LMFDB - Embedded newform 6025.2.a.l.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.50972 q^{2} -0.136405 q^{3} +4.29867 q^{4} +0.342337 q^{6} -4.91163 q^{7} -5.76901 q^{8} -2.98139 q^{9} +O(q^{10})$	\(q-2.50972 q^{2} -0.136405 q^{3} +4.29867 q^{4} +0.342337 q^{6} -4.91163 q^{7} -5.76901 q^{8} -2.98139 q^{9} +3.67330 q^{11} -0.586358 q^{12} -2.24471 q^{13} +12.3268 q^{14} +5.88123 q^{16} +7.15567 q^{17} +7.48245 q^{18} -3.70267 q^{19} +0.669969 q^{21} -9.21894 q^{22} -0.647054 q^{23} +0.786919 q^{24} +5.63358 q^{26} +0.815890 q^{27} -21.1135 q^{28} +7.87622 q^{29} +3.74201 q^{31} -3.22219 q^{32} -0.501055 q^{33} -17.9587 q^{34} -12.8160 q^{36} -10.1019 q^{37} +9.29264 q^{38} +0.306188 q^{39} -4.37151 q^{41} -1.68143 q^{42} -6.82890 q^{43} +15.7903 q^{44} +1.62392 q^{46} -10.8754 q^{47} -0.802227 q^{48} +17.1241 q^{49} -0.976066 q^{51} -9.64926 q^{52} +6.63493 q^{53} -2.04765 q^{54} +28.3353 q^{56} +0.505061 q^{57} -19.7671 q^{58} -10.8955 q^{59} -5.33314 q^{61} -9.39138 q^{62} +14.6435 q^{63} -3.67567 q^{64} +1.25751 q^{66} +0.479655 q^{67} +30.7599 q^{68} +0.0882611 q^{69} +14.9281 q^{71} +17.1997 q^{72} +14.0514 q^{73} +25.3530 q^{74} -15.9166 q^{76} -18.0419 q^{77} -0.768446 q^{78} +5.30373 q^{79} +8.83289 q^{81} +10.9712 q^{82} +13.7939 q^{83} +2.87998 q^{84} +17.1386 q^{86} -1.07435 q^{87} -21.1913 q^{88} -0.507811 q^{89} +11.0252 q^{91} -2.78147 q^{92} -0.510428 q^{93} +27.2942 q^{94} +0.439522 q^{96} +9.41195 q^{97} -42.9767 q^{98} -10.9516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50972	−1.77464	−0.887318	−	0.461157i	$-0.847434\pi$
$2$	−2.50972	−1.77464	−0.887318	+	0.461157i	$0.847434\pi$
$3$	−0.136405	−0.0787532	−0.0393766	−	0.999224i	$-0.512537\pi$
$3$	−0.136405	−0.0787532	−0.0393766	+	0.999224i	$0.512537\pi$
$4$	4.29867	2.14934
$5$	0	0
$5$	0	0
$6$	0.342337	0.139758
$7$	−4.91163	−1.85642	−0.928211	−	0.372054i	$-0.878654\pi$
$7$	−4.91163	−1.85642	−0.928211	+	0.372054i	$0.878654\pi$
$8$	−5.76901	−2.03965
$9$	−2.98139	−0.993798
$10$	0	0
$11$	3.67330	1.10754	0.553771	−	0.832669i	$-0.313188\pi$
$11$	3.67330	1.10754	0.553771	+	0.832669i	$0.313188\pi$
$12$	−0.586358	−0.169267
$13$	−2.24471	−0.622570	−0.311285	−	0.950317i	$-0.600759\pi$
$13$	−2.24471	−0.622570	−0.311285	+	0.950317i	$0.600759\pi$
$14$	12.3268	3.29448
$15$	0	0
$16$	5.88123	1.47031
$17$	7.15567	1.73550	0.867752	−	0.496997i	$-0.165564\pi$
$17$	7.15567	1.73550	0.867752	+	0.496997i	$0.165564\pi$
$18$	7.48245	1.76363
$19$	−3.70267	−0.849450	−0.424725	−	0.905322i	$-0.639629\pi$
$19$	−3.70267	−0.849450	−0.424725	+	0.905322i	$0.639629\pi$
$20$	0	0
$21$	0.669969	0.146199
$22$	−9.21894	−1.96548
$23$	−0.647054	−0.134920	−0.0674600	−	0.997722i	$-0.521490\pi$
$23$	−0.647054	−0.134920	−0.0674600	+	0.997722i	$0.521490\pi$
$24$	0.786919	0.160629
$25$	0	0
$26$	5.63358	1.10484
$27$	0.815890	0.157018
$28$	−21.1135	−3.99007
$29$	7.87622	1.46258	0.731289	−	0.682068i	$-0.238919\pi$
$29$	7.87622	1.46258	0.731289	+	0.682068i	$0.238919\pi$
$30$	0	0
$31$	3.74201	0.672085	0.336043	−	0.941847i	$-0.390911\pi$
$31$	3.74201	0.672085	0.336043	+	0.941847i	$0.390911\pi$
$32$	−3.22219	−0.569609
$33$	−0.501055	−0.0872225
$34$	−17.9587	−3.07989
$35$	0	0
$36$	−12.8160	−2.13601
$37$	−10.1019	−1.66075	−0.830375	−	0.557205i	$-0.811874\pi$
$37$	−10.1019	−1.66075	−0.830375	+	0.557205i	$0.811874\pi$
$38$	9.29264	1.50747
$39$	0.306188	0.0490294
$40$	0	0
$41$	−4.37151	−0.682715	−0.341357	−	0.939934i	$-0.610887\pi$
$41$	−4.37151	−0.682715	−0.341357	+	0.939934i	$0.610887\pi$
$42$	−1.68143	−0.259451
$43$	−6.82890	−1.04140	−0.520699	−	0.853740i	$-0.674329\pi$
$43$	−6.82890	−1.04140	−0.520699	+	0.853740i	$0.674329\pi$
$44$	15.7903	2.38048
$45$	0	0
$46$	1.62392	0.239434
$47$	−10.8754	−1.58634	−0.793172	−	0.608998i	$-0.791572\pi$
$47$	−10.8754	−1.58634	−0.793172	+	0.608998i	$0.791572\pi$
$48$	−0.802227	−0.115791
$49$	17.1241	2.44630
$50$	0	0
$51$	−0.976066	−0.136677
$52$	−9.64926	−1.33811
$53$	6.63493	0.911377	0.455689	−	0.890139i	$-0.349393\pi$
$53$	6.63493	0.911377	0.455689	+	0.890139i	$0.349393\pi$
$54$	−2.04765	−0.278650
$55$	0	0
$56$	28.3353	3.78646
$57$	0.505061	0.0668970
$58$	−19.7671	−2.59554
$59$	−10.8955	−1.41848	−0.709239	−	0.704968i	$-0.750961\pi$
$59$	−10.8955	−1.41848	−0.709239	+	0.704968i	$0.750961\pi$
$60$	0	0
$61$	−5.33314	−0.682838	−0.341419	−	0.939911i	$-0.610908\pi$
$61$	−5.33314	−0.682838	−0.341419	+	0.939911i	$0.610908\pi$
$62$	−9.39138	−1.19271
$63$	14.6435	1.84491
$64$	−3.67567	−0.459459
$65$	0	0
$66$	1.25751	0.154788
$67$	0.479655	0.0585992	0.0292996	−	0.999571i	$-0.490672\pi$
$67$	0.479655	0.0585992	0.0292996	+	0.999571i	$0.490672\pi$
$68$	30.7599	3.73018
$69$	0.0882611	0.0106254
$70$	0	0
$71$	14.9281	1.77163	0.885817	−	0.464034i	$-0.153598\pi$
$71$	14.9281	1.77163	0.885817	+	0.464034i	$0.153598\pi$
$72$	17.1997	2.02700
$73$	14.0514	1.64459	0.822295	−	0.569061i	$-0.192693\pi$
$73$	14.0514	1.64459	0.822295	+	0.569061i	$0.192693\pi$
$74$	25.3530	2.94723
$75$	0	0
$76$	−15.9166	−1.82575
$77$	−18.0419	−2.05606
$78$	−0.768446	−0.0870093
$79$	5.30373	0.596716	0.298358	−	0.954454i	$-0.403561\pi$
$79$	5.30373	0.596716	0.298358	+	0.954454i	$0.403561\pi$
$80$	0	0
$81$	8.83289	0.981432
$82$	10.9712	1.21157
$83$	13.7939	1.51408	0.757039	−	0.653370i	$-0.226645\pi$
$83$	13.7939	1.51408	0.757039	+	0.653370i	$0.226645\pi$
$84$	2.87998	0.314231
$85$	0	0
$86$	17.1386	1.84810
$87$	−1.07435	−0.115183
$88$	−21.1913	−2.25900
$89$	−0.507811	−0.0538279	−0.0269139	−	0.999638i	$-0.508568\pi$
$89$	−0.507811	−0.0538279	−0.0269139	+	0.999638i	$0.508568\pi$
$90$	0	0
$91$	11.0252	1.15575
$92$	−2.78147	−0.289988
$93$	−0.510428	−0.0529289
$94$	27.2942	2.81518
$95$	0	0
$96$	0.439522	0.0448585
$97$	9.41195	0.955639	0.477819	−	0.878458i	$-0.341427\pi$
$97$	9.41195	0.955639	0.477819	+	0.878458i	$0.341427\pi$
$98$	−42.9767	−4.34130
$99$	−10.9516	−1.10067
$100$	0	0
$101$	0.678588	0.0675220	0.0337610	−	0.999430i	$-0.489251\pi$
$101$	0.678588	0.0675220	0.0337610	+	0.999430i	$0.489251\pi$
$102$	2.44965	0.242551
$103$	6.95197	0.684998	0.342499	−	0.939518i	$-0.388727\pi$
$103$	6.95197	0.684998	0.342499	+	0.939518i	$0.388727\pi$
$104$	12.9497	1.26983
$105$	0	0
$106$	−16.6518	−1.61736
$107$	−4.95101	−0.478632	−0.239316	−	0.970942i	$-0.576923\pi$
$107$	−4.95101	−0.478632	−0.239316	+	0.970942i	$0.576923\pi$
$108$	3.50724	0.337484
$109$	−7.21154	−0.690740	−0.345370	−	0.938467i	$-0.612247\pi$
$109$	−7.21154	−0.690740	−0.345370	+	0.938467i	$0.612247\pi$
$110$	0	0
$111$	1.37795	0.130789
$112$	−28.8864	−2.72951
$113$	4.15854	0.391202	0.195601	−	0.980684i	$-0.437334\pi$
$113$	4.15854	0.391202	0.195601	+	0.980684i	$0.437334\pi$
$114$	−1.26756	−0.118718
$115$	0	0
$116$	33.8573	3.14357
$117$	6.69236	0.618709
$118$	27.3447	2.51728
$119$	−35.1460	−3.22183
$120$	0	0
$121$	2.49313	0.226648
$122$	13.3847	1.21179
$123$	0.596294	0.0537660
$124$	16.0857	1.44454
$125$	0	0
$126$	−36.7510	−3.27404
$127$	−1.36731	−0.121329	−0.0606647	−	0.998158i	$-0.519322\pi$
$127$	−1.36731	−0.121329	−0.0606647	+	0.998158i	$0.519322\pi$
$128$	15.6693	1.38498
$129$	0.931494	0.0820135
$130$	0	0
$131$	14.5099	1.26773	0.633866	−	0.773442i	$-0.281467\pi$
$131$	14.5099	1.26773	0.633866	+	0.773442i	$0.281467\pi$
$132$	−2.15387	−0.187470
$133$	18.1861	1.57694
$134$	−1.20380	−0.103992
$135$	0	0
$136$	−41.2811	−3.53983
$137$	−4.47651	−0.382454	−0.191227	−	0.981546i	$-0.561247\pi$
$137$	−4.47651	−0.382454	−0.191227	+	0.981546i	$0.561247\pi$
$138$	−0.221510	−0.0188562
$139$	1.70007	0.144198	0.0720990	−	0.997397i	$-0.477030\pi$
$139$	1.70007	0.144198	0.0720990	+	0.997397i	$0.477030\pi$
$140$	0	0
$141$	1.48346	0.124930
$142$	−37.4652	−3.14401
$143$	−8.24548	−0.689522
$144$	−17.5343	−1.46119
$145$	0	0
$146$	−35.2650	−2.91855
$147$	−2.33581	−0.192654
$148$	−43.4249	−3.56951
$149$	17.7692	1.45571	0.727854	−	0.685732i	$-0.240518\pi$
$149$	17.7692	1.45571	0.727854	+	0.685732i	$0.240518\pi$
$150$	0	0
$151$	−22.3721	−1.82061	−0.910306	−	0.413936i	$-0.864154\pi$
$151$	−22.3721	−1.82061	−0.910306	+	0.413936i	$0.864154\pi$
$152$	21.3607	1.73258
$153$	−21.3339	−1.72474
$154$	45.2800	3.64877
$155$	0	0
$156$	1.31620	0.105381
$157$	15.1043	1.20546	0.602728	−	0.797947i	$-0.294080\pi$
$157$	15.1043	1.20546	0.602728	+	0.797947i	$0.294080\pi$
$158$	−13.3108	−1.05895
$159$	−0.905034	−0.0717739
$160$	0	0
$161$	3.17809	0.250468
$162$	−22.1680	−1.74169
$163$	23.4462	1.83645	0.918226	−	0.396057i	$-0.129622\pi$
$163$	23.4462	1.83645	0.918226	+	0.396057i	$0.129622\pi$
$164$	−18.7917	−1.46738
$165$	0	0
$166$	−34.6188	−2.68694
$167$	−15.7176	−1.21626	−0.608131	−	0.793836i	$-0.708081\pi$
$167$	−15.7176	−1.21626	−0.608131	+	0.793836i	$0.708081\pi$
$168$	−3.86506	−0.298196
$169$	−7.96129	−0.612407
$170$	0	0
$171$	11.0391	0.844182
$172$	−29.3552	−2.23831
$173$	7.80433	0.593352	0.296676	−	0.954978i	$-0.404122\pi$
$173$	7.80433	0.593352	0.296676	+	0.954978i	$0.404122\pi$
$174$	2.69632	0.204407
$175$	0	0
$176$	21.6035	1.62843
$177$	1.48620	0.111710
$178$	1.27446	0.0955249
$179$	8.88874	0.664376	0.332188	−	0.943213i	$-0.392213\pi$
$179$	8.88874	0.664376	0.332188	+	0.943213i	$0.392213\pi$
$180$	0	0
$181$	8.88334	0.660294	0.330147	−	0.943930i	$-0.392902\pi$
$181$	8.88334	0.660294	0.330147	+	0.943930i	$0.392902\pi$
$182$	−27.6701	−2.05104
$183$	0.727465	0.0537757
$184$	3.73286	0.275190
$185$	0	0
$186$	1.28103	0.0939295
$187$	26.2849	1.92214
$188$	−46.7499	−3.40959
$189$	−4.00735	−0.291492
$190$	0	0
$191$	−13.4337	−0.972027	−0.486013	−	0.873951i	$-0.661549\pi$
$191$	−13.4337	−0.972027	−0.486013	+	0.873951i	$0.661549\pi$
$192$	0.501378	0.0361839
$193$	16.0336	1.15412	0.577062	−	0.816701i	$-0.304199\pi$
$193$	16.0336	1.15412	0.577062	+	0.816701i	$0.304199\pi$
$194$	−23.6213	−1.69591
$195$	0	0
$196$	73.6110	5.25793
$197$	−25.0035	−1.78143	−0.890714	−	0.454564i	$-0.849795\pi$
$197$	−25.0035	−1.78143	−0.890714	+	0.454564i	$0.849795\pi$
$198$	27.4853	1.95329
$199$	−15.6642	−1.11040	−0.555202	−	0.831716i	$-0.687359\pi$
$199$	−15.6642	−1.11040	−0.555202	+	0.831716i	$0.687359\pi$
$200$	0	0
$201$	−0.0654272	−0.00461488
$202$	−1.70306	−0.119827
$203$	−38.6851	−2.71516
$204$	−4.19579	−0.293764
$205$	0	0
$206$	−17.4475	−1.21562
$207$	1.92912	0.134083
$208$	−13.2016	−0.915369
$209$	−13.6010	−0.940802
$210$	0	0
$211$	−14.9567	−1.02966	−0.514830	−	0.857292i	$-0.672145\pi$
$211$	−14.9567	−1.02966	−0.514830	+	0.857292i	$0.672145\pi$
$212$	28.5214	1.95886
$213$	−2.03626	−0.139522
$214$	12.4256	0.849398
$215$	0	0
$216$	−4.70687	−0.320262
$217$	−18.3794	−1.24767
$218$	18.0989	1.22581
$219$	−1.91667	−0.129517
$220$	0	0
$221$	−16.0624	−1.08047
$222$	−3.45827	−0.232104
$223$	−8.58921	−0.575176	−0.287588	−	0.957754i	$-0.592853\pi$
$223$	−8.58921	−0.575176	−0.287588	+	0.957754i	$0.592853\pi$
$224$	15.8262	1.05743
$225$	0	0
$226$	−10.4367	−0.694242
$227$	1.83798	0.121991	0.0609955	−	0.998138i	$-0.480572\pi$
$227$	1.83798	0.121991	0.0609955	+	0.998138i	$0.480572\pi$
$228$	2.17109	0.143784
$229$	−15.4431	−1.02051	−0.510256	−	0.860023i	$-0.670449\pi$
$229$	−15.4431	−1.02051	−0.510256	+	0.860023i	$0.670449\pi$
$230$	0	0
$231$	2.46100	0.161922
$232$	−45.4380	−2.98315
$233$	−16.0519	−1.05159	−0.525796	−	0.850610i	$-0.676233\pi$
$233$	−16.0519	−1.05159	−0.525796	+	0.850610i	$0.676233\pi$
$234$	−16.7959	−1.09798
$235$	0	0
$236$	−46.8363	−3.04879
$237$	−0.723453	−0.0469933
$238$	88.2065	5.71758
$239$	−14.0284	−0.907424	−0.453712	−	0.891148i	$-0.649901\pi$
$239$	−14.0284	−0.907424	−0.453712	+	0.891148i	$0.649901\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−6.25704	−0.402218
$243$	−3.65252	−0.234309
$244$	−22.9254	−1.46765
$245$	0	0
$246$	−1.49653	−0.0954151
$247$	8.31141	0.528842
$248$	−21.5877	−1.37082
$249$	−1.88155	−0.119238
$250$	0	0
$251$	9.91869	0.626062	0.313031	−	0.949743i	$-0.398656\pi$
$251$	9.91869	0.626062	0.313031	+	0.949743i	$0.398656\pi$
$252$	62.9476	3.96533
$253$	−2.37682	−0.149429
$254$	3.43157	0.215316
$255$	0	0
$256$	−31.9741	−1.99838
$257$	−8.92738	−0.556875	−0.278437	−	0.960454i	$-0.589816\pi$
$257$	−8.92738	−0.556875	−0.278437	+	0.960454i	$0.589816\pi$
$258$	−2.33778	−0.145544
$259$	49.6170	3.08305
$260$	0	0
$261$	−23.4821	−1.45351
$262$	−36.4156	−2.24977
$263$	32.0302	1.97507	0.987535	−	0.157401i	$-0.0503116\pi$
$263$	32.0302	1.97507	0.987535	+	0.157401i	$0.0503116\pi$
$264$	2.89059	0.177904
$265$	0	0
$266$	−45.6420	−2.79849
$267$	0.0692678	0.00423912
$268$	2.06188	0.125949
$269$	11.1003	0.676794	0.338397	−	0.941003i	$-0.390115\pi$
$269$	11.1003	0.676794	0.338397	+	0.941003i	$0.390115\pi$
$270$	0	0
$271$	−23.4623	−1.42523	−0.712615	−	0.701555i	$-0.752489\pi$
$271$	−23.4623	−1.42523	−0.712615	+	0.701555i	$0.752489\pi$
$272$	42.0841	2.55172
$273$	−1.50388	−0.0910192
$274$	11.2348	0.678717
$275$	0	0
$276$	0.379405	0.0228375
$277$	2.26982	0.136380	0.0681902	−	0.997672i	$-0.478278\pi$
$277$	2.26982	0.136380	0.0681902	+	0.997672i	$0.478278\pi$
$278$	−4.26669	−0.255899
$279$	−11.1564	−0.667917
$280$	0	0
$281$	28.3752	1.69272	0.846360	−	0.532611i	$-0.178789\pi$
$281$	28.3752	1.69272	0.846360	+	0.532611i	$0.178789\pi$
$282$	−3.72306	−0.221705
$283$	−13.5798	−0.807234	−0.403617	−	0.914928i	$-0.632247\pi$
$283$	−13.5798	−0.807234	−0.403617	+	0.914928i	$0.632247\pi$
$284$	64.1708	3.80784
$285$	0	0
$286$	20.6938	1.22365
$287$	21.4712	1.26741
$288$	9.60663	0.566076
$289$	34.2036	2.01197
$290$	0	0
$291$	−1.28383	−0.0752596
$292$	60.4023	3.53478
$293$	−19.1780	−1.12039	−0.560194	−	0.828361i	$-0.689273\pi$
$293$	−19.1780	−1.12039	−0.560194	+	0.828361i	$0.689273\pi$
$294$	5.86222	0.341891
$295$	0	0
$296$	58.2782	3.38735
$297$	2.99701	0.173904
$298$	−44.5956	−2.58335
$299$	1.45245	0.0839971
$300$	0	0
$301$	33.5411	1.93327
$302$	56.1475	3.23092
$303$	−0.0925625	−0.00531757
$304$	−21.7762	−1.24895
$305$	0	0
$306$	53.5419	3.06079
$307$	1.27878	0.0729837	0.0364919	−	0.999334i	$-0.488382\pi$
$307$	1.27878	0.0729837	0.0364919	+	0.999334i	$0.488382\pi$
$308$	−77.5562	−4.41917
$309$	−0.948280	−0.0539458
$310$	0	0
$311$	−13.1036	−0.743035	−0.371517	−	0.928426i	$-0.621162\pi$
$311$	−13.1036	−0.743035	−0.371517	+	0.928426i	$0.621162\pi$
$312$	−1.76640	−0.100003
$313$	−2.00126	−0.113118	−0.0565589	−	0.998399i	$-0.518013\pi$
$313$	−2.00126	−0.113118	−0.0565589	+	0.998399i	$0.518013\pi$
$314$	−37.9076	−2.13925
$315$	0	0
$316$	22.7990	1.28254
$317$	−16.8478	−0.946267	−0.473133	−	0.880991i	$-0.656877\pi$
$317$	−16.8478	−0.946267	−0.473133	+	0.880991i	$0.656877\pi$
$318$	2.27138	0.127373
$319$	28.9317	1.61987
$320$	0	0
$321$	0.675340	0.0376938
$322$	−7.97610	−0.444491
$323$	−26.4951	−1.47422
$324$	37.9697	2.10943
$325$	0	0
$326$	−58.8434	−3.25903
$327$	0.983687	0.0543980
$328$	25.2193	1.39250
$329$	53.4161	2.94492
$330$	0	0
$331$	22.3046	1.22597	0.612987	−	0.790093i	$-0.289968\pi$
$331$	22.3046	1.22597	0.612987	+	0.790093i	$0.289968\pi$
$332$	59.2954	3.25426
$333$	30.1179	1.65045
$334$	39.4467	2.15842
$335$	0	0
$336$	3.94024	0.214958
$337$	15.2251	0.829365	0.414683	−	0.909966i	$-0.363893\pi$
$337$	15.2251	0.829365	0.414683	+	0.909966i	$0.363893\pi$
$338$	19.9806	1.08680
$339$	−0.567244	−0.0308084
$340$	0	0
$341$	13.7455	0.744362
$342$	−27.7050	−1.49812
$343$	−49.7260	−2.68495
$344$	39.3960	2.12409
$345$	0	0
$346$	−19.5866	−1.05298
$347$	3.68813	0.197989	0.0989945	−	0.995088i	$-0.468437\pi$
$347$	3.68813	0.197989	0.0989945	+	0.995088i	$0.468437\pi$
$348$	−4.61829	−0.247566
$349$	23.4819	1.25696	0.628478	−	0.777828i	$-0.283678\pi$
$349$	23.4819	1.25696	0.628478	+	0.777828i	$0.283678\pi$
$350$	0	0
$351$	−1.83143	−0.0977547
$352$	−11.8361	−0.630865
$353$	−27.8978	−1.48485	−0.742424	−	0.669930i	$-0.766324\pi$
$353$	−27.8978	−1.48485	−0.742424	+	0.669930i	$0.766324\pi$
$354$	−3.72994	−0.198244
$355$	0	0
$356$	−2.18291	−0.115694
$357$	4.79408	0.253729
$358$	−22.3082	−1.17903
$359$	−7.47625	−0.394581	−0.197291	−	0.980345i	$-0.563214\pi$
$359$	−7.47625	−0.394581	−0.197291	+	0.980345i	$0.563214\pi$
$360$	0	0
$361$	−5.29025	−0.278434
$362$	−22.2947	−1.17178
$363$	−0.340074	−0.0178493
$364$	47.3936	2.48410
$365$	0	0
$366$	−1.82573	−0.0954324
$367$	15.0515	0.785682	0.392841	−	0.919606i	$-0.371492\pi$
$367$	15.0515	0.785682	0.392841	+	0.919606i	$0.371492\pi$
$368$	−3.80547	−0.198374
$369$	13.0332	0.678481
$370$	0	0
$371$	−32.5883	−1.69190
$372$	−2.19416	−0.113762
$373$	9.75050	0.504862	0.252431	−	0.967615i	$-0.418770\pi$
$373$	9.75050	0.504862	0.252431	+	0.967615i	$0.418770\pi$
$374$	−65.9676	−3.41111
$375$	0	0
$376$	62.7404	3.23559
$377$	−17.6798	−0.910557
$378$	10.0573	0.517292
$379$	−25.3511	−1.30220	−0.651100	−	0.758992i	$-0.725692\pi$
$379$	−25.3511	−1.30220	−0.651100	+	0.758992i	$0.725692\pi$
$380$	0	0
$381$	0.186508	0.00955508
$382$	33.7147	1.72499
$383$	−25.5697	−1.30655	−0.653275	−	0.757121i	$-0.726606\pi$
$383$	−25.5697	−1.30655	−0.653275	+	0.757121i	$0.726606\pi$
$384$	−2.13736	−0.109072
$385$	0	0
$386$	−40.2398	−2.04815
$387$	20.3597	1.03494
$388$	40.4589	2.05399
$389$	−12.7042	−0.644129	−0.322064	−	0.946718i	$-0.604377\pi$
$389$	−12.7042	−0.644129	−0.322064	+	0.946718i	$0.604377\pi$
$390$	0	0
$391$	−4.63010	−0.234154
$392$	−98.7893	−4.98961
$393$	−1.97921	−0.0998381
$394$	62.7517	3.16139
$395$	0	0
$396$	−47.0771	−2.36571
$397$	7.73883	0.388401	0.194200	−	0.980962i	$-0.437789\pi$
$397$	7.73883	0.388401	0.194200	+	0.980962i	$0.437789\pi$
$398$	39.3126	1.97056
$399$	−2.48067	−0.124189
$400$	0	0
$401$	−19.0506	−0.951343	−0.475672	−	0.879623i	$-0.657795\pi$
$401$	−19.0506	−0.951343	−0.475672	+	0.879623i	$0.657795\pi$
$402$	0.164204	0.00818973
$403$	−8.39972	−0.418420
$404$	2.91702	0.145127
$405$	0	0
$406$	97.0886	4.81843
$407$	−37.1075	−1.83935
$408$	5.63093	0.278773
$409$	−23.9095	−1.18225	−0.591123	−	0.806581i	$-0.701315\pi$
$409$	−23.9095	−1.18225	−0.591123	+	0.806581i	$0.701315\pi$
$410$	0	0
$411$	0.610617	0.0301195
$412$	29.8842	1.47229
$413$	53.5149	2.63330
$414$	−4.84155	−0.237949
$415$	0	0
$416$	7.23288	0.354621
$417$	−0.231897	−0.0113561
$418$	34.1347	1.66958
$419$	−25.8224	−1.26151	−0.630753	−	0.775984i	$-0.717254\pi$
$419$	−25.8224	−1.26151	−0.630753	+	0.775984i	$0.717254\pi$
$420$	0	0
$421$	−8.47688	−0.413138	−0.206569	−	0.978432i	$-0.566230\pi$
$421$	−8.47688	−0.413138	−0.206569	+	0.978432i	$0.566230\pi$
$422$	37.5370	1.82727
$423$	32.4239	1.57651
$424$	−38.2770	−1.85889
$425$	0	0
$426$	5.11042	0.247601
$427$	26.1944	1.26764
$428$	−21.2827	−1.02874
$429$	1.12472	0.0543021
$430$	0	0
$431$	−2.78772	−0.134280	−0.0671398	−	0.997744i	$-0.521387\pi$
$431$	−2.78772	−0.134280	−0.0671398	+	0.997744i	$0.521387\pi$
$432$	4.79843	0.230865
$433$	−26.1596	−1.25715	−0.628576	−	0.777748i	$-0.716362\pi$
$433$	−26.1596	−1.25715	−0.628576	+	0.777748i	$0.716362\pi$
$434$	46.1270	2.21417
$435$	0	0
$436$	−31.0000	−1.48463
$437$	2.39582	0.114608
$438$	4.81030	0.229845
$439$	−15.5146	−0.740471	−0.370235	−	0.928938i	$-0.620723\pi$
$439$	−15.5146	−0.740471	−0.370235	+	0.928938i	$0.620723\pi$
$440$	0	0
$441$	−51.0538	−2.43113
$442$	40.3120	1.91745
$443$	−20.0759	−0.953836	−0.476918	−	0.878948i	$-0.658246\pi$
$443$	−20.0759	−0.953836	−0.476918	+	0.878948i	$0.658246\pi$
$444$	5.92336	0.281110
$445$	0	0
$446$	21.5565	1.02073
$447$	−2.42380	−0.114642
$448$	18.0535	0.852950
$449$	7.93192	0.374330	0.187165	−	0.982328i	$-0.440070\pi$
$449$	7.93192	0.374330	0.187165	+	0.982328i	$0.440070\pi$
$450$	0	0
$451$	−16.0579	−0.756135
$452$	17.8762	0.840825
$453$	3.05165	0.143379
$454$	−4.61280	−0.216490
$455$	0	0
$456$	−2.91370	−0.136447
$457$	−12.2810	−0.574481	−0.287240	−	0.957859i	$-0.592738\pi$
$457$	−12.2810	−0.574481	−0.287240	+	0.957859i	$0.592738\pi$
$458$	38.7579	1.81104
$459$	5.83823	0.272505
$460$	0	0
$461$	−16.1896	−0.754024	−0.377012	−	0.926208i	$-0.623048\pi$
$461$	−16.1896	−0.754024	−0.377012	+	0.926208i	$0.623048\pi$
$462$	−6.17640	−0.287352
$463$	−12.0275	−0.558964	−0.279482	−	0.960151i	$-0.590163\pi$
$463$	−12.0275	−0.558964	−0.279482	+	0.960151i	$0.590163\pi$
$464$	46.3219	2.15044
$465$	0	0
$466$	40.2856	1.86620
$467$	18.4120	0.852007	0.426003	−	0.904722i	$-0.359921\pi$
$467$	18.4120	0.852007	0.426003	+	0.904722i	$0.359921\pi$
$468$	28.7682	1.32981
$469$	−2.35589	−0.108785
$470$	0	0
$471$	−2.06030	−0.0949336
$472$	62.8565	2.89320
$473$	−25.0846	−1.15339
$474$	1.81566	0.0833961
$475$	0	0
$476$	−151.081	−6.92479
$477$	−19.7813	−0.905725
$478$	35.2074	1.61035
$479$	−6.21295	−0.283877	−0.141939	−	0.989875i	$-0.545334\pi$
$479$	−6.21295	−0.283877	−0.141939	+	0.989875i	$0.545334\pi$
$480$	0	0
$481$	22.6759	1.03393
$482$	2.50972	0.114314
$483$	−0.433506	−0.0197252
$484$	10.7171	0.487143
$485$	0	0
$486$	9.16677	0.415813
$487$	8.56971	0.388331	0.194165	−	0.980969i	$-0.437800\pi$
$487$	8.56971	0.388331	0.194165	+	0.980969i	$0.437800\pi$
$488$	30.7669	1.39275
$489$	−3.19818	−0.144626
$490$	0	0
$491$	−22.0812	−0.996510	−0.498255	−	0.867031i	$-0.666026\pi$
$491$	−22.0812	−0.996510	−0.498255	+	0.867031i	$0.666026\pi$
$492$	2.56327	0.115561
$493$	56.3596	2.53831
$494$	−20.8593	−0.938503
$495$	0	0
$496$	22.0076	0.988172
$497$	−73.3211	−3.28890
$498$	4.72216	0.211605
$499$	−40.8244	−1.82755	−0.913775	−	0.406221i	$-0.866846\pi$
$499$	−40.8244	−1.82755	−0.913775	+	0.406221i	$0.866846\pi$
$500$	0	0
$501$	2.14395	0.0957846
$502$	−24.8931	−1.11103
$503$	24.4157	1.08864	0.544321	−	0.838877i	$-0.316787\pi$
$503$	24.4157	1.08864	0.544321	+	0.838877i	$0.316787\pi$
$504$	−84.4785	−3.76297
$505$	0	0
$506$	5.96515	0.265183
$507$	1.08596	0.0482290
$508$	−5.87763	−0.260778
$509$	1.69386	0.0750789	0.0375394	−	0.999295i	$-0.488048\pi$
$509$	1.69386	0.0750789	0.0375394	+	0.999295i	$0.488048\pi$
$510$	0	0
$511$	−69.0152	−3.05305
$512$	48.9073	2.16142
$513$	−3.02097	−0.133379
$514$	22.4052	0.988251
$515$	0	0
$516$	4.00419	0.176274
$517$	−39.9487	−1.75694
$518$	−124.525	−5.47130
$519$	−1.06455	−0.0467284
$520$	0	0
$521$	9.06027	0.396937	0.198469	−	0.980107i	$-0.436403\pi$
$521$	9.06027	0.396937	0.198469	+	0.980107i	$0.436403\pi$
$522$	58.9334	2.57945
$523$	−11.6656	−0.510101	−0.255050	−	0.966928i	$-0.582092\pi$
$523$	−11.6656	−0.510101	−0.255050	+	0.966928i	$0.582092\pi$
$524$	62.3731	2.72478
$525$	0	0
$526$	−80.3868	−3.50503
$527$	26.7766	1.16641
$528$	−2.94682	−0.128244
$529$	−22.5813	−0.981797
$530$	0	0
$531$	32.4839	1.40968
$532$	78.1762	3.38937
$533$	9.81276	0.425038
$534$	−0.173842	−0.00752290
$535$	0	0
$536$	−2.76714	−0.119522
$537$	−1.21247	−0.0523218
$538$	−27.8585	−1.20106
$539$	62.9020	2.70938
$540$	0	0
$541$	3.94806	0.169740	0.0848702	−	0.996392i	$-0.472952\pi$
$541$	3.94806	0.169740	0.0848702	+	0.996392i	$0.472952\pi$
$542$	58.8836	2.52927
$543$	−1.21173	−0.0520003
$544$	−23.0569	−0.988558
$545$	0	0
$546$	3.77432	0.161526
$547$	−14.1426	−0.604695	−0.302348	−	0.953198i	$-0.597770\pi$
$547$	−14.1426	−0.604695	−0.302348	+	0.953198i	$0.597770\pi$
$548$	−19.2430	−0.822022
$549$	15.9002	0.678603
$550$	0	0
$551$	−29.1630	−1.24239
$552$	−0.509179	−0.0216721
$553$	−26.0500	−1.10776
$554$	−5.69660	−0.242026
$555$	0	0
$556$	7.30804	0.309930
$557$	10.3719	0.439471	0.219736	−	0.975559i	$-0.429481\pi$
$557$	10.3719	0.439471	0.219736	+	0.975559i	$0.429481\pi$
$558$	27.9994	1.18531
$559$	15.3289	0.648343
$560$	0	0
$561$	−3.58538	−0.151375
$562$	−71.2136	−3.00396
$563$	−4.91493	−0.207140	−0.103570	−	0.994622i	$-0.533027\pi$
$563$	−4.91493	−0.207140	−0.103570	+	0.994622i	$0.533027\pi$
$564$	6.37690	0.268516
$565$	0	0
$566$	34.0814	1.43255
$567$	−43.3839	−1.82195
$568$	−86.1201	−3.61352
$569$	−32.8606	−1.37759	−0.688794	−	0.724957i	$-0.741859\pi$
$569$	−32.8606	−1.37759	−0.688794	+	0.724957i	$0.741859\pi$
$570$	0	0
$571$	7.89831	0.330534	0.165267	−	0.986249i	$-0.447151\pi$
$571$	7.89831	0.330534	0.165267	+	0.986249i	$0.447151\pi$
$572$	−35.4446	−1.48201
$573$	1.83242	0.0765503
$574$	−53.8867	−2.24919
$575$	0	0
$576$	10.9586	0.456609
$577$	−23.4530	−0.976360	−0.488180	−	0.872743i	$-0.662339\pi$
$577$	−23.4530	−0.976360	−0.488180	+	0.872743i	$0.662339\pi$
$578$	−85.8412	−3.57052
$579$	−2.18706	−0.0908909
$580$	0	0
$581$	−67.7506	−2.81077
$582$	3.22206	0.133559
$583$	24.3721	1.00939
$584$	−81.0626	−3.35439
$585$	0	0
$586$	48.1312	1.98828
$587$	−5.07534	−0.209482	−0.104741	−	0.994500i	$-0.533401\pi$
$587$	−5.07534	−0.209482	−0.104741	+	0.994500i	$0.533401\pi$
$588$	−10.0409	−0.414079
$589$	−13.8554	−0.570903
$590$	0	0
$591$	3.41060	0.140293
$592$	−59.4119	−2.44181
$593$	35.2408	1.44717	0.723583	−	0.690237i	$-0.242494\pi$
$593$	35.2408	1.44717	0.723583	+	0.690237i	$0.242494\pi$
$594$	−7.52163	−0.308616
$595$	0	0
$596$	76.3839	3.12880
$597$	2.13666	0.0874478
$598$	−3.64523	−0.149064
$599$	10.9165	0.446038	0.223019	−	0.974814i	$-0.428409\pi$
$599$	10.9165	0.446038	0.223019	+	0.974814i	$0.428409\pi$
$600$	0	0
$601$	11.1702	0.455642	0.227821	−	0.973703i	$-0.426840\pi$
$601$	11.1702	0.455642	0.227821	+	0.973703i	$0.426840\pi$
$602$	−84.1785	−3.43086
$603$	−1.43004	−0.0582358
$604$	−96.1701	−3.91311
$605$	0	0
$606$	0.232305	0.00943676
$607$	41.3033	1.67645	0.838225	−	0.545325i	$-0.183594\pi$
$607$	41.3033	1.67645	0.838225	+	0.545325i	$0.183594\pi$
$608$	11.9307	0.483854
$609$	5.27683	0.213828
$610$	0	0
$611$	24.4121	0.987610
$612$	−91.7073	−3.70705
$613$	−3.25242	−0.131364	−0.0656820	−	0.997841i	$-0.520922\pi$
$613$	−3.25242	−0.131364	−0.0656820	+	0.997841i	$0.520922\pi$
$614$	−3.20937	−0.129520
$615$	0	0
$616$	104.084	4.19366
$617$	42.8047	1.72325	0.861627	−	0.507543i	$-0.169446\pi$
$617$	42.8047	1.72325	0.861627	+	0.507543i	$0.169446\pi$
$618$	2.37991	0.0957341
$619$	−27.3003	−1.09729	−0.548645	−	0.836055i	$-0.684856\pi$
$619$	−27.3003	−1.09729	−0.548645	+	0.836055i	$0.684856\pi$
$620$	0	0
$621$	−0.527924	−0.0211849
$622$	32.8862	1.31862
$623$	2.49418	0.0999273
$624$	1.80076	0.0720883
$625$	0	0
$626$	5.02258	0.200743
$627$	1.85524	0.0740912
$628$	64.9285	2.59093
$629$	−72.2862	−2.88224
$630$	0	0
$631$	−15.6811	−0.624254	−0.312127	−	0.950040i	$-0.601041\pi$
$631$	−15.6811	−0.624254	−0.312127	+	0.950040i	$0.601041\pi$
$632$	−30.5973	−1.21709
$633$	2.04016	0.0810891
$634$	42.2832	1.67928
$635$	0	0
$636$	−3.89045	−0.154266
$637$	−38.4387	−1.52299
$638$	−72.6104	−2.87467
$639$	−44.5064	−1.76065
$640$	0	0
$641$	−0.673614	−0.0266062	−0.0133031	−	0.999912i	$-0.504235\pi$
$641$	−0.673614	−0.0266062	−0.0133031	+	0.999912i	$0.504235\pi$
$642$	−1.69491	−0.0668928
$643$	19.0984	0.753167	0.376583	−	0.926383i	$-0.377099\pi$
$643$	19.0984	0.753167	0.376583	+	0.926383i	$0.377099\pi$
$644$	13.6616	0.538341
$645$	0	0
$646$	66.4951	2.61621
$647$	−21.3540	−0.839512	−0.419756	−	0.907637i	$-0.637884\pi$
$647$	−21.3540	−0.839512	−0.419756	+	0.907637i	$0.637884\pi$
$648$	−50.9570	−2.00178
$649$	−40.0226	−1.57102
$650$	0	0
$651$	2.50703	0.0982583
$652$	100.788	3.94715
$653$	−32.3648	−1.26653	−0.633266	−	0.773934i	$-0.718286\pi$
$653$	−32.3648	−1.26653	−0.633266	+	0.773934i	$0.718286\pi$
$654$	−2.46878	−0.0965368
$655$	0	0
$656$	−25.7098	−1.00380
$657$	−41.8927	−1.63439
$658$	−134.059	−5.22617
$659$	−38.2418	−1.48969	−0.744845	−	0.667238i	$-0.767476\pi$
$659$	−38.2418	−1.48969	−0.744845	+	0.667238i	$0.767476\pi$
$660$	0	0
$661$	−8.46885	−0.329400	−0.164700	−	0.986344i	$-0.552666\pi$
$661$	−8.46885	−0.329400	−0.164700	+	0.986344i	$0.552666\pi$
$662$	−55.9783	−2.17566
$663$	2.19098	0.0850907
$664$	−79.5772	−3.08819
$665$	0	0
$666$	−75.5873	−2.92895
$667$	−5.09634	−0.197331
$668$	−67.5647	−2.61416
$669$	1.17161	0.0452970
$670$	0	0
$671$	−19.5902	−0.756272
$672$	−2.15877	−0.0832764
$673$	−32.5440	−1.25448	−0.627240	−	0.778826i	$-0.715815\pi$
$673$	−32.5440	−1.25448	−0.627240	+	0.778826i	$0.715815\pi$
$674$	−38.2107	−1.47182
$675$	0	0
$676$	−34.2230	−1.31627
$677$	−40.7722	−1.56700	−0.783502	−	0.621389i	$-0.786569\pi$
$677$	−40.7722	−1.56700	−0.783502	+	0.621389i	$0.786569\pi$
$678$	1.42362	0.0546738
$679$	−46.2280	−1.77407
$680$	0	0
$681$	−0.250709	−0.00960718
$682$	−34.4974	−1.32097
$683$	12.1921	0.466518	0.233259	−	0.972415i	$-0.425061\pi$
$683$	12.1921	0.466518	0.233259	+	0.972415i	$0.425061\pi$
$684$	47.4535	1.81443
$685$	0	0
$686$	124.798	4.76481
$687$	2.10652	0.0803686
$688$	−40.1624	−1.53118
$689$	−14.8935	−0.567396
$690$	0	0
$691$	−4.67623	−0.177892	−0.0889462	−	0.996036i	$-0.528350\pi$
$691$	−4.67623	−0.177892	−0.0889462	+	0.996036i	$0.528350\pi$
$692$	33.5482	1.27531
$693$	53.7900	2.04331
$694$	−9.25615	−0.351359
$695$	0	0
$696$	6.19795	0.234933
$697$	−31.2811	−1.18485
$698$	−58.9328	−2.23064
$699$	2.18955	0.0828163
$700$	0	0
$701$	−0.852234	−0.0321884	−0.0160942	−	0.999870i	$-0.505123\pi$
$701$	−0.852234	−0.0321884	−0.0160942	+	0.999870i	$0.505123\pi$
$702$	4.59638	0.173479
$703$	37.4042	1.41072
$704$	−13.5018	−0.508870
$705$	0	0
$706$	70.0155	2.63507
$707$	−3.33297	−0.125349
$708$	6.38869	0.240102
$709$	−13.6717	−0.513451	−0.256726	−	0.966484i	$-0.582644\pi$
$709$	−13.6717	−0.513451	−0.256726	+	0.966484i	$0.582644\pi$
$710$	0	0
$711$	−15.8125	−0.593015
$712$	2.92957	0.109790
$713$	−2.42128	−0.0906777
$714$	−12.0318	−0.450278
$715$	0	0
$716$	38.2098	1.42797
$717$	1.91354	0.0714626
$718$	18.7633	0.700239
$719$	28.9294	1.07888	0.539441	−	0.842023i	$-0.318635\pi$
$719$	28.9294	1.07888	0.539441	+	0.842023i	$0.318635\pi$
$720$	0	0
$721$	−34.1455	−1.27164
$722$	13.2770	0.494119
$723$	0.136405	0.00507294
$724$	38.1866	1.41919
$725$	0	0
$726$	0.853489	0.0316760
$727$	−12.1767	−0.451607	−0.225804	−	0.974173i	$-0.572501\pi$
$727$	−12.1767	−0.451607	−0.225804	+	0.974173i	$0.572501\pi$
$728$	−63.6043	−2.35733
$729$	−26.0005	−0.962980
$730$	0	0
$731$	−48.8654	−1.80735
$732$	3.12713	0.115582
$733$	2.30541	0.0851524	0.0425762	−	0.999093i	$-0.486443\pi$
$733$	2.30541	0.0851524	0.0425762	+	0.999093i	$0.486443\pi$
$734$	−37.7750	−1.39430
$735$	0	0
$736$	2.08493	0.0768516
$737$	1.76192	0.0649011
$738$	−32.7096	−1.20406
$739$	42.4522	1.56163	0.780815	−	0.624763i	$-0.214804\pi$
$739$	42.4522	1.56163	0.780815	+	0.624763i	$0.214804\pi$
$740$	0	0
$741$	−1.13371	−0.0416480
$742$	81.7874	3.00251
$743$	−16.3214	−0.598775	−0.299388	−	0.954132i	$-0.596782\pi$
$743$	−16.3214	−0.598775	−0.299388	+	0.954132i	$0.596782\pi$
$744$	2.94466	0.107957
$745$	0	0
$746$	−24.4710	−0.895946
$747$	−41.1251	−1.50469
$748$	112.990	4.13133
$749$	24.3175	0.888543
$750$	0	0
$751$	15.1395	0.552447	0.276223	−	0.961093i	$-0.410917\pi$
$751$	15.1395	0.552447	0.276223	+	0.961093i	$0.410917\pi$
$752$	−63.9609	−2.33241
$753$	−1.35296	−0.0493044
$754$	44.3713	1.61591
$755$	0	0
$756$	−17.2263	−0.626514
$757$	−39.3617	−1.43062	−0.715312	−	0.698805i	$-0.753715\pi$
$757$	−39.3617	−1.43062	−0.715312	+	0.698805i	$0.753715\pi$
$758$	63.6241	2.31093
$759$	0.324209	0.0117681
$760$	0	0
$761$	47.2917	1.71432	0.857161	−	0.515048i	$-0.172226\pi$
$761$	47.2917	1.71432	0.857161	+	0.515048i	$0.172226\pi$
$762$	−0.468081	−0.0169568
$763$	35.4204	1.28231
$764$	−57.7470	−2.08921
$765$	0	0
$766$	64.1727	2.31865
$767$	24.4573	0.883102
$768$	4.36141	0.157379
$769$	20.6643	0.745175	0.372588	−	0.927997i	$-0.378471\pi$
$769$	20.6643	0.745175	0.372588	+	0.927997i	$0.378471\pi$
$770$	0	0
$771$	1.21774	0.0438557
$772$	68.9231	2.48060
$773$	−6.45358	−0.232119	−0.116060	−	0.993242i	$-0.537026\pi$
$773$	−6.45358	−0.232119	−0.116060	+	0.993242i	$0.537026\pi$
$774$	−51.0969	−1.83664
$775$	0	0
$776$	−54.2976	−1.94917
$777$	−6.76799	−0.242800
$778$	31.8839	1.14309
$779$	16.1862	0.579932
$780$	0	0
$781$	54.8352	1.96216
$782$	11.6202	0.415539
$783$	6.42613	0.229651
$784$	100.711	3.59682
$785$	0	0
$786$	4.96726	0.177176
$787$	−1.35327	−0.0482387	−0.0241193	−	0.999709i	$-0.507678\pi$
$787$	−1.35327	−0.0482387	−0.0241193	+	0.999709i	$0.507678\pi$
$788$	−107.482	−3.82889
$789$	−4.36907	−0.155543
$790$	0	0
$791$	−20.4252	−0.726237
$792$	63.1796	2.24499
$793$	11.9713	0.425115
$794$	−19.4222	−0.689270
$795$	0	0
$796$	−67.3351	−2.38663
$797$	3.89973	0.138136	0.0690678	−	0.997612i	$-0.477998\pi$
$797$	3.89973	0.138136	0.0690678	+	0.997612i	$0.477998\pi$
$798$	6.22578	0.220390
$799$	−77.8209	−2.75311
$800$	0	0
$801$	1.51399	0.0534940
$802$	47.8117	1.68829
$803$	51.6149	1.82145
$804$	−0.281250	−0.00991892
$805$	0	0
$806$	21.0809	0.742543
$807$	−1.51413	−0.0532997
$808$	−3.91478	−0.137721
$809$	5.14954	0.181048	0.0905242	−	0.995894i	$-0.471146\pi$
$809$	5.14954	0.181048	0.0905242	+	0.995894i	$0.471146\pi$
$810$	0	0
$811$	14.5325	0.510304	0.255152	−	0.966901i	$-0.417874\pi$
$811$	14.5325	0.510304	0.255152	+	0.966901i	$0.417874\pi$
$812$	−166.295	−5.83579
$813$	3.20036	0.112241
$814$	93.1292	3.26418
$815$	0	0
$816$	−5.74047	−0.200957
$817$	25.2852	0.884616
$818$	60.0059	2.09806
$819$	−32.8704	−1.14858
$820$	0	0
$821$	−9.87145	−0.344516	−0.172258	−	0.985052i	$-0.555106\pi$
$821$	−9.87145	−0.344516	−0.172258	+	0.985052i	$0.555106\pi$
$822$	−1.53247	−0.0534512
$823$	18.2362	0.635672	0.317836	−	0.948146i	$-0.397044\pi$
$823$	18.2362	0.635672	0.317836	+	0.948146i	$0.397044\pi$
$824$	−40.1060	−1.39716
$825$	0	0
$826$	−134.307	−4.67314
$827$	18.6268	0.647719	0.323859	−	0.946105i	$-0.395020\pi$
$827$	18.6268	0.647719	0.323859	+	0.946105i	$0.395020\pi$
$828$	8.29266	0.288190
$829$	−15.8742	−0.551335	−0.275667	−	0.961253i	$-0.588899\pi$
$829$	−15.8742	−0.551335	−0.275667	+	0.961253i	$0.588899\pi$
$830$	0	0
$831$	−0.309614	−0.0107404
$832$	8.25081	0.286045
$833$	122.535	4.24557
$834$	0.581996	0.0201529
$835$	0	0
$836$	−58.4663	−2.02210
$837$	3.05307	0.105529
$838$	64.8068	2.23872
$839$	−31.8946	−1.10112	−0.550562	−	0.834794i	$-0.685587\pi$
$839$	−31.8946	−1.10112	−0.550562	+	0.834794i	$0.685587\pi$
$840$	0	0
$841$	33.0349	1.13913
$842$	21.2746	0.733170
$843$	−3.87050	−0.133307
$844$	−64.2939	−2.21309
$845$	0	0
$846$	−81.3748	−2.79772
$847$	−12.2453	−0.420755
$848$	39.0215	1.34000
$849$	1.85234	0.0635723
$850$	0	0
$851$	6.53650	0.224068
$852$	−8.75319	−0.299880
$853$	−41.3479	−1.41572	−0.707862	−	0.706351i	$-0.750340\pi$
$853$	−41.3479	−1.41572	−0.707862	+	0.706351i	$0.750340\pi$
$854$	−65.7405	−2.24959
$855$	0	0
$856$	28.5624	0.976243
$857$	22.1387	0.756243	0.378121	−	0.925756i	$-0.376570\pi$
$857$	22.1387	0.756243	0.378121	+	0.925756i	$0.376570\pi$
$858$	−2.82273	−0.0963664
$859$	40.1451	1.36973	0.684867	−	0.728668i	$-0.259860\pi$
$859$	40.1451	1.36973	0.684867	+	0.728668i	$0.259860\pi$
$860$	0	0
$861$	−2.92878	−0.0998124
$862$	6.99638	0.238298
$863$	−35.9288	−1.22303	−0.611515	−	0.791233i	$-0.709440\pi$
$863$	−35.9288	−1.22303	−0.611515	+	0.791233i	$0.709440\pi$
$864$	−2.62895	−0.0894388
$865$	0	0
$866$	65.6532	2.23099
$867$	−4.66552	−0.158450
$868$	−79.0069	−2.68167
$869$	19.4822	0.660888
$870$	0	0
$871$	−1.07669	−0.0364821
$872$	41.6035	1.40887
$873$	−28.0607	−0.949712
$874$	−6.01284	−0.203387
$875$	0	0
$876$	−8.23915	−0.278375
$877$	28.6464	0.967320	0.483660	−	0.875256i	$-0.339307\pi$
$877$	28.6464	0.967320	0.483660	+	0.875256i	$0.339307\pi$
$878$	38.9372	1.31407
$879$	2.61596	0.0882342
$880$	0	0
$881$	−0.746161	−0.0251388	−0.0125694	−	0.999921i	$-0.504001\pi$
$881$	−0.746161	−0.0251388	−0.0125694	+	0.999921i	$0.504001\pi$
$882$	128.130	4.31438
$883$	−27.4728	−0.924532	−0.462266	−	0.886741i	$-0.652963\pi$
$883$	−27.4728	−0.924532	−0.462266	+	0.886741i	$0.652963\pi$
$884$	−69.0469	−2.32230
$885$	0	0
$886$	50.3848	1.69271
$887$	−48.4798	−1.62779	−0.813896	−	0.581011i	$-0.802657\pi$
$887$	−48.4798	−1.62779	−0.813896	+	0.581011i	$0.802657\pi$
$888$	−7.94942	−0.266765
$889$	6.71574	0.225239
$890$	0	0
$891$	32.4459	1.08698
$892$	−36.9222	−1.23625
$893$	40.2681	1.34752
$894$	6.08304	0.203447
$895$	0	0
$896$	−76.9617	−2.57111
$897$	−0.198120	−0.00661504
$898$	−19.9069	−0.664300
$899$	29.4729	0.982977
$900$	0	0
$901$	47.4773	1.58170
$902$	40.3007	1.34187
$903$	−4.57515	−0.152252
$904$	−23.9906	−0.797917
$905$	0	0
$906$	−7.65877	−0.254446
$907$	−56.7140	−1.88316	−0.941578	−	0.336794i	$-0.890657\pi$
$907$	−56.7140	−1.88316	−0.941578	+	0.336794i	$0.890657\pi$
$908$	7.90087	0.262199
$909$	−2.02314	−0.0671032
$910$	0	0
$911$	−4.86575	−0.161210	−0.0806048	−	0.996746i	$-0.525685\pi$
$911$	−4.86575	−0.161210	−0.0806048	+	0.996746i	$0.525685\pi$
$912$	2.97038	0.0983591
$913$	50.6691	1.67690
$914$	30.8218	1.01949
$915$	0	0
$916$	−66.3850	−2.19342
$917$	−71.2671	−2.35345
$918$	−14.6523	−0.483598
$919$	3.50760	0.115705	0.0578526	−	0.998325i	$-0.481575\pi$
$919$	3.50760	0.115705	0.0578526	+	0.998325i	$0.481575\pi$
$920$	0	0
$921$	−0.174431	−0.00574770
$922$	40.6312	1.33812
$923$	−33.5091	−1.10297
$924$	10.5790	0.348024
$925$	0	0
$926$	30.1855	0.991958
$927$	−20.7265	−0.680749
$928$	−25.3787	−0.833097
$929$	41.4175	1.35886	0.679431	−	0.733739i	$-0.262227\pi$
$929$	41.4175	1.35886	0.679431	+	0.733739i	$0.262227\pi$
$930$	0	0
$931$	−63.4050	−2.07801
$932$	−69.0017	−2.26023
$933$	1.78739	0.0585164
$934$	−46.2089	−1.51200
$935$	0	0
$936$	−38.6083	−1.26195
$937$	36.7191	1.19956	0.599780	−	0.800165i	$-0.295255\pi$
$937$	36.7191	1.19956	0.599780	+	0.800165i	$0.295255\pi$
$938$	5.91261	0.193054
$939$	0.272981	0.00890839
$940$	0	0
$941$	−24.6386	−0.803194	−0.401597	−	0.915816i	$-0.631545\pi$
$941$	−24.6386	−0.803194	−0.401597	+	0.915816i	$0.631545\pi$
$942$	5.17076	0.168473
$943$	2.82860	0.0921119
$944$	−64.0792	−2.08560
$945$	0	0
$946$	62.9552	2.04685
$947$	15.9646	0.518778	0.259389	−	0.965773i	$-0.416479\pi$
$947$	15.9646	0.518778	0.259389	+	0.965773i	$0.416479\pi$
$948$	−3.10989	−0.101004
$949$	−31.5412	−1.02387
$950$	0	0
$951$	2.29812	0.0745216
$952$	202.758	6.57141
$953$	16.0014	0.518337	0.259168	−	0.965832i	$-0.416552\pi$
$953$	16.0014	0.518337	0.259168	+	0.965832i	$0.416552\pi$
$954$	49.6455	1.60733
$955$	0	0
$956$	−60.3036	−1.95036
$957$	−3.94642	−0.127570
$958$	15.5927	0.503779
$959$	21.9870	0.709996
$960$	0	0
$961$	−16.9973	−0.548302
$962$	−56.9101	−1.83485
$963$	14.7609	0.475663
$964$	−4.29867	−0.138451
$965$	0	0
$966$	1.08798	0.0350051
$967$	26.6668	0.857548	0.428774	−	0.903412i	$-0.358946\pi$
$967$	26.6668	0.857548	0.428774	+	0.903412i	$0.358946\pi$
$968$	−14.3829	−0.462283
$969$	3.61405	0.116100
$970$	0	0
$971$	44.3408	1.42296	0.711481	−	0.702705i	$-0.248025\pi$
$971$	44.3408	1.42296	0.711481	+	0.702705i	$0.248025\pi$
$972$	−15.7010	−0.503609
$973$	−8.35011	−0.267692
$974$	−21.5075	−0.689146
$975$	0	0
$976$	−31.3654	−1.00398
$977$	−23.8190	−0.762039	−0.381019	−	0.924567i	$-0.624427\pi$
$977$	−23.8190	−0.762039	−0.381019	+	0.924567i	$0.624427\pi$
$978$	8.02651	0.256659
$979$	−1.86534	−0.0596166
$980$	0	0
$981$	21.5004	0.686456
$982$	55.4175	1.76844
$983$	36.8904	1.17662	0.588311	−	0.808635i	$-0.299793\pi$
$983$	36.8904	1.17662	0.588311	+	0.808635i	$0.299793\pi$
$984$	−3.44002	−0.109664
$985$	0	0
$986$	−141.447	−4.50458
$987$	−7.28620	−0.231922
$988$	35.7280	1.13666
$989$	4.41867	0.140505
$990$	0	0
$991$	45.0226	1.43019	0.715095	−	0.699028i	$-0.246384\pi$
$991$	45.0226	1.43019	0.715095	+	0.699028i	$0.246384\pi$
$992$	−12.0575	−0.382826
$993$	−3.04245	−0.0965494
$994$	184.015	5.83661
$995$	0	0
$996$	−8.08817	−0.256283
$997$	−38.0703	−1.20570	−0.602849	−	0.797856i	$-0.705968\pi$
$997$	−38.0703	−1.20570	−0.602849	+	0.797856i	$0.705968\pi$
$998$	102.458	3.24324
$999$	−8.24207	−0.260768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.5	✓	40
5.4	even	2		6025.2.a.o.1.36	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.5	✓	40	1.1	even	1	trivial
6025.2.a.o.1.36	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)

\(f(q)\)	\(=\)	\(q-2.50972 q^{2} -0.136405 q^{3} +4.29867 q^{4} +0.342337 q^{6} -4.91163 q^{7} -5.76901 q^{8} -2.98139 q^{9} +O(q^{10})\)	\(q-2.50972 q^{2} -0.136405 q^{3} +4.29867 q^{4} +0.342337 q^{6} -4.91163 q^{7} -5.76901 q^{8} -2.98139 q^{9} +3.67330 q^{11} -0.586358 q^{12} -2.24471 q^{13} +12.3268 q^{14} +5.88123 q^{16} +7.15567 q^{17} +7.48245 q^{18} -3.70267 q^{19} +0.669969 q^{21} -9.21894 q^{22} -0.647054 q^{23} +0.786919 q^{24} +5.63358 q^{26} +0.815890 q^{27} -21.1135 q^{28} +7.87622 q^{29} +3.74201 q^{31} -3.22219 q^{32} -0.501055 q^{33} -17.9587 q^{34} -12.8160 q^{36} -10.1019 q^{37} +9.29264 q^{38} +0.306188 q^{39} -4.37151 q^{41} -1.68143 q^{42} -6.82890 q^{43} +15.7903 q^{44} +1.62392 q^{46} -10.8754 q^{47} -0.802227 q^{48} +17.1241 q^{49} -0.976066 q^{51} -9.64926 q^{52} +6.63493 q^{53} -2.04765 q^{54} +28.3353 q^{56} +0.505061 q^{57} -19.7671 q^{58} -10.8955 q^{59} -5.33314 q^{61} -9.39138 q^{62} +14.6435 q^{63} -3.67567 q^{64} +1.25751 q^{66} +0.479655 q^{67} +30.7599 q^{68} +0.0882611 q^{69} +14.9281 q^{71} +17.1997 q^{72} +14.0514 q^{73} +25.3530 q^{74} -15.9166 q^{76} -18.0419 q^{77} -0.768446 q^{78} +5.30373 q^{79} +8.83289 q^{81} +10.9712 q^{82} +13.7939 q^{83} +2.87998 q^{84} +17.1386 q^{86} -1.07435 q^{87} -21.1913 q^{88} -0.507811 q^{89} +11.0252 q^{91} -2.78147 q^{92} -0.510428 q^{93} +27.2942 q^{94} +0.439522 q^{96} +9.41195 q^{97} -42.9767 q^{98} -10.9516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more