LMFDB - Embedded newform 1849.4.a.m.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, 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("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.38832 q^{2} +2.26695 q^{3} +11.2573 q^{4} -13.4262 q^{5} -9.94809 q^{6} +4.85010 q^{7} -14.2943 q^{8} -21.8610 q^{9} +O(q^{10})$	\(q-4.38832 q^{2} +2.26695 q^{3} +11.2573 q^{4} -13.4262 q^{5} -9.94809 q^{6} +4.85010 q^{7} -14.2943 q^{8} -21.8610 q^{9} +58.9185 q^{10} +18.1756 q^{11} +25.5198 q^{12} +76.6741 q^{13} -21.2838 q^{14} -30.4365 q^{15} -27.3310 q^{16} +37.3001 q^{17} +95.9328 q^{18} -55.9496 q^{19} -151.144 q^{20} +10.9949 q^{21} -79.7604 q^{22} +76.1313 q^{23} -32.4043 q^{24} +55.2632 q^{25} -336.470 q^{26} -110.765 q^{27} +54.5993 q^{28} +203.259 q^{29} +133.565 q^{30} +130.660 q^{31} +234.291 q^{32} +41.2031 q^{33} -163.685 q^{34} -65.1185 q^{35} -246.096 q^{36} +42.5774 q^{37} +245.525 q^{38} +173.816 q^{39} +191.918 q^{40} +323.655 q^{41} -48.2492 q^{42} +204.609 q^{44} +293.510 q^{45} -334.088 q^{46} -544.173 q^{47} -61.9579 q^{48} -319.477 q^{49} -242.513 q^{50} +84.5574 q^{51} +863.147 q^{52} +669.866 q^{53} +486.073 q^{54} -244.030 q^{55} -69.3286 q^{56} -126.835 q^{57} -891.966 q^{58} -652.224 q^{59} -342.634 q^{60} -461.730 q^{61} -573.376 q^{62} -106.028 q^{63} -809.496 q^{64} -1029.44 q^{65} -180.813 q^{66} +892.354 q^{67} +419.900 q^{68} +172.586 q^{69} +285.761 q^{70} -807.688 q^{71} +312.486 q^{72} -621.347 q^{73} -186.843 q^{74} +125.279 q^{75} -629.844 q^{76} +88.1535 q^{77} -762.761 q^{78} +803.283 q^{79} +366.951 q^{80} +339.147 q^{81} -1420.30 q^{82} +1429.43 q^{83} +123.774 q^{84} -500.799 q^{85} +460.778 q^{87} -259.807 q^{88} -650.143 q^{89} -1288.01 q^{90} +371.877 q^{91} +857.036 q^{92} +296.199 q^{93} +2388.00 q^{94} +751.191 q^{95} +531.126 q^{96} +176.756 q^{97} +1401.96 q^{98} -397.336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.38832	−1.55151	−0.775753	−	0.631037i	$-0.782629\pi$
$2$	−4.38832	−1.55151	−0.775753	+	0.631037i	$0.782629\pi$
$3$	2.26695	0.436274	0.218137	−	0.975918i	$-0.430002\pi$
$3$	2.26695	0.436274	0.218137	+	0.975918i	$0.430002\pi$
$4$	11.2573	1.40717
$5$	−13.4262	−1.20088	−0.600439	−	0.799671i	$-0.705007\pi$
$5$	−13.4262	−1.20088	−0.600439	+	0.799671i	$0.705007\pi$
$6$	−9.94809	−0.676882
$7$	4.85010	0.261881	0.130940	−	0.991390i	$-0.458200\pi$
$7$	4.85010	0.261881	0.130940	+	0.991390i	$0.458200\pi$
$8$	−14.2943	−0.631723
$9$	−21.8610	−0.809665
$10$	58.9185	1.86317
$11$	18.1756	0.498196	0.249098	−	0.968478i	$-0.419866\pi$
$11$	18.1756	0.498196	0.249098	+	0.968478i	$0.419866\pi$
$12$	25.5198	0.613911
$13$	76.6741	1.63581	0.817906	−	0.575351i	$-0.195135\pi$
$13$	76.6741	1.63581	0.817906	+	0.575351i	$0.195135\pi$
$14$	−21.2838	−0.406309
$15$	−30.4365	−0.523912
$16$	−27.3310	−0.427046
$17$	37.3001	0.532153	0.266077	−	0.963952i	$-0.414273\pi$
$17$	37.3001	0.532153	0.266077	+	0.963952i	$0.414273\pi$
$18$	95.9328	1.25620
$19$	−55.9496	−0.675564	−0.337782	−	0.941224i	$-0.609677\pi$
$19$	−55.9496	−0.675564	−0.337782	+	0.941224i	$0.609677\pi$
$20$	−151.144	−1.68984
$21$	10.9949	0.114252
$22$	−79.7604	−0.772953
$23$	76.1313	0.690194	0.345097	−	0.938567i	$-0.387846\pi$
$23$	76.1313	0.690194	0.345097	+	0.938567i	$0.387846\pi$
$24$	−32.4043	−0.275604
$25$	55.2632	0.442106
$26$	−336.470	−2.53797
$27$	−110.765	−0.789510
$28$	54.5993	0.368510
$29$	203.259	1.30153	0.650763	−	0.759281i	$-0.274449\pi$
$29$	203.259	1.30153	0.650763	+	0.759281i	$0.274449\pi$
$30$	133.565	0.812852
$31$	130.660	0.757006	0.378503	−	0.925600i	$-0.376439\pi$
$31$	130.660	0.757006	0.378503	+	0.925600i	$0.376439\pi$
$32$	234.291	1.29429
$33$	41.2031	0.217350
$34$	−163.685	−0.825638
$35$	−65.1185	−0.314487
$36$	−246.096	−1.13933
$37$	42.5774	0.189181	0.0945903	−	0.995516i	$-0.469846\pi$
$37$	42.5774	0.189181	0.0945903	+	0.995516i	$0.469846\pi$
$38$	245.525	1.04814
$39$	173.816	0.713663
$40$	191.918	0.758622
$41$	323.655	1.23284	0.616420	−	0.787418i	$-0.288582\pi$
$41$	323.655	1.23284	0.616420	+	0.787418i	$0.288582\pi$
$42$	−48.2492	−0.177262
$43$	0	0
$43$	0	0
$44$	204.609	0.701045
$45$	293.510	0.972308
$46$	−334.088	−1.07084
$47$	−544.173	−1.68885	−0.844423	−	0.535677i	$-0.820057\pi$
$47$	−544.173	−1.68885	−0.844423	+	0.535677i	$0.820057\pi$
$48$	−61.9579	−0.186309
$49$	−319.477	−0.931418
$50$	−242.513	−0.685930
$51$	84.5574	0.232165
$52$	863.147	2.30186
$53$	669.866	1.73610	0.868049	−	0.496479i	$-0.165374\pi$
$53$	669.866	1.73610	0.868049	+	0.496479i	$0.165374\pi$
$54$	486.073	1.22493
$55$	−244.030	−0.598272
$56$	−69.3286	−0.165436
$57$	−126.835	−0.294731
$58$	−891.966	−2.01933
$59$	−652.224	−1.43919	−0.719596	−	0.694393i	$-0.755673\pi$
$59$	−652.224	−1.43919	−0.719596	+	0.694393i	$0.755673\pi$
$60$	−342.634	−0.737232
$61$	−461.730	−0.969156	−0.484578	−	0.874748i	$-0.661027\pi$
$61$	−461.730	−0.969156	−0.484578	+	0.874748i	$0.661027\pi$
$62$	−573.376	−1.17450
$63$	−106.028	−0.212036
$64$	−809.496	−1.58105
$65$	−1029.44	−1.96441
$66$	−180.813	−0.337219
$67$	892.354	1.62714	0.813570	−	0.581467i	$-0.197521\pi$
$67$	892.354	1.62714	0.813570	+	0.581467i	$0.197521\pi$
$68$	419.900	0.748829
$69$	172.586	0.301114
$70$	285.761	0.487928
$71$	−807.688	−1.35007	−0.675035	−	0.737786i	$-0.735871\pi$
$71$	−807.688	−1.35007	−0.675035	+	0.737786i	$0.735871\pi$
$72$	312.486	0.511484
$73$	−621.347	−0.996208	−0.498104	−	0.867117i	$-0.665970\pi$
$73$	−621.347	−0.996208	−0.498104	+	0.867117i	$0.665970\pi$
$74$	−186.843	−0.293515
$75$	125.279	0.192879
$76$	−629.844	−0.950632
$77$	88.1535	0.130468
$78$	−762.761	−1.10725
$79$	803.283	1.14400	0.572002	−	0.820252i	$-0.306167\pi$
$79$	803.283	1.14400	0.572002	+	0.820252i	$0.306167\pi$
$80$	366.951	0.512830
$81$	339.147	0.465222
$82$	−1420.30	−1.91276
$83$	1429.43	1.89037	0.945183	−	0.326542i	$-0.105884\pi$
$83$	1429.43	1.89037	0.945183	+	0.326542i	$0.105884\pi$
$84$	123.774	0.160772
$85$	−500.799	−0.639051
$86$	0	0
$87$	460.778	0.567822
$88$	−259.807	−0.314722
$89$	−650.143	−0.774326	−0.387163	−	0.922011i	$-0.626545\pi$
$89$	−650.143	−0.774326	−0.387163	+	0.922011i	$0.626545\pi$
$90$	−1288.01	−1.50854
$91$	371.877	0.428388
$92$	857.036	0.971219
$93$	296.199	0.330262
$94$	2388.00	2.62025
$95$	751.191	0.811270
$96$	531.126	0.564664
$97$	176.756	0.185020	0.0925098	−	0.995712i	$-0.470511\pi$
$97$	176.756	0.185020	0.0925098	+	0.995712i	$0.470511\pi$
$98$	1401.96	1.44510
$99$	−397.336	−0.403372
$100$	622.117	0.622117
$101$	−597.796	−0.588940	−0.294470	−	0.955661i	$-0.595143\pi$
$101$	−597.796	−0.588940	−0.294470	+	0.955661i	$0.595143\pi$
$102$	−371.065	−0.360205
$103$	−249.350	−0.238536	−0.119268	−	0.992862i	$-0.538055\pi$
$103$	−249.350	−0.238536	−0.119268	+	0.992862i	$0.538055\pi$
$104$	−1096.00	−1.03338
$105$	−147.620	−0.137202
$106$	−2939.59	−2.69356
$107$	207.203	0.187206	0.0936031	−	0.995610i	$-0.470162\pi$
$107$	207.203	0.187206	0.0936031	+	0.995610i	$0.470162\pi$
$108$	−1246.92	−1.11097
$109$	−1482.95	−1.30313	−0.651565	−	0.758593i	$-0.725887\pi$
$109$	−1482.95	−1.30313	−0.651565	+	0.758593i	$0.725887\pi$
$110$	1070.88	0.928222
$111$	96.5207	0.0825346
$112$	−132.558	−0.111835
$113$	311.204	0.259076	0.129538	−	0.991574i	$-0.458651\pi$
$113$	311.204	0.259076	0.129538	+	0.991574i	$0.458651\pi$
$114$	556.592	0.457277
$115$	−1022.15	−0.828839
$116$	2288.16	1.83147
$117$	−1676.17	−1.32446
$118$	2862.17	2.23291
$119$	180.909	0.139361
$120$	435.068	0.330967
$121$	−1000.65	−0.751801
$122$	2026.22	1.50365
$123$	733.709	0.537856
$124$	1470.88	1.06523
$125$	936.301	0.669962
$126$	465.284	0.328974
$127$	581.417	0.406239	0.203120	−	0.979154i	$-0.434892\pi$
$127$	581.417	0.406239	0.203120	+	0.979154i	$0.434892\pi$
$128$	1678.00	1.15872
$129$	0	0
$130$	4517.52	3.04779
$131$	1902.02	1.26855	0.634277	−	0.773106i	$-0.281298\pi$
$131$	1902.02	1.26855	0.634277	+	0.773106i	$0.281298\pi$
$132$	463.838	0.305848
$133$	−271.361	−0.176917
$134$	−3915.93	−2.52452
$135$	1487.16	0.948105
$136$	−533.177	−0.336173
$137$	−1465.86	−0.914140	−0.457070	−	0.889431i	$-0.651101\pi$
$137$	−1465.86	−0.914140	−0.457070	+	0.889431i	$0.651101\pi$
$138$	−757.361	−0.467180
$139$	−1405.80	−0.857829	−0.428914	−	0.903345i	$-0.641104\pi$
$139$	−1405.80	−0.857829	−0.428914	+	0.903345i	$0.641104\pi$
$140$	−733.061	−0.442536
$141$	−1233.61	−0.736800
$142$	3544.39	2.09464
$143$	1393.60	0.814955
$144$	597.481	0.345764
$145$	−2729.00	−1.56297
$146$	2726.67	1.54562
$147$	−724.236	−0.406354
$148$	479.308	0.266209
$149$	−158.745	−0.0872814	−0.0436407	−	0.999047i	$-0.513896\pi$
$149$	−158.745	−0.0872814	−0.0436407	+	0.999047i	$0.513896\pi$
$150$	−549.764	−0.299253
$151$	−534.424	−0.288019	−0.144009	−	0.989576i	$-0.546000\pi$
$151$	−534.424	−0.288019	−0.144009	+	0.989576i	$0.546000\pi$
$152$	799.758	0.426770
$153$	−815.416	−0.430866
$154$	−386.846	−0.202422
$155$	−1754.27	−0.909071
$156$	1956.71	1.00424
$157$	−1024.29	−0.520681	−0.260341	−	0.965517i	$-0.583835\pi$
$157$	−1024.29	−0.520681	−0.260341	+	0.965517i	$0.583835\pi$
$158$	−3525.06	−1.77493
$159$	1518.55	0.757415
$160$	−3145.64	−1.55428
$161$	369.244	0.180749
$162$	−1488.28	−0.721794
$163$	1083.83	0.520813	0.260406	−	0.965499i	$-0.416143\pi$
$163$	1083.83	0.520813	0.260406	+	0.965499i	$0.416143\pi$
$164$	3643.50	1.73481
$165$	−553.202	−0.261011
$166$	−6272.79	−2.93291
$167$	1093.16	0.506536	0.253268	−	0.967396i	$-0.418495\pi$
$167$	1093.16	0.506536	0.253268	+	0.967396i	$0.418495\pi$
$168$	−157.164	−0.0721755
$169$	3681.92	1.67588
$170$	2197.67	0.991490
$171$	1223.11	0.546981
$172$	0	0
$173$	3208.51	1.41005	0.705024	−	0.709184i	$-0.250936\pi$
$173$	3208.51	1.41005	0.705024	+	0.709184i	$0.250936\pi$
$174$	−2022.04	−0.880979
$175$	268.032	0.115779
$176$	−496.757	−0.212753
$177$	−1478.56	−0.627883
$178$	2853.04	1.20137
$179$	4089.97	1.70781	0.853907	−	0.520426i	$-0.174227\pi$
$179$	4089.97	1.70781	0.853907	+	0.520426i	$0.174227\pi$
$180$	3304.14	1.36820
$181$	−3486.25	−1.43166	−0.715832	−	0.698273i	$-0.753952\pi$
$181$	−3486.25	−1.43166	−0.715832	+	0.698273i	$0.753952\pi$
$182$	−1631.92	−0.664646
$183$	−1046.72	−0.422818
$184$	−1088.24	−0.436012
$185$	−571.653	−0.227183
$186$	−1299.81	−0.512403
$187$	677.952	0.265116
$188$	−6125.94	−2.37649
$189$	−537.222	−0.206758
$190$	−3296.47	−1.25869
$191$	−2471.76	−0.936391	−0.468195	−	0.883625i	$-0.655096\pi$
$191$	−2471.76	−0.936391	−0.468195	+	0.883625i	$0.655096\pi$
$192$	−1835.09	−0.689770
$193$	3382.39	1.26150	0.630751	−	0.775985i	$-0.282747\pi$
$193$	3382.39	1.26150	0.630751	+	0.775985i	$0.282747\pi$
$194$	−775.663	−0.287059
$195$	−2333.69	−0.857021
$196$	−3596.46	−1.31066
$197$	−9.03324	−0.00326696	−0.00163348	−	0.999999i	$-0.500520\pi$
$197$	−9.03324	−0.00326696	−0.00163348	+	0.999999i	$0.500520\pi$
$198$	1743.64	0.625833
$199$	−1093.16	−0.389406	−0.194703	−	0.980862i	$-0.562374\pi$
$199$	−1093.16	−0.389406	−0.194703	+	0.980862i	$0.562374\pi$
$200$	−789.947	−0.279289
$201$	2022.92	0.709879
$202$	2623.32	0.913744
$203$	985.827	0.340845
$204$	951.891	0.326695
$205$	−4345.46	−1.48049
$206$	1094.23	0.370089
$207$	−1664.30	−0.558826
$208$	−2095.58	−0.698568
$209$	−1016.92	−0.336563
$210$	647.804	0.212870
$211$	−5951.57	−1.94181	−0.970907	−	0.239458i	$-0.923030\pi$
$211$	−5951.57	−1.94181	−0.970907	+	0.239458i	$0.923030\pi$
$212$	7540.91	2.44298
$213$	−1830.99	−0.589001
$214$	−909.272	−0.290451
$215$	0	0
$216$	1583.31	0.498752
$217$	633.713	0.198245
$218$	6507.67	2.02181
$219$	−1408.56	−0.434620
$220$	−2747.13	−0.841869
$221$	2859.95	0.870503
$222$	−423.564	−0.128053
$223$	188.773	0.0566869	0.0283434	−	0.999598i	$-0.490977\pi$
$223$	188.773	0.0566869	0.0283434	+	0.999598i	$0.490977\pi$
$224$	1136.34	0.338949
$225$	−1208.11	−0.357958
$226$	−1365.66	−0.401958
$227$	1563.20	0.457064	0.228532	−	0.973536i	$-0.426608\pi$
$227$	1563.20	0.457064	0.228532	+	0.973536i	$0.426608\pi$
$228$	−1427.82	−0.414736
$229$	−2554.51	−0.737147	−0.368573	−	0.929599i	$-0.620154\pi$
$229$	−2554.51	−0.737147	−0.368573	+	0.929599i	$0.620154\pi$
$230$	4485.54	1.28595
$231$	199.839	0.0569198
$232$	−2905.44	−0.822204
$233$	−1786.97	−0.502438	−0.251219	−	0.967930i	$-0.580831\pi$
$233$	−1786.97	−0.502438	−0.251219	+	0.967930i	$0.580831\pi$
$234$	7355.56	2.05491
$235$	7306.18	2.02810
$236$	−7342.31	−2.02519
$237$	1821.00	0.499100
$238$	−793.888	−0.216219
$239$	−4327.04	−1.17110	−0.585551	−	0.810636i	$-0.699122\pi$
$239$	−4327.04	−1.17110	−0.585551	+	0.810636i	$0.699122\pi$
$240$	831.859	0.223735
$241$	1099.66	0.293922	0.146961	−	0.989142i	$-0.453051\pi$
$241$	1099.66	0.293922	0.146961	+	0.989142i	$0.453051\pi$
$242$	4391.16	1.16642
$243$	3759.49	0.992474
$244$	−5197.86	−1.36377
$245$	4289.36	1.11852
$246$	−3219.75	−0.834486
$247$	−4289.89	−1.10510
$248$	−1867.68	−0.478218
$249$	3240.44	0.824717
$250$	−4108.79	−1.03945
$251$	5390.37	1.35553	0.677763	−	0.735281i	$-0.262950\pi$
$251$	5390.37	1.35553	0.677763	+	0.735281i	$0.262950\pi$
$252$	−1193.59	−0.298370
$253$	1383.73	0.343852
$254$	−2551.44	−0.630283
$255$	−1135.29	−0.278801
$256$	−887.626	−0.216706
$257$	5515.79	1.33878	0.669389	−	0.742912i	$-0.266556\pi$
$257$	5515.79	1.33878	0.669389	+	0.742912i	$0.266556\pi$
$258$	0	0
$259$	206.505	0.0495428
$260$	−11588.8	−2.76426
$261$	−4443.44	−1.05380
$262$	−8346.69	−1.96817
$263$	−3768.79	−0.883626	−0.441813	−	0.897107i	$-0.645665\pi$
$263$	−3768.79	−0.883626	−0.441813	+	0.897107i	$0.645665\pi$
$264$	−588.969	−0.137305
$265$	−8993.76	−2.08484
$266$	1190.82	0.274488
$267$	−1473.84	−0.337818
$268$	10045.5	2.28966
$269$	696.594	0.157889	0.0789444	−	0.996879i	$-0.474845\pi$
$269$	696.594	0.157889	0.0789444	+	0.996879i	$0.474845\pi$
$270$	−6526.12	−1.47099
$271$	−4362.22	−0.977809	−0.488905	−	0.872337i	$-0.662603\pi$
$271$	−4362.22	−0.977809	−0.488905	+	0.872337i	$0.662603\pi$
$272$	−1019.45	−0.227254
$273$	843.026	0.186895
$274$	6432.68	1.41829
$275$	1004.44	0.220255
$276$	1942.86	0.423718
$277$	750.747	0.162845	0.0814224	−	0.996680i	$-0.474054\pi$
$277$	750.747	0.162845	0.0814224	+	0.996680i	$0.474054\pi$
$278$	6169.09	1.33093
$279$	−2856.35	−0.612921
$280$	930.821	0.198669
$281$	3887.21	0.825238	0.412619	−	0.910904i	$-0.364614\pi$
$281$	3887.21	0.825238	0.412619	+	0.910904i	$0.364614\pi$
$282$	5413.48	1.14315
$283$	−3762.13	−0.790230	−0.395115	−	0.918632i	$-0.629295\pi$
$283$	−3762.13	−0.790230	−0.395115	+	0.918632i	$0.629295\pi$
$284$	−9092.42	−1.89977
$285$	1702.91	0.353936
$286$	−6115.55	−1.26441
$287$	1569.76	0.322857
$288$	−5121.83	−1.04794
$289$	−3521.70	−0.716813
$290$	11975.7	2.42496
$291$	400.697	0.0807192
$292$	−6994.72	−1.40183
$293$	501.998	0.100092	0.0500461	−	0.998747i	$-0.484063\pi$
$293$	501.998	0.100092	0.0500461	+	0.998747i	$0.484063\pi$
$294$	3178.18	0.630460
$295$	8756.90	1.72829
$296$	−608.612	−0.119510
$297$	−2013.22	−0.393330
$298$	696.625	0.135418
$299$	5837.30	1.12903
$300$	1410.31	0.271414
$301$	0	0
$302$	2345.22	0.446863
$303$	−1355.17	−0.256939
$304$	1529.16	0.288497
$305$	6199.29	1.16384
$306$	3578.30	0.668490
$307$	−169.131	−0.0314424	−0.0157212	−	0.999876i	$-0.505004\pi$
$307$	−169.131	−0.0314424	−0.0157212	+	0.999876i	$0.505004\pi$
$308$	992.375	0.183590
$309$	−565.263	−0.104067
$310$	7698.28	1.41043
$311$	362.992	0.0661845	0.0330922	−	0.999452i	$-0.489464\pi$
$311$	362.992	0.0661845	0.0330922	+	0.999452i	$0.489464\pi$
$312$	−2484.57	−0.450837
$313$	9562.92	1.72693	0.863464	−	0.504411i	$-0.168290\pi$
$313$	9562.92	1.72693	0.863464	+	0.504411i	$0.168290\pi$
$314$	4494.90	0.807840
$315$	1423.55	0.254629
$316$	9042.83	1.60981
$317$	6118.58	1.08408	0.542040	−	0.840352i	$-0.317652\pi$
$317$	6118.58	1.08408	0.542040	+	0.840352i	$0.317652\pi$
$318$	−6663.89	−1.17513
$319$	3694.36	0.648415
$320$	10868.5	1.89864
$321$	469.718	0.0816732
$322$	−1620.36	−0.280432
$323$	−2086.93	−0.359504
$324$	3817.89	0.654645
$325$	4237.26	0.723203
$326$	−4756.21	−0.808044
$327$	−3361.78	−0.568522
$328$	−4626.41	−0.778813
$329$	−2639.29	−0.442277
$330$	2427.63	0.404959
$331$	7770.57	1.29036	0.645180	−	0.764031i	$-0.276783\pi$
$331$	7770.57	1.29036	0.645180	+	0.764031i	$0.276783\pi$
$332$	16091.6	2.66006
$333$	−930.782	−0.153173
$334$	−4797.15	−0.785893
$335$	−11980.9	−1.95400
$336$	−300.502	−0.0487908
$337$	−5681.31	−0.918341	−0.459170	−	0.888348i	$-0.651853\pi$
$337$	−5681.31	−0.918341	−0.459170	+	0.888348i	$0.651853\pi$
$338$	−16157.4	−2.60014
$339$	705.483	0.113028
$340$	−5637.67	−0.899251
$341$	2374.82	0.377137
$342$	−5367.40	−0.848643
$343$	−3213.08	−0.505801
$344$	0	0
$345$	−2317.17	−0.361601
$346$	−14079.9	−2.18770
$347$	8891.95	1.37563	0.687817	−	0.725884i	$-0.258569\pi$
$347$	8891.95	1.37563	0.687817	+	0.725884i	$0.258569\pi$
$348$	5187.13	0.799022
$349$	11446.3	1.75560	0.877800	−	0.479027i	$-0.159011\pi$
$349$	11446.3	1.75560	0.877800	+	0.479027i	$0.159011\pi$
$350$	−1176.21	−0.179632
$351$	−8492.82	−1.29149
$352$	4258.38	0.644809
$353$	2218.77	0.334541	0.167271	−	0.985911i	$-0.446505\pi$
$353$	2218.77	0.334541	0.167271	+	0.985911i	$0.446505\pi$
$354$	6488.38	0.974163
$355$	10844.2	1.62127
$356$	−7318.88	−1.08961
$357$	410.112	0.0607995
$358$	−17948.1	−2.64968
$359$	−732.189	−0.107642	−0.0538210	−	0.998551i	$-0.517140\pi$
$359$	−732.189	−0.107642	−0.0538210	+	0.998551i	$0.517140\pi$
$360$	−4195.51	−0.614229
$361$	−3728.64	−0.543613
$362$	15298.8	2.22123
$363$	−2268.41	−0.327991
$364$	4186.35	0.602814
$365$	8342.34	1.19632
$366$	4593.33	0.656004
$367$	9520.15	1.35408	0.677041	−	0.735946i	$-0.263262\pi$
$367$	9520.15	1.35408	0.677041	+	0.735946i	$0.263262\pi$
$368$	−2080.74	−0.294745
$369$	−7075.41	−0.998187
$370$	2508.60	0.352475
$371$	3248.92	0.454651
$372$	3334.41	0.464734
$373$	13355.2	1.85390	0.926952	−	0.375181i	$-0.122419\pi$
$373$	13355.2	1.85390	0.926952	+	0.375181i	$0.122419\pi$
$374$	−2975.07	−0.411329
$375$	2122.54	0.292287
$376$	7778.55	1.06688
$377$	15584.7	2.12905
$378$	2357.50	0.320785
$379$	4050.20	0.548930	0.274465	−	0.961597i	$-0.411499\pi$
$379$	4050.20	0.548930	0.274465	+	0.961597i	$0.411499\pi$
$380$	8456.42	1.14159
$381$	1318.04	0.177232
$382$	10846.9	1.45282
$383$	13610.9	1.81588	0.907940	−	0.419100i	$-0.137654\pi$
$383$	13610.9	1.81588	0.907940	+	0.419100i	$0.137654\pi$
$384$	3803.94	0.505518
$385$	−1183.57	−0.156676
$386$	−14843.0	−1.95723
$387$	0	0
$388$	1989.81	0.260354
$389$	9483.01	1.23601	0.618004	−	0.786175i	$-0.287941\pi$
$389$	9483.01	1.23601	0.618004	+	0.786175i	$0.287941\pi$
$390$	10241.0	1.32967
$391$	2839.70	0.367289
$392$	4566.68	0.588399
$393$	4311.79	0.553437
$394$	39.6407	0.00506871
$395$	−10785.0	−1.37381
$396$	−4472.95	−0.567611
$397$	10750.0	1.35901	0.679505	−	0.733670i	$-0.262194\pi$
$397$	10750.0	1.35901	0.679505	+	0.733670i	$0.262194\pi$
$398$	4797.12	0.604166
$399$	−615.162	−0.0771845
$400$	−1510.40	−0.188800
$401$	−1329.75	−0.165597	−0.0827986	−	0.996566i	$-0.526386\pi$
$401$	−1329.75	−0.165597	−0.0827986	+	0.996566i	$0.526386\pi$
$402$	−8877.22	−1.10138
$403$	10018.2	1.23832
$404$	−6729.60	−0.828738
$405$	−4553.46	−0.558674
$406$	−4326.12	−0.528823
$407$	773.870	0.0942489
$408$	−1208.69	−0.146664
$409$	9901.11	1.19701	0.598507	−	0.801118i	$-0.295761\pi$
$409$	9901.11	1.19701	0.598507	+	0.801118i	$0.295761\pi$
$410$	19069.3	2.29699
$411$	−3323.04	−0.398816
$412$	−2807.02	−0.335660
$413$	−3163.35	−0.376897
$414$	7303.49	0.867021
$415$	−19191.8	−2.27010
$416$	17964.1	2.11721
$417$	−3186.87	−0.374248
$418$	4462.56	0.522179
$419$	−1906.90	−0.222335	−0.111168	−	0.993802i	$-0.535459\pi$
$419$	−1906.90	−0.222335	−0.111168	+	0.993802i	$0.535459\pi$
$420$	−1661.81	−0.193067
$421$	−4367.85	−0.505644	−0.252822	−	0.967513i	$-0.581359\pi$
$421$	−4367.85	−0.505644	−0.252822	+	0.967513i	$0.581359\pi$
$422$	26117.4	3.01273
$423$	11896.1	1.36740
$424$	−9575.24	−1.09673
$425$	2061.32	0.235268
$426$	8034.95	0.913837
$427$	−2239.44	−0.253803
$428$	2332.55	0.263430
$429$	3159.21	0.355544
$430$	0	0
$431$	−3926.87	−0.438864	−0.219432	−	0.975628i	$-0.570420\pi$
$431$	−3926.87	−0.438864	−0.219432	+	0.975628i	$0.570420\pi$
$432$	3027.32	0.337157
$433$	583.678	0.0647801	0.0323900	−	0.999475i	$-0.489688\pi$
$433$	583.678	0.0647801	0.0323900	+	0.999475i	$0.489688\pi$
$434$	−2780.93	−0.307579
$435$	−6186.50	−0.681885
$436$	−16694.1	−1.83372
$437$	−4259.51	−0.466271
$438$	6181.22	0.674315
$439$	5300.61	0.576274	0.288137	−	0.957589i	$-0.406964\pi$
$439$	5300.61	0.576274	0.288137	+	0.957589i	$0.406964\pi$
$440$	3488.22	0.377942
$441$	6984.06	0.754137
$442$	−12550.4	−1.35059
$443$	755.402	0.0810163	0.0405082	−	0.999179i	$-0.487102\pi$
$443$	755.402	0.0810163	0.0405082	+	0.999179i	$0.487102\pi$
$444$	1086.57	0.116140
$445$	8728.96	0.929871
$446$	−828.396	−0.0879500
$447$	−359.867	−0.0380786
$448$	−3926.14	−0.414046
$449$	−86.8017	−0.00912344	−0.00456172	−	0.999990i	$-0.501452\pi$
$449$	−86.8017	−0.00912344	−0.00456172	+	0.999990i	$0.501452\pi$
$450$	5301.56	0.555373
$451$	5882.63	0.614195
$452$	3503.33	0.364564
$453$	−1211.51	−0.125655
$454$	−6859.83	−0.709136
$455$	−4992.90	−0.514441
$456$	1813.01	0.186189
$457$	−1896.34	−0.194107	−0.0970537	−	0.995279i	$-0.530942\pi$
$457$	−1896.34	−0.194107	−0.0970537	+	0.995279i	$0.530942\pi$
$458$	11210.0	1.14369
$459$	−4131.55	−0.420140
$460$	−11506.7	−1.16632
$461$	−3916.84	−0.395717	−0.197858	−	0.980231i	$-0.563399\pi$
$461$	−3916.84	−0.395717	−0.197858	+	0.980231i	$0.563399\pi$
$462$	−876.959	−0.0883113
$463$	7608.42	0.763700	0.381850	−	0.924224i	$-0.375287\pi$
$463$	7608.42	0.763700	0.381850	+	0.924224i	$0.375287\pi$
$464$	−5555.27	−0.555812
$465$	−3976.83	−0.396604
$466$	7841.78	0.779535
$467$	739.418	0.0732680	0.0366340	−	0.999329i	$-0.488336\pi$
$467$	739.418	0.0732680	0.0366340	+	0.999329i	$0.488336\pi$
$468$	−18869.2	−1.86374
$469$	4328.01	0.426117
$470$	−32061.9	−3.14660
$471$	−2322.00	−0.227160
$472$	9323.07	0.909171
$473$	0	0
$474$	−7991.13	−0.774356
$475$	−3091.96	−0.298671
$476$	2036.56	0.196104
$477$	−14643.9	−1.40566
$478$	18988.4	1.81697
$479$	11617.1	1.10814	0.554069	−	0.832470i	$-0.313074\pi$
$479$	11617.1	1.10814	0.554069	+	0.832470i	$0.313074\pi$
$480$	−7131.01	−0.678092
$481$	3264.58	0.309464
$482$	−4825.64	−0.456021
$483$	837.057	0.0788560
$484$	−11264.6	−1.05791
$485$	−2373.17	−0.222186
$486$	−16497.8	−1.53983
$487$	−11616.8	−1.08092	−0.540458	−	0.841371i	$-0.681749\pi$
$487$	−11616.8	−1.08092	−0.540458	+	0.841371i	$0.681749\pi$
$488$	6600.09	0.612238
$489$	2457.00	0.227217
$490$	−18823.1	−1.73539
$491$	5834.48	0.536265	0.268133	−	0.963382i	$-0.413593\pi$
$491$	5834.48	0.536265	0.268133	+	0.963382i	$0.413593\pi$
$492$	8259.61	0.756854
$493$	7581.59	0.692611
$494$	18825.4	1.71456
$495$	5334.72	0.484400
$496$	−3571.06	−0.323276
$497$	−3917.37	−0.353557
$498$	−14220.1	−1.27955
$499$	−598.307	−0.0536751	−0.0268376	−	0.999640i	$-0.508544\pi$
$499$	−598.307	−0.0536751	−0.0268376	+	0.999640i	$0.508544\pi$
$500$	10540.3	0.942749
$501$	2478.14	0.220989
$502$	−23654.6	−2.10310
$503$	12750.2	1.13022	0.565112	−	0.825014i	$-0.308833\pi$
$503$	12750.2	1.13022	0.565112	+	0.825014i	$0.308833\pi$
$504$	1515.59	0.133948
$505$	8026.14	0.707245
$506$	−6072.26	−0.533488
$507$	8346.71	0.731145
$508$	6545.21	0.571647
$509$	−9554.78	−0.832039	−0.416020	−	0.909356i	$-0.636575\pi$
$509$	−9554.78	−0.832039	−0.416020	+	0.909356i	$0.636575\pi$
$510$	4981.99	0.432562
$511$	−3013.60	−0.260888
$512$	−9528.81	−0.822496
$513$	6197.27	0.533365
$514$	−24205.1	−2.07712
$515$	3347.82	0.286452
$516$	0	0
$517$	−9890.68	−0.841376
$518$	−906.208	−0.0768658
$519$	7273.51	0.615167
$520$	14715.1	1.24096
$521$	7375.83	0.620232	0.310116	−	0.950699i	$-0.399632\pi$
$521$	7375.83	0.620232	0.310116	+	0.950699i	$0.399632\pi$
$522$	19499.2	1.63498
$523$	−8502.64	−0.710888	−0.355444	−	0.934698i	$-0.615670\pi$
$523$	−8502.64	−0.710888	−0.355444	+	0.934698i	$0.615670\pi$
$524$	21411.7	1.78507
$525$	607.615	0.0505114
$526$	16538.7	1.37095
$527$	4873.62	0.402843
$528$	−1126.12	−0.0928185
$529$	−6371.03	−0.523632
$530$	39467.5	3.23464
$531$	14258.2	1.16526
$532$	−3054.81	−0.248952
$533$	24816.0	2.01669
$534$	6467.68	0.524127
$535$	−2781.95	−0.224812
$536$	−12755.5	−1.02790
$537$	9271.74	0.745075
$538$	−3056.88	−0.244965
$539$	−5806.68	−0.464029
$540$	16741.4	1.33414
$541$	12164.9	0.966745	0.483372	−	0.875415i	$-0.339412\pi$
$541$	12164.9	0.966745	0.483372	+	0.875415i	$0.339412\pi$
$542$	19142.8	1.51708
$543$	−7903.15	−0.624598
$544$	8739.08	0.688759
$545$	19910.4	1.56490
$546$	−3699.47	−0.289968
$547$	12391.6	0.968603	0.484301	−	0.874901i	$-0.339074\pi$
$547$	12391.6	0.968603	0.484301	+	0.874901i	$0.339074\pi$
$548$	−16501.7	−1.28635
$549$	10093.9	0.784691
$550$	−4407.82	−0.341727
$551$	−11372.3	−0.879265
$552$	−2466.98	−0.190221
$553$	3896.00	0.299593
$554$	−3294.52	−0.252655
$555$	−1295.91	−0.0991139
$556$	−15825.5	−1.20711
$557$	−12135.5	−0.923157	−0.461578	−	0.887099i	$-0.652717\pi$
$557$	−12135.5	−0.923157	−0.461578	+	0.887099i	$0.652717\pi$
$558$	12534.6	0.950950
$559$	0	0
$560$	1779.75	0.134300
$561$	1536.88	0.115663
$562$	−17058.3	−1.28036
$563$	5346.09	0.400197	0.200098	−	0.979776i	$-0.435874\pi$
$563$	5346.09	0.400197	0.200098	+	0.979776i	$0.435874\pi$
$564$	−13887.2	−1.03680
$565$	−4178.29	−0.311119
$566$	16509.4	1.22605
$567$	1644.90	0.121833
$568$	11545.3	0.852870
$569$	−16220.4	−1.19507	−0.597535	−	0.801843i	$-0.703853\pi$
$569$	−16220.4	−1.19507	−0.597535	+	0.801843i	$0.703853\pi$
$570$	−7472.92	−0.549133
$571$	25303.3	1.85448	0.927241	−	0.374464i	$-0.122173\pi$
$571$	25303.3	1.85448	0.927241	+	0.374464i	$0.122173\pi$
$572$	15688.2	1.14678
$573$	−5603.36	−0.408523
$574$	−6888.61	−0.500914
$575$	4207.26	0.305139
$576$	17696.4	1.28012
$577$	225.432	0.0162649	0.00813245	−	0.999967i	$-0.497411\pi$
$577$	225.432	0.0162649	0.00813245	+	0.999967i	$0.497411\pi$
$578$	15454.4	1.11214
$579$	7667.71	0.550361
$580$	−30721.3	−2.19937
$581$	6932.88	0.495050
$582$	−1758.39	−0.125236
$583$	12175.2	0.864916
$584$	8881.70	0.629328
$585$	22504.6	1.59051
$586$	−2202.93	−0.155294
$587$	−5643.66	−0.396829	−0.198415	−	0.980118i	$-0.563579\pi$
$587$	−5643.66	−0.396829	−0.198415	+	0.980118i	$0.563579\pi$
$588$	−8152.98	−0.571808
$589$	−7310.36	−0.511406
$590$	−38428.1	−2.68146
$591$	−20.4779	−0.00142529
$592$	−1163.68	−0.0807889
$593$	−4561.15	−0.315859	−0.157929	−	0.987450i	$-0.550482\pi$
$593$	−4561.15	−0.315859	−0.157929	+	0.987450i	$0.550482\pi$
$594$	8834.67	0.610254
$595$	−2428.93	−0.167355
$596$	−1787.05	−0.122820
$597$	−2478.13	−0.169888
$598$	−25615.9	−1.75169
$599$	15069.7	1.02793	0.513966	−	0.857811i	$-0.328176\pi$
$599$	15069.7	1.02793	0.513966	+	0.857811i	$0.328176\pi$
$600$	−1790.77	−0.121846
$601$	7606.72	0.516281	0.258140	−	0.966107i	$-0.416890\pi$
$601$	7606.72	0.516281	0.258140	+	0.966107i	$0.416890\pi$
$602$	0	0
$603$	−19507.7	−1.31744
$604$	−6016.20	−0.405291
$605$	13434.9	0.902821
$606$	5946.93	0.398643
$607$	−7572.42	−0.506351	−0.253176	−	0.967420i	$-0.581475\pi$
$607$	−7572.42	−0.506351	−0.253176	+	0.967420i	$0.581475\pi$
$608$	−13108.5	−0.874374
$609$	2234.82	0.148702
$610$	−27204.5	−1.80570
$611$	−41724.0	−2.76264
$612$	−9179.41	−0.606300
$613$	−16577.7	−1.09228	−0.546141	−	0.837693i	$-0.683904\pi$
$613$	−16577.7	−1.09228	−0.546141	+	0.837693i	$0.683904\pi$
$614$	742.201	0.0487831
$615$	−9850.93	−0.645899
$616$	−1260.09	−0.0824196
$617$	1399.11	0.0912904	0.0456452	−	0.998958i	$-0.485466\pi$
$617$	1399.11	0.0912904	0.0456452	+	0.998958i	$0.485466\pi$
$618$	2480.55	0.161460
$619$	22973.1	1.49171	0.745853	−	0.666110i	$-0.232042\pi$
$619$	22973.1	1.49171	0.745853	+	0.666110i	$0.232042\pi$
$620$	−19748.4	−1.27922
$621$	−8432.70	−0.544915
$622$	−1592.92	−0.102686
$623$	−3153.26	−0.202781
$624$	−4750.56	−0.304767
$625$	−19478.9	−1.24665
$626$	−41965.2	−2.67934
$627$	−2305.30	−0.146834
$628$	−11530.7	−0.732686
$629$	1588.14	0.100673
$630$	−6247.00	−0.395058
$631$	−19453.7	−1.22732	−0.613661	−	0.789570i	$-0.710304\pi$
$631$	−19453.7	−1.22732	−0.613661	+	0.789570i	$0.710304\pi$
$632$	−11482.3	−0.722694
$633$	−13491.9	−0.847163
$634$	−26850.3	−1.68196
$635$	−7806.23	−0.487844
$636$	17094.8	1.06581
$637$	−24495.6	−1.52363
$638$	−16212.0	−1.00602
$639$	17656.8	1.09310
$640$	−22529.2	−1.39148
$641$	24542.6	1.51229	0.756143	−	0.654406i	$-0.227081\pi$
$641$	24542.6	1.51229	0.756143	+	0.654406i	$0.227081\pi$
$642$	−2061.27	−0.126716
$643$	27915.1	1.71207	0.856037	−	0.516914i	$-0.172919\pi$
$643$	27915.1	1.71207	0.856037	+	0.516914i	$0.172919\pi$
$644$	4156.71	0.254344
$645$	0	0
$646$	9158.10	0.557772
$647$	25443.2	1.54602	0.773011	−	0.634393i	$-0.218750\pi$
$647$	25443.2	1.54602	0.773011	+	0.634393i	$0.218750\pi$
$648$	−4847.85	−0.293891
$649$	−11854.6	−0.717000
$650$	−18594.4	−1.12205
$651$	1436.59	0.0864893
$652$	12201.1	0.732871
$653$	−22294.3	−1.33605	−0.668027	−	0.744137i	$-0.732861\pi$
$653$	−22294.3	−1.33605	−0.668027	+	0.744137i	$0.732861\pi$
$654$	14752.5	0.882065
$655$	−25537.0	−1.52338
$656$	−8845.80	−0.526480
$657$	13583.2	0.806595
$658$	11582.1	0.686194
$659$	−23249.1	−1.37429	−0.687144	−	0.726522i	$-0.741136\pi$
$659$	−23249.1	−1.37429	−0.687144	+	0.726522i	$0.741136\pi$
$660$	−6227.59	−0.367286
$661$	−6202.69	−0.364987	−0.182494	−	0.983207i	$-0.558417\pi$
$661$	−6202.69	−0.364987	−0.182494	+	0.983207i	$0.558417\pi$
$662$	−34099.7	−2.00200
$663$	6483.36	0.379778
$664$	−20432.6	−1.19419
$665$	3643.35	0.212456
$666$	4084.57	0.237648
$667$	15474.4	0.898306
$668$	12306.1	0.712781
$669$	427.938	0.0247310
$670$	52576.2	3.03163
$671$	−8392.23	−0.482829
$672$	2576.01	0.147875
$673$	4584.75	0.262599	0.131300	−	0.991343i	$-0.458085\pi$
$673$	4584.75	0.262599	0.131300	+	0.991343i	$0.458085\pi$
$674$	24931.4	1.42481
$675$	−6121.24	−0.349047
$676$	41448.6	2.35825
$677$	25888.2	1.46967	0.734835	−	0.678246i	$-0.237260\pi$
$677$	25888.2	1.46967	0.734835	+	0.678246i	$0.237260\pi$
$678$	−3095.89	−0.175364
$679$	857.286	0.0484531
$680$	7158.56	0.403703
$681$	3543.70	0.199405
$682$	−10421.5	−0.585130
$683$	28730.9	1.60960	0.804801	−	0.593544i	$-0.202272\pi$
$683$	28730.9	1.60960	0.804801	+	0.593544i	$0.202272\pi$
$684$	13769.0	0.769694
$685$	19681.0	1.09777
$686$	14100.0	0.784754
$687$	−5790.94	−0.321598
$688$	0	0
$689$	51361.4	2.83993
$690$	10168.5	0.561026
$691$	−4147.66	−0.228342	−0.114171	−	0.993461i	$-0.536421\pi$
$691$	−4147.66	−0.228342	−0.114171	+	0.993461i	$0.536421\pi$
$692$	36119.3	1.98417
$693$	−1927.12	−0.105635
$694$	−39020.7	−2.13430
$695$	18874.5	1.03015
$696$	−6586.48	−0.358707
$697$	12072.4	0.656060
$698$	−50229.8	−2.72382
$699$	−4050.96	−0.219201
$700$	3017.33	0.162921
$701$	−1399.85	−0.0754230	−0.0377115	−	0.999289i	$-0.512007\pi$
$701$	−1399.85	−0.0754230	−0.0377115	+	0.999289i	$0.512007\pi$
$702$	37269.2	2.00375
$703$	−2382.19	−0.127804
$704$	−14713.1	−0.787671
$705$	16562.7	0.884806
$706$	−9736.66	−0.519043
$707$	−2899.37	−0.154232
$708$	−16644.6	−0.883536
$709$	−15953.3	−0.845045	−0.422523	−	0.906352i	$-0.638855\pi$
$709$	−15953.3	−0.845045	−0.422523	+	0.906352i	$0.638855\pi$
$710$	−47587.8	−2.51541
$711$	−17560.5	−0.926260
$712$	9293.32	0.489160
$713$	9947.29	0.522481
$714$	−1799.70	−0.0943307
$715$	−18710.8	−0.978661
$716$	46042.2	2.40318
$717$	−9809.18	−0.510921
$718$	3213.08	0.167007
$719$	−8475.70	−0.439625	−0.219812	−	0.975542i	$-0.570545\pi$
$719$	−8475.70	−0.439625	−0.219812	+	0.975542i	$0.570545\pi$
$720$	−8021.91	−0.415221
$721$	−1209.37	−0.0624679
$722$	16362.5	0.843418
$723$	2492.86	0.128230
$724$	−39245.9	−2.01459
$725$	11232.8	0.575413
$726$	9954.53	0.508880
$727$	−12878.8	−0.657013	−0.328507	−	0.944502i	$-0.606545\pi$
$727$	−12878.8	−0.657013	−0.328507	+	0.944502i	$0.606545\pi$
$728$	−5315.71	−0.270623
$729$	−634.404	−0.0322311
$730$	−36608.9	−1.85610
$731$	0	0
$732$	−11783.3	−0.594976
$733$	8156.30	0.410995	0.205498	−	0.978658i	$-0.434119\pi$
$733$	8156.30	0.410995	0.205498	+	0.978658i	$0.434119\pi$
$734$	−41777.5	−2.10086
$735$	9723.75	0.487981
$736$	17836.9	0.893310
$737$	16219.1	0.810634
$738$	31049.1	1.54869
$739$	−18968.0	−0.944180	−0.472090	−	0.881550i	$-0.656500\pi$
$739$	−18968.0	−0.944180	−0.472090	+	0.881550i	$0.656500\pi$
$740$	−6435.30	−0.319684
$741$	−9724.94	−0.482125
$742$	−14257.3	−0.705393
$743$	−21221.8	−1.04785	−0.523924	−	0.851765i	$-0.675533\pi$
$743$	−21221.8	−1.04785	−0.523924	+	0.851765i	$0.675533\pi$
$744$	−4233.94	−0.208634
$745$	2131.35	0.104814
$746$	−58606.9	−2.87634
$747$	−31248.7	−1.53056
$748$	7631.94	0.373063
$749$	1004.95	0.0490257
$750$	−9314.40	−0.453485
$751$	−889.788	−0.0432341	−0.0216171	−	0.999766i	$-0.506881\pi$
$751$	−889.788	−0.0432341	−0.0216171	+	0.999766i	$0.506881\pi$
$752$	14872.8	0.721216
$753$	12219.7	0.591381
$754$	−68390.7	−3.30324
$755$	7175.30	0.345875
$756$	−6047.70	−0.290943
$757$	−37477.3	−1.79939	−0.899694	−	0.436521i	$-0.856211\pi$
$757$	−37477.3	−1.79939	−0.899694	+	0.436521i	$0.856211\pi$
$758$	−17773.6	−0.851668
$759$	3136.85	0.150014
$760$	−10737.7	−0.512498
$761$	15214.8	0.724750	0.362375	−	0.932032i	$-0.381966\pi$
$761$	15214.8	0.724750	0.362375	+	0.932032i	$0.381966\pi$
$762$	−5783.99	−0.274976
$763$	−7192.47	−0.341265
$764$	−27825.5	−1.31766
$765$	10947.9	0.517417
$766$	−59728.8	−2.81735
$767$	−50008.7	−2.35425
$768$	−2012.20	−0.0945430
$769$	−11493.4	−0.538963	−0.269482	−	0.963006i	$-0.586852\pi$
$769$	−11493.4	−0.538963	−0.269482	+	0.963006i	$0.586852\pi$
$770$	5193.88	0.243083
$771$	12504.0	0.584074
$772$	38076.8	1.77515
$773$	4855.51	0.225926	0.112963	−	0.993599i	$-0.463966\pi$
$773$	4855.51	0.225926	0.112963	+	0.993599i	$0.463966\pi$
$774$	0	0
$775$	7220.68	0.334677
$776$	−2526.60	−0.116881
$777$	468.135	0.0216142
$778$	−41614.5	−1.91767
$779$	−18108.4	−0.832862
$780$	−26271.2	−1.20597
$781$	−14680.2	−0.672599
$782$	−12461.5	−0.569851
$783$	−22514.0	−1.02757
$784$	8731.60	0.397759
$785$	13752.3	0.625274
$786$	−18921.5	−0.858661
$787$	−8470.67	−0.383668	−0.191834	−	0.981427i	$-0.561444\pi$
$787$	−8470.67	−0.383668	−0.191834	+	0.981427i	$0.561444\pi$
$788$	−101.690	−0.00459716
$789$	−8543.65	−0.385503
$790$	47328.2	2.13147
$791$	1509.37	0.0678471
$792$	5679.63	0.254819
$793$	−35402.8	−1.58536
$794$	−47174.5	−2.10851
$795$	−20388.4	−0.909562
$796$	−12306.0	−0.547960
$797$	9100.55	0.404464	0.202232	−	0.979338i	$-0.435180\pi$
$797$	9100.55	0.404464	0.202232	+	0.979338i	$0.435180\pi$
$798$	2699.53	0.119752
$799$	−20297.7	−0.898725
$800$	12947.7	0.572212
$801$	14212.7	0.626945
$802$	5835.36	0.256925
$803$	−11293.4	−0.496307
$804$	22772.7	0.998919
$805$	−4957.55	−0.217057
$806$	−43963.1	−1.92126
$807$	1579.14	0.0688828
$808$	8545.06	0.372047
$809$	26534.7	1.15316	0.576582	−	0.817039i	$-0.304386\pi$
$809$	26534.7	1.15316	0.576582	+	0.817039i	$0.304386\pi$
$810$	19982.0	0.866786
$811$	26348.7	1.14085	0.570424	−	0.821350i	$-0.306779\pi$
$811$	26348.7	1.14085	0.570424	+	0.821350i	$0.306779\pi$
$812$	11097.8	0.479626
$813$	−9888.93	−0.426593
$814$	−3395.99	−0.146228
$815$	−14551.8	−0.625432
$816$	−2311.03	−0.0991451
$817$	0	0
$818$	−43449.2	−1.85717
$819$	−8129.59	−0.346851
$820$	−48918.4	−2.08330
$821$	10423.8	0.443110	0.221555	−	0.975148i	$-0.428887\pi$
$821$	10423.8	0.443110	0.221555	+	0.975148i	$0.428887\pi$
$822$	14582.5	0.618765
$823$	12307.6	0.521284	0.260642	−	0.965436i	$-0.416066\pi$
$823$	12307.6	0.521284	0.260642	+	0.965436i	$0.416066\pi$
$824$	3564.27	0.150688
$825$	2277.02	0.0960917
$826$	13881.8	0.584758
$827$	−10411.3	−0.437771	−0.218886	−	0.975751i	$-0.570242\pi$
$827$	−10411.3	−0.437771	−0.218886	+	0.975751i	$0.570242\pi$
$828$	−18735.6	−0.786362
$829$	46689.3	1.95607	0.978037	−	0.208433i	$-0.0668362\pi$
$829$	46689.3	1.95607	0.978037	+	0.208433i	$0.0668362\pi$
$830$	84219.9	3.52207
$831$	1701.90	0.0710450
$832$	−62067.4	−2.58630
$833$	−11916.5	−0.495657
$834$	13985.0	0.580648
$835$	−14677.0	−0.608287
$836$	−11447.8	−0.473601
$837$	−14472.5	−0.597664
$838$	8368.10	0.344954
$839$	−24447.0	−1.00596	−0.502981	−	0.864297i	$-0.667764\pi$
$839$	−24447.0	−1.00596	−0.502981	+	0.864297i	$0.667764\pi$
$840$	2110.12	0.0866740
$841$	16925.3	0.693971
$842$	19167.5	0.784509
$843$	8812.11	0.360030
$844$	−66998.8	−2.73246
$845$	−49434.2	−2.01253
$846$	−52204.0	−2.12153
$847$	−4853.24	−0.196882
$848$	−18308.1	−0.741394
$849$	−8528.54	−0.344757
$850$	−9045.75	−0.365020
$851$	3241.47	0.130571
$852$	−20612.0	−0.828823
$853$	17525.8	0.703485	0.351742	−	0.936097i	$-0.385589\pi$
$853$	17525.8	0.703485	0.351742	+	0.936097i	$0.385589\pi$
$854$	9827.37	0.393777
$855$	−16421.8	−0.656856
$856$	−2961.81	−0.118262
$857$	−29314.2	−1.16844	−0.584221	−	0.811594i	$-0.698600\pi$
$857$	−29314.2	−1.16844	−0.584221	+	0.811594i	$0.698600\pi$
$858$	−13863.6	−0.551628
$859$	−24641.4	−0.978759	−0.489380	−	0.872071i	$-0.662777\pi$
$859$	−24641.4	−0.978759	−0.489380	+	0.872071i	$0.662777\pi$
$860$	0	0
$861$	3558.56	0.140854
$862$	17232.3	0.680900
$863$	−41609.9	−1.64127	−0.820637	−	0.571450i	$-0.806381\pi$
$863$	−41609.9	−1.64127	−0.820637	+	0.571450i	$0.806381\pi$
$864$	−25951.3	−1.02185
$865$	−43078.1	−1.69329
$866$	−2561.37	−0.100507
$867$	−7983.51	−0.312727
$868$	7133.92	0.278964
$869$	14600.2	0.569938
$870$	27148.3	1.05795
$871$	68420.4	2.66170
$872$	21197.7	0.823217
$873$	−3864.06	−0.149804
$874$	18692.1	0.723421
$875$	4541.15	0.175450
$876$	−15856.7	−0.611583
$877$	1996.11	0.0768572	0.0384286	−	0.999261i	$-0.487765\pi$
$877$	1996.11	0.0768572	0.0384286	+	0.999261i	$0.487765\pi$
$878$	−23260.8	−0.894092
$879$	1138.00	0.0436676
$880$	6669.57	0.255490
$881$	1423.55	0.0544390	0.0272195	−	0.999629i	$-0.491335\pi$
$881$	1423.55	0.0544390	0.0272195	+	0.999629i	$0.491335\pi$
$882$	−30648.3	−1.17005
$883$	15315.8	0.583713	0.291856	−	0.956462i	$-0.405727\pi$
$883$	15315.8	0.583713	0.291856	+	0.956462i	$0.405727\pi$
$884$	32195.5	1.22494
$885$	19851.4	0.754010
$886$	−3314.94	−0.125697
$887$	−11247.8	−0.425779	−0.212889	−	0.977076i	$-0.568287\pi$
$887$	−11247.8	−0.425779	−0.212889	+	0.977076i	$0.568287\pi$
$888$	−1379.69	−0.0521390
$889$	2819.93	0.106386
$890$	−38305.5	−1.44270
$891$	6164.20	0.231772
$892$	2125.08	0.0797680
$893$	30446.3	1.14092
$894$	1579.21	0.0590792
$895$	−54912.8	−2.05087
$896$	8138.47	0.303445
$897$	13232.8	0.492566
$898$	380.914	0.0141551
$899$	26557.8	0.985263
$900$	−13600.1	−0.503706
$901$	24986.1	0.923870
$902$	−25814.8	−0.952927
$903$	0	0
$904$	−4448.43	−0.163665
$905$	46807.2	1.71925
$906$	5316.50	0.194955
$907$	−54031.6	−1.97805	−0.989024	−	0.147757i	$-0.952795\pi$
$907$	−54031.6	−1.97805	−0.989024	+	0.147757i	$0.952795\pi$
$908$	17597.5	0.643165
$909$	13068.4	0.476844
$910$	21910.4	0.798158
$911$	36142.8	1.31445	0.657226	−	0.753694i	$-0.271730\pi$
$911$	36142.8	1.31445	0.657226	+	0.753694i	$0.271730\pi$
$912$	3466.52	0.125864
$913$	25980.8	0.941772
$914$	8321.75	0.301159
$915$	14053.5	0.507752
$916$	−28757.0	−1.03729
$917$	9225.01	0.332210
$918$	18130.6	0.651850
$919$	38701.6	1.38917	0.694585	−	0.719411i	$-0.255588\pi$
$919$	38701.6	1.38917	0.694585	+	0.719411i	$0.255588\pi$
$920$	14611.0	0.523596
$921$	−383.411	−0.0137175
$922$	17188.3	0.613957
$923$	−61928.8	−2.20846
$924$	2249.66	0.0800957
$925$	2352.96	0.0836378
$926$	−33388.2	−1.18489
$927$	5451.02	0.193134
$928$	47621.8	1.68455
$929$	14478.2	0.511317	0.255658	−	0.966767i	$-0.417708\pi$
$929$	14478.2	0.511317	0.255658	+	0.966767i	$0.417708\pi$
$930$	17451.6	0.615333
$931$	17874.6	0.629233
$932$	−20116.5	−0.707015
$933$	822.883	0.0288746
$934$	−3244.80	−0.113676
$935$	−9102.33	−0.318372
$936$	23959.6	0.836692
$937$	32844.8	1.14514	0.572568	−	0.819857i	$-0.305947\pi$
$937$	32844.8	1.14514	0.572568	+	0.819857i	$0.305947\pi$
$938$	−18992.7	−0.661122
$939$	21678.6	0.753414
$940$	82248.2	2.85387
$941$	−29672.5	−1.02795	−0.513973	−	0.857806i	$-0.671827\pi$
$941$	−29672.5	−1.02795	−0.513973	+	0.857806i	$0.671827\pi$
$942$	10189.7	0.352440
$943$	24640.3	0.850899
$944$	17825.9	0.614602
$945$	7212.86	0.248290
$946$	0	0
$947$	−25094.3	−0.861094	−0.430547	−	0.902568i	$-0.641679\pi$
$947$	−25094.3	−0.861094	−0.430547	+	0.902568i	$0.641679\pi$
$948$	20499.6	0.702317
$949$	−47641.2	−1.62961
$950$	13568.5	0.463389
$951$	13870.5	0.472956
$952$	−2585.96	−0.0880374
$953$	5265.49	0.178978	0.0894890	−	0.995988i	$-0.471477\pi$
$953$	5265.49	0.178978	0.0894890	+	0.995988i	$0.471477\pi$
$954$	64262.1	2.18088
$955$	33186.4	1.12449
$956$	−48711.0	−1.64794
$957$	8374.92	0.282887
$958$	−50979.5	−1.71928
$959$	−7109.59	−0.239396
$960$	24638.2	0.828329
$961$	−12719.0	−0.426942
$962$	−14326.0	−0.480135
$963$	−4529.65	−0.151574
$964$	12379.2	0.413597
$965$	−45412.8	−1.51491
$966$	−3673.28	−0.122345
$967$	1250.46	0.0415844	0.0207922	−	0.999784i	$-0.493381\pi$
$967$	1250.46	0.0415844	0.0207922	+	0.999784i	$0.493381\pi$
$968$	14303.5	0.474930
$969$	−4730.95	−0.156842
$970$	10414.2	0.344722
$971$	−43482.9	−1.43711	−0.718554	−	0.695472i	$-0.755196\pi$
$971$	−43482.9	−1.43711	−0.718554	+	0.695472i	$0.755196\pi$
$972$	42321.8	1.39658
$973$	−6818.26	−0.224649
$974$	50978.1	1.67705
$975$	9605.64	0.315515
$976$	12619.5	0.413874
$977$	51010.6	1.67039	0.835196	−	0.549953i	$-0.185354\pi$
$977$	51010.6	1.67039	0.835196	+	0.549953i	$0.185354\pi$
$978$	−10782.1	−0.352529
$979$	−11816.7	−0.385766
$980$	48286.8	1.57394
$981$	32418.8	1.05510
$982$	−25603.5	−0.832018
$983$	−16020.9	−0.519823	−0.259912	−	0.965632i	$-0.583693\pi$
$983$	−16020.9	−0.519823	−0.259912	+	0.965632i	$0.583693\pi$
$984$	−10487.8	−0.339776
$985$	121.282	0.00392322
$986$	−33270.4	−1.07459
$987$	−5983.14	−0.192954
$988$	−48292.7	−1.55506
$989$	0	0
$990$	−23410.5	−0.751549
$991$	−2091.09	−0.0670289	−0.0335144	−	0.999438i	$-0.510670\pi$
$991$	−2091.09	−0.0670289	−0.0335144	+	0.999438i	$0.510670\pi$
$992$	30612.4	0.979783
$993$	17615.5	0.562950
$994$	17190.7	0.548546
$995$	14677.0	0.467629
$996$	36478.8	1.16052
$997$	−54163.4	−1.72053	−0.860267	−	0.509844i	$-0.829703\pi$
$997$	−54163.4	−1.72053	−0.860267	+	0.509844i	$0.829703\pi$
$998$	2625.56	0.0832772
$999$	−4716.09	−0.149360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.18	✓	110
43.42	odd	2	inner	1849.4.a.m.1.93	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.18	✓	110	1.1	even	1	trivial
1849.4.a.m.1.93	yes	110	43.42	odd	2	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-4.38832 q^{2} +2.26695 q^{3} +11.2573 q^{4} -13.4262 q^{5} -9.94809 q^{6} +4.85010 q^{7} -14.2943 q^{8} -21.8610 q^{9} +O(q^{10})\)	\(q-4.38832 q^{2} +2.26695 q^{3} +11.2573 q^{4} -13.4262 q^{5} -9.94809 q^{6} +4.85010 q^{7} -14.2943 q^{8} -21.8610 q^{9} +58.9185 q^{10} +18.1756 q^{11} +25.5198 q^{12} +76.6741 q^{13} -21.2838 q^{14} -30.4365 q^{15} -27.3310 q^{16} +37.3001 q^{17} +95.9328 q^{18} -55.9496 q^{19} -151.144 q^{20} +10.9949 q^{21} -79.7604 q^{22} +76.1313 q^{23} -32.4043 q^{24} +55.2632 q^{25} -336.470 q^{26} -110.765 q^{27} +54.5993 q^{28} +203.259 q^{29} +133.565 q^{30} +130.660 q^{31} +234.291 q^{32} +41.2031 q^{33} -163.685 q^{34} -65.1185 q^{35} -246.096 q^{36} +42.5774 q^{37} +245.525 q^{38} +173.816 q^{39} +191.918 q^{40} +323.655 q^{41} -48.2492 q^{42} +204.609 q^{44} +293.510 q^{45} -334.088 q^{46} -544.173 q^{47} -61.9579 q^{48} -319.477 q^{49} -242.513 q^{50} +84.5574 q^{51} +863.147 q^{52} +669.866 q^{53} +486.073 q^{54} -244.030 q^{55} -69.3286 q^{56} -126.835 q^{57} -891.966 q^{58} -652.224 q^{59} -342.634 q^{60} -461.730 q^{61} -573.376 q^{62} -106.028 q^{63} -809.496 q^{64} -1029.44 q^{65} -180.813 q^{66} +892.354 q^{67} +419.900 q^{68} +172.586 q^{69} +285.761 q^{70} -807.688 q^{71} +312.486 q^{72} -621.347 q^{73} -186.843 q^{74} +125.279 q^{75} -629.844 q^{76} +88.1535 q^{77} -762.761 q^{78} +803.283 q^{79} +366.951 q^{80} +339.147 q^{81} -1420.30 q^{82} +1429.43 q^{83} +123.774 q^{84} -500.799 q^{85} +460.778 q^{87} -259.807 q^{88} -650.143 q^{89} -1288.01 q^{90} +371.877 q^{91} +857.036 q^{92} +296.199 q^{93} +2388.00 q^{94} +751.191 q^{95} +531.126 q^{96} +176.756 q^{97} +1401.96 q^{98} -397.336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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