LMFDB - Embedded newform 1859.4.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.60628 q^{2} +7.07074 q^{3} +13.2178 q^{4} -11.0597 q^{5} -32.5698 q^{6} -9.07530 q^{7} -24.0348 q^{8} +22.9953 q^{9} +O(q^{10})$	\(q-4.60628 q^{2} +7.07074 q^{3} +13.2178 q^{4} -11.0597 q^{5} -32.5698 q^{6} -9.07530 q^{7} -24.0348 q^{8} +22.9953 q^{9} +50.9440 q^{10} -11.0000 q^{11} +93.4598 q^{12} +41.8034 q^{14} -78.2001 q^{15} +4.96838 q^{16} +61.0277 q^{17} -105.923 q^{18} -73.7974 q^{19} -146.185 q^{20} -64.1690 q^{21} +50.6691 q^{22} +32.1202 q^{23} -169.944 q^{24} -2.68347 q^{25} -28.3162 q^{27} -119.956 q^{28} -76.6962 q^{29} +360.212 q^{30} +112.249 q^{31} +169.393 q^{32} -77.7781 q^{33} -281.111 q^{34} +100.370 q^{35} +303.948 q^{36} +149.193 q^{37} +339.932 q^{38} +265.817 q^{40} -172.473 q^{41} +295.581 q^{42} +394.963 q^{43} -145.396 q^{44} -254.321 q^{45} -147.955 q^{46} -257.663 q^{47} +35.1301 q^{48} -260.639 q^{49} +12.3608 q^{50} +431.511 q^{51} -204.844 q^{53} +130.432 q^{54} +121.656 q^{55} +218.123 q^{56} -521.802 q^{57} +353.284 q^{58} +250.278 q^{59} -1033.64 q^{60} -881.262 q^{61} -517.052 q^{62} -208.689 q^{63} -820.017 q^{64} +358.268 q^{66} +822.632 q^{67} +806.654 q^{68} +227.114 q^{69} -462.332 q^{70} -478.539 q^{71} -552.687 q^{72} -439.506 q^{73} -687.223 q^{74} -18.9741 q^{75} -975.442 q^{76} +99.8283 q^{77} +639.472 q^{79} -54.9487 q^{80} -821.089 q^{81} +794.461 q^{82} +419.116 q^{83} -848.175 q^{84} -674.947 q^{85} -1819.31 q^{86} -542.299 q^{87} +264.383 q^{88} -1325.32 q^{89} +1171.47 q^{90} +424.560 q^{92} +793.685 q^{93} +1186.87 q^{94} +816.176 q^{95} +1197.73 q^{96} -47.0779 q^{97} +1200.58 q^{98} -252.948 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * 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 $

$2$	−4.60628	−1.62857	−0.814283	−	0.580468i	$-0.802870\pi$
$2$	−4.60628	−1.62857	−0.814283	+	0.580468i	$0.802870\pi$
$3$	7.07074	1.36076	0.680382	−	0.732858i	$-0.261814\pi$
$3$	7.07074	1.36076	0.680382	+	0.732858i	$0.261814\pi$
$4$	13.2178	1.65223
$5$	−11.0597	−0.989208	−0.494604	−	0.869118i	$-0.664687\pi$
$5$	−11.0597	−0.989208	−0.494604	+	0.869118i	$0.664687\pi$
$6$	−32.5698	−2.21609
$7$	−9.07530	−0.490020	−0.245010	−	0.969521i	$-0.578791\pi$
$7$	−9.07530	−0.490020	−0.245010	+	0.969521i	$0.578791\pi$
$8$	−24.0348	−1.06220
$9$	22.9953	0.851678
$10$	50.9440	1.61099
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	93.4598	2.24829
$13$	0	0
$13$	0	0
$14$	41.8034	0.798030
$15$	−78.2001	−1.34608
$16$	4.96838	0.0776309
$17$	61.0277	0.870671	0.435335	−	0.900268i	$-0.356630\pi$
$17$	61.0277	0.870671	0.435335	+	0.900268i	$0.356630\pi$
$18$	−105.923	−1.38701
$19$	−73.7974	−0.891068	−0.445534	−	0.895265i	$-0.646986\pi$
$19$	−73.7974	−0.891068	−0.445534	+	0.895265i	$0.646986\pi$
$20$	−146.185	−1.63440
$21$	−64.1690	−0.666801
$22$	50.6691	0.491031
$23$	32.1202	0.291197	0.145599	−	0.989344i	$-0.453489\pi$
$23$	32.1202	0.291197	0.145599	+	0.989344i	$0.453489\pi$
$24$	−169.944	−1.44540
$25$	−2.68347	−0.0214677
$26$	0	0
$27$	−28.3162	−0.201832
$28$	−119.956	−0.809625
$29$	−76.6962	−0.491108	−0.245554	−	0.969383i	$-0.578970\pi$
$29$	−76.6962	−0.491108	−0.245554	+	0.969383i	$0.578970\pi$
$30$	360.212	2.19218
$31$	112.249	0.650341	0.325171	−	0.945655i	$-0.394578\pi$
$31$	112.249	0.650341	0.325171	+	0.945655i	$0.394578\pi$
$32$	169.393	0.935771
$33$	−77.7781	−0.410286
$34$	−281.111	−1.41795
$35$	100.370	0.484732
$36$	303.948	1.40717
$37$	149.193	0.662895	0.331447	−	0.943474i	$-0.392463\pi$
$37$	149.193	0.662895	0.331447	+	0.943474i	$0.392463\pi$
$38$	339.932	1.45116
$39$	0	0
$40$	265.817	1.05073
$41$	−172.473	−0.656971	−0.328486	−	0.944509i	$-0.606538\pi$
$41$	−172.473	−0.656971	−0.328486	+	0.944509i	$0.606538\pi$
$42$	295.581	1.08593
$43$	394.963	1.40073	0.700365	−	0.713785i	$-0.253021\pi$
$43$	394.963	1.40073	0.700365	+	0.713785i	$0.253021\pi$
$44$	−145.396	−0.498166
$45$	−254.321	−0.842486
$46$	−147.955	−0.474234
$47$	−257.663	−0.799659	−0.399829	−	0.916590i	$-0.630931\pi$
$47$	−257.663	−0.799659	−0.399829	+	0.916590i	$0.630931\pi$
$48$	35.1301	0.105637
$49$	−260.639	−0.759880
$50$	12.3608	0.0349617
$51$	431.511	1.18478
$52$	0	0
$53$	−204.844	−0.530895	−0.265448	−	0.964125i	$-0.585520\pi$
$53$	−204.844	−0.530895	−0.265448	+	0.964125i	$0.585520\pi$
$54$	130.432	0.328696
$55$	121.656	0.298257
$56$	218.123	0.520498
$57$	−521.802	−1.21253
$58$	353.284	0.799802
$59$	250.278	0.552261	0.276130	−	0.961120i	$-0.410948\pi$
$59$	250.278	0.552261	0.276130	+	0.961120i	$0.410948\pi$
$60$	−1033.64	−2.22403
$61$	−881.262	−1.84974	−0.924870	−	0.380284i	$-0.875826\pi$
$61$	−881.262	−1.84974	−0.924870	+	0.380284i	$0.875826\pi$
$62$	−517.052	−1.05912
$63$	−208.689	−0.417339
$64$	−820.017	−1.60160
$65$	0	0
$66$	358.268	0.668177
$67$	822.632	1.50001	0.750003	−	0.661434i	$-0.230052\pi$
$67$	822.632	1.50001	0.750003	+	0.661434i	$0.230052\pi$
$68$	806.654	1.43855
$69$	227.114	0.396250
$70$	−462.332	−0.789418
$71$	−478.539	−0.799889	−0.399945	−	0.916539i	$-0.630971\pi$
$71$	−478.539	−0.799889	−0.399945	+	0.916539i	$0.630971\pi$
$72$	−552.687	−0.904650
$73$	−439.506	−0.704661	−0.352331	−	0.935876i	$-0.614611\pi$
$73$	−439.506	−0.704661	−0.352331	+	0.935876i	$0.614611\pi$
$74$	−687.223	−1.07957
$75$	−18.9741	−0.0292125
$76$	−975.442	−1.47225
$77$	99.8283	0.147747
$78$	0	0
$79$	639.472	0.910711	0.455356	−	0.890310i	$-0.349512\pi$
$79$	639.472	0.910711	0.455356	+	0.890310i	$0.349512\pi$
$80$	−54.9487	−0.0767931
$81$	−821.089	−1.12632
$82$	794.461	1.06992
$83$	419.116	0.554264	0.277132	−	0.960832i	$-0.410616\pi$
$83$	419.116	0.554264	0.277132	+	0.960832i	$0.410616\pi$
$84$	−848.175	−1.10171
$85$	−674.947	−0.861274
$86$	−1819.31	−2.28118
$87$	−542.299	−0.668282
$88$	264.383	0.320265
$89$	−1325.32	−1.57847	−0.789233	−	0.614094i	$-0.789522\pi$
$89$	−1325.32	−1.57847	−0.789233	+	0.614094i	$0.789522\pi$
$90$	1171.47	1.37204
$91$	0	0
$92$	424.560	0.481124
$93$	793.685	0.884961
$94$	1186.87	1.30230
$95$	816.176	0.881452
$96$	1197.73	1.27336
$97$	−47.0779	−0.0492787	−0.0246394	−	0.999696i	$-0.507844\pi$
$97$	−47.0779	−0.0492787	−0.0246394	+	0.999696i	$0.507844\pi$
$98$	1200.58	1.23752
$99$	−252.948	−0.256790
$100$	−35.4696	−0.0354696
$101$	106.108	0.104536	0.0522681	−	0.998633i	$-0.483355\pi$
$101$	106.108	0.104536	0.0522681	+	0.998633i	$0.483355\pi$
$102$	−1987.66	−1.92949
$103$	852.478	0.815507	0.407753	−	0.913092i	$-0.366312\pi$
$103$	852.478	0.815507	0.407753	+	0.913092i	$0.366312\pi$
$104$	0	0
$105$	709.689	0.659605
$106$	943.568	0.864598
$107$	2002.90	1.80960	0.904801	−	0.425835i	$-0.140020\pi$
$107$	2002.90	1.80960	0.904801	+	0.425835i	$0.140020\pi$
$108$	−374.279	−0.333472
$109$	1238.05	1.08792	0.543960	−	0.839111i	$-0.316924\pi$
$109$	1238.05	1.08792	0.543960	+	0.839111i	$0.316924\pi$
$110$	−560.384	−0.485732
$111$	1054.90	0.902043
$112$	−45.0895	−0.0380407
$113$	−1766.29	−1.47043	−0.735217	−	0.677832i	$-0.762920\pi$
$113$	−1766.29	−1.47043	−0.735217	+	0.677832i	$0.762920\pi$
$114$	2403.57	1.97469
$115$	−355.240	−0.288054
$116$	−1013.76	−0.811423
$117$	0	0
$118$	−1152.85	−0.899393
$119$	−553.845	−0.426646
$120$	1879.52	1.42980
$121$	121.000	0.0909091
$122$	4059.34	3.01242
$123$	−1219.51	−0.893983
$124$	1483.69	1.07451
$125$	1412.14	1.01044
$126$	961.281	0.679665
$127$	2119.63	1.48100	0.740499	−	0.672057i	$-0.234589\pi$
$127$	2119.63	1.48100	0.740499	+	0.672057i	$0.234589\pi$
$128$	2422.09	1.67253
$129$	2792.68	1.90606
$130$	0	0
$131$	1321.97	0.881690	0.440845	−	0.897583i	$-0.354679\pi$
$131$	1321.97	0.881690	0.440845	+	0.897583i	$0.354679\pi$
$132$	−1028.06	−0.677886
$133$	669.734	0.436641
$134$	−3789.27	−2.44286
$135$	313.168	0.199653
$136$	−1466.79	−0.924824
$137$	1034.43	0.645092	0.322546	−	0.946554i	$-0.395461\pi$
$137$	1034.43	0.645092	0.322546	+	0.946554i	$0.395461\pi$
$138$	−1046.15	−0.645320
$139$	−2809.89	−1.71461	−0.857307	−	0.514805i	$-0.827864\pi$
$139$	−2809.89	−1.71461	−0.857307	+	0.514805i	$0.827864\pi$
$140$	1326.67	0.800888
$141$	−1821.86	−1.08815
$142$	2204.29	1.30267
$143$	0	0
$144$	114.249	0.0661165
$145$	848.236	0.485808
$146$	2024.49	1.14759
$147$	−1842.91	−1.03402
$148$	1972.00	1.09525
$149$	94.0228	0.0516956	0.0258478	−	0.999666i	$-0.491771\pi$
$149$	94.0228	0.0516956	0.0258478	+	0.999666i	$0.491771\pi$
$150$	87.4000	0.0475745
$151$	3288.17	1.77210	0.886052	−	0.463586i	$-0.153437\pi$
$151$	3288.17	1.77210	0.886052	+	0.463586i	$0.153437\pi$
$152$	1773.71	0.946490
$153$	1403.35	0.741531
$154$	−459.837	−0.240615
$155$	−1241.44	−0.643323
$156$	0	0
$157$	1997.42	1.01536	0.507679	−	0.861547i	$-0.330504\pi$
$157$	1997.42	1.01536	0.507679	+	0.861547i	$0.330504\pi$
$158$	−2945.59	−1.48315
$159$	−1448.40	−0.722423
$160$	−1873.43	−0.925672
$161$	−291.501	−0.142692
$162$	3782.17	1.83429
$163$	−793.478	−0.381288	−0.190644	−	0.981659i	$-0.561058\pi$
$163$	−793.478	−0.381288	−0.190644	+	0.981659i	$0.561058\pi$
$164$	−2279.72	−1.08547
$165$	860.201	0.405858
$166$	−1930.56	−0.902656
$167$	−1849.37	−0.856937	−0.428468	−	0.903557i	$-0.640947\pi$
$167$	−1849.37	−0.856937	−0.428468	+	0.903557i	$0.640947\pi$
$168$	1542.29	0.708275
$169$	0	0
$170$	3109.00	1.40264
$171$	−1696.99	−0.758903
$172$	5220.56	2.31433
$173$	−1696.07	−0.745377	−0.372688	−	0.927957i	$-0.621564\pi$
$173$	−1696.07	−0.745377	−0.372688	+	0.927957i	$0.621564\pi$
$174$	2497.98	1.08834
$175$	24.3533	0.0105196
$176$	−54.6522	−0.0234066
$177$	1769.65	0.751496
$178$	6104.79	2.57064
$179$	2172.35	0.907088	0.453544	−	0.891234i	$-0.350159\pi$
$179$	2172.35	0.907088	0.453544	+	0.891234i	$0.350159\pi$
$180$	−3361.57	−1.39198
$181$	172.041	0.0706502	0.0353251	−	0.999376i	$-0.488753\pi$
$181$	172.041	0.0706502	0.0353251	+	0.999376i	$0.488753\pi$
$182$	0	0
$183$	−6231.17	−2.51706
$184$	−772.003	−0.309309
$185$	−1650.02	−0.655741
$186$	−3655.94	−1.44122
$187$	−671.305	−0.262517
$188$	−3405.74	−1.32122
$189$	256.978	0.0989016
$190$	−3759.54	−1.43550
$191$	95.4854	0.0361732	0.0180866	−	0.999836i	$-0.494243\pi$
$191$	95.4854	0.0361732	0.0180866	+	0.999836i	$0.494243\pi$
$192$	−5798.12	−2.17939
$193$	3881.98	1.44783	0.723915	−	0.689889i	$-0.242341\pi$
$193$	3881.98	1.44783	0.723915	+	0.689889i	$0.242341\pi$
$194$	216.854	0.0802537
$195$	0	0
$196$	−3445.08	−1.25550
$197$	−2364.73	−0.855227	−0.427614	−	0.903962i	$-0.640646\pi$
$197$	−2364.73	−0.855227	−0.427614	+	0.903962i	$0.640646\pi$
$198$	1165.15	0.418200
$199$	−508.257	−0.181052	−0.0905260	−	0.995894i	$-0.528855\pi$
$199$	−508.257	−0.181052	−0.0905260	+	0.995894i	$0.528855\pi$
$200$	64.4966	0.0228030
$201$	5816.61	2.04115
$202$	−488.764	−0.170244
$203$	696.041	0.240653
$204$	5703.64	1.95752
$205$	1907.50	0.649881
$206$	−3926.76	−1.32811
$207$	738.614	0.248006
$208$	0	0
$209$	811.772	0.268667
$210$	−3269.03	−1.07421
$211$	−2865.92	−0.935063	−0.467531	−	0.883976i	$-0.654857\pi$
$211$	−2865.92	−0.935063	−0.467531	+	0.883976i	$0.654857\pi$
$212$	−2707.59	−0.877161
$213$	−3383.62	−1.08846
$214$	−9225.91	−2.94706
$215$	−4368.17	−1.38561
$216$	680.574	0.214385
$217$	−1018.70	−0.318680
$218$	−5702.79	−1.77175
$219$	−3107.63	−0.958877
$220$	1608.03	0.492789
$221$	0	0
$222$	−4859.17	−1.46904
$223$	5471.48	1.64304	0.821519	−	0.570181i	$-0.193127\pi$
$223$	5471.48	1.64304	0.821519	+	0.570181i	$0.193127\pi$
$224$	−1537.29	−0.458546
$225$	−61.7071	−0.0182836
$226$	8136.05	2.39470
$227$	2886.02	0.843840	0.421920	−	0.906633i	$-0.361356\pi$
$227$	2886.02	0.843840	0.421920	+	0.906633i	$0.361356\pi$
$228$	−6897.09	−2.00338
$229$	−4442.73	−1.28203	−0.641013	−	0.767530i	$-0.721485\pi$
$229$	−4442.73	−1.28203	−0.641013	+	0.767530i	$0.721485\pi$
$230$	1636.33	0.469116
$231$	705.859	0.201048
$232$	1843.38	0.521654
$233$	−146.678	−0.0412410	−0.0206205	−	0.999787i	$-0.506564\pi$
$233$	−146.678	−0.0412410	−0.0206205	+	0.999787i	$0.506564\pi$
$234$	0	0
$235$	2849.67	0.791029
$236$	3308.13	0.912461
$237$	4521.54	1.23926
$238$	2551.17	0.694822
$239$	−500.558	−0.135475	−0.0677373	−	0.997703i	$-0.521578\pi$
$239$	−500.558	−0.135475	−0.0677373	+	0.997703i	$0.521578\pi$
$240$	−388.528	−0.104497
$241$	5125.61	1.37000	0.684999	−	0.728544i	$-0.259803\pi$
$241$	5125.61	1.37000	0.684999	+	0.728544i	$0.259803\pi$
$242$	−557.360	−0.148051
$243$	−5041.17	−1.33083
$244$	−11648.4	−3.05619
$245$	2882.58	0.751680
$246$	5617.42	1.45591
$247$	0	0
$248$	−2697.89	−0.690791
$249$	2963.46	0.754222
$250$	−6504.71	−1.64558
$251$	−592.040	−0.148881	−0.0744407	−	0.997225i	$-0.523717\pi$
$251$	−592.040	−0.148881	−0.0744407	+	0.997225i	$0.523717\pi$
$252$	−2758.42	−0.689540
$253$	−353.323	−0.0877992
$254$	−9763.61	−2.41190
$255$	−4772.37	−1.17199
$256$	−4596.68	−1.12224
$257$	−4455.40	−1.08140	−0.540700	−	0.841215i	$-0.681841\pi$
$257$	−4455.40	−1.08140	−0.540700	+	0.841215i	$0.681841\pi$
$258$	−12863.9	−3.10415
$259$	−1353.97	−0.324832
$260$	0	0
$261$	−1763.65	−0.418266
$262$	−6089.38	−1.43589
$263$	5581.57	1.30865	0.654324	−	0.756214i	$-0.272953\pi$
$263$	5581.57	1.30865	0.654324	+	0.756214i	$0.272953\pi$
$264$	1869.38	0.435805
$265$	2265.51	0.525166
$266$	−3084.98	−0.711099
$267$	−9370.98	−2.14792
$268$	10873.4	2.47835
$269$	−7356.83	−1.66749	−0.833743	−	0.552153i	$-0.813807\pi$
$269$	−7356.83	−1.66749	−0.833743	+	0.552153i	$0.813807\pi$
$270$	−1442.54	−0.325149
$271$	2157.14	0.483532	0.241766	−	0.970335i	$-0.422273\pi$
$271$	2157.14	0.483532	0.241766	+	0.970335i	$0.422273\pi$
$272$	303.209	0.0675910
$273$	0	0
$274$	−4764.89	−1.05058
$275$	29.5182	0.00647277
$276$	3001.95	0.654696
$277$	2630.43	0.570567	0.285283	−	0.958443i	$-0.407912\pi$
$277$	2630.43	0.570567	0.285283	+	0.958443i	$0.407912\pi$
$278$	12943.1	2.79236
$279$	2581.21	0.553881
$280$	−2412.37	−0.514881
$281$	2047.68	0.434712	0.217356	−	0.976092i	$-0.430257\pi$
$281$	2047.68	0.434712	0.217356	+	0.976092i	$0.430257\pi$
$282$	8392.02	1.77212
$283$	5988.84	1.25795	0.628974	−	0.777426i	$-0.283475\pi$
$283$	5988.84	1.25795	0.628974	+	0.777426i	$0.283475\pi$
$284$	−6325.25	−1.32160
$285$	5770.96	1.19945
$286$	0	0
$287$	1565.25	0.321929
$288$	3895.23	0.796975
$289$	−1188.61	−0.241933
$290$	−3907.21	−0.791170
$291$	−332.875	−0.0670567
$292$	−5809.31	−1.16426
$293$	−3740.77	−0.745863	−0.372931	−	0.927859i	$-0.621647\pi$
$293$	−3740.77	−0.745863	−0.372931	+	0.927859i	$0.621647\pi$
$294$	8488.96	1.68397
$295$	−2767.99	−0.546301
$296$	−3585.81	−0.704125
$297$	311.478	0.0608545
$298$	−433.095	−0.0841897
$299$	0	0
$300$	−250.796	−0.0482658
$301$	−3584.41	−0.686385
$302$	−15146.3	−2.88599
$303$	750.262	0.142249
$304$	−366.654	−0.0691744
$305$	9746.48	1.82978
$306$	−6464.23	−1.20763
$307$	8038.83	1.49446	0.747232	−	0.664564i	$-0.231383\pi$
$307$	8038.83	1.49446	0.747232	+	0.664564i	$0.231383\pi$
$308$	1319.51	0.244111
$309$	6027.65	1.10971
$310$	5718.43	1.04769
$311$	7592.61	1.38436	0.692182	−	0.721723i	$-0.256649\pi$
$311$	7592.61	1.38436	0.692182	+	0.721723i	$0.256649\pi$
$312$	0	0
$313$	10297.9	1.85965	0.929825	−	0.368002i	$-0.119958\pi$
$313$	10297.9	1.85965	0.929825	+	0.368002i	$0.119958\pi$
$314$	−9200.66	−1.65358
$315$	2308.04	0.412835
$316$	8452.43	1.50470
$317$	−5216.74	−0.924294	−0.462147	−	0.886803i	$-0.652921\pi$
$317$	−5216.74	−0.924294	−0.462147	+	0.886803i	$0.652921\pi$
$318$	6671.72	1.17651
$319$	843.658	0.148075
$320$	9069.13	1.58431
$321$	14162.0	2.46244
$322$	1342.73	0.232384
$323$	−4503.69	−0.775827
$324$	−10853.0	−1.86094
$325$	0	0
$326$	3654.98	0.620953
$327$	8753.89	1.48040
$328$	4145.36	0.697833
$329$	2338.37	0.391849
$330$	−3962.33	−0.660966
$331$	−6253.97	−1.03852	−0.519259	−	0.854617i	$-0.673792\pi$
$331$	−6253.97	−1.03852	−0.519259	+	0.854617i	$0.673792\pi$
$332$	5539.80	0.915771
$333$	3430.73	0.564573
$334$	8518.71	1.39558
$335$	−9098.04	−1.48382
$336$	−318.816	−0.0517644
$337$	−563.067	−0.0910154	−0.0455077	−	0.998964i	$-0.514491\pi$
$337$	−563.067	−0.0910154	−0.0455077	+	0.998964i	$0.514491\pi$
$338$	0	0
$339$	−12489.0	−2.00091
$340$	−8921.34	−1.42302
$341$	−1234.74	−0.196085
$342$	7816.83	1.23592
$343$	5478.20	0.862377
$344$	−9492.86	−1.48785
$345$	−2511.80	−0.391974
$346$	7812.60	1.21390
$347$	−3535.95	−0.547031	−0.273516	−	0.961868i	$-0.588187\pi$
$347$	−3535.95	−0.547031	−0.273516	+	0.961868i	$0.588187\pi$
$348$	−7168.01	−1.10415
$349$	10061.5	1.54321	0.771607	−	0.636099i	$-0.219453\pi$
$349$	10061.5	1.54321	0.771607	+	0.636099i	$0.219453\pi$
$350$	−112.178	−0.0171319
$351$	0	0
$352$	−1863.32	−0.282145
$353$	703.944	0.106139	0.0530696	−	0.998591i	$-0.483099\pi$
$353$	703.944	0.106139	0.0530696	+	0.998591i	$0.483099\pi$
$354$	−8151.49	−1.22386
$355$	5292.49	0.791257
$356$	−17517.8	−2.60799
$357$	−3916.09	−0.580564
$358$	−10006.4	−1.47725
$359$	−1976.43	−0.290563	−0.145281	−	0.989390i	$-0.546409\pi$
$359$	−1976.43	−0.290563	−0.145281	+	0.989390i	$0.546409\pi$
$360$	6112.54	0.894887
$361$	−1412.94	−0.205998
$362$	−792.467	−0.115058
$363$	855.559	0.123706
$364$	0	0
$365$	4860.79	0.697056
$366$	28702.5	4.09920
$367$	11383.6	1.61912	0.809562	−	0.587034i	$-0.199705\pi$
$367$	11383.6	1.61912	0.809562	+	0.587034i	$0.199705\pi$
$368$	159.586	0.0226059
$369$	−3966.08	−0.559528
$370$	7600.47	1.06792
$371$	1859.02	0.260149
$372$	10490.8	1.46216
$373$	1015.20	0.140925	0.0704626	−	0.997514i	$-0.477552\pi$
$373$	1015.20	0.140925	0.0704626	+	0.997514i	$0.477552\pi$
$374$	3092.22	0.427527
$375$	9984.86	1.37498
$376$	6192.87	0.849396
$377$	0	0
$378$	−1183.71	−0.161068
$379$	337.742	0.0457748	0.0228874	−	0.999738i	$-0.492714\pi$
$379$	337.742	0.0457748	0.0228874	+	0.999738i	$0.492714\pi$
$380$	10788.1	1.45636
$381$	14987.3	2.01529
$382$	−439.833	−0.0589105
$383$	−5319.04	−0.709635	−0.354817	−	0.934936i	$-0.615457\pi$
$383$	−5319.04	−0.709635	−0.354817	+	0.934936i	$0.615457\pi$
$384$	17125.9	2.27592
$385$	−1104.07	−0.146152
$386$	−17881.5	−2.35789
$387$	9082.30	1.19297
$388$	−622.268	−0.0814197
$389$	13487.0	1.75788	0.878941	−	0.476931i	$-0.158251\pi$
$389$	13487.0	1.75788	0.878941	+	0.476931i	$0.158251\pi$
$390$	0	0
$391$	1960.23	0.253537
$392$	6264.40	0.807143
$393$	9347.32	1.19977
$394$	10892.6	1.39279
$395$	−7072.35	−0.900883
$396$	−3343.43	−0.424277
$397$	12545.2	1.58596	0.792979	−	0.609249i	$-0.208529\pi$
$397$	12545.2	1.58596	0.792979	+	0.609249i	$0.208529\pi$
$398$	2341.17	0.294855
$399$	4735.51	0.594165
$400$	−13.3325	−0.00166656
$401$	−5635.79	−0.701840	−0.350920	−	0.936405i	$-0.614131\pi$
$401$	−5635.79	−0.701840	−0.350920	+	0.936405i	$0.614131\pi$
$402$	−26792.9	−3.32416
$403$	0	0
$404$	1402.52	0.172718
$405$	9080.99	1.11417
$406$	−3206.16	−0.391919
$407$	−1641.12	−0.199870
$408$	−10371.3	−1.25847
$409$	−876.359	−0.105949	−0.0529745	−	0.998596i	$-0.516870\pi$
$409$	−876.359	−0.105949	−0.0529745	+	0.998596i	$0.516870\pi$
$410$	−8786.49	−1.05837
$411$	7314.20	0.877818
$412$	11267.9	1.34740
$413$	−2271.34	−0.270619
$414$	−3402.27	−0.403894
$415$	−4635.28	−0.548282
$416$	0	0
$417$	−19868.0	−2.33319
$418$	−3739.25	−0.437542
$419$	3032.23	0.353542	0.176771	−	0.984252i	$-0.443435\pi$
$419$	3032.23	0.353542	0.176771	+	0.984252i	$0.443435\pi$
$420$	9380.55	1.08982
$421$	2570.46	0.297569	0.148785	−	0.988870i	$-0.452464\pi$
$421$	2570.46	0.297569	0.148785	+	0.988870i	$0.452464\pi$
$422$	13201.2	1.52281
$423$	−5925.03	−0.681051
$424$	4923.38	0.563916
$425$	−163.766	−0.0186913
$426$	15585.9	1.77263
$427$	7997.72	0.906409
$428$	26473.9	2.98988
$429$	0	0
$430$	20121.0	2.25656
$431$	12307.0	1.37542	0.687711	−	0.725985i	$-0.258616\pi$
$431$	12307.0	1.37542	0.687711	+	0.725985i	$0.258616\pi$
$432$	−140.686	−0.0156684
$433$	5663.13	0.628528	0.314264	−	0.949336i	$-0.398242\pi$
$433$	5663.13	0.628528	0.314264	+	0.949336i	$0.398242\pi$
$434$	4692.40	0.518992
$435$	5997.65	0.661070
$436$	16364.3	1.79749
$437$	−2370.39	−0.259476
$438$	14314.6	1.56160
$439$	9187.09	0.998807	0.499403	−	0.866370i	$-0.333553\pi$
$439$	9187.09	0.998807	0.499403	+	0.866370i	$0.333553\pi$
$440$	−2923.99	−0.316808
$441$	−5993.47	−0.647173
$442$	0	0
$443$	1242.92	0.133303	0.0666514	−	0.997776i	$-0.478768\pi$
$443$	1242.92	0.133303	0.0666514	+	0.997776i	$0.478768\pi$
$444$	13943.5	1.49038
$445$	14657.6	1.56143
$446$	−25203.2	−2.67580
$447$	664.810	0.0703455
$448$	7441.90	0.784814
$449$	7959.82	0.836630	0.418315	−	0.908302i	$-0.362621\pi$
$449$	7959.82	0.836630	0.418315	+	0.908302i	$0.362621\pi$
$450$	284.240	0.0297761
$451$	1897.21	0.198084
$452$	−23346.6	−2.42949
$453$	23249.8	2.41141
$454$	−13293.8	−1.37425
$455$	0	0
$456$	12541.4	1.28795
$457$	−3892.91	−0.398474	−0.199237	−	0.979951i	$-0.563846\pi$
$457$	−3892.91	−0.398474	−0.199237	+	0.979951i	$0.563846\pi$
$458$	20464.5	2.08786
$459$	−1728.07	−0.175729
$460$	−4695.50	−0.475932
$461$	10509.1	1.06173	0.530866	−	0.847456i	$-0.321867\pi$
$461$	10509.1	1.06173	0.530866	+	0.847456i	$0.321867\pi$
$462$	−3251.39	−0.327420
$463$	8241.46	0.827242	0.413621	−	0.910449i	$-0.364264\pi$
$463$	8241.46	0.827242	0.413621	+	0.910449i	$0.364264\pi$
$464$	−381.056	−0.0381252
$465$	−8777.91	−0.875410
$466$	675.638	0.0671638
$467$	−12855.1	−1.27379	−0.636896	−	0.770949i	$-0.719782\pi$
$467$	−12855.1	−1.27379	−0.636896	+	0.770949i	$0.719782\pi$
$468$	0	0
$469$	−7465.63	−0.735033
$470$	−13126.4	−1.28824
$471$	14123.2	1.38166
$472$	−6015.37	−0.586610
$473$	−4344.60	−0.422336
$474$	−20827.5	−2.01822
$475$	198.033	0.0191292
$476$	−7320.63	−0.704917
$477$	−4710.44	−0.452152
$478$	2305.71	0.220629
$479$	15325.3	1.46186	0.730932	−	0.682450i	$-0.239086\pi$
$479$	15325.3	1.46186	0.730932	+	0.682450i	$0.239086\pi$
$480$	−13246.5	−1.25962
$481$	0	0
$482$	−23610.0	−2.23113
$483$	−2061.12	−0.194171
$484$	1599.36	0.150203
$485$	520.666	0.0487469
$486$	23221.0	2.16734
$487$	−8030.54	−0.747225	−0.373612	−	0.927585i	$-0.621881\pi$
$487$	−8030.54	−0.747225	−0.373612	+	0.927585i	$0.621881\pi$
$488$	21181.0	1.96479
$489$	−5610.47	−0.518843
$490$	−13278.0	−1.22416
$491$	−15805.8	−1.45276	−0.726378	−	0.687295i	$-0.758798\pi$
$491$	−15805.8	−1.45276	−0.726378	+	0.687295i	$0.758798\pi$
$492$	−16119.3	−1.47706
$493$	−4680.60	−0.427593
$494$	0	0
$495$	2797.53	0.254019
$496$	557.697	0.0504866
$497$	4342.89	0.391962
$498$	−13650.5	−1.22830
$499$	−21570.7	−1.93514	−0.967571	−	0.252599i	$-0.918715\pi$
$499$	−21570.7	−1.93514	−0.967571	+	0.252599i	$0.918715\pi$
$500$	18665.4	1.66948
$501$	−13076.4	−1.16609
$502$	2727.10	0.242463
$503$	11088.1	0.982891	0.491446	−	0.870908i	$-0.336469\pi$
$503$	11088.1	0.982891	0.491446	+	0.870908i	$0.336469\pi$
$504$	5015.80	0.443297
$505$	−1173.52	−0.103408
$506$	1627.50	0.142987
$507$	0	0
$508$	28016.9	2.44695
$509$	−119.036	−0.0103658	−0.00518291	−	0.999987i	$-0.501650\pi$
$509$	−119.036	−0.0103658	−0.00518291	+	0.999987i	$0.501650\pi$
$510$	21982.9	1.90866
$511$	3988.65	0.345298
$512$	1796.92	0.155104
$513$	2089.66	0.179846
$514$	20522.8	1.76113
$515$	−9428.14	−0.806706
$516$	36913.2	3.14925
$517$	2834.29	0.241106
$518$	6236.75	0.529010
$519$	−11992.5	−1.01428
$520$	0	0
$521$	9556.50	0.803605	0.401802	−	0.915726i	$-0.368384\pi$
$521$	9556.50	0.803605	0.401802	+	0.915726i	$0.368384\pi$
$522$	8123.88	0.681173
$523$	4242.12	0.354674	0.177337	−	0.984150i	$-0.443252\pi$
$523$	4242.12	0.354674	0.177337	+	0.984150i	$0.443252\pi$
$524$	17473.6	1.45675
$525$	172.196	0.0143147
$526$	−25710.3	−2.13122
$527$	6850.32	0.566233
$528$	−386.431	−0.0318509
$529$	−11135.3	−0.915204
$530$	−10435.6	−0.855268
$531$	5755.21	0.470348
$532$	8852.43	0.721431
$533$	0	0
$534$	43165.4	3.49803
$535$	−22151.4	−1.79007
$536$	−19771.8	−1.59330
$537$	15360.1	1.23433
$538$	33887.6	2.71561
$539$	2867.03	0.229113
$540$	4139.40	0.329873
$541$	−126.757	−0.0100734	−0.00503672	−	0.999987i	$-0.501603\pi$
$541$	−126.757	−0.0100734	−0.00503672	+	0.999987i	$0.501603\pi$
$542$	−9936.41	−0.787464
$543$	1216.45	0.0961382
$544$	10337.6	0.814748
$545$	−13692.4	−1.07618
$546$	0	0
$547$	−7557.48	−0.590740	−0.295370	−	0.955383i	$-0.595443\pi$
$547$	−7557.48	−0.590740	−0.295370	+	0.955383i	$0.595443\pi$
$548$	13673.0	1.06584
$549$	−20264.9	−1.57538
$550$	−135.969	−0.0105413
$551$	5659.98	0.437611
$552$	−5458.63	−0.420896
$553$	−5803.40	−0.446267
$554$	−12116.5	−0.929206
$555$	−11666.9	−0.892308
$556$	−37140.6	−2.83294
$557$	1201.86	0.0914261	0.0457131	−	0.998955i	$-0.485444\pi$
$557$	1201.86	0.0914261	0.0457131	+	0.998955i	$0.485444\pi$
$558$	−11889.8	−0.902032
$559$	0	0
$560$	498.676	0.0376302
$561$	−4746.62	−0.357224
$562$	−9432.17	−0.707958
$563$	15740.5	1.17830	0.589150	−	0.808024i	$-0.299463\pi$
$563$	15740.5	1.17830	0.589150	+	0.808024i	$0.299463\pi$
$564$	−24081.1	−1.79787
$565$	19534.6	1.45456
$566$	−27586.3	−2.04865
$567$	7451.63	0.551921
$568$	11501.6	0.849641
$569$	22176.1	1.63387	0.816935	−	0.576730i	$-0.195671\pi$
$569$	22176.1	1.63387	0.816935	+	0.576730i	$0.195671\pi$
$570$	−26582.7	−1.95338
$571$	24230.9	1.77589	0.887945	−	0.459949i	$-0.152132\pi$
$571$	24230.9	1.77589	0.887945	+	0.459949i	$0.152132\pi$
$572$	0	0
$573$	675.152	0.0492232
$574$	−7209.97	−0.524283
$575$	−86.1936	−0.00625134
$576$	−18856.5	−1.36404
$577$	21484.3	1.55009	0.775044	−	0.631907i	$-0.217727\pi$
$577$	21484.3	1.55009	0.775044	+	0.631907i	$0.217727\pi$
$578$	5475.09	0.394003
$579$	27448.5	1.97015
$580$	11211.8	0.802666
$581$	−3803.60	−0.271600
$582$	1533.32	0.109206
$583$	2253.28	0.160071
$584$	10563.4	0.748489
$585$	0	0
$586$	17231.0	1.21469
$587$	−17875.4	−1.25689	−0.628445	−	0.777854i	$-0.716308\pi$
$587$	−17875.4	−1.25689	−0.628445	+	0.777854i	$0.716308\pi$
$588$	−24359.3	−1.70843
$589$	−8283.71	−0.579498
$590$	12750.1	0.889687
$591$	−16720.4	−1.16376
$592$	741.245	0.0514611
$593$	−5141.31	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$593$	−5141.31	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$594$	−1434.76	−0.0991057
$595$	6125.35	0.422042
$596$	1242.78	0.0854130
$597$	−3593.75	−0.246369
$598$	0	0
$599$	−13302.5	−0.907391	−0.453696	−	0.891157i	$-0.649895\pi$
$599$	−13302.5	−0.907391	−0.453696	+	0.891157i	$0.649895\pi$
$600$	456.038	0.0310295
$601$	−23743.1	−1.61148	−0.805740	−	0.592270i	$-0.798232\pi$
$601$	−23743.1	−1.61148	−0.805740	+	0.592270i	$0.798232\pi$
$602$	16510.8	1.11782
$603$	18916.7	1.27752
$604$	43462.5	2.92792
$605$	−1338.22	−0.0899280
$606$	−3455.92	−0.231662
$607$	14501.6	0.969692	0.484846	−	0.874600i	$-0.338876\pi$
$607$	14501.6	0.969692	0.484846	+	0.874600i	$0.338876\pi$
$608$	−12500.7	−0.833835
$609$	4921.52	0.327472
$610$	−44895.0	−2.97991
$611$	0	0
$612$	18549.3	1.22518
$613$	−20824.4	−1.37209	−0.686043	−	0.727561i	$-0.740654\pi$
$613$	−20824.4	−1.37209	−0.686043	+	0.727561i	$0.740654\pi$
$614$	−37029.1	−2.43383
$615$	13487.4	0.884335
$616$	−2399.35	−0.156936
$617$	−5991.54	−0.390941	−0.195470	−	0.980710i	$-0.562623\pi$
$617$	−5991.54	−0.390941	−0.195470	+	0.980710i	$0.562623\pi$
$618$	−27765.0	−1.80724
$619$	11803.8	0.766451	0.383226	−	0.923655i	$-0.374813\pi$
$619$	11803.8	0.766451	0.383226	+	0.923655i	$0.374813\pi$
$620$	−16409.2	−1.06292
$621$	−909.523	−0.0587728
$622$	−34973.7	−2.25453
$623$	12027.7	0.773480
$624$	0	0
$625$	−15282.4	−0.978071
$626$	−47434.9	−3.02856
$627$	5739.82	0.365592
$628$	26401.5	1.67760
$629$	9104.89	0.577163
$630$	−10631.5	−0.672330
$631$	−5958.64	−0.375927	−0.187963	−	0.982176i	$-0.560189\pi$
$631$	−5958.64	−0.375927	−0.187963	+	0.982176i	$0.560189\pi$
$632$	−15369.6	−0.967355
$633$	−20264.2	−1.27240
$634$	24029.8	1.50527
$635$	−23442.4	−1.46501
$636$	−19144.7	−1.19361
$637$	0	0
$638$	−3886.13	−0.241149
$639$	−11004.1	−0.681248
$640$	−26787.5	−1.65448
$641$	−15028.5	−0.926040	−0.463020	−	0.886348i	$-0.653234\pi$
$641$	−15028.5	−0.926040	−0.463020	+	0.886348i	$0.653234\pi$
$642$	−65233.9	−4.01025
$643$	24509.0	1.50318	0.751588	−	0.659633i	$-0.229288\pi$
$643$	24509.0	1.50318	0.751588	+	0.659633i	$0.229288\pi$
$644$	−3853.01	−0.235760
$645$	−30886.2	−1.88549
$646$	20745.3	1.26349
$647$	6135.42	0.372810	0.186405	−	0.982473i	$-0.440316\pi$
$647$	6135.42	0.372810	0.186405	+	0.982473i	$0.440316\pi$
$648$	19734.7	1.19638
$649$	−2753.05	−0.166513
$650$	0	0
$651$	−7202.93	−0.433648
$652$	−10488.1	−0.629976
$653$	20606.1	1.23488	0.617442	−	0.786616i	$-0.288169\pi$
$653$	20606.1	1.23488	0.617442	+	0.786616i	$0.288169\pi$
$654$	−40322.9	−2.41093
$655$	−14620.6	−0.872174
$656$	−856.913	−0.0510013
$657$	−10106.6	−0.600144
$658$	−10771.2	−0.638152
$659$	−3362.49	−0.198762	−0.0993808	−	0.995049i	$-0.531686\pi$
$659$	−3362.49	−0.198762	−0.0993808	+	0.995049i	$0.531686\pi$
$660$	11370.0	0.670570
$661$	870.203	0.0512057	0.0256028	−	0.999672i	$-0.491849\pi$
$661$	870.203	0.0512057	0.0256028	+	0.999672i	$0.491849\pi$
$662$	28807.6	1.69130
$663$	0	0
$664$	−10073.4	−0.588738
$665$	−7407.04	−0.431929
$666$	−15802.9	−0.919444
$667$	−2463.50	−0.143009
$668$	−24444.6	−1.41586
$669$	38687.4	2.23579
$670$	41908.2	2.41650
$671$	9693.89	0.557717
$672$	−10869.8	−0.623973
$673$	25591.0	1.46577	0.732883	−	0.680355i	$-0.238174\pi$
$673$	25591.0	1.46577	0.732883	+	0.680355i	$0.238174\pi$
$674$	2593.64	0.148225
$675$	75.9856	0.00433287
$676$	0	0
$677$	−1803.36	−0.102376	−0.0511882	−	0.998689i	$-0.516301\pi$
$677$	−1803.36	−0.102376	−0.0511882	+	0.998689i	$0.516301\pi$
$678$	57527.8	3.25862
$679$	427.246	0.0241476
$680$	16222.2	0.914844
$681$	20406.3	1.14827
$682$	5687.57	0.319338
$683$	−35337.2	−1.97971	−0.989853	−	0.142094i	$-0.954617\pi$
$683$	−35337.2	−1.97971	−0.989853	+	0.142094i	$0.954617\pi$
$684$	−22430.6	−1.25388
$685$	−11440.5	−0.638130
$686$	−25234.1	−1.40444
$687$	−31413.4	−1.74453
$688$	1962.33	0.108740
$689$	0	0
$690$	11570.1	0.638356
$691$	7196.38	0.396184	0.198092	−	0.980183i	$-0.436525\pi$
$691$	7196.38	0.396184	0.198092	+	0.980183i	$0.436525\pi$
$692$	−22418.4	−1.23153
$693$	2295.58	0.125832
$694$	16287.6	0.890877
$695$	31076.4	1.69611
$696$	13034.0	0.709848
$697$	−10525.7	−0.572006
$698$	−46346.3	−2.51323
$699$	−1037.12	−0.0561193
$700$	321.897	0.0173808
$701$	22914.0	1.23459	0.617296	−	0.786731i	$-0.288228\pi$
$701$	22914.0	1.23459	0.617296	+	0.786731i	$0.288228\pi$
$702$	0	0
$703$	−11010.0	−0.590684
$704$	9020.19	0.482899
$705$	20149.2	1.07640
$706$	−3242.56	−0.172855
$707$	−962.963	−0.0512248
$708$	23390.9	1.24164
$709$	−12134.0	−0.642738	−0.321369	−	0.946954i	$-0.604143\pi$
$709$	−12134.0	−0.642738	−0.321369	+	0.946954i	$0.604143\pi$
$710$	−24378.7	−1.28861
$711$	14704.8	0.775632
$712$	31853.8	1.67664
$713$	3605.48	0.189377
$714$	18038.6	0.945488
$715$	0	0
$716$	28713.7	1.49872
$717$	−3539.31	−0.184349
$718$	9104.00	0.473201
$719$	−20460.0	−1.06124	−0.530618	−	0.847611i	$-0.678040\pi$
$719$	−20460.0	−1.06124	−0.530618	+	0.847611i	$0.678040\pi$
$720$	−1263.56	−0.0654030
$721$	−7736.50	−0.399615
$722$	6508.39	0.335481
$723$	36241.8	1.86424
$724$	2274.00	0.116730
$725$	205.812	0.0105430
$726$	−3940.95	−0.201463
$727$	18877.3	0.963027	0.481514	−	0.876439i	$-0.340087\pi$
$727$	18877.3	0.963027	0.481514	+	0.876439i	$0.340087\pi$
$728$	0	0
$729$	−13475.4	−0.684619
$730$	−22390.2	−1.13520
$731$	24103.7	1.21957
$732$	−82362.6	−4.15876
$733$	−863.359	−0.0435046	−0.0217523	−	0.999763i	$-0.506925\pi$
$733$	−863.359	−0.0435046	−0.0217523	+	0.999763i	$0.506925\pi$
$734$	−52436.0	−2.63685
$735$	20382.0	1.02286
$736$	5440.93	0.272494
$737$	−9048.95	−0.452269
$738$	18268.9	0.911228
$739$	32792.3	1.63232	0.816160	−	0.577825i	$-0.196099\pi$
$739$	32792.3	1.63232	0.816160	+	0.577825i	$0.196099\pi$
$740$	−21809.7	−1.08343
$741$	0	0
$742$	−8563.16	−0.423671
$743$	−6259.90	−0.309090	−0.154545	−	0.987986i	$-0.549391\pi$
$743$	−6259.90	−0.309090	−0.154545	+	0.987986i	$0.549391\pi$
$744$	−19076.1	−0.940003
$745$	−1039.86	−0.0511377
$746$	−4676.30	−0.229506
$747$	9637.69	0.472054
$748$	−8873.20	−0.433738
$749$	−18176.9	−0.886741
$750$	−45993.1	−2.23924
$751$	−8170.90	−0.397018	−0.198509	−	0.980099i	$-0.563610\pi$
$751$	−8170.90	−0.397018	−0.198509	+	0.980099i	$0.563610\pi$
$752$	−1280.17	−0.0620782
$753$	−4186.16	−0.202593
$754$	0	0
$755$	−36366.1	−1.75298
$756$	3396.69	0.163408
$757$	−30180.2	−1.44903	−0.724517	−	0.689257i	$-0.757937\pi$
$757$	−30180.2	−1.44903	−0.724517	+	0.689257i	$0.757937\pi$
$758$	−1555.73	−0.0745472
$759$	−2498.25	−0.119474
$760$	−19616.6	−0.936276
$761$	5240.04	0.249607	0.124804	−	0.992181i	$-0.460170\pi$
$761$	5240.04	0.249607	0.124804	+	0.992181i	$0.460170\pi$
$762$	−69035.9	−3.28203
$763$	−11235.6	−0.533102
$764$	1262.11	0.0597664
$765$	−15520.6	−0.733528
$766$	24501.0	1.15569
$767$	0	0
$768$	−32501.9	−1.52710
$769$	−17150.8	−0.804259	−0.402129	−	0.915583i	$-0.631730\pi$
$769$	−17150.8	−0.804259	−0.402129	+	0.915583i	$0.631730\pi$
$770$	5085.65	0.238018
$771$	−31502.9	−1.47153
$772$	51311.4	2.39215
$773$	12451.1	0.579349	0.289674	−	0.957125i	$-0.406453\pi$
$773$	12451.1	0.579349	0.289674	+	0.957125i	$0.406453\pi$
$774$	−41835.6	−1.94283
$775$	−301.218	−0.0139614
$776$	1131.51	0.0523437
$777$	−9573.54	−0.442019
$778$	−62124.7	−2.86283
$779$	12728.1	0.585406
$780$	0	0
$781$	5263.93	0.241176
$782$	−9029.35	−0.412901
$783$	2171.75	0.0991211
$784$	−1294.95	−0.0589902
$785$	−22090.8	−1.00440
$786$	−43056.4	−1.95391
$787$	10357.6	0.469133	0.234567	−	0.972100i	$-0.424633\pi$
$787$	10357.6	0.469133	0.234567	+	0.972100i	$0.424633\pi$
$788$	−31256.6	−1.41303
$789$	39465.8	1.78076
$790$	32577.2	1.46715
$791$	16029.6	0.720542
$792$	6079.56	0.272762
$793$	0	0
$794$	−57786.7	−2.58284
$795$	16018.8	0.714627
$796$	−6718.05	−0.299139
$797$	36188.3	1.60835	0.804176	−	0.594391i	$-0.202607\pi$
$797$	36188.3	1.60835	0.804176	+	0.594391i	$0.202607\pi$
$798$	−21813.1	−0.967638
$799$	−15724.6	−0.696239
$800$	−454.560	−0.0200889
$801$	−30476.1	−1.34434
$802$	25960.0	1.14299
$803$	4834.56	0.212463
$804$	76883.0	3.37245
$805$	3223.90	0.141152
$806$	0	0
$807$	−52018.2	−2.26905
$808$	−2550.29	−0.111038
$809$	−26384.0	−1.14661	−0.573307	−	0.819341i	$-0.694340\pi$
$809$	−26384.0	−1.14661	−0.573307	+	0.819341i	$0.694340\pi$
$810$	−41829.6	−1.81450
$811$	18851.8	0.816247	0.408124	−	0.912927i	$-0.366183\pi$
$811$	18851.8	0.816247	0.408124	+	0.912927i	$0.366183\pi$
$812$	9200.15	0.397613
$813$	15252.6	0.657973
$814$	7559.45	0.325502
$815$	8775.61	0.377173
$816$	2143.91	0.0919753
$817$	−29147.3	−1.24815
$818$	4036.76	0.172545
$819$	0	0
$820$	25213.0	1.07375
$821$	13681.0	0.581572	0.290786	−	0.956788i	$-0.406083\pi$
$821$	13681.0	0.581572	0.290786	+	0.956788i	$0.406083\pi$
$822$	−33691.3	−1.42958
$823$	−29100.3	−1.23253	−0.616266	−	0.787538i	$-0.711355\pi$
$823$	−29100.3	−1.23253	−0.616266	+	0.787538i	$0.711355\pi$
$824$	−20489.1	−0.866229
$825$	208.715	0.00880791
$826$	10462.5	0.440721
$827$	5621.57	0.236374	0.118187	−	0.992991i	$-0.462292\pi$
$827$	5621.57	0.236374	0.118187	+	0.992991i	$0.462292\pi$
$828$	9762.88	0.409763
$829$	39283.0	1.64578	0.822892	−	0.568198i	$-0.192359\pi$
$829$	39283.0	1.64578	0.822892	+	0.568198i	$0.192359\pi$
$830$	21351.4	0.892914
$831$	18599.0	0.776407
$832$	0	0
$833$	−15906.2	−0.661606
$834$	91517.4	3.79975
$835$	20453.4	0.847689
$836$	10729.9	0.443900
$837$	−3178.47	−0.131259
$838$	−13967.3	−0.575766
$839$	25102.3	1.03293	0.516465	−	0.856309i	$-0.327248\pi$
$839$	25102.3	1.03293	0.516465	+	0.856309i	$0.327248\pi$
$840$	−17057.2	−0.700631
$841$	−18506.7	−0.758813
$842$	−11840.3	−0.484612
$843$	14478.6	0.591541
$844$	−37881.3	−1.54494
$845$	0	0
$846$	27292.4	1.10914
$847$	−1098.11	−0.0445473
$848$	−1017.74	−0.0412139
$849$	42345.5	1.71177
$850$	754.352	0.0304401
$851$	4792.10	0.193033
$852$	−44724.2	−1.79839
$853$	18708.7	0.750964	0.375482	−	0.926830i	$-0.377477\pi$
$853$	18708.7	0.750964	0.375482	+	0.926830i	$0.377477\pi$
$854$	−36839.7	−1.47615
$855$	18768.2	0.750713
$856$	−48139.2	−1.92215
$857$	−799.595	−0.0318712	−0.0159356	−	0.999873i	$-0.505073\pi$
$857$	−799.595	−0.0318712	−0.0159356	+	0.999873i	$0.505073\pi$
$858$	0	0
$859$	45520.1	1.80806	0.904032	−	0.427464i	$-0.140593\pi$
$859$	45520.1	1.80806	0.904032	+	0.427464i	$0.140593\pi$
$860$	−57737.7	−2.28935
$861$	11067.5	0.438069
$862$	−56689.4	−2.23996
$863$	24324.0	0.959444	0.479722	−	0.877421i	$-0.340737\pi$
$863$	24324.0	0.959444	0.479722	+	0.877421i	$0.340737\pi$
$864$	−4796.55	−0.188868
$865$	18758.0	0.737333
$866$	−26086.0	−1.02360
$867$	−8404.38	−0.329213
$868$	−13465.0	−0.526533
$869$	−7034.19	−0.274590
$870$	−27626.9	−1.07660
$871$	0	0
$872$	−29756.2	−1.15559
$873$	−1082.57	−0.0419696
$874$	10918.7	0.422575
$875$	−12815.6	−0.495138
$876$	−41076.1	−1.58428
$877$	−47616.7	−1.83341	−0.916705	−	0.399564i	$-0.869162\pi$
$877$	−47616.7	−1.83341	−0.916705	+	0.399564i	$0.869162\pi$
$878$	−42318.3	−1.62662
$879$	−26450.0	−1.01494
$880$	604.436	0.0231540
$881$	3889.27	0.148732	0.0743659	−	0.997231i	$-0.476307\pi$
$881$	3889.27	0.148732	0.0743659	+	0.997231i	$0.476307\pi$
$882$	27607.6	1.05396
$883$	−35479.6	−1.35219	−0.676094	−	0.736815i	$-0.736329\pi$
$883$	−35479.6	−1.35219	−0.676094	+	0.736815i	$0.736329\pi$
$884$	0	0
$885$	−19571.7	−0.743386
$886$	−5725.26	−0.217092
$887$	−15204.0	−0.575534	−0.287767	−	0.957700i	$-0.592913\pi$
$887$	−15204.0	−0.575534	−0.287767	+	0.957700i	$0.592913\pi$
$888$	−25354.3	−0.958148
$889$	−19236.3	−0.725719
$890$	−67517.0	−2.54289
$891$	9031.98	0.339599
$892$	72321.1	2.71467
$893$	19014.8	0.712550
$894$	−3062.30	−0.114562
$895$	−24025.5	−0.897299
$896$	−21981.2	−0.819575
$897$	0	0
$898$	−36665.2	−1.36251
$899$	−8609.10	−0.319388
$900$	−815.635	−0.0302087
$901$	−12501.2	−0.462235
$902$	−8739.07	−0.322593
$903$	−25344.4	−0.934008
$904$	42452.5	1.56189
$905$	−1902.71	−0.0698877
$906$	−107095.	−3.92715
$907$	48804.8	1.78670	0.893350	−	0.449362i	$-0.148349\pi$
$907$	48804.8	1.78670	0.893350	+	0.449362i	$0.148349\pi$
$908$	38146.9	1.39422
$909$	2439.99	0.0890311
$910$	0	0
$911$	12662.7	0.460522	0.230261	−	0.973129i	$-0.426042\pi$
$911$	12662.7	0.460522	0.230261	+	0.973129i	$0.426042\pi$
$912$	−2592.51	−0.0941301
$913$	−4610.27	−0.167117
$914$	17931.9	0.648942
$915$	68914.8	2.48989
$916$	−58723.2	−2.11820
$917$	−11997.3	−0.432046
$918$	7959.99	0.286186
$919$	1092.55	0.0392164	0.0196082	−	0.999808i	$-0.493758\pi$
$919$	1092.55	0.0392164	0.0196082	+	0.999808i	$0.493758\pi$
$920$	8538.11	0.305971
$921$	56840.4	2.03361
$922$	−48408.0	−1.72910
$923$	0	0
$924$	9329.93	0.332178
$925$	−400.354	−0.0142309
$926$	−37962.5	−1.34722
$927$	19603.0	0.694549
$928$	−12991.8	−0.459564
$929$	11053.4	0.390365	0.195182	−	0.980767i	$-0.437470\pi$
$929$	11053.4	0.390365	0.195182	+	0.980767i	$0.437470\pi$
$930$	40433.5	1.42566
$931$	19234.5	0.677105
$932$	−1938.76	−0.0681396
$933$	53685.3	1.88379
$934$	59214.0	2.07446
$935$	7424.42	0.259684
$936$	0	0
$937$	−23952.1	−0.835093	−0.417546	−	0.908656i	$-0.637110\pi$
$937$	−23952.1	−0.835093	−0.417546	+	0.908656i	$0.637110\pi$
$938$	34388.8	1.19705
$939$	72813.6	2.53054
$940$	37666.4	1.30696
$941$	−21248.1	−0.736098	−0.368049	−	0.929806i	$-0.619974\pi$
$941$	−21248.1	−0.736098	−0.368049	+	0.929806i	$0.619974\pi$
$942$	−65055.4	−2.25013
$943$	−5539.89	−0.191308
$944$	1243.47	0.0428725
$945$	−2842.09	−0.0978342
$946$	20012.4	0.687802
$947$	−45536.0	−1.56254	−0.781268	−	0.624196i	$-0.785427\pi$
$947$	−45536.0	−1.56254	−0.781268	+	0.624196i	$0.785427\pi$
$948$	59764.9	2.04755
$949$	0	0
$950$	−912.196	−0.0311532
$951$	−36886.2	−1.25775
$952$	13311.5	0.453183
$953$	18283.5	0.621468	0.310734	−	0.950497i	$-0.399425\pi$
$953$	18283.5	0.621468	0.310734	+	0.950497i	$0.399425\pi$
$954$	21697.6	0.736359
$955$	−1056.04	−0.0357828
$956$	−6616.29	−0.223835
$957$	5965.29	0.201495
$958$	−70592.9	−2.38074
$959$	−9387.79	−0.316108
$960$	64125.4	2.15587
$961$	−17191.1	−0.577056
$962$	0	0
$963$	46057.2	1.54120
$964$	67749.4	2.26355
$965$	−42933.5	−1.43220
$966$	9494.12	0.316220
$967$	7703.82	0.256192	0.128096	−	0.991762i	$-0.459113\pi$
$967$	7703.82	0.256192	0.128096	+	0.991762i	$0.459113\pi$
$968$	−2908.21	−0.0965634
$969$	−31844.4	−1.05572
$970$	−2398.34	−0.0793876
$971$	32756.4	1.08260	0.541299	−	0.840830i	$-0.317933\pi$
$971$	32756.4	1.08260	0.541299	+	0.840830i	$0.317933\pi$
$972$	−66633.3	−2.19883
$973$	25500.6	0.840196
$974$	36990.9	1.21690
$975$	0	0
$976$	−4378.45	−0.143597
$977$	33149.2	1.08550	0.542752	−	0.839893i	$-0.317382\pi$
$977$	33149.2	1.08550	0.542752	+	0.839893i	$0.317382\pi$
$978$	25843.4	0.844971
$979$	14578.5	0.475925
$980$	38101.5	1.24195
$981$	28469.2	0.926557
$982$	72805.7	2.36591
$983$	16506.2	0.535571	0.267785	−	0.963479i	$-0.413708\pi$
$983$	16506.2	0.535571	0.267785	+	0.963479i	$0.413708\pi$
$984$	29310.8	0.949586
$985$	26153.1	0.845998
$986$	21560.1	0.696364
$987$	16534.0	0.533214
$988$	0	0
$989$	12686.3	0.407888
$990$	−12886.2	−0.413687
$991$	−15889.2	−0.509320	−0.254660	−	0.967031i	$-0.581964\pi$
$991$	−15889.2	−0.509320	−0.254660	+	0.967031i	$0.581964\pi$
$992$	19014.2	0.608570
$993$	−44220.2	−1.41318
$994$	−20004.6	−0.638336
$995$	5621.16	0.179098
$996$	39170.4	1.24615
$997$	−57994.2	−1.84222	−0.921111	−	0.389300i	$-0.872717\pi$
$997$	−57994.2	−1.84222	−0.921111	+	0.389300i	$0.872717\pi$
$998$	99360.6	3.15151
$999$	−4224.57	−0.133793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.p.1.7	✓	51
13.12	even	2		1859.4.a.q.1.45	yes	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.7	✓	51	1.1	even	1	trivial
1859.4.a.q.1.45	yes	51	13.12	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-4.60628 q^{2} +7.07074 q^{3} +13.2178 q^{4} -11.0597 q^{5} -32.5698 q^{6} -9.07530 q^{7} -24.0348 q^{8} +22.9953 q^{9} +O(q^{10})\)	\(q-4.60628 q^{2} +7.07074 q^{3} +13.2178 q^{4} -11.0597 q^{5} -32.5698 q^{6} -9.07530 q^{7} -24.0348 q^{8} +22.9953 q^{9} +50.9440 q^{10} -11.0000 q^{11} +93.4598 q^{12} +41.8034 q^{14} -78.2001 q^{15} +4.96838 q^{16} +61.0277 q^{17} -105.923 q^{18} -73.7974 q^{19} -146.185 q^{20} -64.1690 q^{21} +50.6691 q^{22} +32.1202 q^{23} -169.944 q^{24} -2.68347 q^{25} -28.3162 q^{27} -119.956 q^{28} -76.6962 q^{29} +360.212 q^{30} +112.249 q^{31} +169.393 q^{32} -77.7781 q^{33} -281.111 q^{34} +100.370 q^{35} +303.948 q^{36} +149.193 q^{37} +339.932 q^{38} +265.817 q^{40} -172.473 q^{41} +295.581 q^{42} +394.963 q^{43} -145.396 q^{44} -254.321 q^{45} -147.955 q^{46} -257.663 q^{47} +35.1301 q^{48} -260.639 q^{49} +12.3608 q^{50} +431.511 q^{51} -204.844 q^{53} +130.432 q^{54} +121.656 q^{55} +218.123 q^{56} -521.802 q^{57} +353.284 q^{58} +250.278 q^{59} -1033.64 q^{60} -881.262 q^{61} -517.052 q^{62} -208.689 q^{63} -820.017 q^{64} +358.268 q^{66} +822.632 q^{67} +806.654 q^{68} +227.114 q^{69} -462.332 q^{70} -478.539 q^{71} -552.687 q^{72} -439.506 q^{73} -687.223 q^{74} -18.9741 q^{75} -975.442 q^{76} +99.8283 q^{77} +639.472 q^{79} -54.9487 q^{80} -821.089 q^{81} +794.461 q^{82} +419.116 q^{83} -848.175 q^{84} -674.947 q^{85} -1819.31 q^{86} -542.299 q^{87} +264.383 q^{88} -1325.32 q^{89} +1171.47 q^{90} +424.560 q^{92} +793.685 q^{93} +1186.87 q^{94} +816.176 q^{95} +1197.73 q^{96} -47.0779 q^{97} +1200.58 q^{98} -252.948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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