LMFDB - Embedded newform 1011.4.a.c.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1011,4,Mod(1,1011)] 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("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1011 = 3 \cdot 337 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1011.a (trivial)

Newform invariants

comment:select newform

sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$59.6509310158$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	1011.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.07541 q^{2} -3.00000 q^{3} +1.45812 q^{4} -6.39601 q^{5} +9.22622 q^{6} +0.626874 q^{7} +20.1189 q^{8} +9.00000 q^{9} +19.6703 q^{10} -35.4878 q^{11} -4.37437 q^{12} -32.9018 q^{13} -1.92789 q^{14} +19.1880 q^{15} -73.5389 q^{16} -12.3485 q^{17} -27.6787 q^{18} +60.9814 q^{19} -9.32616 q^{20} -1.88062 q^{21} +109.139 q^{22} -32.7241 q^{23} -60.3568 q^{24} -84.0911 q^{25} +101.186 q^{26} -27.0000 q^{27} +0.914058 q^{28} +227.951 q^{29} -59.0109 q^{30} +197.472 q^{31} +65.2104 q^{32} +106.463 q^{33} +37.9766 q^{34} -4.00949 q^{35} +13.1231 q^{36} -263.328 q^{37} -187.543 q^{38} +98.7055 q^{39} -128.681 q^{40} -178.522 q^{41} +5.78367 q^{42} -431.571 q^{43} -51.7455 q^{44} -57.5640 q^{45} +100.640 q^{46} +148.368 q^{47} +220.617 q^{48} -342.607 q^{49} +258.614 q^{50} +37.0455 q^{51} -47.9749 q^{52} -659.908 q^{53} +83.0360 q^{54} +226.980 q^{55} +12.6120 q^{56} -182.944 q^{57} -701.042 q^{58} -172.116 q^{59} +27.9785 q^{60} -636.824 q^{61} -607.307 q^{62} +5.64186 q^{63} +387.762 q^{64} +210.440 q^{65} -327.418 q^{66} +100.574 q^{67} -18.0056 q^{68} +98.1722 q^{69} +12.3308 q^{70} -805.302 q^{71} +181.070 q^{72} -65.7876 q^{73} +809.840 q^{74} +252.273 q^{75} +88.9184 q^{76} -22.2463 q^{77} -303.559 q^{78} +416.445 q^{79} +470.355 q^{80} +81.0000 q^{81} +549.026 q^{82} +255.426 q^{83} -2.74218 q^{84} +78.9810 q^{85} +1327.26 q^{86} -683.853 q^{87} -713.976 q^{88} -572.424 q^{89} +177.033 q^{90} -20.6253 q^{91} -47.7157 q^{92} -592.417 q^{93} -456.292 q^{94} -390.038 q^{95} -195.631 q^{96} -1393.23 q^{97} +1053.66 q^{98} -319.390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) $ 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * 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 $

$2$	−3.07541	−1.08732	−0.543660	−	0.839305i	$-0.682962\pi$
$2$	−3.07541	−1.08732	−0.543660	+	0.839305i	$0.682962\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	1.45812	0.182265
$5$	−6.39601	−0.572076	−0.286038	−	0.958218i	$-0.592338\pi$
$5$	−6.39601	−0.572076	−0.286038	+	0.958218i	$0.592338\pi$
$6$	9.22622	0.627765
$7$	0.626874	0.0338480	0.0169240	−	0.999857i	$-0.494613\pi$
$7$	0.626874	0.0338480	0.0169240	+	0.999857i	$0.494613\pi$
$8$	20.1189	0.889140
$9$	9.00000	0.333333
$10$	19.6703	0.622030
$11$	−35.4878	−0.972724	−0.486362	−	0.873757i	$-0.661676\pi$
$11$	−35.4878	−0.972724	−0.486362	+	0.873757i	$0.661676\pi$
$12$	−4.37437	−0.105231
$13$	−32.9018	−0.701948	−0.350974	−	0.936385i	$-0.614149\pi$
$13$	−32.9018	−0.701948	−0.350974	+	0.936385i	$0.614149\pi$
$14$	−1.92789	−0.0368036
$15$	19.1880	0.330288
$16$	−73.5389	−1.14904
$17$	−12.3485	−0.176173	−0.0880867	−	0.996113i	$-0.528075\pi$
$17$	−12.3485	−0.176173	−0.0880867	+	0.996113i	$0.528075\pi$
$18$	−27.6787	−0.362440
$19$	60.9814	0.736321	0.368161	−	0.929762i	$-0.379988\pi$
$19$	60.9814	0.736321	0.368161	+	0.929762i	$0.379988\pi$
$20$	−9.32616	−0.104270
$21$	−1.88062	−0.0195422
$22$	109.139	1.05766
$23$	−32.7241	−0.296671	−0.148336	−	0.988937i	$-0.547392\pi$
$23$	−32.7241	−0.296671	−0.148336	+	0.988937i	$0.547392\pi$
$24$	−60.3568	−0.513345
$25$	−84.0911	−0.672729
$26$	101.186	0.763242
$27$	−27.0000	−0.192450
$28$	0.914058	0.00616931
$29$	227.951	1.45964	0.729818	−	0.683641i	$-0.239605\pi$
$29$	227.951	1.45964	0.729818	+	0.683641i	$0.239605\pi$
$30$	−59.0109	−0.359129
$31$	197.472	1.14410	0.572049	−	0.820219i	$-0.306149\pi$
$31$	197.472	1.14410	0.572049	+	0.820219i	$0.306149\pi$
$32$	65.2104	0.360240
$33$	106.463	0.561602
$34$	37.9766	0.191557
$35$	−4.00949	−0.0193636
$36$	13.1231	0.0607551
$37$	−263.328	−1.17002	−0.585012	−	0.811025i	$-0.698910\pi$
$37$	−263.328	−1.17002	−0.585012	+	0.811025i	$0.698910\pi$
$38$	−187.543	−0.800617
$39$	98.7055	0.405270
$40$	−128.681	−0.508655
$41$	−178.522	−0.680009	−0.340005	−	0.940424i	$-0.610429\pi$
$41$	−178.522	−0.680009	−0.340005	+	0.940424i	$0.610429\pi$
$42$	5.78367	0.0212486
$43$	−431.571	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$43$	−431.571	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$44$	−51.7455	−0.177294
$45$	−57.5640	−0.190692
$46$	100.640	0.322577
$47$	148.368	0.460462	0.230231	−	0.973136i	$-0.426052\pi$
$47$	148.368	0.460462	0.230231	+	0.973136i	$0.426052\pi$
$48$	220.617	0.663401
$49$	−342.607	−0.998854
$50$	258.614	0.731472
$51$	37.0455	0.101714
$52$	−47.9749	−0.127941
$53$	−659.908	−1.71029	−0.855144	−	0.518390i	$-0.826531\pi$
$53$	−659.908	−1.71029	−0.855144	+	0.518390i	$0.826531\pi$
$54$	83.0360	0.209255
$55$	226.980	0.556472
$56$	12.6120	0.0300956
$57$	−182.944	−0.425115
$58$	−701.042	−1.58709
$59$	−172.116	−0.379791	−0.189895	−	0.981804i	$-0.560815\pi$
$59$	−172.116	−0.379791	−0.189895	+	0.981804i	$0.560815\pi$
$60$	27.9785	0.0602001
$61$	−636.824	−1.33667	−0.668336	−	0.743859i	$-0.732993\pi$
$61$	−636.824	−1.33667	−0.668336	+	0.743859i	$0.732993\pi$
$62$	−607.307	−1.24400
$63$	5.64186	0.0112827
$64$	387.762	0.757348
$65$	210.440	0.401568
$66$	−327.418	−0.610642
$67$	100.574	0.183389	0.0916943	−	0.995787i	$-0.470772\pi$
$67$	100.574	0.183389	0.0916943	+	0.995787i	$0.470772\pi$
$68$	−18.0056	−0.0321103
$69$	98.1722	0.171283
$70$	12.3308	0.0210545
$71$	−805.302	−1.34608	−0.673040	−	0.739606i	$-0.735012\pi$
$71$	−805.302	−1.34608	−0.673040	+	0.739606i	$0.735012\pi$
$72$	181.070	0.296380
$73$	−65.7876	−0.105477	−0.0527387	−	0.998608i	$-0.516795\pi$
$73$	−65.7876	−0.105477	−0.0527387	+	0.998608i	$0.516795\pi$
$74$	809.840	1.27219
$75$	252.273	0.388400
$76$	88.9184	0.134206
$77$	−22.2463	−0.0329248
$78$	−303.559	−0.440658
$79$	416.445	0.593085	0.296543	−	0.955020i	$-0.404166\pi$
$79$	416.445	0.593085	0.296543	+	0.955020i	$0.404166\pi$
$80$	470.355	0.657341
$81$	81.0000	0.111111
$82$	549.026	0.739388
$83$	255.426	0.337791	0.168896	−	0.985634i	$-0.445980\pi$
$83$	255.426	0.337791	0.168896	+	0.985634i	$0.445980\pi$
$84$	−2.74218	−0.00356186
$85$	78.9810	0.100785
$86$	1327.26	1.66421
$87$	−683.853	−0.842722
$88$	−713.976	−0.864887
$89$	−572.424	−0.681763	−0.340881	−	0.940106i	$-0.610725\pi$
$89$	−572.424	−0.681763	−0.340881	+	0.940106i	$0.610725\pi$
$90$	177.033	0.207343
$91$	−20.6253	−0.0237595
$92$	−47.7157	−0.0540728
$93$	−592.417	−0.660546
$94$	−456.292	−0.500669
$95$	−390.038	−0.421232
$96$	−195.631	−0.207985
$97$	−1393.23	−1.45836	−0.729180	−	0.684322i	$-0.760098\pi$
$97$	−1393.23	−1.45836	−0.729180	+	0.684322i	$0.760098\pi$
$98$	1053.66	1.08607
$99$	−319.390	−0.324241
$100$	−122.615	−0.122615
$101$	1002.12	0.987279	0.493639	−	0.869667i	$-0.335666\pi$
$101$	1002.12	0.987279	0.493639	+	0.869667i	$0.335666\pi$
$102$	−113.930	−0.110595
$103$	−1122.58	−1.07390	−0.536948	−	0.843615i	$-0.680423\pi$
$103$	−1122.58	−1.07390	−0.536948	+	0.843615i	$0.680423\pi$
$104$	−661.950	−0.624130
$105$	12.0285	0.0111796
$106$	2029.48	1.85963
$107$	1453.02	1.31279	0.656394	−	0.754418i	$-0.272081\pi$
$107$	1453.02	1.31279	0.656394	+	0.754418i	$0.272081\pi$
$108$	−39.3693	−0.0350770
$109$	1763.02	1.54924	0.774619	−	0.632428i	$-0.217941\pi$
$109$	1763.02	1.54924	0.774619	+	0.632428i	$0.217941\pi$
$110$	−698.056	−0.605063
$111$	789.984	0.675513
$112$	−46.0996	−0.0388929
$113$	1736.21	1.44539	0.722693	−	0.691169i	$-0.242904\pi$
$113$	1736.21	1.44539	0.722693	+	0.691169i	$0.242904\pi$
$114$	562.628	0.462236
$115$	209.303	0.169718
$116$	332.381	0.266041
$117$	−296.117	−0.233983
$118$	529.328	0.412954
$119$	−7.74094	−0.00596312
$120$	386.042	0.293672
$121$	−71.6183	−0.0538079
$122$	1958.49	1.45339
$123$	535.565	0.392604
$124$	287.939	0.208529
$125$	1337.35	0.956928
$126$	−17.3510	−0.0122679
$127$	−187.353	−0.130905	−0.0654524	−	0.997856i	$-0.520849\pi$
$127$	−187.353	−0.130905	−0.0654524	+	0.997856i	$0.520849\pi$
$128$	−1714.21	−1.18372
$129$	1294.71	0.883668
$130$	−647.189	−0.436633
$131$	−1032.24	−0.688452	−0.344226	−	0.938887i	$-0.611859\pi$
$131$	−1032.24	−0.688452	−0.344226	+	0.938887i	$0.611859\pi$
$132$	155.236	0.102361
$133$	38.2277	0.0249230
$134$	−309.305	−0.199402
$135$	172.692	0.110096
$136$	−248.438	−0.156643
$137$	2992.13	1.86595	0.932975	−	0.359941i	$-0.117203\pi$
$137$	2992.13	1.86595	0.932975	+	0.359941i	$0.117203\pi$
$138$	−301.919	−0.186240
$139$	126.513	0.0771994	0.0385997	−	0.999255i	$-0.487710\pi$
$139$	126.513	0.0771994	0.0385997	+	0.999255i	$0.487710\pi$
$140$	−5.84632	−0.00352932
$141$	−445.104	−0.265848
$142$	2476.63	1.46362
$143$	1167.61	0.682802
$144$	−661.850	−0.383015
$145$	−1457.98	−0.835023
$146$	202.323	0.114688
$147$	1027.82	0.576689
$148$	−383.964	−0.213255
$149$	−588.770	−0.323718	−0.161859	−	0.986814i	$-0.551749\pi$
$149$	−588.770	−0.323718	−0.161859	+	0.986814i	$0.551749\pi$
$150$	−775.843	−0.422315
$151$	−2457.81	−1.32460	−0.662298	−	0.749241i	$-0.730419\pi$
$151$	−2457.81	−1.32460	−0.662298	+	0.749241i	$0.730419\pi$
$152$	1226.88	0.654692
$153$	−111.136	−0.0587245
$154$	68.4166	0.0357998
$155$	−1263.03	−0.654511
$156$	143.925	0.0738666
$157$	−1073.10	−0.545496	−0.272748	−	0.962085i	$-0.587933\pi$
$157$	−1073.10	−0.545496	−0.272748	+	0.962085i	$0.587933\pi$
$158$	−1280.74	−0.644873
$159$	1979.72	0.987435
$160$	−417.086	−0.206085
$161$	−20.5139	−0.0100417
$162$	−249.108	−0.120813
$163$	−1103.73	−0.530375	−0.265188	−	0.964197i	$-0.585434\pi$
$163$	−1103.73	−0.530375	−0.265188	+	0.964197i	$0.585434\pi$
$164$	−260.306	−0.123942
$165$	−680.940	−0.321279
$166$	−785.540	−0.367287
$167$	383.105	0.177518	0.0887592	−	0.996053i	$-0.471710\pi$
$167$	383.105	0.177518	0.0887592	+	0.996053i	$0.471710\pi$
$168$	−37.8361	−0.0173757
$169$	−1114.47	−0.507269
$170$	−242.899	−0.109585
$171$	548.833	0.245440
$172$	−629.284	−0.278968
$173$	2374.35	1.04346	0.521730	−	0.853111i	$-0.325287\pi$
$173$	2374.35	1.04346	0.521730	+	0.853111i	$0.325287\pi$
$174$	2103.13	0.916308
$175$	−52.7145	−0.0227705
$176$	2609.73	1.11770
$177$	516.349	0.219272
$178$	1760.44	0.741294
$179$	989.435	0.413150	0.206575	−	0.978431i	$-0.433768\pi$
$179$	989.435	0.413150	0.206575	+	0.978431i	$0.433768\pi$
$180$	−83.9354	−0.0347565
$181$	856.314	0.351654	0.175827	−	0.984421i	$-0.443740\pi$
$181$	856.314	0.351654	0.175827	+	0.984421i	$0.443740\pi$
$182$	63.4312	0.0258342
$183$	1910.47	0.771728
$184$	−658.373	−0.263782
$185$	1684.25	0.669342
$186$	1821.92	0.718225
$187$	438.220	0.171368
$188$	216.339	0.0839262
$189$	−16.9256	−0.00651405
$190$	1199.52	0.458014
$191$	−2758.54	−1.04503	−0.522516	−	0.852630i	$-0.675006\pi$
$191$	−2758.54	−1.04503	−0.522516	+	0.852630i	$0.675006\pi$
$192$	−1163.29	−0.437255
$193$	−661.446	−0.246694	−0.123347	−	0.992364i	$-0.539363\pi$
$193$	−661.446	−0.246694	−0.123347	+	0.992364i	$0.539363\pi$
$194$	4284.74	1.58570
$195$	−631.321	−0.231845
$196$	−499.563	−0.182056
$197$	2116.46	0.765439	0.382719	−	0.923865i	$-0.374988\pi$
$197$	2116.46	0.765439	0.382719	+	0.923865i	$0.374988\pi$
$198$	982.254	0.352554
$199$	4202.14	1.49689	0.748446	−	0.663196i	$-0.230800\pi$
$199$	4202.14	1.49689	0.748446	+	0.663196i	$0.230800\pi$
$200$	−1691.82	−0.598150
$201$	−301.721	−0.105879
$202$	−3081.94	−1.07349
$203$	142.897	0.0494058
$204$	54.0168	0.0185389
$205$	1141.82	0.389017
$206$	3452.40	1.16767
$207$	−294.516	−0.0988904
$208$	2419.56	0.806570
$209$	−2164.10	−0.716237
$210$	−36.9924	−0.0121558
$211$	3074.19	1.00302	0.501508	−	0.865153i	$-0.332779\pi$
$211$	3074.19	1.00302	0.501508	+	0.865153i	$0.332779\pi$
$212$	−962.226	−0.311726
$213$	2415.91	0.777160
$214$	−4468.62	−1.42742
$215$	2760.33	0.875596
$216$	−543.211	−0.171115
$217$	123.790	0.0387254
$218$	−5422.01	−1.68452
$219$	197.363	0.0608974
$220$	330.964	0.101426
$221$	406.288	0.123665
$222$	−2429.52	−0.734499
$223$	830.652	0.249438	0.124719	−	0.992192i	$-0.460197\pi$
$223$	830.652	0.249438	0.124719	+	0.992192i	$0.460197\pi$
$224$	40.8787	0.0121934
$225$	−756.820	−0.224243
$226$	−5339.54	−1.57160
$227$	4301.47	1.25770	0.628852	−	0.777525i	$-0.283525\pi$
$227$	4301.47	1.25770	0.628852	+	0.777525i	$0.283525\pi$
$228$	−266.755	−0.0774837
$229$	−1753.52	−0.506007	−0.253003	−	0.967465i	$-0.581418\pi$
$229$	−1753.52	−0.506007	−0.253003	+	0.967465i	$0.581418\pi$
$230$	−643.692	−0.184538
$231$	66.7390	0.0190091
$232$	4586.13	1.29782
$233$	6122.73	1.72152	0.860758	−	0.509015i	$-0.169990\pi$
$233$	6122.73	1.72152	0.860758	+	0.509015i	$0.169990\pi$
$234$	910.678	0.254414
$235$	−948.963	−0.263419
$236$	−250.967	−0.0692227
$237$	−1249.34	−0.342418
$238$	23.8065	0.00648382
$239$	1435.67	0.388561	0.194280	−	0.980946i	$-0.437763\pi$
$239$	1435.67	0.388561	0.194280	+	0.980946i	$0.437763\pi$
$240$	−1411.06	−0.379516
$241$	4852.49	1.29700	0.648498	−	0.761216i	$-0.275397\pi$
$241$	4852.49	1.29700	0.648498	+	0.761216i	$0.275397\pi$
$242$	220.255	0.0585064
$243$	−243.000	−0.0641500
$244$	−928.568	−0.243629
$245$	2191.32	0.571421
$246$	−1647.08	−0.426886
$247$	−2006.40	−0.516859
$248$	3972.93	1.01726
$249$	−766.279	−0.195024
$250$	−4112.89	−1.04049
$251$	6199.92	1.55910	0.779552	−	0.626337i	$-0.215447\pi$
$251$	6199.92	1.55910	0.779552	+	0.626337i	$0.215447\pi$
$252$	8.22653	0.00205644
$253$	1161.30	0.288579
$254$	576.187	0.142335
$255$	−236.943	−0.0581880
$256$	2169.79	0.529734
$257$	−4833.36	−1.17314	−0.586569	−	0.809899i	$-0.699522\pi$
$257$	−4833.36	−1.17314	−0.586569	+	0.809899i	$0.699522\pi$
$258$	−3981.77	−0.960830
$259$	−165.073	−0.0396029
$260$	306.848	0.0731919
$261$	2051.56	0.486546
$262$	3174.56	0.748568
$263$	−7759.70	−1.81933	−0.909665	−	0.415343i	$-0.863661\pi$
$263$	−7759.70	−1.81933	−0.909665	+	0.415343i	$0.863661\pi$
$264$	2141.93	0.499343
$265$	4220.77	0.978415
$266$	−117.566	−0.0270993
$267$	1717.27	0.393616
$268$	146.649	0.0334254
$269$	5774.02	1.30873	0.654365	−	0.756179i	$-0.272936\pi$
$269$	5774.02	1.30873	0.654365	+	0.756179i	$0.272936\pi$
$270$	−531.098	−0.119710
$271$	2900.45	0.650147	0.325073	−	0.945689i	$-0.394611\pi$
$271$	2900.45	0.650147	0.325073	+	0.945689i	$0.394611\pi$
$272$	908.093	0.202431
$273$	61.8759	0.0137176
$274$	−9202.02	−2.02888
$275$	2984.21	0.654380
$276$	143.147	0.0312190
$277$	−6949.43	−1.50740	−0.753702	−	0.657216i	$-0.771734\pi$
$277$	−6949.43	−1.50740	−0.753702	+	0.657216i	$0.771734\pi$
$278$	−389.079	−0.0839404
$279$	1777.25	0.381366
$280$	−80.6666	−0.0172170
$281$	6786.49	1.44074	0.720371	−	0.693589i	$-0.243972\pi$
$281$	6786.49	1.44074	0.720371	+	0.693589i	$0.243972\pi$
$282$	1368.88	0.289062
$283$	4572.74	0.960500	0.480250	−	0.877132i	$-0.340546\pi$
$283$	4572.74	0.960500	0.480250	+	0.877132i	$0.340546\pi$
$284$	−1174.23	−0.245344
$285$	1170.11	0.243198
$286$	−3590.88	−0.742424
$287$	−111.910	−0.0230170
$288$	586.894	0.120080
$289$	−4760.51	−0.968963
$290$	4483.87	0.907938
$291$	4179.69	0.841985
$292$	−95.9263	−0.0192249
$293$	−2756.01	−0.549516	−0.274758	−	0.961513i	$-0.588598\pi$
$293$	−2756.01	−0.549516	−0.274758	+	0.961513i	$0.588598\pi$
$294$	−3160.97	−0.627045
$295$	1100.86	0.217269
$296$	−5297.88	−1.04031
$297$	958.170	0.187201
$298$	1810.71	0.351985
$299$	1076.68	0.208248
$300$	367.845	0.0707919
$301$	−270.541	−0.0518063
$302$	7558.77	1.44026
$303$	−3006.37	−0.570006
$304$	−4484.51	−0.846066
$305$	4073.13	0.764678
$306$	341.789	0.0638523
$307$	6114.43	1.13671	0.568354	−	0.822784i	$-0.307581\pi$
$307$	6114.43	1.13671	0.568354	+	0.822784i	$0.307581\pi$
$308$	−32.4379	−0.00600104
$309$	3367.75	0.620014
$310$	3884.34	0.711664
$311$	−6025.65	−1.09866	−0.549330	−	0.835605i	$-0.685117\pi$
$311$	−6025.65	−1.09866	−0.549330	+	0.835605i	$0.685117\pi$
$312$	1985.85	0.360342
$313$	−8989.39	−1.62336	−0.811678	−	0.584106i	$-0.801445\pi$
$313$	−8989.39	−1.62336	−0.811678	+	0.584106i	$0.801445\pi$
$314$	3300.23	0.593129
$315$	−36.0854	−0.00645454
$316$	607.228	0.108099
$317$	5554.57	0.984151	0.492075	−	0.870553i	$-0.336238\pi$
$317$	5554.57	0.984151	0.492075	+	0.870553i	$0.336238\pi$
$318$	−6088.45	−1.07366
$319$	−8089.48	−1.41982
$320$	−2480.13	−0.433261
$321$	−4359.05	−0.757939
$322$	63.0884	0.0109186
$323$	−753.028	−0.129720
$324$	118.108	0.0202517
$325$	2766.75	0.472221
$326$	3394.43	0.576687
$327$	−5289.07	−0.894454
$328$	−3591.66	−0.604623
$329$	93.0080	0.0155857
$330$	2094.17	0.349334
$331$	−5773.25	−0.958691	−0.479346	−	0.877626i	$-0.659126\pi$
$331$	−5773.25	−0.958691	−0.479346	+	0.877626i	$0.659126\pi$
$332$	372.443	0.0615676
$333$	−2369.95	−0.390008
$334$	−1178.20	−0.193019
$335$	−643.270	−0.104912
$336$	138.299	0.0224548
$337$	−337.000	−0.0544735
$337$	−337.000	−0.0544735
$338$	3427.45	0.551564
$339$	−5208.62	−0.834494
$340$	115.164	0.0183695
$341$	−7007.85	−1.11289
$342$	−1687.88	−0.266872
$343$	−429.789	−0.0676572
$344$	−8682.75	−1.36088
$345$	−627.910	−0.0979870
$346$	−7302.09	−1.13457
$347$	9710.00	1.50219	0.751095	−	0.660194i	$-0.229526\pi$
$347$	9710.00	1.50219	0.751095	+	0.660194i	$0.229526\pi$
$348$	−997.142	−0.153599
$349$	−249.515	−0.0382700	−0.0191350	−	0.999817i	$-0.506091\pi$
$349$	−249.515	−0.0382700	−0.0191350	+	0.999817i	$0.506091\pi$
$350$	162.119	0.0247589
$351$	888.350	0.135090
$352$	−2314.17	−0.350414
$353$	5065.88	0.763823	0.381912	−	0.924199i	$-0.375266\pi$
$353$	5065.88	0.763823	0.381912	+	0.924199i	$0.375266\pi$
$354$	−1587.98	−0.238419
$355$	5150.71	0.770061
$356$	−834.665	−0.124262
$357$	23.2228	0.00344281
$358$	−3042.92	−0.449226
$359$	−5209.49	−0.765867	−0.382934	−	0.923776i	$-0.625086\pi$
$359$	−5209.49	−0.765867	−0.382934	+	0.923776i	$0.625086\pi$
$360$	−1158.13	−0.169552
$361$	−3140.26	−0.457831
$362$	−2633.51	−0.382360
$363$	214.855	0.0310660
$364$	−30.0742	−0.00433054
$365$	420.778	0.0603411
$366$	−5875.48	−0.839116
$367$	−727.035	−0.103408	−0.0517042	−	0.998662i	$-0.516465\pi$
$367$	−727.035	−0.103408	−0.0517042	+	0.998662i	$0.516465\pi$
$368$	2406.49	0.340888
$369$	−1606.69	−0.226670
$370$	−5179.74	−0.727789
$371$	−413.679	−0.0578898
$372$	−863.816	−0.120395
$373$	−9647.78	−1.33926	−0.669629	−	0.742696i	$-0.733547\pi$
$373$	−9647.78	−1.33926	−0.669629	+	0.742696i	$0.733547\pi$
$374$	−1347.70	−0.186332
$375$	−4012.04	−0.552483
$376$	2985.01	0.409415
$377$	−7500.01	−1.02459
$378$	52.0531	0.00708286
$379$	6120.88	0.829574	0.414787	−	0.909919i	$-0.363856\pi$
$379$	6120.88	0.829574	0.414787	+	0.909919i	$0.363856\pi$
$380$	−568.722	−0.0767759
$381$	562.060	0.0755779
$382$	8483.63	1.13628
$383$	−9720.07	−1.29679	−0.648397	−	0.761302i	$-0.724560\pi$
$383$	−9720.07	−1.29679	−0.648397	+	0.761302i	$0.724560\pi$
$384$	5142.63	0.683421
$385$	142.288	0.0188355
$386$	2034.22	0.268235
$387$	−3884.14	−0.510186
$388$	−2031.50	−0.265808
$389$	1247.16	0.162555	0.0812773	−	0.996692i	$-0.474100\pi$
$389$	1247.16	0.162555	0.0812773	+	0.996692i	$0.474100\pi$
$390$	1941.57	0.252090
$391$	404.092	0.0522656
$392$	−6892.89	−0.888121
$393$	3096.72	0.397478
$394$	−6508.97	−0.832277
$395$	−2663.58	−0.339290
$396$	−465.709	−0.0590979
$397$	11284.9	1.42663	0.713315	−	0.700844i	$-0.247193\pi$
$397$	11284.9	1.42663	0.713315	+	0.700844i	$0.247193\pi$
$398$	−12923.3	−1.62760
$399$	−114.683	−0.0143893
$400$	6183.96	0.772996
$401$	6785.59	0.845027	0.422514	−	0.906357i	$-0.361148\pi$
$401$	6785.59	0.845027	0.422514	+	0.906357i	$0.361148\pi$
$402$	927.915	0.115125
$403$	−6497.20	−0.803098
$404$	1461.22	0.179947
$405$	−518.076	−0.0635640
$406$	−439.465	−0.0537199
$407$	9344.92	1.13811
$408$	745.315	0.0904377
$409$	5305.29	0.641393	0.320696	−	0.947182i	$-0.396083\pi$
$409$	5305.29	0.641393	0.320696	+	0.947182i	$0.396083\pi$
$410$	−3511.57	−0.422986
$411$	−8976.40	−1.07731
$412$	−1636.86	−0.195734
$413$	−107.895	−0.0128552
$414$	905.758	0.107526
$415$	−1633.71	−0.193242
$416$	−2145.54	−0.252870
$417$	−379.540	−0.0445711
$418$	6655.47	0.778779
$419$	788.662	0.0919538	0.0459769	−	0.998943i	$-0.485360\pi$
$419$	788.662	0.0919538	0.0459769	+	0.998943i	$0.485360\pi$
$420$	17.5390	0.00203765
$421$	2921.68	0.338228	0.169114	−	0.985597i	$-0.445909\pi$
$421$	2921.68	0.338228	0.169114	+	0.985597i	$0.445909\pi$
$422$	−9454.40	−1.09060
$423$	1335.31	0.153487
$424$	−13276.6	−1.52068
$425$	1038.40	0.118517
$426$	−7429.89	−0.845022
$427$	−399.209	−0.0452437
$428$	2118.68	0.239276
$429$	−3502.84	−0.394216
$430$	−8489.14	−0.952053
$431$	4045.05	0.452072	0.226036	−	0.974119i	$-0.427423\pi$
$431$	4045.05	0.452072	0.226036	+	0.974119i	$0.427423\pi$
$432$	1985.55	0.221134
$433$	1759.83	0.195317	0.0976584	−	0.995220i	$-0.468865\pi$
$433$	1759.83	0.195317	0.0976584	+	0.995220i	$0.468865\pi$
$434$	−380.705	−0.0421070
$435$	4373.93	0.482101
$436$	2570.70	0.282372
$437$	−1995.56	−0.218445
$438$	−606.970	−0.0662150
$439$	9096.98	0.989009	0.494505	−	0.869175i	$-0.335350\pi$
$439$	9096.98	0.989009	0.494505	+	0.869175i	$0.335350\pi$
$440$	4566.59	0.494781
$441$	−3083.46	−0.332951
$442$	−1249.50	−0.134463
$443$	−14592.8	−1.56506	−0.782531	−	0.622611i	$-0.786072\pi$
$443$	−14592.8	−1.56506	−0.782531	+	0.622611i	$0.786072\pi$
$444$	1151.89	0.123123
$445$	3661.23	0.390020
$446$	−2554.59	−0.271219
$447$	1766.31	0.186899
$448$	243.078	0.0256347
$449$	−1851.81	−0.194638	−0.0973191	−	0.995253i	$-0.531027\pi$
$449$	−1851.81	−0.194638	−0.0973191	+	0.995253i	$0.531027\pi$
$450$	2327.53	0.243824
$451$	6335.33	0.661461
$452$	2531.60	0.263444
$453$	7373.44	0.764756
$454$	−13228.8	−1.36753
$455$	131.920	0.0135923
$456$	−3680.64	−0.377987
$457$	4283.78	0.438483	0.219241	−	0.975671i	$-0.429642\pi$
$457$	4283.78	0.438483	0.219241	+	0.975671i	$0.429642\pi$
$458$	5392.77	0.550191
$459$	333.409	0.0339046
$460$	305.190	0.0309338
$461$	187.429	0.0189358	0.00946792	−	0.999955i	$-0.496986\pi$
$461$	187.429	0.0189358	0.00946792	+	0.999955i	$0.496986\pi$
$462$	−205.250	−0.0206690
$463$	10094.8	1.01327	0.506635	−	0.862161i	$-0.330889\pi$
$463$	10094.8	1.01327	0.506635	+	0.862161i	$0.330889\pi$
$464$	−16763.3	−1.67719
$465$	3789.10	0.377882
$466$	−18829.9	−1.87184
$467$	230.158	0.0228061	0.0114031	−	0.999935i	$-0.496370\pi$
$467$	230.158	0.0228061	0.0114031	+	0.999935i	$0.496370\pi$
$468$	−431.774	−0.0426469
$469$	63.0470	0.00620734
$470$	2918.45	0.286421
$471$	3219.31	0.314943
$472$	−3462.80	−0.337687
$473$	15315.5	1.48881
$474$	3842.21	0.372318
$475$	−5128.00	−0.495345
$476$	−11.2872	−0.00108687
$477$	−5939.17	−0.570096
$478$	−4415.28	−0.422490
$479$	−9869.62	−0.941450	−0.470725	−	0.882280i	$-0.656008\pi$
$479$	−9869.62	−0.941450	−0.470725	+	0.882280i	$0.656008\pi$
$480$	1251.26	0.118983
$481$	8663.97	0.821296
$482$	−14923.4	−1.41025
$483$	61.5416	0.00579759
$484$	−104.428	−0.00980731
$485$	8911.10	0.834293
$486$	747.324	0.0697516
$487$	−20185.6	−1.87823	−0.939114	−	0.343606i	$-0.888351\pi$
$487$	−20185.6	−1.87823	−0.939114	+	0.343606i	$0.888351\pi$
$488$	−12812.2	−1.18849
$489$	3311.20	0.306212
$490$	−6739.19	−0.621317
$491$	−13524.2	−1.24305	−0.621526	−	0.783394i	$-0.713487\pi$
$491$	−13524.2	−1.24305	−0.621526	+	0.783394i	$0.713487\pi$
$492$	780.919	0.0715580
$493$	−2814.85	−0.257149
$494$	6170.50	0.561992
$495$	2042.82	0.185491
$496$	−14521.9	−1.31462
$497$	−504.823	−0.0455621
$498$	2356.62	0.212053
$499$	2400.16	0.215323	0.107661	−	0.994188i	$-0.465664\pi$
$499$	2400.16	0.215323	0.107661	+	0.994188i	$0.465664\pi$
$500$	1950.02	0.174415
$501$	−1149.32	−0.102490
$502$	−19067.3	−1.69525
$503$	12653.4	1.12164	0.560822	−	0.827936i	$-0.310485\pi$
$503$	12653.4	1.12164	0.560822	+	0.827936i	$0.310485\pi$
$504$	113.508	0.0100319
$505$	−6409.60	−0.564799
$506$	−3571.48	−0.313778
$507$	3343.41	0.292872
$508$	−273.184	−0.0238594
$509$	−6429.26	−0.559866	−0.279933	−	0.960020i	$-0.590312\pi$
$509$	−6429.26	−0.559866	−0.279933	+	0.960020i	$0.590312\pi$
$510$	728.696	0.0632690
$511$	−41.2405	−0.00357020
$512$	7040.69	0.607729
$513$	−1646.50	−0.141705
$514$	14864.5	1.27558
$515$	7180.04	0.614350
$516$	1887.85	0.161062
$517$	−5265.25	−0.447902
$518$	507.668	0.0430611
$519$	−7123.05	−0.602442
$520$	4233.83	0.357050
$521$	20392.8	1.71483	0.857413	−	0.514629i	$-0.172070\pi$
$521$	20392.8	1.71483	0.857413	+	0.514629i	$0.172070\pi$
$522$	−6309.38	−0.529031
$523$	−3380.52	−0.282638	−0.141319	−	0.989964i	$-0.545134\pi$
$523$	−3380.52	−0.282638	−0.141319	+	0.989964i	$0.545134\pi$
$524$	−1505.13	−0.125481
$525$	158.144	0.0131466
$526$	23864.2	1.97819
$527$	−2438.48	−0.201560
$528$	−7829.19	−0.645306
$529$	−11096.1	−0.911986
$530$	−12980.6	−1.06385
$531$	−1549.05	−0.126597
$532$	55.7406	0.00454260
$533$	5873.69	0.477331
$534$	−5281.31	−0.427986
$535$	−9293.50	−0.751015
$536$	2023.44	0.163058
$537$	−2968.31	−0.238532
$538$	−17757.5	−1.42301
$539$	12158.4	0.971610
$540$	251.806	0.0200667
$541$	21530.4	1.71103	0.855513	−	0.517781i	$-0.173242\pi$
$541$	21530.4	1.71103	0.855513	+	0.517781i	$0.173242\pi$
$542$	−8920.06	−0.706918
$543$	−2568.94	−0.203027
$544$	−805.249	−0.0634647
$545$	−11276.3	−0.886283
$546$	−190.293	−0.0149154
$547$	−25123.4	−1.96380	−0.981900	−	0.189402i	$-0.939345\pi$
$547$	−25123.4	−1.96380	−0.981900	+	0.189402i	$0.939345\pi$
$548$	4362.89	0.340098
$549$	−5731.42	−0.445557
$550$	−9177.64	−0.711520
$551$	13900.8	1.07476
$552$	1975.12	0.152295
$553$	261.058	0.0200747
$554$	21372.3	1.63903
$555$	−5052.74	−0.386445
$556$	184.472	0.0140708
$557$	15035.9	1.14379	0.571894	−	0.820328i	$-0.306209\pi$
$557$	15035.9	1.14379	0.571894	+	0.820328i	$0.306209\pi$
$558$	−5465.76	−0.414667
$559$	14199.5	1.07437
$560$	294.853	0.0222497
$561$	−1314.66	−0.0989394
$562$	−20871.2	−1.56655
$563$	11943.3	0.894050	0.447025	−	0.894521i	$-0.352483\pi$
$563$	11943.3	0.894050	0.447025	+	0.894521i	$0.352483\pi$
$564$	−649.016	−0.0484548
$565$	−11104.8	−0.826871
$566$	−14063.0	−1.04437
$567$	50.7768	0.00376089
$568$	−16201.8	−1.19685
$569$	23367.5	1.72164	0.860822	−	0.508906i	$-0.169950\pi$
$569$	23367.5	1.72164	0.860822	+	0.508906i	$0.169950\pi$
$570$	−3598.57	−0.264434
$571$	5691.02	0.417096	0.208548	−	0.978012i	$-0.433126\pi$
$571$	5691.02	0.417096	0.208548	+	0.978012i	$0.433126\pi$
$572$	1702.52	0.124451
$573$	8275.62	0.603349
$574$	344.170	0.0250268
$575$	2751.80	0.199579
$576$	3489.86	0.252449
$577$	−20456.4	−1.47593	−0.737965	−	0.674839i	$-0.764213\pi$
$577$	−20456.4	−1.47593	−0.737965	+	0.674839i	$0.764213\pi$
$578$	14640.5	1.05357
$579$	1984.34	0.142429
$580$	−2125.91	−0.152196
$581$	160.120	0.0114336
$582$	−12854.2	−0.915507
$583$	23418.6	1.66364
$584$	−1323.58	−0.0937841
$585$	1893.96	0.133856
$586$	8475.86	0.597499
$587$	−23187.8	−1.63043	−0.815215	−	0.579159i	$-0.803381\pi$
$587$	−23187.8	−1.63043	−0.815215	+	0.579159i	$0.803381\pi$
$588$	1498.69	0.105110
$589$	12042.1	0.842424
$590$	−3385.59	−0.236241
$591$	−6349.38	−0.441926
$592$	19364.8	1.34441
$593$	18929.0	1.31083	0.655413	−	0.755271i	$-0.272495\pi$
$593$	18929.0	1.31083	0.655413	+	0.755271i	$0.272495\pi$
$594$	−2946.76	−0.203547
$595$	49.5111	0.00341136
$596$	−858.499	−0.0590025
$597$	−12606.4	−0.864231
$598$	−3311.23	−0.226432
$599$	4828.08	0.329332	0.164666	−	0.986349i	$-0.447345\pi$
$599$	4828.08	0.329332	0.164666	+	0.986349i	$0.447345\pi$
$600$	5075.47	0.345342
$601$	927.828	0.0629732	0.0314866	−	0.999504i	$-0.489976\pi$
$601$	927.828	0.0629732	0.0314866	+	0.999504i	$0.489976\pi$
$602$	832.022	0.0563301
$603$	905.164	0.0611295
$604$	−3583.79	−0.241428
$605$	458.071	0.0307822
$606$	9245.82	0.619779
$607$	−7528.38	−0.503406	−0.251703	−	0.967805i	$-0.580991\pi$
$607$	−7528.38	−0.503406	−0.251703	+	0.967805i	$0.580991\pi$
$608$	3976.62	0.265252
$609$	−428.690	−0.0285244
$610$	−12526.5	−0.831450
$611$	−4881.58	−0.323220
$612$	−162.050	−0.0107034
$613$	1196.39	0.0788281	0.0394140	−	0.999223i	$-0.487451\pi$
$613$	1196.39	0.0788281	0.0394140	+	0.999223i	$0.487451\pi$
$614$	−18804.4	−1.23597
$615$	−3425.47	−0.224599
$616$	−447.573	−0.0292747
$617$	−12548.6	−0.818781	−0.409390	−	0.912359i	$-0.634259\pi$
$617$	−12548.6	−0.818781	−0.409390	+	0.912359i	$0.634259\pi$
$618$	−10357.2	−0.674154
$619$	25924.5	1.68335	0.841676	−	0.539982i	$-0.181569\pi$
$619$	25924.5	1.68335	0.841676	+	0.539982i	$0.181569\pi$
$620$	−1841.66	−0.119295
$621$	883.549	0.0570944
$622$	18531.3	1.19460
$623$	−358.838	−0.0230763
$624$	−7258.69	−0.465673
$625$	1957.70	0.125293
$626$	27646.0	1.76511
$627$	6492.29	0.413520
$628$	−1564.72	−0.0994250
$629$	3251.70	0.206127
$630$	110.977	0.00701816
$631$	−5850.88	−0.369128	−0.184564	−	0.982820i	$-0.559087\pi$
$631$	−5850.88	−0.369128	−0.184564	+	0.982820i	$0.559087\pi$
$632$	8378.43	0.527335
$633$	−9222.58	−0.579091
$634$	−17082.6	−1.07009
$635$	1198.31	0.0748875
$636$	2886.68	0.179975
$637$	11272.4	0.701144
$638$	24878.4	1.54380
$639$	−7247.72	−0.448694
$640$	10964.1	0.677178
$641$	4024.73	0.247999	0.123999	−	0.992282i	$-0.460428\pi$
$641$	4024.73	0.247999	0.123999	+	0.992282i	$0.460428\pi$
$642$	13405.8	0.824122
$643$	29091.5	1.78423	0.892113	−	0.451813i	$-0.149223\pi$
$643$	29091.5	1.78423	0.892113	+	0.451813i	$0.149223\pi$
$644$	−29.9117	−0.00183026
$645$	−8281.00	−0.505525
$646$	2315.87	0.141047
$647$	13487.2	0.819528	0.409764	−	0.912192i	$-0.365611\pi$
$647$	13487.2	0.819528	0.409764	+	0.912192i	$0.365611\pi$
$648$	1629.63	0.0987933
$649$	6108.03	0.369432
$650$	−8508.89	−0.513455
$651$	−371.370	−0.0223581
$652$	−1609.38	−0.0966689
$653$	−27515.4	−1.64894	−0.824472	−	0.565902i	$-0.808528\pi$
$653$	−27515.4	−1.64894	−0.824472	+	0.565902i	$0.808528\pi$
$654$	16266.0	0.972557
$655$	6602.21	0.393847
$656$	13128.3	0.781361
$657$	−592.088	−0.0351591
$658$	−286.038	−0.0169467
$659$	−9953.61	−0.588372	−0.294186	−	0.955748i	$-0.595049\pi$
$659$	−9953.61	−0.588372	−0.294186	+	0.955748i	$0.595049\pi$
$660$	−992.893	−0.0585581
$661$	−21997.1	−1.29438	−0.647192	−	0.762327i	$-0.724057\pi$
$661$	−21997.1	−1.29438	−0.647192	+	0.762327i	$0.724057\pi$
$662$	17755.1	1.04240
$663$	−1218.86	−0.0713978
$664$	5138.90	0.300344
$665$	−244.504	−0.0142579
$666$	7288.56	0.424063
$667$	−7459.49	−0.433032
$668$	558.614	0.0323554
$669$	−2491.96	−0.144013
$670$	1978.32	0.114073
$671$	22599.5	1.30021
$672$	−122.636	−0.00703986
$673$	−1005.66	−0.0576009	−0.0288004	−	0.999585i	$-0.509169\pi$
$673$	−1005.66	−0.0576009	−0.0288004	+	0.999585i	$0.509169\pi$
$674$	1036.41	0.0592301
$675$	2270.46	0.129467
$676$	−1625.03	−0.0924575
$677$	−19805.8	−1.12437	−0.562184	−	0.827012i	$-0.690039\pi$
$677$	−19805.8	−1.12437	−0.562184	+	0.827012i	$0.690039\pi$
$678$	16018.6	0.907362
$679$	−873.378	−0.0493626
$680$	1589.01	0.0896116
$681$	−12904.4	−0.726135
$682$	21552.0	1.21007
$683$	−27280.2	−1.52833	−0.764165	−	0.645021i	$-0.776849\pi$
$683$	−27280.2	−1.52833	−0.764165	+	0.645021i	$0.776849\pi$
$684$	800.265	0.0447353
$685$	−19137.7	−1.06747
$686$	1321.78	0.0735651
$687$	5260.55	0.292143
$688$	31737.3	1.75868
$689$	21712.2	1.20053
$690$	1931.08	0.106543
$691$	5837.46	0.321371	0.160685	−	0.987006i	$-0.448630\pi$
$691$	5837.46	0.321371	0.160685	+	0.987006i	$0.448630\pi$
$692$	3462.09	0.190186
$693$	−200.217	−0.0109749
$694$	−29862.2	−1.63336
$695$	−809.179	−0.0441639
$696$	−13758.4	−0.749297
$697$	2204.47	0.119800
$698$	767.359	0.0416117
$699$	−18368.2	−0.993917
$700$	−76.8642	−0.00415028
$701$	−1828.03	−0.0984934	−0.0492467	−	0.998787i	$-0.515682\pi$
$701$	−1828.03	−0.0984934	−0.0492467	+	0.998787i	$0.515682\pi$
$702$	−2732.04	−0.146886
$703$	−16058.1	−0.861513
$704$	−13760.8	−0.736691
$705$	2846.89	0.152085
$706$	−15579.6	−0.830520
$707$	628.206	0.0334174
$708$	752.901	0.0399657
$709$	18879.7	1.00006	0.500029	−	0.866009i	$-0.333323\pi$
$709$	18879.7	1.00006	0.500029	+	0.866009i	$0.333323\pi$
$710$	−15840.5	−0.837303
$711$	3748.01	0.197695
$712$	−11516.6	−0.606182
$713$	−6462.09	−0.339421
$714$	−71.4196	−0.00374343
$715$	−7468.06	−0.390615
$716$	1442.72	0.0753029
$717$	−4307.02	−0.224336
$718$	16021.3	0.832743
$719$	−2085.03	−0.108148	−0.0540739	−	0.998537i	$-0.517221\pi$
$719$	−2085.03	−0.108148	−0.0540739	+	0.998537i	$0.517221\pi$
$720$	4233.19	0.219114
$721$	−703.717	−0.0363492
$722$	9657.59	0.497809
$723$	−14557.5	−0.748821
$724$	1248.61	0.0640942
$725$	−19168.7	−0.981940
$726$	−660.766	−0.0337787
$727$	37635.8	1.91999	0.959997	−	0.280012i	$-0.0903384\pi$
$727$	37635.8	1.91999	0.959997	+	0.280012i	$0.0903384\pi$
$728$	−414.959	−0.0211255
$729$	729.000	0.0370370
$730$	−1294.06	−0.0656101
$731$	5329.25	0.269644
$732$	2785.70	0.140659
$733$	24488.4	1.23397	0.616986	−	0.786974i	$-0.288354\pi$
$733$	24488.4	1.23397	0.616986	+	0.786974i	$0.288354\pi$
$734$	2235.93	0.112438
$735$	−6573.95	−0.329910
$736$	−2133.95	−0.106873
$737$	−3569.14	−0.178387
$738$	4941.24	0.246463
$739$	36430.0	1.81339	0.906697	−	0.421783i	$-0.138595\pi$
$739$	36430.0	1.81339	0.906697	+	0.421783i	$0.138595\pi$
$740$	2455.84	0.121998
$741$	6019.20	0.298409
$742$	1272.23	0.0629448
$743$	8604.14	0.424839	0.212419	−	0.977179i	$-0.431866\pi$
$743$	8604.14	0.424839	0.212419	+	0.977179i	$0.431866\pi$
$744$	−11918.8	−0.587317
$745$	3765.78	0.185191
$746$	29670.8	1.45620
$747$	2298.84	0.112597
$748$	638.978	0.0312344
$749$	910.858	0.0444353
$750$	12338.7	0.600726
$751$	5463.80	0.265482	0.132741	−	0.991151i	$-0.457622\pi$
$751$	5463.80	0.265482	0.132741	+	0.991151i	$0.457622\pi$
$752$	−10910.8	−0.529091
$753$	−18599.7	−0.900149
$754$	23065.6	1.11406
$755$	15720.2	0.757769
$756$	−24.6796	−0.00118729
$757$	3360.73	0.161358	0.0806789	−	0.996740i	$-0.474291\pi$
$757$	3360.73	0.161358	0.0806789	+	0.996740i	$0.474291\pi$
$758$	−18824.2	−0.902012
$759$	−3483.91	−0.166611
$760$	−7847.14	−0.374534
$761$	−11156.6	−0.531439	−0.265720	−	0.964050i	$-0.585610\pi$
$761$	−11156.6	−0.531439	−0.265720	+	0.964050i	$0.585610\pi$
$762$	−1728.56	−0.0821774
$763$	1105.19	0.0524386
$764$	−4022.29	−0.190473
$765$	710.829	0.0335949
$766$	29893.2	1.41003
$767$	5662.95	0.266593
$768$	−6509.38	−0.305842
$769$	36857.3	1.72836	0.864179	−	0.503184i	$-0.167838\pi$
$769$	36857.3	1.72836	0.864179	+	0.503184i	$0.167838\pi$
$770$	−437.593	−0.0204802
$771$	14500.1	0.677312
$772$	−964.469	−0.0449637
$773$	−31568.6	−1.46888	−0.734439	−	0.678675i	$-0.762554\pi$
$773$	−31568.6	−1.46888	−0.734439	+	0.678675i	$0.762554\pi$
$774$	11945.3	0.554736
$775$	−16605.7	−0.769668
$776$	−28030.3	−1.29669
$777$	495.220	0.0228648
$778$	−3835.54	−0.176749
$779$	−10886.5	−0.500705
$780$	−920.543	−0.0422573
$781$	28578.4	1.30937
$782$	−1242.75	−0.0568294
$783$	−6154.68	−0.280907
$784$	25194.9	1.14773
$785$	6863.57	0.312065
$786$	−9523.67	−0.432186
$787$	−36167.3	−1.63815	−0.819075	−	0.573687i	$-0.805513\pi$
$787$	−36167.3	−1.63815	−0.819075	+	0.573687i	$0.805513\pi$
$788$	3086.06	0.139513
$789$	23279.1	1.05039
$790$	8191.60	0.368917
$791$	1088.38	0.0489234
$792$	−6425.78	−0.288296
$793$	20952.7	0.938275
$794$	−34705.6	−1.55120
$795$	−12662.3	−0.564888
$796$	6127.23	0.272831
$797$	37911.1	1.68492	0.842459	−	0.538760i	$-0.181107\pi$
$797$	37911.1	1.68492	0.842459	+	0.538760i	$0.181107\pi$
$798$	352.697	0.0156458
$799$	−1832.12	−0.0811211
$800$	−5483.61	−0.242344
$801$	−5151.82	−0.227254
$802$	−20868.4	−0.918815
$803$	2334.65	0.102600
$804$	−439.946	−0.0192981
$805$	131.207	0.00574463
$806$	19981.5	0.873225
$807$	−17322.1	−0.755596
$808$	20161.7	0.877828
$809$	−12913.0	−0.561181	−0.280591	−	0.959828i	$-0.590530\pi$
$809$	−12913.0	−0.561181	−0.280591	+	0.959828i	$0.590530\pi$
$810$	1593.30	0.0691144
$811$	−8100.77	−0.350748	−0.175374	−	0.984502i	$-0.556113\pi$
$811$	−8100.77	−0.350748	−0.175374	+	0.984502i	$0.556113\pi$
$812$	208.361	0.00900496
$813$	−8701.35	−0.375362
$814$	−28739.4	−1.23749
$815$	7059.49	0.303415
$816$	−2724.28	−0.116874
$817$	−26317.8	−1.12698
$818$	−16315.9	−0.697399
$819$	−185.628	−0.00791985
$820$	1664.92	0.0709043
$821$	33772.7	1.43566	0.717830	−	0.696218i	$-0.245135\pi$
$821$	33772.7	1.43566	0.717830	+	0.696218i	$0.245135\pi$
$822$	27606.1	1.17138
$823$	−25659.5	−1.08680	−0.543398	−	0.839475i	$-0.682862\pi$
$823$	−25659.5	−1.08680	−0.543398	+	0.839475i	$0.682862\pi$
$824$	−22585.2	−0.954843
$825$	−8952.62	−0.377806
$826$	331.822	0.0139777
$827$	−14976.3	−0.629717	−0.314859	−	0.949139i	$-0.601957\pi$
$827$	−14976.3	−0.629717	−0.314859	+	0.949139i	$0.601957\pi$
$828$	−429.441	−0.0180243
$829$	18792.0	0.787301	0.393651	−	0.919260i	$-0.371212\pi$
$829$	18792.0	0.787301	0.393651	+	0.919260i	$0.371212\pi$
$830$	5024.32	0.210116
$831$	20848.3	0.870300
$832$	−12758.1	−0.531619
$833$	4230.68	0.175972
$834$	1167.24	0.0484630
$835$	−2450.34	−0.101554
$836$	−3155.51	−0.130545
$837$	−5331.75	−0.220182
$838$	−2425.45	−0.0999832
$839$	−564.556	−0.0232308	−0.0116154	−	0.999933i	$-0.503697\pi$
$839$	−564.556	−0.0232308	−0.0116154	+	0.999933i	$0.503697\pi$
$840$	242.000	0.00994022
$841$	27572.7	1.13054
$842$	−8985.34	−0.367762
$843$	−20359.5	−0.831812
$844$	4482.55	0.182815
$845$	7128.15	0.290196
$846$	−4106.63	−0.166890
$847$	−44.8956	−0.00182129
$848$	48528.8	1.96520
$849$	−13718.2	−0.554545
$850$	−3193.49	−0.128866
$851$	8617.16	0.347112
$852$	3522.68	0.141649
$853$	32738.6	1.31412	0.657062	−	0.753836i	$-0.271799\pi$
$853$	32738.6	1.31412	0.657062	+	0.753836i	$0.271799\pi$
$854$	1227.73	0.0491944
$855$	−3510.34	−0.140411
$856$	29233.1	1.16725
$857$	−41123.4	−1.63915	−0.819574	−	0.572974i	$-0.805790\pi$
$857$	−41123.4	−1.63915	−0.819574	+	0.572974i	$0.805790\pi$
$858$	10772.6	0.428639
$859$	29929.5	1.18880	0.594400	−	0.804169i	$-0.297389\pi$
$859$	29929.5	1.18880	0.594400	+	0.804169i	$0.297389\pi$
$860$	4024.90	0.159591
$861$	335.731	0.0132888
$862$	−12440.2	−0.491547
$863$	11753.2	0.463594	0.231797	−	0.972764i	$-0.425539\pi$
$863$	11753.2	0.463594	0.231797	+	0.972764i	$0.425539\pi$
$864$	−1760.68	−0.0693282
$865$	−15186.4	−0.596938
$866$	−5412.20	−0.212372
$867$	14281.5	0.559431
$868$	180.501	0.00705830
$869$	−14778.7	−0.576908
$870$	−13451.6	−0.524198
$871$	−3309.06	−0.128729
$872$	35470.2	1.37749
$873$	−12539.1	−0.486120
$874$	6137.16	0.237520
$875$	838.348	0.0323901
$876$	287.779	0.0110995
$877$	−2655.34	−0.102240	−0.0511201	−	0.998693i	$-0.516279\pi$
$877$	−2655.34	−0.102240	−0.0511201	+	0.998693i	$0.516279\pi$
$878$	−27976.9	−1.07537
$879$	8268.04	0.317263
$880$	−16691.8	−0.639411
$881$	39985.3	1.52910	0.764550	−	0.644564i	$-0.222961\pi$
$881$	39985.3	1.52910	0.764550	+	0.644564i	$0.222961\pi$
$882$	9482.90	0.362025
$883$	31708.2	1.20845	0.604227	−	0.796812i	$-0.293482\pi$
$883$	31708.2	1.20845	0.604227	+	0.796812i	$0.293482\pi$
$884$	592.417	0.0225398
$885$	−3302.57	−0.125440
$886$	44878.6	1.70172
$887$	5808.90	0.219892	0.109946	−	0.993938i	$-0.464932\pi$
$887$	5808.90	0.219892	0.109946	+	0.993938i	$0.464932\pi$
$888$	15893.6	0.600625
$889$	−117.447	−0.00443087
$890$	−11259.8	−0.424077
$891$	−2874.51	−0.108080
$892$	1211.19	0.0454638
$893$	9047.70	0.339048
$894$	−5432.12	−0.203219
$895$	−6328.43	−0.236353
$896$	−1074.59	−0.0400666
$897$	−3230.04	−0.120232
$898$	5695.08	0.211634
$899$	45014.0	1.66997
$900$	−1103.54	−0.0408717
$901$	8148.86	0.301307
$902$	−19483.7	−0.719220
$903$	811.622	0.0299104
$904$	34930.6	1.28515
$905$	−5476.99	−0.201173
$906$	−22676.3	−0.831534
$907$	4357.57	0.159527	0.0797633	−	0.996814i	$-0.474584\pi$
$907$	4357.57	0.159527	0.0797633	+	0.996814i	$0.474584\pi$
$908$	6272.07	0.229236
$909$	9019.12	0.329093
$910$	−405.706	−0.0147791
$911$	51248.6	1.86382	0.931911	−	0.362688i	$-0.118141\pi$
$911$	51248.6	1.86382	0.931911	+	0.362688i	$0.118141\pi$
$912$	13453.5	0.488476
$913$	−9064.51	−0.328578
$914$	−13174.4	−0.476771
$915$	−12219.4	−0.441487
$916$	−2556.84	−0.0922274
$917$	−647.084	−0.0233027
$918$	−1025.37	−0.0368651
$919$	−12655.3	−0.454256	−0.227128	−	0.973865i	$-0.572934\pi$
$919$	−12655.3	−0.454256	−0.227128	+	0.973865i	$0.572934\pi$
$920$	4210.96	0.150903
$921$	−18343.3	−0.656278
$922$	−576.419	−0.0205893
$923$	26495.9	0.944879
$924$	97.3137	0.00346470
$925$	22143.5	0.787108
$926$	−31045.5	−1.10175
$927$	−10103.2	−0.357965
$928$	14864.8	0.525819
$929$	−6790.37	−0.239812	−0.119906	−	0.992785i	$-0.538259\pi$
$929$	−6790.37	−0.239812	−0.119906	+	0.992785i	$0.538259\pi$
$930$	−11653.0	−0.410879
$931$	−20892.7	−0.735478
$932$	8927.68	0.313772
$933$	18077.0	0.634312
$934$	−707.830	−0.0247975
$935$	−2802.86	−0.0980356
$936$	−5957.55	−0.208043
$937$	−24731.5	−0.862266	−0.431133	−	0.902288i	$-0.641886\pi$
$937$	−24731.5	−0.862266	−0.431133	+	0.902288i	$0.641886\pi$
$938$	−193.895	−0.00674936
$939$	26968.2	0.937244
$940$	−1383.70	−0.0480122
$941$	18436.9	0.638711	0.319356	−	0.947635i	$-0.396534\pi$
$941$	18436.9	0.638711	0.319356	+	0.947635i	$0.396534\pi$
$942$	−9900.68	−0.342443
$943$	5841.95	0.201739
$944$	12657.2	0.436397
$945$	108.256	0.00372653
$946$	−47101.4	−1.61881
$947$	−54223.8	−1.86065	−0.930326	−	0.366735i	$-0.880476\pi$
$947$	−54223.8	−1.86065	−0.930326	+	0.366735i	$0.880476\pi$
$948$	−1821.68	−0.0624109
$949$	2164.53	0.0740397
$950$	15770.7	0.538598
$951$	−16663.7	−0.568200
$952$	−155.739	−0.00530204
$953$	−37694.7	−1.28127	−0.640635	−	0.767846i	$-0.721329\pi$
$953$	−37694.7	−1.28127	−0.640635	+	0.767846i	$0.721329\pi$
$954$	18265.4	0.619877
$955$	17643.6	0.597837
$956$	2093.39	0.0708212
$957$	24268.4	0.819736
$958$	30353.1	1.02366
$959$	1875.69	0.0631587
$960$	7440.39	0.250143
$961$	9204.27	0.308961
$962$	−26645.2	−0.893011
$963$	13077.1	0.437596
$964$	7075.52	0.236397
$965$	4230.61	0.141128
$966$	−189.265	−0.00630384
$967$	−21563.9	−0.717113	−0.358556	−	0.933508i	$-0.616731\pi$
$967$	−21563.9	−0.717113	−0.358556	+	0.933508i	$0.616731\pi$
$968$	−1440.88	−0.0478427
$969$	2259.08	0.0748940
$970$	−27405.2	−0.907144
$971$	−32139.3	−1.06220	−0.531101	−	0.847308i	$-0.678222\pi$
$971$	−32139.3	−1.06220	−0.531101	+	0.847308i	$0.678222\pi$
$972$	−354.324	−0.0116923
$973$	79.3078	0.00261304
$974$	62078.9	2.04223
$975$	−8300.26	−0.272637
$976$	46831.3	1.53590
$977$	−19268.7	−0.630974	−0.315487	−	0.948930i	$-0.602168\pi$
$977$	−19268.7	−0.630974	−0.315487	+	0.948930i	$0.602168\pi$
$978$	−10183.3	−0.332951
$979$	20314.1	0.663167
$980$	3195.21	0.104150
$981$	15867.2	0.516413
$982$	41592.4	1.35159
$983$	−43065.2	−1.39732	−0.698660	−	0.715454i	$-0.746220\pi$
$983$	−43065.2	−1.39732	−0.698660	+	0.715454i	$0.746220\pi$
$984$	10775.0	0.349079
$985$	−13536.9	−0.437889
$986$	8656.81	0.279603
$987$	−279.024	−0.00899842
$988$	−2925.58	−0.0942055
$989$	14122.8	0.454072
$990$	−6282.50	−0.201688
$991$	−50160.6	−1.60788	−0.803938	−	0.594713i	$-0.797266\pi$
$991$	−50160.6	−1.60788	−0.803938	+	0.594713i	$0.797266\pi$
$992$	12877.2	0.412150
$993$	17319.8	0.553501
$994$	1552.53	0.0495406
$995$	−26876.9	−0.856336
$996$	−1117.33	−0.0355461
$997$	14973.2	0.475634	0.237817	−	0.971310i	$-0.423568\pi$
$997$	14973.2	0.475634	0.237817	+	0.971310i	$0.423568\pi$
$998$	−7381.48	−0.234125
$999$	7109.86	0.225171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1011.4.a.c.1.12	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1011.4.a.c.1.12	✓	46	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:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1011.a (trivial)

\(f(q)\)	\(=\)	\(q-3.07541 q^{2} -3.00000 q^{3} +1.45812 q^{4} -6.39601 q^{5} +9.22622 q^{6} +0.626874 q^{7} +20.1189 q^{8} +9.00000 q^{9} +19.6703 q^{10} -35.4878 q^{11} -4.37437 q^{12} -32.9018 q^{13} -1.92789 q^{14} +19.1880 q^{15} -73.5389 q^{16} -12.3485 q^{17} -27.6787 q^{18} +60.9814 q^{19} -9.32616 q^{20} -1.88062 q^{21} +109.139 q^{22} -32.7241 q^{23} -60.3568 q^{24} -84.0911 q^{25} +101.186 q^{26} -27.0000 q^{27} +0.914058 q^{28} +227.951 q^{29} -59.0109 q^{30} +197.472 q^{31} +65.2104 q^{32} +106.463 q^{33} +37.9766 q^{34} -4.00949 q^{35} +13.1231 q^{36} -263.328 q^{37} -187.543 q^{38} +98.7055 q^{39} -128.681 q^{40} -178.522 q^{41} +5.78367 q^{42} -431.571 q^{43} -51.7455 q^{44} -57.5640 q^{45} +100.640 q^{46} +148.368 q^{47} +220.617 q^{48} -342.607 q^{49} +258.614 q^{50} +37.0455 q^{51} -47.9749 q^{52} -659.908 q^{53} +83.0360 q^{54} +226.980 q^{55} +12.6120 q^{56} -182.944 q^{57} -701.042 q^{58} -172.116 q^{59} +27.9785 q^{60} -636.824 q^{61} -607.307 q^{62} +5.64186 q^{63} +387.762 q^{64} +210.440 q^{65} -327.418 q^{66} +100.574 q^{67} -18.0056 q^{68} +98.1722 q^{69} +12.3308 q^{70} -805.302 q^{71} +181.070 q^{72} -65.7876 q^{73} +809.840 q^{74} +252.273 q^{75} +88.9184 q^{76} -22.2463 q^{77} -303.559 q^{78} +416.445 q^{79} +470.355 q^{80} +81.0000 q^{81} +549.026 q^{82} +255.426 q^{83} -2.74218 q^{84} +78.9810 q^{85} +1327.26 q^{86} -683.853 q^{87} -713.976 q^{88} -572.424 q^{89} +177.033 q^{90} -20.6253 q^{91} -47.7157 q^{92} -592.417 q^{93} -456.292 q^{94} -390.038 q^{95} -195.631 q^{96} -1393.23 q^{97} +1053.66 q^{98} -319.390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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