LMFDB - Embedded newform 2401.4.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, 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("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46450 q^{2} +5.32585 q^{3} -1.92624 q^{4} -15.0765 q^{5} -13.1256 q^{6} +24.4632 q^{8} +1.36464 q^{9} +O(q^{10})$	\(q-2.46450 q^{2} +5.32585 q^{3} -1.92624 q^{4} -15.0765 q^{5} -13.1256 q^{6} +24.4632 q^{8} +1.36464 q^{9} +37.1561 q^{10} +53.1220 q^{11} -10.2588 q^{12} +52.6503 q^{13} -80.2952 q^{15} -44.8797 q^{16} -118.138 q^{17} -3.36315 q^{18} -43.3288 q^{19} +29.0409 q^{20} -130.919 q^{22} -107.799 q^{23} +130.287 q^{24} +102.301 q^{25} -129.757 q^{26} -136.530 q^{27} +242.757 q^{29} +197.888 q^{30} +171.806 q^{31} -85.0996 q^{32} +282.920 q^{33} +291.152 q^{34} -2.62862 q^{36} +33.9430 q^{37} +106.784 q^{38} +280.407 q^{39} -368.820 q^{40} -192.043 q^{41} +306.594 q^{43} -102.326 q^{44} -20.5740 q^{45} +265.670 q^{46} -328.190 q^{47} -239.023 q^{48} -252.122 q^{50} -629.186 q^{51} -101.417 q^{52} +44.9593 q^{53} +336.478 q^{54} -800.895 q^{55} -230.762 q^{57} -598.275 q^{58} -297.476 q^{59} +154.668 q^{60} +24.7203 q^{61} -423.417 q^{62} +568.766 q^{64} -793.783 q^{65} -697.256 q^{66} +269.322 q^{67} +227.562 q^{68} -574.120 q^{69} +736.450 q^{71} +33.3835 q^{72} +89.8135 q^{73} -83.6525 q^{74} +544.842 q^{75} +83.4614 q^{76} -691.064 q^{78} +162.912 q^{79} +676.630 q^{80} -763.983 q^{81} +473.290 q^{82} -293.556 q^{83} +1781.11 q^{85} -755.601 q^{86} +1292.89 q^{87} +1299.54 q^{88} +274.777 q^{89} +50.7047 q^{90} +207.646 q^{92} +915.014 q^{93} +808.823 q^{94} +653.247 q^{95} -453.227 q^{96} +505.160 q^{97} +72.4924 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * 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 $

$2$	−2.46450	−0.871333	−0.435666	−	0.900108i	$-0.643487\pi$
$2$	−2.46450	−0.871333	−0.435666	+	0.900108i	$0.643487\pi$
$3$	5.32585	1.02496	0.512480	−	0.858699i	$-0.328727\pi$
$3$	5.32585	1.02496	0.512480	+	0.858699i	$0.328727\pi$
$4$	−1.92624	−0.240779
$5$	−15.0765	−1.34848	−0.674242	−	0.738510i	$-0.735530\pi$
$5$	−15.0765	−1.34848	−0.674242	+	0.738510i	$0.735530\pi$
$6$	−13.1256	−0.893081
$7$	0	0
$7$	0	0
$8$	24.4632	1.08113
$9$	1.36464	0.0505422
$10$	37.1561	1.17498
$11$	53.1220	1.45608	0.728041	−	0.685534i	$-0.240431\pi$
$11$	53.1220	1.45608	0.728041	+	0.685534i	$0.240431\pi$
$12$	−10.2588	−0.246789
$13$	52.6503	1.12327	0.561637	−	0.827384i	$-0.310172\pi$
$13$	52.6503	1.12327	0.561637	+	0.827384i	$0.310172\pi$
$14$	0	0
$15$	−80.2952	−1.38214
$16$	−44.8797	−0.701246
$17$	−118.138	−1.68545	−0.842727	−	0.538341i	$-0.819051\pi$
$17$	−118.138	−1.68545	−0.842727	+	0.538341i	$0.819051\pi$
$18$	−3.36315	−0.0440391
$19$	−43.3288	−0.523174	−0.261587	−	0.965180i	$-0.584246\pi$
$19$	−43.3288	−0.523174	−0.261587	+	0.965180i	$0.584246\pi$
$20$	29.0409	0.324687
$21$	0	0
$22$	−130.919	−1.26873
$23$	−107.799	−0.977287	−0.488644	−	0.872483i	$-0.662508\pi$
$23$	−107.799	−0.977287	−0.488644	+	0.872483i	$0.662508\pi$
$24$	130.287	1.10812
$25$	102.301	0.818412
$26$	−129.757	−0.978745
$27$	−136.530	−0.973156
$28$	0	0
$29$	242.757	1.55444	0.777221	−	0.629228i	$-0.216629\pi$
$29$	242.757	1.55444	0.777221	+	0.629228i	$0.216629\pi$
$30$	197.888	1.20431
$31$	171.806	0.995398	0.497699	−	0.867350i	$-0.334178\pi$
$31$	171.806	0.995398	0.497699	+	0.867350i	$0.334178\pi$
$32$	−85.0996	−0.470113
$33$	282.920	1.49242
$34$	291.152	1.46859
$35$	0	0
$36$	−2.62862	−0.0121695
$37$	33.9430	0.150816	0.0754080	−	0.997153i	$-0.475974\pi$
$37$	33.9430	0.150816	0.0754080	+	0.997153i	$0.475974\pi$
$38$	106.784	0.455858
$39$	280.407	1.15131
$40$	−368.820	−1.45789
$41$	−192.043	−0.731515	−0.365757	−	0.930710i	$-0.619190\pi$
$41$	−192.043	−0.731515	−0.365757	+	0.930710i	$0.619190\pi$
$42$	0	0
$43$	306.594	1.08733	0.543664	−	0.839303i	$-0.317036\pi$
$43$	306.594	1.08733	0.543664	+	0.839303i	$0.317036\pi$
$44$	−102.326	−0.350594
$45$	−20.5740	−0.0681554
$46$	265.670	0.851542
$47$	−328.190	−1.01854	−0.509270	−	0.860607i	$-0.670084\pi$
$47$	−328.190	−1.01854	−0.509270	+	0.860607i	$0.670084\pi$
$48$	−239.023	−0.718749
$49$	0	0
$50$	−252.122	−0.713109
$51$	−629.186	−1.72752
$52$	−101.417	−0.270461
$53$	44.9593	0.116521	0.0582607	−	0.998301i	$-0.481445\pi$
$53$	44.9593	0.116521	0.0582607	+	0.998301i	$0.481445\pi$
$54$	336.478	0.847942
$55$	−800.895	−1.96350
$56$	0	0
$57$	−230.762	−0.536232
$58$	−598.275	−1.35444
$59$	−297.476	−0.656409	−0.328205	−	0.944607i	$-0.606444\pi$
$59$	−297.476	−0.656409	−0.328205	+	0.944607i	$0.606444\pi$
$60$	154.668	0.332792
$61$	24.7203	0.0518870	0.0259435	−	0.999663i	$-0.491741\pi$
$61$	24.7203	0.0518870	0.0259435	+	0.999663i	$0.491741\pi$
$62$	−423.417	−0.867322
$63$	0	0
$64$	568.766	1.11087
$65$	−793.783	−1.51472
$66$	−697.256	−1.30040
$67$	269.322	0.491088	0.245544	−	0.969385i	$-0.421033\pi$
$67$	269.322	0.491088	0.245544	+	0.969385i	$0.421033\pi$
$68$	227.562	0.405823
$69$	−574.120	−1.00168
$70$	0	0
$71$	736.450	1.23099	0.615497	−	0.788139i	$-0.288955\pi$
$71$	736.450	1.23099	0.615497	+	0.788139i	$0.288955\pi$
$72$	33.3835	0.0546428
$73$	89.8135	0.143998	0.0719991	−	0.997405i	$-0.477062\pi$
$73$	89.8135	0.143998	0.0719991	+	0.997405i	$0.477062\pi$
$74$	−83.6525	−0.131411
$75$	544.842	0.838839
$76$	83.4614	0.125969
$77$	0	0
$78$	−691.064	−1.00317
$79$	162.912	0.232014	0.116007	−	0.993248i	$-0.462991\pi$
$79$	162.912	0.232014	0.116007	+	0.993248i	$0.462991\pi$
$80$	676.630	0.945619
$81$	−763.983	−1.04799
$82$	473.290	0.637393
$83$	−293.556	−0.388216	−0.194108	−	0.980980i	$-0.562181\pi$
$83$	−293.556	−0.388216	−0.194108	+	0.980980i	$0.562181\pi$
$84$	0	0
$85$	1781.11	2.27281
$86$	−755.601	−0.947425
$87$	1292.89	1.59324
$88$	1299.54	1.57422
$89$	274.777	0.327262	0.163631	−	0.986522i	$-0.447679\pi$
$89$	274.777	0.327262	0.163631	+	0.986522i	$0.447679\pi$
$90$	50.7047	0.0593860
$91$	0	0
$92$	207.646	0.235311
$93$	915.014	1.02024
$94$	808.823	0.887487
$95$	653.247	0.705492
$96$	−453.227	−0.481847
$97$	505.160	0.528776	0.264388	−	0.964416i	$-0.414830\pi$
$97$	505.160	0.528776	0.264388	+	0.964416i	$0.414830\pi$
$98$	0	0
$99$	72.4924	0.0735935
$100$	−197.057	−0.197057
$101$	−23.7146	−0.0233633	−0.0116816	−	0.999932i	$-0.503718\pi$
$101$	−23.7146	−0.0233633	−0.0116816	+	0.999932i	$0.503718\pi$
$102$	1550.63	1.50525
$103$	−579.926	−0.554774	−0.277387	−	0.960758i	$-0.589468\pi$
$103$	−579.926	−0.554774	−0.277387	+	0.960758i	$0.589468\pi$
$104$	1287.99	1.21441
$105$	0	0
$106$	−110.802	−0.101529
$107$	−858.140	−0.775322	−0.387661	−	0.921802i	$-0.626717\pi$
$107$	−858.140	−0.775322	−0.387661	+	0.921802i	$0.626717\pi$
$108$	262.989	0.234316
$109$	319.537	0.280790	0.140395	−	0.990096i	$-0.455163\pi$
$109$	319.537	0.280790	0.140395	+	0.990096i	$0.455163\pi$
$110$	1973.81	1.71086
$111$	180.775	0.154580
$112$	0	0
$113$	1613.00	1.34282	0.671410	−	0.741086i	$-0.265689\pi$
$113$	1613.00	1.34282	0.671410	+	0.741086i	$0.265689\pi$
$114$	568.714	0.467236
$115$	1625.23	1.31786
$116$	−467.607	−0.374278
$117$	71.8486	0.0567727
$118$	733.131	0.571951
$119$	0	0
$120$	−1964.28	−1.49428
$121$	1490.95	1.12017
$122$	−60.9231	−0.0452108
$123$	−1022.79	−0.749773
$124$	−330.940	−0.239671
$125$	342.215	0.244869
$126$	0	0
$127$	−1918.68	−1.34059	−0.670295	−	0.742095i	$-0.733832\pi$
$127$	−1918.68	−1.34059	−0.670295	+	0.742095i	$0.733832\pi$
$128$	−720.927	−0.497825
$129$	1632.87	1.11447
$130$	1956.28	1.31982
$131$	1453.89	0.969669	0.484835	−	0.874606i	$-0.338880\pi$
$131$	1453.89	0.969669	0.484835	+	0.874606i	$0.338880\pi$
$132$	−544.970	−0.359345
$133$	0	0
$134$	−663.744	−0.427901
$135$	2058.40	1.31229
$136$	−2890.04	−1.82220
$137$	−2197.04	−1.37011	−0.685056	−	0.728490i	$-0.740222\pi$
$137$	−2197.04	−1.37011	−0.685056	+	0.728490i	$0.740222\pi$
$138$	1414.92	0.872796
$139$	−876.395	−0.534783	−0.267392	−	0.963588i	$-0.586162\pi$
$139$	−876.395	−0.534783	−0.267392	+	0.963588i	$0.586162\pi$
$140$	0	0
$141$	−1747.89	−1.04396
$142$	−1814.98	−1.07260
$143$	2796.89	1.63558
$144$	−61.2446	−0.0354425
$145$	−3659.93	−2.09614
$146$	−221.345	−0.125470
$147$	0	0
$148$	−65.3822	−0.0363134
$149$	1615.14	0.888037	0.444019	−	0.896018i	$-0.353552\pi$
$149$	1615.14	0.888037	0.444019	+	0.896018i	$0.353552\pi$
$150$	−1342.76	−0.730908
$151$	−245.593	−0.132358	−0.0661789	−	0.997808i	$-0.521081\pi$
$151$	−245.593	−0.132358	−0.0661789	+	0.997808i	$0.521081\pi$
$152$	−1059.96	−0.565620
$153$	−161.216	−0.0851866
$154$	0	0
$155$	−2590.24	−1.34228
$156$	−540.130	−0.277212
$157$	2484.88	1.26316	0.631578	−	0.775313i	$-0.282408\pi$
$157$	2484.88	1.26316	0.631578	+	0.775313i	$0.282408\pi$
$158$	−401.498	−0.202161
$159$	239.446	0.119430
$160$	1283.01	0.633941
$161$	0	0
$162$	1882.84	0.913146
$163$	−628.589	−0.302055	−0.151027	−	0.988530i	$-0.548258\pi$
$163$	−628.589	−0.302055	−0.151027	+	0.988530i	$0.548258\pi$
$164$	369.920	0.176134
$165$	−4265.44	−2.01251
$166$	723.468	0.338265
$167$	−484.477	−0.224491	−0.112245	−	0.993681i	$-0.535804\pi$
$167$	−484.477	−0.224491	−0.112245	+	0.993681i	$0.535804\pi$
$168$	0	0
$169$	575.050	0.261743
$170$	−4389.56	−1.98037
$171$	−59.1281	−0.0264423
$172$	−590.572	−0.261806
$173$	3566.90	1.56755	0.783775	−	0.621045i	$-0.213292\pi$
$173$	3566.90	1.56755	0.783775	+	0.621045i	$0.213292\pi$
$174$	−3186.32	−1.38824
$175$	0	0
$176$	−2384.10	−1.02107
$177$	−1584.31	−0.672793
$178$	−677.188	−0.285154
$179$	−2130.86	−0.889767	−0.444883	−	0.895589i	$-0.646755\pi$
$179$	−2130.86	−0.889767	−0.444883	+	0.895589i	$0.646755\pi$
$180$	39.6304	0.0164104
$181$	−1026.46	−0.421524	−0.210762	−	0.977537i	$-0.567594\pi$
$181$	−1026.46	−0.421524	−0.210762	+	0.977537i	$0.567594\pi$
$182$	0	0
$183$	131.656	0.0531820
$184$	−2637.11	−1.05658
$185$	−511.742	−0.203373
$186$	−2255.05	−0.888970
$187$	−6275.74	−2.45416
$188$	632.170	0.245243
$189$	0	0
$190$	−1609.93	−0.614718
$191$	−4779.78	−1.81075	−0.905374	−	0.424616i	$-0.860409\pi$
$191$	−4779.78	−1.81075	−0.905374	+	0.424616i	$0.860409\pi$
$192$	3029.16	1.13860
$193$	4252.62	1.58606	0.793031	−	0.609181i	$-0.208502\pi$
$193$	4252.62	1.58606	0.793031	+	0.609181i	$0.208502\pi$
$194$	−1244.97	−0.460740
$195$	−4227.56	−1.55252
$196$	0	0
$197$	2620.40	0.947694	0.473847	−	0.880607i	$-0.342865\pi$
$197$	2620.40	0.947694	0.473847	+	0.880607i	$0.342865\pi$
$198$	−178.658	−0.0641244
$199$	−1160.83	−0.413512	−0.206756	−	0.978393i	$-0.566291\pi$
$199$	−1160.83	−0.413512	−0.206756	+	0.978393i	$0.566291\pi$
$200$	2502.62	0.884811
$201$	1434.37	0.503346
$202$	58.4447	0.0203572
$203$	0	0
$204$	1211.96	0.415952
$205$	2895.34	0.986436
$206$	1429.23	0.483393
$207$	−147.107	−0.0493942
$208$	−2362.93	−0.787691
$209$	−2301.71	−0.761783
$210$	0	0
$211$	−1775.92	−0.579430	−0.289715	−	0.957113i	$-0.593560\pi$
$211$	−1775.92	−0.579430	−0.289715	+	0.957113i	$0.593560\pi$
$212$	−86.6023	−0.0280560
$213$	3922.22	1.26172
$214$	2114.89	0.675564
$215$	−4622.37	−1.46625
$216$	−3339.96	−1.05211
$217$	0	0
$218$	−787.499	−0.244661
$219$	478.333	0.147592
$220$	1542.71	0.472771
$221$	−6220.01	−1.89323
$222$	−445.520	−0.134691
$223$	−1966.53	−0.590531	−0.295266	−	0.955415i	$-0.595408\pi$
$223$	−1966.53	−0.590531	−0.295266	+	0.955415i	$0.595408\pi$
$224$	0	0
$225$	139.605	0.0413643
$226$	−3975.25	−1.17004
$227$	−528.470	−0.154519	−0.0772594	−	0.997011i	$-0.524617\pi$
$227$	−528.470	−0.154519	−0.0772594	+	0.997011i	$0.524617\pi$
$228$	444.503	0.129114
$229$	−2034.09	−0.586971	−0.293485	−	0.955964i	$-0.594815\pi$
$229$	−2034.09	−0.586971	−0.293485	+	0.955964i	$0.594815\pi$
$230$	−4005.38	−1.14829
$231$	0	0
$232$	5938.61	1.68056
$233$	−4203.71	−1.18195	−0.590975	−	0.806690i	$-0.701257\pi$
$233$	−4203.71	−1.18195	−0.590975	+	0.806690i	$0.701257\pi$
$234$	−177.071	−0.0494679
$235$	4947.96	1.37349
$236$	573.010	0.158050
$237$	867.646	0.237805
$238$	0	0
$239$	−5398.76	−1.46116	−0.730579	−	0.682828i	$-0.760750\pi$
$239$	−5398.76	−1.46116	−0.730579	+	0.682828i	$0.760750\pi$
$240$	3603.63	0.969222
$241$	−4480.66	−1.19761	−0.598806	−	0.800894i	$-0.704358\pi$
$241$	−4480.66	−1.19761	−0.598806	+	0.800894i	$0.704358\pi$
$242$	−3674.45	−0.976043
$243$	−382.546	−0.100989
$244$	−47.6170	−0.0124933
$245$	0	0
$246$	2520.67	0.653302
$247$	−2281.27	−0.587667
$248$	4202.94	1.07616
$249$	−1563.43	−0.397906
$250$	−843.389	−0.213363
$251$	−5476.97	−1.37730	−0.688652	−	0.725092i	$-0.741797\pi$
$251$	−5476.97	−1.37730	−0.688652	+	0.725092i	$0.741797\pi$
$252$	0	0
$253$	−5726.49	−1.42301
$254$	4728.58	1.16810
$255$	9485.94	2.32954
$256$	−2773.40	−0.677100
$257$	2065.76	0.501396	0.250698	−	0.968065i	$-0.419340\pi$
$257$	2065.76	0.501396	0.250698	+	0.968065i	$0.419340\pi$
$258$	−4024.21	−0.971072
$259$	0	0
$260$	1529.01	0.364713
$261$	331.276	0.0785649
$262$	−3583.11	−0.844905
$263$	−2381.48	−0.558360	−0.279180	−	0.960239i	$-0.590063\pi$
$263$	−2381.48	−0.558360	−0.279180	+	0.960239i	$0.590063\pi$
$264$	6921.13	1.61351
$265$	−677.830	−0.157127
$266$	0	0
$267$	1463.42	0.335430
$268$	−518.778	−0.118244
$269$	33.4245	0.00757594	0.00378797	−	0.999993i	$-0.498794\pi$
$269$	33.4245	0.00757594	0.00378797	+	0.999993i	$0.498794\pi$
$270$	−5072.92	−1.14344
$271$	3851.04	0.863225	0.431612	−	0.902059i	$-0.357945\pi$
$271$	3851.04	0.863225	0.431612	+	0.902059i	$0.357945\pi$
$272$	5302.01	1.18192
$273$	0	0
$274$	5414.60	1.19382
$275$	5434.46	1.19167
$276$	1105.89	0.241184
$277$	−7074.52	−1.53454	−0.767269	−	0.641326i	$-0.778385\pi$
$277$	−7074.52	−1.53454	−0.767269	+	0.641326i	$0.778385\pi$
$278$	2159.88	0.465974
$279$	234.454	0.0503096
$280$	0	0
$281$	−6116.24	−1.29845	−0.649225	−	0.760597i	$-0.724907\pi$
$281$	−6116.24	−1.29845	−0.649225	+	0.760597i	$0.724907\pi$
$282$	4307.67	0.909638
$283$	−8375.20	−1.75920	−0.879600	−	0.475714i	$-0.842190\pi$
$283$	−8375.20	−1.75920	−0.879600	+	0.475714i	$0.842190\pi$
$284$	−1418.58	−0.296398
$285$	3479.09	0.723101
$286$	−6892.93	−1.42513
$287$	0	0
$288$	−116.130	−0.0237606
$289$	9043.64	1.84076
$290$	9019.90	1.82644
$291$	2690.41	0.541974
$292$	−173.002	−0.0346718
$293$	−2448.96	−0.488292	−0.244146	−	0.969738i	$-0.578508\pi$
$293$	−2448.96	−0.488292	−0.244146	+	0.969738i	$0.578508\pi$
$294$	0	0
$295$	4484.91	0.885158
$296$	830.354	0.163052
$297$	−7252.75	−1.41699
$298$	−3980.52	−0.773776
$299$	−5675.64	−1.09776
$300$	−1049.49	−0.201975
$301$	0	0
$302$	605.263	0.115328
$303$	−126.300	−0.0239464
$304$	1944.58	0.366873
$305$	−372.695	−0.0699688
$306$	397.317	0.0742258
$307$	−8585.22	−1.59604	−0.798020	−	0.602631i	$-0.794119\pi$
$307$	−8585.22	−1.59604	−0.798020	+	0.602631i	$0.794119\pi$
$308$	0	0
$309$	−3088.59	−0.568621
$310$	6383.65	1.16957
$311$	−7568.94	−1.38005	−0.690024	−	0.723786i	$-0.742400\pi$
$311$	−7568.94	−1.38005	−0.690024	+	0.723786i	$0.742400\pi$
$312$	6859.66	1.24472
$313$	10321.0	1.86383	0.931917	−	0.362671i	$-0.118135\pi$
$313$	10321.0	1.86383	0.931917	+	0.362671i	$0.118135\pi$
$314$	−6124.00	−1.10063
$315$	0	0
$316$	−313.808	−0.0558641
$317$	6969.60	1.23486	0.617432	−	0.786624i	$-0.288173\pi$
$317$	6969.60	1.23486	0.617432	+	0.786624i	$0.288173\pi$
$318$	−590.116	−0.104063
$319$	12895.7	2.26339
$320$	−8575.01	−1.49799
$321$	−4570.32	−0.794674
$322$	0	0
$323$	5118.78	0.881786
$324$	1471.61	0.252334
$325$	5386.20	0.919300
$326$	1549.16	0.263190
$327$	1701.80	0.287798
$328$	−4697.99	−0.790864
$329$	0	0
$330$	10512.2	1.75357
$331$	1577.21	0.261907	0.130953	−	0.991389i	$-0.458196\pi$
$331$	1577.21	0.261907	0.130953	+	0.991389i	$0.458196\pi$
$332$	565.457	0.0934744
$333$	46.3199	0.00762257
$334$	1193.99	0.195606
$335$	−4060.44	−0.662225
$336$	0	0
$337$	3218.99	0.520324	0.260162	−	0.965565i	$-0.416224\pi$
$337$	3218.99	0.520324	0.260162	+	0.965565i	$0.416224\pi$
$338$	−1417.21	−0.228065
$339$	8590.61	1.37634
$340$	−3430.84	−0.547246
$341$	9126.70	1.44938
$342$	145.721	0.0230401
$343$	0	0
$344$	7500.27	1.17555
$345$	8655.73	1.35075
$346$	−8790.62	−1.36586
$347$	4918.74	0.760956	0.380478	−	0.924790i	$-0.375759\pi$
$347$	4918.74	0.760956	0.380478	+	0.924790i	$0.375759\pi$
$348$	−2490.40	−0.383620
$349$	−10252.6	−1.57252	−0.786262	−	0.617893i	$-0.787986\pi$
$349$	−10252.6	−1.57252	−0.786262	+	0.617893i	$0.787986\pi$
$350$	0	0
$351$	−7188.34	−1.09312
$352$	−4520.66	−0.684523
$353$	−1096.36	−0.165307	−0.0826535	−	0.996578i	$-0.526339\pi$
$353$	−1096.36	−0.165307	−0.0826535	+	0.996578i	$0.526339\pi$
$354$	3904.54	0.586226
$355$	−11103.1	−1.65998
$356$	−529.285	−0.0787979
$357$	0	0
$358$	5251.51	0.775283
$359$	7374.17	1.08410	0.542052	−	0.840345i	$-0.317647\pi$
$359$	7374.17	1.08410	0.542052	+	0.840345i	$0.317647\pi$
$360$	−503.306	−0.0736849
$361$	−4981.62	−0.726289
$362$	2529.70	0.367287
$363$	7940.57	1.14813
$364$	0	0
$365$	−1354.07	−0.194179
$366$	−324.467	−0.0463392
$367$	1633.31	0.232311	0.116156	−	0.993231i	$-0.462943\pi$
$367$	1633.31	0.232311	0.116156	+	0.993231i	$0.462943\pi$
$368$	4837.98	0.685319
$369$	−262.070	−0.0369724
$370$	1261.19	0.177206
$371$	0	0
$372$	−1762.53	−0.245653
$373$	4669.99	0.648265	0.324132	−	0.946012i	$-0.394928\pi$
$373$	4669.99	0.648265	0.324132	+	0.946012i	$0.394928\pi$
$374$	15466.6	2.13839
$375$	1822.59	0.250981
$376$	−8028.57	−1.10118
$377$	12781.2	1.74606
$378$	0	0
$379$	1548.23	0.209835	0.104917	−	0.994481i	$-0.466542\pi$
$379$	1548.23	0.209835	0.104917	+	0.994481i	$0.466542\pi$
$380$	−1258.31	−0.169868
$381$	−10218.6	−1.37405
$382$	11779.8	1.57776
$383$	−5494.41	−0.733032	−0.366516	−	0.930412i	$-0.619449\pi$
$383$	−5494.41	−0.733032	−0.366516	+	0.930412i	$0.619449\pi$
$384$	−3839.55	−0.510250
$385$	0	0
$386$	−10480.6	−1.38199
$387$	418.390	0.0549560
$388$	−973.058	−0.127318
$389$	5363.71	0.699103	0.349551	−	0.936917i	$-0.386334\pi$
$389$	5363.71	0.699103	0.349551	+	0.936917i	$0.386334\pi$
$390$	10418.8	1.35276
$391$	12735.2	1.64717
$392$	0	0
$393$	7743.18	0.993872
$394$	−6457.97	−0.825756
$395$	−2456.15	−0.312867
$396$	−139.637	−0.0177198
$397$	3223.98	0.407574	0.203787	−	0.979015i	$-0.434675\pi$
$397$	3223.98	0.407574	0.203787	+	0.979015i	$0.434675\pi$
$398$	2860.86	0.360306
$399$	0	0
$400$	−4591.26	−0.573908
$401$	−2350.48	−0.292711	−0.146356	−	0.989232i	$-0.546754\pi$
$401$	−2350.48	−0.292711	−0.146356	+	0.989232i	$0.546754\pi$
$402$	−3535.00	−0.438581
$403$	9045.65	1.11810
$404$	45.6799	0.00562540
$405$	11518.2	1.41320
$406$	0	0
$407$	1803.12	0.219600
$408$	−15391.9	−1.86768
$409$	−6433.75	−0.777820	−0.388910	−	0.921276i	$-0.627148\pi$
$409$	−6433.75	−0.777820	−0.388910	+	0.921276i	$0.627148\pi$
$410$	−7135.57	−0.859514
$411$	−11701.1	−1.40431
$412$	1117.07	0.133578
$413$	0	0
$414$	362.544	0.0430388
$415$	4425.80	0.523503
$416$	−4480.52	−0.528066
$417$	−4667.55	−0.548131
$418$	5672.57	0.663767
$419$	−14066.4	−1.64007	−0.820034	−	0.572315i	$-0.806045\pi$
$419$	−14066.4	−1.64007	−0.820034	+	0.572315i	$0.806045\pi$
$420$	0	0
$421$	−12822.8	−1.48442	−0.742212	−	0.670165i	$-0.766223\pi$
$421$	−12822.8	−1.48442	−0.742212	+	0.670165i	$0.766223\pi$
$422$	4376.77	0.504876
$423$	−447.860	−0.0514792
$424$	1099.85	0.125975
$425$	−12085.7	−1.37940
$426$	−9666.31	−1.09938
$427$	0	0
$428$	1652.98	0.186682
$429$	14895.8	1.67640
$430$	11391.8	1.27759
$431$	−13778.0	−1.53982	−0.769910	−	0.638152i	$-0.779699\pi$
$431$	−13778.0	−1.53982	−0.769910	+	0.638152i	$0.779699\pi$
$432$	6127.43	0.682421
$433$	−4999.34	−0.554857	−0.277428	−	0.960746i	$-0.589482\pi$
$433$	−4999.34	−0.554857	−0.277428	+	0.960746i	$0.589482\pi$
$434$	0	0
$435$	−19492.2	−2.14846
$436$	−615.503	−0.0676084
$437$	4670.79	0.511291
$438$	−1178.85	−0.128602
$439$	−1999.46	−0.217379	−0.108689	−	0.994076i	$-0.534665\pi$
$439$	−1999.46	−0.217379	−0.108689	+	0.994076i	$0.534665\pi$
$440$	−19592.5	−2.12281
$441$	0	0
$442$	15329.2	1.64963
$443$	−9396.19	−1.00773	−0.503867	−	0.863781i	$-0.668090\pi$
$443$	−9396.19	−1.00773	−0.503867	+	0.863781i	$0.668090\pi$
$444$	−348.215	−0.0372198
$445$	−4142.68	−0.441307
$446$	4846.51	0.514549
$447$	8602.00	0.910202
$448$	0	0
$449$	−7690.77	−0.808351	−0.404176	−	0.914681i	$-0.632442\pi$
$449$	−7690.77	−0.808351	−0.404176	+	0.914681i	$0.632442\pi$
$450$	−344.056	−0.0360421
$451$	−10201.7	−1.06514
$452$	−3107.03	−0.323324
$453$	−1307.99	−0.135661
$454$	1302.41	0.134637
$455$	0	0
$456$	−5645.19	−0.579737
$457$	−10652.9	−1.09042	−0.545211	−	0.838299i	$-0.683551\pi$
$457$	−10652.9	−1.09042	−0.545211	+	0.838299i	$0.683551\pi$
$458$	5013.01	0.511447
$459$	16129.4	1.64021
$460$	−3130.58	−0.317313
$461$	−9246.40	−0.934160	−0.467080	−	0.884215i	$-0.654694\pi$
$461$	−9246.40	−0.934160	−0.467080	+	0.884215i	$0.654694\pi$
$462$	0	0
$463$	7842.26	0.787172	0.393586	−	0.919288i	$-0.371234\pi$
$463$	7842.26	0.787172	0.393586	+	0.919288i	$0.371234\pi$
$464$	−10894.9	−1.09005
$465$	−13795.2	−1.37578
$466$	10360.1	1.02987
$467$	3043.06	0.301533	0.150767	−	0.988569i	$-0.451826\pi$
$467$	3043.06	0.301533	0.150767	+	0.988569i	$0.451826\pi$
$468$	−138.397	−0.0136697
$469$	0	0
$470$	−12194.2	−1.19676
$471$	13234.1	1.29468
$472$	−7277.23	−0.709665
$473$	16286.9	1.58324
$474$	−2138.31	−0.207207
$475$	−4432.60	−0.428171
$476$	0	0
$477$	61.3533	0.00588925
$478$	13305.3	1.27316
$479$	−11177.2	−1.06618	−0.533091	−	0.846058i	$-0.678970\pi$
$479$	−11177.2	−1.06618	−0.533091	+	0.846058i	$0.678970\pi$
$480$	6833.09	0.649764
$481$	1787.11	0.169408
$482$	11042.6	1.04352
$483$	0	0
$484$	−2871.92	−0.269714
$485$	−7616.06	−0.713046
$486$	942.786	0.0879951
$487$	−17937.6	−1.66906	−0.834530	−	0.550963i	$-0.814261\pi$
$487$	−17937.6	−1.66906	−0.834530	+	0.550963i	$0.814261\pi$
$488$	604.737	0.0560966
$489$	−3347.77	−0.309594
$490$	0	0
$491$	8601.67	0.790607	0.395304	−	0.918551i	$-0.370639\pi$
$491$	8601.67	0.790607	0.395304	+	0.918551i	$0.370639\pi$
$492$	1970.14	0.180530
$493$	−28678.9	−2.61994
$494$	5622.19	0.512054
$495$	−1092.93	−0.0992398
$496$	−7710.62	−0.698018
$497$	0	0
$498$	3853.08	0.346708
$499$	−2713.20	−0.243406	−0.121703	−	0.992567i	$-0.538836\pi$
$499$	−2713.20	−0.243406	−0.121703	+	0.992567i	$0.538836\pi$
$500$	−659.187	−0.0589595
$501$	−2580.25	−0.230094
$502$	13498.0	1.20009
$503$	−6557.17	−0.581252	−0.290626	−	0.956837i	$-0.593863\pi$
$503$	−6557.17	−0.581252	−0.290626	+	0.956837i	$0.593863\pi$
$504$	0	0
$505$	357.534	0.0315050
$506$	14112.9	1.23991
$507$	3062.63	0.268276
$508$	3695.82	0.322787
$509$	−13865.7	−1.20744	−0.603719	−	0.797197i	$-0.706315\pi$
$509$	−13865.7	−1.20744	−0.603719	+	0.797197i	$0.706315\pi$
$510$	−23378.1	−2.02980
$511$	0	0
$512$	12602.5	1.08780
$513$	5915.68	0.509130
$514$	−5091.08	−0.436883
$515$	8743.26	0.748105
$516$	−3145.30	−0.268341
$517$	−17434.1	−1.48308
$518$	0	0
$519$	18996.7	1.60668
$520$	−19418.5	−1.63761
$521$	313.003	0.0263204	0.0131602	−	0.999913i	$-0.495811\pi$
$521$	313.003	0.0263204	0.0131602	+	0.999913i	$0.495811\pi$
$522$	−816.429	−0.0684562
$523$	9153.87	0.765336	0.382668	−	0.923886i	$-0.375005\pi$
$523$	9153.87	0.765336	0.382668	+	0.923886i	$0.375005\pi$
$524$	−2800.53	−0.233476
$525$	0	0
$526$	5869.17	0.486517
$527$	−20296.9	−1.67770
$528$	−12697.4	−1.04656
$529$	−546.413	−0.0449095
$530$	1670.51	0.136910
$531$	−405.948	−0.0331764
$532$	0	0
$533$	−10111.1	−0.821691
$534$	−3606.60	−0.292271
$535$	12937.8	1.04551
$536$	6588.48	0.530931
$537$	−11348.7	−0.911975
$538$	−82.3748	−0.00660117
$539$	0	0
$540$	−3964.96	−0.315972
$541$	22154.2	1.76060	0.880298	−	0.474421i	$-0.157343\pi$
$541$	22154.2	1.76060	0.880298	+	0.474421i	$0.157343\pi$
$542$	−9490.88	−0.752156
$543$	−5466.74	−0.432045
$544$	10053.5	0.792355
$545$	−4817.50	−0.378641
$546$	0	0
$547$	16387.9	1.28098	0.640492	−	0.767965i	$-0.278731\pi$
$547$	16387.9	1.28098	0.640492	+	0.767965i	$0.278731\pi$
$548$	4232.01	0.329895
$549$	33.7342	0.00262248
$550$	−13393.2	−1.03834
$551$	−10518.4	−0.813243
$552$	−14044.8	−1.08295
$553$	0	0
$554$	17435.2	1.33709
$555$	−2725.46	−0.208449
$556$	1688.14	0.128765
$557$	10513.7	0.799781	0.399891	−	0.916563i	$-0.369048\pi$
$557$	10513.7	0.799781	0.399891	+	0.916563i	$0.369048\pi$
$558$	−577.811	−0.0438364
$559$	16142.3	1.22137
$560$	0	0
$561$	−33423.6	−2.51541
$562$	15073.5	1.13138
$563$	11173.8	0.836444	0.418222	−	0.908345i	$-0.362653\pi$
$563$	11173.8	0.836444	0.418222	+	0.908345i	$0.362653\pi$
$564$	3366.84	0.251365
$565$	−24318.5	−1.81077
$566$	20640.7	1.53285
$567$	0	0
$568$	18015.9	1.33087
$569$	−10298.8	−0.758784	−0.379392	−	0.925236i	$-0.623867\pi$
$569$	−10298.8	−0.758784	−0.379392	+	0.925236i	$0.623867\pi$
$570$	−8574.23	−0.630061
$571$	8184.84	0.599869	0.299934	−	0.953960i	$-0.403035\pi$
$571$	8184.84	0.599869	0.299934	+	0.953960i	$0.403035\pi$
$572$	−5387.47	−0.393813
$573$	−25456.4	−1.85594
$574$	0	0
$575$	−11028.0	−0.799823
$576$	776.160	0.0561459
$577$	19772.1	1.42656	0.713278	−	0.700881i	$-0.247210\pi$
$577$	19772.1	1.42656	0.713278	+	0.700881i	$0.247210\pi$
$578$	−22288.1	−1.60391
$579$	22648.8	1.62565
$580$	7049.89	0.504708
$581$	0	0
$582$	−6630.51	−0.472240
$583$	2388.33	0.169665
$584$	2197.13	0.155681
$585$	−1083.23	−0.0765571
$586$	6035.46	0.425465
$587$	−15550.9	−1.09345	−0.546724	−	0.837313i	$-0.684125\pi$
$587$	−15550.9	−1.09345	−0.546724	+	0.837313i	$0.684125\pi$
$588$	0	0
$589$	−7444.16	−0.520766
$590$	−11053.1	−0.771267
$591$	13955.8	0.971348
$592$	−1523.35	−0.105759
$593$	9536.24	0.660382	0.330191	−	0.943914i	$-0.392887\pi$
$593$	9536.24	0.660382	0.330191	+	0.943914i	$0.392887\pi$
$594$	17874.4	1.23467
$595$	0	0
$596$	−3111.14	−0.213821
$597$	−6182.39	−0.423833
$598$	13987.6	0.956515
$599$	9332.69	0.636600	0.318300	−	0.947990i	$-0.396888\pi$
$599$	9332.69	0.636600	0.318300	+	0.947990i	$0.396888\pi$
$600$	13328.6	0.906895
$601$	19089.2	1.29561	0.647807	−	0.761805i	$-0.275686\pi$
$601$	19089.2	1.29561	0.647807	+	0.761805i	$0.275686\pi$
$602$	0	0
$603$	367.527	0.0248207
$604$	473.069	0.0318691
$605$	−22478.3	−1.51054
$606$	311.267	0.0208653
$607$	−17906.4	−1.19736	−0.598679	−	0.800989i	$-0.704308\pi$
$607$	−17906.4	−1.19736	−0.598679	+	0.800989i	$0.704308\pi$
$608$	3687.26	0.245951
$609$	0	0
$610$	918.508	0.0609661
$611$	−17279.3	−1.14410
$612$	310.540	0.0205112
$613$	−17760.2	−1.17019	−0.585095	−	0.810965i	$-0.698943\pi$
$613$	−17760.2	−1.17019	−0.585095	+	0.810965i	$0.698943\pi$
$614$	21158.3	1.39068
$615$	15420.1	1.01106
$616$	0	0
$617$	−29078.3	−1.89732	−0.948662	−	0.316291i	$-0.897562\pi$
$617$	−29078.3	−1.89732	−0.948662	+	0.316291i	$0.897562\pi$
$618$	7611.84	0.495458
$619$	−5388.35	−0.349880	−0.174940	−	0.984579i	$-0.555973\pi$
$619$	−5388.35	−0.349880	−0.174940	+	0.984579i	$0.555973\pi$
$620$	4989.42	0.323193
$621$	14717.8	0.951053
$622$	18653.7	1.20248
$623$	0	0
$624$	−12584.6	−0.807351
$625$	−17947.1	−1.14861
$626$	−25436.2	−1.62402
$627$	−12258.6	−0.780797
$628$	−4786.47	−0.304142
$629$	−4009.96	−0.254193
$630$	0	0
$631$	24689.4	1.55764	0.778818	−	0.627250i	$-0.215820\pi$
$631$	24689.4	1.55764	0.778818	+	0.627250i	$0.215820\pi$
$632$	3985.36	0.250837
$633$	−9458.30	−0.593892
$634$	−17176.6	−1.07598
$635$	28927.0	1.80777
$636$	−461.230	−0.0287562
$637$	0	0
$638$	−31781.6	−1.97217
$639$	1004.99	0.0622171
$640$	10869.1	0.671309
$641$	−19704.6	−1.21418	−0.607088	−	0.794635i	$-0.707662\pi$
$641$	−19704.6	−1.21418	−0.607088	+	0.794635i	$0.707662\pi$
$642$	11263.6	0.692425
$643$	−3172.50	−0.194574	−0.0972870	−	0.995256i	$-0.531016\pi$
$643$	−3172.50	−0.194574	−0.0972870	+	0.995256i	$0.531016\pi$
$644$	0	0
$645$	−24618.0	−1.50284
$646$	−12615.2	−0.768329
$647$	6414.46	0.389766	0.194883	−	0.980827i	$-0.437567\pi$
$647$	6414.46	0.389766	0.194883	+	0.980827i	$0.437567\pi$
$648$	−18689.5	−1.13301
$649$	−15802.5	−0.955785
$650$	−13274.3	−0.801016
$651$	0	0
$652$	1210.81	0.0727285
$653$	−4862.47	−0.291399	−0.145699	−	0.989329i	$-0.546543\pi$
$653$	−4862.47	−0.291399	−0.145699	+	0.989329i	$0.546543\pi$
$654$	−4194.10	−0.250768
$655$	−21919.6	−1.30758
$656$	8618.84	0.512972
$657$	122.563	0.00727799
$658$	0	0
$659$	−9401.87	−0.555759	−0.277879	−	0.960616i	$-0.589632\pi$
$659$	−9401.87	−0.555759	−0.277879	+	0.960616i	$0.589632\pi$
$660$	8216.25	0.484572
$661$	−3117.40	−0.183438	−0.0917191	−	0.995785i	$-0.529236\pi$
$661$	−3117.40	−0.183438	−0.0917191	+	0.995785i	$0.529236\pi$
$662$	−3887.02	−0.228208
$663$	−33126.8	−1.94048
$664$	−7181.31	−0.419712
$665$	0	0
$666$	−114.155	−0.00664179
$667$	−26168.9	−1.51914
$668$	933.216	0.0540527
$669$	−10473.4	−0.605271
$670$	10007.0	0.577018
$671$	1313.19	0.0755516
$672$	0	0
$673$	24698.7	1.41466	0.707330	−	0.706884i	$-0.249900\pi$
$673$	24698.7	1.41466	0.707330	+	0.706884i	$0.249900\pi$
$674$	−7933.19	−0.453376
$675$	−13967.2	−0.796442
$676$	−1107.68	−0.0630224
$677$	−11169.3	−0.634076	−0.317038	−	0.948413i	$-0.602688\pi$
$677$	−11169.3	−0.634076	−0.317038	+	0.948413i	$0.602688\pi$
$678$	−21171.6	−1.19925
$679$	0	0
$680$	43571.8	2.45721
$681$	−2814.55	−0.158376
$682$	−22492.8	−1.26289
$683$	−8263.66	−0.462958	−0.231479	−	0.972840i	$-0.574356\pi$
$683$	−8263.66	−0.462958	−0.231479	+	0.972840i	$0.574356\pi$
$684$	113.895	0.00636677
$685$	33123.7	1.84758
$686$	0	0
$687$	−10833.2	−0.601621
$688$	−13759.9	−0.762485
$689$	2367.12	0.130885
$690$	−21332.1	−1.17695
$691$	−10392.1	−0.572120	−0.286060	−	0.958212i	$-0.592346\pi$
$691$	−10392.1	−0.572120	−0.286060	+	0.958212i	$0.592346\pi$
$692$	−6870.68	−0.377434
$693$	0	0
$694$	−12122.2	−0.663046
$695$	13213.0	0.721147
$696$	31628.1	1.72250
$697$	22687.6	1.23293
$698$	25267.6	1.37019
$699$	−22388.3	−1.21145
$700$	0	0
$701$	−6318.15	−0.340418	−0.170209	−	0.985408i	$-0.554444\pi$
$701$	−6318.15	−0.340418	−0.170209	+	0.985408i	$0.554444\pi$
$702$	17715.7	0.952471
$703$	−1470.71	−0.0789029
$704$	30214.0	1.61752
$705$	26352.1	1.40777
$706$	2701.98	0.144037
$707$	0	0
$708$	3051.76	0.161995
$709$	−24977.7	−1.32307	−0.661536	−	0.749913i	$-0.730095\pi$
$709$	−24977.7	−1.32307	−0.661536	+	0.749913i	$0.730095\pi$
$710$	27363.6	1.44639
$711$	222.317	0.0117265
$712$	6721.92	0.353813
$713$	−18520.5	−0.972790
$714$	0	0
$715$	−42167.3	−2.20555
$716$	4104.55	0.214238
$717$	−28753.0	−1.49763
$718$	−18173.6	−0.944616
$719$	24964.4	1.29487	0.647437	−	0.762119i	$-0.275841\pi$
$719$	24964.4	1.29487	0.647437	+	0.762119i	$0.275841\pi$
$720$	923.356	0.0477937
$721$	0	0
$722$	12277.2	0.632840
$723$	−23863.3	−1.22750
$724$	1977.19	0.101494
$725$	24834.4	1.27217
$726$	−19569.5	−1.00040
$727$	−3995.84	−0.203848	−0.101924	−	0.994792i	$-0.532500\pi$
$727$	−3995.84	−0.203848	−0.101924	+	0.994792i	$0.532500\pi$
$728$	0	0
$729$	18590.2	0.944478
$730$	3337.12	0.169195
$731$	−36220.5	−1.83264
$732$	−253.601	−0.0128051
$733$	−13810.7	−0.695920	−0.347960	−	0.937509i	$-0.613126\pi$
$733$	−13810.7	−0.695920	−0.347960	+	0.937509i	$0.613126\pi$
$734$	−4025.30	−0.202420
$735$	0	0
$736$	9173.64	0.459436
$737$	14306.9	0.715064
$738$	645.871	0.0322152
$739$	16262.8	0.809523	0.404761	−	0.914422i	$-0.367355\pi$
$739$	16262.8	0.809523	0.404761	+	0.914422i	$0.367355\pi$
$740$	985.735	0.0489680
$741$	−12149.7	−0.602335
$742$	0	0
$743$	4025.38	0.198757	0.0993787	−	0.995050i	$-0.468314\pi$
$743$	4025.38	0.198757	0.0993787	+	0.995050i	$0.468314\pi$
$744$	22384.2	1.10302
$745$	−24350.7	−1.19750
$746$	−11509.2	−0.564854
$747$	−400.597	−0.0196213
$748$	12088.6	0.590911
$749$	0	0
$750$	−4491.76	−0.218688
$751$	4233.96	0.205725	0.102862	−	0.994696i	$-0.467200\pi$
$751$	4233.96	0.205725	0.102862	+	0.994696i	$0.467200\pi$
$752$	14729.1	0.714247
$753$	−29169.5	−1.41168
$754$	−31499.3	−1.52140
$755$	3702.68	0.178483
$756$	0	0
$757$	31783.6	1.52602	0.763009	−	0.646388i	$-0.223721\pi$
$757$	31783.6	1.52602	0.763009	+	0.646388i	$0.223721\pi$
$758$	−3815.63	−0.182836
$759$	−30498.4	−1.45853
$760$	15980.5	0.762730
$761$	−5.18268	−0.000246875 0	−0.000123438	−	1.00000i	$-0.500039\pi$
$761$	−5.18268	−0.000246875 0	−0.000123438		1.00000i	$0.500039\pi$
$762$	25183.7	1.19726
$763$	0	0
$764$	9206.98	0.435991
$765$	2430.58	0.114873
$766$	13541.0	0.638715
$767$	−15662.2	−0.737327
$768$	−14770.7	−0.694000
$769$	10354.5	0.485557	0.242779	−	0.970082i	$-0.421941\pi$
$769$	10354.5	0.485557	0.242779	+	0.970082i	$0.421941\pi$
$770$	0	0
$771$	11001.9	0.513911
$772$	−8191.54	−0.381891
$773$	−9765.09	−0.454367	−0.227184	−	0.973852i	$-0.572952\pi$
$773$	−9765.09	−0.454367	−0.227184	+	0.973852i	$0.572952\pi$
$774$	−1031.12	−0.0478849
$775$	17576.0	0.814645
$776$	12357.8	0.571676
$777$	0	0
$778$	−13218.9	−0.609151
$779$	8320.99	0.382709
$780$	8143.29	0.373816
$781$	39121.7	1.79243
$782$	−31385.8	−1.43524
$783$	−33143.6	−1.51271
$784$	0	0
$785$	−37463.4	−1.70335
$786$	−19083.1	−0.865993
$787$	34382.8	1.55732	0.778661	−	0.627444i	$-0.215899\pi$
$787$	34382.8	1.55732	0.778661	+	0.627444i	$0.215899\pi$
$788$	−5047.50	−0.228185
$789$	−12683.4	−0.572296
$790$	6053.19	0.272611
$791$	0	0
$792$	1773.40	0.0795643
$793$	1301.53	0.0582832
$794$	−7945.50	−0.355133
$795$	−3610.02	−0.161049
$796$	2236.03	0.0995652
$797$	16064.2	0.713958	0.356979	−	0.934112i	$-0.383807\pi$
$797$	16064.2	0.713958	0.356979	+	0.934112i	$0.383807\pi$
$798$	0	0
$799$	38771.7	1.71670
$800$	−8705.81	−0.384746
$801$	374.971	0.0165405
$802$	5792.76	0.255049
$803$	4771.07	0.209673
$804$	−2762.93	−0.121195
$805$	0	0
$806$	−22293.0	−0.974240
$807$	178.014	0.00776504
$808$	−580.135	−0.0252588
$809$	17005.2	0.739024	0.369512	−	0.929226i	$-0.379525\pi$
$809$	17005.2	0.739024	0.369512	+	0.929226i	$0.379525\pi$
$810$	−28386.6	−1.23136
$811$	−10448.1	−0.452382	−0.226191	−	0.974083i	$-0.572627\pi$
$811$	−10448.1	−0.452382	−0.226191	+	0.974083i	$0.572627\pi$
$812$	0	0
$813$	20510.0	0.884770
$814$	−4443.79	−0.191345
$815$	9476.94	0.407316
$816$	28237.7	1.21142
$817$	−13284.3	−0.568862
$818$	15856.0	0.677740
$819$	0	0
$820$	−5577.11	−0.237514
$821$	19087.8	0.811410	0.405705	−	0.914004i	$-0.367026\pi$
$821$	19087.8	0.811410	0.405705	+	0.914004i	$0.367026\pi$
$822$	28837.3	1.22362
$823$	26572.7	1.12547	0.562737	−	0.826636i	$-0.309748\pi$
$823$	26572.7	1.12547	0.562737	+	0.826636i	$0.309748\pi$
$824$	−14186.8	−0.599784
$825$	28943.1	1.22142
$826$	0	0
$827$	−31933.9	−1.34275	−0.671373	−	0.741120i	$-0.734295\pi$
$827$	−31933.9	−1.34275	−0.671373	+	0.741120i	$0.734295\pi$
$828$	283.362	0.0118931
$829$	11251.6	0.471392	0.235696	−	0.971827i	$-0.424263\pi$
$829$	11251.6	0.471392	0.235696	+	0.971827i	$0.424263\pi$
$830$	−10907.4	−0.456145
$831$	−37677.8	−1.57284
$832$	29945.7	1.24781
$833$	0	0
$834$	11503.2	0.477605
$835$	7304.22	0.302722
$836$	4433.64	0.183422
$837$	−23456.7	−0.968677
$838$	34666.6	1.42904
$839$	−31635.7	−1.30177	−0.650885	−	0.759177i	$-0.725602\pi$
$839$	−31635.7	−1.30177	−0.650885	+	0.759177i	$0.725602\pi$
$840$	0	0
$841$	34541.9	1.41629
$842$	31601.7	1.29343
$843$	−32574.2	−1.33086
$844$	3420.85	0.139515
$845$	−8669.75	−0.352957
$846$	1103.75	0.0448555
$847$	0	0
$848$	−2017.76	−0.0817102
$849$	−44605.0	−1.80311
$850$	29785.2	1.20191
$851$	−3659.01	−0.147391
$852$	−7555.12	−0.303796
$853$	−6982.48	−0.280276	−0.140138	−	0.990132i	$-0.544755\pi$
$853$	−6982.48	−0.280276	−0.140138	+	0.990132i	$0.544755\pi$
$854$	0	0
$855$	891.446	0.0356571
$856$	−20992.9	−0.838225
$857$	−22904.6	−0.912961	−0.456481	−	0.889733i	$-0.650890\pi$
$857$	−22904.6	−0.912961	−0.456481	+	0.889733i	$0.650890\pi$
$858$	−36710.7	−1.46070
$859$	13443.7	0.533987	0.266993	−	0.963698i	$-0.413970\pi$
$859$	13443.7	0.533987	0.266993	+	0.963698i	$0.413970\pi$
$860$	8903.77	0.353042
$861$	0	0
$862$	33955.9	1.34170
$863$	15183.3	0.598895	0.299447	−	0.954113i	$-0.403198\pi$
$863$	15183.3	0.598895	0.299447	+	0.954113i	$0.403198\pi$
$864$	11618.6	0.457494
$865$	−53776.4	−2.11382
$866$	12320.9	0.483465
$867$	48165.0	1.88670
$868$	0	0
$869$	8654.23	0.337831
$870$	48038.6	1.87202
$871$	14179.9	0.551626
$872$	7816.90	0.303571
$873$	689.362	0.0267255
$874$	−11511.2	−0.445505
$875$	0	0
$876$	−921.382	−0.0355372
$877$	−38226.1	−1.47184	−0.735920	−	0.677069i	$-0.763250\pi$
$877$	−38226.1	−1.47184	−0.735920	+	0.677069i	$0.763250\pi$
$878$	4927.68	0.189409
$879$	−13042.8	−0.500480
$880$	35944.0	1.37690
$881$	12577.5	0.480984	0.240492	−	0.970651i	$-0.422691\pi$
$881$	12577.5	0.480984	0.240492	+	0.970651i	$0.422691\pi$
$882$	0	0
$883$	9515.97	0.362670	0.181335	−	0.983421i	$-0.441958\pi$
$883$	9515.97	0.362670	0.181335	+	0.983421i	$0.441958\pi$
$884$	11981.2	0.455850
$885$	23885.9	0.907251
$886$	23156.9	0.878072
$887$	−39081.9	−1.47942	−0.739709	−	0.672927i	$-0.765037\pi$
$887$	−39081.9	−1.47942	−0.739709	+	0.672927i	$0.765037\pi$
$888$	4422.34	0.167122
$889$	0	0
$890$	10209.6	0.384525
$891$	−40584.3	−1.52596
$892$	3788.00	0.142188
$893$	14220.0	0.532873
$894$	−21199.6	−0.793089
$895$	32126.0	1.19984
$896$	0	0
$897$	−30227.6	−1.12516
$898$	18953.9	0.704343
$899$	41707.2	1.54729
$900$	−268.911	−0.00995968
$901$	−5311.41	−0.196392
$902$	25142.1	0.928095
$903$	0	0
$904$	39459.3	1.45177
$905$	15475.4	0.568419
$906$	3223.54	0.118206
$907$	−2308.99	−0.0845302	−0.0422651	−	0.999106i	$-0.513457\pi$
$907$	−2308.99	−0.0845302	−0.0422651	+	0.999106i	$0.513457\pi$
$908$	1017.96	0.0372050
$909$	−32.3619	−0.00118083
$910$	0	0
$911$	37073.5	1.34830	0.674149	−	0.738595i	$-0.264510\pi$
$911$	37073.5	1.34830	0.674149	+	0.738595i	$0.264510\pi$
$912$	10356.6	0.376030
$913$	−15594.3	−0.565274
$914$	26254.2	0.950121
$915$	−1984.92	−0.0717152
$916$	3918.13	0.141330
$917$	0	0
$918$	−39750.9	−1.42917
$919$	−37505.4	−1.34623	−0.673116	−	0.739537i	$-0.735045\pi$
$919$	−37505.4	−1.34623	−0.673116	+	0.739537i	$0.735045\pi$
$920$	39758.4	1.42478
$921$	−45723.6	−1.63588
$922$	22787.8	0.813964
$923$	38774.3	1.38274
$924$	0	0
$925$	3472.42	0.123430
$926$	−19327.3	−0.685889
$927$	−791.389	−0.0280395
$928$	−20658.5	−0.730764
$929$	−32371.9	−1.14326	−0.571629	−	0.820512i	$-0.693688\pi$
$929$	−32371.9	−1.14326	−0.571629	+	0.820512i	$0.693688\pi$
$930$	33998.4	1.19876
$931$	0	0
$932$	8097.34	0.284589
$933$	−40311.0	−1.41449
$934$	−7499.62	−0.262736
$935$	94616.3	3.30940
$936$	1757.65	0.0613788
$937$	52319.0	1.82411	0.912053	−	0.410073i	$-0.134497\pi$
$937$	52319.0	1.82411	0.912053	+	0.410073i	$0.134497\pi$
$938$	0	0
$939$	54968.3	1.91035
$940$	−9530.93	−0.330707
$941$	−20705.0	−0.717285	−0.358642	−	0.933475i	$-0.616760\pi$
$941$	−20705.0	−0.717285	−0.358642	+	0.933475i	$0.616760\pi$
$942$	−32615.5	−1.12810
$943$	20702.0	0.714900
$944$	13350.7	0.460304
$945$	0	0
$946$	−40139.1	−1.37953
$947$	3779.25	0.129682	0.0648411	−	0.997896i	$-0.479346\pi$
$947$	3779.25	0.129682	0.0648411	+	0.997896i	$0.479346\pi$
$948$	−1671.29	−0.0572584
$949$	4728.70	0.161749
$950$	10924.1	0.373080
$951$	37119.0	1.26569
$952$	0	0
$953$	−25922.9	−0.881140	−0.440570	−	0.897718i	$-0.645224\pi$
$953$	−25922.9	−0.881140	−0.440570	+	0.897718i	$0.645224\pi$
$954$	−151.205	−0.00513150
$955$	72062.4	2.44177
$956$	10399.3	0.351817
$957$	68680.7	2.31989
$958$	27546.3	0.929000
$959$	0	0
$960$	−45669.2	−1.53538
$961$	−273.585	−0.00918348
$962$	−4404.32	−0.147610
$963$	−1171.05	−0.0391865
$964$	8630.80	0.288360
$965$	−64114.6	−2.13878
$966$	0	0
$967$	4427.11	0.147225	0.0736124	−	0.997287i	$-0.476547\pi$
$967$	4427.11	0.147225	0.0736124	+	0.997287i	$0.476547\pi$
$968$	36473.4	1.21105
$969$	27261.9	0.903795
$970$	18769.8	0.621301
$971$	−40981.9	−1.35445	−0.677226	−	0.735775i	$-0.736818\pi$
$971$	−40981.9	−1.35445	−0.677226	+	0.735775i	$0.736818\pi$
$972$	736.875	0.0243161
$973$	0	0
$974$	44207.3	1.45431
$975$	28686.1	0.942245
$976$	−1109.44	−0.0363855
$977$	57928.7	1.89693	0.948466	−	0.316878i	$-0.102635\pi$
$977$	57928.7	1.89693	0.948466	+	0.316878i	$0.102635\pi$
$978$	8250.58	0.269759
$979$	14596.7	0.476519
$980$	0	0
$981$	436.053	0.0141917
$982$	−21198.8	−0.688882
$983$	−44969.5	−1.45911	−0.729554	−	0.683923i	$-0.760272\pi$
$983$	−44969.5	−1.45911	−0.729554	+	0.683923i	$0.760272\pi$
$984$	−25020.8	−0.810603
$985$	−39506.5	−1.27795
$986$	70679.1	2.28284
$987$	0	0
$988$	4394.27	0.141498
$989$	−33050.5	−1.06263
$990$	2693.53	0.0864709
$991$	27688.2	0.887533	0.443766	−	0.896142i	$-0.353642\pi$
$991$	27688.2	0.887533	0.443766	+	0.896142i	$0.353642\pi$
$992$	−14620.6	−0.467950
$993$	8399.96	0.268444
$994$	0	0
$995$	17501.2	0.557615
$996$	3011.54	0.0958075
$997$	−50718.6	−1.61111	−0.805553	−	0.592523i	$-0.798132\pi$
$997$	−50718.6	−1.61111	−0.805553	+	0.592523i	$0.798132\pi$
$998$	6686.68	0.212087
$999$	−4634.23	−0.146767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.11		39
7.6	odd	2		2401.4.a.d.1.11		39
49.6	odd	14		49.4.e.a.36.10	yes	78
49.41	odd	14		49.4.e.a.15.10	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.10	✓	78	49.41	odd	14
49.4.e.a.36.10	yes	78	49.6	odd	14
2401.4.a.c.1.11		39	1.1	even	1	trivial
2401.4.a.d.1.11		39	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46450 q^{2} +5.32585 q^{3} -1.92624 q^{4} -15.0765 q^{5} -13.1256 q^{6} +24.4632 q^{8} +1.36464 q^{9} +O(q^{10})\)	\(q-2.46450 q^{2} +5.32585 q^{3} -1.92624 q^{4} -15.0765 q^{5} -13.1256 q^{6} +24.4632 q^{8} +1.36464 q^{9} +37.1561 q^{10} +53.1220 q^{11} -10.2588 q^{12} +52.6503 q^{13} -80.2952 q^{15} -44.8797 q^{16} -118.138 q^{17} -3.36315 q^{18} -43.3288 q^{19} +29.0409 q^{20} -130.919 q^{22} -107.799 q^{23} +130.287 q^{24} +102.301 q^{25} -129.757 q^{26} -136.530 q^{27} +242.757 q^{29} +197.888 q^{30} +171.806 q^{31} -85.0996 q^{32} +282.920 q^{33} +291.152 q^{34} -2.62862 q^{36} +33.9430 q^{37} +106.784 q^{38} +280.407 q^{39} -368.820 q^{40} -192.043 q^{41} +306.594 q^{43} -102.326 q^{44} -20.5740 q^{45} +265.670 q^{46} -328.190 q^{47} -239.023 q^{48} -252.122 q^{50} -629.186 q^{51} -101.417 q^{52} +44.9593 q^{53} +336.478 q^{54} -800.895 q^{55} -230.762 q^{57} -598.275 q^{58} -297.476 q^{59} +154.668 q^{60} +24.7203 q^{61} -423.417 q^{62} +568.766 q^{64} -793.783 q^{65} -697.256 q^{66} +269.322 q^{67} +227.562 q^{68} -574.120 q^{69} +736.450 q^{71} +33.3835 q^{72} +89.8135 q^{73} -83.6525 q^{74} +544.842 q^{75} +83.4614 q^{76} -691.064 q^{78} +162.912 q^{79} +676.630 q^{80} -763.983 q^{81} +473.290 q^{82} -293.556 q^{83} +1781.11 q^{85} -755.601 q^{86} +1292.89 q^{87} +1299.54 q^{88} +274.777 q^{89} +50.7047 q^{90} +207.646 q^{92} +915.014 q^{93} +808.823 q^{94} +653.247 q^{95} -453.227 q^{96} +505.160 q^{97} +72.4924 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

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