872i	$0.335155\pi$
$744$	−888.016	−0.0437584
$745$	−17750.5	−0.872922
$746$	−11113.3	−0.545423
$747$	630.268	0.0308706
$748$	260.756	0.0127462
$749$	2653.93	0.129469
$750$	−1295.91	−0.0630930
$751$	7373.45	0.358270	0.179135	−	0.983824i	$-0.442670\pi$
$751$	7373.45	0.358270	0.179135	+	0.983824i	$0.442670\pi$
$752$	−34135.9	−1.65533
$753$	15662.9	0.758019
$754$	1069.28	0.0516459
$755$	18054.6	0.870295
$756$	538.320	0.0258975
$757$	−8602.65	−0.413037	−0.206518	−	0.978443i	$-0.566213\pi$
$757$	−8602.65	−0.413037	−0.206518	+	0.978443i	$0.566213\pi$
$758$	23986.4	1.14937
$759$	−12312.0	−0.588797
$760$	6537.51	0.312027
$761$	40771.8	1.94215	0.971075	−	0.238773i	$-0.0767452\pi$
$761$	40771.8	1.94215	0.971075	+	0.238773i	$0.0767452\pi$
$762$	−18120.3	−0.861454
$763$	9139.95	0.433667
$764$	−7385.26	−0.349724
$765$	74.9561	0.00354254
$766$	9204.49	0.434167
$767$	−2622.45	−0.123456
$768$	14479.1	0.680298
$769$	17583.9	0.824569	0.412284	−	0.911055i	$-0.364731\pi$
$769$	17583.9	0.824569	0.412284	+	0.911055i	$0.364731\pi$
$770$	3470.19	0.162412
$771$	1664.61	0.0777553
$772$	−112.103	−0.00522626
$773$	13720.7	0.638419	0.319209	−	0.947684i	$-0.396583\pi$
$773$	13720.7	0.638419	0.319209	+	0.947684i	$0.396583\pi$
$774$	5336.83	0.247840
$775$	527.722	0.0244598
$776$	−22808.7	−1.05513
$777$	2383.80	0.110062
$778$	31002.3	1.42864
$779$	−15634.7	−0.719089
$780$	283.682	0.0130224
$781$	−2167.11	−0.0992895
$782$	−594.895	−0.0272039
$783$	−1741.45	−0.0794819
$784$	25392.6	1.15673
$785$	9395.83	0.427199
$786$	9087.46	0.412390
$787$	33640.8	1.52372	0.761859	−	0.647743i	$-0.224287\pi$
$787$	33640.8	1.52372	0.761859	+	0.647743i	$0.224287\pi$
$788$	−3803.52	−0.171948
$789$	23222.2	1.04782
$790$	6277.70	0.282722
$791$	9267.94	0.416599
$792$	5011.63	0.224849
$793$	2521.97	0.112936
$794$	−27795.7	−1.24236
$795$	−2914.81	−0.130035
$796$	8079.10	0.359744
$797$	1840.48	0.0817983	0.0408991	−	0.999163i	$-0.486978\pi$
$797$	1840.48	0.0817983	0.0408991	+	0.999163i	$0.486978\pi$
$798$	4888.90	0.216874
$799$	−710.778	−0.0314712
$800$	−4106.65	−0.181490
$801$	7251.82	0.319888
$802$	−12712.9	−0.559738
$803$	−24243.6	−1.06543
$804$	3894.95	0.170851
$805$	−2613.45	−0.114425
$806$	−349.954	−0.0152936
$807$	8196.08	0.357516
$808$	5951.56	0.259128
$809$	−3533.20	−0.153549	−0.0767743	−	0.997048i	$-0.524462\pi$
$809$	−3533.20	−0.153549	−0.0767743	+	0.997048i	$0.524462\pi$
$810$	−1399.58	−0.0607113
$811$	19110.4	0.827443	0.413721	−	0.910404i	$-0.364229\pi$
$811$	19110.4	0.827443	0.413721	+	0.910404i	$0.364229\pi$
$812$	−1285.95	−0.0555763
$813$	−12196.8	−0.526152
$814$	−21560.2	−0.928360
$815$	−815.000	−0.0350285
$816$	399.749	0.0171495
$817$	15999.5	0.685132
$818$	1084.21	0.0463431
$819$	−218.366	−0.00931666
$820$	3305.13	0.140756
$821$	1535.72	0.0652824	0.0326412	−	0.999467i	$-0.489608\pi$
$821$	1535.72	0.0652824	0.0326412	+	0.999467i	$0.489608\pi$
$822$	28904.5	1.22647
$823$	22577.8	0.956274	0.478137	−	0.878285i	$-0.341312\pi$
$823$	22577.8	0.956274	0.478137	+	0.878285i	$0.341312\pi$
$824$	−9121.87	−0.385650
$825$	−2978.27	−0.125685
$826$	9553.99	0.402453
$827$	25946.9	1.09101	0.545503	−	0.838109i	$-0.316339\pi$
$827$	25946.9	1.09101	0.545503	+	0.838109i	$0.316339\pi$
$828$	3666.78	0.153900
$829$	−41237.8	−1.72768	−0.863841	−	0.503764i	$-0.831948\pi$
$829$	−41237.8	−1.72768	−0.863841	+	0.503764i	$0.831948\pi$
$830$	−1210.03	−0.0506032
$831$	1877.33	0.0783681
$832$	−346.905	−0.0144553
$833$	528.725	0.0219919
$834$	−13784.7	−0.572333
$835$	6263.86	0.259605
$836$	−14596.5	−0.603863
$837$	569.940	0.0235365
$838$	−35958.5	−1.48230
$839$	33304.0	1.37042	0.685210	−	0.728345i	$-0.259710\pi$
$839$	33304.0	1.37042	0.685210	+	0.728345i	$0.259710\pi$
$840$	1063.81	0.0436964
$841$	−20229.0	−0.829431
$842$	53598.8	2.19375
$843$	25099.2	1.02546
$844$	316.279	0.0128990
$845$	10869.9	0.442529
$846$	13271.6	0.539347
$847$	1243.66	0.0504517
$848$	−15545.0	−0.629502
$849$	−13519.4	−0.546507
$850$	−143.905	−0.00580695
$851$	16237.3	0.654062
$852$	645.411	0.0259524
$853$	−12310.5	−0.494144	−0.247072	−	0.968997i	$-0.579468\pi$
$853$	−12310.5	−0.494144	−0.247072	+	0.968997i	$0.579468\pi$
$854$	−9187.94	−0.368155
$855$	−4195.86	−0.167831
$856$	−7358.41	−0.293815
$857$	−30397.2	−1.21161	−0.605804	−	0.795614i	$-0.707148\pi$
$857$	−30397.2	−1.21161	−0.605804	+	0.795614i	$0.707148\pi$
$858$	1975.01	0.0785848
$859$	−42107.2	−1.67250	−0.836251	−	0.548347i	$-0.815257\pi$
$859$	−42107.2	−1.67250	−0.836251	+	0.548347i	$0.815257\pi$
$860$	−3382.25	−0.134109
$861$	−2544.14	−0.100702
$862$	−27748.4	−1.09642
$863$	−30836.9	−1.21634	−0.608169	−	0.793807i	$-0.708096\pi$
$863$	−30836.9	−1.21634	−0.608169	+	0.793807i	$0.708096\pi$
$864$	−4435.18	−0.174639
$865$	−13322.5	−0.523675
$866$	14079.2	0.552461
$867$	−14730.7	−0.577024
$868$	420.865	0.0164575
$869$	14427.5	0.563198
$870$	3343.34	0.130287
$871$	−1579.96	−0.0614638
$872$	−25341.8	−0.984154
$873$	14638.9	0.567528
$874$	33300.8	1.28881
$875$	−632.193	−0.0244252
$876$	7220.26	0.278482
$877$	10957.6	0.421906	0.210953	−	0.977496i	$-0.432343\pi$
$877$	10957.6	0.421906	0.210953	+	0.977496i	$0.432343\pi$
$878$	−26973.6	−1.03681
$879$	−18758.8	−0.719817
$880$	−15883.4	−0.608443
$881$	−2301.45	−0.0880111	−0.0440055	−	0.999031i	$-0.514012\pi$
$881$	−2301.45	−0.0880111	−0.0440055	+	0.999031i	$0.514012\pi$
$882$	−9872.35	−0.376893
$883$	−29777.9	−1.13489	−0.567444	−	0.823412i	$-0.692068\pi$
$883$	−29777.9	−1.13489	−0.567444	+	0.823412i	$0.692068\pi$
$884$	31.5018	0.00119855
$885$	−8199.63	−0.311444
$886$	16679.3	0.632453
$887$	38638.9	1.46265	0.731324	−	0.682030i	$-0.238903\pi$
$887$	38638.9	1.46265	0.731324	+	0.682030i	$0.238903\pi$
$888$	−6609.43	−0.249772
$889$	−8839.77	−0.333494
$890$	−13922.5	−0.524363
$891$	−3216.53	−0.120940
$892$	20790.5	0.780400
$893$	39787.6	1.49098
$894$	36804.7	1.37688
$895$	12582.1	0.469916
$896$	7910.09	0.294930
$897$	−1487.41	−0.0553657
$898$	−55967.6	−2.07980
$899$	−1361.48	−0.0505095
$900$	886.992	0.0328516
$901$	−323.678	−0.0119681
$902$	23010.5	0.849406
$903$	2603.51	0.0959463
$904$	−25696.7	−0.945420
$905$	1017.09	0.0373582
$906$	−37435.2	−1.37274
$907$	−10749.3	−0.393523	−0.196761	−	0.980451i	$-0.563042\pi$
$907$	−10749.3	−0.393523	−0.196761	+	0.980451i	$0.563042\pi$
$908$	7895.92	0.288585
$909$	−3819.79	−0.139378
$910$	419.233	0.0152719
$911$	−837.297	−0.0304510	−0.0152255	−	0.999884i	$-0.504847\pi$
$911$	−837.297	−0.0304510	−0.0152255	+	0.999884i	$0.504847\pi$
$912$	−22377.0	−0.812473
$913$	−2780.90	−0.100804
$914$	12937.6	0.468203
$915$	7885.47	0.284902
$916$	−19829.7	−0.715276
$917$	4433.21	0.159648
$918$	−155.417	−0.00558774
$919$	31536.4	1.13198	0.565990	−	0.824412i	$-0.308494\pi$
$919$	31536.4	1.13198	0.565990	+	0.824412i	$0.308494\pi$
$920$	7246.17	0.259673
$921$	16065.5	0.574783
$922$	−51032.4	−1.82285
$923$	−261.807	−0.00933639
$924$	−2375.20	−0.0845654
$925$	3927.79	0.139616
$926$	−1676.32	−0.0594895
$927$	5854.54	0.207431
$928$	10594.9	0.374777
$929$	−21888.1	−0.773008	−0.386504	−	0.922288i	$-0.626317\pi$
$929$	−21888.1	−0.773008	−0.386504	+	0.922288i	$0.626317\pi$
$930$	−1094.20	−0.0385811
$931$	−29596.8	−1.04188
$932$	−11448.1	−0.402355
$933$	4392.46	0.154129
$934$	−22856.2	−0.800725
$935$	−330.725	−0.0115678
$936$	605.453	0.0211430
$937$	5902.15	0.205779	0.102889	−	0.994693i	$-0.467191\pi$
$937$	5902.15	0.205779	0.102889	+	0.994693i	$0.467191\pi$
$938$	5756.05	0.200364
$939$	−22456.4	−0.780444
$940$	−8410.99	−0.291847
$941$	−41291.3	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$941$	−41291.3	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$942$	−19481.8	−0.673832
$943$	−17329.5	−0.598436
$944$	−43729.6	−1.50771
$945$	−682.768	−0.0235031
$946$	−23547.4	−0.809295
$947$	−4879.60	−0.167440	−0.0837199	−	0.996489i	$-0.526680\pi$
$947$	−4879.60	−0.167440	−0.0837199	+	0.996489i	$0.526680\pi$
$948$	−4296.82	−0.147209
$949$	−2928.86	−0.100184
$950$	8055.46	0.275109
$951$	5374.49	0.183260
$952$	118.132	0.00402172
$953$	−4355.07	−0.148032	−0.0740161	−	0.997257i	$-0.523582\pi$
$953$	−4355.07	−0.148032	−0.0740161	+	0.997257i	$0.523582\pi$
$954$	6043.70	0.205107
$955$	9366.96	0.317390
$956$	−12130.7	−0.410394
$957$	7683.70	0.259539
$958$	−27173.8	−0.916435
$959$	14100.7	0.474803
$960$	−1084.67	−0.0364663
$961$	−29345.4	−0.985043
$962$	−2604.68	−0.0872955
$963$	4722.72	0.158035
$964$	−3278.35	−0.109532
$965$	142.184	0.00474306
$966$	5418.85	0.180485
$967$	27377.0	0.910428	0.455214	−	0.890382i	$-0.349563\pi$
$967$	27377.0	0.910428	0.455214	+	0.890382i	$0.349563\pi$
$968$	−3448.22	−0.114494
$969$	−465.933	−0.0154468
$970$	−28104.7	−0.930295
$971$	23574.4	0.779135	0.389567	−	0.920998i	$-0.372625\pi$
$971$	23574.4	0.779135	0.389567	+	0.920998i	$0.372625\pi$
$972$	957.952	0.0316114
$973$	−6724.72	−0.221567
$974$	−12725.8	−0.418647
$975$	−359.803	−0.0118184
$976$	42054.1	1.37922
$977$	9611.66	0.314743	0.157372	−	0.987539i	$-0.449698\pi$
$977$	9611.66	0.314743	0.157372	+	0.987539i	$0.449698\pi$
$978$	1689.86	0.0552513
$979$	−31996.8	−1.04456
$980$	6256.67	0.203941
$981$	16264.7	0.529350
$982$	−10811.2	−0.351323
$983$	−20941.2	−0.679470	−0.339735	−	0.940521i	$-0.610337\pi$
$983$	−20941.2	−0.679470	−0.339735	+	0.940521i	$0.610337\pi$
$984$	7054.01	0.228530
$985$	4824.13	0.156050
$986$	371.264	0.0119913
$987$	6474.41	0.208797
$988$	−1763.39	−0.0567824
$989$	17733.9	0.570176
$990$	6175.28	0.198246
$991$	5867.85	0.188091	0.0940456	−	0.995568i	$-0.470020\pi$
$991$	5867.85	0.188091	0.0940456	+	0.995568i	$0.470020\pi$
$992$	−3467.47	−0.110980
$993$	−1699.61	−0.0543157
$994$	953.804	0.0304355
$995$	−10247.0	−0.326483
$996$	828.212	0.0263483
$997$	9198.15	0.292185	0.146092	−	0.989271i	$-0.453330\pi$
$997$	9198.15	0.292185	0.146092	+	0.989271i	$0.453330\pi$
$998$	−23829.2	−0.755813
$999$	4242.02	0.134346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2445.4.a.g.1.33	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2445.4.a.g.1.33	✓	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2445 = 3 \cdot 5 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2445.a (trivial)

\(f(q)\)	\(=\)	\(q+3.45575 q^{2} +3.00000 q^{3} +3.94219 q^{4} -5.00000 q^{5} +10.3672 q^{6} +5.05754 q^{7} -14.0228 q^{8} +9.00000 q^{9} -17.2787 q^{10} -39.7102 q^{11} +11.8266 q^{12} -4.79738 q^{13} +17.4776 q^{14} -15.0000 q^{15} -79.9967 q^{16} -1.66569 q^{17} +31.1017 q^{18} +93.2413 q^{19} -19.7109 q^{20} +15.1726 q^{21} -137.228 q^{22} +103.349 q^{23} -42.0683 q^{24} +25.0000 q^{25} -16.5785 q^{26} +27.0000 q^{27} +19.9378 q^{28} -64.4981 q^{29} -51.8362 q^{30} +21.1089 q^{31} -164.266 q^{32} -119.131 q^{33} -5.75620 q^{34} -25.2877 q^{35} +35.4797 q^{36} +157.112 q^{37} +322.218 q^{38} -14.3921 q^{39} +70.1139 q^{40} -167.680 q^{41} +52.4328 q^{42} +171.593 q^{43} -156.545 q^{44} -45.0000 q^{45} +357.147 q^{46} +426.717 q^{47} -239.990 q^{48} -317.421 q^{49} +86.3937 q^{50} -4.99707 q^{51} -18.9122 q^{52} +194.321 q^{53} +93.3052 q^{54} +198.551 q^{55} -70.9208 q^{56} +279.724 q^{57} -222.889 q^{58} +546.642 q^{59} -59.1328 q^{60} -525.698 q^{61} +72.9470 q^{62} +45.5179 q^{63} +72.3114 q^{64} +23.9869 q^{65} -411.685 q^{66} +329.339 q^{67} -6.56646 q^{68} +310.046 q^{69} -87.3880 q^{70} +54.5730 q^{71} -126.205 q^{72} +610.512 q^{73} +542.939 q^{74} +75.0000 q^{75} +367.575 q^{76} -200.836 q^{77} -49.7356 q^{78} -363.319 q^{79} +399.983 q^{80} +81.0000 q^{81} -579.459 q^{82} +70.0298 q^{83} +59.8134 q^{84} +8.32845 q^{85} +592.981 q^{86} -193.494 q^{87} +556.847 q^{88} +805.758 q^{89} -155.509 q^{90} -24.2629 q^{91} +407.419 q^{92} +63.3267 q^{93} +1474.62 q^{94} -466.206 q^{95} -492.798 q^{96} +1626.55 q^{97} -1096.93 q^{98} -357.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 5 q^{2} + 126 q^{3} + 171 q^{4} - 210 q^{5} + 15 q^{6} - 25 q^{7} + 60 q^{8} + 378 q^{9} - 25 q^{10} + 181 q^{11} + 513 q^{12} + 40 q^{13} + 140 q^{14} - 630 q^{15} + 795 q^{16} + 313 q^{17} + 45 q^{18}+ \cdots + 1629 q^{99}+O(q^{100}) \) 42 * q + 5 * q^2 + 126 * q^3 + 171 * q^4 - 210 * q^5 + 15 * q^6 - 25 * q^7 + 60 * q^8 + 378 * q^9 - 25 * q^10 + 181 * q^11 + 513 * q^12 + 40 * q^13 + 140 * q^14 - 630 * q^15 + 795 * q^16 + 313 * q^17 + 45 * q^18 + 149 * q^19 - 855 * q^20 - 75 * q^21 - 137 * q^22 + 165 * q^23 + 180 * q^24 + 1050 * q^25 + 556 * q^26 + 1134 * q^27 - 31 * q^28 + 691 * q^29 - 75 * q^30 - 114 * q^31 + 710 * q^32 + 543 * q^33 + 69 * q^34 + 125 * q^35 + 1539 * q^36 - 136 * q^37 + 694 * q^38 + 120 * q^39 - 300 * q^40 + 1899 * q^41 + 420 * q^42 + 249 * q^43 + 1850 * q^44 - 1890 * q^45 + 1071 * q^46 + 534 * q^47 + 2385 * q^48 + 2569 * q^49 + 125 * q^50 + 939 * q^51 + 332 * q^52 + 1579 * q^53 + 135 * q^54 - 905 * q^55 + 5138 * q^56 + 447 * q^57 + 478 * q^58 + 2855 * q^59 - 2565 * q^60 - 576 * q^61 + 1851 * q^62 - 225 * q^63 + 3396 * q^64 - 200 * q^65 - 411 * q^66 + 844 * q^67 + 5024 * q^68 + 495 * q^69 - 700 * q^70 + 3751 * q^71 + 540 * q^72 + 1649 * q^73 + 2702 * q^74 + 3150 * q^75 + 724 * q^76 + 3538 * q^77 + 1668 * q^78 + 766 * q^79 - 3975 * q^80 + 3402 * q^81 + 1416 * q^82 + 3283 * q^83 - 93 * q^84 - 1565 * q^85 + 6489 * q^86 + 2073 * q^87 - 2239 * q^88 + 2584 * q^89 - 225 * q^90 + 1564 * q^91 + 3940 * q^92 - 342 * q^93 + 1579 * q^94 - 745 * q^95 + 2130 * q^96 + 1040 * q^97 + 5971 * q^98 + 1629 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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