LMFDB - Embedded newform 6025.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.566303 q^{2} +0.484852 q^{3} -1.67930 q^{4} +0.274573 q^{6} +0.0113879 q^{7} -2.08360 q^{8} -2.76492 q^{9} +O(q^{10})$	\(q+0.566303 q^{2} +0.484852 q^{3} -1.67930 q^{4} +0.274573 q^{6} +0.0113879 q^{7} -2.08360 q^{8} -2.76492 q^{9} -0.725562 q^{11} -0.814212 q^{12} +3.41734 q^{13} +0.00644902 q^{14} +2.17866 q^{16} -3.34481 q^{17} -1.56578 q^{18} +2.32799 q^{19} +0.00552146 q^{21} -0.410888 q^{22} +4.69054 q^{23} -1.01024 q^{24} +1.93525 q^{26} -2.79513 q^{27} -0.0191238 q^{28} +5.86959 q^{29} -0.631035 q^{31} +5.40097 q^{32} -0.351790 q^{33} -1.89417 q^{34} +4.64313 q^{36} -3.86827 q^{37} +1.31835 q^{38} +1.65690 q^{39} -0.320097 q^{41} +0.00312682 q^{42} +3.06079 q^{43} +1.21844 q^{44} +2.65627 q^{46} -10.6540 q^{47} +1.05633 q^{48} -6.99987 q^{49} -1.62174 q^{51} -5.73875 q^{52} -0.842935 q^{53} -1.58289 q^{54} -0.0237279 q^{56} +1.12873 q^{57} +3.32396 q^{58} +10.2157 q^{59} -2.52565 q^{61} -0.357357 q^{62} -0.0314867 q^{63} -1.29872 q^{64} -0.199220 q^{66} -8.96869 q^{67} +5.61694 q^{68} +2.27422 q^{69} +10.7516 q^{71} +5.76098 q^{72} -5.27340 q^{73} -2.19061 q^{74} -3.90940 q^{76} -0.00826265 q^{77} +0.938310 q^{78} +6.07465 q^{79} +6.93953 q^{81} -0.181272 q^{82} +0.282048 q^{83} -0.00927220 q^{84} +1.73333 q^{86} +2.84588 q^{87} +1.51178 q^{88} +4.26717 q^{89} +0.0389165 q^{91} -7.87683 q^{92} -0.305959 q^{93} -6.03339 q^{94} +2.61867 q^{96} -17.9265 q^{97} -3.96405 q^{98} +2.00612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * 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 $

$2$	0.566303	0.400436	0.200218	−	0.979751i	$-0.435835\pi$
$2$	0.566303	0.400436	0.200218	+	0.979751i	$0.435835\pi$
$3$	0.484852	0.279929	0.139965	−	0.990156i	$-0.455301\pi$
$3$	0.484852	0.279929	0.139965	+	0.990156i	$0.455301\pi$
$4$	−1.67930	−0.839651
$5$	0	0
$5$	0	0
$6$	0.274573	0.112094
$7$	0.0113879	0.00430423	0.00215212	−	0.999998i	$-0.499315\pi$
$7$	0.0113879	0.00430423	0.00215212	+	0.999998i	$0.499315\pi$
$8$	−2.08360	−0.736663
$9$	−2.76492	−0.921640
$10$	0	0
$11$	−0.725562	−0.218765	−0.109383	−	0.994000i	$-0.534887\pi$
$11$	−0.725562	−0.218765	−0.109383	+	0.994000i	$0.534887\pi$
$12$	−0.814212	−0.235043
$13$	3.41734	0.947800	0.473900	−	0.880579i	$-0.342846\pi$
$13$	3.41734	0.947800	0.473900	+	0.880579i	$0.342846\pi$
$14$	0.00644902	0.00172357
$15$	0	0
$16$	2.17866	0.544664
$17$	−3.34481	−0.811235	−0.405618	−	0.914043i	$-0.632944\pi$
$17$	−3.34481	−0.811235	−0.405618	+	0.914043i	$0.632944\pi$
$18$	−1.56578	−0.369058
$19$	2.32799	0.534078	0.267039	−	0.963686i	$-0.413955\pi$
$19$	2.32799	0.534078	0.267039	+	0.963686i	$0.413955\pi$
$20$	0	0
$21$	0.00552146	0.00120488
$22$	−0.410888	−0.0876016
$23$	4.69054	0.978046	0.489023	−	0.872271i	$-0.337353\pi$
$23$	4.69054	0.978046	0.489023	+	0.872271i	$0.337353\pi$
$24$	−1.01024	−0.206214
$25$	0	0
$26$	1.93525	0.379534
$27$	−2.79513	−0.537923
$28$	−0.0191238	−0.00361405
$29$	5.86959	1.08996	0.544978	−	0.838451i	$-0.316538\pi$
$29$	5.86959	1.08996	0.544978	+	0.838451i	$0.316538\pi$
$30$	0	0
$31$	−0.631035	−0.113337	−0.0566687	−	0.998393i	$-0.518048\pi$
$31$	−0.631035	−0.113337	−0.0566687	+	0.998393i	$0.518048\pi$
$32$	5.40097	0.954766
$33$	−0.351790	−0.0612388
$34$	−1.89417	−0.324848
$35$	0	0
$36$	4.64313	0.773855
$37$	−3.86827	−0.635939	−0.317970	−	0.948101i	$-0.603001\pi$
$37$	−3.86827	−0.635939	−0.317970	+	0.948101i	$0.603001\pi$
$38$	1.31835	0.213864
$39$	1.65690	0.265317
$40$	0	0
$41$	−0.320097	−0.0499907	−0.0249954	−	0.999688i	$-0.507957\pi$
$41$	−0.320097	−0.0499907	−0.0249954	+	0.999688i	$0.507957\pi$
$42$	0.00312682	0.000482479 0
$43$	3.06079	0.466766	0.233383	−	0.972385i	$-0.425020\pi$
$43$	3.06079	0.466766	0.233383	+	0.972385i	$0.425020\pi$
$44$	1.21844	0.183686
$45$	0	0
$46$	2.65627	0.391645
$47$	−10.6540	−1.55405	−0.777023	−	0.629472i	$-0.783271\pi$
$47$	−10.6540	−1.55405	−0.777023	+	0.629472i	$0.783271\pi$
$48$	1.05633	0.152467
$49$	−6.99987	−0.999981
$50$	0	0
$51$	−1.62174	−0.227089
$52$	−5.73875	−0.795821
$53$	−0.842935	−0.115786	−0.0578930	−	0.998323i	$-0.518438\pi$
$53$	−0.842935	−0.115786	−0.0578930	+	0.998323i	$0.518438\pi$
$54$	−1.58289	−0.215404
$55$	0	0
$56$	−0.0237279	−0.00317077
$57$	1.12873	0.149504
$58$	3.32396	0.436458
$59$	10.2157	1.32997	0.664985	−	0.746857i	$-0.268438\pi$
$59$	10.2157	1.32997	0.664985	+	0.746857i	$0.268438\pi$
$60$	0	0
$61$	−2.52565	−0.323376	−0.161688	−	0.986842i	$-0.551694\pi$
$61$	−2.52565	−0.323376	−0.161688	+	0.986842i	$0.551694\pi$
$62$	−0.357357	−0.0453844
$63$	−0.0314867	−0.00396695
$64$	−1.29872	−0.162341
$65$	0	0
$66$	−0.199220	−0.0245223
$67$	−8.96869	−1.09570	−0.547850	−	0.836577i	$-0.684553\pi$
$67$	−8.96869	−1.09570	−0.547850	+	0.836577i	$0.684553\pi$
$68$	5.61694	0.681154
$69$	2.27422	0.273784
$70$	0	0
$71$	10.7516	1.27598	0.637991	−	0.770044i	$-0.279766\pi$
$71$	10.7516	1.27598	0.637991	+	0.770044i	$0.279766\pi$
$72$	5.76098	0.678938
$73$	−5.27340	−0.617205	−0.308602	−	0.951191i	$-0.599861\pi$
$73$	−5.27340	−0.617205	−0.308602	+	0.951191i	$0.599861\pi$
$74$	−2.19061	−0.254653
$75$	0	0
$76$	−3.90940	−0.448439
$77$	−0.00826265	−0.000941617 0
$78$	0.938310	0.106243
$79$	6.07465	0.683452	0.341726	−	0.939800i	$-0.388989\pi$
$79$	6.07465	0.683452	0.341726	+	0.939800i	$0.388989\pi$
$80$	0	0
$81$	6.93953	0.771059
$82$	−0.181272	−0.0200181
$83$	0.282048	0.0309588	0.0154794	−	0.999880i	$-0.495073\pi$
$83$	0.282048	0.0309588	0.0154794	+	0.999880i	$0.495073\pi$
$84$	−0.00927220	−0.00101168
$85$	0	0
$86$	1.73333	0.186910
$87$	2.84588	0.305110
$88$	1.51178	0.161156
$89$	4.26717	0.452319	0.226160	−	0.974090i	$-0.427383\pi$
$89$	4.26717	0.452319	0.226160	+	0.974090i	$0.427383\pi$
$90$	0	0
$91$	0.0389165	0.00407955
$92$	−7.87683	−0.821217
$93$	−0.305959	−0.0317264
$94$	−6.03339	−0.622297
$95$	0	0
$96$	2.61867	0.267267
$97$	−17.9265	−1.82016	−0.910081	−	0.414431i	$-0.863981\pi$
$97$	−17.9265	−1.82016	−0.910081	+	0.414431i	$0.863981\pi$
$98$	−3.96405	−0.400429
$99$	2.00612	0.201623
$100$	0	0
$101$	−7.00595	−0.697118	−0.348559	−	0.937287i	$-0.613329\pi$
$101$	−7.00595	−0.697118	−0.348559	+	0.937287i	$0.613329\pi$
$102$	−0.918394	−0.0909345
$103$	−3.88113	−0.382419	−0.191210	−	0.981549i	$-0.561241\pi$
$103$	−3.88113	−0.382419	−0.191210	+	0.981549i	$0.561241\pi$
$104$	−7.12037	−0.698210
$105$	0	0
$106$	−0.477357	−0.0463650
$107$	−16.4182	−1.58720	−0.793602	−	0.608438i	$-0.791797\pi$
$107$	−16.4182	−1.58720	−0.793602	+	0.608438i	$0.791797\pi$
$108$	4.69387	0.451668
$109$	1.38684	0.132835	0.0664176	−	0.997792i	$-0.478843\pi$
$109$	1.38684	0.132835	0.0664176	+	0.997792i	$0.478843\pi$
$110$	0	0
$111$	−1.87554	−0.178018
$112$	0.0248104	0.00234436
$113$	−18.0484	−1.69785	−0.848927	−	0.528510i	$-0.822751\pi$
$113$	−18.0484	−1.69785	−0.848927	+	0.528510i	$0.822751\pi$
$114$	0.639203	0.0598669
$115$	0	0
$116$	−9.85681	−0.915182
$117$	−9.44867	−0.873530
$118$	5.78517	0.532568
$119$	−0.0380905	−0.00349175
$120$	0	0
$121$	−10.4736	−0.952142
$122$	−1.43028	−0.129492
$123$	−0.155199	−0.0139939
$124$	1.05970	0.0951638
$125$	0	0
$126$	−0.0178310	−0.00158851
$127$	−7.58960	−0.673468	−0.336734	−	0.941600i	$-0.609322\pi$
$127$	−7.58960	−0.673468	−0.336734	+	0.941600i	$0.609322\pi$
$128$	−11.5374	−1.01977
$129$	1.48403	0.130661
$130$	0	0
$131$	−5.91323	−0.516641	−0.258321	−	0.966059i	$-0.583169\pi$
$131$	−5.91323	−0.516641	−0.258321	+	0.966059i	$0.583169\pi$
$132$	0.590762	0.0514192
$133$	0.0265110	0.00229880
$134$	−5.07899	−0.438758
$135$	0	0
$136$	6.96924	0.597607
$137$	10.9529	0.935773	0.467886	−	0.883789i	$-0.345016\pi$
$137$	10.9529	0.935773	0.467886	+	0.883789i	$0.345016\pi$
$138$	1.28790	0.109633
$139$	−10.9832	−0.931579	−0.465790	−	0.884895i	$-0.654230\pi$
$139$	−10.9832	−0.931579	−0.465790	+	0.884895i	$0.654230\pi$
$140$	0	0
$141$	−5.16561	−0.435023
$142$	6.08867	0.510950
$143$	−2.47949	−0.207346
$144$	−6.02381	−0.501984
$145$	0	0
$146$	−2.98634	−0.247151
$147$	−3.39390	−0.279924
$148$	6.49599	0.533967
$149$	−12.5163	−1.02538	−0.512688	−	0.858575i	$-0.671350\pi$
$149$	−12.5163	−1.02538	−0.512688	+	0.858575i	$0.671350\pi$
$150$	0	0
$151$	6.62555	0.539179	0.269590	−	0.962975i	$-0.413112\pi$
$151$	6.62555	0.539179	0.269590	+	0.962975i	$0.413112\pi$
$152$	−4.85060	−0.393436
$153$	9.24812	0.747666
$154$	−0.00467916	−0.000377058 0
$155$	0	0
$156$	−2.78244	−0.222774
$157$	9.62040	0.767791	0.383896	−	0.923376i	$-0.374582\pi$
$157$	9.62040	0.767791	0.383896	+	0.923376i	$0.374582\pi$
$158$	3.44009	0.273679
$159$	−0.408699	−0.0324119
$160$	0	0
$161$	0.0534156	0.00420974
$162$	3.92987	0.308760
$163$	1.33879	0.104862	0.0524311	−	0.998625i	$-0.483303\pi$
$163$	1.33879	0.104862	0.0524311	+	0.998625i	$0.483303\pi$
$164$	0.537539	0.0419747
$165$	0	0
$166$	0.159724	0.0123970
$167$	19.7748	1.53022	0.765111	−	0.643899i	$-0.222684\pi$
$167$	19.7748	1.53022	0.765111	+	0.643899i	$0.222684\pi$
$168$	−0.0115045	−0.000887592 0
$169$	−1.32177	−0.101675
$170$	0	0
$171$	−6.43671	−0.492227
$172$	−5.13999	−0.391920
$173$	−7.84842	−0.596704	−0.298352	−	0.954456i	$-0.596437\pi$
$173$	−7.84842	−0.596704	−0.298352	+	0.954456i	$0.596437\pi$
$174$	1.61163	0.122177
$175$	0	0
$176$	−1.58075	−0.119154
$177$	4.95310	0.372298
$178$	2.41651	0.181125
$179$	−21.4613	−1.60410	−0.802048	−	0.597260i	$-0.796256\pi$
$179$	−21.4613	−1.60410	−0.802048	+	0.597260i	$0.796256\pi$
$180$	0	0
$181$	13.9253	1.03506	0.517530	−	0.855665i	$-0.326851\pi$
$181$	13.9253	1.03506	0.517530	+	0.855665i	$0.326851\pi$
$182$	0.0220385	0.00163360
$183$	−1.22457	−0.0905225
$184$	−9.77321	−0.720490
$185$	0	0
$186$	−0.173265	−0.0127044
$187$	2.42687	0.177470
$188$	17.8913	1.30486
$189$	−0.0318308	−0.00231535
$190$	0	0
$191$	−16.0944	−1.16455	−0.582274	−	0.812993i	$-0.697837\pi$
$191$	−16.0944	−1.16455	−0.582274	+	0.812993i	$0.697837\pi$
$192$	−0.629689	−0.0454439
$193$	−12.7766	−0.919680	−0.459840	−	0.888002i	$-0.652093\pi$
$193$	−12.7766	−0.919680	−0.459840	+	0.888002i	$0.652093\pi$
$194$	−10.1518	−0.728859
$195$	0	0
$196$	11.7549	0.839635
$197$	−13.4867	−0.960887	−0.480444	−	0.877026i	$-0.659524\pi$
$197$	−13.4867	−0.960887	−0.480444	+	0.877026i	$0.659524\pi$
$198$	1.13607	0.0807371
$199$	−5.85772	−0.415242	−0.207621	−	0.978209i	$-0.566572\pi$
$199$	−5.85772	−0.415242	−0.207621	+	0.978209i	$0.566572\pi$
$200$	0	0
$201$	−4.34848	−0.306718
$202$	−3.96749	−0.279151
$203$	0.0668425	0.00469142
$204$	2.72338	0.190675
$205$	0	0
$206$	−2.19790	−0.153135
$207$	−12.9690	−0.901406
$208$	7.44521	0.516233
$209$	−1.68910	−0.116838
$210$	0	0
$211$	18.8205	1.29566	0.647828	−	0.761787i	$-0.275678\pi$
$211$	18.8205	1.29566	0.647828	+	0.761787i	$0.275678\pi$
$212$	1.41554	0.0972199
$213$	5.21294	0.357185
$214$	−9.29765	−0.635574
$215$	0	0
$216$	5.82393	0.396268
$217$	−0.00718619	−0.000487830 0
$218$	0.785371	0.0531920
$219$	−2.55682	−0.172774
$220$	0	0
$221$	−11.4304	−0.768889
$222$	−1.06212	−0.0712849
$223$	−11.5530	−0.773647	−0.386823	−	0.922154i	$-0.626428\pi$
$223$	−11.5530	−0.773647	−0.386823	+	0.922154i	$0.626428\pi$
$224$	0.0615059	0.00410954
$225$	0	0
$226$	−10.2209	−0.679883
$227$	−9.59140	−0.636604	−0.318302	−	0.947989i	$-0.603113\pi$
$227$	−9.59140	−0.636604	−0.318302	+	0.947989i	$0.603113\pi$
$228$	−1.89548	−0.125531
$229$	4.20557	0.277912	0.138956	−	0.990299i	$-0.455625\pi$
$229$	4.20557	0.277912	0.138956	+	0.990299i	$0.455625\pi$
$230$	0	0
$231$	−0.00400616	−0.000263586 0
$232$	−12.2299	−0.802930
$233$	1.27356	0.0834340	0.0417170	−	0.999129i	$-0.486717\pi$
$233$	1.27356	0.0834340	0.0417170	+	0.999129i	$0.486717\pi$
$234$	−5.35081	−0.349793
$235$	0	0
$236$	−17.1552	−1.11671
$237$	2.94531	0.191318
$238$	−0.0215707	−0.00139822
$239$	−3.30982	−0.214094	−0.107047	−	0.994254i	$-0.534140\pi$
$239$	−3.30982	−0.214094	−0.107047	+	0.994254i	$0.534140\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−5.93120	−0.381272
$243$	11.7500	0.753765
$244$	4.24133	0.271523
$245$	0	0
$246$	−0.0878899	−0.00560365
$247$	7.95554	0.506199
$248$	1.31482	0.0834914
$249$	0.136751	0.00866627
$250$	0	0
$251$	−11.4849	−0.724923	−0.362462	−	0.931999i	$-0.618064\pi$
$251$	−11.4849	−0.724923	−0.362462	+	0.931999i	$0.618064\pi$
$252$	0.0528757	0.00333085
$253$	−3.40328	−0.213962
$254$	−4.29801	−0.269681
$255$	0	0
$256$	−3.93622	−0.246014
$257$	6.71637	0.418956	0.209478	−	0.977813i	$-0.432824\pi$
$257$	6.71637	0.418956	0.209478	+	0.977813i	$0.432824\pi$
$258$	0.840410	0.0523216
$259$	−0.0440516	−0.00273723
$260$	0	0
$261$	−16.2289	−1.00455
$262$	−3.34868	−0.206882
$263$	−5.23417	−0.322753	−0.161377	−	0.986893i	$-0.551593\pi$
$263$	−5.23417	−0.322753	−0.161377	+	0.986893i	$0.551593\pi$
$264$	0.732989	0.0451124
$265$	0	0
$266$	0.0150133	0.000920522 0
$267$	2.06895	0.126617
$268$	15.0611	0.920005
$269$	−15.0578	−0.918087	−0.459044	−	0.888414i	$-0.651808\pi$
$269$	−15.0578	−0.918087	−0.459044	+	0.888414i	$0.651808\pi$
$270$	0	0
$271$	5.19734	0.315716	0.157858	−	0.987462i	$-0.449541\pi$
$271$	5.19734	0.315716	0.157858	+	0.987462i	$0.449541\pi$
$272$	−7.28718	−0.441850
$273$	0.0188687	0.00114199
$274$	6.20268	0.374717
$275$	0	0
$276$	−3.81910	−0.229883
$277$	17.1001	1.02745	0.513723	−	0.857956i	$-0.328266\pi$
$277$	17.1001	1.02745	0.513723	+	0.857956i	$0.328266\pi$
$278$	−6.21979	−0.373038
$279$	1.74476	0.104456
$280$	0	0
$281$	−14.8994	−0.888824	−0.444412	−	0.895823i	$-0.646587\pi$
$281$	−14.8994	−0.888824	−0.444412	+	0.895823i	$0.646587\pi$
$282$	−2.92530	−0.174199
$283$	2.81051	0.167068	0.0835339	−	0.996505i	$-0.473379\pi$
$283$	2.81051	0.167068	0.0835339	+	0.996505i	$0.473379\pi$
$284$	−18.0552	−1.07138
$285$	0	0
$286$	−1.40414	−0.0830288
$287$	−0.00364524	−0.000215172 0
$288$	−14.9333	−0.879950
$289$	−5.81226	−0.341898
$290$	0	0
$291$	−8.69170	−0.509517
$292$	8.85563	0.518237
$293$	28.7943	1.68218	0.841090	−	0.540895i	$-0.181914\pi$
$293$	28.7943	1.68218	0.841090	+	0.540895i	$0.181914\pi$
$294$	−1.92197	−0.112092
$295$	0	0
$296$	8.05991	0.468473
$297$	2.02804	0.117679
$298$	−7.08801	−0.410598
$299$	16.0292	0.926992
$300$	0	0
$301$	0.0348561	0.00200907
$302$	3.75206	0.215907
$303$	−3.39685	−0.195144
$304$	5.07189	0.290893
$305$	0	0
$306$	5.23724	0.299393
$307$	−31.1351	−1.77698	−0.888488	−	0.458900i	$-0.848244\pi$
$307$	−31.1351	−1.77698	−0.888488	+	0.458900i	$0.848244\pi$
$308$	0.0138755	0.000790629 0
$309$	−1.88177	−0.107050
$310$	0	0
$311$	13.7927	0.782114	0.391057	−	0.920366i	$-0.372110\pi$
$311$	13.7927	0.782114	0.391057	+	0.920366i	$0.372110\pi$
$312$	−3.45232	−0.195449
$313$	3.11961	0.176331	0.0881654	−	0.996106i	$-0.471900\pi$
$313$	3.11961	0.176331	0.0881654	+	0.996106i	$0.471900\pi$
$314$	5.44806	0.307452
$315$	0	0
$316$	−10.2012	−0.573861
$317$	−2.78570	−0.156461	−0.0782303	−	0.996935i	$-0.524927\pi$
$317$	−2.78570	−0.156461	−0.0782303	+	0.996935i	$0.524927\pi$
$318$	−0.231447	−0.0129789
$319$	−4.25875	−0.238444
$320$	0	0
$321$	−7.96038	−0.444305
$322$	0.0302494	0.00168573
$323$	−7.78669	−0.433263
$324$	−11.6536	−0.647420
$325$	0	0
$326$	0.758161	0.0419906
$327$	0.672412	0.0371845
$328$	0.666953	0.0368263
$329$	−0.121327	−0.00668898
$330$	0	0
$331$	32.9814	1.81282	0.906411	−	0.422397i	$-0.138811\pi$
$331$	32.9814	1.81282	0.906411	+	0.422397i	$0.138811\pi$
$332$	−0.473643	−0.0259946
$333$	10.6954	0.586107
$334$	11.1985	0.612757
$335$	0	0
$336$	0.0120294	0.000656256 0
$337$	0.552700	0.0301075	0.0150537	−	0.999887i	$-0.495208\pi$
$337$	0.552700	0.0301075	0.0150537	+	0.999887i	$0.495208\pi$
$338$	−0.748522	−0.0407142
$339$	−8.75082	−0.475279
$340$	0	0
$341$	0.457855	0.0247943
$342$	−3.64512	−0.197106
$343$	−0.159430	−0.00860839
$344$	−6.37745	−0.343849
$345$	0	0
$346$	−4.44458	−0.238942
$347$	−10.4477	−0.560863	−0.280431	−	0.959874i	$-0.590478\pi$
$347$	−10.4477	−0.560863	−0.280431	+	0.959874i	$0.590478\pi$
$348$	−4.77909	−0.256186
$349$	25.5041	1.36520	0.682601	−	0.730791i	$-0.260849\pi$
$349$	25.5041	1.36520	0.682601	+	0.730791i	$0.260849\pi$
$350$	0	0
$351$	−9.55192	−0.509844
$352$	−3.91874	−0.208870
$353$	15.4281	0.821155	0.410578	−	0.911826i	$-0.365327\pi$
$353$	15.4281	0.821155	0.410578	+	0.911826i	$0.365327\pi$
$354$	2.80495	0.149081
$355$	0	0
$356$	−7.16586	−0.379790
$357$	−0.0184682	−0.000977442 0
$358$	−12.1536	−0.642338
$359$	23.8394	1.25819	0.629097	−	0.777327i	$-0.283425\pi$
$359$	23.8394	1.25819	0.629097	+	0.777327i	$0.283425\pi$
$360$	0	0
$361$	−13.5805	−0.714761
$362$	7.88595	0.414476
$363$	−5.07813	−0.266532
$364$	−0.0653525	−0.00342540
$365$	0	0
$366$	−0.693475	−0.0362485
$367$	9.39571	0.490452	0.245226	−	0.969466i	$-0.421138\pi$
$367$	9.39571	0.490452	0.245226	+	0.969466i	$0.421138\pi$
$368$	10.2191	0.532706
$369$	0.885041	0.0460734
$370$	0	0
$371$	−0.00959929	−0.000498370 0
$372$	0.513797	0.0266391
$373$	5.54594	0.287158	0.143579	−	0.989639i	$-0.454139\pi$
$373$	5.54594	0.287158	0.143579	+	0.989639i	$0.454139\pi$
$374$	1.37434	0.0710655
$375$	0	0
$376$	22.1987	1.14481
$377$	20.0584	1.03306
$378$	−0.0180259	−0.000927150 0
$379$	−16.7357	−0.859655	−0.429827	−	0.902911i	$-0.641426\pi$
$379$	−16.7357	−0.859655	−0.429827	+	0.902911i	$0.641426\pi$
$380$	0	0
$381$	−3.67983	−0.188524
$382$	−9.11428	−0.466327
$383$	0.215716	0.0110226	0.00551129	−	0.999985i	$-0.498246\pi$
$383$	0.215716	0.0110226	0.00551129	+	0.999985i	$0.498246\pi$
$384$	−5.59394	−0.285465
$385$	0	0
$386$	−7.23542	−0.368273
$387$	−8.46283	−0.430190
$388$	30.1040	1.52830
$389$	−34.5508	−1.75179	−0.875896	−	0.482499i	$-0.839729\pi$
$389$	−34.5508	−1.75179	−0.875896	+	0.482499i	$0.839729\pi$
$390$	0	0
$391$	−15.6890	−0.793425
$392$	14.5849	0.736650
$393$	−2.86704	−0.144623
$394$	−7.63755	−0.384774
$395$	0	0
$396$	−3.36888	−0.169293
$397$	−18.1197	−0.909400	−0.454700	−	0.890645i	$-0.650254\pi$
$397$	−18.1197	−0.909400	−0.454700	+	0.890645i	$0.650254\pi$
$398$	−3.31724	−0.166278
$399$	0.0128539	0.000643501 0
$400$	0	0
$401$	−29.7589	−1.48609	−0.743044	−	0.669242i	$-0.766619\pi$
$401$	−29.7589	−1.48609	−0.743044	+	0.669242i	$0.766619\pi$
$402$	−2.46256	−0.122821
$403$	−2.15646	−0.107421
$404$	11.7651	0.585335
$405$	0	0
$406$	0.0378531	0.00187862
$407$	2.80667	0.139121
$408$	3.37905	0.167288
$409$	11.2104	0.554319	0.277160	−	0.960824i	$-0.410607\pi$
$409$	11.2104	0.554319	0.277160	+	0.960824i	$0.410607\pi$
$410$	0	0
$411$	5.31055	0.261950
$412$	6.51759	0.321099
$413$	0.116336	0.00572450
$414$	−7.34436	−0.360956
$415$	0	0
$416$	18.4570	0.904928
$417$	−5.32521	−0.260776
$418$	−0.956543	−0.0467861
$419$	−4.00205	−0.195513	−0.0977564	−	0.995210i	$-0.531167\pi$
$419$	−4.00205	−0.195513	−0.0977564	+	0.995210i	$0.531167\pi$
$420$	0	0
$421$	30.6511	1.49384	0.746922	−	0.664912i	$-0.231531\pi$
$421$	30.6511	1.49384	0.746922	+	0.664912i	$0.231531\pi$
$422$	10.6581	0.518828
$423$	29.4575	1.43227
$424$	1.75634	0.0852953
$425$	0	0
$426$	2.95210	0.143030
$427$	−0.0287619	−0.00139189
$428$	27.5710	1.33270
$429$	−1.20219	−0.0580422
$430$	0	0
$431$	12.0037	0.578197	0.289099	−	0.957299i	$-0.406644\pi$
$431$	12.0037	0.578197	0.289099	+	0.957299i	$0.406644\pi$
$432$	−6.08963	−0.292987
$433$	−3.75303	−0.180359	−0.0901796	−	0.995926i	$-0.528744\pi$
$433$	−3.75303	−0.180359	−0.0901796	+	0.995926i	$0.528744\pi$
$434$	−0.00406956	−0.000195345 0
$435$	0	0
$436$	−2.32892	−0.111535
$437$	10.9195	0.522353
$438$	−1.44793	−0.0691849
$439$	−24.1433	−1.15230	−0.576149	−	0.817344i	$-0.695445\pi$
$439$	−24.1433	−1.15230	−0.576149	+	0.817344i	$0.695445\pi$
$440$	0	0
$441$	19.3541	0.921622
$442$	−6.47304	−0.307891
$443$	−26.5755	−1.26264	−0.631320	−	0.775522i	$-0.717487\pi$
$443$	−26.5755	−1.26264	−0.631320	+	0.775522i	$0.717487\pi$
$444$	3.14959	0.149473
$445$	0	0
$446$	−6.54250	−0.309796
$447$	−6.06855	−0.287033
$448$	−0.0147898	−0.000698752 0
$449$	15.8987	0.750308	0.375154	−	0.926963i	$-0.377590\pi$
$449$	15.8987	0.750308	0.375154	+	0.926963i	$0.377590\pi$
$450$	0	0
$451$	0.232250	0.0109362
$452$	30.3088	1.42560
$453$	3.21241	0.150932
$454$	−5.43164	−0.254919
$455$	0	0
$456$	−2.35182	−0.110134
$457$	−24.6998	−1.15541	−0.577705	−	0.816246i	$-0.696051\pi$
$457$	−24.6998	−1.15541	−0.577705	+	0.816246i	$0.696051\pi$
$458$	2.38162	0.111286
$459$	9.34918	0.436382
$460$	0	0
$461$	−32.3064	−1.50466	−0.752329	−	0.658788i	$-0.771069\pi$
$461$	−32.3064	−1.50466	−0.752329	+	0.658788i	$0.771069\pi$
$462$	−0.00226870	−0.000105550 0
$463$	−16.6780	−0.775092	−0.387546	−	0.921850i	$-0.626677\pi$
$463$	−16.6780	−0.775092	−0.387546	+	0.921850i	$0.626677\pi$
$464$	12.7878	0.593659
$465$	0	0
$466$	0.721223	0.0334100
$467$	−38.5101	−1.78203	−0.891017	−	0.453971i	$-0.850007\pi$
$467$	−38.5101	−1.78203	−0.891017	+	0.453971i	$0.850007\pi$
$468$	15.8672	0.733460
$469$	−0.102135	−0.00471615
$470$	0	0
$471$	4.66447	0.214927
$472$	−21.2854	−0.979740
$473$	−2.22079	−0.102112
$474$	1.66793	0.0766108
$475$	0	0
$476$	0.0639654	0.00293185
$477$	2.33065	0.106713
$478$	−1.87436	−0.0857311
$479$	4.61086	0.210676	0.105338	−	0.994437i	$-0.466408\pi$
$479$	4.61086	0.210676	0.105338	+	0.994437i	$0.466408\pi$
$480$	0	0
$481$	−13.2192	−0.602743
$482$	−0.566303	−0.0257944
$483$	0.0258987	0.00117843
$484$	17.5883	0.799466
$485$	0	0
$486$	6.65408	0.301835
$487$	23.1281	1.04804	0.524018	−	0.851707i	$-0.324432\pi$
$487$	23.1281	1.04804	0.524018	+	0.851707i	$0.324432\pi$
$488$	5.26244	0.238219
$489$	0.649115	0.0293540
$490$	0	0
$491$	12.1819	0.549761	0.274880	−	0.961478i	$-0.411362\pi$
$491$	12.1819	0.549761	0.274880	+	0.961478i	$0.411362\pi$
$492$	0.260627	0.0117500
$493$	−19.6326	−0.884210
$494$	4.50525	0.202701
$495$	0	0
$496$	−1.37481	−0.0617307
$497$	0.122439	0.00549213
$498$	0.0774427	0.00347029
$499$	10.3843	0.464864	0.232432	−	0.972613i	$-0.425332\pi$
$499$	10.3843	0.464864	0.232432	+	0.972613i	$0.425332\pi$
$500$	0	0
$501$	9.58786	0.428354
$502$	−6.50395	−0.290286
$503$	−9.54023	−0.425378	−0.212689	−	0.977120i	$-0.568222\pi$
$503$	−9.54023	−0.425378	−0.212689	+	0.977120i	$0.568222\pi$
$504$	0.0656057	0.00292231
$505$	0	0
$506$	−1.92729	−0.0856783
$507$	−0.640863	−0.0284617
$508$	12.7452	0.565478
$509$	−26.8693	−1.19096	−0.595481	−	0.803369i	$-0.703039\pi$
$509$	−26.8693	−1.19096	−0.595481	+	0.803369i	$0.703039\pi$
$510$	0	0
$511$	−0.0600531	−0.00265659
$512$	20.8457	0.921261
$513$	−6.50704	−0.287293
$514$	3.80350	0.167765
$515$	0	0
$516$	−2.49213	−0.109710
$517$	7.73014	0.339971
$518$	−0.0249465	−0.00109609
$519$	−3.80532	−0.167035
$520$	0	0
$521$	−34.1340	−1.49544	−0.747720	−	0.664014i	$-0.768851\pi$
$521$	−34.1340	−1.49544	−0.747720	+	0.664014i	$0.768851\pi$
$522$	−9.19049	−0.402257
$523$	−0.440262	−0.0192513	−0.00962566	−	0.999954i	$-0.503064\pi$
$523$	−0.440262	−0.0192513	−0.00962566	+	0.999954i	$0.503064\pi$
$524$	9.93010	0.433798
$525$	0	0
$526$	−2.96413	−0.129242
$527$	2.11069	0.0919432
$528$	−0.766430	−0.0333546
$529$	−0.998809	−0.0434265
$530$	0	0
$531$	−28.2455	−1.22575
$532$	−0.0445200	−0.00193019
$533$	−1.09388	−0.0473812
$534$	1.17165	0.0507022
$535$	0	0
$536$	18.6871	0.807161
$537$	−10.4056	−0.449033
$538$	−8.52725	−0.367636
$539$	5.07884	0.218761
$540$	0	0
$541$	−24.7902	−1.06581	−0.532907	−	0.846174i	$-0.678901\pi$
$541$	−24.7902	−1.06581	−0.532907	+	0.846174i	$0.678901\pi$
$542$	2.94327	0.126424
$543$	6.75172	0.289744
$544$	−18.0652	−0.774540
$545$	0	0
$546$	0.0106854	0.000457293 0
$547$	−19.5952	−0.837831	−0.418916	−	0.908025i	$-0.637590\pi$
$547$	−19.5952	−0.837831	−0.418916	+	0.908025i	$0.637590\pi$
$548$	−18.3933	−0.785722
$549$	6.98322	0.298036
$550$	0	0
$551$	13.6644	0.582121
$552$	−4.73856	−0.201686
$553$	0.0691777	0.00294174
$554$	9.68383	0.411427
$555$	0	0
$556$	18.4440	0.782201
$557$	−16.0104	−0.678382	−0.339191	−	0.940718i	$-0.610153\pi$
$557$	−16.0104	−0.678382	−0.339191	+	0.940718i	$0.610153\pi$
$558$	0.988063	0.0418281
$559$	10.4598	0.442401
$560$	0	0
$561$	1.17667	0.0496791
$562$	−8.43757	−0.355917
$563$	6.74254	0.284164	0.142082	−	0.989855i	$-0.454620\pi$
$563$	6.74254	0.284164	0.142082	+	0.989855i	$0.454620\pi$
$564$	8.67462	0.365268
$565$	0	0
$566$	1.59160	0.0669000
$567$	0.0790269	0.00331882
$568$	−22.4021	−0.939969
$569$	0.129504	0.00542908	0.00271454	−	0.999996i	$-0.499136\pi$
$569$	0.129504	0.00542908	0.00271454	+	0.999996i	$0.499136\pi$
$570$	0	0
$571$	38.4505	1.60910	0.804551	−	0.593883i	$-0.202406\pi$
$571$	38.4505	1.60910	0.804551	+	0.593883i	$0.202406\pi$
$572$	4.16382	0.174098
$573$	−7.80338	−0.325991
$574$	−0.00206431	−8.61626e−5 0
$575$	0	0
$576$	3.59087	0.149620
$577$	32.3194	1.34547	0.672737	−	0.739882i	$-0.265119\pi$
$577$	32.3194	1.34547	0.672737	+	0.739882i	$0.265119\pi$
$578$	−3.29150	−0.136908
$579$	−6.19476	−0.257445
$580$	0	0
$581$	0.00321194	0.000133254 0
$582$	−4.92213	−0.204029
$583$	0.611602	0.0253300
$584$	10.9876	0.454672
$585$	0	0
$586$	16.3063	0.673606
$587$	−2.10246	−0.0867779	−0.0433889	−	0.999058i	$-0.513815\pi$
$587$	−2.10246	−0.0867779	−0.0433889	+	0.999058i	$0.513815\pi$
$588$	5.69938	0.235039
$589$	−1.46905	−0.0605310
$590$	0	0
$591$	−6.53905	−0.268981
$592$	−8.42762	−0.346373
$593$	−2.95679	−0.121421	−0.0607103	−	0.998155i	$-0.519337\pi$
$593$	−2.95679	−0.121421	−0.0607103	+	0.998155i	$0.519337\pi$
$594$	1.14849	0.0471229
$595$	0	0
$596$	21.0186	0.860957
$597$	−2.84012	−0.116239
$598$	9.07737	0.371201
$599$	45.3395	1.85252	0.926262	−	0.376881i	$-0.123004\pi$
$599$	45.3395	1.85252	0.926262	+	0.376881i	$0.123004\pi$
$600$	0	0
$601$	27.0562	1.10365	0.551823	−	0.833961i	$-0.313932\pi$
$601$	27.0562	1.10365	0.551823	+	0.833961i	$0.313932\pi$
$602$	0.0197391	0.000804505 0
$603$	24.7977	1.00984
$604$	−11.1263	−0.452722
$605$	0	0
$606$	−1.92364	−0.0781427
$607$	−12.6166	−0.512091	−0.256045	−	0.966665i	$-0.582420\pi$
$607$	−12.6166	−0.512091	−0.256045	+	0.966665i	$0.582420\pi$
$608$	12.5734	0.509920
$609$	0.0324087	0.00131327
$610$	0	0
$611$	−36.4084	−1.47293
$612$	−15.5304	−0.627779
$613$	23.1758	0.936063	0.468032	−	0.883712i	$-0.344963\pi$
$613$	23.1758	0.936063	0.468032	+	0.883712i	$0.344963\pi$
$614$	−17.6319	−0.711566
$615$	0	0
$616$	0.0172161	0.000693654 0
$617$	8.02149	0.322933	0.161466	−	0.986878i	$-0.448378\pi$
$617$	8.02149	0.322933	0.161466	+	0.986878i	$0.448378\pi$
$618$	−1.06565	−0.0428669
$619$	−24.8438	−0.998558	−0.499279	−	0.866441i	$-0.666402\pi$
$619$	−24.8438	−0.998558	−0.499279	+	0.866441i	$0.666402\pi$
$620$	0	0
$621$	−13.1107	−0.526114
$622$	7.81086	0.313187
$623$	0.0485942	0.00194689
$624$	3.60983	0.144509
$625$	0	0
$626$	1.76664	0.0706093
$627$	−0.818965	−0.0327063
$628$	−16.1555	−0.644676
$629$	12.9386	0.515896
$630$	0	0
$631$	43.0164	1.71246	0.856228	−	0.516598i	$-0.172802\pi$
$631$	43.0164	1.71246	0.856228	+	0.516598i	$0.172802\pi$
$632$	−12.6571	−0.503474
$633$	9.12514	0.362692
$634$	−1.57755	−0.0626525
$635$	0	0
$636$	0.686328	0.0272147
$637$	−23.9210	−0.947783
$638$	−2.41174	−0.0954818
$639$	−29.7274	−1.17600
$640$	0	0
$641$	4.67796	0.184768	0.0923841	−	0.995723i	$-0.470551\pi$
$641$	4.67796	0.184768	0.0923841	+	0.995723i	$0.470551\pi$
$642$	−4.50798	−0.177916
$643$	10.9083	0.430182	0.215091	−	0.976594i	$-0.430995\pi$
$643$	10.9083	0.430182	0.215091	+	0.976594i	$0.430995\pi$
$644$	−0.0897009	−0.00353471
$645$	0	0
$646$	−4.40962	−0.173494
$647$	13.9166	0.547118	0.273559	−	0.961855i	$-0.411799\pi$
$647$	13.9166	0.547118	0.273559	+	0.961855i	$0.411799\pi$
$648$	−14.4592	−0.568011
$649$	−7.41212	−0.290951
$650$	0	0
$651$	−0.00348424	−0.000136558 0
$652$	−2.24823	−0.0880476
$653$	−36.0160	−1.40942	−0.704708	−	0.709498i	$-0.748922\pi$
$653$	−36.0160	−1.40942	−0.704708	+	0.709498i	$0.748922\pi$
$654$	0.380789	0.0148900
$655$	0	0
$656$	−0.697380	−0.0272281
$657$	14.5805	0.568840
$658$	−0.0687079	−0.00267851
$659$	−20.1998	−0.786874	−0.393437	−	0.919352i	$-0.628714\pi$
$659$	−20.1998	−0.786874	−0.393437	+	0.919352i	$0.628714\pi$
$660$	0	0
$661$	17.5698	0.683386	0.341693	−	0.939812i	$-0.389000\pi$
$661$	17.5698	0.683386	0.341693	+	0.939812i	$0.389000\pi$
$662$	18.6775	0.725920
$663$	−5.54203	−0.215235
$664$	−0.587674	−0.0228062
$665$	0	0
$666$	6.05686	0.234698
$667$	27.5316	1.06603
$668$	−33.2079	−1.28485
$669$	−5.60150	−0.216566
$670$	0	0
$671$	1.83252	0.0707435
$672$	0.0298213	0.00115038
$673$	−12.3954	−0.477809	−0.238905	−	0.971043i	$-0.576788\pi$
$673$	−12.3954	−0.477809	−0.238905	+	0.971043i	$0.576788\pi$
$674$	0.312995	0.0120561
$675$	0	0
$676$	2.21965	0.0853712
$677$	15.7457	0.605156	0.302578	−	0.953125i	$-0.402153\pi$
$677$	15.7457	0.605156	0.302578	+	0.953125i	$0.402153\pi$
$678$	−4.95561	−0.190319
$679$	−0.204146	−0.00783440
$680$	0	0
$681$	−4.65041	−0.178204
$682$	0.259285	0.00992853
$683$	−22.9329	−0.877502	−0.438751	−	0.898609i	$-0.644579\pi$
$683$	−22.9329	−0.877502	−0.438751	+	0.898609i	$0.644579\pi$
$684$	10.8092	0.413299
$685$	0	0
$686$	−0.0902854	−0.00344711
$687$	2.03908	0.0777957
$688$	6.66840	0.254231
$689$	−2.88060	−0.109742
$690$	0	0
$691$	32.2536	1.22698	0.613492	−	0.789701i	$-0.289764\pi$
$691$	32.2536	1.22698	0.613492	+	0.789701i	$0.289764\pi$
$692$	13.1799	0.501023
$693$	0.0228456	0.000867831 0
$694$	−5.91657	−0.224590
$695$	0	0
$696$	−5.92967	−0.224764
$697$	1.07066	0.0405542
$698$	14.4430	0.546677
$699$	0.617490	0.0233556
$700$	0	0
$701$	30.7458	1.16125	0.580627	−	0.814170i	$-0.302807\pi$
$701$	30.7458	1.16125	0.580627	+	0.814170i	$0.302807\pi$
$702$	−5.40928	−0.204160
$703$	−9.00529	−0.339641
$704$	0.942306	0.0355145
$705$	0	0
$706$	8.73698	0.328821
$707$	−0.0797833	−0.00300056
$708$	−8.31774	−0.312600
$709$	14.7815	0.555132	0.277566	−	0.960707i	$-0.410472\pi$
$709$	14.7815	0.555132	0.277566	+	0.960707i	$0.410472\pi$
$710$	0	0
$711$	−16.7959	−0.629896
$712$	−8.89107	−0.333207
$713$	−2.95990	−0.110849
$714$	−0.0104586	−0.000391404 0
$715$	0	0
$716$	36.0400	1.34688
$717$	−1.60477	−0.0599312
$718$	13.5003	0.503827
$719$	3.13028	0.116740	0.0583698	−	0.998295i	$-0.481410\pi$
$719$	3.13028	0.116740	0.0583698	+	0.998295i	$0.481410\pi$
$720$	0	0
$721$	−0.0441981	−0.00164602
$722$	−7.69065	−0.286216
$723$	−0.484852	−0.0180318
$724$	−23.3848	−0.869090
$725$	0	0
$726$	−2.87576	−0.106729
$727$	−48.8765	−1.81273	−0.906365	−	0.422495i	$-0.861154\pi$
$727$	−48.8765	−1.81273	−0.906365	+	0.422495i	$0.861154\pi$
$728$	−0.0810863	−0.00300526
$729$	−15.1216	−0.560058
$730$	0	0
$731$	−10.2378	−0.378657
$732$	2.05642	0.0760073
$733$	−31.7570	−1.17297	−0.586486	−	0.809960i	$-0.699489\pi$
$733$	−31.7570	−1.17297	−0.586486	+	0.809960i	$0.699489\pi$
$734$	5.32081	0.196395
$735$	0	0
$736$	25.3335	0.933805
$737$	6.50734	0.239701
$738$	0.501201	0.0184495
$739$	−19.3012	−0.710007	−0.355004	−	0.934865i	$-0.615520\pi$
$739$	−19.3012	−0.710007	−0.355004	+	0.934865i	$0.615520\pi$
$740$	0	0
$741$	3.85726	0.141700
$742$	−0.00543611	−0.000199566 0
$743$	−32.9871	−1.21018	−0.605090	−	0.796157i	$-0.706863\pi$
$743$	−32.9871	−1.21018	−0.605090	+	0.796157i	$0.706863\pi$
$744$	0.637495	0.0233717
$745$	0	0
$746$	3.14068	0.114989
$747$	−0.779840	−0.0285328
$748$	−4.07544	−0.149013
$749$	−0.186969	−0.00683170
$750$	0	0
$751$	14.3548	0.523815	0.261908	−	0.965093i	$-0.415648\pi$
$751$	14.3548	0.523815	0.261908	+	0.965093i	$0.415648\pi$
$752$	−23.2114	−0.846433
$753$	−5.56850	−0.202927
$754$	11.3591	0.413675
$755$	0	0
$756$	0.0534535	0.00194408
$757$	7.75120	0.281722	0.140861	−	0.990029i	$-0.455013\pi$
$757$	7.75120	0.281722	0.140861	+	0.990029i	$0.455013\pi$
$758$	−9.47747	−0.344237
$759$	−1.65009	−0.0598944
$760$	0	0
$761$	−49.3372	−1.78847	−0.894236	−	0.447595i	$-0.852281\pi$
$761$	−49.3372	−1.78847	−0.894236	+	0.447595i	$0.852281\pi$
$762$	−2.08390	−0.0754917
$763$	0.0157932	0.000571754 0
$764$	27.0273	0.977813
$765$	0	0
$766$	0.122161	0.00441384
$767$	34.9105	1.26055
$768$	−1.90848	−0.0688665
$769$	43.2360	1.55913	0.779565	−	0.626321i	$-0.215440\pi$
$769$	43.2360	1.55913	0.779565	+	0.626321i	$0.215440\pi$
$770$	0	0
$771$	3.25645	0.117278
$772$	21.4558	0.772210
$773$	7.24176	0.260468	0.130234	−	0.991483i	$-0.458427\pi$
$773$	7.24176	0.260468	0.130234	+	0.991483i	$0.458427\pi$
$774$	−4.79252	−0.172264
$775$	0	0
$776$	37.3516	1.34085
$777$	−0.0213585	−0.000766231 0
$778$	−19.5662	−0.701482
$779$	−0.745182	−0.0266989
$780$	0	0
$781$	−7.80097	−0.279141
$782$	−8.88470	−0.317716
$783$	−16.4063	−0.586312
$784$	−15.2503	−0.544654
$785$	0	0
$786$	−1.62361	−0.0579124
$787$	−45.5836	−1.62488	−0.812440	−	0.583044i	$-0.801861\pi$
$787$	−45.5836	−1.62488	−0.812440	+	0.583044i	$0.801861\pi$
$788$	22.6482	0.806810
$789$	−2.53780	−0.0903481
$790$	0	0
$791$	−0.205534	−0.00730796
$792$	−4.17995	−0.148528
$793$	−8.63101	−0.306496
$794$	−10.2612	−0.364157
$795$	0	0
$796$	9.83687	0.348659
$797$	30.0258	1.06357	0.531784	−	0.846880i	$-0.321522\pi$
$797$	30.0258	1.06357	0.531784	+	0.846880i	$0.321522\pi$
$798$	0.00727921	0.000257681 0
$799$	35.6356	1.26070
$800$	0	0
$801$	−11.7984	−0.416875
$802$	−16.8525	−0.595084
$803$	3.82618	0.135023
$804$	7.30242	0.257536
$805$	0	0
$806$	−1.22121	−0.0430153
$807$	−7.30078	−0.257000
$808$	14.5976	0.513541
$809$	−33.2838	−1.17020	−0.585098	−	0.810963i	$-0.698944\pi$
$809$	−33.2838	−1.17020	−0.585098	+	0.810963i	$0.698944\pi$
$810$	0	0
$811$	−1.12801	−0.0396098	−0.0198049	−	0.999804i	$-0.506305\pi$
$811$	−1.12801	−0.0396098	−0.0198049	+	0.999804i	$0.506305\pi$
$812$	−0.112249	−0.00393916
$813$	2.51994	0.0883781
$814$	1.58942	0.0557093
$815$	0	0
$816$	−3.53321	−0.123687
$817$	7.12549	0.249289
$818$	6.34849	0.221970
$819$	−0.107601	−0.00375988
$820$	0	0
$821$	−13.8793	−0.484389	−0.242195	−	0.970228i	$-0.577867\pi$
$821$	−13.8793	−0.484389	−0.242195	+	0.970228i	$0.577867\pi$
$822$	3.00738	0.104894
$823$	22.9893	0.801356	0.400678	−	0.916219i	$-0.368775\pi$
$823$	22.9893	0.801356	0.400678	+	0.916219i	$0.368775\pi$
$824$	8.08672	0.281714
$825$	0	0
$826$	0.0658812	0.00229230
$827$	−4.79485	−0.166733	−0.0833666	−	0.996519i	$-0.526567\pi$
$827$	−4.79485	−0.166733	−0.0833666	+	0.996519i	$0.526567\pi$
$828$	21.7788	0.756866
$829$	15.7273	0.546233	0.273116	−	0.961981i	$-0.411946\pi$
$829$	15.7273	0.546233	0.273116	+	0.961981i	$0.411946\pi$
$830$	0	0
$831$	8.29102	0.287612
$832$	−4.43819	−0.153866
$833$	23.4132	0.811220
$834$	−3.01568	−0.104424
$835$	0	0
$836$	2.83651	0.0981028
$837$	1.76383	0.0609668
$838$	−2.26637	−0.0782905
$839$	19.5447	0.674757	0.337378	−	0.941369i	$-0.390460\pi$
$839$	19.5447	0.674757	0.337378	+	0.941369i	$0.390460\pi$
$840$	0	0
$841$	5.45207	0.188003
$842$	17.3578	0.598190
$843$	−7.22400	−0.248808
$844$	−31.6053	−1.08790
$845$	0	0
$846$	16.6818	0.573533
$847$	−0.119272	−0.00409824
$848$	−1.83647	−0.0630645
$849$	1.36268	0.0467672
$850$	0	0
$851$	−18.1443	−0.621978
$852$	−8.75410	−0.299911
$853$	−40.6539	−1.39196	−0.695981	−	0.718060i	$-0.745030\pi$
$853$	−40.6539	−1.39196	−0.695981	+	0.718060i	$0.745030\pi$
$854$	−0.0162880	−0.000557363 0
$855$	0	0
$856$	34.2088	1.16923
$857$	54.3820	1.85765	0.928826	−	0.370516i	$-0.120819\pi$
$857$	54.3820	1.85765	0.928826	+	0.370516i	$0.120819\pi$
$858$	−0.680802	−0.0232422
$859$	−1.26608	−0.0431980	−0.0215990	−	0.999767i	$-0.506876\pi$
$859$	−1.26608	−0.0431980	−0.0215990	+	0.999767i	$0.506876\pi$
$860$	0	0
$861$	−0.00176740	−6.02329e−5 0
$862$	6.79772	0.231531
$863$	32.2104	1.09645	0.548227	−	0.836330i	$-0.315303\pi$
$863$	32.2104	1.09645	0.548227	+	0.836330i	$0.315303\pi$
$864$	−15.0964	−0.513591
$865$	0	0
$866$	−2.12535	−0.0722224
$867$	−2.81808	−0.0957072
$868$	0.0120678	0.000409607 0
$869$	−4.40754	−0.149515
$870$	0	0
$871$	−30.6491	−1.03850
$872$	−2.88962	−0.0978547
$873$	49.5654	1.67753
$874$	6.18377	0.209169
$875$	0	0
$876$	4.29367	0.145070
$877$	6.29719	0.212641	0.106320	−	0.994332i	$-0.466093\pi$
$877$	6.29719	0.212641	0.106320	+	0.994332i	$0.466093\pi$
$878$	−13.6724	−0.461422
$879$	13.9610	0.470892
$880$	0	0
$881$	57.5590	1.93921	0.969606	−	0.244672i	$-0.0786804\pi$
$881$	57.5590	1.93921	0.969606	+	0.244672i	$0.0786804\pi$
$882$	10.9603	0.369051
$883$	32.3394	1.08831	0.544153	−	0.838986i	$-0.316851\pi$
$883$	32.3394	1.08831	0.544153	+	0.838986i	$0.316851\pi$
$884$	19.1950	0.645598
$885$	0	0
$886$	−15.0498	−0.505607
$887$	48.0712	1.61407	0.807037	−	0.590501i	$-0.201070\pi$
$887$	48.0712	1.61407	0.807037	+	0.590501i	$0.201070\pi$
$888$	3.90786	0.131139
$889$	−0.0864299	−0.00289877
$890$	0	0
$891$	−5.03506	−0.168681
$892$	19.4010	0.649593
$893$	−24.8024	−0.829982
$894$	−3.43664	−0.114938
$895$	0	0
$896$	−0.131387	−0.00438934
$897$	7.77178	0.259492
$898$	9.00350	0.300451
$899$	−3.70392	−0.123533
$900$	0	0
$901$	2.81946	0.0939297
$902$	0.131524	0.00437926
$903$	0.0169000	0.000562398 0
$904$	37.6057	1.25075
$905$	0	0
$906$	1.81920	0.0604387
$907$	−12.1591	−0.403736	−0.201868	−	0.979413i	$-0.564701\pi$
$907$	−12.1591	−0.403736	−0.201868	+	0.979413i	$0.564701\pi$
$908$	16.1069	0.534525
$909$	19.3709	0.642491
$910$	0	0
$911$	24.1684	0.800735	0.400368	−	0.916355i	$-0.368882\pi$
$911$	24.1684	0.800735	0.400368	+	0.916355i	$0.368882\pi$
$912$	2.45912	0.0814295
$913$	−0.204643	−0.00677270
$914$	−13.9876	−0.462668
$915$	0	0
$916$	−7.06242	−0.233349
$917$	−0.0673395	−0.00222375
$918$	5.29446	0.174743
$919$	−48.9327	−1.61414	−0.807070	−	0.590456i	$-0.798948\pi$
$919$	−48.9327	−1.61414	−0.807070	+	0.590456i	$0.798948\pi$
$920$	0	0
$921$	−15.0959	−0.497428
$922$	−18.2952	−0.602520
$923$	36.7420	1.20938
$924$	0.00672756	0.000221320 0
$925$	0	0
$926$	−9.44478	−0.310375
$927$	10.7310	0.352453
$928$	31.7015	1.04065
$929$	9.72985	0.319226	0.159613	−	0.987180i	$-0.448975\pi$
$929$	9.72985	0.319226	0.159613	+	0.987180i	$0.448975\pi$
$930$	0	0
$931$	−16.2956	−0.534068
$932$	−2.13870	−0.0700554
$933$	6.68743	0.218937
$934$	−21.8083	−0.713591
$935$	0	0
$936$	19.6872	0.643498
$937$	9.84296	0.321555	0.160778	−	0.986991i	$-0.448600\pi$
$937$	9.84296	0.321555	0.160778	+	0.986991i	$0.448600\pi$
$938$	−0.0578392	−0.00188852
$939$	1.51255	0.0493602
$940$	0	0
$941$	−0.317180	−0.0103398	−0.00516989	−	0.999987i	$-0.501646\pi$
$941$	−0.317180	−0.0103398	−0.00516989	+	0.999987i	$0.501646\pi$
$942$	2.64150	0.0860647
$943$	−1.50143	−0.0488932
$944$	22.2565	0.724386
$945$	0	0
$946$	−1.25764	−0.0408894
$947$	1.48939	0.0483986	0.0241993	−	0.999707i	$-0.492296\pi$
$947$	1.48939	0.0483986	0.0241993	+	0.999707i	$0.492296\pi$
$948$	−4.94606	−0.160640
$949$	−18.0210	−0.584987
$950$	0	0
$951$	−1.35065	−0.0437979
$952$	0.0793652	0.00257224
$953$	1.32360	0.0428756	0.0214378	−	0.999770i	$-0.493176\pi$
$953$	1.32360	0.0428756	0.0214378	+	0.999770i	$0.493176\pi$
$954$	1.31985	0.0427318
$955$	0	0
$956$	5.55818	0.179764
$957$	−2.06486	−0.0667476
$958$	2.61114	0.0843621
$959$	0.124731	0.00402778
$960$	0	0
$961$	−30.6018	−0.987155
$962$	−7.48606	−0.241360
$963$	45.3949	1.46283
$964$	1.67930	0.0540867
$965$	0	0
$966$	0.0146665	0.000471886 0
$967$	32.1292	1.03320	0.516602	−	0.856226i	$-0.327197\pi$
$967$	32.1292	1.03320	0.516602	+	0.856226i	$0.327197\pi$
$968$	21.8227	0.701408
$969$	−3.77539	−0.121283
$970$	0	0
$971$	−35.3208	−1.13350	−0.566749	−	0.823891i	$-0.691799\pi$
$971$	−35.3208	−1.13350	−0.566749	+	0.823891i	$0.691799\pi$
$972$	−19.7319	−0.632900
$973$	−0.125075	−0.00400974
$974$	13.0975	0.419672
$975$	0	0
$976$	−5.50252	−0.176131
$977$	37.2050	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$977$	37.2050	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$978$	0.367596	0.0117544
$979$	−3.09610	−0.0989517
$980$	0	0
$981$	−3.83450	−0.122426
$982$	6.89864	0.220144
$983$	−30.5031	−0.972897	−0.486449	−	0.873709i	$-0.661708\pi$
$983$	−30.5031	−0.972897	−0.486449	+	0.873709i	$0.661708\pi$
$984$	0.323373	0.0103088
$985$	0	0
$986$	−11.1180	−0.354070
$987$	−0.0588257	−0.00187244
$988$	−13.3598	−0.425030
$989$	14.3568	0.456518
$990$	0	0
$991$	−15.8243	−0.502675	−0.251337	−	0.967900i	$-0.580870\pi$
$991$	−15.8243	−0.502675	−0.251337	+	0.967900i	$0.580870\pi$
$992$	−3.40821	−0.108211
$993$	15.9911	0.507462
$994$	0.0693374	0.00219925
$995$	0	0
$996$	−0.229647	−0.00727664
$997$	31.5702	0.999838	0.499919	−	0.866072i	$-0.333363\pi$
$997$	31.5702	0.999838	0.499919	+	0.866072i	$0.333363\pi$
$998$	5.88064	0.186149
$999$	10.8123	0.342087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.16		25
5.4	even	2		1205.2.a.e.1.10	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.10	✓	25	5.4	even	2
6025.2.a.j.1.16		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.566303 q^{2} +0.484852 q^{3} -1.67930 q^{4} +0.274573 q^{6} +0.0113879 q^{7} -2.08360 q^{8} -2.76492 q^{9} +O(q^{10})\)	\(q+0.566303 q^{2} +0.484852 q^{3} -1.67930 q^{4} +0.274573 q^{6} +0.0113879 q^{7} -2.08360 q^{8} -2.76492 q^{9} -0.725562 q^{11} -0.814212 q^{12} +3.41734 q^{13} +0.00644902 q^{14} +2.17866 q^{16} -3.34481 q^{17} -1.56578 q^{18} +2.32799 q^{19} +0.00552146 q^{21} -0.410888 q^{22} +4.69054 q^{23} -1.01024 q^{24} +1.93525 q^{26} -2.79513 q^{27} -0.0191238 q^{28} +5.86959 q^{29} -0.631035 q^{31} +5.40097 q^{32} -0.351790 q^{33} -1.89417 q^{34} +4.64313 q^{36} -3.86827 q^{37} +1.31835 q^{38} +1.65690 q^{39} -0.320097 q^{41} +0.00312682 q^{42} +3.06079 q^{43} +1.21844 q^{44} +2.65627 q^{46} -10.6540 q^{47} +1.05633 q^{48} -6.99987 q^{49} -1.62174 q^{51} -5.73875 q^{52} -0.842935 q^{53} -1.58289 q^{54} -0.0237279 q^{56} +1.12873 q^{57} +3.32396 q^{58} +10.2157 q^{59} -2.52565 q^{61} -0.357357 q^{62} -0.0314867 q^{63} -1.29872 q^{64} -0.199220 q^{66} -8.96869 q^{67} +5.61694 q^{68} +2.27422 q^{69} +10.7516 q^{71} +5.76098 q^{72} -5.27340 q^{73} -2.19061 q^{74} -3.90940 q^{76} -0.00826265 q^{77} +0.938310 q^{78} +6.07465 q^{79} +6.93953 q^{81} -0.181272 q^{82} +0.282048 q^{83} -0.00927220 q^{84} +1.73333 q^{86} +2.84588 q^{87} +1.51178 q^{88} +4.26717 q^{89} +0.0389165 q^{91} -7.87683 q^{92} -0.305959 q^{93} -6.03339 q^{94} +2.61867 q^{96} -17.9265 q^{97} -3.96405 q^{98} +2.00612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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