LMFDB - Embedded newform 6025.2.a.l.1.15

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.23402 q^{2} -3.02124 q^{3} -0.477193 q^{4} +3.72827 q^{6} +0.346766 q^{7} +3.05691 q^{8} +6.12789 q^{9} +O(q^{10})$	\(q-1.23402 q^{2} -3.02124 q^{3} -0.477193 q^{4} +3.72827 q^{6} +0.346766 q^{7} +3.05691 q^{8} +6.12789 q^{9} +3.53617 q^{11} +1.44171 q^{12} -0.754848 q^{13} -0.427916 q^{14} -2.81790 q^{16} +6.52353 q^{17} -7.56194 q^{18} +2.80797 q^{19} -1.04766 q^{21} -4.36371 q^{22} -5.53569 q^{23} -9.23565 q^{24} +0.931498 q^{26} -9.45009 q^{27} -0.165474 q^{28} +10.6084 q^{29} -7.44480 q^{31} -2.63647 q^{32} -10.6836 q^{33} -8.05017 q^{34} -2.92418 q^{36} -8.79104 q^{37} -3.46509 q^{38} +2.28058 q^{39} +9.37710 q^{41} +1.29284 q^{42} -2.18851 q^{43} -1.68744 q^{44} +6.83115 q^{46} +0.847346 q^{47} +8.51355 q^{48} -6.87975 q^{49} -19.7091 q^{51} +0.360208 q^{52} -2.80306 q^{53} +11.6616 q^{54} +1.06003 q^{56} -8.48355 q^{57} -13.0909 q^{58} -8.40776 q^{59} -8.32945 q^{61} +9.18704 q^{62} +2.12494 q^{63} +8.88926 q^{64} +13.1838 q^{66} -2.43662 q^{67} -3.11298 q^{68} +16.7246 q^{69} -4.81460 q^{71} +18.7324 q^{72} -8.19214 q^{73} +10.8483 q^{74} -1.33994 q^{76} +1.22622 q^{77} -2.81428 q^{78} -0.918522 q^{79} +10.1673 q^{81} -11.5715 q^{82} +0.583411 q^{83} +0.499937 q^{84} +2.70067 q^{86} -32.0504 q^{87} +10.8098 q^{88} +13.9038 q^{89} -0.261755 q^{91} +2.64159 q^{92} +22.4925 q^{93} -1.04564 q^{94} +7.96540 q^{96} +2.05714 q^{97} +8.48976 q^{98} +21.6693 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * 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 $

$2$	−1.23402	−0.872584	−0.436292	−	0.899805i	$-0.643709\pi$
$2$	−1.23402	−0.872584	−0.436292	+	0.899805i	$0.643709\pi$
$3$	−3.02124	−1.74431	−0.872157	−	0.489227i	$-0.837279\pi$
$3$	−3.02124	−1.74431	−0.872157	+	0.489227i	$0.837279\pi$
$4$	−0.477193	−0.238596
$5$	0	0
$5$	0	0
$6$	3.72827	1.52206
$7$	0.346766	0.131065	0.0655326	−	0.997850i	$-0.479125\pi$
$7$	0.346766	0.131065	0.0655326	+	0.997850i	$0.479125\pi$
$8$	3.05691	1.08078
$9$	6.12789	2.04263
$10$	0	0
$11$	3.53617	1.06620	0.533098	−	0.846053i	$-0.321028\pi$
$11$	3.53617	1.06620	0.533098	+	0.846053i	$0.321028\pi$
$12$	1.44171	0.416187
$13$	−0.754848	−0.209357	−0.104679	−	0.994506i	$-0.533381\pi$
$13$	−0.754848	−0.209357	−0.104679	+	0.994506i	$0.533381\pi$
$14$	−0.427916	−0.114365
$15$	0	0
$16$	−2.81790	−0.704475
$17$	6.52353	1.58219	0.791094	−	0.611695i	$-0.209512\pi$
$17$	6.52353	1.58219	0.791094	+	0.611695i	$0.209512\pi$
$18$	−7.56194	−1.78237
$19$	2.80797	0.644193	0.322096	−	0.946707i	$-0.395612\pi$
$19$	2.80797	0.644193	0.322096	+	0.946707i	$0.395612\pi$
$20$	0	0
$21$	−1.04766	−0.228619
$22$	−4.36371	−0.930347
$23$	−5.53569	−1.15427	−0.577135	−	0.816649i	$-0.695829\pi$
$23$	−5.53569	−1.15427	−0.577135	+	0.816649i	$0.695829\pi$
$24$	−9.23565	−1.88522
$25$	0	0
$26$	0.931498	0.182682
$27$	−9.45009	−1.81867
$28$	−0.165474	−0.0312717
$29$	10.6084	1.96992	0.984961	−	0.172778i	$-0.0552743\pi$
$29$	10.6084	1.96992	0.984961	+	0.172778i	$0.0552743\pi$
$30$	0	0
$31$	−7.44480	−1.33713	−0.668563	−	0.743655i	$-0.733090\pi$
$31$	−7.44480	−1.33713	−0.668563	+	0.743655i	$0.733090\pi$
$32$	−2.63647	−0.466066
$33$	−10.6836	−1.85978
$34$	−8.05017	−1.38059
$35$	0	0
$36$	−2.92418	−0.487364
$37$	−8.79104	−1.44524	−0.722619	−	0.691247i	$-0.757062\pi$
$37$	−8.79104	−1.44524	−0.722619	+	0.691247i	$0.757062\pi$
$38$	−3.46509	−0.562113
$39$	2.28058	0.365185
$40$	0	0
$41$	9.37710	1.46446	0.732229	−	0.681059i	$-0.238480\pi$
$41$	9.37710	1.46446	0.732229	+	0.681059i	$0.238480\pi$
$42$	1.29284	0.199489
$43$	−2.18851	−0.333745	−0.166872	−	0.985978i	$-0.553367\pi$
$43$	−2.18851	−0.333745	−0.166872	+	0.985978i	$0.553367\pi$
$44$	−1.68744	−0.254391
$45$	0	0
$46$	6.83115	1.00720
$47$	0.847346	0.123598	0.0617991	−	0.998089i	$-0.480316\pi$
$47$	0.847346	0.123598	0.0617991	+	0.998089i	$0.480316\pi$
$48$	8.51355	1.22883
$49$	−6.87975	−0.982822
$50$	0	0
$51$	−19.7091	−2.75983
$52$	0.360208	0.0499519
$53$	−2.80306	−0.385030	−0.192515	−	0.981294i	$-0.561664\pi$
$53$	−2.80306	−0.385030	−0.192515	+	0.981294i	$0.561664\pi$
$54$	11.6616	1.58694
$55$	0	0
$56$	1.06003	0.141653
$57$	−8.48355	−1.12367
$58$	−13.0909	−1.71892
$59$	−8.40776	−1.09460	−0.547299	−	0.836937i	$-0.684344\pi$
$59$	−8.40776	−1.09460	−0.547299	+	0.836937i	$0.684344\pi$
$60$	0	0
$61$	−8.32945	−1.06648	−0.533238	−	0.845965i	$-0.679025\pi$
$61$	−8.32945	−1.06648	−0.533238	+	0.845965i	$0.679025\pi$
$62$	9.18704	1.16676
$63$	2.12494	0.267717
$64$	8.88926	1.11116
$65$	0	0
$66$	13.1838	1.62282
$67$	−2.43662	−0.297681	−0.148840	−	0.988861i	$-0.547554\pi$
$67$	−2.43662	−0.297681	−0.148840	+	0.988861i	$0.547554\pi$
$68$	−3.11298	−0.377505
$69$	16.7246	2.01341
$70$	0	0
$71$	−4.81460	−0.571388	−0.285694	−	0.958321i	$-0.592224\pi$
$71$	−4.81460	−0.571388	−0.285694	+	0.958321i	$0.592224\pi$
$72$	18.7324	2.20763
$73$	−8.19214	−0.958817	−0.479409	−	0.877592i	$-0.659149\pi$
$73$	−8.19214	−0.958817	−0.479409	+	0.877592i	$0.659149\pi$
$74$	10.8483	1.26109
$75$	0	0
$76$	−1.33994	−0.153702
$77$	1.22622	0.139741
$78$	−2.81428	−0.318654
$79$	−0.918522	−0.103342	−0.0516709	−	0.998664i	$-0.516455\pi$
$79$	−0.918522	−0.103342	−0.0516709	+	0.998664i	$0.516455\pi$
$80$	0	0
$81$	10.1673	1.12970
$82$	−11.5715	−1.27786
$83$	0.583411	0.0640377	0.0320188	−	0.999487i	$-0.489806\pi$
$83$	0.583411	0.0640377	0.0320188	+	0.999487i	$0.489806\pi$
$84$	0.499937	0.0545476
$85$	0	0
$86$	2.70067	0.291221
$87$	−32.0504	−3.43616
$88$	10.8098	1.15232
$89$	13.9038	1.47380	0.736902	−	0.676000i	$-0.236288\pi$
$89$	13.9038	1.47380	0.736902	+	0.676000i	$0.236288\pi$
$90$	0	0
$91$	−0.261755	−0.0274394
$92$	2.64159	0.275405
$93$	22.4925	2.33237
$94$	−1.04564	−0.107850
$95$	0	0
$96$	7.96540	0.812965
$97$	2.05714	0.208871	0.104435	−	0.994532i	$-0.466696\pi$
$97$	2.05714	0.208871	0.104435	+	0.994532i	$0.466696\pi$
$98$	8.48976	0.857595
$99$	21.6693	2.17784
$100$	0	0
$101$	−17.2872	−1.72014	−0.860072	−	0.510173i	$-0.829581\pi$
$101$	−17.2872	−1.72014	−0.860072	+	0.510173i	$0.829581\pi$
$102$	24.3215	2.40819
$103$	−19.9121	−1.96199	−0.980997	−	0.194022i	$-0.937847\pi$
$103$	−19.9121	−1.96199	−0.980997	+	0.194022i	$0.937847\pi$
$104$	−2.30750	−0.226269
$105$	0	0
$106$	3.45903	0.335971
$107$	−0.424967	−0.0410831	−0.0205415	−	0.999789i	$-0.506539\pi$
$107$	−0.424967	−0.0410831	−0.0205415	+	0.999789i	$0.506539\pi$
$108$	4.50952	0.433928
$109$	15.9081	1.52372	0.761858	−	0.647744i	$-0.224287\pi$
$109$	15.9081	1.52372	0.761858	+	0.647744i	$0.224287\pi$
$110$	0	0
$111$	26.5598	2.52095
$112$	−0.977151	−0.0923321
$113$	5.74648	0.540583	0.270292	−	0.962778i	$-0.412880\pi$
$113$	5.74648	0.540583	0.270292	+	0.962778i	$0.412880\pi$
$114$	10.4689	0.980500
$115$	0	0
$116$	−5.06223	−0.470016
$117$	−4.62562	−0.427639
$118$	10.3754	0.955129
$119$	2.26214	0.207370
$120$	0	0
$121$	1.50453	0.136776
$122$	10.2787	0.930591
$123$	−28.3305	−2.55447
$124$	3.55261	0.319034
$125$	0	0
$126$	−2.62222	−0.233606
$127$	−7.81763	−0.693702	−0.346851	−	0.937920i	$-0.612749\pi$
$127$	−7.81763	−0.693702	−0.346851	+	0.937920i	$0.612749\pi$
$128$	−5.69659	−0.503512
$129$	6.61202	0.582156
$130$	0	0
$131$	17.3249	1.51368	0.756841	−	0.653599i	$-0.226742\pi$
$131$	17.3249	1.51368	0.756841	+	0.653599i	$0.226742\pi$
$132$	5.09815	0.443737
$133$	0.973708	0.0844312
$134$	3.00684	0.259752
$135$	0	0
$136$	19.9418	1.71000
$137$	17.5916	1.50295	0.751474	−	0.659763i	$-0.229343\pi$
$137$	17.5916	1.50295	0.751474	+	0.659763i	$0.229343\pi$
$138$	−20.6385	−1.75687
$139$	15.7446	1.33544	0.667719	−	0.744413i	$-0.267271\pi$
$139$	15.7446	1.33544	0.667719	+	0.744413i	$0.267271\pi$
$140$	0	0
$141$	−2.56003	−0.215594
$142$	5.94132	0.498584
$143$	−2.66928	−0.223216
$144$	−17.2678	−1.43898
$145$	0	0
$146$	10.1093	0.836649
$147$	20.7854	1.71435
$148$	4.19502	0.344829
$149$	−15.3801	−1.25999	−0.629993	−	0.776601i	$-0.716942\pi$
$149$	−15.3801	−1.25999	−0.629993	+	0.776601i	$0.716942\pi$
$150$	0	0
$151$	6.07573	0.494436	0.247218	−	0.968960i	$-0.420484\pi$
$151$	6.07573	0.494436	0.247218	+	0.968960i	$0.420484\pi$
$152$	8.58371	0.696231
$153$	39.9754	3.23182
$154$	−1.51319	−0.121936
$155$	0	0
$156$	−1.08828	−0.0871318
$157$	−0.0151969	−0.00121284	−0.000606422	−	1.00000i	$-0.500193\pi$
$157$	−0.0151969	−0.00121284	−0.000606422		1.00000i	$0.500193\pi$
$158$	1.13348	0.0901744
$159$	8.46871	0.671612
$160$	0	0
$161$	−1.91959	−0.151285
$162$	−12.5467	−0.985761
$163$	−21.7836	−1.70622	−0.853110	−	0.521730i	$-0.825287\pi$
$163$	−21.7836	−1.70622	−0.853110	+	0.521730i	$0.825287\pi$
$164$	−4.47469	−0.349414
$165$	0	0
$166$	−0.719941	−0.0558783
$167$	0.949747	0.0734936	0.0367468	−	0.999325i	$-0.488300\pi$
$167$	0.949747	0.0734936	0.0367468	+	0.999325i	$0.488300\pi$
$168$	−3.20261	−0.247086
$169$	−12.4302	−0.956170
$170$	0	0
$171$	17.2069	1.31585
$172$	1.04434	0.0796304
$173$	1.50566	0.114473	0.0572367	−	0.998361i	$-0.481771\pi$
$173$	1.50566	0.114473	0.0572367	+	0.998361i	$0.481771\pi$
$174$	39.5508	2.99834
$175$	0	0
$176$	−9.96459	−0.751109
$177$	25.4019	1.90932
$178$	−17.1576	−1.28602
$179$	2.14103	0.160028	0.0800140	−	0.996794i	$-0.474504\pi$
$179$	2.14103	0.160028	0.0800140	+	0.996794i	$0.474504\pi$
$180$	0	0
$181$	−10.0692	−0.748435	−0.374218	−	0.927341i	$-0.622089\pi$
$181$	−10.0692	−0.748435	−0.374218	+	0.927341i	$0.622089\pi$
$182$	0.323012	0.0239432
$183$	25.1653	1.86027
$184$	−16.9221	−1.24751
$185$	0	0
$186$	−27.7562	−2.03519
$187$	23.0683	1.68692
$188$	−0.404348	−0.0294901
$189$	−3.27697	−0.238364
$190$	0	0
$191$	−9.95581	−0.720377	−0.360189	−	0.932879i	$-0.617288\pi$
$191$	−9.95581	−0.720377	−0.360189	+	0.932879i	$0.617288\pi$
$192$	−26.8566	−1.93821
$193$	14.9404	1.07543	0.537716	−	0.843126i	$-0.319287\pi$
$193$	14.9404	1.07543	0.537716	+	0.843126i	$0.319287\pi$
$194$	−2.53855	−0.182257
$195$	0	0
$196$	3.28297	0.234498
$197$	−8.42731	−0.600421	−0.300211	−	0.953873i	$-0.597057\pi$
$197$	−8.42731	−0.600421	−0.300211	+	0.953873i	$0.597057\pi$
$198$	−26.7403	−1.90035
$199$	−27.3440	−1.93836	−0.969182	−	0.246347i	$-0.920770\pi$
$199$	−27.3440	−1.93836	−0.969182	+	0.246347i	$0.920770\pi$
$200$	0	0
$201$	7.36162	0.519249
$202$	21.3328	1.50097
$203$	3.67861	0.258188
$204$	9.40506	0.658486
$205$	0	0
$206$	24.5719	1.71201
$207$	−33.9221	−2.35775
$208$	2.12709	0.147487
$209$	9.92948	0.686836
$210$	0	0
$211$	−13.0812	−0.900548	−0.450274	−	0.892890i	$-0.648674\pi$
$211$	−13.0812	−0.900548	−0.450274	+	0.892890i	$0.648674\pi$
$212$	1.33760	0.0918667
$213$	14.5461	0.996679
$214$	0.524417	0.0358484
$215$	0	0
$216$	−28.8881	−1.96558
$217$	−2.58160	−0.175251
$218$	−19.6309	−1.32957
$219$	24.7504	1.67248
$220$	0	0
$221$	−4.92427	−0.331243
$222$	−32.7754	−2.19974
$223$	−0.758712	−0.0508071	−0.0254036	−	0.999677i	$-0.508087\pi$
$223$	−0.758712	−0.0508071	−0.0254036	+	0.999677i	$0.508087\pi$
$224$	−0.914236	−0.0610850
$225$	0	0
$226$	−7.09128	−0.471705
$227$	27.7348	1.84082	0.920411	−	0.390951i	$-0.127854\pi$
$227$	27.7348	1.84082	0.920411	+	0.390951i	$0.127854\pi$
$228$	4.04829	0.268105
$229$	−3.29040	−0.217436	−0.108718	−	0.994073i	$-0.534674\pi$
$229$	−3.29040	−0.217436	−0.108718	+	0.994073i	$0.534674\pi$
$230$	0	0
$231$	−3.70472	−0.243752
$232$	32.4288	2.12905
$233$	−14.5606	−0.953896	−0.476948	−	0.878931i	$-0.658257\pi$
$233$	−14.5606	−0.953896	−0.476948	+	0.878931i	$0.658257\pi$
$234$	5.70812	0.373151
$235$	0	0
$236$	4.01212	0.261167
$237$	2.77507	0.180260
$238$	−2.79152	−0.180948
$239$	9.83634	0.636260	0.318130	−	0.948047i	$-0.396945\pi$
$239$	9.83634	0.636260	0.318130	+	0.948047i	$0.396945\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−1.85662	−0.119348
$243$	−2.36765	−0.151885
$244$	3.97476	0.254458
$245$	0	0
$246$	34.9604	2.22899
$247$	−2.11959	−0.134866
$248$	−22.7581	−1.44514
$249$	−1.76262	−0.111702
$250$	0	0
$251$	−25.1578	−1.58795	−0.793973	−	0.607953i	$-0.791991\pi$
$251$	−25.1578	−1.58795	−0.793973	+	0.607953i	$0.791991\pi$
$252$	−1.01401	−0.0638764
$253$	−19.5752	−1.23068
$254$	9.64711	0.605314
$255$	0	0
$256$	−10.7488	−0.671800
$257$	−20.9079	−1.30420	−0.652099	−	0.758134i	$-0.726111\pi$
$257$	−20.9079	−1.30420	−0.652099	+	0.758134i	$0.726111\pi$
$258$	−8.15936	−0.507980
$259$	−3.04843	−0.189420
$260$	0	0
$261$	65.0068	4.02382
$262$	−21.3793	−1.32082
$263$	−2.24186	−0.138239	−0.0691196	−	0.997608i	$-0.522019\pi$
$263$	−2.24186	−0.138239	−0.0691196	+	0.997608i	$0.522019\pi$
$264$	−32.6589	−2.01001
$265$	0	0
$266$	−1.20158	−0.0736733
$267$	−42.0068	−2.57078
$268$	1.16274	0.0710256
$269$	−10.5367	−0.642436	−0.321218	−	0.947005i	$-0.604092\pi$
$269$	−10.5367	−0.642436	−0.321218	+	0.947005i	$0.604092\pi$
$270$	0	0
$271$	0.193596	0.0117601	0.00588005	−	0.999983i	$-0.498128\pi$
$271$	0.193596	0.0117601	0.00588005	+	0.999983i	$0.498128\pi$
$272$	−18.3827	−1.11461
$273$	0.790826	0.0478630
$274$	−21.7083	−1.31145
$275$	0	0
$276$	−7.98088	−0.480392
$277$	21.6859	1.30298	0.651491	−	0.758657i	$-0.274144\pi$
$277$	21.6859	1.30298	0.651491	+	0.758657i	$0.274144\pi$
$278$	−19.4291	−1.16528
$279$	−45.6209	−2.73125
$280$	0	0
$281$	−15.9688	−0.952619	−0.476310	−	0.879278i	$-0.658026\pi$
$281$	−15.9688	−0.952619	−0.476310	+	0.879278i	$0.658026\pi$
$282$	3.15914	0.188124
$283$	25.7847	1.53274	0.766372	−	0.642397i	$-0.222060\pi$
$283$	25.7847	1.53274	0.766372	+	0.642397i	$0.222060\pi$
$284$	2.29749	0.136331
$285$	0	0
$286$	3.29394	0.194775
$287$	3.25166	0.191939
$288$	−16.1560	−0.952000
$289$	25.5564	1.50332
$290$	0	0
$291$	−6.21510	−0.364336
$292$	3.90923	0.228770
$293$	13.1712	0.769467	0.384733	−	0.923028i	$-0.374293\pi$
$293$	13.1712	0.769467	0.384733	+	0.923028i	$0.374293\pi$
$294$	−25.6496	−1.49591
$295$	0	0
$296$	−26.8734	−1.56198
$297$	−33.4172	−1.93906
$298$	18.9793	1.09944
$299$	4.17860	0.241655
$300$	0	0
$301$	−0.758901	−0.0437423
$302$	−7.49758	−0.431437
$303$	52.2289	3.00047
$304$	−7.91259	−0.453818
$305$	0	0
$306$	−49.3305	−2.82004
$307$	18.0418	1.02970	0.514851	−	0.857279i	$-0.327847\pi$
$307$	18.0418	1.02970	0.514851	+	0.857279i	$0.327847\pi$
$308$	−0.585146	−0.0333418
$309$	60.1591	3.42233
$310$	0	0
$311$	10.7148	0.607579	0.303790	−	0.952739i	$-0.401748\pi$
$311$	10.7148	0.607579	0.303790	+	0.952739i	$0.401748\pi$
$312$	6.97151	0.394684
$313$	−12.1791	−0.688405	−0.344202	−	0.938896i	$-0.611851\pi$
$313$	−12.1791	−0.688405	−0.344202	+	0.938896i	$0.611851\pi$
$314$	0.0187533	0.00105831
$315$	0	0
$316$	0.438312	0.0246570
$317$	−22.5994	−1.26931	−0.634653	−	0.772797i	$-0.718857\pi$
$317$	−22.5994	−1.26931	−0.634653	+	0.772797i	$0.718857\pi$
$318$	−10.4506	−0.586038
$319$	37.5130	2.10032
$320$	0	0
$321$	1.28393	0.0716617
$322$	2.36881	0.132009
$323$	18.3179	1.01923
$324$	−4.85178	−0.269543
$325$	0	0
$326$	26.8814	1.48882
$327$	−48.0621	−2.65784
$328$	28.6649	1.58276
$329$	0.293831	0.0161994
$330$	0	0
$331$	−11.1920	−0.615171	−0.307585	−	0.951521i	$-0.599521\pi$
$331$	−11.1920	−0.615171	−0.307585	+	0.951521i	$0.599521\pi$
$332$	−0.278400	−0.0152792
$333$	−53.8705	−2.95208
$334$	−1.17201	−0.0641294
$335$	0	0
$336$	2.95221	0.161056
$337$	−20.6367	−1.12415	−0.562077	−	0.827085i	$-0.689997\pi$
$337$	−20.6367	−1.12415	−0.562077	+	0.827085i	$0.689997\pi$
$338$	15.3391	0.834339
$339$	−17.3615	−0.942947
$340$	0	0
$341$	−26.3261	−1.42564
$342$	−21.2337	−1.14819
$343$	−4.81302	−0.259879
$344$	−6.69008	−0.360705
$345$	0	0
$346$	−1.85802	−0.0998876
$347$	−7.49109	−0.402143	−0.201071	−	0.979577i	$-0.564442\pi$
$347$	−7.49109	−0.402143	−0.201071	+	0.979577i	$0.564442\pi$
$348$	15.2942	0.819856
$349$	5.44464	0.291445	0.145722	−	0.989326i	$-0.453449\pi$
$349$	5.44464	0.291445	0.145722	+	0.989326i	$0.453449\pi$
$350$	0	0
$351$	7.13338	0.380752
$352$	−9.32301	−0.496918
$353$	28.1388	1.49768	0.748839	−	0.662752i	$-0.230612\pi$
$353$	28.1388	1.49768	0.748839	+	0.662752i	$0.230612\pi$
$354$	−31.3464	−1.66604
$355$	0	0
$356$	−6.63481	−0.351644
$357$	−6.83445	−0.361718
$358$	−2.64207	−0.139638
$359$	−10.2480	−0.540867	−0.270433	−	0.962739i	$-0.587167\pi$
$359$	−10.2480	−0.540867	−0.270433	+	0.962739i	$0.587167\pi$
$360$	0	0
$361$	−11.1153	−0.585016
$362$	12.4256	0.653073
$363$	−4.54555	−0.238580
$364$	0.124908	0.00654695
$365$	0	0
$366$	−31.0545	−1.62324
$367$	−21.0823	−1.10049	−0.550244	−	0.835004i	$-0.685465\pi$
$367$	−21.0823	−1.10049	−0.550244	+	0.835004i	$0.685465\pi$
$368$	15.5990	0.813155
$369$	57.4618	2.99134
$370$	0	0
$371$	−0.972004	−0.0504639
$372$	−10.7333	−0.556495
$373$	−20.9465	−1.08457	−0.542284	−	0.840195i	$-0.682440\pi$
$373$	−20.9465	−1.08457	−0.542284	+	0.840195i	$0.682440\pi$
$374$	−28.4668	−1.47198
$375$	0	0
$376$	2.59026	0.133582
$377$	−8.00770	−0.412417
$378$	4.04385	0.207993
$379$	−11.2856	−0.579703	−0.289851	−	0.957072i	$-0.593606\pi$
$379$	−11.2856	−0.579703	−0.289851	+	0.957072i	$0.593606\pi$
$380$	0	0
$381$	23.6189	1.21003
$382$	12.2857	0.628590
$383$	20.0503	1.02452	0.512261	−	0.858830i	$-0.328808\pi$
$383$	20.0503	1.02452	0.512261	+	0.858830i	$0.328808\pi$
$384$	17.2108	0.878283
$385$	0	0
$386$	−18.4368	−0.938406
$387$	−13.4109	−0.681717
$388$	−0.981652	−0.0498358
$389$	26.4625	1.34170	0.670851	−	0.741592i	$-0.265929\pi$
$389$	26.4625	1.34170	0.670851	+	0.741592i	$0.265929\pi$
$390$	0	0
$391$	−36.1122	−1.82627
$392$	−21.0308	−1.06221
$393$	−52.3426	−2.64034
$394$	10.3995	0.523918
$395$	0	0
$396$	−10.3404	−0.519626
$397$	31.0903	1.56038	0.780188	−	0.625545i	$-0.215123\pi$
$397$	31.0903	1.56038	0.780188	+	0.625545i	$0.215123\pi$
$398$	33.7430	1.69139
$399$	−2.94181	−0.147274
$400$	0	0
$401$	−6.25499	−0.312359	−0.156180	−	0.987729i	$-0.549918\pi$
$401$	−6.25499	−0.312359	−0.156180	+	0.987729i	$0.549918\pi$
$402$	−9.08439	−0.453088
$403$	5.61970	0.279937
$404$	8.24935	0.410420
$405$	0	0
$406$	−4.53948	−0.225291
$407$	−31.0867	−1.54091
$408$	−60.2490	−2.98277
$409$	−39.3733	−1.94689	−0.973443	−	0.228929i	$-0.926478\pi$
$409$	−39.3733	−1.94689	−0.973443	+	0.228929i	$0.926478\pi$
$410$	0	0
$411$	−53.1483	−2.62161
$412$	9.50190	0.468125
$413$	−2.91552	−0.143464
$414$	41.8605	2.05733
$415$	0	0
$416$	1.99013	0.0975743
$417$	−47.5682	−2.32942
$418$	−12.2532	−0.599323
$419$	−19.8585	−0.970149	−0.485075	−	0.874473i	$-0.661208\pi$
$419$	−19.8585	−0.970149	−0.485075	+	0.874473i	$0.661208\pi$
$420$	0	0
$421$	4.56232	0.222354	0.111177	−	0.993801i	$-0.464538\pi$
$421$	4.56232	0.222354	0.111177	+	0.993801i	$0.464538\pi$
$422$	16.1425	0.785805
$423$	5.19244	0.252465
$424$	−8.56869	−0.416132
$425$	0	0
$426$	−17.9501	−0.869687
$427$	−2.88837	−0.139778
$428$	0.202791	0.00980227
$429$	8.06452	0.389359
$430$	0	0
$431$	−1.31383	−0.0632850	−0.0316425	−	0.999499i	$-0.510074\pi$
$431$	−1.31383	−0.0632850	−0.0316425	+	0.999499i	$0.510074\pi$
$432$	26.6294	1.28121
$433$	−27.1928	−1.30680	−0.653402	−	0.757011i	$-0.726659\pi$
$433$	−27.1928	−1.30680	−0.653402	+	0.757011i	$0.726659\pi$
$434$	3.18575	0.152921
$435$	0	0
$436$	−7.59122	−0.363553
$437$	−15.5440	−0.743573
$438$	−30.5425	−1.45938
$439$	−36.6639	−1.74987	−0.874936	−	0.484238i	$-0.839097\pi$
$439$	−36.6639	−1.74987	−0.874936	+	0.484238i	$0.839097\pi$
$440$	0	0
$441$	−42.1583	−2.00754
$442$	6.07666	0.289037
$443$	−19.4622	−0.924676	−0.462338	−	0.886704i	$-0.652989\pi$
$443$	−19.4622	−0.924676	−0.462338	+	0.886704i	$0.652989\pi$
$444$	−12.6742	−0.601489
$445$	0	0
$446$	0.936266	0.0443335
$447$	46.4669	2.19781
$448$	3.08249	0.145634
$449$	−1.23717	−0.0583854	−0.0291927	−	0.999574i	$-0.509294\pi$
$449$	−1.23717	−0.0583854	−0.0291927	+	0.999574i	$0.509294\pi$
$450$	0	0
$451$	33.1591	1.56140
$452$	−2.74218	−0.128981
$453$	−18.3562	−0.862452
$454$	−34.2253	−1.60627
$455$	0	0
$456$	−25.9334	−1.21444
$457$	38.3425	1.79358	0.896792	−	0.442452i	$-0.145891\pi$
$457$	38.3425	1.79358	0.896792	+	0.442452i	$0.145891\pi$
$458$	4.06042	0.189731
$459$	−61.6479	−2.87748
$460$	0	0
$461$	−22.7537	−1.05974	−0.529872	−	0.848078i	$-0.677760\pi$
$461$	−22.7537	−1.05974	−0.529872	+	0.848078i	$0.677760\pi$
$462$	4.57170	0.212695
$463$	−5.53817	−0.257381	−0.128690	−	0.991685i	$-0.541077\pi$
$463$	−5.53817	−0.257381	−0.128690	+	0.991685i	$0.541077\pi$
$464$	−29.8933	−1.38776
$465$	0	0
$466$	17.9681	0.832355
$467$	−15.9884	−0.739857	−0.369928	−	0.929060i	$-0.620618\pi$
$467$	−15.9884	−0.739857	−0.369928	+	0.929060i	$0.620618\pi$
$468$	2.20732	0.102033
$469$	−0.844937	−0.0390156
$470$	0	0
$471$	0.0459134	0.00211558
$472$	−25.7017	−1.18302
$473$	−7.73896	−0.355838
$474$	−3.42450	−0.157292
$475$	0	0
$476$	−1.07948	−0.0494777
$477$	−17.1768	−0.786472
$478$	−12.1382	−0.555190
$479$	36.1150	1.65014	0.825068	−	0.565033i	$-0.191137\pi$
$479$	36.1150	1.65014	0.825068	+	0.565033i	$0.191137\pi$
$480$	0	0
$481$	6.63590	0.302571
$482$	1.23402	0.0562081
$483$	5.79953	0.263888
$484$	−0.717953	−0.0326342
$485$	0	0
$486$	2.92173	0.132532
$487$	−22.3499	−1.01277	−0.506385	−	0.862308i	$-0.669018\pi$
$487$	−22.3499	−1.01277	−0.506385	+	0.862308i	$0.669018\pi$
$488$	−25.4624	−1.15263
$489$	65.8134	2.97618
$490$	0	0
$491$	4.06555	0.183476	0.0917379	−	0.995783i	$-0.470758\pi$
$491$	4.06555	0.183476	0.0917379	+	0.995783i	$0.470758\pi$
$492$	13.5191	0.609488
$493$	69.2039	3.11679
$494$	2.61562	0.117682
$495$	0	0
$496$	20.9787	0.941972
$497$	−1.66954	−0.0748890
$498$	2.17511	0.0974692
$499$	0.381380	0.0170729	0.00853645	−	0.999964i	$-0.497283\pi$
$499$	0.381380	0.0170729	0.00853645	+	0.999964i	$0.497283\pi$
$500$	0	0
$501$	−2.86941	−0.128196
$502$	31.0452	1.38562
$503$	23.4577	1.04593	0.522964	−	0.852355i	$-0.324826\pi$
$503$	23.4577	1.04593	0.522964	+	0.852355i	$0.324826\pi$
$504$	6.49575	0.289344
$505$	0	0
$506$	24.1561	1.07387
$507$	37.5546	1.66786
$508$	3.73052	0.165515
$509$	31.7115	1.40559	0.702794	−	0.711394i	$-0.251936\pi$
$509$	31.7115	1.40559	0.702794	+	0.711394i	$0.251936\pi$
$510$	0	0
$511$	−2.84075	−0.125667
$512$	24.6574	1.08971
$513$	−26.5356	−1.17157
$514$	25.8008	1.13802
$515$	0	0
$516$	−3.15521	−0.138900
$517$	2.99636	0.131780
$518$	3.76183	0.165285
$519$	−4.54896	−0.199677
$520$	0	0
$521$	18.8780	0.827060	0.413530	−	0.910491i	$-0.364296\pi$
$521$	18.8780	0.827060	0.413530	+	0.910491i	$0.364296\pi$
$522$	−80.2197	−3.51112
$523$	−30.6501	−1.34024	−0.670118	−	0.742254i	$-0.733757\pi$
$523$	−30.6501	−1.34024	−0.670118	+	0.742254i	$0.733757\pi$
$524$	−8.26731	−0.361159
$525$	0	0
$526$	2.76650	0.120625
$527$	−48.5664	−2.11559
$528$	30.1054	1.31017
$529$	7.64382	0.332340
$530$	0	0
$531$	−51.5218	−2.23586
$532$	−0.464647	−0.0201450
$533$	−7.07829	−0.306595
$534$	51.8373	2.24322
$535$	0	0
$536$	−7.44853	−0.321728
$537$	−6.46856	−0.279139
$538$	13.0025	0.560580
$539$	−24.3280	−1.04788
$540$	0	0
$541$	40.5167	1.74195	0.870975	−	0.491327i	$-0.163488\pi$
$541$	40.5167	1.74195	0.870975	+	0.491327i	$0.163488\pi$
$542$	−0.238901	−0.0102617
$543$	30.4214	1.30551
$544$	−17.1991	−0.737404
$545$	0	0
$546$	−0.975895	−0.0417645
$547$	28.5232	1.21956	0.609781	−	0.792570i	$-0.291257\pi$
$547$	28.5232	1.21956	0.609781	+	0.792570i	$0.291257\pi$
$548$	−8.39457	−0.358598
$549$	−51.0419	−2.17842
$550$	0	0
$551$	29.7880	1.26901
$552$	51.1256	2.17605
$553$	−0.318512	−0.0135445
$554$	−26.7609	−1.13696
$555$	0	0
$556$	−7.51321	−0.318631
$557$	25.2959	1.07182	0.535911	−	0.844275i	$-0.319968\pi$
$557$	25.2959	1.07182	0.535911	+	0.844275i	$0.319968\pi$
$558$	56.2971	2.38325
$559$	1.65199	0.0698719
$560$	0	0
$561$	−69.6950	−2.94252
$562$	19.7058	0.831241
$563$	−0.337011	−0.0142033	−0.00710166	−	0.999975i	$-0.502261\pi$
$563$	−0.337011	−0.0142033	−0.00710166	+	0.999975i	$0.502261\pi$
$564$	1.22163	0.0514399
$565$	0	0
$566$	−31.8189	−1.33745
$567$	3.52568	0.148065
$568$	−14.7178	−0.617545
$569$	6.70949	0.281276	0.140638	−	0.990061i	$-0.455085\pi$
$569$	6.70949	0.281276	0.140638	+	0.990061i	$0.455085\pi$
$570$	0	0
$571$	−24.4061	−1.02136	−0.510682	−	0.859770i	$-0.670607\pi$
$571$	−24.4061	−1.02136	−0.510682	+	0.859770i	$0.670607\pi$
$572$	1.27376	0.0532586
$573$	30.0789	1.25656
$574$	−4.01261	−0.167483
$575$	0	0
$576$	54.4723	2.26968
$577$	35.1659	1.46397	0.731987	−	0.681318i	$-0.238593\pi$
$577$	35.1659	1.46397	0.731987	+	0.681318i	$0.238593\pi$
$578$	−31.5372	−1.31177
$579$	−45.1385	−1.87589
$580$	0	0
$581$	0.202307	0.00839310
$582$	7.66957	0.317914
$583$	−9.91210	−0.410517
$584$	−25.0426	−1.03627
$585$	0	0
$586$	−16.2535	−0.671425
$587$	−19.0706	−0.787129	−0.393564	−	0.919297i	$-0.628758\pi$
$587$	−19.0706	−0.787129	−0.393564	+	0.919297i	$0.628758\pi$
$588$	−9.91864	−0.409038
$589$	−20.9048	−0.861367
$590$	0	0
$591$	25.4609	1.04732
$592$	24.7723	1.01813
$593$	28.8167	1.18336	0.591680	−	0.806173i	$-0.298465\pi$
$593$	28.8167	1.18336	0.591680	+	0.806173i	$0.298465\pi$
$594$	41.2375	1.69199
$595$	0	0
$596$	7.33927	0.300628
$597$	82.6127	3.38111
$598$	−5.15648	−0.210864
$599$	−46.7786	−1.91132	−0.955661	−	0.294468i	$-0.904858\pi$
$599$	−46.7786	−1.91132	−0.955661	+	0.294468i	$0.904858\pi$
$600$	0	0
$601$	32.3702	1.32041	0.660205	−	0.751086i	$-0.270470\pi$
$601$	32.3702	1.32041	0.660205	+	0.751086i	$0.270470\pi$
$602$	0.936499	0.0381689
$603$	−14.9313	−0.608052
$604$	−2.89930	−0.117971
$605$	0	0
$606$	−64.4515	−2.61816
$607$	−9.75940	−0.396122	−0.198061	−	0.980190i	$-0.563464\pi$
$607$	−9.75940	−0.396122	−0.198061	+	0.980190i	$0.563464\pi$
$608$	−7.40312	−0.300236
$609$	−11.1140	−0.450361
$610$	0	0
$611$	−0.639618	−0.0258762
$612$	−19.0760	−0.771102
$613$	−29.6233	−1.19648	−0.598238	−	0.801319i	$-0.704132\pi$
$613$	−29.6233	−1.19648	−0.598238	+	0.801319i	$0.704132\pi$
$614$	−22.2640	−0.898502
$615$	0	0
$616$	3.74845	0.151029
$617$	−8.39374	−0.337919	−0.168960	−	0.985623i	$-0.554041\pi$
$617$	−8.39374	−0.337919	−0.168960	+	0.985623i	$0.554041\pi$
$618$	−74.2376	−2.98627
$619$	12.5361	0.503869	0.251935	−	0.967744i	$-0.418933\pi$
$619$	12.5361	0.503869	0.251935	+	0.967744i	$0.418933\pi$
$620$	0	0
$621$	52.3127	2.09924
$622$	−13.2223	−0.530164
$623$	4.82137	0.193164
$624$	−6.42644	−0.257263
$625$	0	0
$626$	15.0293	0.600691
$627$	−29.9993	−1.19806
$628$	0.00725185	0.000289380 0
$629$	−57.3486	−2.28664
$630$	0	0
$631$	−23.7553	−0.945682	−0.472841	−	0.881148i	$-0.656772\pi$
$631$	−23.7553	−0.945682	−0.472841	+	0.881148i	$0.656772\pi$
$632$	−2.80784	−0.111690
$633$	39.5215	1.57084
$634$	27.8881	1.10758
$635$	0	0
$636$	−4.04121	−0.160244
$637$	5.19317	0.205761
$638$	−46.2918	−1.83271
$639$	−29.5033	−1.16713
$640$	0	0
$641$	−26.2334	−1.03616	−0.518078	−	0.855333i	$-0.673352\pi$
$641$	−26.2334	−1.03616	−0.518078	+	0.855333i	$0.673352\pi$
$642$	−1.58439	−0.0625309
$643$	0.792640	0.0312587	0.0156293	−	0.999878i	$-0.495025\pi$
$643$	0.792640	0.0312587	0.0156293	+	0.999878i	$0.495025\pi$
$644$	0.916013	0.0360960
$645$	0	0
$646$	−22.6046	−0.889368
$647$	33.2566	1.30745	0.653725	−	0.756732i	$-0.273205\pi$
$647$	33.2566	1.30745	0.653725	+	0.756732i	$0.273205\pi$
$648$	31.0806	1.22096
$649$	−29.7313	−1.16706
$650$	0	0
$651$	7.79964	0.305692
$652$	10.3950	0.407098
$653$	−37.1590	−1.45415	−0.727073	−	0.686560i	$-0.759120\pi$
$653$	−37.1590	−1.45415	−0.727073	+	0.686560i	$0.759120\pi$
$654$	59.3096	2.31919
$655$	0	0
$656$	−26.4237	−1.03167
$657$	−50.2005	−1.95851
$658$	−0.362593	−0.0141353
$659$	27.2821	1.06276	0.531380	−	0.847133i	$-0.321674\pi$
$659$	27.2821	1.06276	0.531380	+	0.847133i	$0.321674\pi$
$660$	0	0
$661$	7.01637	0.272905	0.136453	−	0.990647i	$-0.456430\pi$
$661$	7.01637	0.272905	0.136453	+	0.990647i	$0.456430\pi$
$662$	13.8112	0.536788
$663$	14.8774	0.577791
$664$	1.78343	0.0692106
$665$	0	0
$666$	66.4773	2.57594
$667$	−58.7245	−2.27382
$668$	−0.453213	−0.0175353
$669$	2.29225	0.0886235
$670$	0	0
$671$	−29.4544	−1.13707
$672$	2.76213	0.106551
$673$	9.24238	0.356268	0.178134	−	0.984006i	$-0.442994\pi$
$673$	9.24238	0.356268	0.178134	+	0.984006i	$0.442994\pi$
$674$	25.4661	0.980918
$675$	0	0
$676$	5.93161	0.228139
$677$	−9.75895	−0.375067	−0.187534	−	0.982258i	$-0.560049\pi$
$677$	−9.75895	−0.375067	−0.187534	+	0.982258i	$0.560049\pi$
$678$	21.4244	0.822801
$679$	0.713345	0.0273757
$680$	0	0
$681$	−83.7934	−3.21097
$682$	32.4870	1.24399
$683$	23.5895	0.902629	0.451314	−	0.892365i	$-0.350955\pi$
$683$	23.5895	0.902629	0.451314	+	0.892365i	$0.350955\pi$
$684$	−8.21103	−0.313956
$685$	0	0
$686$	5.93937	0.226766
$687$	9.94108	0.379276
$688$	6.16701	0.235115
$689$	2.11588	0.0806087
$690$	0	0
$691$	15.4267	0.586858	0.293429	−	0.955981i	$-0.405204\pi$
$691$	15.4267	0.586858	0.293429	+	0.955981i	$0.405204\pi$
$692$	−0.718491	−0.0273129
$693$	7.51416	0.285439
$694$	9.24416	0.350904
$695$	0	0
$696$	−97.9750	−3.71373
$697$	61.1718	2.31705
$698$	−6.71880	−0.254310
$699$	43.9910	1.66389
$700$	0	0
$701$	−0.966074	−0.0364881	−0.0182441	−	0.999834i	$-0.505808\pi$
$701$	−0.966074	−0.0364881	−0.0182441	+	0.999834i	$0.505808\pi$
$702$	−8.80274	−0.332238
$703$	−24.6850	−0.931012
$704$	31.4340	1.18471
$705$	0	0
$706$	−34.7239	−1.30685
$707$	−5.99462	−0.225451
$708$	−12.1216	−0.455557
$709$	39.0688	1.46726	0.733630	−	0.679549i	$-0.237825\pi$
$709$	39.0688	1.46726	0.733630	+	0.679549i	$0.237825\pi$
$710$	0	0
$711$	−5.62860	−0.211089
$712$	42.5027	1.59286
$713$	41.2121	1.54340
$714$	8.43386	0.315629
$715$	0	0
$716$	−1.02168	−0.0381821
$717$	−29.7179	−1.10984
$718$	12.6462	0.471952
$719$	−47.0735	−1.75554	−0.877772	−	0.479078i	$-0.840971\pi$
$719$	−47.0735	−1.75554	−0.877772	+	0.479078i	$0.840971\pi$
$720$	0	0
$721$	−6.90482	−0.257149
$722$	13.7165	0.510475
$723$	3.02124	0.112361
$724$	4.80494	0.178574
$725$	0	0
$726$	5.60931	0.208181
$727$	−15.1998	−0.563731	−0.281865	−	0.959454i	$-0.590953\pi$
$727$	−15.1998	−0.563731	−0.281865	+	0.959454i	$0.590953\pi$
$728$	−0.800162	−0.0296560
$729$	−23.3487	−0.864768
$730$	0	0
$731$	−14.2768	−0.528047
$732$	−12.0087	−0.443854
$733$	−39.5629	−1.46129	−0.730644	−	0.682758i	$-0.760780\pi$
$733$	−39.5629	−1.46129	−0.730644	+	0.682758i	$0.760780\pi$
$734$	26.0160	0.960269
$735$	0	0
$736$	14.5947	0.537966
$737$	−8.61633	−0.317386
$738$	−70.9091	−2.61020
$739$	−18.9052	−0.695439	−0.347720	−	0.937599i	$-0.613044\pi$
$739$	−18.9052	−0.695439	−0.347720	+	0.937599i	$0.613044\pi$
$740$	0	0
$741$	6.40380	0.235249
$742$	1.19947	0.0440340
$743$	47.1115	1.72835	0.864177	−	0.503188i	$-0.167840\pi$
$743$	47.1115	1.72835	0.864177	+	0.503188i	$0.167840\pi$
$744$	68.7576	2.52078
$745$	0	0
$746$	25.8484	0.946377
$747$	3.57508	0.130805
$748$	−11.0080	−0.402494
$749$	−0.147364	−0.00538456
$750$	0	0
$751$	7.72621	0.281933	0.140967	−	0.990014i	$-0.454979\pi$
$751$	7.72621	0.281933	0.140967	+	0.990014i	$0.454979\pi$
$752$	−2.38774	−0.0870718
$753$	76.0077	2.76988
$754$	9.88166	0.359869
$755$	0	0
$756$	1.56375	0.0568729
$757$	0.671245	0.0243968	0.0121984	−	0.999926i	$-0.496117\pi$
$757$	0.671245	0.0243968	0.0121984	+	0.999926i	$0.496117\pi$
$758$	13.9267	0.505840
$759$	59.1412	2.14669
$760$	0	0
$761$	−15.4764	−0.561019	−0.280510	−	0.959851i	$-0.590503\pi$
$761$	−15.4764	−0.561019	−0.280510	+	0.959851i	$0.590503\pi$
$762$	−29.1462	−1.05586
$763$	5.51637	0.199706
$764$	4.75085	0.171880
$765$	0	0
$766$	−24.7425	−0.893982
$767$	6.34658	0.229162
$768$	32.4747	1.17183
$769$	16.5268	0.595971	0.297986	−	0.954570i	$-0.403685\pi$
$769$	16.5268	0.595971	0.297986	+	0.954570i	$0.403685\pi$
$770$	0	0
$771$	63.1677	2.27493
$772$	−7.12945	−0.256595
$773$	−3.57733	−0.128668	−0.0643338	−	0.997928i	$-0.520492\pi$
$773$	−3.57733	−0.128668	−0.0643338	+	0.997928i	$0.520492\pi$
$774$	16.5494	0.594855
$775$	0	0
$776$	6.28848	0.225743
$777$	9.21004	0.330408
$778$	−32.6553	−1.17075
$779$	26.3306	0.943393
$780$	0	0
$781$	−17.0253	−0.609212
$782$	44.5632	1.59358
$783$	−100.250	−3.58264
$784$	19.3865	0.692374
$785$	0	0
$786$	64.5919	2.30392
$787$	29.7428	1.06022	0.530109	−	0.847930i	$-0.322151\pi$
$787$	29.7428	1.06022	0.530109	+	0.847930i	$0.322151\pi$
$788$	4.02146	0.143258
$789$	6.77320	0.241132
$790$	0	0
$791$	1.99268	0.0708516
$792$	66.2410	2.35377
$793$	6.28747	0.223275
$794$	−38.3660	−1.36156
$795$	0	0
$796$	13.0484	0.462487
$797$	−22.6010	−0.800567	−0.400284	−	0.916391i	$-0.631088\pi$
$797$	−22.6010	−0.800567	−0.400284	+	0.916391i	$0.631088\pi$
$798$	3.63025	0.128509
$799$	5.52769	0.195555
$800$	0	0
$801$	85.2011	3.01043
$802$	7.71879	0.272560
$803$	−28.9688	−1.02229
$804$	−3.51291	−0.123891
$805$	0	0
$806$	−6.93482	−0.244269
$807$	31.8340	1.12061
$808$	−52.8455	−1.85910
$809$	−33.6487	−1.18302	−0.591512	−	0.806296i	$-0.701469\pi$
$809$	−33.6487	−1.18302	−0.591512	+	0.806296i	$0.701469\pi$
$810$	0	0
$811$	−10.6295	−0.373251	−0.186626	−	0.982431i	$-0.559755\pi$
$811$	−10.6295	−0.373251	−0.186626	+	0.982431i	$0.559755\pi$
$812$	−1.75541	−0.0616027
$813$	−0.584899	−0.0205133
$814$	38.3616	1.34457
$815$	0	0
$816$	55.5384	1.94423
$817$	−6.14528	−0.214996
$818$	48.5875	1.69882
$819$	−1.60401	−0.0560486
$820$	0	0
$821$	19.6519	0.685855	0.342927	−	0.939362i	$-0.388582\pi$
$821$	19.6519	0.685855	0.342927	+	0.939362i	$0.388582\pi$
$822$	65.5861	2.28758
$823$	−12.9183	−0.450302	−0.225151	−	0.974324i	$-0.572288\pi$
$823$	−12.9183	−0.450302	−0.225151	+	0.974324i	$0.572288\pi$
$824$	−60.8694	−2.12048
$825$	0	0
$826$	3.59782	0.125184
$827$	−10.7457	−0.373663	−0.186832	−	0.982392i	$-0.559822\pi$
$827$	−10.7457	−0.373663	−0.186832	+	0.982392i	$0.559822\pi$
$828$	16.1874	0.562550
$829$	−12.5838	−0.437052	−0.218526	−	0.975831i	$-0.570125\pi$
$829$	−12.5838	−0.437052	−0.218526	+	0.975831i	$0.570125\pi$
$830$	0	0
$831$	−65.5184	−2.27281
$832$	−6.71004	−0.232629
$833$	−44.8803	−1.55501
$834$	58.7001	2.03262
$835$	0	0
$836$	−4.73828	−0.163877
$837$	70.3541	2.43179
$838$	24.5058	0.846537
$839$	−27.5912	−0.952556	−0.476278	−	0.879295i	$-0.658014\pi$
$839$	−27.5912	−0.952556	−0.476278	+	0.879295i	$0.658014\pi$
$840$	0	0
$841$	83.5371	2.88059
$842$	−5.63000	−0.194023
$843$	48.2456	1.66167
$844$	6.24227	0.214868
$845$	0	0
$846$	−6.40758	−0.220297
$847$	0.521720	0.0179265
$848$	7.89874	0.271244
$849$	−77.9019	−2.67358
$850$	0	0
$851$	48.6644	1.66820
$852$	−6.94128	−0.237804
$853$	−33.6751	−1.15301	−0.576507	−	0.817092i	$-0.695585\pi$
$853$	−33.6751	−1.15301	−0.576507	+	0.817092i	$0.695585\pi$
$854$	3.56431	0.121968
$855$	0	0
$856$	−1.29908	−0.0444018
$857$	19.3208	0.659986	0.329993	−	0.943983i	$-0.392954\pi$
$857$	19.3208	0.659986	0.329993	+	0.943983i	$0.392954\pi$
$858$	−9.95178	−0.339748
$859$	−8.30812	−0.283469	−0.141735	−	0.989905i	$-0.545268\pi$
$859$	−8.30812	−0.283469	−0.141735	+	0.989905i	$0.545268\pi$
$860$	0	0
$861$	−9.82403	−0.334802
$862$	1.62130	0.0552215
$863$	−0.00795328	−0.000270733 0	−0.000135366	−	1.00000i	$-0.500043\pi$
$863$	−0.00795328	−0.000270733 0	−0.000135366		1.00000i	$0.500043\pi$
$864$	24.9149	0.847620
$865$	0	0
$866$	33.5565	1.14030
$867$	−77.2121	−2.62226
$868$	1.23192	0.0418142
$869$	−3.24805	−0.110183
$870$	0	0
$871$	1.83928	0.0623217
$872$	48.6295	1.64680
$873$	12.6059	0.426645
$874$	19.1817	0.648830
$875$	0	0
$876$	−11.8107	−0.399047
$877$	9.79164	0.330640	0.165320	−	0.986240i	$-0.447134\pi$
$877$	9.79164	0.330640	0.165320	+	0.986240i	$0.447134\pi$
$878$	45.2440	1.52691
$879$	−39.7932	−1.34219
$880$	0	0
$881$	−0.237489	−0.00800121	−0.00400061	−	0.999992i	$-0.501273\pi$
$881$	−0.237489	−0.00800121	−0.00400061	+	0.999992i	$0.501273\pi$
$882$	52.0243	1.75175
$883$	48.7890	1.64188	0.820940	−	0.571014i	$-0.193450\pi$
$883$	48.7890	1.64188	0.820940	+	0.571014i	$0.193450\pi$
$884$	2.34983	0.0790333
$885$	0	0
$886$	24.0167	0.806858
$887$	−11.6958	−0.392707	−0.196353	−	0.980533i	$-0.562910\pi$
$887$	−11.6958	−0.392707	−0.196353	+	0.980533i	$0.562910\pi$
$888$	81.1909	2.72459
$889$	−2.71088	−0.0909201
$890$	0	0
$891$	35.9534	1.20449
$892$	0.362052	0.0121224
$893$	2.37932	0.0796210
$894$	−57.3411	−1.91777
$895$	0	0
$896$	−1.97538	−0.0659929
$897$	−12.6246	−0.421522
$898$	1.52669	0.0509462
$899$	−78.9771	−2.63403
$900$	0	0
$901$	−18.2858	−0.609189
$902$	−40.9190	−1.36245
$903$	2.29282	0.0763003
$904$	17.5665	0.584252
$905$	0	0
$906$	22.6520	0.752562
$907$	22.6606	0.752433	0.376216	−	0.926532i	$-0.377225\pi$
$907$	22.6606	0.752433	0.376216	+	0.926532i	$0.377225\pi$
$908$	−13.2348	−0.439214
$909$	−105.934	−3.51362
$910$	0	0
$911$	29.7712	0.986365	0.493182	−	0.869926i	$-0.335834\pi$
$911$	29.7712	0.986365	0.493182	+	0.869926i	$0.335834\pi$
$912$	23.9058	0.791601
$913$	2.06304	0.0682768
$914$	−47.3154	−1.56505
$915$	0	0
$916$	1.57015	0.0518794
$917$	6.00767	0.198391
$918$	76.0748	2.51084
$919$	4.77698	0.157578	0.0787890	−	0.996891i	$-0.474895\pi$
$919$	4.77698	0.157578	0.0787890	+	0.996891i	$0.474895\pi$
$920$	0	0
$921$	−54.5087	−1.79612
$922$	28.0785	0.924716
$923$	3.63429	0.119624
$924$	1.76786	0.0581585
$925$	0	0
$926$	6.83422	0.224586
$927$	−122.019	−4.00763
$928$	−27.9686	−0.918113
$929$	−38.3148	−1.25707	−0.628533	−	0.777783i	$-0.716344\pi$
$929$	−38.3148	−1.25707	−0.628533	+	0.777783i	$0.716344\pi$
$930$	0	0
$931$	−19.3182	−0.633127
$932$	6.94821	0.227596
$933$	−32.3719	−1.05981
$934$	19.7301	0.645587
$935$	0	0
$936$	−14.1401	−0.462184
$937$	18.5468	0.605898	0.302949	−	0.953007i	$-0.402029\pi$
$937$	18.5468	0.605898	0.302949	+	0.953007i	$0.402029\pi$
$938$	1.04267	0.0340444
$939$	36.7960	1.20079
$940$	0	0
$941$	21.5041	0.701012	0.350506	−	0.936560i	$-0.386010\pi$
$941$	21.5041	0.701012	0.350506	+	0.936560i	$0.386010\pi$
$942$	−0.0566581	−0.00184602
$943$	−51.9087	−1.69038
$944$	23.6922	0.771117
$945$	0	0
$946$	9.55004	0.310498
$947$	−46.9313	−1.52506	−0.762532	−	0.646951i	$-0.776044\pi$
$947$	−46.9313	−1.52506	−0.762532	+	0.646951i	$0.776044\pi$
$948$	−1.32425	−0.0430095
$949$	6.18382	0.200735
$950$	0	0
$951$	68.2781	2.21407
$952$	6.91514	0.224121
$953$	−17.0216	−0.551384	−0.275692	−	0.961246i	$-0.588907\pi$
$953$	−17.0216	−0.551384	−0.275692	+	0.961246i	$0.588907\pi$
$954$	21.1965	0.686264
$955$	0	0
$956$	−4.69383	−0.151809
$957$	−113.336	−3.66362
$958$	−44.5667	−1.43988
$959$	6.10015	0.196984
$960$	0	0
$961$	24.4251	0.787906
$962$	−8.18884	−0.264019
$963$	−2.60415	−0.0839174
$964$	0.477193	0.0153694
$965$	0	0
$966$	−7.15674	−0.230264
$967$	12.2869	0.395120	0.197560	−	0.980291i	$-0.436698\pi$
$967$	12.2869	0.395120	0.197560	+	0.980291i	$0.436698\pi$
$968$	4.59922	0.147824
$969$	−55.3427	−1.77786
$970$	0	0
$971$	60.1927	1.93168	0.965838	−	0.259146i	$-0.0834411\pi$
$971$	60.1927	1.93168	0.965838	+	0.259146i	$0.0834411\pi$
$972$	1.12983	0.0362392
$973$	5.45968	0.175029
$974$	27.5802	0.883726
$975$	0	0
$976$	23.4716	0.751307
$977$	39.6803	1.26949	0.634743	−	0.772723i	$-0.281106\pi$
$977$	39.6803	1.26949	0.634743	+	0.772723i	$0.281106\pi$
$978$	−81.2151	−2.59697
$979$	49.1664	1.57137
$980$	0	0
$981$	97.4828	3.11239
$982$	−5.01697	−0.160098
$983$	30.2807	0.965804	0.482902	−	0.875674i	$-0.339583\pi$
$983$	30.2807	0.965804	0.482902	+	0.875674i	$0.339583\pi$
$984$	−86.6036	−2.76082
$985$	0	0
$986$	−85.3990	−2.71966
$987$	−0.887732	−0.0282568
$988$	1.01145	0.0321787
$989$	12.1149	0.385232
$990$	0	0
$991$	−36.6638	−1.16466	−0.582332	−	0.812951i	$-0.697860\pi$
$991$	−36.6638	−1.16466	−0.582332	+	0.812951i	$0.697860\pi$
$992$	19.6280	0.623189
$993$	33.8139	1.07305
$994$	2.06024	0.0653470
$995$	0	0
$996$	0.841112	0.0266516
$997$	2.46754	0.0781478	0.0390739	−	0.999236i	$-0.487559\pi$
$997$	2.46754	0.0781478	0.0390739	+	0.999236i	$0.487559\pi$
$998$	−0.470630	−0.0148975
$999$	83.0761	2.62841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.15	✓	40
5.4	even	2		6025.2.a.o.1.26	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.15	✓	40	1.1	even	1	trivial
6025.2.a.o.1.26	yes	40	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.23402 q^{2} -3.02124 q^{3} -0.477193 q^{4} +3.72827 q^{6} +0.346766 q^{7} +3.05691 q^{8} +6.12789 q^{9} +O(q^{10})\)	\(q-1.23402 q^{2} -3.02124 q^{3} -0.477193 q^{4} +3.72827 q^{6} +0.346766 q^{7} +3.05691 q^{8} +6.12789 q^{9} +3.53617 q^{11} +1.44171 q^{12} -0.754848 q^{13} -0.427916 q^{14} -2.81790 q^{16} +6.52353 q^{17} -7.56194 q^{18} +2.80797 q^{19} -1.04766 q^{21} -4.36371 q^{22} -5.53569 q^{23} -9.23565 q^{24} +0.931498 q^{26} -9.45009 q^{27} -0.165474 q^{28} +10.6084 q^{29} -7.44480 q^{31} -2.63647 q^{32} -10.6836 q^{33} -8.05017 q^{34} -2.92418 q^{36} -8.79104 q^{37} -3.46509 q^{38} +2.28058 q^{39} +9.37710 q^{41} +1.29284 q^{42} -2.18851 q^{43} -1.68744 q^{44} +6.83115 q^{46} +0.847346 q^{47} +8.51355 q^{48} -6.87975 q^{49} -19.7091 q^{51} +0.360208 q^{52} -2.80306 q^{53} +11.6616 q^{54} +1.06003 q^{56} -8.48355 q^{57} -13.0909 q^{58} -8.40776 q^{59} -8.32945 q^{61} +9.18704 q^{62} +2.12494 q^{63} +8.88926 q^{64} +13.1838 q^{66} -2.43662 q^{67} -3.11298 q^{68} +16.7246 q^{69} -4.81460 q^{71} +18.7324 q^{72} -8.19214 q^{73} +10.8483 q^{74} -1.33994 q^{76} +1.22622 q^{77} -2.81428 q^{78} -0.918522 q^{79} +10.1673 q^{81} -11.5715 q^{82} +0.583411 q^{83} +0.499937 q^{84} +2.70067 q^{86} -32.0504 q^{87} +10.8098 q^{88} +13.9038 q^{89} -0.261755 q^{91} +2.64159 q^{92} +22.4925 q^{93} -1.04564 q^{94} +7.96540 q^{96} +2.05714 q^{97} +8.48976 q^{98} +21.6693 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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