LMFDB - Embedded newform 950.4.b.d.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,4,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$56.0518145055$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.4.b.d.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +4.00000 q^{6} -31.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +4.00000 q^{6} -31.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +57.0000 q^{11} -8.00000i q^{12} +52.0000i q^{13} -62.0000 q^{14} +16.0000 q^{16} +69.0000i q^{17} -46.0000i q^{18} -19.0000 q^{19} +62.0000 q^{21} -114.000i q^{22} +72.0000i q^{23} -16.0000 q^{24} +104.000 q^{26} +100.000i q^{27} +124.000i q^{28} +150.000 q^{29} +32.0000 q^{31} -32.0000i q^{32} +114.000i q^{33} +138.000 q^{34} -92.0000 q^{36} -226.000i q^{37} +38.0000i q^{38} -104.000 q^{39} -258.000 q^{41} -124.000i q^{42} +67.0000i q^{43} -228.000 q^{44} +144.000 q^{46} +579.000i q^{47} +32.0000i q^{48} -618.000 q^{49} -138.000 q^{51} -208.000i q^{52} +432.000i q^{53} +200.000 q^{54} +248.000 q^{56} -38.0000i q^{57} -300.000i q^{58} +330.000 q^{59} -13.0000 q^{61} -64.0000i q^{62} -713.000i q^{63} -64.0000 q^{64} +228.000 q^{66} -856.000i q^{67} -276.000i q^{68} -144.000 q^{69} +642.000 q^{71} +184.000i q^{72} +487.000i q^{73} -452.000 q^{74} +76.0000 q^{76} -1767.00i q^{77} +208.000i q^{78} +700.000 q^{79} +421.000 q^{81} +516.000i q^{82} +12.0000i q^{83} -248.000 q^{84} +134.000 q^{86} +300.000i q^{87} +456.000i q^{88} +600.000 q^{89} +1612.00 q^{91} -288.000i q^{92} +64.0000i q^{93} +1158.00 q^{94} +64.0000 q^{96} +1424.00i q^{97} +1236.00i q^{98} +1311.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 8 q^{6} + 46 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 + 8 * q^6 + 46 * q^9	$ 2 q - 8 q^{4} + 8 q^{6} + 46 q^{9} + 114 q^{11} - 124 q^{14} + 32 q^{16} - 38 q^{19} + 124 q^{21} - 32 q^{24} + 208 q^{26} + 300 q^{29} + 64 q^{31} + 276 q^{34} - 184 q^{36} - 208 q^{39} - 516 q^{41} - 456 q^{44} + 288 q^{46} - 1236 q^{49} - 276 q^{51} + 400 q^{54} + 496 q^{56} + 660 q^{59} - 26 q^{61} - 128 q^{64} + 456 q^{66} - 288 q^{69} + 1284 q^{71} - 904 q^{74} + 152 q^{76} + 1400 q^{79} + 842 q^{81} - 496 q^{84} + 268 q^{86} + 1200 q^{89} + 3224 q^{91} + 2316 q^{94} + 128 q^{96} + 2622 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 + 8 * q^6 + 46 * q^9 + 114 * q^11 - 124 * q^14 + 32 * q^16 - 38 * q^19 + 124 * q^21 - 32 * q^24 + 208 * q^26 + 300 * q^29 + 64 * q^31 + 276 * q^34 - 184 * q^36 - 208 * q^39 - 516 * q^41 - 456 * q^44 + 288 * q^46 - 1236 * q^49 - 276 * q^51 + 400 * q^54 + 496 * q^56 + 660 * q^59 - 26 * q^61 - 128 * q^64 + 456 * q^66 - 288 * q^69 + 1284 * q^71 - 904 * q^74 + 152 * q^76 + 1400 * q^79 + 842 * q^81 - 496 * q^84 + 268 * q^86 + 1200 * q^89 + 3224 * q^91 + 2316 * q^94 + 128 * q^96 + 2622 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	2.00000i	0.384900i	0.981307	+	0.192450i	$0.0616434\pi$
$3$	2.00000i	0.384900i	−0.981307	+	0.192450i	$0.938357\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	4.00000	0.272166
$7$	− 31.0000i	− 1.67384i	−0.547323	−	0.836921i	$-0.684353\pi$
$7$	− 31.0000i	− 1.67384i	0.547323	−	0.836921i	$-0.315647\pi$
$8$	8.00000i	0.353553i
$9$	23.0000	0.851852
$10$	0	0
$11$	57.0000	1.56238	0.781188	−	0.624295i	$-0.214614\pi$
$11$	57.0000	1.56238	0.781188	+	0.624295i	$0.214614\pi$
$12$	− 8.00000i	− 0.192450i
$13$	52.0000i	1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$	52.0000i	1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−62.0000	−1.18359
$15$	0	0
$16$	16.0000	0.250000
$17$	69.0000i	0.984409i	0.870480	+	0.492205i	$0.163809\pi$
$17$	69.0000i	0.984409i	−0.870480	+	0.492205i	$0.836191\pi$
$18$	− 46.0000i	− 0.602350i
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	62.0000	0.644262
$22$	− 114.000i	− 1.10477i
$23$	72.0000i	0.652741i	0.945242	+	0.326370i	$0.105826\pi$
$23$	72.0000i	0.652741i	−0.945242	+	0.326370i	$0.894174\pi$
$24$	−16.0000	−0.136083
$25$	0	0
$26$	104.000	0.784465
$27$	100.000i	0.712778i
$28$	124.000i	0.836921i
$29$	150.000	0.960493	0.480247	−	0.877134i	$-0.340547\pi$
$29$	150.000	0.960493	0.480247	+	0.877134i	$0.340547\pi$
$30$	0	0
$31$	32.0000	0.185399	0.0926995	−	0.995694i	$-0.470450\pi$
$31$	32.0000	0.185399	0.0926995	+	0.995694i	$0.470450\pi$
$32$	− 32.0000i	− 0.176777i
$33$	114.000i	0.601359i
$34$	138.000	0.696082
$35$	0	0
$36$	−92.0000	−0.425926
$37$	− 226.000i	− 1.00417i	−0.864819	−	0.502083i	$-0.832567\pi$
$37$	− 226.000i	− 1.00417i	0.864819	−	0.502083i	$-0.167433\pi$
$38$	38.0000i	0.162221i
$39$	−104.000	−0.427008
$40$	0	0
$41$	−258.000	−0.982752	−0.491376	−	0.870948i	$-0.663506\pi$
$41$	−258.000	−0.982752	−0.491376	+	0.870948i	$0.663506\pi$
$42$	− 124.000i	− 0.455562i
$43$	67.0000i	0.237614i	0.992917	+	0.118807i	$0.0379070\pi$
$43$	67.0000i	0.237614i	−0.992917	+	0.118807i	$0.962093\pi$
$44$	−228.000	−0.781188
$45$	0	0
$46$	144.000	0.461557
$47$	579.000i	1.79693i	0.439043	+	0.898466i	$0.355318\pi$
$47$	579.000i	1.79693i	−0.439043	+	0.898466i	$0.644682\pi$
$48$	32.0000i	0.0962250i
$49$	−618.000	−1.80175
$50$	0	0
$51$	−138.000	−0.378899
$52$	− 208.000i	− 0.554700i
$53$	432.000i	1.11962i	0.828622	+	0.559809i	$0.189126\pi$
$53$	432.000i	1.11962i	−0.828622	+	0.559809i	$0.810874\pi$
$54$	200.000	0.504010
$55$	0	0
$56$	248.000	0.591793
$57$	− 38.0000i	− 0.0883022i
$58$	− 300.000i	− 0.679171i
$59$	330.000	0.728175	0.364088	−	0.931365i	$-0.381381\pi$
$59$	330.000	0.728175	0.364088	+	0.931365i	$0.381381\pi$
$60$	0	0
$61$	−13.0000	−0.0272865	−0.0136433	−	0.999907i	$-0.504343\pi$
$61$	−13.0000	−0.0272865	−0.0136433	+	0.999907i	$0.504343\pi$
$62$	− 64.0000i	− 0.131097i
$63$	− 713.000i	− 1.42587i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	228.000	0.425225
$67$	− 856.000i	− 1.56085i	−0.625249	−	0.780426i	$-0.715002\pi$
$67$	− 856.000i	− 1.56085i	0.625249	−	0.780426i	$-0.284998\pi$
$68$	− 276.000i	− 0.492205i
$69$	−144.000	−0.251240
$70$	0	0
$71$	642.000	1.07312	0.536559	−	0.843863i	$-0.319724\pi$
$71$	642.000	1.07312	0.536559	+	0.843863i	$0.319724\pi$
$72$	184.000i	0.301175i
$73$	487.000i	0.780809i	0.920643	+	0.390404i	$0.127665\pi$
$73$	487.000i	0.780809i	−0.920643	+	0.390404i	$0.872335\pi$
$74$	−452.000	−0.710053
$75$	0	0
$76$	76.0000	0.114708
$77$	− 1767.00i	− 2.61517i
$78$	208.000i	0.301941i
$79$	700.000	0.996913	0.498457	−	0.866915i	$-0.333900\pi$
$79$	700.000	0.996913	0.498457	+	0.866915i	$0.333900\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	516.000i	0.694911i
$83$	12.0000i	0.0158695i	0.999969	+	0.00793477i	$0.00252574\pi$
$83$	12.0000i	0.0158695i	−0.999969	+	0.00793477i	$0.997474\pi$
$84$	−248.000	−0.322131
$85$	0	0
$86$	134.000	0.168019
$87$	300.000i	0.369694i
$88$	456.000i	0.552384i
$89$	600.000	0.714605	0.357303	−	0.933989i	$-0.383696\pi$
$89$	600.000	0.714605	0.357303	+	0.933989i	$0.383696\pi$
$90$	0	0
$91$	1612.00	1.85696
$92$	− 288.000i	− 0.326370i
$93$	64.0000i	0.0713601i
$94$	1158.00	1.27062
$95$	0	0
$96$	64.0000	0.0680414
$97$	1424.00i	1.49057i	0.666746	+	0.745285i	$0.267687\pi$
$97$	1424.00i	1.49057i	−0.666746	+	0.745285i	$0.732313\pi$
$98$	1236.00i	1.27403i
$99$	1311.00	1.33091
$100$	0	0
$101$	1062.00	1.04627	0.523133	−	0.852251i	$-0.324763\pi$
$101$	1062.00	1.04627	0.523133	+	0.852251i	$0.324763\pi$
$102$	276.000i	0.267922i
$103$	− 1178.00i	− 1.12691i	−0.826147	−	0.563455i	$-0.809472\pi$
$103$	− 1178.00i	− 1.12691i	0.826147	−	0.563455i	$-0.190528\pi$
$104$	−416.000	−0.392232
$105$	0	0
$106$	864.000	0.791690
$107$	114.000i	0.102998i	0.998673	+	0.0514990i	$0.0163999\pi$
$107$	114.000i	0.102998i	−0.998673	+	0.0514990i	$0.983600\pi$
$108$	− 400.000i	− 0.356389i
$109$	−1460.00	−1.28296	−0.641480	−	0.767140i	$-0.721679\pi$
$109$	−1460.00	−1.28296	−0.641480	+	0.767140i	$0.721679\pi$
$110$	0	0
$111$	452.000	0.386504
$112$	− 496.000i	− 0.418461i
$113$	822.000i	0.684312i	0.939643	+	0.342156i	$0.111157\pi$
$113$	822.000i	0.684312i	−0.939643	+	0.342156i	$0.888843\pi$
$114$	−76.0000	−0.0624391
$115$	0	0
$116$	−600.000	−0.480247
$117$	1196.00i	0.945045i
$118$	− 660.000i	− 0.514898i
$119$	2139.00	1.64775
$120$	0	0
$121$	1918.00	1.44102
$122$	26.0000i	0.0192945i
$123$	− 516.000i	− 0.378261i
$124$	−128.000	−0.0926995
$125$	0	0
$126$	−1426.00	−1.00824
$127$	− 2086.00i	− 1.45750i	−0.684780	−	0.728750i	$-0.740102\pi$
$127$	− 2086.00i	− 1.45750i	0.684780	−	0.728750i	$-0.259898\pi$
$128$	128.000i	0.0883883i
$129$	−134.000	−0.0914577
$130$	0	0
$131$	−93.0000	−0.0620263	−0.0310132	−	0.999519i	$-0.509873\pi$
$131$	−93.0000	−0.0620263	−0.0310132	+	0.999519i	$0.509873\pi$
$132$	− 456.000i	− 0.300680i
$133$	589.000i	0.384006i
$134$	−1712.00	−1.10369
$135$	0	0
$136$	−552.000	−0.348041
$137$	1269.00i	0.791372i	0.918386	+	0.395686i	$0.129493\pi$
$137$	1269.00i	0.791372i	−0.918386	+	0.395686i	$0.870507\pi$
$138$	288.000i	0.177654i
$139$	1975.00	1.20516	0.602580	−	0.798058i	$-0.294139\pi$
$139$	1975.00	1.20516	0.602580	+	0.798058i	$0.294139\pi$
$140$	0	0
$141$	−1158.00	−0.691640
$142$	− 1284.00i	− 0.758809i
$143$	2964.00i	1.73330i
$144$	368.000	0.212963
$145$	0	0
$146$	974.000	0.552115
$147$	− 1236.00i	− 0.693494i
$148$	904.000i	0.502083i
$149$	1695.00	0.931945	0.465973	−	0.884799i	$-0.345705\pi$
$149$	1695.00	0.931945	0.465973	+	0.884799i	$0.345705\pi$
$150$	0	0
$151$	1802.00	0.971157	0.485578	−	0.874193i	$-0.338609\pi$
$151$	1802.00	0.971157	0.485578	+	0.874193i	$0.338609\pi$
$152$	− 152.000i	− 0.0811107i
$153$	1587.00i	0.838571i
$154$	−3534.00	−1.84921
$155$	0	0
$156$	416.000	0.213504
$157$	− 3226.00i	− 1.63989i	−0.572442	−	0.819945i	$-0.694004\pi$
$157$	− 3226.00i	− 1.63989i	0.572442	−	0.819945i	$-0.305996\pi$
$158$	− 1400.00i	− 0.704924i
$159$	−864.000	−0.430941
$160$	0	0
$161$	2232.00	1.09259
$162$	− 842.000i	− 0.408357i
$163$	− 1268.00i	− 0.609309i	−0.952463	−	0.304655i	$-0.901459\pi$
$163$	− 1268.00i	− 0.609309i	0.952463	−	0.304655i	$-0.0985411\pi$
$164$	1032.00	0.491376
$165$	0	0
$166$	24.0000	0.0112215
$167$	654.000i	0.303042i	0.988454	+	0.151521i	$0.0484171\pi$
$167$	654.000i	0.303042i	−0.988454	+	0.151521i	$0.951583\pi$
$168$	496.000i	0.227781i
$169$	−507.000	−0.230769
$170$	0	0
$171$	−437.000	−0.195428
$172$	− 268.000i	− 0.118807i
$173$	1362.00i	0.598560i	0.954165	+	0.299280i	$0.0967465\pi$
$173$	1362.00i	0.598560i	−0.954165	+	0.299280i	$0.903253\pi$
$174$	600.000	0.261413
$175$	0	0
$176$	912.000	0.390594
$177$	660.000i	0.280275i
$178$	− 1200.00i	− 0.505302i
$179$	210.000	0.0876879	0.0438440	−	0.999038i	$-0.486040\pi$
$179$	210.000	0.0876879	0.0438440	+	0.999038i	$0.486040\pi$
$180$	0	0
$181$	2.00000	0.000821319 0	0.000410660	−	1.00000i	$-0.499869\pi$
$181$	2.00000	0.000821319 0	0.000410660		1.00000i	$0.499869\pi$
$182$	− 3224.00i	− 1.31307i
$183$	− 26.0000i	− 0.0105026i
$184$	−576.000	−0.230779
$185$	0	0
$186$	128.000	0.0504592
$187$	3933.00i	1.53802i
$188$	− 2316.00i	− 0.898466i
$189$	3100.00	1.19308
$190$	0	0
$191$	−2643.00	−1.00126	−0.500630	−	0.865661i	$-0.666898\pi$
$191$	−2643.00	−1.00126	−0.500630	+	0.865661i	$0.666898\pi$
$192$	− 128.000i	− 0.0481125i
$193$	− 3248.00i	− 1.21138i	−0.795701	−	0.605690i	$-0.792897\pi$
$193$	− 3248.00i	− 1.21138i	0.795701	−	0.605690i	$-0.207103\pi$
$194$	2848.00	1.05399
$195$	0	0
$196$	2472.00	0.900875
$197$	− 3126.00i	− 1.13055i	−0.824903	−	0.565275i	$-0.808770\pi$
$197$	− 3126.00i	− 1.13055i	0.824903	−	0.565275i	$-0.191230\pi$
$198$	− 2622.00i	− 0.941098i
$199$	2995.00	1.06688	0.533442	−	0.845837i	$-0.320898\pi$
$199$	2995.00	1.06688	0.533442	+	0.845837i	$0.320898\pi$
$200$	0	0
$201$	1712.00	0.600772
$202$	− 2124.00i	− 0.739822i
$203$	− 4650.00i	− 1.60771i
$204$	552.000	0.189450
$205$	0	0
$206$	−2356.00	−0.796846
$207$	1656.00i	0.556038i
$208$	832.000i	0.277350i
$209$	−1083.00	−0.358434
$210$	0	0
$211$	−4318.00	−1.40883	−0.704416	−	0.709788i	$-0.748791\pi$
$211$	−4318.00	−1.40883	−0.704416	+	0.709788i	$0.748791\pi$
$212$	− 1728.00i	− 0.559809i
$213$	1284.00i	0.413043i
$214$	228.000	0.0728307
$215$	0	0
$216$	−800.000	−0.252005
$217$	− 992.000i	− 0.310329i
$218$	2920.00i	0.907190i
$219$	−974.000	−0.300533
$220$	0	0
$221$	−3588.00	−1.09210
$222$	− 904.000i	− 0.273300i
$223$	− 518.000i	− 0.155551i	−0.996971	−	0.0777754i	$-0.975218\pi$
$223$	− 518.000i	− 0.155551i	0.996971	−	0.0777754i	$-0.0247817\pi$
$224$	−992.000	−0.295896
$225$	0	0
$226$	1644.00	0.483882
$227$	2844.00i	0.831555i	0.909466	+	0.415777i	$0.136490\pi$
$227$	2844.00i	0.831555i	−0.909466	+	0.415777i	$0.863510\pi$
$228$	152.000i	0.0441511i
$229$	−1745.00	−0.503550	−0.251775	−	0.967786i	$-0.581014\pi$
$229$	−1745.00	−0.503550	−0.251775	+	0.967786i	$0.581014\pi$
$230$	0	0
$231$	3534.00	1.00658
$232$	1200.00i	0.339586i
$233$	− 5283.00i	− 1.48541i	−0.669618	−	0.742706i	$-0.733542\pi$
$233$	− 5283.00i	− 1.48541i	0.669618	−	0.742706i	$-0.266458\pi$
$234$	2392.00	0.668248
$235$	0	0
$236$	−1320.00	−0.364088
$237$	1400.00i	0.383712i
$238$	− 4278.00i	− 1.16513i
$239$	−465.000	−0.125851	−0.0629254	−	0.998018i	$-0.520043\pi$
$239$	−465.000	−0.125851	−0.0629254	+	0.998018i	$0.520043\pi$
$240$	0	0
$241$	−7078.00	−1.89184	−0.945921	−	0.324396i	$-0.894839\pi$
$241$	−7078.00	−1.89184	−0.945921	+	0.324396i	$0.894839\pi$
$242$	− 3836.00i	− 1.01896i
$243$	3542.00i	0.935059i
$244$	52.0000	0.0136433
$245$	0	0
$246$	−1032.00	−0.267471
$247$	− 988.000i	− 0.254514i
$248$	256.000i	0.0655485i
$249$	−24.0000	−0.00610819
$250$	0	0
$251$	3567.00	0.897000	0.448500	−	0.893783i	$-0.351958\pi$
$251$	3567.00	0.897000	0.448500	+	0.893783i	$0.351958\pi$
$252$	2852.00i	0.712933i
$253$	4104.00i	1.01983i
$254$	−4172.00	−1.03061
$255$	0	0
$256$	256.000	0.0625000
$257$	− 1896.00i	− 0.460192i	−0.973168	−	0.230096i	$-0.926096\pi$
$257$	− 1896.00i	− 0.460192i	0.973168	−	0.230096i	$-0.0739039\pi$
$258$	268.000i	0.0646704i
$259$	−7006.00	−1.68082
$260$	0	0
$261$	3450.00	0.818198
$262$	186.000i	0.0438592i
$263$	57.0000i	0.0133641i	0.999978	+	0.00668207i	$0.00212699\pi$
$263$	57.0000i	0.0133641i	−0.999978	+	0.00668207i	$0.997873\pi$
$264$	−912.000	−0.212613
$265$	0	0
$266$	1178.00	0.271533
$267$	1200.00i	0.275052i
$268$	3424.00i	0.780426i
$269$	−2700.00	−0.611977	−0.305989	−	0.952035i	$-0.598987\pi$
$269$	−2700.00	−0.611977	−0.305989	+	0.952035i	$0.598987\pi$
$270$	0	0
$271$	3872.00	0.867923	0.433962	−	0.900931i	$-0.357115\pi$
$271$	3872.00	0.867923	0.433962	+	0.900931i	$0.357115\pi$
$272$	1104.00i	0.246102i
$273$	3224.00i	0.714745i
$274$	2538.00	0.559585
$275$	0	0
$276$	576.000	0.125620
$277$	− 7711.00i	− 1.67260i	−0.548275	−	0.836298i	$-0.684715\pi$
$277$	− 7711.00i	− 1.67260i	0.548275	−	0.836298i	$-0.315285\pi$
$278$	− 3950.00i	− 0.852177i
$279$	736.000	0.157932
$280$	0	0
$281$	−6858.00	−1.45592	−0.727961	−	0.685619i	$-0.759532\pi$
$281$	−6858.00	−1.45592	−0.727961	+	0.685619i	$0.759532\pi$
$282$	2316.00i	0.489063i
$283$	1807.00i	0.379558i	0.981827	+	0.189779i	$0.0607772\pi$
$283$	1807.00i	0.379558i	−0.981827	+	0.189779i	$0.939223\pi$
$284$	−2568.00	−0.536559
$285$	0	0
$286$	5928.00	1.22563
$287$	7998.00i	1.64497i
$288$	− 736.000i	− 0.150588i
$289$	152.000	0.0309383
$290$	0	0
$291$	−2848.00	−0.573721
$292$	− 1948.00i	− 0.390404i
$293$	3012.00i	0.600556i	0.953852	+	0.300278i	$0.0970795\pi$
$293$	3012.00i	0.600556i	−0.953852	+	0.300278i	$0.902921\pi$
$294$	−2472.00	−0.490374
$295$	0	0
$296$	1808.00	0.355027
$297$	5700.00i	1.11363i
$298$	− 3390.00i	− 0.658985i
$299$	−3744.00	−0.724151
$300$	0	0
$301$	2077.00	0.397729
$302$	− 3604.00i	− 0.686712i
$303$	2124.00i	0.402708i
$304$	−304.000	−0.0573539
$305$	0	0
$306$	3174.00	0.592959
$307$	− 1096.00i	− 0.203753i	−0.994797	−	0.101876i	$-0.967515\pi$
$307$	− 1096.00i	− 0.203753i	0.994797	−	0.101876i	$-0.0324846\pi$
$308$	7068.00i	1.30759i
$309$	2356.00	0.433748
$310$	0	0
$311$	1947.00	0.354998	0.177499	−	0.984121i	$-0.443199\pi$
$311$	1947.00	0.354998	0.177499	+	0.984121i	$0.443199\pi$
$312$	− 832.000i	− 0.150970i
$313$	− 7598.00i	− 1.37209i	−0.727559	−	0.686045i	$-0.759345\pi$
$313$	− 7598.00i	− 1.37209i	0.727559	−	0.686045i	$-0.240655\pi$
$314$	−6452.00	−1.15958
$315$	0	0
$316$	−2800.00	−0.498457
$317$	8334.00i	1.47661i	0.674469	+	0.738303i	$0.264373\pi$
$317$	8334.00i	1.47661i	−0.674469	+	0.738303i	$0.735627\pi$
$318$	1728.00i	0.304721i
$319$	8550.00	1.50065
$320$	0	0
$321$	−228.000	−0.0396440
$322$	− 4464.00i	− 0.772575i
$323$	− 1311.00i	− 0.225839i
$324$	−1684.00	−0.288752
$325$	0	0
$326$	−2536.00	−0.430847
$327$	− 2920.00i	− 0.493812i
$328$	− 2064.00i	− 0.347455i
$329$	17949.0	3.00778
$330$	0	0
$331$	−8368.00	−1.38957	−0.694784	−	0.719219i	$-0.744500\pi$
$331$	−8368.00	−1.38957	−0.694784	+	0.719219i	$0.744500\pi$
$332$	− 48.0000i	− 0.00793477i
$333$	− 5198.00i	− 0.855401i
$334$	1308.00	0.214283
$335$	0	0
$336$	992.000	0.161066
$337$	− 10336.0i	− 1.67074i	−0.549692	−	0.835368i	$-0.685255\pi$
$337$	− 10336.0i	− 1.67074i	0.549692	−	0.835368i	$-0.314745\pi$
$338$	1014.00i	0.163178i
$339$	−1644.00	−0.263392
$340$	0	0
$341$	1824.00	0.289663
$342$	874.000i	0.138189i
$343$	8525.00i	1.34200i
$344$	−536.000	−0.0840093
$345$	0	0
$346$	2724.00	0.423246
$347$	6879.00i	1.06422i	0.846675	+	0.532110i	$0.178601\pi$
$347$	6879.00i	1.06422i	−0.846675	+	0.532110i	$0.821399\pi$
$348$	− 1200.00i	− 0.184847i
$349$	6355.00	0.974714	0.487357	−	0.873203i	$-0.337961\pi$
$349$	6355.00	0.974714	0.487357	+	0.873203i	$0.337961\pi$
$350$	0	0
$351$	−5200.00	−0.790756
$352$	− 1824.00i	− 0.276192i
$353$	− 7218.00i	− 1.08832i	−0.838983	−	0.544158i	$-0.816849\pi$
$353$	− 7218.00i	− 1.08832i	0.838983	−	0.544158i	$-0.183151\pi$
$354$	1320.00	0.198184
$355$	0	0
$356$	−2400.00	−0.357303
$357$	4278.00i	0.634218i
$358$	− 420.000i	− 0.0620047i
$359$	−1665.00	−0.244778	−0.122389	−	0.992482i	$-0.539056\pi$
$359$	−1665.00	−0.244778	−0.122389	+	0.992482i	$0.539056\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	− 4.00000i	0 0.000580761i
$363$	3836.00i	0.554650i
$364$	−6448.00	−0.928481
$365$	0	0
$366$	−52.0000	−0.00742646
$367$	13064.0i	1.85813i	0.369911	+	0.929067i	$0.379388\pi$
$367$	13064.0i	1.85813i	−0.369911	+	0.929067i	$0.620612\pi$
$368$	1152.00i	0.163185i
$369$	−5934.00	−0.837159
$370$	0	0
$371$	13392.0	1.87406
$372$	− 256.000i	− 0.0356801i
$373$	10492.0i	1.45645i	0.685339	+	0.728224i	$0.259654\pi$
$373$	10492.0i	1.45645i	−0.685339	+	0.728224i	$0.740346\pi$
$374$	7866.00	1.08754
$375$	0	0
$376$	−4632.00	−0.635312
$377$	7800.00i	1.06557i
$378$	− 6200.00i	− 0.843634i
$379$	−7610.00	−1.03140	−0.515698	−	0.856770i	$-0.672468\pi$
$379$	−7610.00	−1.03140	−0.515698	+	0.856770i	$0.672468\pi$
$380$	0	0
$381$	4172.00	0.560992
$382$	5286.00i	0.707998i
$383$	− 4008.00i	− 0.534724i	−0.963596	−	0.267362i	$-0.913848\pi$
$383$	− 4008.00i	− 0.534724i	0.963596	−	0.267362i	$-0.0861519\pi$
$384$	−256.000	−0.0340207
$385$	0	0
$386$	−6496.00	−0.856574
$387$	1541.00i	0.202412i
$388$	− 5696.00i	− 0.745285i
$389$	3525.00	0.459446	0.229723	−	0.973256i	$-0.426218\pi$
$389$	3525.00	0.459446	0.229723	+	0.973256i	$0.426218\pi$
$390$	0	0
$391$	−4968.00	−0.642564
$392$	− 4944.00i	− 0.637015i
$393$	− 186.000i	− 0.0238739i
$394$	−6252.00	−0.799419
$395$	0	0
$396$	−5244.00	−0.665457
$397$	6629.00i	0.838035i	0.907978	+	0.419018i	$0.137625\pi$
$397$	6629.00i	0.838035i	−0.907978	+	0.419018i	$0.862375\pi$
$398$	− 5990.00i	− 0.754401i
$399$	−1178.00	−0.147804
$400$	0	0
$401$	−10848.0	−1.35093	−0.675465	−	0.737392i	$-0.736057\pi$
$401$	−10848.0	−1.35093	−0.675465	+	0.737392i	$0.736057\pi$
$402$	− 3424.00i	− 0.424810i
$403$	1664.00i	0.205682i
$404$	−4248.00	−0.523133
$405$	0	0
$406$	−9300.00	−1.13683
$407$	− 12882.0i	− 1.56889i
$408$	− 1104.00i	− 0.133961i
$409$	3040.00	0.367526	0.183763	−	0.982971i	$-0.441172\pi$
$409$	3040.00	0.367526	0.183763	+	0.982971i	$0.441172\pi$
$410$	0	0
$411$	−2538.00	−0.304599
$412$	4712.00i	0.563455i
$413$	− 10230.0i	− 1.21885i
$414$	3312.00	0.393179
$415$	0	0
$416$	1664.00	0.196116
$417$	3950.00i	0.463867i
$418$	2166.00i	0.253451i
$419$	3900.00	0.454719	0.227360	−	0.973811i	$-0.426991\pi$
$419$	3900.00	0.454719	0.227360	+	0.973811i	$0.426991\pi$
$420$	0	0
$421$	4412.00	0.510755	0.255377	−	0.966841i	$-0.417800\pi$
$421$	4412.00	0.510755	0.255377	+	0.966841i	$0.417800\pi$
$422$	8636.00i	0.996194i
$423$	13317.0i	1.53072i
$424$	−3456.00	−0.395845
$425$	0	0
$426$	2568.00	0.292066
$427$	403.000i	0.0456734i
$428$	− 456.000i	− 0.0514990i
$429$	−5928.00	−0.667148
$430$	0	0
$431$	432.000	0.0482801	0.0241400	−	0.999709i	$-0.492315\pi$
$431$	432.000	0.0482801	0.0241400	+	0.999709i	$0.492315\pi$
$432$	1600.00i	0.178195i
$433$	2002.00i	0.222194i	0.993810	+	0.111097i	$0.0354364\pi$
$433$	2002.00i	0.222194i	−0.993810	+	0.111097i	$0.964564\pi$
$434$	−1984.00	−0.219436
$435$	0	0
$436$	5840.00	0.641480
$437$	− 1368.00i	− 0.149749i
$438$	1948.00i	0.212509i
$439$	1690.00	0.183734	0.0918671	−	0.995771i	$-0.470717\pi$
$439$	1690.00	0.183734	0.0918671	+	0.995771i	$0.470717\pi$
$440$	0	0
$441$	−14214.0	−1.53482
$442$	7176.00i	0.772234i
$443$	1977.00i	0.212032i	0.994364	+	0.106016i	$0.0338095\pi$
$443$	1977.00i	0.212032i	−0.994364	+	0.106016i	$0.966191\pi$
$444$	−1808.00	−0.193252
$445$	0	0
$446$	−1036.00	−0.109991
$447$	3390.00i	0.358706i
$448$	1984.00i	0.209230i
$449$	2760.00	0.290095	0.145047	−	0.989425i	$-0.453667\pi$
$449$	2760.00	0.290095	0.145047	+	0.989425i	$0.453667\pi$
$450$	0	0
$451$	−14706.0	−1.53543
$452$	− 3288.00i	− 0.342156i
$453$	3604.00i	0.373798i
$454$	5688.00	0.587998
$455$	0	0
$456$	304.000	0.0312195
$457$	4499.00i	0.460513i	0.973130	+	0.230256i	$0.0739565\pi$
$457$	4499.00i	0.460513i	−0.973130	+	0.230256i	$0.926044\pi$
$458$	3490.00i	0.356063i
$459$	−6900.00	−0.701665
$460$	0	0
$461$	−11643.0	−1.17629	−0.588144	−	0.808756i	$-0.700141\pi$
$461$	−11643.0	−1.17629	−0.588144	+	0.808756i	$0.700141\pi$
$462$	− 7068.00i	− 0.711760i
$463$	1537.00i	0.154277i	0.997020	+	0.0771387i	$0.0245784\pi$
$463$	1537.00i	0.154277i	−0.997020	+	0.0771387i	$0.975422\pi$
$464$	2400.00	0.240123
$465$	0	0
$466$	−10566.0	−1.05034
$467$	− 7641.00i	− 0.757138i	−0.925573	−	0.378569i	$-0.876416\pi$
$467$	− 7641.00i	− 0.757138i	0.925573	−	0.378569i	$-0.123584\pi$
$468$	− 4784.00i	− 0.472522i
$469$	−26536.0	−2.61262
$470$	0	0
$471$	6452.00	0.631194
$472$	2640.00i	0.257449i
$473$	3819.00i	0.371243i
$474$	2800.00	0.271325
$475$	0	0
$476$	−8556.00	−0.823873
$477$	9936.00i	0.953749i
$478$	930.000i	0.0889900i
$479$	8580.00	0.818435	0.409217	−	0.912437i	$-0.365802\pi$
$479$	8580.00	0.818435	0.409217	+	0.912437i	$0.365802\pi$
$480$	0	0
$481$	11752.0	1.11402
$482$	14156.0i	1.33773i
$483$	4464.00i	0.420536i
$484$	−7672.00	−0.720511
$485$	0	0
$486$	7084.00	0.661187
$487$	12134.0i	1.12904i	0.825418	+	0.564522i	$0.190939\pi$
$487$	12134.0i	1.12904i	−0.825418	+	0.564522i	$0.809061\pi$
$488$	− 104.000i	− 0.00964725i
$489$	2536.00	0.234523
$490$	0	0
$491$	−5508.00	−0.506258	−0.253129	−	0.967433i	$-0.581460\pi$
$491$	−5508.00	−0.506258	−0.253129	+	0.967433i	$0.581460\pi$
$492$	2064.00i	0.189131i
$493$	10350.0i	0.945518i
$494$	−1976.00	−0.179969
$495$	0	0
$496$	512.000	0.0463498
$497$	− 19902.0i	− 1.79623i
$498$	48.0000i	0.00431914i
$499$	11905.0	1.06802	0.534009	−	0.845479i	$-0.320685\pi$
$499$	11905.0	1.06802	0.534009	+	0.845479i	$0.320685\pi$
$500$	0	0
$501$	−1308.00	−0.116641
$502$	− 7134.00i	− 0.634275i
$503$	− 9108.00i	− 0.807367i	−0.914899	−	0.403684i	$-0.867730\pi$
$503$	− 9108.00i	− 0.807367i	0.914899	−	0.403684i	$-0.132270\pi$
$504$	5704.00	0.504120
$505$	0	0
$506$	8208.00	0.721127
$507$	− 1014.00i	− 0.0888231i
$508$	8344.00i	0.728750i
$509$	2520.00	0.219444	0.109722	−	0.993962i	$-0.465004\pi$
$509$	2520.00	0.219444	0.109722	+	0.993962i	$0.465004\pi$
$510$	0	0
$511$	15097.0	1.30695
$512$	− 512.000i	− 0.0441942i
$513$	− 1900.00i	− 0.163523i
$514$	−3792.00	−0.325405
$515$	0	0
$516$	536.000	0.0457288
$517$	33003.0i	2.80749i
$518$	14012.0i	1.18852i
$519$	−2724.00	−0.230386
$520$	0	0
$521$	21612.0	1.81735	0.908675	−	0.417505i	$-0.137095\pi$
$521$	21612.0	1.81735	0.908675	+	0.417505i	$0.137095\pi$
$522$	− 6900.00i	− 0.578553i
$523$	9022.00i	0.754311i	0.926150	+	0.377155i	$0.123098\pi$
$523$	9022.00i	0.754311i	−0.926150	+	0.377155i	$0.876902\pi$
$524$	372.000	0.0310132
$525$	0	0
$526$	114.000	0.00944988
$527$	2208.00i	0.182509i
$528$	1824.00i	0.150340i
$529$	6983.00	0.573929
$530$	0	0
$531$	7590.00	0.620297
$532$	− 2356.00i	− 0.192003i
$533$	− 13416.0i	− 1.09027i
$534$	2400.00	0.194491
$535$	0	0
$536$	6848.00	0.551844
$537$	420.000i	0.0337511i
$538$	5400.00i	0.432733i
$539$	−35226.0	−2.81501
$540$	0	0
$541$	−9253.00	−0.735337	−0.367669	−	0.929957i	$-0.619844\pi$
$541$	−9253.00	−0.735337	−0.367669	+	0.929957i	$0.619844\pi$
$542$	− 7744.00i	− 0.613715i
$543$	4.00000i	0 0.000316126i
$544$	2208.00	0.174021
$545$	0	0
$546$	6448.00	0.505401
$547$	13244.0i	1.03523i	0.855613	+	0.517617i	$0.173181\pi$
$547$	13244.0i	1.03523i	−0.855613	+	0.517617i	$0.826819\pi$
$548$	− 5076.00i	− 0.395686i
$549$	−299.000	−0.0232441
$550$	0	0
$551$	−2850.00	−0.220352
$552$	− 1152.00i	− 0.0888268i
$553$	− 21700.0i	− 1.66868i
$554$	−15422.0	−1.18270
$555$	0	0
$556$	−7900.00	−0.602580
$557$	1569.00i	0.119355i	0.998218	+	0.0596774i	$0.0190072\pi$
$557$	1569.00i	0.119355i	−0.998218	+	0.0596774i	$0.980993\pi$
$558$	− 1472.00i	− 0.111675i
$559$	−3484.00	−0.263609
$560$	0	0
$561$	−7866.00	−0.591984
$562$	13716.0i	1.02949i
$563$	15762.0i	1.17991i	0.807436	+	0.589955i	$0.200854\pi$
$563$	15762.0i	1.17991i	−0.807436	+	0.589955i	$0.799146\pi$
$564$	4632.00	0.345820
$565$	0	0
$566$	3614.00	0.268388
$567$	− 13051.0i	− 0.966650i
$568$	5136.00i	0.379405i
$569$	13800.0	1.01674	0.508371	−	0.861138i	$-0.330248\pi$
$569$	13800.0	1.01674	0.508371	+	0.861138i	$0.330248\pi$
$570$	0	0
$571$	−4348.00	−0.318666	−0.159333	−	0.987225i	$-0.550934\pi$
$571$	−4348.00	−0.318666	−0.159333	+	0.987225i	$0.550934\pi$
$572$	− 11856.0i	− 0.866651i
$573$	− 5286.00i	− 0.385385i
$574$	15996.0	1.16317
$575$	0	0
$576$	−1472.00	−0.106481
$577$	3539.00i	0.255339i	0.991817	+	0.127669i	$0.0407497\pi$
$577$	3539.00i	0.255339i	−0.991817	+	0.127669i	$0.959250\pi$
$578$	− 304.000i	− 0.0218767i
$579$	6496.00	0.466260
$580$	0	0
$581$	372.000	0.0265631
$582$	5696.00i	0.405682i
$583$	24624.0i	1.74927i
$584$	−3896.00	−0.276058
$585$	0	0
$586$	6024.00	0.424657
$587$	− 6321.00i	− 0.444456i	−0.974995	−	0.222228i	$-0.928667\pi$
$587$	− 6321.00i	− 0.444456i	0.974995	−	0.222228i	$-0.0713329\pi$
$588$	4944.00i	0.346747i
$589$	−608.000	−0.0425335
$590$	0	0
$591$	6252.00	0.435149
$592$	− 3616.00i	− 0.251042i
$593$	− 13278.0i	− 0.919498i	−0.888049	−	0.459749i	$-0.847939\pi$
$593$	− 13278.0i	− 0.919498i	0.888049	−	0.459749i	$-0.152061\pi$
$594$	11400.0	0.787454
$595$	0	0
$596$	−6780.00	−0.465973
$597$	5990.00i	0.410644i
$598$	7488.00i	0.512052i
$599$	−20400.0	−1.39152	−0.695761	−	0.718274i	$-0.744933\pi$
$599$	−20400.0	−1.39152	−0.695761	+	0.718274i	$0.744933\pi$
$600$	0	0
$601$	−22198.0	−1.50661	−0.753307	−	0.657669i	$-0.771543\pi$
$601$	−22198.0	−1.50661	−0.753307	+	0.657669i	$0.771543\pi$
$602$	− 4154.00i	− 0.281237i
$603$	− 19688.0i	− 1.32961i
$604$	−7208.00	−0.485578
$605$	0	0
$606$	4248.00	0.284758
$607$	9824.00i	0.656909i	0.944520	+	0.328455i	$0.106528\pi$
$607$	9824.00i	0.656909i	−0.944520	+	0.328455i	$0.893472\pi$
$608$	608.000i	0.0405554i
$609$	9300.00	0.618810
$610$	0	0
$611$	−30108.0	−1.99352
$612$	− 6348.00i	− 0.419285i
$613$	4327.00i	0.285099i	0.989788	+	0.142550i	$0.0455301\pi$
$613$	4327.00i	0.285099i	−0.989788	+	0.142550i	$0.954470\pi$
$614$	−2192.00	−0.144075
$615$	0	0
$616$	14136.0	0.924603
$617$	− 14151.0i	− 0.923335i	−0.887053	−	0.461668i	$-0.847251\pi$
$617$	− 14151.0i	− 0.923335i	0.887053	−	0.461668i	$-0.152749\pi$
$618$	− 4712.00i	− 0.306706i
$619$	−22460.0	−1.45839	−0.729195	−	0.684306i	$-0.760105\pi$
$619$	−22460.0	−1.45839	−0.729195	+	0.684306i	$0.760105\pi$
$620$	0	0
$621$	−7200.00	−0.465259
$622$	− 3894.00i	− 0.251021i
$623$	− 18600.0i	− 1.19614i
$624$	−1664.00	−0.106752
$625$	0	0
$626$	−15196.0	−0.970215
$627$	− 2166.00i	− 0.137961i
$628$	12904.0i	0.819945i
$629$	15594.0	0.988511
$630$	0	0
$631$	−16363.0	−1.03233	−0.516165	−	0.856489i	$-0.672641\pi$
$631$	−16363.0	−1.03233	−0.516165	+	0.856489i	$0.672641\pi$
$632$	5600.00i	0.352462i
$633$	− 8636.00i	− 0.542259i
$634$	16668.0	1.04412
$635$	0	0
$636$	3456.00	0.215471
$637$	− 32136.0i	− 1.99886i
$638$	− 17100.0i	− 1.06112i
$639$	14766.0	0.914138
$640$	0	0
$641$	5592.00	0.344572	0.172286	−	0.985047i	$-0.444885\pi$
$641$	5592.00	0.344572	0.172286	+	0.985047i	$0.444885\pi$
$642$	456.000i	0.0280325i
$643$	− 16553.0i	− 1.01522i	−0.861587	−	0.507610i	$-0.830529\pi$
$643$	− 16553.0i	− 1.01522i	0.861587	−	0.507610i	$-0.169471\pi$
$644$	−8928.00	−0.546293
$645$	0	0
$646$	−2622.00	−0.159692
$647$	− 4611.00i	− 0.280181i	−0.990139	−	0.140091i	$-0.955261\pi$
$647$	− 4611.00i	− 0.280181i	0.990139	−	0.140091i	$-0.0447394\pi$
$648$	3368.00i	0.204178i
$649$	18810.0	1.13768
$650$	0	0
$651$	1984.00	0.119446
$652$	5072.00i	0.304655i
$653$	− 16413.0i	− 0.983599i	−0.870708	−	0.491800i	$-0.836339\pi$
$653$	− 16413.0i	− 0.983599i	0.870708	−	0.491800i	$-0.163661\pi$
$654$	−5840.00	−0.349177
$655$	0	0
$656$	−4128.00	−0.245688
$657$	11201.0i	0.665133i
$658$	− 35898.0i	− 2.12682i
$659$	−27390.0	−1.61906	−0.809532	−	0.587076i	$-0.800279\pi$
$659$	−27390.0	−1.61906	−0.809532	+	0.587076i	$0.800279\pi$
$660$	0	0
$661$	26912.0	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$661$	26912.0	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$662$	16736.0i	0.982573i
$663$	− 7176.00i	− 0.420351i
$664$	−96.0000	−0.00561073
$665$	0	0
$666$	−10396.0	−0.604860
$667$	10800.0i	0.626953i
$668$	− 2616.00i	− 0.151521i
$669$	1036.00	0.0598716
$670$	0	0
$671$	−741.000	−0.0426319
$672$	− 1984.00i	− 0.113891i
$673$	21562.0i	1.23500i	0.786571	+	0.617499i	$0.211854\pi$
$673$	21562.0i	1.23500i	−0.786571	+	0.617499i	$0.788146\pi$
$674$	−20672.0	−1.18139
$675$	0	0
$676$	2028.00	0.115385
$677$	− 21966.0i	− 1.24700i	−0.781822	−	0.623502i	$-0.785709\pi$
$677$	− 21966.0i	− 1.24700i	0.781822	−	0.623502i	$-0.214291\pi$
$678$	3288.00i	0.186246i
$679$	44144.0	2.49498
$680$	0	0
$681$	−5688.00	−0.320066
$682$	− 3648.00i	− 0.204823i
$683$	− 15348.0i	− 0.859846i	−0.902866	−	0.429923i	$-0.858541\pi$
$683$	− 15348.0i	− 0.859846i	0.902866	−	0.429923i	$-0.141459\pi$
$684$	1748.00	0.0977141
$685$	0	0
$686$	17050.0	0.948939
$687$	− 3490.00i	− 0.193816i
$688$	1072.00i	0.0594035i
$689$	−22464.0	−1.24210
$690$	0	0
$691$	8147.00	0.448519	0.224259	−	0.974529i	$-0.428004\pi$
$691$	8147.00	0.448519	0.224259	+	0.974529i	$0.428004\pi$
$692$	− 5448.00i	− 0.299280i
$693$	− 40641.0i	− 2.22774i
$694$	13758.0	0.752517
$695$	0	0
$696$	−2400.00	−0.130707
$697$	− 17802.0i	− 0.967430i
$698$	− 12710.0i	− 0.689227i
$699$	10566.0	0.571735
$700$	0	0
$701$	14982.0	0.807222	0.403611	−	0.914931i	$-0.367755\pi$
$701$	14982.0	0.807222	0.403611	+	0.914931i	$0.367755\pi$
$702$	10400.0i	0.559149i
$703$	4294.00i	0.230372i
$704$	−3648.00	−0.195297
$705$	0	0
$706$	−14436.0	−0.769555
$707$	− 32922.0i	− 1.75129i
$708$	− 2640.00i	− 0.140137i
$709$	−21890.0	−1.15952	−0.579758	−	0.814789i	$-0.696853\pi$
$709$	−21890.0	−1.15952	−0.579758	+	0.814789i	$0.696853\pi$
$710$	0	0
$711$	16100.0	0.849222
$712$	4800.00i	0.252651i
$713$	2304.00i	0.121018i
$714$	8556.00	0.448460
$715$	0	0
$716$	−840.000	−0.0438440
$717$	− 930.000i	− 0.0484400i
$718$	3330.00i	0.173084i
$719$	27015.0	1.40124	0.700619	−	0.713536i	$-0.252907\pi$
$719$	27015.0	1.40124	0.700619	+	0.713536i	$0.252907\pi$
$720$	0	0
$721$	−36518.0	−1.88627
$722$	− 722.000i	− 0.0372161i
$723$	− 14156.0i	− 0.728171i
$724$	−8.00000	−0.000410660 0
$725$	0	0
$726$	7672.00	0.392196
$727$	− 13021.0i	− 0.664267i	−0.943232	−	0.332134i	$-0.892232\pi$
$727$	− 13021.0i	− 0.664267i	0.943232	−	0.332134i	$-0.107768\pi$
$728$	12896.0i	0.656535i
$729$	4283.00	0.217599
$730$	0	0
$731$	−4623.00	−0.233909
$732$	104.000i	0.00525130i
$733$	6262.00i	0.315542i	0.987476	+	0.157771i	$0.0504308\pi$
$733$	6262.00i	0.315542i	−0.987476	+	0.157771i	$0.949569\pi$
$734$	26128.0	1.31390
$735$	0	0
$736$	2304.00	0.115389
$737$	− 48792.0i	− 2.43864i
$738$	11868.0i	0.591961i
$739$	10855.0	0.540335	0.270168	−	0.962813i	$-0.412921\pi$
$739$	10855.0	0.540335	0.270168	+	0.962813i	$0.412921\pi$
$740$	0	0
$741$	1976.00	0.0979624
$742$	− 26784.0i	− 1.32516i
$743$	14892.0i	0.735309i	0.929962	+	0.367654i	$0.119839\pi$
$743$	14892.0i	0.735309i	−0.929962	+	0.367654i	$0.880161\pi$
$744$	−512.000	−0.0252296
$745$	0	0
$746$	20984.0	1.02986
$747$	276.000i	0.0135185i
$748$	− 15732.0i	− 0.769009i
$749$	3534.00	0.172403
$750$	0	0
$751$	28952.0	1.40676	0.703378	−	0.710816i	$-0.251674\pi$
$751$	28952.0	1.40676	0.703378	+	0.710816i	$0.251674\pi$
$752$	9264.00i	0.449233i
$753$	7134.00i	0.345256i
$754$	15600.0	0.753473
$755$	0	0
$756$	−12400.0	−0.596539
$757$	− 3541.00i	− 0.170013i	−0.996380	−	0.0850065i	$-0.972909\pi$
$757$	− 3541.00i	− 0.170013i	0.996380	−	0.0850065i	$-0.0270911\pi$
$758$	15220.0i	0.729308i
$759$	−8208.00	−0.392532
$760$	0	0
$761$	22617.0	1.07735	0.538676	−	0.842513i	$-0.318925\pi$
$761$	22617.0	1.07735	0.538676	+	0.842513i	$0.318925\pi$
$762$	− 8344.00i	− 0.396681i
$763$	45260.0i	2.14747i
$764$	10572.0	0.500630
$765$	0	0
$766$	−8016.00	−0.378107
$767$	17160.0i	0.807838i
$768$	512.000i	0.0240563i
$769$	−11495.0	−0.539038	−0.269519	−	0.962995i	$-0.586865\pi$
$769$	−11495.0	−0.539038	−0.269519	+	0.962995i	$0.586865\pi$
$770$	0	0
$771$	3792.00	0.177128
$772$	12992.0i	0.605690i
$773$	14622.0i	0.680358i	0.940361	+	0.340179i	$0.110488\pi$
$773$	14622.0i	0.680358i	−0.940361	+	0.340179i	$0.889512\pi$
$774$	3082.00	0.143127
$775$	0	0
$776$	−11392.0	−0.526996
$777$	− 14012.0i	− 0.646947i
$778$	− 7050.00i	− 0.324878i
$779$	4902.00	0.225459
$780$	0	0
$781$	36594.0	1.67661
$782$	9936.00i	0.454361i
$783$	15000.0i	0.684618i
$784$	−9888.00	−0.450437
$785$	0	0
$786$	−372.000	−0.0168814
$787$	7124.00i	0.322672i	0.986900	+	0.161336i	$0.0515803\pi$
$787$	7124.00i	0.322672i	−0.986900	+	0.161336i	$0.948420\pi$
$788$	12504.0i	0.565275i
$789$	−114.000	−0.00514386
$790$	0	0
$791$	25482.0	1.14543
$792$	10488.0i	0.470549i
$793$	− 676.000i	− 0.0302717i
$794$	13258.0	0.592580
$795$	0	0
$796$	−11980.0	−0.533442
$797$	− 3576.00i	− 0.158932i	−0.996838	−	0.0794658i	$-0.974679\pi$
$797$	− 3576.00i	− 0.158932i	0.996838	−	0.0794658i	$-0.0253214\pi$
$798$	2356.00i	0.104513i
$799$	−39951.0	−1.76892
$800$	0	0
$801$	13800.0	0.608738
$802$	21696.0i	0.955252i
$803$	27759.0i	1.21992i
$804$	−6848.00	−0.300386
$805$	0	0
$806$	3328.00	0.145439
$807$	− 5400.00i	− 0.235550i
$808$	8496.00i	0.369911i
$809$	−42855.0	−1.86242	−0.931212	−	0.364477i	$-0.881248\pi$
$809$	−42855.0	−1.86242	−0.931212	+	0.364477i	$0.881248\pi$
$810$	0	0
$811$	−15568.0	−0.674065	−0.337032	−	0.941493i	$-0.609423\pi$
$811$	−15568.0	−0.674065	−0.337032	+	0.941493i	$0.609423\pi$
$812$	18600.0i	0.803857i
$813$	7744.00i	0.334064i
$814$	−25764.0	−1.10937
$815$	0	0
$816$	−2208.00	−0.0947248
$817$	− 1273.00i	− 0.0545124i
$818$	− 6080.00i	− 0.259880i
$819$	37076.0	1.58186
$820$	0	0
$821$	2517.00	0.106996	0.0534981	−	0.998568i	$-0.482963\pi$
$821$	2517.00	0.106996	0.0534981	+	0.998568i	$0.482963\pi$
$822$	5076.00i	0.215384i
$823$	9727.00i	0.411983i	0.978554	+	0.205991i	$0.0660419\pi$
$823$	9727.00i	0.411983i	−0.978554	+	0.205991i	$0.933958\pi$
$824$	9424.00	0.398423
$825$	0	0
$826$	−20460.0	−0.861858
$827$	28224.0i	1.18675i	0.804925	+	0.593376i	$0.202205\pi$
$827$	28224.0i	1.18675i	−0.804925	+	0.593376i	$0.797795\pi$
$828$	− 6624.00i	− 0.278019i
$829$	−3080.00	−0.129038	−0.0645192	−	0.997916i	$-0.520551\pi$
$829$	−3080.00	−0.129038	−0.0645192	+	0.997916i	$0.520551\pi$
$830$	0	0
$831$	15422.0	0.643782
$832$	− 3328.00i	− 0.138675i
$833$	− 42642.0i	− 1.77366i
$834$	7900.00	0.328003
$835$	0	0
$836$	4332.00	0.179217
$837$	3200.00i	0.132148i
$838$	− 7800.00i	− 0.321535i
$839$	−26790.0	−1.10238	−0.551188	−	0.834381i	$-0.685825\pi$
$839$	−26790.0	−1.10238	−0.551188	+	0.834381i	$0.685825\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	− 8824.00i	− 0.361158i
$843$	− 13716.0i	− 0.560385i
$844$	17272.0	0.704416
$845$	0	0
$846$	26634.0	1.08238
$847$	− 59458.0i	− 2.41204i
$848$	6912.00i	0.279905i
$849$	−3614.00	−0.146092
$850$	0	0
$851$	16272.0	0.655461
$852$	− 5136.00i	− 0.206522i
$853$	− 19178.0i	− 0.769803i	−0.922958	−	0.384902i	$-0.874235\pi$
$853$	− 19178.0i	− 0.769803i	0.922958	−	0.384902i	$-0.125765\pi$
$854$	806.000	0.0322960
$855$	0	0
$856$	−912.000	−0.0364153
$857$	− 2406.00i	− 0.0959013i	−0.998850	−	0.0479506i	$-0.984731\pi$
$857$	− 2406.00i	− 0.0959013i	0.998850	−	0.0479506i	$-0.0152690\pi$
$858$	11856.0i	0.471745i
$859$	−9125.00	−0.362446	−0.181223	−	0.983442i	$-0.558006\pi$
$859$	−9125.00	−0.362446	−0.181223	+	0.983442i	$0.558006\pi$
$860$	0	0
$861$	−15996.0	−0.633150
$862$	− 864.000i	− 0.0341392i
$863$	− 8898.00i	− 0.350975i	−0.984482	−	0.175488i	$-0.943850\pi$
$863$	− 8898.00i	− 0.350975i	0.984482	−	0.175488i	$-0.0561502\pi$
$864$	3200.00	0.126003
$865$	0	0
$866$	4004.00	0.157115
$867$	304.000i	0.0119082i
$868$	3968.00i	0.155164i
$869$	39900.0	1.55755
$870$	0	0
$871$	44512.0	1.73161
$872$	− 11680.0i	− 0.453595i
$873$	32752.0i	1.26974i
$874$	−2736.00	−0.105889
$875$	0	0
$876$	3896.00	0.150267
$877$	− 15886.0i	− 0.611667i	−0.952085	−	0.305834i	$-0.901065\pi$
$877$	− 15886.0i	− 0.611667i	0.952085	−	0.305834i	$-0.0989351\pi$
$878$	− 3380.00i	− 0.129920i
$879$	−6024.00	−0.231154
$880$	0	0
$881$	−25683.0	−0.982159	−0.491080	−	0.871115i	$-0.663398\pi$
$881$	−25683.0	−0.982159	−0.491080	+	0.871115i	$0.663398\pi$
$882$	28428.0i	1.08528i
$883$	28267.0i	1.07730i	0.842528	+	0.538652i	$0.181066\pi$
$883$	28267.0i	1.07730i	−0.842528	+	0.538652i	$0.818934\pi$
$884$	14352.0	0.546052
$885$	0	0
$886$	3954.00	0.149929
$887$	− 2466.00i	− 0.0933486i	−0.998910	−	0.0466743i	$-0.985138\pi$
$887$	− 2466.00i	− 0.0933486i	0.998910	−	0.0466743i	$-0.0148623\pi$
$888$	3616.00i	0.136650i
$889$	−64666.0	−2.43963
$890$	0	0
$891$	23997.0	0.902278
$892$	2072.00i	0.0777754i
$893$	− 11001.0i	− 0.412245i
$894$	6780.00	0.253643
$895$	0	0
$896$	3968.00	0.147948
$897$	− 7488.00i	− 0.278726i
$898$	− 5520.00i	− 0.205128i
$899$	4800.00	0.178074
$900$	0	0
$901$	−29808.0	−1.10216
$902$	29412.0i	1.08571i
$903$	4154.00i	0.153086i
$904$	−6576.00	−0.241941
$905$	0	0
$906$	7208.00	0.264315
$907$	29324.0i	1.07353i	0.843733	+	0.536763i	$0.180353\pi$
$907$	29324.0i	1.07353i	−0.843733	+	0.536763i	$0.819647\pi$
$908$	− 11376.0i	− 0.415777i
$909$	24426.0	0.891264
$910$	0	0
$911$	47142.0	1.71447	0.857236	−	0.514924i	$-0.172180\pi$
$911$	47142.0	1.71447	0.857236	+	0.514924i	$0.172180\pi$
$912$	− 608.000i	− 0.0220755i
$913$	684.000i	0.0247942i
$914$	8998.00	0.325632
$915$	0	0
$916$	6980.00	0.251775
$917$	2883.00i	0.103822i
$918$	13800.0i	0.496152i
$919$	39940.0	1.43362	0.716811	−	0.697267i	$-0.245601\pi$
$919$	39940.0	1.43362	0.716811	+	0.697267i	$0.245601\pi$
$920$	0	0
$921$	2192.00	0.0784244
$922$	23286.0i	0.831761i
$923$	33384.0i	1.19052i
$924$	−14136.0	−0.503290
$925$	0	0
$926$	3074.00	0.109091
$927$	− 27094.0i	− 0.959961i
$928$	− 4800.00i	− 0.169793i
$929$	4410.00	0.155745	0.0778727	−	0.996963i	$-0.475187\pi$
$929$	4410.00	0.155745	0.0778727	+	0.996963i	$0.475187\pi$
$930$	0	0
$931$	11742.0	0.413350
$932$	21132.0i	0.742706i
$933$	3894.00i	0.136639i
$934$	−15282.0	−0.535377
$935$	0	0
$936$	−9568.00	−0.334124
$937$	− 41671.0i	− 1.45286i	−0.687239	−	0.726431i	$-0.741178\pi$
$937$	− 41671.0i	− 1.45286i	0.687239	−	0.726431i	$-0.258822\pi$
$938$	53072.0i	1.84740i
$939$	15196.0	0.528118
$940$	0	0
$941$	4062.00	0.140720	0.0703599	−	0.997522i	$-0.477585\pi$
$941$	4062.00	0.140720	0.0703599	+	0.997522i	$0.477585\pi$
$942$	− 12904.0i	− 0.446322i
$943$	− 18576.0i	− 0.641482i
$944$	5280.00	0.182044
$945$	0	0
$946$	7638.00	0.262508
$947$	− 45036.0i	− 1.54538i	−0.634785	−	0.772689i	$-0.718911\pi$
$947$	− 45036.0i	− 1.54538i	0.634785	−	0.772689i	$-0.281089\pi$
$948$	− 5600.00i	− 0.191856i
$949$	−25324.0	−0.866230
$950$	0	0
$951$	−16668.0	−0.568346
$952$	17112.0i	0.582566i
$953$	− 26508.0i	− 0.901027i	−0.892770	−	0.450513i	$-0.851241\pi$
$953$	− 26508.0i	− 0.901027i	0.892770	−	0.450513i	$-0.148759\pi$
$954$	19872.0	0.674402
$955$	0	0
$956$	1860.00	0.0629254
$957$	17100.0i	0.577601i
$958$	− 17160.0i	− 0.578721i
$959$	39339.0	1.32463
$960$	0	0
$961$	−28767.0	−0.965627
$962$	− 23504.0i	− 0.787733i
$963$	2622.00i	0.0877391i
$964$	28312.0	0.945921
$965$	0	0
$966$	8928.00	0.297364
$967$	− 15976.0i	− 0.531286i	−0.964071	−	0.265643i	$-0.914416\pi$
$967$	− 15976.0i	− 0.531286i	0.964071	−	0.265643i	$-0.0855842\pi$
$968$	15344.0i	0.509478i
$969$	2622.00	0.0869255
$970$	0	0
$971$	−39468.0	−1.30442	−0.652208	−	0.758040i	$-0.726157\pi$
$971$	−39468.0	−1.30442	−0.652208	+	0.758040i	$0.726157\pi$
$972$	− 14168.0i	− 0.467530i
$973$	− 61225.0i	− 2.01725i
$974$	24268.0	0.798354
$975$	0	0
$976$	−208.000	−0.00682164
$977$	21804.0i	0.713994i	0.934106	+	0.356997i	$0.116199\pi$
$977$	21804.0i	0.713994i	−0.934106	+	0.356997i	$0.883801\pi$
$978$	− 5072.00i	− 0.165833i
$979$	34200.0	1.11648
$980$	0	0
$981$	−33580.0	−1.09289
$982$	11016.0i	0.357978i
$983$	− 11268.0i	− 0.365609i	−0.983149	−	0.182804i	$-0.941483\pi$
$983$	− 11268.0i	− 0.365609i	0.983149	−	0.182804i	$-0.0585175\pi$
$984$	4128.00	0.133736
$985$	0	0
$986$	20700.0	0.668582
$987$	35898.0i	1.15770i
$988$	3952.00i	0.127257i
$989$	−4824.00	−0.155100
$990$	0	0
$991$	−778.000	−0.0249384	−0.0124692	−	0.999922i	$-0.503969\pi$
$991$	−778.000	−0.0249384	−0.0124692	+	0.999922i	$0.503969\pi$
$992$	− 1024.00i	− 0.0327742i
$993$	− 16736.0i	− 0.534845i
$994$	−39804.0	−1.27013
$995$	0	0
$996$	96.0000	0.00305409
$997$	389.000i	0.0123568i	0.999981	+	0.00617841i	$0.00196666\pi$
$997$	389.000i	0.0123568i	−0.999981	+	0.00617841i	$0.998033\pi$
$998$	− 23810.0i	− 0.755203i
$999$	22600.0	0.715748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.4.b.d.799.1		2
5.2	odd	4		950.4.a.d.1.1		1
5.3	odd	4		38.4.a.a.1.1	✓	1
5.4	even	2	inner	950.4.b.d.799.2		2
15.8	even	4		342.4.a.d.1.1		1
20.3	even	4		304.4.a.a.1.1		1
35.13	even	4		1862.4.a.a.1.1		1
40.3	even	4		1216.4.a.b.1.1		1
40.13	odd	4		1216.4.a.e.1.1		1
95.18	even	4		722.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.a.a.1.1	✓	1	5.3	odd	4
304.4.a.a.1.1		1	20.3	even	4
342.4.a.d.1.1		1	15.8	even	4
722.4.a.d.1.1		1	95.18	even	4
950.4.a.d.1.1		1	5.2	odd	4
950.4.b.d.799.1		2	1.1	even	1	trivial
950.4.b.d.799.2		2	5.4	even	2	inner
1216.4.a.b.1.1		1	40.3	even	4
1216.4.a.e.1.1		1	40.13	odd	4
1862.4.a.a.1.1		1	35.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +4.00000 q^{6} -31.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +4.00000 q^{6} -31.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +57.0000 q^{11} -8.00000i q^{12} +52.0000i q^{13} -62.0000 q^{14} +16.0000 q^{16} +69.0000i q^{17} -46.0000i q^{18} -19.0000 q^{19} +62.0000 q^{21} -114.000i q^{22} +72.0000i q^{23} -16.0000 q^{24} +104.000 q^{26} +100.000i q^{27} +124.000i q^{28} +150.000 q^{29} +32.0000 q^{31} -32.0000i q^{32} +114.000i q^{33} +138.000 q^{34} -92.0000 q^{36} -226.000i q^{37} +38.0000i q^{38} -104.000 q^{39} -258.000 q^{41} -124.000i q^{42} +67.0000i q^{43} -228.000 q^{44} +144.000 q^{46} +579.000i q^{47} +32.0000i q^{48} -618.000 q^{49} -138.000 q^{51} -208.000i q^{52} +432.000i q^{53} +200.000 q^{54} +248.000 q^{56} -38.0000i q^{57} -300.000i q^{58} +330.000 q^{59} -13.0000 q^{61} -64.0000i q^{62} -713.000i q^{63} -64.0000 q^{64} +228.000 q^{66} -856.000i q^{67} -276.000i q^{68} -144.000 q^{69} +642.000 q^{71} +184.000i q^{72} +487.000i q^{73} -452.000 q^{74} +76.0000 q^{76} -1767.00i q^{77} +208.000i q^{78} +700.000 q^{79} +421.000 q^{81} +516.000i q^{82} +12.0000i q^{83} -248.000 q^{84} +134.000 q^{86} +300.000i q^{87} +456.000i q^{88} +600.000 q^{89} +1612.00 q^{91} -288.000i q^{92} +64.0000i q^{93} +1158.00 q^{94} +64.0000 q^{96} +1424.00i q^{97} +1236.00i q^{98} +1311.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 8 q^{6} + 46 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 + 8 * q^6 + 46 * q^9	\( 2 q - 8 q^{4} + 8 q^{6} + 46 q^{9} + 114 q^{11} - 124 q^{14} + 32 q^{16} - 38 q^{19} + 124 q^{21} - 32 q^{24} + 208 q^{26} + 300 q^{29} + 64 q^{31} + 276 q^{34} - 184 q^{36} - 208 q^{39} - 516 q^{41} - 456 q^{44} + 288 q^{46} - 1236 q^{49} - 276 q^{51} + 400 q^{54} + 496 q^{56} + 660 q^{59} - 26 q^{61} - 128 q^{64} + 456 q^{66} - 288 q^{69} + 1284 q^{71} - 904 q^{74} + 152 q^{76} + 1400 q^{79} + 842 q^{81} - 496 q^{84} + 268 q^{86} + 1200 q^{89} + 3224 q^{91} + 2316 q^{94} + 128 q^{96} + 2622 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 + 8 * q^6 + 46 * q^9 + 114 * q^11 - 124 * q^14 + 32 * q^16 - 38 * q^19 + 124 * q^21 - 32 * q^24 + 208 * q^26 + 300 * q^29 + 64 * q^31 + 276 * q^34 - 184 * q^36 - 208 * q^39 - 516 * q^41 - 456 * q^44 + 288 * q^46 - 1236 * q^49 - 276 * q^51 + 400 * q^54 + 496 * q^56 + 660 * q^59 - 26 * q^61 - 128 * q^64 + 456 * q^66 - 288 * q^69 + 1284 * q^71 - 904 * q^74 + 152 * q^76 + 1400 * q^79 + 842 * q^81 - 496 * q^84 + 268 * q^86 + 1200 * q^89 + 3224 * q^91 + 2316 * q^94 + 128 * q^96 + 2622 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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