LMFDB - Embedded newform 3525.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 $ x^7 - x^6 - 9x^5 + 10x^4 + 16x^3 - 15x^2 - 6*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.704785$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.704785 q^{2} +1.00000 q^{3} -1.50328 q^{4} +0.704785 q^{6} -2.27680 q^{7} -2.46906 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.704785 q^{2} +1.00000 q^{3} -1.50328 q^{4} +0.704785 q^{6} -2.27680 q^{7} -2.46906 q^{8} +1.00000 q^{9} -3.62148 q^{11} -1.50328 q^{12} +2.61726 q^{13} -1.60466 q^{14} +1.26640 q^{16} -3.46186 q^{17} +0.704785 q^{18} +0.827286 q^{19} -2.27680 q^{21} -2.55236 q^{22} +4.30944 q^{23} -2.46906 q^{24} +1.84460 q^{26} +1.00000 q^{27} +3.42267 q^{28} +9.52468 q^{29} -4.55940 q^{31} +5.83066 q^{32} -3.62148 q^{33} -2.43987 q^{34} -1.50328 q^{36} +5.75353 q^{37} +0.583059 q^{38} +2.61726 q^{39} -7.54433 q^{41} -1.60466 q^{42} -7.37461 q^{43} +5.44409 q^{44} +3.03723 q^{46} +1.00000 q^{47} +1.26640 q^{48} -1.81617 q^{49} -3.46186 q^{51} -3.93447 q^{52} -0.695625 q^{53} +0.704785 q^{54} +5.62156 q^{56} +0.827286 q^{57} +6.71285 q^{58} +12.8192 q^{59} +8.98704 q^{61} -3.21339 q^{62} -2.27680 q^{63} +1.57656 q^{64} -2.55236 q^{66} +12.4327 q^{67} +5.20414 q^{68} +4.30944 q^{69} +4.88208 q^{71} -2.46906 q^{72} +2.59364 q^{73} +4.05500 q^{74} -1.24364 q^{76} +8.24539 q^{77} +1.84460 q^{78} +7.18573 q^{79} +1.00000 q^{81} -5.31713 q^{82} +13.4641 q^{83} +3.42267 q^{84} -5.19752 q^{86} +9.52468 q^{87} +8.94164 q^{88} +13.5136 q^{89} -5.95898 q^{91} -6.47829 q^{92} -4.55940 q^{93} +0.704785 q^{94} +5.83066 q^{96} -18.2314 q^{97} -1.28001 q^{98} -3.62148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.704785	0.498358	0.249179	−	0.968457i	$-0.419839\pi$
$2$	0.704785	0.498358	0.249179	+	0.968457i	$0.419839\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.50328	−0.751639
$5$	0	0
$5$	0	0
$6$	0.704785	0.287727
$7$	−2.27680	−0.860551	−0.430275	−	0.902698i	$-0.641584\pi$
$7$	−2.27680	−0.860551	−0.430275	+	0.902698i	$0.641584\pi$
$8$	−2.46906	−0.872944
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.62148	−1.09192	−0.545958	−	0.837812i	$-0.683834\pi$
$11$	−3.62148	−1.09192	−0.545958	+	0.837812i	$0.683834\pi$
$12$	−1.50328	−0.433959
$13$	2.61726	0.725897	0.362948	−	0.931809i	$-0.381770\pi$
$13$	2.61726	0.725897	0.362948	+	0.931809i	$0.381770\pi$
$14$	−1.60466	−0.428862
$15$	0	0
$16$	1.26640	0.316600
$17$	−3.46186	−0.839625	−0.419812	−	0.907611i	$-0.637904\pi$
$17$	−3.46186	−0.839625	−0.419812	+	0.907611i	$0.637904\pi$
$18$	0.704785	0.166119
$19$	0.827286	0.189792	0.0948962	−	0.995487i	$-0.469748\pi$
$19$	0.827286	0.189792	0.0948962	+	0.995487i	$0.469748\pi$
$20$	0	0
$21$	−2.27680	−0.496839
$22$	−2.55236	−0.544166
$23$	4.30944	0.898581	0.449290	−	0.893386i	$-0.351677\pi$
$23$	4.30944	0.898581	0.449290	+	0.893386i	$0.351677\pi$
$24$	−2.46906	−0.503994
$25$	0	0
$26$	1.84460	0.361757
$27$	1.00000	0.192450
$28$	3.42267	0.646823
$29$	9.52468	1.76869	0.884344	−	0.466835i	$-0.154606\pi$
$29$	9.52468	1.76869	0.884344	+	0.466835i	$0.154606\pi$
$30$	0	0
$31$	−4.55940	−0.818892	−0.409446	−	0.912334i	$-0.634278\pi$
$31$	−4.55940	−0.818892	−0.409446	+	0.912334i	$0.634278\pi$
$32$	5.83066	1.03072
$33$	−3.62148	−0.630419
$34$	−2.43987	−0.418434
$35$	0	0
$36$	−1.50328	−0.250546
$37$	5.75353	0.945875	0.472937	−	0.881096i	$-0.343194\pi$
$37$	5.75353	0.945875	0.472937	+	0.881096i	$0.343194\pi$
$38$	0.583059	0.0945846
$39$	2.61726	0.419097
$40$	0	0
$41$	−7.54433	−1.17823	−0.589113	−	0.808050i	$-0.700523\pi$
$41$	−7.54433	−1.17823	−0.589113	+	0.808050i	$0.700523\pi$
$42$	−1.60466	−0.247604
$43$	−7.37461	−1.12462	−0.562309	−	0.826927i	$-0.690087\pi$
$43$	−7.37461	−1.12462	−0.562309	+	0.826927i	$0.690087\pi$
$44$	5.44409	0.820727
$45$	0	0
$46$	3.03723	0.447815
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	1.26640	0.182789
$49$	−1.81617	−0.259453
$50$	0	0
$51$	−3.46186	−0.484758
$52$	−3.93447	−0.545612
$53$	−0.695625	−0.0955514	−0.0477757	−	0.998858i	$-0.515213\pi$
$53$	−0.695625	−0.0955514	−0.0477757	+	0.998858i	$0.515213\pi$
$54$	0.704785	0.0959091
$55$	0	0
$56$	5.62156	0.751212
$57$	0.827286	0.109577
$58$	6.71285	0.881441
$59$	12.8192	1.66892	0.834459	−	0.551071i	$-0.185781\pi$
$59$	12.8192	1.66892	0.834459	+	0.551071i	$0.185781\pi$
$60$	0	0
$61$	8.98704	1.15067	0.575336	−	0.817917i	$-0.304871\pi$
$61$	8.98704	1.15067	0.575336	+	0.817917i	$0.304871\pi$
$62$	−3.21339	−0.408101
$63$	−2.27680	−0.286850
$64$	1.57656	0.197070
$65$	0	0
$66$	−2.55236	−0.314174
$67$	12.4327	1.51890	0.759449	−	0.650567i	$-0.225469\pi$
$67$	12.4327	1.51890	0.759449	+	0.650567i	$0.225469\pi$
$68$	5.20414	0.631095
$69$	4.30944	0.518796
$70$	0	0
$71$	4.88208	0.579396	0.289698	−	0.957118i	$-0.406445\pi$
$71$	4.88208	0.579396	0.289698	+	0.957118i	$0.406445\pi$
$72$	−2.46906	−0.290981
$73$	2.59364	0.303562	0.151781	−	0.988414i	$-0.451499\pi$
$73$	2.59364	0.303562	0.151781	+	0.988414i	$0.451499\pi$
$74$	4.05500	0.471384
$75$	0	0
$76$	−1.24364	−0.142655
$77$	8.24539	0.939650
$78$	1.84460	0.208860
$79$	7.18573	0.808458	0.404229	−	0.914658i	$-0.367540\pi$
$79$	7.18573	0.808458	0.404229	+	0.914658i	$0.367540\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.31713	−0.587179
$83$	13.4641	1.47788	0.738939	−	0.673773i	$-0.235327\pi$
$83$	13.4641	1.47788	0.738939	+	0.673773i	$0.235327\pi$
$84$	3.42267	0.373444
$85$	0	0
$86$	−5.19752	−0.560463
$87$	9.52468	1.02115
$88$	8.94164	0.953182
$89$	13.5136	1.43244	0.716218	−	0.697876i	$-0.245871\pi$
$89$	13.5136	1.43244	0.716218	+	0.697876i	$0.245871\pi$
$90$	0	0
$91$	−5.95898	−0.624671
$92$	−6.47829	−0.675408
$93$	−4.55940	−0.472787
$94$	0.704785	0.0726930
$95$	0	0
$96$	5.83066	0.595089
$97$	−18.2314	−1.85112	−0.925559	−	0.378605i	$-0.876404\pi$
$97$	−18.2314	−1.85112	−0.925559	+	0.378605i	$0.876404\pi$
$98$	−1.28001	−0.129300
$99$	−3.62148	−0.363972
$100$	0	0
$101$	−2.65138	−0.263822	−0.131911	−	0.991262i	$-0.542111\pi$
$101$	−2.65138	−0.263822	−0.131911	+	0.991262i	$0.542111\pi$
$102$	−2.43987	−0.241583
$103$	18.5587	1.82864	0.914320	−	0.404994i	$-0.132726\pi$
$103$	18.5587	1.82864	0.914320	+	0.404994i	$0.132726\pi$
$104$	−6.46216	−0.633667
$105$	0	0
$106$	−0.490266	−0.0476188
$107$	−4.72900	−0.457169	−0.228585	−	0.973524i	$-0.573410\pi$
$107$	−4.72900	−0.457169	−0.228585	+	0.973524i	$0.573410\pi$
$108$	−1.50328	−0.144653
$109$	−7.58813	−0.726811	−0.363406	−	0.931631i	$-0.618386\pi$
$109$	−7.58813	−0.726811	−0.363406	+	0.931631i	$0.618386\pi$
$110$	0	0
$111$	5.75353	0.546101
$112$	−2.88335	−0.272451
$113$	−1.35530	−0.127496	−0.0637480	−	0.997966i	$-0.520305\pi$
$113$	−1.35530	−0.127496	−0.0637480	+	0.997966i	$0.520305\pi$
$114$	0.583059	0.0546085
$115$	0	0
$116$	−14.3182	−1.32942
$117$	2.61726	0.241966
$118$	9.03478	0.831719
$119$	7.88198	0.722540
$120$	0	0
$121$	2.11511	0.192283
$122$	6.33393	0.573447
$123$	−7.54433	−0.680250
$124$	6.85404	0.615511
$125$	0	0
$126$	−1.60466	−0.142954
$127$	13.1884	1.17028	0.585140	−	0.810932i	$-0.301040\pi$
$127$	13.1884	1.17028	0.585140	+	0.810932i	$0.301040\pi$
$128$	−10.5502	−0.932513
$129$	−7.37461	−0.649299
$130$	0	0
$131$	0.825961	0.0721645	0.0360823	−	0.999349i	$-0.488512\pi$
$131$	0.825961	0.0721645	0.0360823	+	0.999349i	$0.488512\pi$
$132$	5.44409	0.473847
$133$	−1.88357	−0.163326
$134$	8.76239	0.756955
$135$	0	0
$136$	8.54754	0.732945
$137$	8.81044	0.752727	0.376363	−	0.926472i	$-0.377174\pi$
$137$	8.81044	0.752727	0.376363	+	0.926472i	$0.377174\pi$
$138$	3.03723	0.258546
$139$	−0.0402889	−0.00341726	−0.00170863	−	0.999999i	$-0.500544\pi$
$139$	−0.0402889	−0.00341726	−0.00170863	+	0.999999i	$0.500544\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	3.44082	0.288747
$143$	−9.47834	−0.792619
$144$	1.26640	0.105533
$145$	0	0
$146$	1.82796	0.151283
$147$	−1.81617	−0.149795
$148$	−8.64916	−0.710956
$149$	2.79429	0.228917	0.114459	−	0.993428i	$-0.463487\pi$
$149$	2.79429	0.228917	0.114459	+	0.993428i	$0.463487\pi$
$150$	0	0
$151$	8.95527	0.728770	0.364385	−	0.931248i	$-0.381279\pi$
$151$	8.95527	0.728770	0.364385	+	0.931248i	$0.381279\pi$
$152$	−2.04262	−0.165678
$153$	−3.46186	−0.279875
$154$	5.81123	0.468282
$155$	0	0
$156$	−3.93447	−0.315009
$157$	−0.0468607	−0.00373989	−0.00186995	−	0.999998i	$-0.500595\pi$
$157$	−0.0468607	−0.00373989	−0.00186995	+	0.999998i	$0.500595\pi$
$158$	5.06439	0.402902
$159$	−0.695625	−0.0551666
$160$	0	0
$161$	−9.81175	−0.773274
$162$	0.704785	0.0553731
$163$	4.80530	0.376381	0.188190	−	0.982133i	$-0.439738\pi$
$163$	4.80530	0.376381	0.188190	+	0.982133i	$0.439738\pi$
$164$	11.3412	0.885601
$165$	0	0
$166$	9.48930	0.736513
$167$	4.05372	0.313686	0.156843	−	0.987624i	$-0.449868\pi$
$167$	4.05372	0.313686	0.156843	+	0.987624i	$0.449868\pi$
$168$	5.62156	0.433713
$169$	−6.14996	−0.473074
$170$	0	0
$171$	0.827286	0.0632642
$172$	11.0861	0.845307
$173$	5.78131	0.439545	0.219772	−	0.975551i	$-0.429469\pi$
$173$	5.78131	0.439545	0.219772	+	0.975551i	$0.429469\pi$
$174$	6.71285	0.508900
$175$	0	0
$176$	−4.58624	−0.345701
$177$	12.8192	0.963550
$178$	9.52417	0.713867
$179$	−23.6311	−1.76627	−0.883136	−	0.469117i	$-0.844572\pi$
$179$	−23.6311	−1.76627	−0.883136	+	0.469117i	$0.844572\pi$
$180$	0	0
$181$	−15.9556	−1.18597	−0.592987	−	0.805212i	$-0.702051\pi$
$181$	−15.9556	−1.18597	−0.592987	+	0.805212i	$0.702051\pi$
$182$	−4.19980	−0.311310
$183$	8.98704	0.664341
$184$	−10.6403	−0.784410
$185$	0	0
$186$	−3.21339	−0.235617
$187$	12.5371	0.916801
$188$	−1.50328	−0.109638
$189$	−2.27680	−0.165613
$190$	0	0
$191$	−5.67130	−0.410361	−0.205180	−	0.978724i	$-0.565778\pi$
$191$	−5.67130	−0.410361	−0.205180	+	0.978724i	$0.565778\pi$
$192$	1.57656	0.113778
$193$	14.2922	1.02878	0.514389	−	0.857557i	$-0.328019\pi$
$193$	14.2922	1.02878	0.514389	+	0.857557i	$0.328019\pi$
$194$	−12.8492	−0.922520
$195$	0	0
$196$	2.73021	0.195015
$197$	−6.22370	−0.443421	−0.221710	−	0.975113i	$-0.571164\pi$
$197$	−6.22370	−0.443421	−0.221710	+	0.975113i	$0.571164\pi$
$198$	−2.55236	−0.181389
$199$	24.0381	1.70401	0.852007	−	0.523530i	$-0.175385\pi$
$199$	24.0381	1.70401	0.852007	+	0.523530i	$0.175385\pi$
$200$	0	0
$201$	12.4327	0.876936
$202$	−1.86865	−0.131478
$203$	−21.6858	−1.52205
$204$	5.20414	0.364363
$205$	0	0
$206$	13.0799	0.911317
$207$	4.30944	0.299527
$208$	3.31450	0.229819
$209$	−2.99600	−0.207238
$210$	0	0
$211$	−6.62285	−0.455936	−0.227968	−	0.973669i	$-0.573208\pi$
$211$	−6.62285	−0.455936	−0.227968	+	0.973669i	$0.573208\pi$
$212$	1.04572	0.0718201
$213$	4.88208	0.334514
$214$	−3.33293	−0.227834
$215$	0	0
$216$	−2.46906	−0.167998
$217$	10.3808	0.704698
$218$	−5.34800	−0.362212
$219$	2.59364	0.175262
$220$	0	0
$221$	−9.06059	−0.609481
$222$	4.05500	0.272154
$223$	15.6238	1.04625	0.523125	−	0.852256i	$-0.324766\pi$
$223$	15.6238	1.04625	0.523125	+	0.852256i	$0.324766\pi$
$224$	−13.2753	−0.886990
$225$	0	0
$226$	−0.955196	−0.0635387
$227$	10.1006	0.670402	0.335201	−	0.942147i	$-0.391196\pi$
$227$	10.1006	0.670402	0.335201	+	0.942147i	$0.391196\pi$
$228$	−1.24364	−0.0823621
$229$	−17.7986	−1.17616	−0.588082	−	0.808801i	$-0.700117\pi$
$229$	−17.7986	−1.17616	−0.588082	+	0.808801i	$0.700117\pi$
$230$	0	0
$231$	8.24539	0.542507
$232$	−23.5170	−1.54397
$233$	7.62122	0.499283	0.249641	−	0.968338i	$-0.419687\pi$
$233$	7.62122	0.499283	0.249641	+	0.968338i	$0.419687\pi$
$234$	1.84460	0.120586
$235$	0	0
$236$	−19.2708	−1.25442
$237$	7.18573	0.466763
$238$	5.55510	0.360084
$239$	−7.31608	−0.473238	−0.236619	−	0.971603i	$-0.576039\pi$
$239$	−7.31608	−0.473238	−0.236619	+	0.971603i	$0.576039\pi$
$240$	0	0
$241$	−19.6662	−1.26681	−0.633405	−	0.773820i	$-0.718343\pi$
$241$	−19.6662	−1.26681	−0.633405	+	0.773820i	$0.718343\pi$
$242$	1.49070	0.0958257
$243$	1.00000	0.0641500
$244$	−13.5100	−0.864890
$245$	0	0
$246$	−5.31713	−0.339008
$247$	2.16522	0.137770
$248$	11.2574	0.714846
$249$	13.4641	0.853253
$250$	0	0
$251$	−17.2705	−1.09010	−0.545051	−	0.838403i	$-0.683490\pi$
$251$	−17.2705	−1.09010	−0.545051	+	0.838403i	$0.683490\pi$
$252$	3.42267	0.215608
$253$	−15.6066	−0.981175
$254$	9.29497	0.583219
$255$	0	0
$256$	−10.5887	−0.661795
$257$	−8.26886	−0.515797	−0.257899	−	0.966172i	$-0.583030\pi$
$257$	−8.26886	−0.515797	−0.257899	+	0.966172i	$0.583030\pi$
$258$	−5.19752	−0.323583
$259$	−13.0997	−0.813973
$260$	0	0
$261$	9.52468	0.589563
$262$	0.582125	0.0359638
$263$	21.6756	1.33657	0.668286	−	0.743904i	$-0.267028\pi$
$263$	21.6756	1.33657	0.668286	+	0.743904i	$0.267028\pi$
$264$	8.94164	0.550320
$265$	0	0
$266$	−1.32751	−0.0813949
$267$	13.5136	0.827018
$268$	−18.6898	−1.14166
$269$	−7.83425	−0.477662	−0.238831	−	0.971061i	$-0.576764\pi$
$269$	−7.83425	−0.477662	−0.238831	+	0.971061i	$0.576764\pi$
$270$	0	0
$271$	−26.4316	−1.60560	−0.802801	−	0.596246i	$-0.796658\pi$
$271$	−26.4316	−1.60560	−0.802801	+	0.596246i	$0.796658\pi$
$272$	−4.38411	−0.265825
$273$	−5.95898	−0.360654
$274$	6.20947	0.375128
$275$	0	0
$276$	−6.47829	−0.389947
$277$	−13.4301	−0.806937	−0.403469	−	0.914993i	$-0.632196\pi$
$277$	−13.4301	−0.806937	−0.403469	+	0.914993i	$0.632196\pi$
$278$	−0.0283950	−0.00170302
$279$	−4.55940	−0.272964
$280$	0	0
$281$	25.6430	1.52974	0.764868	−	0.644187i	$-0.222804\pi$
$281$	25.6430	1.52974	0.764868	+	0.644187i	$0.222804\pi$
$282$	0.704785	0.0419693
$283$	27.4891	1.63406	0.817029	−	0.576597i	$-0.195620\pi$
$283$	27.4891	1.63406	0.817029	+	0.576597i	$0.195620\pi$
$284$	−7.33912	−0.435497
$285$	0	0
$286$	−6.68020	−0.395008
$287$	17.1770	1.01392
$288$	5.83066	0.343575
$289$	−5.01551	−0.295030
$290$	0	0
$291$	−18.2314	−1.06874
$292$	−3.89896	−0.228169
$293$	−2.74634	−0.160443	−0.0802215	−	0.996777i	$-0.525563\pi$
$293$	−2.74634	−0.160443	−0.0802215	+	0.996777i	$0.525563\pi$
$294$	−1.28001	−0.0746516
$295$	0	0
$296$	−14.2058	−0.825695
$297$	−3.62148	−0.210140
$298$	1.96938	0.114083
$299$	11.2789	0.652277
$300$	0	0
$301$	16.7905	0.967791
$302$	6.31154	0.363188
$303$	−2.65138	−0.152318
$304$	1.04768	0.0600883
$305$	0	0
$306$	−2.43987	−0.139478
$307$	27.3425	1.56052	0.780261	−	0.625455i	$-0.215086\pi$
$307$	27.3425	1.56052	0.780261	+	0.625455i	$0.215086\pi$
$308$	−12.3951	−0.706277
$309$	18.5587	1.05577
$310$	0	0
$311$	17.6116	0.998660	0.499330	−	0.866412i	$-0.333579\pi$
$311$	17.6116	0.998660	0.499330	+	0.866412i	$0.333579\pi$
$312$	−6.46216	−0.365848
$313$	16.7688	0.947829	0.473914	−	0.880571i	$-0.342841\pi$
$313$	16.7688	0.947829	0.473914	+	0.880571i	$0.342841\pi$
$314$	−0.0330267	−0.00186381
$315$	0	0
$316$	−10.8021	−0.607668
$317$	30.4275	1.70898	0.854489	−	0.519469i	$-0.173870\pi$
$317$	30.4275	1.70898	0.854489	+	0.519469i	$0.173870\pi$
$318$	−0.490266	−0.0274927
$319$	−34.4934	−1.93126
$320$	0	0
$321$	−4.72900	−0.263947
$322$	−6.91517	−0.385368
$323$	−2.86395	−0.159354
$324$	−1.50328	−0.0835154
$325$	0	0
$326$	3.38671	0.187572
$327$	−7.58813	−0.419625
$328$	18.6274	1.02853
$329$	−2.27680	−0.125524
$330$	0	0
$331$	−21.2742	−1.16933	−0.584667	−	0.811273i	$-0.698775\pi$
$331$	−21.2742	−1.16933	−0.584667	+	0.811273i	$0.698775\pi$
$332$	−20.2403	−1.11083
$333$	5.75353	0.315292
$334$	2.85700	0.156328
$335$	0	0
$336$	−2.88335	−0.157299
$337$	−28.5913	−1.55747	−0.778734	−	0.627354i	$-0.784138\pi$
$337$	−28.5913	−1.55747	−0.778734	+	0.627354i	$0.784138\pi$
$338$	−4.33440	−0.235760
$339$	−1.35530	−0.0736098
$340$	0	0
$341$	16.5118	0.894162
$342$	0.583059	0.0315282
$343$	20.0727	1.08382
$344$	18.2083	0.981728
$345$	0	0
$346$	4.07458	0.219051
$347$	−28.8981	−1.55133	−0.775666	−	0.631143i	$-0.782586\pi$
$347$	−28.8981	−1.55133	−0.775666	+	0.631143i	$0.782586\pi$
$348$	−14.3182	−0.767538
$349$	0.564887	0.0302377	0.0151188	−	0.999886i	$-0.495187\pi$
$349$	0.564887	0.0302377	0.0151188	+	0.999886i	$0.495187\pi$
$350$	0	0
$351$	2.61726	0.139699
$352$	−21.1156	−1.12547
$353$	11.0561	0.588459	0.294230	−	0.955735i	$-0.404937\pi$
$353$	11.0561	0.588459	0.294230	+	0.955735i	$0.404937\pi$
$354$	9.03478	0.480193
$355$	0	0
$356$	−20.3147	−1.07668
$357$	7.88198	0.417159
$358$	−16.6548	−0.880236
$359$	35.0118	1.84785	0.923926	−	0.382572i	$-0.124961\pi$
$359$	35.0118	1.84785	0.923926	+	0.382572i	$0.124961\pi$
$360$	0	0
$361$	−18.3156	−0.963979
$362$	−11.2453	−0.591040
$363$	2.11511	0.111014
$364$	8.95800	0.469527
$365$	0	0
$366$	6.33393	0.331080
$367$	26.6971	1.39358	0.696790	−	0.717275i	$-0.254611\pi$
$367$	26.6971	1.39358	0.696790	+	0.717275i	$0.254611\pi$
$368$	5.45748	0.284491
$369$	−7.54433	−0.392742
$370$	0	0
$371$	1.58380	0.0822268
$372$	6.85404	0.355365
$373$	−10.9715	−0.568080	−0.284040	−	0.958812i	$-0.591675\pi$
$373$	−10.9715	−0.568080	−0.284040	+	0.958812i	$0.591675\pi$
$374$	8.83593	0.456895
$375$	0	0
$376$	−2.46906	−0.127332
$377$	24.9285	1.28389
$378$	−1.60466	−0.0825346
$379$	−19.7260	−1.01326	−0.506629	−	0.862164i	$-0.669108\pi$
$379$	−19.7260	−1.01326	−0.506629	+	0.862164i	$0.669108\pi$
$380$	0	0
$381$	13.1884	0.675661
$382$	−3.99705	−0.204507
$383$	−7.76936	−0.396996	−0.198498	−	0.980101i	$-0.563606\pi$
$383$	−7.76936	−0.396996	−0.198498	+	0.980101i	$0.563606\pi$
$384$	−10.5502	−0.538387
$385$	0	0
$386$	10.0730	0.512700
$387$	−7.37461	−0.374873
$388$	27.4068	1.39137
$389$	−23.9114	−1.21236	−0.606178	−	0.795329i	$-0.707298\pi$
$389$	−23.9114	−1.21236	−0.606178	+	0.795329i	$0.707298\pi$
$390$	0	0
$391$	−14.9187	−0.754471
$392$	4.48423	0.226488
$393$	0.825961	0.0416642
$394$	−4.38637	−0.220982
$395$	0	0
$396$	5.44409	0.273576
$397$	−10.9897	−0.551557	−0.275779	−	0.961221i	$-0.588936\pi$
$397$	−10.9897	−0.551557	−0.275779	+	0.961221i	$0.588936\pi$
$398$	16.9417	0.849210
$399$	−1.88357	−0.0942963
$400$	0	0
$401$	31.7109	1.58357	0.791784	−	0.610801i	$-0.209153\pi$
$401$	31.7109	1.58357	0.791784	+	0.610801i	$0.209153\pi$
$402$	8.76239	0.437028
$403$	−11.9331	−0.594431
$404$	3.98576	0.198299
$405$	0	0
$406$	−15.2838	−0.758524
$407$	−20.8363	−1.03282
$408$	8.54754	0.423166
$409$	−4.05508	−0.200511	−0.100255	−	0.994962i	$-0.531966\pi$
$409$	−4.05508	−0.200511	−0.100255	+	0.994962i	$0.531966\pi$
$410$	0	0
$411$	8.81044	0.434587
$412$	−27.8988	−1.37448
$413$	−29.1868	−1.43619
$414$	3.03723	0.149272
$415$	0	0
$416$	15.2603	0.748199
$417$	−0.0402889	−0.00197296
$418$	−2.11154	−0.103279
$419$	23.9652	1.17078	0.585388	−	0.810753i	$-0.300942\pi$
$419$	23.9652	1.17078	0.585388	+	0.810753i	$0.300942\pi$
$420$	0	0
$421$	−16.1016	−0.784742	−0.392371	−	0.919807i	$-0.628345\pi$
$421$	−16.1016	−0.784742	−0.392371	+	0.919807i	$0.628345\pi$
$422$	−4.66769	−0.227219
$423$	1.00000	0.0486217
$424$	1.71754	0.0834110
$425$	0	0
$426$	3.44082	0.166708
$427$	−20.4617	−0.990212
$428$	7.10900	0.343626
$429$	−9.47834	−0.457619
$430$	0	0
$431$	19.5695	0.942630	0.471315	−	0.881965i	$-0.343779\pi$
$431$	19.5695	0.942630	0.471315	+	0.881965i	$0.343779\pi$
$432$	1.26640	0.0609297
$433$	−17.7866	−0.854770	−0.427385	−	0.904070i	$-0.640565\pi$
$433$	−17.7866	−0.854770	−0.427385	+	0.904070i	$0.640565\pi$
$434$	7.31626	0.351192
$435$	0	0
$436$	11.4071	0.546300
$437$	3.56514	0.170544
$438$	1.82796	0.0873431
$439$	16.9533	0.809136	0.404568	−	0.914508i	$-0.367422\pi$
$439$	16.9533	0.809136	0.404568	+	0.914508i	$0.367422\pi$
$440$	0	0
$441$	−1.81617	−0.0864843
$442$	−6.38577	−0.303740
$443$	−13.4508	−0.639068	−0.319534	−	0.947575i	$-0.603526\pi$
$443$	−13.4508	−0.639068	−0.319534	+	0.947575i	$0.603526\pi$
$444$	−8.64916	−0.410471
$445$	0	0
$446$	11.0115	0.521407
$447$	2.79429	0.132166
$448$	−3.58951	−0.169588
$449$	−4.11853	−0.194366	−0.0971828	−	0.995267i	$-0.530983\pi$
$449$	−4.11853	−0.194366	−0.0971828	+	0.995267i	$0.530983\pi$
$450$	0	0
$451$	27.3216	1.28653
$452$	2.03739	0.0958309
$453$	8.95527	0.420755
$454$	7.11877	0.334100
$455$	0	0
$456$	−2.04262	−0.0956543
$457$	−20.9471	−0.979865	−0.489933	−	0.871760i	$-0.662979\pi$
$457$	−20.9471	−0.979865	−0.489933	+	0.871760i	$0.662979\pi$
$458$	−12.5442	−0.586151
$459$	−3.46186	−0.161586
$460$	0	0
$461$	−12.8097	−0.596608	−0.298304	−	0.954471i	$-0.596421\pi$
$461$	−12.8097	−0.596608	−0.298304	+	0.954471i	$0.596421\pi$
$462$	5.81123	0.270363
$463$	10.0835	0.468620	0.234310	−	0.972162i	$-0.424717\pi$
$463$	10.0835	0.468620	0.234310	+	0.972162i	$0.424717\pi$
$464$	12.0621	0.559967
$465$	0	0
$466$	5.37132	0.248822
$467$	−11.2811	−0.522026	−0.261013	−	0.965335i	$-0.584057\pi$
$467$	−11.2811	−0.522026	−0.261013	+	0.965335i	$0.584057\pi$
$468$	−3.93447	−0.181871
$469$	−28.3068	−1.30709
$470$	0	0
$471$	−0.0468607	−0.00215923
$472$	−31.6513	−1.45687
$473$	26.7070	1.22799
$474$	5.06439	0.232615
$475$	0	0
$476$	−11.8488	−0.543089
$477$	−0.695625	−0.0318505
$478$	−5.15626	−0.235842
$479$	38.1043	1.74103	0.870516	−	0.492140i	$-0.163785\pi$
$479$	38.1043	1.74103	0.870516	+	0.492140i	$0.163785\pi$
$480$	0	0
$481$	15.0585	0.686607
$482$	−13.8604	−0.631325
$483$	−9.81175	−0.446450
$484$	−3.17960	−0.144527
$485$	0	0
$486$	0.704785	0.0319697
$487$	−12.7375	−0.577191	−0.288596	−	0.957451i	$-0.593188\pi$
$487$	−12.7375	−0.577191	−0.288596	+	0.957451i	$0.593188\pi$
$488$	−22.1895	−1.00447
$489$	4.80530	0.217303
$490$	0	0
$491$	6.06381	0.273656	0.136828	−	0.990595i	$-0.456309\pi$
$491$	6.06381	0.273656	0.136828	+	0.990595i	$0.456309\pi$
$492$	11.3412	0.511302
$493$	−32.9731	−1.48504
$494$	1.52602	0.0686587
$495$	0	0
$496$	−5.77402	−0.259261
$497$	−11.1155	−0.498600
$498$	9.48930	0.425226
$499$	−33.3406	−1.49253	−0.746265	−	0.665650i	$-0.768155\pi$
$499$	−33.3406	−1.49253	−0.746265	+	0.665650i	$0.768155\pi$
$500$	0	0
$501$	4.05372	0.181107
$502$	−12.1720	−0.543261
$503$	−11.6999	−0.521674	−0.260837	−	0.965383i	$-0.583999\pi$
$503$	−11.6999	−0.521674	−0.260837	+	0.965383i	$0.583999\pi$
$504$	5.62156	0.250404
$505$	0	0
$506$	−10.9993	−0.488977
$507$	−6.14996	−0.273129
$508$	−19.8258	−0.879628
$509$	−20.2558	−0.897825	−0.448912	−	0.893576i	$-0.648188\pi$
$509$	−20.2558	−0.897825	−0.448912	+	0.893576i	$0.648188\pi$
$510$	0	0
$511$	−5.90520	−0.261231
$512$	13.6376	0.602702
$513$	0.827286	0.0365256
$514$	−5.82777	−0.257052
$515$	0	0
$516$	11.0861	0.488038
$517$	−3.62148	−0.159272
$518$	−9.23244	−0.405650
$519$	5.78131	0.253771
$520$	0	0
$521$	8.78508	0.384881	0.192441	−	0.981309i	$-0.438360\pi$
$521$	8.78508	0.384881	0.192441	+	0.981309i	$0.438360\pi$
$522$	6.71285	0.293814
$523$	−13.5464	−0.592342	−0.296171	−	0.955135i	$-0.595710\pi$
$523$	−13.5464	−0.592342	−0.296171	+	0.955135i	$0.595710\pi$
$524$	−1.24165	−0.0542417
$525$	0	0
$526$	15.2766	0.666092
$527$	15.7840	0.687562
$528$	−4.58624	−0.199591
$529$	−4.42871	−0.192553
$530$	0	0
$531$	12.8192	0.556306
$532$	2.83153	0.122762
$533$	−19.7455	−0.855271
$534$	9.52417	0.412151
$535$	0	0
$536$	−30.6971	−1.32591
$537$	−23.6311	−1.01976
$538$	−5.52146	−0.238047
$539$	6.57722	0.283301
$540$	0	0
$541$	8.96283	0.385342	0.192671	−	0.981263i	$-0.438285\pi$
$541$	8.96283	0.385342	0.192671	+	0.981263i	$0.438285\pi$
$542$	−18.6286	−0.800166
$543$	−15.9556	−0.684722
$544$	−20.1849	−0.865422
$545$	0	0
$546$	−4.19980	−0.179735
$547$	29.7905	1.27375	0.636875	−	0.770967i	$-0.280227\pi$
$547$	29.7905	1.27375	0.636875	+	0.770967i	$0.280227\pi$
$548$	−13.2445	−0.565779
$549$	8.98704	0.383557
$550$	0	0
$551$	7.87964	0.335684
$552$	−10.6403	−0.452880
$553$	−16.3605	−0.695719
$554$	−9.46534	−0.402144
$555$	0	0
$556$	0.0605654	0.00256855
$557$	17.7643	0.752697	0.376349	−	0.926478i	$-0.377179\pi$
$557$	17.7643	0.752697	0.376349	+	0.926478i	$0.377179\pi$
$558$	−3.21339	−0.136034
$559$	−19.3013	−0.816357
$560$	0	0
$561$	12.5371	0.529315
$562$	18.0728	0.762356
$563$	46.2829	1.95059	0.975296	−	0.220901i	$-0.0708999\pi$
$563$	46.2829	1.95059	0.975296	+	0.220901i	$0.0708999\pi$
$564$	−1.50328	−0.0632994
$565$	0	0
$566$	19.3739	0.814346
$567$	−2.27680	−0.0956167
$568$	−12.0541	−0.505780
$569$	−22.8534	−0.958064	−0.479032	−	0.877798i	$-0.659012\pi$
$569$	−22.8534	−0.958064	−0.479032	+	0.877798i	$0.659012\pi$
$570$	0	0
$571$	32.4950	1.35987	0.679937	−	0.733270i	$-0.262007\pi$
$571$	32.4950	1.35987	0.679937	+	0.733270i	$0.262007\pi$
$572$	14.2486	0.595763
$573$	−5.67130	−0.236922
$574$	12.1061	0.505297
$575$	0	0
$576$	1.57656	0.0656899
$577$	24.9222	1.03752	0.518762	−	0.854918i	$-0.326393\pi$
$577$	24.9222	1.03752	0.518762	+	0.854918i	$0.326393\pi$
$578$	−3.53486	−0.147031
$579$	14.2922	0.593965
$580$	0	0
$581$	−30.6551	−1.27179
$582$	−12.8492	−0.532617
$583$	2.51919	0.104334
$584$	−6.40384	−0.264993
$585$	0	0
$586$	−1.93558	−0.0799581
$587$	−9.72402	−0.401353	−0.200677	−	0.979658i	$-0.564314\pi$
$587$	−9.72402	−0.401353	−0.200677	+	0.979658i	$0.564314\pi$
$588$	2.73021	0.112592
$589$	−3.77192	−0.155419
$590$	0	0
$591$	−6.22370	−0.256009
$592$	7.28628	0.299464
$593$	−18.8660	−0.774735	−0.387367	−	0.921925i	$-0.626616\pi$
$593$	−18.8660	−0.774735	−0.387367	+	0.921925i	$0.626616\pi$
$594$	−2.55236	−0.104725
$595$	0	0
$596$	−4.20060	−0.172063
$597$	24.0381	0.983813
$598$	7.94921	0.325068
$599$	6.81447	0.278432	0.139216	−	0.990262i	$-0.455542\pi$
$599$	6.81447	0.278432	0.139216	+	0.990262i	$0.455542\pi$
$600$	0	0
$601$	34.5851	1.41076	0.705379	−	0.708831i	$-0.250777\pi$
$601$	34.5851	1.41076	0.705379	+	0.708831i	$0.250777\pi$
$602$	11.8337	0.482307
$603$	12.4327	0.506299
$604$	−13.4623	−0.547772
$605$	0	0
$606$	−1.86865	−0.0759089
$607$	−9.60064	−0.389678	−0.194839	−	0.980835i	$-0.562418\pi$
$607$	−9.60064	−0.389678	−0.194839	+	0.980835i	$0.562418\pi$
$608$	4.82362	0.195624
$609$	−21.6858	−0.878754
$610$	0	0
$611$	2.61726	0.105883
$612$	5.20414	0.210365
$613$	42.6046	1.72078	0.860392	−	0.509633i	$-0.170219\pi$
$613$	42.6046	1.72078	0.860392	+	0.509633i	$0.170219\pi$
$614$	19.2706	0.777699
$615$	0	0
$616$	−20.3584	−0.820261
$617$	−3.21229	−0.129322	−0.0646609	−	0.997907i	$-0.520597\pi$
$617$	−3.21229	−0.129322	−0.0646609	+	0.997907i	$0.520597\pi$
$618$	13.0799	0.526149
$619$	−44.1165	−1.77319	−0.886596	−	0.462544i	$-0.846937\pi$
$619$	−44.1165	−1.77319	−0.886596	+	0.462544i	$0.846937\pi$
$620$	0	0
$621$	4.30944	0.172932
$622$	12.4124	0.497691
$623$	−30.7678	−1.23268
$624$	3.31450	0.132686
$625$	0	0
$626$	11.8184	0.472358
$627$	−2.99600	−0.119649
$628$	0.0704447	0.00281105
$629$	−19.9179	−0.794180
$630$	0	0
$631$	−14.3389	−0.570823	−0.285411	−	0.958405i	$-0.592130\pi$
$631$	−14.3389	−0.570823	−0.285411	+	0.958405i	$0.592130\pi$
$632$	−17.7420	−0.705738
$633$	−6.62285	−0.263235
$634$	21.4448	0.851683
$635$	0	0
$636$	1.04572	0.0414654
$637$	−4.75338	−0.188336
$638$	−24.3104	−0.962460
$639$	4.88208	0.193132
$640$	0	0
$641$	9.27241	0.366238	0.183119	−	0.983091i	$-0.441381\pi$
$641$	9.27241	0.366238	0.183119	+	0.983091i	$0.441381\pi$
$642$	−3.33293	−0.131540
$643$	−0.154793	−0.00610443	−0.00305221	−	0.999995i	$-0.500972\pi$
$643$	−0.154793	−0.00610443	−0.00305221	+	0.999995i	$0.500972\pi$
$644$	14.7498	0.581223
$645$	0	0
$646$	−2.01847	−0.0794156
$647$	30.7744	1.20987	0.604934	−	0.796276i	$-0.293200\pi$
$647$	30.7744	1.20987	0.604934	+	0.796276i	$0.293200\pi$
$648$	−2.46906	−0.0969938
$649$	−46.4244	−1.82232
$650$	0	0
$651$	10.3808	0.406857
$652$	−7.22371	−0.282902
$653$	28.1772	1.10266	0.551330	−	0.834287i	$-0.314120\pi$
$653$	28.1772	1.10266	0.551330	+	0.834287i	$0.314120\pi$
$654$	−5.34800	−0.209123
$655$	0	0
$656$	−9.55415	−0.373027
$657$	2.59364	0.101187
$658$	−1.60466	−0.0625560
$659$	15.2954	0.595823	0.297911	−	0.954594i	$-0.403710\pi$
$659$	15.2954	0.595823	0.297911	+	0.954594i	$0.403710\pi$
$660$	0	0
$661$	−2.50273	−0.0973449	−0.0486724	−	0.998815i	$-0.515499\pi$
$661$	−2.50273	−0.0973449	−0.0486724	+	0.998815i	$0.515499\pi$
$662$	−14.9937	−0.582748
$663$	−9.06059	−0.351884
$664$	−33.2437	−1.29010
$665$	0	0
$666$	4.05500	0.157128
$667$	41.0460	1.58931
$668$	−6.09386	−0.235779
$669$	15.6238	0.604053
$670$	0	0
$671$	−32.5464	−1.25644
$672$	−13.2753	−0.512104
$673$	27.8567	1.07380	0.536899	−	0.843646i	$-0.319596\pi$
$673$	27.8567	1.07380	0.536899	+	0.843646i	$0.319596\pi$
$674$	−20.1507	−0.776177
$675$	0	0
$676$	9.24510	0.355581
$677$	−12.0506	−0.463142	−0.231571	−	0.972818i	$-0.574387\pi$
$677$	−12.0506	−0.463142	−0.231571	+	0.972818i	$0.574387\pi$
$678$	−0.955196	−0.0366841
$679$	41.5093	1.59298
$680$	0	0
$681$	10.1006	0.387057
$682$	11.6372	0.445613
$683$	8.78007	0.335960	0.167980	−	0.985790i	$-0.446276\pi$
$683$	8.78007	0.335960	0.167980	+	0.985790i	$0.446276\pi$
$684$	−1.24364	−0.0475518
$685$	0	0
$686$	14.1469	0.540132
$687$	−17.7986	−0.679058
$688$	−9.33922	−0.356054
$689$	−1.82063	−0.0693604
$690$	0	0
$691$	−34.2462	−1.30279	−0.651393	−	0.758741i	$-0.725815\pi$
$691$	−34.2462	−1.30279	−0.651393	+	0.758741i	$0.725815\pi$
$692$	−8.69091	−0.330379
$693$	8.24539	0.313217
$694$	−20.3670	−0.773120
$695$	0	0
$696$	−23.5170	−0.891409
$697$	26.1174	0.989269
$698$	0.398124	0.0150692
$699$	7.62122	0.288261
$700$	0	0
$701$	33.8420	1.27819	0.639097	−	0.769126i	$-0.279308\pi$
$701$	33.8420	1.27819	0.639097	+	0.769126i	$0.279308\pi$
$702$	1.84460	0.0696201
$703$	4.75982	0.179520
$704$	−5.70947	−0.215184
$705$	0	0
$706$	7.79221	0.293264
$707$	6.03667	0.227032
$708$	−19.2708	−0.724242
$709$	14.3001	0.537052	0.268526	−	0.963272i	$-0.413463\pi$
$709$	14.3001	0.537052	0.268526	+	0.963272i	$0.413463\pi$
$710$	0	0
$711$	7.18573	0.269486
$712$	−33.3658	−1.25044
$713$	−19.6484	−0.735840
$714$	5.55510	0.207894
$715$	0	0
$716$	35.5241	1.32760
$717$	−7.31608	−0.273224
$718$	24.6758	0.920892
$719$	14.8833	0.555054	0.277527	−	0.960718i	$-0.410485\pi$
$719$	14.8833	0.555054	0.277527	+	0.960718i	$0.410485\pi$
$720$	0	0
$721$	−42.2544	−1.57364
$722$	−12.9086	−0.480407
$723$	−19.6662	−0.731393
$724$	23.9858	0.891424
$725$	0	0
$726$	1.49070	0.0553250
$727$	−43.0563	−1.59687	−0.798434	−	0.602082i	$-0.794338\pi$
$727$	−43.0563	−1.59687	−0.798434	+	0.602082i	$0.794338\pi$
$728$	14.7131	0.545303
$729$	1.00000	0.0370370
$730$	0	0
$731$	25.5299	0.944257
$732$	−13.5100	−0.499345
$733$	−23.3140	−0.861121	−0.430561	−	0.902562i	$-0.641684\pi$
$733$	−23.3140	−0.861121	−0.430561	+	0.902562i	$0.641684\pi$
$734$	18.8157	0.694502
$735$	0	0
$736$	25.1269	0.926189
$737$	−45.0248	−1.65851
$738$	−5.31713	−0.195726
$739$	0.233787	0.00859999	0.00429999	−	0.999991i	$-0.498631\pi$
$739$	0.233787	0.00859999	0.00429999	+	0.999991i	$0.498631\pi$
$740$	0	0
$741$	2.16522	0.0795414
$742$	1.11624	0.0409784
$743$	−32.8601	−1.20552	−0.602760	−	0.797922i	$-0.705933\pi$
$743$	−32.8601	−1.20552	−0.602760	+	0.797922i	$0.705933\pi$
$744$	11.2574	0.412717
$745$	0	0
$746$	−7.73251	−0.283107
$747$	13.4641	0.492626
$748$	−18.8467	−0.689103
$749$	10.7670	0.393417
$750$	0	0
$751$	−4.22639	−0.154223	−0.0771116	−	0.997022i	$-0.524570\pi$
$751$	−4.22639	−0.154223	−0.0771116	+	0.997022i	$0.524570\pi$
$752$	1.26640	0.0461809
$753$	−17.2705	−0.629371
$754$	17.5693	0.639835
$755$	0	0
$756$	3.42267	0.124481
$757$	1.80156	0.0654789	0.0327395	−	0.999464i	$-0.489577\pi$
$757$	1.80156	0.0654789	0.0327395	+	0.999464i	$0.489577\pi$
$758$	−13.9026	−0.504965
$759$	−15.6066	−0.566482
$760$	0	0
$761$	−25.8915	−0.938565	−0.469282	−	0.883048i	$-0.655487\pi$
$761$	−25.8915	−0.938565	−0.469282	+	0.883048i	$0.655487\pi$
$762$	9.29497	0.336721
$763$	17.2767	0.625458
$764$	8.52554	0.308443
$765$	0	0
$766$	−5.47573	−0.197846
$767$	33.5511	1.21146
$768$	−10.5887	−0.382088
$769$	−24.7428	−0.892250	−0.446125	−	0.894971i	$-0.647196\pi$
$769$	−24.7428	−0.892250	−0.446125	+	0.894971i	$0.647196\pi$
$770$	0	0
$771$	−8.26886	−0.297796
$772$	−21.4852	−0.773270
$773$	42.4437	1.52660	0.763298	−	0.646047i	$-0.223579\pi$
$773$	42.4437	1.52660	0.763298	+	0.646047i	$0.223579\pi$
$774$	−5.19752	−0.186821
$775$	0	0
$776$	45.0144	1.61592
$777$	−13.0997	−0.469948
$778$	−16.8524	−0.604187
$779$	−6.24132	−0.223619
$780$	0	0
$781$	−17.6803	−0.632652
$782$	−10.5145	−0.375997
$783$	9.52468	0.340384
$784$	−2.30000	−0.0821428
$785$	0	0
$786$	0.582125	0.0207637
$787$	−14.9474	−0.532817	−0.266409	−	0.963860i	$-0.585837\pi$
$787$	−14.9474	−0.532817	−0.266409	+	0.963860i	$0.585837\pi$
$788$	9.35596	0.333292
$789$	21.6756	0.771670
$790$	0	0
$791$	3.08575	0.109717
$792$	8.94164	0.317727
$793$	23.5214	0.835269
$794$	−7.74538	−0.274873
$795$	0	0
$796$	−36.1359	−1.28080
$797$	−7.05175	−0.249786	−0.124893	−	0.992170i	$-0.539859\pi$
$797$	−7.05175	−0.249786	−0.124893	+	0.992170i	$0.539859\pi$
$798$	−1.32751	−0.0469933
$799$	−3.46186	−0.122472
$800$	0	0
$801$	13.5136	0.477479
$802$	22.3494	0.789184
$803$	−9.39280	−0.331465
$804$	−18.6898	−0.659139
$805$	0	0
$806$	−8.41028	−0.296239
$807$	−7.83425	−0.275778
$808$	6.54642	0.230302
$809$	14.5596	0.511887	0.255944	−	0.966692i	$-0.417614\pi$
$809$	14.5596	0.511887	0.255944	+	0.966692i	$0.417614\pi$
$810$	0	0
$811$	23.6618	0.830878	0.415439	−	0.909621i	$-0.363628\pi$
$811$	23.6618	0.830878	0.415439	+	0.909621i	$0.363628\pi$
$812$	32.5998	1.14403
$813$	−26.4316	−0.926995
$814$	−14.6851	−0.514713
$815$	0	0
$816$	−4.38411	−0.153474
$817$	−6.10092	−0.213444
$818$	−2.85796	−0.0999262
$819$	−5.95898	−0.208224
$820$	0	0
$821$	31.0604	1.08402	0.542008	−	0.840374i	$-0.317664\pi$
$821$	31.0604	1.08402	0.542008	+	0.840374i	$0.317664\pi$
$822$	6.20947	0.216580
$823$	−27.3374	−0.952923	−0.476462	−	0.879195i	$-0.658081\pi$
$823$	−27.3374	−0.952923	−0.476462	+	0.879195i	$0.658081\pi$
$824$	−45.8224	−1.59630
$825$	0	0
$826$	−20.5704	−0.715736
$827$	34.8391	1.21147	0.605736	−	0.795665i	$-0.292879\pi$
$827$	34.8391	1.21147	0.605736	+	0.795665i	$0.292879\pi$
$828$	−6.47829	−0.225136
$829$	−28.2044	−0.979581	−0.489790	−	0.871840i	$-0.662927\pi$
$829$	−28.2044	−0.979581	−0.489790	+	0.871840i	$0.662927\pi$
$830$	0	0
$831$	−13.4301	−0.465885
$832$	4.12626	0.143052
$833$	6.28733	0.217843
$834$	−0.0283950	−0.000983239 0
$835$	0	0
$836$	4.50382	0.155768
$837$	−4.55940	−0.157596
$838$	16.8903	0.583466
$839$	−25.7809	−0.890055	−0.445027	−	0.895517i	$-0.646806\pi$
$839$	−25.7809	−0.890055	−0.445027	+	0.895517i	$0.646806\pi$
$840$	0	0
$841$	61.7195	2.12826
$842$	−11.3481	−0.391083
$843$	25.6430	0.883193
$844$	9.95599	0.342699
$845$	0	0
$846$	0.704785	0.0242310
$847$	−4.81569	−0.165469
$848$	−0.880940	−0.0302516
$849$	27.4891	0.943424
$850$	0	0
$851$	24.7945	0.849945
$852$	−7.33912	−0.251434
$853$	−13.5299	−0.463255	−0.231627	−	0.972805i	$-0.574405\pi$
$853$	−13.5299	−0.463255	−0.231627	+	0.972805i	$0.574405\pi$
$854$	−14.4211	−0.493480
$855$	0	0
$856$	11.6762	0.399083
$857$	−2.61031	−0.0891664	−0.0445832	−	0.999006i	$-0.514196\pi$
$857$	−2.61031	−0.0891664	−0.0445832	+	0.999006i	$0.514196\pi$
$858$	−6.68020	−0.228058
$859$	−6.12774	−0.209076	−0.104538	−	0.994521i	$-0.533336\pi$
$859$	−6.12774	−0.209076	−0.104538	+	0.994521i	$0.533336\pi$
$860$	0	0
$861$	17.1770	0.585389
$862$	13.7923	0.469768
$863$	−21.5168	−0.732440	−0.366220	−	0.930528i	$-0.619348\pi$
$863$	−21.5168	−0.732440	−0.366220	+	0.930528i	$0.619348\pi$
$864$	5.83066	0.198363
$865$	0	0
$866$	−12.5357	−0.425982
$867$	−5.01551	−0.170336
$868$	−15.6053	−0.529678
$869$	−26.0230	−0.882769
$870$	0	0
$871$	32.5396	1.10256
$872$	18.7355	0.634465
$873$	−18.2314	−0.617039
$874$	2.51266	0.0849919
$875$	0	0
$876$	−3.89896	−0.131734
$877$	7.78499	0.262880	0.131440	−	0.991324i	$-0.458040\pi$
$877$	7.78499	0.262880	0.131440	+	0.991324i	$0.458040\pi$
$878$	11.9484	0.403239
$879$	−2.74634	−0.0926318
$880$	0	0
$881$	−7.47286	−0.251767	−0.125883	−	0.992045i	$-0.540177\pi$
$881$	−7.47286	−0.251767	−0.125883	+	0.992045i	$0.540177\pi$
$882$	−1.28001	−0.0431001
$883$	−22.9237	−0.771445	−0.385722	−	0.922615i	$-0.626048\pi$
$883$	−22.9237	−0.771445	−0.385722	+	0.922615i	$0.626048\pi$
$884$	13.6206	0.458110
$885$	0	0
$886$	−9.47994	−0.318485
$887$	4.51506	0.151601	0.0758004	−	0.997123i	$-0.475849\pi$
$887$	4.51506	0.151601	0.0758004	+	0.997123i	$0.475849\pi$
$888$	−14.2058	−0.476716
$889$	−30.0273	−1.00708
$890$	0	0
$891$	−3.62148	−0.121324
$892$	−23.4870	−0.786402
$893$	0.827286	0.0276841
$894$	1.96938	0.0658658
$895$	0	0
$896$	24.0207	0.802474
$897$	11.2789	0.376592
$898$	−2.90268	−0.0968637
$899$	−43.4268	−1.44836
$900$	0	0
$901$	2.40816	0.0802273
$902$	19.2559	0.641151
$903$	16.7905	0.558754
$904$	3.34632	0.111297
$905$	0	0
$906$	6.31154	0.209687
$907$	34.7998	1.15551	0.577754	−	0.816211i	$-0.303929\pi$
$907$	34.7998	1.15551	0.577754	+	0.816211i	$0.303929\pi$
$908$	−15.1840	−0.503900
$909$	−2.65138	−0.0879408
$910$	0	0
$911$	−1.02311	−0.0338970	−0.0169485	−	0.999856i	$-0.505395\pi$
$911$	−1.02311	−0.0338970	−0.0169485	+	0.999856i	$0.505395\pi$
$912$	1.04768	0.0346920
$913$	−48.7600	−1.61372
$914$	−14.7632	−0.488324
$915$	0	0
$916$	26.7562	0.884051
$917$	−1.88055	−0.0621012
$918$	−2.43987	−0.0805277
$919$	9.95049	0.328236	0.164118	−	0.986441i	$-0.447522\pi$
$919$	9.95049	0.328236	0.164118	+	0.986441i	$0.447522\pi$
$920$	0	0
$921$	27.3425	0.900967
$922$	−9.02809	−0.297324
$923$	12.7777	0.420582
$924$	−12.3951	−0.407769
$925$	0	0
$926$	7.10670	0.233541
$927$	18.5587	0.609546
$928$	55.5351	1.82303
$929$	48.9134	1.60480	0.802398	−	0.596789i	$-0.203557\pi$
$929$	48.9134	1.60480	0.802398	+	0.596789i	$0.203557\pi$
$930$	0	0
$931$	−1.50249	−0.0492422
$932$	−11.4568	−0.375280
$933$	17.6116	0.576577
$934$	−7.95074	−0.260156
$935$	0	0
$936$	−6.46216	−0.211222
$937$	−37.8886	−1.23777	−0.618884	−	0.785483i	$-0.712415\pi$
$937$	−37.8886	−1.23777	−0.618884	+	0.785483i	$0.712415\pi$
$938$	−19.9502	−0.651398
$939$	16.7688	0.547229
$940$	0	0
$941$	18.0263	0.587641	0.293820	−	0.955861i	$-0.405073\pi$
$941$	18.0263	0.587641	0.293820	+	0.955861i	$0.405073\pi$
$942$	−0.0330267	−0.00107607
$943$	−32.5119	−1.05873
$944$	16.2342	0.528380
$945$	0	0
$946$	18.8227	0.611979
$947$	11.9915	0.389672	0.194836	−	0.980836i	$-0.437583\pi$
$947$	11.9915	0.389672	0.194836	+	0.980836i	$0.437583\pi$
$948$	−10.8021	−0.350838
$949$	6.78822	0.220355
$950$	0	0
$951$	30.4275	0.986679
$952$	−19.4611	−0.630737
$953$	−36.4759	−1.18157	−0.590786	−	0.806829i	$-0.701182\pi$
$953$	−36.4759	−1.18157	−0.590786	+	0.806829i	$0.701182\pi$
$954$	−0.490266	−0.0158729
$955$	0	0
$956$	10.9981	0.355704
$957$	−34.4934	−1.11501
$958$	26.8554	0.867658
$959$	−20.0596	−0.647760
$960$	0	0
$961$	−10.2119	−0.329417
$962$	10.6130	0.342176
$963$	−4.72900	−0.152390
$964$	29.5637	0.952184
$965$	0	0
$966$	−6.91517	−0.222492
$967$	46.5953	1.49840	0.749201	−	0.662342i	$-0.230438\pi$
$967$	46.5953	1.49840	0.749201	+	0.662342i	$0.230438\pi$
$968$	−5.22233	−0.167852
$969$	−2.86395	−0.0920034
$970$	0	0
$971$	−0.0330024	−0.00105910	−0.000529549	−	1.00000i	$-0.500169\pi$
$971$	−0.0330024	−0.00105910	−0.000529549		1.00000i	$0.500169\pi$
$972$	−1.50328	−0.0482177
$973$	0.0917299	0.00294073
$974$	−8.97720	−0.287648
$975$	0	0
$976$	11.3812	0.364303
$977$	4.93863	0.158001	0.0790004	−	0.996875i	$-0.474827\pi$
$977$	4.93863	0.158001	0.0790004	+	0.996875i	$0.474827\pi$
$978$	3.38671	0.108295
$979$	−48.9391	−1.56410
$980$	0	0
$981$	−7.58813	−0.242270
$982$	4.27368	0.136379
$983$	36.7760	1.17297	0.586486	−	0.809960i	$-0.300511\pi$
$983$	36.7760	1.17297	0.586486	+	0.809960i	$0.300511\pi$
$984$	18.6274	0.593820
$985$	0	0
$986$	−23.2390	−0.740080
$987$	−2.27680	−0.0724714
$988$	−3.25493	−0.103553
$989$	−31.7805	−1.01056
$990$	0	0
$991$	14.9934	0.476281	0.238141	−	0.971231i	$-0.423462\pi$
$991$	14.9934	0.476281	0.238141	+	0.971231i	$0.423462\pi$
$992$	−26.5843	−0.844051
$993$	−21.2742	−0.675116
$994$	−7.83406	−0.248481
$995$	0	0
$996$	−20.2403	−0.641338
$997$	−9.99544	−0.316559	−0.158279	−	0.987394i	$-0.550595\pi$
$997$	−9.99544	−0.316559	−0.158279	+	0.987394i	$0.550595\pi$
$998$	−23.4979	−0.743814
$999$	5.75353	0.182034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.z.1.5	✓	7
5.4	even	2		3525.2.a.ba.1.3	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.z.1.5	✓	7	1.1	even	1	trivial
3525.2.a.ba.1.3	yes	7	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.704785 q^{2} +1.00000 q^{3} -1.50328 q^{4} +0.704785 q^{6} -2.27680 q^{7} -2.46906 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.704785 q^{2} +1.00000 q^{3} -1.50328 q^{4} +0.704785 q^{6} -2.27680 q^{7} -2.46906 q^{8} +1.00000 q^{9} -3.62148 q^{11} -1.50328 q^{12} +2.61726 q^{13} -1.60466 q^{14} +1.26640 q^{16} -3.46186 q^{17} +0.704785 q^{18} +0.827286 q^{19} -2.27680 q^{21} -2.55236 q^{22} +4.30944 q^{23} -2.46906 q^{24} +1.84460 q^{26} +1.00000 q^{27} +3.42267 q^{28} +9.52468 q^{29} -4.55940 q^{31} +5.83066 q^{32} -3.62148 q^{33} -2.43987 q^{34} -1.50328 q^{36} +5.75353 q^{37} +0.583059 q^{38} +2.61726 q^{39} -7.54433 q^{41} -1.60466 q^{42} -7.37461 q^{43} +5.44409 q^{44} +3.03723 q^{46} +1.00000 q^{47} +1.26640 q^{48} -1.81617 q^{49} -3.46186 q^{51} -3.93447 q^{52} -0.695625 q^{53} +0.704785 q^{54} +5.62156 q^{56} +0.827286 q^{57} +6.71285 q^{58} +12.8192 q^{59} +8.98704 q^{61} -3.21339 q^{62} -2.27680 q^{63} +1.57656 q^{64} -2.55236 q^{66} +12.4327 q^{67} +5.20414 q^{68} +4.30944 q^{69} +4.88208 q^{71} -2.46906 q^{72} +2.59364 q^{73} +4.05500 q^{74} -1.24364 q^{76} +8.24539 q^{77} +1.84460 q^{78} +7.18573 q^{79} +1.00000 q^{81} -5.31713 q^{82} +13.4641 q^{83} +3.42267 q^{84} -5.19752 q^{86} +9.52468 q^{87} +8.94164 q^{88} +13.5136 q^{89} -5.95898 q^{91} -6.47829 q^{92} -4.55940 q^{93} +0.704785 q^{94} +5.83066 q^{96} -18.2314 q^{97} -1.28001 q^{98} -3.62148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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