LMFDB - Embedded newform 294.5.c.b.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,5,Mod(97,294)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.7
Root			$-1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	294.97
Dual form			294.5.c.b.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -41.5951i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -41.5951i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} -117.649i q^{10} -50.8054 q^{11} +41.5692i q^{12} +166.901i q^{13} +216.135 q^{15} +64.0000 q^{16} -538.223i q^{17} -76.3675 q^{18} -398.856i q^{19} -332.761i q^{20} -143.699 q^{22} -573.259 q^{23} +117.576i q^{24} -1105.16 q^{25} +472.068i q^{26} -140.296i q^{27} -831.611 q^{29} +611.321 q^{30} +1007.01i q^{31} +181.019 q^{32} -263.993i q^{33} -1522.32i q^{34} -216.000 q^{36} +918.266 q^{37} -1128.13i q^{38} -867.244 q^{39} -941.191i q^{40} -1588.51i q^{41} -377.140 q^{43} -406.443 q^{44} +1123.07i q^{45} -1621.42 q^{46} -3705.96i q^{47} +332.554i q^{48} -3125.85 q^{50} +2796.69 q^{51} +1335.21i q^{52} -3325.51 q^{53} -396.817i q^{54} +2113.26i q^{55} +2072.51 q^{57} -2352.15 q^{58} -6266.08i q^{59} +1729.08 q^{60} -3785.94i q^{61} +2848.26i q^{62} +512.000 q^{64} +6942.28 q^{65} -746.684i q^{66} +4124.52 q^{67} -4305.78i q^{68} -2978.74i q^{69} +1664.42 q^{71} -610.940 q^{72} +3977.44i q^{73} +2597.25 q^{74} -5742.56i q^{75} -3190.84i q^{76} -2452.94 q^{78} +11870.3 q^{79} -2662.09i q^{80} +729.000 q^{81} -4492.99i q^{82} +5629.74i q^{83} -22387.5 q^{85} -1066.71 q^{86} -4321.18i q^{87} -1149.59 q^{88} +12517.7i q^{89} +3176.52i q^{90} -4586.07 q^{92} -5232.58 q^{93} -10482.0i q^{94} -16590.5 q^{95} +940.604i q^{96} -4818.49i q^{97} +1371.75 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{4} - 216 q^{9}+O(q^{10}) $ 8 * q + 64 * q^4 - 216 * q^9	$ 8 q + 64 q^{4} - 216 q^{9} + 512 q^{16} - 1312 q^{22} - 272 q^{23} - 2808 q^{25} + 400 q^{29} + 3168 q^{30} - 1728 q^{36} - 3328 q^{37} + 656 q^{43} - 2400 q^{46} + 800 q^{50} + 7200 q^{51} + 9264 q^{53} + 1152 q^{57} - 11488 q^{58} + 4096 q^{64} - 15696 q^{65} + 26816 q^{67} + 28192 q^{71} - 4512 q^{74} + 9216 q^{78} + 19728 q^{79} + 5832 q^{81} - 49632 q^{85} + 5888 q^{86} - 10496 q^{88} - 2176 q^{92} + 15264 q^{93} - 92752 q^{95}+O(q^{100}) $ 8 * q + 64 * q^4 - 216 * q^9 + 512 * q^16 - 1312 * q^22 - 272 * q^23 - 2808 * q^25 + 400 * q^29 + 3168 * q^30 - 1728 * q^36 - 3328 * q^37 + 656 * q^43 - 2400 * q^46 + 800 * q^50 + 7200 * q^51 + 9264 * q^53 + 1152 * q^57 - 11488 * q^58 + 4096 * q^64 - 15696 * q^65 + 26816 * q^67 + 28192 * q^71 - 4512 * q^74 + 9216 * q^78 + 19728 * q^79 + 5832 * q^81 - 49632 * q^85 + 5888 * q^86 - 10496 * q^88 - 2176 * q^92 + 15264 * q^93 - 92752 * q^95

Display 100 coefficients 10 coefficients

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
$5$	− 41.5951i	− 1.66381i	−0.554921	−	0.831903i	$-0.687252\pi$
$5$	− 41.5951i	− 1.66381i	0.554921	−	0.831903i	$-0.312748\pi$
$6$	14.6969i	0.408248i
$7$	0	0
$7$	0	0
$8$	22.6274	0.353553
$9$	−27.0000	−0.333333
$10$	− 117.649i	− 1.17649i
$11$	−50.8054	−0.419879	−0.209940	−	0.977714i	$-0.567327\pi$
$11$	−50.8054	−0.419879	−0.209940	+	0.977714i	$0.567327\pi$
$12$	41.5692i	0.288675i
$13$	166.901i	0.987582i	0.869581	+	0.493791i	$0.164389\pi$
$13$	166.901i	0.987582i	−0.869581	+	0.493791i	$0.835611\pi$
$14$	0	0
$15$	216.135	0.960599
$16$	64.0000	0.250000
$17$	− 538.223i	− 1.86236i	−0.364556	−	0.931181i	$-0.618779\pi$
$17$	− 538.223i	− 1.86236i	0.364556	−	0.931181i	$-0.381221\pi$
$18$	−76.3675	−0.235702
$19$	− 398.856i	− 1.10486i	−0.833558	−	0.552431i	$-0.813700\pi$
$19$	− 398.856i	− 1.10486i	0.833558	−	0.552431i	$-0.186300\pi$
$20$	− 332.761i	− 0.831903i
$21$	0	0
$22$	−143.699	−0.296899
$23$	−573.259	−1.08367	−0.541833	−	0.840486i	$-0.682269\pi$
$23$	−573.259	−1.08367	−0.541833	+	0.840486i	$0.682269\pi$
$24$	117.576i	0.204124i
$25$	−1105.16	−1.76825
$26$	472.068i	0.698326i
$27$	− 140.296i	− 0.192450i
$28$	0	0
$29$	−831.611	−0.988836	−0.494418	−	0.869224i	$-0.664619\pi$
$29$	−831.611	−0.988836	−0.494418	+	0.869224i	$0.664619\pi$
$30$	611.321	0.679246
$31$	1007.01i	1.04788i	0.851756	+	0.523939i	$0.175538\pi$
$31$	1007.01i	1.04788i	−0.851756	+	0.523939i	$0.824462\pi$
$32$	181.019	0.176777
$33$	− 263.993i	− 0.242417i
$34$	− 1522.32i	− 1.31689i
$35$	0	0
$36$	−216.000	−0.166667
$37$	918.266	0.670757	0.335379	−	0.942083i	$-0.391136\pi$
$37$	918.266	0.670757	0.335379	+	0.942083i	$0.391136\pi$
$38$	− 1128.13i	− 0.781256i
$39$	−867.244	−0.570180
$40$	− 941.191i	− 0.588244i
$41$	− 1588.51i	− 0.944979i	−0.881336	−	0.472490i	$-0.843355\pi$
$41$	− 1588.51i	− 0.944979i	0.881336	−	0.472490i	$-0.156645\pi$
$42$	0	0
$43$	−377.140	−0.203970	−0.101985	−	0.994786i	$-0.532519\pi$
$43$	−377.140	−0.203970	−0.101985	+	0.994786i	$0.532519\pi$
$44$	−406.443	−0.209940
$45$	1123.07i	0.554602i
$46$	−1621.42	−0.766267
$47$	− 3705.96i	− 1.67766i	−0.544392	−	0.838831i	$-0.683240\pi$
$47$	− 3705.96i	− 1.67766i	0.544392	−	0.838831i	$-0.316760\pi$
$48$	332.554i	0.144338i
$49$	0	0
$50$	−3125.85	−1.25034
$51$	2796.69	1.07524
$52$	1335.21i	0.493791i
$53$	−3325.51	−1.18388	−0.591938	−	0.805984i	$-0.701637\pi$
$53$	−3325.51	−1.18388	−0.591938	+	0.805984i	$0.701637\pi$
$54$	− 396.817i	− 0.136083i
$55$	2113.26i	0.698597i
$56$	0	0
$57$	2072.51	0.637893
$58$	−2352.15	−0.699213
$59$	− 6266.08i	− 1.80008i	−0.435807	−	0.900040i	$-0.643537\pi$
$59$	− 6266.08i	− 1.80008i	0.435807	−	0.900040i	$-0.356463\pi$
$60$	1729.08	0.480299
$61$	− 3785.94i	− 1.01745i	−0.860928	−	0.508726i	$-0.830116\pi$
$61$	− 3785.94i	− 1.01745i	0.860928	−	0.508726i	$-0.169884\pi$
$62$	2848.26i	0.740962i
$63$	0	0
$64$	512.000	0.125000
$65$	6942.28	1.64314
$66$	− 746.684i	− 0.171415i
$67$	4124.52	0.918806	0.459403	−	0.888228i	$-0.348063\pi$
$67$	4124.52	0.918806	0.459403	+	0.888228i	$0.348063\pi$
$68$	− 4305.78i	− 0.931181i
$69$	− 2978.74i	− 0.625654i
$70$	0	0
$71$	1664.42	0.330177	0.165088	−	0.986279i	$-0.447209\pi$
$71$	1664.42	0.330177	0.165088	+	0.986279i	$0.447209\pi$
$72$	−610.940	−0.117851
$73$	3977.44i	0.746377i	0.927756	+	0.373188i	$0.121736\pi$
$73$	3977.44i	0.746377i	−0.927756	+	0.373188i	$0.878264\pi$
$74$	2597.25	0.474297
$75$	− 5742.56i	− 1.02090i
$76$	− 3190.84i	− 0.552431i
$77$	0	0
$78$	−2452.94	−0.403178
$79$	11870.3	1.90198	0.950990	−	0.309221i	$-0.100068\pi$
$79$	11870.3	1.90198	0.950990	+	0.309221i	$0.100068\pi$
$80$	− 2662.09i	− 0.415951i
$81$	729.000	0.111111
$82$	− 4492.99i	− 0.668201i
$83$	5629.74i	0.817206i	0.912712	+	0.408603i	$0.133984\pi$
$83$	5629.74i	0.817206i	−0.912712	+	0.408603i	$0.866016\pi$
$84$	0	0
$85$	−22387.5	−3.09861
$86$	−1066.71	−0.144228
$87$	− 4321.18i	− 0.570905i
$88$	−1149.59	−0.148450
$89$	12517.7i	1.58032i	0.612903	+	0.790158i	$0.290002\pi$
$89$	12517.7i	1.58032i	−0.612903	+	0.790158i	$0.709998\pi$
$90$	3176.52i	0.392163i
$91$	0	0
$92$	−4586.07	−0.541833
$93$	−5232.58	−0.604993
$94$	− 10482.0i	− 1.18629i
$95$	−16590.5	−1.83828
$96$	940.604i	0.102062i
$97$	− 4818.49i	− 0.512115i	−0.966662	−	0.256058i	$-0.917576\pi$
$97$	− 4818.49i	− 0.512115i	0.966662	−	0.256058i	$-0.0824237\pi$
$98$	0	0
$99$	1371.75	0.139960
$100$	−8841.25	−0.884125
$101$	15057.0i	1.47604i	0.674781	+	0.738018i	$0.264238\pi$
$101$	15057.0i	1.47604i	−0.674781	+	0.738018i	$0.735762\pi$
$102$	7910.23	0.760306
$103$	2728.68i	0.257204i	0.991696	+	0.128602i	$0.0410490\pi$
$103$	2728.68i	0.257204i	−0.991696	+	0.128602i	$0.958951\pi$
$104$	3776.54i	0.349163i
$105$	0	0
$106$	−9405.95	−0.837126
$107$	11425.7	0.997964	0.498982	−	0.866612i	$-0.333707\pi$
$107$	11425.7	0.997964	0.498982	+	0.866612i	$0.333707\pi$
$108$	− 1122.37i	− 0.0962250i
$109$	−4437.60	−0.373504	−0.186752	−	0.982407i	$-0.559796\pi$
$109$	−4437.60	−0.373504	−0.186752	+	0.982407i	$0.559796\pi$
$110$	5977.19i	0.493983i
$111$	4771.45i	0.387262i
$112$	0	0
$113$	4817.56	0.377286	0.188643	−	0.982046i	$-0.439591\pi$
$113$	4817.56	0.377286	0.188643	+	0.982046i	$0.439591\pi$
$114$	5861.95	0.451058
$115$	23844.8i	1.80301i
$116$	−6652.89	−0.494418
$117$	− 4506.33i	− 0.329194i
$118$	− 17723.1i	− 1.27285i
$119$	0	0
$120$	4890.57	0.339623
$121$	−12059.8	−0.823701
$122$	− 10708.3i	− 0.719448i
$123$	8254.14	0.545584
$124$	8056.09i	0.523939i
$125$	19972.2i	1.27822i
$126$	0	0
$127$	14684.0	0.910413	0.455206	−	0.890386i	$-0.349566\pi$
$127$	14684.0	0.910413	0.455206	+	0.890386i	$0.349566\pi$
$128$	1448.15	0.0883883
$129$	− 1959.68i	− 0.117762i
$130$	19635.7	1.16188
$131$	− 12445.1i	− 0.725194i	−0.931946	−	0.362597i	$-0.881890\pi$
$131$	− 12445.1i	− 0.725194i	0.931946	−	0.362597i	$-0.118110\pi$
$132$	− 2111.94i	− 0.121209i
$133$	0	0
$134$	11665.9	0.649694
$135$	−5835.64	−0.320200
$136$	− 12178.6i	− 0.658445i
$137$	−18361.3	−0.978276	−0.489138	−	0.872206i	$-0.662689\pi$
$137$	−18361.3	−0.978276	−0.489138	+	0.872206i	$0.662689\pi$
$138$	− 8425.15i	− 0.442405i
$139$	− 5698.83i	− 0.294955i	−0.989065	−	0.147477i	$-0.952885\pi$
$139$	− 5698.83i	− 0.294955i	0.989065	−	0.147477i	$-0.0471154\pi$
$140$	0	0
$141$	19256.7	0.968599
$142$	4707.70	0.233470
$143$	− 8479.48i	− 0.414665i
$144$	−1728.00	−0.0833333
$145$	34591.0i	1.64523i
$146$	11249.9i	0.527768i
$147$	0	0
$148$	7346.13	0.335379
$149$	−8444.98	−0.380387	−0.190194	−	0.981747i	$-0.560912\pi$
$149$	−8444.98	−0.380387	−0.190194	+	0.981747i	$0.560912\pi$
$150$	− 16242.4i	− 0.721885i
$151$	−3358.39	−0.147291	−0.0736456	−	0.997284i	$-0.523463\pi$
$151$	−3358.39	−0.147291	−0.0736456	+	0.997284i	$0.523463\pi$
$152$	− 9025.07i	− 0.390628i
$153$	14532.0i	0.620788i
$154$	0	0
$155$	41886.8	1.74347
$156$	−6937.96	−0.285090
$157$	34388.6i	1.39513i	0.716522	+	0.697565i	$0.245733\pi$
$157$	34388.6i	1.39513i	−0.716522	+	0.697565i	$0.754267\pi$
$158$	33574.2	1.34490
$159$	− 17279.8i	− 0.683511i
$160$	− 7529.53i	− 0.294122i
$161$	0	0
$162$	2061.92	0.0785674
$163$	−12829.8	−0.482887	−0.241443	−	0.970415i	$-0.577621\pi$
$163$	−12829.8	−0.482887	−0.241443	+	0.970415i	$0.577621\pi$
$164$	− 12708.1i	− 0.472490i
$165$	−10980.8	−0.403335
$166$	15923.3i	0.577852i
$167$	− 25297.3i	− 0.907073i	−0.891238	−	0.453536i	$-0.850162\pi$
$167$	− 25297.3i	− 0.907073i	0.891238	−	0.453536i	$-0.149838\pi$
$168$	0	0
$169$	704.964	0.0246827
$170$	−63321.3	−2.19105
$171$	10769.1i	0.368288i
$172$	−3017.12	−0.101985
$173$	34086.6i	1.13892i	0.822021	+	0.569458i	$0.192847\pi$
$173$	34086.6i	1.13892i	−0.822021	+	0.569458i	$0.807153\pi$
$174$	− 12222.1i	− 0.403691i
$175$	0	0
$176$	−3251.54	−0.104970
$177$	32559.5	1.03928
$178$	35405.4i	1.11745i
$179$	56453.3	1.76191	0.880954	−	0.473202i	$-0.156902\pi$
$179$	56453.3	1.76191	0.880954	+	0.473202i	$0.156902\pi$
$180$	8984.55i	0.277301i
$181$	− 59004.4i	− 1.80105i	−0.434799	−	0.900527i	$-0.643181\pi$
$181$	− 59004.4i	− 1.80105i	0.434799	−	0.900527i	$-0.356819\pi$
$182$	0	0
$183$	19672.3	0.587427
$184$	−12971.4	−0.383134
$185$	− 38195.4i	− 1.11601i
$186$	−14800.0	−0.427795
$187$	27344.6i	0.781967i
$188$	− 29647.6i	− 0.838831i
$189$	0	0
$190$	−46924.9	−1.29986
$191$	5105.75	0.139956	0.0699782	−	0.997549i	$-0.477707\pi$
$191$	5105.75	0.139956	0.0699782	+	0.997549i	$0.477707\pi$
$192$	2660.43i	0.0721688i
$193$	−9513.64	−0.255407	−0.127703	−	0.991812i	$-0.540761\pi$
$193$	−9513.64	−0.255407	−0.127703	+	0.991812i	$0.540761\pi$
$194$	− 13628.8i	− 0.362120i
$195$	36073.2i	0.948670i
$196$	0	0
$197$	37171.3	0.957800	0.478900	−	0.877869i	$-0.341036\pi$
$197$	37171.3	0.957800	0.478900	+	0.877869i	$0.341036\pi$
$198$	3879.88	0.0989665
$199$	65207.0i	1.64660i	0.567607	+	0.823300i	$0.307869\pi$
$199$	65207.0i	1.64660i	−0.567607	+	0.823300i	$0.692131\pi$
$200$	−25006.8	−0.625171
$201$	21431.6i	0.530473i
$202$	42587.8i	1.04372i
$203$	0	0
$204$	22373.5	0.537618
$205$	−66074.3	−1.57226
$206$	7717.87i	0.181871i
$207$	15478.0	0.361222
$208$	10681.7i	0.246895i
$209$	20264.0i	0.463909i
$210$	0	0
$211$	−45787.8	−1.02845	−0.514227	−	0.857654i	$-0.671921\pi$
$211$	−45787.8	−1.02845	−0.514227	+	0.857654i	$0.671921\pi$
$212$	−26604.0	−0.591938
$213$	8648.59i	0.190628i
$214$	32316.7	0.705667
$215$	15687.2i	0.339366i
$216$	− 3174.54i	− 0.0680414i
$217$	0	0
$218$	−12551.4	−0.264107
$219$	−20667.4	−0.430921
$220$	16906.1i	0.349299i
$221$	89830.1	1.83924
$222$	13495.7i	0.273835i
$223$	− 22007.9i	− 0.442557i	−0.975211	−	0.221278i	$-0.928977\pi$
$223$	− 22007.9i	− 0.442557i	0.975211	−	0.221278i	$-0.0710229\pi$
$224$	0	0
$225$	29839.2	0.589417
$226$	13626.1	0.266781
$227$	− 30415.8i	− 0.590266i	−0.955456	−	0.295133i	$-0.904636\pi$
$227$	− 30415.8i	− 0.590266i	0.955456	−	0.295133i	$-0.0953640\pi$
$228$	16580.1	0.318946
$229$	29832.4i	0.568875i	0.958695	+	0.284438i	$0.0918069\pi$
$229$	29832.4i	0.568875i	−0.958695	+	0.284438i	$0.908193\pi$
$230$	67443.2i	1.27492i
$231$	0	0
$232$	−18817.2	−0.349606
$233$	72528.6	1.33597	0.667986	−	0.744173i	$-0.267156\pi$
$233$	72528.6	1.33597	0.667986	+	0.744173i	$0.267156\pi$
$234$	− 12745.8i	− 0.232775i
$235$	−154150.	−2.79130
$236$	− 50128.6i	− 0.900040i
$237$	61679.7i	1.09811i
$238$	0	0
$239$	−27512.1	−0.481646	−0.240823	−	0.970569i	$-0.577417\pi$
$239$	−27512.1	−0.481646	−0.240823	+	0.970569i	$0.577417\pi$
$240$	13832.6	0.240150
$241$	− 43396.2i	− 0.747167i	−0.927597	−	0.373583i	$-0.878129\pi$
$241$	− 43396.2i	− 0.747167i	0.927597	−	0.373583i	$-0.121871\pi$
$242$	−34110.3	−0.582445
$243$	3788.00i	0.0641500i
$244$	− 30287.5i	− 0.508726i
$245$	0	0
$246$	23346.2	0.385786
$247$	66569.5	1.09114
$248$	22786.1i	0.370481i
$249$	−29253.0	−0.471814
$250$	56489.8i	0.903837i
$251$	26874.3i	0.426569i	0.976990	+	0.213285i	$0.0684162\pi$
$251$	26874.3i	0.426569i	−0.976990	+	0.213285i	$0.931584\pi$
$252$	0	0
$253$	29124.6	0.455008
$254$	41532.7	0.643759
$255$	− 116329.i	− 1.78898i
$256$	4096.00	0.0625000
$257$	− 29457.4i	− 0.445993i	−0.974819	−	0.222997i	$-0.928416\pi$
$257$	− 29457.4i	− 0.445993i	0.974819	−	0.222997i	$-0.0715839\pi$
$258$	− 5542.80i	− 0.0832703i
$259$	0	0
$260$	55538.3	0.821572
$261$	22453.5	0.329612
$262$	− 35199.9i	− 0.512790i
$263$	37760.5	0.545917	0.272958	−	0.962026i	$-0.411998\pi$
$263$	37760.5	0.545917	0.272958	+	0.962026i	$0.411998\pi$
$264$	− 5973.47i	− 0.0857075i
$265$	138325.i	1.96974i
$266$	0	0
$267$	−65043.8	−0.912396
$268$	32996.2	0.459403
$269$	11042.4i	0.152602i	0.997085	+	0.0763009i	$0.0243110\pi$
$269$	11042.4i	0.152602i	−0.997085	+	0.0763009i	$0.975689\pi$
$270$	−16505.7	−0.226415
$271$	− 102273.i	− 1.39258i	−0.717759	−	0.696292i	$-0.754832\pi$
$271$	− 102273.i	− 1.39258i	0.717759	−	0.696292i	$-0.245168\pi$
$272$	− 34446.3i	− 0.465591i
$273$	0	0
$274$	−51933.5	−0.691745
$275$	56147.9	0.742451
$276$	− 23829.9i	− 0.312827i
$277$	134841.	1.75736	0.878682	−	0.477407i	$-0.158423\pi$
$277$	134841.	1.75736	0.878682	+	0.477407i	$0.158423\pi$
$278$	− 16118.7i	− 0.208565i
$279$	− 27189.3i	− 0.349293i
$280$	0	0
$281$	82794.0	1.04854	0.524272	−	0.851551i	$-0.324338\pi$
$281$	82794.0	1.04854	0.524272	+	0.851551i	$0.324338\pi$
$282$	54466.2	0.684903
$283$	95866.4i	1.19700i	0.801124	+	0.598499i	$0.204236\pi$
$283$	95866.4i	1.19700i	−0.801124	+	0.598499i	$0.795764\pi$
$284$	13315.4	0.165088
$285$	− 86206.5i	− 1.06133i
$286$	− 23983.6i	− 0.293212i
$287$	0	0
$288$	−4887.52	−0.0589256
$289$	−206163.	−2.46840
$290$	97838.1i	1.16335i
$291$	25037.6	0.295670
$292$	31819.5i	0.373188i
$293$	− 84355.5i	− 0.982603i	−0.870989	−	0.491302i	$-0.836521\pi$
$293$	− 84355.5i	− 0.982603i	0.870989	−	0.491302i	$-0.163479\pi$
$294$	0	0
$295$	−260638.	−2.99498
$296$	20778.0	0.237148
$297$	7127.80i	0.0808058i
$298$	−23886.0	−0.268975
$299$	− 95677.7i	− 1.07021i
$300$	− 45940.5i	− 0.510450i
$301$	0	0
$302$	−9498.95	−0.104151
$303$	−78238.7	−0.852190
$304$	− 25526.8i	− 0.276216i
$305$	−157477.	−1.69284
$306$	41102.8i	0.438963i
$307$	− 150073.i	− 1.59230i	−0.605097	−	0.796152i	$-0.706866\pi$
$307$	− 150073.i	− 1.59230i	0.605097	−	0.796152i	$-0.293134\pi$
$308$	0	0
$309$	−14178.6	−0.148497
$310$	118474.	1.23282
$311$	34385.3i	0.355511i	0.984075	+	0.177755i	$0.0568835\pi$
$311$	34385.3i	0.355511i	−0.984075	+	0.177755i	$0.943116\pi$
$312$	−19623.5	−0.201589
$313$	15921.2i	0.162512i	0.996693	+	0.0812562i	$0.0258932\pi$
$313$	15921.2i	0.162512i	−0.996693	+	0.0812562i	$0.974107\pi$
$314$	97265.5i	0.986506i
$315$	0	0
$316$	94962.1	0.950990
$317$	87737.9	0.873109	0.436555	−	0.899678i	$-0.356199\pi$
$317$	87737.9	0.873109	0.436555	+	0.899678i	$0.356199\pi$
$318$	− 48874.7i	− 0.483315i
$319$	42250.3	0.415192
$320$	− 21296.7i	− 0.207976i
$321$	59369.6i	0.576175i
$322$	0	0
$323$	−214673.	−2.05766
$324$	5832.00	0.0555556
$325$	− 184452.i	− 1.74629i
$326$	−36288.2	−0.341453
$327$	− 23058.5i	− 0.215643i
$328$	− 35943.9i	− 0.334101i
$329$	0	0
$330$	−31058.4	−0.285201
$331$	6459.71	0.0589600	0.0294800	−	0.999565i	$-0.490615\pi$
$331$	6459.71	0.0589600	0.0294800	+	0.999565i	$0.490615\pi$
$332$	45037.9i	0.408603i
$333$	−24793.2	−0.223586
$334$	− 71551.7i	− 0.641397i
$335$	− 171560.i	− 1.52871i
$336$	0	0
$337$	−146729.	−1.29198	−0.645992	−	0.763344i	$-0.723556\pi$
$337$	−146729.	−1.29198	−0.645992	+	0.763344i	$0.723556\pi$
$338$	1993.94	0.0174533
$339$	25032.8i	0.217826i
$340$	−179100.	−1.54930
$341$	− 51161.6i	− 0.439982i
$342$	30459.6i	0.260419i
$343$	0	0
$344$	−8533.70	−0.0721142
$345$	−123901.	−1.04097
$346$	96411.5i	0.805335i
$347$	−4334.80	−0.0360007	−0.0180003	−	0.999838i	$-0.505730\pi$
$347$	−4334.80	−0.0360007	−0.0180003	+	0.999838i	$0.505730\pi$
$348$	− 34569.4i	− 0.285452i
$349$	− 90514.5i	− 0.743135i	−0.928406	−	0.371567i	$-0.878821\pi$
$349$	− 90514.5i	− 0.743135i	0.928406	−	0.371567i	$-0.121179\pi$
$350$	0	0
$351$	23415.6	0.190060
$352$	−9196.76	−0.0742249
$353$	− 44031.5i	− 0.353358i	−0.984269	−	0.176679i	$-0.943465\pi$
$353$	− 44031.5i	− 0.353358i	0.984269	−	0.176679i	$-0.0565354\pi$
$354$	92092.2	0.734880
$355$	− 69231.9i	− 0.549350i
$356$	100141.i	0.790158i
$357$	0	0
$358$	159674.	1.24586
$359$	113177.	0.878148	0.439074	−	0.898451i	$-0.355307\pi$
$359$	113177.	0.878148	0.439074	+	0.898451i	$0.355307\pi$
$360$	25412.1i	0.196081i
$361$	−28764.7	−0.220722
$362$	− 166890.i	− 1.27354i
$363$	− 62664.6i	− 0.475564i
$364$	0	0
$365$	165442.	1.24183
$366$	55641.8	0.415373
$367$	− 26013.8i	− 0.193140i	−0.995326	−	0.0965698i	$-0.969213\pi$
$367$	− 26013.8i	− 0.193140i	0.995326	−	0.0965698i	$-0.0307871\pi$
$368$	−36688.6	−0.270916
$369$	42889.8i	0.314993i
$370$	− 108033.i	− 0.789138i
$371$	0	0
$372$	−41860.7	−0.302496
$373$	99384.4	0.714333	0.357167	−	0.934041i	$-0.383743\pi$
$373$	99384.4	0.714333	0.357167	+	0.934041i	$0.383743\pi$
$374$	77342.3i	0.552934i
$375$	−103778.	−0.737980
$376$	− 83856.2i	− 0.593143i
$377$	− 138797.i	− 0.976556i
$378$	0	0
$379$	259493.	1.80654	0.903269	−	0.429074i	$-0.141160\pi$
$379$	259493.	1.80654	0.903269	+	0.429074i	$0.141160\pi$
$380$	−132724.	−0.919139
$381$	76300.5i	0.525627i
$382$	14441.2	0.0989642
$383$	− 18421.4i	− 0.125581i	−0.998027	−	0.0627906i	$-0.980000\pi$
$383$	− 18421.4i	− 0.125581i	0.998027	−	0.0627906i	$-0.0200000\pi$
$384$	7524.83i	0.0510310i
$385$	0	0
$386$	−26908.6	−0.180600
$387$	10182.8	0.0679899
$388$	− 38547.9i	− 0.256058i
$389$	255533.	1.68868	0.844340	−	0.535808i	$-0.179993\pi$
$389$	255533.	1.68868	0.844340	+	0.535808i	$0.179993\pi$
$390$	102030.i	0.670811i
$391$	308541.i	2.01818i
$392$	0	0
$393$	64666.4	0.418691
$394$	105136.	0.677267
$395$	− 493745.i	− 3.16453i
$396$	10974.0	0.0699799
$397$	− 119517.i	− 0.758315i	−0.925332	−	0.379158i	$-0.876214\pi$
$397$	− 119517.i	− 0.758315i	0.925332	−	0.379158i	$-0.123786\pi$
$398$	184433.i	1.16432i
$399$	0	0
$400$	−70730.0	−0.442062
$401$	−188404.	−1.17166	−0.585829	−	0.810434i	$-0.699231\pi$
$401$	−188404.	−1.17166	−0.585829	+	0.810434i	$0.699231\pi$
$402$	60617.8i	0.375101i
$403$	−168071.	−1.03487
$404$	120456.i	0.738018i
$405$	− 30322.9i	− 0.184867i
$406$	0	0
$407$	−46652.9	−0.281637
$408$	63281.8	0.380153
$409$	− 150328.i	− 0.898656i	−0.893367	−	0.449328i	$-0.851663\pi$
$409$	− 150328.i	− 0.898656i	0.893367	−	0.449328i	$-0.148337\pi$
$410$	−186886.	−1.11176
$411$	− 95407.9i	− 0.564808i
$412$	21829.4i	0.128602i
$413$	0	0
$414$	43778.4	0.255422
$415$	234170.	1.35967
$416$	30212.4i	0.174581i
$417$	29612.0	0.170292
$418$	57315.3i	0.328033i
$419$	− 34182.7i	− 0.194706i	−0.995250	−	0.0973529i	$-0.968962\pi$
$419$	− 34182.7i	− 0.194706i	0.995250	−	0.0973529i	$-0.0310376\pi$
$420$	0	0
$421$	−4727.28	−0.0266715	−0.0133357	−	0.999911i	$-0.504245\pi$
$421$	−4727.28	−0.0266715	−0.0133357	+	0.999911i	$0.504245\pi$
$422$	−129508.	−0.727227
$423$	100061.i	0.559221i
$424$	−75247.6	−0.418563
$425$	594820.i	3.29312i
$426$	24461.9i	0.134794i
$427$	0	0
$428$	91405.5	0.498982
$429$	44060.7	0.239407
$430$	44370.1i	0.239968i
$431$	−123779.	−0.666333	−0.333166	−	0.942868i	$-0.608117\pi$
$431$	−123779.	−0.666333	−0.333166	+	0.942868i	$0.608117\pi$
$432$	− 8978.95i	− 0.0481125i
$433$	47907.6i	0.255522i	0.991805	+	0.127761i	$0.0407791\pi$
$433$	47907.6i	0.255522i	−0.991805	+	0.127761i	$0.959221\pi$
$434$	0	0
$435$	−179740.	−0.949875
$436$	−35500.8	−0.186752
$437$	228647.i	1.19730i
$438$	−58456.2	−0.304707
$439$	67802.6i	0.351817i	0.984406	+	0.175909i	$0.0562863\pi$
$439$	67802.6i	0.351817i	−0.984406	+	0.175909i	$0.943714\pi$
$440$	47817.5i	0.246991i
$441$	0	0
$442$	254078.	1.30054
$443$	−185643.	−0.945955	−0.472978	−	0.881074i	$-0.656821\pi$
$443$	−185643.	−0.945955	−0.472978	+	0.881074i	$0.656821\pi$
$444$	38171.6i	0.193631i
$445$	520675.	2.62934
$446$	− 62247.8i	− 0.312935i
$447$	− 43881.4i	− 0.219617i
$448$	0	0
$449$	−241853.	−1.19966	−0.599832	−	0.800126i	$-0.704766\pi$
$449$	−241853.	−1.19966	−0.599832	+	0.800126i	$0.704766\pi$
$450$	84398.0	0.416780
$451$	80704.9i	0.396777i
$452$	38540.5	0.188643
$453$	− 17450.7i	− 0.0850386i
$454$	− 86029.0i	− 0.417381i
$455$	0	0
$456$	46895.6	0.225529
$457$	−150814.	−0.722119	−0.361059	−	0.932543i	$-0.617585\pi$
$457$	−150814.	−0.722119	−0.361059	+	0.932543i	$0.617585\pi$
$458$	84378.8i	0.402256i
$459$	−75510.6	−0.358412
$460$	190758.i	0.901504i
$461$	− 41729.4i	− 0.196354i	−0.995169	−	0.0981771i	$-0.968699\pi$
$461$	− 41729.4i	− 0.196354i	0.995169	−	0.0981771i	$-0.0313012\pi$
$462$	0	0
$463$	176509.	0.823388	0.411694	−	0.911322i	$-0.364937\pi$
$463$	176509.	0.823388	0.411694	+	0.911322i	$0.364937\pi$
$464$	−53223.1	−0.247209
$465$	217650.i	1.00659i
$466$	205142.	0.944676
$467$	− 38443.6i	− 0.176275i	−0.996108	−	0.0881374i	$-0.971909\pi$
$467$	− 38443.6i	− 0.176275i	0.996108	−	0.0881374i	$-0.0280915\pi$
$468$	− 36050.7i	− 0.164597i
$469$	0	0
$470$	−436001.	−1.97375
$471$	−178688.	−0.805479
$472$	− 141785.i	− 0.636425i
$473$	19160.7	0.0856426
$474$	174456.i	0.776480i
$475$	440798.i	1.95367i
$476$	0	0
$477$	89788.6	0.394625
$478$	−77816.0	−0.340575
$479$	− 308594.i	− 1.34498i	−0.740105	−	0.672492i	$-0.765224\pi$
$479$	− 308594.i	− 1.34498i	0.740105	−	0.672492i	$-0.234776\pi$
$480$	39124.6	0.169811
$481$	153260.i	0.662427i
$482$	− 122743.i	− 0.528327i
$483$	0	0
$484$	−96478.5	−0.411851
$485$	−200426.	−0.852060
$486$	10714.1i	0.0453609i
$487$	1010.73	0.00426162	0.00213081	−	0.999998i	$-0.499322\pi$
$487$	1010.73	0.00426162	0.00213081	+	0.999998i	$0.499322\pi$
$488$	− 85666.1i	− 0.359724i
$489$	− 66665.7i	− 0.278795i
$490$	0	0
$491$	−153528.	−0.636833	−0.318416	−	0.947951i	$-0.603151\pi$
$491$	−153528.	−0.636833	−0.318416	+	0.947951i	$0.603151\pi$
$492$	66033.1	0.272792
$493$	447592.i	1.84157i
$494$	188287.	0.771554
$495$	− 57057.9i	− 0.232866i
$496$	64448.7i	0.261970i
$497$	0	0
$498$	−82739.9	−0.333623
$499$	−248518.	−0.998060	−0.499030	−	0.866585i	$-0.666310\pi$
$499$	−248518.	−0.998060	−0.499030	+	0.866585i	$0.666310\pi$
$500$	159777.i	0.639109i
$501$	131449.	0.523699
$502$	76012.0i	0.301630i
$503$	− 5243.36i	− 0.0207240i	−0.999946	−	0.0103620i	$-0.996702\pi$
$503$	− 5243.36i	− 0.0207240i	0.999946	−	0.0103620i	$-0.00329839\pi$
$504$	0	0
$505$	626300.	2.45584
$506$	82376.9	0.321740
$507$	3663.10i	0.0142506i
$508$	117472.	0.455206
$509$	294325.i	1.13604i	0.823016	+	0.568018i	$0.192290\pi$
$509$	294325.i	1.13604i	−0.823016	+	0.568018i	$0.807710\pi$
$510$	− 329027.i	− 1.26500i
$511$	0	0
$512$	11585.2	0.0441942
$513$	−55957.9	−0.212631
$514$	− 83318.2i	− 0.315365i
$515$	113500.	0.427938
$516$	− 15677.4i	− 0.0588810i
$517$	188282.i	0.704415i
$518$	0	0
$519$	−177119.	−0.657553
$520$	157086.	0.580939
$521$	313225.i	1.15393i	0.816767	+	0.576967i	$0.195764\pi$
$521$	313225.i	1.15393i	−0.816767	+	0.576967i	$0.804236\pi$
$522$	63508.1	0.233071
$523$	− 499433.i	− 1.82589i	−0.408087	−	0.912943i	$-0.633804\pi$
$523$	− 499433.i	− 1.82589i	0.408087	−	0.912943i	$-0.366196\pi$
$524$	− 99560.4i	− 0.362597i
$525$	0	0
$526$	106803.	0.386022
$527$	541996.	1.95153
$528$	− 16895.5i	− 0.0606043i
$529$	48784.8	0.174330
$530$	391242.i	1.39282i
$531$	169184.i	0.600027i
$532$	0	0
$533$	265124.	0.933244
$534$	−183972.	−0.645161
$535$	− 475253.i	− 1.66042i
$536$	93327.2	0.324847
$537$	293340.i	1.01724i
$538$	31232.7i	0.107906i
$539$	0	0
$540$	−46685.1	−0.160100
$541$	−343522.	−1.17371	−0.586855	−	0.809692i	$-0.699634\pi$
$541$	−343522.	−1.17371	−0.586855	+	0.809692i	$0.699634\pi$
$542$	− 289271.i	− 0.984706i
$543$	306596.	1.03984
$544$	− 97428.7i	− 0.329222i
$545$	184583.i	0.621438i
$546$	0	0
$547$	184552.	0.616800	0.308400	−	0.951257i	$-0.400206\pi$
$547$	184552.	0.616800	0.308400	+	0.951257i	$0.400206\pi$
$548$	−146890.	−0.489138
$549$	102220.i	0.339151i
$550$	158810.	0.524992
$551$	331693.i	1.09253i
$552$	− 67401.2i	− 0.221202i
$553$	0	0
$554$	381387.	1.24264
$555$	198469.	0.644328
$556$	− 45590.6i	− 0.147477i
$557$	−88192.7	−0.284264	−0.142132	−	0.989848i	$-0.545396\pi$
$557$	−88192.7	−0.284264	−0.142132	+	0.989848i	$0.545396\pi$
$558$	− 76903.0i	− 0.246987i
$559$	− 62945.1i	− 0.201437i
$560$	0	0
$561$	−142087.	−0.451469
$562$	234177.	0.741432
$563$	439990.i	1.38812i	0.719919	+	0.694058i	$0.244179\pi$
$563$	439990.i	1.38812i	−0.719919	+	0.694058i	$0.755821\pi$
$564$	154054.	0.484299
$565$	− 200387.i	− 0.627730i
$566$	271151.i	0.846405i
$567$	0	0
$568$	37661.6	0.116735
$569$	159194.	0.491702	0.245851	−	0.969308i	$-0.420933\pi$
$569$	159194.	0.491702	0.245851	+	0.969308i	$0.420933\pi$
$570$	− 243829.i	− 0.750474i
$571$	−51154.0	−0.156894	−0.0784472	−	0.996918i	$-0.524996\pi$
$571$	−51154.0	−0.156894	−0.0784472	+	0.996918i	$0.524996\pi$
$572$	− 67835.9i	− 0.207332i
$573$	26530.3i	0.0808039i
$574$	0	0
$575$	633541.	1.91619
$576$	−13824.0	−0.0416667
$577$	− 355696.i	− 1.06838i	−0.845363	−	0.534192i	$-0.820616\pi$
$577$	− 355696.i	− 1.06838i	0.845363	−	0.534192i	$-0.179384\pi$
$578$	−583117.	−1.74542
$579$	− 49434.3i	− 0.147459i
$580$	276728.i	0.822616i
$581$	0	0
$582$	70817.1	0.209070
$583$	168954.	0.497084
$584$	89999.3i	0.263884i
$585$	−187442.	−0.547715
$586$	− 238593.i	− 0.694805i
$587$	34149.9i	0.0991091i	0.998771	+	0.0495546i	$0.0157802\pi$
$587$	34149.9i	0.0991091i	−0.998771	+	0.0495546i	$0.984220\pi$
$588$	0	0
$589$	401652.	1.15776
$590$	−737197.	−2.11777
$591$	193148.i	0.552986i
$592$	58769.0	0.167689
$593$	352700.i	1.00299i	0.865161	+	0.501495i	$0.167216\pi$
$593$	352700.i	1.00299i	−0.865161	+	0.501495i	$0.832784\pi$
$594$	20160.5i	0.0571383i
$595$	0	0
$596$	−67559.9	−0.190194
$597$	−338825.	−0.950665
$598$	− 270617.i	− 0.756751i
$599$	−473487.	−1.31964	−0.659818	−	0.751425i	$-0.729367\pi$
$599$	−473487.	−1.31964	−0.659818	+	0.751425i	$0.729367\pi$
$600$	− 129939.i	− 0.360942i
$601$	− 226280.i	− 0.626466i	−0.949676	−	0.313233i	$-0.898588\pi$
$601$	− 226280.i	− 0.626466i	0.949676	−	0.313233i	$-0.101412\pi$
$602$	0	0
$603$	−111362.	−0.306269
$604$	−26867.1	−0.0736456
$605$	501630.i	1.37048i
$606$	−221292.	−0.602589
$607$	− 313074.i	− 0.849709i	−0.905262	−	0.424855i	$-0.860325\pi$
$607$	− 313074.i	− 0.849709i	0.905262	−	0.424855i	$-0.139675\pi$
$608$	− 72200.6i	− 0.195314i
$609$	0	0
$610$	−445412.	−1.19702
$611$	618529.	1.65683
$612$	116256.i	0.310394i
$613$	−338434.	−0.900643	−0.450321	−	0.892867i	$-0.648691\pi$
$613$	−338434.	−0.900643	−0.450321	+	0.892867i	$0.648691\pi$
$614$	− 424471.i	− 1.12593i
$615$	− 343332.i	− 0.907746i
$616$	0	0
$617$	−517289.	−1.35882	−0.679411	−	0.733758i	$-0.737765\pi$
$617$	−517289.	−1.35882	−0.679411	+	0.733758i	$0.737765\pi$
$618$	−40103.2	−0.105003
$619$	− 72706.8i	− 0.189755i	−0.995489	−	0.0948776i	$-0.969754\pi$
$619$	− 72706.8i	− 0.189755i	0.995489	−	0.0948776i	$-0.0302460\pi$
$620$	335094.	0.871733
$621$	80426.0i	0.208551i
$622$	97256.4i	0.251384i
$623$	0	0
$624$	−55503.6	−0.142545
$625$	140022.	0.358457
$626$	45031.9i	0.114914i
$627$	−105295.	−0.267838
$628$	275108.i	0.697565i
$629$	− 494232.i	− 1.24919i
$630$	0	0
$631$	−487488.	−1.22435	−0.612174	−	0.790723i	$-0.709705\pi$
$631$	−487488.	−1.22435	−0.612174	+	0.790723i	$0.709705\pi$
$632$	268593.	0.672452
$633$	− 237921.i	− 0.593779i
$634$	248160.	0.617381
$635$	− 610785.i	− 1.51475i
$636$	− 138239.i	− 0.341755i
$637$	0	0
$638$	119502.	0.293585
$639$	−44939.4	−0.110059
$640$	− 60236.2i	− 0.147061i
$641$	55174.0	0.134282	0.0671410	−	0.997743i	$-0.478612\pi$
$641$	55174.0	0.134282	0.0671410	+	0.997743i	$0.478612\pi$
$642$	167923.i	0.407417i
$643$	− 516872.i	− 1.25015i	−0.780566	−	0.625074i	$-0.785069\pi$
$643$	− 516872.i	− 1.25015i	0.780566	−	0.625074i	$-0.214931\pi$
$644$	0	0
$645$	−81513.0	−0.195933
$646$	−607187.	−1.45498
$647$	110801.i	0.264689i	0.991204	+	0.132345i	$0.0422506\pi$
$647$	110801.i	0.264689i	−0.991204	+	0.132345i	$0.957749\pi$
$648$	16495.4	0.0392837
$649$	318351.i	0.755816i
$650$	− 521709.i	− 1.23481i
$651$	0	0
$652$	−102639.	−0.241443
$653$	56939.6	0.133533	0.0667664	−	0.997769i	$-0.478732\pi$
$653$	56939.6	0.133533	0.0667664	+	0.997769i	$0.478732\pi$
$654$	− 65219.2i	− 0.152482i
$655$	−517654.	−1.20658
$656$	− 101665.i	− 0.236245i
$657$	− 107391.i	− 0.248792i
$658$	0	0
$659$	−336817.	−0.775573	−0.387786	−	0.921749i	$-0.626760\pi$
$659$	−336817.	−0.775573	−0.387786	+	0.921749i	$0.626760\pi$
$660$	−87846.4	−0.201668
$661$	435886.i	0.997631i	0.866708	+	0.498816i	$0.166232\pi$
$661$	435886.i	0.997631i	−0.866708	+	0.498816i	$0.833768\pi$
$662$	18270.8	0.0416910
$663$	466771.i	1.06188i
$664$	127386.i	0.288926i
$665$	0	0
$666$	−70125.7	−0.158099
$667$	476729.	1.07157
$668$	− 202379.i	− 0.453536i
$669$	114356.	0.255510
$670$	− 485245.i	− 1.08096i
$671$	192346.i	0.427207i
$672$	0	0
$673$	602595.	1.33044	0.665220	−	0.746647i	$-0.268338\pi$
$673$	602595.	1.33044	0.665220	+	0.746647i	$0.268338\pi$
$674$	−415013.	−0.913571
$675$	155049.i	0.340300i
$676$	5639.71	0.0123414
$677$	187554.i	0.409212i	0.978844	+	0.204606i	$0.0655912\pi$
$677$	187554.i	0.409212i	−0.978844	+	0.204606i	$0.934409\pi$
$678$	70803.4i	0.154026i
$679$	0	0
$680$	−506570.	−1.09552
$681$	158045.	0.340790
$682$	− 144707.i	− 0.311115i
$683$	−720934.	−1.54545	−0.772723	−	0.634743i	$-0.781106\pi$
$683$	−720934.	−1.54545	−0.772723	+	0.634743i	$0.781106\pi$
$684$	86152.8i	0.184144i
$685$	763739.i	1.62766i
$686$	0	0
$687$	−155014.	−0.328440
$688$	−24137.0	−0.0509924
$689$	− 555031.i	− 1.16917i
$690$	−350445.	−0.736075
$691$	370485.i	0.775916i	0.921677	+	0.387958i	$0.126819\pi$
$691$	370485.i	0.775916i	−0.921677	+	0.387958i	$0.873181\pi$
$692$	272693.i	0.569458i
$693$	0	0
$694$	−12260.7	−0.0254563
$695$	−237043.	−0.490748
$696$	− 97777.1i	− 0.201845i
$697$	−854972.	−1.75989
$698$	− 256014.i	− 0.525476i
$699$	376870.i	0.771324i
$700$	0	0
$701$	−703763.	−1.43216	−0.716078	−	0.698020i	$-0.754065\pi$
$701$	−703763.	−1.43216	−0.716078	+	0.698020i	$0.754065\pi$
$702$	66229.3	0.134393
$703$	− 366256.i	− 0.741095i
$704$	−26012.4	−0.0524849
$705$	− 800985.i	− 1.61156i
$706$	− 124540.i	− 0.249862i
$707$	0	0
$708$	260476.	0.519638
$709$	251584.	0.500484	0.250242	−	0.968183i	$-0.419490\pi$
$709$	251584.	0.500484	0.250242	+	0.968183i	$0.419490\pi$
$710$	− 195817.i	− 0.388449i
$711$	−320497.	−0.633993
$712$	283243.i	0.558726i
$713$	− 577278.i	− 1.13555i
$714$	0	0
$715$	−352705.	−0.689922
$716$	451626.	0.880954
$717$	− 142957.i	− 0.278079i
$718$	320112.	0.620945
$719$	− 804606.i	− 1.55642i	−0.628007	−	0.778208i	$-0.716129\pi$
$719$	− 804606.i	− 1.55642i	0.628007	−	0.778208i	$-0.283871\pi$
$720$	71876.4i	0.138650i
$721$	0	0
$722$	−81358.9	−0.156074
$723$	225493.	0.431377
$724$	− 472035.i	− 0.900527i
$725$	919060.	1.74851
$726$	− 177242.i	− 0.336275i
$727$	− 745416.i	− 1.41036i	−0.709029	−	0.705180i	$-0.750866\pi$
$727$	− 745416.i	− 1.41036i	0.709029	−	0.705180i	$-0.249134\pi$
$728$	0	0
$729$	−19683.0	−0.0370370
$730$	467942.	0.878104
$731$	202985.i	0.379866i
$732$	157379.	0.293713
$733$	150285.i	0.279710i	0.990172	+	0.139855i	$0.0446636\pi$
$733$	150285.i	0.279710i	−0.990172	+	0.139855i	$0.955336\pi$
$734$	− 73578.1i	− 0.136570i
$735$	0	0
$736$	−103771.	−0.191567
$737$	−209548.	−0.385787
$738$	121311.i	0.222734i
$739$	737144.	1.34978	0.674890	−	0.737918i	$-0.264191\pi$
$739$	737144.	1.34978	0.674890	+	0.737918i	$0.264191\pi$
$740$	− 305563.i	− 0.558005i
$741$	345905.i	0.629971i
$742$	0	0
$743$	106915.	0.193670	0.0968351	−	0.995300i	$-0.469128\pi$
$743$	106915.	0.193670	0.0968351	+	0.995300i	$0.469128\pi$
$744$	−118400.	−0.213897
$745$	351270.i	0.632891i
$746$	281102.	0.505110
$747$	− 152003.i	− 0.272402i
$748$	218757.i	0.390984i
$749$	0	0
$750$	−293530.	−0.521830
$751$	582205.	1.03228	0.516138	−	0.856505i	$-0.327369\pi$
$751$	582205.	1.03228	0.516138	+	0.856505i	$0.327369\pi$
$752$	− 237181.i	− 0.419415i
$753$	−139643.	−0.246280
$754$	− 392577.i	− 0.690530i
$755$	139693.i	0.245064i
$756$	0	0
$757$	207115.	0.361426	0.180713	−	0.983536i	$-0.442160\pi$
$757$	207115.	0.361426	0.180713	+	0.983536i	$0.442160\pi$
$758$	733957.	1.27742
$759$	151336.i	0.262699i
$760$	−375399.	−0.649929
$761$	− 1.12435e6i	− 1.94148i	−0.240135	−	0.970740i	$-0.577192\pi$
$761$	− 1.12435e6i	− 1.94148i	0.240135	−	0.970740i	$-0.422808\pi$
$762$	215810.i	0.371674i
$763$	0	0
$764$	40846.0	0.0699782
$765$	604461.	1.03287
$766$	− 52103.5i	− 0.0887993i
$767$	1.04582e6	1.77773
$768$	21283.4i	0.0360844i
$769$	483502.i	0.817609i	0.912622	+	0.408804i	$0.134054\pi$
$769$	483502.i	0.817609i	−0.912622	+	0.408804i	$0.865946\pi$
$770$	0	0
$771$	153065.	0.257494
$772$	−76109.1	−0.127703
$773$	− 396591.i	− 0.663719i	−0.943329	−	0.331860i	$-0.892324\pi$
$773$	− 396591.i	− 0.663719i	0.943329	−	0.331860i	$-0.107676\pi$
$774$	28801.3	0.0480761
$775$	− 1.11290e6i	− 1.85291i
$776$	− 109030.i	− 0.181060i
$777$	0	0
$778$	722756.	1.19408
$779$	−633586.	−1.04407
$780$	288585.i	0.474335i
$781$	−84561.6	−0.138634
$782$	872686.i	1.42707i
$783$	116672.i	0.190302i
$784$	0	0
$785$	1.43040e6	2.32123
$786$	182904.	0.296059
$787$	345917.i	0.558500i	0.960218	+	0.279250i	$0.0900858\pi$
$787$	345917.i	0.558500i	−0.960218	+	0.279250i	$0.909914\pi$
$788$	297370.	0.478900
$789$	196209.i	0.315185i
$790$	− 1.39652e6i	− 2.23766i
$791$	0	0
$792$	31039.1	0.0494832
$793$	631879.	1.00482
$794$	− 338046.i	− 0.536210i
$795$	−718757.	−1.13723
$796$	521656.i	0.823300i
$797$	944899.i	1.48754i	0.668435	+	0.743770i	$0.266964\pi$
$797$	944899.i	1.48754i	−0.668435	+	0.743770i	$0.733036\pi$
$798$	0	0
$799$	−1.99463e6	−3.12441
$800$	−200055.	−0.312585
$801$	− 337977.i	− 0.526772i
$802$	−532887.	−0.828488
$803$	− 202075.i	− 0.313388i
$804$	171453.i	0.265236i
$805$	0	0
$806$	−475378.	−0.731760
$807$	−57378.1	−0.0881047
$808$	340702.i	0.521858i
$809$	82296.7	0.125744	0.0628718	−	0.998022i	$-0.479974\pi$
$809$	82296.7	0.125744	0.0628718	+	0.998022i	$0.479974\pi$
$810$	− 85766.0i	− 0.130721i
$811$	1.05525e6i	1.60440i	0.597054	+	0.802201i	$0.296338\pi$
$811$	1.05525e6i	1.60440i	−0.597054	+	0.802201i	$0.703662\pi$
$812$	0	0
$813$	531425.	0.804009
$814$	−131954.	−0.199147
$815$	533658.i	0.803430i
$816$	178988.	0.268809
$817$	150424.i	0.225359i
$818$	− 425192.i	− 0.635446i
$819$	0	0
$820$	−528594.	−0.786131
$821$	194688.	0.288837	0.144419	−	0.989517i	$-0.453869\pi$
$821$	194688.	0.288837	0.144419	+	0.989517i	$0.453869\pi$
$822$	− 269854.i	− 0.399379i
$823$	−667481.	−0.985461	−0.492731	−	0.870182i	$-0.664001\pi$
$823$	−667481.	−0.985461	−0.492731	+	0.870182i	$0.664001\pi$
$824$	61742.9i	0.0909354i
$825$	291753.i	0.428654i
$826$	0	0
$827$	−725361.	−1.06058	−0.530289	−	0.847817i	$-0.677917\pi$
$827$	−725361.	−1.06058	−0.530289	+	0.847817i	$0.677917\pi$
$828$	123824.	0.180611
$829$	− 272431.i	− 0.396412i	−0.980160	−	0.198206i	$-0.936488\pi$
$829$	− 272431.i	− 0.396412i	0.980160	−	0.198206i	$-0.0635116\pi$
$830$	662332.	0.961434
$831$	700653.i	1.01461i
$832$	85453.5i	0.123448i
$833$	0	0
$834$	83755.3	0.120415
$835$	−1.05225e6	−1.50919
$836$	162112.i	0.231954i
$837$	141280.	0.201664
$838$	− 96683.4i	− 0.137678i
$839$	50997.6i	0.0724479i	0.999344	+	0.0362239i	$0.0115330\pi$
$839$	50997.6i	0.0724479i	−0.999344	+	0.0362239i	$0.988467\pi$
$840$	0	0
$841$	−15703.6	−0.0222028
$842$	−13370.8	−0.0188596
$843$	430210.i	0.605377i
$844$	−366303.	−0.514227
$845$	− 29323.1i	− 0.0410673i
$846$	283015.i	0.395429i
$847$	0	0
$848$	−212832.	−0.295969
$849$	−498136.	−0.691087
$850$	1.68241e6i	2.32859i
$851$	−526404.	−0.726876
$852$	69188.7i	0.0953139i
$853$	− 81836.7i	− 0.112473i	−0.998417	−	0.0562367i	$-0.982090\pi$
$853$	− 81836.7i	− 0.112473i	0.998417	−	0.0562367i	$-0.0179102\pi$
$854$	0	0
$855$	447942.	0.612759
$856$	258534.	0.352834
$857$	505238.i	0.687914i	0.938985	+	0.343957i	$0.111768\pi$
$857$	505238.i	0.687914i	−0.938985	+	0.343957i	$0.888232\pi$
$858$	124622.	0.169286
$859$	1.03668e6i	1.40494i	0.711711	+	0.702472i	$0.247920\pi$
$859$	1.03668e6i	1.40494i	−0.711711	+	0.702472i	$0.752080\pi$
$860$	125498.i	0.169683i
$861$	0	0
$862$	−350099.	−0.471168
$863$	918585.	1.23338	0.616691	−	0.787205i	$-0.288473\pi$
$863$	918585.	1.23338	0.616691	+	0.787205i	$0.288473\pi$
$864$	− 25396.3i	− 0.0340207i
$865$	1.41784e6	1.89493
$866$	135503.i	0.180681i
$867$	− 1.07125e6i	− 1.42513i
$868$	0	0
$869$	−603073.	−0.798602
$870$	−508382.	−0.671663
$871$	688387.i	0.907396i
$872$	−100411.	−0.132054
$873$	130099.i	0.170705i
$874$	646713.i	0.846620i
$875$	0	0
$876$	−165339.	−0.215460
$877$	175139.	0.227711	0.113855	−	0.993497i	$-0.463680\pi$
$877$	175139.	0.227711	0.113855	+	0.993497i	$0.463680\pi$
$878$	191775.i	0.248772i
$879$	438324.	0.567306
$880$	135248.i	0.174649i
$881$	− 56505.5i	− 0.0728012i	−0.999337	−	0.0364006i	$-0.988411\pi$
$881$	− 56505.5i	− 0.0728012i	0.999337	−	0.0364006i	$-0.0115892\pi$
$882$	0	0
$883$	−351813.	−0.451222	−0.225611	−	0.974217i	$-0.572438\pi$
$883$	−351813.	−0.451222	−0.225611	+	0.974217i	$0.572438\pi$
$884$	718641.	0.919618
$885$	− 1.35432e6i	− 1.72915i
$886$	−525077.	−0.668891
$887$	− 152362.i	− 0.193655i	−0.995301	−	0.0968275i	$-0.969130\pi$
$887$	− 152362.i	− 0.193655i	0.995301	−	0.0968275i	$-0.0308695\pi$
$888$	107966.i	0.136918i
$889$	0	0
$890$	1.47269e6	1.85922
$891$	−37037.1	−0.0466532
$892$	− 176063.i	− 0.221278i
$893$	−1.47814e6	−1.85359
$894$	− 124115.i	− 0.155293i
$895$	− 2.34818e6i	− 2.93147i
$896$	0	0
$897$	497156.	0.617885
$898$	−684065.	−0.848290
$899$	− 837442.i	− 1.03618i
$900$	238714.	0.294708
$901$	1.78986e6i	2.20480i
$902$	228268.i	0.280564i
$903$	0	0
$904$	109009.	0.133391
$905$	−2.45429e6	−2.99661
$906$	− 49358.0i	− 0.0601314i
$907$	1.40476e6	1.70760	0.853801	−	0.520600i	$-0.174292\pi$
$907$	1.40476e6	1.70760	0.853801	+	0.520600i	$0.174292\pi$
$908$	− 243327.i	− 0.295133i
$909$	− 406540.i	− 0.492012i
$910$	0	0
$911$	1.44879e6	1.74570	0.872849	−	0.487990i	$-0.162270\pi$
$911$	1.44879e6	1.74570	0.872849	+	0.487990i	$0.162270\pi$
$912$	132641.	0.159473
$913$	− 286021.i	− 0.343128i
$914$	−426566.	−0.510615
$915$	− 818274.i	− 0.977364i
$916$	238659.i	0.284438i
$917$	0	0
$918$	−213576.	−0.253435
$919$	−661628.	−0.783399	−0.391699	−	0.920093i	$-0.628113\pi$
$919$	−661628.	−0.783399	−0.391699	+	0.920093i	$0.628113\pi$
$920$	539546.i	0.637460i
$921$	779802.	0.919317
$922$	− 118029.i	− 0.138843i
$923$	277794.i	0.326077i
$924$	0	0
$925$	−1.01483e6	−1.18607
$926$	499243.	0.582224
$927$	− 73674.3i	− 0.0857347i
$928$	−150538.	−0.174803
$929$	1.25868e6i	1.45843i	0.684287	+	0.729213i	$0.260114\pi$
$929$	1.25868e6i	1.45843i	−0.684287	+	0.729213i	$0.739886\pi$
$930$	615607.i	0.711767i
$931$	0	0
$932$	580229.	0.667986
$933$	−178671.	−0.205254
$934$	− 108735.i	− 0.124645i
$935$	1.13740e6	1.30104
$936$	− 101967.i	− 0.116388i
$937$	232757.i	0.265109i	0.991176	+	0.132554i	$0.0423179\pi$
$937$	232757.i	0.265109i	−0.991176	+	0.132554i	$0.957682\pi$
$938$	0	0
$939$	−82728.8	−0.0938265
$940$	−1.23320e6	−1.39565
$941$	− 679488.i	− 0.767366i	−0.923465	−	0.383683i	$-0.874656\pi$
$941$	− 679488.i	− 0.767366i	0.923465	−	0.383683i	$-0.125344\pi$
$942$	−505406.	−0.569559
$943$	910628.i	1.02404i
$944$	− 401029.i	− 0.450020i
$945$	0	0
$946$	54194.8	0.0605585
$947$	778814.	0.868428	0.434214	−	0.900810i	$-0.357026\pi$
$947$	778814.	0.868428	0.434214	+	0.900810i	$0.357026\pi$
$948$	493437.i	0.549054i
$949$	−663840.	−0.737108
$950$	1.24676e6i	1.38146i
$951$	455899.i	0.504090i
$952$	0	0
$953$	838192.	0.922907	0.461453	−	0.887164i	$-0.347328\pi$
$953$	838192.	0.922907	0.461453	+	0.887164i	$0.347328\pi$
$954$	253961.	0.279042
$955$	− 212374.i	− 0.232860i
$956$	−220097.	−0.240823
$957$	219539.i	0.239711i
$958$	− 872836.i	− 0.951047i
$959$	0	0
$960$	110661.	0.120075
$961$	−90550.7	−0.0980494
$962$	433484.i	0.468407i
$963$	−308494.	−0.332655
$964$	− 347170.i	− 0.373583i
$965$	395721.i	0.424947i
$966$	0	0
$967$	974955.	1.04263	0.521317	−	0.853363i	$-0.325441\pi$
$967$	974955.	1.04263	0.521317	+	0.853363i	$0.325441\pi$
$968$	−272882.	−0.291222
$969$	− 1.11547e6i	− 1.18799i
$970$	−566890.	−0.602497
$971$	− 656480.i	− 0.696278i	−0.937443	−	0.348139i	$-0.886814\pi$
$971$	− 656480.i	− 0.696278i	0.937443	−	0.348139i	$-0.113186\pi$
$972$	30304.0i	0.0320750i
$973$	0	0
$974$	2858.76	0.00301342
$975$	958440.	1.00822
$976$	− 242300.i	− 0.254363i
$977$	−668819.	−0.700679	−0.350340	−	0.936623i	$-0.613934\pi$
$977$	−668819.	−0.700679	−0.350340	+	0.936623i	$0.613934\pi$
$978$	− 188559.i	− 0.197138i
$979$	− 635966.i	− 0.663542i
$980$	0	0
$981$	119815.	0.124501
$982$	−434244.	−0.450309
$983$	− 1.21781e6i	− 1.26029i	−0.776476	−	0.630146i	$-0.782995\pi$
$983$	− 1.21781e6i	− 1.26029i	0.776476	−	0.630146i	$-0.217005\pi$
$984$	186770.	0.192893
$985$	− 1.54614e6i	− 1.59359i
$986$	1.26598e6i	1.30219i
$987$	0	0
$988$	532556.	0.545571
$989$	216199.	0.221035
$990$	− 161384.i	− 0.164661i
$991$	1.09800e6	1.11803	0.559017	−	0.829156i	$-0.311178\pi$
$991$	1.09800e6	1.11803	0.559017	+	0.829156i	$0.311178\pi$
$992$	182289.i	0.185241i
$993$	33565.7i	0.0340406i
$994$	0	0
$995$	2.71229e6	2.73962
$996$	−234024.	−0.235907
$997$	639475.i	0.643329i	0.946854	+	0.321664i	$0.104242\pi$
$997$	639475.i	0.643329i	−0.946854	+	0.321664i	$0.895758\pi$
$998$	−702915.	−0.705735
$999$	− 128829.i	− 0.129087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.c.b.97.7	yes	8
3.2	odd	2		882.5.c.f.685.4		8
7.2	even	3		294.5.g.e.31.1		8
7.3	odd	6		294.5.g.e.19.1		8
7.4	even	3		294.5.g.g.19.2		8
7.5	odd	6		294.5.g.g.31.2		8
7.6	odd	2	inner	294.5.c.b.97.6	✓	8
21.20	even	2		882.5.c.f.685.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.5.c.b.97.6	✓	8	7.6	odd	2	inner
294.5.c.b.97.7	yes	8	1.1	even	1	trivial
294.5.g.e.19.1		8	7.3	odd	6
294.5.g.e.31.1		8	7.2	even	3
294.5.g.g.19.2		8	7.4	even	3
294.5.g.g.31.2		8	7.5	odd	6
882.5.c.f.685.1		8	21.20	even	2
882.5.c.f.685.4		8	3.2	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -41.5951i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -41.5951i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} -117.649i q^{10} -50.8054 q^{11} +41.5692i q^{12} +166.901i q^{13} +216.135 q^{15} +64.0000 q^{16} -538.223i q^{17} -76.3675 q^{18} -398.856i q^{19} -332.761i q^{20} -143.699 q^{22} -573.259 q^{23} +117.576i q^{24} -1105.16 q^{25} +472.068i q^{26} -140.296i q^{27} -831.611 q^{29} +611.321 q^{30} +1007.01i q^{31} +181.019 q^{32} -263.993i q^{33} -1522.32i q^{34} -216.000 q^{36} +918.266 q^{37} -1128.13i q^{38} -867.244 q^{39} -941.191i q^{40} -1588.51i q^{41} -377.140 q^{43} -406.443 q^{44} +1123.07i q^{45} -1621.42 q^{46} -3705.96i q^{47} +332.554i q^{48} -3125.85 q^{50} +2796.69 q^{51} +1335.21i q^{52} -3325.51 q^{53} -396.817i q^{54} +2113.26i q^{55} +2072.51 q^{57} -2352.15 q^{58} -6266.08i q^{59} +1729.08 q^{60} -3785.94i q^{61} +2848.26i q^{62} +512.000 q^{64} +6942.28 q^{65} -746.684i q^{66} +4124.52 q^{67} -4305.78i q^{68} -2978.74i q^{69} +1664.42 q^{71} -610.940 q^{72} +3977.44i q^{73} +2597.25 q^{74} -5742.56i q^{75} -3190.84i q^{76} -2452.94 q^{78} +11870.3 q^{79} -2662.09i q^{80} +729.000 q^{81} -4492.99i q^{82} +5629.74i q^{83} -22387.5 q^{85} -1066.71 q^{86} -4321.18i q^{87} -1149.59 q^{88} +12517.7i q^{89} +3176.52i q^{90} -4586.07 q^{92} -5232.58 q^{93} -10482.0i q^{94} -16590.5 q^{95} +940.604i q^{96} -4818.49i q^{97} +1371.75 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{4} - 216 q^{9}+O(q^{10}) \) 8 * q + 64 * q^4 - 216 * q^9	\( 8 q + 64 q^{4} - 216 q^{9} + 512 q^{16} - 1312 q^{22} - 272 q^{23} - 2808 q^{25} + 400 q^{29} + 3168 q^{30} - 1728 q^{36} - 3328 q^{37} + 656 q^{43} - 2400 q^{46} + 800 q^{50} + 7200 q^{51} + 9264 q^{53} + 1152 q^{57} - 11488 q^{58} + 4096 q^{64} - 15696 q^{65} + 26816 q^{67} + 28192 q^{71} - 4512 q^{74} + 9216 q^{78} + 19728 q^{79} + 5832 q^{81} - 49632 q^{85} + 5888 q^{86} - 10496 q^{88} - 2176 q^{92} + 15264 q^{93} - 92752 q^{95}+O(q^{100}) \) 8 * q + 64 * q^4 - 216 * q^9 + 512 * q^16 - 1312 * q^22 - 272 * q^23 - 2808 * q^25 + 400 * q^29 + 3168 * q^30 - 1728 * q^36 - 3328 * q^37 + 656 * q^43 - 2400 * q^46 + 800 * q^50 + 7200 * q^51 + 9264 * q^53 + 1152 * q^57 - 11488 * q^58 + 4096 * q^64 - 15696 * q^65 + 26816 * q^67 + 28192 * q^71 - 4512 * q^74 + 9216 * q^78 + 19728 * q^79 + 5832 * q^81 - 49632 * q^85 + 5888 * q^86 - 10496 * q^88 - 2176 * q^92 + 15264 * q^93 - 92752 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more