LMFDB - Embedded newform 294.5.c.a.97.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,5,Mod(97,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.97"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	294.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,32,0,0,0,0,-108,0,324,0,0,0,396,256,0,0,0,0,0,-192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(22)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.3
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.97
Dual form			294.5.c.a.97.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.82843 q^{2} -5.19615i q^{3} +8.00000 q^{4} +14.1536i q^{5} -14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +40.0324i q^{10} +64.0294 q^{11} -41.5692i q^{12} -228.919i q^{13} +73.5442 q^{15} +64.0000 q^{16} -225.455i q^{17} -76.3675 q^{18} +294.737i q^{19} +113.229i q^{20} +181.103 q^{22} +709.499 q^{23} -117.576i q^{24} +424.676 q^{25} -647.481i q^{26} +140.296i q^{27} +740.397 q^{29} +208.014 q^{30} -666.713i q^{31} +181.019 q^{32} -332.707i q^{33} -637.683i q^{34} -216.000 q^{36} -833.765 q^{37} +833.642i q^{38} -1189.50 q^{39} +320.259i q^{40} -2817.60i q^{41} +3066.41 q^{43} +512.235 q^{44} -382.147i q^{45} +2006.77 q^{46} +613.726i q^{47} -332.554i q^{48} +1201.17 q^{50} -1171.50 q^{51} -1831.35i q^{52} -1152.60 q^{53} +396.817i q^{54} +906.246i q^{55} +1531.50 q^{57} +2094.16 q^{58} -3492.59i q^{59} +588.353 q^{60} -2272.21i q^{61} -1885.75i q^{62} +512.000 q^{64} +3240.03 q^{65} -941.037i q^{66} -8674.62 q^{67} -1803.64i q^{68} -3686.66i q^{69} -353.591 q^{71} -610.940 q^{72} +4069.95i q^{73} -2358.24 q^{74} -2206.68i q^{75} +2357.90i q^{76} -3364.41 q^{78} +6472.83 q^{79} +905.829i q^{80} +729.000 q^{81} -7969.38i q^{82} -8225.83i q^{83} +3191.00 q^{85} +8673.11 q^{86} -3847.22i q^{87} +1448.82 q^{88} +15538.3i q^{89} -1080.87i q^{90} +5675.99 q^{92} -3464.34 q^{93} +1735.88i q^{94} -4171.58 q^{95} -940.604i q^{96} +1558.61i q^{97} -1728.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{4} - 108 q^{9} + 324 q^{11} + 396 q^{15} + 256 q^{16} - 192 q^{22} - 624 q^{23} + 952 q^{25} + 2724 q^{29} - 288 q^{30} - 864 q^{36} - 2792 q^{37} - 1296 q^{39} - 632 q^{43} + 2592 q^{44} + 9792 q^{46}+ \cdots - 8748 q^{99}+O(q^{100}) $ 4 * q + 32 * q^4 - 108 * q^9 + 324 * q^11 + 396 * q^15 + 256 * q^16 - 192 * q^22 - 624 * q^23 + 952 * q^25 + 2724 * q^29 - 288 * q^30 - 864 * q^36 - 2792 * q^37 - 1296 * q^39 - 632 * q^43 + 2592 * q^44 + 9792 * q^46 + 2112 * q^50 - 1224 * q^51 + 2076 * q^53 + 2664 * q^57 + 672 * q^58 + 3168 * q^60 + 2048 * q^64 + 1488 * q^65 - 29200 * q^67 - 9696 * q^71 - 1536 * q^74 - 9792 * q^78 - 7948 * q^79 + 2916 * q^81 + 1224 * q^85 + 36480 * q^86 - 1536 * q^88 - 4992 * q^92 - 22716 * q^93 - 6504 * q^95 - 8748 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.82843	0.707107
$2$	2.82843	0.707107
$3$	− 5.19615i	− 0.577350i
$3$	− 5.19615i	− 0.577350i
$4$	8.00000	0.500000
$5$	14.1536i	0.566143i	0.959099	+	0.283072i	$0.0913534\pi$
$5$	14.1536i	0.566143i	−0.959099	+	0.283072i	$0.908647\pi$
$6$	− 14.6969i	− 0.408248i
$7$	0	0
$7$	0	0
$8$	22.6274	0.353553
$9$	−27.0000	−0.333333
$10$	40.0324i	0.400324i
$11$	64.0294	0.529169	0.264584	−	0.964363i	$-0.414765\pi$
$11$	64.0294	0.529169	0.264584	+	0.964363i	$0.414765\pi$
$12$	− 41.5692i	− 0.288675i
$13$	− 228.919i	− 1.35455i	−0.735729	−	0.677276i	$-0.763161\pi$
$13$	− 228.919i	− 1.35455i	0.735729	−	0.677276i	$-0.236839\pi$
$14$	0	0
$15$	73.5442	0.326863
$16$	64.0000	0.250000
$17$	− 225.455i	− 0.780121i	−0.920789	−	0.390061i	$-0.872454\pi$
$17$	− 225.455i	− 0.780121i	0.920789	−	0.390061i	$-0.127546\pi$
$18$	−76.3675	−0.235702
$19$	294.737i	0.816446i	0.912882	+	0.408223i	$0.133851\pi$
$19$	294.737i	0.816446i	−0.912882	+	0.408223i	$0.866149\pi$
$20$	113.229i	0.283072i
$21$	0	0
$22$	181.103	0.374179
$23$	709.499	1.34121	0.670604	−	0.741816i	$-0.266035\pi$
$23$	709.499	1.34121	0.670604	+	0.741816i	$0.266035\pi$
$24$	− 117.576i	− 0.204124i
$25$	424.676	0.679482
$26$	− 647.481i	− 0.957812i
$27$	140.296i	0.192450i
$28$	0	0
$29$	740.397	0.880377	0.440188	−	0.897905i	$-0.354912\pi$
$29$	740.397	0.880377	0.440188	+	0.897905i	$0.354912\pi$
$30$	208.014	0.231127
$31$	− 666.713i	− 0.693770i	−0.937908	−	0.346885i	$-0.887239\pi$
$31$	− 666.713i	− 0.693770i	0.937908	−	0.346885i	$-0.112761\pi$
$32$	181.019	0.176777
$33$	− 332.707i	− 0.305516i
$34$	− 637.683i	− 0.551629i
$35$	0	0
$36$	−216.000	−0.166667
$37$	−833.765	−0.609032	−0.304516	−	0.952507i	$-0.598495\pi$
$37$	−833.765	−0.609032	−0.304516	+	0.952507i	$0.598495\pi$
$38$	833.642i	0.577315i
$39$	−1189.50	−0.782050
$40$	320.259i	0.200162i
$41$	− 2817.60i	− 1.67615i	−0.545558	−	0.838073i	$-0.683682\pi$
$41$	− 2817.60i	− 1.67615i	0.545558	−	0.838073i	$-0.316318\pi$
$42$	0	0
$43$	3066.41	1.65841	0.829207	−	0.558942i	$-0.188793\pi$
$43$	3066.41	1.65841	0.829207	+	0.558942i	$0.188793\pi$
$44$	512.235	0.264584
$45$	− 382.147i	− 0.188714i
$46$	2006.77	0.948377
$47$	613.726i	0.277830i	0.990304	+	0.138915i	$0.0443614\pi$
$47$	613.726i	0.277830i	−0.990304	+	0.138915i	$0.955639\pi$
$48$	− 332.554i	− 0.144338i
$49$	0	0
$50$	1201.17	0.480466
$51$	−1171.50	−0.450403
$52$	− 1831.35i	− 0.677276i
$53$	−1152.60	−0.410324	−0.205162	−	0.978728i	$-0.565772\pi$
$53$	−1152.60	−0.410324	−0.205162	+	0.978728i	$0.565772\pi$
$54$	396.817i	0.136083i
$55$	906.246i	0.299585i
$56$	0	0
$57$	1531.50	0.471375
$58$	2094.16	0.622520
$59$	− 3492.59i	− 1.00333i	−0.865062	−	0.501665i	$-0.832721\pi$
$59$	− 3492.59i	− 1.00333i	0.865062	−	0.501665i	$-0.167279\pi$
$60$	588.353	0.163431
$61$	− 2272.21i	− 0.610645i	−0.952249	−	0.305323i	$-0.901236\pi$
$61$	− 2272.21i	− 0.610645i	0.952249	−	0.305323i	$-0.0987643\pi$
$62$	− 1885.75i	− 0.490569i
$63$	0	0
$64$	512.000	0.125000
$65$	3240.03	0.766870
$66$	− 941.037i	− 0.216032i
$67$	−8674.62	−1.93242	−0.966208	−	0.257764i	$-0.917014\pi$
$67$	−8674.62	−1.93242	−0.966208	+	0.257764i	$0.917014\pi$
$68$	− 1803.64i	− 0.390061i
$69$	− 3686.66i	− 0.774346i
$70$	0	0
$71$	−353.591	−0.0701431	−0.0350715	−	0.999385i	$-0.511166\pi$
$71$	−353.591	−0.0701431	−0.0350715	+	0.999385i	$0.511166\pi$
$72$	−610.940	−0.117851
$73$	4069.95i	0.763736i	0.924217	+	0.381868i	$0.124719\pi$
$73$	4069.95i	0.763736i	−0.924217	+	0.381868i	$0.875281\pi$
$74$	−2358.24	−0.430650
$75$	− 2206.68i	− 0.392299i
$76$	2357.90i	0.408223i
$77$	0	0
$78$	−3364.41	−0.552993
$79$	6472.83	1.03715	0.518573	−	0.855033i	$-0.326464\pi$
$79$	6472.83	1.03715	0.518573	+	0.855033i	$0.326464\pi$
$80$	905.829i	0.141536i
$81$	729.000	0.111111
$82$	− 7969.38i	− 1.18521i
$83$	− 8225.83i	− 1.19405i	−0.802222	−	0.597026i	$-0.796349\pi$
$83$	− 8225.83i	− 1.19405i	0.802222	−	0.597026i	$-0.203651\pi$
$84$	0	0
$85$	3191.00	0.441660
$86$	8673.11	1.17268
$87$	− 3847.22i	− 0.508286i
$88$	1448.82	0.187089
$89$	15538.3i	1.96166i	0.194878	+	0.980828i	$0.437569\pi$
$89$	15538.3i	1.96166i	−0.194878	+	0.980828i	$0.562431\pi$
$90$	− 1080.87i	− 0.133441i
$91$	0	0
$92$	5675.99	0.670604
$93$	−3464.34	−0.400548
$94$	1735.88i	0.196455i
$95$	−4171.58	−0.462225
$96$	− 940.604i	− 0.102062i
$97$	1558.61i	0.165651i	0.996564	+	0.0828254i	$0.0263944\pi$
$97$	1558.61i	0.165651i	−0.996564	+	0.0828254i	$0.973606\pi$
$98$	0	0
$99$	−1728.79	−0.176390
$100$	3397.41	0.339741
$101$	15735.3i	1.54253i	0.636516	+	0.771264i	$0.280375\pi$
$101$	15735.3i	1.54253i	−0.636516	+	0.771264i	$0.719625\pi$
$102$	−3313.50	−0.318483
$103$	− 33.7287i	− 0.00317926i	−0.999999	−	0.00158963i	$-0.999494\pi$
$103$	− 33.7287i	− 0.00317926i	0.999999	−	0.00158963i	$-0.000505995\pi$
$104$	− 5179.85i	− 0.478906i
$105$	0	0
$106$	−3260.05	−0.290143
$107$	−5446.46	−0.475715	−0.237858	−	0.971300i	$-0.576445\pi$
$107$	−5446.46	−0.475715	−0.237858	+	0.971300i	$0.576445\pi$
$108$	1122.37i	0.0962250i
$109$	16697.8	1.40542	0.702709	−	0.711477i	$-0.251974\pi$
$109$	16697.8	1.40542	0.702709	+	0.711477i	$0.251974\pi$
$110$	2563.25i	0.211839i
$111$	4332.37i	0.351625i
$112$	0	0
$113$	9455.64	0.740515	0.370258	−	0.928929i	$-0.379269\pi$
$113$	9455.64	0.740515	0.370258	+	0.928929i	$0.379269\pi$
$114$	4331.73	0.333313
$115$	10041.9i	0.759315i
$116$	5923.18	0.440188
$117$	6180.82i	0.451517i
$118$	− 9878.54i	− 0.709461i
$119$	0	0
$120$	1664.11	0.115563
$121$	−10541.2	−0.719980
$122$	− 6426.79i	− 0.431792i
$123$	−14640.7	−0.967724
$124$	− 5333.70i	− 0.346885i
$125$	14856.7i	0.950827i
$126$	0	0
$127$	−2380.07	−0.147564	−0.0737822	−	0.997274i	$-0.523507\pi$
$127$	−2380.07	−0.147564	−0.0737822	+	0.997274i	$0.523507\pi$
$128$	1448.15	0.0883883
$129$	− 15933.5i	− 0.957486i
$130$	9164.17	0.542259
$131$	4339.79i	0.252887i	0.991974	+	0.126443i	$0.0403562\pi$
$131$	4339.79i	0.252887i	−0.991974	+	0.126443i	$0.959644\pi$
$132$	− 2661.65i	− 0.152758i
$133$	0	0
$134$	−24535.5	−1.36642
$135$	−1985.69	−0.108954
$136$	− 5101.46i	− 0.275814i
$137$	−30759.2	−1.63883	−0.819414	−	0.573202i	$-0.805701\pi$
$137$	−30759.2	−1.63883	−0.819414	+	0.573202i	$0.805701\pi$
$138$	− 10427.5i	− 0.547546i
$139$	27186.6i	1.40710i	0.710644	+	0.703551i	$0.248404\pi$
$139$	27186.6i	1.40710i	−0.710644	+	0.703551i	$0.751596\pi$
$140$	0	0
$141$	3189.01	0.160405
$142$	−1000.11	−0.0495987
$143$	− 14657.6i	− 0.716786i
$144$	−1728.00	−0.0833333
$145$	10479.3i	0.498419i
$146$	11511.6i	0.540043i
$147$	0	0
$148$	−6670.12	−0.304516
$149$	−5826.92	−0.262462	−0.131231	−	0.991352i	$-0.541893\pi$
$149$	−5826.92	−0.262462	−0.131231	+	0.991352i	$0.541893\pi$
$150$	− 6241.44i	− 0.277397i
$151$	25186.8	1.10463	0.552317	−	0.833634i	$-0.313744\pi$
$151$	25186.8	1.10463	0.552317	+	0.833634i	$0.313744\pi$
$152$	6669.14i	0.288657i
$153$	6087.29i	0.260040i
$154$	0	0
$155$	9436.37	0.392773
$156$	−9515.99	−0.391025
$157$	23896.0i	0.969453i	0.874666	+	0.484726i	$0.161081\pi$
$157$	23896.0i	0.969453i	−0.874666	+	0.484726i	$0.838919\pi$
$158$	18307.9	0.733373
$159$	5989.09i	0.236901i
$160$	2562.07i	0.100081i
$161$	0	0
$162$	2061.92	0.0785674
$163$	−42585.9	−1.60284	−0.801422	−	0.598100i	$-0.795923\pi$
$163$	−42585.9	−1.60284	−0.801422	+	0.598100i	$0.795923\pi$
$164$	− 22540.8i	− 0.838073i
$165$	4708.99	0.172966
$166$	− 23266.2i	− 0.844323i
$167$	− 26356.3i	− 0.945043i	−0.881319	−	0.472521i	$-0.843344\pi$
$167$	− 26356.3i	− 0.945043i	0.881319	−	0.472521i	$-0.156656\pi$
$168$	0	0
$169$	−23843.0	−0.834809
$170$	9025.50	0.312301
$171$	− 7957.90i	− 0.272149i
$172$	24531.3	0.829207
$173$	− 28019.2i	− 0.936188i	−0.883679	−	0.468094i	$-0.844941\pi$
$173$	− 28019.2i	− 0.936188i	0.883679	−	0.468094i	$-0.155059\pi$
$174$	− 10881.6i	− 0.359412i
$175$	0	0
$176$	4097.88	0.132292
$177$	−18148.0	−0.579273
$178$	43948.9i	1.38710i
$179$	25398.5	0.792687	0.396343	−	0.918102i	$-0.370279\pi$
$179$	25398.5	0.792687	0.396343	+	0.918102i	$0.370279\pi$
$180$	− 3057.17i	− 0.0943572i
$181$	44097.2i	1.34603i	0.739630	+	0.673014i	$0.235001\pi$
$181$	44097.2i	1.34603i	−0.739630	+	0.673014i	$0.764999\pi$
$182$	0	0
$183$	−11806.8	−0.352556
$184$	16054.1	0.474188
$185$	− 11800.8i	− 0.344799i
$186$	−9798.64	−0.283230
$187$	− 14435.8i	− 0.412816i
$188$	4909.81i	0.138915i
$189$	0	0
$190$	−11799.0	−0.326843
$191$	−64559.1	−1.76966	−0.884832	−	0.465911i	$-0.845727\pi$
$191$	−64559.1	−1.76966	−0.884832	+	0.465911i	$0.845727\pi$
$192$	− 2660.43i	− 0.0721688i
$193$	36674.6	0.984579	0.492290	−	0.870432i	$-0.336160\pi$
$193$	36674.6	0.984579	0.492290	+	0.870432i	$0.336160\pi$
$194$	4408.41i	0.117133i
$195$	− 16835.7i	− 0.442753i
$196$	0	0
$197$	−73147.0	−1.88480	−0.942398	−	0.334494i	$-0.891434\pi$
$197$	−73147.0	−1.88480	−0.942398	+	0.334494i	$0.891434\pi$
$198$	−4889.77	−0.124726
$199$	− 1401.03i	− 0.0353786i	−0.999844	−	0.0176893i	$-0.994369\pi$
$199$	− 1401.03i	− 0.0353786i	0.999844	−	0.0176893i	$-0.00563097\pi$
$200$	9609.33	0.240233
$201$	45074.6i	1.11568i
$202$	44506.2i	1.09073i
$203$	0	0
$204$	−9371.99	−0.225202
$205$	39879.2	0.948939
$206$	− 95.3993i	− 0.00224807i
$207$	−19156.5	−0.447069
$208$	− 14650.8i	− 0.338638i
$209$	18871.8i	0.432038i
$210$	0	0
$211$	58231.7	1.30796	0.653980	−	0.756512i	$-0.273098\pi$
$211$	58231.7	1.30796	0.653980	+	0.756512i	$0.273098\pi$
$212$	−9220.80	−0.205162
$213$	1837.31i	0.0404971i
$214$	−15404.9	−0.336381
$215$	43400.6i	0.938900i
$216$	3174.54i	0.0680414i
$217$	0	0
$218$	47228.4	0.993781
$219$	21148.1	0.440943
$220$	7249.97i	0.149793i
$221$	−51611.0	−1.05671
$222$	12253.8i	0.248636i
$223$	61050.9i	1.22767i	0.789434	+	0.613836i	$0.210374\pi$
$223$	61050.9i	1.22767i	−0.789434	+	0.613836i	$0.789626\pi$
$224$	0	0
$225$	−11466.3	−0.226494
$226$	26744.6	0.523623
$227$	24993.7i	0.485041i	0.970146	+	0.242520i	$0.0779742\pi$
$227$	24993.7i	0.485041i	−0.970146	+	0.242520i	$0.922026\pi$
$228$	12252.0	0.235688
$229$	18928.9i	0.360956i	0.983579	+	0.180478i	$0.0577644\pi$
$229$	18928.9i	0.360956i	−0.983579	+	0.180478i	$0.942236\pi$
$230$	28402.9i	0.536917i
$231$	0	0
$232$	16753.3	0.311260
$233$	6684.74	0.123132	0.0615662	−	0.998103i	$-0.480390\pi$
$233$	6684.74	0.123132	0.0615662	+	0.998103i	$0.480390\pi$
$234$	17482.0i	0.319271i
$235$	−8686.42	−0.157291
$236$	− 27940.7i	− 0.501665i
$237$	− 33633.8i	− 0.598796i
$238$	0	0
$239$	−96461.0	−1.68871	−0.844356	−	0.535782i	$-0.820017\pi$
$239$	−96461.0	−1.68871	−0.844356	+	0.535782i	$0.820017\pi$
$240$	4706.83	0.0817157
$241$	54700.2i	0.941792i	0.882189	+	0.470896i	$0.156069\pi$
$241$	54700.2i	0.941792i	−0.882189	+	0.470896i	$0.843931\pi$
$242$	−29815.1	−0.509103
$243$	− 3788.00i	− 0.0641500i
$244$	− 18177.7i	− 0.305323i
$245$	0	0
$246$	−41410.1	−0.684284
$247$	67471.0	1.10592
$248$	− 15086.0i	− 0.245285i
$249$	−42742.6	−0.689386
$250$	42021.0i	0.672336i
$251$	− 108137.i	− 1.71643i	−0.513286	−	0.858217i	$-0.671572\pi$
$251$	− 108137.i	− 1.71643i	0.513286	−	0.858217i	$-0.328428\pi$
$252$	0	0
$253$	45428.8	0.709725
$254$	−6731.84	−0.104344
$255$	− 16580.9i	− 0.254993i
$256$	4096.00	0.0625000
$257$	− 35886.1i	− 0.543325i	−0.962393	−	0.271663i	$-0.912427\pi$
$257$	− 35886.1i	− 0.543325i	0.962393	−	0.271663i	$-0.0875735\pi$
$258$	− 45066.8i	− 0.677045i
$259$	0	0
$260$	25920.2	0.383435
$261$	−19990.7	−0.293459
$262$	12274.8i	0.178818i
$263$	−65431.6	−0.945967	−0.472984	−	0.881071i	$-0.656823\pi$
$263$	−65431.6	−0.945967	−0.472984	+	0.881071i	$0.656823\pi$
$264$	− 7528.29i	− 0.108016i
$265$	− 16313.4i	− 0.232302i
$266$	0	0
$267$	80739.2	1.13256
$268$	−69396.9	−0.966208
$269$	− 69211.3i	− 0.956472i	−0.878231	−	0.478236i	$-0.841276\pi$
$269$	− 69211.3i	− 0.956472i	0.878231	−	0.478236i	$-0.158724\pi$
$270$	−5616.39	−0.0770423
$271$	− 6550.55i	− 0.0891947i	−0.999005	−	0.0445973i	$-0.985800\pi$
$271$	− 6550.55i	− 0.0891947i	0.999005	−	0.0445973i	$-0.0142005\pi$
$272$	− 14429.1i	− 0.195030i
$273$	0	0
$274$	−87000.1	−1.15883
$275$	27191.8	0.359561
$276$	− 29493.3i	− 0.387173i
$277$	79103.2	1.03094	0.515471	−	0.856907i	$-0.327617\pi$
$277$	79103.2	1.03094	0.515471	+	0.856907i	$0.327617\pi$
$278$	76895.4i	0.994972i
$279$	18001.2i	0.231257i
$280$	0	0
$281$	34363.1	0.435191	0.217596	−	0.976039i	$-0.430179\pi$
$281$	34363.1	0.435191	0.217596	+	0.976039i	$0.430179\pi$
$282$	9019.89	0.113424
$283$	91912.3i	1.14763i	0.818986	+	0.573813i	$0.194537\pi$
$283$	91912.3i	1.14763i	−0.818986	+	0.573813i	$0.805463\pi$
$284$	−2828.73	−0.0350715
$285$	21676.2i	0.266866i
$286$	− 41457.8i	− 0.506844i
$287$	0	0
$288$	−4887.52	−0.0589256
$289$	32691.0	0.391411
$290$	29639.8i	0.352436i
$291$	8098.77	0.0956385
$292$	32559.6i	0.381868i
$293$	23218.2i	0.270453i	0.990815	+	0.135227i	$0.0431763\pi$
$293$	23218.2i	0.270453i	−0.990815	+	0.135227i	$0.956824\pi$
$294$	0	0
$295$	49432.7	0.568028
$296$	−18865.9	−0.215325
$297$	8983.08i	0.101839i
$298$	−16481.0	−0.185589
$299$	− 162418.i	− 1.81673i
$300$	− 17653.5i	− 0.196150i
$301$	0	0
$302$	71239.0	0.781095
$303$	81763.1	0.890579
$304$	18863.2i	0.204112i
$305$	32159.9	0.345713
$306$	17217.4i	0.183876i
$307$	− 66385.9i	− 0.704367i	−0.935931	−	0.352183i	$-0.885439\pi$
$307$	− 66385.9i	− 0.704367i	0.935931	−	0.352183i	$-0.114561\pi$
$308$	0	0
$309$	−175.260	−0.00183555
$310$	26690.1	0.277733
$311$	− 95700.5i	− 0.989449i	−0.869050	−	0.494724i	$-0.835269\pi$
$311$	− 95700.5i	− 0.989449i	0.869050	−	0.494724i	$-0.164731\pi$
$312$	−26915.3	−0.276497
$313$	− 47904.0i	− 0.488971i	−0.969653	−	0.244486i	$-0.921381\pi$
$313$	− 47904.0i	− 0.488971i	0.969653	−	0.244486i	$-0.0786191\pi$
$314$	67588.2i	0.685507i
$315$	0	0
$316$	51782.6	0.518573
$317$	−34128.2	−0.339621	−0.169811	−	0.985477i	$-0.554316\pi$
$317$	−34128.2	−0.339621	−0.169811	+	0.985477i	$0.554316\pi$
$318$	16939.7i	0.167514i
$319$	47407.2	0.465868
$320$	7246.63i	0.0707679i
$321$	28300.7i	0.274654i
$322$	0	0
$323$	66450.0	0.636927
$324$	5832.00	0.0555556
$325$	− 97216.5i	− 0.920393i
$326$	−120451.	−1.13338
$327$	− 86764.2i	− 0.811418i
$328$	− 63755.1i	− 0.592607i
$329$	0	0
$330$	13319.0	0.122305
$331$	133285.	1.21654	0.608270	−	0.793730i	$-0.291864\pi$
$331$	133285.	1.21654	0.608270	+	0.793730i	$0.291864\pi$
$332$	− 65806.6i	− 0.597026i
$333$	22511.6	0.203011
$334$	− 74546.9i	− 0.668246i
$335$	− 122777.i	− 1.09402i
$336$	0	0
$337$	−49734.4	−0.437922	−0.218961	−	0.975734i	$-0.570267\pi$
$337$	−49734.4	−0.437922	−0.218961	+	0.975734i	$0.570267\pi$
$338$	−67438.1	−0.590299
$339$	− 49133.0i	− 0.427537i
$340$	25528.0	0.220830
$341$	− 42689.2i	− 0.367121i
$342$	− 22508.3i	− 0.192438i
$343$	0	0
$344$	69384.9	0.586338
$345$	52179.5	0.438391
$346$	− 79250.2i	− 0.661985i
$347$	18769.5	0.155882	0.0779408	−	0.996958i	$-0.475165\pi$
$347$	18769.5	0.155882	0.0779408	+	0.996958i	$0.475165\pi$
$348$	− 30777.7i	− 0.254143i
$349$	− 4574.17i	− 0.0375545i	−0.999824	−	0.0187772i	$-0.994023\pi$
$349$	− 4574.17i	− 0.0375545i	0.999824	−	0.0187772i	$-0.00597733\pi$
$350$	0	0
$351$	32116.5	0.260683
$352$	11590.6	0.0935447
$353$	60893.0i	0.488673i	0.969691	+	0.244336i	$0.0785701\pi$
$353$	60893.0i	0.488673i	−0.969691	+	0.244336i	$0.921430\pi$
$354$	−51330.4	−0.409608
$355$	− 5004.58i	− 0.0397110i
$356$	124306.i	0.980828i
$357$	0	0
$358$	71837.7	0.560514
$359$	232118.	1.80103	0.900513	−	0.434830i	$-0.143192\pi$
$359$	232118.	1.80103	0.900513	+	0.434830i	$0.143192\pi$
$360$	− 8646.99i	− 0.0667206i
$361$	43451.1	0.333416
$362$	124726.i	0.951786i
$363$	54773.8i	0.415681i
$364$	0	0
$365$	−57604.4	−0.432384
$366$	−33394.6	−0.249295
$367$	− 144718.i	− 1.07446i	−0.843436	−	0.537229i	$-0.819471\pi$
$367$	− 144718.i	− 1.07446i	0.843436	−	0.537229i	$-0.180529\pi$
$368$	45407.9	0.335302
$369$	76075.3i	0.558716i
$370$	− 33377.6i	− 0.243810i
$371$	0	0
$372$	−27714.7	−0.200274
$373$	−148883.	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$373$	−148883.	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$374$	− 40830.5i	− 0.291905i
$375$	77197.5	0.548960
$376$	13887.0i	0.0982276i
$377$	− 169491.i	− 1.19252i
$378$	0	0
$379$	140667.	0.979299	0.489649	−	0.871919i	$-0.337125\pi$
$379$	140667.	0.979299	0.489649	+	0.871919i	$0.337125\pi$
$380$	−33372.7	−0.231113
$381$	12367.2i	0.0851963i
$382$	−182601.	−1.25134
$383$	− 29322.3i	− 0.199895i	−0.994993	−	0.0999473i	$-0.968133\pi$
$383$	− 29322.3i	− 0.199895i	0.994993	−	0.0999473i	$-0.0318674\pi$
$384$	− 7524.83i	− 0.0510310i
$385$	0	0
$386$	103731.	0.696202
$387$	−82793.0	−0.552805
$388$	12468.9i	0.0828254i
$389$	132420.	0.875092	0.437546	−	0.899196i	$-0.355848\pi$
$389$	132420.	0.875092	0.437546	+	0.899196i	$0.355848\pi$
$390$	− 47618.4i	− 0.313073i
$391$	− 159960.i	− 1.04630i
$392$	0	0
$393$	22550.2	0.146004
$394$	−206891.	−1.33275
$395$	91613.7i	0.587173i
$396$	−13830.4	−0.0881948
$397$	− 34227.6i	− 0.217168i	−0.994087	−	0.108584i	$-0.965368\pi$
$397$	− 34227.6i	− 0.217168i	0.994087	−	0.108584i	$-0.0346316\pi$
$398$	− 3962.70i	− 0.0250164i
$399$	0	0
$400$	27179.3	0.169870
$401$	−179081.	−1.11368	−0.556841	−	0.830619i	$-0.687987\pi$
$401$	−179081.	−1.11368	−0.556841	+	0.830619i	$0.687987\pi$
$402$	127490.i	0.788906i
$403$	−152623.	−0.939747
$404$	125883.i	0.771264i
$405$	10318.0i	0.0629048i
$406$	0	0
$407$	−53385.5	−0.322281
$408$	−26508.0	−0.159242
$409$	49766.8i	0.297504i	0.988875	+	0.148752i	$0.0475257\pi$
$409$	49766.8i	0.297504i	−0.988875	+	0.148752i	$0.952474\pi$
$410$	112795.	0.671001
$411$	159829.i	0.946178i
$412$	− 269.830i	− 0.00158963i
$413$	0	0
$414$	−54182.7	−0.316126
$415$	116425.	0.676005
$416$	− 41438.8i	− 0.239453i
$417$	141266.	0.812391
$418$	53377.6i	0.305497i
$419$	− 43951.2i	− 0.250347i	−0.992135	−	0.125174i	$-0.960051\pi$
$419$	− 43951.2i	− 0.250347i	0.992135	−	0.125174i	$-0.0399488\pi$
$420$	0	0
$421$	−218257.	−1.23141	−0.615707	−	0.787975i	$-0.711129\pi$
$421$	−218257.	−1.23141	−0.615707	+	0.787975i	$0.711129\pi$
$422$	164704.	0.924867
$423$	− 16570.6i	− 0.0926099i
$424$	−26080.4	−0.145071
$425$	− 95745.4i	− 0.530078i
$426$	5196.71i	0.0286358i
$427$	0	0
$428$	−43571.7	−0.237858
$429$	−76162.9	−0.413837
$430$	122756.i	0.663902i
$431$	−76739.6	−0.413109	−0.206555	−	0.978435i	$-0.566225\pi$
$431$	−76739.6	−0.413109	−0.206555	+	0.978435i	$0.566225\pi$
$432$	8978.95i	0.0481125i
$433$	216713.i	1.15587i	0.816083	+	0.577935i	$0.196141\pi$
$433$	216713.i	1.15587i	−0.816083	+	0.577935i	$0.803859\pi$
$434$	0	0
$435$	54451.9	0.287763
$436$	133582.	0.702709
$437$	209116.i	1.09502i
$438$	59815.8	0.311794
$439$	− 23762.1i	− 0.123298i	−0.998098	−	0.0616489i	$-0.980364\pi$
$439$	− 23762.1i	− 0.123298i	0.998098	−	0.0616489i	$-0.0196359\pi$
$440$	20506.0i	0.105919i
$441$	0	0
$442$	−145978.	−0.747210
$443$	174865.	0.891035	0.445517	−	0.895273i	$-0.353020\pi$
$443$	174865.	0.891035	0.445517	+	0.895273i	$0.353020\pi$
$444$	34658.9i	0.175812i
$445$	−219922.	−1.11058
$446$	172678.i	0.868095i
$447$	30277.6i	0.151532i
$448$	0	0
$449$	−195154.	−0.968023	−0.484011	−	0.875062i	$-0.660821\pi$
$449$	−195154.	−0.968023	−0.484011	+	0.875062i	$0.660821\pi$
$450$	−32431.5	−0.160155
$451$	− 180409.i	− 0.886965i
$452$	75645.1	0.370258
$453$	− 130874.i	− 0.637761i
$454$	70692.8i	0.342976i
$455$	0	0
$456$	34653.9	0.166656
$457$	58472.2	0.279974	0.139987	−	0.990153i	$-0.455294\pi$
$457$	58472.2	0.279974	0.139987	+	0.990153i	$0.455294\pi$
$458$	53539.0i	0.255234i
$459$	31630.5	0.150134
$460$	80335.6i	0.379658i
$461$	307243.i	1.44571i	0.691002	+	0.722853i	$0.257169\pi$
$461$	307243.i	1.44571i	−0.691002	+	0.722853i	$0.742831\pi$
$462$	0	0
$463$	−17772.2	−0.0829049	−0.0414524	−	0.999140i	$-0.513199\pi$
$463$	−17772.2	−0.0829049	−0.0414524	+	0.999140i	$0.513199\pi$
$464$	47385.4	0.220094
$465$	− 49032.8i	− 0.226768i
$466$	18907.3	0.0870678
$467$	− 64965.1i	− 0.297883i	−0.988846	−	0.148942i	$-0.952413\pi$
$467$	− 64965.1i	− 0.297883i	0.988846	−	0.148942i	$-0.0475867\pi$
$468$	49446.5i	0.225759i
$469$	0	0
$470$	−24568.9	−0.111222
$471$	124167.	0.559714
$472$	− 79028.3i	− 0.354731i
$473$	196340.	0.877581
$474$	− 95130.7i	− 0.423413i
$475$	125168.i	0.554760i
$476$	0	0
$477$	31120.2	0.136775
$478$	−272833.	−1.19410
$479$	210937.i	0.919351i	0.888087	+	0.459675i	$0.152034\pi$
$479$	210937.i	0.919351i	−0.888087	+	0.459675i	$0.847966\pi$
$480$	13312.9	0.0577817
$481$	190865.i	0.824965i
$482$	154716.i	0.665948i
$483$	0	0
$484$	−84329.8	−0.359990
$485$	−22059.9	−0.0937821
$486$	− 10714.1i	− 0.0453609i
$487$	−228888.	−0.965084	−0.482542	−	0.875873i	$-0.660286\pi$
$487$	−228888.	−0.965084	−0.482542	+	0.875873i	$0.660286\pi$
$488$	− 51414.3i	− 0.215896i
$489$	221283.i	0.925402i
$490$	0	0
$491$	140350.	0.582169	0.291085	−	0.956697i	$-0.405984\pi$
$491$	140350.	0.582169	0.291085	+	0.956697i	$0.405984\pi$
$492$	−117126.	−0.483862
$493$	− 166926.i	− 0.686801i
$494$	190837.	0.782002
$495$	− 24468.6i	− 0.0998618i
$496$	− 42669.6i	− 0.173442i
$497$	0	0
$498$	−120894.	−0.487470
$499$	−345327.	−1.38685	−0.693424	−	0.720529i	$-0.743899\pi$
$499$	−345327.	−1.38685	−0.693424	+	0.720529i	$0.743899\pi$
$500$	118853.i	0.475414i
$501$	−136951.	−0.545621
$502$	− 305858.i	− 1.21370i
$503$	− 58979.0i	− 0.233110i	−0.993184	−	0.116555i	$-0.962815\pi$
$503$	− 58979.0i	− 0.233110i	0.993184	−	0.116555i	$-0.0371851\pi$
$504$	0	0
$505$	−222711.	−0.873291
$506$	128492.	0.501852
$507$	123892.i	0.481977i
$508$	−19040.5	−0.0737822
$509$	− 23848.7i	− 0.0920511i	−0.998940	−	0.0460255i	$-0.985344\pi$
$509$	− 23848.7i	− 0.0920511i	0.998940	−	0.0460255i	$-0.0146556\pi$
$510$	− 46897.9i	− 0.180307i
$511$	0	0
$512$	11585.2	0.0441942
$513$	−41350.5	−0.157125
$514$	− 101501.i	− 0.384189i
$515$	477.382	0.00179991
$516$	− 127468.i	− 0.478743i
$517$	39296.5i	0.147019i
$518$	0	0
$519$	−145592.	−0.540509
$520$	73313.4	0.271129
$521$	481708.i	1.77463i	0.461163	+	0.887315i	$0.347432\pi$
$521$	481708.i	1.77463i	−0.461163	+	0.887315i	$0.652568\pi$
$522$	−56542.3	−0.207507
$523$	461410.i	1.68688i	0.537226	+	0.843438i	$0.319472\pi$
$523$	461410.i	1.68688i	−0.537226	+	0.843438i	$0.680528\pi$
$524$	34718.3i	0.126443i
$525$	0	0
$526$	−185068.	−0.668900
$527$	−150314.	−0.541225
$528$	− 21293.2i	− 0.0763790i
$529$	223547.	0.798837
$530$	− 46141.3i	− 0.164262i
$531$	94299.9i	0.334443i
$532$	0	0
$533$	−645003.	−2.27043
$534$	228365.	0.800842
$535$	− 77086.9i	− 0.269323i
$536$	−196284.	−0.683212
$537$	− 131974.i	− 0.457658i
$538$	− 195759.i	− 0.676328i
$539$	0	0
$540$	−15885.5	−0.0544772
$541$	−508196.	−1.73635	−0.868174	−	0.496260i	$-0.834706\pi$
$541$	−508196.	−1.73635	−0.868174	+	0.496260i	$0.834706\pi$
$542$	− 18527.7i	− 0.0630702i
$543$	229136.	0.777130
$544$	− 40811.7i	− 0.137907i
$545$	236333.i	0.795668i
$546$	0	0
$547$	40170.8	0.134257	0.0671283	−	0.997744i	$-0.478616\pi$
$547$	40170.8	0.134257	0.0671283	+	0.997744i	$0.478616\pi$
$548$	−246073.	−0.819414
$549$	61349.7i	0.203548i
$550$	76910.0	0.254248
$551$	218222.i	0.718780i
$552$	− 83419.7i	− 0.273773i
$553$	0	0
$554$	223738.	0.728987
$555$	−61318.5	−0.199070
$556$	217493.i	0.703551i
$557$	−78460.4	−0.252895	−0.126447	−	0.991973i	$-0.540358\pi$
$557$	−78460.4	−0.252895	−0.126447	+	0.991973i	$0.540358\pi$
$558$	50915.2i	0.163523i
$559$	− 701959.i	− 2.24641i
$560$	0	0
$561$	−75010.4	−0.238339
$562$	97193.7	0.307727
$563$	− 410625.i	− 1.29547i	−0.761864	−	0.647737i	$-0.775716\pi$
$563$	− 410625.i	− 1.29547i	0.761864	−	0.647737i	$-0.224284\pi$
$564$	25512.1	0.0802025
$565$	133831.i	0.419238i
$566$	259967.i	0.811495i
$567$	0	0
$568$	−8000.86	−0.0247993
$569$	−148809.	−0.459625	−0.229812	−	0.973235i	$-0.573811\pi$
$569$	−148809.	−0.459625	−0.229812	+	0.973235i	$0.573811\pi$
$570$	61309.5i	0.188703i
$571$	72292.6	0.221729	0.110864	−	0.993836i	$-0.464638\pi$
$571$	72292.6	0.221729	0.110864	+	0.993836i	$0.464638\pi$
$572$	− 117261.i	− 0.358393i
$573$	335459.i	1.02172i
$574$	0	0
$575$	301307.	0.911326
$576$	−13824.0	−0.0416667
$577$	− 557335.i	− 1.67404i	−0.547176	−	0.837018i	$-0.684297\pi$
$577$	− 557335.i	− 1.67404i	0.547176	−	0.837018i	$-0.315703\pi$
$578$	92464.2	0.276769
$579$	− 190567.i	− 0.568447i
$580$	83834.1i	0.249210i
$581$	0	0
$582$	22906.8	0.0676267
$583$	−73800.4	−0.217131
$584$	92092.4i	0.270021i
$585$	−87480.7	−0.255623
$586$	65670.9i	0.191239i
$587$	− 308119.i	− 0.894217i	−0.894480	−	0.447109i	$-0.852454\pi$
$587$	− 308119.i	− 0.894217i	0.894480	−	0.447109i	$-0.147546\pi$
$588$	0	0
$589$	196505.	0.566426
$590$	139817.	0.401657
$591$	380083.i	1.08819i
$592$	−53360.9	−0.152258
$593$	231870.i	0.659378i	0.944090	+	0.329689i	$0.106944\pi$
$593$	231870.i	0.659378i	−0.944090	+	0.329689i	$0.893056\pi$
$594$	25408.0i	0.0720108i
$595$	0	0
$596$	−46615.3	−0.131231
$597$	−7279.95	−0.0204258
$598$	− 459387.i	− 1.28462i
$599$	−334083.	−0.931110	−0.465555	−	0.885019i	$-0.654145\pi$
$599$	−334083.	−0.931110	−0.465555	+	0.885019i	$0.654145\pi$
$600$	− 49931.5i	− 0.138699i
$601$	645072.i	1.78591i	0.450147	+	0.892955i	$0.351372\pi$
$601$	645072.i	1.78591i	−0.450147	+	0.892955i	$0.648628\pi$
$602$	0	0
$603$	234215.	0.644139
$604$	201494.	0.552317
$605$	− 149196.i	− 0.407612i
$606$	231261.	0.629734
$607$	− 139306.i	− 0.378088i	−0.981969	−	0.189044i	$-0.939461\pi$
$607$	− 139306.i	− 0.378088i	0.981969	−	0.189044i	$-0.0605388\pi$
$608$	53353.1i	0.144329i
$609$	0	0
$610$	90962.0	0.244456
$611$	140494.	0.376335
$612$	48698.3i	0.130020i
$613$	−407331.	−1.08399	−0.541997	−	0.840381i	$-0.682331\pi$
$613$	−407331.	−1.08399	−0.541997	+	0.840381i	$0.682331\pi$
$614$	− 187768.i	− 0.498063i
$615$	− 207218.i	− 0.547870i
$616$	0	0
$617$	276504.	0.726325	0.363163	−	0.931726i	$-0.381697\pi$
$617$	276504.	0.726325	0.363163	+	0.931726i	$0.381697\pi$
$618$	−495.709	−0.00129793
$619$	223901.i	0.584352i	0.956365	+	0.292176i	$0.0943793\pi$
$619$	223901.i	0.584352i	−0.956365	+	0.292176i	$0.905621\pi$
$620$	75491.0	0.196387
$621$	99539.9i	0.258115i
$622$	− 270682.i	− 0.699646i
$623$	0	0
$624$	−76127.9	−0.195513
$625$	55147.5	0.141178
$626$	− 135493.i	− 0.345755i
$627$	98061.0	0.249437
$628$	191168.i	0.484726i
$629$	187976.i	0.475119i
$630$	0	0
$631$	299528.	0.752278	0.376139	−	0.926563i	$-0.377251\pi$
$631$	299528.	0.752278	0.376139	+	0.926563i	$0.377251\pi$
$632$	146463.	0.366686
$633$	− 302581.i	− 0.755151i
$634$	−96529.1	−0.240148
$635$	− 33686.4i	− 0.0835425i
$636$	47912.7i	0.118450i
$637$	0	0
$638$	134088.	0.329418
$639$	9546.97	0.0233810
$640$	20496.6i	0.0500405i
$641$	577884.	1.40645	0.703226	−	0.710967i	$-0.251742\pi$
$641$	577884.	1.40645	0.703226	+	0.710967i	$0.251742\pi$
$642$	80046.3i	0.194210i
$643$	− 135320.i	− 0.327295i	−0.986519	−	0.163647i	$-0.947674\pi$
$643$	− 135320.i	− 0.327295i	0.986519	−	0.163647i	$-0.0523259\pi$
$644$	0	0
$645$	225516.	0.542074
$646$	187949.	0.450375
$647$	218100.i	0.521011i	0.965472	+	0.260506i	$0.0838892\pi$
$647$	218100.i	0.521011i	−0.965472	+	0.260506i	$0.916111\pi$
$648$	16495.4	0.0392837
$649$	− 223629.i	− 0.530931i
$650$	− 274970.i	− 0.650816i
$651$	0	0
$652$	−340688.	−0.801422
$653$	144254.	0.338301	0.169150	−	0.985590i	$-0.445898\pi$
$653$	144254.	0.338301	0.169150	+	0.985590i	$0.445898\pi$
$654$	− 245406.i	− 0.573759i
$655$	−61423.6	−0.143170
$656$	− 180327.i	− 0.419037i
$657$	− 109889.i	− 0.254579i
$658$	0	0
$659$	−159392.	−0.367024	−0.183512	−	0.983017i	$-0.558747\pi$
$659$	−159392.	−0.367024	−0.183512	+	0.983017i	$0.558747\pi$
$660$	37671.9	0.0864828
$661$	352962.i	0.807839i	0.914795	+	0.403919i	$0.132352\pi$
$661$	352962.i	0.807839i	−0.914795	+	0.403919i	$0.867648\pi$
$662$	376988.	0.860223
$663$	268178.i	0.610094i
$664$	− 186129.i	− 0.422161i
$665$	0	0
$666$	63672.5	0.143550
$667$	525311.	1.18077
$668$	− 210850.i	− 0.472521i
$669$	317230.	0.708797
$670$	− 347265.i	− 0.773592i
$671$	− 145488.i	− 0.323135i
$672$	0	0
$673$	504858.	1.11465	0.557326	−	0.830294i	$-0.311827\pi$
$673$	504858.	1.11465	0.557326	+	0.830294i	$0.311827\pi$
$674$	−140670.	−0.309658
$675$	59580.4i	0.130766i
$676$	−190744.	−0.417404
$677$	195706.i	0.426999i	0.976943	+	0.213500i	$0.0684862\pi$
$677$	195706.i	0.426999i	−0.976943	+	0.213500i	$0.931514\pi$
$678$	− 138969.i	− 0.302314i
$679$	0	0
$680$	72204.0	0.156150
$681$	129871.	0.280039
$682$	− 120743.i	− 0.259594i
$683$	−234441.	−0.502566	−0.251283	−	0.967914i	$-0.580852\pi$
$683$	−234441.	−0.502566	−0.251283	+	0.967914i	$0.580852\pi$
$684$	− 63663.2i	− 0.136074i
$685$	− 435352.i	− 0.927812i
$686$	0	0
$687$	98357.4	0.208398
$688$	196250.	0.414603
$689$	263852.i	0.555805i
$690$	147586.	0.309989
$691$	89309.2i	0.187042i	0.995617	+	0.0935212i	$0.0298123\pi$
$691$	89309.2i	0.187042i	−0.995617	+	0.0935212i	$0.970188\pi$
$692$	− 224153.i	− 0.468094i
$693$	0	0
$694$	53088.3	0.110225
$695$	−384788.	−0.796622
$696$	− 87052.5i	− 0.179706i
$697$	−635243.	−1.30760
$698$	− 12937.7i	− 0.0265550i
$699$	− 34734.9i	− 0.0710905i
$700$	0	0
$701$	122213.	0.248704	0.124352	−	0.992238i	$-0.460315\pi$
$701$	122213.	0.248704	0.124352	+	0.992238i	$0.460315\pi$
$702$	90839.1	0.184331
$703$	− 245741.i	− 0.497242i
$704$	32783.1	0.0661461
$705$	45135.9i	0.0908122i
$706$	172231.i	0.345544i
$707$	0	0
$708$	−145184.	−0.289636
$709$	84019.8	0.167143	0.0835717	−	0.996502i	$-0.473367\pi$
$709$	84019.8	0.167143	0.0835717	+	0.996502i	$0.473367\pi$
$710$	− 14155.1i	− 0.0280799i
$711$	−174766.	−0.345715
$712$	351591.i	0.693550i
$713$	− 473032.i	− 0.930489i
$714$	0	0
$715$	207457.	0.405804
$716$	203188.	0.396343
$717$	501226.i	0.974979i
$718$	656529.	1.27352
$719$	− 759119.i	− 1.46843i	−0.678919	−	0.734213i	$-0.737551\pi$
$719$	− 759119.i	− 1.46843i	0.678919	−	0.734213i	$-0.262449\pi$
$720$	− 24457.4i	− 0.0471786i
$721$	0	0
$722$	122898.	0.235760
$723$	284231.	0.543744
$724$	352778.i	0.673014i
$725$	314429.	0.598200
$726$	154924.i	0.293931i
$727$	92384.1i	0.174795i	0.996174	+	0.0873974i	$0.0278550\pi$
$727$	92384.1i	0.174795i	−0.996174	+	0.0873974i	$0.972145\pi$
$728$	0	0
$729$	−19683.0	−0.0370370
$730$	−162930.	−0.305742
$731$	− 691337.i	− 1.29376i
$732$	−94454.1	−0.176278
$733$	− 3352.68i	− 0.00623999i	−0.999995	−	0.00312000i	$-0.999007\pi$
$733$	− 3352.68i	− 0.00623999i	0.999995	−	0.00312000i	$-0.000993127\pi$
$734$	− 409324.i	− 0.759757i
$735$	0	0
$736$	128433.	0.237094
$737$	−555431.	−1.02257
$738$	215173.i	0.395072i
$739$	−27185.6	−0.0497795	−0.0248897	−	0.999690i	$-0.507923\pi$
$739$	−27185.6	−0.0497795	−0.0248897	+	0.999690i	$0.507923\pi$
$740$	− 94406.0i	− 0.172400i
$741$	− 350589.i	− 0.638502i
$742$	0	0
$743$	773801.	1.40169	0.700845	−	0.713314i	$-0.252807\pi$
$743$	773801.	1.40169	0.700845	+	0.713314i	$0.252807\pi$
$744$	−78389.1	−0.141615
$745$	− 82471.7i	− 0.148591i
$746$	−421105.	−0.756681
$747$	222097.i	0.398017i
$748$	− 115486.i	− 0.206408i
$749$	0	0
$750$	218348.	0.388174
$751$	197844.	0.350787	0.175394	−	0.984498i	$-0.443880\pi$
$751$	197844.	0.350787	0.175394	+	0.984498i	$0.443880\pi$
$752$	39278.5i	0.0694574i
$753$	−561897.	−0.990984
$754$	− 479393.i	− 0.843236i
$755$	356483.i	0.625381i
$756$	0	0
$757$	−770706.	−1.34492	−0.672461	−	0.740132i	$-0.734763\pi$
$757$	−770706.	−1.34492	−0.672461	+	0.740132i	$0.734763\pi$
$758$	397868.	0.692469
$759$	− 236055.i	− 0.409760i
$760$	−94392.2	−0.163421
$761$	152140.i	0.262708i	0.991336	+	0.131354i	$0.0419325\pi$
$761$	152140.i	0.262708i	−0.991336	+	0.131354i	$0.958068\pi$
$762$	34979.7i	0.0602429i
$763$	0	0
$764$	−516473.	−0.884832
$765$	−86156.9	−0.147220
$766$	− 82936.1i	− 0.141347i
$767$	−799521.	−1.35906
$768$	− 21283.4i	− 0.0360844i
$769$	− 961897.i	− 1.62658i	−0.581857	−	0.813291i	$-0.697674\pi$
$769$	− 961897.i	− 1.62658i	0.581857	−	0.813291i	$-0.302326\pi$
$770$	0	0
$771$	−186470.	−0.313689
$772$	293397.	0.492290
$773$	− 151069.i	− 0.252823i	−0.991978	−	0.126411i	$-0.959654\pi$
$773$	− 151069.i	− 0.252823i	0.991978	−	0.126411i	$-0.0403459\pi$
$774$	−234174.	−0.390892
$775$	− 283137.i	− 0.471404i
$776$	35267.3i	0.0585664i
$777$	0	0
$778$	374540.	0.618783
$779$	830452.	1.36848
$780$	− 134685.i	− 0.221376i
$781$	−22640.3	−0.0371175
$782$	− 452435.i	− 0.739849i
$783$	103875.i	0.169429i
$784$	0	0
$785$	−338215.	−0.548849
$786$	63781.7	0.103241
$787$	− 198891.i	− 0.321118i	−0.987026	−	0.160559i	$-0.948670\pi$
$787$	− 198891.i	− 0.321118i	0.987026	−	0.160559i	$-0.0513297\pi$
$788$	−585176.	−0.942398
$789$	339993.i	0.546154i
$790$	259123.i	0.415194i
$791$	0	0
$792$	−39118.2	−0.0623632
$793$	−520153.	−0.827150
$794$	− 96810.3i	− 0.153561i
$795$	−84767.0	−0.134120
$796$	− 11208.2i	− 0.0176893i
$797$	990756.i	1.55973i	0.625947	+	0.779866i	$0.284713\pi$
$797$	990756.i	1.55973i	−0.625947	+	0.779866i	$0.715287\pi$
$798$	0	0
$799$	138368.	0.216741
$800$	76874.6	0.120117
$801$	− 419533.i	− 0.653885i
$802$	−506518.	−0.787492
$803$	260597.i	0.404145i
$804$	360597.i	0.557840i
$805$	0	0
$806$	−431684.	−0.664501
$807$	−359632.	−0.552219
$808$	356050.i	0.545366i
$809$	−92288.6	−0.141010	−0.0705052	−	0.997511i	$-0.522461\pi$
$809$	−92288.6	−0.141010	−0.0705052	+	0.997511i	$0.522461\pi$
$810$	29183.6i	0.0444804i
$811$	617125.i	0.938277i	0.883125	+	0.469139i	$0.155436\pi$
$811$	617125.i	0.938277i	−0.883125	+	0.469139i	$0.844564\pi$
$812$	0	0
$813$	−34037.6	−0.0514966
$814$	−150997.	−0.227887
$815$	− 602743.i	− 0.907439i
$816$	−74975.9	−0.112601
$817$	903784.i	1.35401i
$818$	140762.i	0.210367i
$819$	0	0
$820$	319033.	0.474469
$821$	307066.	0.455559	0.227780	−	0.973713i	$-0.426853\pi$
$821$	307066.	0.455559	0.227780	+	0.973713i	$0.426853\pi$
$822$	452066.i	0.669049i
$823$	846858.	1.25029	0.625146	−	0.780508i	$-0.285040\pi$
$823$	846858.	1.25029	0.625146	+	0.780508i	$0.285040\pi$
$824$	− 763.194i	− 0.00112404i
$825$	− 141293.i	− 0.207592i
$826$	0	0
$827$	294059.	0.429956	0.214978	−	0.976619i	$-0.431032\pi$
$827$	294059.	0.429956	0.214978	+	0.976619i	$0.431032\pi$
$828$	−153252.	−0.223535
$829$	1.03438e6i	1.50513i	0.658520	+	0.752563i	$0.271183\pi$
$829$	1.03438e6i	1.50513i	−0.658520	+	0.752563i	$0.728817\pi$
$830$	329299.	0.478007
$831$	− 411032.i	− 0.595215i
$832$	− 117207.i	− 0.169319i
$833$	0	0
$834$	399560.	0.574447
$835$	373036.	0.535030
$836$	150975.i	0.216019i
$837$	93537.2	0.133516
$838$	− 124313.i	− 0.177022i
$839$	− 307258.i	− 0.436495i	−0.975893	−	0.218248i	$-0.929966\pi$
$839$	− 307258.i	− 0.436495i	0.975893	−	0.218248i	$-0.0700340\pi$
$840$	0	0
$841$	−159093.	−0.224937
$842$	−617324.	−0.870741
$843$	− 178556.i	− 0.251258i
$844$	465853.	0.653980
$845$	− 337463.i	− 0.472621i
$846$	− 46868.7i	− 0.0654851i
$847$	0	0
$848$	−73766.4	−0.102581
$849$	477590.	0.662583
$850$	− 270809.i	− 0.374822i
$851$	−591555.	−0.816838
$852$	14698.5i	0.0202486i
$853$	− 70737.4i	− 0.0972190i	−0.998818	−	0.0486095i	$-0.984521\pi$
$853$	− 70737.4i	− 0.0972190i	0.998818	−	0.0486095i	$-0.0154790\pi$
$854$	0	0
$855$	112633.	0.154075
$856$	−123239.	−0.168191
$857$	329863.i	0.449130i	0.974459	+	0.224565i	$0.0720961\pi$
$857$	329863.i	0.449130i	−0.974459	+	0.224565i	$0.927904\pi$
$858$	−215421.	−0.292627
$859$	69962.5i	0.0948154i	0.998876	+	0.0474077i	$0.0150960\pi$
$859$	69962.5i	0.0948154i	−0.998876	+	0.0474077i	$0.984904\pi$
$860$	347205.i	0.469450i
$861$	0	0
$862$	−217052.	−0.292113
$863$	−772223.	−1.03686	−0.518431	−	0.855119i	$-0.673484\pi$
$863$	−772223.	−1.03686	−0.518431	+	0.855119i	$0.673484\pi$
$864$	25396.3i	0.0340207i
$865$	396572.	0.530017
$866$	612957.i	0.817324i
$867$	− 169868.i	− 0.225981i
$868$	0	0
$869$	414451.	0.548825
$870$	154013.	0.203479
$871$	1.98579e6i	2.61756i
$872$	377827.	0.496890
$873$	− 42082.4i	− 0.0552169i
$874$	591468.i	0.774299i
$875$	0	0
$876$	169185.	0.220472
$877$	242520.	0.315317	0.157659	−	0.987494i	$-0.449605\pi$
$877$	242520.	0.315317	0.157659	+	0.987494i	$0.449605\pi$
$878$	− 67209.3i	− 0.0871847i
$879$	120645.	0.156146
$880$	57999.7i	0.0748963i
$881$	− 646528.i	− 0.832982i	−0.909140	−	0.416491i	$-0.863260\pi$
$881$	− 646528.i	− 0.832982i	0.909140	−	0.416491i	$-0.136740\pi$
$882$	0	0
$883$	−461877.	−0.592387	−0.296193	−	0.955128i	$-0.595717\pi$
$883$	−461877.	−0.592387	−0.296193	+	0.955128i	$0.595717\pi$
$884$	−412888.	−0.528357
$885$	− 256860.i	− 0.327951i
$886$	494592.	0.630057
$887$	215226.i	0.273557i	0.990602	+	0.136778i	$0.0436748\pi$
$887$	215226.i	0.273557i	−0.990602	+	0.136778i	$0.956325\pi$
$888$	98030.3i	0.124318i
$889$	0	0
$890$	−622034.	−0.785297
$891$	46677.5	0.0587965
$892$	488407.i	0.613836i
$893$	−180888.	−0.226833
$894$	85637.9i	0.107150i
$895$	359479.i	0.448774i
$896$	0	0
$897$	−843948.	−1.04889
$898$	−551980.	−0.684496
$899$	− 493632.i	− 0.610779i
$900$	−91730.1	−0.113247
$901$	259860.i	0.320103i
$902$	− 510275.i	− 0.627179i
$903$	0	0
$904$	213957.	0.261812
$905$	−624134.	−0.762045
$906$	− 370168.i	− 0.450965i
$907$	1.09827e6	1.33504	0.667519	−	0.744592i	$-0.267356\pi$
$907$	1.09827e6	1.33504	0.667519	+	0.744592i	$0.267356\pi$
$908$	199949.i	0.242520i
$909$	− 424854.i	− 0.514176i
$910$	0	0
$911$	−1.32312e6	−1.59427	−0.797133	−	0.603803i	$-0.793651\pi$
$911$	−1.32312e6	−1.59427	−0.797133	+	0.603803i	$0.793651\pi$
$912$	98015.9	0.117844
$913$	− 526695.i	− 0.631855i
$914$	165384.	0.197971
$915$	− 167108.i	− 0.199597i
$916$	151431.i	0.180478i
$917$	0	0
$918$	89464.5	0.106161
$919$	516528.	0.611594	0.305797	−	0.952097i	$-0.401077\pi$
$919$	516528.	0.611594	0.305797	+	0.952097i	$0.401077\pi$
$920$	227223.i	0.268459i
$921$	−344951.	−0.406666
$922$	869014.i	1.02227i
$923$	80943.8i	0.0950124i
$924$	0	0
$925$	−354080.	−0.413826
$926$	−50267.5	−0.0586226
$927$	910.676i	0.00105975i
$928$	134026.	0.155630
$929$	− 1.23939e6i	− 1.43608i	−0.696003	−	0.718039i	$-0.745040\pi$
$929$	− 1.23939e6i	− 1.43608i	0.696003	−	0.718039i	$-0.254960\pi$
$930$	− 138686.i	− 0.160349i
$931$	0	0
$932$	53477.9	0.0615662
$933$	−497274.	−0.571259
$934$	− 183749.i	− 0.210635i
$935$	204318.	0.233713
$936$	139856.i	0.159635i
$937$	1.15260e6i	1.31281i	0.754411	+	0.656403i	$0.227923\pi$
$937$	1.15260e6i	1.31281i	−0.754411	+	0.656403i	$0.772077\pi$
$938$	0	0
$939$	−248917.	−0.282308
$940$	−69491.3	−0.0786457
$941$	107507.i	0.121411i	0.998156	+	0.0607057i	$0.0193351\pi$
$941$	107507.i	0.121411i	−0.998156	+	0.0607057i	$0.980665\pi$
$942$	351199.	0.395777
$943$	− 1.99909e6i	− 2.24806i
$944$	− 223526.i	− 0.250832i
$945$	0	0
$946$	555334.	0.620543
$947$	−412614.	−0.460092	−0.230046	−	0.973180i	$-0.573888\pi$
$947$	−412614.	−0.460092	−0.230046	+	0.973180i	$0.573888\pi$
$948$	− 269070.i	− 0.299398i
$949$	931689.	1.03452
$950$	354028.i	0.392275i
$951$	177335.i	0.196080i
$952$	0	0
$953$	1.43052e6	1.57510	0.787550	−	0.616251i	$-0.211349\pi$
$953$	1.43052e6	1.57510	0.787550	+	0.616251i	$0.211349\pi$
$954$	88021.3	0.0967143
$955$	− 913742.i	− 1.00188i
$956$	−771688.	−0.844356
$957$	− 246335.i	− 0.268969i
$958$	596619.i	0.650079i
$959$	0	0
$960$	37654.6	0.0408579
$961$	479015.	0.518683
$962$	539847.i	0.583338i
$963$	147055.	0.158572
$964$	437602.i	0.470896i
$965$	519077.i	0.557413i
$966$	0	0
$967$	−344533.	−0.368449	−0.184225	−	0.982884i	$-0.558977\pi$
$967$	−344533.	−0.368449	−0.184225	+	0.982884i	$0.558977\pi$
$968$	−238521.	−0.254551
$969$	− 345284.i	− 0.367730i
$970$	−62394.8	−0.0663139
$971$	1.45316e6i	1.54126i	0.637283	+	0.770630i	$0.280058\pi$
$971$	1.45316e6i	1.54126i	−0.637283	+	0.770630i	$0.719942\pi$
$972$	− 30304.0i	− 0.0320750i
$973$	0	0
$974$	−647393.	−0.682417
$975$	−505152.	−0.531389
$976$	− 145422.i	− 0.152661i
$977$	1.54571e6	1.61934	0.809669	−	0.586887i	$-0.199647\pi$
$977$	1.54571e6	1.61934	0.809669	+	0.586887i	$0.199647\pi$
$978$	625883.i	0.654358i
$979$	994907.i	1.03805i
$980$	0	0
$981$	−450840.	−0.468473
$982$	396970.	0.411656
$983$	134268.i	0.138952i	0.997584	+	0.0694761i	$0.0221328\pi$
$983$	134268.i	0.138952i	−0.997584	+	0.0694761i	$0.977867\pi$
$984$	−331281.	−0.342142
$985$	− 1.03529e6i	− 1.06706i
$986$	− 472139.i	− 0.485641i
$987$	0	0
$988$	539768.	0.552959
$989$	2.17561e6	2.22428
$990$	− 69207.7i	− 0.0706129i
$991$	−791191.	−0.805627	−0.402814	−	0.915282i	$-0.631968\pi$
$991$	−791191.	−0.805627	−0.402814	+	0.915282i	$0.631968\pi$
$992$	− 120688.i	− 0.122642i
$993$	− 692571.i	− 0.702369i
$994$	0	0
$995$	19829.5	0.0200293
$996$	−341941.	−0.344693
$997$	672757.i	0.676811i	0.941000	+	0.338406i	$0.109888\pi$
$997$	672757.i	0.676811i	−0.941000	+	0.338406i	$0.890112\pi$
$998$	−976732.	−0.980650
$999$	− 116974.i	− 0.117208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.c.a.97.3		4
3.2	odd	2		882.5.c.a.685.1		4
7.2	even	3		294.5.g.c.31.1		4
7.3	odd	6		294.5.g.c.19.1		4
7.4	even	3		42.5.g.a.19.1	✓	4
7.5	odd	6		42.5.g.a.31.1	yes	4
7.6	odd	2	inner	294.5.c.a.97.4		4
21.5	even	6		126.5.n.b.73.2		4
21.11	odd	6		126.5.n.b.19.2		4
21.20	even	2		882.5.c.a.685.2		4
28.11	odd	6		336.5.bh.d.145.2		4
28.19	even	6		336.5.bh.d.241.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.1	✓	4	7.4	even	3
42.5.g.a.31.1	yes	4	7.5	odd	6
126.5.n.b.19.2		4	21.11	odd	6
126.5.n.b.73.2		4	21.5	even	6
294.5.c.a.97.3		4	1.1	even	1	trivial
294.5.c.a.97.4		4	7.6	odd	2	inner
294.5.g.c.19.1		4	7.3	odd	6
294.5.g.c.31.1		4	7.2	even	3
336.5.bh.d.145.2		4	28.11	odd	6
336.5.bh.d.241.2		4	28.19	even	6
882.5.c.a.685.1		4	3.2	odd	2
882.5.c.a.685.2		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	294.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} -5.19615i q^{3} +8.00000 q^{4} +14.1536i q^{5} -14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +40.0324i q^{10} +64.0294 q^{11} -41.5692i q^{12} -228.919i q^{13} +73.5442 q^{15} +64.0000 q^{16} -225.455i q^{17} -76.3675 q^{18} +294.737i q^{19} +113.229i q^{20} +181.103 q^{22} +709.499 q^{23} -117.576i q^{24} +424.676 q^{25} -647.481i q^{26} +140.296i q^{27} +740.397 q^{29} +208.014 q^{30} -666.713i q^{31} +181.019 q^{32} -332.707i q^{33} -637.683i q^{34} -216.000 q^{36} -833.765 q^{37} +833.642i q^{38} -1189.50 q^{39} +320.259i q^{40} -2817.60i q^{41} +3066.41 q^{43} +512.235 q^{44} -382.147i q^{45} +2006.77 q^{46} +613.726i q^{47} -332.554i q^{48} +1201.17 q^{50} -1171.50 q^{51} -1831.35i q^{52} -1152.60 q^{53} +396.817i q^{54} +906.246i q^{55} +1531.50 q^{57} +2094.16 q^{58} -3492.59i q^{59} +588.353 q^{60} -2272.21i q^{61} -1885.75i q^{62} +512.000 q^{64} +3240.03 q^{65} -941.037i q^{66} -8674.62 q^{67} -1803.64i q^{68} -3686.66i q^{69} -353.591 q^{71} -610.940 q^{72} +4069.95i q^{73} -2358.24 q^{74} -2206.68i q^{75} +2357.90i q^{76} -3364.41 q^{78} +6472.83 q^{79} +905.829i q^{80} +729.000 q^{81} -7969.38i q^{82} -8225.83i q^{83} +3191.00 q^{85} +8673.11 q^{86} -3847.22i q^{87} +1448.82 q^{88} +15538.3i q^{89} -1080.87i q^{90} +5675.99 q^{92} -3464.34 q^{93} +1735.88i q^{94} -4171.58 q^{95} -940.604i q^{96} +1558.61i q^{97} -1728.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{4} - 108 q^{9} + 324 q^{11} + 396 q^{15} + 256 q^{16} - 192 q^{22} - 624 q^{23} + 952 q^{25} + 2724 q^{29} - 288 q^{30} - 864 q^{36} - 2792 q^{37} - 1296 q^{39} - 632 q^{43} + 2592 q^{44} + 9792 q^{46}+ \cdots - 8748 q^{99}+O(q^{100}) \) 4 * q + 32 * q^4 - 108 * q^9 + 324 * q^11 + 396 * q^15 + 256 * q^16 - 192 * q^22 - 624 * q^23 + 952 * q^25 + 2724 * q^29 - 288 * q^30 - 864 * q^36 - 2792 * q^37 - 1296 * q^39 - 632 * q^43 + 2592 * q^44 + 9792 * q^46 + 2112 * q^50 - 1224 * q^51 + 2076 * q^53 + 2664 * q^57 + 672 * q^58 + 3168 * q^60 + 2048 * q^64 + 1488 * q^65 - 29200 * q^67 - 9696 * q^71 - 1536 * q^74 - 9792 * q^78 - 7948 * q^79 + 2916 * q^81 + 1224 * q^85 + 36480 * q^86 - 1536 * q^88 - 4992 * q^92 - 22716 * q^93 - 6504 * q^95 - 8748 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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