LMFDB - Embedded newform 825.4.c.e.199.2

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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.e.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +3.00000 q^{6} +36.0000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +3.00000 q^{6} +36.0000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +11.0000 q^{11} -21.0000i q^{12} -2.00000i q^{13} -36.0000 q^{14} +41.0000 q^{16} +66.0000i q^{17} -9.00000i q^{18} -140.000 q^{19} +108.000 q^{21} +11.0000i q^{22} +68.0000i q^{23} +45.0000 q^{24} +2.00000 q^{26} +27.0000i q^{27} +252.000i q^{28} -150.000 q^{29} -128.000 q^{31} +161.000i q^{32} -33.0000i q^{33} -66.0000 q^{34} -63.0000 q^{36} -314.000i q^{37} -140.000i q^{38} -6.00000 q^{39} -118.000 q^{41} +108.000i q^{42} -172.000i q^{43} +77.0000 q^{44} -68.0000 q^{46} -324.000i q^{47} -123.000i q^{48} -953.000 q^{49} +198.000 q^{51} -14.0000i q^{52} -82.0000i q^{53} -27.0000 q^{54} -540.000 q^{56} +420.000i q^{57} -150.000i q^{58} +740.000 q^{59} +122.000 q^{61} -128.000i q^{62} -324.000i q^{63} +167.000 q^{64} +33.0000 q^{66} -124.000i q^{67} +462.000i q^{68} +204.000 q^{69} -988.000 q^{71} -135.000i q^{72} -2.00000i q^{73} +314.000 q^{74} -980.000 q^{76} +396.000i q^{77} -6.00000i q^{78} -1100.00 q^{79} +81.0000 q^{81} -118.000i q^{82} +868.000i q^{83} +756.000 q^{84} +172.000 q^{86} +450.000i q^{87} +165.000i q^{88} +470.000 q^{89} +72.0000 q^{91} +476.000i q^{92} +384.000i q^{93} +324.000 q^{94} +483.000 q^{96} +1186.00i q^{97} -953.000i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 14 q^{4} + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q + 14 * q^4 + 6 * q^6 - 18 * q^9	$ 2 q + 14 q^{4} + 6 q^{6} - 18 q^{9} + 22 q^{11} - 72 q^{14} + 82 q^{16} - 280 q^{19} + 216 q^{21} + 90 q^{24} + 4 q^{26} - 300 q^{29} - 256 q^{31} - 132 q^{34} - 126 q^{36} - 12 q^{39} - 236 q^{41} + 154 q^{44} - 136 q^{46} - 1906 q^{49} + 396 q^{51} - 54 q^{54} - 1080 q^{56} + 1480 q^{59} + 244 q^{61} + 334 q^{64} + 66 q^{66} + 408 q^{69} - 1976 q^{71} + 628 q^{74} - 1960 q^{76} - 2200 q^{79} + 162 q^{81} + 1512 q^{84} + 344 q^{86} + 940 q^{89} + 144 q^{91} + 648 q^{94} + 966 q^{96} - 198 q^{99}+O(q^{100}) $ 2 * q + 14 * q^4 + 6 * q^6 - 18 * q^9 + 22 * q^11 - 72 * q^14 + 82 * q^16 - 280 * q^19 + 216 * q^21 + 90 * q^24 + 4 * q^26 - 300 * q^29 - 256 * q^31 - 132 * q^34 - 126 * q^36 - 12 * q^39 - 236 * q^41 + 154 * q^44 - 136 * q^46 - 1906 * q^49 + 396 * q^51 - 54 * q^54 - 1080 * q^56 + 1480 * q^59 + 244 * q^61 + 334 * q^64 + 66 * q^66 + 408 * q^69 - 1976 * q^71 + 628 * q^74 - 1960 * q^76 - 2200 * q^79 + 162 * q^81 + 1512 * q^84 + 344 * q^86 + 940 * q^89 + 144 * q^91 + 648 * q^94 + 966 * q^96 - 198 * 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 $

$2$	1.00000i	0.353553i	0.984251	+	0.176777i	$0.0565670\pi$
$2$	1.00000i	0.353553i	−0.984251	+	0.176777i	$0.943433\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	7.00000	0.875000
$5$	0	0
$5$	0	0
$6$	3.00000	0.204124
$7$	36.0000i	1.94382i	0.235358	+	0.971909i	$0.424374\pi$
$7$	36.0000i	1.94382i	−0.235358	+	0.971909i	$0.575626\pi$
$8$	15.0000i	0.662913i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	− 21.0000i	− 0.505181i
$13$	− 2.00000i	− 0.0426692i	−0.999772	−	0.0213346i	$-0.993208\pi$
$13$	− 2.00000i	− 0.0426692i	0.999772	−	0.0213346i	$-0.00679154\pi$
$14$	−36.0000	−0.687243
$15$	0	0
$16$	41.0000	0.640625
$17$	66.0000i	0.941609i	0.882238	+	0.470804i	$0.156036\pi$
$17$	66.0000i	0.941609i	−0.882238	+	0.470804i	$0.843964\pi$
$18$	− 9.00000i	− 0.117851i
$19$	−140.000	−1.69043	−0.845216	−	0.534425i	$-0.820528\pi$
$19$	−140.000	−1.69043	−0.845216	+	0.534425i	$0.820528\pi$
$20$	0	0
$21$	108.000	1.12226
$22$	11.0000i	0.106600i
$23$	68.0000i	0.616477i	0.951309	+	0.308239i	$0.0997395\pi$
$23$	68.0000i	0.616477i	−0.951309	+	0.308239i	$0.900260\pi$
$24$	45.0000	0.382733
$25$	0	0
$26$	2.00000	0.0150859
$27$	27.0000i	0.192450i
$28$	252.000i	1.70084i
$29$	−150.000	−0.960493	−0.480247	−	0.877134i	$-0.659453\pi$
$29$	−150.000	−0.960493	−0.480247	+	0.877134i	$0.659453\pi$
$30$	0	0
$31$	−128.000	−0.741596	−0.370798	−	0.928714i	$-0.620916\pi$
$31$	−128.000	−0.741596	−0.370798	+	0.928714i	$0.620916\pi$
$32$	161.000i	0.889408i
$33$	− 33.0000i	− 0.174078i
$34$	−66.0000	−0.332909
$35$	0	0
$36$	−63.0000	−0.291667
$37$	− 314.000i	− 1.39517i	−0.716502	−	0.697585i	$-0.754258\pi$
$37$	− 314.000i	− 1.39517i	0.716502	−	0.697585i	$-0.245742\pi$
$38$	− 140.000i	− 0.597658i
$39$	−6.00000	−0.0246351
$40$	0	0
$41$	−118.000	−0.449476	−0.224738	−	0.974419i	$-0.572153\pi$
$41$	−118.000	−0.449476	−0.224738	+	0.974419i	$0.572153\pi$
$42$	108.000i	0.396780i
$43$	− 172.000i	− 0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$	− 172.000i	− 0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	77.0000	0.263822
$45$	0	0
$46$	−68.0000	−0.217958
$47$	− 324.000i	− 1.00554i	−0.864421	−	0.502769i	$-0.832315\pi$
$47$	− 324.000i	− 1.00554i	0.864421	−	0.502769i	$-0.167685\pi$
$48$	− 123.000i	− 0.369865i
$49$	−953.000	−2.77843
$50$	0	0
$51$	198.000	0.543638
$52$	− 14.0000i	− 0.0373356i
$53$	− 82.0000i	− 0.212520i	−0.994338	−	0.106260i	$-0.966112\pi$
$53$	− 82.0000i	− 0.212520i	0.994338	−	0.106260i	$-0.0338876\pi$
$54$	−27.0000	−0.0680414
$55$	0	0
$56$	−540.000	−1.28858
$57$	420.000i	0.975971i
$58$	− 150.000i	− 0.339586i
$59$	740.000	1.63288	0.816439	−	0.577432i	$-0.195945\pi$
$59$	740.000	1.63288	0.816439	+	0.577432i	$0.195945\pi$
$60$	0	0
$61$	122.000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	122.000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	− 128.000i	− 0.262194i
$63$	− 324.000i	− 0.647939i
$64$	167.000	0.326172
$65$	0	0
$66$	33.0000	0.0615457
$67$	− 124.000i	− 0.226105i	−0.993589	−	0.113052i	$-0.963937\pi$
$67$	− 124.000i	− 0.226105i	0.993589	−	0.113052i	$-0.0360628\pi$
$68$	462.000i	0.823908i
$69$	204.000	0.355923
$70$	0	0
$71$	−988.000	−1.65147	−0.825733	−	0.564062i	$-0.809238\pi$
$71$	−988.000	−1.65147	−0.825733	+	0.564062i	$0.809238\pi$
$72$	− 135.000i	− 0.220971i
$73$	− 2.00000i	− 0.00320661i	−0.999999	−	0.00160330i	$-0.999490\pi$
$73$	− 2.00000i	− 0.00320661i	0.999999	−	0.00160330i	$-0.000510348\pi$
$74$	314.000	0.493267
$75$	0	0
$76$	−980.000	−1.47913
$77$	396.000i	0.586083i
$78$	− 6.00000i	− 0.00870982i
$79$	−1100.00	−1.56658	−0.783289	−	0.621658i	$-0.786460\pi$
$79$	−1100.00	−1.56658	−0.783289	+	0.621658i	$0.786460\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 118.000i	− 0.158914i
$83$	868.000i	1.14790i	0.818892	+	0.573948i	$0.194589\pi$
$83$	868.000i	1.14790i	−0.818892	+	0.573948i	$0.805411\pi$
$84$	756.000	0.981981
$85$	0	0
$86$	172.000	0.215666
$87$	450.000i	0.554541i
$88$	165.000i	0.199876i
$89$	470.000	0.559774	0.279887	−	0.960033i	$-0.409703\pi$
$89$	470.000	0.559774	0.279887	+	0.960033i	$0.409703\pi$
$90$	0	0
$91$	72.0000	0.0829412
$92$	476.000i	0.539418i
$93$	384.000i	0.428161i
$94$	324.000	0.355511
$95$	0	0
$96$	483.000	0.513500
$97$	1186.00i	1.24144i	0.784031	+	0.620722i	$0.213160\pi$
$97$	1186.00i	1.24144i	−0.784031	+	0.620722i	$0.786840\pi$
$98$	− 953.000i	− 0.982322i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	1502.00	1.47975	0.739874	−	0.672745i	$-0.234885\pi$
$101$	1502.00	1.47975	0.739874	+	0.672745i	$0.234885\pi$
$102$	198.000i	0.192205i
$103$	− 32.0000i	− 0.0306122i	−0.999883	−	0.0153061i	$-0.995128\pi$
$103$	− 32.0000i	− 0.0306122i	0.999883	−	0.0153061i	$-0.00487227\pi$
$104$	30.0000	0.0282860
$105$	0	0
$106$	82.0000	0.0751372
$107$	1116.00i	1.00830i	0.863617	+	0.504149i	$0.168194\pi$
$107$	1116.00i	1.00830i	−0.863617	+	0.504149i	$0.831806\pi$
$108$	189.000i	0.168394i
$109$	2190.00	1.92444	0.962220	−	0.272273i	$-0.0877755\pi$
$109$	2190.00	1.92444	0.962220	+	0.272273i	$0.0877755\pi$
$110$	0	0
$111$	−942.000	−0.805502
$112$	1476.00i	1.24526i
$113$	1398.00i	1.16383i	0.813250	+	0.581915i	$0.197696\pi$
$113$	1398.00i	1.16383i	−0.813250	+	0.581915i	$0.802304\pi$
$114$	−420.000	−0.345058
$115$	0	0
$116$	−1050.00	−0.840431
$117$	18.0000i	0.0142231i
$118$	740.000i	0.577310i
$119$	−2376.00	−1.83032
$120$	0	0
$121$	121.000	0.0909091
$122$	122.000i	0.0905357i
$123$	354.000i	0.259505i
$124$	−896.000	−0.648897
$125$	0	0
$126$	324.000	0.229081
$127$	− 44.0000i	− 0.0307431i	−0.999882	−	0.0153715i	$-0.995107\pi$
$127$	− 44.0000i	− 0.0307431i	0.999882	−	0.0153715i	$-0.00489310\pi$
$128$	1455.00i	1.00473i
$129$	−516.000	−0.352180
$130$	0	0
$131$	−1308.00	−0.872370	−0.436185	−	0.899857i	$-0.643671\pi$
$131$	−1308.00	−0.872370	−0.436185	+	0.899857i	$0.643671\pi$
$132$	− 231.000i	− 0.152318i
$133$	− 5040.00i	− 3.28589i
$134$	124.000	0.0799401
$135$	0	0
$136$	−990.000	−0.624204
$137$	1626.00i	1.01400i	0.861945	+	0.507002i	$0.169246\pi$
$137$	1626.00i	1.01400i	−0.861945	+	0.507002i	$0.830754\pi$
$138$	204.000i	0.125838i
$139$	−180.000	−0.109837	−0.0549187	−	0.998491i	$-0.517490\pi$
$139$	−180.000	−0.109837	−0.0549187	+	0.998491i	$0.517490\pi$
$140$	0	0
$141$	−972.000	−0.580547
$142$	− 988.000i	− 0.583881i
$143$	− 22.0000i	− 0.0128653i
$144$	−369.000	−0.213542
$145$	0	0
$146$	2.00000	0.00113371
$147$	2859.00i	1.60412i
$148$	− 2198.00i	− 1.22077i
$149$	−1430.00	−0.786243	−0.393121	−	0.919487i	$-0.628605\pi$
$149$	−1430.00	−0.786243	−0.393121	+	0.919487i	$0.628605\pi$
$150$	0	0
$151$	−1948.00	−1.04984	−0.524921	−	0.851151i	$-0.675905\pi$
$151$	−1948.00	−1.04984	−0.524921	+	0.851151i	$0.675905\pi$
$152$	− 2100.00i	− 1.12061i
$153$	− 594.000i	− 0.313870i
$154$	−396.000	−0.207212
$155$	0	0
$156$	−42.0000	−0.0215557
$157$	646.000i	0.328385i	0.986428	+	0.164192i	$0.0525018\pi$
$157$	646.000i	0.328385i	−0.986428	+	0.164192i	$0.947498\pi$
$158$	− 1100.00i	− 0.553869i
$159$	−246.000	−0.122699
$160$	0	0
$161$	−2448.00	−1.19832
$162$	81.0000i	0.0392837i
$163$	− 3052.00i	− 1.46657i	−0.679921	−	0.733286i	$-0.737986\pi$
$163$	− 3052.00i	− 1.46657i	0.679921	−	0.733286i	$-0.262014\pi$
$164$	−826.000	−0.393291
$165$	0	0
$166$	−868.000	−0.405843
$167$	1216.00i	0.563455i	0.959495	+	0.281727i	$0.0909073\pi$
$167$	1216.00i	0.563455i	−0.959495	+	0.281727i	$0.909093\pi$
$168$	1620.00i	0.743963i
$169$	2193.00	0.998179
$170$	0	0
$171$	1260.00	0.563477
$172$	− 1204.00i	− 0.533745i
$173$	3858.00i	1.69548i	0.530411	+	0.847741i	$0.322038\pi$
$173$	3858.00i	1.69548i	−0.530411	+	0.847741i	$0.677962\pi$
$174$	−450.000	−0.196060
$175$	0	0
$176$	451.000	0.193156
$177$	− 2220.00i	− 0.942742i
$178$	470.000i	0.197910i
$179$	380.000	0.158673	0.0793367	−	0.996848i	$-0.474720\pi$
$179$	380.000	0.158673	0.0793367	+	0.996848i	$0.474720\pi$
$180$	0	0
$181$	−538.000	−0.220935	−0.110467	−	0.993880i	$-0.535235\pi$
$181$	−538.000	−0.220935	−0.110467	+	0.993880i	$0.535235\pi$
$182$	72.0000i	0.0293241i
$183$	− 366.000i	− 0.147844i
$184$	−1020.00	−0.408671
$185$	0	0
$186$	−384.000	−0.151378
$187$	726.000i	0.283906i
$188$	− 2268.00i	− 0.879845i
$189$	−972.000	−0.374088
$190$	0	0
$191$	1412.00	0.534915	0.267457	−	0.963570i	$-0.413817\pi$
$191$	1412.00	0.534915	0.267457	+	0.963570i	$0.413817\pi$
$192$	− 501.000i	− 0.188315i
$193$	638.000i	0.237949i	0.992897	+	0.118975i	$0.0379607\pi$
$193$	638.000i	0.237949i	−0.992897	+	0.118975i	$0.962039\pi$
$194$	−1186.00	−0.438917
$195$	0	0
$196$	−6671.00	−2.43112
$197$	3686.00i	1.33308i	0.745470	+	0.666540i	$0.232225\pi$
$197$	3686.00i	1.33308i	−0.745470	+	0.666540i	$0.767775\pi$
$198$	− 99.0000i	− 0.0355335i
$199$	240.000	0.0854932	0.0427466	−	0.999086i	$-0.486389\pi$
$199$	240.000	0.0854932	0.0427466	+	0.999086i	$0.486389\pi$
$200$	0	0
$201$	−372.000	−0.130542
$202$	1502.00i	0.523170i
$203$	− 5400.00i	− 1.86702i
$204$	1386.00	0.475683
$205$	0	0
$206$	32.0000	0.0108230
$207$	− 612.000i	− 0.205492i
$208$	− 82.0000i	− 0.0273350i
$209$	−1540.00	−0.509684
$210$	0	0
$211$	5092.00	1.66136	0.830682	−	0.556747i	$-0.187951\pi$
$211$	5092.00	1.66136	0.830682	+	0.556747i	$0.187951\pi$
$212$	− 574.000i	− 0.185955i
$213$	2964.00i	0.953474i
$214$	−1116.00	−0.356487
$215$	0	0
$216$	−405.000	−0.127578
$217$	− 4608.00i	− 1.44153i
$218$	2190.00i	0.680392i
$219$	−6.00000	−0.00185134
$220$	0	0
$221$	132.000	0.0401777
$222$	− 942.000i	− 0.284788i
$223$	3808.00i	1.14351i	0.820425	+	0.571755i	$0.193737\pi$
$223$	3808.00i	1.14351i	−0.820425	+	0.571755i	$0.806263\pi$
$224$	−5796.00	−1.72885
$225$	0	0
$226$	−1398.00	−0.411476
$227$	− 44.0000i	− 0.0128651i	−0.999979	−	0.00643256i	$-0.997952\pi$
$227$	− 44.0000i	− 0.0128651i	0.999979	−	0.00643256i	$-0.00204756\pi$
$228$	2940.00i	0.853975i
$229$	2650.00	0.764703	0.382351	−	0.924017i	$-0.375114\pi$
$229$	2650.00	0.764703	0.382351	+	0.924017i	$0.375114\pi$
$230$	0	0
$231$	1188.00	0.338375
$232$	− 2250.00i	− 0.636723i
$233$	5718.00i	1.60772i	0.594819	+	0.803860i	$0.297224\pi$
$233$	5718.00i	1.60772i	−0.594819	+	0.803860i	$0.702776\pi$
$234$	−18.0000	−0.00502862
$235$	0	0
$236$	5180.00	1.42877
$237$	3300.00i	0.904464i
$238$	− 2376.00i	− 0.647114i
$239$	6520.00	1.76462	0.882309	−	0.470670i	$-0.155988\pi$
$239$	6520.00	1.76462	0.882309	+	0.470670i	$0.155988\pi$
$240$	0	0
$241$	−2438.00	−0.651641	−0.325820	−	0.945432i	$-0.605640\pi$
$241$	−2438.00	−0.651641	−0.325820	+	0.945432i	$0.605640\pi$
$242$	121.000i	0.0321412i
$243$	− 243.000i	− 0.0641500i
$244$	854.000	0.224065
$245$	0	0
$246$	−354.000	−0.0917488
$247$	280.000i	0.0721294i
$248$	− 1920.00i	− 0.491613i
$249$	2604.00	0.662738
$250$	0	0
$251$	−5268.00	−1.32475	−0.662377	−	0.749171i	$-0.730452\pi$
$251$	−5268.00	−1.32475	−0.662377	+	0.749171i	$0.730452\pi$
$252$	− 2268.00i	− 0.566947i
$253$	748.000i	0.185875i
$254$	44.0000	0.0108693
$255$	0	0
$256$	−119.000	−0.0290527
$257$	− 5574.00i	− 1.35290i	−0.736486	−	0.676452i	$-0.763516\pi$
$257$	− 5574.00i	− 1.35290i	0.736486	−	0.676452i	$-0.236484\pi$
$258$	− 516.000i	− 0.124515i
$259$	11304.0	2.71196
$260$	0	0
$261$	1350.00	0.320164
$262$	− 1308.00i	− 0.308429i
$263$	− 2472.00i	− 0.579582i	−0.957090	−	0.289791i	$-0.906414\pi$
$263$	− 2472.00i	− 0.579582i	0.957090	−	0.289791i	$-0.0935858\pi$
$264$	495.000	0.115398
$265$	0	0
$266$	5040.00	1.16174
$267$	− 1410.00i	− 0.323186i
$268$	− 868.000i	− 0.197842i
$269$	−4410.00	−0.999563	−0.499781	−	0.866152i	$-0.666586\pi$
$269$	−4410.00	−0.999563	−0.499781	+	0.866152i	$0.666586\pi$
$270$	0	0
$271$	−1308.00	−0.293193	−0.146597	−	0.989196i	$-0.546832\pi$
$271$	−1308.00	−0.293193	−0.146597	+	0.989196i	$0.546832\pi$
$272$	2706.00i	0.603218i
$273$	− 216.000i	− 0.0478861i
$274$	−1626.00	−0.358505
$275$	0	0
$276$	1428.00	0.311433
$277$	226.000i	0.0490217i	0.999700	+	0.0245109i	$0.00780283\pi$
$277$	226.000i	0.0490217i	−0.999700	+	0.0245109i	$0.992197\pi$
$278$	− 180.000i	− 0.0388334i
$279$	1152.00	0.247199
$280$	0	0
$281$	522.000	0.110818	0.0554091	−	0.998464i	$-0.482354\pi$
$281$	522.000	0.110818	0.0554091	+	0.998464i	$0.482354\pi$
$282$	− 972.000i	− 0.205254i
$283$	1508.00i	0.316754i	0.987379	+	0.158377i	$0.0506261\pi$
$283$	1508.00i	0.316754i	−0.987379	+	0.158377i	$0.949374\pi$
$284$	−6916.00	−1.44503
$285$	0	0
$286$	22.0000	0.00454856
$287$	− 4248.00i	− 0.873699i
$288$	− 1449.00i	− 0.296469i
$289$	557.000	0.113373
$290$	0	0
$291$	3558.00	0.716748
$292$	− 14.0000i	− 0.00280578i
$293$	4658.00i	0.928748i	0.885639	+	0.464374i	$0.153721\pi$
$293$	4658.00i	0.928748i	−0.885639	+	0.464374i	$0.846279\pi$
$294$	−2859.00	−0.567144
$295$	0	0
$296$	4710.00	0.924876
$297$	297.000i	0.0580259i
$298$	− 1430.00i	− 0.277979i
$299$	136.000	0.0263046
$300$	0	0
$301$	6192.00	1.18572
$302$	− 1948.00i	− 0.371175i
$303$	− 4506.00i	− 0.854333i
$304$	−5740.00	−1.08293
$305$	0	0
$306$	594.000	0.110970
$307$	6476.00i	1.20392i	0.798525	+	0.601962i	$0.205614\pi$
$307$	6476.00i	1.20392i	−0.798525	+	0.601962i	$0.794386\pi$
$308$	2772.00i	0.512823i
$309$	−96.0000	−0.0176739
$310$	0	0
$311$	5652.00	1.03053	0.515266	−	0.857030i	$-0.327693\pi$
$311$	5652.00	1.03053	0.515266	+	0.857030i	$0.327693\pi$
$312$	− 90.0000i	− 0.0163309i
$313$	5638.00i	1.01814i	0.860724	+	0.509071i	$0.170011\pi$
$313$	5638.00i	1.01814i	−0.860724	+	0.509071i	$0.829989\pi$
$314$	−646.000	−0.116102
$315$	0	0
$316$	−7700.00	−1.37076
$317$	1506.00i	0.266831i	0.991060	+	0.133415i	$0.0425945\pi$
$317$	1506.00i	0.266831i	−0.991060	+	0.133415i	$0.957406\pi$
$318$	− 246.000i	− 0.0433805i
$319$	−1650.00	−0.289600
$320$	0	0
$321$	3348.00	0.582141
$322$	− 2448.00i	− 0.423670i
$323$	− 9240.00i	− 1.59173i
$324$	567.000	0.0972222
$325$	0	0
$326$	3052.00	0.518511
$327$	− 6570.00i	− 1.11108i
$328$	− 1770.00i	− 0.297963i
$329$	11664.0	1.95458
$330$	0	0
$331$	−7268.00	−1.20690	−0.603452	−	0.797399i	$-0.706209\pi$
$331$	−7268.00	−1.20690	−0.603452	+	0.797399i	$0.706209\pi$
$332$	6076.00i	1.00441i
$333$	2826.00i	0.465057i
$334$	−1216.00	−0.199211
$335$	0	0
$336$	4428.00	0.718950
$337$	− 7254.00i	− 1.17255i	−0.810111	−	0.586277i	$-0.800593\pi$
$337$	− 7254.00i	− 1.17255i	0.810111	−	0.586277i	$-0.199407\pi$
$338$	2193.00i	0.352910i
$339$	4194.00	0.671937
$340$	0	0
$341$	−1408.00	−0.223600
$342$	1260.00i	0.199219i
$343$	− 21960.0i	− 3.45693i
$344$	2580.00	0.404373
$345$	0	0
$346$	−3858.00	−0.599443
$347$	2276.00i	0.352110i	0.984380	+	0.176055i	$0.0563336\pi$
$347$	2276.00i	0.352110i	−0.984380	+	0.176055i	$0.943666\pi$
$348$	3150.00i	0.485223i
$349$	−4610.00	−0.707071	−0.353535	−	0.935421i	$-0.615021\pi$
$349$	−4610.00	−0.707071	−0.353535	+	0.935421i	$0.615021\pi$
$350$	0	0
$351$	54.0000	0.00821170
$352$	1771.00i	0.268167i
$353$	− 4602.00i	− 0.693880i	−0.937887	−	0.346940i	$-0.887221\pi$
$353$	− 4602.00i	− 0.693880i	0.937887	−	0.346940i	$-0.112779\pi$
$354$	2220.00	0.333310
$355$	0	0
$356$	3290.00	0.489802
$357$	7128.00i	1.05673i
$358$	380.000i	0.0560995i
$359$	4160.00	0.611578	0.305789	−	0.952099i	$-0.401080\pi$
$359$	4160.00	0.611578	0.305789	+	0.952099i	$0.401080\pi$
$360$	0	0
$361$	12741.0	1.85756
$362$	− 538.000i	− 0.0781123i
$363$	− 363.000i	− 0.0524864i
$364$	504.000	0.0725736
$365$	0	0
$366$	366.000	0.0522708
$367$	− 5024.00i	− 0.714579i	−0.933994	−	0.357290i	$-0.883701\pi$
$367$	− 5024.00i	− 0.714579i	0.933994	−	0.357290i	$-0.116299\pi$
$368$	2788.00i	0.394931i
$369$	1062.00	0.149825
$370$	0	0
$371$	2952.00	0.413100
$372$	2688.00i	0.374641i
$373$	− 10842.0i	− 1.50503i	−0.658573	−	0.752517i	$-0.728840\pi$
$373$	− 10842.0i	− 1.50503i	0.658573	−	0.752517i	$-0.271160\pi$
$374$	−726.000	−0.100376
$375$	0	0
$376$	4860.00	0.666583
$377$	300.000i	0.0409835i
$378$	− 972.000i	− 0.132260i
$379$	1540.00	0.208719	0.104359	−	0.994540i	$-0.466721\pi$
$379$	1540.00	0.208719	0.104359	+	0.994540i	$0.466721\pi$
$380$	0	0
$381$	−132.000	−0.0177495
$382$	1412.00i	0.189121i
$383$	9468.00i	1.26317i	0.775309	+	0.631583i	$0.217594\pi$
$383$	9468.00i	1.26317i	−0.775309	+	0.631583i	$0.782406\pi$
$384$	4365.00	0.580079
$385$	0	0
$386$	−638.000	−0.0841278
$387$	1548.00i	0.203331i
$388$	8302.00i	1.08626i
$389$	10590.0	1.38029	0.690147	−	0.723669i	$-0.257546\pi$
$389$	10590.0	1.38029	0.690147	+	0.723669i	$0.257546\pi$
$390$	0	0
$391$	−4488.00	−0.580481
$392$	− 14295.0i	− 1.84185i
$393$	3924.00i	0.503663i
$394$	−3686.00	−0.471315
$395$	0	0
$396$	−693.000	−0.0879408
$397$	− 7434.00i	− 0.939803i	−0.882719	−	0.469901i	$-0.844289\pi$
$397$	− 7434.00i	− 0.939803i	0.882719	−	0.469901i	$-0.155711\pi$
$398$	240.000i	0.0302264i
$399$	−15120.0	−1.89711
$400$	0	0
$401$	11402.0	1.41992	0.709961	−	0.704241i	$-0.248713\pi$
$401$	11402.0	1.41992	0.709961	+	0.704241i	$0.248713\pi$
$402$	− 372.000i	− 0.0461534i
$403$	256.000i	0.0316433i
$404$	10514.0	1.29478
$405$	0	0
$406$	5400.00	0.660092
$407$	− 3454.00i	− 0.420660i
$408$	2970.00i	0.360385i
$409$	510.000	0.0616574	0.0308287	−	0.999525i	$-0.490185\pi$
$409$	510.000	0.0616574	0.0308287	+	0.999525i	$0.490185\pi$
$410$	0	0
$411$	4878.00	0.585436
$412$	− 224.000i	− 0.0267857i
$413$	26640.0i	3.17402i
$414$	612.000	0.0726526
$415$	0	0
$416$	322.000	0.0379504
$417$	540.000i	0.0634147i
$418$	− 1540.00i	− 0.180201i
$419$	−2420.00	−0.282159	−0.141080	−	0.989998i	$-0.545057\pi$
$419$	−2420.00	−0.282159	−0.141080	+	0.989998i	$0.545057\pi$
$420$	0	0
$421$	−8178.00	−0.946725	−0.473363	−	0.880868i	$-0.656960\pi$
$421$	−8178.00	−0.946725	−0.473363	+	0.880868i	$0.656960\pi$
$422$	5092.00i	0.587381i
$423$	2916.00i	0.335179i
$424$	1230.00	0.140882
$425$	0	0
$426$	−2964.00	−0.337104
$427$	4392.00i	0.497761i
$428$	7812.00i	0.882260i
$429$	−66.0000	−0.00742776
$430$	0	0
$431$	−6768.00	−0.756388	−0.378194	−	0.925726i	$-0.623455\pi$
$431$	−6768.00	−0.756388	−0.378194	+	0.925726i	$0.623455\pi$
$432$	1107.00i	0.123288i
$433$	478.000i	0.0530513i	0.999648	+	0.0265257i	$0.00844437\pi$
$433$	478.000i	0.0530513i	−0.999648	+	0.0265257i	$0.991556\pi$
$434$	4608.00	0.509657
$435$	0	0
$436$	15330.0	1.68388
$437$	− 9520.00i	− 1.04211i
$438$	− 6.00000i	0 0.000654546i
$439$	3260.00	0.354422	0.177211	−	0.984173i	$-0.443292\pi$
$439$	3260.00	0.354422	0.177211	+	0.984173i	$0.443292\pi$
$440$	0	0
$441$	8577.00	0.926142
$442$	132.000i	0.0142050i
$443$	− 6812.00i	− 0.730582i	−0.930893	−	0.365291i	$-0.880969\pi$
$443$	− 6812.00i	− 0.730582i	0.930893	−	0.365291i	$-0.119031\pi$
$444$	−6594.00	−0.704814
$445$	0	0
$446$	−3808.00	−0.404292
$447$	4290.00i	0.453937i
$448$	6012.00i	0.634019i
$449$	−15290.0	−1.60708	−0.803541	−	0.595250i	$-0.797053\pi$
$449$	−15290.0	−1.60708	−0.803541	+	0.595250i	$0.797053\pi$
$450$	0	0
$451$	−1298.00	−0.135522
$452$	9786.00i	1.01835i
$453$	5844.00i	0.606126i
$454$	44.0000	0.00454851
$455$	0	0
$456$	−6300.00	−0.646984
$457$	− 12854.0i	− 1.31572i	−0.753140	−	0.657861i	$-0.771462\pi$
$457$	− 12854.0i	− 1.31572i	0.753140	−	0.657861i	$-0.228538\pi$
$458$	2650.00i	0.270363i
$459$	−1782.00	−0.181213
$460$	0	0
$461$	6782.00	0.685183	0.342591	−	0.939485i	$-0.388695\pi$
$461$	6782.00	0.685183	0.342591	+	0.939485i	$0.388695\pi$
$462$	1188.00i	0.119634i
$463$	6408.00i	0.643207i	0.946874	+	0.321604i	$0.104222\pi$
$463$	6408.00i	0.643207i	−0.946874	+	0.321604i	$0.895778\pi$
$464$	−6150.00	−0.615316
$465$	0	0
$466$	−5718.00	−0.568415
$467$	10476.0i	1.03805i	0.854758	+	0.519027i	$0.173706\pi$
$467$	10476.0i	1.03805i	−0.854758	+	0.519027i	$0.826294\pi$
$468$	126.000i	0.0124452i
$469$	4464.00	0.439506
$470$	0	0
$471$	1938.00	0.189593
$472$	11100.0i	1.08246i
$473$	− 1892.00i	− 0.183920i
$474$	−3300.00	−0.319776
$475$	0	0
$476$	−16632.0	−1.60153
$477$	738.000i	0.0708400i
$478$	6520.00i	0.623887i
$479$	−1920.00	−0.183146	−0.0915731	−	0.995798i	$-0.529190\pi$
$479$	−1920.00	−0.183146	−0.0915731	+	0.995798i	$0.529190\pi$
$480$	0	0
$481$	−628.000	−0.0595308
$482$	− 2438.00i	− 0.230390i
$483$	7344.00i	0.691850i
$484$	847.000	0.0795455
$485$	0	0
$486$	243.000	0.0226805
$487$	8416.00i	0.783091i	0.920159	+	0.391546i	$0.128059\pi$
$487$	8416.00i	0.783091i	−0.920159	+	0.391546i	$0.871941\pi$
$488$	1830.00i	0.169755i
$489$	−9156.00	−0.846725
$490$	0	0
$491$	17732.0	1.62980	0.814902	−	0.579598i	$-0.196791\pi$
$491$	17732.0	1.62980	0.814902	+	0.579598i	$0.196791\pi$
$492$	2478.00i	0.227067i
$493$	− 9900.00i	− 0.904409i
$494$	−280.000	−0.0255016
$495$	0	0
$496$	−5248.00	−0.475085
$497$	− 35568.0i	− 3.21015i
$498$	2604.00i	0.234313i
$499$	5580.00	0.500591	0.250296	−	0.968169i	$-0.419472\pi$
$499$	5580.00	0.500591	0.250296	+	0.968169i	$0.419472\pi$
$500$	0	0
$501$	3648.00	0.325311
$502$	− 5268.00i	− 0.468371i
$503$	− 12512.0i	− 1.10911i	−0.832147	−	0.554555i	$-0.812888\pi$
$503$	− 12512.0i	− 1.10911i	0.832147	−	0.554555i	$-0.187112\pi$
$504$	4860.00	0.429527
$505$	0	0
$506$	−748.000	−0.0657167
$507$	− 6579.00i	− 0.576299i
$508$	− 308.000i	− 0.0269002i
$509$	22390.0	1.94974	0.974872	−	0.222767i	$-0.0715091\pi$
$509$	22390.0	1.94974	0.974872	+	0.222767i	$0.0715091\pi$
$510$	0	0
$511$	72.0000	0.00623306
$512$	11521.0i	0.994455i
$513$	− 3780.00i	− 0.325324i
$514$	5574.00	0.478324
$515$	0	0
$516$	−3612.00	−0.308158
$517$	− 3564.00i	− 0.303181i
$518$	11304.0i	0.958821i
$519$	11574.0	0.978887
$520$	0	0
$521$	882.000	0.0741672	0.0370836	−	0.999312i	$-0.488193\pi$
$521$	882.000	0.0741672	0.0370836	+	0.999312i	$0.488193\pi$
$522$	1350.00i	0.113195i
$523$	− 18172.0i	− 1.51932i	−0.650319	−	0.759662i	$-0.725365\pi$
$523$	− 18172.0i	− 1.51932i	0.650319	−	0.759662i	$-0.274635\pi$
$524$	−9156.00	−0.763324
$525$	0	0
$526$	2472.00	0.204913
$527$	− 8448.00i	− 0.698293i
$528$	− 1353.00i	− 0.111518i
$529$	7543.00	0.619956
$530$	0	0
$531$	−6660.00	−0.544293
$532$	− 35280.0i	− 2.87515i
$533$	236.000i	0.0191788i
$534$	1410.00	0.114263
$535$	0	0
$536$	1860.00	0.149888
$537$	− 1140.00i	− 0.0916101i
$538$	− 4410.00i	− 0.353399i
$539$	−10483.0	−0.837727
$540$	0	0
$541$	−17998.0	−1.43030	−0.715152	−	0.698969i	$-0.753643\pi$
$541$	−17998.0	−1.43030	−0.715152	+	0.698969i	$0.753643\pi$
$542$	− 1308.00i	− 0.103659i
$543$	1614.00i	0.127557i
$544$	−10626.0	−0.837474
$545$	0	0
$546$	216.000	0.0169303
$547$	− 4164.00i	− 0.325484i	−0.986669	−	0.162742i	$-0.947966\pi$
$547$	− 4164.00i	− 0.325484i	0.986669	−	0.162742i	$-0.0520338\pi$
$548$	11382.0i	0.887254i
$549$	−1098.00	−0.0853579
$550$	0	0
$551$	21000.0	1.62365
$552$	3060.00i	0.235946i
$553$	− 39600.0i	− 3.04514i
$554$	−226.000	−0.0173318
$555$	0	0
$556$	−1260.00	−0.0961077
$557$	13366.0i	1.01676i	0.861133	+	0.508380i	$0.169756\pi$
$557$	13366.0i	1.01676i	−0.861133	+	0.508380i	$0.830244\pi$
$558$	1152.00i	0.0873979i
$559$	−344.000	−0.0260280
$560$	0	0
$561$	2178.00	0.163913
$562$	522.000i	0.0391801i
$563$	− 24612.0i	− 1.84240i	−0.389087	−	0.921201i	$-0.627210\pi$
$563$	− 24612.0i	− 1.84240i	0.389087	−	0.921201i	$-0.372790\pi$
$564$	−6804.00	−0.507979
$565$	0	0
$566$	−1508.00	−0.111989
$567$	2916.00i	0.215980i
$568$	− 14820.0i	− 1.09478i
$569$	70.0000	0.00515739	0.00257869	−	0.999997i	$-0.499179\pi$
$569$	70.0000	0.00515739	0.00257869	+	0.999997i	$0.499179\pi$
$570$	0	0
$571$	−12348.0	−0.904987	−0.452494	−	0.891768i	$-0.649465\pi$
$571$	−12348.0	−0.904987	−0.452494	+	0.891768i	$0.649465\pi$
$572$	− 154.000i	− 0.0112571i
$573$	− 4236.00i	− 0.308833i
$574$	4248.00	0.308899
$575$	0	0
$576$	−1503.00	−0.108724
$577$	23426.0i	1.69019i	0.534620	+	0.845093i	$0.320455\pi$
$577$	23426.0i	1.69019i	−0.534620	+	0.845093i	$0.679545\pi$
$578$	557.000i	0.0400833i
$579$	1914.00	0.137380
$580$	0	0
$581$	−31248.0	−2.23130
$582$	3558.00i	0.253409i
$583$	− 902.000i	− 0.0640772i
$584$	30.0000	0.00212570
$585$	0	0
$586$	−4658.00	−0.328362
$587$	21036.0i	1.47913i	0.673086	+	0.739564i	$0.264968\pi$
$587$	21036.0i	1.47913i	−0.673086	+	0.739564i	$0.735032\pi$
$588$	20013.0i	1.40361i
$589$	17920.0	1.25362
$590$	0	0
$591$	11058.0	0.769654
$592$	− 12874.0i	− 0.893781i
$593$	2798.00i	0.193761i	0.995296	+	0.0968803i	$0.0308864\pi$
$593$	2798.00i	0.193761i	−0.995296	+	0.0968803i	$0.969114\pi$
$594$	−297.000	−0.0205152
$595$	0	0
$596$	−10010.0	−0.687962
$597$	− 720.000i	− 0.0493595i
$598$	136.000i	0.00930009i
$599$	11100.0	0.757151	0.378576	−	0.925570i	$-0.376414\pi$
$599$	11100.0	0.757151	0.378576	+	0.925570i	$0.376414\pi$
$600$	0	0
$601$	15242.0	1.03450	0.517250	−	0.855835i	$-0.326956\pi$
$601$	15242.0	1.03450	0.517250	+	0.855835i	$0.326956\pi$
$602$	6192.00i	0.419214i
$603$	1116.00i	0.0753682i
$604$	−13636.0	−0.918611
$605$	0	0
$606$	4506.00	0.302052
$607$	13876.0i	0.927857i	0.885873	+	0.463929i	$0.153561\pi$
$607$	13876.0i	0.927857i	−0.885873	+	0.463929i	$0.846439\pi$
$608$	− 22540.0i	− 1.50348i
$609$	−16200.0	−1.07793
$610$	0	0
$611$	−648.000	−0.0429055
$612$	− 4158.00i	− 0.274636i
$613$	− 8722.00i	− 0.574679i	−0.957829	−	0.287340i	$-0.907229\pi$
$613$	− 8722.00i	− 0.574679i	0.957829	−	0.287340i	$-0.0927708\pi$
$614$	−6476.00	−0.425652
$615$	0	0
$616$	−5940.00	−0.388522
$617$	− 8014.00i	− 0.522904i	−0.965217	−	0.261452i	$-0.915799\pi$
$617$	− 8014.00i	− 0.522904i	0.965217	−	0.261452i	$-0.0842012\pi$
$618$	− 96.0000i	− 0.00624868i
$619$	−26020.0	−1.68955	−0.844776	−	0.535121i	$-0.820266\pi$
$619$	−26020.0	−1.68955	−0.844776	+	0.535121i	$0.820266\pi$
$620$	0	0
$621$	−1836.00	−0.118641
$622$	5652.00i	0.364348i
$623$	16920.0i	1.08810i
$624$	−246.000	−0.0157819
$625$	0	0
$626$	−5638.00	−0.359968
$627$	4620.00i	0.294266i
$628$	4522.00i	0.287337i
$629$	20724.0	1.31370
$630$	0	0
$631$	−23528.0	−1.48437	−0.742183	−	0.670197i	$-0.766209\pi$
$631$	−23528.0	−1.48437	−0.742183	+	0.670197i	$0.766209\pi$
$632$	− 16500.0i	− 1.03850i
$633$	− 15276.0i	− 0.959189i
$634$	−1506.00	−0.0943390
$635$	0	0
$636$	−1722.00	−0.107361
$637$	1906.00i	0.118553i
$638$	− 1650.00i	− 0.102389i
$639$	8892.00	0.550488
$640$	0	0
$641$	−18998.0	−1.17063	−0.585317	−	0.810805i	$-0.699030\pi$
$641$	−18998.0	−1.17063	−0.585317	+	0.810805i	$0.699030\pi$
$642$	3348.00i	0.205818i
$643$	4348.00i	0.266669i	0.991071	+	0.133335i	$0.0425685\pi$
$643$	4348.00i	0.266669i	−0.991071	+	0.133335i	$0.957431\pi$
$644$	−17136.0	−1.04853
$645$	0	0
$646$	9240.00	0.562760
$647$	31916.0i	1.93933i	0.244435	+	0.969666i	$0.421398\pi$
$647$	31916.0i	1.93933i	−0.244435	+	0.969666i	$0.578602\pi$
$648$	1215.00i	0.0736570i
$649$	8140.00	0.492331
$650$	0	0
$651$	−13824.0	−0.832266
$652$	− 21364.0i	− 1.28325i
$653$	− 25682.0i	− 1.53907i	−0.638603	−	0.769536i	$-0.720487\pi$
$653$	− 25682.0i	− 1.53907i	0.638603	−	0.769536i	$-0.279513\pi$
$654$	6570.00	0.392825
$655$	0	0
$656$	−4838.00	−0.287945
$657$	18.0000i	0.00106887i
$658$	11664.0i	0.691049i
$659$	−14940.0	−0.883126	−0.441563	−	0.897230i	$-0.645576\pi$
$659$	−14940.0	−0.883126	−0.441563	+	0.897230i	$0.645576\pi$
$660$	0	0
$661$	4502.00	0.264913	0.132457	−	0.991189i	$-0.457714\pi$
$661$	4502.00	0.264913	0.132457	+	0.991189i	$0.457714\pi$
$662$	− 7268.00i	− 0.426705i
$663$	− 396.000i	− 0.0231966i
$664$	−13020.0	−0.760955
$665$	0	0
$666$	−2826.00	−0.164422
$667$	− 10200.0i	− 0.592122i
$668$	8512.00i	0.493023i
$669$	11424.0	0.660205
$670$	0	0
$671$	1342.00	0.0772091
$672$	17388.0i	0.998150i
$673$	− 5362.00i	− 0.307117i	−0.988140	−	0.153559i	$-0.950927\pi$
$673$	− 5362.00i	− 0.307117i	0.988140	−	0.153559i	$-0.0490734\pi$
$674$	7254.00	0.414560
$675$	0	0
$676$	15351.0	0.873407
$677$	14566.0i	0.826908i	0.910525	+	0.413454i	$0.135678\pi$
$677$	14566.0i	0.826908i	−0.910525	+	0.413454i	$0.864322\pi$
$678$	4194.00i	0.237566i
$679$	−42696.0	−2.41314
$680$	0	0
$681$	−132.000	−0.00742768
$682$	− 1408.00i	− 0.0790544i
$683$	− 11852.0i	− 0.663989i	−0.943281	−	0.331994i	$-0.892279\pi$
$683$	− 11852.0i	− 0.663989i	0.943281	−	0.331994i	$-0.107721\pi$
$684$	8820.00	0.493043
$685$	0	0
$686$	21960.0	1.22221
$687$	− 7950.00i	− 0.441501i
$688$	− 7052.00i	− 0.390778i
$689$	−164.000	−0.00906807
$690$	0	0
$691$	−1828.00	−0.100637	−0.0503187	−	0.998733i	$-0.516024\pi$
$691$	−1828.00	−0.100637	−0.0503187	+	0.998733i	$0.516024\pi$
$692$	27006.0i	1.48355i
$693$	− 3564.00i	− 0.195361i
$694$	−2276.00	−0.124490
$695$	0	0
$696$	−6750.00	−0.367612
$697$	− 7788.00i	− 0.423230i
$698$	− 4610.00i	− 0.249987i
$699$	17154.0	0.928217
$700$	0	0
$701$	23182.0	1.24903	0.624516	−	0.781012i	$-0.285296\pi$
$701$	23182.0	1.24903	0.624516	+	0.781012i	$0.285296\pi$
$702$	54.0000i	0.00290327i
$703$	43960.0i	2.35844i
$704$	1837.00	0.0983445
$705$	0	0
$706$	4602.00	0.245324
$707$	54072.0i	2.87636i
$708$	− 15540.0i	− 0.824900i
$709$	33850.0	1.79304	0.896519	−	0.443006i	$-0.146088\pi$
$709$	33850.0	1.79304	0.896519	+	0.443006i	$0.146088\pi$
$710$	0	0
$711$	9900.00	0.522193
$712$	7050.00i	0.371081i
$713$	− 8704.00i	− 0.457177i
$714$	−7128.00	−0.373612
$715$	0	0
$716$	2660.00	0.138839
$717$	− 19560.0i	− 1.01880i
$718$	4160.00i	0.216225i
$719$	7140.00	0.370344	0.185172	−	0.982706i	$-0.440716\pi$
$719$	7140.00	0.370344	0.185172	+	0.982706i	$0.440716\pi$
$720$	0	0
$721$	1152.00	0.0595045
$722$	12741.0i	0.656746i
$723$	7314.00i	0.376225i
$724$	−3766.00	−0.193318
$725$	0	0
$726$	363.000	0.0185567
$727$	8896.00i	0.453830i	0.973915	+	0.226915i	$0.0728640\pi$
$727$	8896.00i	0.453830i	−0.973915	+	0.226915i	$0.927136\pi$
$728$	1080.00i	0.0549828i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	11352.0	0.574376
$732$	− 2562.00i	− 0.129364i
$733$	13038.0i	0.656984i	0.944507	+	0.328492i	$0.106540\pi$
$733$	13038.0i	0.656984i	−0.944507	+	0.328492i	$0.893460\pi$
$734$	5024.00	0.252642
$735$	0	0
$736$	−10948.0	−0.548300
$737$	− 1364.00i	− 0.0681731i
$738$	1062.00i	0.0529712i
$739$	−11620.0	−0.578415	−0.289207	−	0.957266i	$-0.593392\pi$
$739$	−11620.0	−0.578415	−0.289207	+	0.957266i	$0.593392\pi$
$740$	0	0
$741$	840.000	0.0416440
$742$	2952.00i	0.146053i
$743$	1328.00i	0.0655715i	0.999462	+	0.0327857i	$0.0104379\pi$
$743$	1328.00i	0.0655715i	−0.999462	+	0.0327857i	$0.989562\pi$
$744$	−5760.00	−0.283833
$745$	0	0
$746$	10842.0	0.532110
$747$	− 7812.00i	− 0.382632i
$748$	5082.00i	0.248418i
$749$	−40176.0	−1.95995
$750$	0	0
$751$	−37808.0	−1.83706	−0.918531	−	0.395349i	$-0.870624\pi$
$751$	−37808.0	−1.83706	−0.918531	+	0.395349i	$0.870624\pi$
$752$	− 13284.0i	− 0.644172i
$753$	15804.0i	0.764847i
$754$	−300.000	−0.0144899
$755$	0	0
$756$	−6804.00	−0.327327
$757$	34326.0i	1.64808i	0.566529	+	0.824042i	$0.308286\pi$
$757$	34326.0i	1.64808i	−0.566529	+	0.824042i	$0.691714\pi$
$758$	1540.00i	0.0737933i
$759$	2244.00	0.107315
$760$	0	0
$761$	4282.00	0.203972	0.101986	−	0.994786i	$-0.467480\pi$
$761$	4282.00	0.203972	0.101986	+	0.994786i	$0.467480\pi$
$762$	− 132.000i	− 0.00627540i
$763$	78840.0i	3.74076i
$764$	9884.00	0.468050
$765$	0	0
$766$	−9468.00	−0.446596
$767$	− 1480.00i	− 0.0696737i
$768$	357.000i	0.0167736i
$769$	−24410.0	−1.14466	−0.572332	−	0.820022i	$-0.693961\pi$
$769$	−24410.0	−1.14466	−0.572332	+	0.820022i	$0.693961\pi$
$770$	0	0
$771$	−16722.0	−0.781100
$772$	4466.00i	0.208206i
$773$	− 8162.00i	− 0.379776i	−0.981806	−	0.189888i	$-0.939188\pi$
$773$	− 8162.00i	− 0.379776i	0.981806	−	0.189888i	$-0.0608125\pi$
$774$	−1548.00	−0.0718885
$775$	0	0
$776$	−17790.0	−0.822969
$777$	− 33912.0i	− 1.56575i
$778$	10590.0i	0.488008i
$779$	16520.0	0.759808
$780$	0	0
$781$	−10868.0	−0.497935
$782$	− 4488.00i	− 0.205231i
$783$	− 4050.00i	− 0.184847i
$784$	−39073.0	−1.77993
$785$	0	0
$786$	−3924.00	−0.178072
$787$	26596.0i	1.20463i	0.798258	+	0.602316i	$0.205755\pi$
$787$	26596.0i	1.20463i	−0.798258	+	0.602316i	$0.794245\pi$
$788$	25802.0i	1.16644i
$789$	−7416.00	−0.334622
$790$	0	0
$791$	−50328.0	−2.26227
$792$	− 1485.00i	− 0.0666252i
$793$	− 244.000i	− 0.0109265i
$794$	7434.00	0.332271
$795$	0	0
$796$	1680.00	0.0748066
$797$	− 24614.0i	− 1.09394i	−0.837151	−	0.546972i	$-0.815781\pi$
$797$	− 24614.0i	− 1.09394i	0.837151	−	0.546972i	$-0.184219\pi$
$798$	− 15120.0i	− 0.670730i
$799$	21384.0	0.946823
$800$	0	0
$801$	−4230.00	−0.186591
$802$	11402.0i	0.502018i
$803$	− 22.0000i	0 0.000966828i
$804$	−2604.00	−0.114224
$805$	0	0
$806$	−256.000	−0.0111876
$807$	13230.0i	0.577098i
$808$	22530.0i	0.980944i
$809$	−39930.0	−1.73531	−0.867654	−	0.497169i	$-0.834373\pi$
$809$	−39930.0	−1.73531	−0.867654	+	0.497169i	$0.834373\pi$
$810$	0	0
$811$	2412.00	0.104435	0.0522175	−	0.998636i	$-0.483371\pi$
$811$	2412.00	0.104435	0.0522175	+	0.998636i	$0.483371\pi$
$812$	− 37800.0i	− 1.63365i
$813$	3924.00i	0.169275i
$814$	3454.00	0.148726
$815$	0	0
$816$	8118.00	0.348268
$817$	24080.0i	1.03115i
$818$	510.000i	0.0217992i
$819$	−648.000	−0.0276471
$820$	0	0
$821$	−6018.00	−0.255822	−0.127911	−	0.991786i	$-0.540827\pi$
$821$	−6018.00	−0.255822	−0.127911	+	0.991786i	$0.540827\pi$
$822$	4878.00i	0.206983i
$823$	− 34632.0i	− 1.46682i	−0.679785	−	0.733412i	$-0.737927\pi$
$823$	− 34632.0i	− 1.46682i	0.679785	−	0.733412i	$-0.262073\pi$
$824$	480.000	0.0202932
$825$	0	0
$826$	−26640.0	−1.12218
$827$	− 40044.0i	− 1.68376i	−0.539668	−	0.841878i	$-0.681450\pi$
$827$	− 40044.0i	− 1.68376i	0.539668	−	0.841878i	$-0.318550\pi$
$828$	− 4284.00i	− 0.179806i
$829$	44090.0	1.84718	0.923588	−	0.383386i	$-0.125242\pi$
$829$	44090.0	1.84718	0.923588	+	0.383386i	$0.125242\pi$
$830$	0	0
$831$	678.000	0.0283027
$832$	− 334.000i	− 0.0139175i
$833$	− 62898.0i	− 2.61619i
$834$	−540.000	−0.0224205
$835$	0	0
$836$	−10780.0	−0.445974
$837$	− 3456.00i	− 0.142720i
$838$	− 2420.00i	− 0.0997584i
$839$	23780.0	0.978518	0.489259	−	0.872138i	$-0.337267\pi$
$839$	23780.0	0.978518	0.489259	+	0.872138i	$0.337267\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	− 8178.00i	− 0.334718i
$843$	− 1566.00i	− 0.0639809i
$844$	35644.0	1.45369
$845$	0	0
$846$	−2916.00	−0.118504
$847$	4356.00i	0.176711i
$848$	− 3362.00i	− 0.136146i
$849$	4524.00	0.182878
$850$	0	0
$851$	21352.0	0.860091
$852$	20748.0i	0.834290i
$853$	4078.00i	0.163691i	0.996645	+	0.0818453i	$0.0260813\pi$
$853$	4078.00i	0.163691i	−0.996645	+	0.0818453i	$0.973919\pi$
$854$	−4392.00	−0.175985
$855$	0	0
$856$	−16740.0	−0.668413
$857$	30666.0i	1.22232i	0.791506	+	0.611161i	$0.209297\pi$
$857$	30666.0i	1.22232i	−0.791506	+	0.611161i	$0.790703\pi$
$858$	− 66.0000i	− 0.00262611i
$859$	−4780.00	−0.189862	−0.0949310	−	0.995484i	$-0.530263\pi$
$859$	−4780.00	−0.189862	−0.0949310	+	0.995484i	$0.530263\pi$
$860$	0	0
$861$	−12744.0	−0.504430
$862$	− 6768.00i	− 0.267423i
$863$	9428.00i	0.371880i	0.982561	+	0.185940i	$0.0595331\pi$
$863$	9428.00i	0.371880i	−0.982561	+	0.185940i	$0.940467\pi$
$864$	−4347.00	−0.171167
$865$	0	0
$866$	−478.000	−0.0187565
$867$	− 1671.00i	− 0.0654558i
$868$	− 32256.0i	− 1.26134i
$869$	−12100.0	−0.472341
$870$	0	0
$871$	−248.000	−0.00964771
$872$	32850.0i	1.27574i
$873$	− 10674.0i	− 0.413815i
$874$	9520.00	0.368443
$875$	0	0
$876$	−42.0000	−0.00161992
$877$	15266.0i	0.587795i	0.955837	+	0.293897i	$0.0949524\pi$
$877$	15266.0i	0.587795i	−0.955837	+	0.293897i	$0.905048\pi$
$878$	3260.00i	0.125307i
$879$	13974.0	0.536213
$880$	0	0
$881$	−5118.00	−0.195721	−0.0978603	−	0.995200i	$-0.531200\pi$
$881$	−5118.00	−0.195721	−0.0978603	+	0.995200i	$0.531200\pi$
$882$	8577.00i	0.327441i
$883$	44188.0i	1.68408i	0.539413	+	0.842041i	$0.318646\pi$
$883$	44188.0i	1.68408i	−0.539413	+	0.842041i	$0.681354\pi$
$884$	924.000	0.0351555
$885$	0	0
$886$	6812.00	0.258300
$887$	− 16864.0i	− 0.638374i	−0.947692	−	0.319187i	$-0.896590\pi$
$887$	− 16864.0i	− 0.638374i	0.947692	−	0.319187i	$-0.103410\pi$
$888$	− 14130.0i	− 0.533977i
$889$	1584.00	0.0597589
$890$	0	0
$891$	891.000	0.0335013
$892$	26656.0i	1.00057i
$893$	45360.0i	1.69979i
$894$	−4290.00	−0.160491
$895$	0	0
$896$	−52380.0	−1.95301
$897$	− 408.000i	− 0.0151870i
$898$	− 15290.0i	− 0.568189i
$899$	19200.0	0.712298
$900$	0	0
$901$	5412.00	0.200111
$902$	− 1298.00i	− 0.0479143i
$903$	− 18576.0i	− 0.684574i
$904$	−20970.0	−0.771518
$905$	0	0
$906$	−5844.00	−0.214298
$907$	− 37924.0i	− 1.38836i	−0.719800	−	0.694182i	$-0.755766\pi$
$907$	− 37924.0i	− 1.38836i	0.719800	−	0.694182i	$-0.244234\pi$
$908$	− 308.000i	− 0.0112570i
$909$	−13518.0	−0.493249
$910$	0	0
$911$	−36628.0	−1.33210	−0.666048	−	0.745909i	$-0.732015\pi$
$911$	−36628.0	−1.33210	−0.666048	+	0.745909i	$0.732015\pi$
$912$	17220.0i	0.625232i
$913$	9548.00i	0.346104i
$914$	12854.0	0.465178
$915$	0	0
$916$	18550.0	0.669115
$917$	− 47088.0i	− 1.69573i
$918$	− 1782.00i	− 0.0640684i
$919$	21300.0	0.764551	0.382275	−	0.924048i	$-0.375141\pi$
$919$	21300.0	0.764551	0.382275	+	0.924048i	$0.375141\pi$
$920$	0	0
$921$	19428.0	0.695086
$922$	6782.00i	0.242249i
$923$	1976.00i	0.0704668i
$924$	8316.00	0.296078
$925$	0	0
$926$	−6408.00	−0.227408
$927$	288.000i	0.0102041i
$928$	− 24150.0i	− 0.854270i
$929$	−31450.0	−1.11070	−0.555350	−	0.831616i	$-0.687416\pi$
$929$	−31450.0	−1.11070	−0.555350	+	0.831616i	$0.687416\pi$
$930$	0	0
$931$	133420.	4.69674
$932$	40026.0i	1.40675i
$933$	− 16956.0i	− 0.594978i
$934$	−10476.0	−0.367008
$935$	0	0
$936$	−270.000	−0.00942866
$937$	− 6174.00i	− 0.215257i	−0.994191	−	0.107628i	$-0.965674\pi$
$937$	− 6174.00i	− 0.215257i	0.994191	−	0.107628i	$-0.0343257\pi$
$938$	4464.00i	0.155389i
$939$	16914.0	0.587825
$940$	0	0
$941$	20422.0	0.707479	0.353740	−	0.935344i	$-0.384910\pi$
$941$	20422.0	0.707479	0.353740	+	0.935344i	$0.384910\pi$
$942$	1938.00i	0.0670313i
$943$	− 8024.00i	− 0.277092i
$944$	30340.0	1.04606
$945$	0	0
$946$	1892.00	0.0650256
$947$	12156.0i	0.417125i	0.978009	+	0.208562i	$0.0668784\pi$
$947$	12156.0i	0.417125i	−0.978009	+	0.208562i	$0.933122\pi$
$948$	23100.0i	0.791406i
$949$	−4.00000	−0.000136823 0
$950$	0	0
$951$	4518.00	0.154055
$952$	− 35640.0i	− 1.21334i
$953$	− 14442.0i	− 0.490894i	−0.969410	−	0.245447i	$-0.921065\pi$
$953$	− 14442.0i	− 0.490894i	0.969410	−	0.245447i	$-0.0789348\pi$
$954$	−738.000	−0.0250457
$955$	0	0
$956$	45640.0	1.54404
$957$	4950.00i	0.167200i
$958$	− 1920.00i	− 0.0647520i
$959$	−58536.0	−1.97104
$960$	0	0
$961$	−13407.0	−0.450035
$962$	− 628.000i	− 0.0210473i
$963$	− 10044.0i	− 0.336099i
$964$	−17066.0	−0.570186
$965$	0	0
$966$	−7344.00	−0.244606
$967$	33356.0i	1.10926i	0.832096	+	0.554631i	$0.187141\pi$
$967$	33356.0i	1.10926i	−0.832096	+	0.554631i	$0.812859\pi$
$968$	1815.00i	0.0602648i
$969$	−27720.0	−0.918983
$970$	0	0
$971$	3852.00	0.127309	0.0636543	−	0.997972i	$-0.479725\pi$
$971$	3852.00	0.127309	0.0636543	+	0.997972i	$0.479725\pi$
$972$	− 1701.00i	− 0.0561313i
$973$	− 6480.00i	− 0.213504i
$974$	−8416.00	−0.276865
$975$	0	0
$976$	5002.00	0.164047
$977$	− 37454.0i	− 1.22647i	−0.789901	−	0.613234i	$-0.789868\pi$
$977$	− 37454.0i	− 1.22647i	0.789901	−	0.613234i	$-0.210132\pi$
$978$	− 9156.00i	− 0.299363i
$979$	5170.00	0.168778
$980$	0	0
$981$	−19710.0	−0.641480
$982$	17732.0i	0.576223i
$983$	16228.0i	0.526544i	0.964722	+	0.263272i	$0.0848017\pi$
$983$	16228.0i	0.526544i	−0.964722	+	0.263272i	$0.915198\pi$
$984$	−5310.00	−0.172029
$985$	0	0
$986$	9900.00	0.319757
$987$	− 34992.0i	− 1.12848i
$988$	1960.00i	0.0631133i
$989$	11696.0	0.376048
$990$	0	0
$991$	−23728.0	−0.760590	−0.380295	−	0.924865i	$-0.624178\pi$
$991$	−23728.0	−0.760590	−0.380295	+	0.924865i	$0.624178\pi$
$992$	− 20608.0i	− 0.659581i
$993$	21804.0i	0.696807i
$994$	35568.0	1.13496
$995$	0	0
$996$	18228.0	0.579896
$997$	41306.0i	1.31211i	0.754713	+	0.656055i	$0.227776\pi$
$997$	41306.0i	1.31211i	−0.754713	+	0.656055i	$0.772224\pi$
$998$	5580.00i	0.176986i
$999$	8478.00	0.268501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.e.199.2		2
5.2	odd	4		825.4.a.d.1.1		1
5.3	odd	4		165.4.a.b.1.1	✓	1
5.4	even	2	inner	825.4.c.e.199.1		2
15.2	even	4		2475.4.a.g.1.1		1
15.8	even	4		495.4.a.b.1.1		1
55.43	even	4		1815.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.b.1.1	✓	1	5.3	odd	4
495.4.a.b.1.1		1	15.8	even	4
825.4.a.d.1.1		1	5.2	odd	4
825.4.c.e.199.1		2	5.4	even	2	inner
825.4.c.e.199.2		2	1.1	even	1	trivial
1815.4.a.c.1.1		1	55.43	even	4
2475.4.a.g.1.1		1	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +3.00000 q^{6} +36.0000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +3.00000 q^{6} +36.0000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +11.0000 q^{11} -21.0000i q^{12} -2.00000i q^{13} -36.0000 q^{14} +41.0000 q^{16} +66.0000i q^{17} -9.00000i q^{18} -140.000 q^{19} +108.000 q^{21} +11.0000i q^{22} +68.0000i q^{23} +45.0000 q^{24} +2.00000 q^{26} +27.0000i q^{27} +252.000i q^{28} -150.000 q^{29} -128.000 q^{31} +161.000i q^{32} -33.0000i q^{33} -66.0000 q^{34} -63.0000 q^{36} -314.000i q^{37} -140.000i q^{38} -6.00000 q^{39} -118.000 q^{41} +108.000i q^{42} -172.000i q^{43} +77.0000 q^{44} -68.0000 q^{46} -324.000i q^{47} -123.000i q^{48} -953.000 q^{49} +198.000 q^{51} -14.0000i q^{52} -82.0000i q^{53} -27.0000 q^{54} -540.000 q^{56} +420.000i q^{57} -150.000i q^{58} +740.000 q^{59} +122.000 q^{61} -128.000i q^{62} -324.000i q^{63} +167.000 q^{64} +33.0000 q^{66} -124.000i q^{67} +462.000i q^{68} +204.000 q^{69} -988.000 q^{71} -135.000i q^{72} -2.00000i q^{73} +314.000 q^{74} -980.000 q^{76} +396.000i q^{77} -6.00000i q^{78} -1100.00 q^{79} +81.0000 q^{81} -118.000i q^{82} +868.000i q^{83} +756.000 q^{84} +172.000 q^{86} +450.000i q^{87} +165.000i q^{88} +470.000 q^{89} +72.0000 q^{91} +476.000i q^{92} +384.000i q^{93} +324.000 q^{94} +483.000 q^{96} +1186.00i q^{97} -953.000i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 14 q^{4} + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q + 14 * q^4 + 6 * q^6 - 18 * q^9	\( 2 q + 14 q^{4} + 6 q^{6} - 18 q^{9} + 22 q^{11} - 72 q^{14} + 82 q^{16} - 280 q^{19} + 216 q^{21} + 90 q^{24} + 4 q^{26} - 300 q^{29} - 256 q^{31} - 132 q^{34} - 126 q^{36} - 12 q^{39} - 236 q^{41} + 154 q^{44} - 136 q^{46} - 1906 q^{49} + 396 q^{51} - 54 q^{54} - 1080 q^{56} + 1480 q^{59} + 244 q^{61} + 334 q^{64} + 66 q^{66} + 408 q^{69} - 1976 q^{71} + 628 q^{74} - 1960 q^{76} - 2200 q^{79} + 162 q^{81} + 1512 q^{84} + 344 q^{86} + 940 q^{89} + 144 q^{91} + 648 q^{94} + 966 q^{96} - 198 q^{99}+O(q^{100}) \) 2 * q + 14 * q^4 + 6 * q^6 - 18 * q^9 + 22 * q^11 - 72 * q^14 + 82 * q^16 - 280 * q^19 + 216 * q^21 + 90 * q^24 + 4 * q^26 - 300 * q^29 - 256 * q^31 - 132 * q^34 - 126 * q^36 - 12 * q^39 - 236 * q^41 + 154 * q^44 - 136 * q^46 - 1906 * q^49 + 396 * q^51 - 54 * q^54 - 1080 * q^56 + 1480 * q^59 + 244 * q^61 + 334 * q^64 + 66 * q^66 + 408 * q^69 - 1976 * q^71 + 628 * q^74 - 1960 * q^76 - 2200 * q^79 + 162 * q^81 + 1512 * q^84 + 344 * q^86 + 940 * q^89 + 144 * q^91 + 648 * q^94 + 966 * q^96 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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