LMFDB - Embedded newform 750.4.c.e.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,4,Mod(499,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("750.499");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	750.c (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:	$44.2514325043$
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} + 99x^{6} + 3541x^{4} + 54684x^{2} + 309136 $ x^8 + 99x^6 + 3541x^4 + 54684*x^2 + 309136
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			499.2
Root			$4.58789i$ of defining polynomial
Character	$\chi$	$=$	750.499
Dual form			750.4.c.e.499.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} -6.00000 q^{6} +1.17164i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} -6.00000 q^{6} +1.17164i q^{7} +8.00000i q^{8} -9.00000 q^{9} +49.8906 q^{11} +12.0000i q^{12} -85.7043i q^{13} +2.34328 q^{14} +16.0000 q^{16} +112.699i q^{17} +18.0000i q^{18} +71.6223 q^{19} +3.51492 q^{21} -99.7812i q^{22} +212.980i q^{23} +24.0000 q^{24} -171.409 q^{26} +27.0000i q^{27} -4.68656i q^{28} +99.4253 q^{29} -18.4385 q^{31} -32.0000i q^{32} -149.672i q^{33} +225.398 q^{34} +36.0000 q^{36} +215.788i q^{37} -143.245i q^{38} -257.113 q^{39} +367.036 q^{41} -7.02985i q^{42} -104.120i q^{43} -199.562 q^{44} +425.961 q^{46} -410.887i q^{47} -48.0000i q^{48} +341.627 q^{49} +338.097 q^{51} +342.817i q^{52} -650.147i q^{53} +54.0000 q^{54} -9.37313 q^{56} -214.867i q^{57} -198.851i q^{58} +660.030 q^{59} +50.8175 q^{61} +36.8770i q^{62} -10.5448i q^{63} -64.0000 q^{64} -299.344 q^{66} +431.856i q^{67} -450.797i q^{68} +638.941 q^{69} -1129.02 q^{71} -72.0000i q^{72} -1174.32i q^{73} +431.576 q^{74} -286.489 q^{76} +58.4539i q^{77} +514.226i q^{78} -778.556 q^{79} +81.0000 q^{81} -734.072i q^{82} -838.296i q^{83} -14.0597 q^{84} -208.241 q^{86} -298.276i q^{87} +399.125i q^{88} +350.223 q^{89} +100.415 q^{91} -851.922i q^{92} +55.3155i q^{93} -821.774 q^{94} -96.0000 q^{96} +565.871i q^{97} -683.255i q^{98} -449.015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} - 48 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 - 48 * q^6 - 72 * q^9	$ 8 q - 32 q^{4} - 48 q^{6} - 72 q^{9} - 30 q^{11} + 12 q^{14} + 128 q^{16} + 128 q^{19} + 18 q^{21} + 192 q^{24} - 516 q^{26} + 252 q^{29} + 174 q^{31} + 52 q^{34} + 288 q^{36} - 774 q^{39} - 78 q^{41} + 120 q^{44} - 520 q^{46} - 238 q^{49} + 78 q^{51} + 432 q^{54} - 48 q^{56} + 1530 q^{59} + 1310 q^{61} - 512 q^{64} + 180 q^{66} - 780 q^{69} - 3780 q^{71} + 3924 q^{74} - 512 q^{76} + 1974 q^{79} + 648 q^{81} - 72 q^{84} - 3408 q^{86} + 2814 q^{89} - 3884 q^{91} + 520 q^{94} - 768 q^{96} + 270 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 - 48 * q^6 - 72 * q^9 - 30 * q^11 + 12 * q^14 + 128 * q^16 + 128 * q^19 + 18 * q^21 + 192 * q^24 - 516 * q^26 + 252 * q^29 + 174 * q^31 + 52 * q^34 + 288 * q^36 - 774 * q^39 - 78 * q^41 + 120 * q^44 - 520 * q^46 - 238 * q^49 + 78 * q^51 + 432 * q^54 - 48 * q^56 + 1530 * q^59 + 1310 * q^61 - 512 * q^64 + 180 * q^66 - 780 * q^69 - 3780 * q^71 + 3924 * q^74 - 512 * q^76 + 1974 * q^79 + 648 * q^81 - 72 * q^84 - 3408 * q^86 + 2814 * q^89 - 3884 * q^91 + 520 * q^94 - 768 * q^96 + 270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	1.17164i	0.0632627i	0.999500	+	0.0316313i	$0.0100702\pi$
$7$	1.17164i	0.0632627i	−0.999500	+	0.0316313i	$0.989930\pi$
$8$	8.00000i	0.353553i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	49.8906	1.36751	0.683754	−	0.729713i	$-0.260346\pi$
$11$	49.8906	1.36751	0.683754	+	0.729713i	$0.260346\pi$
$12$	12.0000i	0.288675i
$13$	− 85.7043i	− 1.82847i	−0.405185	−	0.914235i	$-0.632793\pi$
$13$	− 85.7043i	− 1.82847i	0.405185	−	0.914235i	$-0.367207\pi$
$14$	2.34328	0.0447335
$15$	0	0
$16$	16.0000	0.250000
$17$	112.699i	1.60786i	0.594726	+	0.803928i	$0.297260\pi$
$17$	112.699i	1.60786i	−0.594726	+	0.803928i	$0.702740\pi$
$18$	18.0000i	0.235702i
$19$	71.6223	0.864804	0.432402	−	0.901681i	$-0.357666\pi$
$19$	71.6223	0.864804	0.432402	+	0.901681i	$0.357666\pi$
$20$	0	0
$21$	3.51492	0.0365247
$22$	− 99.7812i	− 0.966974i
$23$	212.980i	1.93085i	0.260685	+	0.965424i	$0.416051\pi$
$23$	212.980i	1.93085i	−0.260685	+	0.965424i	$0.583949\pi$
$24$	24.0000	0.204124
$25$	0	0
$26$	−171.409	−1.29292
$27$	27.0000i	0.192450i
$28$	− 4.68656i	− 0.0316313i
$29$	99.4253	0.636649	0.318324	−	0.947982i	$-0.396880\pi$
$29$	99.4253	0.636649	0.318324	+	0.947982i	$0.396880\pi$
$30$	0	0
$31$	−18.4385	−0.106828	−0.0534138	−	0.998572i	$-0.517010\pi$
$31$	−18.4385	−0.106828	−0.0534138	+	0.998572i	$0.517010\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 149.672i	− 0.789531i
$34$	225.398	1.13693
$35$	0	0
$36$	36.0000	0.166667
$37$	215.788i	0.958794i	0.877598	+	0.479397i	$0.159145\pi$
$37$	215.788i	0.958794i	−0.877598	+	0.479397i	$0.840855\pi$
$38$	− 143.245i	− 0.611509i
$39$	−257.113	−1.05567
$40$	0	0
$41$	367.036	1.39808	0.699042	−	0.715081i	$-0.253610\pi$
$41$	367.036	1.39808	0.699042	+	0.715081i	$0.253610\pi$
$42$	− 7.02985i	− 0.0258269i
$43$	− 104.120i	− 0.369261i	−0.982808	−	0.184630i	$-0.940891\pi$
$43$	− 104.120i	− 0.369261i	0.982808	−	0.184630i	$-0.0591088\pi$
$44$	−199.562	−0.683754
$45$	0	0
$46$	425.961	1.36532
$47$	− 410.887i	− 1.27519i	−0.770371	−	0.637596i	$-0.779929\pi$
$47$	− 410.887i	− 1.27519i	0.770371	−	0.637596i	$-0.220071\pi$
$48$	− 48.0000i	− 0.144338i
$49$	341.627	0.995998
$50$	0	0
$51$	338.097	0.928296
$52$	342.817i	0.914235i
$53$	− 650.147i	− 1.68499i	−0.538702	−	0.842496i	$-0.681085\pi$
$53$	− 650.147i	− 1.68499i	0.538702	−	0.842496i	$-0.318915\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	−9.37313	−0.0223667
$57$	− 214.867i	− 0.499295i
$58$	− 198.851i	− 0.450179i
$59$	660.030	1.45642	0.728208	−	0.685356i	$-0.240353\pi$
$59$	660.030	1.45642	0.728208	+	0.685356i	$0.240353\pi$
$60$	0	0
$61$	50.8175	0.106664	0.0533321	−	0.998577i	$-0.483016\pi$
$61$	50.8175	0.106664	0.0533321	+	0.998577i	$0.483016\pi$
$62$	36.8770i	0.0755385i
$63$	− 10.5448i	− 0.0210876i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−299.344	−0.558283
$67$	431.856i	0.787458i	0.919227	+	0.393729i	$0.128815\pi$
$67$	431.856i	0.787458i	−0.919227	+	0.393729i	$0.871185\pi$
$68$	− 450.797i	− 0.803928i
$69$	638.941	1.11478
$70$	0	0
$71$	−1129.02	−1.88718	−0.943591	−	0.331114i	$-0.892575\pi$
$71$	−1129.02	−1.88718	−0.943591	+	0.331114i	$0.892575\pi$
$72$	− 72.0000i	− 0.117851i
$73$	− 1174.32i	− 1.88279i	−0.337303	−	0.941396i	$-0.609515\pi$
$73$	− 1174.32i	− 1.88279i	0.337303	−	0.941396i	$-0.390485\pi$
$74$	431.576	0.677969
$75$	0	0
$76$	−286.489	−0.432402
$77$	58.4539i	0.0865122i
$78$	514.226i	0.746470i
$79$	−778.556	−1.10879	−0.554395	−	0.832254i	$-0.687050\pi$
$79$	−778.556	−1.10879	−0.554395	+	0.832254i	$0.687050\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 734.072i	− 0.988594i
$83$	− 838.296i	− 1.10861i	−0.832312	−	0.554307i	$-0.812983\pi$
$83$	− 838.296i	− 1.10861i	0.832312	−	0.554307i	$-0.187017\pi$
$84$	−14.0597	−0.0182624
$85$	0	0
$86$	−208.241	−0.261107
$87$	− 298.276i	− 0.367569i
$88$	399.125i	0.483487i
$89$	350.223	0.417118	0.208559	−	0.978010i	$-0.433123\pi$
$89$	350.223	0.417118	0.208559	+	0.978010i	$0.433123\pi$
$90$	0	0
$91$	100.415	0.115674
$92$	− 851.922i	− 0.965424i
$93$	55.3155i	0.0616769i
$94$	−821.774	−0.901697
$95$	0	0
$96$	−96.0000	−0.102062
$97$	565.871i	0.592325i	0.955138	+	0.296162i	$0.0957069\pi$
$97$	565.871i	0.592325i	−0.955138	+	0.296162i	$0.904293\pi$
$98$	− 683.255i	− 0.704277i
$99$	−449.015	−0.455836
$100$	0	0
$101$	368.459	0.363001	0.181500	−	0.983391i	$-0.441905\pi$
$101$	368.459	0.363001	0.181500	+	0.983391i	$0.441905\pi$
$102$	− 676.195i	− 0.656405i
$103$	− 54.7994i	− 0.0524228i	−0.999656	−	0.0262114i	$-0.991656\pi$
$103$	− 54.7994i	− 0.0524228i	0.999656	−	0.0262114i	$-0.00834430\pi$
$104$	685.635	0.646462
$105$	0	0
$106$	−1300.29	−1.19147
$107$	1253.09i	1.13215i	0.824352	+	0.566077i	$0.191540\pi$
$107$	1253.09i	1.13215i	−0.824352	+	0.566077i	$0.808460\pi$
$108$	− 108.000i	− 0.0962250i
$109$	−83.5093	−0.0733830	−0.0366915	−	0.999327i	$-0.511682\pi$
$109$	−83.5093	−0.0733830	−0.0366915	+	0.999327i	$0.511682\pi$
$110$	0	0
$111$	647.365	0.553560
$112$	18.7463i	0.0158157i
$113$	523.142i	0.435513i	0.976003	+	0.217757i	$0.0698739\pi$
$113$	523.142i	0.435513i	−0.976003	+	0.217757i	$0.930126\pi$
$114$	−429.734	−0.353055
$115$	0	0
$116$	−397.701	−0.318324
$117$	771.339i	0.609490i
$118$	− 1320.06i	− 1.02984i
$119$	−132.043	−0.101717
$120$	0	0
$121$	1158.07	0.870077
$122$	− 101.635i	− 0.0754229i
$123$	− 1101.11i	− 0.807184i
$124$	73.7540	0.0534138
$125$	0	0
$126$	−21.0895	−0.0149112
$127$	− 1010.40i	− 0.705969i	−0.935629	−	0.352985i	$-0.885167\pi$
$127$	− 1010.40i	− 0.705969i	0.935629	−	0.352985i	$-0.114833\pi$
$128$	128.000i	0.0883883i
$129$	−312.361	−0.213193
$130$	0	0
$131$	1464.73	0.976900	0.488450	−	0.872592i	$-0.337562\pi$
$131$	1464.73	0.976900	0.488450	+	0.872592i	$0.337562\pi$
$132$	598.687i	0.394765i
$133$	83.9156i	0.0547098i
$134$	863.713	0.556817
$135$	0	0
$136$	−901.593	−0.568463
$137$	− 2638.35i	− 1.64532i	−0.568531	−	0.822662i	$-0.692488\pi$
$137$	− 2638.35i	− 1.64532i	0.568531	−	0.822662i	$-0.307512\pi$
$138$	− 1277.88i	− 0.788265i
$139$	480.546	0.293233	0.146616	−	0.989193i	$-0.453162\pi$
$139$	480.546	0.293233	0.146616	+	0.989193i	$0.453162\pi$
$140$	0	0
$141$	−1232.66	−0.736232
$142$	2258.04i	1.33444i
$143$	− 4275.84i	− 2.50045i
$144$	−144.000	−0.0833333
$145$	0	0
$146$	−2348.64	−1.33134
$147$	− 1024.88i	− 0.575040i
$148$	− 863.153i	− 0.479397i
$149$	−442.453	−0.243269	−0.121635	−	0.992575i	$-0.538814\pi$
$149$	−442.453	−0.243269	−0.121635	+	0.992575i	$0.538814\pi$
$150$	0	0
$151$	2565.65	1.38271	0.691356	−	0.722515i	$-0.257014\pi$
$151$	2565.65	1.38271	0.691356	+	0.722515i	$0.257014\pi$
$152$	572.978i	0.305754i
$153$	− 1014.29i	− 0.535952i
$154$	116.908	0.0611733
$155$	0	0
$156$	1028.45	0.527834
$157$	1868.68i	0.949916i	0.880008	+	0.474958i	$0.157537\pi$
$157$	1868.68i	0.949916i	−0.880008	+	0.474958i	$0.842463\pi$
$158$	1557.11i	0.784033i
$159$	−1950.44	−0.972831
$160$	0	0
$161$	−249.537	−0.122151
$162$	− 162.000i	− 0.0785674i
$163$	− 1213.96i	− 0.583341i	−0.956519	−	0.291670i	$-0.905789\pi$
$163$	− 1213.96i	− 0.583341i	0.956519	−	0.291670i	$-0.0942110\pi$
$164$	−1468.14	−0.699042
$165$	0	0
$166$	−1676.59	−0.783908
$167$	1291.33i	0.598360i	0.954197	+	0.299180i	$0.0967131\pi$
$167$	1291.33i	0.598360i	−0.954197	+	0.299180i	$0.903287\pi$
$168$	28.1194i	0.0129134i
$169$	−5148.23	−2.34330
$170$	0	0
$171$	−644.601	−0.288268
$172$	416.481i	0.184630i
$173$	1210.43i	0.531951i	0.963980	+	0.265976i	$0.0856940\pi$
$173$	1210.43i	0.531951i	−0.963980	+	0.265976i	$0.914306\pi$
$174$	−596.552	−0.259911
$175$	0	0
$176$	798.250	0.341877
$177$	− 1980.09i	− 0.840863i
$178$	− 700.445i	− 0.294947i
$179$	1499.92	0.626310	0.313155	−	0.949702i	$-0.398614\pi$
$179$	1499.92	0.626310	0.313155	+	0.949702i	$0.398614\pi$
$180$	0	0
$181$	−683.859	−0.280833	−0.140417	−	0.990092i	$-0.544844\pi$
$181$	−683.859	−0.280833	−0.140417	+	0.990092i	$0.544844\pi$
$182$	− 200.829i	− 0.0817938i
$183$	− 152.452i	− 0.0615826i
$184$	−1703.84	−0.682658
$185$	0	0
$186$	110.631	0.0436122
$187$	5622.63i	2.19876i
$188$	1643.55i	0.637596i
$189$	−31.6343	−0.0121749
$190$	0	0
$191$	−1837.34	−0.696048	−0.348024	−	0.937486i	$-0.613147\pi$
$191$	−1837.34	−0.696048	−0.348024	+	0.937486i	$0.613147\pi$
$192$	192.000i	0.0721688i
$193$	− 1110.75i	− 0.414266i	−0.978313	−	0.207133i	$-0.933587\pi$
$193$	− 1110.75i	− 0.414266i	0.978313	−	0.207133i	$-0.0664132\pi$
$194$	1131.74	0.418837
$195$	0	0
$196$	−1366.51	−0.497999
$197$	− 3267.34i	− 1.18167i	−0.806794	−	0.590833i	$-0.798799\pi$
$197$	− 3267.34i	− 1.18167i	0.806794	−	0.590833i	$-0.201201\pi$
$198$	898.031i	0.322325i
$199$	4232.28	1.50763	0.753815	−	0.657087i	$-0.228212\pi$
$199$	4232.28	1.50763	0.753815	+	0.657087i	$0.228212\pi$
$200$	0	0
$201$	1295.57	0.454639
$202$	− 736.919i	− 0.256680i
$203$	116.491i	0.0402761i
$204$	−1352.39	−0.464148
$205$	0	0
$206$	−109.599	−0.0370685
$207$	− 1916.82i	− 0.643616i
$208$	− 1371.27i	− 0.457117i
$209$	3573.28	1.18263
$210$	0	0
$211$	3245.46	1.05889	0.529447	−	0.848343i	$-0.322399\pi$
$211$	3245.46	1.05889	0.529447	+	0.848343i	$0.322399\pi$
$212$	2600.59i	0.842496i
$213$	3387.06i	1.08956i
$214$	2506.17	0.800554
$215$	0	0
$216$	−216.000	−0.0680414
$217$	− 21.6033i	− 0.00675819i
$218$	167.019i	0.0518896i
$219$	−3522.96	−1.08703
$220$	0	0
$221$	9658.81	2.93992
$222$	− 1294.73i	− 0.391426i
$223$	1128.12i	0.338763i	0.985551	+	0.169382i	$0.0541771\pi$
$223$	1128.12i	0.338763i	−0.985551	+	0.169382i	$0.945823\pi$
$224$	37.4925	0.0111834
$225$	0	0
$226$	1046.28	0.307955
$227$	135.889i	0.0397325i	0.999803	+	0.0198663i	$0.00632404\pi$
$227$	135.889i	0.0397325i	−0.999803	+	0.0198663i	$0.993676\pi$
$228$	859.467i	0.249647i
$229$	−5271.97	−1.52132	−0.760659	−	0.649151i	$-0.775124\pi$
$229$	−5271.97	−1.52132	−0.760659	+	0.649151i	$0.775124\pi$
$230$	0	0
$231$	175.362	0.0499478
$232$	795.403i	0.225089i
$233$	− 2990.28i	− 0.840771i	−0.907346	−	0.420385i	$-0.861895\pi$
$233$	− 2990.28i	− 0.840771i	0.907346	−	0.420385i	$-0.138105\pi$
$234$	1542.68	0.430974
$235$	0	0
$236$	−2640.12	−0.728208
$237$	2335.67i	0.640160i
$238$	264.086i	0.0719250i
$239$	1002.48	0.271317	0.135658	−	0.990756i	$-0.456685\pi$
$239$	1002.48	0.271317	0.135658	+	0.990756i	$0.456685\pi$
$240$	0	0
$241$	332.728	0.0889332	0.0444666	−	0.999011i	$-0.485841\pi$
$241$	332.728	0.0889332	0.0444666	+	0.999011i	$0.485841\pi$
$242$	− 2316.14i	− 0.615237i
$243$	− 243.000i	− 0.0641500i
$244$	−203.270	−0.0533321
$245$	0	0
$246$	−2202.22	−0.570765
$247$	− 6138.34i	− 1.58127i
$248$	− 147.508i	− 0.0377692i
$249$	−2514.89	−0.640058
$250$	0	0
$251$	5348.48	1.34499	0.672497	−	0.740100i	$-0.265222\pi$
$251$	5348.48	1.34499	0.672497	+	0.740100i	$0.265222\pi$
$252$	42.1791i	0.0105438i
$253$	10625.7i	2.64045i
$254$	−2020.79	−0.499196
$255$	0	0
$256$	256.000	0.0625000
$257$	− 3154.96i	− 0.765763i	−0.923797	−	0.382882i	$-0.874932\pi$
$257$	− 3154.96i	− 0.765763i	0.923797	−	0.382882i	$-0.125068\pi$
$258$	624.722i	0.150750i
$259$	−252.826	−0.0606558
$260$	0	0
$261$	−894.828	−0.212216
$262$	− 2929.46i	− 0.690773i
$263$	− 261.673i	− 0.0613516i	−0.999529	−	0.0306758i	$-0.990234\pi$
$263$	− 261.673i	− 0.0613516i	0.999529	−	0.0306758i	$-0.00976594\pi$
$264$	1197.37	0.279141
$265$	0	0
$266$	167.831	0.0386857
$267$	− 1050.67i	− 0.240823i
$268$	− 1727.43i	− 0.393729i
$269$	6412.33	1.45341	0.726704	−	0.686951i	$-0.241051\pi$
$269$	6412.33	1.45341	0.726704	+	0.686951i	$0.241051\pi$
$270$	0	0
$271$	−2283.52	−0.511859	−0.255929	−	0.966695i	$-0.582381\pi$
$271$	−2283.52	−0.511859	−0.255929	+	0.966695i	$0.582381\pi$
$272$	1803.19i	0.401964i
$273$	− 301.244i	− 0.0667843i
$274$	−5276.70	−1.16342
$275$	0	0
$276$	−2555.77	−0.557388
$277$	4856.57i	1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$277$	4856.57i	1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$278$	− 961.091i	− 0.207347i
$279$	165.947	0.0356092
$280$	0	0
$281$	−1696.24	−0.360103	−0.180051	−	0.983657i	$-0.557626\pi$
$281$	−1696.24	−0.360103	−0.180051	+	0.983657i	$0.557626\pi$
$282$	2465.32i	0.520595i
$283$	1340.52i	0.281574i	0.990040	+	0.140787i	$0.0449632\pi$
$283$	1340.52i	0.281574i	−0.990040	+	0.140787i	$0.955037\pi$
$284$	4516.08	0.943591
$285$	0	0
$286$	−8551.68	−1.76808
$287$	430.035i	0.0884465i
$288$	288.000i	0.0589256i
$289$	−7788.10	−1.58520
$290$	0	0
$291$	1697.61	0.341979
$292$	4697.28i	0.941396i
$293$	4196.78i	0.836787i	0.908266	+	0.418393i	$0.137407\pi$
$293$	4196.78i	0.836787i	−0.908266	+	0.418393i	$0.862593\pi$
$294$	−2049.76	−0.406614
$295$	0	0
$296$	−1726.31	−0.338985
$297$	1347.05i	0.263177i
$298$	884.905i	0.172017i
$299$	18253.3	3.53050
$300$	0	0
$301$	121.992	0.0233604
$302$	− 5131.29i	− 0.977725i
$303$	− 1105.38i	− 0.209579i
$304$	1145.96	0.216201
$305$	0	0
$306$	−2028.58	−0.378975
$307$	− 7126.26i	− 1.32481i	−0.749145	−	0.662406i	$-0.769535\pi$
$307$	− 7126.26i	− 1.32481i	0.749145	−	0.662406i	$-0.230465\pi$
$308$	− 233.816i	− 0.0432561i
$309$	−164.398	−0.0302663
$310$	0	0
$311$	−2132.43	−0.388808	−0.194404	−	0.980922i	$-0.562277\pi$
$311$	−2132.43	−0.388808	−0.194404	+	0.980922i	$0.562277\pi$
$312$	− 2056.90i	− 0.373235i
$313$	6460.50i	1.16667i	0.812230	+	0.583337i	$0.198253\pi$
$313$	6460.50i	1.16667i	−0.812230	+	0.583337i	$0.801747\pi$
$314$	3737.36	0.671692
$315$	0	0
$316$	3114.23	0.554395
$317$	6402.20i	1.13433i	0.823603	+	0.567166i	$0.191960\pi$
$317$	6402.20i	1.13433i	−0.823603	+	0.567166i	$0.808040\pi$
$318$	3900.88i	0.687895i
$319$	4960.39	0.870622
$320$	0	0
$321$	3759.26	0.653650
$322$	499.073i	0.0863735i
$323$	8071.77i	1.39048i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	−2427.92	−0.412484
$327$	250.528i	0.0423677i
$328$	2936.29i	0.494297i
$329$	481.412	0.0806720
$330$	0	0
$331$	7771.13	1.29045	0.645226	−	0.763991i	$-0.276763\pi$
$331$	7771.13	1.29045	0.645226	+	0.763991i	$0.276763\pi$
$332$	3353.18i	0.554307i
$333$	− 1942.09i	− 0.319598i
$334$	2582.66	0.423105
$335$	0	0
$336$	56.2388	0.00913118
$337$	− 2272.52i	− 0.367335i	−0.982988	−	0.183668i	$-0.941203\pi$
$337$	− 2272.52i	− 0.367335i	0.982988	−	0.183668i	$-0.0587970\pi$
$338$	10296.5i	1.65696i
$339$	1569.42	0.251444
$340$	0	0
$341$	−919.908	−0.146087
$342$	1289.20i	0.203836i
$343$	802.137i	0.126272i
$344$	832.963	0.130553
$345$	0	0
$346$	2420.87	0.376146
$347$	− 1975.56i	− 0.305630i	−0.988255	−	0.152815i	$-0.951166\pi$
$347$	− 1975.56i	− 0.305630i	0.988255	−	0.152815i	$-0.0488339\pi$
$348$	1193.10i	0.183785i
$349$	−3714.14	−0.569666	−0.284833	−	0.958577i	$-0.591938\pi$
$349$	−3714.14	−0.569666	−0.284833	+	0.958577i	$0.591938\pi$
$350$	0	0
$351$	2314.02	0.351889
$352$	− 1596.50i	− 0.241743i
$353$	8006.05i	1.20714i	0.797312	+	0.603568i	$0.206255\pi$
$353$	8006.05i	1.20714i	−0.797312	+	0.603568i	$0.793745\pi$
$354$	−3960.18	−0.594580
$355$	0	0
$356$	−1400.89	−0.208559
$357$	396.129i	0.0587265i
$358$	− 2999.85i	− 0.442868i
$359$	−2051.14	−0.301546	−0.150773	−	0.988568i	$-0.548176\pi$
$359$	−2051.14	−0.301546	−0.150773	+	0.988568i	$0.548176\pi$
$360$	0	0
$361$	−1729.25	−0.252114
$362$	1367.72i	0.198579i
$363$	− 3474.22i	− 0.502339i
$364$	−401.659	−0.0578369
$365$	0	0
$366$	−304.905	−0.0435454
$367$	3184.85i	0.452991i	0.974012	+	0.226496i	$0.0727269\pi$
$367$	3184.85i	0.452991i	−0.974012	+	0.226496i	$0.927273\pi$
$368$	3407.69i	0.482712i
$369$	−3303.33	−0.466028
$370$	0	0
$371$	761.739	0.106597
$372$	− 221.262i	− 0.0308384i
$373$	909.773i	0.126290i	0.998004	+	0.0631451i	$0.0201131\pi$
$373$	909.773i	0.126290i	−0.998004	+	0.0631451i	$0.979887\pi$
$374$	11245.3	1.55476
$375$	0	0
$376$	3287.09	0.450848
$377$	− 8521.18i	− 1.16409i
$378$	63.2686i	0.00860896i
$379$	−5483.27	−0.743158	−0.371579	−	0.928401i	$-0.621183\pi$
$379$	−5483.27	−0.743158	−0.371579	+	0.928401i	$0.621183\pi$
$380$	0	0
$381$	−3031.19	−0.407592
$382$	3674.68i	0.492180i
$383$	4194.65i	0.559625i	0.960055	+	0.279813i	$0.0902723\pi$
$383$	4194.65i	0.559625i	−0.960055	+	0.279813i	$0.909728\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	−2221.49	−0.292930
$387$	937.083i	0.123087i
$388$	− 2263.48i	− 0.296162i
$389$	2824.52	0.368146	0.184073	−	0.982913i	$-0.441072\pi$
$389$	2824.52	0.368146	0.184073	+	0.982913i	$0.441072\pi$
$390$	0	0
$391$	−24002.7	−3.10453
$392$	2733.02i	0.352138i
$393$	− 4394.18i	− 0.564013i
$394$	−6534.68	−0.835564
$395$	0	0
$396$	1796.06	0.227918
$397$	7741.76i	0.978709i	0.872085	+	0.489355i	$0.162768\pi$
$397$	7741.76i	0.978709i	−0.872085	+	0.489355i	$0.837232\pi$
$398$	− 8464.56i	− 1.06605i
$399$	251.747	0.0315867
$400$	0	0
$401$	−2814.29	−0.350472	−0.175236	−	0.984527i	$-0.556069\pi$
$401$	−2814.29	−0.350472	−0.175236	+	0.984527i	$0.556069\pi$
$402$	− 2591.14i	− 0.321478i
$403$	1580.26i	0.195331i
$404$	−1473.84	−0.181500
$405$	0	0
$406$	232.982	0.0284795
$407$	10765.8i	1.31116i
$408$	2704.78i	0.328202i
$409$	10004.9	1.20956	0.604778	−	0.796394i	$-0.293262\pi$
$409$	10004.9	1.20956	0.604778	+	0.796394i	$0.293262\pi$
$410$	0	0
$411$	−7915.04	−0.949928
$412$	219.198i	0.0262114i
$413$	773.318i	0.0921368i
$414$	−3833.65	−0.455105
$415$	0	0
$416$	−2742.54	−0.323231
$417$	− 1441.64i	− 0.169298i
$418$	− 7146.56i	− 0.836243i
$419$	−5584.69	−0.651145	−0.325573	−	0.945517i	$-0.605557\pi$
$419$	−5584.69	−0.651145	−0.325573	+	0.945517i	$0.605557\pi$
$420$	0	0
$421$	88.0019	0.0101875	0.00509377	−	0.999987i	$-0.498379\pi$
$421$	88.0019	0.0101875	0.00509377	+	0.999987i	$0.498379\pi$
$422$	− 6490.92i	− 0.748751i
$423$	3697.98i	0.425064i
$424$	5201.18	0.595735
$425$	0	0
$426$	6774.11	0.770439
$427$	59.5398i	0.00674786i
$428$	− 5012.35i	− 0.566077i
$429$	−12827.5	−1.44363
$430$	0	0
$431$	10870.3	1.21486	0.607430	−	0.794373i	$-0.292201\pi$
$431$	10870.3	1.21486	0.607430	+	0.794373i	$0.292201\pi$
$432$	432.000i	0.0481125i
$433$	5154.52i	0.572080i	0.958218	+	0.286040i	$0.0923390\pi$
$433$	5154.52i	0.572080i	−0.958218	+	0.286040i	$0.907661\pi$
$434$	−43.2066	−0.00477876
$435$	0	0
$436$	334.037	0.0366915
$437$	15254.1i	1.66980i
$438$	7045.92i	0.768647i
$439$	6775.15	0.736584	0.368292	−	0.929710i	$-0.379943\pi$
$439$	6775.15	0.736584	0.368292	+	0.929710i	$0.379943\pi$
$440$	0	0
$441$	−3074.65	−0.331999
$442$	− 19317.6i	− 2.07884i
$443$	− 1162.58i	− 0.124686i	−0.998055	−	0.0623430i	$-0.980143\pi$
$443$	− 1162.58i	− 0.124686i	0.998055	−	0.0623430i	$-0.0198573\pi$
$444$	−2589.46	−0.276780
$445$	0	0
$446$	2256.23	0.239542
$447$	1327.36i	0.140452i
$448$	− 74.9850i	− 0.00790783i
$449$	14295.0	1.50250	0.751250	−	0.660017i	$-0.229451\pi$
$449$	14295.0	1.50250	0.751250	+	0.660017i	$0.229451\pi$
$450$	0	0
$451$	18311.7	1.91189
$452$	− 2092.57i	− 0.217757i
$453$	− 7696.94i	− 0.798309i
$454$	271.778	0.0280951
$455$	0	0
$456$	1718.93	0.176527
$457$	− 11821.2i	− 1.21001i	−0.796223	−	0.605003i	$-0.793172\pi$
$457$	− 11821.2i	− 1.21001i	0.796223	−	0.605003i	$-0.206828\pi$
$458$	10543.9i	1.07573i
$459$	−3042.88	−0.309432
$460$	0	0
$461$	−13808.6	−1.39508	−0.697539	−	0.716547i	$-0.745722\pi$
$461$	−13808.6	−1.39508	−0.697539	+	0.716547i	$0.745722\pi$
$462$	− 350.723i	− 0.0353184i
$463$	19289.1i	1.93616i	0.250643	+	0.968080i	$0.419358\pi$
$463$	19289.1i	1.93616i	−0.250643	+	0.968080i	$0.580642\pi$
$464$	1590.81	0.159162
$465$	0	0
$466$	−5980.55	−0.594515
$467$	1240.07i	0.122877i	0.998111	+	0.0614386i	$0.0195688\pi$
$467$	1240.07i	0.122877i	−0.998111	+	0.0614386i	$0.980431\pi$
$468$	− 3085.36i	− 0.304745i
$469$	−505.981	−0.0498167
$470$	0	0
$471$	5606.04	0.548434
$472$	5280.24i	0.514921i
$473$	− 5194.63i	− 0.504967i
$474$	4671.34	0.452662
$475$	0	0
$476$	528.172	0.0508586
$477$	5851.33i	0.561664i
$478$	− 2004.95i	− 0.191850i
$479$	−405.216	−0.0386530	−0.0193265	−	0.999813i	$-0.506152\pi$
$479$	−405.216	−0.0386530	−0.0193265	+	0.999813i	$0.506152\pi$
$480$	0	0
$481$	18494.0	1.75312
$482$	− 665.456i	− 0.0628853i
$483$	748.610i	0.0705237i
$484$	−4632.29	−0.435038
$485$	0	0
$486$	−486.000	−0.0453609
$487$	5943.30i	0.553011i	0.961012	+	0.276506i	$0.0891764\pi$
$487$	5943.30i	0.553011i	−0.961012	+	0.276506i	$0.910824\pi$
$488$	406.540i	0.0377115i
$489$	−3641.87	−0.336792
$490$	0	0
$491$	−2685.38	−0.246822	−0.123411	−	0.992356i	$-0.539383\pi$
$491$	−2685.38	−0.246822	−0.123411	+	0.992356i	$0.539383\pi$
$492$	4404.43i	0.403592i
$493$	11205.2i	1.02364i
$494$	−12276.7	−1.11813
$495$	0	0
$496$	−295.016	−0.0267069
$497$	− 1322.80i	− 0.119388i
$498$	5029.77i	0.452590i
$499$	−5624.29	−0.504565	−0.252282	−	0.967654i	$-0.581181\pi$
$499$	−5624.29	−0.504565	−0.252282	+	0.967654i	$0.581181\pi$
$500$	0	0
$501$	3873.99	0.345463
$502$	− 10697.0i	− 0.951054i
$503$	− 12926.8i	− 1.14588i	−0.819598	−	0.572939i	$-0.805803\pi$
$503$	− 12926.8i	− 1.14588i	0.819598	−	0.572939i	$-0.194197\pi$
$504$	84.3581	0.00745558
$505$	0	0
$506$	21251.4	1.86708
$507$	15444.7i	1.35291i
$508$	4041.58i	0.352985i
$509$	−2592.91	−0.225793	−0.112897	−	0.993607i	$-0.536013\pi$
$509$	−2592.91	−0.225793	−0.112897	+	0.993607i	$0.536013\pi$
$510$	0	0
$511$	1375.88	0.119110
$512$	− 512.000i	− 0.0441942i
$513$	1933.80i	0.166432i
$514$	−6309.92	−0.541476
$515$	0	0
$516$	1249.44	0.106596
$517$	− 20499.4i	− 1.74383i
$518$	505.653i	0.0428902i
$519$	3631.30	0.307122
$520$	0	0
$521$	−14070.2	−1.18316	−0.591581	−	0.806245i	$-0.701496\pi$
$521$	−14070.2	−1.18316	−0.591581	+	0.806245i	$0.701496\pi$
$522$	1789.66i	0.150060i
$523$	8494.96i	0.710246i	0.934820	+	0.355123i	$0.115561\pi$
$523$	8494.96i	0.710246i	−0.934820	+	0.355123i	$0.884439\pi$
$524$	−5858.91	−0.488450
$525$	0	0
$526$	−523.347	−0.0433821
$527$	− 2078.00i	− 0.171763i
$528$	− 2394.75i	− 0.197383i
$529$	−33193.7	−2.72817
$530$	0	0
$531$	−5940.27	−0.485472
$532$	− 335.662i	− 0.0273549i
$533$	− 31456.6i	− 2.55635i
$534$	−2101.34	−0.170288
$535$	0	0
$536$	−3454.85	−0.278408
$537$	− 4499.77i	− 0.361600i
$538$	− 12824.7i	− 1.02771i
$539$	17044.0	1.36203
$540$	0	0
$541$	−4666.81	−0.370872	−0.185436	−	0.982656i	$-0.559370\pi$
$541$	−4666.81	−0.370872	−0.185436	+	0.982656i	$0.559370\pi$
$542$	4567.03i	0.361939i
$543$	2051.58i	0.162139i
$544$	3606.37	0.284232
$545$	0	0
$546$	−602.488	−0.0472237
$547$	− 14150.5i	− 1.10609i	−0.833152	−	0.553044i	$-0.813466\pi$
$547$	− 14150.5i	− 1.10609i	0.833152	−	0.553044i	$-0.186534\pi$
$548$	10553.4i	0.822662i
$549$	−457.357	−0.0355547
$550$	0	0
$551$	7121.07	0.550577
$552$	5111.53i	0.394133i
$553$	− 912.189i	− 0.0701450i
$554$	9713.15	0.744895
$555$	0	0
$556$	−1922.18	−0.146616
$557$	− 13330.0i	− 1.01402i	−0.861939	−	0.507012i	$-0.830750\pi$
$557$	− 13330.0i	− 1.01402i	0.861939	−	0.507012i	$-0.169250\pi$
$558$	− 331.893i	− 0.0251795i
$559$	−8923.56	−0.675182
$560$	0	0
$561$	16867.9	1.26945
$562$	3392.47i	0.254631i
$563$	− 23875.6i	− 1.78728i	−0.448786	−	0.893639i	$-0.648144\pi$
$563$	− 23875.6i	− 1.78728i	0.448786	−	0.893639i	$-0.351856\pi$
$564$	4930.64	0.368116
$565$	0	0
$566$	2681.03	0.199103
$567$	94.9029i	0.00702919i
$568$	− 9032.15i	− 0.667219i
$569$	−15232.6	−1.12229	−0.561145	−	0.827717i	$-0.689639\pi$
$569$	−15232.6	−1.12229	−0.561145	+	0.827717i	$0.689639\pi$
$570$	0	0
$571$	471.515	0.0345574	0.0172787	−	0.999851i	$-0.494500\pi$
$571$	471.515	0.0345574	0.0172787	+	0.999851i	$0.494500\pi$
$572$	17103.4i	1.25022i
$573$	5512.01i	0.401863i
$574$	860.069	0.0625411
$575$	0	0
$576$	576.000	0.0416667
$577$	24235.3i	1.74857i	0.485410	+	0.874287i	$0.338670\pi$
$577$	24235.3i	1.74857i	−0.485410	+	0.874287i	$0.661330\pi$
$578$	15576.2i	1.12091i
$579$	−3332.24	−0.239176
$580$	0	0
$581$	982.182	0.0701338
$582$	− 3395.23i	− 0.241816i
$583$	− 32436.2i	− 2.30424i
$584$	9394.56	0.665668
$585$	0	0
$586$	8393.56	0.591698
$587$	− 2119.03i	− 0.148998i	−0.997221	−	0.0744989i	$-0.976264\pi$
$587$	− 2119.03i	− 0.148998i	0.997221	−	0.0744989i	$-0.0237357\pi$
$588$	4099.53i	0.287520i
$589$	−1320.61	−0.0923849
$590$	0	0
$591$	−9802.01	−0.682235
$592$	3452.61i	0.239698i
$593$	16046.5i	1.11122i	0.831444	+	0.555609i	$0.187515\pi$
$593$	16046.5i	1.11122i	−0.831444	+	0.555609i	$0.812485\pi$
$594$	2694.09	0.186094
$595$	0	0
$596$	1769.81	0.121635
$597$	− 12696.8i	− 0.870430i
$598$	− 36506.7i	− 2.49644i
$599$	20791.2	1.41820	0.709102	−	0.705106i	$-0.249100\pi$
$599$	20791.2	1.41820	0.709102	+	0.705106i	$0.249100\pi$
$600$	0	0
$601$	1658.25	0.112548	0.0562740	−	0.998415i	$-0.482078\pi$
$601$	1658.25	0.112548	0.0562740	+	0.998415i	$0.482078\pi$
$602$	− 243.983i	− 0.0165183i
$603$	− 3886.71i	− 0.262486i
$604$	−10262.6	−0.691356
$605$	0	0
$606$	−2210.76	−0.148194
$607$	− 21758.6i	− 1.45495i	−0.686134	−	0.727475i	$-0.740694\pi$
$607$	− 21758.6i	− 1.45495i	0.686134	−	0.727475i	$-0.259306\pi$
$608$	− 2291.91i	− 0.152877i
$609$	349.472	0.0232534
$610$	0	0
$611$	−35214.8	−2.33165
$612$	4057.17i	0.267976i
$613$	− 26445.4i	− 1.74245i	−0.490886	−	0.871224i	$-0.663327\pi$
$613$	− 26445.4i	− 1.74245i	0.490886	−	0.871224i	$-0.336673\pi$
$614$	−14252.5	−0.936783
$615$	0	0
$616$	−467.631	−0.0305867
$617$	7287.91i	0.475527i	0.971323	+	0.237763i	$0.0764143\pi$
$617$	7287.91i	0.475527i	−0.971323	+	0.237763i	$0.923586\pi$
$618$	328.797i	0.0214015i
$619$	−15032.1	−0.976077	−0.488039	−	0.872822i	$-0.662287\pi$
$619$	−15032.1	−0.976077	−0.488039	+	0.872822i	$0.662287\pi$
$620$	0	0
$621$	−5750.47	−0.371592
$622$	4264.87i	0.274929i
$623$	410.335i	0.0263880i
$624$	−4113.81	−0.263917
$625$	0	0
$626$	12921.0	0.824963
$627$	− 10719.8i	− 0.682790i
$628$	− 7474.72i	− 0.474958i
$629$	−24319.1	−1.54160
$630$	0	0
$631$	−29321.4	−1.84987	−0.924934	−	0.380127i	$-0.875880\pi$
$631$	−29321.4	−1.84987	−0.924934	+	0.380127i	$0.875880\pi$
$632$	− 6228.45i	− 0.392017i
$633$	− 9736.38i	− 0.611353i
$634$	12804.4	0.802094
$635$	0	0
$636$	7801.77	0.486415
$637$	− 29278.9i	− 1.82115i
$638$	− 9920.78i	− 0.615623i
$639$	10161.2	0.629060
$640$	0	0
$641$	−11353.4	−0.699580	−0.349790	−	0.936828i	$-0.613747\pi$
$641$	−11353.4	−0.699580	−0.349790	+	0.936828i	$0.613747\pi$
$642$	− 7518.52i	− 0.462200i
$643$	5624.78i	0.344976i	0.985012	+	0.172488i	$0.0551807\pi$
$643$	5624.78i	0.344976i	−0.985012	+	0.172488i	$0.944819\pi$
$644$	998.146	0.0610753
$645$	0	0
$646$	16143.5	0.983219
$647$	6911.62i	0.419975i	0.977704	+	0.209988i	$0.0673423\pi$
$647$	6911.62i	0.419975i	−0.977704	+	0.209988i	$0.932658\pi$
$648$	648.000i	0.0392837i
$649$	32929.3	1.99166
$650$	0	0
$651$	−64.8099	−0.00390184
$652$	4855.83i	0.291670i
$653$	− 10042.6i	− 0.601832i	−0.953651	−	0.300916i	$-0.902708\pi$
$653$	− 10042.6i	− 0.601832i	0.953651	−	0.300916i	$-0.0972924\pi$
$654$	501.056	0.0299585
$655$	0	0
$656$	5872.58	0.349521
$657$	10568.9i	0.627597i
$658$	− 962.824i	− 0.0570437i
$659$	31966.3	1.88957	0.944787	−	0.327685i	$-0.106269\pi$
$659$	31966.3	1.88957	0.944787	+	0.327685i	$0.106269\pi$
$660$	0	0
$661$	−19680.5	−1.15807	−0.579035	−	0.815303i	$-0.696570\pi$
$661$	−19680.5	−1.15807	−0.579035	+	0.815303i	$0.696570\pi$
$662$	− 15542.3i	− 0.912488i
$663$	− 28976.4i	− 1.69736i
$664$	6706.37	0.391954
$665$	0	0
$666$	−3884.19	−0.225990
$667$	21175.6i	1.22927i
$668$	− 5165.32i	− 0.299180i
$669$	3384.35	0.195585
$670$	0	0
$671$	2535.31	0.145864
$672$	− 112.478i	− 0.00645672i
$673$	20937.4i	1.19923i	0.800290	+	0.599613i	$0.204679\pi$
$673$	20937.4i	1.19923i	−0.800290	+	0.599613i	$0.795321\pi$
$674$	−4545.04	−0.259745
$675$	0	0
$676$	20592.9	1.17165
$677$	12063.9i	0.684865i	0.939542	+	0.342433i	$0.111251\pi$
$677$	12063.9i	0.684865i	−0.939542	+	0.342433i	$0.888749\pi$
$678$	− 3138.85i	− 0.177798i
$679$	−662.998	−0.0374720
$680$	0	0
$681$	407.667	0.0229396
$682$	1839.82i	0.103299i
$683$	511.020i	0.0286291i	0.999898	+	0.0143145i	$0.00455661\pi$
$683$	511.020i	0.0286291i	−0.999898	+	0.0143145i	$0.995443\pi$
$684$	2578.40	0.144134
$685$	0	0
$686$	1604.27	0.0892879
$687$	15815.9i	0.878334i
$688$	− 1665.93i	− 0.0923151i
$689$	−55720.4	−3.08096
$690$	0	0
$691$	−1659.58	−0.0913653	−0.0456826	−	0.998956i	$-0.514546\pi$
$691$	−1659.58	−0.0913653	−0.0456826	+	0.998956i	$0.514546\pi$
$692$	− 4841.73i	− 0.265976i
$693$	− 526.085i	− 0.0288374i
$694$	−3951.12	−0.216113
$695$	0	0
$696$	2386.21	0.129955
$697$	41364.7i	2.24792i
$698$	7428.29i	0.402815i
$699$	−8970.83	−0.485419
$700$	0	0
$701$	31336.6	1.68840	0.844199	−	0.536030i	$-0.180076\pi$
$701$	31336.6	1.68840	0.844199	+	0.536030i	$0.180076\pi$
$702$	− 4628.03i	− 0.248823i
$703$	15455.2i	0.829169i
$704$	−3193.00	−0.170938
$705$	0	0
$706$	16012.1	0.853574
$707$	431.702i	0.0229644i
$708$	7920.36i	0.420431i
$709$	12733.6	0.674502	0.337251	−	0.941415i	$-0.390503\pi$
$709$	12733.6	0.674502	0.337251	+	0.941415i	$0.390503\pi$
$710$	0	0
$711$	7007.01	0.369597
$712$	2801.78i	0.147474i
$713$	− 3927.04i	− 0.206268i
$714$	792.258	0.0415259
$715$	0	0
$716$	−5999.70	−0.313155
$717$	− 3007.43i	− 0.156645i
$718$	4102.28i	0.213225i
$719$	3601.98	0.186831	0.0934153	−	0.995627i	$-0.470222\pi$
$719$	3601.98	0.186831	0.0934153	+	0.995627i	$0.470222\pi$
$720$	0	0
$721$	64.2053	0.00331641
$722$	3458.50i	0.178271i
$723$	− 998.184i	− 0.0513456i
$724$	2735.44	0.140417
$725$	0	0
$726$	−6948.43	−0.355207
$727$	− 5690.14i	− 0.290283i	−0.989411	−	0.145141i	$-0.953636\pi$
$727$	− 5690.14i	− 0.290283i	0.989411	−	0.145141i	$-0.0463637\pi$
$728$	803.318i	0.0408969i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	11734.3	0.593718
$732$	609.810i	0.0307913i
$733$	4102.52i	0.206726i	0.994644	+	0.103363i	$0.0329603\pi$
$733$	4102.52i	0.206726i	−0.994644	+	0.103363i	$0.967040\pi$
$734$	6369.70	0.320313
$735$	0	0
$736$	6815.37	0.341329
$737$	21545.6i	1.07685i
$738$	6606.65i	0.329531i
$739$	23471.4	1.16835	0.584174	−	0.811628i	$-0.301419\pi$
$739$	23471.4	1.16835	0.584174	+	0.811628i	$0.301419\pi$
$740$	0	0
$741$	−18415.0	−0.912945
$742$	− 1523.48i	− 0.0753755i
$743$	18.4319i	0 0.000910095i	1.00000		0.000455048i	$0.000144846\pi$
$743$	18.4319i	0 0.000910095i	−1.00000		0.000455048i	$0.999855\pi$
$744$	−442.524	−0.0218061
$745$	0	0
$746$	1819.55	0.0893007
$747$	7544.66i	0.369538i
$748$	− 22490.5i	− 1.09938i
$749$	−1468.17	−0.0716231
$750$	0	0
$751$	−21161.4	−1.02821	−0.514107	−	0.857726i	$-0.671877\pi$
$751$	−21161.4	−1.02821	−0.514107	+	0.857726i	$0.671877\pi$
$752$	− 6574.19i	− 0.318798i
$753$	− 16045.5i	− 0.776532i
$754$	−17042.4	−0.823138
$755$	0	0
$756$	126.537	0.00608745
$757$	− 8489.09i	− 0.407584i	−0.979014	−	0.203792i	$-0.934673\pi$
$757$	− 8489.09i	− 0.407584i	0.979014	−	0.203792i	$-0.0653267\pi$
$758$	10966.5i	0.525492i
$759$	31877.2	1.52446
$760$	0	0
$761$	−16312.2	−0.777024	−0.388512	−	0.921444i	$-0.627011\pi$
$761$	−16312.2	−0.777024	−0.388512	+	0.921444i	$0.627011\pi$
$762$	6062.37i	0.288211i
$763$	− 97.8429i	− 0.00464240i
$764$	7349.35	0.348024
$765$	0	0
$766$	8389.29	0.395715
$767$	− 56567.4i	− 2.66301i
$768$	− 768.000i	− 0.0360844i
$769$	−15365.3	−0.720529	−0.360265	−	0.932850i	$-0.617314\pi$
$769$	−15365.3	−0.720529	−0.360265	+	0.932850i	$0.617314\pi$
$770$	0	0
$771$	−9464.88	−0.442113
$772$	4442.99i	0.207133i
$773$	− 30950.6i	− 1.44013i	−0.693909	−	0.720063i	$-0.744113\pi$
$773$	− 30950.6i	− 1.44013i	0.693909	−	0.720063i	$-0.255887\pi$
$774$	1874.17	0.0870355
$775$	0	0
$776$	−4526.97	−0.209418
$777$	758.479i	0.0350197i
$778$	− 5649.04i	− 0.260319i
$779$	26288.0	1.20907
$780$	0	0
$781$	−56327.4	−2.58073
$782$	48005.4i	2.19523i
$783$	2684.48i	0.122523i
$784$	5466.04	0.248999
$785$	0	0
$786$	−8788.37	−0.398818
$787$	− 19386.9i	− 0.878103i	−0.898462	−	0.439051i	$-0.855315\pi$
$787$	− 19386.9i	− 0.878103i	0.898462	−	0.439051i	$-0.144685\pi$
$788$	13069.4i	0.590833i
$789$	−785.020	−0.0354214
$790$	0	0
$791$	−612.934	−0.0275517
$792$	− 3592.12i	− 0.161162i
$793$	− 4355.28i	− 0.195032i
$794$	15483.5	0.692052
$795$	0	0
$796$	−16929.1	−0.753815
$797$	− 29756.3i	− 1.32249i	−0.750171	−	0.661244i	$-0.770029\pi$
$797$	− 29756.3i	− 1.32249i	0.750171	−	0.661244i	$-0.229971\pi$
$798$	− 503.494i	− 0.0223352i
$799$	46306.6	2.05033
$800$	0	0
$801$	−3152.00	−0.139039
$802$	5628.59i	0.247821i
$803$	− 58587.6i	− 2.57473i
$804$	−5182.28	−0.227319
$805$	0	0
$806$	3160.52	0.138120
$807$	− 19237.0i	− 0.839126i
$808$	2947.67i	0.128340i
$809$	−40337.8	−1.75303	−0.876514	−	0.481376i	$-0.840137\pi$
$809$	−40337.8	−1.75303	−0.876514	+	0.481376i	$0.840137\pi$
$810$	0	0
$811$	84.9612	0.00367866	0.00183933	−	0.999998i	$-0.499415\pi$
$811$	84.9612	0.00367866	0.00183933	+	0.999998i	$0.499415\pi$
$812$	− 465.963i	− 0.0201381i
$813$	6850.55i	0.295522i
$814$	21531.6	0.927128
$815$	0	0
$816$	5409.56	0.232074
$817$	− 7457.34i	− 0.319338i
$818$	− 20009.7i	− 0.855286i
$819$	−903.732	−0.0385580
$820$	0	0
$821$	18701.0	0.794969	0.397485	−	0.917609i	$-0.369883\pi$
$821$	18701.0	0.794969	0.397485	+	0.917609i	$0.369883\pi$
$822$	15830.1i	0.671700i
$823$	− 15804.2i	− 0.669379i	−0.942328	−	0.334689i	$-0.891369\pi$
$823$	− 15804.2i	− 0.669379i	0.942328	−	0.334689i	$-0.108631\pi$
$824$	438.395	0.0185343
$825$	0	0
$826$	1546.64	0.0651506
$827$	36570.0i	1.53768i	0.639440	+	0.768841i	$0.279166\pi$
$827$	36570.0i	1.53768i	−0.639440	+	0.768841i	$0.720834\pi$
$828$	7667.30i	0.321808i
$829$	23227.9	0.973146	0.486573	−	0.873640i	$-0.338247\pi$
$829$	23227.9	0.973146	0.486573	+	0.873640i	$0.338247\pi$
$830$	0	0
$831$	14569.7	0.608205
$832$	5485.08i	0.228559i
$833$	38501.1i	1.60142i
$834$	−2883.27	−0.119712
$835$	0	0
$836$	−14293.1	−0.591313
$837$	− 497.840i	− 0.0205590i
$838$	11169.4i	0.460429i
$839$	−18133.9	−0.746188	−0.373094	−	0.927793i	$-0.621703\pi$
$839$	−18133.9	−0.746188	−0.373094	+	0.927793i	$0.621703\pi$
$840$	0	0
$841$	−14503.6	−0.594678
$842$	− 176.004i	− 0.00720367i
$843$	5088.71i	0.207906i
$844$	−12981.8	−0.529447
$845$	0	0
$846$	7395.96	0.300566
$847$	1356.85i	0.0550434i
$848$	− 10402.4i	− 0.421248i
$849$	4021.55	0.162567
$850$	0	0
$851$	−45958.7	−1.85128
$852$	− 13548.2i	− 0.544782i
$853$	38445.0i	1.54318i	0.636120	+	0.771590i	$0.280538\pi$
$853$	38445.0i	1.54318i	−0.636120	+	0.771590i	$0.719462\pi$
$854$	119.080	0.00477146
$855$	0	0
$856$	−10024.7	−0.400277
$857$	4061.04i	0.161870i	0.996719	+	0.0809349i	$0.0257906\pi$
$857$	4061.04i	0.161870i	−0.996719	+	0.0809349i	$0.974209\pi$
$858$	25655.0i	1.02080i
$859$	30569.6	1.21423	0.607113	−	0.794616i	$-0.292328\pi$
$859$	30569.6	1.21423	0.607113	+	0.794616i	$0.292328\pi$
$860$	0	0
$861$	1290.10	0.0510646
$862$	− 21740.6i	− 0.859036i
$863$	4791.08i	0.188981i	0.995526	+	0.0944903i	$0.0301221\pi$
$863$	4791.08i	0.188981i	−0.995526	+	0.0944903i	$0.969878\pi$
$864$	864.000	0.0340207
$865$	0	0
$866$	10309.0	0.404522
$867$	23364.3i	0.915217i
$868$	86.4132i	0.00337910i
$869$	−38842.7	−1.51628
$870$	0	0
$871$	37012.0	1.43984
$872$	− 668.075i	− 0.0259448i
$873$	− 5092.84i	− 0.197442i
$874$	30508.3	1.18073
$875$	0	0
$876$	14091.8	0.543515
$877$	12653.8i	0.487215i	0.969874	+	0.243607i	$0.0783308\pi$
$877$	12653.8i	0.487215i	−0.969874	+	0.243607i	$0.921669\pi$
$878$	− 13550.3i	− 0.520843i
$879$	12590.3	0.483119
$880$	0	0
$881$	36192.9	1.38407	0.692037	−	0.721862i	$-0.256714\pi$
$881$	36192.9	1.38407	0.692037	+	0.721862i	$0.256714\pi$
$882$	6149.29i	0.234759i
$883$	17507.8i	0.667252i	0.942705	+	0.333626i	$0.108272\pi$
$883$	17507.8i	0.667252i	−0.942705	+	0.333626i	$0.891728\pi$
$884$	−38635.2	−1.46996
$885$	0	0
$886$	−2325.16	−0.0881663
$887$	− 14273.0i	− 0.540295i	−0.962819	−	0.270147i	$-0.912928\pi$
$887$	− 14273.0i	− 0.540295i	0.962819	−	0.270147i	$-0.0870724\pi$
$888$	5178.92i	0.195713i
$889$	1183.82	0.0446615
$890$	0	0
$891$	4041.14	0.151945
$892$	− 4512.46i	− 0.169382i
$893$	− 29428.7i	− 1.10279i
$894$	2654.72	0.0993143
$895$	0	0
$896$	−149.970	−0.00559168
$897$	− 54760.0i	− 2.03833i
$898$	− 28590.0i	− 1.06243i
$899$	−1833.25	−0.0680116
$900$	0	0
$901$	73271.1	2.70923
$902$	− 36623.3i	− 1.35191i
$903$	− 365.975i	− 0.0134871i
$904$	−4185.13	−0.153977
$905$	0	0
$906$	−15393.9	−0.564490
$907$	11460.3i	0.419550i	0.977750	+	0.209775i	$0.0672731\pi$
$907$	11460.3i	0.419550i	−0.977750	+	0.209775i	$0.932727\pi$
$908$	− 543.556i	− 0.0198663i
$909$	−3316.13	−0.121000
$910$	0	0
$911$	36058.3	1.31138	0.655689	−	0.755031i	$-0.272378\pi$
$911$	36058.3	1.31138	0.655689	+	0.755031i	$0.272378\pi$
$912$	− 3437.87i	− 0.124824i
$913$	− 41823.1i	− 1.51604i
$914$	−23642.4	−0.855603
$915$	0	0
$916$	21087.9	0.760659
$917$	1716.14i	0.0618013i
$918$	6085.75i	0.218802i
$919$	14258.3	0.511793	0.255897	−	0.966704i	$-0.417629\pi$
$919$	14258.3	0.511793	0.255897	+	0.966704i	$0.417629\pi$
$920$	0	0
$921$	−21378.8	−0.764880
$922$	27617.2i	0.986469i
$923$	96761.8i	3.45065i
$924$	−701.447	−0.0249739
$925$	0	0
$926$	38578.2	1.36907
$927$	493.195i	0.0174743i
$928$	− 3181.61i	− 0.112545i
$929$	1576.41	0.0556732	0.0278366	−	0.999612i	$-0.491138\pi$
$929$	1576.41	0.0556732	0.0278366	+	0.999612i	$0.491138\pi$
$930$	0	0
$931$	24468.1	0.861343
$932$	11961.1i	0.420385i
$933$	6397.30i	0.224478i
$934$	2480.14	0.0868873
$935$	0	0
$936$	−6170.71	−0.215487
$937$	10728.3i	0.374043i	0.982356	+	0.187021i	$0.0598834\pi$
$937$	10728.3i	0.374043i	−0.982356	+	0.187021i	$0.940117\pi$
$938$	1011.96i	0.0352257i
$939$	19381.5	0.673579
$940$	0	0
$941$	−36007.1	−1.24739	−0.623696	−	0.781667i	$-0.714370\pi$
$941$	−36007.1	−1.24739	−0.623696	+	0.781667i	$0.714370\pi$
$942$	− 11212.1i	− 0.387802i
$943$	78171.5i	2.69949i
$944$	10560.5	0.364104
$945$	0	0
$946$	−10389.3	−0.357065
$947$	− 6303.70i	− 0.216307i	−0.994134	−	0.108154i	$-0.965506\pi$
$947$	− 6303.70i	− 0.216307i	0.994134	−	0.108154i	$-0.0344938\pi$
$948$	− 9342.68i	− 0.320080i
$949$	−100644.	−3.44263
$950$	0	0
$951$	19206.6	0.654907
$952$	− 1056.34i	− 0.0359625i
$953$	− 13372.1i	− 0.454526i	−0.973833	−	0.227263i	$-0.927022\pi$
$953$	− 13372.1i	− 0.454526i	0.973833	−	0.227263i	$-0.0729777\pi$
$954$	11702.7	0.397157
$955$	0	0
$956$	−4009.90	−0.135658
$957$	− 14881.2i	− 0.502654i
$958$	810.432i	0.0273318i
$959$	3091.20	0.104088
$960$	0	0
$961$	−29451.0	−0.988588
$962$	− 36988.0i	− 1.23965i
$963$	− 11277.8i	− 0.377385i
$964$	−1330.91	−0.0444666
$965$	0	0
$966$	1497.22	0.0498678
$967$	32389.5i	1.07712i	0.842587	+	0.538560i	$0.181032\pi$
$967$	32389.5i	1.07712i	−0.842587	+	0.538560i	$0.818968\pi$
$968$	9264.58i	0.307619i
$969$	24215.3	0.802795
$970$	0	0
$971$	−37729.4	−1.24696	−0.623478	−	0.781841i	$-0.714281\pi$
$971$	−37729.4	−1.24696	−0.623478	+	0.781841i	$0.714281\pi$
$972$	972.000i	0.0320750i
$973$	563.027i	0.0185507i
$974$	11886.6	0.391038
$975$	0	0
$976$	813.080	0.0266660
$977$	14705.9i	0.481558i	0.970580	+	0.240779i	$0.0774029\pi$
$977$	14705.9i	0.481558i	−0.970580	+	0.240779i	$0.922597\pi$
$978$	7283.75i	0.238148i
$979$	17472.8	0.570413
$980$	0	0
$981$	751.584	0.0244610
$982$	5370.75i	0.174529i
$983$	30404.2i	0.986514i	0.869884	+	0.493257i	$0.164194\pi$
$983$	30404.2i	0.986514i	−0.869884	+	0.493257i	$0.835806\pi$
$984$	8808.87	0.285383
$985$	0	0
$986$	22410.3	0.723823
$987$	− 1444.24i	− 0.0465760i
$988$	24553.4i	0.790634i
$989$	22175.6	0.712986
$990$	0	0
$991$	7107.76	0.227836	0.113918	−	0.993490i	$-0.463660\pi$
$991$	7107.76	0.227836	0.113918	+	0.993490i	$0.463660\pi$
$992$	590.032i	0.0188846i
$993$	− 23313.4i	− 0.745043i
$994$	−2645.61	−0.0844202
$995$	0	0
$996$	10059.5	0.320029
$997$	30604.9i	0.972184i	0.873908	+	0.486092i	$0.161578\pi$
$997$	30604.9i	0.972184i	−0.873908	+	0.486092i	$0.838422\pi$
$998$	11248.6i	0.356781i
$999$	−5826.28	−0.184520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.4.c.e.499.2		8
5.2	odd	4		750.4.a.m.1.3	yes	4
5.3	odd	4		750.4.a.l.1.2	✓	4
5.4	even	2	inner	750.4.c.e.499.7		8
15.2	even	4		2250.4.a.m.1.3		4
15.8	even	4		2250.4.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.4.a.l.1.2	✓	4	5.3	odd	4
750.4.a.m.1.3	yes	4	5.2	odd	4
750.4.c.e.499.2		8	1.1	even	1	trivial
750.4.c.e.499.7		8	5.4	even	2	inner
2250.4.a.m.1.3		4	15.2	even	4
2250.4.a.z.1.2		4	15.8	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	750.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} -6.00000 q^{6} +1.17164i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} -6.00000 q^{6} +1.17164i q^{7} +8.00000i q^{8} -9.00000 q^{9} +49.8906 q^{11} +12.0000i q^{12} -85.7043i q^{13} +2.34328 q^{14} +16.0000 q^{16} +112.699i q^{17} +18.0000i q^{18} +71.6223 q^{19} +3.51492 q^{21} -99.7812i q^{22} +212.980i q^{23} +24.0000 q^{24} -171.409 q^{26} +27.0000i q^{27} -4.68656i q^{28} +99.4253 q^{29} -18.4385 q^{31} -32.0000i q^{32} -149.672i q^{33} +225.398 q^{34} +36.0000 q^{36} +215.788i q^{37} -143.245i q^{38} -257.113 q^{39} +367.036 q^{41} -7.02985i q^{42} -104.120i q^{43} -199.562 q^{44} +425.961 q^{46} -410.887i q^{47} -48.0000i q^{48} +341.627 q^{49} +338.097 q^{51} +342.817i q^{52} -650.147i q^{53} +54.0000 q^{54} -9.37313 q^{56} -214.867i q^{57} -198.851i q^{58} +660.030 q^{59} +50.8175 q^{61} +36.8770i q^{62} -10.5448i q^{63} -64.0000 q^{64} -299.344 q^{66} +431.856i q^{67} -450.797i q^{68} +638.941 q^{69} -1129.02 q^{71} -72.0000i q^{72} -1174.32i q^{73} +431.576 q^{74} -286.489 q^{76} +58.4539i q^{77} +514.226i q^{78} -778.556 q^{79} +81.0000 q^{81} -734.072i q^{82} -838.296i q^{83} -14.0597 q^{84} -208.241 q^{86} -298.276i q^{87} +399.125i q^{88} +350.223 q^{89} +100.415 q^{91} -851.922i q^{92} +55.3155i q^{93} -821.774 q^{94} -96.0000 q^{96} +565.871i q^{97} -683.255i q^{98} -449.015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} - 48 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 - 48 * q^6 - 72 * q^9	\( 8 q - 32 q^{4} - 48 q^{6} - 72 q^{9} - 30 q^{11} + 12 q^{14} + 128 q^{16} + 128 q^{19} + 18 q^{21} + 192 q^{24} - 516 q^{26} + 252 q^{29} + 174 q^{31} + 52 q^{34} + 288 q^{36} - 774 q^{39} - 78 q^{41} + 120 q^{44} - 520 q^{46} - 238 q^{49} + 78 q^{51} + 432 q^{54} - 48 q^{56} + 1530 q^{59} + 1310 q^{61} - 512 q^{64} + 180 q^{66} - 780 q^{69} - 3780 q^{71} + 3924 q^{74} - 512 q^{76} + 1974 q^{79} + 648 q^{81} - 72 q^{84} - 3408 q^{86} + 2814 q^{89} - 3884 q^{91} + 520 q^{94} - 768 q^{96} + 270 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 - 48 * q^6 - 72 * q^9 - 30 * q^11 + 12 * q^14 + 128 * q^16 + 128 * q^19 + 18 * q^21 + 192 * q^24 - 516 * q^26 + 252 * q^29 + 174 * q^31 + 52 * q^34 + 288 * q^36 - 774 * q^39 - 78 * q^41 + 120 * q^44 - 520 * q^46 - 238 * q^49 + 78 * q^51 + 432 * q^54 - 48 * q^56 + 1530 * q^59 + 1310 * q^61 - 512 * q^64 + 180 * q^66 - 780 * q^69 - 3780 * q^71 + 3924 * q^74 - 512 * q^76 + 1974 * q^79 + 648 * q^81 - 72 * q^84 - 3408 * q^86 + 2814 * q^89 - 3884 * q^91 + 520 * q^94 - 768 * q^96 + 270 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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