LMFDB - Embedded newform 6025.2.a.j.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.25748 q^{2} +2.42991 q^{3} -0.418732 q^{4} +3.05557 q^{6} -3.44014 q^{7} -3.04152 q^{8} +2.90444 q^{9} +O(q^{10})$	\(q+1.25748 q^{2} +2.42991 q^{3} -0.418732 q^{4} +3.05557 q^{6} -3.44014 q^{7} -3.04152 q^{8} +2.90444 q^{9} +6.10481 q^{11} -1.01748 q^{12} -2.91218 q^{13} -4.32592 q^{14} -2.98720 q^{16} -2.89053 q^{17} +3.65229 q^{18} +0.435190 q^{19} -8.35922 q^{21} +7.67670 q^{22} +0.0375202 q^{23} -7.39060 q^{24} -3.66202 q^{26} -0.232203 q^{27} +1.44050 q^{28} -1.49920 q^{29} -3.02438 q^{31} +2.32668 q^{32} +14.8341 q^{33} -3.63480 q^{34} -1.21618 q^{36} -6.11186 q^{37} +0.547245 q^{38} -7.07632 q^{39} -0.436153 q^{41} -10.5116 q^{42} +3.05957 q^{43} -2.55628 q^{44} +0.0471811 q^{46} -8.14790 q^{47} -7.25861 q^{48} +4.83457 q^{49} -7.02371 q^{51} +1.21942 q^{52} +0.115328 q^{53} -0.291992 q^{54} +10.4633 q^{56} +1.05747 q^{57} -1.88522 q^{58} -10.3018 q^{59} -1.01774 q^{61} -3.80311 q^{62} -9.99168 q^{63} +8.90016 q^{64} +18.6537 q^{66} +0.262383 q^{67} +1.21036 q^{68} +0.0911705 q^{69} +2.18460 q^{71} -8.83391 q^{72} -7.24400 q^{73} -7.68557 q^{74} -0.182228 q^{76} -21.0014 q^{77} -8.89837 q^{78} -3.71002 q^{79} -9.27755 q^{81} -0.548456 q^{82} -3.99801 q^{83} +3.50027 q^{84} +3.84737 q^{86} -3.64291 q^{87} -18.5679 q^{88} -8.60342 q^{89} +10.0183 q^{91} -0.0157109 q^{92} -7.34895 q^{93} -10.2459 q^{94} +5.65361 q^{96} -0.615933 q^{97} +6.07940 q^{98} +17.7310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.25748	0.889176	0.444588	−	0.895735i	$-0.353350\pi$
$2$	1.25748	0.889176	0.444588	+	0.895735i	$0.353350\pi$
$3$	2.42991	1.40291	0.701453	−	0.712716i	$-0.252535\pi$
$3$	2.42991	1.40291	0.701453	+	0.712716i	$0.252535\pi$
$4$	−0.418732	−0.209366
$5$	0	0
$5$	0	0
$6$	3.05557	1.24743
$7$	−3.44014	−1.30025	−0.650126	−	0.759827i	$-0.725284\pi$
$7$	−3.44014	−1.30025	−0.650126	+	0.759827i	$0.725284\pi$
$8$	−3.04152	−1.07534
$9$	2.90444	0.968146
$10$	0	0
$11$	6.10481	1.84067	0.920334	−	0.391133i	$-0.127917\pi$
$11$	6.10481	1.84067	0.920334	+	0.391133i	$0.127917\pi$
$12$	−1.01748	−0.293721
$13$	−2.91218	−0.807693	−0.403847	−	0.914827i	$-0.632327\pi$
$13$	−2.91218	−0.807693	−0.403847	+	0.914827i	$0.632327\pi$
$14$	−4.32592	−1.15615
$15$	0	0
$16$	−2.98720	−0.746800
$17$	−2.89053	−0.701057	−0.350528	−	0.936552i	$-0.613998\pi$
$17$	−2.89053	−0.701057	−0.350528	+	0.936552i	$0.613998\pi$
$18$	3.65229	0.860853
$19$	0.435190	0.0998395	0.0499197	−	0.998753i	$-0.484103\pi$
$19$	0.435190	0.0998395	0.0499197	+	0.998753i	$0.484103\pi$
$20$	0	0
$21$	−8.35922	−1.82413
$22$	7.67670	1.63668
$23$	0.0375202	0.00782350	0.00391175	−	0.999992i	$-0.498755\pi$
$23$	0.0375202	0.00782350	0.00391175	+	0.999992i	$0.498755\pi$
$24$	−7.39060	−1.50860
$25$	0	0
$26$	−3.66202	−0.718182
$27$	−0.232203	−0.0446876
$28$	1.44050	0.272228
$29$	−1.49920	−0.278394	−0.139197	−	0.990265i	$-0.544452\pi$
$29$	−1.49920	−0.278394	−0.139197	+	0.990265i	$0.544452\pi$
$30$	0	0
$31$	−3.02438	−0.543194	−0.271597	−	0.962411i	$-0.587552\pi$
$31$	−3.02438	−0.543194	−0.271597	+	0.962411i	$0.587552\pi$
$32$	2.32668	0.411303
$33$	14.8341	2.58229
$34$	−3.63480	−0.623363
$35$	0	0
$36$	−1.21618	−0.202697
$37$	−6.11186	−1.00478	−0.502392	−	0.864640i	$-0.667546\pi$
$37$	−6.11186	−1.00478	−0.502392	+	0.864640i	$0.667546\pi$
$38$	0.547245	0.0887749
$39$	−7.07632	−1.13312
$40$	0	0
$41$	−0.436153	−0.0681156	−0.0340578	−	0.999420i	$-0.510843\pi$
$41$	−0.436153	−0.0681156	−0.0340578	+	0.999420i	$0.510843\pi$
$42$	−10.5116	−1.62197
$43$	3.05957	0.466581	0.233290	−	0.972407i	$-0.425051\pi$
$43$	3.05957	0.466581	0.233290	+	0.972407i	$0.425051\pi$
$44$	−2.55628	−0.385374
$45$	0	0
$46$	0.0471811	0.00695647
$47$	−8.14790	−1.18849	−0.594247	−	0.804283i	$-0.702550\pi$
$47$	−8.14790	−1.18849	−0.594247	+	0.804283i	$0.702550\pi$
$48$	−7.25861	−1.04769
$49$	4.83457	0.690653
$50$	0	0
$51$	−7.02371	−0.983517
$52$	1.21942	0.169104
$53$	0.115328	0.0158415	0.00792073	−	0.999969i	$-0.497479\pi$
$53$	0.115328	0.0158415	0.00792073	+	0.999969i	$0.497479\pi$
$54$	−0.291992	−0.0397351
$55$	0	0
$56$	10.4633	1.39821
$57$	1.05747	0.140065
$58$	−1.88522	−0.247541
$59$	−10.3018	−1.34118	−0.670589	−	0.741829i	$-0.733958\pi$
$59$	−10.3018	−1.34118	−0.670589	+	0.741829i	$0.733958\pi$
$60$	0	0
$61$	−1.01774	−0.130308	−0.0651542	−	0.997875i	$-0.520754\pi$
$61$	−1.01774	−0.130308	−0.0651542	+	0.997875i	$0.520754\pi$
$62$	−3.80311	−0.482995
$63$	−9.99168	−1.25883
$64$	8.90016	1.11252
$65$	0	0
$66$	18.6537	2.29611
$67$	0.262383	0.0320552	0.0160276	−	0.999872i	$-0.494898\pi$
$67$	0.262383	0.0320552	0.0160276	+	0.999872i	$0.494898\pi$
$68$	1.21036	0.146777
$69$	0.0911705	0.0109756
$70$	0	0
$71$	2.18460	0.259264	0.129632	−	0.991562i	$-0.458620\pi$
$71$	2.18460	0.259264	0.129632	+	0.991562i	$0.458620\pi$
$72$	−8.83391	−1.04109
$73$	−7.24400	−0.847846	−0.423923	−	0.905698i	$-0.639347\pi$
$73$	−7.24400	−0.847846	−0.423923	+	0.905698i	$0.639347\pi$
$74$	−7.68557	−0.893429
$75$	0	0
$76$	−0.182228	−0.0209030
$77$	−21.0014	−2.39333
$78$	−8.89837	−1.00754
$79$	−3.71002	−0.417410	−0.208705	−	0.977979i	$-0.566925\pi$
$79$	−3.71002	−0.417410	−0.208705	+	0.977979i	$0.566925\pi$
$80$	0	0
$81$	−9.27755	−1.03084
$82$	−0.548456	−0.0605668
$83$	−3.99801	−0.438838	−0.219419	−	0.975631i	$-0.570416\pi$
$83$	−3.99801	−0.438838	−0.219419	+	0.975631i	$0.570416\pi$
$84$	3.50027	0.381911
$85$	0	0
$86$	3.84737	0.414872
$87$	−3.64291	−0.390561
$88$	−18.5679	−1.97934
$89$	−8.60342	−0.911960	−0.455980	−	0.889990i	$-0.650711\pi$
$89$	−8.60342	−0.911960	−0.455980	+	0.889990i	$0.650711\pi$
$90$	0	0
$91$	10.0183	1.05020
$92$	−0.0157109	−0.00163798
$93$	−7.34895	−0.762051
$94$	−10.2459	−1.05678
$95$	0	0
$96$	5.65361	0.577019
$97$	−0.615933	−0.0625386	−0.0312693	−	0.999511i	$-0.509955\pi$
$97$	−0.615933	−0.0625386	−0.0312693	+	0.999511i	$0.509955\pi$
$98$	6.07940	0.614112
$99$	17.7310	1.78204
$100$	0	0
$101$	5.45701	0.542993	0.271497	−	0.962439i	$-0.412481\pi$
$101$	5.45701	0.542993	0.271497	+	0.962439i	$0.412481\pi$
$102$	−8.83221	−0.874520
$103$	−6.11470	−0.602499	−0.301250	−	0.953545i	$-0.597404\pi$
$103$	−6.11470	−0.602499	−0.301250	+	0.953545i	$0.597404\pi$
$104$	8.85745	0.868545
$105$	0	0
$106$	0.145023	0.0140859
$107$	0.399986	0.0386681	0.0193341	−	0.999813i	$-0.493845\pi$
$107$	0.399986	0.0386681	0.0193341	+	0.999813i	$0.493845\pi$
$108$	0.0972310	0.00935606
$109$	−17.9680	−1.72102	−0.860512	−	0.509430i	$-0.829856\pi$
$109$	−17.9680	−1.72102	−0.860512	+	0.509430i	$0.829856\pi$
$110$	0	0
$111$	−14.8512	−1.40962
$112$	10.2764	0.971027
$113$	16.1077	1.51528	0.757642	−	0.652671i	$-0.226352\pi$
$113$	16.1077	1.51528	0.757642	+	0.652671i	$0.226352\pi$
$114$	1.32975	0.124543
$115$	0	0
$116$	0.627763	0.0582863
$117$	−8.45825	−0.781966
$118$	−12.9543	−1.19254
$119$	9.94383	0.911550
$120$	0	0
$121$	26.2687	2.38806
$122$	−1.27979	−0.115867
$123$	−1.05981	−0.0955599
$124$	1.26640	0.113726
$125$	0	0
$126$	−12.5644	−1.11932
$127$	−19.9234	−1.76791	−0.883956	−	0.467570i	$-0.845130\pi$
$127$	−19.9234	−1.76791	−0.883956	+	0.467570i	$0.845130\pi$
$128$	6.53846	0.577924
$129$	7.43447	0.654569
$130$	0	0
$131$	−15.4494	−1.34982	−0.674910	−	0.737900i	$-0.735817\pi$
$131$	−15.4494	−1.34982	−0.674910	+	0.737900i	$0.735817\pi$
$132$	−6.21152	−0.540643
$133$	−1.49712	−0.129816
$134$	0.329943	0.0285027
$135$	0	0
$136$	8.79160	0.753874
$137$	−5.30038	−0.452842	−0.226421	−	0.974030i	$-0.572703\pi$
$137$	−5.30038	−0.452842	−0.226421	+	0.974030i	$0.572703\pi$
$138$	0.114646	0.00975927
$139$	22.6764	1.92339	0.961693	−	0.274129i	$-0.0883895\pi$
$139$	22.6764	1.92339	0.961693	+	0.274129i	$0.0883895\pi$
$140$	0	0
$141$	−19.7986	−1.66735
$142$	2.74710	0.230531
$143$	−17.7783	−1.48670
$144$	−8.67614	−0.723012
$145$	0	0
$146$	−9.10921	−0.753884
$147$	11.7475	0.968921
$148$	2.55923	0.210368
$149$	−12.3612	−1.01267	−0.506335	−	0.862337i	$-0.669000\pi$
$149$	−12.3612	−1.01267	−0.506335	+	0.862337i	$0.669000\pi$
$150$	0	0
$151$	−9.45769	−0.769656	−0.384828	−	0.922988i	$-0.625739\pi$
$151$	−9.45769	−0.769656	−0.384828	+	0.922988i	$0.625739\pi$
$152$	−1.32364	−0.107361
$153$	−8.39537	−0.678725
$154$	−26.4089	−2.12809
$155$	0	0
$156$	2.96308	0.237237
$157$	9.24840	0.738103	0.369051	−	0.929409i	$-0.379683\pi$
$157$	9.24840	0.738103	0.369051	+	0.929409i	$0.379683\pi$
$158$	−4.66529	−0.371151
$159$	0.280235	0.0222241
$160$	0	0
$161$	−0.129075	−0.0101725
$162$	−11.6664	−0.916597
$163$	−13.3085	−1.04241	−0.521203	−	0.853433i	$-0.674516\pi$
$163$	−13.3085	−1.04241	−0.521203	+	0.853433i	$0.674516\pi$
$164$	0.182631	0.0142611
$165$	0	0
$166$	−5.02743	−0.390204
$167$	12.5141	0.968367	0.484183	−	0.874967i	$-0.339117\pi$
$167$	12.5141	0.968367	0.484183	+	0.874967i	$0.339117\pi$
$168$	25.4247	1.96156
$169$	−4.51921	−0.347631
$170$	0	0
$171$	1.26398	0.0966592
$172$	−1.28114	−0.0976861
$173$	16.9914	1.29183	0.645916	−	0.763409i	$-0.276476\pi$
$173$	16.9914	1.29183	0.645916	+	0.763409i	$0.276476\pi$
$174$	−4.58090	−0.347277
$175$	0	0
$176$	−18.2363	−1.37461
$177$	−25.0324	−1.88155
$178$	−10.8187	−0.810893
$179$	13.0149	0.972782	0.486391	−	0.873741i	$-0.338313\pi$
$179$	13.0149	0.972782	0.486391	+	0.873741i	$0.338313\pi$
$180$	0	0
$181$	−5.50027	−0.408832	−0.204416	−	0.978884i	$-0.565530\pi$
$181$	−5.50027	−0.408832	−0.204416	+	0.978884i	$0.565530\pi$
$182$	12.5979	0.933816
$183$	−2.47302	−0.182811
$184$	−0.114118	−0.00841292
$185$	0	0
$186$	−9.24120	−0.677597
$187$	−17.6461	−1.29041
$188$	3.41179	0.248830
$189$	0.798813	0.0581051
$190$	0	0
$191$	4.98997	0.361062	0.180531	−	0.983569i	$-0.442218\pi$
$191$	4.98997	0.361062	0.180531	+	0.983569i	$0.442218\pi$
$192$	21.6266	1.56076
$193$	20.5174	1.47688	0.738438	−	0.674321i	$-0.235564\pi$
$193$	20.5174	1.47688	0.738438	+	0.674321i	$0.235564\pi$
$194$	−0.774527	−0.0556078
$195$	0	0
$196$	−2.02439	−0.144599
$197$	1.57731	0.112378	0.0561892	−	0.998420i	$-0.482105\pi$
$197$	1.57731	0.112378	0.0561892	+	0.998420i	$0.482105\pi$
$198$	22.2965	1.58454
$199$	18.3247	1.29901	0.649503	−	0.760359i	$-0.274977\pi$
$199$	18.3247	1.29901	0.649503	+	0.760359i	$0.274977\pi$
$200$	0	0
$201$	0.637567	0.0449705
$202$	6.86211	0.482816
$203$	5.15745	0.361982
$204$	2.94105	0.205915
$205$	0	0
$206$	−7.68914	−0.535728
$207$	0.108975	0.00757429
$208$	8.69926	0.603185
$209$	2.65675	0.183771
$210$	0	0
$211$	25.8400	1.77890	0.889448	−	0.457036i	$-0.151089\pi$
$211$	25.8400	1.77890	0.889448	+	0.457036i	$0.151089\pi$
$212$	−0.0482914	−0.00331667
$213$	5.30836	0.363723
$214$	0.502976	0.0343828
$215$	0	0
$216$	0.706251	0.0480543
$217$	10.4043	0.706289
$218$	−22.5945	−1.53029
$219$	−17.6022	−1.18945
$220$	0	0
$221$	8.41775	0.566239
$222$	−18.6752	−1.25340
$223$	−6.13852	−0.411066	−0.205533	−	0.978650i	$-0.565893\pi$
$223$	−6.13852	−0.411066	−0.205533	+	0.978650i	$0.565893\pi$
$224$	−8.00411	−0.534797
$225$	0	0
$226$	20.2552	1.34735
$227$	16.2377	1.07774	0.538868	−	0.842390i	$-0.318852\pi$
$227$	16.2377	1.07774	0.538868	+	0.842390i	$0.318852\pi$
$228$	−0.442797	−0.0293249
$229$	−25.1507	−1.66200	−0.831002	−	0.556269i	$-0.812232\pi$
$229$	−25.1507	−1.66200	−0.831002	+	0.556269i	$0.812232\pi$
$230$	0	0
$231$	−51.0314	−3.35762
$232$	4.55984	0.299368
$233$	14.1976	0.930117	0.465059	−	0.885280i	$-0.346033\pi$
$233$	14.1976	0.930117	0.465059	+	0.885280i	$0.346033\pi$
$234$	−10.6361	−0.695305
$235$	0	0
$236$	4.31369	0.280797
$237$	−9.01500	−0.585587
$238$	12.5042	0.810528
$239$	−10.1054	−0.653666	−0.326833	−	0.945082i	$-0.605981\pi$
$239$	−10.1054	−0.653666	−0.326833	+	0.945082i	$0.605981\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	33.0325	2.12341
$243$	−21.8470	−1.40148
$244$	0.426161	0.0272822
$245$	0	0
$246$	−1.33270	−0.0849695
$247$	−1.26735	−0.0806397
$248$	9.19870	0.584118
$249$	−9.71478	−0.615649
$250$	0	0
$251$	26.8384	1.69402	0.847012	−	0.531574i	$-0.178399\pi$
$251$	26.8384	1.69402	0.847012	+	0.531574i	$0.178399\pi$
$252$	4.18384	0.263557
$253$	0.229054	0.0144005
$254$	−25.0533	−1.57199
$255$	0	0
$256$	−9.57831	−0.598645
$257$	−6.47501	−0.403900	−0.201950	−	0.979396i	$-0.564728\pi$
$257$	−6.47501	−0.403900	−0.201950	+	0.979396i	$0.564728\pi$
$258$	9.34874	0.582027
$259$	21.0257	1.30647
$260$	0	0
$261$	−4.35433	−0.269526
$262$	−19.4274	−1.20023
$263$	7.24781	0.446919	0.223460	−	0.974713i	$-0.428265\pi$
$263$	7.24781	0.446919	0.223460	+	0.974713i	$0.428265\pi$
$264$	−45.1182	−2.77683
$265$	0	0
$266$	−1.88260	−0.115430
$267$	−20.9055	−1.27940
$268$	−0.109868	−0.00671128
$269$	32.2305	1.96513	0.982565	−	0.185917i	$-0.0595255\pi$
$269$	32.2305	1.96513	0.982565	+	0.185917i	$0.0595255\pi$
$270$	0	0
$271$	−2.03102	−0.123376	−0.0616879	−	0.998095i	$-0.519648\pi$
$271$	−2.03102	−0.123376	−0.0616879	+	0.998095i	$0.519648\pi$
$272$	8.63459	0.523549
$273$	24.3435	1.47334
$274$	−6.66515	−0.402656
$275$	0	0
$276$	−0.0381760	−0.00229793
$277$	−25.3320	−1.52205	−0.761025	−	0.648723i	$-0.775304\pi$
$277$	−25.3320	−1.52205	−0.761025	+	0.648723i	$0.775304\pi$
$278$	28.5152	1.71023
$279$	−8.78412	−0.525892
$280$	0	0
$281$	−25.0267	−1.49297	−0.746483	−	0.665404i	$-0.768259\pi$
$281$	−25.0267	−1.49297	−0.746483	+	0.665404i	$0.768259\pi$
$282$	−24.8965	−1.48256
$283$	−8.12232	−0.482822	−0.241411	−	0.970423i	$-0.577610\pi$
$283$	−8.12232	−0.482822	−0.241411	+	0.970423i	$0.577610\pi$
$284$	−0.914760	−0.0542810
$285$	0	0
$286$	−22.3559	−1.32193
$287$	1.50043	0.0885674
$288$	6.75770	0.398201
$289$	−8.64483	−0.508520
$290$	0	0
$291$	−1.49666	−0.0877358
$292$	3.03329	0.177510
$293$	−1.24229	−0.0725753	−0.0362877	−	0.999341i	$-0.511553\pi$
$293$	−1.24229	−0.0725753	−0.0362877	+	0.999341i	$0.511553\pi$
$294$	14.7724	0.861542
$295$	0	0
$296$	18.5893	1.08048
$297$	−1.41756	−0.0822550
$298$	−15.5440	−0.900442
$299$	−0.109266	−0.00631899
$300$	0	0
$301$	−10.5254	−0.606672
$302$	−11.8929	−0.684359
$303$	13.2600	0.761769
$304$	−1.30000	−0.0745601
$305$	0	0
$306$	−10.5570	−0.603506
$307$	−28.3495	−1.61799	−0.808997	−	0.587813i	$-0.799989\pi$
$307$	−28.3495	−1.61799	−0.808997	+	0.587813i	$0.799989\pi$
$308$	8.79396	0.501082
$309$	−14.8581	−0.845250
$310$	0	0
$311$	−17.7992	−1.00930	−0.504651	−	0.863323i	$-0.668379\pi$
$311$	−17.7992	−1.00930	−0.504651	+	0.863323i	$0.668379\pi$
$312$	21.5228	1.21849
$313$	−31.5016	−1.78057	−0.890287	−	0.455401i	$-0.849496\pi$
$313$	−31.5016	−1.78057	−0.890287	+	0.455401i	$0.849496\pi$
$314$	11.6297	0.656303
$315$	0	0
$316$	1.55350	0.0873915
$317$	−11.4499	−0.643091	−0.321546	−	0.946894i	$-0.604202\pi$
$317$	−11.4499	−0.643091	−0.321546	+	0.946894i	$0.604202\pi$
$318$	0.352391	0.0197611
$319$	−9.15232	−0.512431
$320$	0	0
$321$	0.971928	0.0542477
$322$	−0.162310	−0.00904516
$323$	−1.25793	−0.0699931
$324$	3.88481	0.215823
$325$	0	0
$326$	−16.7353	−0.926882
$327$	−43.6606	−2.41444
$328$	1.32657	0.0732474
$329$	28.0299	1.54534
$330$	0	0
$331$	−18.2040	−1.00058	−0.500292	−	0.865857i	$-0.666774\pi$
$331$	−18.2040	−1.00058	−0.500292	+	0.865857i	$0.666774\pi$
$332$	1.67409	0.0918778
$333$	−17.7515	−0.972777
$334$	15.7362	0.861048
$335$	0	0
$336$	24.9706	1.36226
$337$	2.20700	0.120223	0.0601115	−	0.998192i	$-0.480854\pi$
$337$	2.20700	0.120223	0.0601115	+	0.998192i	$0.480854\pi$
$338$	−5.68283	−0.309105
$339$	39.1401	2.12580
$340$	0	0
$341$	−18.4632	−0.999841
$342$	1.58944	0.0859471
$343$	7.44938	0.402229
$344$	−9.30575	−0.501732
$345$	0	0
$346$	21.3664	1.14867
$347$	16.6349	0.893008	0.446504	−	0.894782i	$-0.352669\pi$
$347$	16.6349	0.893008	0.446504	+	0.894782i	$0.352669\pi$
$348$	1.52540	0.0817702
$349$	13.9627	0.747405	0.373702	−	0.927549i	$-0.378088\pi$
$349$	13.9627	0.747405	0.373702	+	0.927549i	$0.378088\pi$
$350$	0	0
$351$	0.676218	0.0360939
$352$	14.2039	0.757072
$353$	6.49106	0.345484	0.172742	−	0.984967i	$-0.444737\pi$
$353$	6.49106	0.345484	0.172742	+	0.984967i	$0.444737\pi$
$354$	−31.4778	−1.67303
$355$	0	0
$356$	3.60253	0.190934
$357$	24.1626	1.27882
$358$	16.3661	0.864974
$359$	30.0584	1.58642	0.793211	−	0.608948i	$-0.208408\pi$
$359$	30.0584	1.58642	0.793211	+	0.608948i	$0.208408\pi$
$360$	0	0
$361$	−18.8106	−0.990032
$362$	−6.91651	−0.363524
$363$	63.8304	3.35023
$364$	−4.19499	−0.219877
$365$	0	0
$366$	−3.10978	−0.162551
$367$	26.8651	1.40235	0.701173	−	0.712992i	$-0.252660\pi$
$367$	26.8651	1.40235	0.701173	+	0.712992i	$0.252660\pi$
$368$	−0.112080	−0.00584259
$369$	−1.26678	−0.0659459
$370$	0	0
$371$	−0.396743	−0.0205979
$372$	3.07724	0.159548
$373$	−16.6377	−0.861469	−0.430734	−	0.902479i	$-0.641745\pi$
$373$	−16.6377	−0.861469	−0.430734	+	0.902479i	$0.641745\pi$
$374$	−22.1897	−1.14740
$375$	0	0
$376$	24.7820	1.27803
$377$	4.36594	0.224857
$378$	1.00449	0.0516656
$379$	32.1591	1.65190	0.825952	−	0.563741i	$-0.190638\pi$
$379$	32.1591	1.65190	0.825952	+	0.563741i	$0.190638\pi$
$380$	0	0
$381$	−48.4119	−2.48022
$382$	6.27481	0.321047
$383$	4.63427	0.236800	0.118400	−	0.992966i	$-0.462223\pi$
$383$	4.63427	0.236800	0.118400	+	0.992966i	$0.462223\pi$
$384$	15.8878	0.810773
$385$	0	0
$386$	25.8003	1.31320
$387$	8.88634	0.451718
$388$	0.257911	0.0130935
$389$	−37.5478	−1.90375	−0.951874	−	0.306489i	$-0.900846\pi$
$389$	−37.5478	−1.90375	−0.951874	+	0.306489i	$0.900846\pi$
$390$	0	0
$391$	−0.108453	−0.00548472
$392$	−14.7044	−0.742686
$393$	−37.5406	−1.89367
$394$	1.98344	0.0999243
$395$	0	0
$396$	−7.42456	−0.373098
$397$	4.56801	0.229262	0.114631	−	0.993408i	$-0.463431\pi$
$397$	4.56801	0.229262	0.114631	+	0.993408i	$0.463431\pi$
$398$	23.0431	1.15504
$399$	−3.63785	−0.182120
$400$	0	0
$401$	−4.51361	−0.225399	−0.112699	−	0.993629i	$-0.535950\pi$
$401$	−4.51361	−0.225399	−0.112699	+	0.993629i	$0.535950\pi$
$402$	0.801730	0.0399867
$403$	8.80754	0.438735
$404$	−2.28503	−0.113684
$405$	0	0
$406$	6.48542	0.321866
$407$	−37.3117	−1.84947
$408$	21.3628	1.05761
$409$	−8.25303	−0.408086	−0.204043	−	0.978962i	$-0.565408\pi$
$409$	−8.25303	−0.408086	−0.204043	+	0.978962i	$0.565408\pi$
$410$	0	0
$411$	−12.8794	−0.635295
$412$	2.56042	0.126143
$413$	35.4396	1.74387
$414$	0.137035	0.00673488
$415$	0	0
$416$	−6.77571	−0.332207
$417$	55.1015	2.69833
$418$	3.34083	0.163405
$419$	24.3109	1.18767	0.593833	−	0.804588i	$-0.297614\pi$
$419$	24.3109	1.18767	0.593833	+	0.804588i	$0.297614\pi$
$420$	0	0
$421$	28.2937	1.37895	0.689475	−	0.724310i	$-0.257841\pi$
$421$	28.2937	1.37895	0.689475	+	0.724310i	$0.257841\pi$
$422$	32.4934	1.58175
$423$	−23.6651	−1.15064
$424$	−0.350771	−0.0170350
$425$	0	0
$426$	6.67518	0.323414
$427$	3.50117	0.169434
$428$	−0.167487	−0.00809579
$429$	−43.1996	−2.08570
$430$	0	0
$431$	−18.6546	−0.898561	−0.449280	−	0.893391i	$-0.648320\pi$
$431$	−18.6546	−0.898561	−0.449280	+	0.893391i	$0.648320\pi$
$432$	0.693638	0.0333727
$433$	16.7317	0.804072	0.402036	−	0.915624i	$-0.368303\pi$
$433$	16.7317	0.804072	0.402036	+	0.915624i	$0.368303\pi$
$434$	13.0832	0.628015
$435$	0	0
$436$	7.52379	0.360324
$437$	0.0163284	0.000781094 0
$438$	−22.1345	−1.05763
$439$	36.5936	1.74652	0.873260	−	0.487255i	$-0.162002\pi$
$439$	36.5936	1.74652	0.873260	+	0.487255i	$0.162002\pi$
$440$	0	0
$441$	14.0417	0.668653
$442$	10.5852	0.503486
$443$	22.6142	1.07443	0.537216	−	0.843445i	$-0.319476\pi$
$443$	22.6142	1.07443	0.537216	+	0.843445i	$0.319476\pi$
$444$	6.21869	0.295126
$445$	0	0
$446$	−7.71910	−0.365510
$447$	−30.0366	−1.42068
$448$	−30.6178	−1.44656
$449$	−4.96373	−0.234253	−0.117126	−	0.993117i	$-0.537368\pi$
$449$	−4.96373	−0.234253	−0.117126	+	0.993117i	$0.537368\pi$
$450$	0	0
$451$	−2.66263	−0.125378
$452$	−6.74480	−0.317249
$453$	−22.9813	−1.07975
$454$	20.4187	0.958297
$455$	0	0
$456$	−3.21632	−0.150618
$457$	−23.3650	−1.09297	−0.546485	−	0.837469i	$-0.684035\pi$
$457$	−23.3650	−1.09297	−0.546485	+	0.837469i	$0.684035\pi$
$458$	−31.6266	−1.47781
$459$	0.671191	0.0313285
$460$	0	0
$461$	6.46899	0.301291	0.150645	−	0.988588i	$-0.451865\pi$
$461$	6.46899	0.301291	0.150645	+	0.988588i	$0.451865\pi$
$462$	−64.1712	−2.98552
$463$	−1.70184	−0.0790913	−0.0395456	−	0.999218i	$-0.512591\pi$
$463$	−1.70184	−0.0790913	−0.0395456	+	0.999218i	$0.512591\pi$
$464$	4.47840	0.207905
$465$	0	0
$466$	17.8533	0.827038
$467$	26.8597	1.24292	0.621460	−	0.783446i	$-0.286540\pi$
$467$	26.8597	1.24292	0.621460	+	0.783446i	$0.286540\pi$
$468$	3.54174	0.163717
$469$	−0.902636	−0.0416798
$470$	0	0
$471$	22.4727	1.03549
$472$	31.3331	1.44222
$473$	18.6781	0.858820
$474$	−11.3362	−0.520690
$475$	0	0
$476$	−4.16380	−0.190848
$477$	0.334962	0.0153369
$478$	−12.7074	−0.581224
$479$	−0.239763	−0.0109551	−0.00547754	−	0.999985i	$-0.501744\pi$
$479$	−0.239763	−0.0109551	−0.00547754	+	0.999985i	$0.501744\pi$
$480$	0	0
$481$	17.7988	0.811557
$482$	−1.25748	−0.0572769
$483$	−0.313639	−0.0142711
$484$	−10.9995	−0.499979
$485$	0	0
$486$	−27.4722	−1.24617
$487$	20.0006	0.906316	0.453158	−	0.891430i	$-0.350297\pi$
$487$	20.0006	0.906316	0.453158	+	0.891430i	$0.350297\pi$
$488$	3.09548	0.140126
$489$	−32.3385	−1.46240
$490$	0	0
$491$	27.0575	1.22109	0.610544	−	0.791982i	$-0.290951\pi$
$491$	27.0575	1.22109	0.610544	+	0.791982i	$0.290951\pi$
$492$	0.443777	0.0200070
$493$	4.33348	0.195170
$494$	−1.59368	−0.0717029
$495$	0	0
$496$	9.03442	0.405657
$497$	−7.51532	−0.337108
$498$	−12.2162	−0.547420
$499$	−40.8570	−1.82901	−0.914506	−	0.404572i	$-0.867420\pi$
$499$	−40.8570	−1.82901	−0.914506	+	0.404572i	$0.867420\pi$
$500$	0	0
$501$	30.4080	1.35853
$502$	33.7489	1.50629
$503$	11.8362	0.527752	0.263876	−	0.964557i	$-0.414999\pi$
$503$	11.8362	0.527752	0.263876	+	0.964557i	$0.414999\pi$
$504$	30.3899	1.35367
$505$	0	0
$506$	0.288031	0.0128046
$507$	−10.9812	−0.487694
$508$	8.34255	0.370141
$509$	33.7105	1.49419	0.747095	−	0.664717i	$-0.231448\pi$
$509$	33.7105	1.49419	0.747095	+	0.664717i	$0.231448\pi$
$510$	0	0
$511$	24.9204	1.10241
$512$	−25.1215	−1.11022
$513$	−0.101053	−0.00446158
$514$	−8.14223	−0.359138
$515$	0	0
$516$	−3.11305	−0.137044
$517$	−49.7414	−2.18762
$518$	26.4394	1.16168
$519$	41.2875	1.81232
$520$	0	0
$521$	10.1651	0.445342	0.222671	−	0.974894i	$-0.428522\pi$
$521$	10.1651	0.445342	0.222671	+	0.974894i	$0.428522\pi$
$522$	−5.47550	−0.239656
$523$	−18.5411	−0.810745	−0.405373	−	0.914152i	$-0.632858\pi$
$523$	−18.5411	−0.810745	−0.405373	+	0.914152i	$0.632858\pi$
$524$	6.46916	0.282606
$525$	0	0
$526$	9.11401	0.397390
$527$	8.74206	0.380810
$528$	−44.3124	−1.92845
$529$	−22.9986	−0.999939
$530$	0	0
$531$	−29.9209	−1.29846
$532$	0.626890	0.0271791
$533$	1.27016	0.0550166
$534$	−26.2883	−1.13761
$535$	0	0
$536$	−0.798044	−0.0344702
$537$	31.6251	1.36472
$538$	40.5294	1.74735
$539$	29.5141	1.27126
$540$	0	0
$541$	16.2722	0.699599	0.349799	−	0.936825i	$-0.386250\pi$
$541$	16.2722	0.699599	0.349799	+	0.936825i	$0.386250\pi$
$542$	−2.55398	−0.109703
$543$	−13.3651	−0.573553
$544$	−6.72534	−0.288347
$545$	0	0
$546$	30.6116	1.31006
$547$	−34.0181	−1.45451	−0.727254	−	0.686369i	$-0.759204\pi$
$547$	−34.0181	−1.45451	−0.727254	+	0.686369i	$0.759204\pi$
$548$	2.21944	0.0948098
$549$	−2.95597	−0.126158
$550$	0	0
$551$	−0.652436	−0.0277947
$552$	−0.277297	−0.0118025
$553$	12.7630	0.542738
$554$	−31.8545	−1.35337
$555$	0	0
$556$	−9.49533	−0.402692
$557$	−6.49624	−0.275255	−0.137627	−	0.990484i	$-0.543948\pi$
$557$	−6.49624	−0.275255	−0.137627	+	0.990484i	$0.543948\pi$
$558$	−11.0459	−0.467610
$559$	−8.91003	−0.376854
$560$	0	0
$561$	−42.8784	−1.81033
$562$	−31.4707	−1.32751
$563$	4.51807	0.190414	0.0952070	−	0.995457i	$-0.469649\pi$
$563$	4.51807	0.190414	0.0952070	+	0.995457i	$0.469649\pi$
$564$	8.29032	0.349085
$565$	0	0
$566$	−10.2137	−0.429314
$567$	31.9161	1.34035
$568$	−6.64449	−0.278797
$569$	19.3782	0.812374	0.406187	−	0.913790i	$-0.366858\pi$
$569$	19.3782	0.812374	0.406187	+	0.913790i	$0.366858\pi$
$570$	0	0
$571$	27.9986	1.17171	0.585853	−	0.810417i	$-0.300760\pi$
$571$	27.9986	1.17171	0.585853	+	0.810417i	$0.300760\pi$
$572$	7.44434	0.311264
$573$	12.1252	0.506536
$574$	1.88676	0.0787520
$575$	0	0
$576$	25.8500	1.07708
$577$	36.6737	1.52674	0.763372	−	0.645959i	$-0.223542\pi$
$577$	36.6737	1.52674	0.763372	+	0.645959i	$0.223542\pi$
$578$	−10.8707	−0.452163
$579$	49.8554	2.07192
$580$	0	0
$581$	13.7537	0.570600
$582$	−1.88203	−0.0780125
$583$	0.704053	0.0291589
$584$	22.0327	0.911722
$585$	0	0
$586$	−1.56216	−0.0645322
$587$	37.3165	1.54022	0.770109	−	0.637912i	$-0.220202\pi$
$587$	37.3165	1.54022	0.770109	+	0.637912i	$0.220202\pi$
$588$	−4.91907	−0.202859
$589$	−1.31618	−0.0542322
$590$	0	0
$591$	3.83271	0.157657
$592$	18.2573	0.750372
$593$	−2.82141	−0.115861	−0.0579307	−	0.998321i	$-0.518450\pi$
$593$	−2.82141	−0.115861	−0.0579307	+	0.998321i	$0.518450\pi$
$594$	−1.78256	−0.0731392
$595$	0	0
$596$	5.17604	0.212019
$597$	44.5274	1.82238
$598$	−0.137400	−0.00561869
$599$	−41.0397	−1.67684	−0.838419	−	0.545026i	$-0.816520\pi$
$599$	−41.0397	−1.67684	−0.838419	+	0.545026i	$0.816520\pi$
$600$	0	0
$601$	22.5878	0.921375	0.460687	−	0.887562i	$-0.347603\pi$
$601$	22.5878	0.921375	0.460687	+	0.887562i	$0.347603\pi$
$602$	−13.2355	−0.539438
$603$	0.762076	0.0310342
$604$	3.96024	0.161140
$605$	0	0
$606$	16.6743	0.677346
$607$	−7.99865	−0.324655	−0.162328	−	0.986737i	$-0.551900\pi$
$607$	−7.99865	−0.324655	−0.162328	+	0.986737i	$0.551900\pi$
$608$	1.01255	0.0410643
$609$	12.5321	0.507827
$610$	0	0
$611$	23.7282	0.959939
$612$	3.51541	0.142102
$613$	−36.9494	−1.49237	−0.746187	−	0.665737i	$-0.768117\pi$
$613$	−36.9494	−1.49237	−0.746187	+	0.665737i	$0.768117\pi$
$614$	−35.6491	−1.43868
$615$	0	0
$616$	63.8761	2.57364
$617$	14.3909	0.579354	0.289677	−	0.957124i	$-0.406452\pi$
$617$	14.3909	0.579354	0.289677	+	0.957124i	$0.406452\pi$
$618$	−18.6839	−0.751576
$619$	−8.64732	−0.347565	−0.173782	−	0.984784i	$-0.555599\pi$
$619$	−8.64732	−0.347565	−0.173782	+	0.984784i	$0.555599\pi$
$620$	0	0
$621$	−0.00871232	−0.000349613 0
$622$	−22.3823	−0.897448
$623$	29.5970	1.18578
$624$	21.1384	0.846213
$625$	0	0
$626$	−39.6127	−1.58324
$627$	6.45566	0.257814
$628$	−3.87260	−0.154534
$629$	17.6665	0.704410
$630$	0	0
$631$	−29.5033	−1.17451	−0.587254	−	0.809403i	$-0.699791\pi$
$631$	−29.5033	−1.17451	−0.587254	+	0.809403i	$0.699791\pi$
$632$	11.2841	0.448857
$633$	62.7887	2.49563
$634$	−14.3981	−0.571821
$635$	0	0
$636$	−0.117343	−0.00465297
$637$	−14.0791	−0.557836
$638$	−11.5089	−0.455642
$639$	6.34503	0.251005
$640$	0	0
$641$	−40.8613	−1.61392	−0.806961	−	0.590604i	$-0.798889\pi$
$641$	−40.8613	−1.61392	−0.806961	+	0.590604i	$0.798889\pi$
$642$	1.22218	0.0482358
$643$	−38.6132	−1.52275	−0.761377	−	0.648309i	$-0.775477\pi$
$643$	−38.6132	−1.52275	−0.761377	+	0.648309i	$0.775477\pi$
$644$	0.0540477	0.00212978
$645$	0	0
$646$	−1.58183	−0.0622362
$647$	−0.729963	−0.0286978	−0.0143489	−	0.999897i	$-0.504568\pi$
$647$	−0.729963	−0.0286978	−0.0143489	+	0.999897i	$0.504568\pi$
$648$	28.2178	1.10850
$649$	−62.8904	−2.46866
$650$	0	0
$651$	25.2814	0.990858
$652$	5.57271	0.218244
$653$	−14.7794	−0.578362	−0.289181	−	0.957274i	$-0.593383\pi$
$653$	−14.7794	−0.578362	−0.289181	+	0.957274i	$0.593383\pi$
$654$	−54.9025	−2.14686
$655$	0	0
$656$	1.30288	0.0508687
$657$	−21.0397	−0.820839
$658$	35.2472	1.37408
$659$	−4.67319	−0.182042	−0.0910208	−	0.995849i	$-0.529013\pi$
$659$	−4.67319	−0.182042	−0.0910208	+	0.995849i	$0.529013\pi$
$660$	0	0
$661$	0.560779	0.0218118	0.0109059	−	0.999941i	$-0.496528\pi$
$661$	0.560779	0.0218118	0.0109059	+	0.999941i	$0.496528\pi$
$662$	−22.8913	−0.889696
$663$	20.4543	0.794380
$664$	12.1600	0.471900
$665$	0	0
$666$	−22.3223	−0.864970
$667$	−0.0562502	−0.00217802
$668$	−5.24004	−0.202743
$669$	−14.9160	−0.576687
$670$	0	0
$671$	−6.21312	−0.239855
$672$	−19.4492	−0.750270
$673$	16.5422	0.637655	0.318827	−	0.947813i	$-0.396711\pi$
$673$	16.5422	0.637655	0.318827	+	0.947813i	$0.396711\pi$
$674$	2.77527	0.106899
$675$	0	0
$676$	1.89234	0.0727822
$677$	27.2288	1.04649	0.523243	−	0.852183i	$-0.324722\pi$
$677$	27.2288	1.04649	0.523243	+	0.852183i	$0.324722\pi$
$678$	49.2181	1.89021
$679$	2.11890	0.0813158
$680$	0	0
$681$	39.4561	1.51196
$682$	−23.2173	−0.889035
$683$	10.6627	0.407996	0.203998	−	0.978971i	$-0.434606\pi$
$683$	10.6627	0.407996	0.203998	+	0.978971i	$0.434606\pi$
$684$	−0.529270	−0.0202372
$685$	0	0
$686$	9.36749	0.357652
$687$	−61.1138	−2.33164
$688$	−9.13955	−0.348442
$689$	−0.335855	−0.0127951
$690$	0	0
$691$	17.2235	0.655212	0.327606	−	0.944814i	$-0.393758\pi$
$691$	17.2235	0.655212	0.327606	+	0.944814i	$0.393758\pi$
$692$	−7.11484	−0.270466
$693$	−60.9973	−2.31710
$694$	20.9181	0.794041
$695$	0	0
$696$	11.0800	0.419986
$697$	1.26071	0.0477529
$698$	17.5578	0.664574
$699$	34.4989	1.30487
$700$	0	0
$701$	−24.1883	−0.913580	−0.456790	−	0.889575i	$-0.651001\pi$
$701$	−24.1883	−0.913580	−0.456790	+	0.889575i	$0.651001\pi$
$702$	0.850334	0.0320938
$703$	−2.65982	−0.100317
$704$	54.3338	2.04778
$705$	0	0
$706$	8.16241	0.307196
$707$	−18.7729	−0.706027
$708$	10.4818	0.393932
$709$	−20.1645	−0.757293	−0.378647	−	0.925541i	$-0.623610\pi$
$709$	−20.1645	−0.757293	−0.378647	+	0.925541i	$0.623610\pi$
$710$	0	0
$711$	−10.7755	−0.404114
$712$	26.1675	0.980667
$713$	−0.113475	−0.00424968
$714$	30.3841	1.13709
$715$	0	0
$716$	−5.44977	−0.203668
$717$	−24.5552	−0.917032
$718$	37.7980	1.41061
$719$	51.1719	1.90839	0.954196	−	0.299183i	$-0.0967142\pi$
$719$	51.1719	1.90839	0.954196	+	0.299183i	$0.0967142\pi$
$720$	0	0
$721$	21.0354	0.783400
$722$	−23.6541	−0.880313
$723$	−2.42991	−0.0903691
$724$	2.30314	0.0855956
$725$	0	0
$726$	80.2657	2.97894
$727$	−1.28264	−0.0475705	−0.0237852	−	0.999717i	$-0.507572\pi$
$727$	−1.28264	−0.0475705	−0.0237852	+	0.999717i	$0.507572\pi$
$728$	−30.4709	−1.12933
$729$	−25.2534	−0.935311
$730$	0	0
$731$	−8.84379	−0.327099
$732$	1.03553	0.0382743
$733$	34.6260	1.27894	0.639470	−	0.768816i	$-0.279154\pi$
$733$	34.6260	1.27894	0.639470	+	0.768816i	$0.279154\pi$
$734$	33.7824	1.24693
$735$	0	0
$736$	0.0872975	0.00321783
$737$	1.60180	0.0590030
$738$	−1.59296	−0.0586375
$739$	−16.5790	−0.609868	−0.304934	−	0.952373i	$-0.598634\pi$
$739$	−16.5790	−0.609868	−0.304934	+	0.952373i	$0.598634\pi$
$740$	0	0
$741$	−3.07955	−0.113130
$742$	−0.498899	−0.0183151
$743$	−46.9842	−1.72368	−0.861842	−	0.507177i	$-0.830689\pi$
$743$	−46.9842	−1.72368	−0.861842	+	0.507177i	$0.830689\pi$
$744$	22.3520	0.819463
$745$	0	0
$746$	−20.9217	−0.765997
$747$	−11.6120	−0.424860
$748$	7.38900	0.270169
$749$	−1.37601	−0.0502782
$750$	0	0
$751$	0.574306	0.0209567	0.0104784	−	0.999945i	$-0.496665\pi$
$751$	0.574306	0.0209567	0.0104784	+	0.999945i	$0.496665\pi$
$752$	24.3394	0.887567
$753$	65.2147	2.37656
$754$	5.49010	0.199938
$755$	0	0
$756$	−0.334489	−0.0121652
$757$	−30.4564	−1.10696	−0.553479	−	0.832863i	$-0.686700\pi$
$757$	−30.4564	−1.10696	−0.553479	+	0.832863i	$0.686700\pi$
$758$	40.4396	1.46883
$759$	0.556578	0.0202025
$760$	0	0
$761$	42.4908	1.54029	0.770144	−	0.637870i	$-0.220184\pi$
$761$	42.4908	1.54029	0.770144	+	0.637870i	$0.220184\pi$
$762$	−60.8772	−2.20535
$763$	61.8125	2.23776
$764$	−2.08946	−0.0755940
$765$	0	0
$766$	5.82752	0.210557
$767$	30.0006	1.08326
$768$	−23.2744	−0.839842
$769$	−53.7911	−1.93976	−0.969878	−	0.243593i	$-0.921674\pi$
$769$	−53.7911	−1.93976	−0.969878	+	0.243593i	$0.921674\pi$
$770$	0	0
$771$	−15.7337	−0.566634
$772$	−8.59130	−0.309208
$773$	−54.0892	−1.94545	−0.972726	−	0.231956i	$-0.925488\pi$
$773$	−54.0892	−1.94545	−0.972726	+	0.231956i	$0.925488\pi$
$774$	11.1744	0.401657
$775$	0	0
$776$	1.87337	0.0672502
$777$	51.0903	1.83286
$778$	−47.2158	−1.69277
$779$	−0.189809	−0.00680063
$780$	0	0
$781$	13.3365	0.477219
$782$	−0.136378	−0.00487688
$783$	0.348119	0.0124408
$784$	−14.4418	−0.515779
$785$	0	0
$786$	−47.2067	−1.68381
$787$	25.8938	0.923015	0.461507	−	0.887136i	$-0.347309\pi$
$787$	25.8938	0.923015	0.461507	+	0.887136i	$0.347309\pi$
$788$	−0.660469	−0.0235282
$789$	17.6115	0.626986
$790$	0	0
$791$	−55.4127	−1.97025
$792$	−53.9293	−1.91629
$793$	2.96385	0.105249
$794$	5.74421	0.203854
$795$	0	0
$796$	−7.67315	−0.271968
$797$	28.5753	1.01219	0.506095	−	0.862478i	$-0.331089\pi$
$797$	28.5753	1.01219	0.506095	+	0.862478i	$0.331089\pi$
$798$	−4.57454	−0.161937
$799$	23.5518	0.833201
$800$	0	0
$801$	−24.9881	−0.882911
$802$	−5.67580	−0.200419
$803$	−44.2232	−1.56060
$804$	−0.266970	−0.00941529
$805$	0	0
$806$	11.0753	0.390112
$807$	78.3172	2.75689
$808$	−16.5976	−0.583902
$809$	−50.2451	−1.76653	−0.883263	−	0.468879i	$-0.844658\pi$
$809$	−50.2451	−1.76653	−0.883263	+	0.468879i	$0.844658\pi$
$810$	0	0
$811$	38.8564	1.36443	0.682217	−	0.731150i	$-0.261016\pi$
$811$	38.8564	1.36443	0.682217	+	0.731150i	$0.261016\pi$
$812$	−2.15959	−0.0757868
$813$	−4.93519	−0.173085
$814$	−46.9189	−1.64451
$815$	0	0
$816$	20.9812	0.734490
$817$	1.33150	0.0465832
$818$	−10.3781	−0.362860
$819$	29.0976	1.01675
$820$	0	0
$821$	33.0877	1.15477	0.577385	−	0.816472i	$-0.304073\pi$
$821$	33.0877	1.15477	0.577385	+	0.816472i	$0.304073\pi$
$822$	−16.1957	−0.564889
$823$	−0.254874	−0.00888435	−0.00444218	−	0.999990i	$-0.501414\pi$
$823$	−0.254874	−0.00888435	−0.00444218	+	0.999990i	$0.501414\pi$
$824$	18.5980	0.647891
$825$	0	0
$826$	44.5647	1.55061
$827$	48.2635	1.67829	0.839143	−	0.543910i	$-0.183057\pi$
$827$	48.2635	1.67829	0.839143	+	0.543910i	$0.183057\pi$
$828$	−0.0456314	−0.00158580
$829$	−40.0346	−1.39046	−0.695230	−	0.718787i	$-0.744698\pi$
$829$	−40.0346	−1.39046	−0.695230	+	0.718787i	$0.744698\pi$
$830$	0	0
$831$	−61.5543	−2.13529
$832$	−25.9189	−0.898575
$833$	−13.9745	−0.484187
$834$	69.2893	2.39929
$835$	0	0
$836$	−1.11247	−0.0384755
$837$	0.702271	0.0242740
$838$	30.5706	1.05604
$839$	−17.5710	−0.606619	−0.303309	−	0.952892i	$-0.598092\pi$
$839$	−17.5710	−0.606619	−0.303309	+	0.952892i	$0.598092\pi$
$840$	0	0
$841$	−26.7524	−0.922497
$842$	35.5789	1.22613
$843$	−60.8125	−2.09449
$844$	−10.8200	−0.372441
$845$	0	0
$846$	−29.7585	−1.02312
$847$	−90.3679	−3.10508
$848$	−0.344507	−0.0118304
$849$	−19.7365	−0.677354
$850$	0	0
$851$	−0.229318	−0.00786092
$852$	−2.22278	−0.0761512
$853$	−19.5879	−0.670676	−0.335338	−	0.942098i	$-0.608851\pi$
$853$	−19.5879	−0.670676	−0.335338	+	0.942098i	$0.608851\pi$
$854$	4.40267	0.150656
$855$	0	0
$856$	−1.21656	−0.0415813
$857$	−9.38946	−0.320738	−0.160369	−	0.987057i	$-0.551268\pi$
$857$	−9.38946	−0.320738	−0.160369	+	0.987057i	$0.551268\pi$
$858$	−54.3228	−1.85455
$859$	−40.9326	−1.39660	−0.698301	−	0.715804i	$-0.746060\pi$
$859$	−40.9326	−1.39660	−0.698301	+	0.715804i	$0.746060\pi$
$860$	0	0
$861$	3.64590	0.124252
$862$	−23.4579	−0.798979
$863$	−10.2287	−0.348190	−0.174095	−	0.984729i	$-0.555700\pi$
$863$	−10.2287	−0.348190	−0.174095	+	0.984729i	$0.555700\pi$
$864$	−0.540263	−0.0183801
$865$	0	0
$866$	21.0398	0.714962
$867$	−21.0061	−0.713405
$868$	−4.35661	−0.147873
$869$	−22.6490	−0.768313
$870$	0	0
$871$	−0.764108	−0.0258908
$872$	54.6501	1.85069
$873$	−1.78894	−0.0605465
$874$	0.0205327	0.000694530 0
$875$	0	0
$876$	7.37062	0.249030
$877$	12.6843	0.428319	0.214160	−	0.976799i	$-0.431299\pi$
$877$	12.6843	0.428319	0.214160	+	0.976799i	$0.431299\pi$
$878$	46.0160	1.55296
$879$	−3.01864	−0.101816
$880$	0	0
$881$	30.5518	1.02931	0.514657	−	0.857396i	$-0.327919\pi$
$881$	30.5518	1.02931	0.514657	+	0.857396i	$0.327919\pi$
$882$	17.6572	0.594550
$883$	−11.1859	−0.376435	−0.188217	−	0.982127i	$-0.560271\pi$
$883$	−11.1859	−0.376435	−0.188217	+	0.982127i	$0.560271\pi$
$884$	−3.52478	−0.118551
$885$	0	0
$886$	28.4370	0.955359
$887$	17.5867	0.590504	0.295252	−	0.955419i	$-0.404596\pi$
$887$	17.5867	0.590504	0.295252	+	0.955419i	$0.404596\pi$
$888$	45.1703	1.51582
$889$	68.5392	2.29873
$890$	0	0
$891$	−56.6377	−1.89743
$892$	2.57040	0.0860633
$893$	−3.54589	−0.118659
$894$	−37.7706	−1.26324
$895$	0	0
$896$	−22.4932	−0.751446
$897$	−0.265505	−0.00886495
$898$	−6.24181	−0.208292
$899$	4.53414	0.151222
$900$	0	0
$901$	−0.333358	−0.0111058
$902$	−3.34822	−0.111483
$903$	−25.5756	−0.851104
$904$	−48.9918	−1.62944
$905$	0	0
$906$	−28.8986	−0.960092
$907$	1.47883	0.0491036	0.0245518	−	0.999699i	$-0.492184\pi$
$907$	1.47883	0.0491036	0.0245518	+	0.999699i	$0.492184\pi$
$908$	−6.79926	−0.225641
$909$	15.8496	0.525697
$910$	0	0
$911$	−39.8388	−1.31992	−0.659960	−	0.751301i	$-0.729427\pi$
$911$	−39.8388	−1.31992	−0.659960	+	0.751301i	$0.729427\pi$
$912$	−3.15888	−0.104601
$913$	−24.4071	−0.807756
$914$	−29.3812	−0.971843
$915$	0	0
$916$	10.5314	0.347967
$917$	53.1481	1.75510
$918$	0.844013	0.0278566
$919$	−10.1754	−0.335655	−0.167828	−	0.985816i	$-0.553675\pi$
$919$	−10.1754	−0.335655	−0.167828	+	0.985816i	$0.553675\pi$
$920$	0	0
$921$	−68.8867	−2.26989
$922$	8.13465	0.267900
$923$	−6.36194	−0.209406
$924$	21.3685	0.702972
$925$	0	0
$926$	−2.14004	−0.0703261
$927$	−17.7598	−0.583307
$928$	−3.48816	−0.114504
$929$	15.1566	0.497273	0.248636	−	0.968597i	$-0.420018\pi$
$929$	15.1566	0.497273	0.248636	+	0.968597i	$0.420018\pi$
$930$	0	0
$931$	2.10396	0.0689544
$932$	−5.94500	−0.194735
$933$	−43.2505	−1.41596
$934$	33.7757	1.10517
$935$	0	0
$936$	25.7259	0.840878
$937$	−21.5489	−0.703973	−0.351987	−	0.936005i	$-0.614494\pi$
$937$	−21.5489	−0.703973	−0.351987	+	0.936005i	$0.614494\pi$
$938$	−1.13505	−0.0370607
$939$	−76.5458	−2.49798
$940$	0	0
$941$	4.96936	0.161996	0.0809982	−	0.996714i	$-0.474189\pi$
$941$	4.96936	0.161996	0.0809982	+	0.996714i	$0.474189\pi$
$942$	28.2591	0.920732
$943$	−0.0163645	−0.000532903 0
$944$	30.7735	1.00159
$945$	0	0
$946$	23.4874	0.763642
$947$	−43.1691	−1.40281	−0.701403	−	0.712765i	$-0.747443\pi$
$947$	−43.1691	−1.40281	−0.701403	+	0.712765i	$0.747443\pi$
$948$	3.77487	0.122602
$949$	21.0958	0.684799
$950$	0	0
$951$	−27.8222	−0.902197
$952$	−30.2444	−0.980225
$953$	29.6499	0.960455	0.480228	−	0.877144i	$-0.340554\pi$
$953$	29.6499	0.960455	0.480228	+	0.877144i	$0.340554\pi$
$954$	0.421210	0.0136372
$955$	0	0
$956$	4.23147	0.136855
$957$	−22.2393	−0.718893
$958$	−0.301499	−0.00974099
$959$	18.2341	0.588808
$960$	0	0
$961$	−21.8531	−0.704940
$962$	22.3818	0.721617
$963$	1.16174	0.0374364
$964$	0.418732	0.0134865
$965$	0	0
$966$	−0.394397	−0.0126895
$967$	46.8305	1.50597	0.752984	−	0.658038i	$-0.228614\pi$
$967$	46.8305	1.50597	0.752984	+	0.658038i	$0.228614\pi$
$968$	−79.8967	−2.56798
$969$	−3.05665	−0.0981938
$970$	0	0
$971$	−30.5519	−0.980456	−0.490228	−	0.871594i	$-0.663087\pi$
$971$	−30.5519	−0.980456	−0.490228	+	0.871594i	$0.663087\pi$
$972$	9.14802	0.293423
$973$	−78.0100	−2.50088
$974$	25.1505	0.805874
$975$	0	0
$976$	3.04020	0.0973143
$977$	12.3905	0.396406	0.198203	−	0.980161i	$-0.436489\pi$
$977$	12.3905	0.396406	0.198203	+	0.980161i	$0.436489\pi$
$978$	−40.6652	−1.30033
$979$	−52.5222	−1.67862
$980$	0	0
$981$	−52.1870	−1.66620
$982$	34.0244	1.08576
$983$	−25.7281	−0.820599	−0.410299	−	0.911951i	$-0.634576\pi$
$983$	−25.7281	−0.820599	−0.410299	+	0.911951i	$0.634576\pi$
$984$	3.22343	0.102759
$985$	0	0
$986$	5.44928	0.173541
$987$	68.1101	2.16797
$988$	0.530681	0.0168832
$989$	0.114796	0.00365029
$990$	0	0
$991$	−50.3530	−1.59951	−0.799757	−	0.600323i	$-0.795039\pi$
$991$	−50.3530	−1.59951	−0.799757	+	0.600323i	$0.795039\pi$
$992$	−7.03676	−0.223417
$993$	−44.2341	−1.40373
$994$	−9.45040	−0.299748
$995$	0	0
$996$	4.06789	0.128896
$997$	40.3647	1.27836	0.639181	−	0.769057i	$-0.279274\pi$
$997$	40.3647	1.27836	0.639181	+	0.769057i	$0.279274\pi$
$998$	−51.3771	−1.62631
$999$	1.41919	0.0449013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.19		25
5.4	even	2		1205.2.a.e.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.7	✓	25	5.4	even	2
6025.2.a.j.1.19		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)

\(f(q)\)	\(=\)	\(q+1.25748 q^{2} +2.42991 q^{3} -0.418732 q^{4} +3.05557 q^{6} -3.44014 q^{7} -3.04152 q^{8} +2.90444 q^{9} +O(q^{10})\)	\(q+1.25748 q^{2} +2.42991 q^{3} -0.418732 q^{4} +3.05557 q^{6} -3.44014 q^{7} -3.04152 q^{8} +2.90444 q^{9} +6.10481 q^{11} -1.01748 q^{12} -2.91218 q^{13} -4.32592 q^{14} -2.98720 q^{16} -2.89053 q^{17} +3.65229 q^{18} +0.435190 q^{19} -8.35922 q^{21} +7.67670 q^{22} +0.0375202 q^{23} -7.39060 q^{24} -3.66202 q^{26} -0.232203 q^{27} +1.44050 q^{28} -1.49920 q^{29} -3.02438 q^{31} +2.32668 q^{32} +14.8341 q^{33} -3.63480 q^{34} -1.21618 q^{36} -6.11186 q^{37} +0.547245 q^{38} -7.07632 q^{39} -0.436153 q^{41} -10.5116 q^{42} +3.05957 q^{43} -2.55628 q^{44} +0.0471811 q^{46} -8.14790 q^{47} -7.25861 q^{48} +4.83457 q^{49} -7.02371 q^{51} +1.21942 q^{52} +0.115328 q^{53} -0.291992 q^{54} +10.4633 q^{56} +1.05747 q^{57} -1.88522 q^{58} -10.3018 q^{59} -1.01774 q^{61} -3.80311 q^{62} -9.99168 q^{63} +8.90016 q^{64} +18.6537 q^{66} +0.262383 q^{67} +1.21036 q^{68} +0.0911705 q^{69} +2.18460 q^{71} -8.83391 q^{72} -7.24400 q^{73} -7.68557 q^{74} -0.182228 q^{76} -21.0014 q^{77} -8.89837 q^{78} -3.71002 q^{79} -9.27755 q^{81} -0.548456 q^{82} -3.99801 q^{83} +3.50027 q^{84} +3.84737 q^{86} -3.64291 q^{87} -18.5679 q^{88} -8.60342 q^{89} +10.0183 q^{91} -0.0157109 q^{92} -7.34895 q^{93} -10.2459 q^{94} +5.65361 q^{96} -0.615933 q^{97} +6.07940 q^{98} +17.7310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 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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