LMFDB - Embedded newform 432.2.y.e.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11640 - 0.868135i) q^{2} +(0.492685 + 1.93837i) q^{4} +(2.41406 - 0.646846i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.13273 - 2.59170i) q^{8} +O(q^{10})$	\(q+(-1.11640 - 0.868135i) q^{2} +(0.492685 + 1.93837i) q^{4} +(2.41406 - 0.646846i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.13273 - 2.59170i) q^{8} +(-3.25660 - 1.37359i) q^{10} +(-0.356120 + 1.32906i) q^{11} +(1.42802 + 5.32945i) q^{13} +(-4.56486 - 0.630943i) q^{14} +(-3.51452 + 1.91001i) q^{16} -5.37452 q^{17} +(4.71269 - 4.71269i) q^{19} +(2.44320 + 4.36064i) q^{20} +(1.55137 - 1.17460i) q^{22} +(2.88877 + 1.66783i) q^{23} +(1.07916 - 0.623053i) q^{25} +(3.03244 - 7.18949i) q^{26} +(4.54846 + 4.66730i) q^{28} +(3.03883 + 0.814251i) q^{29} +(0.621800 - 1.07699i) q^{31} +(5.58175 + 0.918755i) q^{32} +(6.00010 + 4.66581i) q^{34} +(5.75853 - 5.75853i) q^{35} +(-5.86087 - 5.86087i) q^{37} +(-9.35247 + 1.16998i) q^{38} +(1.05805 - 6.98923i) q^{40} +(2.81108 + 1.62298i) q^{41} +(1.61636 - 6.03232i) q^{43} +(-2.75166 - 0.0354845i) q^{44} +(-1.77711 - 4.36981i) q^{46} +(-2.17485 - 3.76695i) q^{47} +(1.80902 - 3.13331i) q^{49} +(-1.74566 - 0.241281i) q^{50} +(-9.62685 + 5.39376i) q^{52} +(0.134334 + 0.134334i) q^{53} +3.43879i q^{55} +(-1.02604 - 9.15923i) q^{56} +(-2.68566 - 3.54714i) q^{58} +(2.21088 - 0.592405i) q^{59} +(-2.29879 - 0.615960i) q^{61} +(-1.62915 + 0.662542i) q^{62} +(-5.43384 - 5.87140i) q^{64} +(6.89466 + 11.9419i) q^{65} +(-0.0300838 - 0.112274i) q^{67} +(-2.64794 - 10.4178i) q^{68} +(-11.4280 + 1.42963i) q^{70} +3.21118i q^{71} +9.75441i q^{73} +(1.45503 + 11.6311i) q^{74} +(11.4568 + 6.81304i) q^{76} +(1.16043 + 4.33078i) q^{77} +(1.11184 + 1.92576i) q^{79} +(-7.24880 + 6.88423i) q^{80} +(-1.72932 - 4.25229i) q^{82} +(-5.74772 - 1.54010i) q^{83} +(-12.9744 + 3.47649i) q^{85} +(-7.04136 + 5.33125i) q^{86} +(3.04114 + 2.42842i) q^{88} +6.12376i q^{89} +(12.7129 + 12.7129i) q^{91} +(-1.80962 + 6.42122i) q^{92} +(-0.842224 + 6.09347i) q^{94} +(8.32833 - 14.4251i) q^{95} +(-2.21495 - 3.83640i) q^{97} +(-4.73971 + 1.92755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.11640	−	0.868135i	−0.789412	−	0.613864i
$2$	−1.11640	−	0.868135i	−0.789412	−	0.613864i
$3$		0			0
$3$		0			0
$4$	0.492685	+	1.93837i	0.246342	+	0.969183i
$5$	2.41406	−	0.646846i	1.07960	−	0.289278i	0.325169	−	0.945656i	$-0.394579\pi$
$5$	2.41406	−	0.646846i	1.07960	−	0.289278i	0.754433	+	0.656378i	$0.227912\pi$
$6$		0			0
$7$	2.82197	−	1.62927i	1.06661	−	0.615805i	0.139353	−	0.990243i	$-0.455498\pi$
$7$	2.82197	−	1.62927i	1.06661	−	0.615805i	0.927252	+	0.374438i	$0.122164\pi$
$8$	1.13273	−	2.59170i	0.400481	−	0.916305i
$9$		0			0
$10$	−3.25660	−	1.37359i	−1.02983	−	0.434369i
$11$	−0.356120	+	1.32906i	−0.107374	+	0.400726i	−0.998604	−	0.0528265i	$-0.983177\pi$
$11$	−0.356120	+	1.32906i	−0.107374	+	0.400726i	0.891229	+	0.453553i	$0.149844\pi$
$12$		0			0
$13$	1.42802	+	5.32945i	0.396062	+	1.47812i	0.819964	+	0.572415i	$0.193993\pi$
$13$	1.42802	+	5.32945i	0.396062	+	1.47812i	−0.423903	+	0.905708i	$0.639340\pi$
$14$	−4.56486	−	0.630943i	−1.22001	−	0.168627i
$15$		0			0
$16$	−3.51452	+	1.91001i	−0.878631	+	0.477501i
$17$	−5.37452			−1.30351			−0.651756	−	0.758428i	$-0.725968\pi$
$17$	−5.37452			−1.30351			−0.651756	+	0.758428i	$0.725968\pi$
$18$		0			0
$19$	4.71269	−	4.71269i	1.08116	−	1.08116i	0.0847630	−	0.996401i	$-0.472987\pi$
$19$	4.71269	−	4.71269i	1.08116	−	1.08116i	0.996401	−	0.0847630i	$-0.0270133\pi$
$20$	2.44320	+	4.36064i	0.546315	+	0.975070i
$21$		0			0
$22$	1.55137	−	1.17460i	0.330754	−	0.250425i
$23$	2.88877	+	1.66783i	0.602351	+	0.347767i	0.769966	−	0.638085i	$-0.220273\pi$
$23$	2.88877	+	1.66783i	0.602351	+	0.347767i	−0.167615	+	0.985853i	$0.553607\pi$
$24$		0			0
$25$	1.07916	−	0.623053i	0.215832	−	0.124611i
$26$	3.03244	−	7.18949i	0.594710	−	1.40998i
$27$		0			0
$28$	4.54846	+	4.66730i	0.859577	+	0.882037i
$29$	3.03883	+	0.814251i	0.564296	+	0.151203i	0.529679	−	0.848198i	$-0.322312\pi$
$29$	3.03883	+	0.814251i	0.564296	+	0.151203i	0.0346168	+	0.999401i	$0.488979\pi$
$30$		0			0
$31$	0.621800	−	1.07699i	0.111679	−	0.193433i	−0.804769	−	0.593589i	$-0.797711\pi$
$31$	0.621800	−	1.07699i	0.111679	−	0.193433i	0.916447	+	0.400156i	$0.131044\pi$
$32$	5.58175	+	0.918755i	0.986723	+	0.162414i
$33$		0			0
$34$	6.00010	+	4.66581i	1.02901	+	0.800179i
$35$	5.75853	−	5.75853i	0.973369	−	0.973369i
$36$		0			0
$37$	−5.86087	−	5.86087i	−0.963521	−	0.963521i	0.0358368	−	0.999358i	$-0.488590\pi$
$37$	−5.86087	−	5.86087i	−0.963521	−	0.963521i	−0.999358	+	0.0358368i	$0.988590\pi$
$38$	−9.35247	+	1.16998i	−1.51717	+	0.189796i
$39$		0			0
$40$	1.05805	−	6.98923i	0.167292	−	1.10509i
$41$	2.81108	+	1.62298i	0.439017	+	0.253467i	0.703181	−	0.711011i	$-0.251763\pi$
$41$	2.81108	+	1.62298i	0.439017	+	0.253467i	−0.264163	+	0.964478i	$0.585096\pi$
$42$		0			0
$43$	1.61636	−	6.03232i	0.246492	−	0.919920i	−0.726136	−	0.687551i	$-0.758686\pi$
$43$	1.61636	−	6.03232i	0.246492	−	0.919920i	0.972628	−	0.232369i	$-0.0746476\pi$
$44$	−2.75166	−	0.0354845i	−0.414828	−	0.00534949i
$45$		0			0
$46$	−1.77711	−	4.36981i	−0.262021	−	0.644293i
$47$	−2.17485	−	3.76695i	−0.317234	−	0.549466i	0.662676	−	0.748907i	$-0.269421\pi$
$47$	−2.17485	−	3.76695i	−0.317234	−	0.549466i	−0.979910	+	0.199441i	$0.936088\pi$
$48$		0			0
$49$	1.80902	−	3.13331i	0.258431	−	0.447615i
$50$	−1.74566	−	0.241281i	−0.246874	−	0.0341223i
$51$		0			0
$52$	−9.62685	+	5.39376i	−1.33500	+	0.747980i
$53$	0.134334	+	0.134334i	0.0184522	+	0.0184522i	0.716273	−	0.697820i	$-0.245847\pi$
$53$	0.134334	+	0.134334i	0.0184522	+	0.0184522i	−0.697820	+	0.716273i	$0.745847\pi$
$54$		0			0
$55$			3.43879i			0.463686i
$56$	−1.02604	−	9.15923i	−0.137110	−	1.22395i
$57$		0			0
$58$	−2.68566	−	3.54714i	−0.352644	−	0.465762i
$59$	2.21088	−	0.592405i	0.287833	−	0.0771245i	−0.112014	−	0.993707i	$-0.535730\pi$
$59$	2.21088	−	0.592405i	0.287833	−	0.0771245i	0.399846	+	0.916582i	$0.369063\pi$
$60$		0			0
$61$	−2.29879	−	0.615960i	−0.294330	−	0.0788656i	0.108632	−	0.994082i	$-0.465353\pi$
$61$	−2.29879	−	0.615960i	−0.294330	−	0.0788656i	−0.402963	+	0.915216i	$0.632020\pi$
$62$	−1.62915	+	0.662542i	−0.206902	+	0.0841429i
$63$		0			0
$64$	−5.43384	−	5.87140i	−0.679230	−	0.733925i
$65$	6.89466	+	11.9419i	0.855178	+	1.48121i
$66$		0			0
$67$	−0.0300838	−	0.112274i	−0.00367532	−	0.0137165i	0.964064	−	0.265671i	$-0.0855934\pi$
$67$	−0.0300838	−	0.112274i	−0.00367532	−	0.0137165i	−0.967739	+	0.251954i	$0.918927\pi$
$68$	−2.64794	−	10.4178i	−0.321110	−	1.26334i
$69$		0			0
$70$	−11.4280	+	1.42963i	−1.36591	+	0.170873i
$71$			3.21118i			0.381097i	0.981678	+	0.190548i	$0.0610266\pi$
$71$			3.21118i			0.381097i	−0.981678	+	0.190548i	$0.938973\pi$
$72$		0			0
$73$			9.75441i			1.14167i	0.821066	+	0.570833i	$0.193380\pi$
$73$			9.75441i			1.14167i	−0.821066	+	0.570833i	$0.806620\pi$
$74$	1.45503	+	11.6311i	0.169144	+	1.35209i
$75$		0			0
$76$	11.4568	+	6.81304i	1.31418	+	0.781509i
$77$	1.16043	+	4.33078i	0.132243	+	0.493538i
$78$		0			0
$79$	1.11184	+	1.92576i	0.125092	+	0.216665i	0.921769	−	0.387740i	$-0.126744\pi$
$79$	1.11184	+	1.92576i	0.125092	+	0.216665i	−0.796677	+	0.604405i	$0.793411\pi$
$80$	−7.24880	+	6.88423i	−0.810440	+	0.769680i
$81$		0			0
$82$	−1.72932	−	4.25229i	−0.190971	−	0.469586i
$83$	−5.74772	−	1.54010i	−0.630895	−	0.169048i	−0.0708190	−	0.997489i	$-0.522561\pi$
$83$	−5.74772	−	1.54010i	−0.630895	−	0.169048i	−0.560076	+	0.828441i	$0.689228\pi$
$84$		0			0
$85$	−12.9744	+	3.47649i	−1.40727	+	0.377078i
$86$	−7.04136	+	5.33125i	−0.759289	+	0.574883i
$87$		0			0
$88$	3.04114	+	2.42842i	0.324186	+	0.258871i
$89$			6.12376i			0.649118i	0.945866	+	0.324559i	$0.105216\pi$
$89$			6.12376i			0.649118i	−0.945866	+	0.324559i	$0.894784\pi$
$90$		0			0
$91$	12.7129	+	12.7129i	1.33268	+	1.33268i
$92$	−1.80962	+	6.42122i	−0.188666	+	0.669458i
$93$		0			0
$94$	−0.842224	+	6.09347i	−0.0868688	+	0.628494i
$95$	8.32833	−	14.4251i	0.854469	−	1.47998i
$96$		0			0
$97$	−2.21495	−	3.83640i	−0.224894	−	0.389528i	0.731394	−	0.681956i	$-0.238870\pi$
$97$	−2.21495	−	3.83640i	−0.224894	−	0.389528i	−0.956288	+	0.292428i	$0.905537\pi$
$98$	−4.73971	+	1.92755i	−0.478783	+	0.194712i
$99$		0			0
$100$	1.73939	+	1.78484i	0.173939	+	0.178484i
$101$	4.62330	−	17.2544i	0.460035	−	1.71688i	−0.212811	−	0.977093i	$-0.568262\pi$
$101$	4.62330	−	17.2544i	0.460035	−	1.71688i	0.672847	−	0.739782i	$-0.265071\pi$
$102$		0			0
$103$	−8.73448	−	5.04285i	−0.860634	−	0.496887i	0.00359067	−	0.999994i	$-0.498857\pi$
$103$	−8.73448	−	5.04285i	−0.860634	−	0.496887i	−0.864224	+	0.503106i	$0.832190\pi$
$104$	15.4299	+	2.33582i	1.51303	+	0.229046i
$105$		0			0
$106$	−0.0333502	−	0.266591i	−0.00323926	−	0.0258936i
$107$	−3.59876	−	3.59876i	−0.347905	−	0.347905i	0.511423	−	0.859329i	$-0.329118\pi$
$107$	−3.59876	−	3.59876i	−0.347905	−	0.347905i	−0.859329	+	0.511423i	$0.829118\pi$
$108$		0			0
$109$	−7.27011	+	7.27011i	−0.696351	+	0.696351i	−0.963621	−	0.267271i	$-0.913878\pi$
$109$	−7.27011	+	7.27011i	−0.696351	+	0.696351i	0.267271	+	0.963621i	$0.413878\pi$
$110$	2.98533	−	3.83905i	0.284640	−	0.366039i
$111$		0			0
$112$	−6.80598	+	11.1161i	−0.643105	+	1.05037i
$113$	−5.81099	+	10.0649i	−0.546652	+	0.946828i	0.451849	+	0.892094i	$0.350764\pi$
$113$	−5.81099	+	10.0649i	−0.546652	+	0.946828i	−0.998501	+	0.0547341i	$0.982569\pi$
$114$		0			0
$115$	8.05251	+	2.15766i	0.750900	+	0.201203i
$116$	−0.0811335	+	6.29153i	−0.00753306	+	0.584154i
$117$		0			0
$118$	−2.98251	−	1.25799i	−0.274562	−	0.115807i
$119$	−15.1667	+	8.75652i	−1.39033	+	0.802709i
$120$		0			0
$121$	7.88670	+	4.55339i	0.716973	+	0.413945i
$122$	2.03163	+	2.68332i	0.183935	+	0.242936i
$123$		0			0
$124$	2.39395	+	0.674660i	0.214983	+	0.0605863i
$125$	−6.63394	+	6.63394i	−0.593358	+	0.593358i
$126$		0			0
$127$	−7.37772			−0.654667			−0.327333	−	0.944909i	$-0.606150\pi$
$127$	−7.37772			−0.654667			−0.327333	+	0.944909i	$0.606150\pi$
$128$	0.969157	+	11.2721i	0.0856622	+	0.996324i
$129$		0			0
$130$	2.67000	−	19.3174i	0.234175	−	1.69425i
$131$	3.93512	+	14.6861i	0.343813	+	1.28313i	0.893992	+	0.448082i	$0.147893\pi$
$131$	3.93512	+	14.6861i	0.343813	+	1.28313i	−0.550179	+	0.835047i	$0.685440\pi$
$132$		0			0
$133$	5.62085	−	20.9773i	0.487389	−	1.81896i
$134$	−0.0638837	+	0.151459i	−0.00551871	+	0.0130841i
$135$		0			0
$136$	−6.08788	+	13.9292i	−0.522032	+	1.19442i
$137$	−11.5397	+	6.66247i	−0.985906	+	0.569213i	−0.904048	−	0.427431i	$-0.859419\pi$
$137$	−11.5397	+	6.66247i	−0.985906	+	0.569213i	−0.0818576	+	0.996644i	$0.526085\pi$
$138$		0			0
$139$	−16.2127	+	4.34417i	−1.37514	+	0.368468i	−0.869354	−	0.494191i	$-0.835465\pi$
$139$	−16.2127	+	4.34417i	−1.37514	+	0.368468i	−0.505787	+	0.862658i	$0.668798\pi$
$140$	13.9993	+	8.32500i	1.18315	+	0.703591i
$141$		0			0
$142$	2.78774	−	3.58495i	0.233942	−	0.300843i
$143$	−7.59170			−0.634849
$144$		0			0
$145$	7.86261			0.652955
$146$	8.46814	−	10.8898i	0.700828	−	0.901245i
$147$		0			0
$148$	8.47295	−	14.2481i	0.696472	−	1.17118i
$149$	−12.7771	+	3.42362i	−1.04674	+	0.280474i	−0.740905	−	0.671610i	$-0.765603\pi$
$149$	−12.7771	+	3.42362i	−1.04674	+	0.280474i	−0.305838	+	0.952084i	$0.598937\pi$
$150$		0			0
$151$	−10.3438	+	5.97202i	−0.841769	+	0.485996i	−0.857865	−	0.513875i	$-0.828210\pi$
$151$	−10.3438	+	5.97202i	−0.841769	+	0.485996i	0.0160959	+	0.999870i	$0.494876\pi$
$152$	−6.87567	−	17.5521i	−0.557691	−	1.42366i
$153$		0			0
$154$	2.46420	−	5.84228i	0.198571	−	0.470784i
$155$	0.804418	−	3.00213i	0.0646124	−	0.241137i
$156$		0			0
$157$	−3.88412	−	14.4957i	−0.309986	−	1.15689i	−0.928567	−	0.371164i	$-0.878959\pi$
$157$	−3.88412	−	14.4957i	−0.309986	−	1.15689i	0.618581	−	0.785721i	$-0.287708\pi$
$158$	0.430566	−	3.11514i	0.0342540	−	0.247827i
$159$		0			0
$160$	14.0690	−	1.39260i	1.11225	−	0.110095i
$161$	10.8694			0.856627
$162$		0			0
$163$	16.4303	−	16.4303i	1.28692	−	1.28692i	0.350278	−	0.936646i	$-0.386087\pi$
$163$	16.4303	−	16.4303i	1.28692	−	1.28692i	0.936646	−	0.350278i	$-0.113913\pi$
$164$	−1.76095	+	6.24852i	−0.137507	+	0.487927i
$165$		0			0
$166$	5.07973	+	6.70916i	0.394263	+	0.520732i
$167$	−11.8153	−	6.82158i	−0.914297	−	0.527870i	−0.0324861	−	0.999472i	$-0.510342\pi$
$167$	−11.8153	−	6.82158i	−0.914297	−	0.527870i	−0.881811	+	0.471602i	$0.843676\pi$
$168$		0			0
$169$	−15.1054	+	8.72112i	−1.16196	+	0.670855i
$170$	17.5027	+	7.38241i	1.34239	+	0.566205i
$171$		0			0
$172$	12.4892	+	0.161057i	0.952292	+	0.0122805i
$173$	4.31671	+	1.15666i	0.328193	+	0.0879391i	0.419153	−	0.907915i	$-0.362327\pi$
$173$	4.31671	+	1.15666i	0.328193	+	0.0879391i	−0.0909602	+	0.995855i	$0.528994\pi$
$174$		0			0
$175$	2.03024	−	3.51648i	0.153472	−	0.265821i
$176$	−1.28692	−	5.35120i	−0.0970050	−	0.403362i
$177$		0			0
$178$	5.31625	−	6.83655i	0.398470	−	0.512421i
$179$	17.9090	−	17.9090i	1.33858	−	1.33858i	0.441146	−	0.897435i	$-0.354572\pi$
$179$	17.9090	−	17.9090i	1.33858	−	1.33858i	0.897435	−	0.441146i	$-0.145428\pi$
$180$		0			0
$181$	9.03811	+	9.03811i	0.671797	+	0.671797i	0.958130	−	0.286333i	$-0.0924363\pi$
$181$	9.03811	+	9.03811i	0.671797	+	0.671797i	−0.286333	+	0.958130i	$0.592436\pi$
$182$	−3.15614	−	25.2292i	−0.233949	−	1.87011i
$183$		0			0
$184$	7.59473	−	5.59763i	0.559891	−	0.412663i
$185$	−17.9396	−	10.3574i	−1.31894	−	0.761493i
$186$		0			0
$187$	1.91398	−	7.14305i	0.139964	−	0.522352i
$188$	6.23021	−	6.07157i	0.454385	−	0.442815i
$189$		0			0
$190$	−21.8207	+	8.87402i	−1.58304	+	0.643789i
$191$	−5.50837	−	9.54078i	−0.398572	−	0.690346i	0.594978	−	0.803742i	$-0.297161\pi$
$191$	−5.50837	−	9.54078i	−0.398572	−	0.690346i	−0.993550	+	0.113395i	$0.963827\pi$
$192$		0			0
$193$	−8.22204	+	14.2410i	−0.591836	+	1.02509i	0.402149	+	0.915574i	$0.368263\pi$
$193$	−8.22204	+	14.2410i	−0.591836	+	1.02509i	−0.993985	+	0.109515i	$0.965070\pi$
$194$	−0.857753	+	6.20582i	−0.0615831	+	0.445552i
$195$		0			0
$196$	6.96477	+	1.96280i	0.497484	+	0.140200i
$197$	−2.20874	−	2.20874i	−0.157366	−	0.157366i	0.624033	−	0.781398i	$-0.285493\pi$
$197$	−2.20874	−	2.20874i	−0.157366	−	0.157366i	−0.781398	+	0.624033i	$0.785493\pi$
$198$		0			0
$199$			11.9387i			0.846312i	0.906057	+	0.423156i	$0.139078\pi$
$199$			11.9387i			0.846312i	−0.906057	+	0.423156i	$0.860922\pi$
$200$	−0.392371	−	3.50261i	−0.0277448	−	0.247672i
$201$		0			0
$202$	−20.1406	+	15.2491i	−1.41709	+	1.07292i
$203$	9.90212	−	2.65326i	0.694992	−	0.186223i
$204$		0			0
$205$	7.83594	+	2.09963i	0.547286	+	0.146645i
$206$	5.37327	+	13.2125i	0.374373	+	0.920561i
$207$		0			0
$208$	−15.1981	−	16.0029i	−1.05380	−	1.10960i
$209$	4.58515	+	7.94172i	0.317162	+	0.549340i
$210$		0			0
$211$	−1.55584	−	5.80646i	−0.107108	−	0.399733i	0.891468	−	0.453084i	$-0.149676\pi$
$211$	−1.55584	−	5.80646i	−0.107108	−	0.399733i	−0.998576	+	0.0533513i	$0.983010\pi$
$212$	−0.194205	+	0.326574i	−0.0133380	+	0.0224292i
$213$		0			0
$214$	0.893437	+	7.14186i	0.0610741	+	0.488207i
$215$		−	15.6079i		−	1.06445i
$216$		0			0
$217$		−	4.05231i		−	0.275089i
$218$	14.4278	−	1.80490i	0.977172	−	0.122243i
$219$		0			0
$220$	−6.66562	+	1.69424i	−0.449396	+	0.114225i
$221$	−7.67493	−	28.6432i	−0.516271	−	1.92675i
$222$		0			0
$223$	4.14191	+	7.17400i	0.277363	+	0.480407i	0.970729	−	0.240179i	$-0.0772062\pi$
$223$	4.14191	+	7.17400i	0.277363	+	0.480407i	−0.693366	+	0.720586i	$0.743873\pi$
$224$	17.2484	−	6.50145i	1.15246	−	0.434396i
$225$		0			0
$226$	15.2251	−	6.19173i	1.01276	−	0.411868i
$227$	17.3293	+	4.64336i	1.15018	+	0.308191i	0.783039	−	0.621973i	$-0.213669\pi$
$227$	17.3293	+	4.64336i	1.15018	+	0.308191i	0.367145	+	0.930164i	$0.380335\pi$
$228$		0			0
$229$	−9.17552	+	2.45857i	−0.606335	+	0.162467i	−0.548908	−	0.835883i	$-0.684956\pi$
$229$	−9.17552	+	2.45857i	−0.606335	+	0.162467i	−0.0574270	+	0.998350i	$0.518290\pi$
$230$	−7.11666	−	9.39947i	−0.469258	−	0.619783i
$231$		0			0
$232$	5.55247	−	6.95341i	0.364538	−	0.456514i
$233$			6.39614i			0.419025i	0.977806	+	0.209512i	$0.0671877\pi$
$233$			6.39614i			0.419025i	−0.977806	+	0.209512i	$0.932812\pi$
$234$		0			0
$235$	−7.68686	−	7.68686i	−0.501435	−	0.501435i
$236$	2.23757	+	3.99363i	0.145653	+	0.259963i
$237$		0			0
$238$	24.5339	+	3.39102i	1.59030	+	0.219807i
$239$	−12.4015	+	21.4800i	−0.802187	+	1.38943i	0.115987	+	0.993251i	$0.462997\pi$
$239$	−12.4015	+	21.4800i	−0.802187	+	1.38943i	−0.918174	+	0.396178i	$0.870336\pi$
$240$		0			0
$241$	4.32533	+	7.49168i	0.278619	+	0.482582i	0.971042	−	0.238910i	$-0.0767901\pi$
$241$	4.32533	+	7.49168i	0.278619	+	0.482582i	−0.692423	+	0.721492i	$0.743457\pi$
$242$	−4.85174	−	11.9301i	−0.311881	−	0.766897i
$243$		0			0
$244$	0.0613754	−	4.75938i	0.00392916	−	0.304688i
$245$	2.34031	−	8.73415i	0.149517	−	0.558005i
$246$		0			0
$247$	31.8458	+	18.3862i	2.02630	+	1.16989i
$248$	−2.08690	−	2.83146i	−0.132519	−	0.179798i
$249$		0			0
$250$	13.1653	−	1.64696i	0.832645	−	0.104163i
$251$	1.34312	+	1.34312i	0.0847772	+	0.0847772i	0.748224	−	0.663446i	$-0.230907\pi$
$251$	1.34312	+	1.34312i	0.0847772	+	0.0847772i	−0.663446	+	0.748224i	$0.730907\pi$
$252$		0			0
$253$	−3.24540	+	3.24540i	−0.204037	+	0.204037i
$254$	8.23647	+	6.40486i	0.516802	+	0.401876i
$255$		0			0
$256$	8.70376	−	13.4255i	0.543985	−	0.839095i
$257$	13.0905	−	22.6734i	0.816563	−	1.41433i	−0.0916380	−	0.995792i	$-0.529210\pi$
$257$	13.0905	−	22.6734i	0.816563	−	1.41433i	0.908201	−	0.418535i	$-0.137456\pi$
$258$		0			0
$259$	−26.0881	−	6.99029i	−1.62104	−	0.434356i
$260$	−19.7509	+	19.2480i	−1.22490	+	1.19371i
$261$		0			0
$262$	8.35634	−	19.8117i	0.516256	−	1.22397i
$263$	−6.75594	+	3.90054i	−0.416589	+	0.240518i	−0.693617	−	0.720344i	$-0.743984\pi$
$263$	−6.75594	+	3.90054i	−0.416589	+	0.240518i	0.277028	+	0.960862i	$0.410651\pi$
$264$		0			0
$265$	0.411185	+	0.237398i	0.0252589	+	0.0145832i
$266$	−24.4862	+	18.5393i	−1.50135	+	1.13672i
$267$		0			0
$268$	0.202807	−	0.113629i	0.0123884	−	0.00694101i
$269$	−4.79063	+	4.79063i	−0.292090	+	0.292090i	−0.837905	−	0.545815i	$-0.816220\pi$
$269$	−4.79063	+	4.79063i	−0.292090	+	0.292090i	0.545815	+	0.837905i	$0.316220\pi$
$270$		0			0
$271$	−24.8625			−1.51029			−0.755144	−	0.655559i	$-0.772433\pi$
$271$	−24.8625			−1.51029			−0.755144	+	0.655559i	$0.772433\pi$
$272$	18.8889	−	10.2654i	1.14531	−	0.622429i
$273$		0			0
$274$	18.6668	+	2.58008i	1.12770	+	0.155868i
$275$	0.443764	+	1.65615i	0.0267599	+	0.0998695i
$276$		0			0
$277$	−0.238901	+	0.891589i	−0.0143541	+	0.0535704i	−0.972731	−	0.231934i	$-0.925495\pi$
$277$	−0.238901	+	0.891589i	−0.0143541	+	0.0535704i	0.958377	+	0.285505i	$0.0921612\pi$
$278$	21.8711	+	9.22496i	1.31174	+	0.553276i
$279$		0			0
$280$	−8.40153	−	21.4473i	−0.502088	−	1.28172i
$281$	24.6632	−	14.2393i	1.47128	−	0.849446i	0.471804	−	0.881703i	$-0.343603\pi$
$281$	24.6632	−	14.2393i	1.47128	−	0.849446i	0.999480	+	0.0322571i	$0.0102695\pi$
$282$		0			0
$283$	6.41436	−	1.71872i	0.381294	−	0.102167i	−0.0630806	−	0.998008i	$-0.520093\pi$
$283$	6.41436	−	1.71872i	0.381294	−	0.102167i	0.444375	+	0.895841i	$0.353426\pi$
$284$	−6.22444	+	1.58210i	−0.369353	+	0.0938803i
$285$		0			0
$286$	8.47535	+	6.59061i	0.501158	+	0.389711i
$287$	10.5771			0.624344
$288$		0			0
$289$	11.8855			0.699145
$290$	−8.77780	−	6.82581i	−0.515450	−	0.400825i
$291$		0			0
$292$	−18.9076	+	4.80585i	−1.10648	+	0.281241i
$293$	9.42116	−	2.52439i	0.550390	−	0.147477i	0.0271023	−	0.999633i	$-0.491372\pi$
$293$	9.42116	−	2.52439i	0.550390	−	0.147477i	0.523288	+	0.852156i	$0.324705\pi$
$294$		0			0
$295$	4.95402	−	2.86020i	0.288434	−	0.166527i
$296$	−21.8284	+	8.55084i	−1.26875	+	0.497008i
$297$		0			0
$298$	17.2365	+	7.27015i	0.998484	+	0.421148i
$299$	−4.76340	+	17.7773i	−0.275475	+	1.02809i
$300$		0			0
$301$	−5.26694	−	19.6565i	−0.303582	−	1.13298i
$302$	16.7323	+	2.31270i	0.962838	+	0.133081i
$303$		0			0
$304$	−7.56159	+	25.5641i	−0.433687	+	1.46620i
$305$	−5.94786			−0.340574
$306$		0			0
$307$	−4.55233	+	4.55233i	−0.259815	+	0.259815i	−0.824979	−	0.565164i	$-0.808813\pi$
$307$	−4.55233	+	4.55233i	−0.259815	+	0.259815i	0.565164	+	0.824979i	$0.308813\pi$
$308$	−7.82291	+	4.38305i	−0.445752	+	0.249747i
$309$		0			0
$310$	−3.50430	+	2.65322i	−0.199031	+	0.150693i
$311$	5.56997	+	3.21582i	0.315844	+	0.182353i	0.649539	−	0.760329i	$-0.274962\pi$
$311$	5.56997	+	3.21582i	0.315844	+	0.182353i	−0.333695	+	0.942681i	$0.608295\pi$
$312$		0			0
$313$	−2.90181	+	1.67536i	−0.164020	+	0.0946969i	−0.579763	−	0.814785i	$-0.696855\pi$
$313$	−2.90181	+	1.67536i	−0.164020	+	0.0946969i	0.415743	+	0.909482i	$0.363522\pi$
$314$	−8.24803	+	19.5549i	−0.465463	+	1.10355i
$315$		0			0
$316$	−3.18504	+	3.10394i	−0.179173	+	0.174610i
$317$	14.6346	+	3.92134i	0.821963	+	0.220244i	0.645204	−	0.764010i	$-0.276772\pi$
$317$	14.6346	+	3.92134i	0.821963	+	0.220244i	0.176758	+	0.984254i	$0.443439\pi$
$318$		0			0
$319$	−2.16438	+	3.74881i	−0.121182	+	0.209893i
$320$	−16.9155	−	10.6591i	−0.945607	−	0.595860i
$321$		0			0
$322$	−12.1345	−	9.43609i	−0.676232	−	0.525853i
$323$	−25.3284	+	25.3284i	−1.40931	+	1.40931i
$324$		0			0
$325$	4.86159	+	4.86159i	0.269672	+	0.269672i
$326$	−32.6065	+	4.07904i	−1.80591	+	0.225917i
$327$		0			0
$328$	7.39048	−	5.44709i	0.408071	−	0.300765i
$329$	−12.2747	−	7.08682i	−0.676728	−	0.390709i
$330$		0			0
$331$	−2.68206	+	10.0096i	−0.147420	+	0.550177i	0.852216	+	0.523190i	$0.175258\pi$
$331$	−2.68206	+	10.0096i	−0.147420	+	0.550177i	−0.999636	+	0.0269876i	$0.991409\pi$
$332$	0.153458	−	11.9000i	0.00842212	−	0.653096i
$333$		0			0
$334$	7.26854	+	17.8729i	0.397717	+	0.977961i
$335$	−0.145248	−	0.251578i	−0.00793577	−	0.0137452i
$336$		0			0
$337$	6.52225	−	11.2969i	0.355289	−	0.615379i	−0.631878	−	0.775068i	$-0.717716\pi$
$337$	6.52225	−	11.2969i	0.355289	−	0.615379i	0.987167	+	0.159689i	$0.0510490\pi$
$338$	24.4348	+	3.37731i	1.32908	+	0.183701i
$339$		0			0
$340$	−13.1310	−	23.4364i	−0.712129	−	1.27102i
$341$	1.20995	+	1.20995i	0.0655223	+	0.0655223i
$342$		0			0
$343$			11.0203i			0.595038i
$344$	−13.8031	−	11.0221i	−0.744212	−	0.594272i
$345$		0			0
$346$	−3.81503	−	5.03877i	−0.205097	−	0.270886i
$347$	−23.5314	+	6.30523i	−1.26323	+	0.338482i	−0.827435	−	0.561562i	$-0.810201\pi$
$347$	−23.5314	+	6.30523i	−1.26323	+	0.338482i	−0.435798	+	0.900044i	$0.643534\pi$
$348$		0			0
$349$	27.7772	+	7.44289i	1.48688	+	0.398409i	0.908683	−	0.417487i	$-0.137089\pi$
$349$	27.7772	+	7.44289i	1.48688	+	0.398409i	0.578199	+	0.815896i	$0.303756\pi$
$350$	−5.31933	+	2.16326i	−0.284330	+	0.115631i
$351$		0			0
$352$	−3.20885	+	7.09128i	−0.171032	+	0.377967i
$353$	−17.6048	−	30.4924i	−0.937010	−	1.62295i	−0.771011	−	0.636822i	$-0.780248\pi$
$353$	−17.6048	−	30.4924i	−0.937010	−	1.62295i	−0.165999	−	0.986126i	$-0.553085\pi$
$354$		0			0
$355$	2.07714	+	7.75199i	0.110243	+	0.411433i
$356$	−11.8701	+	3.01708i	−0.629114	+	0.159905i
$357$		0			0
$358$	−35.5410	+	4.44613i	−1.87840	+	0.234985i
$359$			17.6127i			0.929564i	0.885425	+	0.464782i	$0.153867\pi$
$359$			17.6127i			0.929564i	−0.885425	+	0.464782i	$0.846133\pi$
$360$		0			0
$361$		−	25.4188i		−	1.33783i
$362$	−2.24382	−	17.9364i	−0.117933	−	0.942717i
$363$		0			0
$364$	−18.3788	+	30.9058i	−0.963312	+	1.61990i
$365$	6.30960	+	23.5477i	0.330259	+	1.23255i
$366$		0			0
$367$	−8.31959	−	14.4100i	−0.434279	−	0.752193i	0.562957	−	0.826486i	$-0.309663\pi$
$367$	−8.31959	−	14.4100i	−0.434279	−	0.752193i	−0.997236	+	0.0742925i	$0.976330\pi$
$368$	−13.3382	−	0.344068i	−0.695304	−	0.0179358i
$369$		0			0
$370$	11.0361	+	27.1370i	0.573737	+	1.41078i
$371$	0.597954	+	0.160221i	0.0310442	+	0.00831828i
$372$		0			0
$373$	−3.22714	+	0.864710i	−0.167095	+	0.0447730i	−0.341397	−	0.939919i	$-0.610900\pi$
$373$	−3.22714	+	0.864710i	−0.167095	+	0.0447730i	0.174302	+	0.984692i	$0.444233\pi$
$374$	−8.33789	+	6.31290i	−0.431142	+	0.326432i
$375$		0			0
$376$	−12.2263	+	1.36962i	−0.630525	+	0.0706329i
$377$			17.3580i			0.893984i
$378$		0			0
$379$	−10.2384	−	10.2384i	−0.525910	−	0.525910i	0.393440	−	0.919350i	$-0.371285\pi$
$379$	−10.2384	−	10.2384i	−0.525910	−	0.525910i	−0.919350	+	0.393440i	$0.871285\pi$
$380$	32.0644	+	9.03633i	1.64487	+	0.463554i
$381$		0			0
$382$	−2.13315	+	15.4333i	−0.109142	+	0.789637i
$383$	−5.44755	+	9.43544i	−0.278357	+	0.482128i	−0.970977	−	0.239175i	$-0.923123\pi$
$383$	−5.44755	+	9.43544i	−0.278357	+	0.482128i	0.692620	+	0.721303i	$0.256456\pi$
$384$		0			0
$385$	5.60270	+	9.70416i	0.285540	+	0.494570i
$386$	21.5422	−	8.76077i	1.09647	−	0.445911i
$387$		0			0
$388$	6.34508	−	6.18352i	0.322123	−	0.313921i
$389$	−3.72849	+	13.9149i	−0.189042	+	0.705513i	0.804687	+	0.593699i	$0.202333\pi$
$389$	−3.72849	+	13.9149i	−0.189042	+	0.705513i	−0.993729	+	0.111815i	$0.964334\pi$
$390$		0			0
$391$	−15.5258	−	8.96381i	−0.785172	−	0.453319i
$392$	−6.07147	−	8.23763i	−0.306656	−	0.416063i
$393$		0			0
$394$	0.548346	+	4.38330i	0.0276253	+	0.220828i
$395$	3.92972	+	3.92972i	0.197725	+	0.197725i
$396$		0			0
$397$	15.4247	−	15.4247i	0.774145	−	0.774145i	−0.204683	−	0.978828i	$-0.565616\pi$
$397$	15.4247	−	15.4247i	0.774145	−	0.774145i	0.978828	+	0.204683i	$0.0656165\pi$
$398$	10.3644	−	13.3283i	0.519520	−	0.668089i
$399$		0			0
$400$	−2.60270	+	4.25093i	−0.130135	+	0.212547i
$401$	3.21720	−	5.57235i	0.160659	−	0.278270i	−0.774446	−	0.632640i	$-0.781971\pi$
$401$	3.21720	−	5.57235i	0.160659	−	0.278270i	0.935105	+	0.354370i	$0.115305\pi$
$402$		0			0
$403$	6.62770	+	1.77589i	0.330149	+	0.0884633i
$404$	35.7231	+	0.460674i	1.77729	+	0.0229194i
$405$		0			0
$406$	−13.3581	−	5.63428i	−0.662951	−	0.279624i
$407$	9.87661	−	5.70227i	0.489566	−	0.282651i
$408$		0			0
$409$	31.8642	+	18.3968i	1.57558	+	0.909663i	0.995465	+	0.0951294i	$0.0303265\pi$
$409$	31.8642	+	18.3968i	1.57558	+	0.909663i	0.580117	+	0.814533i	$0.303007\pi$
$410$	−6.92526	−	9.14668i	−0.342014	−	0.451722i
$411$		0			0
$412$	5.47155	−	19.4152i	0.269564	−	0.956516i
$413$	5.27387	−	5.27387i	0.259510	−	0.259510i
$414$		0			0
$415$	−14.8716			−0.730017
$416$	3.07439	+	31.0596i	0.150735	+	1.52282i
$417$		0			0
$418$	1.77563	−	12.8466i	0.0868489	−	0.628350i
$419$	5.78093	+	21.5747i	0.282417	+	1.05399i	0.950706	+	0.310093i	$0.100360\pi$
$419$	5.78093	+	21.5747i	0.282417	+	1.05399i	−0.668290	+	0.743901i	$0.732973\pi$
$420$		0			0
$421$	2.33477	−	8.71347i	0.113790	−	0.424669i	−0.885404	−	0.464822i	$-0.846118\pi$
$421$	2.33477	−	8.71347i	0.113790	−	0.424669i	0.999194	+	0.0401539i	$0.0127848\pi$
$422$	−3.30386	+	7.83299i	−0.160829	+	0.381304i
$423$		0			0
$424$	0.500319	−	0.195990i	0.0242977	−	0.00951812i
$425$	−5.79996	+	3.34861i	−0.281340	+	0.162431i
$426$		0			0
$427$	−7.49070	+	2.00713i	−0.362500	+	0.0971316i
$428$	5.20266	−	8.74877i	0.251480	−	0.422888i
$429$		0			0
$430$	−13.5498	+	17.4246i	−0.653428	+	0.840291i
$431$	2.82883			0.136260			0.0681299	−	0.997676i	$-0.478297\pi$
$431$	2.82883			0.136260			0.0681299	+	0.997676i	$0.478297\pi$
$432$		0			0
$433$	−9.90919			−0.476205			−0.238103	−	0.971240i	$-0.576525\pi$
$433$	−9.90919			−0.476205			−0.238103	+	0.971240i	$0.576525\pi$
$434$	−3.51795	+	4.52399i	−0.168867	+	0.217158i
$435$		0			0
$436$	−17.6740	−	10.5103i	−0.846432	−	0.503351i
$437$	21.4739	−	5.75390i	1.02723	−	0.275246i
$438$		0			0
$439$	5.53112	−	3.19339i	0.263986	−	0.152412i	−0.362166	−	0.932114i	$-0.617963\pi$
$439$	5.53112	−	3.19339i	0.263986	−	0.152412i	0.626151	+	0.779701i	$0.284629\pi$
$440$	8.91231	+	3.89522i	0.424878	+	0.185697i
$441$		0			0
$442$	−16.2979	+	38.6401i	−0.775212	+	1.83792i
$443$	4.33005	−	16.1600i	0.205727	−	0.767783i	−0.783500	−	0.621392i	$-0.786568\pi$
$443$	4.33005	−	16.1600i	0.205727	−	0.767783i	0.989227	−	0.146391i	$-0.0467658\pi$
$444$		0			0
$445$	3.96113	+	14.7831i	0.187776	+	0.700788i
$446$	1.60398	−	11.6048i	0.0759507	−	0.549502i
$447$		0			0
$448$	−24.9002	−	7.71576i	−1.17643	−	0.364535i
$449$	23.7209			1.11946			0.559729	−	0.828676i	$-0.310905\pi$
$449$	23.7209			1.11946			0.559729	+	0.828676i	$0.310905\pi$
$450$		0			0
$451$	−3.15812	+	3.15812i	−0.148710	+	0.148710i
$452$	−22.3725	−	6.30498i	−1.05231	−	0.296562i
$453$		0			0
$454$	−15.3153	−	20.2280i	−0.718781	−	0.949346i
$455$	38.9131	+	22.4665i	1.82427	+	1.05324i
$456$		0			0
$457$	−25.8782	+	14.9408i	−1.21053	+	0.698901i	−0.962875	−	0.269946i	$-0.912994\pi$
$457$	−25.8782	+	14.9408i	−1.21053	+	0.698901i	−0.247657	+	0.968848i	$0.579661\pi$
$458$	12.3779	+	5.22084i	0.578381	+	0.243954i
$459$		0			0
$460$	−0.214994	+	16.6718i	−0.0100241	+	0.777325i
$461$	−26.9785	−	7.22887i	−1.25651	−	0.336682i	−0.431665	−	0.902034i	$-0.642074\pi$
$461$	−26.9785	−	7.22887i	−1.25651	−	0.336682i	−0.824850	+	0.565352i	$0.808740\pi$
$462$		0			0
$463$	9.00954	−	15.6050i	0.418709	−	0.725225i	−0.577101	−	0.816673i	$-0.695816\pi$
$463$	9.00954	−	15.6050i	0.418709	−	0.725225i	0.995810	+	0.0914480i	$0.0291495\pi$
$464$	−12.2353	+	2.94247i	−0.568008	+	0.136601i
$465$		0			0
$466$	5.55271	−	7.14063i	0.257224	−	0.330783i
$467$	−3.24566	+	3.24566i	−0.150191	+	0.150191i	−0.778204	−	0.628012i	$-0.783869\pi$
$467$	−3.24566	+	3.24566i	−0.150191	+	0.150191i	0.628012	+	0.778204i	$0.283869\pi$
$468$		0			0
$469$	−0.267820	−	0.267820i	−0.0123668	−	0.0123668i
$470$	1.90836	+	15.2548i	0.0880260	+	0.703652i
$471$		0			0
$472$	0.969000	−	6.40099i	0.0446019	−	0.294629i
$473$	7.44169	+	4.29646i	0.342169	+	0.197552i
$474$		0			0
$475$	2.14949	−	8.02199i	0.0986252	−	0.368074i
$476$	−24.4458	−	25.0845i	−1.12047	−	1.14975i
$477$		0			0
$478$	32.4926	−	13.2141i	1.48618	−	0.604398i
$479$	1.27156	+	2.20241i	0.0580991	+	0.100631i	0.893612	−	0.448840i	$-0.148163\pi$
$479$	1.27156	+	2.20241i	0.0580991	+	0.100631i	−0.835513	+	0.549471i	$0.814829\pi$
$480$		0			0
$481$	22.8657	−	39.6046i	1.04259	−	1.80582i
$482$	1.67501	−	12.1187i	0.0762946	−	0.551990i
$483$		0			0
$484$	−4.94048	+	17.5307i	−0.224567	+	0.796850i
$485$	−7.82859	−	7.82859i	−0.355478	−	0.355478i
$486$		0			0
$487$		−	26.4554i		−	1.19881i	−0.800447	−	0.599404i	$-0.795404\pi$
$487$		−	26.4554i		−	1.19881i	0.800447	−	0.599404i	$-0.204596\pi$
$488$	−4.20030	+	5.26007i	−0.190139	+	0.238112i
$489$		0			0
$490$	−10.1951	+	7.71908i	−0.460569	+	0.348712i
$491$	21.9322	−	5.87672i	0.989787	−	0.265213i	0.272626	−	0.962120i	$-0.412108\pi$
$491$	21.9322	−	5.87672i	0.989787	−	0.265213i	0.717161	+	0.696907i	$0.245441\pi$
$492$		0			0
$493$	−16.3322	−	4.37621i	−0.735567	−	0.197095i
$494$	−19.5909	−	48.1727i	−0.881436	−	2.16739i
$495$		0			0
$496$	−0.128275	+	4.97275i	−0.00575973	+	0.223283i
$497$	5.23187	+	9.06186i	0.234681	+	0.406480i
$498$		0			0
$499$	7.34516	+	27.4125i	0.328815	+	1.22715i	0.910421	+	0.413683i	$0.135758\pi$
$499$	7.34516	+	27.4125i	0.328815	+	1.22715i	−0.581606	+	0.813470i	$0.697576\pi$
$500$	−16.1274	−	9.59057i	−0.721241	−	0.428903i
$501$		0			0
$502$	−0.333447	−	2.66547i	−0.0148825	−	0.118966i
$503$		−	32.0583i		−	1.42941i	−0.699427	−	0.714704i	$-0.746561\pi$
$503$		−	32.0583i		−	1.42941i	0.699427	−	0.714704i	$-0.253439\pi$
$504$		0			0
$505$		−	44.6437i		−	1.98662i
$506$	6.44060	−	0.805711i	0.286320	−	0.0358182i
$507$		0			0
$508$	−3.63489	−	14.3007i	−0.161272	−	0.634492i
$509$	−7.15242	−	26.6932i	−0.317025	−	1.18316i	−0.922089	−	0.386978i	$-0.873519\pi$
$509$	−7.15242	−	26.6932i	−0.317025	−	1.18316i	0.605064	−	0.796177i	$-0.293148\pi$
$510$		0			0
$511$	15.8925	+	27.5267i	0.703044	+	1.21771i
$512$	−21.3720	+	7.43218i	−0.944518	+	0.328459i
$513$		0			0
$514$	−34.2977	+	13.9482i	−1.51281	+	0.615229i
$515$	−24.3475	−	6.52390i	−1.07288	−	0.287477i
$516$		0			0
$517$	5.78101	−	1.54902i	0.254248	−	0.0681256i
$518$	23.0562	+	30.4519i	1.01303	+	1.33798i
$519$		0			0
$520$	38.7597	−	4.34195i	1.69972	−	0.190407i
$521$			6.90291i			0.302422i	0.988502	+	0.151211i	$0.0483173\pi$
$521$			6.90291i			0.302422i	−0.988502	+	0.151211i	$0.951683\pi$
$522$		0			0
$523$	14.2754	+	14.2754i	0.624219	+	0.624219i	0.946607	−	0.322389i	$-0.104486\pi$
$523$	14.2754	+	14.2754i	0.624219	+	0.624219i	−0.322389	+	0.946607i	$0.604486\pi$
$524$	−26.5282	+	14.8633i	−1.15889	+	0.649307i
$525$		0			0
$526$	10.9285	+	1.51051i	0.476505	+	0.0658613i
$527$	−3.34188	+	5.78830i	−0.145574	+	0.252142i
$528$		0			0
$529$	−5.93666	−	10.2826i	−0.258116	−	0.447069i
$530$	−0.252953	−	0.621994i	−0.0109876	−	0.0270177i
$531$		0			0
$532$	43.4310	+	0.560072i	1.88297	+	0.0242822i
$533$	−4.63529	+	17.2992i	−0.200777	+	0.749310i
$534$		0			0
$535$	−11.0155	−	6.35979i	−0.476241	−	0.274958i
$536$	−0.325058	−	0.0492083i	−0.0140404	−	0.00212547i
$537$		0			0
$538$	9.50716	−	1.18933i	0.409883	−	0.0512758i
$539$	3.52012	+	3.52012i	0.151622	+	0.151622i
$540$		0			0
$541$	−15.3215	+	15.3215i	−0.658723	+	0.658723i	−0.955078	−	0.296355i	$-0.904229\pi$
$541$	−15.3215	+	15.3215i	−0.658723	+	0.658723i	0.296355	+	0.955078i	$0.404229\pi$
$542$	27.7564	+	21.5840i	1.19224	+	0.927111i
$543$		0			0
$544$	−29.9992	−	4.93787i	−1.28621	−	0.211709i
$545$	−12.8479	+	22.2532i	−0.550342	+	0.953220i
$546$		0			0
$547$	4.09038	+	1.09601i	0.174892	+	0.0468622i	0.345202	−	0.938528i	$-0.387810\pi$
$547$	4.09038	+	1.09601i	0.174892	+	0.0468622i	−0.170310	+	0.985390i	$0.554477\pi$
$548$	−18.5997	−	19.0857i	−0.794542	−	0.815302i
$549$		0			0
$550$	0.942343	−	2.23417i	0.0401816	−	0.0952651i
$551$	18.1584	−	10.4837i	0.773572	−	0.446622i
$552$		0			0
$553$	6.27515	+	3.62296i	0.266847	+	0.154064i
$554$	1.04073	−	0.787970i	0.0442163	−	0.0334776i
$555$		0			0
$556$	−16.4083	−	29.2858i	−0.695868	−	1.24199i
$557$	−3.77104	+	3.77104i	−0.159784	+	0.159784i	−0.782471	−	0.622687i	$-0.786041\pi$
$557$	−3.77104	+	3.77104i	−0.159784	+	0.159784i	0.622687	+	0.782471i	$0.286041\pi$
$558$		0			0
$559$	34.4571			1.45738
$560$	−9.23967	+	31.2373i	−0.390447	+	1.32002i
$561$		0			0
$562$	−39.8956	−	5.51426i	−1.68289	−	0.232605i
$563$	−4.72321	−	17.6273i	−0.199060	−	0.742901i	−0.991178	−	0.132534i	$-0.957689\pi$
$563$	−4.72321	−	17.6273i	−0.199060	−	0.742901i	0.792119	−	0.610367i	$-0.208978\pi$
$564$		0			0
$565$	−7.51763	+	28.0562i	−0.316269	+	1.18033i
$566$	−8.65306	−	3.64975i	−0.363715	−	0.153411i
$567$		0			0
$568$	8.32242	+	3.63740i	0.349201	+	0.152622i
$569$	10.5687	−	6.10184i	0.443062	−	0.255802i	−0.261833	−	0.965113i	$-0.584327\pi$
$569$	10.5687	−	6.10184i	0.443062	−	0.255802i	0.704896	+	0.709311i	$0.250994\pi$
$570$		0			0
$571$	10.1445	−	2.71820i	0.424533	−	0.113753i	−0.0402258	−	0.999191i	$-0.512808\pi$
$571$	10.1445	−	2.71820i	0.424533	−	0.113753i	0.464759	+	0.885437i	$0.346141\pi$
$572$	−3.74031	−	14.7155i	−0.156390	−	0.615285i
$573$		0			0
$574$	−11.8082	−	9.18231i	−0.492864	−	0.383262i
$575$	4.15660			0.173342
$576$		0			0
$577$	−11.0011			−0.457982			−0.228991	−	0.973429i	$-0.573543\pi$
$577$	−11.0011			−0.457982			−0.228991	+	0.973429i	$0.573543\pi$
$578$	−13.2689	−	10.3182i	−0.551914	−	0.429180i
$579$		0			0
$580$	3.87379	+	15.2406i	0.160850	+	0.632832i
$581$	−18.7291	+	5.01846i	−0.777016	+	0.208201i
$582$		0			0
$583$	−0.226378	+	0.130699i	−0.00937560	+	0.00541300i
$584$	25.2805	+	11.0491i	1.04612	+	0.457216i
$585$		0			0
$586$	−12.7093	−	5.36061i	−0.525015	−	0.221445i
$587$	4.43586	−	16.5549i	0.183088	−	0.683292i	−0.811944	−	0.583735i	$-0.801591\pi$
$587$	4.43586	−	16.5549i	0.183088	−	0.683292i	0.995032	−	0.0995570i	$-0.0317426\pi$
$588$		0			0
$589$	−2.14516	−	8.00586i	−0.0883900	−	0.329876i
$590$	−8.01369	−	1.10763i	−0.329918	−	0.0456005i
$591$		0			0
$592$	31.7925	+	9.40387i	1.30666	+	0.386497i
$593$	−38.5906			−1.58472			−0.792362	−	0.610051i	$-0.791149\pi$
$593$	−38.5906			−1.58472			−0.792362	+	0.610051i	$0.791149\pi$
$594$		0			0
$595$	−30.9493	+	30.9493i	−1.26880	+	1.26880i
$596$	−12.9313	−	23.0800i	−0.529688	−	0.945393i
$597$		0			0
$598$	20.7509	−	15.7112i	0.848568	−	0.642479i
$599$	4.83678	+	2.79252i	0.197626	+	0.114099i	0.595547	−	0.803320i	$-0.296935\pi$
$599$	4.83678	+	2.79252i	0.197626	+	0.114099i	−0.397922	+	0.917419i	$0.630268\pi$
$600$		0			0
$601$	29.8602	−	17.2398i	1.21802	−	0.703227i	0.253529	−	0.967328i	$-0.418409\pi$
$601$	29.8602	−	17.2398i	1.21802	−	0.703227i	0.964495	+	0.264101i	$0.0850753\pi$
$602$	−11.1845	+	26.5169i	−0.455846	+	1.08075i
$603$		0			0
$604$	−16.6722	−	17.1078i	−0.678382	−	0.696107i
$605$	21.9843	+	5.89068i	0.893790	+	0.239490i
$606$		0			0
$607$	7.58467	−	13.1370i	0.307852	−	0.533216i	−0.670040	−	0.742325i	$-0.733723\pi$
$607$	7.58467	−	13.1370i	0.307852	−	0.533216i	0.977892	+	0.209109i	$0.0670564\pi$
$608$	30.6348	−	21.9752i	1.24241	−	0.891212i
$609$		0			0
$610$	6.64018	+	5.16355i	0.268853	+	0.209066i
$611$	16.9700	−	16.9700i	0.686534	−	0.686534i
$612$		0			0
$613$	7.90551	+	7.90551i	0.319301	+	0.319301i	0.848498	−	0.529198i	$-0.177507\pi$
$613$	7.90551	+	7.90551i	0.319301	+	0.319301i	−0.529198	+	0.848498i	$0.677507\pi$
$614$	9.03424	−	1.13017i	0.364592	−	0.0456100i
$615$		0			0
$616$	12.5386	+	1.89812i	0.505193	+	0.0764775i
$617$	25.0266	+	14.4491i	1.00753	+	0.581700i	0.910468	−	0.413578i	$-0.135721\pi$
$617$	25.0266	+	14.4491i	1.00753	+	0.581700i	0.0970648	+	0.995278i	$0.469055\pi$
$618$		0			0
$619$	8.96627	−	33.4626i	0.360385	−	1.34497i	−0.513186	−	0.858277i	$-0.671535\pi$
$619$	8.96627	−	33.4626i	0.360385	−	1.34497i	0.873571	−	0.486697i	$-0.161798\pi$
$620$	6.21555	+	0.0801537i	0.249622	+	0.00321905i
$621$		0			0
$622$	−3.42653	−	8.42562i	−0.137391	−	0.337837i
$623$	9.97724	+	17.2811i	0.399730	+	0.692352i
$624$		0			0
$625$	−14.8389	+	25.7017i	−0.593555	+	1.02807i
$626$	4.69400	+	0.648793i	0.187610	+	0.0259310i
$627$		0			0
$628$	26.1844	−	14.6707i	1.04487	−	0.585423i
$629$	31.4994	+	31.4994i	1.25596	+	1.25596i
$630$		0			0
$631$		−	30.4132i		−	1.21073i	−0.795948	−	0.605365i	$-0.793027\pi$
$631$		−	30.4132i		−	1.21073i	0.795948	−	0.605365i	$-0.206973\pi$
$632$	6.25041	−	0.700185i	0.248628	−	0.0278519i
$633$		0			0
$634$	−12.9338	−	17.0826i	−0.513667	−	0.678437i
$635$	−17.8103	+	4.77225i	−0.706779	+	0.189381i
$636$		0			0
$637$	19.2821	+	5.16663i	0.763985	+	0.204709i
$638$	5.67077	−	2.30619i	0.224508	−	0.0913029i
$639$		0			0
$640$	9.63093	+	26.5847i	0.380696	+	1.05085i
$641$	6.19753	+	10.7344i	0.244788	+	0.423985i	0.962072	−	0.272796i	$-0.0879484\pi$
$641$	6.19753	+	10.7344i	0.244788	+	0.423985i	−0.717284	+	0.696781i	$0.754615\pi$
$642$		0			0
$643$	6.97693	+	26.0383i	0.275143	+	1.02685i	0.955745	+	0.294195i	$0.0950516\pi$
$643$	6.97693	+	26.0383i	0.275143	+	1.02685i	−0.680602	+	0.732653i	$0.738282\pi$
$644$	5.35518	+	21.0688i	0.211024	+	0.830229i
$645$		0			0
$646$	50.2651	−	6.28809i	1.97765	−	0.247402i
$647$		−	1.44109i		−	0.0566551i	−0.999599	−	0.0283275i	$-0.990982\pi$
$647$		−	1.44109i		−	0.0566551i	0.999599	−	0.0283275i	$-0.00901814\pi$
$648$		0			0
$649$			3.14936i			0.123623i
$650$	−1.20695	−	9.64798i	−0.0473405	−	0.378425i
$651$		0			0
$652$	39.9430	+	23.7530i	1.56429	+	0.930241i
$653$	−3.87857	−	14.4750i	−0.151780	−	0.566451i	−0.999360	−	0.0357824i	$-0.988608\pi$
$653$	−3.87857	−	14.4750i	−0.151780	−	0.566451i	0.847580	−	0.530668i	$-0.178059\pi$
$654$		0			0
$655$	18.9993	+	32.9077i	0.742363	+	1.28581i
$656$	−12.9795	−	0.334815i	−0.506765	−	0.0130723i
$657$		0			0
$658$	7.55116	+	18.5678i	0.294375	+	0.723849i
$659$	5.05876	+	1.35549i	0.197061	+	0.0528024i	0.356000	−	0.934486i	$-0.384140\pi$
$659$	5.05876	+	1.35549i	0.197061	+	0.0528024i	−0.158938	+	0.987289i	$0.550807\pi$
$660$		0			0
$661$	19.8188	−	5.31043i	0.770862	−	0.206552i	0.148110	−	0.988971i	$-0.452681\pi$
$661$	19.8188	−	5.31043i	0.770862	−	0.206552i	0.622752	+	0.782419i	$0.286014\pi$
$662$	11.6839	−	8.84630i	0.454109	−	0.343821i
$663$		0			0
$664$	−10.5021	+	13.1519i	−0.407561	+	0.510392i
$665$		−	54.2763i		−	2.10474i
$666$		0			0
$667$	7.42045	+	7.42045i	0.287321	+	0.287321i
$668$	7.40149	−	26.2633i	0.286372	−	1.01616i
$669$		0			0
$670$	−0.0562483	+	0.406956i	−0.00217306	+	0.0157221i
$671$	1.63729	−	2.83588i	0.0632071	−	0.109478i
$672$		0			0
$673$	7.01009	+	12.1418i	0.270219	+	0.468033i	0.968918	−	0.247383i	$-0.0795706\pi$
$673$	7.01009	+	12.1418i	0.270219	+	0.468033i	−0.698699	+	0.715416i	$0.746237\pi$
$674$	−17.0886	+	6.94959i	−0.658229	+	0.267688i
$675$		0			0
$676$	−24.3469	−	24.9831i	−0.936420	−	0.960888i
$677$	−4.35650	+	16.2587i	−0.167434	+	0.624872i	0.830283	+	0.557342i	$0.188179\pi$
$677$	−4.35650	+	16.2587i	−0.167434	+	0.624872i	−0.997717	+	0.0675306i	$0.978488\pi$
$678$		0			0
$679$	−12.5010	−	7.21748i	−0.479746	−	0.276982i
$680$	−5.68651	+	37.5638i	−0.218068	+	1.44050i
$681$		0			0
$682$	−0.300384	−	2.40118i	−0.0115023	−	0.0919459i
$683$	−26.6987	−	26.6987i	−1.02160	−	1.02160i	−0.999762	−	0.0218370i	$-0.993049\pi$
$683$	−26.6987	−	26.6987i	−1.02160	−	1.02160i	−0.0218370	−	0.999762i	$-0.506951\pi$
$684$		0			0
$685$	−23.5480	+	23.5480i	−0.899724	+	0.899724i
$686$	9.56706	−	12.3030i	0.365272	−	0.469730i
$687$		0			0
$688$	5.84105	+	24.2880i	0.222688	+	0.925970i
$689$	−0.524096	+	0.907760i	−0.0199665	+	0.0345829i
$690$		0			0
$691$	−28.2719	−	7.57544i	−1.07551	−	0.288183i	−0.322757	−	0.946482i	$-0.604610\pi$
$691$	−28.2719	−	7.57544i	−1.07551	−	0.288183i	−0.752757	+	0.658299i	$0.771276\pi$
$692$	−0.115252	+	8.93723i	−0.00438121	+	0.339742i
$693$		0			0
$694$	31.7442	+	13.3893i	1.20499	+	0.508251i
$695$	−36.3284	+	20.9742i	−1.37801	+	0.795597i
$696$		0			0
$697$	−15.1082	−	8.72273i	−0.572264	−	0.330397i
$698$	−24.5490	−	32.4236i	−0.929194	−	1.22725i
$699$		0			0
$700$	7.81648	+	2.20283i	0.295435	+	0.0832592i
$701$	28.6250	−	28.6250i	1.08115	−	1.08115i	0.0847476	−	0.996402i	$-0.472992\pi$
$701$	28.6250	−	28.6250i	1.08115	−	1.08115i	0.996402	−	0.0847476i	$-0.0270084\pi$
$702$		0			0
$703$	−55.2409			−2.08345
$704$	9.73854	−	5.13097i	0.367035	−	0.193381i
$705$		0			0
$706$	−6.81757	+	49.3250i	−0.256583	+	1.85637i
$707$	−15.0652	−	56.2240i	−0.566584	−	2.11452i
$708$		0			0
$709$	6.98798	−	26.0795i	0.262439	−	0.979437i	−0.701360	−	0.712807i	$-0.747423\pi$
$709$	6.98798	−	26.0795i	0.262439	−	0.979437i	0.963799	−	0.266629i	$-0.0859099\pi$
$710$	4.41086	−	10.4575i	0.165537	−	0.392464i
$711$		0			0
$712$	15.8710	+	6.93658i	0.594790	+	0.259959i
$713$	3.59248	−	2.07412i	0.134539	−	0.0776764i
$714$		0			0
$715$	−18.3268	+	4.91066i	−0.685384	+	0.183648i
$716$	43.5377	+	25.8907i	1.62708	+	0.967581i
$717$		0			0
$718$	15.2902	−	19.6628i	0.570626	−	0.733809i
$719$	−3.06518			−0.114312			−0.0571560	−	0.998365i	$-0.518203\pi$
$719$	−3.06518			−0.114312			−0.0571560	+	0.998365i	$0.518203\pi$
$720$		0			0
$721$	−32.8646			−1.22394
$722$	−22.0669	+	28.3775i	−0.821247	+	1.05610i
$723$		0			0
$724$	−13.0662	+	21.9721i	−0.485602	+	0.816587i
$725$	3.78670	−	1.01464i	0.140635	−	0.0376829i
$726$		0			0
$727$	−12.5849	+	7.26589i	−0.466748	+	0.269477i	−0.714877	−	0.699250i	$-0.753517\pi$
$727$	−12.5849	+	7.26589i	−0.466748	+	0.269477i	0.248130	+	0.968727i	$0.420184\pi$
$728$	47.3484	−	18.5478i	1.75485	−	0.687427i
$729$		0			0
$730$	13.3986	−	31.7662i	0.495904	−	1.17572i
$731$	−8.68713	+	32.4208i	−0.321305	+	1.19913i
$732$		0			0
$733$	−1.26777	−	4.73140i	−0.0468263	−	0.174758i	0.938552	−	0.345137i	$-0.112168\pi$
$733$	−1.26777	−	4.73140i	−0.0468263	−	0.174758i	−0.985379	+	0.170379i	$0.945501\pi$
$734$	−3.22181	+	23.3098i	−0.118919	+	0.860379i
$735$		0			0
$736$	14.5921	+	11.9635i	0.537871	+	0.440980i
$737$	0.159933			0.00589119
$738$		0			0
$739$	27.6544	−	27.6544i	1.01728	−	1.01728i	0.0174359	−	0.999848i	$-0.494450\pi$
$739$	27.6544	−	27.6544i	1.01728	−	1.01728i	0.999848	−	0.0174359i	$-0.00555030\pi$
$740$	11.2379	−	39.8764i	0.413114	−	1.46589i
$741$		0			0
$742$	−0.528461	−	0.697976i	−0.0194004	−	0.0256235i
$743$	−16.0882	−	9.28853i	−0.590219	−	0.340763i	0.174965	−	0.984575i	$-0.444019\pi$
$743$	−16.0882	−	9.28853i	−0.590219	−	0.340763i	−0.765184	+	0.643812i	$0.777352\pi$
$744$		0			0
$745$	−28.6302	+	16.5297i	−1.04893	+	0.605600i
$746$	4.35346	+	1.83623i	0.159391	+	0.0672293i
$747$		0			0
$748$	14.7888	+	0.190712i	0.540733	+	0.00697313i
$749$	−16.0189	−	4.29226i	−0.585320	−	0.156836i
$750$		0			0
$751$	17.4576	−	30.2374i	0.637037	−	1.10338i	−0.349043	−	0.937107i	$-0.613493\pi$
$751$	17.4576	−	30.2374i	0.637037	−	1.10338i	0.986080	−	0.166273i	$-0.0531733\pi$
$752$	14.8385	+	9.08506i	0.541103	+	0.331298i
$753$		0			0
$754$	15.0691	−	19.3785i	0.548785	−	0.705722i
$755$	−21.1077	+	21.1077i	−0.768187	+	0.768187i
$756$		0			0
$757$	15.4255	+	15.4255i	0.560649	+	0.560649i	0.929492	−	0.368843i	$-0.120246\pi$
$757$	15.4255	+	15.4255i	0.560649	+	0.560649i	−0.368843	+	0.929492i	$0.620246\pi$
$758$	2.54181	+	20.3184i	0.0923225	+	0.737997i
$759$		0			0
$760$	−27.9518	−	37.9243i	−1.01392	−	1.37566i
$761$	−14.7108	−	8.49331i	−0.533268	−	0.307882i	0.209078	−	0.977899i	$-0.432954\pi$
$761$	−14.7108	−	8.49331i	−0.533268	−	0.307882i	−0.742346	+	0.670017i	$0.766287\pi$
$762$		0			0
$763$	−8.67111	+	32.3610i	−0.313915	+	1.17155i
$764$	15.7796	−	15.3778i	0.570887	−	0.556350i
$765$		0			0
$766$	14.2729	−	5.80449i	0.515699	−	0.209725i
$767$	6.31438	+	10.9368i	0.227999	+	0.394906i
$768$		0			0
$769$	−21.5351	+	37.2999i	−0.776575	+	1.34507i	0.157330	+	0.987546i	$0.449712\pi$
$769$	−21.5351	+	37.2999i	−0.776575	+	1.34507i	−0.933905	+	0.357522i	$0.883622\pi$
$770$	2.16968	−	15.6976i	0.0781898	−	0.565702i
$771$		0			0
$772$	−31.6551	−	8.92101i	−1.13929	−	0.321074i
$773$	−32.8660	−	32.8660i	−1.18211	−	1.18211i	−0.979198	−	0.202909i	$-0.934961\pi$
$773$	−32.8660	−	32.8660i	−1.18211	−	1.18211i	−0.202909	−	0.979198i	$-0.565039\pi$
$774$		0			0
$775$		−	1.54966i		−	0.0556653i
$776$	−12.4518	+	1.39488i	−0.446992	+	0.0500731i
$777$		0			0
$778$	16.2425	−	12.2977i	0.582321	−	0.440895i
$779$	20.8963	−	5.59915i	0.748689	−	0.200611i
$780$		0			0
$781$	−4.26785	−	1.14357i	−0.152716	−	0.0409200i
$782$	9.55113	+	23.4856i	0.341548	+	0.839844i
$783$		0			0
$784$	−0.373194	+	14.4673i	−0.0133284	+	0.516690i
$785$	−18.7530	−	32.4812i	−0.669324	−	1.15930i
$786$		0			0
$787$	1.55972	+	5.82094i	0.0555978	+	0.207494i	0.988137	−	0.153575i	$-0.0490786\pi$
$787$	1.55972	+	5.82094i	0.0555978	+	0.207494i	−0.932539	+	0.361069i	$0.882412\pi$
$788$	3.19313	−	5.36955i	0.113750	−	0.191282i
$789$		0			0
$790$	−0.975601	−	7.79865i	−0.0347103	−	0.277463i
$791$			37.8706i			1.34652i
$792$		0			0
$793$		−	13.1309i		−	0.466292i
$794$	−30.6109	+	3.82938i	−1.08634	+	0.135900i
$795$		0			0
$796$	−23.1416	+	5.88201i	−0.820231	+	0.208482i
$797$	13.4797	+	50.3069i	0.477475	+	1.78196i	0.611788	+	0.791022i	$0.290451\pi$
$797$	13.4797	+	50.3069i	0.477475	+	1.78196i	−0.134313	+	0.990939i	$0.542883\pi$
$798$		0			0
$799$	11.6888	+	20.2455i	0.413519	+	0.716236i
$800$	6.59603	−	2.48624i	0.233205	−	0.0879019i
$801$		0			0
$802$	−8.42922	+	3.42799i	−0.297646	+	0.121047i
$803$	−12.9642	−	3.47374i	−0.457496	−	0.122586i
$804$		0			0
$805$	26.2394	−	7.03082i	0.924816	−	0.247804i
$806$	−5.85744	−	7.73633i	−0.206319	−	0.272501i
$807$		0			0
$808$	−39.4813	−	31.5268i	−1.38895	−	1.10911i
$809$		−	12.2452i		−	0.430520i	−0.976557	−	0.215260i	$-0.930940\pi$
$809$		−	12.2452i		−	0.430520i	0.976557	−	0.215260i	$-0.0690599\pi$
$810$		0			0
$811$	34.8977	+	34.8977i	1.22542	+	1.22542i	0.965677	+	0.259747i	$0.0836390\pi$
$811$	34.8977	+	34.8977i	1.22542	+	1.22542i	0.259747	+	0.965677i	$0.416361\pi$
$812$	10.0216	+	17.8867i	0.351690	+	0.627700i
$813$		0			0
$814$	−15.9766	−	2.20824i	−0.559978	−	0.0773987i
$815$	29.0360	−	50.2918i	1.01709	−	1.76164i
$816$		0			0
$817$	−20.8110	−	36.0458i	−0.728086	−	1.26108i
$818$	−19.6022	−	48.2005i	−0.685374	−	1.68529i
$819$		0			0
$820$	−0.209212	+	16.2234i	−0.00730598	+	0.566545i
$821$	−2.10293	+	7.84823i	−0.0733926	+	0.273905i	−0.992864	−	0.119252i	$-0.961950\pi$
$821$	−2.10293	+	7.84823i	−0.0733926	+	0.273905i	0.919471	+	0.393157i	$0.128617\pi$
$822$		0			0
$823$	−11.0255	−	6.36556i	−0.384324	−	0.221890i	0.295374	−	0.955382i	$-0.404556\pi$
$823$	−11.0255	−	6.36556i	−0.384324	−	0.221890i	−0.679698	+	0.733492i	$0.737889\pi$
$824$	−22.9634	+	16.9250i	−0.799968	+	0.589609i
$825$		0			0
$826$	−10.4662	+	1.30930i	−0.364164	+	0.0455565i
$827$	−7.95914	−	7.95914i	−0.276766	−	0.276766i	0.555050	−	0.831817i	$-0.312699\pi$
$827$	−7.95914	−	7.95914i	−0.276766	−	0.276766i	−0.831817	+	0.555050i	$0.812699\pi$
$828$		0			0
$829$	21.1944	−	21.1944i	0.736113	−	0.736113i	−0.235710	−	0.971823i	$-0.575742\pi$
$829$	21.1944	−	21.1944i	0.736113	−	0.736113i	0.971823	+	0.235710i	$0.0757416\pi$
$830$	16.6026	+	12.9105i	0.576284	+	0.448131i
$831$		0			0
$832$	23.5317	−	37.3439i	0.815814	−	1.29467i
$833$	−9.72259	+	16.8400i	−0.336868	+	0.583472i
$834$		0			0
$835$	−32.9354	−	8.82503i	−1.13978	−	0.305403i
$836$	−13.1349	+	12.8005i	−0.454281	+	0.442713i
$837$		0			0
$838$	12.2759	−	29.1046i	0.424066	−	1.00540i
$839$	34.4751	−	19.9042i	1.19021	−	0.687169i	0.231858	−	0.972750i	$-0.425520\pi$
$839$	34.4751	−	19.9042i	1.19021	−	0.687169i	0.958355	+	0.285580i	$0.0921864\pi$
$840$		0			0
$841$	−16.5433	−	9.55126i	−0.570458	−	0.329354i
$842$	−10.1710	+	7.70080i	−0.350516	+	0.265387i
$843$		0			0
$844$	10.4885	−	5.87653i	0.361029	−	0.202279i
$845$	−30.8242	+	30.8242i	−1.06039	+	1.06039i
$846$		0			0
$847$	29.6747			1.01964
$848$	−0.728701	−	0.215542i	−0.0250237	−	0.00740174i
$849$		0			0
$850$	9.38211	+	1.29677i	0.321804	+	0.0444789i
$851$	−7.15576	−	26.7057i	−0.245296	−	0.915459i
$852$		0			0
$853$	−12.8592	+	47.9910i	−0.440289	+	1.64318i	0.287794	+	0.957692i	$0.407078\pi$
$853$	−12.8592	+	47.9910i	−0.440289	+	1.64318i	−0.728083	+	0.685489i	$0.759589\pi$
$854$	10.1050	+	4.26218i	0.345788	+	0.145849i
$855$		0			0
$856$	−13.4033	+	5.25049i	−0.458117	+	0.179458i
$857$	1.84308	−	1.06410i	0.0629582	−	0.0363490i	−0.468190	−	0.883628i	$-0.655094\pi$
$857$	1.84308	−	1.06410i	0.0629582	−	0.0363490i	0.531149	+	0.847279i	$0.321761\pi$
$858$		0			0
$859$	9.11407	−	2.44211i	0.310968	−	0.0833237i	−0.0999599	−	0.994991i	$-0.531871\pi$
$859$	9.11407	−	2.44211i	0.310968	−	0.0833237i	0.410928	+	0.911668i	$0.365205\pi$
$860$	30.2539	−	7.68978i	1.03165	−	0.262219i
$861$		0			0
$862$	−3.15810	−	2.45580i	−0.107565	−	0.0836450i
$863$	−1.35198			−0.0460219			−0.0230110	−	0.999735i	$-0.507325\pi$
$863$	−1.35198			−0.0460219			−0.0230110	+	0.999735i	$0.507325\pi$
$864$		0			0
$865$	11.1690			0.379757
$866$	11.0626	+	8.60251i	0.375922	+	0.292325i
$867$		0			0
$868$	7.85486	−	1.99651i	0.266611	−	0.0677660i
$869$	−2.95540	+	0.791896i	−0.100255	+	0.0268632i
$870$		0			0
$871$	0.555400	−	0.320660i	0.0188190	−	0.0108652i
$872$	10.6069	+	27.0771i	0.359195	+	0.916945i
$873$		0			0
$874$	−28.9685	−	12.2186i	−0.979875	−	0.413299i
$875$	−7.91234	+	29.5293i	−0.267486	+	0.998271i
$876$		0			0
$877$	−4.48959	−	16.7554i	−0.151603	−	0.565789i	−0.999372	−	0.0354241i	$-0.988722\pi$
$877$	−4.48959	−	16.7554i	−0.151603	−	0.565789i	0.847770	−	0.530364i	$-0.177945\pi$
$878$	−8.94722	−	1.23666i	−0.301954	−	0.0417353i
$879$		0			0
$880$	−6.56810	−	12.0857i	−0.221411	−	0.407409i
$881$	−4.49503			−0.151441			−0.0757207	−	0.997129i	$-0.524126\pi$
$881$	−4.49503			−0.151441			−0.0757207	+	0.997129i	$0.524126\pi$
$882$		0			0
$883$	7.21822	−	7.21822i	0.242913	−	0.242913i	−0.575141	−	0.818054i	$-0.695053\pi$
$883$	7.21822	−	7.21822i	0.242913	−	0.242913i	0.818054	+	0.575141i	$0.195053\pi$
$884$	51.7397	−	28.9889i	1.74019	−	0.975002i
$885$		0			0
$886$	−18.8631	+	14.2819i	−0.633717	+	0.479809i
$887$	−32.3743	−	18.6913i	−1.08702	−	0.627592i	−0.154240	−	0.988033i	$-0.549293\pi$
$887$	−32.3743	−	18.6913i	−1.08702	−	0.627592i	−0.932782	+	0.360441i	$0.882626\pi$
$888$		0			0
$889$	−20.8197	+	12.0203i	−0.698271	+	0.403147i
$890$	8.41157	−	19.9427i	0.281956	−	0.668479i
$891$		0			0
$892$	−11.8652	+	11.5631i	−0.397276	+	0.387160i
$893$	−28.0018	−	7.50307i	−0.937046	−	0.251081i
$894$		0			0
$895$	31.6491	−	54.8178i	1.05791	−	1.83236i
$896$	21.1002	+	30.2306i	0.704909	+	1.00993i
$897$		0			0
$898$	−26.4819	−	20.5929i	−0.883714	−	0.687195i
$899$	2.76648	−	2.76648i	0.0922674	−	0.0922674i
$900$		0			0
$901$	−0.721983	−	0.721983i	−0.0240527	−	0.0240527i
$902$	6.26738	−	0.784042i	0.208681	−	0.0261057i
$903$		0			0
$904$	19.5030	+	26.4612i	0.648660	+	0.880086i
$905$	27.6648	+	15.9723i	0.919610	+	0.530937i
$906$		0			0
$907$	7.32597	−	27.3409i	0.243255	−	0.907840i	−0.730998	−	0.682380i	$-0.760945\pi$
$907$	7.32597	−	27.3409i	0.243255	−	0.907840i	0.974253	−	0.225460i	$-0.0723884\pi$
$908$	−0.462673	+	35.8782i	−0.0153544	+	1.19066i
$909$		0			0
$910$	−23.9385	−	58.8633i	−0.793554	−	1.95130i
$911$	12.2805	+	21.2704i	0.406871	+	0.704721i	0.994537	−	0.104383i	$-0.0332867\pi$
$911$	12.2805	+	21.2704i	0.406871	+	0.704721i	−0.587667	+	0.809103i	$0.699953\pi$
$912$		0			0
$913$	4.09376	−	7.09060i	0.135484	−	0.234665i
$914$	41.8610	+	5.78592i	1.38464	+	0.191381i
$915$		0			0
$916$	−9.28625	−	16.5742i	−0.306826	−	0.547627i
$917$	35.0323	+	35.0323i	1.15687	+	1.15687i
$918$		0			0
$919$		−	21.3619i		−	0.704665i	−0.935875	−	0.352332i	$-0.885389\pi$
$919$		−	21.3619i		−	0.704665i	0.935875	−	0.352332i	$-0.114611\pi$
$920$	14.7133	−	18.4257i	0.485085	−	0.607476i
$921$		0			0
$922$	23.8431	+	31.4913i	0.785231	+	1.03711i
$923$	−17.1138	+	4.58563i	−0.563308	+	0.150938i
$924$		0			0
$925$	−9.97644	−	2.67318i	−0.328023	−	0.0878936i
$926$	−23.6054	+	9.59986i	−0.775723	+	0.315471i
$927$		0			0
$928$	16.2139	+	7.33688i	0.532246	+	0.240845i
$929$	−0.783906	−	1.35776i	−0.0257191	−	0.0445468i	0.852879	−	0.522108i	$-0.174854\pi$
$929$	−0.783906	−	1.35776i	−0.0257191	−	0.0445468i	−0.878598	+	0.477561i	$0.841521\pi$
$930$		0			0
$931$	−6.24097	−	23.2916i	−0.204540	−	0.763352i
$932$	−12.3981	+	3.15128i	−0.406112	+	0.103224i
$933$		0			0
$934$	6.44112	−	0.805776i	0.210760	−	0.0263658i
$935$		−	18.4818i		−	0.604420i
$936$		0			0
$937$			40.1161i			1.31054i	0.755396	+	0.655269i	$0.227445\pi$
$937$			40.1161i			1.31054i	−0.755396	+	0.655269i	$0.772555\pi$
$938$	0.0664897	+	0.531498i	0.00217097	+	0.0173540i
$939$		0			0
$940$	11.1127	−	18.6871i	0.362458	−	0.609507i
$941$	10.7101	+	39.9706i	0.349139	+	1.30300i	0.887702	+	0.460419i	$0.152301\pi$
$941$	10.7101	+	39.9706i	0.349139	+	1.30300i	−0.538562	+	0.842586i	$0.681032\pi$
$942$		0			0
$943$	5.41372	+	9.37683i	0.176295	+	0.305352i
$944$	−6.63871	+	6.30482i	−0.216072	+	0.205204i
$945$		0			0
$946$	−4.57797	−	11.2569i	−0.148843	−	0.365995i
$947$	−31.9411	−	8.55860i	−1.03795	−	0.278117i	−0.300685	−	0.953724i	$-0.597215\pi$
$947$	−31.9411	−	8.55860i	−1.03795	−	0.278117i	−0.737263	+	0.675606i	$0.763882\pi$
$948$		0			0
$949$	−51.9856	+	13.9295i	−1.68752	+	0.452171i
$950$	−9.36385	+	7.08968i	−0.303803	+	0.230020i
$951$		0			0
$952$	5.51446	+	49.2265i	0.178725	+	1.59544i
$953$		−	6.18680i		−	0.200410i	−0.994967	−	0.100205i	$-0.968050\pi$
$953$		−	6.18680i		−	0.200410i	0.994967	−	0.100205i	$-0.0319499\pi$
$954$		0			0
$955$	−19.4690	−	19.4690i	−0.630001	−	0.630001i
$956$	−47.7462	−	13.4558i	−1.54422	−	0.435191i
$957$		0			0
$958$	0.492420	−	3.56265i	0.0159094	−	0.115104i
$959$	−21.7099	+	37.6026i	−0.701048	+	1.21425i
$960$		0			0
$961$	14.7267	+	25.5074i	0.475056	+	0.822821i
$962$	−59.9094	+	24.3639i	−1.93156	+	0.785525i
$963$		0			0
$964$	−12.3906	+	12.0751i	−0.399074	+	0.388913i
$965$	−10.6368	+	39.6971i	−0.342410	+	1.27789i
$966$		0			0
$967$	25.0282	+	14.4500i	0.804851	+	0.464681i	0.845165	−	0.534506i	$-0.179502\pi$
$967$	25.0282	+	14.4500i	0.804851	+	0.464681i	−0.0403133	+	0.999187i	$0.512836\pi$
$968$	20.7345	−	15.2822i	0.666434	−	0.491189i
$969$		0			0
$970$	1.94354	+	15.5361i	0.0624034	+	0.498833i
$971$	41.1803	+	41.1803i	1.32154	+	1.32154i	0.912531	+	0.409008i	$0.134125\pi$
$971$	41.1803	+	41.1803i	1.32154	+	1.32154i	0.409008	+	0.912531i	$0.365875\pi$
$972$		0			0
$973$	−38.6739	+	38.6739i	−1.23983	+	1.23983i
$974$	−22.9668	+	29.5347i	−0.735905	+	0.946354i
$975$		0			0
$976$	9.25566	−	2.22590i	0.296266	−	0.0712495i
$977$	18.1859	−	31.4990i	0.581820	−	1.00774i	−0.413444	−	0.910530i	$-0.635674\pi$
$977$	18.1859	−	31.4990i	0.581820	−	1.00774i	0.995264	−	0.0972120i	$-0.0309925\pi$
$978$		0			0
$979$	−8.13884	−	2.18080i	−0.260119	−	0.0696986i
$980$	18.0830	+	0.233193i	0.577641	+	0.00744907i
$981$		0			0
$982$	−29.5868	−	12.4794i	−0.944154	−	0.398232i
$983$	48.0347	−	27.7329i	1.53207	−	0.884541i	0.532803	−	0.846239i	$-0.321139\pi$
$983$	48.0347	−	27.7329i	1.53207	−	0.884541i	0.999266	−	0.0383018i	$-0.0121948\pi$
$984$		0			0
$985$	−6.76074	−	3.90331i	−0.215415	−	0.124370i
$986$	14.4341	+	19.0642i	0.459676	+	0.607127i
$987$		0			0
$988$	−19.9492	+	70.7874i	−0.634669	+	2.25205i
$989$	14.7302	−	14.7302i	0.468393	−	0.468393i
$990$		0			0
$991$	15.3724			0.488321			0.244161	−	0.969735i	$-0.421488\pi$
$991$	15.3724			0.488321			0.244161	+	0.969735i	$0.421488\pi$
$992$	4.46022	−	5.44020i	0.141612	−	0.172727i
$993$		0			0
$994$	2.02607	−	14.6586i	0.0642631	−	0.464943i
$995$	7.72250	+	28.8208i	0.244820	+	0.913679i
$996$		0			0
$997$	−7.71233	+	28.7828i	−0.244252	+	0.911561i	0.729506	+	0.683974i	$0.239750\pi$
$997$	−7.71233	+	28.7828i	−0.244252	+	0.911561i	−0.973758	+	0.227586i	$0.926917\pi$
$998$	15.5976	−	36.9798i	0.493735	−	1.17058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.3		72
3.2	odd	2		144.2.x.e.85.16	yes	72
4.3	odd	2		1728.2.bc.e.1009.16		72
9.2	odd	6		144.2.x.e.133.8	yes	72
9.7	even	3	inner	432.2.y.e.181.11		72
12.11	even	2		576.2.bb.e.49.12		72
16.3	odd	4		1728.2.bc.e.145.3		72
16.13	even	4	inner	432.2.y.e.253.11		72
36.7	odd	6		1728.2.bc.e.1585.3		72
36.11	even	6		576.2.bb.e.241.17		72
48.29	odd	4		144.2.x.e.13.8	✓	72
48.35	even	4		576.2.bb.e.337.17		72
144.29	odd	12		144.2.x.e.61.16	yes	72
144.61	even	12	inner	432.2.y.e.397.3		72
144.83	even	12		576.2.bb.e.529.12		72
144.115	odd	12		1728.2.bc.e.721.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.8	✓	72	48.29	odd	4
144.2.x.e.61.16	yes	72	144.29	odd	12
144.2.x.e.85.16	yes	72	3.2	odd	2
144.2.x.e.133.8	yes	72	9.2	odd	6
432.2.y.e.37.3		72	1.1	even	1	trivial
432.2.y.e.181.11		72	9.7	even	3	inner
432.2.y.e.253.11		72	16.13	even	4	inner
432.2.y.e.397.3		72	144.61	even	12	inner
576.2.bb.e.49.12		72	12.11	even	2
576.2.bb.e.241.17		72	36.11	even	6
576.2.bb.e.337.17		72	48.35	even	4
576.2.bb.e.529.12		72	144.83	even	12
1728.2.bc.e.145.3		72	16.3	odd	4
1728.2.bc.e.721.16		72	144.115	odd	12
1728.2.bc.e.1009.16		72	4.3	odd	2
1728.2.bc.e.1585.3		72	36.7	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11640 - 0.868135i) q^{2} +(0.492685 + 1.93837i) q^{4} +(2.41406 - 0.646846i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.13273 - 2.59170i) q^{8} +O(q^{10})\)	\(q+(-1.11640 - 0.868135i) q^{2} +(0.492685 + 1.93837i) q^{4} +(2.41406 - 0.646846i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.13273 - 2.59170i) q^{8} +(-3.25660 - 1.37359i) q^{10} +(-0.356120 + 1.32906i) q^{11} +(1.42802 + 5.32945i) q^{13} +(-4.56486 - 0.630943i) q^{14} +(-3.51452 + 1.91001i) q^{16} -5.37452 q^{17} +(4.71269 - 4.71269i) q^{19} +(2.44320 + 4.36064i) q^{20} +(1.55137 - 1.17460i) q^{22} +(2.88877 + 1.66783i) q^{23} +(1.07916 - 0.623053i) q^{25} +(3.03244 - 7.18949i) q^{26} +(4.54846 + 4.66730i) q^{28} +(3.03883 + 0.814251i) q^{29} +(0.621800 - 1.07699i) q^{31} +(5.58175 + 0.918755i) q^{32} +(6.00010 + 4.66581i) q^{34} +(5.75853 - 5.75853i) q^{35} +(-5.86087 - 5.86087i) q^{37} +(-9.35247 + 1.16998i) q^{38} +(1.05805 - 6.98923i) q^{40} +(2.81108 + 1.62298i) q^{41} +(1.61636 - 6.03232i) q^{43} +(-2.75166 - 0.0354845i) q^{44} +(-1.77711 - 4.36981i) q^{46} +(-2.17485 - 3.76695i) q^{47} +(1.80902 - 3.13331i) q^{49} +(-1.74566 - 0.241281i) q^{50} +(-9.62685 + 5.39376i) q^{52} +(0.134334 + 0.134334i) q^{53} +3.43879i q^{55} +(-1.02604 - 9.15923i) q^{56} +(-2.68566 - 3.54714i) q^{58} +(2.21088 - 0.592405i) q^{59} +(-2.29879 - 0.615960i) q^{61} +(-1.62915 + 0.662542i) q^{62} +(-5.43384 - 5.87140i) q^{64} +(6.89466 + 11.9419i) q^{65} +(-0.0300838 - 0.112274i) q^{67} +(-2.64794 - 10.4178i) q^{68} +(-11.4280 + 1.42963i) q^{70} +3.21118i q^{71} +9.75441i q^{73} +(1.45503 + 11.6311i) q^{74} +(11.4568 + 6.81304i) q^{76} +(1.16043 + 4.33078i) q^{77} +(1.11184 + 1.92576i) q^{79} +(-7.24880 + 6.88423i) q^{80} +(-1.72932 - 4.25229i) q^{82} +(-5.74772 - 1.54010i) q^{83} +(-12.9744 + 3.47649i) q^{85} +(-7.04136 + 5.33125i) q^{86} +(3.04114 + 2.42842i) q^{88} +6.12376i q^{89} +(12.7129 + 12.7129i) q^{91} +(-1.80962 + 6.42122i) q^{92} +(-0.842224 + 6.09347i) q^{94} +(8.32833 - 14.4251i) q^{95} +(-2.21495 - 3.83640i) q^{97} +(-4.73971 + 1.92755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

L-functions

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