LMFDB - Embedded newform 2401.4.a.d.1.2

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:	$0$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-5.47147 q^{2} -8.31145 q^{3} +21.9370 q^{4} -5.94042 q^{5} +45.4758 q^{6} -76.2558 q^{8} +42.0802 q^{9} +O(q^{10})$	\(q-5.47147 q^{2} -8.31145 q^{3} +21.9370 q^{4} -5.94042 q^{5} +45.4758 q^{6} -76.2558 q^{8} +42.0802 q^{9} +32.5028 q^{10} -31.3620 q^{11} -182.328 q^{12} -17.0041 q^{13} +49.3735 q^{15} +241.736 q^{16} +55.8707 q^{17} -230.240 q^{18} -16.2635 q^{19} -130.315 q^{20} +171.596 q^{22} +83.9619 q^{23} +633.796 q^{24} -89.7115 q^{25} +93.0377 q^{26} -125.338 q^{27} -100.389 q^{29} -270.145 q^{30} -153.655 q^{31} -712.602 q^{32} +260.664 q^{33} -305.695 q^{34} +923.112 q^{36} -98.3114 q^{37} +88.9854 q^{38} +141.329 q^{39} +452.991 q^{40} +330.022 q^{41} -340.833 q^{43} -687.988 q^{44} -249.974 q^{45} -459.395 q^{46} +79.8981 q^{47} -2009.17 q^{48} +490.854 q^{50} -464.367 q^{51} -373.020 q^{52} +56.1969 q^{53} +685.783 q^{54} +186.303 q^{55} +135.173 q^{57} +549.278 q^{58} -196.150 q^{59} +1083.10 q^{60} +555.209 q^{61} +840.719 q^{62} +1965.10 q^{64} +101.012 q^{65} -1426.21 q^{66} -379.405 q^{67} +1225.64 q^{68} -697.845 q^{69} +1049.60 q^{71} -3208.86 q^{72} -1202.26 q^{73} +537.908 q^{74} +745.632 q^{75} -356.773 q^{76} -773.278 q^{78} +937.794 q^{79} -1436.01 q^{80} -94.4241 q^{81} -1805.71 q^{82} +598.368 q^{83} -331.895 q^{85} +1864.86 q^{86} +834.382 q^{87} +2391.54 q^{88} +988.706 q^{89} +1367.72 q^{90} +1841.87 q^{92} +1277.10 q^{93} -437.160 q^{94} +96.6121 q^{95} +5922.76 q^{96} -890.642 q^{97} -1319.72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.47147	−1.93446	−0.967228	−	0.253908i	$-0.918284\pi$
$2$	−5.47147	−1.93446	−0.967228	+	0.253908i	$0.918284\pi$
$3$	−8.31145	−1.59954	−0.799769	−	0.600307i	$-0.795045\pi$
$3$	−8.31145	−1.59954	−0.799769	+	0.600307i	$0.795045\pi$
$4$	21.9370	2.74212
$5$	−5.94042	−0.531327	−0.265663	−	0.964066i	$-0.585591\pi$
$5$	−5.94042	−0.531327	−0.265663	+	0.964066i	$0.585591\pi$
$6$	45.4758	3.09424
$7$	0	0
$7$	0	0
$8$	−76.2558	−3.37006
$9$	42.0802	1.55852
$10$	32.5028	1.02783
$11$	−31.3620	−0.859637	−0.429818	−	0.902915i	$-0.641422\pi$
$11$	−31.3620	−0.859637	−0.429818	+	0.902915i	$0.641422\pi$
$12$	−182.328	−4.38613
$13$	−17.0041	−0.362777	−0.181388	−	0.983412i	$-0.558059\pi$
$13$	−17.0041	−0.362777	−0.181388	+	0.983412i	$0.558059\pi$
$14$	0	0
$15$	49.3735	0.849878
$16$	241.736	3.77712
$17$	55.8707	0.797096	0.398548	−	0.917147i	$-0.369514\pi$
$17$	55.8707	0.797096	0.398548	+	0.917147i	$0.369514\pi$
$18$	−230.240	−3.01490
$19$	−16.2635	−0.196374	−0.0981871	−	0.995168i	$-0.531304\pi$
$19$	−16.2635	−0.196374	−0.0981871	+	0.995168i	$0.531304\pi$
$20$	−130.315	−1.45696
$21$	0	0
$22$	171.596	1.66293
$23$	83.9619	0.761186	0.380593	−	0.924743i	$-0.375720\pi$
$23$	83.9619	0.761186	0.380593	+	0.924743i	$0.375720\pi$
$24$	633.796	5.39055
$25$	−89.7115	−0.717692
$26$	93.0377	0.701776
$27$	−125.338	−0.893382
$28$	0	0
$29$	−100.389	−0.642823	−0.321411	−	0.946940i	$-0.604157\pi$
$29$	−100.389	−0.642823	−0.321411	+	0.946940i	$0.604157\pi$
$30$	−270.145	−1.64405
$31$	−153.655	−0.890234	−0.445117	−	0.895472i	$-0.646838\pi$
$31$	−153.655	−0.890234	−0.445117	+	0.895472i	$0.646838\pi$
$32$	−712.602	−3.93661
$33$	260.664	1.37502
$34$	−305.695	−1.54195
$35$	0	0
$36$	923.112	4.27367
$37$	−98.3114	−0.436819	−0.218409	−	0.975857i	$-0.570087\pi$
$37$	−98.3114	−0.436819	−0.218409	+	0.975857i	$0.570087\pi$
$38$	88.9854	0.379877
$39$	141.329	0.580276
$40$	452.991	1.79061
$41$	330.022	1.25709	0.628547	−	0.777772i	$-0.283650\pi$
$41$	330.022	1.25709	0.628547	+	0.777772i	$0.283650\pi$
$42$	0	0
$43$	−340.833	−1.20876	−0.604378	−	0.796698i	$-0.706578\pi$
$43$	−340.833	−1.20876	−0.604378	+	0.796698i	$0.706578\pi$
$44$	−687.988	−2.35723
$45$	−249.974	−0.828086
$46$	−459.395	−1.47248
$47$	79.8981	0.247965	0.123982	−	0.992284i	$-0.460433\pi$
$47$	79.8981	0.247965	0.123982	+	0.992284i	$0.460433\pi$
$48$	−2009.17	−6.04165
$49$	0	0
$50$	490.854	1.38834
$51$	−464.367	−1.27499
$52$	−373.020	−0.994779
$53$	56.1969	0.145646	0.0728230	−	0.997345i	$-0.476799\pi$
$53$	56.1969	0.145646	0.0728230	+	0.997345i	$0.476799\pi$
$54$	685.783	1.72821
$55$	186.303	0.456748
$56$	0	0
$57$	135.173	0.314108
$58$	549.278	1.24351
$59$	−196.150	−0.432822	−0.216411	−	0.976302i	$-0.569435\pi$
$59$	−196.150	−0.432822	−0.216411	+	0.976302i	$0.569435\pi$
$60$	1083.10	2.33047
$61$	555.209	1.16536	0.582682	−	0.812700i	$-0.302003\pi$
$61$	555.209	1.16536	0.582682	+	0.812700i	$0.302003\pi$
$62$	840.719	1.72212
$63$	0	0
$64$	1965.10	3.83808
$65$	101.012	0.192753
$66$	−1426.21	−2.65992
$67$	−379.405	−0.691817	−0.345909	−	0.938268i	$-0.612429\pi$
$67$	−379.405	−0.691817	−0.345909	+	0.938268i	$0.612429\pi$
$68$	1225.64	2.18574
$69$	−697.845	−1.21755
$70$	0	0
$71$	1049.60	1.75443	0.877215	−	0.480097i	$-0.159398\pi$
$71$	1049.60	1.75443	0.877215	+	0.480097i	$0.159398\pi$
$72$	−3208.86	−5.25233
$73$	−1202.26	−1.92758	−0.963791	−	0.266658i	$-0.914081\pi$
$73$	−1202.26	−1.92758	−0.963791	+	0.266658i	$0.914081\pi$
$74$	537.908	0.845007
$75$	745.632	1.14798
$76$	−356.773	−0.538482
$77$	0	0
$78$	−773.278	−1.12252
$79$	937.794	1.33557	0.667785	−	0.744354i	$-0.267242\pi$
$79$	937.794	1.33557	0.667785	+	0.744354i	$0.267242\pi$
$80$	−1436.01	−2.00688
$81$	−94.4241	−0.129525
$82$	−1805.71	−2.43179
$83$	598.368	0.791318	0.395659	−	0.918397i	$-0.370516\pi$
$83$	598.368	0.791318	0.395659	+	0.918397i	$0.370516\pi$
$84$	0	0
$85$	−331.895	−0.423519
$86$	1864.86	2.33829
$87$	834.382	1.02822
$88$	2391.54	2.89703
$89$	988.706	1.17756	0.588779	−	0.808294i	$-0.299609\pi$
$89$	988.706	1.17756	0.588779	+	0.808294i	$0.299609\pi$
$90$	1367.72	1.60190
$91$	0	0
$92$	1841.87	2.08727
$93$	1277.10	1.42396
$94$	−437.160	−0.479677
$95$	96.6121	0.104339
$96$	5922.76	6.29676
$97$	−890.642	−0.932279	−0.466139	−	0.884711i	$-0.654355\pi$
$97$	−890.642	−0.932279	−0.466139	+	0.884711i	$0.654355\pi$
$98$	0	0
$99$	−1319.72	−1.33977
$100$	−1968.00	−1.96800
$101$	1603.04	1.57929	0.789647	−	0.613562i	$-0.210264\pi$
$101$	1603.04	1.57929	0.789647	+	0.613562i	$0.210264\pi$
$102$	2540.77	2.46641
$103$	594.523	0.568738	0.284369	−	0.958715i	$-0.408216\pi$
$103$	594.523	0.568738	0.284369	+	0.958715i	$0.408216\pi$
$104$	1296.66	1.22258
$105$	0	0
$106$	−307.480	−0.281746
$107$	−896.895	−0.810337	−0.405169	−	0.914242i	$-0.632787\pi$
$107$	−896.895	−0.810337	−0.405169	+	0.914242i	$0.632787\pi$
$108$	−2749.54	−2.44976
$109$	−769.690	−0.676357	−0.338179	−	0.941082i	$-0.609811\pi$
$109$	−769.690	−0.676357	−0.338179	+	0.941082i	$0.609811\pi$
$110$	−1019.35	−0.883560
$111$	817.110	0.698709
$112$	0	0
$113$	−927.016	−0.771737	−0.385869	−	0.922554i	$-0.626098\pi$
$113$	−927.016	−0.771737	−0.385869	+	0.922554i	$0.626098\pi$
$114$	−739.597	−0.607628
$115$	−498.769	−0.404438
$116$	−2202.24	−1.76270
$117$	−715.537	−0.565397
$118$	1073.23	0.837275
$119$	0	0
$120$	−3765.01	−2.86414
$121$	−347.423	−0.261024
$122$	−3037.81	−2.25435
$123$	−2742.96	−2.01077
$124$	−3370.73	−2.44113
$125$	1275.48	0.912656
$126$	0	0
$127$	1705.02	1.19131	0.595653	−	0.803242i	$-0.296893\pi$
$127$	1705.02	1.19131	0.595653	+	0.803242i	$0.296893\pi$
$128$	−5051.16	−3.48800
$129$	2832.81	1.93345
$130$	−552.682	−0.372873
$131$	999.018	0.666295	0.333147	−	0.942875i	$-0.391889\pi$
$131$	999.018	0.666295	0.333147	+	0.942875i	$0.391889\pi$
$132$	5718.18	3.77048
$133$	0	0
$134$	2075.91	1.33829
$135$	744.560	0.474678
$136$	−4260.47	−2.68627
$137$	−1162.27	−0.724813	−0.362407	−	0.932020i	$-0.618045\pi$
$137$	−1162.27	−0.724813	−0.362407	+	0.932020i	$0.618045\pi$
$138$	3818.24	2.35529
$139$	−514.875	−0.314181	−0.157090	−	0.987584i	$-0.550211\pi$
$139$	−514.875	−0.314181	−0.157090	+	0.987584i	$0.550211\pi$
$140$	0	0
$141$	−664.069	−0.396629
$142$	−5742.86	−3.39387
$143$	533.284	0.311857
$144$	10172.3	5.88673
$145$	596.355	0.341549
$146$	6578.11	3.72883
$147$	0	0
$148$	−2156.66	−1.19781
$149$	−3532.50	−1.94224	−0.971120	−	0.238592i	$-0.923314\pi$
$149$	−3532.50	−1.94224	−0.971120	+	0.238592i	$0.923314\pi$
$150$	−4079.70	−2.22071
$151$	−1363.65	−0.734914	−0.367457	−	0.930040i	$-0.619772\pi$
$151$	−1363.65	−0.734914	−0.367457	+	0.930040i	$0.619772\pi$
$152$	1240.19	0.661793
$153$	2351.05	1.24229
$154$	0	0
$155$	912.775	0.473005
$156$	3100.33	1.59119
$157$	−715.357	−0.363642	−0.181821	−	0.983332i	$-0.558199\pi$
$157$	−715.357	−0.363642	−0.181821	+	0.983332i	$0.558199\pi$
$158$	−5131.11	−2.58360
$159$	−467.078	−0.232967
$160$	4233.15	2.09163
$161$	0	0
$162$	516.639	0.250561
$163$	−568.767	−0.273308	−0.136654	−	0.990619i	$-0.543635\pi$
$163$	−568.767	−0.273308	−0.136654	+	0.990619i	$0.543635\pi$
$164$	7239.70	3.44711
$165$	−1548.45	−0.730587
$166$	−3273.95	−1.53077
$167$	−3050.15	−1.41334	−0.706671	−	0.707543i	$-0.749804\pi$
$167$	−3050.15	−1.41334	−0.706671	+	0.707543i	$0.749804\pi$
$168$	0	0
$169$	−1907.86	−0.868393
$170$	1815.95	0.819279
$171$	−684.372	−0.306054
$172$	−7476.84	−3.31456
$173$	−209.546	−0.0920894	−0.0460447	−	0.998939i	$-0.514662\pi$
$173$	−209.546	−0.0920894	−0.0460447	+	0.998939i	$0.514662\pi$
$174$	−4565.29	−1.98905
$175$	0	0
$176$	−7581.32	−3.24695
$177$	1630.29	0.692316
$178$	−5409.67	−2.27793
$179$	−407.642	−0.170215	−0.0851077	−	0.996372i	$-0.527123\pi$
$179$	−407.642	−0.170215	−0.0851077	+	0.996372i	$0.527123\pi$
$180$	−5483.67	−2.27071
$181$	−2336.27	−0.959411	−0.479706	−	0.877429i	$-0.659257\pi$
$181$	−2336.27	−0.959411	−0.479706	+	0.877429i	$0.659257\pi$
$182$	0	0
$183$	−4614.59	−1.86405
$184$	−6402.59	−2.56524
$185$	584.011	0.232094
$186$	−6987.59	−2.75460
$187$	−1752.22	−0.685214
$188$	1752.72	0.679950
$189$	0	0
$190$	−528.610	−0.201839
$191$	351.022	0.132979	0.0664896	−	0.997787i	$-0.478820\pi$
$191$	351.022	0.132979	0.0664896	+	0.997787i	$0.478820\pi$
$192$	−16332.8	−6.13916
$193$	−3855.48	−1.43795	−0.718974	−	0.695037i	$-0.755388\pi$
$193$	−3855.48	−1.43795	−0.718974	+	0.695037i	$0.755388\pi$
$194$	4873.12	1.80345
$195$	−839.553	−0.308316
$196$	0	0
$197$	−1929.74	−0.697909	−0.348954	−	0.937140i	$-0.613463\pi$
$197$	−1929.74	−0.697909	−0.348954	+	0.937140i	$0.613463\pi$
$198$	7220.80	2.59172
$199$	−2013.21	−0.717148	−0.358574	−	0.933501i	$-0.616737\pi$
$199$	−2013.21	−0.717148	−0.358574	+	0.933501i	$0.616737\pi$
$200$	6841.02	2.41867
$201$	3153.41	1.10659
$202$	−8771.00	−3.05507
$203$	0	0
$204$	−10186.8	−3.49617
$205$	−1960.47	−0.667928
$206$	−3252.91	−1.10020
$207$	3533.13	1.18633
$208$	−4110.51	−1.37025
$209$	510.057	0.168810
$210$	0	0
$211$	2854.21	0.931242	0.465621	−	0.884984i	$-0.345831\pi$
$211$	2854.21	0.931242	0.465621	+	0.884984i	$0.345831\pi$
$212$	1232.79	0.399379
$213$	−8723.70	−2.80628
$214$	4907.33	1.56756
$215$	2024.69	0.642244
$216$	9557.75	3.01075
$217$	0	0
$218$	4211.34	1.30838
$219$	9992.50	3.08324
$220$	4086.94	1.25246
$221$	−950.034	−0.289168
$222$	−4470.80	−1.35162
$223$	2319.01	0.696379	0.348190	−	0.937424i	$-0.386797\pi$
$223$	2319.01	0.696379	0.348190	+	0.937424i	$0.386797\pi$
$224$	0	0
$225$	−3775.07	−1.11854
$226$	5072.14	1.49289
$227$	−2196.59	−0.642260	−0.321130	−	0.947035i	$-0.604063\pi$
$227$	−2196.59	−0.642260	−0.321130	+	0.947035i	$0.604063\pi$
$228$	2965.30	0.861323
$229$	−755.333	−0.217964	−0.108982	−	0.994044i	$-0.534759\pi$
$229$	−755.333	−0.217964	−0.108982	+	0.994044i	$0.534759\pi$
$230$	2729.00	0.782369
$231$	0	0
$232$	7655.28	2.16635
$233$	−1779.03	−0.500206	−0.250103	−	0.968219i	$-0.580465\pi$
$233$	−1779.03	−0.500206	−0.250103	+	0.968219i	$0.580465\pi$
$234$	3915.04	1.09374
$235$	−474.628	−0.131750
$236$	−4302.93	−1.18685
$237$	−7794.43	−2.13630
$238$	0	0
$239$	−1788.86	−0.484148	−0.242074	−	0.970258i	$-0.577828\pi$
$239$	−1788.86	−0.484148	−0.242074	+	0.970258i	$0.577828\pi$
$240$	11935.3	3.21009
$241$	7019.47	1.87620	0.938099	−	0.346366i	$-0.112585\pi$
$241$	7019.47	1.87620	0.938099	+	0.346366i	$0.112585\pi$
$242$	1900.92	0.504940
$243$	4168.93	1.10056
$244$	12179.6	3.19557
$245$	0	0
$246$	15008.0	3.88975
$247$	276.547	0.0712400
$248$	11717.1	3.00015
$249$	−4973.30	−1.26574
$250$	−6978.73	−1.76549
$251$	−1234.68	−0.310488	−0.155244	−	0.987876i	$-0.549616\pi$
$251$	−1234.68	−0.310488	−0.155244	+	0.987876i	$0.549616\pi$
$252$	0	0
$253$	−2633.22	−0.654343
$254$	−9328.95	−2.30453
$255$	2758.53	0.677435
$256$	11916.5	2.90930
$257$	5898.84	1.43175	0.715875	−	0.698229i	$-0.246028\pi$
$257$	5898.84	1.43175	0.715875	+	0.698229i	$0.246028\pi$
$258$	−15499.7	−3.74018
$259$	0	0
$260$	2215.89	0.528553
$261$	−4224.41	−1.00185
$262$	−5466.10	−1.28892
$263$	−1493.78	−0.350230	−0.175115	−	0.984548i	$-0.556030\pi$
$263$	−1493.78	−0.350230	−0.175115	+	0.984548i	$0.556030\pi$
$264$	−19877.1	−4.63391
$265$	−333.833	−0.0773857
$266$	0	0
$267$	−8217.58	−1.88355
$268$	−8323.01	−1.89705
$269$	−1800.43	−0.408082	−0.204041	−	0.978962i	$-0.565408\pi$
$269$	−1800.43	−0.408082	−0.204041	+	0.978962i	$0.565408\pi$
$270$	−4073.84	−0.918244
$271$	−4285.36	−0.960579	−0.480289	−	0.877110i	$-0.659468\pi$
$271$	−4285.36	−0.960579	−0.480289	+	0.877110i	$0.659468\pi$
$272$	13505.9	3.01073
$273$	0	0
$274$	6359.32	1.40212
$275$	2813.53	0.616954
$276$	−15308.6	−3.33866
$277$	−7496.93	−1.62616	−0.813081	−	0.582151i	$-0.802211\pi$
$277$	−7496.93	−1.62616	−0.813081	+	0.582151i	$0.802211\pi$
$278$	2817.12	0.607769
$279$	−6465.83	−1.38745
$280$	0	0
$281$	4336.93	0.920710	0.460355	−	0.887735i	$-0.347722\pi$
$281$	4336.93	0.920710	0.460355	+	0.887735i	$0.347722\pi$
$282$	3633.43	0.767262
$283$	5677.47	1.19255	0.596273	−	0.802782i	$-0.296647\pi$
$283$	5677.47	1.19255	0.596273	+	0.802782i	$0.296647\pi$
$284$	23025.1	4.81087
$285$	−802.986	−0.166894
$286$	−2917.85	−0.603273
$287$	0	0
$288$	−29986.4	−6.13530
$289$	−1791.46	−0.364637
$290$	−3262.94	−0.660712
$291$	7402.53	1.49122
$292$	−26373.9	−5.28567
$293$	−9139.86	−1.82238	−0.911189	−	0.411989i	$-0.864834\pi$
$293$	−9139.86	−1.82238	−0.911189	+	0.411989i	$0.864834\pi$
$294$	0	0
$295$	1165.21	0.229970
$296$	7496.82	1.47211
$297$	3930.85	0.767984
$298$	19328.0	3.75718
$299$	−1427.70	−0.276141
$300$	16356.9	3.14789
$301$	0	0
$302$	7461.16	1.42166
$303$	−13323.6	−2.52614
$304$	−3931.47	−0.741728
$305$	−3298.17	−0.619189
$306$	−12863.7	−2.40316
$307$	−7230.81	−1.34425	−0.672124	−	0.740439i	$-0.734618\pi$
$307$	−7230.81	−1.34425	−0.672124	+	0.740439i	$0.734618\pi$
$308$	0	0
$309$	−4941.34	−0.909719
$310$	−4994.22	−0.915009
$311$	−6610.68	−1.20533	−0.602665	−	0.797995i	$-0.705894\pi$
$311$	−6610.68	−1.20533	−0.602665	+	0.797995i	$0.705894\pi$
$312$	−10777.2	−1.95557
$313$	−1840.05	−0.332288	−0.166144	−	0.986102i	$-0.553132\pi$
$313$	−1840.05	−0.332288	−0.166144	+	0.986102i	$0.553132\pi$
$314$	3914.06	0.703449
$315$	0	0
$316$	20572.4	3.66230
$317$	−396.617	−0.0702720	−0.0351360	−	0.999383i	$-0.511186\pi$
$317$	−396.617	−0.0702720	−0.0351360	+	0.999383i	$0.511186\pi$
$318$	2555.60	0.450664
$319$	3148.42	0.552594
$320$	−11673.5	−2.03928
$321$	7454.50	1.29617
$322$	0	0
$323$	−908.655	−0.156529
$324$	−2071.38	−0.355175
$325$	1525.47	0.260362
$326$	3111.99	0.528703
$327$	6397.24	1.08186
$328$	−25166.1	−4.23648
$329$	0	0
$330$	8472.31	1.41329
$331$	−3629.46	−0.602698	−0.301349	−	0.953514i	$-0.597437\pi$
$331$	−3629.46	−0.602698	−0.301349	+	0.953514i	$0.597437\pi$
$332$	13126.4	2.16989
$333$	−4136.96	−0.680793
$334$	16688.8	2.73405
$335$	2253.83	0.367581
$336$	0	0
$337$	5660.54	0.914984	0.457492	−	0.889214i	$-0.348748\pi$
$337$	5660.54	0.914984	0.457492	+	0.889214i	$0.348748\pi$
$338$	10438.8	1.67987
$339$	7704.84	1.23442
$340$	−7280.78	−1.16134
$341$	4818.93	0.765278
$342$	3744.52	0.592048
$343$	0	0
$344$	25990.5	4.07358
$345$	4145.49	0.646915
$346$	1146.52	0.178143
$347$	−7216.34	−1.11641	−0.558204	−	0.829704i	$-0.688509\pi$
$347$	−7216.34	−1.11641	−0.558204	+	0.829704i	$0.688509\pi$
$348$	18303.8	2.81951
$349$	−4188.40	−0.642407	−0.321203	−	0.947010i	$-0.604087\pi$
$349$	−4188.40	−0.642407	−0.321203	+	0.947010i	$0.604087\pi$
$350$	0	0
$351$	2131.27	0.324098
$352$	22348.7	3.38405
$353$	−4390.31	−0.661962	−0.330981	−	0.943637i	$-0.607380\pi$
$353$	−4390.31	−0.661962	−0.330981	+	0.943637i	$0.607380\pi$
$354$	−8920.07	−1.33925
$355$	−6235.06	−0.932176
$356$	21689.2	3.22901
$357$	0	0
$358$	2230.40	0.329275
$359$	−4323.72	−0.635646	−0.317823	−	0.948150i	$-0.602952\pi$
$359$	−4323.72	−0.635646	−0.317823	+	0.948150i	$0.602952\pi$
$360$	19061.9	2.79070
$361$	−6594.50	−0.961437
$362$	12782.8	1.85594
$363$	2887.59	0.417519
$364$	0	0
$365$	7141.90	1.02418
$366$	25248.6	3.60592
$367$	−392.234	−0.0557887	−0.0278943	−	0.999611i	$-0.508880\pi$
$367$	−392.234	−0.0557887	−0.0278943	+	0.999611i	$0.508880\pi$
$368$	20296.6	2.87509
$369$	13887.4	1.95921
$370$	−3195.40	−0.448975
$371$	0	0
$372$	28015.6	3.90469
$373$	9325.44	1.29451	0.647256	−	0.762273i	$-0.275917\pi$
$373$	9325.44	1.29451	0.647256	+	0.762273i	$0.275917\pi$
$374$	9587.21	1.32552
$375$	−10601.0	−1.45983
$376$	−6092.70	−0.835656
$377$	1707.04	0.233201
$378$	0	0
$379$	−3958.07	−0.536445	−0.268222	−	0.963357i	$-0.586436\pi$
$379$	−3958.07	−0.536445	−0.268222	+	0.963357i	$0.586436\pi$
$380$	2119.38	0.286110
$381$	−14171.2	−1.90554
$382$	−1920.60	−0.257243
$383$	−6961.61	−0.928778	−0.464389	−	0.885631i	$-0.653726\pi$
$383$	−6961.61	−0.928778	−0.464389	+	0.885631i	$0.653726\pi$
$384$	41982.4	5.57919
$385$	0	0
$386$	21095.2	2.78165
$387$	−14342.3	−1.88388
$388$	−19538.0	−2.55642
$389$	2562.10	0.333942	0.166971	−	0.985962i	$-0.446601\pi$
$389$	2562.10	0.333942	0.166971	+	0.985962i	$0.446601\pi$
$390$	4593.59	0.596424
$391$	4691.01	0.606738
$392$	0	0
$393$	−8303.28	−1.06576
$394$	10558.5	1.35007
$395$	−5570.89	−0.709625
$396$	−28950.7	−3.67380
$397$	−1905.59	−0.240903	−0.120452	−	0.992719i	$-0.538434\pi$
$397$	−1905.59	−0.240903	−0.120452	+	0.992719i	$0.538434\pi$
$398$	11015.2	1.38729
$399$	0	0
$400$	−21686.5	−2.71081
$401$	2882.06	0.358911	0.179456	−	0.983766i	$-0.442566\pi$
$401$	2882.06	0.358911	0.179456	+	0.983766i	$0.442566\pi$
$402$	−17253.8	−2.14065
$403$	2612.77	0.322957
$404$	35165.9	4.33062
$405$	560.918	0.0688204
$406$	0	0
$407$	3083.25	0.375506
$408$	35410.7	4.29679
$409$	12270.4	1.48345	0.741726	−	0.670703i	$-0.234007\pi$
$409$	12270.4	1.48345	0.741726	+	0.670703i	$0.234007\pi$
$410$	10726.7	1.29208
$411$	9660.14	1.15937
$412$	13042.0	1.55955
$413$	0	0
$414$	−19331.4	−2.29490
$415$	−3554.55	−0.420449
$416$	12117.2	1.42811
$417$	4279.36	0.502544
$418$	−2790.76	−0.326557
$419$	12244.4	1.42763	0.713817	−	0.700333i	$-0.246965\pi$
$419$	12244.4	1.42763	0.713817	+	0.700333i	$0.246965\pi$
$420$	0	0
$421$	−8011.38	−0.927436	−0.463718	−	0.885983i	$-0.653485\pi$
$421$	−8011.38	−0.927436	−0.463718	+	0.885983i	$0.653485\pi$
$422$	−15616.7	−1.80145
$423$	3362.13	0.386459
$424$	−4285.34	−0.490836
$425$	−5012.24	−0.572069
$426$	47731.4	5.42863
$427$	0	0
$428$	−19675.2	−2.22205
$429$	−4432.37	−0.498827
$430$	−11078.0	−1.24239
$431$	2972.81	0.332239	0.166120	−	0.986106i	$-0.446876\pi$
$431$	2972.81	0.332239	0.166120	+	0.986106i	$0.446876\pi$
$432$	−30298.7	−3.37441
$433$	13572.8	1.50639	0.753194	−	0.657799i	$-0.228512\pi$
$433$	13572.8	1.50639	0.753194	+	0.657799i	$0.228512\pi$
$434$	0	0
$435$	−4956.57	−0.546321
$436$	−16884.7	−1.85465
$437$	−1365.52	−0.149477
$438$	−54673.6	−5.96440
$439$	−1950.61	−0.212067	−0.106033	−	0.994363i	$-0.533815\pi$
$439$	−1950.61	−0.212067	−0.106033	+	0.994363i	$0.533815\pi$
$440$	−14206.7	−1.53927
$441$	0	0
$442$	5198.08	0.559383
$443$	−881.162	−0.0945040	−0.0472520	−	0.998883i	$-0.515046\pi$
$443$	−881.162	−0.0945040	−0.0472520	+	0.998883i	$0.515046\pi$
$444$	17924.9	1.91595
$445$	−5873.32	−0.625668
$446$	−12688.4	−1.34712
$447$	29360.2	3.10669
$448$	0	0
$449$	7552.21	0.793788	0.396894	−	0.917864i	$-0.370088\pi$
$449$	7552.21	0.793788	0.396894	+	0.917864i	$0.370088\pi$
$450$	20655.2	2.16377
$451$	−10350.2	−1.08064
$452$	−20335.9	−2.11620
$453$	11333.9	1.17552
$454$	12018.6	1.24242
$455$	0	0
$456$	−10307.8	−1.05856
$457$	−8349.10	−0.854605	−0.427303	−	0.904109i	$-0.640536\pi$
$457$	−8349.10	−0.854605	−0.427303	+	0.904109i	$0.640536\pi$
$458$	4132.78	0.421643
$459$	−7002.72	−0.712112
$460$	−10941.5	−1.10902
$461$	−15061.3	−1.52163	−0.760816	−	0.648968i	$-0.775201\pi$
$461$	−15061.3	−1.52163	−0.760816	+	0.648968i	$0.775201\pi$
$462$	0	0
$463$	−1425.28	−0.143063	−0.0715316	−	0.997438i	$-0.522789\pi$
$463$	−1425.28	−0.143063	−0.0715316	+	0.997438i	$0.522789\pi$
$464$	−24267.7	−2.42802
$465$	−7586.48	−0.756591
$466$	9733.91	0.967628
$467$	−5825.91	−0.577282	−0.288641	−	0.957437i	$-0.593203\pi$
$467$	−5825.91	−0.577282	−0.288641	+	0.957437i	$0.593203\pi$
$468$	−15696.7	−1.55039
$469$	0	0
$470$	2596.91	0.254865
$471$	5945.66	0.581659
$472$	14957.5	1.45864
$473$	10689.2	1.03909
$474$	42647.0	4.13257
$475$	1459.02	0.140936
$476$	0	0
$477$	2364.78	0.226993
$478$	9787.67	0.936564
$479$	15712.4	1.49878	0.749391	−	0.662128i	$-0.230346\pi$
$479$	15712.4	1.49878	0.749391	+	0.662128i	$0.230346\pi$
$480$	−35183.6	−3.34564
$481$	1671.70	0.158468
$482$	−38406.8	−3.62943
$483$	0	0
$484$	−7621.42	−0.715761
$485$	5290.79	0.495345
$486$	−22810.2	−2.12899
$487$	9379.06	0.872702	0.436351	−	0.899776i	$-0.356271\pi$
$487$	9379.06	0.872702	0.436351	+	0.899776i	$0.356271\pi$
$488$	−42337.9	−3.92735
$489$	4727.27	0.437167
$490$	0	0
$491$	−11122.3	−1.02228	−0.511142	−	0.859496i	$-0.670778\pi$
$491$	−11122.3	−1.02228	−0.511142	+	0.859496i	$0.670778\pi$
$492$	−60172.4	−5.51378
$493$	−5608.83	−0.512392
$494$	−1513.12	−0.137811
$495$	7839.68	0.711853
$496$	−37143.9	−3.36252
$497$	0	0
$498$	27211.3	2.44853
$499$	7625.34	0.684082	0.342041	−	0.939685i	$-0.388882\pi$
$499$	7625.34	0.684082	0.342041	+	0.939685i	$0.388882\pi$
$500$	27980.1	2.50261
$501$	25351.2	2.26069
$502$	6755.53	0.600625
$503$	−4142.41	−0.367199	−0.183600	−	0.983001i	$-0.558775\pi$
$503$	−4142.41	−0.367199	−0.183600	+	0.983001i	$0.558775\pi$
$504$	0	0
$505$	−9522.73	−0.839121
$506$	14407.6	1.26580
$507$	15857.1	1.38903
$508$	37402.9	3.26671
$509$	7993.20	0.696056	0.348028	−	0.937484i	$-0.386851\pi$
$509$	7993.20	0.696056	0.348028	+	0.937484i	$0.386851\pi$
$510$	−15093.2	−1.31047
$511$	0	0
$512$	−24791.4	−2.13991
$513$	2038.44	0.175437
$514$	−32275.3	−2.76966
$515$	−3531.71	−0.302186
$516$	62143.4	5.30176
$517$	−2505.77	−0.213160
$518$	0	0
$519$	1741.63	0.147301
$520$	−7702.73	−0.649590
$521$	6911.38	0.581176	0.290588	−	0.956848i	$-0.406149\pi$
$521$	6911.38	0.581176	0.290588	+	0.956848i	$0.406149\pi$
$522$	23113.7	1.93804
$523$	−996.464	−0.0833123	−0.0416561	−	0.999132i	$-0.513263\pi$
$523$	−996.464	−0.0833123	−0.0416561	+	0.999132i	$0.513263\pi$
$524$	21915.4	1.82706
$525$	0	0
$526$	8173.19	0.677506
$527$	−8584.82	−0.709603
$528$	63011.7	5.19362
$529$	−5117.39	−0.420596
$530$	1826.56	0.149699
$531$	−8254.01	−0.674564
$532$	0	0
$533$	−5611.75	−0.456045
$534$	44962.2	3.64364
$535$	5327.93	0.430554
$536$	28931.9	2.33147
$537$	3388.09	0.272266
$538$	9851.00	0.789418
$539$	0	0
$540$	16333.4	1.30163
$541$	18728.1	1.48833	0.744164	−	0.667997i	$-0.232848\pi$
$541$	18728.1	1.48833	0.744164	+	0.667997i	$0.232848\pi$
$542$	23447.2	1.85820
$543$	19417.8	1.53462
$544$	−39813.6	−3.13786
$545$	4572.28	0.359367
$546$	0	0
$547$	−4275.09	−0.334168	−0.167084	−	0.985943i	$-0.553435\pi$
$547$	−4275.09	−0.334168	−0.167084	+	0.985943i	$0.553435\pi$
$548$	−25496.7	−1.98753
$549$	23363.3	1.81625
$550$	−15394.2	−1.19347
$551$	1632.69	0.126234
$552$	53214.8	4.10321
$553$	0	0
$554$	41019.2	3.14574
$555$	−4853.97	−0.371243
$556$	−11294.8	−0.861522
$557$	−7727.55	−0.587840	−0.293920	−	0.955830i	$-0.594960\pi$
$557$	−7727.55	−0.587840	−0.293920	+	0.955830i	$0.594960\pi$
$558$	35377.6	2.68397
$559$	5795.57	0.438509
$560$	0	0
$561$	14563.5	1.09603
$562$	−23729.4	−1.78107
$563$	26041.0	1.94938	0.974688	−	0.223568i	$-0.0717705\pi$
$563$	26041.0	1.94938	0.974688	+	0.223568i	$0.0717705\pi$
$564$	−14567.7	−1.08761
$565$	5506.86	0.410045
$566$	−31064.1	−2.30693
$567$	0	0
$568$	−80038.1	−5.91254
$569$	−8405.33	−0.619279	−0.309640	−	0.950854i	$-0.600208\pi$
$569$	−8405.33	−0.619279	−0.309640	+	0.950854i	$0.600208\pi$
$570$	4393.52	0.322849
$571$	21210.5	1.55452	0.777259	−	0.629181i	$-0.216609\pi$
$571$	21210.5	1.55452	0.777259	+	0.629181i	$0.216609\pi$
$572$	11698.7	0.855149
$573$	−2917.50	−0.212705
$574$	0	0
$575$	−7532.35	−0.546297
$576$	82691.7	5.98175
$577$	−8728.47	−0.629759	−0.314879	−	0.949132i	$-0.601964\pi$
$577$	−8728.47	−0.629759	−0.314879	+	0.949132i	$0.601964\pi$
$578$	9801.94	0.705375
$579$	32044.7	2.30005
$580$	13082.2	0.936569
$581$	0	0
$582$	−40502.7	−2.88469
$583$	−1762.45	−0.125203
$584$	91679.1	6.49607
$585$	4250.59	0.300411
$586$	50008.5	3.52531
$587$	−8173.80	−0.574734	−0.287367	−	0.957821i	$-0.592780\pi$
$587$	−8173.80	−0.574734	−0.287367	+	0.957821i	$0.592780\pi$
$588$	0	0
$589$	2498.97	0.174819
$590$	−6375.41	−0.444867
$591$	16038.9	1.11633
$592$	−23765.4	−1.64992
$593$	22537.1	1.56069	0.780344	−	0.625350i	$-0.215044\pi$
$593$	22537.1	1.56069	0.780344	+	0.625350i	$0.215044\pi$
$594$	−21507.6	−1.48563
$595$	0	0
$596$	−77492.4	−5.32586
$597$	16732.7	1.14711
$598$	7811.62	0.534182
$599$	2877.18	0.196258	0.0981290	−	0.995174i	$-0.468714\pi$
$599$	2877.18	0.196258	0.0981290	+	0.995174i	$0.468714\pi$
$600$	−56858.8	−3.86875
$601$	−23044.0	−1.56403	−0.782015	−	0.623259i	$-0.785808\pi$
$601$	−23044.0	−1.56403	−0.782015	+	0.623259i	$0.785808\pi$
$602$	0	0
$603$	−15965.4	−1.07821
$604$	−29914.3	−2.01523
$605$	2063.84	0.138689
$606$	72899.7	4.88671
$607$	−10804.4	−0.722464	−0.361232	−	0.932476i	$-0.617644\pi$
$607$	−10804.4	−0.722464	−0.361232	+	0.932476i	$0.617644\pi$
$608$	11589.4	0.773048
$609$	0	0
$610$	18045.9	1.19780
$611$	−1358.60	−0.0899559
$612$	51574.9	3.40652
$613$	4265.22	0.281028	0.140514	−	0.990079i	$-0.455124\pi$
$613$	4265.22	0.281028	0.140514	+	0.990079i	$0.455124\pi$
$614$	39563.2	2.60039
$615$	16294.3	1.06838
$616$	0	0
$617$	3703.83	0.241670	0.120835	−	0.992673i	$-0.461443\pi$
$617$	3703.83	0.241670	0.120835	+	0.992673i	$0.461443\pi$
$618$	27036.4	1.75981
$619$	−12490.2	−0.811020	−0.405510	−	0.914091i	$-0.632906\pi$
$619$	−12490.2	−0.811020	−0.405510	+	0.914091i	$0.632906\pi$
$620$	20023.5	1.29704
$621$	−10523.6	−0.680030
$622$	36170.1	2.33166
$623$	0	0
$624$	34164.3	2.19177
$625$	3637.08	0.232773
$626$	10067.8	0.642796
$627$	−4239.31	−0.270019
$628$	−15692.8	−0.997150
$629$	−5492.73	−0.348187
$630$	0	0
$631$	15181.8	0.957807	0.478904	−	0.877868i	$-0.341034\pi$
$631$	15181.8	0.957807	0.478904	+	0.877868i	$0.341034\pi$
$632$	−71512.3	−4.50096
$633$	−23722.6	−1.48956
$634$	2170.08	0.135938
$635$	−10128.5	−0.632973
$636$	−10246.3	−0.638823
$637$	0	0
$638$	−17226.5	−1.06897
$639$	44167.3	2.73432
$640$	30006.0	1.85327
$641$	192.595	0.0118675	0.00593374	−	0.999982i	$-0.498111\pi$
$641$	192.595	0.0118675	0.00593374	+	0.999982i	$0.498111\pi$
$642$	−40787.1	−2.50738
$643$	3816.68	0.234083	0.117041	−	0.993127i	$-0.462659\pi$
$643$	3816.68	0.234083	0.117041	+	0.993127i	$0.462659\pi$
$644$	0	0
$645$	−16828.1	−1.02729
$646$	4971.68	0.302799
$647$	25724.7	1.56312	0.781562	−	0.623827i	$-0.214423\pi$
$647$	25724.7	1.56312	0.781562	+	0.623827i	$0.214423\pi$
$648$	7200.39	0.436509
$649$	6151.65	0.372070
$650$	−8346.55	−0.503659
$651$	0	0
$652$	−12477.0	−0.749445
$653$	−20684.5	−1.23958	−0.619792	−	0.784766i	$-0.712783\pi$
$653$	−20684.5	−1.23958	−0.619792	+	0.784766i	$0.712783\pi$
$654$	−35002.3	−2.09281
$655$	−5934.58	−0.354020
$656$	79778.1	4.74819
$657$	−50591.2	−3.00418
$658$	0	0
$659$	−32697.6	−1.93280	−0.966402	−	0.257034i	$-0.917255\pi$
$659$	−32697.6	−1.93280	−0.966402	+	0.257034i	$0.917255\pi$
$660$	−33968.4	−2.00336
$661$	−2649.90	−0.155929	−0.0779647	−	0.996956i	$-0.524842\pi$
$661$	−2649.90	−0.155929	−0.0779647	+	0.996956i	$0.524842\pi$
$662$	19858.5	1.16589
$663$	7896.15	0.462536
$664$	−45629.0	−2.66679
$665$	0	0
$666$	22635.3	1.31696
$667$	−8428.89	−0.489307
$668$	−66911.2	−3.87556
$669$	−19274.4	−1.11389
$670$	−12331.7	−0.711070
$671$	−17412.5	−1.00179
$672$	0	0
$673$	24753.8	1.41782	0.708908	−	0.705301i	$-0.249188\pi$
$673$	24753.8	1.41782	0.708908	+	0.705301i	$0.249188\pi$
$674$	−30971.5	−1.77000
$675$	11244.3	0.641173
$676$	−41852.7	−2.38124
$677$	3242.33	0.184066	0.0920332	−	0.995756i	$-0.470663\pi$
$677$	3242.33	0.184066	0.0920332	+	0.995756i	$0.470663\pi$
$678$	−42156.8	−2.38794
$679$	0	0
$680$	25308.9	1.42728
$681$	18256.9	1.02732
$682$	−26366.7	−1.48040
$683$	14539.2	0.814532	0.407266	−	0.913309i	$-0.366482\pi$
$683$	14539.2	0.814532	0.407266	+	0.913309i	$0.366482\pi$
$684$	−15013.1	−0.839238
$685$	6904.36	0.385113
$686$	0	0
$687$	6277.91	0.348642
$688$	−82391.4	−4.56561
$689$	−955.580	−0.0528370
$690$	−22681.9	−1.25143
$691$	25800.1	1.42038	0.710191	−	0.704009i	$-0.248609\pi$
$691$	25800.1	1.42038	0.710191	+	0.704009i	$0.248609\pi$
$692$	−4596.80	−0.252521
$693$	0	0
$694$	39484.0	2.15964
$695$	3058.57	0.166933
$696$	−63626.5	−3.46517
$697$	18438.6	1.00202
$698$	22916.7	1.24271
$699$	14786.3	0.800100
$700$	0	0
$701$	−2115.64	−0.113990	−0.0569948	−	0.998374i	$-0.518152\pi$
$701$	−2115.64	−0.113990	−0.0569948	+	0.998374i	$0.518152\pi$
$702$	−11661.2	−0.626954
$703$	1598.89	0.0857799
$704$	−61629.5	−3.29936
$705$	3944.85	0.210740
$706$	24021.4	1.28054
$707$	0	0
$708$	35763.6	1.89841
$709$	13900.0	0.736282	0.368141	−	0.929770i	$-0.379994\pi$
$709$	13900.0	0.736282	0.368141	+	0.929770i	$0.379994\pi$
$710$	34114.9	1.80325
$711$	39462.5	2.08152
$712$	−75394.6	−3.96844
$713$	−12901.2	−0.677634
$714$	0	0
$715$	−3167.93	−0.165698
$716$	−8942.43	−0.466752
$717$	14868.0	0.774414
$718$	23657.1	1.22963
$719$	2606.78	0.135211	0.0676053	−	0.997712i	$-0.478464\pi$
$719$	2606.78	0.135211	0.0676053	+	0.997712i	$0.478464\pi$
$720$	−60427.5	−3.12778
$721$	0	0
$722$	36081.6	1.85986
$723$	−58342.0	−3.00105
$724$	−51250.7	−2.63082
$725$	9006.09	0.461348
$726$	−15799.4	−0.807672
$727$	−6258.07	−0.319256	−0.159628	−	0.987177i	$-0.551029\pi$
$727$	−6258.07	−0.319256	−0.159628	+	0.987177i	$0.551029\pi$
$728$	0	0
$729$	−32100.4	−1.63087
$730$	−39076.7	−1.98123
$731$	−19042.6	−0.963495
$732$	−101230.	−5.11144
$733$	−24301.9	−1.22457	−0.612287	−	0.790636i	$-0.709750\pi$
$733$	−24301.9	−1.22457	−0.612287	+	0.790636i	$0.709750\pi$
$734$	2146.10	0.107921
$735$	0	0
$736$	−59831.5	−2.99649
$737$	11898.9	0.594711
$738$	−75984.5	−3.79001
$739$	18601.7	0.925949	0.462974	−	0.886372i	$-0.346782\pi$
$739$	18601.7	0.925949	0.462974	+	0.886372i	$0.346782\pi$
$740$	12811.4	0.636429
$741$	−2298.51	−0.113951
$742$	0	0
$743$	−17243.2	−0.851400	−0.425700	−	0.904864i	$-0.639972\pi$
$743$	−17243.2	−0.851400	−0.425700	+	0.904864i	$0.639972\pi$
$744$	−97386.0	−4.79885
$745$	20984.5	1.03196
$746$	−51023.9	−2.50418
$747$	25179.4	1.23329
$748$	−38438.4	−1.87894
$749$	0	0
$750$	58003.3	2.82398
$751$	34010.8	1.65256	0.826279	−	0.563261i	$-0.190454\pi$
$751$	34010.8	1.65256	0.826279	+	0.563261i	$0.190454\pi$
$752$	19314.2	0.936592
$753$	10262.0	0.496637
$754$	−9340.00	−0.451118
$755$	8100.63	0.390480
$756$	0	0
$757$	−14797.7	−0.710479	−0.355239	−	0.934775i	$-0.615601\pi$
$757$	−14797.7	−0.710479	−0.355239	+	0.934775i	$0.615601\pi$
$758$	21656.5	1.03773
$759$	21885.8	1.04665
$760$	−7367.23	−0.351628
$761$	−2783.77	−0.132604	−0.0663019	−	0.997800i	$-0.521120\pi$
$761$	−2783.77	−0.132604	−0.0663019	+	0.997800i	$0.521120\pi$
$762$	77537.1	3.68618
$763$	0	0
$764$	7700.36	0.364646
$765$	−13966.2	−0.660064
$766$	38090.3	1.79668
$767$	3335.36	0.157018
$768$	−99043.2	−4.65353
$769$	−7457.20	−0.349692	−0.174846	−	0.984596i	$-0.555943\pi$
$769$	−7457.20	−0.349692	−0.174846	+	0.984596i	$0.555943\pi$
$770$	0	0
$771$	−49027.9	−2.29014
$772$	−84577.7	−3.94303
$773$	−37733.9	−1.75575	−0.877875	−	0.478889i	$-0.841040\pi$
$773$	−37733.9	−1.75575	−0.877875	+	0.478889i	$0.841040\pi$
$774$	78473.5	3.64428
$775$	13784.6	0.638914
$776$	67916.7	3.14184
$777$	0	0
$778$	−14018.4	−0.645997
$779$	−5367.33	−0.246861
$780$	−18417.3	−0.845441
$781$	−32917.6	−1.50817
$782$	−25666.7	−1.17371
$783$	12582.6	0.574286
$784$	0	0
$785$	4249.52	0.193213
$786$	45431.2	2.06167
$787$	−28221.0	−1.27823	−0.639116	−	0.769110i	$-0.720700\pi$
$787$	−28221.0	−1.27823	−0.639116	+	0.769110i	$0.720700\pi$
$788$	−42332.6	−1.91375
$789$	12415.5	0.560207
$790$	30480.9	1.37274
$791$	0	0
$792$	100636.	4.51509
$793$	−9440.85	−0.422767
$794$	10426.4	0.466017
$795$	2774.64	0.123781
$796$	−44163.7	−1.96651
$797$	−36891.8	−1.63962	−0.819808	−	0.572639i	$-0.805920\pi$
$797$	−36891.8	−1.63962	−0.819808	+	0.572639i	$0.805920\pi$
$798$	0	0
$799$	4463.96	0.197652
$800$	63928.6	2.82527
$801$	41604.9	1.83525
$802$	−15769.1	−0.694298
$803$	37705.2	1.65702
$804$	69176.3	3.03440
$805$	0	0
$806$	−14295.7	−0.624746
$807$	14964.2	0.652744
$808$	−122241.	−5.32232
$809$	−43891.6	−1.90747	−0.953736	−	0.300645i	$-0.902798\pi$
$809$	−43891.6	−1.90747	−0.953736	+	0.300645i	$0.902798\pi$
$810$	−3069.05	−0.133130
$811$	30637.5	1.32655	0.663274	−	0.748377i	$-0.269167\pi$
$811$	30637.5	1.32655	0.663274	+	0.748377i	$0.269167\pi$
$812$	0	0
$813$	35617.5	1.53648
$814$	−16869.9	−0.726400
$815$	3378.71	0.145216
$816$	−112254.	−4.81578
$817$	5543.14	0.237368
$818$	−67137.1	−2.86967
$819$	0	0
$820$	−43006.8	−1.83154
$821$	−4659.92	−0.198090	−0.0990452	−	0.995083i	$-0.531579\pi$
$821$	−4659.92	−0.198090	−0.0990452	+	0.995083i	$0.531579\pi$
$822$	−52855.2	−2.24275
$823$	−33362.3	−1.41304	−0.706522	−	0.707691i	$-0.749737\pi$
$823$	−33362.3	−1.41304	−0.706522	+	0.707691i	$0.749737\pi$
$824$	−45335.8	−1.91668
$825$	−23384.5	−0.986842
$826$	0	0
$827$	28780.2	1.21014	0.605071	−	0.796172i	$-0.293145\pi$
$827$	28780.2	1.21014	0.605071	+	0.796172i	$0.293145\pi$
$828$	77506.3	3.25305
$829$	6245.58	0.261662	0.130831	−	0.991405i	$-0.458235\pi$
$829$	6245.58	0.261662	0.130831	+	0.991405i	$0.458235\pi$
$830$	19448.6	0.813340
$831$	62310.3	2.60111
$832$	−33414.8	−1.39237
$833$	0	0
$834$	−23414.4	−0.972150
$835$	18119.2	0.750946
$836$	11189.1	0.462899
$837$	19258.8	0.795319
$838$	−66994.9	−2.76169
$839$	30037.0	1.23598	0.617992	−	0.786184i	$-0.287946\pi$
$839$	30037.0	1.23598	0.617992	+	0.786184i	$0.287946\pi$
$840$	0	0
$841$	−14311.0	−0.586779
$842$	43834.0	1.79408
$843$	−36046.2	−1.47271
$844$	62612.8	2.55358
$845$	11333.5	0.461400
$846$	−18395.8	−0.747588
$847$	0	0
$848$	13584.8	0.550122
$849$	−47188.0	−1.90752
$850$	27424.3	1.10664
$851$	−8254.42	−0.332500
$852$	−191372.	−7.69517
$853$	−48986.9	−1.96633	−0.983164	−	0.182725i	$-0.941508\pi$
$853$	−48986.9	−1.96633	−0.983164	+	0.182725i	$0.941508\pi$
$854$	0	0
$855$	4065.45	0.162615
$856$	68393.5	2.73089
$857$	20113.8	0.801722	0.400861	−	0.916139i	$-0.368711\pi$
$857$	20113.8	0.801722	0.400861	+	0.916139i	$0.368711\pi$
$858$	24251.6	0.964959
$859$	9690.60	0.384912	0.192456	−	0.981306i	$-0.438355\pi$
$859$	9690.60	0.384912	0.192456	+	0.981306i	$0.438355\pi$
$860$	44415.6	1.76111
$861$	0	0
$862$	−16265.6	−0.642703
$863$	5575.65	0.219927	0.109964	−	0.993936i	$-0.464927\pi$
$863$	5575.65	0.219927	0.109964	+	0.993936i	$0.464927\pi$
$864$	89316.2	3.51690
$865$	1244.79	0.0489296
$866$	−74263.0	−2.91404
$867$	14889.7	0.583252
$868$	0	0
$869$	−29411.1	−1.14811
$870$	27119.7	1.05683
$871$	6451.46	0.250975
$872$	58693.3	2.27937
$873$	−37478.4	−1.45298
$874$	7471.38	0.289157
$875$	0	0
$876$	219205.	8.45463
$877$	12300.0	0.473593	0.236796	−	0.971559i	$-0.423903\pi$
$877$	12300.0	0.473593	0.236796	+	0.971559i	$0.423903\pi$
$878$	10672.7	0.410234
$879$	75965.5	2.91496
$880$	45036.2	1.72519
$881$	−11529.2	−0.440895	−0.220448	−	0.975399i	$-0.570752\pi$
$881$	−11529.2	−0.440895	−0.220448	+	0.975399i	$0.570752\pi$
$882$	0	0
$883$	37773.8	1.43963	0.719813	−	0.694168i	$-0.244227\pi$
$883$	37773.8	1.43963	0.719813	+	0.694168i	$0.244227\pi$
$884$	−20840.9	−0.792935
$885$	−9684.58	−0.367846
$886$	4821.25	0.182814
$887$	−29725.1	−1.12522	−0.562611	−	0.826722i	$-0.690203\pi$
$887$	−29725.1	−1.12522	−0.562611	+	0.826722i	$0.690203\pi$
$888$	−62309.4	−2.35469
$889$	0	0
$890$	32135.7	1.21033
$891$	2961.33	0.111345
$892$	50872.2	1.90956
$893$	−1299.42	−0.0486938
$894$	−160643.	−6.00975
$895$	2421.56	0.0904401
$896$	0	0
$897$	11866.3	0.441698
$898$	−41321.7	−1.53555
$899$	15425.3	0.572263
$900$	−82813.7	−3.06718
$901$	3139.76	0.116094
$902$	56630.6	2.09046
$903$	0	0
$904$	70690.4	2.60080
$905$	13878.4	0.509761
$906$	−62013.0	−2.27400
$907$	−10993.3	−0.402454	−0.201227	−	0.979545i	$-0.564493\pi$
$907$	−10993.3	−0.402454	−0.201227	+	0.979545i	$0.564493\pi$
$908$	−48186.6	−1.76116
$909$	67456.3	2.46137
$910$	0	0
$911$	−20418.8	−0.742596	−0.371298	−	0.928514i	$-0.621087\pi$
$911$	−20418.8	−0.742596	−0.371298	+	0.928514i	$0.621087\pi$
$912$	32676.2	1.18642
$913$	−18766.0	−0.680246
$914$	45681.9	1.65320
$915$	27412.6	0.990418
$916$	−16569.7	−0.597685
$917$	0	0
$918$	38315.2	1.37755
$919$	18964.4	0.680716	0.340358	−	0.940296i	$-0.389452\pi$
$919$	18964.4	0.680716	0.340358	+	0.940296i	$0.389452\pi$
$920$	38034.0	1.36298
$921$	60098.5	2.15018
$922$	82407.2	2.94353
$923$	−17847.5	−0.636467
$924$	0	0
$925$	8819.66	0.313501
$926$	7798.36	0.276750
$927$	25017.6	0.886393
$928$	71537.8	2.53054
$929$	16012.5	0.565505	0.282753	−	0.959193i	$-0.408752\pi$
$929$	16012.5	0.565505	0.282753	+	0.959193i	$0.408752\pi$
$930$	41509.2	1.46359
$931$	0	0
$932$	−39026.5	−1.37163
$933$	54944.3	1.92797
$934$	31876.3	1.11673
$935$	10408.9	0.364072
$936$	54563.9	1.90542
$937$	35277.0	1.22994	0.614968	−	0.788552i	$-0.289169\pi$
$937$	35277.0	1.22994	0.614968	+	0.788552i	$0.289169\pi$
$938$	0	0
$939$	15293.5	0.531507
$940$	−10411.9	−0.361276
$941$	−9007.59	−0.312050	−0.156025	−	0.987753i	$-0.549868\pi$
$941$	−9007.59	−0.312050	−0.156025	+	0.987753i	$0.549868\pi$
$942$	−32531.5	−1.12519
$943$	27709.3	0.956882
$944$	−47416.3	−1.63482
$945$	0	0
$946$	−58485.7	−2.01008
$947$	1132.23	0.0388517	0.0194258	−	0.999811i	$-0.493816\pi$
$947$	1132.23	0.0388517	0.0194258	+	0.999811i	$0.493816\pi$
$948$	−170986.	−5.85799
$949$	20443.3	0.699283
$950$	−7983.01	−0.272635
$951$	3296.46	0.112403
$952$	0	0
$953$	28711.3	0.975919	0.487960	−	0.872866i	$-0.337741\pi$
$953$	28711.3	0.975919	0.487960	+	0.872866i	$0.337741\pi$
$954$	−12938.8	−0.439108
$955$	−2085.21	−0.0706554
$956$	−39242.1	−1.32759
$957$	−26167.9	−0.883896
$958$	−85969.8	−2.89933
$959$	0	0
$960$	97023.7	3.26190
$961$	−6181.12	−0.207483
$962$	−9146.67	−0.306549
$963$	−37741.5	−1.26293
$964$	153986.	5.14477
$965$	22903.2	0.764020
$966$	0	0
$967$	16889.7	0.561672	0.280836	−	0.959756i	$-0.409388\pi$
$967$	16889.7	0.561672	0.280836	+	0.959756i	$0.409388\pi$
$968$	26493.1	0.879668
$969$	7552.24	0.250374
$970$	−28948.4	−0.958223
$971$	−40282.8	−1.33134	−0.665672	−	0.746244i	$-0.731855\pi$
$971$	−40282.8	−1.33134	−0.665672	+	0.746244i	$0.731855\pi$
$972$	91453.7	3.01788
$973$	0	0
$974$	−51317.3	−1.68820
$975$	−12678.8	−0.416459
$976$	134214.	4.40172
$977$	6838.51	0.223934	0.111967	−	0.993712i	$-0.464285\pi$
$977$	6838.51	0.223934	0.111967	+	0.993712i	$0.464285\pi$
$978$	−25865.1	−0.845681
$979$	−31007.8	−1.01227
$980$	0	0
$981$	−32388.7	−1.05412
$982$	60855.3	1.97757
$983$	59622.8	1.93456	0.967280	−	0.253712i	$-0.0816515\pi$
$983$	59622.8	1.93456	0.967280	+	0.253712i	$0.0816515\pi$
$984$	209167.	6.77642
$985$	11463.4	0.370818
$986$	30688.6	0.991199
$987$	0	0
$988$	6066.61	0.195349
$989$	−28617.0	−0.920088
$990$	−42894.6	−1.37705
$991$	−6381.97	−0.204571	−0.102285	−	0.994755i	$-0.532616\pi$
$991$	−6381.97	−0.204571	−0.102285	+	0.994755i	$0.532616\pi$
$992$	109495.	3.50451
$993$	30166.0	0.964038
$994$	0	0
$995$	11959.3	0.381040
$996$	−109099.	−3.47083
$997$	25158.8	0.799185	0.399592	−	0.916693i	$-0.369152\pi$
$997$	25158.8	0.799185	0.399592	+	0.916693i	$0.369152\pi$
$998$	−41721.8	−1.32333
$999$	12322.2	0.390246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.d.1.2		39
7.6	odd	2		2401.4.a.c.1.2		39
49.8	even	7		49.4.e.a.15.13	✓	78
49.43	even	7		49.4.e.a.36.13	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.13	✓	78	49.8	even	7
49.4.e.a.36.13	yes	78	49.43	even	7
2401.4.a.c.1.2		39	7.6	odd	2
2401.4.a.d.1.2		39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.47147 q^{2} -8.31145 q^{3} +21.9370 q^{4} -5.94042 q^{5} +45.4758 q^{6} -76.2558 q^{8} +42.0802 q^{9} +O(q^{10})\)	\(q-5.47147 q^{2} -8.31145 q^{3} +21.9370 q^{4} -5.94042 q^{5} +45.4758 q^{6} -76.2558 q^{8} +42.0802 q^{9} +32.5028 q^{10} -31.3620 q^{11} -182.328 q^{12} -17.0041 q^{13} +49.3735 q^{15} +241.736 q^{16} +55.8707 q^{17} -230.240 q^{18} -16.2635 q^{19} -130.315 q^{20} +171.596 q^{22} +83.9619 q^{23} +633.796 q^{24} -89.7115 q^{25} +93.0377 q^{26} -125.338 q^{27} -100.389 q^{29} -270.145 q^{30} -153.655 q^{31} -712.602 q^{32} +260.664 q^{33} -305.695 q^{34} +923.112 q^{36} -98.3114 q^{37} +88.9854 q^{38} +141.329 q^{39} +452.991 q^{40} +330.022 q^{41} -340.833 q^{43} -687.988 q^{44} -249.974 q^{45} -459.395 q^{46} +79.8981 q^{47} -2009.17 q^{48} +490.854 q^{50} -464.367 q^{51} -373.020 q^{52} +56.1969 q^{53} +685.783 q^{54} +186.303 q^{55} +135.173 q^{57} +549.278 q^{58} -196.150 q^{59} +1083.10 q^{60} +555.209 q^{61} +840.719 q^{62} +1965.10 q^{64} +101.012 q^{65} -1426.21 q^{66} -379.405 q^{67} +1225.64 q^{68} -697.845 q^{69} +1049.60 q^{71} -3208.86 q^{72} -1202.26 q^{73} +537.908 q^{74} +745.632 q^{75} -356.773 q^{76} -773.278 q^{78} +937.794 q^{79} -1436.01 q^{80} -94.4241 q^{81} -1805.71 q^{82} +598.368 q^{83} -331.895 q^{85} +1864.86 q^{86} +834.382 q^{87} +2391.54 q^{88} +988.706 q^{89} +1367.72 q^{90} +1841.87 q^{92} +1277.10 q^{93} -437.160 q^{94} +96.6121 q^{95} +5922.76 q^{96} -890.642 q^{97} -1319.72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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