LMFDB - Embedded newform 2401.4.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-3.74761 q^{2} -2.12177 q^{3} +6.04460 q^{4} -10.5286 q^{5} +7.95158 q^{6} +7.32810 q^{8} -22.4981 q^{9} +O(q^{10})$	\(q-3.74761 q^{2} -2.12177 q^{3} +6.04460 q^{4} -10.5286 q^{5} +7.95158 q^{6} +7.32810 q^{8} -22.4981 q^{9} +39.4572 q^{10} -24.8183 q^{11} -12.8253 q^{12} -69.8668 q^{13} +22.3393 q^{15} -75.8196 q^{16} +75.4735 q^{17} +84.3141 q^{18} -127.523 q^{19} -63.6412 q^{20} +93.0093 q^{22} -24.6521 q^{23} -15.5486 q^{24} -14.1483 q^{25} +261.834 q^{26} +105.024 q^{27} +160.417 q^{29} -83.7191 q^{30} +43.6957 q^{31} +225.518 q^{32} +52.6588 q^{33} -282.845 q^{34} -135.992 q^{36} +201.423 q^{37} +477.905 q^{38} +148.241 q^{39} -77.1547 q^{40} +169.269 q^{41} -393.700 q^{43} -150.017 q^{44} +236.874 q^{45} +92.3865 q^{46} -241.776 q^{47} +160.872 q^{48} +53.0225 q^{50} -160.138 q^{51} -422.316 q^{52} +418.806 q^{53} -393.588 q^{54} +261.302 q^{55} +270.574 q^{57} -601.182 q^{58} -149.042 q^{59} +135.032 q^{60} +182.185 q^{61} -163.755 q^{62} -238.596 q^{64} +735.600 q^{65} -197.345 q^{66} -968.160 q^{67} +456.207 q^{68} +52.3061 q^{69} -364.523 q^{71} -164.868 q^{72} +490.670 q^{73} -754.856 q^{74} +30.0196 q^{75} -770.822 q^{76} -555.551 q^{78} +1160.20 q^{79} +798.275 q^{80} +384.612 q^{81} -634.355 q^{82} -493.308 q^{83} -794.631 q^{85} +1475.43 q^{86} -340.369 q^{87} -181.871 q^{88} -858.289 q^{89} -887.710 q^{90} -149.012 q^{92} -92.7124 q^{93} +906.081 q^{94} +1342.64 q^{95} -478.497 q^{96} +552.977 q^{97} +558.364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.74761	−1.32498	−0.662490	−	0.749070i	$-0.730500\pi$
$2$	−3.74761	−1.32498	−0.662490	+	0.749070i	$0.730500\pi$
$3$	−2.12177	−0.408335	−0.204168	−	0.978936i	$-0.565449\pi$
$3$	−2.12177	−0.408335	−0.204168	+	0.978936i	$0.565449\pi$
$4$	6.04460	0.755574
$5$	−10.5286	−0.941708	−0.470854	−	0.882211i	$-0.656054\pi$
$5$	−10.5286	−0.941708	−0.470854	+	0.882211i	$0.656054\pi$
$6$	7.95158	0.541037
$7$	0	0
$7$	0	0
$8$	7.32810	0.323859
$9$	−22.4981	−0.833262
$10$	39.4572	1.24774
$11$	−24.8183	−0.680272	−0.340136	−	0.940376i	$-0.610473\pi$
$11$	−24.8183	−0.680272	−0.340136	+	0.940376i	$0.610473\pi$
$12$	−12.8253	−0.308528
$13$	−69.8668	−1.49058	−0.745291	−	0.666740i	$-0.767689\pi$
$13$	−69.8668	−1.49058	−0.745291	+	0.666740i	$0.767689\pi$
$14$	0	0
$15$	22.3393	0.384533
$16$	−75.8196	−1.18468
$17$	75.4735	1.07676	0.538382	−	0.842701i	$-0.319036\pi$
$17$	75.4735	1.07676	0.538382	+	0.842701i	$0.319036\pi$
$18$	84.3141	1.10406
$19$	−127.523	−1.53977	−0.769886	−	0.638181i	$-0.779687\pi$
$19$	−127.523	−1.53977	−0.769886	+	0.638181i	$0.779687\pi$
$20$	−63.6412	−0.711530
$21$	0	0
$22$	93.0093	0.901348
$23$	−24.6521	−0.223492	−0.111746	−	0.993737i	$-0.535644\pi$
$23$	−24.6521	−0.223492	−0.111746	+	0.993737i	$0.535644\pi$
$24$	−15.5486	−0.132243
$25$	−14.1483	−0.113187
$26$	261.834	1.97499
$27$	105.024	0.748586
$28$	0	0
$29$	160.417	1.02720	0.513599	−	0.858030i	$-0.328312\pi$
$29$	160.417	1.02720	0.513599	+	0.858030i	$0.328312\pi$
$30$	−83.7191	−0.509498
$31$	43.6957	0.253161	0.126580	−	0.991956i	$-0.459600\pi$
$31$	43.6957	0.253161	0.126580	+	0.991956i	$0.459600\pi$
$32$	225.518	1.24582
$33$	52.6588	0.277779
$34$	−282.845	−1.42669
$35$	0	0
$36$	−135.992	−0.629592
$37$	201.423	0.894967	0.447483	−	0.894292i	$-0.352320\pi$
$37$	201.423	0.894967	0.447483	+	0.894292i	$0.352320\pi$
$38$	477.905	2.04017
$39$	148.241	0.608657
$40$	−77.1547	−0.304981
$41$	169.269	0.644766	0.322383	−	0.946609i	$-0.395516\pi$
$41$	169.269	0.644766	0.322383	+	0.946609i	$0.395516\pi$
$42$	0	0
$43$	−393.700	−1.39625	−0.698124	−	0.715977i	$-0.745982\pi$
$43$	−393.700	−1.39625	−0.698124	+	0.715977i	$0.745982\pi$
$44$	−150.017	−0.513996
$45$	236.874	0.784689
$46$	92.3865	0.296123
$47$	−241.776	−0.750353	−0.375176	−	0.926953i	$-0.622418\pi$
$47$	−241.776	−0.750353	−0.375176	+	0.926953i	$0.622418\pi$
$48$	160.872	0.483747
$49$	0	0
$50$	53.0225	0.149970
$51$	−160.138	−0.439681
$52$	−422.316	−1.12625
$53$	418.806	1.08542	0.542712	−	0.839919i	$-0.317398\pi$
$53$	418.806	1.08542	0.542712	+	0.839919i	$0.317398\pi$
$54$	−393.588	−0.991862
$55$	261.302	0.640618
$56$	0	0
$57$	270.574	0.628744
$58$	−601.182	−1.36102
$59$	−149.042	−0.328876	−0.164438	−	0.986387i	$-0.552581\pi$
$59$	−149.042	−0.328876	−0.164438	+	0.986387i	$0.552581\pi$
$60$	135.032	0.290543
$61$	182.185	0.382400	0.191200	−	0.981551i	$-0.438762\pi$
$61$	182.185	0.382400	0.191200	+	0.981551i	$0.438762\pi$
$62$	−163.755	−0.335433
$63$	0	0
$64$	−238.596	−0.466008
$65$	735.600	1.40369
$66$	−197.345	−0.368052
$67$	−968.160	−1.76537	−0.882683	−	0.469968i	$-0.844265\pi$
$67$	−968.160	−1.76537	−0.882683	+	0.469968i	$0.844265\pi$
$68$	456.207	0.813576
$69$	52.3061	0.0912597
$70$	0	0
$71$	−364.523	−0.609309	−0.304655	−	0.952463i	$-0.598541\pi$
$71$	−364.523	−0.609309	−0.304655	+	0.952463i	$0.598541\pi$
$72$	−164.868	−0.269860
$73$	490.670	0.786692	0.393346	−	0.919390i	$-0.371317\pi$
$73$	490.670	0.786692	0.393346	+	0.919390i	$0.371317\pi$
$74$	−754.856	−1.18581
$75$	30.0196	0.0462181
$76$	−770.822	−1.16341
$77$	0	0
$78$	−555.551	−0.806459
$79$	1160.20	1.65232	0.826158	−	0.563439i	$-0.190522\pi$
$79$	1160.20	1.65232	0.826158	+	0.563439i	$0.190522\pi$
$80$	798.275	1.11562
$81$	384.612	0.527588
$82$	−634.355	−0.854303
$83$	−493.308	−0.652381	−0.326190	−	0.945304i	$-0.605765\pi$
$83$	−493.308	−0.652381	−0.326190	+	0.945304i	$0.605765\pi$
$84$	0	0
$85$	−794.631	−1.01400
$86$	1475.43	1.85000
$87$	−340.369	−0.419441
$88$	−181.871	−0.220312
$89$	−858.289	−1.02223	−0.511115	−	0.859512i	$-0.670767\pi$
$89$	−858.289	−1.02223	−0.511115	+	0.859512i	$0.670767\pi$
$90$	−887.710	−1.03970
$91$	0	0
$92$	−149.012	−0.168865
$93$	−92.7124	−0.103375
$94$	906.081	0.994203
$95$	1342.64	1.45002
$96$	−478.497	−0.508713
$97$	552.977	0.578828	0.289414	−	0.957204i	$-0.406540\pi$
$97$	552.977	0.578828	0.289414	+	0.957204i	$0.406540\pi$
$98$	0	0
$99$	558.364	0.566845
$100$	−85.5210	−0.0855210
$101$	705.841	0.695385	0.347692	−	0.937609i	$-0.386965\pi$
$101$	705.841	0.695385	0.347692	+	0.937609i	$0.386965\pi$
$102$	600.133	0.582569
$103$	−1345.93	−1.28755	−0.643777	−	0.765214i	$-0.722633\pi$
$103$	−1345.93	−1.28755	−0.643777	+	0.765214i	$0.722633\pi$
$104$	−511.990	−0.482738
$105$	0	0
$106$	−1569.52	−1.43816
$107$	1798.34	1.62479	0.812395	−	0.583107i	$-0.198163\pi$
$107$	1798.34	1.62479	0.812395	+	0.583107i	$0.198163\pi$
$108$	634.826	0.565612
$109$	1832.52	1.61031	0.805153	−	0.593067i	$-0.202083\pi$
$109$	1832.52	1.61031	0.805153	+	0.593067i	$0.202083\pi$
$110$	−979.259	−0.848806
$111$	−427.374	−0.365447
$112$	0	0
$113$	908.265	0.756127	0.378064	−	0.925780i	$-0.376590\pi$
$113$	908.265	0.756127	0.378064	+	0.925780i	$0.376590\pi$
$114$	−1014.01	−0.833073
$115$	259.552	0.210464
$116$	969.658	0.776125
$117$	1571.87	1.24204
$118$	558.553	0.435754
$119$	0	0
$120$	163.705	0.124534
$121$	−715.053	−0.537230
$122$	−682.760	−0.506673
$123$	−359.151	−0.263281
$124$	264.123	0.191282
$125$	1465.04	1.04830
$126$	0	0
$127$	−72.5998	−0.0507259	−0.0253629	−	0.999678i	$-0.508074\pi$
$127$	−72.5998	−0.0507259	−0.0253629	+	0.999678i	$0.508074\pi$
$128$	−909.977	−0.628370
$129$	835.342	0.570138
$130$	−2756.74	−1.85986
$131$	−533.858	−0.356057	−0.178028	−	0.984025i	$-0.556972\pi$
$131$	−533.858	−0.356057	−0.178028	+	0.984025i	$0.556972\pi$
$132$	318.301	0.209883
$133$	0	0
$134$	3628.29	2.33908
$135$	−1105.75	−0.704949
$136$	553.077	0.348720
$137$	1295.40	0.807834	0.403917	−	0.914796i	$-0.367648\pi$
$137$	1295.40	0.807834	0.403917	+	0.914796i	$0.367648\pi$
$138$	−196.023	−0.120917
$139$	531.648	0.324416	0.162208	−	0.986757i	$-0.448138\pi$
$139$	531.648	0.324416	0.162208	+	0.986757i	$0.448138\pi$
$140$	0	0
$141$	512.993	0.306396
$142$	1366.09	0.807323
$143$	1733.97	1.01400
$144$	1705.80	0.987150
$145$	−1688.97	−0.967320
$146$	−1838.84	−1.04235
$147$	0	0
$148$	1217.52	0.676214
$149$	−523.443	−0.287799	−0.143900	−	0.989592i	$-0.545964\pi$
$149$	−523.443	−0.287799	−0.143900	+	0.989592i	$0.545964\pi$
$150$	−112.502	−0.0612382
$151$	2182.48	1.17621	0.588105	−	0.808785i	$-0.299874\pi$
$151$	2182.48	1.17621	0.588105	+	0.808785i	$0.299874\pi$
$152$	−934.498	−0.498669
$153$	−1698.01	−0.897227
$154$	0	0
$155$	−460.055	−0.238403
$156$	896.059	0.459886
$157$	1869.64	0.950405	0.475203	−	0.879876i	$-0.342375\pi$
$157$	1869.64	0.950405	0.475203	+	0.879876i	$0.342375\pi$
$158$	−4347.99	−2.18929
$159$	−888.611	−0.443217
$160$	−2374.39	−1.17320
$161$	0	0
$162$	−1441.38	−0.699044
$163$	189.761	0.0911856	0.0455928	−	0.998960i	$-0.485482\pi$
$163$	189.761	0.0911856	0.0455928	+	0.998960i	$0.485482\pi$
$164$	1023.16	0.487169
$165$	−554.424	−0.261587
$166$	1848.73	0.864392
$167$	−1865.13	−0.864242	−0.432121	−	0.901816i	$-0.642235\pi$
$167$	−1865.13	−0.864242	−0.432121	+	0.901816i	$0.642235\pi$
$168$	0	0
$169$	2684.37	1.22183
$170$	2977.97	1.34353
$171$	2869.01	1.28303
$172$	−2379.76	−1.05497
$173$	3805.80	1.67254	0.836270	−	0.548318i	$-0.184732\pi$
$173$	3805.80	1.67254	0.836270	+	0.548318i	$0.184732\pi$
$174$	1275.57	0.555752
$175$	0	0
$176$	1881.71	0.805906
$177$	316.234	0.134292
$178$	3216.54	1.35444
$179$	−3577.56	−1.49385	−0.746927	−	0.664906i	$-0.768471\pi$
$179$	−3577.56	−1.49385	−0.746927	+	0.664906i	$0.768471\pi$
$180$	1431.80	0.592891
$181$	−450.904	−0.185168	−0.0925841	−	0.995705i	$-0.529513\pi$
$181$	−450.904	−0.185168	−0.0925841	+	0.995705i	$0.529513\pi$
$182$	0	0
$183$	−386.556	−0.156148
$184$	−180.653	−0.0723799
$185$	−2120.71	−0.842797
$186$	347.450	0.136969
$187$	−1873.12	−0.732493
$188$	−1461.44	−0.566947
$189$	0	0
$190$	−5031.68	−1.92124
$191$	373.838	0.141623	0.0708114	−	0.997490i	$-0.477441\pi$
$191$	373.838	0.141623	0.0708114	+	0.997490i	$0.477441\pi$
$192$	506.247	0.190288
$193$	842.713	0.314299	0.157150	−	0.987575i	$-0.449769\pi$
$193$	842.713	0.314299	0.157150	+	0.987575i	$0.449769\pi$
$194$	−2072.34	−0.766936
$195$	−1560.78	−0.573177
$196$	0	0
$197$	4816.08	1.74178	0.870892	−	0.491475i	$-0.163542\pi$
$197$	4816.08	1.74178	0.870892	+	0.491475i	$0.163542\pi$
$198$	−2092.53	−0.751059
$199$	−259.694	−0.0925086	−0.0462543	−	0.998930i	$-0.514728\pi$
$199$	−259.694	−0.0925086	−0.0462543	+	0.998930i	$0.514728\pi$
$200$	−103.680	−0.0366566
$201$	2054.22	0.720862
$202$	−2645.22	−0.921371
$203$	0	0
$204$	−967.967	−0.332212
$205$	−1782.17	−0.607181
$206$	5044.01	1.70598
$207$	554.625	0.186227
$208$	5297.27	1.76586
$209$	3164.89	1.04746
$210$	0	0
$211$	351.257	0.114604	0.0573022	−	0.998357i	$-0.481750\pi$
$211$	351.257	0.114604	0.0573022	+	0.998357i	$0.481750\pi$
$212$	2531.51	0.820118
$213$	773.436	0.248803
$214$	−6739.50	−2.15282
$215$	4145.11	1.31486
$216$	769.624	0.242436
$217$	0	0
$218$	−6867.57	−2.13363
$219$	−1041.09	−0.321234
$220$	1579.47	0.484034
$221$	−5273.09	−1.60501
$222$	1601.63	0.484210
$223$	−6224.05	−1.86903	−0.934514	−	0.355928i	$-0.884165\pi$
$223$	−6224.05	−1.86903	−0.934514	+	0.355928i	$0.884165\pi$
$224$	0	0
$225$	318.311	0.0943142
$226$	−3403.82	−1.00185
$227$	87.6518	0.0256284	0.0128142	−	0.999918i	$-0.495921\pi$
$227$	87.6518	0.0256284	0.0128142	+	0.999918i	$0.495921\pi$
$228$	1635.51	0.475063
$229$	6023.73	1.73825	0.869125	−	0.494593i	$-0.164683\pi$
$229$	6023.73	1.73825	0.869125	+	0.494593i	$0.164683\pi$
$230$	−972.701	−0.278861
$231$	0	0
$232$	1175.55	0.332667
$233$	−4796.72	−1.34868	−0.674342	−	0.738419i	$-0.735573\pi$
$233$	−4796.72	−1.34868	−0.674342	+	0.738419i	$0.735573\pi$
$234$	−5890.75	−1.64569
$235$	2545.56	0.706613
$236$	−900.901	−0.248490
$237$	−2461.68	−0.674699
$238$	0	0
$239$	989.486	0.267801	0.133901	−	0.990995i	$-0.457250\pi$
$239$	989.486	0.267801	0.133901	+	0.990995i	$0.457250\pi$
$240$	−1693.76	−0.455549
$241$	7182.71	1.91983	0.959915	−	0.280293i	$-0.0904315\pi$
$241$	7182.71	1.91983	0.959915	+	0.280293i	$0.0904315\pi$
$242$	2679.74	0.711819
$243$	−3651.70	−0.964019
$244$	1101.24	0.288932
$245$	0	0
$246$	1345.96	0.348842
$247$	8909.59	2.29516
$248$	320.207	0.0819885
$249$	1046.69	0.266390
$250$	−5490.40	−1.38897
$251$	3471.69	0.873033	0.436516	−	0.899696i	$-0.356212\pi$
$251$	3471.69	0.873033	0.436516	+	0.899696i	$0.356212\pi$
$252$	0	0
$253$	611.823	0.152035
$254$	272.076	0.0672108
$255$	1686.03	0.414051
$256$	5319.01	1.29859
$257$	−6365.67	−1.54506	−0.772528	−	0.634981i	$-0.781008\pi$
$257$	−6365.67	−1.54506	−0.772528	+	0.634981i	$0.781008\pi$
$258$	−3130.54	−0.755421
$259$	0	0
$260$	4446.40	1.06059
$261$	−3609.08	−0.855925
$262$	2000.69	0.471768
$263$	−3175.14	−0.744439	−0.372219	−	0.928145i	$-0.621403\pi$
$263$	−3175.14	−0.744439	−0.372219	+	0.928145i	$0.621403\pi$
$264$	385.889	0.0899614
$265$	−4409.45	−1.02215
$266$	0	0
$267$	1821.10	0.417413
$268$	−5852.14	−1.33387
$269$	−4415.89	−1.00090	−0.500449	−	0.865766i	$-0.666832\pi$
$269$	−4415.89	−1.00090	−0.500449	+	0.865766i	$0.666832\pi$
$270$	4143.94	0.934044
$271$	3046.33	0.682846	0.341423	−	0.939910i	$-0.389091\pi$
$271$	3046.33	0.682846	0.341423	+	0.939910i	$0.389091\pi$
$272$	−5722.37	−1.27562
$273$	0	0
$274$	−4854.65	−1.07036
$275$	351.138	0.0769978
$276$	316.169	0.0689535
$277$	4133.65	0.896632	0.448316	−	0.893875i	$-0.352024\pi$
$277$	4133.65	0.896632	0.448316	+	0.893875i	$0.352024\pi$
$278$	−1992.41	−0.429845
$279$	−983.070	−0.210949
$280$	0	0
$281$	278.315	0.0590849	0.0295424	−	0.999564i	$-0.490595\pi$
$281$	278.315	0.0590849	0.0295424	+	0.999564i	$0.490595\pi$
$282$	−1922.50	−0.405968
$283$	4721.42	0.991729	0.495865	−	0.868400i	$-0.334851\pi$
$283$	4721.42	0.991729	0.495865	+	0.868400i	$0.334851\pi$
$284$	−2203.40	−0.460379
$285$	−2848.77	−0.592093
$286$	−6498.26	−1.34353
$287$	0	0
$288$	−5073.72	−1.03810
$289$	783.243	0.159423
$290$	6329.61	1.28168
$291$	−1173.29	−0.236356
$292$	2965.90	0.594405
$293$	−2303.09	−0.459207	−0.229604	−	0.973284i	$-0.573743\pi$
$293$	−2303.09	−0.459207	−0.229604	+	0.973284i	$0.573743\pi$
$294$	0	0
$295$	1569.21	0.309705
$296$	1476.05	0.289843
$297$	−2606.51	−0.509242
$298$	1961.66	0.381329
$299$	1722.36	0.333133
$300$	181.456	0.0349213
$301$	0	0
$302$	−8179.08	−1.55845
$303$	−1497.63	−0.283950
$304$	9668.71	1.82414
$305$	−1918.16	−0.360109
$306$	6363.47	1.18881
$307$	2129.29	0.395847	0.197923	−	0.980217i	$-0.436580\pi$
$307$	2129.29	0.395847	0.197923	+	0.980217i	$0.436580\pi$
$308$	0	0
$309$	2855.75	0.525753
$310$	1724.11	0.315880
$311$	−2685.36	−0.489623	−0.244811	−	0.969571i	$-0.578726\pi$
$311$	−2685.36	−0.489623	−0.244811	+	0.969571i	$0.578726\pi$
$312$	1086.33	0.197119
$313$	−7808.95	−1.41018	−0.705092	−	0.709115i	$-0.749095\pi$
$313$	−7808.95	−1.41018	−0.705092	+	0.709115i	$0.749095\pi$
$314$	−7006.69	−1.25927
$315$	0	0
$316$	7012.95	1.24845
$317$	7865.75	1.39364	0.696821	−	0.717245i	$-0.254597\pi$
$317$	7865.75	1.39364	0.696821	+	0.717245i	$0.254597\pi$
$318$	3330.17	0.587254
$319$	−3981.28	−0.698774
$320$	2512.09	0.438843
$321$	−3815.68	−0.663459
$322$	0	0
$323$	−9624.57	−1.65797
$324$	2324.82	0.398632
$325$	988.499	0.168714
$326$	−711.152	−0.120819
$327$	−3888.19	−0.657545
$328$	1240.42	0.208813
$329$	0	0
$330$	2077.76	0.346598
$331$	4140.80	0.687611	0.343805	−	0.939041i	$-0.388284\pi$
$331$	4140.80	0.687611	0.343805	+	0.939041i	$0.388284\pi$
$332$	−2981.85	−0.492922
$333$	−4531.64	−0.745742
$334$	6989.80	1.14510
$335$	10193.4	1.66246
$336$	0	0
$337$	−7690.88	−1.24317	−0.621586	−	0.783346i	$-0.713511\pi$
$337$	−7690.88	−1.24317	−0.621586	+	0.783346i	$0.713511\pi$
$338$	−10060.0	−1.61890
$339$	−1927.13	−0.308753
$340$	−4803.22	−0.766151
$341$	−1084.45	−0.172218
$342$	−10751.9	−1.70000
$343$	0	0
$344$	−2885.07	−0.452188
$345$	−550.711	−0.0859399
$346$	−14262.6	−2.21608
$347$	−3531.07	−0.546276	−0.273138	−	0.961975i	$-0.588062\pi$
$347$	−3531.07	−0.546276	−0.273138	+	0.961975i	$0.588062\pi$
$348$	−2057.39	−0.316919
$349$	−8587.75	−1.31717	−0.658584	−	0.752507i	$-0.728844\pi$
$349$	−8587.75	−1.31717	−0.658584	+	0.752507i	$0.728844\pi$
$350$	0	0
$351$	−7337.67	−1.11583
$352$	−5596.97	−0.847498
$353$	−4472.60	−0.674369	−0.337184	−	0.941439i	$-0.609475\pi$
$353$	−4472.60	−0.674369	−0.337184	+	0.941439i	$0.609475\pi$
$354$	−1185.12	−0.177934
$355$	3837.92	0.573791
$356$	−5188.01	−0.772371
$357$	0	0
$358$	13407.3	1.97933
$359$	−592.139	−0.0870526	−0.0435263	−	0.999052i	$-0.513859\pi$
$359$	−592.139	−0.0870526	−0.0435263	+	0.999052i	$0.513859\pi$
$360$	1735.83	0.254129
$361$	9403.00	1.37090
$362$	1689.81	0.245344
$363$	1517.18	0.219370
$364$	0	0
$365$	−5166.07	−0.740834
$366$	1448.66	0.206893
$367$	−2510.98	−0.357145	−0.178573	−	0.983927i	$-0.557148\pi$
$367$	−2510.98	−0.357145	−0.178573	+	0.983927i	$0.557148\pi$
$368$	1869.11	0.264767
$369$	−3808.23	−0.537259
$370$	7947.59	1.11669
$371$	0	0
$372$	−560.409	−0.0781071
$373$	3425.10	0.475455	0.237728	−	0.971332i	$-0.423597\pi$
$373$	3425.10	0.475455	0.237728	+	0.971332i	$0.423597\pi$
$374$	7019.73	0.970540
$375$	−3108.48	−0.428057
$376$	−1771.75	−0.243009
$377$	−11207.8	−1.53112
$378$	0	0
$379$	10087.4	1.36716	0.683581	−	0.729875i	$-0.260422\pi$
$379$	10087.4	1.36716	0.683581	+	0.729875i	$0.260422\pi$
$380$	8115.69	1.09559
$381$	154.040	0.0207132
$382$	−1401.00	−0.187647
$383$	10008.6	1.33529	0.667647	−	0.744478i	$-0.267301\pi$
$383$	10008.6	1.33529	0.667647	+	0.744478i	$0.267301\pi$
$384$	1930.76	0.256586
$385$	0	0
$386$	−3158.16	−0.416441
$387$	8857.49	1.16344
$388$	3342.52	0.437347
$389$	621.457	0.0810003	0.0405001	−	0.999180i	$-0.487105\pi$
$389$	621.457	0.0810003	0.0405001	+	0.999180i	$0.487105\pi$
$390$	5849.18	0.759449
$391$	−1860.58	−0.240648
$392$	0	0
$393$	1132.73	0.145391
$394$	−18048.8	−2.30783
$395$	−12215.3	−1.55600
$396$	3375.08	0.428294
$397$	645.634	0.0816208	0.0408104	−	0.999167i	$-0.487006\pi$
$397$	645.634	0.0816208	0.0408104	+	0.999167i	$0.487006\pi$
$398$	973.232	0.122572
$399$	0	0
$400$	1072.72	0.134090
$401$	3757.43	0.467923	0.233962	−	0.972246i	$-0.424831\pi$
$401$	3757.43	0.467923	0.233962	+	0.972246i	$0.424831\pi$
$402$	−7698.40	−0.955128
$403$	−3052.88	−0.377357
$404$	4266.53	0.525415
$405$	−4049.43	−0.496834
$406$	0	0
$407$	−4998.98	−0.608821
$408$	−1173.50	−0.142395
$409$	−5103.22	−0.616963	−0.308482	−	0.951230i	$-0.599821\pi$
$409$	−5103.22	−0.616963	−0.308482	+	0.951230i	$0.599821\pi$
$410$	6678.88	0.804503
$411$	−2748.54	−0.329867
$412$	−8135.57	−0.972842
$413$	0	0
$414$	−2078.52	−0.246748
$415$	5193.85	0.614352
$416$	−15756.2	−1.85700
$417$	−1128.04	−0.132471
$418$	−11860.8	−1.38787
$419$	−8583.18	−1.00075	−0.500377	−	0.865808i	$-0.666805\pi$
$419$	−8583.18	−1.00075	−0.500377	+	0.865808i	$0.666805\pi$
$420$	0	0
$421$	12301.8	1.42412	0.712061	−	0.702118i	$-0.247762\pi$
$421$	12301.8	1.42412	0.712061	+	0.702118i	$0.247762\pi$
$422$	−1316.37	−0.151849
$423$	5439.48	0.625241
$424$	3069.05	0.351524
$425$	−1067.82	−0.121875
$426$	−2898.54	−0.329659
$427$	0	0
$428$	10870.3	1.22765
$429$	−3679.10	−0.414052
$430$	−15534.3	−1.74216
$431$	6137.21	0.685891	0.342946	−	0.939355i	$-0.388575\pi$
$431$	6137.21	0.685891	0.342946	+	0.939355i	$0.388575\pi$
$432$	−7962.86	−0.886836
$433$	−2764.10	−0.306777	−0.153388	−	0.988166i	$-0.549019\pi$
$433$	−2764.10	−0.306777	−0.153388	+	0.988166i	$0.549019\pi$
$434$	0	0
$435$	3583.61	0.394991
$436$	11076.8	1.21671
$437$	3143.70	0.344127
$438$	3901.60	0.425629
$439$	1642.99	0.178623	0.0893116	−	0.996004i	$-0.471533\pi$
$439$	1642.99	0.178623	0.0893116	+	0.996004i	$0.471533\pi$
$440$	1914.85	0.207470
$441$	0	0
$442$	19761.5	2.12660
$443$	10061.1	1.07905	0.539525	−	0.841969i	$-0.318604\pi$
$443$	10061.1	1.07905	0.539525	+	0.841969i	$0.318604\pi$
$444$	−2583.30	−0.276122
$445$	9036.60	0.962642
$446$	23325.3	2.47643
$447$	1110.63	0.117519
$448$	0	0
$449$	−5420.98	−0.569781	−0.284891	−	0.958560i	$-0.591957\pi$
$449$	−5420.98	−0.569781	−0.284891	+	0.958560i	$0.591957\pi$
$450$	−1192.90	−0.124965
$451$	−4200.97	−0.438616
$452$	5490.09	0.571310
$453$	−4630.72	−0.480288
$454$	−328.485	−0.0339572
$455$	0	0
$456$	1982.79	0.203624
$457$	−6944.96	−0.710879	−0.355439	−	0.934699i	$-0.615669\pi$
$457$	−6944.96	−0.710879	−0.355439	+	0.934699i	$0.615669\pi$
$458$	−22574.6	−2.30315
$459$	7926.50	0.806051
$460$	1568.89	0.159021
$461$	11840.6	1.19626	0.598128	−	0.801401i	$-0.295912\pi$
$461$	11840.6	1.19626	0.598128	+	0.801401i	$0.295912\pi$
$462$	0	0
$463$	−374.035	−0.0375440	−0.0187720	−	0.999824i	$-0.505976\pi$
$463$	−374.035	−0.0375440	−0.0187720	+	0.999824i	$0.505976\pi$
$464$	−12162.8	−1.21690
$465$	976.133	0.0973486
$466$	17976.2	1.78698
$467$	−16584.3	−1.64332	−0.821660	−	0.569978i	$-0.806952\pi$
$467$	−16584.3	−1.64332	−0.821660	+	0.569978i	$0.806952\pi$
$468$	9501.31	0.938457
$469$	0	0
$470$	−9539.77	−0.936249
$471$	−3966.95	−0.388084
$472$	−1092.20	−0.106509
$473$	9770.96	0.949829
$474$	9225.44	0.893963
$475$	1804.23	0.174282
$476$	0	0
$477$	−9422.33	−0.904442
$478$	−3708.21	−0.354832
$479$	−13055.4	−1.24534	−0.622668	−	0.782486i	$-0.713951\pi$
$479$	−13055.4	−1.24534	−0.622668	+	0.782486i	$0.713951\pi$
$480$	5037.91	0.479059
$481$	−14072.8	−1.33402
$482$	−26918.0	−2.54374
$483$	0	0
$484$	−4322.20	−0.405917
$485$	−5822.08	−0.545086
$486$	13685.1	1.27731
$487$	−4778.92	−0.444669	−0.222334	−	0.974970i	$-0.571368\pi$
$487$	−4778.92	−0.444669	−0.222334	+	0.974970i	$0.571368\pi$
$488$	1335.07	0.123844
$489$	−402.631	−0.0372343
$490$	0	0
$491$	10883.8	1.00036	0.500181	−	0.865921i	$-0.333267\pi$
$491$	10883.8	1.00036	0.500181	+	0.865921i	$0.333267\pi$
$492$	−2170.92	−0.198928
$493$	12107.2	1.10605
$494$	−33389.7	−3.04104
$495$	−5878.80	−0.533802
$496$	−3312.99	−0.299915
$497$	0	0
$498$	−3922.58	−0.352962
$499$	−6654.05	−0.596946	−0.298473	−	0.954418i	$-0.596477\pi$
$499$	−6654.05	−0.596946	−0.298473	+	0.954418i	$0.596477\pi$
$500$	8855.57	0.792066
$501$	3957.39	0.352900
$502$	−13010.6	−1.15675
$503$	−14468.0	−1.28249	−0.641247	−	0.767335i	$-0.721583\pi$
$503$	−14468.0	−1.28249	−0.641247	+	0.767335i	$0.721583\pi$
$504$	0	0
$505$	−7431.53	−0.654849
$506$	−2292.87	−0.201444
$507$	−5695.61	−0.498917
$508$	−438.836	−0.0383272
$509$	−22651.9	−1.97255	−0.986274	−	0.165118i	$-0.947200\pi$
$509$	−22651.9	−1.97255	−0.986274	+	0.165118i	$0.947200\pi$
$510$	−6318.57	−0.548610
$511$	0	0
$512$	−12653.8	−1.09223
$513$	−13392.9	−1.15265
$514$	23856.0	2.04717
$515$	14170.7	1.21250
$516$	5049.30	0.430781
$517$	6000.45	0.510444
$518$	0	0
$519$	−8075.04	−0.682957
$520$	5390.55	0.454598
$521$	−5394.36	−0.453611	−0.226805	−	0.973940i	$-0.572828\pi$
$521$	−5394.36	−0.453611	−0.226805	+	0.973940i	$0.572828\pi$
$522$	13525.4	1.13408
$523$	−7186.35	−0.600836	−0.300418	−	0.953808i	$-0.597126\pi$
$523$	−7186.35	−0.600836	−0.300418	+	0.953808i	$0.597126\pi$
$524$	−3226.96	−0.269027
$525$	0	0
$526$	11899.2	0.986367
$527$	3297.87	0.272595
$528$	−3992.57	−0.329080
$529$	−11559.3	−0.950051
$530$	16524.9	1.35433
$531$	3353.17	0.274040
$532$	0	0
$533$	−11826.3	−0.961076
$534$	−6824.76	−0.553064
$535$	−18934.1	−1.53008
$536$	−7094.77	−0.571730
$537$	7590.78	0.609993
$538$	16549.0	1.32617
$539$	0	0
$540$	−6683.83	−0.532641
$541$	−16883.7	−1.34175	−0.670873	−	0.741572i	$-0.734081\pi$
$541$	−16883.7	−1.34175	−0.670873	+	0.741572i	$0.734081\pi$
$542$	−11416.5	−0.904758
$543$	956.716	0.0756107
$544$	17020.6	1.34146
$545$	−19293.9	−1.51644
$546$	0	0
$547$	815.039	0.0637085	0.0318542	−	0.999493i	$-0.489859\pi$
$547$	815.039	0.0637085	0.0318542	+	0.999493i	$0.489859\pi$
$548$	7830.15	0.610379
$549$	−4098.82	−0.318640
$550$	−1315.93	−0.102021
$551$	−20456.8	−1.58165
$552$	383.304	0.0295553
$553$	0	0
$554$	−15491.3	−1.18802
$555$	4499.66	0.344144
$556$	3213.60	0.245121
$557$	−5494.36	−0.417960	−0.208980	−	0.977920i	$-0.567014\pi$
$557$	−5494.36	−0.417960	−0.208980	+	0.977920i	$0.567014\pi$
$558$	3684.17	0.279504
$559$	27506.5	2.08122
$560$	0	0
$561$	3974.34	0.299103
$562$	−1043.02	−0.0782864
$563$	−17540.4	−1.31304	−0.656520	−	0.754309i	$-0.727972\pi$
$563$	−17540.4	−1.31304	−0.656520	+	0.754309i	$0.727972\pi$
$564$	3100.83	0.231505
$565$	−9562.77	−0.712051
$566$	−17694.1	−1.31402
$567$	0	0
$568$	−2671.26	−0.197330
$569$	6764.24	0.498368	0.249184	−	0.968456i	$-0.419838\pi$
$569$	6764.24	0.498368	0.249184	+	0.968456i	$0.419838\pi$
$570$	10676.1	0.784512
$571$	−22185.9	−1.62601	−0.813006	−	0.582256i	$-0.802170\pi$
$571$	−22185.9	−1.62601	−0.813006	+	0.582256i	$0.802170\pi$
$572$	10481.2	0.766153
$573$	−793.198	−0.0578296
$574$	0	0
$575$	348.786	0.0252963
$576$	5367.95	0.388307
$577$	−16818.0	−1.21342	−0.606711	−	0.794923i	$-0.707511\pi$
$577$	−16818.0	−1.21342	−0.606711	+	0.794923i	$0.707511\pi$
$578$	−2935.29	−0.211232
$579$	−1788.04	−0.128340
$580$	−10209.1	−0.730882
$581$	0	0
$582$	4397.04	0.313167
$583$	−10394.0	−0.738383
$584$	3595.67	0.254777
$585$	−16549.6	−1.16964
$586$	8631.07	0.608441
$587$	−4586.41	−0.322489	−0.161245	−	0.986914i	$-0.551551\pi$
$587$	−4586.41	−0.322489	−0.161245	+	0.986914i	$0.551551\pi$
$588$	0	0
$589$	−5572.19	−0.389810
$590$	−5880.79	−0.410353
$591$	−10218.6	−0.711232
$592$	−15271.8	−1.06025
$593$	−24911.7	−1.72513	−0.862565	−	0.505946i	$-0.831143\pi$
$593$	−24911.7	−1.72513	−0.862565	+	0.505946i	$0.831143\pi$
$594$	9768.18	0.674736
$595$	0	0
$596$	−3164.00	−0.217454
$597$	551.011	0.0377745
$598$	−6454.74	−0.441395
$599$	−22215.8	−1.51538	−0.757690	−	0.652615i	$-0.773672\pi$
$599$	−22215.8	−1.51538	−0.757690	+	0.652615i	$0.773672\pi$
$600$	219.986	0.0149682
$601$	5145.11	0.349207	0.174604	−	0.984639i	$-0.444136\pi$
$601$	5145.11	0.349207	0.174604	+	0.984639i	$0.444136\pi$
$602$	0	0
$603$	21781.7	1.47101
$604$	13192.2	0.888714
$605$	7528.51	0.505913
$606$	5612.55	0.376228
$607$	−8531.66	−0.570493	−0.285247	−	0.958454i	$-0.592076\pi$
$607$	−8531.66	−0.570493	−0.285247	+	0.958454i	$0.592076\pi$
$608$	−28758.6	−1.91828
$609$	0	0
$610$	7188.51	0.477138
$611$	16892.1	1.11846
$612$	−10263.8	−0.677922
$613$	25594.5	1.68639	0.843193	−	0.537612i	$-0.180673\pi$
$613$	25594.5	1.68639	0.843193	+	0.537612i	$0.180673\pi$
$614$	−7979.75	−0.524490
$615$	3781.36	0.247934
$616$	0	0
$617$	19723.7	1.28695	0.643475	−	0.765467i	$-0.277492\pi$
$617$	19723.7	1.28695	0.643475	+	0.765467i	$0.277492\pi$
$618$	−10702.2	−0.696613
$619$	−17569.6	−1.14084	−0.570421	−	0.821353i	$-0.693220\pi$
$619$	−17569.6	−1.14084	−0.570421	+	0.821353i	$0.693220\pi$
$620$	−2780.85	−0.180132
$621$	−2589.05	−0.167303
$622$	10063.7	0.648741
$623$	0	0
$624$	−11239.6	−0.721065
$625$	−13656.3	−0.874002
$626$	29264.9	1.86847
$627$	−6715.18	−0.427717
$628$	11301.2	0.718102
$629$	15202.1	0.963669
$630$	0	0
$631$	6568.63	0.414410	0.207205	−	0.978297i	$-0.433563\pi$
$631$	6568.63	0.414410	0.207205	+	0.978297i	$0.433563\pi$
$632$	8502.07	0.535117
$633$	−745.287	−0.0467970
$634$	−29477.8	−1.84655
$635$	764.375	0.0477690
$636$	−5371.30	−0.334883
$637$	0	0
$638$	14920.3	0.925863
$639$	8201.07	0.507714
$640$	9580.79	0.591741
$641$	−9487.18	−0.584588	−0.292294	−	0.956328i	$-0.594419\pi$
$641$	−9487.18	−0.584588	−0.292294	+	0.956328i	$0.594419\pi$
$642$	14299.7	0.879071
$643$	−14736.0	−0.903781	−0.451890	−	0.892073i	$-0.649250\pi$
$643$	−14736.0	−0.903781	−0.451890	+	0.892073i	$0.649250\pi$
$644$	0	0
$645$	−8794.99	−0.536903
$646$	36069.1	2.19678
$647$	14799.4	0.899266	0.449633	−	0.893213i	$-0.351555\pi$
$647$	14799.4	0.899266	0.449633	+	0.893213i	$0.351555\pi$
$648$	2818.47	0.170864
$649$	3698.98	0.223725
$650$	−3704.51	−0.223543
$651$	0	0
$652$	1147.03	0.0688975
$653$	−4218.99	−0.252836	−0.126418	−	0.991977i	$-0.540348\pi$
$653$	−4218.99	−0.252836	−0.126418	+	0.991977i	$0.540348\pi$
$654$	14571.4	0.871235
$655$	5620.79	0.335301
$656$	−12833.9	−0.763843
$657$	−11039.1	−0.655521
$658$	0	0
$659$	14315.2	0.846190	0.423095	−	0.906085i	$-0.360944\pi$
$659$	14315.2	0.846190	0.423095	+	0.906085i	$0.360944\pi$
$660$	−3351.27	−0.197648
$661$	−2885.51	−0.169793	−0.0848965	−	0.996390i	$-0.527056\pi$
$661$	−2885.51	−0.169793	−0.0848965	+	0.996390i	$0.527056\pi$
$662$	−15518.1	−0.911071
$663$	11188.3	0.655380
$664$	−3615.01	−0.211280
$665$	0	0
$666$	16982.8	0.988094
$667$	−3954.62	−0.229571
$668$	−11274.0	−0.652999
$669$	13206.0	0.763190
$670$	−38200.8	−2.20273
$671$	−4521.53	−0.260136
$672$	0	0
$673$	13411.8	0.768181	0.384091	−	0.923295i	$-0.374515\pi$
$673$	13411.8	0.768181	0.384091	+	0.923295i	$0.374515\pi$
$674$	28822.4	1.64718
$675$	−1485.91	−0.0847300
$676$	16225.9	0.923185
$677$	19235.2	1.09198	0.545990	−	0.837792i	$-0.316154\pi$
$677$	19235.2	1.09198	0.545990	+	0.837792i	$0.316154\pi$
$678$	7222.14	0.409092
$679$	0	0
$680$	−5823.13	−0.328392
$681$	−185.977	−0.0104650
$682$	4064.11	0.228186
$683$	18647.8	1.04471	0.522357	−	0.852727i	$-0.325053\pi$
$683$	18647.8	1.04471	0.522357	+	0.852727i	$0.325053\pi$
$684$	17342.0	0.969428
$685$	−13638.7	−0.760743
$686$	0	0
$687$	−12781.0	−0.709789
$688$	29850.2	1.65411
$689$	−29260.6	−1.61791
$690$	2063.85	0.113869
$691$	−14962.9	−0.823756	−0.411878	−	0.911239i	$-0.635127\pi$
$691$	−14962.9	−0.823756	−0.411878	+	0.911239i	$0.635127\pi$
$692$	23004.5	1.26373
$693$	0	0
$694$	13233.1	0.723805
$695$	−5597.52	−0.305505
$696$	−2494.26	−0.135840
$697$	12775.3	0.694261
$698$	32183.6	1.74522
$699$	10177.5	0.550715
$700$	0	0
$701$	6461.83	0.348160	0.174080	−	0.984732i	$-0.444305\pi$
$701$	6461.83	0.348160	0.174080	+	0.984732i	$0.444305\pi$
$702$	27498.7	1.47845
$703$	−25686.0	−1.37805
$704$	5921.55	0.317012
$705$	−5401.10	−0.288535
$706$	16761.6	0.893526
$707$	0	0
$708$	1911.51	0.101467
$709$	23997.5	1.27115	0.635575	−	0.772039i	$-0.280763\pi$
$709$	23997.5	1.27115	0.635575	+	0.772039i	$0.280763\pi$
$710$	−14383.1	−0.760262
$711$	−26102.3	−1.37681
$712$	−6289.63	−0.331059
$713$	−1077.19	−0.0565794
$714$	0	0
$715$	−18256.3	−0.954893
$716$	−21624.9	−1.12872
$717$	−2099.46	−0.109353
$718$	2219.11	0.115343
$719$	−19265.0	−0.999254	−0.499627	−	0.866241i	$-0.666529\pi$
$719$	−19265.0	−0.999254	−0.499627	+	0.866241i	$0.666529\pi$
$720$	−17959.7	−0.929607
$721$	0	0
$722$	−35238.8	−1.81642
$723$	−15240.1	−0.783934
$724$	−2725.53	−0.139908
$725$	−2269.64	−0.116265
$726$	−5685.80	−0.290661
$727$	14268.1	0.727890	0.363945	−	0.931421i	$-0.381430\pi$
$727$	14268.1	0.727890	0.363945	+	0.931421i	$0.381430\pi$
$728$	0	0
$729$	−2636.44	−0.133945
$730$	19360.4	0.981591
$731$	−29713.9	−1.50343
$732$	−2336.57	−0.117981
$733$	8658.32	0.436292	0.218146	−	0.975916i	$-0.429999\pi$
$733$	8658.32	0.436292	0.218146	+	0.975916i	$0.429999\pi$
$734$	9410.20	0.473211
$735$	0	0
$736$	−5559.48	−0.278431
$737$	24028.1	1.20093
$738$	14271.8	0.711858
$739$	20025.5	0.996820	0.498410	−	0.866942i	$-0.333917\pi$
$739$	20025.5	0.996820	0.498410	+	0.866942i	$0.333917\pi$
$740$	−12818.8	−0.636796
$741$	−18904.1	−0.937193
$742$	0	0
$743$	28577.0	1.41102	0.705511	−	0.708699i	$-0.250717\pi$
$743$	28577.0	1.41102	0.705511	+	0.708699i	$0.250717\pi$
$744$	−679.406	−0.0334788
$745$	5511.13	0.271023
$746$	−12835.9	−0.629969
$747$	11098.5	0.543604
$748$	−11322.3	−0.553453
$749$	0	0
$750$	11649.4	0.567167
$751$	−13794.4	−0.670262	−0.335131	−	0.942172i	$-0.608780\pi$
$751$	−13794.4	−0.670262	−0.335131	+	0.942172i	$0.608780\pi$
$752$	18331.3	0.888929
$753$	−7366.14	−0.356490
$754$	42002.6	2.02871
$755$	−22978.5	−1.10765
$756$	0	0
$757$	−2175.08	−0.104431	−0.0522157	−	0.998636i	$-0.516628\pi$
$757$	−2175.08	−0.104431	−0.0522157	+	0.998636i	$0.516628\pi$
$758$	−37803.6	−1.81146
$759$	−1298.15	−0.0620814
$760$	9838.96	0.469601
$761$	−7698.40	−0.366711	−0.183355	−	0.983047i	$-0.558696\pi$
$761$	−7698.40	−0.366711	−0.183355	+	0.983047i	$0.558696\pi$
$762$	−577.283	−0.0274446
$763$	0	0
$764$	2259.70	0.107007
$765$	17877.7	0.844926
$766$	−37508.5	−1.76924
$767$	10413.1	0.490216
$768$	−11285.7	−0.530259
$769$	5192.10	0.243474	0.121737	−	0.992562i	$-0.461153\pi$
$769$	5192.10	0.243474	0.121737	+	0.992562i	$0.461153\pi$
$770$	0	0
$771$	13506.5	0.630901
$772$	5093.86	0.237477
$773$	−36881.8	−1.71610	−0.858050	−	0.513566i	$-0.828324\pi$
$773$	−36881.8	−1.71610	−0.858050	+	0.513566i	$0.828324\pi$
$774$	−33194.4	−1.54154
$775$	−618.222	−0.0286544
$776$	4052.27	0.187459
$777$	0	0
$778$	−2328.98	−0.107324
$779$	−21585.6	−0.992793
$780$	−9434.26	−0.433078
$781$	9046.84	0.414496
$782$	6972.73	0.318854
$783$	16847.6	0.768946
$784$	0	0
$785$	−19684.7	−0.895004
$786$	−4245.02	−0.192640
$787$	14140.8	0.640490	0.320245	−	0.947335i	$-0.396235\pi$
$787$	14140.8	0.640490	0.320245	+	0.947335i	$0.396235\pi$
$788$	29111.2	1.31605
$789$	6736.92	0.303981
$790$	45778.3	2.06167
$791$	0	0
$792$	4091.74	0.183578
$793$	−12728.7	−0.569999
$794$	−2419.59	−0.108146
$795$	9355.84	0.417381
$796$	−1569.74	−0.0698971
$797$	36572.3	1.62542	0.812708	−	0.582671i	$-0.197992\pi$
$797$	36572.3	1.62542	0.812708	+	0.582671i	$0.197992\pi$
$798$	0	0
$799$	−18247.6	−0.807954
$800$	−3190.70	−0.141010
$801$	19309.9	0.851786
$802$	−14081.4	−0.619989
$803$	−12177.6	−0.535165
$804$	12416.9	0.544665
$805$	0	0
$806$	11441.0	0.499990
$807$	9369.51	0.408702
$808$	5172.47	0.225207
$809$	−29543.5	−1.28392	−0.641962	−	0.766737i	$-0.721879\pi$
$809$	−29543.5	−1.28392	−0.641962	+	0.766737i	$0.721879\pi$
$810$	15175.7	0.658295
$811$	−319.871	−0.0138498	−0.00692489	−	0.999976i	$-0.502204\pi$
$811$	−319.871	−0.0138498	−0.00692489	+	0.999976i	$0.502204\pi$
$812$	0	0
$813$	−6463.62	−0.278830
$814$	18734.2	0.806676
$815$	−1997.92	−0.0858702
$816$	12141.6	0.520882
$817$	50205.6	2.14990
$818$	19124.9	0.817464
$819$	0	0
$820$	−10772.5	−0.458771
$821$	−19324.1	−0.821459	−0.410729	−	0.911757i	$-0.634726\pi$
$821$	−19324.1	−0.821459	−0.410729	+	0.911757i	$0.634726\pi$
$822$	10300.5	0.437068
$823$	971.792	0.0411598	0.0205799	−	0.999788i	$-0.493449\pi$
$823$	971.792	0.0411598	0.0205799	+	0.999788i	$0.493449\pi$
$824$	−9863.07	−0.416986
$825$	−745.034	−0.0314409
$826$	0	0
$827$	34455.0	1.44875	0.724375	−	0.689406i	$-0.242128\pi$
$827$	34455.0	1.44875	0.724375	+	0.689406i	$0.242128\pi$
$828$	3352.48	0.140709
$829$	−1897.35	−0.0794907	−0.0397453	−	0.999210i	$-0.512655\pi$
$829$	−1897.35	−0.0794907	−0.0397453	+	0.999210i	$0.512655\pi$
$830$	−19464.5	−0.814005
$831$	−8770.67	−0.366127
$832$	16669.9	0.694623
$833$	0	0
$834$	4227.45	0.175521
$835$	19637.3	0.813863
$836$	19130.5	0.791438
$837$	4589.09	0.189513
$838$	32166.4	1.32598
$839$	31645.4	1.30217	0.651085	−	0.759005i	$-0.274314\pi$
$839$	31645.4	1.30217	0.651085	+	0.759005i	$0.274314\pi$
$840$	0	0
$841$	1344.71	0.0551358
$842$	−46102.6	−1.88693
$843$	−590.520	−0.0241265
$844$	2123.21	0.0865921
$845$	−28262.6	−1.15061
$846$	−20385.1	−0.828432
$847$	0	0
$848$	−31753.7	−1.28588
$849$	−10017.8	−0.404958
$850$	4001.79	0.161483
$851$	−4965.50	−0.200018
$852$	4675.11	0.187989
$853$	19554.6	0.784919	0.392460	−	0.919769i	$-0.371624\pi$
$853$	19554.6	0.784919	0.392460	+	0.919769i	$0.371624\pi$
$854$	0	0
$855$	−30206.7	−1.20824
$856$	13178.4	0.526203
$857$	31638.5	1.26109	0.630543	−	0.776154i	$-0.282832\pi$
$857$	31638.5	1.26109	0.630543	+	0.776154i	$0.282832\pi$
$858$	13787.8	0.548612
$859$	27689.8	1.09984	0.549921	−	0.835217i	$-0.314658\pi$
$859$	27689.8	1.09984	0.549921	+	0.835217i	$0.314658\pi$
$860$	25055.5	0.993473
$861$	0	0
$862$	−22999.9	−0.908793
$863$	10138.3	0.399898	0.199949	−	0.979806i	$-0.435922\pi$
$863$	10138.3	0.399898	0.199949	+	0.979806i	$0.435922\pi$
$864$	23684.7	0.932604
$865$	−40069.8	−1.57504
$866$	10358.8	0.406473
$867$	−1661.86	−0.0650979
$868$	0	0
$869$	−28794.2	−1.12402
$870$	−13430.0	−0.523356
$871$	67642.2	2.63142
$872$	13428.9	0.521513
$873$	−12440.9	−0.482315
$874$	−11781.4	−0.455962
$875$	0	0
$876$	−6292.96	−0.242716
$877$	7447.14	0.286741	0.143371	−	0.989669i	$-0.454206\pi$
$877$	7447.14	0.286741	0.143371	+	0.989669i	$0.454206\pi$
$878$	−6157.29	−0.236672
$879$	4886.63	0.187511
$880$	−19811.8	−0.758928
$881$	−31134.6	−1.19064	−0.595319	−	0.803490i	$-0.702974\pi$
$881$	−31134.6	−1.19064	−0.595319	+	0.803490i	$0.702974\pi$
$882$	0	0
$883$	22384.2	0.853103	0.426551	−	0.904463i	$-0.359728\pi$
$883$	22384.2	0.853103	0.426551	+	0.904463i	$0.359728\pi$
$884$	−31873.7	−1.21270
$885$	−3329.51	−0.126463
$886$	−37705.3	−1.42972
$887$	1330.91	0.0503806	0.0251903	−	0.999683i	$-0.491981\pi$
$887$	1330.91	0.0503806	0.0251903	+	0.999683i	$0.491981\pi$
$888$	−3131.84	−0.118353
$889$	0	0
$890$	−33865.7	−1.27548
$891$	−9545.41	−0.358904
$892$	−37621.8	−1.41219
$893$	30831.8	1.15537
$894$	−4162.20	−0.155710
$895$	37666.8	1.40677
$896$	0	0
$897$	−3654.46	−0.136030
$898$	20315.7	0.754950
$899$	7009.55	0.260046
$900$	1924.06	0.0712614
$901$	31608.7	1.16875
$902$	15743.6	0.581158
$903$	0	0
$904$	6655.85	0.244879
$905$	4747.40	0.174374
$906$	17354.2	0.636372
$907$	−10551.4	−0.386275	−0.193138	−	0.981172i	$-0.561866\pi$
$907$	−10551.4	−0.386275	−0.193138	+	0.981172i	$0.561866\pi$
$908$	529.820	0.0193642
$909$	−15880.1	−0.579438
$910$	0	0
$911$	51333.0	1.86689	0.933446	−	0.358717i	$-0.116786\pi$
$911$	51333.0	1.86689	0.933446	+	0.358717i	$0.116786\pi$
$912$	−20514.8	−0.744861
$913$	12243.1	0.443797
$914$	26027.0	0.941901
$915$	4069.89	0.147045
$916$	36411.0	1.31338
$917$	0	0
$918$	−29705.4	−1.06800
$919$	−5383.60	−0.193241	−0.0966205	−	0.995321i	$-0.530803\pi$
$919$	−5383.60	−0.193241	−0.0966205	+	0.995321i	$0.530803\pi$
$920$	1902.02	0.0681607
$921$	−4517.87	−0.161638
$922$	−44374.1	−1.58502
$923$	25468.1	0.908225
$924$	0	0
$925$	−2849.80	−0.101298
$926$	1401.74	0.0497451
$927$	30280.7	1.07287
$928$	36177.0	1.27971
$929$	−8269.28	−0.292041	−0.146021	−	0.989282i	$-0.546647\pi$
$929$	−8269.28	−0.292041	−0.146021	+	0.989282i	$0.546647\pi$
$930$	−3658.17	−0.128985
$931$	0	0
$932$	−28994.2	−1.01903
$933$	5697.72	0.199930
$934$	62151.5	2.17737
$935$	19721.4	0.689795
$936$	11518.8	0.402248
$937$	−12441.0	−0.433757	−0.216879	−	0.976199i	$-0.569588\pi$
$937$	−12441.0	−0.433757	−0.216879	+	0.976199i	$0.569588\pi$
$938$	0	0
$939$	16568.8	0.575828
$940$	15386.9	0.533899
$941$	−30423.2	−1.05395	−0.526975	−	0.849881i	$-0.676674\pi$
$941$	−30423.2	−1.05395	−0.526975	+	0.849881i	$0.676674\pi$
$942$	14866.6	0.514204
$943$	−4172.84	−0.144100
$944$	11300.3	0.389613
$945$	0	0
$946$	−36617.8	−1.25851
$947$	−44106.6	−1.51349	−0.756744	−	0.653712i	$-0.773211\pi$
$947$	−44106.6	−1.51349	−0.756744	+	0.653712i	$0.773211\pi$
$948$	−14879.9	−0.509785
$949$	−34281.5	−1.17263
$950$	−6761.56	−0.230920
$951$	−16689.3	−0.569074
$952$	0	0
$953$	−14111.5	−0.479660	−0.239830	−	0.970815i	$-0.577092\pi$
$953$	−14111.5	−0.479660	−0.239830	+	0.970815i	$0.577092\pi$
$954$	35311.2	1.19837
$955$	−3935.99	−0.133367
$956$	5981.04	0.202344
$957$	8447.38	0.285334
$958$	48926.6	1.65005
$959$	0	0
$960$	−5330.08	−0.179195
$961$	−27881.7	−0.935910
$962$	52739.4	1.76755
$963$	−40459.3	−1.35388
$964$	43416.6	1.45057
$965$	−8872.59	−0.295978
$966$	0	0
$967$	39015.5	1.29747	0.648735	−	0.761015i	$-0.275298\pi$
$967$	39015.5	1.29747	0.648735	+	0.761015i	$0.275298\pi$
$968$	−5239.97	−0.173987
$969$	20421.1	0.677009
$970$	21818.9	0.722229
$971$	41897.6	1.38471	0.692357	−	0.721555i	$-0.256572\pi$
$971$	41897.6	1.38471	0.692357	+	0.721555i	$0.256572\pi$
$972$	−22073.0	−0.728388
$973$	0	0
$974$	17909.6	0.589178
$975$	−2097.37	−0.0688919
$976$	−13813.2	−0.453023
$977$	58600.3	1.91892	0.959462	−	0.281837i	$-0.0909437\pi$
$977$	58600.3	1.91892	0.959462	+	0.281837i	$0.0909437\pi$
$978$	1508.90	0.0493348
$979$	21301.3	0.695395
$980$	0	0
$981$	−41228.2	−1.34181
$982$	−40788.1	−1.32546
$983$	32003.9	1.03842	0.519210	−	0.854647i	$-0.326226\pi$
$983$	32003.9	1.03842	0.519210	+	0.854647i	$0.326226\pi$
$984$	−2631.89	−0.0852659
$985$	−50706.6	−1.64025
$986$	−45373.3	−1.46550
$987$	0	0
$988$	53854.9	1.73416
$989$	9705.52	0.312050
$990$	22031.4	0.707278
$991$	−30356.2	−0.973054	−0.486527	−	0.873666i	$-0.661736\pi$
$991$	−30356.2	−0.973054	−0.486527	+	0.873666i	$0.661736\pi$
$992$	9854.16	0.315393
$993$	−8785.85	−0.280776
$994$	0	0
$995$	2734.22	0.0871161
$996$	6326.81	0.201278
$997$	−11554.4	−0.367033	−0.183516	−	0.983017i	$-0.558748\pi$
$997$	−11554.4	−0.367033	−0.183516	+	0.983017i	$0.558748\pi$
$998$	24936.8	0.790943
$999$	21154.2	0.669959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.8		39
7.6	odd	2		2401.4.a.d.1.8		39
49.6	odd	14		49.4.e.a.36.11	yes	78
49.41	odd	14		49.4.e.a.15.11	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.11	✓	78	49.41	odd	14
49.4.e.a.36.11	yes	78	49.6	odd	14
2401.4.a.c.1.8		39	1.1	even	1	trivial
2401.4.a.d.1.8		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)

\(f(q)\)	\(=\)	\(q-3.74761 q^{2} -2.12177 q^{3} +6.04460 q^{4} -10.5286 q^{5} +7.95158 q^{6} +7.32810 q^{8} -22.4981 q^{9} +O(q^{10})\)	\(q-3.74761 q^{2} -2.12177 q^{3} +6.04460 q^{4} -10.5286 q^{5} +7.95158 q^{6} +7.32810 q^{8} -22.4981 q^{9} +39.4572 q^{10} -24.8183 q^{11} -12.8253 q^{12} -69.8668 q^{13} +22.3393 q^{15} -75.8196 q^{16} +75.4735 q^{17} +84.3141 q^{18} -127.523 q^{19} -63.6412 q^{20} +93.0093 q^{22} -24.6521 q^{23} -15.5486 q^{24} -14.1483 q^{25} +261.834 q^{26} +105.024 q^{27} +160.417 q^{29} -83.7191 q^{30} +43.6957 q^{31} +225.518 q^{32} +52.6588 q^{33} -282.845 q^{34} -135.992 q^{36} +201.423 q^{37} +477.905 q^{38} +148.241 q^{39} -77.1547 q^{40} +169.269 q^{41} -393.700 q^{43} -150.017 q^{44} +236.874 q^{45} +92.3865 q^{46} -241.776 q^{47} +160.872 q^{48} +53.0225 q^{50} -160.138 q^{51} -422.316 q^{52} +418.806 q^{53} -393.588 q^{54} +261.302 q^{55} +270.574 q^{57} -601.182 q^{58} -149.042 q^{59} +135.032 q^{60} +182.185 q^{61} -163.755 q^{62} -238.596 q^{64} +735.600 q^{65} -197.345 q^{66} -968.160 q^{67} +456.207 q^{68} +52.3061 q^{69} -364.523 q^{71} -164.868 q^{72} +490.670 q^{73} -754.856 q^{74} +30.0196 q^{75} -770.822 q^{76} -555.551 q^{78} +1160.20 q^{79} +798.275 q^{80} +384.612 q^{81} -634.355 q^{82} -493.308 q^{83} -794.631 q^{85} +1475.43 q^{86} -340.369 q^{87} -181.871 q^{88} -858.289 q^{89} -887.710 q^{90} -149.012 q^{92} -92.7124 q^{93} +906.081 q^{94} +1342.64 q^{95} -478.497 q^{96} +552.977 q^{97} +558.364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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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