LMFDB - Embedded newform 1014.4.b.a.337.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,4,Mod(337,1014)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1014.337"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1014.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-6,-8,0,0,0,0,18,-64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$59.8279367458$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.4.b.a.337.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +16.0000i q^{5} -6.00000i q^{6} +28.0000i q^{7} -8.00000i q^{8} +9.00000 q^{9} -32.0000 q^{10} +34.0000i q^{11} +12.0000 q^{12} -56.0000 q^{14} -48.0000i q^{15} +16.0000 q^{16} -138.000 q^{17} +18.0000i q^{18} -108.000i q^{19} -64.0000i q^{20} -84.0000i q^{21} -68.0000 q^{22} +52.0000 q^{23} +24.0000i q^{24} -131.000 q^{25} -27.0000 q^{27} -112.000i q^{28} -190.000 q^{29} +96.0000 q^{30} +176.000i q^{31} +32.0000i q^{32} -102.000i q^{33} -276.000i q^{34} -448.000 q^{35} -36.0000 q^{36} +342.000i q^{37} +216.000 q^{38} +128.000 q^{40} -240.000i q^{41} +168.000 q^{42} +140.000 q^{43} -136.000i q^{44} +144.000i q^{45} +104.000i q^{46} +454.000i q^{47} -48.0000 q^{48} -441.000 q^{49} -262.000i q^{50} +414.000 q^{51} +198.000 q^{53} -54.0000i q^{54} -544.000 q^{55} +224.000 q^{56} +324.000i q^{57} -380.000i q^{58} -154.000i q^{59} +192.000i q^{60} +34.0000 q^{61} -352.000 q^{62} +252.000i q^{63} -64.0000 q^{64} +204.000 q^{66} +656.000i q^{67} +552.000 q^{68} -156.000 q^{69} -896.000i q^{70} -550.000i q^{71} -72.0000i q^{72} +614.000i q^{73} -684.000 q^{74} +393.000 q^{75} +432.000i q^{76} -952.000 q^{77} +8.00000 q^{79} +256.000i q^{80} +81.0000 q^{81} +480.000 q^{82} -762.000i q^{83} +336.000i q^{84} -2208.00i q^{85} +280.000i q^{86} +570.000 q^{87} +272.000 q^{88} -444.000i q^{89} -288.000 q^{90} -208.000 q^{92} -528.000i q^{93} -908.000 q^{94} +1728.00 q^{95} -96.0000i q^{96} -1022.00i q^{97} -882.000i q^{98} +306.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9} - 64 q^{10} + 24 q^{12} - 112 q^{14} + 32 q^{16} - 276 q^{17} - 136 q^{22} + 104 q^{23} - 262 q^{25} - 54 q^{27} - 380 q^{29} + 192 q^{30} - 896 q^{35} - 72 q^{36} + 432 q^{38}+ \cdots + 3456 q^{95}+O(q^{100}) $ 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9 - 64 * q^10 + 24 * q^12 - 112 * q^14 + 32 * q^16 - 276 * q^17 - 136 * q^22 + 104 * q^23 - 262 * q^25 - 54 * q^27 - 380 * q^29 + 192 * q^30 - 896 * q^35 - 72 * q^36 + 432 * q^38 + 256 * q^40 + 336 * q^42 + 280 * q^43 - 96 * q^48 - 882 * q^49 + 828 * q^51 + 396 * q^53 - 1088 * q^55 + 448 * q^56 + 68 * q^61 - 704 * q^62 - 128 * q^64 + 408 * q^66 + 1104 * q^68 - 312 * q^69 - 1368 * q^74 + 786 * q^75 - 1904 * q^77 + 16 * q^79 + 162 * q^81 + 960 * q^82 + 1140 * q^87 + 544 * q^88 - 576 * q^90 - 416 * q^92 - 1816 * q^94 + 3456 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.00000	−0.500000
$5$	16.0000i	1.43108i	0.698570	+	0.715542i	$0.253820\pi$
$5$	16.0000i	1.43108i	−0.698570	+	0.715542i	$0.746180\pi$
$6$	− 6.00000i	− 0.408248i
$7$	28.0000i	1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$	28.0000i	1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	− 8.00000i	− 0.353553i
$9$	9.00000	0.333333
$10$	−32.0000	−1.01193
$11$	34.0000i	0.931944i	0.884799	+	0.465972i	$0.154295\pi$
$11$	34.0000i	0.931944i	−0.884799	+	0.465972i	$0.845705\pi$
$12$	12.0000	0.288675
$13$	0	0
$13$	0	0
$14$	−56.0000	−1.06904
$15$	− 48.0000i	− 0.826236i
$16$	16.0000	0.250000
$17$	−138.000	−1.96882	−0.984409	−	0.175893i	$-0.943719\pi$
$17$	−138.000	−1.96882	−0.984409	+	0.175893i	$0.943719\pi$
$18$	18.0000i	0.235702i
$19$	− 108.000i	− 1.30405i	−0.758199	−	0.652024i	$-0.773920\pi$
$19$	− 108.000i	− 1.30405i	0.758199	−	0.652024i	$-0.226080\pi$
$20$	− 64.0000i	− 0.715542i
$21$	− 84.0000i	− 0.872872i
$22$	−68.0000	−0.658984
$23$	52.0000	0.471424	0.235712	−	0.971823i	$-0.424258\pi$
$23$	52.0000	0.471424	0.235712	+	0.971823i	$0.424258\pi$
$24$	24.0000i	0.204124i
$25$	−131.000	−1.04800
$26$	0	0
$27$	−27.0000	−0.192450
$28$	− 112.000i	− 0.755929i
$29$	−190.000	−1.21662	−0.608312	−	0.793698i	$-0.708153\pi$
$29$	−190.000	−1.21662	−0.608312	+	0.793698i	$0.708153\pi$
$30$	96.0000	0.584237
$31$	176.000i	1.01969i	0.860265	+	0.509847i	$0.170298\pi$
$31$	176.000i	1.01969i	−0.860265	+	0.509847i	$0.829702\pi$
$32$	32.0000i	0.176777i
$33$	− 102.000i	− 0.538058i
$34$	− 276.000i	− 1.39216i
$35$	−448.000	−2.16359
$36$	−36.0000	−0.166667
$37$	342.000i	1.51958i	0.650169	+	0.759790i	$0.274698\pi$
$37$	342.000i	1.51958i	−0.650169	+	0.759790i	$0.725302\pi$
$38$	216.000	0.922101
$39$	0	0
$40$	128.000	0.505964
$41$	− 240.000i	− 0.914188i	−0.889418	−	0.457094i	$-0.848890\pi$
$41$	− 240.000i	− 0.914188i	0.889418	−	0.457094i	$-0.151110\pi$
$42$	168.000	0.617213
$43$	140.000	0.496507	0.248253	−	0.968695i	$-0.420143\pi$
$43$	140.000	0.496507	0.248253	+	0.968695i	$0.420143\pi$
$44$	− 136.000i	− 0.465972i
$45$	144.000i	0.477028i
$46$	104.000i	0.333347i
$47$	454.000i	1.40899i	0.709707	+	0.704497i	$0.248827\pi$
$47$	454.000i	1.40899i	−0.709707	+	0.704497i	$0.751173\pi$
$48$	−48.0000	−0.144338
$49$	−441.000	−1.28571
$50$	− 262.000i	− 0.741048i
$51$	414.000	1.13670
$52$	0	0
$53$	198.000	0.513158	0.256579	−	0.966523i	$-0.417405\pi$
$53$	198.000	0.513158	0.256579	+	0.966523i	$0.417405\pi$
$54$	− 54.0000i	− 0.136083i
$55$	−544.000	−1.33369
$56$	224.000	0.534522
$57$	324.000i	0.752892i
$58$	− 380.000i	− 0.860284i
$59$	− 154.000i	− 0.339815i	−0.985460	−	0.169908i	$-0.945653\pi$
$59$	− 154.000i	− 0.339815i	0.985460	−	0.169908i	$-0.0543469\pi$
$60$	192.000i	0.413118i
$61$	34.0000	0.0713648	0.0356824	−	0.999363i	$-0.488640\pi$
$61$	34.0000	0.0713648	0.0356824	+	0.999363i	$0.488640\pi$
$62$	−352.000	−0.721033
$63$	252.000i	0.503953i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	204.000	0.380465
$67$	656.000i	1.19617i	0.801434	+	0.598083i	$0.204071\pi$
$67$	656.000i	1.19617i	−0.801434	+	0.598083i	$0.795929\pi$
$68$	552.000	0.984409
$69$	−156.000	−0.272177
$70$	− 896.000i	− 1.52989i
$71$	− 550.000i	− 0.919338i	−0.888090	−	0.459669i	$-0.847968\pi$
$71$	− 550.000i	− 0.919338i	0.888090	−	0.459669i	$-0.152032\pi$
$72$	− 72.0000i	− 0.117851i
$73$	614.000i	0.984428i	0.870474	+	0.492214i	$0.163812\pi$
$73$	614.000i	0.984428i	−0.870474	+	0.492214i	$0.836188\pi$
$74$	−684.000	−1.07451
$75$	393.000	0.605063
$76$	432.000i	0.652024i
$77$	−952.000	−1.40897
$78$	0	0
$79$	8.00000	0.0113933	0.00569665	−	0.999984i	$-0.498187\pi$
$79$	8.00000	0.0113933	0.00569665	+	0.999984i	$0.498187\pi$
$80$	256.000i	0.357771i
$81$	81.0000	0.111111
$82$	480.000	0.646428
$83$	− 762.000i	− 1.00772i	−0.863787	−	0.503858i	$-0.831914\pi$
$83$	− 762.000i	− 1.00772i	0.863787	−	0.503858i	$-0.168086\pi$
$84$	336.000i	0.436436i
$85$	− 2208.00i	− 2.81754i
$86$	280.000i	0.351083i
$87$	570.000	0.702419
$88$	272.000	0.329492
$89$	− 444.000i	− 0.528808i	−0.964412	−	0.264404i	$-0.914825\pi$
$89$	− 444.000i	− 0.528808i	0.964412	−	0.264404i	$-0.0851752\pi$
$90$	−288.000	−0.337310
$91$	0	0
$92$	−208.000	−0.235712
$93$	− 528.000i	− 0.588721i
$94$	−908.000	−0.996309
$95$	1728.00	1.86620
$96$	− 96.0000i	− 0.102062i
$97$	− 1022.00i	− 1.06978i	−0.844923	−	0.534889i	$-0.820354\pi$
$97$	− 1022.00i	− 1.06978i	0.844923	−	0.534889i	$-0.179646\pi$
$98$	− 882.000i	− 0.909137i
$99$	306.000i	0.310648i
$100$	524.000	0.524000
$101$	1190.00	1.17237	0.586185	−	0.810177i	$-0.300629\pi$
$101$	1190.00	1.17237	0.586185	+	0.810177i	$0.300629\pi$
$102$	828.000i	0.803767i
$103$	224.000	0.214285	0.107143	−	0.994244i	$-0.465830\pi$
$103$	224.000	0.214285	0.107143	+	0.994244i	$0.465830\pi$
$104$	0	0
$105$	1344.00	1.24915
$106$	396.000i	0.362858i
$107$	−640.000	−0.578235	−0.289117	−	0.957294i	$-0.593362\pi$
$107$	−640.000	−0.578235	−0.289117	+	0.957294i	$0.593362\pi$
$108$	108.000	0.0962250
$109$	1934.00i	1.69948i	0.527200	+	0.849741i	$0.323242\pi$
$109$	1934.00i	1.69948i	−0.527200	+	0.849741i	$0.676758\pi$
$110$	− 1088.00i	− 0.943061i
$111$	− 1026.00i	− 0.877330i
$112$	448.000i	0.377964i
$113$	−418.000	−0.347983	−0.173992	−	0.984747i	$-0.555667\pi$
$113$	−418.000	−0.347983	−0.173992	+	0.984747i	$0.555667\pi$
$114$	−648.000	−0.532375
$115$	832.000i	0.674647i
$116$	760.000	0.608312
$117$	0	0
$118$	308.000	0.240286
$119$	− 3864.00i	− 2.97657i
$120$	−384.000	−0.292119
$121$	175.000	0.131480
$122$	68.0000i	0.0504625i
$123$	720.000i	0.527807i
$124$	− 704.000i	− 0.509847i
$125$	− 96.0000i	− 0.0686920i
$126$	−504.000	−0.356348
$127$	1040.00	0.726654	0.363327	−	0.931662i	$-0.381641\pi$
$127$	1040.00	0.726654	0.363327	+	0.931662i	$0.381641\pi$
$128$	− 128.000i	− 0.0883883i
$129$	−420.000	−0.286658
$130$	0	0
$131$	−568.000	−0.378827	−0.189414	−	0.981897i	$-0.560659\pi$
$131$	−568.000	−0.378827	−0.189414	+	0.981897i	$0.560659\pi$
$132$	408.000i	0.269029i
$133$	3024.00	1.97153
$134$	−1312.00	−0.845817
$135$	− 432.000i	− 0.275412i
$136$	1104.00i	0.696082i
$137$	528.000i	0.329271i	0.986355	+	0.164635i	$0.0526447\pi$
$137$	528.000i	0.329271i	−0.986355	+	0.164635i	$0.947355\pi$
$138$	− 312.000i	− 0.192458i
$139$	−1556.00	−0.949483	−0.474742	−	0.880125i	$-0.657459\pi$
$139$	−1556.00	−0.949483	−0.474742	+	0.880125i	$0.657459\pi$
$140$	1792.00	1.08180
$141$	− 1362.00i	− 0.813483i
$142$	1100.00	0.650070
$143$	0	0
$144$	144.000	0.0833333
$145$	− 3040.00i	− 1.74109i
$146$	−1228.00	−0.696096
$147$	1323.00	0.742307
$148$	− 1368.00i	− 0.759790i
$149$	− 1524.00i	− 0.837926i	−0.908003	−	0.418963i	$-0.862394\pi$
$149$	− 1524.00i	− 0.837926i	0.908003	−	0.418963i	$-0.137606\pi$
$150$	786.000i	0.427844i
$151$	− 3024.00i	− 1.62973i	−0.579649	−	0.814866i	$-0.696810\pi$
$151$	− 3024.00i	− 1.62973i	0.579649	−	0.814866i	$-0.303190\pi$
$152$	−864.000	−0.461050
$153$	−1242.00	−0.656273
$154$	− 1904.00i	− 0.996290i
$155$	−2816.00	−1.45927
$156$	0	0
$157$	2198.00	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	2198.00	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	16.0000i	0.00805628i
$159$	−594.000	−0.296272
$160$	−512.000	−0.252982
$161$	1456.00i	0.712726i
$162$	162.000i	0.0785674i
$163$	− 268.000i	− 0.128781i	−0.997925	−	0.0643907i	$-0.979490\pi$
$163$	− 268.000i	− 0.128781i	0.997925	−	0.0643907i	$-0.0205104\pi$
$164$	960.000i	0.457094i
$165$	1632.00	0.770006
$166$	1524.00	0.712562
$167$	702.000i	0.325284i	0.986685	+	0.162642i	$0.0520015\pi$
$167$	702.000i	0.325284i	−0.986685	+	0.162642i	$0.947998\pi$
$168$	−672.000	−0.308607
$169$	0	0
$170$	4416.00	1.99230
$171$	− 972.000i	− 0.434682i
$172$	−560.000	−0.248253
$173$	−2066.00	−0.907948	−0.453974	−	0.891015i	$-0.649994\pi$
$173$	−2066.00	−0.907948	−0.453974	+	0.891015i	$0.649994\pi$
$174$	1140.00i	0.496685i
$175$	− 3668.00i	− 1.58443i
$176$	544.000i	0.232986i
$177$	462.000i	0.196192i
$178$	888.000	0.373924
$179$	276.000	0.115247	0.0576235	−	0.998338i	$-0.481648\pi$
$179$	276.000	0.115247	0.0576235	+	0.998338i	$0.481648\pi$
$180$	− 576.000i	− 0.238514i
$181$	3474.00	1.42663	0.713316	−	0.700843i	$-0.247192\pi$
$181$	3474.00	1.42663	0.713316	+	0.700843i	$0.247192\pi$
$182$	0	0
$183$	−102.000	−0.0412025
$184$	− 416.000i	− 0.166674i
$185$	−5472.00	−2.17465
$186$	1056.00	0.416289
$187$	− 4692.00i	− 1.83483i
$188$	− 1816.00i	− 0.704497i
$189$	− 756.000i	− 0.290957i
$190$	3456.00i	1.31960i
$191$	−3920.00	−1.48503	−0.742516	−	0.669828i	$-0.766368\pi$
$191$	−3920.00	−1.48503	−0.742516	+	0.669828i	$0.766368\pi$
$192$	192.000	0.0721688
$193$	2186.00i	0.815294i	0.913140	+	0.407647i	$0.133651\pi$
$193$	2186.00i	0.815294i	−0.913140	+	0.407647i	$0.866349\pi$
$194$	2044.00	0.756447
$195$	0	0
$196$	1764.00	0.642857
$197$	1368.00i	0.494751i	0.968920	+	0.247376i	$0.0795681\pi$
$197$	1368.00i	0.494751i	−0.968920	+	0.247376i	$0.920432\pi$
$198$	−612.000	−0.219661
$199$	1072.00	0.381870	0.190935	−	0.981603i	$-0.438848\pi$
$199$	1072.00	0.381870	0.190935	+	0.981603i	$0.438848\pi$
$200$	1048.00i	0.370524i
$201$	− 1968.00i	− 0.690607i
$202$	2380.00i	0.828991i
$203$	− 5320.00i	− 1.83936i
$204$	−1656.00	−0.568349
$205$	3840.00	1.30828
$206$	448.000i	0.151523i
$207$	468.000	0.157141
$208$	0	0
$209$	3672.00	1.21530
$210$	2688.00i	0.883284i
$211$	5444.00	1.77621	0.888105	−	0.459640i	$-0.152022\pi$
$211$	5444.00	1.77621	0.888105	+	0.459640i	$0.152022\pi$
$212$	−792.000	−0.256579
$213$	1650.00i	0.530780i
$214$	− 1280.00i	− 0.408874i
$215$	2240.00i	0.710543i
$216$	216.000i	0.0680414i
$217$	−4928.00	−1.54163
$218$	−3868.00	−1.20172
$219$	− 1842.00i	− 0.568360i
$220$	2176.00	0.666845
$221$	0	0
$222$	2052.00	0.620366
$223$	− 96.0000i	− 0.0288280i	−0.999896	−	0.0144140i	$-0.995412\pi$
$223$	− 96.0000i	− 0.0288280i	0.999896	−	0.0144140i	$-0.00458827\pi$
$224$	−896.000	−0.267261
$225$	−1179.00	−0.349333
$226$	− 836.000i	− 0.246061i
$227$	− 198.000i	− 0.0578930i	−0.999581	−	0.0289465i	$-0.990785\pi$
$227$	− 198.000i	− 0.0578930i	0.999581	−	0.0289465i	$-0.00921525\pi$
$228$	− 1296.00i	− 0.376446i
$229$	5922.00i	1.70889i	0.519538	+	0.854447i	$0.326104\pi$
$229$	5922.00i	1.70889i	−0.519538	+	0.854447i	$0.673896\pi$
$230$	−1664.00	−0.477047
$231$	2856.00	0.813468
$232$	1520.00i	0.430142i
$233$	5114.00	1.43789	0.718947	−	0.695065i	$-0.244624\pi$
$233$	5114.00	1.43789	0.718947	+	0.695065i	$0.244624\pi$
$234$	0	0
$235$	−7264.00	−2.01639
$236$	616.000i	0.169908i
$237$	−24.0000	−0.00657792
$238$	7728.00	2.10476
$239$	5226.00i	1.41440i	0.707013	+	0.707200i	$0.250042\pi$
$239$	5226.00i	1.41440i	−0.707013	+	0.707200i	$0.749958\pi$
$240$	− 768.000i	− 0.206559i
$241$	− 762.000i	− 0.203671i	−0.994801	−	0.101836i	$-0.967528\pi$
$241$	− 762.000i	− 0.203671i	0.994801	−	0.101836i	$-0.0324716\pi$
$242$	350.000i	0.0929705i
$243$	−243.000	−0.0641500
$244$	−136.000	−0.0356824
$245$	− 7056.00i	− 1.83996i
$246$	−1440.00	−0.373216
$247$	0	0
$248$	1408.00	0.360516
$249$	2286.00i	0.581805i
$250$	192.000	0.0485726
$251$	−3240.00	−0.814769	−0.407384	−	0.913257i	$-0.633559\pi$
$251$	−3240.00	−0.814769	−0.407384	+	0.913257i	$0.633559\pi$
$252$	− 1008.00i	− 0.251976i
$253$	1768.00i	0.439341i
$254$	2080.00i	0.513822i
$255$	6624.00i	1.62671i
$256$	256.000	0.0625000
$257$	1386.00	0.336406	0.168203	−	0.985752i	$-0.446204\pi$
$257$	1386.00	0.336406	0.168203	+	0.985752i	$0.446204\pi$
$258$	− 840.000i	− 0.202698i
$259$	−9576.00	−2.29739
$260$	0	0
$261$	−1710.00	−0.405542
$262$	− 1136.00i	− 0.267871i
$263$	3300.00	0.773714	0.386857	−	0.922140i	$-0.373561\pi$
$263$	3300.00	0.773714	0.386857	+	0.922140i	$0.373561\pi$
$264$	−816.000	−0.190232
$265$	3168.00i	0.734372i
$266$	6048.00i	1.39409i
$267$	1332.00i	0.305307i
$268$	− 2624.00i	− 0.598083i
$269$	4290.00	0.972364	0.486182	−	0.873858i	$-0.338389\pi$
$269$	4290.00	0.972364	0.486182	+	0.873858i	$0.338389\pi$
$270$	864.000	0.194746
$271$	2452.00i	0.549625i	0.961498	+	0.274813i	$0.0886158\pi$
$271$	2452.00i	0.549625i	−0.961498	+	0.274813i	$0.911384\pi$
$272$	−2208.00	−0.492205
$273$	0	0
$274$	−1056.00	−0.232830
$275$	− 4454.00i	− 0.976677i
$276$	624.000	0.136088
$277$	42.0000	0.00911024	0.00455512	−	0.999990i	$-0.498550\pi$
$277$	42.0000	0.00911024	0.00455512	+	0.999990i	$0.498550\pi$
$278$	− 3112.00i	− 0.671386i
$279$	1584.00i	0.339898i
$280$	3584.00i	0.764946i
$281$	− 2288.00i	− 0.485732i	−0.970060	−	0.242866i	$-0.921912\pi$
$281$	− 2288.00i	− 0.485732i	0.970060	−	0.242866i	$-0.0780875\pi$
$282$	2724.00	0.575219
$283$	−1156.00	−0.242816	−0.121408	−	0.992603i	$-0.538741\pi$
$283$	−1156.00	−0.242816	−0.121408	+	0.992603i	$0.538741\pi$
$284$	2200.00i	0.459669i
$285$	−5184.00	−1.07745
$286$	0	0
$287$	6720.00	1.38212
$288$	288.000i	0.0589256i
$289$	14131.0	2.87625
$290$	6080.00	1.23114
$291$	3066.00i	0.617636i
$292$	− 2456.00i	− 0.492214i
$293$	− 8684.00i	− 1.73148i	−0.500491	−	0.865742i	$-0.666847\pi$
$293$	− 8684.00i	− 1.73148i	0.500491	−	0.865742i	$-0.333153\pi$
$294$	2646.00i	0.524891i
$295$	2464.00	0.486304
$296$	2736.00	0.537253
$297$	− 918.000i	− 0.179353i
$298$	3048.00	0.592503
$299$	0	0
$300$	−1572.00	−0.302532
$301$	3920.00i	0.750648i
$302$	6048.00	1.15240
$303$	−3570.00	−0.676868
$304$	− 1728.00i	− 0.326012i
$305$	544.000i	0.102129i
$306$	− 2484.00i	− 0.464055i
$307$	− 7552.00i	− 1.40396i	−0.712197	−	0.701979i	$-0.752300\pi$
$307$	− 7552.00i	− 1.40396i	0.712197	−	0.701979i	$-0.247700\pi$
$308$	3808.00	0.704484
$309$	−672.000	−0.123718
$310$	− 5632.00i	− 1.03186i
$311$	−2652.00	−0.483541	−0.241770	−	0.970334i	$-0.577728\pi$
$311$	−2652.00	−0.483541	−0.241770	+	0.970334i	$0.577728\pi$
$312$	0	0
$313$	−4426.00	−0.799273	−0.399636	−	0.916674i	$-0.630864\pi$
$313$	−4426.00	−0.799273	−0.399636	+	0.916674i	$0.630864\pi$
$314$	4396.00i	0.790066i
$315$	−4032.00	−0.721198
$316$	−32.0000	−0.00569665
$317$	4944.00i	0.875971i	0.898982	+	0.437985i	$0.144308\pi$
$317$	4944.00i	0.875971i	−0.898982	+	0.437985i	$0.855692\pi$
$318$	− 1188.00i	− 0.209496i
$319$	− 6460.00i	− 1.13383i
$320$	− 1024.00i	− 0.178885i
$321$	1920.00	0.333844
$322$	−2912.00	−0.503973
$323$	14904.0i	2.56743i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	536.000	0.0910623
$327$	− 5802.00i	− 0.981197i
$328$	−1920.00	−0.323214
$329$	−12712.0	−2.13020
$330$	3264.00i	0.544477i
$331$	6088.00i	1.01096i	0.862839	+	0.505478i	$0.168684\pi$
$331$	6088.00i	1.01096i	−0.862839	+	0.505478i	$0.831316\pi$
$332$	3048.00i	0.503858i
$333$	3078.00i	0.506527i
$334$	−1404.00	−0.230010
$335$	−10496.0	−1.71181
$336$	− 1344.00i	− 0.218218i
$337$	−6638.00	−1.07298	−0.536491	−	0.843906i	$-0.680250\pi$
$337$	−6638.00	−1.07298	−0.536491	+	0.843906i	$0.680250\pi$
$338$	0	0
$339$	1254.00	0.200908
$340$	8832.00i	1.40877i
$341$	−5984.00	−0.950298
$342$	1944.00	0.307367
$343$	− 2744.00i	− 0.431959i
$344$	− 1120.00i	− 0.175542i
$345$	− 2496.00i	− 0.389508i
$346$	− 4132.00i	− 0.642016i
$347$	−2292.00	−0.354585	−0.177293	−	0.984158i	$-0.556734\pi$
$347$	−2292.00	−0.354585	−0.177293	+	0.984158i	$0.556734\pi$
$348$	−2280.00	−0.351209
$349$	− 9866.00i	− 1.51322i	−0.653865	−	0.756612i	$-0.726853\pi$
$349$	− 9866.00i	− 1.51322i	0.653865	−	0.756612i	$-0.273147\pi$
$350$	7336.00	1.12036
$351$	0	0
$352$	−1088.00	−0.164746
$353$	− 2368.00i	− 0.357042i	−0.983936	−	0.178521i	$-0.942869\pi$
$353$	− 2368.00i	− 0.357042i	0.983936	−	0.178521i	$-0.0571313\pi$
$354$	−924.000	−0.138729
$355$	8800.00	1.31565
$356$	1776.00i	0.264404i
$357$	11592.0i	1.71853i
$358$	552.000i	0.0814919i
$359$	5070.00i	0.745360i	0.927960	+	0.372680i	$0.121561\pi$
$359$	5070.00i	0.745360i	−0.927960	+	0.372680i	$0.878439\pi$
$360$	1152.00	0.168655
$361$	−4805.00	−0.700539
$362$	6948.00i	1.00878i
$363$	−525.000	−0.0759101
$364$	0	0
$365$	−9824.00	−1.40880
$366$	− 204.000i	− 0.0291346i
$367$	−8584.00	−1.22093	−0.610465	−	0.792043i	$-0.709017\pi$
$367$	−8584.00	−1.22093	−0.610465	+	0.792043i	$0.709017\pi$
$368$	832.000	0.117856
$369$	− 2160.00i	− 0.304729i
$370$	− 10944.0i	− 1.53771i
$371$	5544.00i	0.775822i
$372$	2112.00i	0.294360i
$373$	4994.00	0.693243	0.346621	−	0.938005i	$-0.387329\pi$
$373$	4994.00	0.693243	0.346621	+	0.938005i	$0.387329\pi$
$374$	9384.00	1.29742
$375$	288.000i	0.0396593i
$376$	3632.00	0.498155
$377$	0	0
$378$	1512.00	0.205738
$379$	− 1300.00i	− 0.176191i	−0.996112	−	0.0880957i	$-0.971922\pi$
$379$	− 1300.00i	− 0.176191i	0.996112	−	0.0880957i	$-0.0280781\pi$
$380$	−6912.00	−0.933100
$381$	−3120.00	−0.419534
$382$	− 7840.00i	− 1.05008i
$383$	4590.00i	0.612371i	0.951972	+	0.306185i	$0.0990528\pi$
$383$	4590.00i	0.612371i	−0.951972	+	0.306185i	$0.900947\pi$
$384$	384.000i	0.0510310i
$385$	− 15232.0i	− 2.01635i
$386$	−4372.00	−0.576500
$387$	1260.00	0.165502
$388$	4088.00i	0.534889i
$389$	−3510.00	−0.457491	−0.228746	−	0.973486i	$-0.573462\pi$
$389$	−3510.00	−0.457491	−0.228746	+	0.973486i	$0.573462\pi$
$390$	0	0
$391$	−7176.00	−0.928148
$392$	3528.00i	0.454569i
$393$	1704.00	0.218716
$394$	−2736.00	−0.349842
$395$	128.000i	0.0163048i
$396$	− 1224.00i	− 0.155324i
$397$	6230.00i	0.787594i	0.919197	+	0.393797i	$0.128839\pi$
$397$	6230.00i	0.787594i	−0.919197	+	0.393797i	$0.871161\pi$
$398$	2144.00i	0.270023i
$399$	−9072.00	−1.13827
$400$	−2096.00	−0.262000
$401$	− 7500.00i	− 0.933995i	−0.884259	−	0.466998i	$-0.845336\pi$
$401$	− 7500.00i	− 0.933995i	0.884259	−	0.466998i	$-0.154664\pi$
$402$	3936.00	0.488333
$403$	0	0
$404$	−4760.00	−0.586185
$405$	1296.00i	0.159009i
$406$	10640.0	1.30063
$407$	−11628.0	−1.41616
$408$	− 3312.00i	− 0.401883i
$409$	− 8254.00i	− 0.997883i	−0.866636	−	0.498941i	$-0.833722\pi$
$409$	− 8254.00i	− 0.997883i	0.866636	−	0.498941i	$-0.166278\pi$
$410$	7680.00i	0.925093i
$411$	− 1584.00i	− 0.190105i
$412$	−896.000	−0.107143
$413$	4312.00	0.513752
$414$	936.000i	0.111116i
$415$	12192.0	1.44212
$416$	0	0
$417$	4668.00	0.548185
$418$	7344.00i	0.859346i
$419$	−14808.0	−1.72653	−0.863267	−	0.504747i	$-0.831586\pi$
$419$	−14808.0	−1.72653	−0.863267	+	0.504747i	$0.831586\pi$
$420$	−5376.00	−0.624576
$421$	− 10354.0i	− 1.19863i	−0.800513	−	0.599315i	$-0.795440\pi$
$421$	− 10354.0i	− 1.19863i	0.800513	−	0.599315i	$-0.204560\pi$
$422$	10888.0i	1.25597i
$423$	4086.00i	0.469665i
$424$	− 1584.00i	− 0.181429i
$425$	18078.0	2.06332
$426$	−3300.00	−0.375318
$427$	952.000i	0.107893i
$428$	2560.00	0.289117
$429$	0	0
$430$	−4480.00	−0.502430
$431$	15486.0i	1.73071i	0.501163	+	0.865353i	$0.332906\pi$
$431$	15486.0i	1.73071i	−0.501163	+	0.865353i	$0.667094\pi$
$432$	−432.000	−0.0481125
$433$	2018.00	0.223970	0.111985	−	0.993710i	$-0.464279\pi$
$433$	2018.00	0.223970	0.111985	+	0.993710i	$0.464279\pi$
$434$	− 9856.00i	− 1.09010i
$435$	9120.00i	1.00522i
$436$	− 7736.00i	− 0.849741i
$437$	− 5616.00i	− 0.614759i
$438$	3684.00	0.401891
$439$	−8792.00	−0.955853	−0.477926	−	0.878400i	$-0.658611\pi$
$439$	−8792.00	−0.955853	−0.477926	+	0.878400i	$0.658611\pi$
$440$	4352.00i	0.471531i
$441$	−3969.00	−0.428571
$442$	0	0
$443$	−2760.00	−0.296008	−0.148004	−	0.988987i	$-0.547285\pi$
$443$	−2760.00	−0.296008	−0.148004	+	0.988987i	$0.547285\pi$
$444$	4104.00i	0.438665i
$445$	7104.00	0.756768
$446$	192.000	0.0203844
$447$	4572.00i	0.483777i
$448$	− 1792.00i	− 0.188982i
$449$	9532.00i	1.00188i	0.865483	+	0.500939i	$0.167012\pi$
$449$	9532.00i	1.00188i	−0.865483	+	0.500939i	$0.832988\pi$
$450$	− 2358.00i	− 0.247016i
$451$	8160.00	0.851972
$452$	1672.00	0.173992
$453$	9072.00i	0.940927i
$454$	396.000	0.0409366
$455$	0	0
$456$	2592.00	0.266188
$457$	− 12862.0i	− 1.31654i	−0.752782	−	0.658270i	$-0.771288\pi$
$457$	− 12862.0i	− 1.31654i	0.752782	−	0.658270i	$-0.228712\pi$
$458$	−11844.0	−1.20837
$459$	3726.00	0.378899
$460$	− 3328.00i	− 0.337323i
$461$	6744.00i	0.681344i	0.940182	+	0.340672i	$0.110654\pi$
$461$	6744.00i	0.681344i	−0.940182	+	0.340672i	$0.889346\pi$
$462$	5712.00i	0.575208i
$463$	− 9572.00i	− 0.960796i	−0.877051	−	0.480398i	$-0.840492\pi$
$463$	− 9572.00i	− 0.960796i	0.877051	−	0.480398i	$-0.159508\pi$
$464$	−3040.00	−0.304156
$465$	8448.00	0.842509
$466$	10228.0i	1.01674i
$467$	−9104.00	−0.902105	−0.451052	−	0.892498i	$-0.648951\pi$
$467$	−9104.00	−0.902105	−0.451052	+	0.892498i	$0.648951\pi$
$468$	0	0
$469$	−18368.0	−1.80843
$470$	− 14528.0i	− 1.42580i
$471$	−6594.00	−0.645086
$472$	−1232.00	−0.120143
$473$	4760.00i	0.462717i
$474$	− 48.0000i	− 0.00465129i
$475$	14148.0i	1.36664i
$476$	15456.0i	1.48829i
$477$	1782.00	0.171053
$478$	−10452.0	−1.00013
$479$	− 18870.0i	− 1.79998i	−0.435906	−	0.899992i	$-0.643572\pi$
$479$	− 18870.0i	− 1.79998i	0.435906	−	0.899992i	$-0.356428\pi$
$480$	1536.00	0.146059
$481$	0	0
$482$	1524.00	0.144017
$483$	− 4368.00i	− 0.411493i
$484$	−700.000	−0.0657400
$485$	16352.0	1.53094
$486$	− 486.000i	− 0.0453609i
$487$	1744.00i	0.162276i	0.996703	+	0.0811378i	$0.0258554\pi$
$487$	1744.00i	0.162276i	−0.996703	+	0.0811378i	$0.974145\pi$
$488$	− 272.000i	− 0.0252313i
$489$	804.000i	0.0743520i
$490$	14112.0	1.30105
$491$	−13360.0	−1.22796	−0.613980	−	0.789322i	$-0.710432\pi$
$491$	−13360.0	−1.22796	−0.613980	+	0.789322i	$0.710432\pi$
$492$	− 2880.00i	− 0.263903i
$493$	26220.0	2.39531
$494$	0	0
$495$	−4896.00	−0.444563
$496$	2816.00i	0.254924i
$497$	15400.0	1.38991
$498$	−4572.00	−0.411398
$499$	− 17368.0i	− 1.55811i	−0.626954	−	0.779057i	$-0.715698\pi$
$499$	− 17368.0i	− 1.55811i	0.626954	−	0.779057i	$-0.284302\pi$
$500$	384.000i	0.0343460i
$501$	− 2106.00i	− 0.187803i
$502$	− 6480.00i	− 0.576129i
$503$	−5828.00	−0.516616	−0.258308	−	0.966063i	$-0.583165\pi$
$503$	−5828.00	−0.516616	−0.258308	+	0.966063i	$0.583165\pi$
$504$	2016.00	0.178174
$505$	19040.0i	1.67776i
$506$	−3536.00	−0.310661
$507$	0	0
$508$	−4160.00	−0.363327
$509$	− 10744.0i	− 0.935598i	−0.883835	−	0.467799i	$-0.845047\pi$
$509$	− 10744.0i	− 0.935598i	0.883835	−	0.467799i	$-0.154953\pi$
$510$	−13248.0	−1.15026
$511$	−17192.0	−1.48832
$512$	512.000i	0.0441942i
$513$	2916.00i	0.250964i
$514$	2772.00i	0.237875i
$515$	3584.00i	0.306660i
$516$	1680.00	0.143329
$517$	−15436.0	−1.31310
$518$	− 19152.0i	− 1.62450i
$519$	6198.00	0.524204
$520$	0	0
$521$	−12234.0	−1.02875	−0.514377	−	0.857564i	$-0.671977\pi$
$521$	−12234.0	−1.02875	−0.514377	+	0.857564i	$0.671977\pi$
$522$	− 3420.00i	− 0.286761i
$523$	1812.00	0.151498	0.0757488	−	0.997127i	$-0.475865\pi$
$523$	1812.00	0.151498	0.0757488	+	0.997127i	$0.475865\pi$
$524$	2272.00	0.189414
$525$	11004.0i	0.914769i
$526$	6600.00i	0.547098i
$527$	− 24288.0i	− 2.00759i
$528$	− 1632.00i	− 0.134515i
$529$	−9463.00	−0.777760
$530$	−6336.00	−0.519280
$531$	− 1386.00i	− 0.113272i
$532$	−12096.0	−0.985767
$533$	0	0
$534$	−2664.00	−0.215885
$535$	− 10240.0i	− 0.827502i
$536$	5248.00	0.422909
$537$	−828.000	−0.0665379
$538$	8580.00i	0.687565i
$539$	− 14994.0i	− 1.19821i
$540$	1728.00i	0.137706i
$541$	6098.00i	0.484609i	0.970200	+	0.242305i	$0.0779033\pi$
$541$	6098.00i	0.484609i	−0.970200	+	0.242305i	$0.922097\pi$
$542$	−4904.00	−0.388644
$543$	−10422.0	−0.823666
$544$	− 4416.00i	− 0.348041i
$545$	−30944.0	−2.43210
$546$	0	0
$547$	−18332.0	−1.43294	−0.716471	−	0.697616i	$-0.754244\pi$
$547$	−18332.0	−1.43294	−0.716471	+	0.697616i	$0.754244\pi$
$548$	− 2112.00i	− 0.164635i
$549$	306.000	0.0237883
$550$	8908.00	0.690615
$551$	20520.0i	1.58654i
$552$	1248.00i	0.0962290i
$553$	224.000i	0.0172250i
$554$	84.0000i	0.00644191i
$555$	16416.0	1.25553
$556$	6224.00	0.474742
$557$	− 20004.0i	− 1.52172i	−0.648917	−	0.760859i	$-0.724778\pi$
$557$	− 20004.0i	− 1.52172i	0.648917	−	0.760859i	$-0.275222\pi$
$558$	−3168.00	−0.240344
$559$	0	0
$560$	−7168.00	−0.540899
$561$	14076.0i	1.05934i
$562$	4576.00	0.343464
$563$	−10988.0	−0.822538	−0.411269	−	0.911514i	$-0.634914\pi$
$563$	−10988.0	−0.822538	−0.411269	+	0.911514i	$0.634914\pi$
$564$	5448.00i	0.406741i
$565$	− 6688.00i	− 0.497993i
$566$	− 2312.00i	− 0.171697i
$567$	2268.00i	0.167984i
$568$	−4400.00	−0.325035
$569$	−11062.0	−0.815014	−0.407507	−	0.913202i	$-0.633602\pi$
$569$	−11062.0	−0.815014	−0.407507	+	0.913202i	$0.633602\pi$
$570$	− 10368.0i	− 0.761873i
$571$	708.000	0.0518895	0.0259447	−	0.999663i	$-0.491741\pi$
$571$	708.000	0.0518895	0.0259447	+	0.999663i	$0.491741\pi$
$572$	0	0
$573$	11760.0	0.857384
$574$	13440.0i	0.977308i
$575$	−6812.00	−0.494052
$576$	−576.000	−0.0416667
$577$	2094.00i	0.151082i	0.997143	+	0.0755410i	$0.0240684\pi$
$577$	2094.00i	0.151082i	−0.997143	+	0.0755410i	$0.975932\pi$
$578$	28262.0i	2.03381i
$579$	− 6558.00i	− 0.470710i
$580$	12160.0i	0.870546i
$581$	21336.0	1.52352
$582$	−6132.00	−0.436735
$583$	6732.00i	0.478235i
$584$	4912.00	0.348048
$585$	0	0
$586$	17368.0	1.22434
$587$	17854.0i	1.25539i	0.778460	+	0.627695i	$0.216001\pi$
$587$	17854.0i	1.25539i	−0.778460	+	0.627695i	$0.783999\pi$
$588$	−5292.00	−0.371154
$589$	19008.0	1.32973
$590$	4928.00i	0.343869i
$591$	− 4104.00i	− 0.285645i
$592$	5472.00i	0.379895i
$593$	23948.0i	1.65839i	0.558958	+	0.829196i	$0.311201\pi$
$593$	23948.0i	1.65839i	−0.558958	+	0.829196i	$0.688799\pi$
$594$	1836.00	0.126822
$595$	61824.0	4.25973
$596$	6096.00i	0.418963i
$597$	−3216.00	−0.220473
$598$	0	0
$599$	−18068.0	−1.23245	−0.616226	−	0.787570i	$-0.711339\pi$
$599$	−18068.0	−1.23245	−0.616226	+	0.787570i	$0.711339\pi$
$600$	− 3144.00i	− 0.213922i
$601$	19942.0	1.35350	0.676748	−	0.736215i	$-0.263389\pi$
$601$	19942.0	1.35350	0.676748	+	0.736215i	$0.263389\pi$
$602$	−7840.00	−0.530788
$603$	5904.00i	0.398722i
$604$	12096.0i	0.814866i
$605$	2800.00i	0.188159i
$606$	− 7140.00i	− 0.478618i
$607$	26376.0	1.76370	0.881852	−	0.471526i	$-0.156296\pi$
$607$	26376.0	1.76370	0.881852	+	0.471526i	$0.156296\pi$
$608$	3456.00	0.230525
$609$	15960.0i	1.06196i
$610$	−1088.00	−0.0722161
$611$	0	0
$612$	4968.00	0.328136
$613$	19426.0i	1.27995i	0.768396	+	0.639975i	$0.221055\pi$
$613$	19426.0i	1.27995i	−0.768396	+	0.639975i	$0.778945\pi$
$614$	15104.0	0.992749
$615$	−11520.0	−0.755335
$616$	7616.00i	0.498145i
$617$	8024.00i	0.523556i	0.965128	+	0.261778i	$0.0843088\pi$
$617$	8024.00i	0.523556i	−0.965128	+	0.261778i	$0.915691\pi$
$618$	− 1344.00i	− 0.0874816i
$619$	− 20648.0i	− 1.34073i	−0.742031	−	0.670366i	$-0.766137\pi$
$619$	− 20648.0i	− 1.34073i	0.742031	−	0.670366i	$-0.233863\pi$
$620$	11264.0	0.729634
$621$	−1404.00	−0.0907256
$622$	− 5304.00i	− 0.341915i
$623$	12432.0	0.799482
$624$	0	0
$625$	−14839.0	−0.949696
$626$	− 8852.00i	− 0.565171i
$627$	−11016.0	−0.701653
$628$	−8792.00	−0.558661
$629$	− 47196.0i	− 2.99178i
$630$	− 8064.00i	− 0.509964i
$631$	12280.0i	0.774737i	0.921925	+	0.387369i	$0.126616\pi$
$631$	12280.0i	0.774737i	−0.921925	+	0.387369i	$0.873384\pi$
$632$	− 64.0000i	− 0.00402814i
$633$	−16332.0	−1.02550
$634$	−9888.00	−0.619405
$635$	16640.0i	1.03990i
$636$	2376.00	0.148136
$637$	0	0
$638$	12920.0	0.801736
$639$	− 4950.00i	− 0.306446i
$640$	2048.00	0.126491
$641$	15878.0	0.978383	0.489191	−	0.872176i	$-0.337292\pi$
$641$	15878.0	0.978383	0.489191	+	0.872176i	$0.337292\pi$
$642$	3840.00i	0.236063i
$643$	21520.0i	1.31985i	0.751330	+	0.659927i	$0.229413\pi$
$643$	21520.0i	1.31985i	−0.751330	+	0.659927i	$0.770587\pi$
$644$	− 5824.00i	− 0.356363i
$645$	− 6720.00i	− 0.410232i
$646$	−29808.0	−1.81545
$647$	−7312.00	−0.444304	−0.222152	−	0.975012i	$-0.571308\pi$
$647$	−7312.00	−0.444304	−0.222152	+	0.975012i	$0.571308\pi$
$648$	− 648.000i	− 0.0392837i
$649$	5236.00	0.316689
$650$	0	0
$651$	14784.0	0.890062
$652$	1072.00i	0.0643907i
$653$	3090.00	0.185178	0.0925889	−	0.995704i	$-0.470486\pi$
$653$	3090.00	0.185178	0.0925889	+	0.995704i	$0.470486\pi$
$654$	11604.0	0.693811
$655$	− 9088.00i	− 0.542134i
$656$	− 3840.00i	− 0.228547i
$657$	5526.00i	0.328143i
$658$	− 25424.0i	− 1.50628i
$659$	−13428.0	−0.793749	−0.396875	−	0.917873i	$-0.629905\pi$
$659$	−13428.0	−0.793749	−0.396875	+	0.917873i	$0.629905\pi$
$660$	−6528.00	−0.385003
$661$	22598.0i	1.32974i	0.746958	+	0.664872i	$0.231514\pi$
$661$	22598.0i	1.32974i	−0.746958	+	0.664872i	$0.768486\pi$
$662$	−12176.0	−0.714854
$663$	0	0
$664$	−6096.00	−0.356281
$665$	48384.0i	2.82143i
$666$	−6156.00	−0.358168
$667$	−9880.00	−0.573546
$668$	− 2808.00i	− 0.162642i
$669$	288.000i	0.0166438i
$670$	− 20992.0i	− 1.21044i
$671$	1156.00i	0.0665080i
$672$	2688.00	0.154303
$673$	−6178.00	−0.353855	−0.176927	−	0.984224i	$-0.556616\pi$
$673$	−6178.00	−0.353855	−0.176927	+	0.984224i	$0.556616\pi$
$674$	− 13276.0i	− 0.758713i
$675$	3537.00	0.201688
$676$	0	0
$677$	22398.0	1.27153	0.635764	−	0.771883i	$-0.280685\pi$
$677$	22398.0	1.27153	0.635764	+	0.771883i	$0.280685\pi$
$678$	2508.00i	0.142064i
$679$	28616.0	1.61735
$680$	−17664.0	−0.996152
$681$	594.000i	0.0334246i
$682$	− 11968.0i	− 0.671962i
$683$	11410.0i	0.639226i	0.947548	+	0.319613i	$0.103553\pi$
$683$	11410.0i	0.639226i	−0.947548	+	0.319613i	$0.896447\pi$
$684$	3888.00i	0.217341i
$685$	−8448.00	−0.471214
$686$	5488.00	0.305441
$687$	− 17766.0i	− 0.986631i
$688$	2240.00	0.124127
$689$	0	0
$690$	4992.00	0.275423
$691$	− 32488.0i	− 1.78857i	−0.447498	−	0.894285i	$-0.647685\pi$
$691$	− 32488.0i	− 1.78857i	0.447498	−	0.894285i	$-0.352315\pi$
$692$	8264.00	0.453974
$693$	−8568.00	−0.469656
$694$	− 4584.00i	− 0.250729i
$695$	− 24896.0i	− 1.35879i
$696$	− 4560.00i	− 0.248342i
$697$	33120.0i	1.79987i
$698$	19732.0	1.07001
$699$	−15342.0	−0.830168
$700$	14672.0i	0.792214i
$701$	−5094.00	−0.274462	−0.137231	−	0.990539i	$-0.543820\pi$
$701$	−5094.00	−0.274462	−0.137231	+	0.990539i	$0.543820\pi$
$702$	0	0
$703$	36936.0	1.98160
$704$	− 2176.00i	− 0.116493i
$705$	21792.0	1.16416
$706$	4736.00	0.252467
$707$	33320.0i	1.77246i
$708$	− 1848.00i	− 0.0980962i
$709$	25418.0i	1.34639i	0.739463	+	0.673197i	$0.235079\pi$
$709$	25418.0i	1.34639i	−0.739463	+	0.673197i	$0.764921\pi$
$710$	17600.0i	0.930305i
$711$	72.0000	0.00379777
$712$	−3552.00	−0.186962
$713$	9152.00i	0.480708i
$714$	−23184.0	−1.21518
$715$	0	0
$716$	−1104.00	−0.0576235
$717$	− 15678.0i	− 0.816605i
$718$	−10140.0	−0.527049
$719$	20428.0	1.05958	0.529788	−	0.848130i	$-0.322271\pi$
$719$	20428.0	1.05958	0.529788	+	0.848130i	$0.322271\pi$
$720$	2304.00i	0.119257i
$721$	6272.00i	0.323969i
$722$	− 9610.00i	− 0.495356i
$723$	2286.00i	0.117590i
$724$	−13896.0	−0.713316
$725$	24890.0	1.27502
$726$	− 1050.00i	− 0.0536765i
$727$	38336.0	1.95571	0.977857	−	0.209276i	$-0.0671107\pi$
$727$	38336.0	1.95571	0.977857	+	0.209276i	$0.0671107\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	− 19648.0i	− 0.996171i
$731$	−19320.0	−0.977532
$732$	408.000	0.0206012
$733$	166.000i	0.00836473i	0.999991	+	0.00418237i	$0.00133129\pi$
$733$	166.000i	0.00836473i	−0.999991	+	0.00418237i	$0.998669\pi$
$734$	− 17168.0i	− 0.863328i
$735$	21168.0i	1.06230i
$736$	1664.00i	0.0833368i
$737$	−22304.0	−1.11476
$738$	4320.00	0.215476
$739$	− 25248.0i	− 1.25678i	−0.777897	−	0.628392i	$-0.783714\pi$
$739$	− 25248.0i	− 1.25678i	0.777897	−	0.628392i	$-0.216286\pi$
$740$	21888.0	1.08732
$741$	0	0
$742$	−11088.0	−0.548589
$743$	4442.00i	0.219329i	0.993969	+	0.109664i	$0.0349776\pi$
$743$	4442.00i	0.219329i	−0.993969	+	0.109664i	$0.965022\pi$
$744$	−4224.00	−0.208144
$745$	24384.0	1.19914
$746$	9988.00i	0.490197i
$747$	− 6858.00i	− 0.335905i
$748$	18768.0i	0.917414i
$749$	− 17920.0i	− 0.874209i
$750$	−576.000	−0.0280434
$751$	19848.0	0.964399	0.482200	−	0.876061i	$-0.339838\pi$
$751$	19848.0	0.964399	0.482200	+	0.876061i	$0.339838\pi$
$752$	7264.00i	0.352248i
$753$	9720.00	0.470407
$754$	0	0
$755$	48384.0	2.33228
$756$	3024.00i	0.145479i
$757$	−29166.0	−1.40034	−0.700169	−	0.713977i	$-0.746892\pi$
$757$	−29166.0	−1.40034	−0.700169	+	0.713977i	$0.746892\pi$
$758$	2600.00	0.124586
$759$	− 5304.00i	− 0.253653i
$760$	− 13824.0i	− 0.659802i
$761$	− 6240.00i	− 0.297240i	−0.988894	−	0.148620i	$-0.952517\pi$
$761$	− 6240.00i	− 0.297240i	0.988894	−	0.148620i	$-0.0474832\pi$
$762$	− 6240.00i	− 0.296655i
$763$	−54152.0	−2.56938
$764$	15680.0	0.742516
$765$	− 19872.0i	− 0.939181i
$766$	−9180.00	−0.433012
$767$	0	0
$768$	−768.000	−0.0360844
$769$	39750.0i	1.86401i	0.362449	+	0.932004i	$0.381941\pi$
$769$	39750.0i	1.86401i	−0.362449	+	0.932004i	$0.618059\pi$
$770$	30464.0	1.42577
$771$	−4158.00	−0.194224
$772$	− 8744.00i	− 0.407647i
$773$	− 9764.00i	− 0.454317i	−0.973858	−	0.227158i	$-0.927057\pi$
$773$	− 9764.00i	− 0.454317i	0.973858	−	0.227158i	$-0.0729435\pi$
$774$	2520.00i	0.117028i
$775$	− 23056.0i	− 1.06864i
$776$	−8176.00	−0.378223
$777$	28728.0	1.32640
$778$	− 7020.00i	− 0.323495i
$779$	−25920.0	−1.19214
$780$	0	0
$781$	18700.0	0.856772
$782$	− 14352.0i	− 0.656300i
$783$	5130.00	0.234140
$784$	−7056.00	−0.321429
$785$	35168.0i	1.59898i
$786$	3408.00i	0.154656i
$787$	− 36016.0i	− 1.63130i	−0.578547	−	0.815649i	$-0.696380\pi$
$787$	− 36016.0i	− 1.63130i	0.578547	−	0.815649i	$-0.303620\pi$
$788$	− 5472.00i	− 0.247376i
$789$	−9900.00	−0.446704
$790$	−256.000	−0.0115292
$791$	− 11704.0i	− 0.526102i
$792$	2448.00	0.109831
$793$	0	0
$794$	−12460.0	−0.556913
$795$	− 9504.00i	− 0.423990i
$796$	−4288.00	−0.190935
$797$	22290.0	0.990655	0.495328	−	0.868706i	$-0.335048\pi$
$797$	22290.0	0.990655	0.495328	+	0.868706i	$0.335048\pi$
$798$	− 18144.0i	− 0.804875i
$799$	− 62652.0i	− 2.77405i
$800$	− 4192.00i	− 0.185262i
$801$	− 3996.00i	− 0.176269i
$802$	15000.0	0.660434
$803$	−20876.0	−0.917432
$804$	7872.00i	0.345304i
$805$	−23296.0	−1.01997
$806$	0	0
$807$	−12870.0	−0.561395
$808$	− 9520.00i	− 0.414496i
$809$	−25578.0	−1.11159	−0.555794	−	0.831320i	$-0.687586\pi$
$809$	−25578.0	−1.11159	−0.555794	+	0.831320i	$0.687586\pi$
$810$	−2592.00	−0.112437
$811$	− 29900.0i	− 1.29461i	−0.762230	−	0.647306i	$-0.775895\pi$
$811$	− 29900.0i	− 1.29461i	0.762230	−	0.647306i	$-0.224105\pi$
$812$	21280.0i	0.919682i
$813$	− 7356.00i	− 0.317326i
$814$	− 23256.0i	− 1.00138i
$815$	4288.00	0.184297
$816$	6624.00	0.284174
$817$	− 15120.0i	− 0.647469i
$818$	16508.0	0.705610
$819$	0	0
$820$	−15360.0	−0.654140
$821$	− 16412.0i	− 0.697665i	−0.937185	−	0.348832i	$-0.886578\pi$
$821$	− 16412.0i	− 0.697665i	0.937185	−	0.348832i	$-0.113422\pi$
$822$	3168.00	0.134424
$823$	−18552.0	−0.785762	−0.392881	−	0.919589i	$-0.628522\pi$
$823$	−18552.0	−0.785762	−0.392881	+	0.919589i	$0.628522\pi$
$824$	− 1792.00i	− 0.0757613i
$825$	13362.0i	0.563885i
$826$	8624.00i	0.363278i
$827$	− 28662.0i	− 1.20517i	−0.798055	−	0.602585i	$-0.794137\pi$
$827$	− 28662.0i	− 1.20517i	0.798055	−	0.602585i	$-0.205863\pi$
$828$	−1872.00	−0.0785706
$829$	3686.00	0.154427	0.0772136	−	0.997015i	$-0.475398\pi$
$829$	3686.00	0.154427	0.0772136	+	0.997015i	$0.475398\pi$
$830$	24384.0i	1.01974i
$831$	−126.000	−0.00525980
$832$	0	0
$833$	60858.0	2.53134
$834$	9336.00i	0.387625i
$835$	−11232.0	−0.465508
$836$	−14688.0	−0.607650
$837$	− 4752.00i	− 0.196240i
$838$	− 29616.0i	− 1.22084i
$839$	13370.0i	0.550159i	0.961421	+	0.275080i	$0.0887042\pi$
$839$	13370.0i	0.550159i	−0.961421	+	0.275080i	$0.911296\pi$
$840$	− 10752.0i	− 0.441642i
$841$	11711.0	0.480175
$842$	20708.0	0.847559
$843$	6864.00i	0.280437i
$844$	−21776.0	−0.888105
$845$	0	0
$846$	−8172.00	−0.332103
$847$	4900.00i	0.198779i
$848$	3168.00	0.128290
$849$	3468.00	0.140190
$850$	36156.0i	1.45899i
$851$	17784.0i	0.716366i
$852$	− 6600.00i	− 0.265390i
$853$	11398.0i	0.457515i	0.973483	+	0.228757i	$0.0734662\pi$
$853$	11398.0i	0.457515i	−0.973483	+	0.228757i	$0.926534\pi$
$854$	−1904.00	−0.0762922
$855$	15552.0	0.622067
$856$	5120.00i	0.204437i
$857$	−7990.00	−0.318475	−0.159238	−	0.987240i	$-0.550904\pi$
$857$	−7990.00	−0.318475	−0.159238	+	0.987240i	$0.550904\pi$
$858$	0	0
$859$	7652.00	0.303938	0.151969	−	0.988385i	$-0.451439\pi$
$859$	7652.00	0.303938	0.151969	+	0.988385i	$0.451439\pi$
$860$	− 8960.00i	− 0.355271i
$861$	−20160.0	−0.797969
$862$	−30972.0	−1.22379
$863$	1022.00i	0.0403120i	0.999797	+	0.0201560i	$0.00641629\pi$
$863$	1022.00i	0.0403120i	−0.999797	+	0.0201560i	$0.993584\pi$
$864$	− 864.000i	− 0.0340207i
$865$	− 33056.0i	− 1.29935i
$866$	4036.00i	0.158371i
$867$	−42393.0	−1.66060
$868$	19712.0	0.770817
$869$	272.000i	0.0106179i
$870$	−18240.0	−0.710798
$871$	0	0
$872$	15472.0	0.600858
$873$	− 9198.00i	− 0.356592i
$874$	11232.0	0.434700
$875$	2688.00	0.103853
$876$	7368.00i	0.284180i
$877$	15546.0i	0.598576i	0.954163	+	0.299288i	$0.0967491\pi$
$877$	15546.0i	0.598576i	−0.954163	+	0.299288i	$0.903251\pi$
$878$	− 17584.0i	− 0.675890i
$879$	26052.0i	0.999673i
$880$	−8704.00	−0.333422
$881$	−11310.0	−0.432513	−0.216256	−	0.976337i	$-0.569385\pi$
$881$	−11310.0	−0.432513	−0.216256	+	0.976337i	$0.569385\pi$
$882$	− 7938.00i	− 0.303046i
$883$	−17260.0	−0.657809	−0.328904	−	0.944363i	$-0.606679\pi$
$883$	−17260.0	−0.657809	−0.328904	+	0.944363i	$0.606679\pi$
$884$	0	0
$885$	−7392.00	−0.280768
$886$	− 5520.00i	− 0.209309i
$887$	832.000	0.0314947	0.0157474	−	0.999876i	$-0.494987\pi$
$887$	832.000	0.0314947	0.0157474	+	0.999876i	$0.494987\pi$
$888$	−8208.00	−0.310183
$889$	29120.0i	1.09860i
$890$	14208.0i	0.535116i
$891$	2754.00i	0.103549i
$892$	384.000i	0.0144140i
$893$	49032.0	1.83739
$894$	−9144.00	−0.342082
$895$	4416.00i	0.164928i
$896$	3584.00	0.133631
$897$	0	0
$898$	−19064.0	−0.708434
$899$	− 33440.0i	− 1.24059i
$900$	4716.00	0.174667
$901$	−27324.0	−1.01032
$902$	16320.0i	0.602435i
$903$	− 11760.0i	− 0.433387i
$904$	3344.00i	0.123031i
$905$	55584.0i	2.04163i
$906$	−18144.0	−0.665336
$907$	−31740.0	−1.16197	−0.580986	−	0.813913i	$-0.697333\pi$
$907$	−31740.0	−1.16197	−0.580986	+	0.813913i	$0.697333\pi$
$908$	792.000i	0.0289465i
$909$	10710.0	0.390790
$910$	0	0
$911$	−23568.0	−0.857127	−0.428563	−	0.903512i	$-0.640980\pi$
$911$	−23568.0	−0.857127	−0.428563	+	0.903512i	$0.640980\pi$
$912$	5184.00i	0.188223i
$913$	25908.0	0.939134
$914$	25724.0	0.930935
$915$	− 1632.00i	− 0.0589642i
$916$	− 23688.0i	− 0.854447i
$917$	− 15904.0i	− 0.572733i
$918$	7452.00i	0.267922i
$919$	−18864.0	−0.677112	−0.338556	−	0.940946i	$-0.609938\pi$
$919$	−18864.0	−0.677112	−0.338556	+	0.940946i	$0.609938\pi$
$920$	6656.00	0.238524
$921$	22656.0i	0.810576i
$922$	−13488.0	−0.481783
$923$	0	0
$924$	−11424.0	−0.406734
$925$	− 44802.0i	− 1.59252i
$926$	19144.0	0.679385
$927$	2016.00	0.0714284
$928$	− 6080.00i	− 0.215071i
$929$	19536.0i	0.689941i	0.938613	+	0.344971i	$0.112111\pi$
$929$	19536.0i	0.689941i	−0.938613	+	0.344971i	$0.887889\pi$
$930$	16896.0i	0.595744i
$931$	47628.0i	1.67663i
$932$	−20456.0	−0.718947
$933$	7956.00	0.279172
$934$	− 18208.0i	− 0.637884i
$935$	75072.0	2.62579
$936$	0	0
$937$	18174.0	0.633638	0.316819	−	0.948486i	$-0.397385\pi$
$937$	18174.0	0.633638	0.316819	+	0.948486i	$0.397385\pi$
$938$	− 36736.0i	− 1.27876i
$939$	13278.0	0.461460
$940$	29056.0	1.00819
$941$	− 51172.0i	− 1.77275i	−0.462966	−	0.886376i	$-0.653215\pi$
$941$	− 51172.0i	− 1.77275i	0.462966	−	0.886376i	$-0.346785\pi$
$942$	− 13188.0i	− 0.456145i
$943$	− 12480.0i	− 0.430970i
$944$	− 2464.00i	− 0.0849538i
$945$	12096.0	0.416384
$946$	−9520.00	−0.327190
$947$	3726.00i	0.127855i	0.997955	+	0.0639275i	$0.0203626\pi$
$947$	3726.00i	0.127855i	−0.997955	+	0.0639275i	$0.979637\pi$
$948$	96.0000	0.00328896
$949$	0	0
$950$	−28296.0	−0.966362
$951$	− 14832.0i	− 0.505742i
$952$	−30912.0	−1.05238
$953$	40498.0	1.37656	0.688279	−	0.725447i	$-0.258367\pi$
$953$	40498.0	1.37656	0.688279	+	0.725447i	$0.258367\pi$
$954$	3564.00i	0.120953i
$955$	− 62720.0i	− 2.12521i
$956$	− 20904.0i	− 0.707200i
$957$	19380.0i	0.654615i
$958$	37740.0	1.27278
$959$	−14784.0	−0.497810
$960$	3072.00i	0.103280i
$961$	−1185.00	−0.0397771
$962$	0	0
$963$	−5760.00	−0.192745
$964$	3048.00i	0.101836i
$965$	−34976.0	−1.16675
$966$	8736.00	0.290969
$967$	− 28568.0i	− 0.950036i	−0.879976	−	0.475018i	$-0.842442\pi$
$967$	− 28568.0i	− 0.950036i	0.879976	−	0.475018i	$-0.157558\pi$
$968$	− 1400.00i	− 0.0464852i
$969$	− 44712.0i	− 1.48231i
$970$	32704.0i	1.08254i
$971$	−8676.00	−0.286742	−0.143371	−	0.989669i	$-0.545794\pi$
$971$	−8676.00	−0.286742	−0.143371	+	0.989669i	$0.545794\pi$
$972$	972.000	0.0320750
$973$	− 43568.0i	− 1.43548i
$974$	−3488.00	−0.114746
$975$	0	0
$976$	544.000	0.0178412
$977$	2796.00i	0.0915578i	0.998952	+	0.0457789i	$0.0145770\pi$
$977$	2796.00i	0.0915578i	−0.998952	+	0.0457789i	$0.985423\pi$
$978$	−1608.00	−0.0525748
$979$	15096.0	0.492819
$980$	28224.0i	0.919982i
$981$	17406.0i	0.566494i
$982$	− 26720.0i	− 0.868299i
$983$	− 406.000i	− 0.0131733i	−0.999978	−	0.00658667i	$-0.997903\pi$
$983$	− 406.000i	− 0.0131733i	0.999978	−	0.00658667i	$-0.00209662\pi$
$984$	5760.00	0.186608
$985$	−21888.0	−0.708030
$986$	52440.0i	1.69374i
$987$	38136.0	1.22987
$988$	0	0
$989$	7280.00	0.234065
$990$	− 9792.00i	− 0.314354i
$991$	−23232.0	−0.744691	−0.372346	−	0.928094i	$-0.621446\pi$
$991$	−23232.0	−0.744691	−0.372346	+	0.928094i	$0.621446\pi$
$992$	−5632.00	−0.180258
$993$	− 18264.0i	− 0.583676i
$994$	30800.0i	0.982814i
$995$	17152.0i	0.546487i
$996$	− 9144.00i	− 0.290902i
$997$	6110.00	0.194088	0.0970440	−	0.995280i	$-0.469061\pi$
$997$	6110.00	0.194088	0.0970440	+	0.995280i	$0.469061\pi$
$998$	34736.0	1.10175
$999$	− 9234.00i	− 0.292443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.4.b.a.337.2		2
13.5	odd	4		1014.4.a.i.1.1		1
13.8	odd	4		78.4.a.a.1.1	✓	1
13.12	even	2	inner	1014.4.b.a.337.1		2
39.8	even	4		234.4.a.k.1.1		1
52.47	even	4		624.4.a.f.1.1		1
65.34	odd	4		1950.4.a.o.1.1		1
104.21	odd	4		2496.4.a.q.1.1		1
104.99	even	4		2496.4.a.g.1.1		1
156.47	odd	4		1872.4.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.4.a.a.1.1	✓	1	13.8	odd	4
234.4.a.k.1.1		1	39.8	even	4
624.4.a.f.1.1		1	52.47	even	4
1014.4.a.i.1.1		1	13.5	odd	4
1014.4.b.a.337.1		2	13.12	even	2	inner
1014.4.b.a.337.2		2	1.1	even	1	trivial
1872.4.a.o.1.1		1	156.47	odd	4
1950.4.a.o.1.1		1	65.34	odd	4
2496.4.a.g.1.1		1	104.99	even	4
2496.4.a.q.1.1		1	104.21	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +16.0000i q^{5} -6.00000i q^{6} +28.0000i q^{7} -8.00000i q^{8} +9.00000 q^{9} -32.0000 q^{10} +34.0000i q^{11} +12.0000 q^{12} -56.0000 q^{14} -48.0000i q^{15} +16.0000 q^{16} -138.000 q^{17} +18.0000i q^{18} -108.000i q^{19} -64.0000i q^{20} -84.0000i q^{21} -68.0000 q^{22} +52.0000 q^{23} +24.0000i q^{24} -131.000 q^{25} -27.0000 q^{27} -112.000i q^{28} -190.000 q^{29} +96.0000 q^{30} +176.000i q^{31} +32.0000i q^{32} -102.000i q^{33} -276.000i q^{34} -448.000 q^{35} -36.0000 q^{36} +342.000i q^{37} +216.000 q^{38} +128.000 q^{40} -240.000i q^{41} +168.000 q^{42} +140.000 q^{43} -136.000i q^{44} +144.000i q^{45} +104.000i q^{46} +454.000i q^{47} -48.0000 q^{48} -441.000 q^{49} -262.000i q^{50} +414.000 q^{51} +198.000 q^{53} -54.0000i q^{54} -544.000 q^{55} +224.000 q^{56} +324.000i q^{57} -380.000i q^{58} -154.000i q^{59} +192.000i q^{60} +34.0000 q^{61} -352.000 q^{62} +252.000i q^{63} -64.0000 q^{64} +204.000 q^{66} +656.000i q^{67} +552.000 q^{68} -156.000 q^{69} -896.000i q^{70} -550.000i q^{71} -72.0000i q^{72} +614.000i q^{73} -684.000 q^{74} +393.000 q^{75} +432.000i q^{76} -952.000 q^{77} +8.00000 q^{79} +256.000i q^{80} +81.0000 q^{81} +480.000 q^{82} -762.000i q^{83} +336.000i q^{84} -2208.00i q^{85} +280.000i q^{86} +570.000 q^{87} +272.000 q^{88} -444.000i q^{89} -288.000 q^{90} -208.000 q^{92} -528.000i q^{93} -908.000 q^{94} +1728.00 q^{95} -96.0000i q^{96} -1022.00i q^{97} -882.000i q^{98} +306.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9} - 64 q^{10} + 24 q^{12} - 112 q^{14} + 32 q^{16} - 276 q^{17} - 136 q^{22} + 104 q^{23} - 262 q^{25} - 54 q^{27} - 380 q^{29} + 192 q^{30} - 896 q^{35} - 72 q^{36} + 432 q^{38}+ \cdots + 3456 q^{95}+O(q^{100}) \) 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9 - 64 * q^10 + 24 * q^12 - 112 * q^14 + 32 * q^16 - 276 * q^17 - 136 * q^22 + 104 * q^23 - 262 * q^25 - 54 * q^27 - 380 * q^29 + 192 * q^30 - 896 * q^35 - 72 * q^36 + 432 * q^38 + 256 * q^40 + 336 * q^42 + 280 * q^43 - 96 * q^48 - 882 * q^49 + 828 * q^51 + 396 * q^53 - 1088 * q^55 + 448 * q^56 + 68 * q^61 - 704 * q^62 - 128 * q^64 + 408 * q^66 + 1104 * q^68 - 312 * q^69 - 1368 * q^74 + 786 * q^75 - 1904 * q^77 + 16 * q^79 + 162 * q^81 + 960 * q^82 + 1140 * q^87 + 544 * q^88 - 576 * q^90 - 416 * q^92 - 1816 * q^94 + 3456 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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