LMFDB - Embedded newform 2401.4.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.28751 q^{2} -1.89643 q^{3} -6.34231 q^{4} -17.6887 q^{5} +2.44167 q^{6} +18.4659 q^{8} -23.4036 q^{9} +O(q^{10})$	\(q-1.28751 q^{2} -1.89643 q^{3} -6.34231 q^{4} -17.6887 q^{5} +2.44167 q^{6} +18.4659 q^{8} -23.4036 q^{9} +22.7744 q^{10} -54.3663 q^{11} +12.0277 q^{12} -22.3458 q^{13} +33.5452 q^{15} +26.9635 q^{16} -18.8788 q^{17} +30.1324 q^{18} -142.319 q^{19} +112.187 q^{20} +69.9972 q^{22} -68.8535 q^{23} -35.0192 q^{24} +187.889 q^{25} +28.7704 q^{26} +95.5866 q^{27} -21.1393 q^{29} -43.1899 q^{30} +288.230 q^{31} -182.443 q^{32} +103.102 q^{33} +24.3066 q^{34} +148.433 q^{36} +22.6074 q^{37} +183.237 q^{38} +42.3771 q^{39} -326.637 q^{40} -300.537 q^{41} +392.938 q^{43} +344.808 q^{44} +413.978 q^{45} +88.6496 q^{46} -110.833 q^{47} -51.1342 q^{48} -241.909 q^{50} +35.8022 q^{51} +141.724 q^{52} -650.948 q^{53} -123.069 q^{54} +961.667 q^{55} +269.897 q^{57} +27.2171 q^{58} +158.468 q^{59} -212.755 q^{60} +66.3396 q^{61} -371.100 q^{62} +19.1895 q^{64} +395.267 q^{65} -132.744 q^{66} +755.351 q^{67} +119.735 q^{68} +130.575 q^{69} +418.935 q^{71} -432.168 q^{72} +92.4344 q^{73} -29.1073 q^{74} -356.318 q^{75} +902.629 q^{76} -54.5610 q^{78} -647.958 q^{79} -476.948 q^{80} +450.623 q^{81} +386.944 q^{82} -458.608 q^{83} +333.940 q^{85} -505.912 q^{86} +40.0891 q^{87} -1003.92 q^{88} -528.397 q^{89} -533.001 q^{90} +436.690 q^{92} -546.607 q^{93} +142.699 q^{94} +2517.43 q^{95} +345.989 q^{96} +1090.75 q^{97} +1272.36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.28751	−0.455204	−0.227602	−	0.973754i	$-0.573089\pi$
$2$	−1.28751	−0.455204	−0.227602	+	0.973754i	$0.573089\pi$
$3$	−1.89643	−0.364967	−0.182484	−	0.983209i	$-0.558414\pi$
$3$	−1.89643	−0.364967	−0.182484	+	0.983209i	$0.558414\pi$
$4$	−6.34231	−0.792789
$5$	−17.6887	−1.58212	−0.791061	−	0.611737i	$-0.790471\pi$
$5$	−17.6887	−1.58212	−0.791061	+	0.611737i	$0.790471\pi$
$6$	2.44167	0.166135
$7$	0	0
$7$	0	0
$8$	18.4659	0.816085
$9$	−23.4036	−0.866799
$10$	22.7744	0.720189
$11$	−54.3663	−1.49019	−0.745093	−	0.666960i	$-0.767595\pi$
$11$	−54.3663	−1.49019	−0.745093	+	0.666960i	$0.767595\pi$
$12$	12.0277	0.289342
$13$	−22.3458	−0.476738	−0.238369	−	0.971175i	$-0.576613\pi$
$13$	−22.3458	−0.476738	−0.238369	+	0.971175i	$0.576613\pi$
$14$	0	0
$15$	33.5452	0.577423
$16$	26.9635	0.421304
$17$	−18.8788	−0.269340	−0.134670	−	0.990891i	$-0.542997\pi$
$17$	−18.8788	−0.269340	−0.134670	+	0.990891i	$0.542997\pi$
$18$	30.1324	0.394570
$19$	−142.319	−1.71843	−0.859214	−	0.511616i	$-0.829047\pi$
$19$	−142.319	−1.71843	−0.859214	+	0.511616i	$0.829047\pi$
$20$	112.187	1.25429
$21$	0	0
$22$	69.9972	0.678339
$23$	−68.8535	−0.624215	−0.312107	−	0.950047i	$-0.601035\pi$
$23$	−68.8535	−0.624215	−0.312107	+	0.950047i	$0.601035\pi$
$24$	−35.0192	−0.297844
$25$	187.889	1.50311
$26$	28.7704	0.217013
$27$	95.5866	0.681321
$28$	0	0
$29$	−21.1393	−0.135361	−0.0676804	−	0.997707i	$-0.521560\pi$
$29$	−21.1393	−0.135361	−0.0676804	+	0.997707i	$0.521560\pi$
$30$	−43.1899	−0.262845
$31$	288.230	1.66993	0.834963	−	0.550307i	$-0.185489\pi$
$31$	288.230	1.66993	0.834963	+	0.550307i	$0.185489\pi$
$32$	−182.443	−1.00786
$33$	103.102	0.543869
$34$	24.3066	0.122604
$35$	0	0
$36$	148.433	0.687189
$37$	22.6074	0.100450	0.0502248	−	0.998738i	$-0.484006\pi$
$37$	22.6074	0.100450	0.0502248	+	0.998738i	$0.484006\pi$
$38$	183.237	0.782235
$39$	42.3771	0.173994
$40$	−326.637	−1.29115
$41$	−300.537	−1.14478	−0.572390	−	0.819982i	$-0.693983\pi$
$41$	−300.537	−1.14478	−0.572390	+	0.819982i	$0.693983\pi$
$42$	0	0
$43$	392.938	1.39355	0.696773	−	0.717292i	$-0.254619\pi$
$43$	392.938	1.39355	0.696773	+	0.717292i	$0.254619\pi$
$44$	344.808	1.18140
$45$	413.978	1.37138
$46$	88.6496	0.284145
$47$	−110.833	−0.343971	−0.171986	−	0.985099i	$-0.555018\pi$
$47$	−110.833	−0.343971	−0.171986	+	0.985099i	$0.555018\pi$
$48$	−51.1342	−0.153762
$49$	0	0
$50$	−241.909	−0.684223
$51$	35.8022	0.0983001
$52$	141.724	0.377953
$53$	−650.948	−1.68707	−0.843534	−	0.537075i	$-0.819529\pi$
$53$	−650.948	−1.68707	−0.843534	+	0.537075i	$0.819529\pi$
$54$	−123.069	−0.310140
$55$	961.667	2.35766
$56$	0	0
$57$	269.897	0.627170
$58$	27.2171	0.0616168
$59$	158.468	0.349674	0.174837	−	0.984597i	$-0.444060\pi$
$59$	158.468	0.349674	0.174837	+	0.984597i	$0.444060\pi$
$60$	−212.755	−0.457775
$61$	66.3396	0.139244	0.0696222	−	0.997573i	$-0.477821\pi$
$61$	66.3396	0.139244	0.0696222	+	0.997573i	$0.477821\pi$
$62$	−371.100	−0.760157
$63$	0	0
$64$	19.1895	0.0374795
$65$	395.267	0.754259
$66$	−132.744	−0.247571
$67$	755.351	1.37733	0.688663	−	0.725082i	$-0.258198\pi$
$67$	755.351	1.37733	0.688663	+	0.725082i	$0.258198\pi$
$68$	119.735	0.213530
$69$	130.575	0.227818
$70$	0	0
$71$	418.935	0.700259	0.350129	−	0.936701i	$-0.386138\pi$
$71$	418.935	0.700259	0.350129	+	0.936701i	$0.386138\pi$
$72$	−432.168	−0.707381
$73$	92.4344	0.148200	0.0741002	−	0.997251i	$-0.476392\pi$
$73$	92.4344	0.148200	0.0741002	+	0.997251i	$0.476392\pi$
$74$	−29.1073	−0.0457251
$75$	−356.318	−0.548587
$76$	902.629	1.36235
$77$	0	0
$78$	−54.5610	−0.0792027
$79$	−647.958	−0.922798	−0.461399	−	0.887193i	$-0.652652\pi$
$79$	−647.958	−0.922798	−0.461399	+	0.887193i	$0.652652\pi$
$80$	−476.948	−0.666555
$81$	450.623	0.618139
$82$	386.944	0.521108
$83$	−458.608	−0.606491	−0.303245	−	0.952913i	$-0.598070\pi$
$83$	−458.608	−0.606491	−0.303245	+	0.952913i	$0.598070\pi$
$84$	0	0
$85$	333.940	0.426128
$86$	−505.912	−0.634348
$87$	40.0891	0.0494023
$88$	−1003.92	−1.21612
$89$	−528.397	−0.629325	−0.314663	−	0.949204i	$-0.601891\pi$
$89$	−528.397	−0.629325	−0.314663	+	0.949204i	$0.601891\pi$
$90$	−533.001	−0.624259
$91$	0	0
$92$	436.690	0.494871
$93$	−546.607	−0.609468
$94$	142.699	0.156577
$95$	2517.43	2.71876
$96$	345.989	0.367837
$97$	1090.75	1.14174	0.570871	−	0.821040i	$-0.306606\pi$
$97$	1090.75	1.14174	0.570871	+	0.821040i	$0.306606\pi$
$98$	0	0
$99$	1272.36	1.29169
$100$	−1191.65	−1.19165
$101$	−936.958	−0.923077	−0.461539	−	0.887120i	$-0.652702\pi$
$101$	−936.958	−0.923077	−0.461539	+	0.887120i	$0.652702\pi$
$102$	−46.0957	−0.0447466
$103$	419.044	0.400870	0.200435	−	0.979707i	$-0.435764\pi$
$103$	419.044	0.400870	0.200435	+	0.979707i	$0.435764\pi$
$104$	−412.634	−0.389059
$105$	0	0
$106$	838.103	0.767960
$107$	1198.06	1.08244	0.541218	−	0.840882i	$-0.317963\pi$
$107$	1198.06	1.08244	0.541218	+	0.840882i	$0.317963\pi$
$108$	−606.240	−0.540144
$109$	438.237	0.385096	0.192548	−	0.981288i	$-0.438325\pi$
$109$	438.237	0.385096	0.192548	+	0.981288i	$0.438325\pi$
$110$	−1238.16	−1.07322
$111$	−42.8733	−0.0366608
$112$	0	0
$113$	993.291	0.826911	0.413456	−	0.910524i	$-0.364322\pi$
$113$	993.291	0.826911	0.413456	+	0.910524i	$0.364322\pi$
$114$	−347.495	−0.285490
$115$	1217.93	0.987584
$116$	134.072	0.107313
$117$	522.971	0.413236
$118$	−204.029	−0.159173
$119$	0	0
$120$	619.443	0.471226
$121$	1624.69	1.22066
$122$	−85.4129	−0.0633846
$123$	569.945	0.417807
$124$	−1828.05	−1.32390
$125$	−1112.42	−0.795986
$126$	0	0
$127$	666.342	0.465577	0.232789	−	0.972527i	$-0.425215\pi$
$127$	666.342	0.465577	0.232789	+	0.972527i	$0.425215\pi$
$128$	1434.84	0.990803
$129$	−745.177	−0.508599
$130$	−508.910	−0.343342
$131$	168.033	0.112070	0.0560348	−	0.998429i	$-0.482154\pi$
$131$	168.033	0.112070	0.0560348	+	0.998429i	$0.482154\pi$
$132$	−653.903	−0.431174
$133$	0	0
$134$	−972.523	−0.626964
$135$	−1690.80	−1.07793
$136$	−348.613	−0.219804
$137$	971.627	0.605925	0.302962	−	0.953002i	$-0.402024\pi$
$137$	971.627	0.605925	0.302962	+	0.953002i	$0.402024\pi$
$138$	−168.117	−0.103704
$139$	−337.975	−0.206235	−0.103118	−	0.994669i	$-0.532882\pi$
$139$	−337.975	−0.206235	−0.103118	+	0.994669i	$0.532882\pi$
$140$	0	0
$141$	210.186	0.125538
$142$	−539.383	−0.318761
$143$	1214.86	0.710429
$144$	−631.042	−0.365186
$145$	373.926	0.214158
$146$	−119.010	−0.0674614
$147$	0	0
$148$	−143.383	−0.0796354
$149$	2799.07	1.53898	0.769492	−	0.638656i	$-0.220509\pi$
$149$	2799.07	1.53898	0.769492	+	0.638656i	$0.220509\pi$
$150$	458.763	0.249719
$151$	575.482	0.310146	0.155073	−	0.987903i	$-0.450439\pi$
$151$	575.482	0.310146	0.155073	+	0.987903i	$0.450439\pi$
$152$	−2628.04	−1.40238
$153$	441.830	0.233463
$154$	0	0
$155$	−5098.41	−2.64203
$156$	−268.769	−0.137941
$157$	1627.03	0.827077	0.413538	−	0.910487i	$-0.364293\pi$
$157$	1627.03	0.827077	0.413538	+	0.910487i	$0.364293\pi$
$158$	834.254	0.420061
$159$	1234.48	0.615725
$160$	3227.17	1.59456
$161$	0	0
$162$	−580.183	−0.281379
$163$	920.984	0.442558	0.221279	−	0.975210i	$-0.428977\pi$
$163$	920.984	0.442558	0.221279	+	0.975210i	$0.428977\pi$
$164$	1906.10	0.907569
$165$	−1823.73	−0.860468
$166$	590.463	0.276077
$167$	−130.808	−0.0606122	−0.0303061	−	0.999541i	$-0.509648\pi$
$167$	−130.808	−0.0606122	−0.0303061	+	0.999541i	$0.509648\pi$
$168$	0	0
$169$	−1697.67	−0.772721
$170$	−429.952	−0.193975
$171$	3330.76	1.48953
$172$	−2492.14	−1.10479
$173$	1969.75	0.865648	0.432824	−	0.901478i	$-0.357517\pi$
$173$	1969.75	0.865648	0.432824	+	0.901478i	$0.357517\pi$
$174$	−51.6151	−0.0224881
$175$	0	0
$176$	−1465.90	−0.627822
$177$	−300.522	−0.127619
$178$	680.317	0.286471
$179$	1611.27	0.672806	0.336403	−	0.941718i	$-0.390790\pi$
$179$	1611.27	0.672806	0.336403	+	0.941718i	$0.390790\pi$
$180$	−2625.58	−1.08722
$181$	254.621	0.104563	0.0522813	−	0.998632i	$-0.483351\pi$
$181$	254.621	0.104563	0.0522813	+	0.998632i	$0.483351\pi$
$182$	0	0
$183$	−125.808	−0.0508197
$184$	−1271.44	−0.509412
$185$	−399.895	−0.158924
$186$	703.763	0.277432
$187$	1026.37	0.401366
$188$	702.938	0.272697
$189$	0	0
$190$	−3241.22	−1.23759
$191$	−1642.15	−0.622104	−0.311052	−	0.950393i	$-0.600681\pi$
$191$	−1642.15	−0.622104	−0.311052	+	0.950393i	$0.600681\pi$
$192$	−36.3915	−0.0136788
$193$	−4606.52	−1.71805	−0.859027	−	0.511930i	$-0.828931\pi$
$193$	−4606.52	−1.71805	−0.859027	+	0.511930i	$0.828931\pi$
$194$	−1404.35	−0.519726
$195$	−749.594	−0.275280
$196$	0	0
$197$	−3277.42	−1.18531	−0.592655	−	0.805456i	$-0.701920\pi$
$197$	−3277.42	−1.18531	−0.592655	+	0.805456i	$0.701920\pi$
$198$	−1638.18	−0.587983
$199$	−3912.42	−1.39369	−0.696844	−	0.717222i	$-0.745413\pi$
$199$	−3912.42	−1.39369	−0.696844	+	0.717222i	$0.745413\pi$
$200$	3469.54	1.22667
$201$	−1432.47	−0.502679
$202$	1206.34	0.420188
$203$	0	0
$204$	−227.069	−0.0779313
$205$	5316.09	1.81118
$206$	−539.524	−0.182478
$207$	1611.42	0.541069
$208$	−602.519	−0.200852
$209$	7737.33	2.56078
$210$	0	0
$211$	2003.79	0.653775	0.326888	−	0.945063i	$-0.394000\pi$
$211$	2003.79	0.653775	0.326888	+	0.945063i	$0.394000\pi$
$212$	4128.52	1.33749
$213$	−794.478	−0.255572
$214$	−1542.51	−0.492730
$215$	−6950.55	−2.20476
$216$	1765.09	0.556015
$217$	0	0
$218$	−564.235	−0.175297
$219$	−175.295	−0.0540883
$220$	−6099.20	−1.86913
$221$	421.860	0.128405
$222$	55.1999	0.0166882
$223$	−4124.26	−1.23848	−0.619240	−	0.785201i	$-0.712559\pi$
$223$	−4124.26	−1.23848	−0.619240	+	0.785201i	$0.712559\pi$
$224$	0	0
$225$	−4397.27	−1.30290
$226$	−1278.87	−0.376413
$227$	−823.029	−0.240645	−0.120322	−	0.992735i	$-0.538393\pi$
$227$	−823.029	−0.240645	−0.120322	+	0.992735i	$0.538393\pi$
$228$	−1711.77	−0.497214
$229$	−4266.41	−1.23114	−0.615572	−	0.788081i	$-0.711075\pi$
$229$	−4266.41	−1.23114	−0.615572	+	0.788081i	$0.711075\pi$
$230$	−1568.09	−0.449552
$231$	0	0
$232$	−390.356	−0.110466
$233$	−4824.74	−1.35656	−0.678281	−	0.734802i	$-0.737275\pi$
$233$	−4824.74	−1.35656	−0.678281	+	0.734802i	$0.737275\pi$
$234$	−673.330	−0.188107
$235$	1960.49	0.544205
$236$	−1005.05	−0.277218
$237$	1228.80	0.336791
$238$	0	0
$239$	4187.81	1.13342	0.566709	−	0.823918i	$-0.308216\pi$
$239$	4187.81	1.13342	0.566709	+	0.823918i	$0.308216\pi$
$240$	904.496	0.243271
$241$	−153.223	−0.0409541	−0.0204770	−	0.999790i	$-0.506518\pi$
$241$	−153.223	−0.0409541	−0.0204770	+	0.999790i	$0.506518\pi$
$242$	−2091.81	−0.555647
$243$	−3435.41	−0.906921
$244$	−420.746	−0.110392
$245$	0	0
$246$	−733.811	−0.190187
$247$	3180.22	0.819241
$248$	5322.43	1.36280
$249$	869.715	0.221349
$250$	1432.26	0.362336
$251$	2366.18	0.595028	0.297514	−	0.954718i	$-0.403843\pi$
$251$	2366.18	0.595028	0.297514	+	0.954718i	$0.403843\pi$
$252$	0	0
$253$	3743.31	0.930196
$254$	−857.923	−0.211933
$255$	−633.293	−0.155523
$256$	−2000.88	−0.488497
$257$	−4954.58	−1.20256	−0.601280	−	0.799038i	$-0.705342\pi$
$257$	−4954.58	−1.20256	−0.601280	+	0.799038i	$0.705342\pi$
$258$	959.424	0.231516
$259$	0	0
$260$	−2506.91	−0.597968
$261$	494.735	0.117331
$262$	−216.344	−0.0510145
$263$	−1260.39	−0.295508	−0.147754	−	0.989024i	$-0.547204\pi$
$263$	−1260.39	−0.295508	−0.147754	+	0.989024i	$0.547204\pi$
$264$	1903.86	0.443843
$265$	11514.4	2.66915
$266$	0	0
$267$	1002.07	0.229683
$268$	−4790.67	−1.09193
$269$	1053.08	0.238690	0.119345	−	0.992853i	$-0.461921\pi$
$269$	1053.08	0.238690	0.119345	+	0.992853i	$0.461921\pi$
$270$	2176.92	0.490679
$271$	−6277.44	−1.40711	−0.703556	−	0.710640i	$-0.748405\pi$
$271$	−6277.44	−1.40711	−0.703556	+	0.710640i	$0.748405\pi$
$272$	−509.037	−0.113474
$273$	0	0
$274$	−1250.98	−0.275819
$275$	−10214.8	−2.23992
$276$	−828.151	−0.180612
$277$	3996.31	0.866842	0.433421	−	0.901192i	$-0.357306\pi$
$277$	3996.31	0.866842	0.433421	+	0.901192i	$0.357306\pi$
$278$	435.147	0.0938790
$279$	−6745.62	−1.44749
$280$	0	0
$281$	−2357.95	−0.500583	−0.250291	−	0.968171i	$-0.580526\pi$
$281$	−2357.95	−0.500583	−0.250291	+	0.968171i	$0.580526\pi$
$282$	−270.617	−0.0571455
$283$	1782.36	0.374383	0.187191	−	0.982323i	$-0.440062\pi$
$283$	1782.36	0.374383	0.187191	+	0.982323i	$0.440062\pi$
$284$	−2657.02	−0.555158
$285$	−4774.11	−0.992260
$286$	−1564.14	−0.323390
$287$	0	0
$288$	4269.82	0.873616
$289$	−4556.59	−0.927456
$290$	−481.434	−0.0974854
$291$	−2068.53	−0.416699
$292$	−586.248	−0.117492
$293$	−1402.33	−0.279607	−0.139804	−	0.990179i	$-0.544647\pi$
$293$	−1402.33	−0.279607	−0.139804	+	0.990179i	$0.544647\pi$
$294$	0	0
$295$	−2803.08	−0.553227
$296$	417.466	0.0819755
$297$	−5196.69	−1.01529
$298$	−3603.83	−0.700552
$299$	1538.58	0.297587
$300$	2259.88	0.434914
$301$	0	0
$302$	−740.939	−0.141180
$303$	1776.87	0.336893
$304$	−3837.40	−0.723981
$305$	−1173.46	−0.220302
$306$	−568.862	−0.106273
$307$	1807.51	0.336027	0.168013	−	0.985785i	$-0.446265\pi$
$307$	1807.51	0.336027	0.168013	+	0.985785i	$0.446265\pi$
$308$	0	0
$309$	−794.686	−0.146304
$310$	6564.26	1.20266
$311$	−9638.08	−1.75732	−0.878658	−	0.477451i	$-0.841561\pi$
$311$	−9638.08	−1.75732	−0.878658	+	0.477451i	$0.841561\pi$
$312$	782.530	0.141994
$313$	−5013.10	−0.905294	−0.452647	−	0.891690i	$-0.649520\pi$
$313$	−5013.10	−0.905294	−0.452647	+	0.891690i	$0.649520\pi$
$314$	−2094.82	−0.376489
$315$	0	0
$316$	4109.56	0.731584
$317$	7945.53	1.40778	0.703889	−	0.710310i	$-0.251445\pi$
$317$	7945.53	1.40778	0.703889	+	0.710310i	$0.251445\pi$
$318$	−1589.40	−0.280280
$319$	1149.26	0.201713
$320$	−339.437	−0.0592972
$321$	−2272.03	−0.395054
$322$	0	0
$323$	2686.80	0.462841
$324$	−2858.00	−0.490054
$325$	−4198.52	−0.716591
$326$	−1185.78	−0.201454
$327$	−831.083	−0.140547
$328$	−5549.68	−0.934237
$329$	0	0
$330$	2348.07	0.391688
$331$	4886.27	0.811402	0.405701	−	0.914006i	$-0.367028\pi$
$331$	4886.27	0.811402	0.405701	+	0.914006i	$0.367028\pi$
$332$	2908.63	0.480819
$333$	−529.094	−0.0870697
$334$	168.417	0.0275909
$335$	−13361.2	−2.17910
$336$	0	0
$337$	−7719.95	−1.24787	−0.623936	−	0.781476i	$-0.714467\pi$
$337$	−7719.95	−1.24787	−0.623936	+	0.781476i	$0.714467\pi$
$338$	2185.77	0.351745
$339$	−1883.70	−0.301796
$340$	−2117.95	−0.337830
$341$	−15670.0	−2.48850
$342$	−4288.40	−0.678041
$343$	0	0
$344$	7255.95	1.13725
$345$	−2309.71	−0.360436
$346$	−2536.07	−0.394046
$347$	−986.272	−0.152582	−0.0762908	−	0.997086i	$-0.524308\pi$
$347$	−986.272	−0.152582	−0.0762908	+	0.997086i	$0.524308\pi$
$348$	−254.257	−0.0391656
$349$	10931.2	1.67661	0.838304	−	0.545203i	$-0.183547\pi$
$349$	10931.2	1.67661	0.838304	+	0.545203i	$0.183547\pi$
$350$	0	0
$351$	−2135.96	−0.324812
$352$	9918.74	1.50191
$353$	−8667.34	−1.30684	−0.653422	−	0.756994i	$-0.726667\pi$
$353$	−8667.34	−1.30684	−0.653422	+	0.756994i	$0.726667\pi$
$354$	386.926	0.0580929
$355$	−7410.40	−1.10790
$356$	3351.26	0.498922
$357$	0	0
$358$	−2074.53	−0.306264
$359$	2302.46	0.338493	0.169247	−	0.985574i	$-0.445867\pi$
$359$	2302.46	0.338493	0.169247	+	0.985574i	$0.445867\pi$
$360$	7644.47	1.11916
$361$	13395.6	1.95299
$362$	−327.828	−0.0475973
$363$	−3081.11	−0.445499
$364$	0	0
$365$	−1635.04	−0.234471
$366$	161.979	0.0231333
$367$	−544.880	−0.0775000	−0.0387500	−	0.999249i	$-0.512338\pi$
$367$	−544.880	−0.0775000	−0.0387500	+	0.999249i	$0.512338\pi$
$368$	−1856.53	−0.262984
$369$	7033.63	0.992293
$370$	514.870	0.0723427
$371$	0	0
$372$	3466.75	0.483180
$373$	−386.955	−0.0537152	−0.0268576	−	0.999639i	$-0.508550\pi$
$373$	−386.955	−0.0537152	−0.0268576	+	0.999639i	$0.508550\pi$
$374$	−1321.46	−0.182703
$375$	2109.63	0.290509
$376$	−2046.63	−0.280710
$377$	472.373	0.0645317
$378$	0	0
$379$	4226.13	0.572776	0.286388	−	0.958114i	$-0.407545\pi$
$379$	4226.13	0.572776	0.286388	+	0.958114i	$0.407545\pi$
$380$	−15966.3	−2.15541
$381$	−1263.67	−0.169920
$382$	2114.29	0.283184
$383$	−4573.07	−0.610112	−0.305056	−	0.952334i	$-0.598675\pi$
$383$	−4573.07	−0.610112	−0.305056	+	0.952334i	$0.598675\pi$
$384$	−2721.06	−0.361611
$385$	0	0
$386$	5930.95	0.782065
$387$	−9196.15	−1.20792
$388$	−6917.89	−0.905161
$389$	12725.1	1.65859	0.829294	−	0.558813i	$-0.188743\pi$
$389$	12725.1	1.65859	0.829294	+	0.558813i	$0.188743\pi$
$390$	965.111	0.125308
$391$	1299.87	0.168126
$392$	0	0
$393$	−318.662	−0.0409017
$394$	4219.71	0.539558
$395$	11461.5	1.45998
$396$	−8069.74	−1.02404
$397$	−10949.5	−1.38422	−0.692112	−	0.721790i	$-0.743320\pi$
$397$	−10949.5	−1.38422	−0.692112	+	0.721790i	$0.743320\pi$
$398$	5037.28	0.634413
$399$	0	0
$400$	5066.14	0.633268
$401$	−945.233	−0.117712	−0.0588562	−	0.998266i	$-0.518745\pi$
$401$	−945.233	−0.117712	−0.0588562	+	0.998266i	$0.518745\pi$
$402$	1844.32	0.228821
$403$	−6440.72	−0.796117
$404$	5942.48	0.731806
$405$	−7970.93	−0.977972
$406$	0	0
$407$	−1229.08	−0.149689
$408$	661.119	0.0802212
$409$	107.347	0.0129779	0.00648893	−	0.999979i	$-0.497934\pi$
$409$	107.347	0.0129779	0.00648893	+	0.999979i	$0.497934\pi$
$410$	−6844.53	−0.824457
$411$	−1842.62	−0.221143
$412$	−2657.71	−0.317806
$413$	0	0
$414$	−2074.72	−0.246297
$415$	8112.16	0.959543
$416$	4076.83	0.480488
$417$	640.945	0.0752691
$418$	−9961.90	−1.16568
$419$	3428.70	0.399768	0.199884	−	0.979820i	$-0.435943\pi$
$419$	3428.70	0.399768	0.199884	+	0.979820i	$0.435943\pi$
$420$	0	0
$421$	11485.5	1.32962	0.664810	−	0.747013i	$-0.268513\pi$
$421$	11485.5	1.32962	0.664810	+	0.747013i	$0.268513\pi$
$422$	−2579.90	−0.297601
$423$	2593.89	0.298154
$424$	−12020.3	−1.37679
$425$	−3547.11	−0.404848
$426$	1022.90	0.116337
$427$	0	0
$428$	−7598.47	−0.858144
$429$	−2303.88	−0.259283
$430$	8948.91	1.00362
$431$	2944.25	0.329048	0.164524	−	0.986373i	$-0.447391\pi$
$431$	2944.25	0.329048	0.164524	+	0.986373i	$0.447391\pi$
$432$	2577.35	0.287043
$433$	−11899.5	−1.32068	−0.660338	−	0.750969i	$-0.729587\pi$
$433$	−11899.5	−1.32068	−0.660338	+	0.750969i	$0.729587\pi$
$434$	0	0
$435$	−709.122	−0.0781605
$436$	−2779.43	−0.305300
$437$	9799.13	1.07267
$438$	225.694	0.0246212
$439$	17180.0	1.86778	0.933892	−	0.357555i	$-0.116390\pi$
$439$	17180.0	1.86778	0.933892	+	0.357555i	$0.116390\pi$
$440$	17758.0	1.92405
$441$	0	0
$442$	−543.150	−0.0584502
$443$	4903.56	0.525903	0.262952	−	0.964809i	$-0.415304\pi$
$443$	4903.56	0.525903	0.262952	+	0.964809i	$0.415304\pi$
$444$	271.916	0.0290643
$445$	9346.64	0.995670
$446$	5310.04	0.563761
$447$	−5308.23	−0.561679
$448$	0	0
$449$	7514.56	0.789831	0.394915	−	0.918717i	$-0.370774\pi$
$449$	7514.56	0.789831	0.394915	+	0.918717i	$0.370774\pi$
$450$	5661.54	0.593083
$451$	16339.1	1.70593
$452$	−6299.77	−0.655567
$453$	−1091.36	−0.113193
$454$	1059.66	0.109542
$455$	0	0
$456$	4983.88	0.511824
$457$	14195.6	1.45305	0.726523	−	0.687142i	$-0.241135\pi$
$457$	14195.6	1.45305	0.726523	+	0.687142i	$0.241135\pi$
$458$	5493.05	0.560422
$459$	−1804.56	−0.183507
$460$	−7724.47	−0.782946
$461$	−3041.35	−0.307266	−0.153633	−	0.988128i	$-0.549097\pi$
$461$	−3041.35	−0.307266	−0.153633	+	0.988128i	$0.549097\pi$
$462$	0	0
$463$	6496.24	0.652064	0.326032	−	0.945359i	$-0.394288\pi$
$463$	6496.24	0.652064	0.326032	+	0.945359i	$0.394288\pi$
$464$	−569.988	−0.0570281
$465$	9668.75	0.964253
$466$	6211.90	0.617513
$467$	−5072.36	−0.502614	−0.251307	−	0.967907i	$-0.580860\pi$
$467$	−5072.36	−0.502614	−0.251307	+	0.967907i	$0.580860\pi$
$468$	−3316.84	−0.327609
$469$	0	0
$470$	−2524.15	−0.247724
$471$	−3085.54	−0.301856
$472$	2926.25	0.285363
$473$	−21362.6	−2.07664
$474$	−1582.10	−0.153309
$475$	−26740.1	−2.58299
$476$	0	0
$477$	15234.5	1.46235
$478$	−5391.85	−0.515936
$479$	−16661.5	−1.58932	−0.794661	−	0.607054i	$-0.792351\pi$
$479$	−16661.5	−1.58932	−0.794661	+	0.607054i	$0.792351\pi$
$480$	−6120.09	−0.581964
$481$	−505.180	−0.0478882
$482$	197.276	0.0186425
$483$	0	0
$484$	−10304.3	−0.967722
$485$	−19293.9	−1.80638
$486$	4423.13	0.412834
$487$	6337.12	0.589656	0.294828	−	0.955550i	$-0.404738\pi$
$487$	6337.12	0.589656	0.294828	+	0.955550i	$0.404738\pi$
$488$	1225.02	0.113635
$489$	−1746.58	−0.161519
$490$	0	0
$491$	16578.4	1.52378	0.761888	−	0.647709i	$-0.224273\pi$
$491$	16578.4	1.52378	0.761888	+	0.647709i	$0.224273\pi$
$492$	−3614.77	−0.331233
$493$	399.083	0.0364580
$494$	−4094.57	−0.372922
$495$	−22506.4	−2.04361
$496$	7771.69	0.703547
$497$	0	0
$498$	−1119.77	−0.100759
$499$	8376.16	0.751439	0.375720	−	0.926733i	$-0.377396\pi$
$499$	8376.16	0.751439	0.375720	+	0.926733i	$0.377396\pi$
$500$	7055.34	0.631049
$501$	248.068	0.0221215
$502$	−3046.48	−0.270859
$503$	17261.2	1.53010	0.765051	−	0.643970i	$-0.222714\pi$
$503$	17261.2	1.53010	0.765051	+	0.643970i	$0.222714\pi$
$504$	0	0
$505$	16573.5	1.46042
$506$	−4819.55	−0.423429
$507$	3219.50	0.282018
$508$	−4226.15	−0.369105
$509$	11454.8	0.997497	0.498748	−	0.866747i	$-0.333793\pi$
$509$	11454.8	0.997497	0.498748	+	0.866747i	$0.333793\pi$
$510$	815.372	0.0707946
$511$	0	0
$512$	−8902.53	−0.768438
$513$	−13603.8	−1.17080
$514$	6379.07	0.547410
$515$	−7412.33	−0.634226
$516$	4726.15	0.403212
$517$	6025.58	0.512581
$518$	0	0
$519$	−3735.48	−0.315933
$520$	7298.95	0.615539
$521$	15668.6	1.31757	0.658784	−	0.752332i	$-0.271071\pi$
$521$	15668.6	1.31757	0.658784	+	0.752332i	$0.271071\pi$
$522$	−636.976	−0.0534094
$523$	3653.52	0.305463	0.152732	−	0.988268i	$-0.451193\pi$
$523$	3653.52	0.305463	0.152732	+	0.988268i	$0.451193\pi$
$524$	−1065.72	−0.0888475
$525$	0	0
$526$	1622.76	0.134517
$527$	−5441.43	−0.449777
$528$	2779.98	0.229134
$529$	−7426.20	−0.610356
$530$	−14824.9	−1.21501
$531$	−3708.71	−0.303097
$532$	0	0
$533$	6715.72	0.545760
$534$	−1290.17	−0.104553
$535$	−21192.1	−1.71255
$536$	13948.2	1.12401
$537$	−3055.66	−0.245552
$538$	−1355.86	−0.108653
$539$	0	0
$540$	10723.6	0.854574
$541$	10062.6	0.799673	0.399836	−	0.916587i	$-0.369067\pi$
$541$	10062.6	0.799673	0.399836	+	0.916587i	$0.369067\pi$
$542$	8082.27	0.640523
$543$	−482.870	−0.0381620
$544$	3444.30	0.271458
$545$	−7751.82	−0.609269
$546$	0	0
$547$	734.682	0.0574273	0.0287137	−	0.999588i	$-0.490859\pi$
$547$	734.682	0.0574273	0.0287137	+	0.999588i	$0.490859\pi$
$548$	−6162.37	−0.480371
$549$	−1552.58	−0.120697
$550$	13151.7	1.01962
$551$	3008.51	0.232608
$552$	2411.19	0.185919
$553$	0	0
$554$	−5145.30	−0.394590
$555$	758.372	0.0580020
$556$	2143.55	0.163501
$557$	3149.41	0.239578	0.119789	−	0.992799i	$-0.461778\pi$
$557$	3149.41	0.239578	0.119789	+	0.992799i	$0.461778\pi$
$558$	8685.06	0.658903
$559$	−8780.50	−0.664357
$560$	0	0
$561$	−1946.43	−0.146485
$562$	3035.89	0.227867
$563$	−24155.8	−1.80825	−0.904125	−	0.427269i	$-0.859476\pi$
$563$	−24155.8	−1.80825	−0.904125	+	0.427269i	$0.859476\pi$
$564$	−1333.07	−0.0995254
$565$	−17570.0	−1.30828
$566$	−2294.81	−0.170421
$567$	0	0
$568$	7736.00	0.571471
$569$	−3957.28	−0.291560	−0.145780	−	0.989317i	$-0.546569\pi$
$569$	−3957.28	−0.291560	−0.145780	+	0.989317i	$0.546569\pi$
$570$	6146.72	0.451681
$571$	26858.4	1.96845	0.984227	−	0.176911i	$-0.0566106\pi$
$571$	26858.4	1.96845	0.984227	+	0.176911i	$0.0566106\pi$
$572$	−7705.00	−0.563221
$573$	3114.22	0.227048
$574$	0	0
$575$	−12936.8	−0.938265
$576$	−449.103	−0.0324872
$577$	−11321.0	−0.816807	−0.408403	−	0.912802i	$-0.633914\pi$
$577$	−11321.0	−0.816807	−0.408403	+	0.912802i	$0.633914\pi$
$578$	5866.66	0.422182
$579$	8735.92	0.627034
$580$	−2371.55	−0.169782
$581$	0	0
$582$	2663.25	0.189683
$583$	35389.6	2.51405
$584$	1706.88	0.120944
$585$	−9250.65	−0.653791
$586$	1805.51	0.127278
$587$	−13346.6	−0.938457	−0.469228	−	0.883077i	$-0.655468\pi$
$587$	−13346.6	−0.938457	−0.469228	+	0.883077i	$0.655468\pi$
$588$	0	0
$589$	−41020.5	−2.86965
$590$	3609.00	0.251831
$591$	6215.37	0.432600
$592$	609.575	0.0423199
$593$	−44.0713	−0.00305193	−0.00152596	−	0.999999i	$-0.500486\pi$
$593$	−44.0713	−0.00305193	−0.00152596	+	0.999999i	$0.500486\pi$
$594$	6690.79	0.462166
$595$	0	0
$596$	−17752.6	−1.22009
$597$	7419.61	0.508651
$598$	−1980.94	−0.135463
$599$	9857.44	0.672394	0.336197	−	0.941792i	$-0.390859\pi$
$599$	9857.44	0.672394	0.336197	+	0.941792i	$0.390859\pi$
$600$	−6579.72	−0.447693
$601$	211.872	0.0143801	0.00719004	−	0.999974i	$-0.497711\pi$
$601$	211.872	0.0143801	0.00719004	+	0.999974i	$0.497711\pi$
$602$	0	0
$603$	−17677.9	−1.19386
$604$	−3649.89	−0.245880
$605$	−28738.6	−1.93123
$606$	−2287.74	−0.153355
$607$	−8525.32	−0.570069	−0.285035	−	0.958517i	$-0.592005\pi$
$607$	−8525.32	−0.570069	−0.285035	+	0.958517i	$0.592005\pi$
$608$	25965.0	1.73194
$609$	0	0
$610$	1510.84	0.100282
$611$	2476.65	0.163984
$612$	−2802.23	−0.185087
$613$	−17462.6	−1.15058	−0.575290	−	0.817949i	$-0.695111\pi$
$613$	−17462.6	−1.15058	−0.575290	+	0.817949i	$0.695111\pi$
$614$	−2327.19	−0.152961
$615$	−10081.6	−0.661022
$616$	0	0
$617$	−5038.50	−0.328756	−0.164378	−	0.986397i	$-0.552562\pi$
$617$	−5038.50	−0.328756	−0.164378	+	0.986397i	$0.552562\pi$
$618$	1023.17	0.0665984
$619$	−2817.27	−0.182933	−0.0914665	−	0.995808i	$-0.529155\pi$
$619$	−2817.27	−0.182933	−0.0914665	+	0.995808i	$0.529155\pi$
$620$	32335.7	2.09457
$621$	−6581.47	−0.425290
$622$	12409.1	0.799937
$623$	0	0
$624$	1142.63	0.0733044
$625$	−3808.84	−0.243766
$626$	6454.42	0.412093
$627$	−14673.3	−0.934600
$628$	−10319.1	−0.655698
$629$	−426.800	−0.0270551
$630$	0	0
$631$	−25505.9	−1.60915	−0.804575	−	0.593850i	$-0.797607\pi$
$631$	−25505.9	−1.60915	−0.804575	+	0.593850i	$0.797607\pi$
$632$	−11965.1	−0.753081
$633$	−3800.04	−0.238607
$634$	−10230.0	−0.640826
$635$	−11786.7	−0.736600
$636$	−7829.43	−0.488140
$637$	0	0
$638$	−1479.69	−0.0918205
$639$	−9804.56	−0.606984
$640$	−25380.4	−1.56757
$641$	−8549.68	−0.526821	−0.263410	−	0.964684i	$-0.584847\pi$
$641$	−8549.68	−0.526821	−0.263410	+	0.964684i	$0.584847\pi$
$642$	2925.26	0.179830
$643$	−5867.35	−0.359853	−0.179927	−	0.983680i	$-0.557586\pi$
$643$	−5867.35	−0.359853	−0.179927	+	0.983680i	$0.557586\pi$
$644$	0	0
$645$	13181.2	0.804665
$646$	−3459.28	−0.210687
$647$	11791.9	0.716519	0.358259	−	0.933622i	$-0.383370\pi$
$647$	11791.9	0.716519	0.358259	+	0.933622i	$0.383370\pi$
$648$	8321.16	0.504454
$649$	−8615.30	−0.521079
$650$	5405.65	0.326195
$651$	0	0
$652$	−5841.17	−0.350856
$653$	−3103.93	−0.186013	−0.0930063	−	0.995666i	$-0.529648\pi$
$653$	−3103.93	−0.186013	−0.0930063	+	0.995666i	$0.529648\pi$
$654$	1070.03	0.0639777
$655$	−2972.28	−0.177308
$656$	−8103.51	−0.482300
$657$	−2163.30	−0.128460
$658$	0	0
$659$	−24085.7	−1.42374	−0.711870	−	0.702311i	$-0.752152\pi$
$659$	−24085.7	−1.42374	−0.711870	+	0.702311i	$0.752152\pi$
$660$	11566.7	0.682170
$661$	13968.3	0.821944	0.410972	−	0.911648i	$-0.365189\pi$
$661$	13968.3	0.821944	0.410972	+	0.911648i	$0.365189\pi$
$662$	−6291.13	−0.369353
$663$	−800.027	−0.0468634
$664$	−8468.60	−0.494948
$665$	0	0
$666$	681.215	0.0396345
$667$	1455.51	0.0844943
$668$	829.626	0.0480527
$669$	7821.36	0.452005
$670$	17202.6	0.991934
$671$	−3606.64	−0.207500
$672$	0	0
$673$	2683.77	0.153717	0.0768585	−	0.997042i	$-0.475511\pi$
$673$	2683.77	0.153717	0.0768585	+	0.997042i	$0.475511\pi$
$674$	9939.53	0.568036
$675$	17959.7	1.02410
$676$	10767.1	0.612605
$677$	−18991.2	−1.07812	−0.539062	−	0.842266i	$-0.681221\pi$
$677$	−18991.2	−1.07812	−0.539062	+	0.842266i	$0.681221\pi$
$678$	2425.29	0.137379
$679$	0	0
$680$	6166.50	0.347757
$681$	1560.81	0.0878275
$682$	20175.3	1.13277
$683$	−10784.0	−0.604156	−0.302078	−	0.953283i	$-0.597680\pi$
$683$	−10784.0	−0.604156	−0.302078	+	0.953283i	$0.597680\pi$
$684$	−21124.8	−1.18088
$685$	−17186.8	−0.958648
$686$	0	0
$687$	8090.92	0.449327
$688$	10595.0	0.587107
$689$	14545.9	0.804290
$690$	2973.77	0.164072
$691$	23442.0	1.29056	0.645278	−	0.763948i	$-0.276742\pi$
$691$	23442.0	1.29056	0.645278	+	0.763948i	$0.276742\pi$
$692$	−12492.8	−0.686276
$693$	0	0
$694$	1269.84	0.0694558
$695$	5978.33	0.326289
$696$	740.280	0.0403165
$697$	5673.76	0.308334
$698$	−14074.1	−0.763199
$699$	9149.75	0.495101
$700$	0	0
$701$	−9964.55	−0.536884	−0.268442	−	0.963296i	$-0.586509\pi$
$701$	−9964.55	−0.536884	−0.268442	+	0.963296i	$0.586509\pi$
$702$	2750.07	0.147856
$703$	−3217.46	−0.172616
$704$	−1043.26	−0.0558514
$705$	−3717.92	−0.198617
$706$	11159.3	0.594880
$707$	0	0
$708$	1906.01	0.101175
$709$	−18551.9	−0.982693	−0.491347	−	0.870964i	$-0.663495\pi$
$709$	−18551.9	−0.982693	−0.491347	+	0.870964i	$0.663495\pi$
$710$	9540.97	0.504319
$711$	15164.5	0.799880
$712$	−9757.32	−0.513583
$713$	−19845.7	−1.04239
$714$	0	0
$715$	−21489.2	−1.12399
$716$	−10219.2	−0.533394
$717$	−7941.87	−0.413660
$718$	−2964.44	−0.154083
$719$	28785.2	1.49305	0.746526	−	0.665356i	$-0.231720\pi$
$719$	28785.2	1.49305	0.746526	+	0.665356i	$0.231720\pi$
$720$	11162.3	0.577769
$721$	0	0
$722$	−17247.0	−0.889011
$723$	290.575	0.0149469
$724$	−1614.89	−0.0828962
$725$	−3971.84	−0.203463
$726$	3966.96	0.202793
$727$	25151.4	1.28310	0.641550	−	0.767081i	$-0.278292\pi$
$727$	25151.4	1.28310	0.641550	+	0.767081i	$0.278292\pi$
$728$	0	0
$729$	−5651.83	−0.287143
$730$	2105.14	0.106732
$731$	−7418.18	−0.375337
$732$	797.914	0.0402893
$733$	27478.0	1.38462	0.692308	−	0.721602i	$-0.256594\pi$
$733$	27478.0	1.38462	0.692308	+	0.721602i	$0.256594\pi$
$734$	701.539	0.0352783
$735$	0	0
$736$	12561.8	0.629124
$737$	−41065.6	−2.05247
$738$	−9055.88	−0.451696
$739$	615.572	0.0306416	0.0153208	−	0.999883i	$-0.495123\pi$
$739$	615.572	0.0306416	0.0153208	+	0.999883i	$0.495123\pi$
$740$	2536.26	0.125993
$741$	−6031.05	−0.298996
$742$	0	0
$743$	−444.555	−0.0219504	−0.0109752	−	0.999940i	$-0.503494\pi$
$743$	−444.555	−0.0219504	−0.0109752	+	0.999940i	$0.503494\pi$
$744$	−10093.6	−0.497378
$745$	−49511.8	−2.43486
$746$	498.209	0.0244514
$747$	10733.1	0.525706
$748$	−6509.55	−0.318199
$749$	0	0
$750$	−2716.17	−0.132241
$751$	18345.1	0.891376	0.445688	−	0.895188i	$-0.352959\pi$
$751$	18345.1	0.891376	0.445688	+	0.895188i	$0.352959\pi$
$752$	−2988.44	−0.144917
$753$	−4487.28	−0.217166
$754$	−608.186	−0.0293751
$755$	−10179.5	−0.490689
$756$	0	0
$757$	38880.3	1.86675	0.933375	−	0.358904i	$-0.116849\pi$
$757$	38880.3	1.86675	0.933375	+	0.358904i	$0.116849\pi$
$758$	−5441.20	−0.260730
$759$	−7098.90	−0.339491
$760$	46486.5	2.21874
$761$	34487.5	1.64280	0.821401	−	0.570351i	$-0.193193\pi$
$761$	34487.5	1.64280	0.821401	+	0.570351i	$0.193193\pi$
$762$	1626.99	0.0773485
$763$	0	0
$764$	10415.0	0.493198
$765$	−7815.39	−0.369367
$766$	5887.87	0.277725
$767$	−3541.08	−0.166703
$768$	3794.53	0.178285
$769$	−7962.54	−0.373389	−0.186695	−	0.982418i	$-0.559778\pi$
$769$	−7962.54	−0.373389	−0.186695	+	0.982418i	$0.559778\pi$
$770$	0	0
$771$	9395.99	0.438895
$772$	29216.0	1.36206
$773$	−15568.6	−0.724404	−0.362202	−	0.932100i	$-0.617975\pi$
$773$	−15568.6	−0.724404	−0.362202	+	0.932100i	$0.617975\pi$
$774$	11840.1	0.549852
$775$	54155.3	2.51008
$776$	20141.7	0.931759
$777$	0	0
$778$	−16383.8	−0.754996
$779$	42772.0	1.96722
$780$	4754.16	0.218239
$781$	−22775.9	−1.04352
$782$	−1673.60	−0.0765315
$783$	−2020.63	−0.0922241
$784$	0	0
$785$	−28780.0	−1.30854
$786$	410.281	0.0186186
$787$	26353.5	1.19365	0.596823	−	0.802373i	$-0.296429\pi$
$787$	26353.5	1.19365	0.596823	+	0.802373i	$0.296429\pi$
$788$	20786.4	0.939701
$789$	2390.23	0.107851
$790$	−14756.8	−0.664588
$791$	0	0
$792$	23495.4	1.05413
$793$	−1482.41	−0.0663832
$794$	14097.5	0.630105
$795$	−21836.2	−0.974152
$796$	24813.8	1.10490
$797$	−36310.7	−1.61379	−0.806894	−	0.590696i	$-0.798853\pi$
$797$	−36310.7	−1.61379	−0.806894	+	0.590696i	$0.798853\pi$
$798$	0	0
$799$	2092.39	0.0926451
$800$	−34279.0	−1.51493
$801$	12366.4	0.545498
$802$	1217.00	0.0535831
$803$	−5025.32	−0.220846
$804$	9085.15	0.398518
$805$	0	0
$806$	8292.50	0.362396
$807$	−1997.09	−0.0871141
$808$	−17301.8	−0.753309
$809$	−7029.26	−0.305483	−0.152741	−	0.988266i	$-0.548810\pi$
$809$	−7029.26	−0.305483	−0.152741	+	0.988266i	$0.548810\pi$
$810$	10262.7	0.445177
$811$	−29509.8	−1.27772	−0.638858	−	0.769325i	$-0.720593\pi$
$811$	−29509.8	−1.27772	−0.638858	+	0.769325i	$0.720593\pi$
$812$	0	0
$813$	11904.7	0.513550
$814$	1582.46	0.0681389
$815$	−16291.0	−0.700182
$816$	965.351	0.0414143
$817$	−55922.4	−2.39471
$818$	−138.210	−0.00590757
$819$	0	0
$820$	−33716.3	−1.43589
$821$	−28217.8	−1.19952	−0.599761	−	0.800179i	$-0.704738\pi$
$821$	−28217.8	−1.19952	−0.599761	+	0.800179i	$0.704738\pi$
$822$	2372.39	0.100665
$823$	19670.0	0.833114	0.416557	−	0.909110i	$-0.363237\pi$
$823$	19670.0	0.833114	0.416557	+	0.909110i	$0.363237\pi$
$824$	7738.02	0.327144
$825$	19371.7	0.817497
$826$	0	0
$827$	40500.5	1.70295	0.851476	−	0.524394i	$-0.175708\pi$
$827$	40500.5	1.70295	0.851476	+	0.524394i	$0.175708\pi$
$828$	−10220.1	−0.428953
$829$	41083.0	1.72120	0.860599	−	0.509284i	$-0.170090\pi$
$829$	41083.0	1.72120	0.860599	+	0.509284i	$0.170090\pi$
$830$	−10444.5	−0.436788
$831$	−7578.71	−0.316369
$832$	−428.804	−0.0178679
$833$	0	0
$834$	−825.224	−0.0342628
$835$	2313.82	0.0958959
$836$	−49072.6	−2.03016
$837$	27551.0	1.13775
$838$	−4414.49	−0.181976
$839$	18138.9	0.746394	0.373197	−	0.927752i	$-0.378261\pi$
$839$	18138.9	0.746394	0.373197	+	0.927752i	$0.378261\pi$
$840$	0	0
$841$	−23942.1	−0.981677
$842$	−14787.7	−0.605248
$843$	4471.69	0.182696
$844$	−12708.7	−0.518306
$845$	30029.5	1.22254
$846$	−3339.66	−0.135721
$847$	0	0
$848$	−17551.8	−0.710769
$849$	−3380.11	−0.136637
$850$	4566.95	0.184288
$851$	−1556.60	−0.0627022
$852$	5038.83	0.202614
$853$	−33781.0	−1.35597	−0.677983	−	0.735077i	$-0.737146\pi$
$853$	−33781.0	−1.35597	−0.677983	+	0.735077i	$0.737146\pi$
$854$	0	0
$855$	−58916.8	−2.35662
$856$	22123.2	0.883360
$857$	−7731.44	−0.308169	−0.154084	−	0.988058i	$-0.549243\pi$
$857$	−7731.44	−0.308169	−0.154084	+	0.988058i	$0.549243\pi$
$858$	2966.28	0.118027
$859$	44733.8	1.77683	0.888415	−	0.459042i	$-0.151807\pi$
$859$	44733.8	1.77683	0.888415	+	0.459042i	$0.151807\pi$
$860$	44082.6	1.74791
$861$	0	0
$862$	−3790.75	−0.149784
$863$	44308.7	1.74772	0.873861	−	0.486176i	$-0.161608\pi$
$863$	44308.7	1.74772	0.873861	+	0.486176i	$0.161608\pi$
$864$	−17439.1	−0.686679
$865$	−34842.2	−1.36956
$866$	15320.7	0.601177
$867$	8641.24	0.338491
$868$	0	0
$869$	35227.1	1.37514
$870$	913.003	0.0355790
$871$	−16878.9	−0.656624
$872$	8092.43	0.314271
$873$	−25527.5	−0.989661
$874$	−12616.5	−0.488283
$875$	0	0
$876$	1111.78	0.0428806
$877$	−25895.6	−0.997071	−0.498536	−	0.866869i	$-0.666129\pi$
$877$	−25895.6	−0.997071	−0.498536	+	0.866869i	$0.666129\pi$
$878$	−22119.5	−0.850223
$879$	2659.41	0.102047
$880$	25929.9	0.993291
$881$	37589.2	1.43747	0.718735	−	0.695284i	$-0.244721\pi$
$881$	37589.2	1.43747	0.718735	+	0.695284i	$0.244721\pi$
$882$	0	0
$883$	17136.2	0.653091	0.326546	−	0.945181i	$-0.394115\pi$
$883$	17136.2	0.653091	0.326546	+	0.945181i	$0.394115\pi$
$884$	−2675.57	−0.101798
$885$	5315.84	0.201910
$886$	−6313.39	−0.239393
$887$	−10739.1	−0.406522	−0.203261	−	0.979125i	$-0.565154\pi$
$887$	−10739.1	−0.406522	−0.203261	+	0.979125i	$0.565154\pi$
$888$	−791.694	−0.0299184
$889$	0	0
$890$	−12033.9	−0.453233
$891$	−24498.7	−0.921143
$892$	26157.4	0.981854
$893$	15773.6	0.591090
$894$	6834.40	0.255678
$895$	−28501.3	−1.06446
$896$	0	0
$897$	−2917.81	−0.108610
$898$	−9675.08	−0.359534
$899$	−6092.98	−0.226043
$900$	27888.9	1.03292
$901$	12289.1	0.454394
$902$	−21036.7	−0.776548
$903$	0	0
$904$	18342.0	0.674830
$905$	−4503.91	−0.165431
$906$	1405.14	0.0515259
$907$	−37276.9	−1.36467	−0.682337	−	0.731038i	$-0.739036\pi$
$907$	−37276.9	−1.36467	−0.682337	+	0.731038i	$0.739036\pi$
$908$	5219.91	0.190781
$909$	21928.2	0.800122
$910$	0	0
$911$	−8784.15	−0.319464	−0.159732	−	0.987160i	$-0.551063\pi$
$911$	−8784.15	−0.319464	−0.159732	+	0.987160i	$0.551063\pi$
$912$	7277.35	0.264229
$913$	24932.8	0.903784
$914$	−18277.0	−0.661432
$915$	2225.38	0.0804030
$916$	27058.9	0.976038
$917$	0	0
$918$	2323.39	0.0835329
$919$	45883.4	1.64696	0.823478	−	0.567348i	$-0.192031\pi$
$919$	45883.4	1.64696	0.823478	+	0.567348i	$0.192031\pi$
$920$	22490.1	0.805953
$921$	−3427.82	−0.122639
$922$	3915.77	0.139869
$923$	−9361.41	−0.333840
$924$	0	0
$925$	4247.69	0.150987
$926$	−8363.98	−0.296822
$927$	−9807.12	−0.347474
$928$	3856.71	0.136425
$929$	−7436.36	−0.262626	−0.131313	−	0.991341i	$-0.541919\pi$
$929$	−7436.36	−0.262626	−0.131313	+	0.991341i	$0.541919\pi$
$930$	−12448.6	−0.438932
$931$	0	0
$932$	30600.0	1.07547
$933$	18277.9	0.641363
$934$	6530.72	0.228792
$935$	−18155.1	−0.635010
$936$	9657.12	0.337236
$937$	−24305.8	−0.847422	−0.423711	−	0.905797i	$-0.639273\pi$
$937$	−24305.8	−0.847422	−0.423711	+	0.905797i	$0.639273\pi$
$938$	0	0
$939$	9506.96	0.330403
$940$	−12434.0	−0.431440
$941$	−19655.8	−0.680935	−0.340467	−	0.940256i	$-0.610585\pi$
$941$	−19655.8	−0.680935	−0.340467	+	0.940256i	$0.610585\pi$
$942$	3972.67	0.137406
$943$	20693.0	0.714588
$944$	4272.84	0.147319
$945$	0	0
$946$	27504.5	0.945296
$947$	26104.7	0.895763	0.447881	−	0.894093i	$-0.352179\pi$
$947$	26104.7	0.895763	0.447881	+	0.894093i	$0.352179\pi$
$948$	−7793.47	−0.267004
$949$	−2065.52	−0.0706528
$950$	34428.2	1.17579
$951$	−15068.1	−0.513793
$952$	0	0
$953$	35041.7	1.19109	0.595547	−	0.803320i	$-0.296935\pi$
$953$	35041.7	1.19109	0.595547	+	0.803320i	$0.296935\pi$
$954$	−19614.6	−0.665667
$955$	29047.5	0.984245
$956$	−26560.4	−0.898562
$957$	−2179.49	−0.0736186
$958$	21451.9	0.723465
$959$	0	0
$960$	643.716	0.0216415
$961$	53285.7	1.78865
$962$	650.425	0.0217989
$963$	−28038.9	−0.938255
$964$	971.786	0.0324680
$965$	81483.2	2.71817
$966$	0	0
$967$	7654.73	0.254560	0.127280	−	0.991867i	$-0.459375\pi$
$967$	7654.73	0.254560	0.127280	+	0.991867i	$0.459375\pi$
$968$	30001.4	0.996158
$969$	−5095.32	−0.168922
$970$	24841.2	0.822270
$971$	55772.2	1.84327	0.921635	−	0.388058i	$-0.126854\pi$
$971$	55772.2	1.84327	0.921635	+	0.388058i	$0.126854\pi$
$972$	21788.5	0.718997
$973$	0	0
$974$	−8159.12	−0.268414
$975$	7962.19	0.261532
$976$	1788.75	0.0586643
$977$	14042.1	0.459823	0.229912	−	0.973212i	$-0.426156\pi$
$977$	14042.1	0.459823	0.229912	+	0.973212i	$0.426156\pi$
$978$	2248.74	0.0735242
$979$	28727.0	0.937812
$980$	0	0
$981$	−10256.3	−0.333801
$982$	−21344.9	−0.693629
$983$	−10477.8	−0.339969	−0.169985	−	0.985447i	$-0.554372\pi$
$983$	−10477.8	−0.339969	−0.169985	+	0.985447i	$0.554372\pi$
$984$	10524.6	0.340966
$985$	57973.1	1.87531
$986$	−513.824	−0.0165958
$987$	0	0
$988$	−20169.9	−0.649485
$989$	−27055.1	−0.869872
$990$	28977.3	0.930262
$991$	−40266.9	−1.29074	−0.645368	−	0.763872i	$-0.723296\pi$
$991$	−40266.9	−1.29074	−0.645368	+	0.763872i	$0.723296\pi$
$992$	−52585.6	−1.68306
$993$	−9266.46	−0.296135
$994$	0	0
$995$	69205.5	2.20499
$996$	−5516.01	−0.175483
$997$	48152.8	1.52960	0.764801	−	0.644266i	$-0.222837\pi$
$997$	48152.8	1.52960	0.764801	+	0.644266i	$0.222837\pi$
$998$	−10784.4	−0.342058
$999$	2160.97	0.0684384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.17		39
7.6	odd	2		2401.4.a.d.1.17		39
49.20	odd	14		49.4.e.a.8.6	✓	78
49.27	odd	14		49.4.e.a.43.6	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.6	✓	78	49.20	odd	14
49.4.e.a.43.6	yes	78	49.27	odd	14
2401.4.a.c.1.17		39	1.1	even	1	trivial
2401.4.a.d.1.17		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)

\(f(q)\)	\(=\)	\(q-1.28751 q^{2} -1.89643 q^{3} -6.34231 q^{4} -17.6887 q^{5} +2.44167 q^{6} +18.4659 q^{8} -23.4036 q^{9} +O(q^{10})\)	\(q-1.28751 q^{2} -1.89643 q^{3} -6.34231 q^{4} -17.6887 q^{5} +2.44167 q^{6} +18.4659 q^{8} -23.4036 q^{9} +22.7744 q^{10} -54.3663 q^{11} +12.0277 q^{12} -22.3458 q^{13} +33.5452 q^{15} +26.9635 q^{16} -18.8788 q^{17} +30.1324 q^{18} -142.319 q^{19} +112.187 q^{20} +69.9972 q^{22} -68.8535 q^{23} -35.0192 q^{24} +187.889 q^{25} +28.7704 q^{26} +95.5866 q^{27} -21.1393 q^{29} -43.1899 q^{30} +288.230 q^{31} -182.443 q^{32} +103.102 q^{33} +24.3066 q^{34} +148.433 q^{36} +22.6074 q^{37} +183.237 q^{38} +42.3771 q^{39} -326.637 q^{40} -300.537 q^{41} +392.938 q^{43} +344.808 q^{44} +413.978 q^{45} +88.6496 q^{46} -110.833 q^{47} -51.1342 q^{48} -241.909 q^{50} +35.8022 q^{51} +141.724 q^{52} -650.948 q^{53} -123.069 q^{54} +961.667 q^{55} +269.897 q^{57} +27.2171 q^{58} +158.468 q^{59} -212.755 q^{60} +66.3396 q^{61} -371.100 q^{62} +19.1895 q^{64} +395.267 q^{65} -132.744 q^{66} +755.351 q^{67} +119.735 q^{68} +130.575 q^{69} +418.935 q^{71} -432.168 q^{72} +92.4344 q^{73} -29.1073 q^{74} -356.318 q^{75} +902.629 q^{76} -54.5610 q^{78} -647.958 q^{79} -476.948 q^{80} +450.623 q^{81} +386.944 q^{82} -458.608 q^{83} +333.940 q^{85} -505.912 q^{86} +40.0891 q^{87} -1003.92 q^{88} -528.397 q^{89} -533.001 q^{90} +436.690 q^{92} -546.607 q^{93} +142.699 q^{94} +2517.43 q^{95} +345.989 q^{96} +1090.75 q^{97} +1272.36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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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