LMFDB - Embedded newform 529.4.a.m.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.198677 q^{2} -8.81112 q^{3} -7.96053 q^{4} -10.0672 q^{5} +1.75056 q^{6} -25.3475 q^{7} +3.17098 q^{8} +50.6358 q^{9} +2.00012 q^{10} +14.1537 q^{11} +70.1411 q^{12} -4.58325 q^{13} +5.03595 q^{14} +88.7033 q^{15} +63.0542 q^{16} +102.166 q^{17} -10.0601 q^{18} -69.2898 q^{19} +80.1402 q^{20} +223.340 q^{21} -2.81201 q^{22} -27.9399 q^{24} -23.6515 q^{25} +0.910585 q^{26} -208.258 q^{27} +201.779 q^{28} +210.883 q^{29} -17.6233 q^{30} -282.393 q^{31} -37.8953 q^{32} -124.710 q^{33} -20.2979 q^{34} +255.178 q^{35} -403.088 q^{36} +174.114 q^{37} +13.7663 q^{38} +40.3836 q^{39} -31.9229 q^{40} +102.177 q^{41} -44.3724 q^{42} -128.557 q^{43} -112.671 q^{44} -509.761 q^{45} +130.950 q^{47} -555.578 q^{48} +299.495 q^{49} +4.69900 q^{50} -900.193 q^{51} +36.4851 q^{52} +96.8973 q^{53} +41.3759 q^{54} -142.488 q^{55} -80.3765 q^{56} +610.521 q^{57} -41.8975 q^{58} +276.358 q^{59} -706.125 q^{60} -458.018 q^{61} +56.1050 q^{62} -1283.49 q^{63} -496.905 q^{64} +46.1405 q^{65} +24.7770 q^{66} +350.178 q^{67} -813.292 q^{68} -50.6980 q^{70} +765.951 q^{71} +160.565 q^{72} +906.125 q^{73} -34.5925 q^{74} +208.396 q^{75} +551.584 q^{76} -358.761 q^{77} -8.02327 q^{78} -448.567 q^{79} -634.779 q^{80} +467.817 q^{81} -20.3002 q^{82} -430.462 q^{83} -1777.90 q^{84} -1028.52 q^{85} +25.5413 q^{86} -1858.11 q^{87} +44.8812 q^{88} +334.558 q^{89} +101.278 q^{90} +116.174 q^{91} +2488.20 q^{93} -26.0168 q^{94} +697.554 q^{95} +333.900 q^{96} -851.130 q^{97} -59.5027 q^{98} +716.685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.198677	−0.0702428	−0.0351214	−	0.999383i	$-0.511182\pi$
$2$	−0.198677	−0.0702428	−0.0351214	+	0.999383i	$0.511182\pi$
$3$	−8.81112	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$3$	−8.81112	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$4$	−7.96053	−0.995066
$5$	−10.0672	−0.900438	−0.450219	−	0.892918i	$-0.648654\pi$
$5$	−10.0672	−0.900438	−0.450219	+	0.892918i	$0.648654\pi$
$6$	1.75056	0.119111
$7$	−25.3475	−1.36864	−0.684318	−	0.729184i	$-0.739900\pi$
$7$	−25.3475	−1.36864	−0.684318	+	0.729184i	$0.739900\pi$
$8$	3.17098	0.140139
$9$	50.6358	1.87540
$10$	2.00012	0.0632493
$11$	14.1537	0.387955	0.193978	−	0.981006i	$-0.437861\pi$
$11$	14.1537	0.387955	0.193978	+	0.981006i	$0.437861\pi$
$12$	70.1411	1.68733
$13$	−4.58325	−0.0977820	−0.0488910	−	0.998804i	$-0.515569\pi$
$13$	−4.58325	−0.0977820	−0.0488910	+	0.998804i	$0.515569\pi$
$14$	5.03595	0.0961368
$15$	88.7033	1.52687
$16$	63.0542	0.985222
$17$	102.166	1.45758	0.728788	−	0.684739i	$-0.240084\pi$
$17$	102.166	1.45758	0.728788	+	0.684739i	$0.240084\pi$
$18$	−10.0601	−0.131733
$19$	−69.2898	−0.836641	−0.418320	−	0.908300i	$-0.637381\pi$
$19$	−69.2898	−0.836641	−0.418320	+	0.908300i	$0.637381\pi$
$20$	80.1402	0.895995
$21$	223.340	2.32080
$22$	−2.81201	−0.0272511
$23$	0	0
$23$	0	0
$24$	−27.9399	−0.237634
$25$	−23.6515	−0.189212
$26$	0.910585	0.00686848
$27$	−208.258	−1.48442
$28$	201.779	1.36188
$29$	210.883	1.35034	0.675172	−	0.737661i	$-0.264070\pi$
$29$	210.883	1.35034	0.675172	+	0.737661i	$0.264070\pi$
$30$	−17.6233	−0.107252
$31$	−282.393	−1.63611	−0.818054	−	0.575141i	$-0.804947\pi$
$31$	−282.393	−1.63611	−0.818054	+	0.575141i	$0.804947\pi$
$32$	−37.8953	−0.209344
$33$	−124.710	−0.657856
$34$	−20.2979	−0.102384
$35$	255.178	1.23237
$36$	−403.088	−1.86615
$37$	174.114	0.773628	0.386814	−	0.922158i	$-0.373576\pi$
$37$	174.114	0.773628	0.386814	+	0.922158i	$0.373576\pi$
$38$	13.7663	0.0587680
$39$	40.3836	0.165809
$40$	−31.9229	−0.126186
$41$	102.177	0.389204	0.194602	−	0.980882i	$-0.437659\pi$
$41$	102.177	0.389204	0.194602	+	0.980882i	$0.437659\pi$
$42$	−44.3724	−0.163019
$43$	−128.557	−0.455925	−0.227962	−	0.973670i	$-0.573206\pi$
$43$	−128.557	−0.455925	−0.227962	+	0.973670i	$0.573206\pi$
$44$	−112.671	−0.386041
$45$	−509.761	−1.68868
$46$	0	0
$47$	130.950	0.406406	0.203203	−	0.979137i	$-0.434865\pi$
$47$	130.950	0.406406	0.203203	+	0.979137i	$0.434865\pi$
$48$	−555.578	−1.67064
$49$	299.495	0.873164
$50$	4.69900	0.0132908
$51$	−900.193	−2.47161
$52$	36.4851	0.0972995
$53$	96.8973	0.251130	0.125565	−	0.992085i	$-0.459926\pi$
$53$	96.8973	0.251130	0.125565	+	0.992085i	$0.459926\pi$
$54$	41.3759	0.104270
$55$	−142.488	−0.349329
$56$	−80.3765	−0.191799
$57$	610.521	1.41869
$58$	−41.8975	−0.0948519
$59$	276.358	0.609810	0.304905	−	0.952383i	$-0.401375\pi$
$59$	276.358	0.609810	0.304905	+	0.952383i	$0.401375\pi$
$60$	−706.125	−1.51934
$61$	−458.018	−0.961364	−0.480682	−	0.876895i	$-0.659611\pi$
$61$	−458.018	−0.961364	−0.480682	+	0.876895i	$0.659611\pi$
$62$	56.1050	0.114925
$63$	−1283.49	−2.56674
$64$	−496.905	−0.970517
$65$	46.1405	0.0880466
$66$	24.7770	0.0462096
$67$	350.178	0.638523	0.319262	−	0.947667i	$-0.396565\pi$
$67$	350.178	0.638523	0.319262	+	0.947667i	$0.396565\pi$
$68$	−813.292	−1.45038
$69$	0	0
$70$	−50.6980	−0.0865652
$71$	765.951	1.28030	0.640152	−	0.768248i	$-0.278871\pi$
$71$	765.951	1.28030	0.640152	+	0.768248i	$0.278871\pi$
$72$	160.565	0.262817
$73$	906.125	1.45279	0.726397	−	0.687276i	$-0.241194\pi$
$73$	906.125	1.45279	0.726397	+	0.687276i	$0.241194\pi$
$74$	−34.5925	−0.0543418
$75$	208.396	0.320847
$76$	551.584	0.832513
$77$	−358.761	−0.530969
$78$	−8.02327	−0.0116469
$79$	−448.567	−0.638832	−0.319416	−	0.947615i	$-0.603487\pi$
$79$	−448.567	−0.638832	−0.319416	+	0.947615i	$0.603487\pi$
$80$	−634.779	−0.887131
$81$	467.817	0.641724
$82$	−20.3002	−0.0273387
$83$	−430.462	−0.569269	−0.284634	−	0.958636i	$-0.591872\pi$
$83$	−430.462	−0.569269	−0.284634	+	0.958636i	$0.591872\pi$
$84$	−1777.90	−2.30935
$85$	−1028.52	−1.31246
$86$	25.5413	0.0320254
$87$	−1858.11	−2.28978
$88$	44.8812	0.0543676
$89$	334.558	0.398461	0.199231	−	0.979953i	$-0.436156\pi$
$89$	334.558	0.398461	0.199231	+	0.979953i	$0.436156\pi$
$90$	101.278	0.118618
$91$	116.174	0.133828
$92$	0	0
$93$	2488.20	2.77435
$94$	−26.0168	−0.0285471
$95$	697.554	0.753343
$96$	333.900	0.354984
$97$	−851.130	−0.890919	−0.445460	−	0.895302i	$-0.646960\pi$
$97$	−851.130	−0.890919	−0.445460	+	0.895302i	$0.646960\pi$
$98$	−59.5027	−0.0613335
$99$	716.685	0.727571
$100$	188.278	0.188278
$101$	−144.338	−0.142200	−0.0710998	−	0.997469i	$-0.522651\pi$
$101$	−144.338	−0.142200	−0.0710998	+	0.997469i	$0.522651\pi$
$102$	178.847	0.173613
$103$	−491.302	−0.469994	−0.234997	−	0.971996i	$-0.575508\pi$
$103$	−491.302	−0.469994	−0.234997	+	0.971996i	$0.575508\pi$
$104$	−14.5334	−0.0137031
$105$	−2248.41	−2.08973
$106$	−19.2512	−0.0176400
$107$	426.627	0.385455	0.192727	−	0.981252i	$-0.438267\pi$
$107$	426.627	0.385455	0.192727	+	0.981252i	$0.438267\pi$
$108$	1657.84	1.47709
$109$	−507.283	−0.445769	−0.222885	−	0.974845i	$-0.571547\pi$
$109$	−507.283	−0.445769	−0.222885	+	0.974845i	$0.571547\pi$
$110$	28.3091	0.0245379
$111$	−1534.14	−1.31184
$112$	−1598.27	−1.34841
$113$	1242.42	1.03431	0.517155	−	0.855892i	$-0.326991\pi$
$113$	1242.42	1.03431	0.517155	+	0.855892i	$0.326991\pi$
$114$	−121.296	−0.0996529
$115$	0	0
$116$	−1678.74	−1.34368
$117$	−232.077	−0.183380
$118$	−54.9059	−0.0428348
$119$	−2589.64	−1.99489
$120$	281.277	0.213974
$121$	−1130.67	−0.849491
$122$	90.9975	0.0675289
$123$	−900.292	−0.659973
$124$	2248.00	1.62804
$125$	1496.50	1.07081
$126$	255.000	0.180295
$127$	1637.13	1.14387	0.571936	−	0.820298i	$-0.306193\pi$
$127$	1637.13	1.14387	0.571936	+	0.820298i	$0.306193\pi$
$128$	401.886	0.277516
$129$	1132.73	0.773112
$130$	−9.16704	−0.00618464
$131$	716.603	0.477938	0.238969	−	0.971027i	$-0.423191\pi$
$131$	716.603	0.477938	0.238969	+	0.971027i	$0.423191\pi$
$132$	992.758	0.654610
$133$	1756.32	1.14506
$134$	−69.5722	−0.0448517
$135$	2096.57	1.33662
$136$	323.965	0.204263
$137$	−1582.55	−0.986905	−0.493452	−	0.869773i	$-0.664265\pi$
$137$	−1582.55	−0.986905	−0.493452	+	0.869773i	$0.664265\pi$
$138$	0	0
$139$	−1194.38	−0.728822	−0.364411	−	0.931238i	$-0.618730\pi$
$139$	−1194.38	−0.728822	−0.364411	+	0.931238i	$0.618730\pi$
$140$	−2031.35	−1.22629
$141$	−1153.82	−0.689143
$142$	−152.176	−0.0899322
$143$	−64.8700	−0.0379350
$144$	3192.80	1.84769
$145$	−2123.00	−1.21590
$146$	−180.026	−0.102048
$147$	−2638.89	−1.48062
$148$	−1386.04	−0.769811
$149$	1057.27	0.581306	0.290653	−	0.956829i	$-0.406128\pi$
$149$	1057.27	0.581306	0.290653	+	0.956829i	$0.406128\pi$
$150$	−41.4034	−0.0225372
$151$	1115.00	0.600909	0.300454	−	0.953796i	$-0.402862\pi$
$151$	1115.00	0.600909	0.300454	+	0.953796i	$0.402862\pi$
$152$	−219.717	−0.117246
$153$	5173.24	2.73354
$154$	71.2775	0.0372968
$155$	2842.91	1.47321
$156$	−321.475	−0.164991
$157$	1161.37	0.590365	0.295182	−	0.955441i	$-0.404620\pi$
$157$	1161.37	0.590365	0.295182	+	0.955441i	$0.404620\pi$
$158$	89.1197	0.0448733
$159$	−853.774	−0.425841
$160$	381.499	0.188501
$161$	0	0
$162$	−92.9443	−0.0450765
$163$	1603.29	0.770428	0.385214	−	0.922827i	$-0.374128\pi$
$163$	1603.29	0.770428	0.385214	+	0.922827i	$0.374128\pi$
$164$	−813.382	−0.387283
$165$	1255.48	0.592358
$166$	85.5227	0.0399870
$167$	1325.30	0.614102	0.307051	−	0.951693i	$-0.400658\pi$
$167$	1325.30	0.614102	0.307051	+	0.951693i	$0.400658\pi$
$168$	708.207	0.325234
$169$	−2175.99	−0.990439
$170$	204.343	0.0921906
$171$	−3508.54	−1.56904
$172$	1023.38	0.453675
$173$	1133.69	0.498226	0.249113	−	0.968474i	$-0.419861\pi$
$173$	1133.69	0.498226	0.249113	+	0.968474i	$0.419861\pi$
$174$	369.164	0.160840
$175$	599.506	0.258962
$176$	892.451	0.382222
$177$	−2435.02	−1.03405
$178$	−66.4688	−0.0279890
$179$	4006.99	1.67316	0.836581	−	0.547843i	$-0.184551\pi$
$179$	4006.99	1.67316	0.836581	+	0.547843i	$0.184551\pi$
$180$	4057.96	1.68035
$181$	−2791.31	−1.14628	−0.573139	−	0.819458i	$-0.694274\pi$
$181$	−2791.31	−1.14628	−0.573139	+	0.819458i	$0.694274\pi$
$182$	−23.0810	−0.00940044
$183$	4035.65	1.63018
$184$	0	0
$185$	−1752.85	−0.696604
$186$	−494.348	−0.194878
$187$	1446.02	0.565474
$188$	−1042.43	−0.404401
$189$	5278.81	2.03162
$190$	−138.588	−0.0529169
$191$	−3753.90	−1.42211	−0.711055	−	0.703137i	$-0.751782\pi$
$191$	−3753.90	−1.42211	−0.711055	+	0.703137i	$0.751782\pi$
$192$	4378.29	1.64571
$193$	−730.043	−0.272278	−0.136139	−	0.990690i	$-0.543469\pi$
$193$	−730.043	−0.272278	−0.136139	+	0.990690i	$0.543469\pi$
$194$	169.100	0.0625807
$195$	−406.549	−0.149301
$196$	−2384.14	−0.868855
$197$	2028.40	0.733591	0.366795	−	0.930302i	$-0.380455\pi$
$197$	2028.40	0.733591	0.366795	+	0.930302i	$0.380455\pi$
$198$	−142.388	−0.0511066
$199$	−3901.11	−1.38966	−0.694829	−	0.719175i	$-0.744520\pi$
$199$	−3901.11	−1.38966	−0.694829	+	0.719175i	$0.744520\pi$
$200$	−74.9985	−0.0265160
$201$	−3085.46	−1.08274
$202$	28.6766	0.00998850
$203$	−5345.35	−1.84813
$204$	7166.01	2.45942
$205$	−1028.63	−0.350454
$206$	97.6102	0.0330137
$207$	0	0
$208$	−288.993	−0.0963370
$209$	−980.708	−0.324579
$210$	446.706	0.146789
$211$	643.596	0.209986	0.104993	−	0.994473i	$-0.466518\pi$
$211$	643.596	0.209986	0.104993	+	0.994473i	$0.466518\pi$
$212$	−771.354	−0.249891
$213$	−6748.88	−2.17101
$214$	−84.7609	−0.0270754
$215$	1294.21	0.410532
$216$	−660.382	−0.208025
$217$	7157.96	2.23924
$218$	100.785	0.0313121
$219$	−7983.97	−2.46350
$220$	1134.28	0.347606
$221$	−468.251	−0.142525
$222$	304.798	0.0921474
$223$	28.2177	0.00847354	0.00423677	−	0.999991i	$-0.498651\pi$
$223$	28.2177	0.00847354	0.00423677	+	0.999991i	$0.498651\pi$
$224$	960.550	0.286515
$225$	−1197.61	−0.354848
$226$	−246.840	−0.0726528
$227$	−6795.33	−1.98688	−0.993440	−	0.114351i	$-0.963521\pi$
$227$	−6795.33	−1.98688	−0.993440	+	0.114351i	$0.963521\pi$
$228$	−4860.07	−1.41169
$229$	−281.246	−0.0811583	−0.0405791	−	0.999176i	$-0.512920\pi$
$229$	−281.246	−0.0811583	−0.0405791	+	0.999176i	$0.512920\pi$
$230$	0	0
$231$	3161.09	0.900365
$232$	668.706	0.189236
$233$	−1986.40	−0.558512	−0.279256	−	0.960217i	$-0.590088\pi$
$233$	−1986.40	−0.558512	−0.279256	+	0.960217i	$0.590088\pi$
$234$	46.1082	0.0128811
$235$	−1318.30	−0.365943
$236$	−2199.96	−0.606801
$237$	3952.37	1.08327
$238$	514.501	0.140127
$239$	4918.57	1.33120	0.665598	−	0.746311i	$-0.268177\pi$
$239$	4918.57	1.33120	0.665598	+	0.746311i	$0.268177\pi$
$240$	5593.12	1.50431
$241$	−4781.43	−1.27800	−0.639002	−	0.769205i	$-0.720652\pi$
$241$	−4781.43	−1.27800	−0.639002	+	0.769205i	$0.720652\pi$
$242$	224.638	0.0596706
$243$	1500.97	0.396244
$244$	3646.06	0.956620
$245$	−3015.08	−0.786229
$246$	178.867	0.0463583
$247$	317.573	0.0818084
$248$	−895.465	−0.229283
$249$	3792.85	0.965309
$250$	−297.320	−0.0752168
$251$	−3375.15	−0.848755	−0.424378	−	0.905485i	$-0.639507\pi$
$251$	−3375.15	−0.848755	−0.424378	+	0.905485i	$0.639507\pi$
$252$	10217.3	2.55407
$253$	0	0
$254$	−325.259	−0.0803487
$255$	9062.42	2.22553
$256$	3895.39	0.951024
$257$	7028.18	1.70586	0.852930	−	0.522026i	$-0.174824\pi$
$257$	7028.18	1.70586	0.852930	+	0.522026i	$0.174824\pi$
$258$	−225.047	−0.0543055
$259$	−4413.36	−1.05882
$260$	−367.303	−0.0876121
$261$	10678.2	2.53243
$262$	−142.372	−0.0335717
$263$	−7926.76	−1.85850	−0.929249	−	0.369455i	$-0.879544\pi$
$263$	−7926.76	−1.85850	−0.929249	+	0.369455i	$0.879544\pi$
$264$	−395.454	−0.0921912
$265$	−975.485	−0.226127
$266$	−348.940	−0.0804320
$267$	−2947.83	−0.675671
$268$	−2787.60	−0.635373
$269$	−1737.10	−0.393729	−0.196864	−	0.980431i	$-0.563076\pi$
$269$	−1737.10	−0.393729	−0.196864	+	0.980431i	$0.563076\pi$
$270$	−416.540	−0.0938882
$271$	993.779	0.222759	0.111380	−	0.993778i	$-0.464473\pi$
$271$	993.779	0.222759	0.111380	+	0.993778i	$0.464473\pi$
$272$	6441.97	1.43604
$273$	−1023.62	−0.226932
$274$	314.415	0.0693230
$275$	−334.757	−0.0734057
$276$	0	0
$277$	71.1195	0.0154266	0.00771328	−	0.999970i	$-0.497545\pi$
$277$	71.1195	0.0154266	0.00771328	+	0.999970i	$0.497545\pi$
$278$	237.296	0.0511945
$279$	−14299.2	−3.06836
$280$	809.166	0.172703
$281$	4188.95	0.889294	0.444647	−	0.895706i	$-0.353329\pi$
$281$	4188.95	0.889294	0.444647	+	0.895706i	$0.353329\pi$
$282$	229.237	0.0484073
$283$	5653.19	1.18745	0.593723	−	0.804670i	$-0.297658\pi$
$283$	5653.19	1.18745	0.593723	+	0.804670i	$0.297658\pi$
$284$	−6097.37	−1.27399
$285$	−6146.23	−1.27744
$286$	12.8882	0.00266466
$287$	−2589.93	−0.532678
$288$	−1918.86	−0.392603
$289$	5524.81	1.12453
$290$	421.790	0.0854082
$291$	7499.41	1.51073
$292$	−7213.23	−1.44562
$293$	9184.13	1.83120	0.915602	−	0.402087i	$-0.131715\pi$
$293$	9184.13	1.83120	0.915602	+	0.402087i	$0.131715\pi$
$294$	524.285	0.104003
$295$	−2782.15	−0.549096
$296$	552.114	0.108415
$297$	−2947.62	−0.575887
$298$	−210.054	−0.0408325
$299$	0	0
$300$	−1658.94	−0.319264
$301$	3258.60	0.623995
$302$	−221.524	−0.0422095
$303$	1271.78	0.241128
$304$	−4369.02	−0.824277
$305$	4610.96	0.865648
$306$	−1027.80	−0.192011
$307$	−3586.10	−0.666677	−0.333338	−	0.942807i	$-0.608175\pi$
$307$	−3586.10	−0.666677	−0.333338	+	0.942807i	$0.608175\pi$
$308$	2855.93	0.528349
$309$	4328.92	0.796969
$310$	−564.820	−0.103483
$311$	−4763.91	−0.868607	−0.434304	−	0.900767i	$-0.643005\pi$
$311$	−4763.91	−0.868607	−0.434304	+	0.900767i	$0.643005\pi$
$312$	128.056	0.0232363
$313$	−3334.41	−0.602147	−0.301074	−	0.953601i	$-0.597345\pi$
$313$	−3334.41	−0.602147	−0.301074	+	0.953601i	$0.597345\pi$
$314$	−230.737	−0.0414689
$315$	12921.2	2.31119
$316$	3570.83	0.635680
$317$	−4486.63	−0.794935	−0.397467	−	0.917616i	$-0.630111\pi$
$317$	−4486.63	−0.794935	−0.397467	+	0.917616i	$0.630111\pi$
$318$	169.625	0.0299122
$319$	2984.78	0.523873
$320$	5002.44	0.873890
$321$	−3759.06	−0.653615
$322$	0	0
$323$	−7079.04	−1.21947
$324$	−3724.07	−0.638558
$325$	108.401	0.0185015
$326$	−318.537	−0.0541170
$327$	4469.73	0.755891
$328$	324.001	0.0545426
$329$	−3319.26	−0.556222
$330$	−249.435	−0.0416089
$331$	−449.598	−0.0746590	−0.0373295	−	0.999303i	$-0.511885\pi$
$331$	−449.598	−0.0746590	−0.0373295	+	0.999303i	$0.511885\pi$
$332$	3426.70	0.566460
$333$	8816.42	1.45086
$334$	−263.307	−0.0431363
$335$	−3525.31	−0.574950
$336$	14082.5	2.28650
$337$	9504.68	1.53636	0.768179	−	0.640235i	$-0.221163\pi$
$337$	9504.68	1.53636	0.768179	+	0.640235i	$0.221163\pi$
$338$	432.319	0.0695712
$339$	−10947.1	−1.75388
$340$	8187.57	1.30598
$341$	−3996.92	−0.634737
$342$	697.066	0.110213
$343$	1102.74	0.173593
$344$	−407.652	−0.0638928
$345$	0	0
$346$	−225.238	−0.0349968
$347$	−12480.2	−1.93076	−0.965380	−	0.260849i	$-0.915998\pi$
$347$	−12480.2	−1.93076	−0.965380	+	0.260849i	$0.915998\pi$
$348$	14791.6	2.27848
$349$	−6983.74	−1.07115	−0.535575	−	0.844488i	$-0.679905\pi$
$349$	−6983.74	−1.07115	−0.535575	+	0.844488i	$0.679905\pi$
$350$	−119.108	−0.0181902
$351$	954.498	0.145149
$352$	−536.359	−0.0812160
$353$	2371.92	0.357634	0.178817	−	0.983882i	$-0.442773\pi$
$353$	2371.92	0.357634	0.178817	+	0.983882i	$0.442773\pi$
$354$	483.783	0.0726349
$355$	−7710.98	−1.15283
$356$	−2663.26	−0.396495
$357$	22817.6	3.38274
$358$	−796.094	−0.117528
$359$	−8102.23	−1.19114	−0.595570	−	0.803303i	$-0.703074\pi$
$359$	−8102.23	−1.19114	−0.595570	+	0.803303i	$0.703074\pi$
$360$	−1616.44	−0.236650
$361$	−2057.92	−0.300032
$362$	554.568	0.0805177
$363$	9962.49	1.44048
$364$	−924.806	−0.133168
$365$	−9122.14	−1.30815
$366$	−801.789	−0.114509
$367$	−3397.55	−0.483244	−0.241622	−	0.970370i	$-0.577679\pi$
$367$	−3397.55	−0.483244	−0.241622	+	0.970370i	$0.577679\pi$
$368$	0	0
$369$	5173.81	0.729912
$370$	348.249	0.0489314
$371$	−2456.10	−0.343705
$372$	−19807.4	−2.76066
$373$	−111.632	−0.0154962	−0.00774809	−	0.999970i	$-0.502466\pi$
$373$	−111.632	−0.0154962	−0.00774809	+	0.999970i	$0.502466\pi$
$374$	−287.291	−0.0397205
$375$	−13185.9	−1.81578
$376$	415.242	0.0569533
$377$	−966.529	−0.132039
$378$	−1048.78	−0.142707
$379$	4021.13	0.544991	0.272495	−	0.962157i	$-0.412151\pi$
$379$	4021.13	0.544991	0.272495	+	0.962157i	$0.412151\pi$
$380$	−5552.90	−0.749626
$381$	−14424.9	−1.93966
$382$	745.813	0.0998929
$383$	−6352.12	−0.847463	−0.423731	−	0.905788i	$-0.639280\pi$
$383$	−6352.12	−0.847463	−0.423731	+	0.905788i	$0.639280\pi$
$384$	−3541.06	−0.470583
$385$	3611.72	0.478105
$386$	145.043	0.0191256
$387$	−6509.59	−0.855041
$388$	6775.44	0.886523
$389$	3778.39	0.492473	0.246236	−	0.969210i	$-0.420806\pi$
$389$	3778.39	0.492473	0.246236	+	0.969210i	$0.420806\pi$
$390$	80.7719	0.0104873
$391$	0	0
$392$	949.694	0.122364
$393$	−6314.07	−0.810440
$394$	−402.995	−0.0515295
$395$	4515.81	0.575228
$396$	−5705.19	−0.723981
$397$	8840.89	1.11766	0.558831	−	0.829282i	$-0.311250\pi$
$397$	8840.89	1.11766	0.558831	+	0.829282i	$0.311250\pi$
$398$	775.059	0.0976135
$399$	−15475.2	−1.94167
$400$	−1491.33	−0.186416
$401$	−6345.08	−0.790170	−0.395085	−	0.918645i	$-0.629285\pi$
$401$	−6345.08	−0.790170	−0.395085	+	0.918645i	$0.629285\pi$
$402$	613.009	0.0760550
$403$	1294.28	0.159982
$404$	1149.01	0.141498
$405$	−4709.61	−0.577833
$406$	1062.00	0.129818
$407$	2464.37	0.300133
$408$	−2854.50	−0.346369
$409$	−12450.7	−1.50525	−0.752626	−	0.658448i	$-0.771213\pi$
$409$	−12450.7	−1.50525	−0.752626	+	0.658448i	$0.771213\pi$
$410$	204.366	0.0246168
$411$	13944.0	1.67349
$412$	3911.02	0.467675
$413$	−7004.99	−0.834607
$414$	0	0
$415$	4333.54	0.512591
$416$	173.684	0.0204700
$417$	10523.8	1.23586
$418$	194.844	0.0227993
$419$	11026.1	1.28559	0.642794	−	0.766039i	$-0.277775\pi$
$419$	11026.1	1.28559	0.642794	+	0.766039i	$0.277775\pi$
$420$	17898.5	2.07942
$421$	−9350.05	−1.08241	−0.541204	−	0.840891i	$-0.682031\pi$
$421$	−9350.05	−1.08241	−0.541204	+	0.840891i	$0.682031\pi$
$422$	−127.867	−0.0147500
$423$	6630.78	0.762174
$424$	307.260	0.0351931
$425$	−2416.37	−0.275791
$426$	1340.84	0.152498
$427$	11609.6	1.31576
$428$	−3396.18	−0.383553
$429$	571.578	0.0643264
$430$	−257.129	−0.0288369
$431$	−9598.85	−1.07276	−0.536381	−	0.843976i	$-0.680209\pi$
$431$	−9598.85	−1.07276	−0.536381	+	0.843976i	$0.680209\pi$
$432$	−13131.5	−1.46248
$433$	2841.22	0.315336	0.157668	−	0.987492i	$-0.449602\pi$
$433$	2841.22	0.315336	0.157668	+	0.987492i	$0.449602\pi$
$434$	−1422.12	−0.157290
$435$	18706.0	2.06180
$436$	4038.24	0.443570
$437$	0	0
$438$	1586.23	0.173043
$439$	6795.87	0.738836	0.369418	−	0.929263i	$-0.379557\pi$
$439$	6795.87	0.738836	0.369418	+	0.929263i	$0.379557\pi$
$440$	−451.828	−0.0489547
$441$	15165.2	1.63753
$442$	93.0305	0.0100113
$443$	−7238.65	−0.776340	−0.388170	−	0.921588i	$-0.626893\pi$
$443$	−7238.65	−0.776340	−0.388170	+	0.921588i	$0.626893\pi$
$444$	12212.6	1.30537
$445$	−3368.06	−0.358790
$446$	−5.60621	−0.000595205 0
$447$	−9315.69	−0.985720
$448$	12595.3	1.32828
$449$	14383.3	1.51179	0.755893	−	0.654696i	$-0.227203\pi$
$449$	14383.3	1.51179	0.755893	+	0.654696i	$0.227203\pi$
$450$	237.938	0.0249255
$451$	1446.18	0.150993
$452$	−9890.32	−1.02921
$453$	−9824.37	−1.01896
$454$	1350.07	0.139564
$455$	−1169.55	−0.120504
$456$	1935.95	0.198814
$457$	−7446.84	−0.762251	−0.381125	−	0.924523i	$-0.624463\pi$
$457$	−7446.84	−0.762251	−0.381125	+	0.924523i	$0.624463\pi$
$458$	55.8770	0.00570078
$459$	−21276.8	−2.16365
$460$	0	0
$461$	−10563.3	−1.06720	−0.533602	−	0.845735i	$-0.679162\pi$
$461$	−10563.3	−1.06720	−0.533602	+	0.845735i	$0.679162\pi$
$462$	−628.034	−0.0632441
$463$	−1191.98	−0.119646	−0.0598230	−	0.998209i	$-0.519054\pi$
$463$	−1191.98	−0.119646	−0.0598230	+	0.998209i	$0.519054\pi$
$464$	13297.1	1.33039
$465$	−25049.2	−2.49813
$466$	394.651	0.0392314
$467$	18859.4	1.86875	0.934375	−	0.356290i	$-0.115958\pi$
$467$	18859.4	1.86875	0.934375	+	0.356290i	$0.115958\pi$
$468$	1847.45	0.182475
$469$	−8876.13	−0.873906
$470$	261.916	0.0257049
$471$	−10233.0	−1.00108
$472$	876.328	0.0854582
$473$	−1819.56	−0.176878
$474$	−785.244	−0.0760917
$475$	1638.81	0.158302
$476$	20614.9	1.98505
$477$	4906.47	0.470968
$478$	−977.204	−0.0935069
$479$	−4024.11	−0.383854	−0.191927	−	0.981409i	$-0.561474\pi$
$479$	−4024.11	−0.383854	−0.191927	+	0.981409i	$0.561474\pi$
$480$	−3361.43	−0.319641
$481$	−798.010	−0.0756469
$482$	949.959	0.0897706
$483$	0	0
$484$	9000.75	0.845299
$485$	8568.50	0.802217
$486$	−298.207	−0.0278333
$487$	−14938.2	−1.38997	−0.694983	−	0.719026i	$-0.744588\pi$
$487$	−14938.2	−1.38997	−0.694983	+	0.719026i	$0.744588\pi$
$488$	−1452.37	−0.134725
$489$	−14126.8	−1.30641
$490$	599.025	0.0552270
$491$	15589.4	1.43287	0.716436	−	0.697653i	$-0.245772\pi$
$491$	15589.4	1.43287	0.716436	+	0.697653i	$0.245772\pi$
$492$	7166.80	0.656716
$493$	21545.0	1.96823
$494$	−63.0943	−0.00574645
$495$	−7215.01	−0.655132
$496$	−17806.1	−1.61193
$497$	−19414.9	−1.75227
$498$	−753.550	−0.0678060
$499$	−4048.59	−0.363206	−0.181603	−	0.983372i	$-0.558129\pi$
$499$	−4048.59	−0.363206	−0.181603	+	0.983372i	$0.558129\pi$
$500$	−11913.0	−1.06553
$501$	−11677.4	−1.04133
$502$	670.563	0.0596189
$503$	−4367.65	−0.387165	−0.193583	−	0.981084i	$-0.562011\pi$
$503$	−4367.65	−0.387165	−0.193583	+	0.981084i	$0.562011\pi$
$504$	−4069.93	−0.359700
$505$	1453.08	0.128042
$506$	0	0
$507$	19172.9	1.67949
$508$	−13032.4	−1.13823
$509$	−6168.89	−0.537193	−0.268597	−	0.963253i	$-0.586560\pi$
$509$	−6168.89	−0.537193	−0.268597	+	0.963253i	$0.586560\pi$
$510$	−1800.49	−0.156328
$511$	−22968.0	−1.98834
$512$	−3989.01	−0.344318
$513$	14430.1	1.24192
$514$	−1396.34	−0.119824
$515$	4946.03	0.423200
$516$	−9017.14	−0.769297
$517$	1853.44	0.157667
$518$	876.832	0.0743741
$519$	−9989.10	−0.844841
$520$	146.311	0.0123388
$521$	−21832.1	−1.83586	−0.917928	−	0.396748i	$-0.870139\pi$
$521$	−21832.1	−1.83586	−0.917928	+	0.396748i	$0.870139\pi$
$522$	−2121.51	−0.177885
$523$	−12961.9	−1.08372	−0.541858	−	0.840470i	$-0.682279\pi$
$523$	−12961.9	−1.08372	−0.541858	+	0.840470i	$0.682279\pi$
$524$	−5704.54	−0.475580
$525$	−5282.32	−0.439122
$526$	1574.86	0.130546
$527$	−28850.9	−2.38475
$528$	−7863.49	−0.648134
$529$	0	0
$530$	193.806	0.0158838
$531$	13993.6	1.14364
$532$	−13981.3	−1.13941
$533$	−468.302	−0.0380571
$534$	585.665	0.0474610
$535$	−4294.94	−0.347078
$536$	1110.41	0.0894820
$537$	−35306.0	−2.83718
$538$	345.122	0.0276566
$539$	4238.97	0.338748
$540$	−16689.8	−1.33003
$541$	−8551.62	−0.679598	−0.339799	−	0.940498i	$-0.610359\pi$
$541$	−8551.62	−0.679598	−0.339799	+	0.940498i	$0.610359\pi$
$542$	−197.441	−0.0156472
$543$	24594.5	1.94374
$544$	−3871.59	−0.305135
$545$	5106.92	0.401388
$546$	203.370	0.0159403
$547$	9562.02	0.747426	0.373713	−	0.927544i	$-0.378084\pi$
$547$	9562.02	0.747426	0.373713	+	0.927544i	$0.378084\pi$
$548$	12597.9	0.982035
$549$	−23192.1	−1.80294
$550$	66.5083	0.00515622
$551$	−14612.0	−1.12975
$552$	0	0
$553$	11370.0	0.874328
$554$	−14.1298	−0.00108361
$555$	15444.5	1.18123
$556$	9507.92	0.725226
$557$	2940.80	0.223709	0.111854	−	0.993725i	$-0.464321\pi$
$557$	2940.80	0.223709	0.111854	+	0.993725i	$0.464321\pi$
$558$	2840.92	0.215530
$559$	589.209	0.0445812
$560$	16090.1	1.21416
$561$	−12741.1	−0.958875
$562$	−832.246	−0.0624665
$563$	−12352.5	−0.924681	−0.462341	−	0.886702i	$-0.652990\pi$
$563$	−12352.5	−0.924681	−0.462341	+	0.886702i	$0.652990\pi$
$564$	9185.01	0.685743
$565$	−12507.7	−0.931332
$566$	−1123.16	−0.0834095
$567$	−11858.0	−0.878287
$568$	2428.82	0.179421
$569$	−1872.77	−0.137980	−0.0689900	−	0.997617i	$-0.521978\pi$
$569$	−1872.77	−0.137980	−0.0689900	+	0.997617i	$0.521978\pi$
$570$	1221.11	0.0897312
$571$	−20368.8	−1.49283	−0.746416	−	0.665479i	$-0.768227\pi$
$571$	−20368.8	−1.49283	−0.746416	+	0.665479i	$0.768227\pi$
$572$	516.400	0.0377478
$573$	33076.1	2.41147
$574$	514.558	0.0374168
$575$	0	0
$576$	−25161.2	−1.82011
$577$	−4476.69	−0.322993	−0.161497	−	0.986873i	$-0.551632\pi$
$577$	−4476.69	−0.322993	−0.161497	+	0.986873i	$0.551632\pi$
$578$	−1097.65	−0.0789901
$579$	6432.50	0.461702
$580$	16900.2	1.20990
$581$	10911.1	0.779121
$582$	−1489.96	−0.106118
$583$	1371.46	0.0974270
$584$	2873.31	0.203593
$585$	2336.36	0.165122
$586$	−1824.67	−0.128629
$587$	−8331.79	−0.585843	−0.292921	−	0.956137i	$-0.594627\pi$
$587$	−8331.79	−0.585843	−0.292921	+	0.956137i	$0.594627\pi$
$588$	21006.9	1.47332
$589$	19567.0	1.36883
$590$	552.749	0.0385700
$591$	−17872.5	−1.24395
$592$	10978.7	0.762196
$593$	−17672.2	−1.22379	−0.611897	−	0.790937i	$-0.709593\pi$
$593$	−17672.2	−1.22379	−0.611897	+	0.790937i	$0.709593\pi$
$594$	585.623	0.0404519
$595$	26070.4	1.79628
$596$	−8416.39	−0.578437
$597$	34373.1	2.35644
$598$	0	0
$599$	6746.87	0.460217	0.230108	−	0.973165i	$-0.426092\pi$
$599$	6746.87	0.460217	0.230108	+	0.973165i	$0.426092\pi$
$600$	660.821	0.0449632
$601$	19281.7	1.30868	0.654339	−	0.756202i	$-0.272947\pi$
$601$	19281.7	1.30868	0.654339	+	0.756202i	$0.272947\pi$
$602$	−647.407	−0.0438311
$603$	17731.5	1.19749
$604$	−8875.97	−0.597944
$605$	11382.7	0.764914
$606$	−252.673	−0.0169375
$607$	−10210.7	−0.682769	−0.341385	−	0.939924i	$-0.610896\pi$
$607$	−10210.7	−0.682769	−0.341385	+	0.939924i	$0.610896\pi$
$608$	2625.76	0.175146
$609$	47098.5	3.13387
$610$	−916.090	−0.0608055
$611$	−600.179	−0.0397392
$612$	−41181.7	−2.72005
$613$	25743.0	1.69617	0.848085	−	0.529860i	$-0.177756\pi$
$613$	25743.0	1.69617	0.848085	+	0.529860i	$0.177756\pi$
$614$	712.475	0.0468292
$615$	9063.42	0.594264
$616$	−1137.63	−0.0744095
$617$	15056.4	0.982412	0.491206	−	0.871043i	$-0.336556\pi$
$617$	15056.4	0.982412	0.491206	+	0.871043i	$0.336556\pi$
$618$	−860.055	−0.0559813
$619$	18370.6	1.19286	0.596429	−	0.802666i	$-0.296586\pi$
$619$	18370.6	1.19286	0.596429	+	0.802666i	$0.296586\pi$
$620$	−22631.1	−1.46594
$621$	0	0
$622$	946.479	0.0610134
$623$	−8480.20	−0.545348
$624$	2546.35	0.163359
$625$	−12109.2	−0.774987
$626$	662.470	0.0422965
$627$	8641.14	0.550389
$628$	−9245.11	−0.587452
$629$	17788.5	1.12762
$630$	−2567.13	−0.162344
$631$	−23273.2	−1.46829	−0.734145	−	0.678993i	$-0.762417\pi$
$631$	−23273.2	−1.46829	−0.734145	+	0.678993i	$0.762417\pi$
$632$	−1422.40	−0.0895252
$633$	−5670.80	−0.356073
$634$	891.389	0.0558384
$635$	−16481.3	−1.02999
$636$	6796.49	0.423739
$637$	−1372.66	−0.0853797
$638$	−593.005	−0.0367983
$639$	38784.5	2.40108
$640$	−4045.86	−0.249886
$641$	17381.2	1.07101	0.535505	−	0.844532i	$-0.320121\pi$
$641$	17381.2	1.07101	0.535505	+	0.844532i	$0.320121\pi$
$642$	746.838	0.0459118
$643$	28080.8	1.72224	0.861119	−	0.508403i	$-0.169764\pi$
$643$	28080.8	1.72224	0.861119	+	0.508403i	$0.169764\pi$
$644$	0	0
$645$	−11403.4	−0.696139
$646$	1406.44	0.0856588
$647$	−7212.91	−0.438282	−0.219141	−	0.975693i	$-0.570326\pi$
$647$	−7212.91	−0.438282	−0.219141	+	0.975693i	$0.570326\pi$
$648$	1483.44	0.0899306
$649$	3911.50	0.236579
$650$	−21.5367	−0.00129960
$651$	−63069.7	−3.79707
$652$	−12763.1	−0.766626
$653$	10240.4	0.613688	0.306844	−	0.951760i	$-0.400727\pi$
$653$	10240.4	0.613688	0.306844	+	0.951760i	$0.400727\pi$
$654$	−888.031	−0.0530959
$655$	−7214.18	−0.430353
$656$	6442.68	0.383452
$657$	45882.4	2.72457
$658$	659.460	0.0390706
$659$	23388.4	1.38252	0.691261	−	0.722605i	$-0.257055\pi$
$659$	23388.4	1.38252	0.691261	+	0.722605i	$0.257055\pi$
$660$	−9994.29	−0.589435
$661$	−14508.7	−0.853744	−0.426872	−	0.904312i	$-0.640385\pi$
$661$	−14508.7	−0.853744	−0.426872	+	0.904312i	$0.640385\pi$
$662$	89.3245	0.00524426
$663$	4125.81	0.241679
$664$	−1364.99	−0.0797768
$665$	−17681.3	−1.03105
$666$	−1751.62	−0.101913
$667$	0	0
$668$	−10550.1	−0.611072
$669$	−248.630	−0.0143686
$670$	700.397	0.0403861
$671$	−6482.66	−0.372966
$672$	−8463.52	−0.485844
$673$	17715.8	1.01470	0.507352	−	0.861739i	$-0.330624\pi$
$673$	17715.8	1.01470	0.507352	+	0.861739i	$0.330624\pi$
$674$	−1888.36	−0.107918
$675$	4925.61	0.280869
$676$	17322.1	0.985552
$677$	−7260.93	−0.412201	−0.206101	−	0.978531i	$-0.566077\pi$
$677$	−7260.93	−0.412201	−0.206101	+	0.978531i	$0.566077\pi$
$678$	2174.93	0.123197
$679$	21574.0	1.21934
$680$	−3261.43	−0.183926
$681$	59874.5	3.36915
$682$	794.094	0.0445857
$683$	30080.6	1.68522	0.842609	−	0.538526i	$-0.181019\pi$
$683$	30080.6	1.68522	0.842609	+	0.538526i	$0.181019\pi$
$684$	27929.9	1.56129
$685$	15931.8	0.888646
$686$	−219.088	−0.0121936
$687$	2478.09	0.137620
$688$	−8106.06	−0.449187
$689$	−444.105	−0.0245559
$690$	0	0
$691$	−6377.88	−0.351123	−0.175562	−	0.984468i	$-0.556174\pi$
$691$	−6377.88	−0.351123	−0.175562	+	0.984468i	$0.556174\pi$
$692$	−9024.79	−0.495767
$693$	−18166.2	−0.995779
$694$	2479.53	0.135622
$695$	12024.1	0.656259
$696$	−5892.05	−0.320887
$697$	10439.0	0.567294
$698$	1387.51	0.0752406
$699$	17502.4	0.947068
$700$	−4772.38	−0.257685
$701$	−7709.10	−0.415362	−0.207681	−	0.978197i	$-0.566592\pi$
$701$	−7709.10	−0.415362	−0.207681	+	0.978197i	$0.566592\pi$
$702$	−189.636	−0.0101957
$703$	−12064.4	−0.647249
$704$	−7033.05	−0.376517
$705$	11615.7	0.620530
$706$	−471.246	−0.0251212
$707$	3658.60	0.194619
$708$	19384.1	1.02895
$709$	35861.2	1.89957	0.949784	−	0.312906i	$-0.101302\pi$
$709$	35861.2	1.89957	0.949784	+	0.312906i	$0.101302\pi$
$710$	1531.99	0.0809783
$711$	−22713.5	−1.19806
$712$	1060.88	0.0558400
$713$	0	0
$714$	−4533.33	−0.237613
$715$	653.060	0.0341581
$716$	−31897.7	−1.66491
$717$	−43338.1	−2.25731
$718$	1609.72	0.0836690
$719$	9993.59	0.518356	0.259178	−	0.965830i	$-0.416548\pi$
$719$	9993.59	0.518356	0.259178	+	0.965830i	$0.416548\pi$
$720$	−32142.6	−1.66373
$721$	12453.3	0.643251
$722$	408.861	0.0210751
$723$	42129.7	2.16711
$724$	22220.3	1.14062
$725$	−4987.69	−0.255501
$726$	−1979.31	−0.101183
$727$	6104.88	0.311441	0.155720	−	0.987801i	$-0.450230\pi$
$727$	6104.88	0.311441	0.155720	+	0.987801i	$0.450230\pi$
$728$	368.386	0.0187545
$729$	−25856.3	−1.31363
$730$	1812.36	0.0918881
$731$	−13134.1	−0.664545
$732$	−32125.9	−1.62214
$733$	8985.95	0.452802	0.226401	−	0.974034i	$-0.427304\pi$
$733$	8985.95	0.452802	0.226401	+	0.974034i	$0.427304\pi$
$734$	675.014	0.0339444
$735$	26566.2	1.33321
$736$	0	0
$737$	4956.32	0.247718
$738$	−1027.91	−0.0512711
$739$	19935.3	0.992331	0.496165	−	0.868228i	$-0.334741\pi$
$739$	19935.3	0.992331	0.496165	+	0.868228i	$0.334741\pi$
$740$	13953.6	0.693167
$741$	−2798.17	−0.138722
$742$	487.970	0.0241428
$743$	2078.74	0.102640	0.0513201	−	0.998682i	$-0.483657\pi$
$743$	2078.74	0.102640	0.0513201	+	0.998682i	$0.483657\pi$
$744$	7890.05	0.388795
$745$	−10643.7	−0.523430
$746$	22.1786	0.00108849
$747$	−21796.8	−1.06761
$748$	−11511.1	−0.562684
$749$	−10813.9	−0.527547
$750$	2619.73	0.127545
$751$	27501.7	1.33629	0.668143	−	0.744033i	$-0.267090\pi$
$751$	27501.7	1.33629	0.668143	+	0.744033i	$0.267090\pi$
$752$	8256.98	0.400400
$753$	29738.8	1.43923
$754$	192.027	0.00927481
$755$	−11224.9	−0.541081
$756$	−42022.1	−2.02160
$757$	−5803.29	−0.278632	−0.139316	−	0.990248i	$-0.544490\pi$
$757$	−5803.29	−0.278632	−0.139316	+	0.990248i	$0.544490\pi$
$758$	−798.904	−0.0382817
$759$	0	0
$760$	2211.93	0.105573
$761$	−4781.12	−0.227747	−0.113873	−	0.993495i	$-0.536326\pi$
$761$	−4781.12	−0.227747	−0.113873	+	0.993495i	$0.536326\pi$
$762$	2865.90	0.136247
$763$	12858.3	0.610096
$764$	29883.0	1.41509
$765$	−52080.0	−2.46138
$766$	1262.02	0.0595282
$767$	−1266.62	−0.0596284
$768$	−34322.8	−1.61265
$769$	12230.2	0.573516	0.286758	−	0.958003i	$-0.407422\pi$
$769$	12230.2	0.573516	0.286758	+	0.958003i	$0.407422\pi$
$770$	−717.564	−0.0335834
$771$	−61926.1	−2.89263
$772$	5811.53	0.270935
$773$	−28377.2	−1.32038	−0.660191	−	0.751098i	$-0.729525\pi$
$773$	−28377.2	−1.32038	−0.660191	+	0.751098i	$0.729525\pi$
$774$	1293.30	0.0600605
$775$	6679.03	0.309571
$776$	−2698.92	−0.124853
$777$	38886.7	1.79543
$778$	−750.677	−0.0345927
$779$	−7079.82	−0.325624
$780$	3236.35	0.148564
$781$	10841.0	0.496701
$782$	0	0
$783$	−43918.0	−2.00447
$784$	18884.4	0.860260
$785$	−11691.7	−0.531587
$786$	1254.46	0.0569276
$787$	6706.08	0.303743	0.151872	−	0.988400i	$-0.451470\pi$
$787$	6706.08	0.303743	0.151872	+	0.988400i	$0.451470\pi$
$788$	−16147.1	−0.729971
$789$	69843.6	3.15145
$790$	−897.186	−0.0404056
$791$	−31492.2	−1.41559
$792$	2272.60	0.101961
$793$	2099.21	0.0940040
$794$	−1756.48	−0.0785076
$795$	8595.11	0.383443
$796$	31054.9	1.38280
$797$	−24717.7	−1.09855	−0.549277	−	0.835641i	$-0.685097\pi$
$797$	−24717.7	−1.09855	−0.549277	+	0.835641i	$0.685097\pi$
$798$	3074.55	0.136389
$799$	13378.6	0.592368
$800$	896.280	0.0396103
$801$	16940.6	0.747274
$802$	1260.62	0.0555038
$803$	12825.0	0.563618
$804$	24561.9	1.07740
$805$	0	0
$806$	−257.143	−0.0112376
$807$	15305.8	0.667646
$808$	−457.693	−0.0199277
$809$	24194.7	1.05147	0.525736	−	0.850648i	$-0.323790\pi$
$809$	24194.7	1.05147	0.525736	+	0.850648i	$0.323790\pi$
$810$	935.689	0.0405886
$811$	−3717.21	−0.160948	−0.0804741	−	0.996757i	$-0.525643\pi$
$811$	−3717.21	−0.160948	−0.0804741	+	0.996757i	$0.525643\pi$
$812$	42551.8	1.83901
$813$	−8756.30	−0.377733
$814$	−489.612	−0.0210822
$815$	−16140.7	−0.693722
$816$	−56761.0	−2.43509
$817$	8907.69	0.381445
$818$	2473.67	0.105733
$819$	5882.56	0.250981
$820$	8188.48	0.348724
$821$	13895.0	0.590669	0.295335	−	0.955394i	$-0.404569\pi$
$821$	13895.0	0.590669	0.295335	+	0.955394i	$0.404569\pi$
$822$	−2770.35	−0.117551
$823$	−45379.1	−1.92201	−0.961007	−	0.276525i	$-0.910817\pi$
$823$	−45379.1	−1.92201	−0.961007	+	0.276525i	$0.910817\pi$
$824$	−1557.91	−0.0658645
$825$	2949.58	0.124474
$826$	1391.73	0.0586252
$827$	26239.2	1.10330	0.551648	−	0.834077i	$-0.313999\pi$
$827$	26239.2	1.10330	0.551648	+	0.834077i	$0.313999\pi$
$828$	0	0
$829$	24569.3	1.02934	0.514672	−	0.857387i	$-0.327914\pi$
$829$	24569.3	1.02934	0.514672	+	0.857387i	$0.327914\pi$
$830$	−860.974	−0.0360058
$831$	−626.643	−0.0261588
$832$	2277.44	0.0948991
$833$	30598.1	1.27270
$834$	−2090.84	−0.0868105
$835$	−13342.1	−0.552961
$836$	7806.96	0.322978
$837$	58810.6	2.42866
$838$	−2190.63	−0.0903033
$839$	−23214.8	−0.955262	−0.477631	−	0.878561i	$-0.658504\pi$
$839$	−23214.8	−0.955262	−0.477631	+	0.878561i	$0.658504\pi$
$840$	−7129.66	−0.292853
$841$	20082.6	0.823428
$842$	1857.64	0.0760313
$843$	−36909.3	−1.50798
$844$	−5123.36	−0.208949
$845$	21906.2	0.891828
$846$	−1317.38	−0.0535372
$847$	28659.7	1.16264
$848$	6109.79	0.247418
$849$	−49810.9	−2.01355
$850$	480.076	0.0193723
$851$	0	0
$852$	53724.6	2.16030
$853$	35062.1	1.40739	0.703694	−	0.710503i	$-0.251533\pi$
$853$	35062.1	1.40739	0.703694	+	0.710503i	$0.251533\pi$
$854$	−2306.56	−0.0924224
$855$	35321.2	1.41282
$856$	1352.83	0.0540172
$857$	22603.3	0.900950	0.450475	−	0.892789i	$-0.351255\pi$
$857$	22603.3	0.900950	0.450475	+	0.892789i	$0.351255\pi$
$858$	−113.559	−0.00451847
$859$	26669.9	1.05933	0.529665	−	0.848207i	$-0.322318\pi$
$859$	26669.9	1.05933	0.529665	+	0.848207i	$0.322318\pi$
$860$	−10302.6	−0.408506
$861$	22820.1	0.903262
$862$	1907.07	0.0753538
$863$	−22584.1	−0.890814	−0.445407	−	0.895328i	$-0.646941\pi$
$863$	−22584.1	−0.890814	−0.445407	+	0.895328i	$0.646941\pi$
$864$	7891.98	0.310753
$865$	−11413.1	−0.448621
$866$	−564.484	−0.0221501
$867$	−48679.7	−1.90686
$868$	−56981.2	−2.22819
$869$	−6348.89	−0.247838
$870$	−3716.45	−0.144827
$871$	−1604.95	−0.0624361
$872$	−1608.59	−0.0624697
$873$	−43097.6	−1.67083
$874$	0	0
$875$	−37932.6	−1.46555
$876$	63556.6	2.45135
$877$	−35100.3	−1.35149	−0.675743	−	0.737137i	$-0.736177\pi$
$877$	−35100.3	−1.35149	−0.675743	+	0.737137i	$0.736177\pi$
$878$	−1350.18	−0.0518979
$879$	−80922.4	−3.10517
$880$	−8984.49	−0.344167
$881$	−44929.8	−1.71819	−0.859093	−	0.511819i	$-0.828972\pi$
$881$	−44929.8	−1.71819	−0.859093	+	0.511819i	$0.828972\pi$
$882$	−3012.97	−0.115025
$883$	−15789.5	−0.601765	−0.300883	−	0.953661i	$-0.597281\pi$
$883$	−15789.5	−0.601765	−0.300883	+	0.953661i	$0.597281\pi$
$884$	3727.52	0.141821
$885$	24513.9	0.931102
$886$	1438.15	0.0545323
$887$	−9655.87	−0.365516	−0.182758	−	0.983158i	$-0.558502\pi$
$887$	−9655.87	−0.365516	−0.182758	+	0.983158i	$0.558502\pi$
$888$	−4864.74	−0.183840
$889$	−41497.1	−1.56554
$890$	669.155	0.0252024
$891$	6621.35	0.248960
$892$	−224.628	−0.00843173
$893$	−9073.53	−0.340016
$894$	1850.81	0.0692397
$895$	−40339.1	−1.50658
$896$	−10186.8	−0.379818
$897$	0	0
$898$	−2857.63	−0.106192
$899$	−59551.9	−2.20931
$900$	9533.62	0.353097
$901$	9899.57	0.366041
$902$	−287.323	−0.0106062
$903$	−28711.9	−1.05811
$904$	3939.69	0.144947
$905$	28100.6	1.03215
$906$	1951.87	0.0715747
$907$	20754.5	0.759804	0.379902	−	0.925027i	$-0.375958\pi$
$907$	20754.5	0.759804	0.379902	+	0.925027i	$0.375958\pi$
$908$	54094.4	1.97708
$909$	−7308.67	−0.266681
$910$	232.361	0.00846451
$911$	−30666.9	−1.11530	−0.557651	−	0.830076i	$-0.688297\pi$
$911$	−30666.9	−1.11530	−0.557651	+	0.830076i	$0.688297\pi$
$912$	38495.9	1.39773
$913$	−6092.63	−0.220851
$914$	1479.51	0.0535426
$915$	−40627.7	−1.46788
$916$	2238.86	0.0807578
$917$	−18164.1	−0.654123
$918$	4227.20	0.151981
$919$	25701.9	0.922555	0.461277	−	0.887256i	$-0.347391\pi$
$919$	25701.9	0.922555	0.461277	+	0.887256i	$0.347391\pi$
$920$	0	0
$921$	31597.6	1.13048
$922$	2098.68	0.0749635
$923$	−3510.54	−0.125191
$924$	−25163.9	−0.895922
$925$	−4118.07	−0.146380
$926$	236.819	0.00840426
$927$	−24877.4	−0.881427
$928$	−7991.46	−0.282686
$929$	47880.2	1.69096	0.845478	−	0.534009i	$-0.179315\pi$
$929$	47880.2	1.69096	0.845478	+	0.534009i	$0.179315\pi$
$930$	4976.70	0.175476
$931$	−20752.0	−0.730524
$932$	15812.8	0.555756
$933$	41975.4	1.47290
$934$	−3746.91	−0.131266
$935$	−14557.4	−0.509174
$936$	−735.911	−0.0256987
$937$	−30597.8	−1.06680	−0.533398	−	0.845865i	$-0.679085\pi$
$937$	−30597.8	−1.06680	−0.533398	+	0.845865i	$0.679085\pi$
$938$	1763.48	0.0613856
$939$	29379.9	1.02106
$940$	10494.4	0.364138
$941$	18849.7	0.653010	0.326505	−	0.945195i	$-0.394129\pi$
$941$	18849.7	0.653010	0.326505	+	0.945195i	$0.394129\pi$
$942$	2033.05	0.0703188
$943$	0	0
$944$	17425.6	0.600798
$945$	−53142.8	−1.82935
$946$	361.504	0.0124244
$947$	6070.66	0.208310	0.104155	−	0.994561i	$-0.466786\pi$
$947$	6070.66	0.208310	0.104155	+	0.994561i	$0.466786\pi$
$948$	−31463.0	−1.07792
$949$	−4153.00	−0.142057
$950$	−325.593	−0.0111196
$951$	39532.2	1.34797
$952$	−8211.71	−0.279562
$953$	−26206.8	−0.890788	−0.445394	−	0.895335i	$-0.646936\pi$
$953$	−26206.8	−0.890788	−0.445394	+	0.895335i	$0.646936\pi$
$954$	−974.801	−0.0330821
$955$	37791.3	1.28052
$956$	−39154.4	−1.32463
$957$	−26299.2	−0.888331
$958$	799.496	0.0269630
$959$	40113.5	1.35071
$960$	−44077.1	−1.48186
$961$	49955.0	1.67685
$962$	158.546	0.00531365
$963$	21602.6	0.722881
$964$	38062.7	1.27170
$965$	7349.49	0.245169
$966$	0	0
$967$	−42074.3	−1.39919	−0.699595	−	0.714539i	$-0.746636\pi$
$967$	−42074.3	−1.39919	−0.699595	+	0.714539i	$0.746636\pi$
$968$	−3585.34	−0.119047
$969$	62374.2	2.06785
$970$	−1702.36	−0.0563500
$971$	16425.9	0.542875	0.271438	−	0.962456i	$-0.412501\pi$
$971$	16425.9	0.542875	0.271438	+	0.962456i	$0.412501\pi$
$972$	−11948.5	−0.394288
$973$	30274.6	0.997492
$974$	2967.87	0.0976351
$975$	−955.132	−0.0313730
$976$	−28880.0	−0.947157
$977$	17470.1	0.572077	0.286039	−	0.958218i	$-0.407661\pi$
$977$	17470.1	0.572077	0.286039	+	0.958218i	$0.407661\pi$
$978$	2806.67	0.0917662
$979$	4735.24	0.154585
$980$	24001.6	0.782350
$981$	−25686.7	−0.835996
$982$	−3097.25	−0.100649
$983$	17415.6	0.565076	0.282538	−	0.959256i	$-0.408824\pi$
$983$	17415.6	0.565076	0.282538	+	0.959256i	$0.408824\pi$
$984$	−2854.81	−0.0924879
$985$	−20420.3	−0.660553
$986$	−4280.48	−0.138254
$987$	29246.4	0.943186
$988$	−2528.05	−0.0814047
$989$	0	0
$990$	1433.45	0.0460183
$991$	10513.9	0.337018	0.168509	−	0.985700i	$-0.446105\pi$
$991$	10513.9	0.337018	0.168509	+	0.985700i	$0.446105\pi$
$992$	10701.4	0.342509
$993$	3961.46	0.126599
$994$	3857.29	0.123084
$995$	39273.2	1.25130
$996$	−30193.1	−0.960546
$997$	−52110.7	−1.65533	−0.827665	−	0.561223i	$-0.810331\pi$
$997$	−52110.7	−1.65533	−0.827665	+	0.561223i	$0.810331\pi$
$998$	804.360	0.0255126
$999$	−36260.7	−1.14839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.13		25
23.7	odd	22		23.4.c.a.3.3	✓	50
23.10	odd	22		23.4.c.a.8.3	yes	50
23.22	odd	2		529.4.a.n.1.13		25
69.53	even	22		207.4.i.a.118.3		50
69.56	even	22		207.4.i.a.100.3		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.3.3	✓	50	23.7	odd	22
23.4.c.a.8.3	yes	50	23.10	odd	22
207.4.i.a.100.3		50	69.56	even	22
207.4.i.a.118.3		50	69.53	even	22
529.4.a.m.1.13		25	1.1	even	1	trivial
529.4.a.n.1.13		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.198677 q^{2} -8.81112 q^{3} -7.96053 q^{4} -10.0672 q^{5} +1.75056 q^{6} -25.3475 q^{7} +3.17098 q^{8} +50.6358 q^{9} +2.00012 q^{10} +14.1537 q^{11} +70.1411 q^{12} -4.58325 q^{13} +5.03595 q^{14} +88.7033 q^{15} +63.0542 q^{16} +102.166 q^{17} -10.0601 q^{18} -69.2898 q^{19} +80.1402 q^{20} +223.340 q^{21} -2.81201 q^{22} -27.9399 q^{24} -23.6515 q^{25} +0.910585 q^{26} -208.258 q^{27} +201.779 q^{28} +210.883 q^{29} -17.6233 q^{30} -282.393 q^{31} -37.8953 q^{32} -124.710 q^{33} -20.2979 q^{34} +255.178 q^{35} -403.088 q^{36} +174.114 q^{37} +13.7663 q^{38} +40.3836 q^{39} -31.9229 q^{40} +102.177 q^{41} -44.3724 q^{42} -128.557 q^{43} -112.671 q^{44} -509.761 q^{45} +130.950 q^{47} -555.578 q^{48} +299.495 q^{49} +4.69900 q^{50} -900.193 q^{51} +36.4851 q^{52} +96.8973 q^{53} +41.3759 q^{54} -142.488 q^{55} -80.3765 q^{56} +610.521 q^{57} -41.8975 q^{58} +276.358 q^{59} -706.125 q^{60} -458.018 q^{61} +56.1050 q^{62} -1283.49 q^{63} -496.905 q^{64} +46.1405 q^{65} +24.7770 q^{66} +350.178 q^{67} -813.292 q^{68} -50.6980 q^{70} +765.951 q^{71} +160.565 q^{72} +906.125 q^{73} -34.5925 q^{74} +208.396 q^{75} +551.584 q^{76} -358.761 q^{77} -8.02327 q^{78} -448.567 q^{79} -634.779 q^{80} +467.817 q^{81} -20.3002 q^{82} -430.462 q^{83} -1777.90 q^{84} -1028.52 q^{85} +25.5413 q^{86} -1858.11 q^{87} +44.8812 q^{88} +334.558 q^{89} +101.278 q^{90} +116.174 q^{91} +2488.20 q^{93} -26.0168 q^{94} +697.554 q^{95} +333.900 q^{96} -851.130 q^{97} -59.5027 q^{98} +716.685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

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Database

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