LMFDB - Embedded newform 931.2.c.f.930.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(930,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("931.930");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			930.6
Character	$\chi$	$=$	931.930
Dual form			931.2.c.f.930.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27541i q^{2} +2.74153 q^{3} -3.17751 q^{4} +1.16914i q^{5} -6.23811i q^{6} +2.67932i q^{8} +4.51598 q^{9} +O(q^{10})$	\(q-2.27541i q^{2} +2.74153 q^{3} -3.17751 q^{4} +1.16914i q^{5} -6.23811i q^{6} +2.67932i q^{8} +4.51598 q^{9} +2.66029 q^{10} +4.83297 q^{11} -8.71123 q^{12} -3.16090 q^{13} +3.20524i q^{15} -0.258461 q^{16} -3.82680i q^{17} -10.2757i q^{18} +(-3.29194 - 2.85712i) q^{19} -3.71496i q^{20} -10.9970i q^{22} +7.97426 q^{23} +7.34543i q^{24} +3.63310 q^{25} +7.19236i q^{26} +4.15612 q^{27} -7.81752i q^{29} +7.29325 q^{30} +3.32967 q^{31} +5.94674i q^{32} +13.2497 q^{33} -8.70755 q^{34} -14.3496 q^{36} +2.56989i q^{37} +(-6.50114 + 7.49051i) q^{38} -8.66571 q^{39} -3.13251 q^{40} +4.59434 q^{41} -6.25704 q^{43} -15.3568 q^{44} +5.27983i q^{45} -18.1447i q^{46} -1.49025i q^{47} -0.708580 q^{48} -8.26681i q^{50} -10.4913i q^{51} +10.0438 q^{52} +10.1821i q^{53} -9.45688i q^{54} +5.65044i q^{55} +(-9.02494 - 7.83289i) q^{57} -17.7881 q^{58} -11.2476 q^{59} -10.1847i q^{60} +14.3674i q^{61} -7.57638i q^{62} +13.0144 q^{64} -3.69555i q^{65} -30.1486i q^{66} +4.81321i q^{67} +12.1597i q^{68} +21.8617 q^{69} +9.62034i q^{71} +12.0998i q^{72} +3.07389i q^{73} +5.84757 q^{74} +9.96026 q^{75} +(10.4601 + 9.07853i) q^{76} +19.7181i q^{78} -4.04668i q^{79} -0.302179i q^{80} -2.15384 q^{81} -10.4540i q^{82} -4.15553i q^{83} +4.47408 q^{85} +14.2373i q^{86} -21.4320i q^{87} +12.9491i q^{88} -10.9122 q^{89} +12.0138 q^{90} -25.3383 q^{92} +9.12839 q^{93} -3.39094 q^{94} +(3.34039 - 3.84875i) q^{95} +16.3032i q^{96} -0.0766995 q^{97} +21.8256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 40 * q^4 + 40 * q^9	$ 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	2.27541i		−	1.60896i	−0.593979	−	0.804480i	$-0.702444\pi$
$2$		−	2.27541i		−	1.60896i	0.593979	−	0.804480i	$-0.297556\pi$
$3$	2.74153			1.58282			0.791411	−	0.611284i	$-0.209347\pi$
$3$	2.74153			1.58282			0.791411	+	0.611284i	$0.209347\pi$
$4$	−3.17751			−1.58875
$5$			1.16914i			0.522857i	0.965223	+	0.261428i	$0.0841935\pi$
$5$			1.16914i			0.522857i	−0.965223	+	0.261428i	$0.915806\pi$
$6$		−	6.23811i		−	2.54670i
$7$		0			0
$7$		0			0
$8$			2.67932i			0.947281i
$9$	4.51598			1.50533
$10$	2.66029			0.841256
$11$	4.83297			1.45720			0.728598	−	0.684942i	$-0.240172\pi$
$11$	4.83297			1.45720			0.728598	+	0.684942i	$0.240172\pi$
$12$	−8.71123			−2.51472
$13$	−3.16090			−0.876677			−0.438339	−	0.898810i	$-0.644433\pi$
$13$	−3.16090			−0.876677			−0.438339	+	0.898810i	$0.644433\pi$
$14$		0			0
$15$			3.20524i			0.827590i
$16$	−0.258461			−0.0646154
$17$		−	3.82680i		−	0.928135i	−0.885800	−	0.464068i	$-0.846389\pi$
$17$		−	3.82680i		−	0.928135i	0.885800	−	0.464068i	$-0.153611\pi$
$18$		−	10.2757i		−	2.42201i
$19$	−3.29194	−	2.85712i	−0.755222	−	0.655469i
$19$	−3.29194	−	2.85712i	−0.755222	−	0.655469i
$20$		−	3.71496i		−	0.830691i
$21$		0			0
$22$		−	10.9970i		−	2.34457i
$23$	7.97426			1.66275			0.831374	−	0.555713i	$-0.187555\pi$
$23$	7.97426			1.66275			0.831374	+	0.555713i	$0.187555\pi$
$24$			7.34543i			1.49938i
$25$	3.63310			0.726621
$26$			7.19236i			1.41054i
$27$	4.15612			0.799845
$28$		0			0
$29$		−	7.81752i		−	1.45168i	−0.687865	−	0.725839i	$-0.741452\pi$
$29$		−	7.81752i		−	1.45168i	0.687865	−	0.725839i	$-0.258548\pi$
$30$	7.29325			1.33156
$31$	3.32967			0.598026			0.299013	−	0.954249i	$-0.403343\pi$
$31$	3.32967			0.598026			0.299013	+	0.954249i	$0.403343\pi$
$32$			5.94674i			1.05124i
$33$	13.2497			2.30648
$34$	−8.70755			−1.49333
$35$		0			0
$36$	−14.3496			−2.39160
$37$			2.56989i			0.422488i	0.977433	+	0.211244i	$0.0677514\pi$
$37$			2.56989i			0.422488i	−0.977433	+	0.211244i	$0.932249\pi$
$38$	−6.50114	+	7.49051i	−1.05462	+	1.21512i
$39$	−8.66571			−1.38762
$40$	−3.13251			−0.495293
$41$	4.59434			0.717515			0.358757	−	0.933431i	$-0.383201\pi$
$41$	4.59434			0.717515			0.358757	+	0.933431i	$0.383201\pi$
$42$		0			0
$43$	−6.25704			−0.954189			−0.477095	−	0.878852i	$-0.658310\pi$
$43$	−6.25704			−0.954189			−0.477095	+	0.878852i	$0.658310\pi$
$44$	−15.3568			−2.31512
$45$			5.27983i			0.787071i
$46$		−	18.1447i		−	2.67530i
$47$		−	1.49025i		−	0.217376i	−0.994076	−	0.108688i	$-0.965335\pi$
$47$		−	1.49025i		−	0.217376i	0.994076	−	0.108688i	$-0.0346649\pi$
$48$	−0.708580			−0.102275
$49$		0			0
$50$		−	8.26681i		−	1.16910i
$51$		−	10.4913i		−	1.46907i
$52$	10.0438			1.39282
$53$			10.1821i			1.39862i	0.714818	+	0.699311i	$0.246510\pi$
$53$			10.1821i			1.39862i	−0.714818	+	0.699311i	$0.753490\pi$
$54$		−	9.45688i		−	1.28692i
$55$			5.65044i			0.761905i
$56$		0			0
$57$	−9.02494	−	7.83289i	−1.19538	−	1.03749i
$58$	−17.7881			−2.33569
$59$	−11.2476			−1.46432			−0.732158	−	0.681134i	$-0.761487\pi$
$59$	−11.2476			−1.46432			−0.732158	+	0.681134i	$0.761487\pi$
$60$		−	10.1847i		−	1.31484i
$61$			14.3674i			1.83956i	0.392437	+	0.919779i	$0.371632\pi$
$61$			14.3674i			1.83956i	−0.392437	+	0.919779i	$0.628368\pi$
$62$		−	7.57638i		−	0.962201i
$63$		0			0
$64$	13.0144			1.62680
$65$		−	3.69555i		−	0.458377i
$66$		−	30.1486i		−	3.71104i
$67$			4.81321i			0.588028i	0.955801	+	0.294014i	$0.0949912\pi$
$67$			4.81321i			0.588028i	−0.955801	+	0.294014i	$0.905009\pi$
$68$			12.1597i			1.47458i
$69$	21.8617			2.63184
$70$		0			0
$71$			9.62034i			1.14172i	0.821046	+	0.570862i	$0.193391\pi$
$71$			9.62034i			1.14172i	−0.821046	+	0.570862i	$0.806609\pi$
$72$			12.0998i			1.42597i
$73$			3.07389i			0.359771i	0.983688	+	0.179886i	$0.0575728\pi$
$73$			3.07389i			0.359771i	−0.983688	+	0.179886i	$0.942427\pi$
$74$	5.84757			0.679766
$75$	9.96026			1.15011
$76$	10.4601	+	9.07853i	1.19986	+	1.04138i
$77$		0			0
$78$			19.7181i			2.23263i
$79$		−	4.04668i		−	0.455287i	−0.973745	−	0.227643i	$-0.926898\pi$
$79$		−	4.04668i		−	0.455287i	0.973745	−	0.227643i	$-0.0731021\pi$
$80$		−	0.302179i		−	0.0337846i
$81$	−2.15384			−0.239316
$82$		−	10.4540i		−	1.15445i
$83$		−	4.15553i		−	0.456129i	−0.973646	−	0.228065i	$-0.926760\pi$
$83$		−	4.15553i		−	0.456129i	0.973646	−	0.228065i	$-0.0732397\pi$
$84$		0			0
$85$	4.47408			0.485282
$86$			14.2373i			1.53525i
$87$		−	21.4320i		−	2.29775i
$88$			12.9491i			1.38037i
$89$	−10.9122			−1.15669			−0.578343	−	0.815794i	$-0.696300\pi$
$89$	−10.9122			−1.15669			−0.578343	+	0.815794i	$0.696300\pi$
$90$	12.0138			1.26637
$91$		0			0
$92$	−25.3383			−2.64170
$93$	9.12839			0.946570
$94$	−3.39094			−0.349749
$95$	3.34039	−	3.84875i	0.342717	−	0.394873i
$96$			16.3032i			1.66393i
$97$	−0.0766995			−0.00778765			−0.00389383	−	0.999992i	$-0.501239\pi$
$97$	−0.0766995			−0.00778765			−0.00389383	+	0.999992i	$0.501239\pi$
$98$		0			0
$99$	21.8256			2.19356
$100$	−11.5442			−1.15442
$101$			19.8342i			1.97357i	0.162028	+	0.986786i	$0.448196\pi$
$101$			19.8342i			1.97357i	−0.162028	+	0.986786i	$0.551804\pi$
$102$	−23.8720			−2.36368
$103$	−12.4783			−1.22953			−0.614763	−	0.788712i	$-0.710748\pi$
$103$	−12.4783			−1.22953			−0.614763	+	0.788712i	$0.710748\pi$
$104$		−	8.46906i		−	0.830460i
$105$		0			0
$106$	23.1685			2.25033
$107$			5.13599i			0.496515i	0.968694	+	0.248258i	$0.0798580\pi$
$107$			5.13599i			0.496515i	−0.968694	+	0.248258i	$0.920142\pi$
$108$	−13.2061			−1.27076
$109$			1.35773i			0.130047i	0.997884	+	0.0650235i	$0.0207122\pi$
$109$			1.35773i			0.130047i	−0.997884	+	0.0650235i	$0.979288\pi$
$110$	12.8571			1.22587
$111$			7.04544i			0.668723i
$112$		0			0
$113$		−	5.51308i		−	0.518627i	−0.965793	−	0.259313i	$-0.916504\pi$
$113$		−	5.51308i		−	0.518627i	0.965793	−	0.259313i	$-0.0834963\pi$
$114$	−17.8231	+	20.5355i	−1.66928	+	1.92332i
$115$			9.32306i			0.869380i
$116$			24.8402i			2.30636i
$117$	−14.2746			−1.31969
$118$			25.5930i			2.35603i
$119$		0			0
$120$	−8.58786			−0.783960
$121$	12.3576			1.12342
$122$	32.6918			2.95978
$123$	12.5955			1.13570
$124$	−10.5801			−0.950117
$125$			10.0933i			0.902776i
$126$		0			0
$127$		−	2.26205i		−	0.200725i	−0.994951	−	0.100362i	$-0.968000\pi$
$127$		−	2.26205i		−	0.200725i	0.994951	−	0.100362i	$-0.0320002\pi$
$128$		−	17.7196i		−	1.56621i
$129$	−17.1539			−1.51031
$130$	−8.40891			−0.737510
$131$		−	4.40394i		−	0.384774i	−0.981319	−	0.192387i	$-0.938377\pi$
$131$		−	4.40394i		−	0.384774i	0.981319	−	0.192387i	$-0.0616229\pi$
$132$	−42.1011			−3.66443
$133$		0			0
$134$	10.9521			0.946113
$135$			4.85910i			0.418204i
$136$	10.2532			0.879205
$137$	−19.0541			−1.62790			−0.813949	−	0.580936i	$-0.802687\pi$
$137$	−19.0541			−1.62790			−0.813949	+	0.580936i	$0.802687\pi$
$138$		−	49.7444i		−	4.23452i
$139$			5.50466i			0.466899i	0.972369	+	0.233449i	$0.0750013\pi$
$139$			5.50466i			0.466899i	−0.972369	+	0.233449i	$0.924999\pi$
$140$		0			0
$141$		−	4.08558i		−	0.344068i
$142$	21.8902			1.83699
$143$	−15.2766			−1.27749
$144$	−1.16721			−0.0972673
$145$	9.13981			0.759020
$146$	6.99437			0.578858
$147$		0			0
$148$		−	8.16586i		−	0.671229i
$149$	−0.401567			−0.0328976			−0.0164488	−	0.999865i	$-0.505236\pi$
$149$	−0.401567			−0.0328976			−0.0164488	+	0.999865i	$0.505236\pi$
$150$		−	22.6637i		−	1.85048i
$151$		−	10.3075i		−	0.838812i	−0.907799	−	0.419406i	$-0.862238\pi$
$151$		−	10.3075i		−	0.838812i	0.907799	−	0.419406i	$-0.137762\pi$
$152$	7.65514	−	8.82014i	0.620914	−	0.715408i
$153$		−	17.2818i		−	1.39715i
$154$		0			0
$155$			3.89286i			0.312682i
$156$	27.5354			2.20459
$157$			1.13960i			0.0909503i	0.998965	+	0.0454752i	$0.0144802\pi$
$157$			1.13960i			0.0909503i	−0.998965	+	0.0454752i	$0.985520\pi$
$158$	−9.20787			−0.732539
$159$			27.9146i			2.21377i
$160$	−6.95259			−0.549651
$161$		0			0
$162$			4.90088i			0.385049i
$163$	14.1956			1.11189			0.555944	−	0.831220i	$-0.312357\pi$
$163$	14.1956			1.11189			0.555944	+	0.831220i	$0.312357\pi$
$164$	−14.5985			−1.13995
$165$			15.4908i			1.20596i
$166$	−9.45556			−0.733894
$167$	−7.77749			−0.601840			−0.300920	−	0.953649i	$-0.597294\pi$
$167$	−7.77749			−0.601840			−0.300920	+	0.953649i	$0.597294\pi$
$168$		0			0
$169$	−3.00869			−0.231437
$170$		−	10.1804i		−	0.780799i
$171$	−14.8663	−	12.9027i	−1.13686	−	0.986696i
$172$	19.8818			1.51597
$173$	14.2130			1.08059			0.540295	−	0.841475i	$-0.318313\pi$
$173$	14.2130			1.08059			0.540295	+	0.841475i	$0.318313\pi$
$174$	−48.7666			−3.69699
$175$		0			0
$176$	−1.24914			−0.0941572
$177$	−30.8357			−2.31775
$178$			24.8297i			1.86106i
$179$			18.3047i			1.36816i	0.729406	+	0.684081i	$0.239796\pi$
$179$			18.3047i			1.36816i	−0.729406	+	0.684081i	$0.760204\pi$
$180$		−	16.7767i		−	1.25046i
$181$	−4.18931			−0.311389			−0.155694	−	0.987805i	$-0.549761\pi$
$181$	−4.18931			−0.311389			−0.155694	+	0.987805i	$0.549761\pi$
$182$		0			0
$183$			39.3887i			2.91169i
$184$			21.3656i			1.57509i
$185$	−3.00457			−0.220901
$186$		−	20.7709i		−	1.52299i
$187$		−	18.4948i		−	1.35247i
$188$			4.73529i			0.345357i
$189$		0			0
$190$	−8.75749	−	7.60077i	−0.635335	−	0.551418i
$191$	4.18712			0.302969			0.151485	−	0.988460i	$-0.451595\pi$
$191$	4.18712			0.302969			0.151485	+	0.988460i	$0.451595\pi$
$192$	35.6793			2.57493
$193$		−	10.3873i		−	0.747696i	−0.927490	−	0.373848i	$-0.878038\pi$
$193$		−	10.3873i		−	0.747696i	0.927490	−	0.373848i	$-0.121962\pi$
$194$			0.174523i			0.0125300i
$195$		−	10.1315i		−	0.725529i
$196$		0			0
$197$	−0.756466			−0.0538960			−0.0269480	−	0.999637i	$-0.508579\pi$
$197$	−0.756466			−0.0538960			−0.0269480	+	0.999637i	$0.508579\pi$
$198$		−	49.6623i		−	3.52935i
$199$		−	11.0783i		−	0.785318i	−0.919684	−	0.392659i	$-0.871555\pi$
$199$		−	11.0783i		−	0.785318i	0.919684	−	0.392659i	$-0.128445\pi$
$200$			9.73423i			0.688314i
$201$			13.1956i			0.930744i
$202$	45.1309			3.17540
$203$		0			0
$204$			33.3361i			2.33400i
$205$			5.37144i			0.375158i
$206$			28.3934i			1.97826i
$207$	36.0116			2.50298
$208$	0.816972			0.0566468
$209$	−15.9098	−	13.8084i	−1.10051	−	0.955147i
$210$		0			0
$211$		−	26.4941i		−	1.82393i	−0.410270	−	0.911964i	$-0.634566\pi$
$211$		−	26.4941i		−	1.82393i	0.410270	−	0.911964i	$-0.365434\pi$
$212$		−	32.3537i		−	2.22206i
$213$			26.3744i			1.80715i
$214$	11.6865			0.798873
$215$		−	7.31537i		−	0.498904i
$216$			11.1355i			0.757678i
$217$		0			0
$218$	3.08940			0.209240
$219$			8.42716i			0.569454i
$220$		−	17.9543i		−	1.21048i
$221$			12.0961i			0.813675i
$222$	16.0313			1.07595
$223$	10.1635			0.680598			0.340299	−	0.940317i	$-0.389472\pi$
$223$	10.1635			0.680598			0.340299	+	0.940317i	$0.389472\pi$
$224$		0			0
$225$	16.4070			1.09380
$226$	−12.5445			−0.834450
$227$	6.15741			0.408682			0.204341	−	0.978900i	$-0.434495\pi$
$227$	6.15741			0.408682			0.204341	+	0.978900i	$0.434495\pi$
$228$	28.6768	+	24.8891i	1.89917	+	1.64832i
$229$		−	2.15457i		−	0.142378i	−0.997463	−	0.0711891i	$-0.977321\pi$
$229$		−	2.15457i		−	0.142378i	0.997463	−	0.0711891i	$-0.0226794\pi$
$230$	21.2138			1.39880
$231$		0			0
$232$	20.9456			1.37515
$233$	−23.4900			−1.53888			−0.769442	−	0.638717i	$-0.779465\pi$
$233$	−23.4900			−1.53888			−0.769442	+	0.638717i	$0.779465\pi$
$234$			32.4806i			2.12332i
$235$	1.74232			0.113656
$236$	35.7394			2.32644
$237$		−	11.0941i		−	0.720638i
$238$		0			0
$239$	0.173031			0.0111924			0.00559622	−	0.999984i	$-0.498219\pi$
$239$	0.173031			0.0111924			0.00559622	+	0.999984i	$0.498219\pi$
$240$		−	0.828431i		−	0.0534750i
$241$	26.4793			1.70568			0.852841	−	0.522171i	$-0.174878\pi$
$241$	26.4793			1.70568			0.852841	+	0.522171i	$0.174878\pi$
$242$		−	28.1187i		−	1.80754i
$243$	−18.3732			−1.17864
$244$		−	45.6525i		−	2.92260i
$245$		0			0
$246$		−	28.6600i		−	1.82729i
$247$	10.4055	+	9.03110i	0.662086	+	0.574635i
$248$			8.92124i			0.566499i
$249$		−	11.3925i		−	0.721972i
$250$	22.9665			1.45253
$251$		−	22.9698i		−	1.44984i	−0.688833	−	0.724920i	$-0.741877\pi$
$251$		−	22.9698i		−	1.44984i	0.688833	−	0.724920i	$-0.258123\pi$
$252$		0			0
$253$	38.5394			2.42295
$254$	−5.14711			−0.322958
$255$	12.2658			0.768115
$256$	−14.2907			−0.893167
$257$	11.7982			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$257$	11.7982			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$258$			39.0321i			2.43003i
$259$		0			0
$260$			11.7426i			0.728248i
$261$		−	35.3038i		−	2.18525i
$262$	−10.0208			−0.619086
$263$	10.5199			0.648685			0.324343	−	0.945940i	$-0.394857\pi$
$263$	10.5199			0.648685			0.324343	+	0.945940i	$0.394857\pi$
$264$			35.5002i			2.18489i
$265$	−11.9044			−0.731279
$266$		0			0
$267$	−29.9160			−1.83083
$268$		−	15.2940i		−	0.934231i
$269$	−7.66911			−0.467594			−0.233797	−	0.972285i	$-0.575115\pi$
$269$	−7.66911			−0.467594			−0.233797	+	0.972285i	$0.575115\pi$
$270$	11.0565			0.672874
$271$			12.2336i			0.743136i	0.928406	+	0.371568i	$0.121180\pi$
$271$			12.2336i			0.743136i	−0.928406	+	0.371568i	$0.878820\pi$
$272$			0.989080i			0.0599718i
$273$		0			0
$274$			43.3559i			2.61922i
$275$	17.5587			1.05883
$276$	−69.4656			−4.18134
$277$	29.7219			1.78582			0.892909	−	0.450236i	$-0.148660\pi$
$277$	29.7219			1.78582			0.892909	+	0.450236i	$0.148660\pi$
$278$	12.5254			0.751222
$279$	15.0367			0.900226
$280$		0			0
$281$		−	19.2002i		−	1.14539i	−0.819769	−	0.572695i	$-0.805898\pi$
$281$		−	19.2002i		−	1.14539i	0.819769	−	0.572695i	$-0.194102\pi$
$282$	−9.29637			−0.553591
$283$		−	2.60845i		−	0.155056i	−0.996990	−	0.0775280i	$-0.975297\pi$
$283$		−	2.60845i		−	0.155056i	0.996990	−	0.0775280i	$-0.0247027\pi$
$284$		−	30.5687i		−	1.81392i
$285$	9.15777	−	10.5514i	0.542460	−	0.625014i
$286$			34.7605i			2.05543i
$287$		0			0
$288$			26.8554i			1.58247i
$289$	2.35560			0.138565
$290$		−	20.7968i		−	1.22123i
$291$	−0.210274			−0.0123265
$292$		−	9.76730i		−	0.571588i
$293$	−16.2593			−0.949880			−0.474940	−	0.880018i	$-0.657530\pi$
$293$	−16.2593			−0.949880			−0.474940	+	0.880018i	$0.657530\pi$
$294$		0			0
$295$		−	13.1501i		−	0.765628i
$296$	−6.88556			−0.400215
$297$	20.0864			1.16553
$298$			0.913731i			0.0529310i
$299$	−25.2059			−1.45769
$300$	−31.6488			−1.82724
$301$		0			0
$302$	−23.4538			−1.34962
$303$			54.3759i			3.12382i
$304$	0.850838	+	0.738457i	0.0487989	+	0.0423534i
$305$	−16.7976			−0.961826
$306$	−39.3232			−2.24796
$307$	−13.0254			−0.743399			−0.371700	−	0.928353i	$-0.621225\pi$
$307$	−13.0254			−0.743399			−0.371700	+	0.928353i	$0.621225\pi$
$308$		0			0
$309$	−34.2097			−1.94612
$310$	8.85787			0.503093
$311$		−	13.7240i		−	0.778217i	−0.921192	−	0.389108i	$-0.872783\pi$
$311$		−	13.7240i		−	0.778217i	0.921192	−	0.389108i	$-0.127217\pi$
$312$		−	23.2182i		−	1.31447i
$313$		−	30.3329i		−	1.71452i	−0.514886	−	0.857258i	$-0.672166\pi$
$313$		−	30.3329i		−	1.71452i	0.514886	−	0.857258i	$-0.327834\pi$
$314$	2.59307			0.146335
$315$		0			0
$316$			12.8583i			0.723339i
$317$			29.4680i			1.65509i	0.561403	+	0.827543i	$0.310262\pi$
$317$			29.4680i			1.65509i	−0.561403	+	0.827543i	$0.689738\pi$
$318$	63.5172			3.56187
$319$		−	37.7819i		−	2.11538i
$320$			15.2157i			0.850582i
$321$			14.0805i			0.785896i
$322$		0			0
$323$	−10.9336	+	12.5976i	−0.608364	+	0.700948i
$324$	6.84384			0.380213
$325$	−11.4839			−0.637012
$326$		−	32.3009i		−	1.78898i
$327$			3.72226i			0.205841i
$328$			12.3097i			0.679688i
$329$		0			0
$330$	35.2481			1.94034
$331$		−	5.84518i		−	0.321280i	−0.987013	−	0.160640i	$-0.948644\pi$
$331$		−	5.84518i		−	0.321280i	0.987013	−	0.160640i	$-0.0513558\pi$
$332$			13.2042i			0.724677i
$333$			11.6056i			0.635983i
$334$			17.6970i			0.968337i
$335$	−5.62734			−0.307454
$336$		0			0
$337$		−	11.7323i		−	0.639097i	−0.947570	−	0.319548i	$-0.896469\pi$
$337$		−	11.7323i		−	0.639097i	0.947570	−	0.319548i	$-0.103531\pi$
$338$			6.84601i			0.372374i
$339$		−	15.1143i		−	0.820895i
$340$	−14.2164			−0.770993
$341$	16.0922			0.871441
$342$	−29.3590	+	33.8270i	−1.58756	+	1.82916i
$343$		0			0
$344$		−	16.7646i		−	0.903886i
$345$			25.5594i			1.37607i
$346$		−	32.3403i		−	1.73863i
$347$	−16.8159			−0.902724			−0.451362	−	0.892341i	$-0.649062\pi$
$347$	−16.8159			−0.902724			−0.451362	+	0.892341i	$0.649062\pi$
$348$			68.1002i			3.65056i
$349$			2.01576i			0.107901i	0.998544	+	0.0539506i	$0.0171814\pi$
$349$			2.01576i			0.107901i	−0.998544	+	0.0539506i	$0.982819\pi$
$350$		0			0
$351$	−13.1371			−0.701206
$352$			28.7404i			1.53187i
$353$			18.8112i			1.00122i	0.865673	+	0.500610i	$0.166891\pi$
$353$			18.8112i			1.00122i	−0.865673	+	0.500610i	$0.833109\pi$
$354$			70.1640i			3.72917i
$355$	−11.2476			−0.596958
$356$	34.6734			1.83769
$357$		0			0
$358$	41.6509			2.20132
$359$	−20.9198			−1.10411			−0.552053	−	0.833809i	$-0.686155\pi$
$359$	−20.9198			−1.10411			−0.552053	+	0.833809i	$0.686155\pi$
$360$	−14.1463			−0.745578
$361$	2.67368	+	18.8109i	0.140720	+	0.990049i
$362$			9.53240i			0.501012i
$363$	33.8787			1.77817
$364$		0			0
$365$	−3.59382			−0.188109
$366$	89.6255			4.68480
$367$			21.2155i			1.10744i	0.832703	+	0.553720i	$0.186792\pi$
$367$			21.2155i			1.10744i	−0.832703	+	0.553720i	$0.813208\pi$
$368$	−2.06104			−0.107439
$369$	20.7479			1.08010
$370$			6.83665i			0.355420i
$371$		0			0
$372$	−29.0055			−1.50387
$373$		−	2.42009i		−	0.125307i	−0.998035	−	0.0626537i	$-0.980044\pi$
$373$		−	2.42009i		−	0.125307i	0.998035	−	0.0626537i	$-0.0199564\pi$
$374$	−42.0833			−2.17608
$375$			27.6712i			1.42893i
$376$	3.99286			0.205916
$377$			24.7104i			1.27265i
$378$		0			0
$379$		−	10.5823i		−	0.543576i	−0.962357	−	0.271788i	$-0.912385\pi$
$379$		−	10.5823i		−	0.543576i	0.962357	−	0.271788i	$-0.0876149\pi$
$380$	−10.6141	+	12.2294i	−0.544492	+	0.627356i
$381$		−	6.20149i		−	0.317712i
$382$		−	9.52743i		−	0.487466i
$383$	27.2735			1.39361			0.696805	−	0.717260i	$-0.254604\pi$
$383$	27.2735			1.39361			0.696805	+	0.717260i	$0.254604\pi$
$384$		−	48.5788i		−	2.47903i
$385$		0			0
$386$	−23.6355			−1.20301
$387$	−28.2567			−1.43637
$388$	0.243713			0.0123727
$389$	4.38743			0.222452			0.111226	−	0.993795i	$-0.464522\pi$
$389$	4.38743			0.222452			0.111226	+	0.993795i	$0.464522\pi$
$390$	−23.0533			−1.16735
$391$		−	30.5159i		−	1.54326i
$392$		0			0
$393$		−	12.0735i		−	0.609029i
$394$			1.72127i			0.0867165i
$395$	4.73115			0.238050
$396$	−69.3511			−3.48502
$397$		−	2.84978i		−	0.143026i	−0.997440	−	0.0715132i	$-0.977217\pi$
$397$		−	2.84978i		−	0.143026i	0.997440	−	0.0715132i	$-0.0227828\pi$
$398$	−25.2077			−1.26355
$399$		0			0
$400$	−0.939017			−0.0469509
$401$		−	25.8321i		−	1.28999i	−0.764186	−	0.644996i	$-0.776859\pi$
$401$		−	25.8321i		−	1.28999i	0.764186	−	0.644996i	$-0.223141\pi$
$402$	30.0254			1.49753
$403$	−10.5248			−0.524276
$404$		−	63.0232i		−	3.13552i
$405$		−	2.51815i		−	0.125128i
$406$		0			0
$407$			12.4202i			0.615647i
$408$	28.1095			1.39163
$409$	18.9579			0.937409			0.468705	−	0.883355i	$-0.344721\pi$
$409$	18.9579			0.937409			0.468705	+	0.883355i	$0.344721\pi$
$410$	12.2222			0.603614
$411$	−52.2373			−2.57667
$412$	39.6500			1.95341
$413$		0			0
$414$		−	81.9414i		−	4.02720i
$415$	4.85842			0.238490
$416$		−	18.7971i		−	0.921602i
$417$			15.0912i			0.739018i
$418$	−31.4198	+	36.2014i	−1.53679	+	1.77067i
$419$			8.56462i			0.418409i	0.977872	+	0.209204i	$0.0670874\pi$
$419$			8.56462i			0.418409i	−0.977872	+	0.209204i	$0.932913\pi$
$420$		0			0
$421$			17.7095i			0.863110i	0.902087	+	0.431555i	$0.142035\pi$
$421$			17.7095i			0.863110i	−0.902087	+	0.431555i	$0.857965\pi$
$422$	−60.2850			−2.93463
$423$		−	6.72996i		−	0.327222i
$424$	−27.2811			−1.32489
$425$		−	13.9032i		−	0.674402i
$426$	60.0128			2.90763
$427$		0			0
$428$		−	16.3197i		−	0.788841i
$429$	−41.8811			−2.02204
$430$	−16.6455			−0.802717
$431$		−	1.99351i		−	0.0960239i	−0.998847	−	0.0480120i	$-0.984711\pi$
$431$		−	1.99351i		−	0.0960239i	0.998847	−	0.0480120i	$-0.0152886\pi$
$432$	−1.07420			−0.0516823
$433$	−0.241849			−0.0116225			−0.00581127	−	0.999983i	$-0.501850\pi$
$433$	−0.241849			−0.0116225			−0.00581127	+	0.999983i	$0.501850\pi$
$434$		0			0
$435$	25.0570			1.20139
$436$		−	4.31420i		−	0.206613i
$437$	−26.2508	−	22.7835i	−1.25574	−	1.08988i
$438$	19.1753			0.916230
$439$	−7.41257			−0.353782			−0.176891	−	0.984230i	$-0.556604\pi$
$439$	−7.41257			−0.353782			−0.176891	+	0.984230i	$0.556604\pi$
$440$	−15.1393			−0.721738
$441$		0			0
$442$	27.5237			1.30917
$443$	17.6396			0.838082			0.419041	−	0.907967i	$-0.362366\pi$
$443$	17.6396			0.838082			0.419041	+	0.907967i	$0.362366\pi$
$444$		−	22.3869i		−	1.06244i
$445$		−	12.7579i		−	0.604781i
$446$		−	23.1262i		−	1.09506i
$447$	−1.10091			−0.0520711
$448$		0			0
$449$			10.1988i			0.481313i	0.970610	+	0.240657i	$0.0773628\pi$
$449$			10.1988i			0.481313i	−0.970610	+	0.240657i	$0.922637\pi$
$450$		−	37.3328i		−	1.75988i
$451$	22.2043			1.04556
$452$			17.5179i			0.823970i
$453$		−	28.2583i		−	1.32769i
$454$		−	14.0107i		−	0.657552i
$455$		0			0
$456$	20.9868	−	24.1807i	0.982797	−	1.13236i
$457$	−11.2279			−0.525218			−0.262609	−	0.964902i	$-0.584583\pi$
$457$	−11.2279			−0.525218			−0.262609	+	0.964902i	$0.584583\pi$
$458$	−4.90254			−0.229081
$459$		−	15.9046i		−	0.742364i
$460$		−	29.6241i		−	1.38123i
$461$		−	20.3775i		−	0.949073i	−0.880236	−	0.474537i	$-0.842616\pi$
$461$		−	20.3775i		−	0.949073i	0.880236	−	0.474537i	$-0.157384\pi$
$462$		0			0
$463$	−40.1530			−1.86607			−0.933034	−	0.359787i	$-0.882849\pi$
$463$	−40.1530			−1.86607			−0.933034	+	0.359787i	$0.882849\pi$
$464$			2.02053i			0.0938007i
$465$			10.6724i			0.494921i
$466$			53.4496i			2.47600i
$467$		−	32.4601i		−	1.50208i	−0.660259	−	0.751038i	$-0.729554\pi$
$467$		−	32.4601i		−	1.50208i	0.660259	−	0.751038i	$-0.270446\pi$
$468$	45.3576			2.09666
$469$		0			0
$470$		−	3.96450i		−	0.182869i
$471$			3.12426i			0.143958i
$472$		−	30.1360i		−	1.38712i
$473$	−30.2401			−1.39044
$474$	−25.2436			−1.15948
$475$	−11.9599	−	10.3802i	−0.548760	−	0.476278i
$476$		0			0
$477$			45.9823i			2.10538i
$478$		−	0.393717i		−	0.0180082i
$479$		−	7.20892i		−	0.329384i	−0.986345	−	0.164692i	$-0.947337\pi$
$479$		−	7.20892i		−	0.329384i	0.986345	−	0.164692i	$-0.0526630\pi$
$480$	−19.0607			−0.870000
$481$		−	8.12319i		−	0.370385i
$482$		−	60.2514i		−	2.74437i
$483$		0			0
$484$	−39.2664			−1.78484
$485$		−	0.0896727i		−	0.00407183i
$486$			41.8065i			1.89638i
$487$			4.18721i			0.189741i	0.995490	+	0.0948703i	$0.0302436\pi$
$487$			4.18721i			0.189741i	−0.995490	+	0.0948703i	$0.969756\pi$
$488$	−38.4948			−1.74258
$489$	38.9178			1.75992
$490$		0			0
$491$	6.25015			0.282065			0.141033	−	0.990005i	$-0.454958\pi$
$491$	6.25015			0.282065			0.141033	+	0.990005i	$0.454958\pi$
$492$	−40.0223			−1.80435
$493$	−29.9161			−1.34735
$494$	20.5495	−	23.6768i	0.924565	−	1.06527i
$495$			25.5173i			1.14692i
$496$	−0.860591			−0.0386417
$497$		0			0
$498$	−25.9227			−1.16162
$499$	25.5489			1.14373			0.571863	−	0.820349i	$-0.306221\pi$
$499$	25.5489			1.14373			0.571863	+	0.820349i	$0.306221\pi$
$500$		−	32.0717i		−	1.43429i
$501$	−21.3222			−0.952607
$502$	−52.2658			−2.33274
$503$			32.4478i			1.44678i	0.690442	+	0.723388i	$0.257416\pi$
$503$			32.4478i			1.44678i	−0.690442	+	0.723388i	$0.742584\pi$
$504$		0			0
$505$	−23.1890			−1.03190
$506$		−	87.6930i		−	3.89843i
$507$	−8.24840			−0.366324
$508$			7.18770i			0.318902i
$509$	−11.0850			−0.491336			−0.245668	−	0.969354i	$-0.579007\pi$
$509$	−11.0850			−0.491336			−0.245668	+	0.969354i	$0.579007\pi$
$510$		−	27.9098i		−	1.23587i
$511$		0			0
$512$		−	2.92200i		−	0.129136i
$513$	−13.6817	−	11.8745i	−0.604060	−	0.524274i
$514$		−	26.8458i		−	1.18412i
$515$		−	14.5890i		−	0.642866i
$516$	54.5065			2.39951
$517$		−	7.20235i		−	0.316759i
$518$		0			0
$519$	38.9652			1.71038
$520$	9.90155			0.434212
$521$	20.0540			0.878581			0.439291	−	0.898345i	$-0.355230\pi$
$521$	20.0540			0.878581			0.439291	+	0.898345i	$0.355230\pi$
$522$	−80.3308			−3.51598
$523$	28.7156			1.25565			0.627823	−	0.778356i	$-0.283946\pi$
$523$	28.7156			1.25565			0.627823	+	0.778356i	$0.283946\pi$
$524$			13.9936i			0.611311i
$525$		0			0
$526$		−	23.9371i		−	1.04371i
$527$		−	12.7420i		−	0.555049i
$528$	−3.42455			−0.149034
$529$	40.5889			1.76473
$530$			27.0873i			1.17660i
$531$	−50.7941			−2.20428
$532$		0			0
$533$	−14.5223			−0.629029
$534$			68.0712i			2.94573i
$535$	−6.00471			−0.259606
$536$	−12.8961			−0.557028
$537$			50.1830i			2.16556i
$538$			17.4504i			0.752340i
$539$		0			0
$540$		−	15.4398i		−	0.664424i
$541$	−15.2970			−0.657667			−0.328834	−	0.944388i	$-0.606656\pi$
$541$	−15.2970			−0.657667			−0.328834	+	0.944388i	$0.606656\pi$
$542$	27.8364			1.19568
$543$	−11.4851			−0.492873
$544$	22.7570			0.975698
$545$	−1.58738			−0.0679959
$546$		0			0
$547$			42.6215i			1.82236i	0.412005	+	0.911182i	$0.364829\pi$
$547$			42.6215i			1.82236i	−0.412005	+	0.911182i	$0.635171\pi$
$548$	60.5444			2.58633
$549$			64.8830i			2.76914i
$550$		−	39.9533i		−	1.70361i
$551$	−22.3356	+	25.7348i	−0.951530	+	1.09634i
$552$			58.5744i			2.49309i
$553$		0			0
$554$		−	67.6297i		−	2.87331i
$555$	−8.23713			−0.349647
$556$		−	17.4911i		−	0.741787i
$557$	1.59552			0.0676045			0.0338023	−	0.999429i	$-0.489238\pi$
$557$	1.59552			0.0676045			0.0338023	+	0.999429i	$0.489238\pi$
$558$		−	34.2148i		−	1.44843i
$559$	19.7779			0.836516
$560$		0			0
$561$		−	50.7041i		−	2.14073i
$562$	−43.6885			−1.84289
$563$	21.1634			0.891930			0.445965	−	0.895050i	$-0.352861\pi$
$563$	21.1634			0.891930			0.445965	+	0.895050i	$0.352861\pi$
$564$			12.9819i			0.546639i
$565$	6.44558			0.271168
$566$	−5.93529			−0.249479
$567$		0			0
$568$	−25.7759			−1.08153
$569$		−	32.8207i		−	1.37592i	−0.725751	−	0.687958i	$-0.758507\pi$
$569$		−	32.8207i		−	1.37592i	0.725751	−	0.687958i	$-0.241493\pi$
$570$	−24.0089	−	20.8377i	−1.00562	−	0.872796i
$571$	−16.2332			−0.679337			−0.339668	−	0.940545i	$-0.610315\pi$
$571$	−16.2332			−0.679337			−0.339668	+	0.940545i	$0.610315\pi$
$572$	48.5414			2.02962
$573$	11.4791			0.479547
$574$		0			0
$575$	28.9713			1.20819
$576$	58.7727			2.44886
$577$			35.6119i			1.48254i	0.671206	+	0.741271i	$0.265777\pi$
$577$			35.6119i			1.48254i	−0.671206	+	0.741271i	$0.734223\pi$
$578$		−	5.35997i		−	0.222945i
$579$		−	28.4772i		−	1.18347i
$580$	−29.0418			−1.20590
$581$		0			0
$582$			0.478460i			0.0198328i
$583$			49.2099i			2.03806i
$584$	−8.23592			−0.340805
$585$		−	16.6890i		−	0.690007i
$586$			36.9967i			1.52832i
$587$			47.0084i			1.94024i	0.242618	+	0.970122i	$0.421994\pi$
$587$			47.0084i			1.94024i	−0.242618	+	0.970122i	$0.578006\pi$
$588$		0			0
$589$	−10.9611	−	9.51328i	−0.451643	−	0.391988i
$590$	−29.9219			−1.23187
$591$	−2.07388			−0.0853078
$592$		−	0.664218i		−	0.0272992i
$593$		−	22.9384i		−	0.941965i	−0.882142	−	0.470983i	$-0.843899\pi$
$593$		−	22.9384i		−	0.941965i	0.882142	−	0.470983i	$-0.156101\pi$
$594$		−	45.7048i		−	1.87529i
$595$		0			0
$596$	1.27598			0.0522662
$597$		−	30.3714i		−	1.24302i
$598$			57.3538i			2.34537i
$599$		−	11.8708i		−	0.485028i	−0.970148	−	0.242514i	$-0.922028\pi$
$599$		−	11.8708i		−	0.485028i	0.970148	−	0.242514i	$-0.0779721\pi$
$600$			26.6867i			1.08948i
$601$	−17.5890			−0.717471			−0.358736	−	0.933439i	$-0.616792\pi$
$601$	−17.5890			−0.717471			−0.358736	+	0.933439i	$0.616792\pi$
$602$		0			0
$603$			21.7364i			0.885174i
$604$			32.7521i			1.33267i
$605$			14.4478i			0.587387i
$606$	123.728			5.02610
$607$	−22.0200			−0.893763			−0.446882	−	0.894593i	$-0.647465\pi$
$607$	−22.0200			−0.893763			−0.446882	+	0.894593i	$0.647465\pi$
$608$	16.9906	−	19.5763i	0.689059	−	0.793923i
$609$		0			0
$610$			38.2214i			1.54754i
$611$			4.71055i			0.190568i
$612$			54.9129i			2.21972i
$613$	−21.4893			−0.867944			−0.433972	−	0.900926i	$-0.642888\pi$
$613$	−21.4893			−0.867944			−0.433972	+	0.900926i	$0.642888\pi$
$614$			29.6382i			1.19610i
$615$			14.7260i			0.593808i
$616$		0			0
$617$	16.0661			0.646795			0.323398	−	0.946263i	$-0.395175\pi$
$617$	16.0661			0.646795			0.323398	+	0.946263i	$0.395175\pi$
$618$			77.8412i			3.13123i
$619$			25.1393i			1.01043i	0.862993	+	0.505216i	$0.168587\pi$
$619$			25.1393i			1.01043i	−0.862993	+	0.505216i	$0.831413\pi$
$620$		−	12.3696i		−	0.496775i
$621$	33.1420			1.32994
$622$	−31.2278			−1.25212
$623$		0			0
$624$	2.23975			0.0896619
$625$	6.36496			0.254598
$626$	−69.0199			−2.75859
$627$	−43.6173	−	37.8561i	−1.74191	−	1.51183i
$628$		−	3.62110i		−	0.144498i
$629$	9.83447			0.392126
$630$		0			0
$631$	−13.8267			−0.550432			−0.275216	−	0.961382i	$-0.588749\pi$
$631$	−13.8267			−0.550432			−0.275216	+	0.961382i	$0.588749\pi$
$632$	10.8423			0.431285
$633$		−	72.6343i		−	2.88696i
$634$	67.0518			2.66297
$635$	2.64467			0.104950
$636$		−	88.6988i		−	3.51713i
$637$		0			0
$638$	−85.9694			−3.40356
$639$			43.4453i			1.71867i
$640$	20.7168			0.818902
$641$		−	1.19608i		−	0.0472424i	−0.999721	−	0.0236212i	$-0.992480\pi$
$641$		−	1.19608i		−	0.0472424i	0.999721	−	0.0236212i	$-0.00751956\pi$
$642$	32.0389			1.26448
$643$		−	28.4311i		−	1.12121i	−0.828082	−	0.560606i	$-0.810568\pi$
$643$		−	28.4311i		−	1.12121i	0.828082	−	0.560606i	$-0.189432\pi$
$644$		0			0
$645$		−	20.0553i		−	0.789677i
$646$	28.6647	+	24.8786i	1.12780	+	0.978834i
$647$			5.56921i			0.218948i	0.993990	+	0.109474i	$0.0349167\pi$
$647$			5.56921i			0.218948i	−0.993990	+	0.109474i	$0.965083\pi$
$648$		−	5.77082i		−	0.226699i
$649$	−54.3595			−2.13380
$650$			26.1306i			1.02493i
$651$		0			0
$652$	−45.1067			−1.76652
$653$	8.89967			0.348271			0.174135	−	0.984722i	$-0.444287\pi$
$653$	8.89967			0.348271			0.174135	+	0.984722i	$0.444287\pi$
$654$	8.46967			0.331190
$655$	5.14884			0.201182
$656$	−1.18746			−0.0463625
$657$			13.8816i			0.541574i
$658$		0			0
$659$			23.7329i			0.924502i	0.886749	+	0.462251i	$0.152958\pi$
$659$			23.7329i			0.924502i	−0.886749	+	0.462251i	$0.847042\pi$
$660$		−	49.2223i		−	1.91597i
$661$	−14.4296			−0.561245			−0.280622	−	0.959818i	$-0.590541\pi$
$661$	−14.4296			−0.561245			−0.280622	+	0.959818i	$0.590541\pi$
$662$	−13.3002			−0.516927
$663$			33.1619i			1.28790i
$664$	11.1340			0.432083
$665$		0			0
$666$	26.4075			1.02327
$667$		−	62.3390i		−	2.41377i
$668$	24.7130			0.956176
$669$	27.8635			1.07727
$670$			12.8045i			0.494682i
$671$			69.4373i			2.68060i
$672$		0			0
$673$			18.9024i			0.728634i	0.931275	+	0.364317i	$0.118697\pi$
$673$			18.9024i			0.728634i	−0.931275	+	0.364317i	$0.881303\pi$
$674$	−26.6957			−1.02828
$675$	15.0996			0.581184
$676$	9.56012			0.367697
$677$	−31.4337			−1.20809			−0.604047	−	0.796949i	$-0.706446\pi$
$677$	−31.4337			−1.20809			−0.604047	+	0.796949i	$0.706446\pi$
$678$	−34.3912			−1.32079
$679$		0			0
$680$			11.9875i			0.459699i
$681$	16.8807			0.646871
$682$		−	36.6164i		−	1.40211i
$683$			51.0246i			1.95240i	0.216867	+	0.976201i	$0.430416\pi$
$683$			51.0246i			1.95240i	−0.216867	+	0.976201i	$0.569584\pi$
$684$	47.2379	+	40.9985i	1.80619	+	1.56762i
$685$		−	22.2769i		−	0.851158i
$686$		0			0
$687$		−	5.90683i		−	0.225359i
$688$	1.61720			0.0616553
$689$		−	32.1847i		−	1.22614i
$690$	58.1583			2.21405
$691$			33.1060i			1.25941i	0.776834	+	0.629705i	$0.216824\pi$
$691$			33.1060i			1.25941i	−0.776834	+	0.629705i	$0.783176\pi$
$692$	−45.1618			−1.71679
$693$		0			0
$694$			38.2631i			1.45245i
$695$	−6.43573			−0.244121
$696$	57.4230			2.17661
$697$		−	17.5816i		−	0.665951i
$698$	4.58669			0.173609
$699$	−64.3986			−2.43578
$700$		0			0
$701$	26.4032			0.997234			0.498617	−	0.866822i	$-0.333841\pi$
$701$	26.4032			0.997234			0.498617	+	0.866822i	$0.333841\pi$
$702$			29.8923i			1.12821i
$703$	7.34251	−	8.45992i	0.276928	−	0.319072i
$704$	62.8981			2.37056
$705$	4.77662			0.179898
$706$	42.8033			1.61092
$707$		0			0
$708$	97.9807			3.68234
$709$	16.9388			0.636150			0.318075	−	0.948066i	$-0.396964\pi$
$709$	16.9388			0.636150			0.318075	+	0.948066i	$0.396964\pi$
$710$			25.5928i			0.960482i
$711$		−	18.2747i		−	0.685356i
$712$		−	29.2371i		−	1.09571i
$713$	26.5517			0.994368
$714$		0			0
$715$		−	17.8605i		−	0.667944i
$716$		−	58.1635i		−	2.17367i
$717$	0.474369			0.0177156
$718$			47.6012i			1.77646i
$719$		−	24.1831i		−	0.901879i	−0.892555	−	0.450939i	$-0.851089\pi$
$719$		−	24.1831i		−	0.901879i	0.892555	−	0.450939i	$-0.148911\pi$
$720$		−	1.36463i		−	0.0508569i
$721$		0			0
$722$	42.8027	−	6.08372i	1.59295	−	0.226413i
$723$	72.5938			2.69979
$724$	13.3115			0.494720
$725$		−	28.4019i		−	1.05482i
$726$		−	77.0881i		−	2.86101i
$727$			12.7784i			0.473926i	0.971519	+	0.236963i	$0.0761521\pi$
$727$			12.7784i			0.473926i	−0.971519	+	0.236963i	$0.923848\pi$
$728$		0			0
$729$	−43.9090			−1.62626
$730$			8.17742i			0.302660i
$731$			23.9444i			0.885617i
$732$		−	125.158i		−	4.62597i
$733$			33.0362i			1.22022i	0.792316	+	0.610111i	$0.208875\pi$
$733$			33.0362i			1.22022i	−0.792316	+	0.610111i	$0.791125\pi$
$734$	48.2741			1.78183
$735$		0			0
$736$			47.4209i			1.74796i
$737$			23.2621i			0.856871i
$738$		−	47.2102i		−	1.73783i
$739$	−12.6368			−0.464850			−0.232425	−	0.972614i	$-0.574666\pi$
$739$	−12.6368			−0.464850			−0.232425	+	0.972614i	$0.574666\pi$
$740$	9.54706			0.350957
$741$	28.5270	+	24.7590i	1.04796	+	0.909545i
$742$		0			0
$743$			14.5981i			0.535552i	0.963481	+	0.267776i	$0.0862887\pi$
$743$			14.5981i			0.535552i	−0.963481	+	0.267776i	$0.913711\pi$
$744$			24.4578i			0.896668i
$745$		−	0.469489i		−	0.0172008i
$746$	−5.50670			−0.201615
$747$		−	18.7663i		−	0.686624i
$748$			58.7674i			2.14875i
$749$		0			0
$750$	62.9634			2.29910
$751$		−	50.6540i		−	1.84839i	−0.381918	−	0.924196i	$-0.624736\pi$
$751$		−	50.6540i		−	1.84839i	0.381918	−	0.924196i	$-0.375264\pi$
$752$			0.385173i			0.0140458i
$753$		−	62.9724i		−	2.29484i
$754$	56.2265			2.04765
$755$	12.0509			0.438579
$756$		0			0
$757$	2.35093			0.0854460			0.0427230	−	0.999087i	$-0.486397\pi$
$757$	2.35093			0.0854460			0.0427230	+	0.999087i	$0.486397\pi$
$758$	−24.0791			−0.874592
$759$	105.657			3.83510
$760$	10.3120	+	8.94996i	0.374056	+	0.324649i
$761$			18.3009i			0.663405i	0.943384	+	0.331703i	$0.107623\pi$
$761$			18.3009i			0.663405i	−0.943384	+	0.331703i	$0.892377\pi$
$762$	−14.1110			−0.511186
$763$		0			0
$764$	−13.3046			−0.481344
$765$	20.2049			0.730508
$766$		−	62.0585i		−	2.24226i
$767$	35.5527			1.28373
$768$	−39.1783			−1.41373
$769$		−	38.6463i		−	1.39362i	−0.717255	−	0.696811i	$-0.754602\pi$
$769$		−	38.6463i		−	1.39362i	0.717255	−	0.696811i	$-0.245398\pi$
$770$		0			0
$771$	32.3451			1.16488
$772$			33.0058i			1.18791i
$773$	40.2540			1.44784			0.723918	−	0.689886i	$-0.242340\pi$
$773$	40.2540			1.44784			0.723918	+	0.689886i	$0.242340\pi$
$774$			64.2956i			2.31106i
$775$	12.0970			0.434538
$776$		−	0.205502i		−	0.00737710i
$777$		0			0
$778$		−	9.98322i		−	0.357916i
$779$	−15.1243	−	13.1266i	−0.541883	−	0.470309i
$780$			32.1928i			1.15269i
$781$			46.4948i			1.66372i
$782$	−69.4363			−2.48304
$783$		−	32.4905i		−	1.16112i
$784$		0			0
$785$	−1.33236			−0.0475540
$786$	−27.4723			−0.979904
$787$	11.3040			0.402945			0.201473	−	0.979494i	$-0.435427\pi$
$787$	11.3040			0.402945			0.201473	+	0.979494i	$0.435427\pi$
$788$	2.40368			0.0856275
$789$	28.8406			1.02675
$790$		−	10.7653i		−	0.383013i
$791$		0			0
$792$			58.4777i			2.07792i
$793$		−	45.4140i		−	1.61270i
$794$	−6.48443			−0.230124
$795$	−32.6361			−1.15748
$796$			35.2013i			1.24768i
$797$	−24.2678			−0.859611			−0.429806	−	0.902921i	$-0.641418\pi$
$797$	−24.2678			−0.859611			−0.429806	+	0.902921i	$0.641418\pi$
$798$		0			0
$799$	−5.70290			−0.201754
$800$			21.6051i			0.763856i
$801$	−49.2791			−1.74119
$802$	−58.7787			−2.07555
$803$			14.8560i			0.524257i
$804$		−	41.9290i		−	1.47872i
$805$		0			0
$806$			23.9482i			0.843539i
$807$	−21.0251			−0.740118
$808$	−53.1420			−1.86953
$809$	26.7437			0.940258			0.470129	−	0.882598i	$-0.344207\pi$
$809$	26.7437			0.940258			0.470129	+	0.882598i	$0.344207\pi$
$810$	−5.72983			−0.201326
$811$	−22.8881			−0.803711			−0.401855	−	0.915703i	$-0.631635\pi$
$811$	−22.8881			−0.803711			−0.401855	+	0.915703i	$0.631635\pi$
$812$		0			0
$813$			33.5387i			1.17625i
$814$	28.2611			0.990552
$815$			16.5967i			0.581358i
$816$			2.71159i			0.0949247i
$817$	20.5978	+	17.8771i	0.720624	+	0.625442i
$818$		−	43.1371i		−	1.50825i
$819$		0			0
$820$		−	17.0678i		−	0.596033i
$821$	−34.4857			−1.20356			−0.601780	−	0.798662i	$-0.705542\pi$
$821$	−34.4857			−1.20356			−0.601780	+	0.798662i	$0.705542\pi$
$822$			118.861i			4.14577i
$823$	17.6994			0.616964			0.308482	−	0.951230i	$-0.400179\pi$
$823$	17.6994			0.616964			0.308482	+	0.951230i	$0.400179\pi$
$824$		−	33.4334i		−	1.16471i
$825$	48.1376			1.67594
$826$		0			0
$827$			19.4111i			0.674991i	0.941327	+	0.337496i	$0.109580\pi$
$827$			19.4111i			0.674991i	−0.941327	+	0.337496i	$0.890420\pi$
$828$	−114.427			−3.97662
$829$	−0.0311598			−0.00108222			−0.000541112	−	1.00000i	$-0.500172\pi$
$829$	−0.0311598			−0.00108222			−0.000541112		1.00000i	$0.500172\pi$
$830$		−	11.0549i		−	0.383721i
$831$	81.4836			2.82663
$832$	−41.1372			−1.42617
$833$		0			0
$834$	34.3387			1.18905
$835$		−	9.09301i		−	0.314676i
$836$	50.5536	+	43.8763i	1.74843	+	1.51749i
$837$	13.8385			0.478328
$838$	19.4880			0.673203
$839$	−13.9635			−0.482075			−0.241037	−	0.970516i	$-0.577488\pi$
$839$	−13.9635			−0.482075			−0.241037	+	0.970516i	$0.577488\pi$
$840$		0			0
$841$	−32.1137			−1.10737
$842$	40.2965			1.38871
$843$		−	52.6380i		−	1.81295i
$844$			84.1852i			2.89777i
$845$		−	3.51759i		−	0.121009i
$846$	−15.3135			−0.526487
$847$		0			0
$848$		−	2.63168i		−	0.0903724i
$849$		−	7.15113i		−	0.245426i
$850$	−31.6354			−1.08509
$851$			20.4930i			0.702491i
$852$		−	83.8050i		−	2.87111i
$853$			3.34953i			0.114686i	0.998355	+	0.0573428i	$0.0182628\pi$
$853$			3.34953i			0.114686i	−0.998355	+	0.0573428i	$0.981737\pi$
$854$		0			0
$855$	15.0851	−	17.3809i	0.515901	−	0.594413i
$856$	−13.7610			−0.470340
$857$	−30.1832			−1.03104			−0.515519	−	0.856878i	$-0.672401\pi$
$857$	−30.1832			−1.03104			−0.515519	+	0.856878i	$0.672401\pi$
$858$			95.2969i			3.25338i
$859$		−	26.2227i		−	0.894708i	−0.894357	−	0.447354i	$-0.852366\pi$
$859$		−	26.2227i		−	0.894708i	0.894357	−	0.447354i	$-0.147634\pi$
$860$			23.2447i			0.792636i
$861$		0			0
$862$	−4.53606			−0.154499
$863$			25.5260i			0.868916i	0.900692	+	0.434458i	$0.143060\pi$
$863$			25.5260i			0.868916i	−0.900692	+	0.434458i	$0.856940\pi$
$864$			24.7153i			0.840833i
$865$			16.6170i			0.564994i
$866$			0.550308i			0.0187002i
$867$	6.45796			0.219324
$868$		0			0
$869$		−	19.5575i		−	0.663442i
$870$		−	57.0151i		−	1.93299i
$871$		−	15.2141i		−	0.515510i
$872$	−3.63779			−0.123191
$873$	−0.346374			−0.0117230
$874$	−51.8418	+	59.7313i	−1.75358	+	2.02044i
$875$		0			0
$876$		−	26.7773i		−	0.904723i
$877$		−	47.1052i		−	1.59063i	−0.606197	−	0.795314i	$-0.707306\pi$
$877$		−	47.1052i		−	1.59063i	0.606197	−	0.795314i	$-0.292694\pi$
$878$			16.8667i			0.569222i
$879$	−44.5754			−1.50349
$880$		−	1.46042i		−	0.0492308i
$881$		−	18.3361i		−	0.617759i	−0.951101	−	0.308879i	$-0.900046\pi$
$881$		−	18.3361i		−	0.617759i	0.951101	−	0.308879i	$-0.0999540\pi$
$882$		0			0
$883$	5.56291			0.187207			0.0936034	−	0.995610i	$-0.470161\pi$
$883$	5.56291			0.187207			0.0936034	+	0.995610i	$0.470161\pi$
$884$		−	38.4356i		−	1.29273i
$885$		−	36.0514i		−	1.21185i
$886$		−	40.1374i		−	1.34844i
$887$	16.4588			0.552633			0.276317	−	0.961067i	$-0.410886\pi$
$887$	16.4588			0.552633			0.276317	+	0.961067i	$0.410886\pi$
$888$	−18.8770			−0.633469
$889$		0			0
$890$	−29.0294			−0.973069
$891$	−10.4094			−0.348730
$892$	−32.2946			−1.08130
$893$	−4.25784	+	4.90582i	−0.142483	+	0.164167i
$894$			2.50502i			0.0837804i
$895$	−21.4009			−0.715352
$896$		0			0
$897$	−69.1027			−2.30727
$898$	23.2066			0.774414
$899$		−	26.0298i		−	0.868142i
$900$	−52.1335			−1.73778
$901$	38.9649			1.29811
$902$		−	50.5239i		−	1.68226i
$903$		0			0
$904$	14.7713			0.491286
$905$		−	4.89790i		−	0.162812i
$906$	−64.2993			−2.13620
$907$		−	16.7411i		−	0.555880i	−0.960598	−	0.277940i	$-0.910348\pi$
$907$		−	16.7411i		−	0.555880i	0.960598	−	0.277940i	$-0.0896516\pi$
$908$	−19.5652			−0.649294
$909$			89.5707i			2.97087i
$910$		0			0
$911$		−	48.8253i		−	1.61765i	−0.588047	−	0.808827i	$-0.700103\pi$
$911$		−	48.8253i		−	1.61765i	0.588047	−	0.808827i	$-0.299897\pi$
$912$	2.33260	+	2.02450i	0.0772401	+	0.0670379i
$913$		−	20.0836i		−	0.664669i
$914$			25.5481i			0.845055i
$915$	−46.0510			−1.52240
$916$			6.84617i			0.226204i
$917$		0			0
$918$	−36.1896			−1.19443
$919$	43.4426			1.43304			0.716520	−	0.697566i	$-0.245734\pi$
$919$	43.4426			1.43304			0.716520	+	0.697566i	$0.245734\pi$
$920$	−24.9794			−0.823547
$921$	−35.7095			−1.17667
$922$	−46.3672			−1.52702
$923$		−	30.4090i		−	1.00092i
$924$		0			0
$925$			9.33669i			0.306988i
$926$			91.3647i			3.00243i
$927$	−56.3519			−1.85084
$928$	46.4888			1.52607
$929$		−	48.1965i		−	1.58128i	−0.612283	−	0.790639i	$-0.709749\pi$
$929$		−	48.1965i		−	1.58128i	0.612283	−	0.790639i	$-0.290251\pi$
$930$	24.2841			0.796308
$931$		0			0
$932$	74.6398			2.44491
$933$		−	37.6248i		−	1.23178i
$934$	−73.8602			−2.41678
$935$	21.6231			0.707151
$936$		−	38.2461i		−	1.25011i
$937$		−	21.5927i		−	0.705404i	−0.935736	−	0.352702i	$-0.885263\pi$
$937$		−	21.5927i		−	0.705404i	0.935736	−	0.352702i	$-0.114737\pi$
$938$		0			0
$939$		−	83.1585i		−	2.71378i
$940$	−5.53624			−0.180572
$941$	−31.2582			−1.01899			−0.509494	−	0.860474i	$-0.670167\pi$
$941$	−31.2582			−1.01899			−0.509494	+	0.860474i	$0.670167\pi$
$942$	7.10898			0.231623
$943$	36.6364			1.19305
$944$	2.90708			0.0946174
$945$		0			0
$946$			68.8087i			2.23716i
$947$	36.2070			1.17657			0.588284	−	0.808654i	$-0.299804\pi$
$947$	36.2070			1.17657			0.588284	+	0.808654i	$0.299804\pi$
$948$			35.2515i			1.14492i
$949$		−	9.71627i		−	0.315403i
$950$	−23.6193	+	27.2138i	−0.766312	+	0.882933i
$951$			80.7873i			2.61971i
$952$		0			0
$953$		−	16.5137i		−	0.534931i	−0.963567	−	0.267465i	$-0.913814\pi$
$953$		−	16.5137i		−	0.534931i	0.963567	−	0.267465i	$-0.0861861\pi$
$954$	104.629			3.38748
$955$			4.89534i			0.158410i
$956$	−0.549807			−0.0177820
$957$		−	103.580i		−	3.34827i
$958$	−16.4033			−0.529965
$959$		0			0
$960$			41.7142i			1.34632i
$961$	−19.9133			−0.642364
$962$	−18.4836			−0.595935
$963$			23.1941i			0.747418i
$964$	−84.1382			−2.70991
$965$	12.1443			0.390938
$966$		0			0
$967$	24.4926			0.787628			0.393814	−	0.919190i	$-0.371155\pi$
$967$	24.4926			0.787628			0.393814	+	0.919190i	$0.371155\pi$
$968$			33.1099i			1.06419i
$969$	−29.9749	+	34.5366i	−0.962933	+	1.10948i
$970$	−0.204042			−0.00655141
$971$	1.45611			0.0467287			0.0233644	−	0.999727i	$-0.492562\pi$
$971$	1.45611			0.0467287			0.0233644	+	0.999727i	$0.492562\pi$
$972$	58.3809			1.87257
$973$		0			0
$974$	9.52764			0.305285
$975$	−31.4834			−1.00828
$976$		−	3.71342i		−	0.118864i
$977$			32.4852i			1.03929i	0.854381	+	0.519647i	$0.173937\pi$
$977$			32.4852i			1.03929i	−0.854381	+	0.519647i	$0.826063\pi$
$978$		−	88.5540i		−	2.83164i
$979$	−52.7381			−1.68552
$980$		0			0
$981$			6.13149i			0.195763i
$982$		−	14.2217i		−	0.453832i
$983$	−20.4031			−0.650759			−0.325379	−	0.945584i	$-0.605492\pi$
$983$	−20.4031			−0.650759			−0.325379	+	0.945584i	$0.605492\pi$
$984$			33.7474i			1.07583i
$985$		−	0.884418i		−	0.0281799i
$986$			68.0715i			2.16784i
$987$		0			0
$988$	−33.0635	−	28.6964i	−1.05189	−	0.912953i
$989$	−49.8953			−1.58658
$990$	58.0624			1.84534
$991$			8.01254i			0.254527i	0.991869	+	0.127263i	$0.0406193\pi$
$991$			8.01254i			0.254527i	−0.991869	+	0.127263i	$0.959381\pi$
$992$			19.8007i			0.628672i
$993$		−	16.0247i		−	0.508529i
$994$		0			0
$995$	12.9521			0.410609
$996$			36.1998i			1.14704i
$997$		−	19.3154i		−	0.611724i	−0.952076	−	0.305862i	$-0.901055\pi$
$997$		−	19.3154i		−	0.611724i	0.952076	−	0.305862i	$-0.0989445\pi$
$998$		−	58.1343i		−	1.84021i
$999$			10.6808i			0.337925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.c.f.930.6	yes	40
7.2	even	3		931.2.o.i.227.5		80
7.3	odd	6		931.2.o.i.607.36		80
7.4	even	3		931.2.o.i.607.35		80
7.5	odd	6		931.2.o.i.227.6		80
7.6	odd	2	inner	931.2.c.f.930.5	✓	40
19.18	odd	2	inner	931.2.c.f.930.35	yes	40
133.18	odd	6		931.2.o.i.607.6		80
133.37	odd	6		931.2.o.i.227.36		80
133.75	even	6		931.2.o.i.227.35		80
133.94	even	6		931.2.o.i.607.5		80
133.132	even	2	inner	931.2.c.f.930.36	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.c.f.930.5	✓	40	7.6	odd	2	inner
931.2.c.f.930.6	yes	40	1.1	even	1	trivial
931.2.c.f.930.35	yes	40	19.18	odd	2	inner
931.2.c.f.930.36	yes	40	133.132	even	2	inner
931.2.o.i.227.5		80	7.2	even	3
931.2.o.i.227.6		80	7.5	odd	6
931.2.o.i.227.35		80	133.75	even	6
931.2.o.i.227.36		80	133.37	odd	6
931.2.o.i.607.5		80	133.94	even	6
931.2.o.i.607.6		80	133.18	odd	6
931.2.o.i.607.35		80	7.4	even	3
931.2.o.i.607.36		80	7.3	odd	6

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.27541i q^{2} +2.74153 q^{3} -3.17751 q^{4} +1.16914i q^{5} -6.23811i q^{6} +2.67932i q^{8} +4.51598 q^{9} +O(q^{10})\)	\(q-2.27541i q^{2} +2.74153 q^{3} -3.17751 q^{4} +1.16914i q^{5} -6.23811i q^{6} +2.67932i q^{8} +4.51598 q^{9} +2.66029 q^{10} +4.83297 q^{11} -8.71123 q^{12} -3.16090 q^{13} +3.20524i q^{15} -0.258461 q^{16} -3.82680i q^{17} -10.2757i q^{18} +(-3.29194 - 2.85712i) q^{19} -3.71496i q^{20} -10.9970i q^{22} +7.97426 q^{23} +7.34543i q^{24} +3.63310 q^{25} +7.19236i q^{26} +4.15612 q^{27} -7.81752i q^{29} +7.29325 q^{30} +3.32967 q^{31} +5.94674i q^{32} +13.2497 q^{33} -8.70755 q^{34} -14.3496 q^{36} +2.56989i q^{37} +(-6.50114 + 7.49051i) q^{38} -8.66571 q^{39} -3.13251 q^{40} +4.59434 q^{41} -6.25704 q^{43} -15.3568 q^{44} +5.27983i q^{45} -18.1447i q^{46} -1.49025i q^{47} -0.708580 q^{48} -8.26681i q^{50} -10.4913i q^{51} +10.0438 q^{52} +10.1821i q^{53} -9.45688i q^{54} +5.65044i q^{55} +(-9.02494 - 7.83289i) q^{57} -17.7881 q^{58} -11.2476 q^{59} -10.1847i q^{60} +14.3674i q^{61} -7.57638i q^{62} +13.0144 q^{64} -3.69555i q^{65} -30.1486i q^{66} +4.81321i q^{67} +12.1597i q^{68} +21.8617 q^{69} +9.62034i q^{71} +12.0998i q^{72} +3.07389i q^{73} +5.84757 q^{74} +9.96026 q^{75} +(10.4601 + 9.07853i) q^{76} +19.7181i q^{78} -4.04668i q^{79} -0.302179i q^{80} -2.15384 q^{81} -10.4540i q^{82} -4.15553i q^{83} +4.47408 q^{85} +14.2373i q^{86} -21.4320i q^{87} +12.9491i q^{88} -10.9122 q^{89} +12.0138 q^{90} -25.3383 q^{92} +9.12839 q^{93} -3.39094 q^{94} +(3.34039 - 3.84875i) q^{95} +16.3032i q^{96} -0.0766995 q^{97} +21.8256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 40 * q^4 + 40 * q^9	\( 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Introduction

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