LMFDB - Embedded newform 825.4.c.k.199.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, 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("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.36142572544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 53x^{4} + 632x^{2} + 484 $ x^6 + 53x^4 + 632x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.5
Root			$5.97123i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.k.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.97123i q^{2} -3.00000i q^{3} -16.7131 q^{4} +14.9137 q^{6} +5.48376i q^{7} -43.3148i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.97123i q^{2} -3.00000i q^{3} -16.7131 q^{4} +14.9137 q^{6} +5.48376i q^{7} -43.3148i q^{8} -9.00000 q^{9} +11.0000 q^{11} +50.1393i q^{12} -24.5738i q^{13} -27.2610 q^{14} +81.6231 q^{16} -59.3687i q^{17} -44.7411i q^{18} -5.89234 q^{19} +16.4513 q^{21} +54.6835i q^{22} +68.4570i q^{23} -129.945 q^{24} +122.162 q^{26} +27.0000i q^{27} -91.6506i q^{28} +265.022 q^{29} -196.554 q^{31} +59.2482i q^{32} -33.0000i q^{33} +295.135 q^{34} +150.418 q^{36} +166.575i q^{37} -29.2922i q^{38} -73.7214 q^{39} +424.101 q^{41} +81.7830i q^{42} +177.351i q^{43} -183.844 q^{44} -340.316 q^{46} +141.148i q^{47} -244.869i q^{48} +312.928 q^{49} -178.106 q^{51} +410.704i q^{52} +339.828i q^{53} -134.223 q^{54} +237.528 q^{56} +17.6770i q^{57} +1317.48i q^{58} -416.784 q^{59} +662.146 q^{61} -977.115i q^{62} -49.3538i q^{63} +358.448 q^{64} +164.051 q^{66} +313.713i q^{67} +992.235i q^{68} +205.371 q^{69} -153.693 q^{71} +389.834i q^{72} -153.866i q^{73} -828.084 q^{74} +98.4793 q^{76} +60.3213i q^{77} -366.486i q^{78} -403.000 q^{79} +81.0000 q^{81} +2108.30i q^{82} +652.313i q^{83} -274.952 q^{84} -881.650 q^{86} -795.065i q^{87} -476.463i q^{88} -1226.77 q^{89} +134.757 q^{91} -1144.13i q^{92} +589.662i q^{93} -701.677 q^{94} +177.745 q^{96} +959.746i q^{97} +1555.64i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	4.97123i	1.75759i	0.477195	+	0.878797i	$0.341653\pi$
$2$	4.97123i	1.75759i	−0.477195	+	0.878797i	$0.658347\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−16.7131	−2.08914
$5$	0	0
$5$	0	0
$6$	14.9137	1.01475
$7$	5.48376i	0.296095i	0.988980	+	0.148048i	$0.0472989\pi$
$7$	5.48376i	0.296095i	−0.988980	+	0.148048i	$0.952701\pi$
$8$	− 43.3148i	− 1.91426i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	50.1393i	1.20616i
$13$	− 24.5738i	− 0.524272i	−0.965031	−	0.262136i	$-0.915573\pi$
$13$	− 24.5738i	− 0.524272i	0.965031	−	0.262136i	$-0.0844270\pi$
$14$	−27.2610	−0.520415
$15$	0	0
$16$	81.6231	1.27536
$17$	− 59.3687i	− 0.847001i	−0.905896	−	0.423501i	$-0.860801\pi$
$17$	− 59.3687i	− 0.847001i	0.905896	−	0.423501i	$-0.139199\pi$
$18$	− 44.7411i	− 0.585865i
$19$	−5.89234	−0.0711471	−0.0355736	−	0.999367i	$-0.511326\pi$
$19$	−5.89234	−0.0711471	−0.0355736	+	0.999367i	$0.511326\pi$
$20$	0	0
$21$	16.4513	0.170951
$22$	54.6835i	0.529935i
$23$	68.4570i	0.620621i	0.950635	+	0.310310i	$0.100433\pi$
$23$	68.4570i	0.620621i	−0.950635	+	0.310310i	$0.899567\pi$
$24$	−129.945	−1.10520
$25$	0	0
$26$	122.162	0.921458
$27$	27.0000i	0.192450i
$28$	− 91.6506i	− 0.618584i
$29$	265.022	1.69701	0.848505	−	0.529187i	$-0.177503\pi$
$29$	265.022	1.69701	0.848505	+	0.529187i	$0.177503\pi$
$30$	0	0
$31$	−196.554	−1.13878	−0.569389	−	0.822068i	$-0.692820\pi$
$31$	−196.554	−1.13878	−0.569389	+	0.822068i	$0.692820\pi$
$32$	59.2482i	0.327303i
$33$	− 33.0000i	− 0.174078i
$34$	295.135	1.48868
$35$	0	0
$36$	150.418	0.696379
$37$	166.575i	0.740131i	0.929006	+	0.370065i	$0.120665\pi$
$37$	166.575i	0.740131i	−0.929006	+	0.370065i	$0.879335\pi$
$38$	− 29.2922i	− 0.125048i
$39$	−73.7214	−0.302689
$40$	0	0
$41$	424.101	1.61545	0.807725	−	0.589559i	$-0.200699\pi$
$41$	424.101	1.61545	0.807725	+	0.589559i	$0.200699\pi$
$42$	81.7830i	0.300462i
$43$	177.351i	0.628970i	0.949262	+	0.314485i	$0.101832\pi$
$43$	177.351i	0.628970i	−0.949262	+	0.314485i	$0.898168\pi$
$44$	−183.844	−0.629899
$45$	0	0
$46$	−340.316	−1.09080
$47$	141.148i	0.438053i	0.975719	+	0.219026i	$0.0702881\pi$
$47$	141.148i	0.438053i	−0.975719	+	0.219026i	$0.929712\pi$
$48$	− 244.869i	− 0.736330i
$49$	312.928	0.912328
$50$	0	0
$51$	−178.106	−0.489016
$52$	410.704i	1.09528i
$53$	339.828i	0.880736i	0.897817	+	0.440368i	$0.145152\pi$
$53$	339.828i	0.880736i	−0.897817	+	0.440368i	$0.854848\pi$
$54$	−134.223	−0.338249
$55$	0	0
$56$	237.528	0.566804
$57$	17.6770i	0.0410768i
$58$	1317.48i	2.98266i
$59$	−416.784	−0.919672	−0.459836	−	0.888004i	$-0.652092\pi$
$59$	−416.784	−0.919672	−0.459836	+	0.888004i	$0.652092\pi$
$60$	0	0
$61$	662.146	1.38982	0.694911	−	0.719096i	$-0.255444\pi$
$61$	662.146	1.38982	0.694911	+	0.719096i	$0.255444\pi$
$62$	− 977.115i	− 2.00151i
$63$	− 49.3538i	− 0.0986984i
$64$	358.448	0.700094
$65$	0	0
$66$	164.051	0.305958
$67$	313.713i	0.572032i	0.958225	+	0.286016i	$0.0923311\pi$
$67$	313.713i	0.572032i	−0.958225	+	0.286016i	$0.907669\pi$
$68$	992.235i	1.76950i
$69$	205.371	0.358316
$70$	0	0
$71$	−153.693	−0.256902	−0.128451	−	0.991716i	$-0.541000\pi$
$71$	−153.693	−0.256902	−0.128451	+	0.991716i	$0.541000\pi$
$72$	389.834i	0.638088i
$73$	− 153.866i	− 0.246694i	−0.992364	−	0.123347i	$-0.960637\pi$
$73$	− 153.866i	− 0.246694i	0.992364	−	0.123347i	$-0.0393628\pi$
$74$	−828.084	−1.30085
$75$	0	0
$76$	98.4793	0.148636
$77$	60.3213i	0.0892760i
$78$	− 366.486i	− 0.532004i
$79$	−403.000	−0.573938	−0.286969	−	0.957940i	$-0.592648\pi$
$79$	−403.000	−0.573938	−0.286969	+	0.957940i	$0.592648\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	2108.30i	2.83931i
$83$	652.313i	0.862659i	0.902195	+	0.431329i	$0.141955\pi$
$83$	652.313i	0.862659i	−0.902195	+	0.431329i	$0.858045\pi$
$84$	−274.952	−0.357139
$85$	0	0
$86$	−881.650	−1.10547
$87$	− 795.065i	− 0.979769i
$88$	− 476.463i	− 0.577172i
$89$	−1226.77	−1.46109	−0.730545	−	0.682864i	$-0.760734\pi$
$89$	−1226.77	−1.46109	−0.730545	+	0.682864i	$0.760734\pi$
$90$	0	0
$91$	134.757	0.155234
$92$	− 1144.13i	− 1.29656i
$93$	589.662i	0.657474i
$94$	−701.677	−0.769919
$95$	0	0
$96$	177.745	0.188969
$97$	959.746i	1.00461i	0.864690	+	0.502306i	$0.167515\pi$
$97$	959.746i	1.00461i	−0.864690	+	0.502306i	$0.832485\pi$
$98$	1555.64i	1.60350i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−1258.52	−1.23988	−0.619939	−	0.784650i	$-0.712843\pi$
$101$	−1258.52	−1.23988	−0.619939	+	0.784650i	$0.712843\pi$
$102$	− 885.406i	− 0.859492i
$103$	493.175i	0.471786i	0.971779	+	0.235893i	$0.0758015\pi$
$103$	493.175i	0.471786i	−0.971779	+	0.235893i	$0.924198\pi$
$104$	−1064.41	−1.00360
$105$	0	0
$106$	−1689.36	−1.54798
$107$	− 1099.05i	− 0.992983i	−0.868042	−	0.496492i	$-0.834621\pi$
$107$	− 1099.05i	− 0.992983i	0.868042	−	0.496492i	$-0.165379\pi$
$108$	− 451.254i	− 0.402055i
$109$	−1275.04	−1.12043	−0.560216	−	0.828347i	$-0.689282\pi$
$109$	−1275.04	−1.12043	−0.560216	+	0.828347i	$0.689282\pi$
$110$	0	0
$111$	499.726	0.427315
$112$	447.601i	0.377628i
$113$	946.433i	0.787902i	0.919131	+	0.393951i	$0.128892\pi$
$113$	946.433i	0.787902i	−0.919131	+	0.393951i	$0.871108\pi$
$114$	−87.8765	−0.0721964
$115$	0	0
$116$	−4429.34	−3.54529
$117$	221.164i	0.174757i
$118$	− 2071.93i	− 1.61641i
$119$	325.563	0.250793
$120$	0	0
$121$	121.000	0.0909091
$122$	3291.68i	2.44274i
$123$	− 1272.30i	− 0.932681i
$124$	3285.03	2.37907
$125$	0	0
$126$	245.349	0.173472
$127$	2260.77i	1.57962i	0.613354	+	0.789808i	$0.289820\pi$
$127$	2260.77i	1.57962i	−0.613354	+	0.789808i	$0.710180\pi$
$128$	2255.91i	1.55778i
$129$	532.052	0.363136
$130$	0	0
$131$	−57.1277	−0.0381013	−0.0190507	−	0.999819i	$-0.506064\pi$
$131$	−57.1277	−0.0381013	−0.0190507	+	0.999819i	$0.506064\pi$
$132$	551.533i	0.363672i
$133$	− 32.3122i	− 0.0210663i
$134$	−1559.54	−1.00540
$135$	0	0
$136$	−2571.54	−1.62138
$137$	1919.27i	1.19689i	0.801162	+	0.598447i	$0.204215\pi$
$137$	1919.27i	1.19689i	−0.801162	+	0.598447i	$0.795785\pi$
$138$	1020.95i	0.629774i
$139$	1690.46	1.03153	0.515766	−	0.856729i	$-0.327507\pi$
$139$	1690.46	1.03153	0.515766	+	0.856729i	$0.327507\pi$
$140$	0	0
$141$	423.443	0.252910
$142$	− 764.044i	− 0.451529i
$143$	− 270.312i	− 0.158074i
$144$	−734.608	−0.425120
$145$	0	0
$146$	764.904	0.433588
$147$	− 938.785i	− 0.526733i
$148$	− 2783.99i	− 1.54624i
$149$	2077.88	1.14246	0.571231	−	0.820789i	$-0.306466\pi$
$149$	2077.88	1.14246	0.571231	+	0.820789i	$0.306466\pi$
$150$	0	0
$151$	2711.16	1.46113	0.730566	−	0.682842i	$-0.239256\pi$
$151$	2711.16	1.46113	0.730566	+	0.682842i	$0.239256\pi$
$152$	255.226i	0.136194i
$153$	534.318i	0.282334i
$154$	−299.871	−0.156911
$155$	0	0
$156$	1232.11	0.632359
$157$	2341.23i	1.19013i	0.803677	+	0.595066i	$0.202874\pi$
$157$	2341.23i	1.19013i	−0.803677	+	0.595066i	$0.797126\pi$
$158$	− 2003.41i	− 1.00875i
$159$	1019.48	0.508493
$160$	0	0
$161$	−375.402	−0.183763
$162$	402.669i	0.195288i
$163$	− 3523.01i	− 1.69291i	−0.532464	−	0.846453i	$-0.678734\pi$
$163$	− 3523.01i	− 1.69291i	0.532464	−	0.846453i	$-0.321266\pi$
$164$	−7088.05	−3.37490
$165$	0	0
$166$	−3242.80	−1.51620
$167$	4011.90i	1.85898i	0.368842	+	0.929492i	$0.379754\pi$
$167$	4011.90i	1.85898i	−0.368842	+	0.929492i	$0.620246\pi$
$168$	− 712.584i	− 0.327244i
$169$	1593.13	0.725138
$170$	0	0
$171$	53.0310	0.0237157
$172$	− 2964.08i	− 1.31400i
$173$	− 3325.30i	− 1.46137i	−0.682713	−	0.730687i	$-0.739200\pi$
$173$	− 3325.30i	− 1.46137i	0.682713	−	0.730687i	$-0.260800\pi$
$174$	3952.45	1.72204
$175$	0	0
$176$	897.854	0.384536
$177$	1250.35i	0.530973i
$178$	− 6098.54i	− 2.56800i
$179$	26.6350	0.0111217	0.00556087	−	0.999985i	$-0.498230\pi$
$179$	26.6350	0.0111217	0.00556087	+	0.999985i	$0.498230\pi$
$180$	0	0
$181$	1934.25	0.794320	0.397160	−	0.917749i	$-0.369996\pi$
$181$	1934.25	0.794320	0.397160	+	0.917749i	$0.369996\pi$
$182$	669.906i	0.272839i
$183$	− 1986.44i	− 0.802414i
$184$	2965.21	1.18803
$185$	0	0
$186$	−2931.34	−1.15557
$187$	− 653.055i	− 0.255380i
$188$	− 2359.01i	− 0.915153i
$189$	−148.061	−0.0569835
$190$	0	0
$191$	−3341.59	−1.26591	−0.632956	−	0.774188i	$-0.718158\pi$
$191$	−3341.59	−1.26591	−0.632956	+	0.774188i	$0.718158\pi$
$192$	− 1075.34i	− 0.404200i
$193$	1293.97i	0.482600i	0.970451	+	0.241300i	$0.0775737\pi$
$193$	1293.97i	0.482600i	−0.970451	+	0.241300i	$0.922426\pi$
$194$	−4771.12	−1.76570
$195$	0	0
$196$	−5230.01	−1.90598
$197$	− 2301.17i	− 0.832240i	−0.909310	−	0.416120i	$-0.863390\pi$
$197$	− 2301.17i	− 0.832240i	0.909310	−	0.416120i	$-0.136610\pi$
$198$	− 492.152i	− 0.176645i
$199$	3039.64	1.08279	0.541393	−	0.840770i	$-0.317897\pi$
$199$	3039.64	1.08279	0.541393	+	0.840770i	$0.317897\pi$
$200$	0	0
$201$	941.139	0.330263
$202$	− 6256.40i	− 2.17920i
$203$	1453.31i	0.502476i
$204$	2976.70	1.02162
$205$	0	0
$206$	−2451.69	−0.829209
$207$	− 616.113i	− 0.206874i
$208$	− 2005.79i	− 0.668636i
$209$	−64.8157	−0.0214517
$210$	0	0
$211$	2807.86	0.916119	0.458060	−	0.888921i	$-0.348545\pi$
$211$	2807.86	0.916119	0.458060	+	0.888921i	$0.348545\pi$
$212$	− 5679.58i	− 1.83998i
$213$	461.080i	0.148322i
$214$	5463.63	1.74526
$215$	0	0
$216$	1169.50	0.368400
$217$	− 1077.85i	− 0.337187i
$218$	− 6338.53i	− 1.96926i
$219$	−461.598	−0.142429
$220$	0	0
$221$	−1458.91	−0.444059
$222$	2484.25i	0.751046i
$223$	− 1443.09i	− 0.433348i	−0.976244	−	0.216674i	$-0.930479\pi$
$223$	− 1443.09i	− 0.433348i	0.976244	−	0.216674i	$-0.0695209\pi$
$224$	−324.903	−0.0969129
$225$	0	0
$226$	−4704.94	−1.38481
$227$	3658.71i	1.06977i	0.844926	+	0.534884i	$0.179645\pi$
$227$	3658.71i	1.06977i	−0.844926	+	0.534884i	$0.820355\pi$
$228$	− 295.438i	− 0.0858151i
$229$	1695.50	0.489265	0.244632	−	0.969616i	$-0.421333\pi$
$229$	1695.50	0.489265	0.244632	+	0.969616i	$0.421333\pi$
$230$	0	0
$231$	180.964	0.0515435
$232$	− 11479.4i	− 3.24853i
$233$	5782.24i	1.62578i	0.582417	+	0.812890i	$0.302107\pi$
$233$	5782.24i	1.62578i	−0.582417	+	0.812890i	$0.697893\pi$
$234$	−1099.46	−0.307153
$235$	0	0
$236$	6965.76	1.92132
$237$	1209.00i	0.331363i
$238$	1618.45i	0.440792i
$239$	5836.16	1.57954	0.789770	−	0.613404i	$-0.210200\pi$
$239$	5836.16	1.57954	0.789770	+	0.613404i	$0.210200\pi$
$240$	0	0
$241$	−982.308	−0.262556	−0.131278	−	0.991346i	$-0.541908\pi$
$241$	−982.308	−0.262556	−0.131278	+	0.991346i	$0.541908\pi$
$242$	601.519i	0.159781i
$243$	− 243.000i	− 0.0641500i
$244$	−11066.5	−2.90353
$245$	0	0
$246$	6324.91	1.63927
$247$	144.797i	0.0373005i
$248$	8513.70i	2.17992i
$249$	1956.94	0.498056
$250$	0	0
$251$	4320.23	1.08642	0.543209	−	0.839598i	$-0.317209\pi$
$251$	4320.23	1.08642	0.543209	+	0.839598i	$0.317209\pi$
$252$	824.856i	0.206195i
$253$	753.027i	0.187124i
$254$	−11238.8	−2.77633
$255$	0	0
$256$	−8347.07	−2.03786
$257$	− 6224.29i	− 1.51074i	−0.655298	−	0.755371i	$-0.727457\pi$
$257$	− 6224.29i	− 1.51074i	0.655298	−	0.755371i	$-0.272543\pi$
$258$	2644.95i	0.638246i
$259$	−913.459	−0.219149
$260$	0	0
$261$	−2385.20	−0.565670
$262$	− 283.995i	− 0.0669666i
$263$	2588.95i	0.607002i	0.952831	+	0.303501i	$0.0981555\pi$
$263$	2588.95i	0.607002i	−0.952831	+	0.303501i	$0.901844\pi$
$264$	−1429.39	−0.333230
$265$	0	0
$266$	160.631	0.0370260
$267$	3680.30i	0.843561i
$268$	− 5243.12i	− 1.19505i
$269$	5871.53	1.33083	0.665415	−	0.746473i	$-0.268254\pi$
$269$	5871.53	1.33083	0.665415	+	0.746473i	$0.268254\pi$
$270$	0	0
$271$	−3306.93	−0.741261	−0.370630	−	0.928780i	$-0.620858\pi$
$271$	−3306.93	−0.741261	−0.370630	+	0.928780i	$0.620858\pi$
$272$	− 4845.85i	− 1.08023i
$273$	− 404.270i	− 0.0896247i
$274$	−9541.14	−2.10366
$275$	0	0
$276$	−3432.39	−0.748571
$277$	− 2861.37i	− 0.620660i	−0.950629	−	0.310330i	$-0.899560\pi$
$277$	− 2861.37i	− 0.620660i	0.950629	−	0.310330i	$-0.100440\pi$
$278$	8403.66i	1.81302i
$279$	1768.99	0.379593
$280$	0	0
$281$	−2988.05	−0.634349	−0.317174	−	0.948367i	$-0.602734\pi$
$281$	−2988.05	−0.634349	−0.317174	+	0.948367i	$0.602734\pi$
$282$	2105.03i	0.444513i
$283$	− 1454.60i	− 0.305536i	−0.988262	−	0.152768i	$-0.951181\pi$
$283$	− 1454.60i	− 0.305536i	0.988262	−	0.152768i	$-0.0488188\pi$
$284$	2568.69	0.536704
$285$	0	0
$286$	1343.78	0.277830
$287$	2325.67i	0.478327i
$288$	− 533.234i	− 0.109101i
$289$	1388.36	0.282589
$290$	0	0
$291$	2879.24	0.580014
$292$	2571.58i	0.515378i
$293$	8586.52i	1.71205i	0.516937	+	0.856023i	$0.327072\pi$
$293$	8586.52i	1.71205i	−0.516937	+	0.856023i	$0.672928\pi$
$294$	4666.92	0.925782
$295$	0	0
$296$	7215.19	1.41681
$297$	297.000i	0.0580259i
$298$	10329.6i	2.00798i
$299$	1682.25	0.325374
$300$	0	0
$301$	−972.547	−0.186235
$302$	13477.8i	2.56808i
$303$	3775.57i	0.715844i
$304$	−480.951	−0.0907382
$305$	0	0
$306$	−2656.22	−0.496228
$307$	529.029i	0.0983495i	0.998790	+	0.0491748i	$0.0156591\pi$
$307$	529.029i	0.0983495i	−0.998790	+	0.0491748i	$0.984341\pi$
$308$	− 1008.16i	− 0.186510i
$309$	1479.53	0.272386
$310$	0	0
$311$	−5008.00	−0.913111	−0.456555	−	0.889695i	$-0.650917\pi$
$311$	−5008.00	−0.913111	−0.456555	+	0.889695i	$0.650917\pi$
$312$	3193.23i	0.579426i
$313$	− 7858.53i	− 1.41914i	−0.704635	−	0.709570i	$-0.748889\pi$
$313$	− 7858.53i	− 1.41914i	0.704635	−	0.709570i	$-0.251111\pi$
$314$	−11638.8	−2.09177
$315$	0	0
$316$	6735.39	1.19904
$317$	7747.04i	1.37261i	0.727315	+	0.686304i	$0.240768\pi$
$317$	7747.04i	1.37261i	−0.727315	+	0.686304i	$0.759232\pi$
$318$	5068.09i	0.893724i
$319$	2915.24	0.511668
$320$	0	0
$321$	−3297.15	−0.573299
$322$	− 1866.21i	− 0.322980i
$323$	349.820i	0.0602617i
$324$	−1353.76	−0.232126
$325$	0	0
$326$	17513.7	2.97544
$327$	3825.13i	0.646882i
$328$	− 18369.9i	− 3.09240i
$329$	−774.019	−0.129705
$330$	0	0
$331$	1355.08	0.225022	0.112511	−	0.993650i	$-0.464111\pi$
$331$	1355.08	0.225022	0.112511	+	0.993650i	$0.464111\pi$
$332$	− 10902.2i	− 1.80221i
$333$	− 1499.18i	− 0.246710i
$334$	−19944.1	−3.26734
$335$	0	0
$336$	1342.80	0.218024
$337$	2596.97i	0.419780i	0.977725	+	0.209890i	$0.0673106\pi$
$337$	2596.97i	0.419780i	−0.977725	+	0.209890i	$0.932689\pi$
$338$	7919.81i	1.27450i
$339$	2839.30	0.454896
$340$	0	0
$341$	−2162.09	−0.343355
$342$	263.629i	0.0416826i
$343$	3596.95i	0.566231i
$344$	7681.91	1.20401
$345$	0	0
$346$	16530.8	2.56850
$347$	266.820i	0.0412785i	0.999787	+	0.0206392i	$0.00657014\pi$
$347$	266.820i	0.0412785i	−0.999787	+	0.0206392i	$0.993430\pi$
$348$	13288.0i	2.04687i
$349$	10549.4	1.61804	0.809021	−	0.587780i	$-0.199998\pi$
$349$	10549.4	1.61804	0.809021	+	0.587780i	$0.199998\pi$
$350$	0	0
$351$	663.492	0.100896
$352$	651.730i	0.0986856i
$353$	− 7152.63i	− 1.07846i	−0.842159	−	0.539229i	$-0.818716\pi$
$353$	− 7152.63i	− 1.07846i	0.842159	−	0.539229i	$-0.181284\pi$
$354$	−6215.79	−0.933235
$355$	0	0
$356$	20503.1	3.05242
$357$	− 976.690i	− 0.144795i
$358$	132.409i	0.0195475i
$359$	−359.182	−0.0528047	−0.0264024	−	0.999651i	$-0.508405\pi$
$359$	−359.182	−0.0528047	−0.0264024	+	0.999651i	$0.508405\pi$
$360$	0	0
$361$	−6824.28	−0.994938
$362$	9615.62i	1.39609i
$363$	− 363.000i	− 0.0524864i
$364$	−2252.20	−0.324306
$365$	0	0
$366$	9875.04	1.41032
$367$	9042.47i	1.28614i	0.765808	+	0.643070i	$0.222339\pi$
$367$	9042.47i	1.28614i	−0.765808	+	0.643070i	$0.777661\pi$
$368$	5587.67i	0.791515i
$369$	−3816.91	−0.538483
$370$	0	0
$371$	−1863.54	−0.260781
$372$	− 9855.08i	− 1.37355i
$373$	11929.0i	1.65592i	0.560787	+	0.827960i	$0.310499\pi$
$373$	11929.0i	1.65592i	−0.560787	+	0.827960i	$0.689501\pi$
$374$	3246.49	0.448855
$375$	0	0
$376$	6113.78	0.838549
$377$	− 6512.59i	− 0.889696i
$378$	− 736.047i	− 0.100154i
$379$	−6556.08	−0.888557	−0.444279	−	0.895889i	$-0.646540\pi$
$379$	−6556.08	−0.888557	−0.444279	+	0.895889i	$0.646540\pi$
$380$	0	0
$381$	6782.32	0.911992
$382$	− 16611.8i	− 2.22496i
$383$	− 10703.1i	− 1.42795i	−0.700172	−	0.713975i	$-0.746893\pi$
$383$	− 10703.1i	− 1.42795i	0.700172	−	0.713975i	$-0.253107\pi$
$384$	6767.74	0.899388
$385$	0	0
$386$	−6432.60	−0.848214
$387$	− 1596.15i	− 0.209657i
$388$	− 16040.3i	− 2.09878i
$389$	6450.30	0.840728	0.420364	−	0.907355i	$-0.361902\pi$
$389$	6450.30	0.840728	0.420364	+	0.907355i	$0.361902\pi$
$390$	0	0
$391$	4064.20	0.525667
$392$	− 13554.4i	− 1.74644i
$393$	171.383i	0.0219978i
$394$	11439.6	1.46274
$395$	0	0
$396$	1654.60	0.209966
$397$	− 12526.0i	− 1.58353i	−0.610828	−	0.791764i	$-0.709163\pi$
$397$	− 12526.0i	− 1.58353i	0.610828	−	0.791764i	$-0.290837\pi$
$398$	15110.7i	1.90310i
$399$	−96.9365	−0.0121626
$400$	0	0
$401$	9119.52	1.13568	0.567839	−	0.823139i	$-0.307779\pi$
$401$	9119.52	1.13568	0.567839	+	0.823139i	$0.307779\pi$
$402$	4678.62i	0.580468i
$403$	4830.08i	0.597030i
$404$	21033.8	2.59028
$405$	0	0
$406$	−7224.76	−0.883150
$407$	1832.33i	0.223158i
$408$	7714.63i	0.936106i
$409$	596.921	0.0721658	0.0360829	−	0.999349i	$-0.488512\pi$
$409$	596.921	0.0721658	0.0360829	+	0.999349i	$0.488512\pi$
$410$	0	0
$411$	5757.82	0.691027
$412$	− 8242.49i	− 0.985627i
$413$	− 2285.54i	− 0.272310i
$414$	3062.84	0.363600
$415$	0	0
$416$	1455.95	0.171596
$417$	− 5071.38i	− 0.595555i
$418$	− 322.214i	− 0.0377033i
$419$	−11560.5	−1.34789	−0.673944	−	0.738782i	$-0.735401\pi$
$419$	−11560.5	−1.34789	−0.673944	+	0.738782i	$0.735401\pi$
$420$	0	0
$421$	15182.6	1.75761	0.878805	−	0.477182i	$-0.158342\pi$
$421$	15182.6	1.75761	0.878805	+	0.477182i	$0.158342\pi$
$422$	13958.5i	1.61017i
$423$	− 1270.33i	− 0.146018i
$424$	14719.6	1.68596
$425$	0	0
$426$	−2292.13	−0.260691
$427$	3631.05i	0.411519i
$428$	18368.5i	2.07448i
$429$	−810.935	−0.0912641
$430$	0	0
$431$	−14902.7	−1.66551	−0.832757	−	0.553639i	$-0.813239\pi$
$431$	−14902.7	−1.66551	−0.832757	+	0.553639i	$0.813239\pi$
$432$	2203.82i	0.245443i
$433$	2269.85i	0.251922i	0.992035	+	0.125961i	$0.0402014\pi$
$433$	2269.85i	0.251922i	−0.992035	+	0.125961i	$0.959799\pi$
$434$	5358.26	0.592637
$435$	0	0
$436$	21309.9	2.34074
$437$	− 403.372i	− 0.0441554i
$438$	− 2294.71i	− 0.250332i
$439$	13418.7	1.45886	0.729431	−	0.684054i	$-0.239785\pi$
$439$	13418.7	1.45886	0.729431	+	0.684054i	$0.239785\pi$
$440$	0	0
$441$	−2816.36	−0.304109
$442$	− 7252.59i	− 0.780476i
$443$	− 11507.5i	− 1.23417i	−0.786896	−	0.617086i	$-0.788313\pi$
$443$	− 11507.5i	− 1.23417i	0.786896	−	0.617086i	$-0.211687\pi$
$444$	−8351.98	−0.892719
$445$	0	0
$446$	7173.94	0.761650
$447$	− 6233.65i	− 0.659601i
$448$	1965.64i	0.207294i
$449$	16203.8	1.70313	0.851564	−	0.524250i	$-0.175654\pi$
$449$	16203.8	1.70313	0.851564	+	0.524250i	$0.175654\pi$
$450$	0	0
$451$	4665.11	0.487077
$452$	− 15817.8i	− 1.64604i
$453$	− 8133.48i	− 0.843585i
$454$	−18188.3	−1.88022
$455$	0	0
$456$	765.677	0.0786318
$457$	4912.79i	0.502868i	0.967874	+	0.251434i	$0.0809022\pi$
$457$	4912.79i	0.502868i	−0.967874	+	0.251434i	$0.919098\pi$
$458$	8428.70i	0.859929i
$459$	1602.95	0.163005
$460$	0	0
$461$	−14270.8	−1.44178	−0.720888	−	0.693051i	$-0.756266\pi$
$461$	−14270.8	−1.44178	−0.720888	+	0.693051i	$0.756266\pi$
$462$	899.613i	0.0905926i
$463$	− 6656.46i	− 0.668146i	−0.942547	−	0.334073i	$-0.891577\pi$
$463$	− 6656.46i	− 0.668146i	0.942547	−	0.334073i	$-0.108423\pi$
$464$	21631.9	2.16430
$465$	0	0
$466$	−28744.8	−2.85746
$467$	19347.7i	1.91714i	0.284853	+	0.958571i	$0.408055\pi$
$467$	19347.7i	1.91714i	−0.284853	+	0.958571i	$0.591945\pi$
$468$	− 3696.34i	− 0.365093i
$469$	−1720.33	−0.169376
$470$	0	0
$471$	7023.70	0.687123
$472$	18052.9i	1.76050i
$473$	1950.86i	0.189642i
$474$	−6010.22	−0.582402
$475$	0	0
$476$	−5441.18	−0.523941
$477$	− 3058.45i	− 0.293579i
$478$	29012.9i	2.77619i
$479$	−9826.69	−0.937355	−0.468678	−	0.883369i	$-0.655269\pi$
$479$	−9826.69	−0.937355	−0.468678	+	0.883369i	$0.655269\pi$
$480$	0	0
$481$	4093.39	0.388030
$482$	− 4883.28i	− 0.461467i
$483$	1126.21i	0.106095i
$484$	−2022.29	−0.189922
$485$	0	0
$486$	1208.01	0.112750
$487$	10278.1i	0.956353i	0.878264	+	0.478176i	$0.158702\pi$
$487$	10278.1i	0.956353i	−0.878264	+	0.478176i	$0.841298\pi$
$488$	− 28680.7i	− 2.66048i
$489$	−10569.0	−0.977400
$490$	0	0
$491$	11397.1	1.04755	0.523773	−	0.851858i	$-0.324524\pi$
$491$	11397.1	1.04755	0.523773	+	0.851858i	$0.324524\pi$
$492$	21264.1i	1.94850i
$493$	− 15734.0i	− 1.43737i
$494$	−719.819	−0.0655591
$495$	0	0
$496$	−16043.3	−1.45235
$497$	− 842.817i	− 0.0760674i
$498$	9728.39i	0.875381i
$499$	9179.17	0.823479	0.411740	−	0.911302i	$-0.364921\pi$
$499$	9179.17	0.823479	0.411740	+	0.911302i	$0.364921\pi$
$500$	0	0
$501$	12035.7	1.07329
$502$	21476.9i	1.90948i
$503$	− 6782.80i	− 0.601253i	−0.953742	−	0.300626i	$-0.902804\pi$
$503$	− 6782.80i	− 0.601253i	0.953742	−	0.300626i	$-0.0971957\pi$
$504$	−2137.75	−0.188935
$505$	0	0
$506$	−3743.47	−0.328889
$507$	− 4779.39i	− 0.418659i
$508$	− 37784.6i	− 3.30004i
$509$	−6814.24	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$509$	−6814.24	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$510$	0	0
$511$	843.765	0.0730449
$512$	− 23447.9i	− 2.02395i
$513$	− 159.093i	− 0.0136923i
$514$	30942.4	2.65527
$515$	0	0
$516$	−8892.23	−0.758641
$517$	1552.62i	0.132078i
$518$	− 4541.01i	− 0.385175i
$519$	−9975.89	−0.843724
$520$	0	0
$521$	206.712	0.0173824	0.00869118	−	0.999962i	$-0.497233\pi$
$521$	206.712	0.0173824	0.00869118	+	0.999962i	$0.497233\pi$
$522$	− 11857.4i	− 0.994219i
$523$	11375.9i	0.951118i	0.879684	+	0.475559i	$0.157754\pi$
$523$	11375.9i	0.951118i	−0.879684	+	0.475559i	$0.842246\pi$
$524$	954.781	0.0795989
$525$	0	0
$526$	−12870.3	−1.06686
$527$	11669.1i	0.964547i
$528$	− 2693.56i	− 0.222012i
$529$	7480.63	0.614830
$530$	0	0
$531$	3751.06	0.306557
$532$	540.036i	0.0440104i
$533$	− 10421.8i	− 0.846936i
$534$	−18295.6	−1.48264
$535$	0	0
$536$	13588.4	1.09502
$537$	− 79.9049i	− 0.00642114i
$538$	29188.7i	2.33906i
$539$	3442.21	0.275077
$540$	0	0
$541$	−10228.1	−0.812831	−0.406415	−	0.913688i	$-0.633221\pi$
$541$	−10228.1	−0.812831	−0.406415	+	0.913688i	$0.633221\pi$
$542$	− 16439.5i	− 1.30284i
$543$	− 5802.76i	− 0.458601i
$544$	3517.49	0.277226
$545$	0	0
$546$	2009.72	0.157524
$547$	− 15538.9i	− 1.21461i	−0.794467	−	0.607307i	$-0.792250\pi$
$547$	− 15538.9i	− 1.21461i	0.794467	−	0.607307i	$-0.207750\pi$
$548$	− 32077.0i	− 2.50048i
$549$	−5959.31	−0.463274
$550$	0	0
$551$	−1561.60	−0.120737
$552$	− 8895.62i	− 0.685911i
$553$	− 2209.96i	− 0.169940i
$554$	14224.5	1.09087
$555$	0	0
$556$	−28252.8	−2.15501
$557$	− 5191.17i	− 0.394896i	−0.980313	−	0.197448i	$-0.936735\pi$
$557$	− 5191.17i	− 0.394896i	0.980313	−	0.197448i	$-0.0632653\pi$
$558$	8794.03i	0.667170i
$559$	4358.17	0.329752
$560$	0	0
$561$	−1959.17	−0.147444
$562$	− 14854.3i	− 1.11493i
$563$	− 13722.9i	− 1.02727i	−0.858009	−	0.513635i	$-0.828299\pi$
$563$	− 13722.9i	− 1.02727i	0.858009	−	0.513635i	$-0.171701\pi$
$564$	−7077.04	−0.528364
$565$	0	0
$566$	7231.13	0.537009
$567$	444.184i	0.0328995i
$568$	6657.20i	0.491778i
$569$	−23209.0	−1.70997	−0.854986	−	0.518652i	$-0.826434\pi$
$569$	−23209.0	−1.70997	−0.854986	+	0.518652i	$0.826434\pi$
$570$	0	0
$571$	−13130.5	−0.962337	−0.481168	−	0.876628i	$-0.659787\pi$
$571$	−13130.5	−0.962337	−0.481168	+	0.876628i	$0.659787\pi$
$572$	4517.75i	0.330239i
$573$	10024.8i	0.730874i
$574$	−11561.4	−0.840705
$575$	0	0
$576$	−3226.03	−0.233365
$577$	− 12261.0i	− 0.884633i	−0.896859	−	0.442317i	$-0.854157\pi$
$577$	− 12261.0i	− 0.884633i	0.896859	−	0.442317i	$-0.145843\pi$
$578$	6901.86i	0.496677i
$579$	3881.90	0.278629
$580$	0	0
$581$	−3577.13	−0.255429
$582$	14313.3i	1.01943i
$583$	3738.11i	0.265552i
$584$	−6664.69	−0.472238
$585$	0	0
$586$	−42685.5	−3.00908
$587$	− 3553.42i	− 0.249856i	−0.992166	−	0.124928i	$-0.960130\pi$
$587$	− 3553.42i	− 0.249856i	0.992166	−	0.124928i	$-0.0398700\pi$
$588$	15690.0i	1.10042i
$589$	1158.16	0.0810208
$590$	0	0
$591$	−6903.50	−0.480494
$592$	13596.4i	0.943933i
$593$	− 1942.83i	− 0.134540i	−0.997735	−	0.0672701i	$-0.978571\pi$
$593$	− 1942.83i	− 0.134540i	0.997735	−	0.0672701i	$-0.0214289\pi$
$594$	−1476.45	−0.101986
$595$	0	0
$596$	−34727.9	−2.38676
$597$	− 9118.92i	− 0.625147i
$598$	8362.84i	0.571876i
$599$	−18585.4	−1.26774	−0.633871	−	0.773439i	$-0.718535\pi$
$599$	−18585.4	−1.26774	−0.633871	+	0.773439i	$0.718535\pi$
$600$	0	0
$601$	8010.10	0.543658	0.271829	−	0.962346i	$-0.412371\pi$
$601$	8010.10	0.543658	0.271829	+	0.962346i	$0.412371\pi$
$602$	− 4834.75i	− 0.327325i
$603$	− 2823.42i	− 0.190677i
$604$	−45311.9	−3.05251
$605$	0	0
$606$	−18769.2	−1.25816
$607$	− 1537.69i	− 0.102822i	−0.998678	−	0.0514111i	$-0.983628\pi$
$607$	− 1537.69i	− 0.102822i	0.998678	−	0.0514111i	$-0.0163719\pi$
$608$	− 349.110i	− 0.0232867i
$609$	4359.94	0.290105
$610$	0	0
$611$	3468.53	0.229659
$612$	− 8930.11i	− 0.589834i
$613$	− 2298.75i	− 0.151461i	−0.997128	−	0.0757304i	$-0.975871\pi$
$613$	− 2298.75i	− 0.151461i	0.997128	−	0.0757304i	$-0.0241289\pi$
$614$	−2629.93	−0.172859
$615$	0	0
$616$	2612.81	0.170898
$617$	6089.51i	0.397333i	0.980067	+	0.198666i	$0.0636610\pi$
$617$	6089.51i	0.397333i	−0.980067	+	0.198666i	$0.936339\pi$
$618$	7355.06i	0.478744i
$619$	−12255.4	−0.795775	−0.397887	−	0.917434i	$-0.630257\pi$
$619$	−12255.4	−0.795775	−0.397887	+	0.917434i	$0.630257\pi$
$620$	0	0
$621$	−1848.34	−0.119439
$622$	− 24895.9i	− 1.60488i
$623$	− 6727.29i	− 0.432622i
$624$	−6017.36	−0.386037
$625$	0	0
$626$	39066.6	2.49427
$627$	194.447i	0.0123851i
$628$	− 39129.3i	− 2.48635i
$629$	9889.36	0.626891
$630$	0	0
$631$	−25746.5	−1.62433	−0.812165	−	0.583428i	$-0.801711\pi$
$631$	−25746.5	−1.62433	−0.812165	+	0.583428i	$0.801711\pi$
$632$	17455.9i	1.09867i
$633$	− 8423.58i	− 0.528922i
$634$	−38512.3	−2.41249
$635$	0	0
$636$	−17038.8	−1.06231
$637$	− 7689.84i	− 0.478308i
$638$	14492.3i	0.899305i
$639$	1383.24	0.0856340
$640$	0	0
$641$	−598.022	−0.0368494	−0.0184247	−	0.999830i	$-0.505865\pi$
$641$	−598.022	−0.0368494	−0.0184247	+	0.999830i	$0.505865\pi$
$642$	− 16390.9i	− 1.00763i
$643$	− 14610.9i	− 0.896109i	−0.894006	−	0.448054i	$-0.852117\pi$
$643$	− 14610.9i	− 0.896109i	0.894006	−	0.448054i	$-0.147883\pi$
$644$	6274.13	0.383906
$645$	0	0
$646$	−1739.04	−0.105916
$647$	− 17252.3i	− 1.04831i	−0.851622	−	0.524156i	$-0.824381\pi$
$647$	− 17252.3i	− 1.04831i	0.851622	−	0.524156i	$-0.175619\pi$
$648$	− 3508.50i	− 0.212696i
$649$	−4584.63	−0.277292
$650$	0	0
$651$	−3233.56	−0.194675
$652$	58880.5i	3.53671i
$653$	17768.6i	1.06484i	0.846481	+	0.532418i	$0.178717\pi$
$653$	17768.6i	1.06484i	−0.846481	+	0.532418i	$0.821283\pi$
$654$	−19015.6	−1.13696
$655$	0	0
$656$	34616.4	2.06028
$657$	1384.80i	0.0822314i
$658$	− 3847.82i	− 0.227969i
$659$	17594.9	1.04006	0.520031	−	0.854147i	$-0.325920\pi$
$659$	17594.9	1.04006	0.520031	+	0.854147i	$0.325920\pi$
$660$	0	0
$661$	23355.9	1.37434	0.687170	−	0.726497i	$-0.258853\pi$
$661$	23355.9	1.37434	0.687170	+	0.726497i	$0.258853\pi$
$662$	6736.44i	0.395497i
$663$	4376.74i	0.256378i
$664$	28254.8	1.65136
$665$	0	0
$666$	7452.76	0.433617
$667$	18142.6i	1.05320i
$668$	− 67051.4i	− 3.88368i
$669$	−4329.28	−0.250194
$670$	0	0
$671$	7283.61	0.419047
$672$	974.708i	0.0559527i
$673$	2340.47i	0.134054i	0.997751	+	0.0670271i	$0.0213514\pi$
$673$	2340.47i	0.134054i	−0.997751	+	0.0670271i	$0.978649\pi$
$674$	−12910.1	−0.737803
$675$	0	0
$676$	−26626.1	−1.51491
$677$	− 16562.2i	− 0.940234i	−0.882604	−	0.470117i	$-0.844212\pi$
$677$	− 16562.2i	− 0.940234i	0.882604	−	0.470117i	$-0.155788\pi$
$678$	14114.8i	0.799522i
$679$	−5263.01	−0.297461
$680$	0	0
$681$	10976.1	0.617630
$682$	− 10748.3i	− 0.603478i
$683$	− 22303.4i	− 1.24951i	−0.780821	−	0.624755i	$-0.785199\pi$
$683$	− 22303.4i	− 1.24951i	0.780821	−	0.624755i	$-0.214801\pi$
$684$	−886.313	−0.0495454
$685$	0	0
$686$	−17881.3	−0.995204
$687$	− 5086.49i	− 0.282477i
$688$	14475.9i	0.802163i
$689$	8350.87	0.461745
$690$	0	0
$691$	6244.91	0.343802	0.171901	−	0.985114i	$-0.445009\pi$
$691$	6244.91	0.343802	0.171901	+	0.985114i	$0.445009\pi$
$692$	55576.0i	3.05301i
$693$	− 542.892i	− 0.0297587i
$694$	−1326.42	−0.0725508
$695$	0	0
$696$	−34438.1	−1.87554
$697$	− 25178.3i	− 1.36829i
$698$	52443.5i	2.84386i
$699$	17346.7	0.938645
$700$	0	0
$701$	−15277.7	−0.823154	−0.411577	−	0.911375i	$-0.635022\pi$
$701$	−15277.7	−0.823154	−0.411577	+	0.911375i	$0.635022\pi$
$702$	3298.37i	0.177335i
$703$	− 981.519i	− 0.0526582i
$704$	3942.93	0.211086
$705$	0	0
$706$	35557.3	1.89549
$707$	− 6901.43i	− 0.367122i
$708$	− 20897.3i	− 1.10928i
$709$	11732.1	0.621449	0.310725	−	0.950500i	$-0.399428\pi$
$709$	11732.1	0.621449	0.310725	+	0.950500i	$0.399428\pi$
$710$	0	0
$711$	3627.00	0.191313
$712$	53137.2i	2.79691i
$713$	− 13455.5i	− 0.706750i
$714$	4855.35	0.254491
$715$	0	0
$716$	−445.153	−0.0232349
$717$	− 17508.5i	− 0.911947i
$718$	− 1785.57i	− 0.0928093i
$719$	19006.2	0.985828	0.492914	−	0.870078i	$-0.335932\pi$
$719$	19006.2	0.985828	0.492914	+	0.870078i	$0.335932\pi$
$720$	0	0
$721$	−2704.45	−0.139694
$722$	− 33925.1i	− 1.74870i
$723$	2946.92i	0.151587i
$724$	−32327.4	−1.65945
$725$	0	0
$726$	1804.56	0.0922498
$727$	2650.77i	0.135229i	0.997712	+	0.0676146i	$0.0215388\pi$
$727$	2650.77i	0.135229i	−0.997712	+	0.0676146i	$0.978461\pi$
$728$	− 5836.96i	− 0.297160i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	10529.1	0.532738
$732$	33199.5i	1.67635i
$733$	8854.22i	0.446164i	0.974800	+	0.223082i	$0.0716117\pi$
$733$	8854.22i	0.446164i	−0.974800	+	0.223082i	$0.928388\pi$
$734$	−44952.2	−2.26051
$735$	0	0
$736$	−4055.96	−0.203131
$737$	3450.84i	0.172474i
$738$	− 18974.7i	− 0.946435i
$739$	−17174.8	−0.854921	−0.427460	−	0.904034i	$-0.640592\pi$
$739$	−17174.8	−0.854921	−0.427460	+	0.904034i	$0.640592\pi$
$740$	0	0
$741$	434.391	0.0215354
$742$	− 9264.06i	− 0.458348i
$743$	9800.30i	0.483901i	0.970289	+	0.241950i	$0.0777871\pi$
$743$	9800.30i	0.483901i	−0.970289	+	0.241950i	$0.922213\pi$
$744$	25541.1	1.25858
$745$	0	0
$746$	−59301.6	−2.91044
$747$	− 5870.82i	− 0.287553i
$748$	10914.6i	0.533525i
$749$	6026.92	0.294017
$750$	0	0
$751$	2781.25	0.135139	0.0675695	−	0.997715i	$-0.478476\pi$
$751$	2781.25	0.135139	0.0675695	+	0.997715i	$0.478476\pi$
$752$	11520.9i	0.558675i
$753$	− 12960.7i	− 0.627243i
$754$	32375.6	1.56372
$755$	0	0
$756$	2474.57	0.119046
$757$	3010.87i	0.144560i	0.997384	+	0.0722800i	$0.0230275\pi$
$757$	3010.87i	0.144560i	−0.997384	+	0.0722800i	$0.976972\pi$
$758$	− 32591.8i	− 1.56172i
$759$	2259.08	0.108036
$760$	0	0
$761$	−2709.54	−0.129068	−0.0645340	−	0.997916i	$-0.520556\pi$
$761$	−2709.54	−0.129068	−0.0645340	+	0.997916i	$0.520556\pi$
$762$	33716.5i	1.60291i
$763$	− 6992.03i	− 0.331754i
$764$	55848.4	2.64466
$765$	0	0
$766$	53207.7	2.50976
$767$	10242.0i	0.482159i
$768$	25041.2i	1.17656i
$769$	28121.1	1.31869	0.659345	−	0.751841i	$-0.270834\pi$
$769$	28121.1	1.31869	0.659345	+	0.751841i	$0.270834\pi$
$770$	0	0
$771$	−18672.9	−0.872227
$772$	− 21626.2i	− 1.00822i
$773$	− 4274.61i	− 0.198897i	−0.995043	−	0.0994483i	$-0.968292\pi$
$773$	− 4274.61i	− 0.198897i	0.995043	−	0.0994483i	$-0.0317078\pi$
$774$	7934.85	0.368491
$775$	0	0
$776$	41571.2	1.92309
$777$	2740.38i	0.126526i
$778$	32065.9i	1.47766i
$779$	−2498.95	−0.114935
$780$	0	0
$781$	−1690.63	−0.0774589
$782$	20204.1i	0.923909i
$783$	7155.59i	0.326590i
$784$	25542.2	1.16355
$785$	0	0
$786$	−851.985	−0.0386632
$787$	19107.9i	0.865469i	0.901522	+	0.432734i	$0.142451\pi$
$787$	19107.9i	0.865469i	−0.901522	+	0.432734i	$0.857549\pi$
$788$	38459.6i	1.73866i
$789$	7766.85	0.350453
$790$	0	0
$791$	−5190.01	−0.233294
$792$	4288.17i	0.192391i
$793$	− 16271.4i	− 0.728645i
$794$	62269.4	2.78320
$795$	0	0
$796$	−50801.9	−2.26209
$797$	27518.4i	1.22303i	0.791234	+	0.611513i	$0.209439\pi$
$797$	27518.4i	1.22303i	−0.791234	+	0.611513i	$0.790561\pi$
$798$	− 481.893i	− 0.0213770i
$799$	8379.74	0.371031
$800$	0	0
$801$	11040.9	0.487030
$802$	45335.2i	1.99606i
$803$	− 1692.53i	− 0.0743811i
$804$	−15729.4	−0.689965
$805$	0	0
$806$	−24011.4	−1.04934
$807$	− 17614.6i	− 0.768356i
$808$	54512.7i	2.37345i
$809$	−21986.6	−0.955511	−0.477755	−	0.878493i	$-0.658550\pi$
$809$	−21986.6	−0.955511	−0.477755	+	0.878493i	$0.658550\pi$
$810$	0	0
$811$	11835.1	0.512437	0.256218	−	0.966619i	$-0.417523\pi$
$811$	11835.1	0.512437	0.256218	+	0.966619i	$0.417523\pi$
$812$	− 24289.4i	− 1.04974i
$813$	9920.79i	0.427967i
$814$	−9108.93	−0.392221
$815$	0	0
$816$	−14537.6	−0.623672
$817$	− 1045.01i	− 0.0447494i
$818$	2967.43i	0.126838i
$819$	−1212.81	−0.0517448
$820$	0	0
$821$	−7890.58	−0.335424	−0.167712	−	0.985836i	$-0.553638\pi$
$821$	−7890.58	−0.335424	−0.167712	+	0.985836i	$0.553638\pi$
$822$	28623.4i	1.21455i
$823$	− 1000.74i	− 0.0423861i	−0.999775	−	0.0211930i	$-0.993254\pi$
$823$	− 1000.74i	− 0.0423861i	0.999775	−	0.0211930i	$-0.00674646\pi$
$824$	21361.8	0.903123
$825$	0	0
$826$	11362.0	0.478611
$827$	22764.2i	0.957181i	0.878038	+	0.478590i	$0.158852\pi$
$827$	22764.2i	0.957181i	−0.878038	+	0.478590i	$0.841148\pi$
$828$	10297.2i	0.432188i
$829$	−39835.8	−1.66894	−0.834471	−	0.551051i	$-0.814227\pi$
$829$	−39835.8	−1.66894	−0.834471	+	0.551051i	$0.814227\pi$
$830$	0	0
$831$	−8584.10	−0.358338
$832$	− 8808.43i	− 0.367040i
$833$	− 18578.1i	− 0.772742i
$834$	25211.0	1.04674
$835$	0	0
$836$	1083.27	0.0448155
$837$	− 5306.96i	− 0.219158i
$838$	− 57469.7i	− 2.36904i
$839$	−23330.9	−0.960037	−0.480019	−	0.877258i	$-0.659370\pi$
$839$	−23330.9	−0.960037	−0.480019	+	0.877258i	$0.659370\pi$
$840$	0	0
$841$	45847.5	1.87984
$842$	75476.0i	3.08916i
$843$	8964.14i	0.366241i
$844$	−46928.1	−1.91390
$845$	0	0
$846$	6315.09	0.256640
$847$	663.535i	0.0269177i
$848$	27737.8i	1.12326i
$849$	−4363.79	−0.176402
$850$	0	0
$851$	−11403.3	−0.459341
$852$	− 7706.08i	− 0.309866i
$853$	− 22937.3i	− 0.920701i	−0.887737	−	0.460351i	$-0.847724\pi$
$853$	− 22937.3i	− 0.920701i	0.887737	−	0.460351i	$-0.152276\pi$
$854$	−18050.8	−0.723284
$855$	0	0
$856$	−47605.2	−1.90083
$857$	− 38472.3i	− 1.53348i	−0.641961	−	0.766738i	$-0.721879\pi$
$857$	− 38472.3i	− 1.53348i	0.641961	−	0.766738i	$-0.278121\pi$
$858$	− 4031.34i	− 0.160405i
$859$	22970.3	0.912384	0.456192	−	0.889881i	$-0.349213\pi$
$859$	22970.3	0.912384	0.456192	+	0.889881i	$0.349213\pi$
$860$	0	0
$861$	6977.00	0.276162
$862$	− 74084.5i	− 2.92730i
$863$	33587.6i	1.32484i	0.749133	+	0.662420i	$0.230470\pi$
$863$	33587.6i	1.32484i	−0.749133	+	0.662420i	$0.769530\pi$
$864$	−1599.70	−0.0629895
$865$	0	0
$866$	−11284.0	−0.442777
$867$	− 4165.08i	− 0.163153i
$868$	18014.3i	0.704430i
$869$	−4433.00	−0.173049
$870$	0	0
$871$	7709.12	0.299901
$872$	55228.3i	2.14480i
$873$	− 8637.71i	− 0.334871i
$874$	2005.25	0.0776073
$875$	0	0
$876$	7714.74	0.297554
$877$	− 704.130i	− 0.0271115i	−0.999908	−	0.0135558i	$-0.995685\pi$
$877$	− 704.130i	− 0.0271115i	0.999908	−	0.0135558i	$-0.00431506\pi$
$878$	66707.5i	2.56409i
$879$	25759.5	0.988450
$880$	0	0
$881$	9746.33	0.372715	0.186358	−	0.982482i	$-0.440332\pi$
$881$	9746.33	0.372715	0.186358	+	0.982482i	$0.440332\pi$
$882$	− 14000.7i	− 0.534501i
$883$	8774.24i	0.334402i	0.985923	+	0.167201i	$0.0534728\pi$
$883$	8774.24i	0.334402i	−0.985923	+	0.167201i	$0.946527\pi$
$884$	24383.0	0.927701
$885$	0	0
$886$	57206.4	2.16917
$887$	− 13505.1i	− 0.511224i	−0.966779	−	0.255612i	$-0.917723\pi$
$887$	− 13505.1i	− 0.511224i	0.966779	−	0.255612i	$-0.0822770\pi$
$888$	− 21645.6i	− 0.817993i
$889$	−12397.5	−0.467717
$890$	0	0
$891$	891.000	0.0335013
$892$	24118.6i	0.905324i
$893$	− 831.689i	− 0.0311662i
$894$	30988.9	1.15931
$895$	0	0
$896$	−12370.9	−0.461252
$897$	− 5046.75i	− 0.187855i
$898$	80552.8i	2.99341i
$899$	−52091.1	−1.93252
$900$	0	0
$901$	20175.1	0.745984
$902$	23191.3i	0.856083i
$903$	2917.64i	0.107523i
$904$	40994.6	1.50825
$905$	0	0
$906$	40433.4	1.48268
$907$	− 2523.23i	− 0.0923732i	−0.998933	−	0.0461866i	$-0.985293\pi$
$907$	− 2523.23i	− 0.0923732i	0.998933	−	0.0461866i	$-0.0147069\pi$
$908$	− 61148.4i	− 2.23489i
$909$	11326.7	0.413293
$910$	0	0
$911$	−32285.3	−1.17416	−0.587080	−	0.809529i	$-0.699723\pi$
$911$	−32285.3	−1.17416	−0.587080	+	0.809529i	$0.699723\pi$
$912$	1442.85i	0.0523877i
$913$	7175.45i	0.260101i
$914$	−24422.6	−0.883838
$915$	0	0
$916$	−28337.0	−1.02214
$917$	− 313.274i	− 0.0112816i
$918$	7968.65i	0.286497i
$919$	40956.5	1.47011	0.735055	−	0.678008i	$-0.237156\pi$
$919$	40956.5	1.47011	0.735055	+	0.678008i	$0.237156\pi$
$920$	0	0
$921$	1587.09	0.0567821
$922$	− 70943.6i	− 2.53406i
$923$	3776.83i	0.134687i
$924$	−3024.47	−0.107682
$925$	0	0
$926$	33090.8	1.17433
$927$	− 4438.58i	− 0.157262i
$928$	15702.1i	0.555437i
$929$	6728.41	0.237623	0.118812	−	0.992917i	$-0.462092\pi$
$929$	6728.41	0.237623	0.118812	+	0.992917i	$0.462092\pi$
$930$	0	0
$931$	−1843.88	−0.0649095
$932$	− 96639.1i	− 3.39648i
$933$	15024.0i	0.527185i
$934$	−96181.9	−3.36956
$935$	0	0
$936$	9579.69	0.334532
$937$	− 36377.8i	− 1.26831i	−0.773205	−	0.634157i	$-0.781347\pi$
$937$	− 36377.8i	− 1.26831i	0.773205	−	0.634157i	$-0.218653\pi$
$938$	− 8552.13i	− 0.297694i
$939$	−23575.6	−0.819340
$940$	0	0
$941$	25907.0	0.897496	0.448748	−	0.893658i	$-0.351870\pi$
$941$	25907.0	0.897496	0.448748	+	0.893658i	$0.351870\pi$
$942$	34916.4i	1.20768i
$943$	29032.7i	1.00258i
$944$	−34019.2	−1.17291
$945$	0	0
$946$	−9698.15	−0.333313
$947$	37096.3i	1.27293i	0.771304	+	0.636466i	$0.219605\pi$
$947$	37096.3i	1.27293i	−0.771304	+	0.636466i	$0.780395\pi$
$948$	− 20206.2i	− 0.692263i
$949$	−3781.07	−0.129335
$950$	0	0
$951$	23241.1	0.792476
$952$	− 14101.7i	− 0.480084i
$953$	15323.7i	0.520865i	0.965492	+	0.260432i	$0.0838651\pi$
$953$	15323.7i	0.520865i	−0.965492	+	0.260432i	$0.916135\pi$
$954$	15204.3	0.515992
$955$	0	0
$956$	−97540.4	−3.29988
$957$	− 8745.72i	− 0.295412i
$958$	− 48850.7i	− 1.64749i
$959$	−10524.8	−0.354395
$960$	0	0
$961$	8842.46	0.296817
$962$	20349.2i	0.682000i
$963$	9891.45i	0.330994i
$964$	16417.4	0.548516
$965$	0	0
$966$	−5598.62	−0.186473
$967$	− 53388.0i	− 1.77543i	−0.460391	−	0.887716i	$-0.652291\pi$
$967$	− 53388.0i	− 1.77543i	0.460391	−	0.887716i	$-0.347709\pi$
$968$	− 5241.10i	− 0.174024i
$969$	1049.46	0.0347921
$970$	0	0
$971$	−36325.7	−1.20056	−0.600281	−	0.799789i	$-0.704945\pi$
$971$	−36325.7	−1.20056	−0.600281	+	0.799789i	$0.704945\pi$
$972$	4061.28i	0.134018i
$973$	9270.07i	0.305432i
$974$	−51094.6	−1.68088
$975$	0	0
$976$	54046.4	1.77252
$977$	48608.7i	1.59174i	0.605468	+	0.795870i	$0.292986\pi$
$977$	48608.7i	1.59174i	−0.605468	+	0.795870i	$0.707014\pi$
$978$	− 52541.1i	− 1.71787i
$979$	−13494.4	−0.440535
$980$	0	0
$981$	11475.4	0.373477
$982$	56657.7i	1.84116i
$983$	− 31762.6i	− 1.03059i	−0.857013	−	0.515295i	$-0.827682\pi$
$983$	− 31762.6i	− 1.03059i	0.857013	−	0.515295i	$-0.172318\pi$
$984$	−55109.6	−1.78540
$985$	0	0
$986$	78217.2	2.52631
$987$	2322.06i	0.0748854i
$988$	− 2420.01i	− 0.0779258i
$989$	−12140.9	−0.390352
$990$	0	0
$991$	−5073.82	−0.162639	−0.0813195	−	0.996688i	$-0.525913\pi$
$991$	−5073.82	−0.162639	−0.0813195	+	0.996688i	$0.525913\pi$
$992$	− 11645.5i	− 0.372726i
$993$	− 4065.25i	− 0.129916i
$994$	4189.83	0.133696
$995$	0	0
$996$	−32706.5	−1.04051
$997$	24607.0i	0.781657i	0.920464	+	0.390828i	$0.127811\pi$
$997$	24607.0i	0.781657i	−0.920464	+	0.390828i	$0.872189\pi$
$998$	45631.8i	1.44734i
$999$	−4497.54	−0.142438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.k.199.5		6
5.2	odd	4		825.4.a.r.1.1		3
5.3	odd	4		165.4.a.e.1.3	✓	3
5.4	even	2	inner	825.4.c.k.199.2		6
15.2	even	4		2475.4.a.t.1.3		3
15.8	even	4		495.4.a.k.1.1		3
55.43	even	4		1815.4.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.3	✓	3	5.3	odd	4
495.4.a.k.1.1		3	15.8	even	4
825.4.a.r.1.1		3	5.2	odd	4
825.4.c.k.199.2		6	5.4	even	2	inner
825.4.c.k.199.5		6	1.1	even	1	trivial
1815.4.a.r.1.1		3	55.43	even	4
2475.4.a.t.1.3		3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.97123i q^{2} -3.00000i q^{3} -16.7131 q^{4} +14.9137 q^{6} +5.48376i q^{7} -43.3148i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.97123i q^{2} -3.00000i q^{3} -16.7131 q^{4} +14.9137 q^{6} +5.48376i q^{7} -43.3148i q^{8} -9.00000 q^{9} +11.0000 q^{11} +50.1393i q^{12} -24.5738i q^{13} -27.2610 q^{14} +81.6231 q^{16} -59.3687i q^{17} -44.7411i q^{18} -5.89234 q^{19} +16.4513 q^{21} +54.6835i q^{22} +68.4570i q^{23} -129.945 q^{24} +122.162 q^{26} +27.0000i q^{27} -91.6506i q^{28} +265.022 q^{29} -196.554 q^{31} +59.2482i q^{32} -33.0000i q^{33} +295.135 q^{34} +150.418 q^{36} +166.575i q^{37} -29.2922i q^{38} -73.7214 q^{39} +424.101 q^{41} +81.7830i q^{42} +177.351i q^{43} -183.844 q^{44} -340.316 q^{46} +141.148i q^{47} -244.869i q^{48} +312.928 q^{49} -178.106 q^{51} +410.704i q^{52} +339.828i q^{53} -134.223 q^{54} +237.528 q^{56} +17.6770i q^{57} +1317.48i q^{58} -416.784 q^{59} +662.146 q^{61} -977.115i q^{62} -49.3538i q^{63} +358.448 q^{64} +164.051 q^{66} +313.713i q^{67} +992.235i q^{68} +205.371 q^{69} -153.693 q^{71} +389.834i q^{72} -153.866i q^{73} -828.084 q^{74} +98.4793 q^{76} +60.3213i q^{77} -366.486i q^{78} -403.000 q^{79} +81.0000 q^{81} +2108.30i q^{82} +652.313i q^{83} -274.952 q^{84} -881.650 q^{86} -795.065i q^{87} -476.463i q^{88} -1226.77 q^{89} +134.757 q^{91} -1144.13i q^{92} +589.662i q^{93} -701.677 q^{94} +177.745 q^{96} +959.746i q^{97} +1555.64i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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