LMFDB - Embedded newform 525.4.d.n.274.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 48x^{6} + 668x^{4} + 2217x^{2} + 2116 $ x^8 + 48x^6 + 668x^4 + 2217*x^2 + 2116
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.7
Root			$4.60171i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.n.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.60171i q^{2} +3.00000i q^{3} -13.1758 q^{4} -13.8051 q^{6} -7.00000i q^{7} -23.8174i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.60171i q^{2} +3.00000i q^{3} -13.1758 q^{4} -13.8051 q^{6} -7.00000i q^{7} -23.8174i q^{8} -9.00000 q^{9} -52.9465 q^{11} -39.5273i q^{12} +19.6024i q^{13} +32.2120 q^{14} +4.19486 q^{16} -61.5076i q^{17} -41.4154i q^{18} -27.0928 q^{19} +21.0000 q^{21} -243.645i q^{22} +19.2163i q^{23} +71.4523 q^{24} -90.2046 q^{26} -27.0000i q^{27} +92.2304i q^{28} +167.409 q^{29} +225.638 q^{31} -171.236i q^{32} -158.839i q^{33} +283.040 q^{34} +118.582 q^{36} -311.705i q^{37} -124.673i q^{38} -58.8071 q^{39} +12.8071 q^{41} +96.6360i q^{42} -114.311i q^{43} +697.611 q^{44} -88.4281 q^{46} +207.919i q^{47} +12.5846i q^{48} -49.0000 q^{49} +184.523 q^{51} -258.277i q^{52} +227.402i q^{53} +124.246 q^{54} -166.722 q^{56} -81.2784i q^{57} +770.369i q^{58} +605.531 q^{59} -315.981 q^{61} +1038.32i q^{62} +63.0000i q^{63} +821.538 q^{64} +730.934 q^{66} -720.254i q^{67} +810.410i q^{68} -57.6490 q^{69} -56.2766 q^{71} +214.357i q^{72} -1154.36i q^{73} +1434.38 q^{74} +356.969 q^{76} +370.625i q^{77} -270.614i q^{78} -1152.80 q^{79} +81.0000 q^{81} +58.9347i q^{82} +692.581i q^{83} -276.691 q^{84} +526.029 q^{86} +502.227i q^{87} +1261.05i q^{88} -1417.70 q^{89} +137.217 q^{91} -253.190i q^{92} +676.914i q^{93} -956.783 q^{94} +513.708 q^{96} -661.229i q^{97} -225.484i q^{98} +476.518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 - 72 * q^9	$ 8 q - 32 q^{4} - 72 q^{9} + 42 q^{11} + 144 q^{16} - 144 q^{19} + 168 q^{21} - 54 q^{24} + 258 q^{26} + 480 q^{29} + 702 q^{31} + 570 q^{34} + 288 q^{36} - 30 q^{39} + 762 q^{41} + 1950 q^{44} + 1100 q^{46} - 392 q^{49} + 594 q^{51} + 126 q^{56} + 1710 q^{59} + 1374 q^{61} + 2570 q^{64} + 1326 q^{66} - 612 q^{69} - 1362 q^{71} + 6738 q^{74} + 3820 q^{76} - 690 q^{79} + 648 q^{81} - 672 q^{84} - 1080 q^{86} + 396 q^{89} + 70 q^{91} + 3464 q^{94} + 432 q^{96} - 378 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 - 72 * q^9 + 42 * q^11 + 144 * q^16 - 144 * q^19 + 168 * q^21 - 54 * q^24 + 258 * q^26 + 480 * q^29 + 702 * q^31 + 570 * q^34 + 288 * q^36 - 30 * q^39 + 762 * q^41 + 1950 * q^44 + 1100 * q^46 - 392 * q^49 + 594 * q^51 + 126 * q^56 + 1710 * q^59 + 1374 * q^61 + 2570 * q^64 + 1326 * q^66 - 612 * q^69 - 1362 * q^71 + 6738 * q^74 + 3820 * q^76 - 690 * q^79 + 648 * q^81 - 672 * q^84 - 1080 * q^86 + 396 * q^89 + 70 * q^91 + 3464 * q^94 + 432 * q^96 - 378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	4.60171i	1.62695i	0.581599	+	0.813476i	$0.302427\pi$
$2$	4.60171i	1.62695i	−0.581599	+	0.813476i	$0.697573\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−13.1758	−1.64697
$5$	0	0
$5$	0	0
$6$	−13.8051	−0.939321
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 23.8174i	− 1.05259i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−52.9465	−1.45127	−0.725635	−	0.688080i	$-0.758454\pi$
$11$	−52.9465	−1.45127	−0.725635	+	0.688080i	$0.758454\pi$
$12$	− 39.5273i	− 0.950880i
$13$	19.6024i	0.418209i	0.977893	+	0.209105i	$0.0670550\pi$
$13$	19.6024i	0.418209i	−0.977893	+	0.209105i	$0.932945\pi$
$14$	32.2120	0.614930
$15$	0	0
$16$	4.19486	0.0655446
$17$	− 61.5076i	− 0.877516i	−0.898605	−	0.438758i	$-0.855418\pi$
$17$	− 61.5076i	− 0.877516i	0.898605	−	0.438758i	$-0.144582\pi$
$18$	− 41.4154i	− 0.542317i
$19$	−27.0928	−0.327133	−0.163566	−	0.986532i	$-0.552300\pi$
$19$	−27.0928	−0.327133	−0.163566	+	0.986532i	$0.552300\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 243.645i	− 2.36115i
$23$	19.2163i	0.174212i	0.996199	+	0.0871062i	$0.0277619\pi$
$23$	19.2163i	0.174212i	−0.996199	+	0.0871062i	$0.972238\pi$
$24$	71.4523	0.607714
$25$	0	0
$26$	−90.2046	−0.680407
$27$	− 27.0000i	− 0.192450i
$28$	92.2304i	0.622497i
$29$	167.409	1.07197	0.535984	−	0.844228i	$-0.319941\pi$
$29$	167.409	1.07197	0.535984	+	0.844228i	$0.319941\pi$
$30$	0	0
$31$	225.638	1.30728	0.653642	−	0.756804i	$-0.273240\pi$
$31$	225.638	1.30728	0.653642	+	0.756804i	$0.273240\pi$
$32$	− 171.236i	− 0.945954i
$33$	− 158.839i	− 0.837891i
$34$	283.040	1.42768
$35$	0	0
$36$	118.582	0.548991
$37$	− 311.705i	− 1.38497i	−0.721432	−	0.692485i	$-0.756516\pi$
$37$	− 311.705i	− 1.38497i	0.721432	−	0.692485i	$-0.243484\pi$
$38$	− 124.673i	− 0.532229i
$39$	−58.8071	−0.241453
$40$	0	0
$41$	12.8071	0.0487838	0.0243919	−	0.999702i	$-0.492235\pi$
$41$	12.8071	0.0487838	0.0243919	+	0.999702i	$0.492235\pi$
$42$	96.6360i	0.355030i
$43$	− 114.311i	− 0.405403i	−0.979241	−	0.202702i	$-0.935028\pi$
$43$	− 114.311i	− 0.405403i	0.979241	−	0.202702i	$-0.0649721\pi$
$44$	697.611	2.39020
$45$	0	0
$46$	−88.4281	−0.283435
$47$	207.919i	0.645278i	0.946522	+	0.322639i	$0.104570\pi$
$47$	207.919i	0.645278i	−0.946522	+	0.322639i	$0.895430\pi$
$48$	12.5846i	0.0378422i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	184.523	0.506634
$52$	− 258.277i	− 0.688779i
$53$	227.402i	0.589360i	0.955596	+	0.294680i	$0.0952131\pi$
$53$	227.402i	0.589360i	−0.955596	+	0.294680i	$0.904787\pi$
$54$	124.246	0.313107
$55$	0	0
$56$	−166.722	−0.397842
$57$	− 81.2784i	− 0.188870i
$58$	770.369i	1.74404i
$59$	605.531	1.33616	0.668080	−	0.744090i	$-0.267116\pi$
$59$	605.531	1.33616	0.668080	+	0.744090i	$0.267116\pi$
$60$	0	0
$61$	−315.981	−0.663232	−0.331616	−	0.943414i	$-0.607594\pi$
$61$	−315.981	−0.663232	−0.331616	+	0.943414i	$0.607594\pi$
$62$	1038.32i	2.12689i
$63$	63.0000i	0.125988i
$64$	821.538	1.60457
$65$	0	0
$66$	730.934	1.36321
$67$	− 720.254i	− 1.31333i	−0.754183	−	0.656664i	$-0.771967\pi$
$67$	− 720.254i	− 1.31333i	0.754183	−	0.656664i	$-0.228033\pi$
$68$	810.410i	1.44524i
$69$	−57.6490	−0.100582
$70$	0	0
$71$	−56.2766	−0.0940676	−0.0470338	−	0.998893i	$-0.514977\pi$
$71$	−56.2766	−0.0940676	−0.0470338	+	0.998893i	$0.514977\pi$
$72$	214.357i	0.350864i
$73$	− 1154.36i	− 1.85079i	−0.379010	−	0.925393i	$-0.623735\pi$
$73$	− 1154.36i	− 1.85079i	0.379010	−	0.925393i	$-0.376265\pi$
$74$	1434.38	2.25328
$75$	0	0
$76$	356.969	0.538778
$77$	370.625i	0.548528i
$78$	− 270.614i	− 0.392833i
$79$	−1152.80	−1.64177	−0.820885	−	0.571093i	$-0.806520\pi$
$79$	−1152.80	−1.64177	−0.820885	+	0.571093i	$0.806520\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	58.9347i	0.0793689i
$83$	692.581i	0.915911i	0.888975	+	0.457956i	$0.151418\pi$
$83$	692.581i	0.915911i	−0.888975	+	0.457956i	$0.848582\pi$
$84$	−276.691	−0.359399
$85$	0	0
$86$	526.029	0.659571
$87$	502.227i	0.618901i
$88$	1261.05i	1.52759i
$89$	−1417.70	−1.68849	−0.844246	−	0.535956i	$-0.819951\pi$
$89$	−1417.70	−1.68849	−0.844246	+	0.535956i	$0.819951\pi$
$90$	0	0
$91$	137.217	0.158068
$92$	− 253.190i	− 0.286923i
$93$	676.914i	0.754760i
$94$	−956.783	−1.04984
$95$	0	0
$96$	513.708	0.546147
$97$	− 661.229i	− 0.692140i	−0.938209	−	0.346070i	$-0.887516\pi$
$97$	− 661.229i	− 0.692140i	0.938209	−	0.346070i	$-0.112484\pi$
$98$	− 225.484i	− 0.232422i
$99$	476.518	0.483757
$100$	0	0
$101$	187.231	0.184458	0.0922289	−	0.995738i	$-0.470601\pi$
$101$	187.231	0.184458	0.0922289	+	0.995738i	$0.470601\pi$
$102$	849.121i	0.824270i
$103$	1076.28i	1.02961i	0.857308	+	0.514803i	$0.172135\pi$
$103$	1076.28i	1.02961i	−0.857308	+	0.514803i	$0.827865\pi$
$104$	466.879	0.440204
$105$	0	0
$106$	−1046.44	−0.958861
$107$	− 1591.65i	− 1.43805i	−0.694986	−	0.719024i	$-0.744589\pi$
$107$	− 1591.65i	− 1.43805i	0.694986	−	0.719024i	$-0.255411\pi$
$108$	355.746i	0.316960i
$109$	−1706.29	−1.49938	−0.749692	−	0.661786i	$-0.769799\pi$
$109$	−1706.29	−1.49938	−0.749692	+	0.661786i	$0.769799\pi$
$110$	0	0
$111$	935.114	0.799613
$112$	− 29.3640i	− 0.0247735i
$113$	− 560.000i	− 0.466198i	−0.972453	−	0.233099i	$-0.925113\pi$
$113$	− 560.000i	− 0.466198i	0.972453	−	0.233099i	$-0.0748866\pi$
$114$	374.020	0.307282
$115$	0	0
$116$	−2205.74	−1.76550
$117$	− 176.421i	− 0.139403i
$118$	2786.48i	2.17387i
$119$	−430.553	−0.331670
$120$	0	0
$121$	1472.33	1.10618
$122$	− 1454.05i	− 1.07905i
$123$	38.4214i	0.0281653i
$124$	−2972.96	−2.15306
$125$	0	0
$126$	−289.908	−0.204977
$127$	− 2098.96i	− 1.46655i	−0.679931	−	0.733276i	$-0.737990\pi$
$127$	− 2098.96i	− 1.46655i	0.679931	−	0.733276i	$-0.262010\pi$
$128$	2410.60i	1.66460i
$129$	342.934	0.234060
$130$	0	0
$131$	1675.28	1.11733	0.558664	−	0.829394i	$-0.311314\pi$
$131$	1675.28	1.11733	0.558664	+	0.829394i	$0.311314\pi$
$132$	2092.83i	1.37998i
$133$	189.650i	0.123644i
$134$	3314.40	2.13672
$135$	0	0
$136$	−1464.95	−0.923667
$137$	2678.78i	1.67054i	0.549841	+	0.835269i	$0.314688\pi$
$137$	2678.78i	1.67054i	−0.549841	+	0.835269i	$0.685312\pi$
$138$	− 265.284i	− 0.163641i
$139$	−1032.11	−0.629800	−0.314900	−	0.949125i	$-0.601971\pi$
$139$	−1032.11	−0.629800	−0.314900	+	0.949125i	$0.601971\pi$
$140$	0	0
$141$	−623.756	−0.372552
$142$	− 258.969i	− 0.153043i
$143$	− 1037.88i	− 0.606935i
$144$	−37.7537	−0.0218482
$145$	0	0
$146$	5312.02	3.01114
$147$	− 147.000i	− 0.0824786i
$148$	4106.95i	2.28101i
$149$	−1187.33	−0.652815	−0.326408	−	0.945229i	$-0.605838\pi$
$149$	−1187.33	−0.652815	−0.326408	+	0.945229i	$0.605838\pi$
$150$	0	0
$151$	−138.484	−0.0746338	−0.0373169	−	0.999303i	$-0.511881\pi$
$151$	−138.484	−0.0746338	−0.0373169	+	0.999303i	$0.511881\pi$
$152$	645.282i	0.344337i
$153$	553.568i	0.292505i
$154$	−1705.51	−0.892429
$155$	0	0
$156$	774.830	0.397667
$157$	− 441.575i	− 0.224469i	−0.993682	−	0.112234i	$-0.964199\pi$
$157$	− 441.575i	− 0.224469i	0.993682	−	0.112234i	$-0.0358007\pi$
$158$	− 5304.85i	− 2.67108i
$159$	−682.207	−0.340267
$160$	0	0
$161$	134.514	0.0658461
$162$	372.739i	0.180772i
$163$	2116.62i	1.01710i	0.861034	+	0.508548i	$0.169817\pi$
$163$	2116.62i	1.01710i	−0.861034	+	0.508548i	$0.830183\pi$
$164$	−168.744	−0.0803455
$165$	0	0
$166$	−3187.06	−1.49014
$167$	− 843.566i	− 0.390881i	−0.980716	−	0.195440i	$-0.937386\pi$
$167$	− 843.566i	− 0.390881i	0.980716	−	0.195440i	$-0.0626136\pi$
$168$	− 500.166i	− 0.229694i
$169$	1812.75	0.825101
$170$	0	0
$171$	243.835	0.109044
$172$	1506.14i	0.667687i
$173$	− 4319.01i	− 1.89808i	−0.315150	−	0.949042i	$-0.602055\pi$
$173$	− 4319.01i	− 1.89808i	0.315150	−	0.949042i	$-0.397945\pi$
$174$	−2311.11	−1.00692
$175$	0	0
$176$	−222.103	−0.0951229
$177$	1816.59i	0.771432i
$178$	− 6523.84i	− 2.74709i
$179$	421.744	0.176104	0.0880520	−	0.996116i	$-0.471936\pi$
$179$	421.744	0.176104	0.0880520	+	0.996116i	$0.471936\pi$
$180$	0	0
$181$	791.205	0.324916	0.162458	−	0.986715i	$-0.448058\pi$
$181$	791.205	0.324916	0.162458	+	0.986715i	$0.448058\pi$
$182$	631.432i	0.257170i
$183$	− 947.942i	− 0.382917i
$184$	457.684	0.183375
$185$	0	0
$186$	−3114.96	−1.22796
$187$	3256.61i	1.27351i
$188$	− 2739.49i	− 1.06276i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	1790.22	0.678199	0.339100	−	0.940750i	$-0.389878\pi$
$191$	1790.22	0.678199	0.339100	+	0.940750i	$0.389878\pi$
$192$	2464.61i	0.926397i
$193$	− 2301.10i	− 0.858221i	−0.903252	−	0.429111i	$-0.858827\pi$
$193$	− 2301.10i	− 0.858221i	0.903252	−	0.429111i	$-0.141173\pi$
$194$	3042.79	1.12608
$195$	0	0
$196$	645.613	0.235282
$197$	− 3490.59i	− 1.26241i	−0.775617	−	0.631203i	$-0.782561\pi$
$197$	− 3490.59i	− 1.26241i	0.775617	−	0.631203i	$-0.217439\pi$
$198$	2192.80i	0.787048i
$199$	−822.357	−0.292942	−0.146471	−	0.989215i	$-0.546791\pi$
$199$	−822.357	−0.292942	−0.146471	+	0.989215i	$0.546791\pi$
$200$	0	0
$201$	2160.76	0.758251
$202$	861.586i	0.300104i
$203$	− 1171.86i	− 0.405166i
$204$	−2431.23	−0.834413
$205$	0	0
$206$	−4952.75	−1.67512
$207$	− 172.947i	− 0.0580708i
$208$	82.2292i	0.0274114i
$209$	1434.47	0.474757
$210$	0	0
$211$	−2323.79	−0.758181	−0.379091	−	0.925360i	$-0.623763\pi$
$211$	−2323.79	−0.758181	−0.379091	+	0.925360i	$0.623763\pi$
$212$	− 2996.20i	− 0.970660i
$213$	− 168.830i	− 0.0543099i
$214$	7324.34	2.33963
$215$	0	0
$216$	−643.071	−0.202571
$217$	− 1579.47i	− 0.494107i
$218$	− 7851.86i	− 2.43943i
$219$	3463.07	1.06855
$220$	0	0
$221$	1205.70	0.366986
$222$	4303.13i	1.30093i
$223$	− 2526.13i	− 0.758574i	−0.925279	−	0.379287i	$-0.876169\pi$
$223$	− 2526.13i	− 0.758574i	0.925279	−	0.379287i	$-0.123831\pi$
$224$	−1198.65	−0.357537
$225$	0	0
$226$	2576.96	0.758482
$227$	− 3924.06i	− 1.14735i	−0.819082	−	0.573676i	$-0.805517\pi$
$227$	− 3924.06i	− 1.14735i	0.819082	−	0.573676i	$-0.194483\pi$
$228$	1070.91i	0.311064i
$229$	−3591.55	−1.03640	−0.518201	−	0.855259i	$-0.673398\pi$
$229$	−3591.55	−1.03640	−0.518201	+	0.855259i	$0.673398\pi$
$230$	0	0
$231$	−1111.88	−0.316693
$232$	− 3987.26i	− 1.12835i
$233$	4957.57i	1.39391i	0.717115	+	0.696955i	$0.245462\pi$
$233$	4957.57i	1.39391i	−0.717115	+	0.696955i	$0.754538\pi$
$234$	811.841	0.226802
$235$	0	0
$236$	−7978.34	−2.20062
$237$	− 3458.39i	− 0.947877i
$238$	− 1981.28i	− 0.539611i
$239$	5663.57	1.53283	0.766414	−	0.642347i	$-0.222039\pi$
$239$	5663.57	1.53283	0.766414	+	0.642347i	$0.222039\pi$
$240$	0	0
$241$	−2246.64	−0.600493	−0.300246	−	0.953862i	$-0.597069\pi$
$241$	−2246.64	−0.600493	−0.300246	+	0.953862i	$0.597069\pi$
$242$	6775.24i	1.79971i
$243$	243.000i	0.0641500i
$244$	4163.29	1.09232
$245$	0	0
$246$	−176.804	−0.0458236
$247$	− 531.084i	− 0.136810i
$248$	− 5374.12i	− 1.37604i
$249$	−2077.74	−0.528802
$250$	0	0
$251$	−3382.51	−0.850606	−0.425303	−	0.905051i	$-0.639833\pi$
$251$	−3382.51	−0.850606	−0.425303	+	0.905051i	$0.639833\pi$
$252$	− 830.074i	− 0.207499i
$253$	− 1017.44i	− 0.252829i
$254$	9658.79	2.38601
$255$	0	0
$256$	−4520.57	−1.10365
$257$	− 8116.97i	− 1.97013i	−0.172190	−	0.985064i	$-0.555084\pi$
$257$	− 8116.97i	− 1.97013i	0.172190	−	0.985064i	$-0.444916\pi$
$258$	1578.09i	0.380804i
$259$	−2181.93	−0.523470
$260$	0	0
$261$	−1506.68	−0.357323
$262$	7709.17i	1.81784i
$263$	3643.53i	0.854257i	0.904191	+	0.427129i	$0.140475\pi$
$263$	3643.53i	0.854257i	−0.904191	+	0.427129i	$0.859525\pi$
$264$	−3783.15	−0.881957
$265$	0	0
$266$	−872.714	−0.201164
$267$	− 4253.10i	− 0.974851i
$268$	9489.90i	2.16302i
$269$	−7509.24	−1.70203	−0.851015	−	0.525141i	$-0.824013\pi$
$269$	−7509.24	−1.70203	−0.851015	+	0.525141i	$0.824013\pi$
$270$	0	0
$271$	−8350.12	−1.87171	−0.935855	−	0.352385i	$-0.885371\pi$
$271$	−8350.12	−1.87171	−0.935855	+	0.352385i	$0.885371\pi$
$272$	− 258.015i	− 0.0575165i
$273$	411.650i	0.0912608i
$274$	−12327.0	−2.71788
$275$	0	0
$276$	759.571	0.165655
$277$	− 3359.70i	− 0.728753i	−0.931252	−	0.364377i	$-0.881282\pi$
$277$	− 3359.70i	− 0.728753i	0.931252	−	0.364377i	$-0.118718\pi$
$278$	− 4749.47i	− 1.02465i
$279$	−2030.74	−0.435761
$280$	0	0
$281$	6403.33	1.35940	0.679699	−	0.733491i	$-0.262110\pi$
$281$	6403.33	1.35940	0.679699	+	0.733491i	$0.262110\pi$
$282$	− 2870.35i	− 0.606123i
$283$	− 5862.59i	− 1.23143i	−0.787969	−	0.615715i	$-0.788867\pi$
$283$	− 5862.59i	− 1.23143i	0.787969	−	0.615715i	$-0.211133\pi$
$284$	741.487	0.154927
$285$	0	0
$286$	4776.01	0.987453
$287$	− 89.6498i	− 0.0184385i
$288$	1541.12i	0.315318i
$289$	1129.82	0.229965
$290$	0	0
$291$	1983.69	0.399607
$292$	15209.6i	3.04819i
$293$	3866.04i	0.770840i	0.922741	+	0.385420i	$0.125944\pi$
$293$	3866.04i	0.770840i	−0.922741	+	0.385420i	$0.874056\pi$
$294$	676.452	0.134189
$295$	0	0
$296$	−7424.01	−1.45781
$297$	1429.56i	0.279297i
$298$	− 5463.73i	− 1.06210i
$299$	−376.686	−0.0728573
$300$	0	0
$301$	−800.180	−0.153228
$302$	− 637.266i	− 0.121426i
$303$	561.694i	0.106497i
$304$	−113.650	−0.0214418
$305$	0	0
$306$	−2547.36	−0.475892
$307$	− 7084.81i	− 1.31711i	−0.752535	−	0.658553i	$-0.771169\pi$
$307$	− 7084.81i	− 1.31711i	0.752535	−	0.658553i	$-0.228831\pi$
$308$	− 4883.28i	− 0.903411i
$309$	−3228.85	−0.594443
$310$	0	0
$311$	−10616.6	−1.93572	−0.967862	−	0.251483i	$-0.919082\pi$
$311$	−10616.6	−1.93572	−0.967862	+	0.251483i	$0.919082\pi$
$312$	1400.64i	0.254152i
$313$	− 7247.78i	− 1.30885i	−0.756128	−	0.654423i	$-0.772911\pi$
$313$	− 7247.78i	− 1.30885i	0.756128	−	0.654423i	$-0.227089\pi$
$314$	2032.00	0.365199
$315$	0	0
$316$	15189.0	2.70395
$317$	− 6308.24i	− 1.11768i	−0.829274	−	0.558842i	$-0.811246\pi$
$317$	− 6308.24i	− 1.11768i	0.829274	−	0.558842i	$-0.188754\pi$
$318$	− 3139.32i	− 0.553599i
$319$	−8863.72	−1.55572
$320$	0	0
$321$	4774.96	0.830257
$322$	618.997i	0.107128i
$323$	1666.41i	0.287064i
$324$	−1067.24	−0.182997
$325$	0	0
$326$	−9740.09	−1.65477
$327$	− 5118.87i	− 0.865670i
$328$	− 305.033i	− 0.0513494i
$329$	1455.43	0.243892
$330$	0	0
$331$	6656.25	1.10532	0.552660	−	0.833407i	$-0.313613\pi$
$331$	6656.25	1.10532	0.552660	+	0.833407i	$0.313613\pi$
$332$	− 9125.29i	− 1.50848i
$333$	2805.34i	0.461657i
$334$	3881.85	0.635944
$335$	0	0
$336$	88.0920	0.0143030
$337$	11941.8i	1.93030i	0.261691	+	0.965152i	$0.415720\pi$
$337$	11941.8i	1.93030i	−0.261691	+	0.965152i	$0.584280\pi$
$338$	8341.74i	1.34240i
$339$	1680.00	0.269160
$340$	0	0
$341$	−11946.7	−1.89722
$342$	1122.06i	0.177410i
$343$	343.000i	0.0539949i
$344$	−2722.61	−0.426724
$345$	0	0
$346$	19874.9	3.08809
$347$	6390.65i	0.988669i	0.869272	+	0.494335i	$0.164588\pi$
$347$	6390.65i	0.988669i	−0.869272	+	0.494335i	$0.835412\pi$
$348$	− 6617.23i	− 1.01931i
$349$	7760.54	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$349$	7760.54	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$350$	0	0
$351$	529.264	0.0804844
$352$	9066.34i	1.37283i
$353$	5416.46i	0.816684i	0.912829	+	0.408342i	$0.133893\pi$
$353$	5416.46i	0.816684i	−0.912829	+	0.408342i	$0.866107\pi$
$354$	−8359.44	−1.25508
$355$	0	0
$356$	18679.3	2.78090
$357$	− 1291.66i	− 0.191490i
$358$	1940.74i	0.286513i
$359$	2563.26	0.376834	0.188417	−	0.982089i	$-0.439664\pi$
$359$	2563.26	0.376834	0.188417	+	0.982089i	$0.439664\pi$
$360$	0	0
$361$	−6124.98	−0.892984
$362$	3640.90i	0.528623i
$363$	4416.99i	0.638655i
$364$	−1807.94	−0.260334
$365$	0	0
$366$	4362.16	0.622988
$367$	10118.8i	1.43923i	0.694374	+	0.719614i	$0.255681\pi$
$367$	10118.8i	1.43923i	−0.694374	+	0.719614i	$0.744319\pi$
$368$	80.6098i	0.0114187i
$369$	−115.264	−0.0162613
$370$	0	0
$371$	1591.82	0.222757
$372$	− 8918.87i	− 1.24307i
$373$	1870.64i	0.259673i	0.991535	+	0.129837i	$0.0414453\pi$
$373$	1870.64i	0.259673i	−0.991535	+	0.129837i	$0.958555\pi$
$374$	−14986.0	−2.07194
$375$	0	0
$376$	4952.09	0.679215
$377$	3281.62i	0.448307i
$378$	− 869.724i	− 0.118343i
$379$	−3804.87	−0.515681	−0.257841	−	0.966187i	$-0.583011\pi$
$379$	−3804.87	−0.515681	−0.257841	+	0.966187i	$0.583011\pi$
$380$	0	0
$381$	6296.87	0.846715
$382$	8238.10i	1.10340i
$383$	11709.3i	1.56219i	0.624414	+	0.781094i	$0.285338\pi$
$383$	11709.3i	1.56219i	−0.624414	+	0.781094i	$0.714662\pi$
$384$	−7231.79	−0.961056
$385$	0	0
$386$	10589.0	1.39628
$387$	1028.80i	0.135134i
$388$	8712.20i	1.13994i
$389$	1278.24	0.166605	0.0833023	−	0.996524i	$-0.473453\pi$
$389$	1278.24	0.166605	0.0833023	+	0.996524i	$0.473453\pi$
$390$	0	0
$391$	1181.95	0.152874
$392$	1167.05i	0.150370i
$393$	5025.85i	0.645090i
$394$	16062.7	2.05387
$395$	0	0
$396$	−6278.50	−0.796733
$397$	− 2101.91i	− 0.265723i	−0.991135	−	0.132862i	$-0.957583\pi$
$397$	− 2101.91i	− 0.265723i	0.991135	−	0.132862i	$-0.0424166\pi$
$398$	− 3784.25i	− 0.476602i
$399$	−568.949	−0.0713862
$400$	0	0
$401$	−11239.5	−1.39969	−0.699846	−	0.714294i	$-0.746748\pi$
$401$	−11239.5	−1.39969	−0.699846	+	0.714294i	$0.746748\pi$
$402$	9943.21i	1.23364i
$403$	4423.04i	0.546718i
$404$	−2466.92	−0.303797
$405$	0	0
$406$	5392.58	0.659186
$407$	16503.7i	2.00997i
$408$	− 4394.86i	− 0.533279i
$409$	−6751.66	−0.816254	−0.408127	−	0.912925i	$-0.633818\pi$
$409$	−6751.66	−0.816254	−0.408127	+	0.912925i	$0.633818\pi$
$410$	0	0
$411$	−8036.34	−0.964486
$412$	− 14180.9i	− 1.69573i
$413$	− 4238.72i	− 0.505021i
$414$	795.853	0.0944784
$415$	0	0
$416$	3356.63	0.395607
$417$	− 3096.32i	− 0.363615i
$418$	6601.02i	0.772408i
$419$	8449.93	0.985218	0.492609	−	0.870251i	$-0.336043\pi$
$419$	8449.93	0.985218	0.492609	+	0.870251i	$0.336043\pi$
$420$	0	0
$421$	2267.58	0.262506	0.131253	−	0.991349i	$-0.458100\pi$
$421$	2267.58	0.262506	0.131253	+	0.991349i	$0.458100\pi$
$422$	− 10693.4i	− 1.23352i
$423$	− 1871.27i	− 0.215093i
$424$	5416.14	0.620356
$425$	0	0
$426$	776.906	0.0883597
$427$	2211.86i	0.250678i
$428$	20971.3i	2.36842i
$429$	3113.63	0.350414
$430$	0	0
$431$	−3172.81	−0.354591	−0.177296	−	0.984158i	$-0.556735\pi$
$431$	−3172.81	−0.354591	−0.177296	+	0.984158i	$0.556735\pi$
$432$	− 113.261i	− 0.0126141i
$433$	− 13569.4i	− 1.50601i	−0.658013	−	0.753006i	$-0.728603\pi$
$433$	− 13569.4i	− 1.50601i	0.658013	−	0.753006i	$-0.271397\pi$
$434$	7268.25	0.803888
$435$	0	0
$436$	22481.7	2.46944
$437$	− 520.625i	− 0.0569905i
$438$	15936.1i	1.73848i
$439$	12021.7	1.30698	0.653488	−	0.756936i	$-0.273305\pi$
$439$	12021.7	1.30698	0.653488	+	0.756936i	$0.273305\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	5548.26i	0.597068i
$443$	2072.36i	0.222259i	0.993806	+	0.111129i	$0.0354468\pi$
$443$	2072.36i	0.222259i	−0.993806	+	0.111129i	$0.964553\pi$
$444$	−12320.8	−1.31694
$445$	0	0
$446$	11624.5	1.23416
$447$	− 3561.98i	− 0.376903i
$448$	− 5750.77i	− 0.606469i
$449$	−154.727	−0.0162628	−0.00813142	−	0.999967i	$-0.502588\pi$
$449$	−154.727	−0.0162628	−0.00813142	+	0.999967i	$0.502588\pi$
$450$	0	0
$451$	−678.092	−0.0707984
$452$	7378.44i	0.767815i
$453$	− 415.453i	− 0.0430898i
$454$	18057.4	1.86669
$455$	0	0
$456$	−1935.84	−0.198803
$457$	− 4347.26i	− 0.444981i	−0.974935	−	0.222491i	$-0.928581\pi$
$457$	− 4347.26i	− 0.444981i	0.974935	−	0.222491i	$-0.0714187\pi$
$458$	− 16527.3i	− 1.68618i
$459$	−1660.70	−0.168878
$460$	0	0
$461$	−5510.76	−0.556750	−0.278375	−	0.960473i	$-0.589796\pi$
$461$	−5510.76	−0.556750	−0.278375	+	0.960473i	$0.589796\pi$
$462$	− 5116.54i	− 0.515244i
$463$	9166.14i	0.920058i	0.887904	+	0.460029i	$0.152161\pi$
$463$	9166.14i	0.920058i	−0.887904	+	0.460029i	$0.847839\pi$
$464$	702.257	0.0702618
$465$	0	0
$466$	−22813.3	−2.26783
$467$	− 9008.92i	− 0.892683i	−0.894863	−	0.446342i	$-0.852727\pi$
$467$	− 9008.92i	− 0.892683i	0.894863	−	0.446342i	$-0.147273\pi$
$468$	2324.49i	0.229593i
$469$	−5041.78	−0.496392
$470$	0	0
$471$	1324.73	0.129597
$472$	− 14422.2i	− 1.40643i
$473$	6052.39i	0.588349i
$474$	15914.5	1.54215
$475$	0	0
$476$	5672.87	0.546251
$477$	− 2046.62i	− 0.196453i
$478$	26062.1i	2.49384i
$479$	−10128.1	−0.966108	−0.483054	−	0.875590i	$-0.660473\pi$
$479$	−10128.1	−0.966108	−0.483054	+	0.875590i	$0.660473\pi$
$480$	0	0
$481$	6110.15	0.579208
$482$	− 10338.4i	− 0.976973i
$483$	403.543i	0.0380163i
$484$	−19399.1	−1.82185
$485$	0	0
$486$	−1118.22	−0.104369
$487$	954.443i	0.0888089i	0.999014	+	0.0444045i	$0.0141390\pi$
$487$	954.443i	0.0888089i	−0.999014	+	0.0444045i	$0.985861\pi$
$488$	7525.85i	0.698113i
$489$	−6349.86	−0.587220
$490$	0	0
$491$	7336.23	0.674296	0.337148	−	0.941452i	$-0.390538\pi$
$491$	7336.23	0.674296	0.337148	+	0.941452i	$0.390538\pi$
$492$	− 506.231i	− 0.0463875i
$493$	− 10296.9i	− 0.940670i
$494$	2443.90	0.222583
$495$	0	0
$496$	946.519	0.0856854
$497$	393.936i	0.0355542i
$498$	− 9561.18i	− 0.860335i
$499$	−16572.9	−1.48679	−0.743393	−	0.668855i	$-0.766785\pi$
$499$	−16572.9	−1.48679	−0.743393	+	0.668855i	$0.766785\pi$
$500$	0	0
$501$	2530.70	0.225675
$502$	− 15565.3i	− 1.38390i
$503$	13628.8i	1.20811i	0.796944	+	0.604053i	$0.206448\pi$
$503$	13628.8i	1.20811i	−0.796944	+	0.604053i	$0.793552\pi$
$504$	1500.50	0.132614
$505$	0	0
$506$	4681.96	0.411341
$507$	5438.24i	0.476372i
$508$	27655.4i	2.41537i
$509$	8370.77	0.728935	0.364467	−	0.931216i	$-0.381251\pi$
$509$	8370.77	0.728935	0.364467	+	0.931216i	$0.381251\pi$
$510$	0	0
$511$	−8080.50	−0.699531
$512$	− 1517.60i	− 0.130994i
$513$	731.506i	0.0629567i
$514$	37352.0	3.20530
$515$	0	0
$516$	−4518.43	−0.385489
$517$	− 11008.6i	− 0.936473i
$518$	− 10040.6i	− 0.851660i
$519$	12957.0	1.09586
$520$	0	0
$521$	−705.491	−0.0593246	−0.0296623	−	0.999560i	$-0.509443\pi$
$521$	−705.491	−0.0593246	−0.0296623	+	0.999560i	$0.509443\pi$
$522$	− 6933.32i	− 0.581347i
$523$	− 4556.70i	− 0.380977i	−0.981689	−	0.190488i	$-0.938993\pi$
$523$	− 4556.70i	− 0.380977i	0.981689	−	0.190488i	$-0.0610071\pi$
$524$	−22073.1	−1.84021
$525$	0	0
$526$	−16766.5	−1.38984
$527$	− 13878.4i	− 1.14716i
$528$	− 666.309i	− 0.0549193i
$529$	11797.7	0.969650
$530$	0	0
$531$	−5449.78	−0.445387
$532$	− 2498.78i	− 0.203639i
$533$	251.050i	0.0204018i
$534$	19571.5	1.58604
$535$	0	0
$536$	−17154.6	−1.38240
$537$	1265.23i	0.101674i
$538$	− 34555.4i	− 2.76912i
$539$	2594.38	0.207324
$540$	0	0
$541$	−21336.7	−1.69563	−0.847817	−	0.530289i	$-0.822084\pi$
$541$	−21336.7	−1.69563	−0.847817	+	0.530289i	$0.822084\pi$
$542$	− 38424.9i	− 3.04518i
$543$	2373.61i	0.187590i
$544$	−10532.3	−0.830090
$545$	0	0
$546$	−1894.30	−0.148477
$547$	957.875i	0.0748734i	0.999299	+	0.0374367i	$0.0119193\pi$
$547$	957.875i	0.0748734i	−0.999299	+	0.0374367i	$0.988081\pi$
$548$	− 35295.0i	− 2.75133i
$549$	2843.83	0.221077
$550$	0	0
$551$	−4535.58	−0.350676
$552$	1373.05i	0.105871i
$553$	8069.58i	0.620531i
$554$	15460.4	1.18565
$555$	0	0
$556$	13598.8	1.03726
$557$	13357.8i	1.01614i	0.861316	+	0.508069i	$0.169641\pi$
$557$	13357.8i	1.01614i	−0.861316	+	0.508069i	$0.830359\pi$
$558$	− 9344.89i	− 0.708962i
$559$	2240.78	0.169543
$560$	0	0
$561$	−9769.83	−0.735263
$562$	29466.3i	2.21167i
$563$	14988.5i	1.12201i	0.827814	+	0.561003i	$0.189584\pi$
$563$	14988.5i	1.12201i	−0.827814	+	0.561003i	$0.810416\pi$
$564$	8218.48	0.613582
$565$	0	0
$566$	26978.0	2.00348
$567$	− 567.000i	− 0.0419961i
$568$	1340.36i	0.0990148i
$569$	12901.9	0.950572	0.475286	−	0.879831i	$-0.342345\pi$
$569$	12901.9	0.950572	0.475286	+	0.879831i	$0.342345\pi$
$570$	0	0
$571$	−19768.4	−1.44883	−0.724414	−	0.689365i	$-0.757890\pi$
$571$	−19768.4	−1.44883	−0.724414	+	0.689365i	$0.757890\pi$
$572$	13674.8i	0.999604i
$573$	5370.67i	0.391559i
$574$	412.543	0.0299986
$575$	0	0
$576$	−7393.84	−0.534855
$577$	5598.68i	0.403945i	0.979391	+	0.201972i	$0.0647352\pi$
$577$	5598.68i	0.403945i	−0.979391	+	0.201972i	$0.935265\pi$
$578$	5199.10i	0.374142i
$579$	6903.30	0.495494
$580$	0	0
$581$	4848.07	0.346182
$582$	9128.36i	0.650142i
$583$	− 12040.2i	− 0.855321i
$584$	−27493.8	−1.94812
$585$	0	0
$586$	−17790.4	−1.25412
$587$	− 2915.30i	− 0.204987i	−0.994734	−	0.102494i	$-0.967318\pi$
$587$	− 2915.30i	− 0.204987i	0.994734	−	0.102494i	$-0.0326821\pi$
$588$	1936.84i	0.135840i
$589$	−6113.17	−0.427655
$590$	0	0
$591$	10471.8	0.728851
$592$	− 1307.56i	− 0.0907774i
$593$	− 6126.89i	− 0.424285i	−0.977239	−	0.212143i	$-0.931956\pi$
$593$	− 6126.89i	− 0.424285i	0.977239	−	0.212143i	$-0.0680442\pi$
$594$	−6578.40	−0.454403
$595$	0	0
$596$	15643.9	1.07517
$597$	− 2467.07i	− 0.169130i
$598$	− 1733.40i	− 0.118535i
$599$	13503.6	0.921104	0.460552	−	0.887633i	$-0.347652\pi$
$599$	13503.6	0.921104	0.460552	+	0.887633i	$0.347652\pi$
$600$	0	0
$601$	−28199.1	−1.91392	−0.956960	−	0.290220i	$-0.906272\pi$
$601$	−28199.1	−1.91392	−0.956960	+	0.290220i	$0.906272\pi$
$602$	− 3682.20i	− 0.249294i
$603$	6482.29i	0.437776i
$604$	1824.64	0.122920
$605$	0	0
$606$	−2584.76	−0.173265
$607$	13557.2i	0.906543i	0.891372	+	0.453272i	$0.149743\pi$
$607$	13557.2i	0.906543i	−0.891372	+	0.453272i	$0.850257\pi$
$608$	4639.27i	0.309452i
$609$	3515.59	0.233923
$610$	0	0
$611$	−4075.70	−0.269861
$612$	− 7293.69i	− 0.481748i
$613$	− 10357.7i	− 0.682452i	−0.939981	−	0.341226i	$-0.889158\pi$
$613$	− 10357.7i	− 0.682452i	0.939981	−	0.341226i	$-0.110842\pi$
$614$	32602.3	2.14287
$615$	0	0
$616$	8827.35	0.577377
$617$	9433.74i	0.615540i	0.951461	+	0.307770i	$0.0995827\pi$
$617$	9433.74i	0.615540i	−0.951461	+	0.307770i	$0.900417\pi$
$618$	− 14858.3i	− 0.967131i
$619$	5686.15	0.369217	0.184609	−	0.982812i	$-0.440898\pi$
$619$	5686.15	0.369217	0.184609	+	0.982812i	$0.440898\pi$
$620$	0	0
$621$	518.841	0.0335272
$622$	− 48854.4i	− 3.14933i
$623$	9923.89i	0.638190i
$624$	−246.688	−0.0158260
$625$	0	0
$626$	33352.2	2.12943
$627$	4303.41i	0.274101i
$628$	5818.10i	0.369693i
$629$	−19172.2	−1.21533
$630$	0	0
$631$	24059.8	1.51792	0.758959	−	0.651138i	$-0.225708\pi$
$631$	24059.8	1.51792	0.758959	+	0.651138i	$0.225708\pi$
$632$	27456.7i	1.72811i
$633$	− 6971.37i	− 0.437736i
$634$	29028.7	1.81842
$635$	0	0
$636$	8988.60	0.560411
$637$	− 960.517i	− 0.0597442i
$638$	− 40788.3i	− 2.53107i
$639$	506.489	0.0313559
$640$	0	0
$641$	18543.7	1.14264	0.571319	−	0.820728i	$-0.306432\pi$
$641$	18543.7	1.14264	0.571319	+	0.820728i	$0.306432\pi$
$642$	21973.0i	1.35079i
$643$	6491.72i	0.398147i	0.979985	+	0.199073i	$0.0637932\pi$
$643$	6491.72i	0.398147i	−0.979985	+	0.199073i	$0.936207\pi$
$644$	−1772.33	−0.108447
$645$	0	0
$646$	−7668.36	−0.467040
$647$	12238.1i	0.743630i	0.928307	+	0.371815i	$0.121264\pi$
$647$	12238.1i	0.743630i	−0.928307	+	0.371815i	$0.878736\pi$
$648$	− 1929.21i	− 0.116955i
$649$	−32060.7	−1.93913
$650$	0	0
$651$	4738.40	0.285273
$652$	− 27888.1i	− 1.67513i
$653$	− 2507.00i	− 0.150239i	−0.997175	−	0.0751197i	$-0.976066\pi$
$653$	− 2507.00i	− 0.150239i	0.997175	−	0.0751197i	$-0.0239339\pi$
$654$	23555.6	1.40840
$655$	0	0
$656$	53.7240	0.00319752
$657$	10389.2i	0.616928i
$658$	6697.48i	0.396801i
$659$	16501.0	0.975398	0.487699	−	0.873012i	$-0.337836\pi$
$659$	16501.0	0.975398	0.487699	+	0.873012i	$0.337836\pi$
$660$	0	0
$661$	19086.4	1.12311	0.561554	−	0.827440i	$-0.310204\pi$
$661$	19086.4	1.12311	0.561554	+	0.827440i	$0.310204\pi$
$662$	30630.2i	1.79830i
$663$	3617.09i	0.211879i
$664$	16495.5	0.964081
$665$	0	0
$666$	−12909.4	−0.751093
$667$	3216.99i	0.186750i
$668$	11114.6i	0.643770i
$669$	7578.38	0.437963
$670$	0	0
$671$	16730.1	0.962529
$672$	− 3595.96i	− 0.206424i
$673$	− 28326.1i	− 1.62242i	−0.584754	−	0.811211i	$-0.698809\pi$
$673$	− 28326.1i	− 1.62242i	0.584754	−	0.811211i	$-0.301191\pi$
$674$	−54952.8	−3.14051
$675$	0	0
$676$	−23884.3	−1.35892
$677$	− 9012.99i	− 0.511665i	−0.966721	−	0.255833i	$-0.917650\pi$
$677$	− 9012.99i	− 0.511665i	0.966721	−	0.255833i	$-0.0823496\pi$
$678$	7730.88i	0.437910i
$679$	−4628.60	−0.261604
$680$	0	0
$681$	11772.2	0.662424
$682$	− 54975.5i	− 3.08669i
$683$	− 3111.96i	− 0.174343i	−0.996193	−	0.0871713i	$-0.972217\pi$
$683$	− 3111.96i	− 0.174343i	0.996193	−	0.0871713i	$-0.0277827\pi$
$684$	−3212.72	−0.179593
$685$	0	0
$686$	−1578.39	−0.0878471
$687$	− 10774.6i	− 0.598367i
$688$	− 479.520i	− 0.0265720i
$689$	−4457.63	−0.246476
$690$	0	0
$691$	21905.5	1.20597	0.602984	−	0.797753i	$-0.293978\pi$
$691$	21905.5	1.20597	0.602984	+	0.797753i	$0.293978\pi$
$692$	56906.3i	3.12609i
$693$	− 3335.63i	− 0.182843i
$694$	−29408.0	−1.60852
$695$	0	0
$696$	11961.8	0.651451
$697$	− 787.735i	− 0.0428086i
$698$	35711.8i	1.93655i
$699$	−14872.7	−0.804775
$700$	0	0
$701$	−13337.0	−0.718592	−0.359296	−	0.933224i	$-0.616983\pi$
$701$	−13337.0	−0.718592	−0.359296	+	0.933224i	$0.616983\pi$
$702$	2435.52i	0.130944i
$703$	8444.95i	0.453069i
$704$	−43497.5	−2.32866
$705$	0	0
$706$	−24925.0	−1.32870
$707$	− 1310.62i	− 0.0697185i
$708$	− 23935.0i	− 1.27053i
$709$	−31571.2	−1.67233	−0.836164	−	0.548480i	$-0.815207\pi$
$709$	−31571.2	−1.67233	−0.836164	+	0.548480i	$0.815207\pi$
$710$	0	0
$711$	10375.2	0.547257
$712$	33766.0i	1.77729i
$713$	4335.94i	0.227745i
$714$	5943.85	0.311545
$715$	0	0
$716$	−5556.80	−0.290038
$717$	16990.7i	0.884979i
$718$	11795.4i	0.613091i
$719$	1983.80	0.102897	0.0514486	−	0.998676i	$-0.483616\pi$
$719$	1983.80	0.102897	0.0514486	+	0.998676i	$0.483616\pi$
$720$	0	0
$721$	7533.99	0.389155
$722$	− 28185.4i	− 1.45284i
$723$	− 6739.92i	− 0.346695i
$724$	−10424.7	−0.535127
$725$	0	0
$726$	−20325.7	−1.03906
$727$	− 28855.0i	− 1.47204i	−0.676960	−	0.736020i	$-0.736703\pi$
$727$	− 28855.0i	− 1.47204i	0.676960	−	0.736020i	$-0.263297\pi$
$728$	− 3268.15i	− 0.166381i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−7031.02	−0.355748
$732$	12489.9i	0.630654i
$733$	2709.63i	0.136538i	0.997667	+	0.0682691i	$0.0217476\pi$
$733$	2709.63i	0.136538i	−0.997667	+	0.0682691i	$0.978252\pi$
$734$	−46563.8	−2.34156
$735$	0	0
$736$	3290.53	0.164797
$737$	38134.9i	1.90599i
$738$	− 530.412i	− 0.0264563i
$739$	24900.6	1.23949	0.619746	−	0.784802i	$-0.287236\pi$
$739$	24900.6	1.23949	0.619746	+	0.784802i	$0.287236\pi$
$740$	0	0
$741$	1593.25	0.0789872
$742$	7325.08i	0.362415i
$743$	− 14522.6i	− 0.717070i	−0.933516	−	0.358535i	$-0.883276\pi$
$743$	− 14522.6i	− 0.717070i	0.933516	−	0.358535i	$-0.116724\pi$
$744$	16122.4	0.794455
$745$	0	0
$746$	−8608.16	−0.422476
$747$	− 6233.23i	− 0.305304i
$748$	− 42908.4i	− 2.09744i
$749$	−11141.6	−0.543531
$750$	0	0
$751$	−14360.6	−0.697768	−0.348884	−	0.937166i	$-0.613439\pi$
$751$	−14360.6	−0.697768	−0.348884	+	0.937166i	$0.613439\pi$
$752$	872.190i	0.0422945i
$753$	− 10147.5i	− 0.491098i
$754$	−15101.1	−0.729374
$755$	0	0
$756$	2490.22	0.119800
$757$	6200.35i	0.297695i	0.988860	+	0.148848i	$0.0475564\pi$
$757$	6200.35i	0.297695i	−0.988860	+	0.148848i	$0.952444\pi$
$758$	− 17508.9i	− 0.838988i
$759$	3052.31	0.145971
$760$	0	0
$761$	−22218.6	−1.05838	−0.529188	−	0.848505i	$-0.677503\pi$
$761$	−22218.6	−1.05838	−0.529188	+	0.848505i	$0.677503\pi$
$762$	28976.4i	1.37756i
$763$	11944.0i	0.566714i
$764$	−23587.6	−1.11698
$765$	0	0
$766$	−53882.9	−2.54160
$767$	11869.8i	0.558795i
$768$	− 13561.7i	− 0.637195i
$769$	−9799.16	−0.459515	−0.229757	−	0.973248i	$-0.573793\pi$
$769$	−9799.16	−0.459515	−0.229757	+	0.973248i	$0.573793\pi$
$770$	0	0
$771$	24350.9	1.13745
$772$	30318.8i	1.41347i
$773$	− 23174.1i	− 1.07828i	−0.842215	−	0.539141i	$-0.818749\pi$
$773$	− 23174.1i	− 1.07828i	0.842215	−	0.539141i	$-0.181251\pi$
$774$	−4734.26	−0.219857
$775$	0	0
$776$	−15748.8	−0.728541
$777$	− 6545.80i	− 0.302225i
$778$	5882.08i	0.271058i
$779$	−346.981	−0.0159588
$780$	0	0
$781$	2979.65	0.136517
$782$	5439.00i	0.248719i
$783$	− 4520.05i	− 0.206300i
$784$	−205.548	−0.00936352
$785$	0	0
$786$	−23127.5	−1.04953
$787$	− 13218.3i	− 0.598707i	−0.954142	−	0.299353i	$-0.903229\pi$
$787$	− 13218.3i	− 0.598707i	0.954142	−	0.299353i	$-0.0967710\pi$
$788$	45991.2i	2.07915i
$789$	−10930.6	−0.493206
$790$	0	0
$791$	−3920.00	−0.176206
$792$	− 11349.4i	− 0.509198i
$793$	− 6193.97i	− 0.277370i
$794$	9672.41	0.432319
$795$	0	0
$796$	10835.2	0.482466
$797$	− 1421.60i	− 0.0631815i	−0.999501	−	0.0315908i	$-0.989943\pi$
$797$	− 1421.60i	− 0.0631815i	0.999501	−	0.0315908i	$-0.0100573\pi$
$798$	− 2618.14i	− 0.116142i
$799$	12788.6	0.566242
$800$	0	0
$801$	12759.3	0.562831
$802$	− 51721.2i	− 2.27723i
$803$	61119.2i	2.68599i
$804$	−28469.7	−1.24882
$805$	0	0
$806$	−20353.6	−0.889484
$807$	− 22527.7i	− 0.982668i
$808$	− 4459.37i	− 0.194159i
$809$	−11669.3	−0.507131	−0.253566	−	0.967318i	$-0.581603\pi$
$809$	−11669.3	−0.507131	−0.253566	+	0.967318i	$0.581603\pi$
$810$	0	0
$811$	2165.42	0.0937587	0.0468793	−	0.998901i	$-0.485072\pi$
$811$	2165.42	0.0937587	0.0468793	+	0.998901i	$0.485072\pi$
$812$	15440.2i	0.667297i
$813$	− 25050.4i	− 1.08063i
$814$	−75945.1	−3.27012
$815$	0	0
$816$	774.046	0.0332072
$817$	3097.02i	0.132621i
$818$	− 31069.2i	− 1.32801i
$819$	−1234.95	−0.0526894
$820$	0	0
$821$	−37709.7	−1.60302	−0.801509	−	0.597982i	$-0.795969\pi$
$821$	−37709.7	−1.60302	−0.801509	+	0.597982i	$0.795969\pi$
$822$	− 36981.0i	− 1.56917i
$823$	20883.1i	0.884497i	0.896893	+	0.442248i	$0.145819\pi$
$823$	20883.1i	0.884497i	−0.896893	+	0.442248i	$0.854181\pi$
$824$	25634.3	1.08376
$825$	0	0
$826$	19505.4	0.821645
$827$	13018.1i	0.547379i	0.961818	+	0.273690i	$0.0882441\pi$
$827$	13018.1i	0.547379i	−0.961818	+	0.273690i	$0.911756\pi$
$828$	2278.71i	0.0956410i
$829$	−1309.94	−0.0548807	−0.0274404	−	0.999623i	$-0.508736\pi$
$829$	−1309.94	−0.0548807	−0.0274404	+	0.999623i	$0.508736\pi$
$830$	0	0
$831$	10079.1	0.420746
$832$	16104.1i	0.671045i
$833$	3013.87i	0.125359i
$834$	14248.4	0.591585
$835$	0	0
$836$	−18900.2	−0.781912
$837$	− 6092.23i	− 0.251587i
$838$	38884.2i	1.60290i
$839$	−35223.2	−1.44939	−0.724696	−	0.689069i	$-0.758020\pi$
$839$	−35223.2	−1.44939	−0.724696	+	0.689069i	$0.758020\pi$
$840$	0	0
$841$	3636.81	0.149117
$842$	10434.8i	0.427085i
$843$	19210.0i	0.784849i
$844$	30617.7	1.24870
$845$	0	0
$846$	8611.05	0.349946
$847$	− 10306.3i	− 0.418098i
$848$	953.920i	0.0386294i
$849$	17587.8	0.710967
$850$	0	0
$851$	5989.82	0.241279
$852$	2224.46i	0.0894470i
$853$	− 14907.6i	− 0.598390i	−0.954192	−	0.299195i	$-0.903282\pi$
$853$	− 14907.6i	− 0.598390i	0.954192	−	0.299195i	$-0.0967181\pi$
$854$	−10178.4	−0.407841
$855$	0	0
$856$	−37909.1	−1.51368
$857$	30377.1i	1.21081i	0.795919	+	0.605404i	$0.206988\pi$
$857$	30377.1i	1.21081i	−0.795919	+	0.605404i	$0.793012\pi$
$858$	14328.0i	0.570106i
$859$	−24031.5	−0.954535	−0.477267	−	0.878758i	$-0.658373\pi$
$859$	−24031.5	−0.954535	−0.477267	+	0.878758i	$0.658373\pi$
$860$	0	0
$861$	268.949	0.0106455
$862$	− 14600.4i	− 0.576903i
$863$	− 33363.7i	− 1.31601i	−0.753015	−	0.658004i	$-0.771401\pi$
$863$	− 33363.7i	− 1.31601i	0.753015	−	0.658004i	$-0.228599\pi$
$864$	−4623.37	−0.182049
$865$	0	0
$866$	62442.5	2.45021
$867$	3389.45i	0.132770i
$868$	20810.7i	0.813780i
$869$	61036.6	2.38265
$870$	0	0
$871$	14118.7	0.549246
$872$	40639.5i	1.57824i
$873$	5951.06i	0.230713i
$874$	2395.77	0.0927208
$875$	0	0
$876$	−45628.7	−1.75987
$877$	− 4392.19i	− 0.169115i	−0.996419	−	0.0845574i	$-0.973052\pi$
$877$	− 4392.19i	− 0.169115i	0.996419	−	0.0845574i	$-0.0269476\pi$
$878$	55320.3i	2.12639i
$879$	−11598.1	−0.445045
$880$	0	0
$881$	−8132.72	−0.311008	−0.155504	−	0.987835i	$-0.549700\pi$
$881$	−8132.72	−0.311008	−0.155504	+	0.987835i	$0.549700\pi$
$882$	2029.36i	0.0774739i
$883$	− 16582.9i	− 0.632003i	−0.948759	−	0.316002i	$-0.897659\pi$
$883$	− 16582.9i	− 0.632003i	0.948759	−	0.316002i	$-0.102341\pi$
$884$	−15886.0	−0.604415
$885$	0	0
$886$	−9536.40	−0.361605
$887$	9140.65i	0.346012i	0.984921	+	0.173006i	$0.0553481\pi$
$887$	9140.65i	0.346012i	−0.984921	+	0.173006i	$0.944652\pi$
$888$	− 22272.0i	− 0.841667i
$889$	−14692.7	−0.554305
$890$	0	0
$891$	−4288.67	−0.161252
$892$	33283.7i	1.24935i
$893$	− 5633.11i	− 0.211092i
$894$	16391.2	0.613203
$895$	0	0
$896$	16874.2	0.629159
$897$	− 1130.06i	− 0.0420642i
$898$	− 712.009i	− 0.0264589i
$899$	37773.9	1.40137
$900$	0	0
$901$	13987.0	0.517173
$902$	− 3120.38i	− 0.115186i
$903$	− 2400.54i	− 0.0884662i
$904$	−13337.8	−0.490717
$905$	0	0
$906$	1911.80	0.0701051
$907$	− 25359.3i	− 0.928382i	−0.885735	−	0.464191i	$-0.846345\pi$
$907$	− 25359.3i	− 0.928382i	0.885735	−	0.464191i	$-0.153655\pi$
$908$	51702.5i	1.88966i
$909$	−1685.08	−0.0614859
$910$	0	0
$911$	33308.6	1.21138	0.605688	−	0.795702i	$-0.292898\pi$
$911$	33308.6	1.21138	0.605688	+	0.795702i	$0.292898\pi$
$912$	− 340.951i	− 0.0123794i
$913$	− 36669.7i	− 1.32923i
$914$	20004.9	0.723963
$915$	0	0
$916$	47321.4	1.70692
$917$	− 11727.0i	− 0.422311i
$918$	− 7642.09i	− 0.274757i
$919$	5827.47	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$919$	5827.47	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$920$	0	0
$921$	21254.4	0.760431
$922$	− 25358.9i	− 0.905805i
$923$	− 1103.15i	− 0.0393400i
$924$	14649.8	0.521584
$925$	0	0
$926$	−42180.0	−1.49689
$927$	− 9686.56i	− 0.343202i
$928$	− 28666.5i	− 1.01403i
$929$	−19224.3	−0.678934	−0.339467	−	0.940618i	$-0.610247\pi$
$929$	−19224.3	−0.678934	−0.339467	+	0.940618i	$0.610247\pi$
$930$	0	0
$931$	1327.55	0.0467332
$932$	− 65319.8i	− 2.29573i
$933$	− 31849.7i	− 1.11759i
$934$	41456.5	1.45235
$935$	0	0
$936$	−4201.91	−0.146735
$937$	37202.8i	1.29708i	0.761181	+	0.648539i	$0.224620\pi$
$937$	37202.8i	1.29708i	−0.761181	+	0.648539i	$0.775380\pi$
$938$	− 23200.8i	− 0.807605i
$939$	21743.4	0.755663
$940$	0	0
$941$	43155.8	1.49505	0.747523	−	0.664236i	$-0.231243\pi$
$941$	43155.8	1.49505	0.747523	+	0.664236i	$0.231243\pi$
$942$	6096.01i	0.210848i
$943$	246.106i	0.00849874i
$944$	2540.12	0.0875781
$945$	0	0
$946$	−27851.4	−0.957215
$947$	1442.59i	0.0495014i	0.999694	+	0.0247507i	$0.00787919\pi$
$947$	1442.59i	0.0495014i	−0.999694	+	0.0247507i	$0.992121\pi$
$948$	45567.0i	1.56113i
$949$	22628.2	0.774016
$950$	0	0
$951$	18924.7	0.645295
$952$	10254.7i	0.349113i
$953$	2964.70i	0.100773i	0.998730	+	0.0503863i	$0.0160452\pi$
$953$	2964.70i	0.100773i	−0.998730	+	0.0503863i	$0.983955\pi$
$954$	9417.96	0.319620
$955$	0	0
$956$	−74621.9	−2.52452
$957$	− 26591.2i	− 0.898193i
$958$	− 46606.7i	− 1.57181i
$959$	18751.5	0.631404
$960$	0	0
$961$	21121.5	0.708990
$962$	28117.2i	0.942343i
$963$	14324.9i	0.479349i
$964$	29601.2	0.988994
$965$	0	0
$966$	−1856.99	−0.0618506
$967$	59088.1i	1.96499i	0.186292	+	0.982494i	$0.440353\pi$
$967$	59088.1i	1.96499i	−0.186292	+	0.982494i	$0.559647\pi$
$968$	− 35067.1i	− 1.16436i
$969$	−4999.24	−0.165737
$970$	0	0
$971$	−6678.75	−0.220732	−0.110366	−	0.993891i	$-0.535202\pi$
$971$	−6678.75	−0.220732	−0.110366	+	0.993891i	$0.535202\pi$
$972$	− 3201.71i	− 0.105653i
$973$	7224.76i	0.238042i
$974$	−4392.07	−0.144488
$975$	0	0
$976$	−1325.49	−0.0434713
$977$	− 46454.6i	− 1.52120i	−0.649220	−	0.760600i	$-0.724905\pi$
$977$	− 46454.6i	− 1.52120i	0.649220	−	0.760600i	$-0.275095\pi$
$978$	− 29220.3i	− 0.955379i
$979$	75062.2	2.45046
$980$	0	0
$981$	15356.6	0.499795
$982$	33759.2i	1.09705i
$983$	− 3154.80i	− 0.102363i	−0.998689	−	0.0511814i	$-0.983701\pi$
$983$	− 3154.80i	− 0.102363i	0.998689	−	0.0511814i	$-0.0162987\pi$
$984$	915.098	0.0296466
$985$	0	0
$986$	47383.5	1.53042
$987$	4366.30i	0.140811i
$988$	6997.44i	0.225322i
$989$	2196.65	0.0706262
$990$	0	0
$991$	36207.7	1.16062	0.580311	−	0.814395i	$-0.302931\pi$
$991$	36207.7	1.16062	0.580311	+	0.814395i	$0.302931\pi$
$992$	− 38637.3i	− 1.23663i
$993$	19968.8i	0.638157i
$994$	−1812.78	−0.0578450
$995$	0	0
$996$	27375.9	0.870922
$997$	− 18452.9i	− 0.586166i	−0.956087	−	0.293083i	$-0.905319\pi$
$997$	− 18452.9i	− 0.586166i	0.956087	−	0.293083i	$-0.0946813\pi$
$998$	− 76263.9i	− 2.41893i
$999$	−8416.02	−0.266538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.n.274.7		8
5.2	odd	4		525.4.a.u.1.1	yes	4
5.3	odd	4		525.4.a.t.1.4	✓	4
5.4	even	2	inner	525.4.d.n.274.2		8
15.2	even	4		1575.4.a.bk.1.4		4
15.8	even	4		1575.4.a.bj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.t.1.4	✓	4	5.3	odd	4
525.4.a.u.1.1	yes	4	5.2	odd	4
525.4.d.n.274.2		8	5.4	even	2	inner
525.4.d.n.274.7		8	1.1	even	1	trivial
1575.4.a.bj.1.1		4	15.8	even	4
1575.4.a.bk.1.4		4	15.2	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.60171i q^{2} +3.00000i q^{3} -13.1758 q^{4} -13.8051 q^{6} -7.00000i q^{7} -23.8174i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.60171i q^{2} +3.00000i q^{3} -13.1758 q^{4} -13.8051 q^{6} -7.00000i q^{7} -23.8174i q^{8} -9.00000 q^{9} -52.9465 q^{11} -39.5273i q^{12} +19.6024i q^{13} +32.2120 q^{14} +4.19486 q^{16} -61.5076i q^{17} -41.4154i q^{18} -27.0928 q^{19} +21.0000 q^{21} -243.645i q^{22} +19.2163i q^{23} +71.4523 q^{24} -90.2046 q^{26} -27.0000i q^{27} +92.2304i q^{28} +167.409 q^{29} +225.638 q^{31} -171.236i q^{32} -158.839i q^{33} +283.040 q^{34} +118.582 q^{36} -311.705i q^{37} -124.673i q^{38} -58.8071 q^{39} +12.8071 q^{41} +96.6360i q^{42} -114.311i q^{43} +697.611 q^{44} -88.4281 q^{46} +207.919i q^{47} +12.5846i q^{48} -49.0000 q^{49} +184.523 q^{51} -258.277i q^{52} +227.402i q^{53} +124.246 q^{54} -166.722 q^{56} -81.2784i q^{57} +770.369i q^{58} +605.531 q^{59} -315.981 q^{61} +1038.32i q^{62} +63.0000i q^{63} +821.538 q^{64} +730.934 q^{66} -720.254i q^{67} +810.410i q^{68} -57.6490 q^{69} -56.2766 q^{71} +214.357i q^{72} -1154.36i q^{73} +1434.38 q^{74} +356.969 q^{76} +370.625i q^{77} -270.614i q^{78} -1152.80 q^{79} +81.0000 q^{81} +58.9347i q^{82} +692.581i q^{83} -276.691 q^{84} +526.029 q^{86} +502.227i q^{87} +1261.05i q^{88} -1417.70 q^{89} +137.217 q^{91} -253.190i q^{92} +676.914i q^{93} -956.783 q^{94} +513.708 q^{96} -661.229i q^{97} -225.484i q^{98} +476.518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 - 72 * q^9	\( 8 q - 32 q^{4} - 72 q^{9} + 42 q^{11} + 144 q^{16} - 144 q^{19} + 168 q^{21} - 54 q^{24} + 258 q^{26} + 480 q^{29} + 702 q^{31} + 570 q^{34} + 288 q^{36} - 30 q^{39} + 762 q^{41} + 1950 q^{44} + 1100 q^{46} - 392 q^{49} + 594 q^{51} + 126 q^{56} + 1710 q^{59} + 1374 q^{61} + 2570 q^{64} + 1326 q^{66} - 612 q^{69} - 1362 q^{71} + 6738 q^{74} + 3820 q^{76} - 690 q^{79} + 648 q^{81} - 672 q^{84} - 1080 q^{86} + 396 q^{89} + 70 q^{91} + 3464 q^{94} + 432 q^{96} - 378 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 - 72 * q^9 + 42 * q^11 + 144 * q^16 - 144 * q^19 + 168 * q^21 - 54 * q^24 + 258 * q^26 + 480 * q^29 + 702 * q^31 + 570 * q^34 + 288 * q^36 - 30 * q^39 + 762 * q^41 + 1950 * q^44 + 1100 * q^46 - 392 * q^49 + 594 * q^51 + 126 * q^56 + 1710 * q^59 + 1374 * q^61 + 2570 * q^64 + 1326 * q^66 - 612 * q^69 - 1362 * q^71 + 6738 * q^74 + 3820 * q^76 - 690 * q^79 + 648 * q^81 - 672 * q^84 - 1080 * q^86 + 396 * q^89 + 70 * q^91 + 3464 * q^94 + 432 * q^96 - 378 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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