LMFDB - Embedded newform 936.2.ed.d.739.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			739.8
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.d.19.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.376293 + 1.36323i) q^{2} +(-1.71681 + 1.02595i) q^{4} +(-0.0693382 + 0.0693382i) q^{5} +(3.36551 - 0.901786i) q^{7} +(-2.04463 - 1.95435i) q^{8} +(-0.120616 - 0.0684326i) q^{10} +(0.305781 + 0.0819339i) q^{11} +(-3.13155 + 1.78702i) q^{13} +(2.49576 + 4.24864i) q^{14} +(1.89485 - 3.52272i) q^{16} +(5.48889 + 3.16901i) q^{17} +(-0.397336 + 0.106466i) q^{19} +(0.0479027 - 0.190178i) q^{20} +(0.00336858 + 0.447683i) q^{22} +(3.68562 + 6.38369i) q^{23} +4.99038i q^{25} +(-3.61450 - 3.59658i) q^{26} +(-4.85274 + 5.00104i) q^{28} +(3.16915 - 1.82971i) q^{29} +(1.12080 - 1.12080i) q^{31} +(5.51530 + 1.25755i) q^{32} +(-2.25467 + 8.67511i) q^{34} +(-0.170830 + 0.295887i) q^{35} +(0.804964 - 3.00417i) q^{37} +(-0.294652 - 0.501598i) q^{38} +(0.277282 - 0.00626016i) q^{40} +(-1.85187 + 6.91129i) q^{41} +(4.88743 + 2.82176i) q^{43} +(-0.609028 + 0.173052i) q^{44} +(-7.31557 + 7.42650i) q^{46} +(-6.15946 - 6.15946i) q^{47} +(4.45127 - 2.56994i) q^{49} +(-6.80306 + 1.87785i) q^{50} +(3.54287 - 6.28077i) q^{52} -3.89384i q^{53} +(-0.0268835 + 0.0155212i) q^{55} +(-8.64364 - 4.73356i) q^{56} +(3.68685 + 3.63178i) q^{58} +(2.51467 + 9.38488i) q^{59} +(-11.9231 - 6.88378i) q^{61} +(1.94966 + 1.10616i) q^{62} +(0.361046 + 7.99185i) q^{64} +(0.0932273 - 0.341044i) q^{65} +(-3.16917 + 11.8275i) q^{67} +(-12.6746 + 0.190751i) q^{68} +(-0.467645 - 0.121541i) q^{70} +(-1.81764 - 6.78351i) q^{71} +(1.49582 - 1.49582i) q^{73} +(4.39828 - 0.0330948i) q^{74} +(0.572920 - 0.590428i) q^{76} +1.10300 q^{77} +10.3044i q^{79} +(0.112874 + 0.375645i) q^{80} +(-10.1185 + 0.0761368i) q^{82} +(-2.53771 - 2.53771i) q^{83} +(-0.600323 + 0.160856i) q^{85} +(-2.00761 + 7.72451i) q^{86} +(-0.465083 - 0.765128i) q^{88} +(-0.110536 - 0.0296181i) q^{89} +(-8.92775 + 8.83821i) q^{91} +(-12.8768 - 7.17829i) q^{92} +(6.07901 - 10.7145i) q^{94} +(0.0201684 - 0.0349327i) q^{95} +(6.28973 - 1.68533i) q^{97} +(5.17841 + 5.10107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.376293	+	1.36323i	0.266080	+	0.963951i
$2$	0.376293	+	1.36323i	0.266080	+	0.963951i
$3$		0			0
$3$		0			0
$4$	−1.71681	+	1.02595i	−0.858403	+	0.512975i
$5$	−0.0693382	+	0.0693382i	−0.0310090	+	0.0310090i	−0.722441	−	0.691432i	$-0.756980\pi$
$5$	−0.0693382	+	0.0693382i	−0.0310090	+	0.0310090i	0.691432	+	0.722441i	$0.256980\pi$
$6$		0			0
$7$	3.36551	−	0.901786i	1.27204	−	0.340843i	0.441230	−	0.897394i	$-0.354542\pi$
$7$	3.36551	−	0.901786i	1.27204	−	0.340843i	0.830814	+	0.556551i	$0.187876\pi$
$8$	−2.04463	−	1.95435i	−0.722887	−	0.690966i
$9$		0			0
$10$	−0.120616	−	0.0684326i	−0.0381420	−	0.0216403i
$11$	0.305781	+	0.0819339i	0.0921966	+	0.0247040i	0.304622	−	0.952473i	$-0.401470\pi$
$11$	0.305781	+	0.0819339i	0.0921966	+	0.0247040i	−0.212426	+	0.977177i	$0.568136\pi$
$12$		0			0
$13$	−3.13155	+	1.78702i	−0.868534	+	0.495629i
$13$	−3.13155	+	1.78702i	−0.868534	+	0.495629i
$14$	2.49576	+	4.24864i	0.667021	+	1.13550i
$15$		0			0
$16$	1.89485	−	3.52272i	0.473712	−	0.880680i
$17$	5.48889	+	3.16901i	1.33125	+	0.768598i	0.985491	−	0.169725i	$-0.0542880\pi$
$17$	5.48889	+	3.16901i	1.33125	+	0.768598i	0.345760	+	0.938323i	$0.387621\pi$
$18$		0			0
$19$	−0.397336	+	0.106466i	−0.0911550	+	0.0244249i	−0.304108	−	0.952637i	$-0.598358\pi$
$19$	−0.397336	+	0.106466i	−0.0911550	+	0.0244249i	0.212953	+	0.977062i	$0.431692\pi$
$20$	0.0479027	−	0.190178i	0.0107114	−	0.0425251i
$21$		0			0
$22$	0.00336858	+	0.447683i	0.000718183	+	0.0954462i
$23$	3.68562	+	6.38369i	0.768505	+	1.33109i	0.938373	+	0.345624i	$0.112333\pi$
$23$	3.68562	+	6.38369i	0.768505	+	1.33109i	−0.169868	+	0.985467i	$0.554334\pi$
$24$		0			0
$25$			4.99038i			0.998077i
$26$	−3.61450	−	3.59658i	−0.708861	−	0.705348i
$27$		0			0
$28$	−4.85274	+	5.00104i	−0.917082	+	0.945108i
$29$	3.16915	−	1.82971i	0.588496	−	0.339768i	−0.176006	−	0.984389i	$-0.556318\pi$
$29$	3.16915	−	1.82971i	0.588496	−	0.339768i	0.764503	+	0.644621i	$0.222985\pi$
$30$		0			0
$31$	1.12080	−	1.12080i	0.201301	−	0.201301i	−0.599256	−	0.800557i	$-0.704537\pi$
$31$	1.12080	−	1.12080i	0.201301	−	0.201301i	0.800557	+	0.599256i	$0.204537\pi$
$32$	5.51530	+	1.25755i	0.974977	+	0.222305i
$33$		0			0
$34$	−2.25467	+	8.67511i	−0.386672	+	1.48777i
$35$	−0.170830	+	0.295887i	−0.0288756	+	0.0500140i
$36$		0			0
$37$	0.804964	−	3.00417i	0.132335	−	0.493882i	−0.867659	−	0.497159i	$-0.834376\pi$
$37$	0.804964	−	3.00417i	0.132335	−	0.493882i	0.999995	+	0.00327710i	$0.00104314\pi$
$38$	−0.294652	−	0.501598i	−0.0477989	−	0.0813700i
$39$		0			0
$40$	0.277282	−	0.00626016i	0.0438422	−	0.000989819i
$41$	−1.85187	+	6.91129i	−0.289214	+	1.07936i	0.656491	+	0.754334i	$0.272040\pi$
$41$	−1.85187	+	6.91129i	−0.289214	+	1.07936i	−0.945705	+	0.325027i	$0.894627\pi$
$42$		0			0
$43$	4.88743	+	2.82176i	0.745326	+	0.430314i	0.824003	−	0.566586i	$-0.191736\pi$
$43$	4.88743	+	2.82176i	0.745326	+	0.430314i	−0.0786766	+	0.996900i	$0.525069\pi$
$44$	−0.609028	+	0.173052i	−0.0918144	+	0.0260886i
$45$		0			0
$46$	−7.31557	+	7.42650i	−1.07862	+	1.09498i
$47$	−6.15946	−	6.15946i	−0.898449	−	0.898449i	0.0968500	−	0.995299i	$-0.469123\pi$
$47$	−6.15946	−	6.15946i	−0.898449	−	0.898449i	−0.995299	+	0.0968500i	$0.969123\pi$
$48$		0			0
$49$	4.45127	−	2.56994i	0.635896	−	0.367135i
$50$	−6.80306	+	1.87785i	−0.962097	+	0.265568i
$51$		0			0
$52$	3.54287	−	6.28077i	0.491307	−	0.870986i
$53$		−	3.89384i		−	0.534861i	−0.963577	−	0.267430i	$-0.913825\pi$
$53$		−	3.89384i		−	0.534861i	0.963577	−	0.267430i	$-0.0861745\pi$
$54$		0			0
$55$	−0.0268835	+	0.0155212i	−0.00362497	+	0.00209288i
$56$	−8.64364	−	4.73356i	−1.15505	−	0.632549i
$57$		0			0
$58$	3.68685	+	3.63178i	0.484107	+	0.476876i
$59$	2.51467	+	9.38488i	0.327382	+	1.22181i	0.911895	+	0.410423i	$0.134619\pi$
$59$	2.51467	+	9.38488i	0.327382	+	1.22181i	−0.584513	+	0.811385i	$0.698714\pi$
$60$		0			0
$61$	−11.9231	−	6.88378i	−1.52659	−	0.881378i	−0.999502	−	0.0315679i	$-0.989950\pi$
$61$	−11.9231	−	6.88378i	−1.52659	−	0.881378i	−0.527089	−	0.849810i	$-0.676717\pi$
$62$	1.94966	+	1.10616i	0.247607	+	0.140482i
$63$		0			0
$64$	0.361046	+	7.99185i	0.0451307	+	0.998981i
$65$	0.0932273	−	0.341044i	0.0115634	−	0.0423013i
$66$		0			0
$67$	−3.16917	+	11.8275i	−0.387176	+	1.44496i	0.447532	+	0.894268i	$0.352303\pi$
$67$	−3.16917	+	11.8275i	−0.387176	+	1.44496i	−0.834708	+	0.550693i	$0.814363\pi$
$68$	−12.6746	+	0.190751i	−1.53702	+	0.0231319i
$69$		0			0
$70$	−0.467645	−	0.121541i	−0.0558943	−	0.0145270i
$71$	−1.81764	−	6.78351i	−0.215714	−	0.805055i	−0.985914	−	0.167253i	$-0.946510\pi$
$71$	−1.81764	−	6.78351i	−0.215714	−	0.805055i	0.770200	−	0.637802i	$-0.220156\pi$
$72$		0			0
$73$	1.49582	−	1.49582i	0.175072	−	0.175072i	−0.614131	−	0.789204i	$-0.710494\pi$
$73$	1.49582	−	1.49582i	0.175072	−	0.175072i	0.789204	+	0.614131i	$0.210494\pi$
$74$	4.39828	−	0.0330948i	0.511290	−	0.00384719i
$75$		0			0
$76$	0.572920	−	0.590428i	0.0657184	−	0.0677267i
$77$	1.10300			0.125698
$78$		0			0
$79$			10.3044i			1.15933i	0.814854	+	0.579667i	$0.196817\pi$
$79$			10.3044i			1.15933i	−0.814854	+	0.579667i	$0.803183\pi$
$80$	0.112874	+	0.375645i	0.0126196	+	0.0419983i
$81$		0			0
$82$	−10.1185	+	0.0761368i	−1.11741	+	0.00840790i
$83$	−2.53771	−	2.53771i	−0.278550	−	0.278550i	0.553980	−	0.832530i	$-0.313108\pi$
$83$	−2.53771	−	2.53771i	−0.278550	−	0.278550i	−0.832530	+	0.553980i	$0.813108\pi$
$84$		0			0
$85$	−0.600323	+	0.160856i	−0.0651142	+	0.0174473i
$86$	−2.00761	+	7.72451i	−0.216486	+	0.832956i
$87$		0			0
$88$	−0.465083	−	0.765128i	−0.0495781	−	0.0815629i
$89$	−0.110536	−	0.0296181i	−0.0117168	−	0.00313951i	0.252956	−	0.967478i	$-0.418597\pi$
$89$	−0.110536	−	0.0296181i	−0.0117168	−	0.00313951i	−0.264673	+	0.964338i	$0.585264\pi$
$90$		0			0
$91$	−8.92775	+	8.83821i	−0.935882	+	0.926496i
$92$	−12.8768	−	7.17829i	−1.34250	−	0.748388i
$93$		0			0
$94$	6.07901	−	10.7145i	0.627002	−	1.10512i
$95$	0.0201684	−	0.0349327i	0.00206923	−	0.00358402i
$96$		0			0
$97$	6.28973	−	1.68533i	0.638626	−	0.171119i	0.0750449	−	0.997180i	$-0.476090\pi$
$97$	6.28973	−	1.68533i	0.638626	−	0.171119i	0.563581	+	0.826061i	$0.309423\pi$
$98$	5.17841	+	5.10107i	0.523099	+	0.515286i
$99$		0			0
$100$	−5.11989	−	8.56752i	−0.511989	−	0.856752i
$101$	−3.22024	−	5.57761i	−0.320425	−	0.554993i	0.660150	−	0.751133i	$-0.270493\pi$
$101$	−3.22024	−	5.57761i	−0.320425	−	0.554993i	−0.980576	+	0.196140i	$0.937159\pi$
$102$		0			0
$103$	15.5401			1.53121			0.765604	−	0.643312i	$-0.222440\pi$
$103$	15.5401			1.53121			0.765604	+	0.643312i	$0.222440\pi$
$104$	9.89531	+	2.46634i	0.970315	+	0.241844i
$105$		0			0
$106$	5.30822	−	1.46523i	0.515579	−	0.142315i
$107$	0.865163	+	1.49851i	0.0836385	+	0.144866i	0.904810	−	0.425815i	$-0.140013\pi$
$107$	0.865163	+	1.49851i	0.0836385	+	0.144866i	−0.821172	+	0.570681i	$0.806679\pi$
$108$		0			0
$109$	13.2174	−	13.2174i	1.26599	−	1.26599i	0.317853	−	0.948140i	$-0.397038\pi$
$109$	13.2174	−	13.2174i	1.26599	−	1.26599i	0.948140	−	0.317853i	$-0.102962\pi$
$110$	−0.0312751	−	0.0308079i	−0.00298196	−	0.00293742i
$111$		0			0
$112$	3.20040	−	13.5645i	0.302409	−	1.28172i
$113$	6.88323	−	11.9221i	0.647520	−	1.12154i	−0.336193	−	0.941793i	$-0.609140\pi$
$113$	6.88323	−	11.9221i	0.647520	−	1.12154i	0.983713	−	0.179744i	$-0.0575271\pi$
$114$		0			0
$115$	−0.698188	−	0.187079i	−0.0651064	−	0.0174452i
$116$	−3.56362	+	6.39265i	−0.330874	+	0.593542i
$117$		0			0
$118$	−11.8475	+	6.95955i	−1.09065	+	0.640679i
$119$	21.3307	+	5.71554i	1.95538	+	0.523943i
$120$		0			0
$121$	−9.43949	−	5.44989i	−0.858135	−	0.495445i
$122$	4.89763	−	18.8442i	0.443410	−	1.70608i
$123$		0			0
$124$	−0.774310	+	3.07408i	−0.0695351	+	0.276060i
$125$	−0.692716	−	0.692716i	−0.0619584	−	0.0619584i
$126$		0			0
$127$	4.23231	+	7.33057i	0.375557	+	0.650483i	0.990410	−	0.138158i	$-0.0441182\pi$
$127$	4.23231	+	7.33057i	0.375557	+	0.650483i	−0.614853	+	0.788641i	$0.710785\pi$
$128$	−10.7589	+	3.49947i	−0.950961	+	0.309312i
$129$		0			0
$130$	0.500004	−	0.00124220i	0.0438532	−	0.000108948i
$131$	13.5858			1.18700			0.593499	−	0.804835i	$-0.297746\pi$
$131$	13.5858			1.18700			0.593499	+	0.804835i	$0.297746\pi$
$132$		0			0
$133$	−1.24123	+	0.716623i	−0.107628	+	0.0621391i
$134$	−17.3162	+	0.130295i	−1.49589	+	0.0112558i
$135$		0			0
$136$	−5.02941	−	17.2067i	−0.431268	−	1.47546i
$137$	−3.19234	−	11.9140i	−0.272740	−	1.01788i	−0.957341	−	0.288961i	$-0.906690\pi$
$137$	−3.19234	−	11.9140i	−0.272740	−	1.01788i	0.684601	−	0.728918i	$-0.259976\pi$
$138$		0			0
$139$	5.36196	−	9.28718i	0.454795	−	0.787729i	−0.543881	−	0.839162i	$-0.683046\pi$
$139$	5.36196	−	9.28718i	0.454795	−	0.787729i	0.998676	+	0.0514337i	$0.0163791\pi$
$140$	−0.0102827	−	0.683244i	−0.000869047	−	0.0577447i
$141$		0			0
$142$	8.56354	−	5.03045i	0.718636	−	0.422146i
$143$	−1.10399	+	0.289857i	−0.0923199	+	0.0242390i
$144$		0			0
$145$	−0.0928744	+	0.346612i	−0.00771280	+	0.0287846i
$146$	2.60202	+	1.47628i	0.215344	+	0.122178i
$147$		0			0
$148$	1.70016	+	5.98343i	0.139752	+	0.491835i
$149$	−2.96712	−	11.0734i	−0.243076	−	0.907172i	−0.974341	−	0.225078i	$-0.927736\pi$
$149$	−2.96712	−	11.0734i	−0.243076	−	0.907172i	0.731265	−	0.682094i	$-0.238930\pi$
$150$		0			0
$151$	−7.63837	−	7.63837i	−0.621602	−	0.621602i	0.324339	−	0.945941i	$-0.394858\pi$
$151$	−7.63837	−	7.63837i	−0.621602	−	0.621602i	−0.945941	+	0.324339i	$0.894858\pi$
$152$	1.02048	+	0.558849i	0.0827716	+	0.0453286i
$153$		0			0
$154$	0.415051	+	1.50364i	0.0334458	+	0.121167i
$155$			0.155428i			0.0124843i
$156$		0			0
$157$		−	0.295631i		−	0.0235940i	−0.999930	−	0.0117970i	$-0.996245\pi$
$157$		−	0.295631i		−	0.0235940i	0.999930	−	0.0117970i	$-0.00375518\pi$
$158$	−14.0473	+	3.87747i	−1.11754	+	0.308475i
$159$		0			0
$160$	−0.469617	+	0.295225i	−0.0371265	+	0.0233396i
$161$	18.1607	+	18.1607i	1.43127	+	1.43127i
$162$		0			0
$163$	−0.643966	−	2.40331i	−0.0504393	−	0.188242i	0.936110	−	0.351708i	$-0.114399\pi$
$163$	−0.643966	−	2.40331i	−0.0504393	−	0.188242i	−0.986549	+	0.163466i	$0.947732\pi$
$164$	−3.91133	−	13.7653i	−0.305424	−	1.07489i
$165$		0			0
$166$	2.50456	−	4.41441i	0.194392	−	0.342625i
$167$	−2.40443	+	8.97345i	−0.186060	+	0.694386i	0.808341	+	0.588715i	$0.200366\pi$
$167$	−2.40443	+	8.97345i	−0.186060	+	0.694386i	−0.994401	+	0.105672i	$0.966301\pi$
$168$		0			0
$169$	6.61315	−	11.1922i	0.508704	−	0.860942i
$170$	−0.445182	−	0.757851i	−0.0341439	−	0.0581246i
$171$		0			0
$172$	−11.2858	+	0.169849i	−0.860531	+	0.0129508i
$173$	−1.48266	+	2.56803i	−0.112724	+	0.195244i	−0.916868	−	0.399191i	$-0.869291\pi$
$173$	−1.48266	+	2.56803i	−0.112724	+	0.195244i	0.804144	+	0.594435i	$0.202624\pi$
$174$		0			0
$175$	4.50026	+	16.7952i	0.340188	+	1.26960i
$176$	0.868040	−	0.921930i	0.0654310	−	0.0694931i
$177$		0			0
$178$	−0.00121770	−	0.161832i	−9.12705e−5	−	0.0121298i
$179$	−5.42364	+	3.13134i	−0.405382	+	0.234047i	−0.688803	−	0.724948i	$-0.741864\pi$
$179$	−5.42364	+	3.13134i	−0.405382	+	0.234047i	0.283422	+	0.958995i	$0.408530\pi$
$180$		0			0
$181$	−19.6735			−1.46232			−0.731160	−	0.682206i	$-0.761021\pi$
$181$	−19.6735			−1.46232			−0.731160	+	0.682206i	$0.761021\pi$
$182$	−15.4080	−	8.84484i	−1.14212	−	0.655623i
$183$		0			0
$184$	4.94020	−	20.2553i	0.364196	−	1.49324i
$185$	0.152489	+	0.264119i	0.0112112	+	0.0194184i
$186$		0			0
$187$	1.41875	+	1.41875i	0.103749	+	0.103749i
$188$	16.8939	+	4.25530i	1.23211	+	0.310349i
$189$		0			0
$190$	0.0552106	+	0.0143493i	0.00400540	+	0.00104101i
$191$	−6.98944	−	4.03535i	−0.505738	−	0.291988i	0.225342	−	0.974280i	$-0.427650\pi$
$191$	−6.98944	−	4.03535i	−0.505738	−	0.291988i	−0.731080	+	0.682292i	$0.760983\pi$
$192$		0			0
$193$	3.79172	+	1.01599i	0.272934	+	0.0731325i	0.392690	−	0.919671i	$-0.371545\pi$
$193$	3.79172	+	1.01599i	0.272934	+	0.0731325i	−0.119756	+	0.992803i	$0.538211\pi$
$194$	4.66428	+	7.94019i	0.334876	+	0.570073i
$195$		0			0
$196$	−5.00534	+	8.97888i	−0.357524	+	0.641349i
$197$	17.9395	+	4.80687i	1.27813	+	0.342475i	0.833142	−	0.553059i	$-0.186540\pi$
$197$	17.9395	+	4.80687i	1.27813	+	0.342475i	0.444993	+	0.895534i	$0.353206\pi$
$198$		0			0
$199$	0.747531	−	1.29476i	0.0529911	−	0.0917833i	−0.838313	−	0.545189i	$-0.816458\pi$
$199$	0.747531	−	1.29476i	0.0529911	−	0.0917833i	0.891304	+	0.453406i	$0.149791\pi$
$200$	9.75295	−	10.2035i	0.689638	−	0.721497i
$201$		0			0
$202$	6.39183	−	6.48875i	0.449727	−	0.456547i
$203$	9.01580	−	9.01580i	0.632785	−	0.632785i
$204$		0			0
$205$	−0.350811	−	0.607622i	−0.0245017	−	0.0424382i
$206$	5.84762	+	21.1847i	0.407423	+	1.47601i
$207$		0			0
$208$	0.361345	+	14.4177i	0.0250548	+	0.999686i
$209$	−0.130221			−0.00900758
$210$		0			0
$211$	−5.13613	−	8.89604i	−0.353586	−	0.612429i	0.633289	−	0.773915i	$-0.281704\pi$
$211$	−5.13613	−	8.89604i	−0.353586	−	0.612429i	−0.986875	+	0.161487i	$0.948371\pi$
$212$	3.99489	+	6.68498i	0.274370	+	0.459126i
$213$		0			0
$214$	−1.71726	+	1.74330i	−0.117389	+	0.119169i
$215$	−0.534542	+	0.143230i	−0.0364554	+	0.00976820i
$216$		0			0
$217$	2.76134	−	4.78278i	0.187452	−	0.324676i
$218$	22.9919	+	13.0447i	1.55721	+	0.883500i
$219$		0			0
$220$	0.0302298	−	0.0542280i	0.00203809	−	0.00365605i
$221$	−22.8518	−	0.115173i	−1.53718	−	0.00774737i
$222$		0			0
$223$	−4.08977	−	1.09585i	−0.273871	−	0.0733836i	0.119269	−	0.992862i	$-0.461945\pi$
$223$	−4.08977	−	1.09585i	−0.273871	−	0.0733836i	−0.393141	+	0.919478i	$0.628611\pi$
$224$	19.6959	−	0.741341i	1.31598	−	0.0495330i
$225$		0			0
$226$	18.8427	+	4.89724i	1.25340	+	0.325759i
$227$	−20.5241	+	5.49942i	−1.36223	+	0.365009i	−0.864636	−	0.502399i	$-0.832451\pi$
$227$	−20.5241	+	5.49942i	−1.36223	+	0.365009i	−0.497598	+	0.867408i	$0.665784\pi$
$228$		0			0
$229$	−2.65946	−	2.65946i	−0.175742	−	0.175742i	0.613755	−	0.789497i	$-0.289658\pi$
$229$	−2.65946	−	2.65946i	−0.175742	−	0.175742i	−0.789497	+	0.613755i	$0.789658\pi$
$230$	−0.00769145	−	1.02219i	−0.000507159	−	0.0674012i
$231$		0			0
$232$	−10.0556	−	2.45254i	−0.660185	−	0.161017i
$233$		−	12.9659i		−	0.849423i	−0.905329	−	0.424711i	$-0.860376\pi$
$233$		−	12.9659i		−	0.849423i	0.905329	−	0.424711i	$-0.139624\pi$
$234$		0			0
$235$	0.854172			0.0557200
$236$	−13.9456	−	13.5321i	−0.907783	−	0.880865i
$237$		0			0
$238$	0.234985	+	31.2294i	0.0152318	+	2.02430i
$239$	2.00711	−	2.00711i	0.129829	−	0.129829i	−0.639206	−	0.769035i	$-0.720737\pi$
$239$	2.00711	−	2.00711i	0.129829	−	0.129829i	0.769035	+	0.639206i	$0.220737\pi$
$240$		0			0
$241$	−2.01768	−	7.53010i	−0.129970	−	0.485056i	0.869998	−	0.493056i	$-0.164120\pi$
$241$	−2.01768	−	7.53010i	−0.129970	−	0.485056i	−0.999968	+	0.00799977i	$0.997454\pi$
$242$	3.87745	−	14.9190i	0.249252	−	0.959028i
$243$		0			0
$244$	27.5320	−	0.414352i	1.76256	−	0.0265261i
$245$	−0.130448	+	0.486839i	−0.00833402	+	0.0311030i
$246$		0			0
$247$	1.05402	−	1.04345i	0.0670656	−	0.0663929i
$248$	−4.48205	+	0.101191i	−0.284610	+	0.00642561i
$249$		0			0
$250$	0.683668	−	1.20500i	0.0432390	−	0.0762107i
$251$	8.49344	+	4.90369i	0.536101	+	0.309518i	0.743497	−	0.668739i	$-0.233166\pi$
$251$	8.49344	+	4.90369i	0.536101	+	0.309518i	−0.207396	+	0.978257i	$0.566499\pi$
$252$		0			0
$253$	0.603955	+	2.25399i	0.0379703	+	0.141707i
$254$	−8.40069	+	8.52807i	−0.527106	+	0.535099i
$255$		0			0
$256$	−8.81909	−	13.3500i	−0.551193	−	0.834378i
$257$	−8.22290	+	4.74749i	−0.512930	+	0.296140i	−0.734037	−	0.679109i	$-0.762366\pi$
$257$	−8.22290	+	4.74749i	−0.512930	+	0.296140i	0.221107	+	0.975250i	$0.429033\pi$
$258$		0			0
$259$		−	10.8365i		−	0.673345i
$260$	0.189841	+	0.681154i	0.0117735	+	0.0422434i
$261$		0			0
$262$	5.11225	+	18.5206i	0.315836	+	1.14421i
$263$	−0.383169	+	0.221223i	−0.0236272	+	0.0136412i	−0.511767	−	0.859124i	$-0.671009\pi$
$263$	−0.383169	+	0.221223i	−0.0236272	+	0.0136412i	0.488140	+	0.872765i	$0.337676\pi$
$264$		0			0
$265$	0.269992	+	0.269992i	0.0165855	+	0.0165855i
$266$	−1.44399	−	1.42242i	−0.0885367	−	0.0872143i
$267$		0			0
$268$	−6.69359	−	23.5570i	−0.408876	−	1.43897i
$269$	−12.2972	−	7.09981i	−0.749776	−	0.432883i	0.0758371	−	0.997120i	$-0.475837\pi$
$269$	−12.2972	−	7.09981i	−0.749776	−	0.432883i	−0.825613	+	0.564237i	$0.809170\pi$
$270$		0			0
$271$	1.28851	−	4.80880i	0.0782717	−	0.292114i	−0.915684	−	0.401900i	$-0.868350\pi$
$271$	1.28851	−	4.80880i	0.0782717	−	0.292114i	0.993955	+	0.109786i	$0.0350166\pi$
$272$	21.5642	−	13.3310i	1.30752	−	0.808311i
$273$		0			0
$274$	15.0402	−	8.83504i	0.908614	−	0.533744i
$275$	−0.408882	+	1.52597i	−0.0246565	+	0.0920193i
$276$		0			0
$277$	−5.99110	+	10.3769i	−0.359970	+	0.623487i	−0.987955	−	0.154739i	$-0.950546\pi$
$277$	−5.99110	+	10.3769i	−0.359970	+	0.623487i	0.627985	+	0.778225i	$0.283880\pi$
$278$	14.6783	+	3.81489i	0.880344	+	0.228802i
$279$		0			0
$280$	0.927551	−	0.271118i	0.0554318	−	0.0162024i
$281$	5.12419	−	5.12419i	0.305684	−	0.305684i	−0.537549	−	0.843233i	$-0.680650\pi$
$281$	5.12419	−	5.12419i	0.305684	−	0.305684i	0.843233	+	0.537549i	$0.180650\pi$
$282$		0			0
$283$	−10.7351	+	6.19789i	−0.638133	+	0.368426i	−0.783895	−	0.620893i	$-0.786770\pi$
$283$	−10.7351	+	6.19789i	−0.638133	+	0.368426i	0.145762	+	0.989320i	$0.453437\pi$
$284$	10.0801	+	9.78117i	0.598143	+	0.580406i
$285$		0			0
$286$	−0.810564	−	1.39592i	−0.0479297	−	0.0825424i
$287$			24.9300i			1.47157i
$288$		0			0
$289$	11.5853	+	20.0663i	0.681486	+	1.18037i
$290$	−0.507461	+	0.00381838i	−0.0297991	+	0.000224223i
$291$		0			0
$292$	−1.03340	+	4.10267i	−0.0604749	+	0.240091i
$293$	−2.75972	+	0.739465i	−0.161225	+	0.0432000i	−0.338528	−	0.940956i	$-0.609929\pi$
$293$	−2.75972	+	0.739465i	−0.161225	+	0.0432000i	0.177304	+	0.984156i	$0.443262\pi$
$294$		0			0
$295$	−0.825094	−	0.476368i	−0.0480388	−	0.0277352i
$296$	−7.51705	+	4.56924i	−0.436919	+	0.265582i
$297$		0			0
$298$	13.9792	−	8.21174i	0.809792	−	0.475693i
$299$	−22.9494	−	13.4045i	−1.32720	−	0.775204i
$300$		0			0
$301$	18.9933	+	5.08925i	1.09476	+	0.293339i
$302$	7.53861	−	13.2871i	0.433798	−	0.764589i
$303$		0			0
$304$	−0.377842	+	1.60144i	−0.0216707	+	0.0918488i
$305$	1.30403	−	0.349415i	0.0746687	−	0.0200074i
$306$		0			0
$307$	1.31454	−	1.31454i	0.0750248	−	0.0750248i	−0.668599	−	0.743623i	$-0.733106\pi$
$307$	1.31454	−	1.31454i	0.0750248	−	0.0750248i	0.743623	+	0.668599i	$0.233106\pi$
$308$	−1.89363	+	1.13162i	−0.107900	+	0.0644801i
$309$		0			0
$310$	−0.211885	+	0.0584867i	−0.0120343	+	0.00332182i
$311$	26.3976			1.49687			0.748436	−	0.663207i	$-0.230805\pi$
$311$	26.3976			1.49687			0.748436	+	0.663207i	$0.230805\pi$
$312$		0			0
$313$	23.0930			1.30529			0.652647	−	0.757662i	$-0.273658\pi$
$313$	23.0930			1.30529			0.652647	+	0.757662i	$0.273658\pi$
$314$	0.403014	−	0.111244i	0.0227434	−	0.00627787i
$315$		0			0
$316$	−10.5718	−	17.6906i	−0.594710	−	0.995176i
$317$	−13.9691	+	13.9691i	−0.784583	+	0.784583i	−0.980600	−	0.196018i	$-0.937199\pi$
$317$	−13.9691	+	13.9691i	−0.784583	+	0.784583i	0.196018	+	0.980600i	$0.437199\pi$
$318$		0			0
$319$	1.11898	−	0.299830i	0.0626510	−	0.0167873i
$320$	−0.579175	−	0.529106i	−0.0323769	−	0.0295779i
$321$		0			0
$322$	−17.9235	+	31.5911i	−0.998839	+	1.76050i
$323$	−2.51832	−	0.674782i	−0.140123	−	0.0375459i
$324$		0			0
$325$	−8.91789	−	15.6276i	−0.494676	−	0.866864i
$326$	3.03395	−	1.78223i	0.168035	−	0.0987084i
$327$		0			0
$328$	17.2935	−	10.5118i	0.954872	−	0.580419i
$329$	−26.2842	−	15.1752i	−1.44910	−	0.836636i
$330$		0			0
$331$	8.82798	−	2.36545i	0.485229	−	0.130017i	−0.00790714	−	0.999969i	$-0.502517\pi$
$331$	8.82798	−	2.36545i	0.485229	−	0.130017i	0.493137	+	0.869952i	$0.335850\pi$
$332$	6.96032	+	1.75319i	0.381997	+	0.0962188i
$333$		0			0
$334$	−13.1377	+	0.0988542i	−0.718861	+	0.00540906i
$335$	−0.600354	−	1.03984i	−0.0328009	−	0.0568127i
$336$		0			0
$337$		−	8.38992i		−	0.457028i	−0.973541	−	0.228514i	$-0.926613\pi$
$337$		−	8.38992i		−	0.457028i	0.973541	−	0.228514i	$-0.0733867\pi$
$338$	17.7461	+	4.80370i	0.965261	+	0.261287i
$339$		0			0
$340$	0.865609	−	0.892061i	0.0469442	−	0.0483788i
$341$	0.434551	−	0.250888i	0.0235322	−	0.0135863i
$342$		0			0
$343$	−4.58281	+	4.58281i	−0.247448	+	0.247448i
$344$	−4.47830	−	15.3212i	−0.241454	−	0.826064i
$345$		0			0
$346$	−4.05874	−	1.05487i	−0.218199	−	0.0567102i
$347$	−1.54479	+	2.67566i	−0.0829287	+	0.143637i	−0.904507	−	0.426459i	$-0.859761\pi$
$347$	−1.54479	+	2.67566i	−0.0829287	+	0.143637i	0.821578	+	0.570096i	$0.193094\pi$
$348$		0			0
$349$	7.75487	−	28.9416i	0.415109	−	1.54921i	−0.369509	−	0.929227i	$-0.620474\pi$
$349$	7.75487	−	28.9416i	0.415109	−	1.54921i	0.784618	−	0.619980i	$-0.212859\pi$
$350$	−21.2023	+	12.4548i	−1.13331	+	0.665738i
$351$		0			0
$352$	1.58344	+	0.836424i	0.0843978	+	0.0445816i
$353$	6.52845	−	24.3645i	0.347474	−	1.29679i	−0.542220	−	0.840236i	$-0.682416\pi$
$353$	6.52845	−	24.3645i	0.347474	−	1.29679i	0.889695	−	0.456556i	$-0.150917\pi$
$354$		0			0
$355$	0.596389	+	0.344325i	0.0316530	+	0.0182749i
$356$	0.220156	−	0.0625562i	0.0116682	−	0.00331547i
$357$		0			0
$358$	−6.30962	−	6.21538i	−0.333474	−	0.328493i
$359$	9.78353	+	9.78353i	0.516355	+	0.516355i	0.916467	−	0.400111i	$-0.131029\pi$
$359$	9.78353	+	9.78353i	0.516355	+	0.516355i	−0.400111	+	0.916467i	$0.631029\pi$
$360$		0			0
$361$	−16.3079	+	9.41539i	−0.858313	+	0.495547i
$362$	−7.40301	−	26.8196i	−0.389093	−	1.40960i
$363$		0			0
$364$	6.25965	−	24.3329i	0.328095	−	1.27539i
$365$			0.207435i			0.0108576i
$366$		0			0
$367$	7.32432	−	4.22870i	0.382327	−	0.220736i	−0.296504	−	0.955032i	$-0.595821\pi$
$367$	7.32432	−	4.22870i	0.382327	−	0.220736i	0.678830	+	0.734295i	$0.262487\pi$
$368$	29.4716	−	0.887286i	1.53631	−	0.0462530i
$369$		0			0
$370$	−0.302674	+	0.307264i	−0.0157353	+	0.0159739i
$371$	−3.51141	−	13.1048i	−0.182304	−	0.680366i
$372$		0			0
$373$	8.98736	+	5.18886i	0.465348	+	0.268669i	0.714290	−	0.699850i	$-0.246750\pi$
$373$	8.98736	+	5.18886i	0.465348	+	0.268669i	−0.248942	+	0.968518i	$0.580083\pi$
$374$	−1.40022	+	2.46795i	−0.0724037	+	0.127615i
$375$		0			0
$376$	0.556103	+	24.6315i	0.0286788	+	1.27028i
$377$	−6.65461	+	11.3931i	−0.342730	+	0.586776i
$378$		0			0
$379$	1.21827	−	4.54665i	0.0625784	−	0.233546i	−0.927552	−	0.373694i	$-0.878091\pi$
$379$	1.21827	−	4.54665i	0.0625784	−	0.233546i	0.990131	+	0.140148i	$0.0447578\pi$
$380$	0.00121399	+	0.0806645i	6.22761e−5	+	0.00413800i
$381$		0			0
$382$	2.87105	−	11.0467i	0.146895	−	0.565198i
$383$	−5.80376	−	21.6599i	−0.296558	−	1.10677i	−0.939972	−	0.341252i	$-0.889149\pi$
$383$	−5.80376	−	21.6599i	−0.296558	−	1.10677i	0.643414	−	0.765519i	$-0.277518\pi$
$384$		0			0
$385$	−0.0764799	+	0.0764799i	−0.00389778	+	0.00389778i
$386$	0.0417707	+	5.55131i	0.00212607	+	0.282554i
$387$		0			0
$388$	−9.06919	+	9.34634i	−0.460418	+	0.474489i
$389$	−0.255974			−0.0129784			−0.00648920	−	0.999979i	$-0.502066\pi$
$389$	−0.255974			−0.0129784			−0.00648920	+	0.999979i	$0.502066\pi$
$390$		0			0
$391$			46.7191i			2.36269i
$392$	−14.1238	−	3.44475i	−0.713359	−	0.173986i
$393$		0			0
$394$	0.197627	+	26.2645i	0.00995628	+	1.32319i
$395$	−0.714488	−	0.714488i	−0.0359498	−	0.0359498i
$396$		0			0
$397$	−29.9538	+	8.02610i	−1.50334	+	0.402818i	−0.914217	−	0.405226i	$-0.867193\pi$
$397$	−29.9538	+	8.02610i	−1.50334	+	0.402818i	−0.589122	+	0.808044i	$0.700526\pi$
$398$	2.04635	+	0.531849i	0.102574	+	0.0266592i
$399$		0			0
$400$	17.5797	+	9.45603i	0.878986	+	0.472801i
$401$	−20.6707	−	5.53870i	−1.03225	−	0.276590i	−0.297350	−	0.954769i	$-0.596103\pi$
$401$	−20.6707	−	5.53870i	−1.03225	−	0.276590i	−0.734897	+	0.678179i	$0.762769\pi$
$402$		0			0
$403$	−1.50695	+	5.51271i	−0.0750663	+	0.274608i
$404$	11.2509	+	6.27188i	0.559752	+	0.312038i
$405$		0			0
$406$	15.6832	+	8.89805i	0.778345	+	0.441603i
$407$	0.492286	−	0.852665i	0.0244017	−	0.0422650i
$408$		0			0
$409$	−31.2652	+	8.37750i	−1.54597	+	0.414241i	−0.928188	−	0.372112i	$-0.878634\pi$
$409$	−31.2652	+	8.37750i	−1.54597	+	0.414241i	−0.617779	+	0.786352i	$0.711967\pi$
$410$	0.696322	−	0.706881i	0.0343889	−	0.0349104i
$411$		0			0
$412$	−26.6793	+	15.9433i	−1.31439	+	0.785472i
$413$	16.9263	+	29.3172i	0.832889	+	1.44261i
$414$		0			0
$415$	0.351920			0.0172751
$416$	−19.5187	+	5.91787i	−0.956982	+	0.290148i
$417$		0			0
$418$	−0.0490013	−	0.177522i	−0.00239673	−	0.00868286i
$419$	10.4525	+	18.1043i	0.510640	+	0.884454i	0.999924	+	0.0123300i	$0.00392485\pi$
$419$	10.4525	+	18.1043i	0.510640	+	0.884454i	−0.489284	+	0.872125i	$0.662742\pi$
$420$		0			0
$421$	8.42426	−	8.42426i	0.410573	−	0.410573i	−0.471365	−	0.881938i	$-0.656239\pi$
$421$	8.42426	−	8.42426i	0.410573	−	0.410573i	0.881938	+	0.471365i	$0.156239\pi$
$422$	10.1947	−	10.3493i	0.496269	−	0.503794i
$423$		0			0
$424$	−7.60993	+	7.96148i	−0.369571	+	0.386644i
$425$	−15.8146	+	27.3917i	−0.767120	+	1.32869i
$426$		0			0
$427$	−46.3349	−	12.4154i	−2.24230	−	0.600823i
$428$	−3.02271	−	1.68503i	−0.146108	−	0.0814491i
$429$		0			0
$430$	−0.396400	−	0.674808i	−0.0191161	−	0.0325421i
$431$	−21.5916	−	5.78544i	−1.04003	−	0.278675i	−0.301904	−	0.953338i	$-0.597622\pi$
$431$	−21.5916	−	5.78544i	−1.04003	−	0.278675i	−0.738125	+	0.674663i	$0.764289\pi$
$432$		0			0
$433$	−12.3592	−	7.13560i	−0.593946	−	0.342915i	0.172710	−	0.984973i	$-0.444748\pi$
$433$	−12.3592	−	7.13560i	−0.593946	−	0.342915i	−0.766656	+	0.642058i	$0.778081\pi$
$434$	7.55911	+	1.96462i	0.362849	+	0.0943047i
$435$		0			0
$436$	−9.13129	+	36.2520i	−0.437309	+	1.73616i
$437$	−2.14407	−	2.14407i	−0.102565	−	0.102565i
$438$		0			0
$439$	1.78605	+	3.09353i	0.0852434	+	0.147646i	0.905495	−	0.424357i	$-0.139500\pi$
$439$	1.78605	+	3.09353i	0.0852434	+	0.147646i	−0.820251	+	0.572003i	$0.806167\pi$
$440$	0.0853007	+	0.0208046i	0.00406655	+	0.000991819i
$441$		0			0
$442$	−8.44196	−	31.1956i	−0.401543	−	1.48382i
$443$	−8.73925			−0.415214			−0.207607	−	0.978212i	$-0.566568\pi$
$443$	−8.73925			−0.415214			−0.207607	+	0.978212i	$0.566568\pi$
$444$		0			0
$445$	0.00971805	−	0.00561072i	0.000460680	−	0.000265974i
$446$	−0.0450541	−	5.98767i	−0.00213337	−	0.283524i
$447$		0			0
$448$	8.42204	+	26.5711i	0.397904	+	1.25537i
$449$	6.78232	+	25.3120i	0.320077	+	1.19455i	0.919169	+	0.393864i	$0.128862\pi$
$449$	6.78232	+	25.3120i	0.320077	+	1.19455i	−0.599091	+	0.800681i	$0.704471\pi$
$450$		0			0
$451$	−1.13254	+	1.96161i	−0.0533291	+	0.0923687i
$452$	0.414319	+	27.5298i	0.0194879	+	1.29489i
$453$		0			0
$454$	−15.2201	−	25.9098i	−0.714314	−	1.21601i
$455$	0.00620857	−	1.23186i	0.000291062	−	0.0577505i
$456$		0			0
$457$	8.37320	−	31.2492i	0.391682	−	1.46178i	−0.435677	−	0.900103i	$-0.643491\pi$
$457$	8.37320	−	31.2492i	0.391682	−	1.46178i	0.827359	−	0.561674i	$-0.189842\pi$
$458$	2.62473	−	4.62620i	0.122645	−	0.216168i
$459$		0			0
$460$	1.39059	−	0.395128i	0.0648365	−	0.0184230i
$461$	4.21669	+	15.7369i	0.196391	+	0.732941i	0.991902	+	0.127003i	$0.0405356\pi$
$461$	4.21669	+	15.7369i	0.196391	+	0.732941i	−0.795511	+	0.605939i	$0.792798\pi$
$462$		0			0
$463$	−24.8178	−	24.8178i	−1.15338	−	1.15338i	−0.985871	−	0.167509i	$-0.946428\pi$
$463$	−24.8178	−	24.8178i	−1.15338	−	1.15338i	−0.167509	−	0.985871i	$-0.553572\pi$
$464$	−0.440489	−	14.6310i	−0.0204492	−	0.679229i
$465$		0			0
$466$	17.6755	−	4.87897i	0.818802	−	0.226014i
$467$		−	10.5453i		−	0.487976i	−0.969778	−	0.243988i	$-0.921544\pi$
$467$		−	10.5453i		−	0.487976i	0.969778	−	0.243988i	$-0.0784558\pi$
$468$		0			0
$469$			42.6636i			1.97002i
$470$	0.321419	+	1.16443i	0.0148260	+	0.0537114i
$471$		0			0
$472$	13.1997	−	24.1032i	0.607568	−	1.10944i
$473$	1.26329	+	1.26329i	0.0580860	+	0.0580860i
$474$		0			0
$475$	−0.531305	−	1.98286i	−0.0243779	−	0.0909797i
$476$	−42.4845	+	12.0718i	−1.94728	+	0.553308i
$477$		0			0
$478$	3.49143	+	1.98090i	0.159694	+	0.0906042i
$479$	−2.68034	+	10.0032i	−0.122468	+	0.457057i	−0.999737	−	0.0229425i	$-0.992697\pi$
$479$	−2.68034	+	10.0032i	−0.122468	+	0.457057i	0.877269	+	0.480000i	$0.159363\pi$
$480$		0			0
$481$	2.84771	+	10.8462i	0.129845	+	0.494543i
$482$	9.50603	−	5.58410i	0.432988	−	0.254349i
$483$		0			0
$484$	21.7971	−	0.328042i	0.990777	−	0.0149110i
$485$	−0.319261	+	0.552977i	−0.0144969	+	0.0251094i
$486$		0			0
$487$	−6.29726	−	23.5017i	−0.285356	−	1.06496i	−0.948579	−	0.316541i	$-0.897478\pi$
$487$	−6.29726	−	23.5017i	−0.285356	−	1.06496i	0.663222	−	0.748422i	$-0.269188\pi$
$488$	10.9250	+	37.3766i	0.494550	+	1.69196i
$489$		0			0
$490$	−0.712761	+	0.00536316i	−0.0321993	+	0.000242283i
$491$	−28.1909	+	16.2760i	−1.27224	+	0.734525i	−0.975408	−	0.220406i	$-0.929262\pi$
$491$	−28.1909	+	16.2760i	−1.27224	+	0.734525i	−0.296827	+	0.954931i	$0.595928\pi$
$492$		0			0
$493$	23.1935			1.04458
$494$	1.81908	+	1.04423i	0.0818443	+	0.0469821i
$495$		0			0
$496$	−1.82451	−	6.07200i	−0.0819230	−	0.272641i
$497$	−12.2346	−	21.1909i	−0.548795	−	0.950541i
$498$		0			0
$499$	20.4541	+	20.4541i	0.915653	+	0.915653i	0.996710	−	0.0810563i	$-0.0258294\pi$
$499$	20.4541	+	20.4541i	0.915653	+	0.915653i	−0.0810563	+	0.996710i	$0.525829\pi$
$500$	1.89995	+	0.478567i	0.0849684	+	0.0214021i
$501$		0			0
$502$	−3.48885	+	13.4238i	−0.155715	+	0.599132i
$503$	−22.7444	−	13.1315i	−1.01412	−	0.585504i	−0.101726	−	0.994812i	$-0.532437\pi$
$503$	−22.7444	−	13.1315i	−1.01412	−	0.585504i	−0.912396	+	0.409309i	$0.865770\pi$
$504$		0			0
$505$	0.610027	+	0.163456i	0.0271459	+	0.00727371i
$506$	−2.84545	+	1.67149i	−0.126496	+	0.0743069i
$507$		0			0
$508$	−14.7869	−	8.24304i	−0.656061	−	0.365726i
$509$	13.3661	+	3.58144i	0.592443	+	0.158745i	0.542569	−	0.840011i	$-0.317452\pi$
$509$	13.3661	+	3.58144i	0.592443	+	0.158745i	0.0498735	+	0.998756i	$0.484118\pi$
$510$		0			0
$511$	3.68529	−	6.38311i	0.163028	−	0.282372i
$512$	14.8806	−	17.0460i	0.657638	−	0.753334i
$513$		0			0
$514$	−9.56616	−	9.42327i	−0.421945	−	0.415643i
$515$	−1.07752	+	1.07752i	−0.0474812	+	0.0474812i
$516$		0			0
$517$	−1.37878	−	2.38812i	−0.0606386	−	0.105029i
$518$	14.7726	−	4.07769i	0.649072	−	0.179163i
$519$		0			0
$520$	−0.857135	+	0.515112i	−0.0375879	+	0.0225891i
$521$	−0.605870			−0.0265437			−0.0132718	−	0.999912i	$-0.504225\pi$
$521$	−0.605870			−0.0265437			−0.0132718	+	0.999912i	$0.504225\pi$
$522$		0			0
$523$	6.97171	+	12.0753i	0.304851	+	0.528018i	0.977228	−	0.212191i	$-0.0680599\pi$
$523$	6.97171	+	12.0753i	0.304851	+	0.528018i	−0.672377	+	0.740209i	$0.734727\pi$
$524$	−23.3242	+	13.9384i	−1.01892	+	0.608900i
$525$		0			0
$526$	−0.445762	−	0.439104i	−0.0194362	−	0.0191458i
$527$	9.70376	−	2.60011i	0.422702	−	0.113263i
$528$		0			0
$529$	−15.6676	+	27.1371i	−0.681201	+	1.17987i
$530$	−0.266466	+	0.469659i	−0.0115745	+	0.0204007i
$531$		0			0
$532$	1.39573	−	2.50374i	0.0605125	−	0.108551i
$533$	−6.55135	−	24.9523i	−0.283770	−	1.08081i
$534$		0			0
$535$	−0.163893	−	0.0439149i	−0.00708570	−	0.00189861i
$536$	29.5949	−	17.9893i	1.27830	−	0.777018i
$537$		0			0
$538$	5.05133	−	19.4356i	0.217778	−	0.837929i
$539$	1.57168	−	0.421131i	0.0676971	−	0.0181394i
$540$		0			0
$541$	−8.59605	−	8.59605i	−0.369573	−	0.369573i	0.497748	−	0.867321i	$-0.334160\pi$
$541$	−8.59605	−	8.59605i	−0.369573	−	0.369573i	−0.867321	+	0.497748i	$0.834160\pi$
$542$	7.04037	−	0.0529752i	0.302410	−	0.00227548i
$543$		0			0
$544$	26.2877	+	24.3806i	1.12708	+	1.04531i
$545$			1.83294i			0.0785144i
$546$		0			0
$547$	8.02828			0.343264			0.171632	−	0.985161i	$-0.445096\pi$
$547$	8.02828			0.343264			0.171632	+	0.985161i	$0.445096\pi$
$548$	17.7038	+	17.1788i	0.756267	+	0.733841i
$549$		0			0
$550$	−2.23411	+	0.0168105i	−0.0952627	+	0.000716802i
$551$	−1.06441	+	1.06441i	−0.0453456	+	0.0453456i
$552$		0			0
$553$	9.29235	+	34.6795i	0.395151	+	1.47472i
$554$	−16.4005	−	4.26251i	−0.696791	−	0.181097i
$555$		0			0
$556$	0.322749	+	21.4454i	0.0136876	+	0.909488i
$557$	9.27198	−	34.6035i	0.392866	−	1.46620i	−0.432517	−	0.901626i	$-0.642375\pi$
$557$	9.27198	−	34.6035i	0.392866	−	1.46620i	0.825384	−	0.564572i	$-0.190959\pi$
$558$		0			0
$559$	−20.3477	−	0.102553i	−0.860617	−	0.00433751i
$560$	0.718628	+	1.16245i	0.0303676	+	0.0491224i
$561$		0			0
$562$	8.91366	+	5.05726i	0.376000	+	0.213328i
$563$	5.28880	+	3.05349i	0.222897	+	0.128689i	0.607291	−	0.794480i	$-0.292256\pi$
$563$	5.28880	+	3.05349i	0.222897	+	0.128689i	−0.384394	+	0.923169i	$0.625590\pi$
$564$		0			0
$565$	0.349387	+	1.30393i	0.0146988	+	0.0548567i
$566$	−12.4887	−	12.3022i	−0.524939	−	0.517098i
$567$		0			0
$568$	−9.54095	+	17.4221i	−0.400329	+	0.731015i
$569$	16.0840	−	9.28610i	0.674276	−	0.389293i	−0.123419	−	0.992355i	$-0.539386\pi$
$569$	16.0840	−	9.28610i	0.674276	−	0.389293i	0.797695	+	0.603061i	$0.206053\pi$
$570$		0			0
$571$			30.2053i			1.26405i	0.774947	+	0.632026i	$0.217777\pi$
$571$			30.2053i			1.26405i	−0.774947	+	0.632026i	$0.782223\pi$
$572$	1.59795	−	1.63026i	0.0668137	−	0.0681647i
$573$		0			0
$574$	−33.9854	+	9.38100i	−1.41852	+	0.391555i
$575$	−31.8570	+	18.3927i	−1.32853	+	0.767027i
$576$		0			0
$577$	−26.5827	−	26.5827i	−1.10665	−	1.10665i	−0.993588	−	0.113063i	$-0.963934\pi$
$577$	−26.5827	−	26.5827i	−1.10665	−	1.10665i	−0.113063	−	0.993588i	$-0.536066\pi$
$578$	−22.9955	+	23.3442i	−0.956488	+	0.970991i
$579$		0			0
$580$	−0.196159	−	0.690350i	−0.00814508	−	0.0286652i
$581$	−10.8292	−	6.25222i	−0.449269	−	0.259386i
$582$		0			0
$583$	0.319038	−	1.19067i	0.0132132	−	0.0493123i
$584$	−5.98175	+	0.135049i	−0.247527	+	0.00558838i
$585$		0			0
$586$	−2.04653	−	3.48388i	−0.0845412	−	0.143918i
$587$	9.64475	−	35.9947i	0.398081	−	1.48566i	−0.418387	−	0.908269i	$-0.637404\pi$
$587$	9.64475	−	35.9947i	0.398081	−	1.48566i	0.816468	−	0.577391i	$-0.195929\pi$
$588$		0			0
$589$	−0.326006	+	0.564659i	−0.0134329	+	0.0232664i
$590$	0.338923	−	1.30405i	0.0139533	−	0.0536869i
$591$		0			0
$592$	−9.05755	−	8.52811i	−0.372263	−	0.350503i
$593$	−11.5292	+	11.5292i	−0.473447	+	0.473447i	−0.903028	−	0.429581i	$-0.858661\pi$
$593$	−11.5292	+	11.5292i	−0.473447	+	0.473447i	0.429581	+	0.903028i	$0.358661\pi$
$594$		0			0
$595$	−1.87534	+	1.08273i	−0.0768814	+	0.0443875i
$596$	16.4548	+	15.9668i	0.674014	+	0.654027i
$597$		0			0
$598$	9.63778	−	36.3295i	0.394118	−	1.48562i
$599$			16.7701i			0.685208i	0.939480	+	0.342604i	$0.111309\pi$
$599$			16.7701i			0.685208i	−0.939480	+	0.342604i	$0.888691\pi$
$600$		0			0
$601$	−8.91511	−	15.4414i	−0.363655	−	0.629869i	0.624904	−	0.780701i	$-0.285138\pi$
$601$	−8.91511	−	15.4414i	−0.363655	−	0.629869i	−0.988559	+	0.150832i	$0.951805\pi$
$602$	0.209236	+	27.8074i	0.00852782	+	1.13334i
$603$		0			0
$604$	20.9502	+	5.27701i	0.852451	+	0.214719i
$605$	1.03240	−	0.276632i	0.0419732	−	0.0112467i
$606$		0			0
$607$	−7.27664	−	4.20117i	−0.295350	−	0.170520i	0.345002	−	0.938602i	$-0.387878\pi$
$607$	−7.27664	−	4.20117i	−0.295350	−	0.170520i	−0.640352	+	0.768082i	$0.721211\pi$
$608$	−2.32531	+	0.0875235i	−0.0943038	+	0.00354955i
$609$		0			0
$610$	0.967032	+	1.64622i	0.0391540	+	0.0666534i
$611$	30.2957	+	8.28157i	1.22563	+	0.335037i
$612$		0			0
$613$	28.9567	+	7.75893i	1.16955	+	0.313380i	0.790774	−	0.612108i	$-0.209678\pi$
$613$	28.9567	+	7.75893i	1.16955	+	0.313380i	0.378776	+	0.925488i	$0.376345\pi$
$614$	2.28668	+	1.29737i	0.0922828	+	0.0523577i
$615$		0			0
$616$	−2.25523	−	2.15564i	−0.0908656	−	0.0868533i
$617$	29.7623	−	7.97479i	1.19819	−	0.321053i	0.396069	−	0.918221i	$-0.370374\pi$
$617$	29.7623	−	7.97479i	1.19819	−	0.321053i	0.802116	+	0.597168i	$0.203707\pi$
$618$		0			0
$619$	16.2444	−	16.2444i	0.652916	−	0.652916i	−0.300778	−	0.953694i	$-0.597246\pi$
$619$	16.2444	−	16.2444i	0.652916	−	0.652916i	0.953694	+	0.300778i	$0.0972463\pi$
$620$	−0.159462	−	0.266840i	−0.00640414	−	0.0107166i
$621$		0			0
$622$	9.93326	+	35.9861i	0.398287	+	1.44291i
$623$	−0.398720			−0.0159744
$624$		0			0
$625$	−24.8559			−0.994234
$626$	8.68975	+	31.4812i	0.347312	+	1.25824i
$627$		0			0
$628$	0.303303	+	0.507542i	0.0121031	+	0.0202531i
$629$	13.9386	−	13.9386i	0.555768	−	0.555768i
$630$		0			0
$631$	18.9019	−	5.06474i	0.752472	−	0.201624i	0.137858	−	0.990452i	$-0.455978\pi$
$631$	18.9019	−	5.06474i	0.752472	−	0.201624i	0.614614	+	0.788828i	$0.289312\pi$
$632$	20.1384	−	21.0687i	0.801061	−	0.838067i
$633$		0			0
$634$	−24.2996	−	13.7866i	−0.965061	−	0.547538i
$635$	−0.801750	−	0.214828i	−0.0318165	−	0.00852520i
$636$		0			0
$637$	−9.34683	+	16.0024i	−0.370335	+	0.634038i
$638$	0.829804	+	1.41261i	0.0328523	+	0.0559257i
$639$		0			0
$640$	0.503355	−	0.988649i	0.0198969	−	0.0390798i
$641$	−15.3793	−	8.87927i	−0.607448	−	0.350710i	0.164518	−	0.986374i	$-0.447393\pi$
$641$	−15.3793	−	8.87927i	−0.607448	−	0.350710i	−0.771966	+	0.635664i	$0.780726\pi$
$642$		0			0
$643$	−32.3334	+	8.66372i	−1.27511	+	0.341664i	−0.831985	−	0.554798i	$-0.812796\pi$
$643$	−32.3334	+	8.66372i	−1.27511	+	0.341664i	−0.443121	+	0.896462i	$0.646129\pi$
$644$	−49.8105	−	12.5464i	−1.96281	−	0.494399i
$645$		0			0
$646$	−0.0277426	−	3.68697i	−0.00109152	−	0.145062i
$647$	−13.7124	−	23.7505i	−0.539089	−	0.933730i	−0.998953	−	0.0457408i	$-0.985435\pi$
$647$	−13.7124	−	23.7505i	−0.539089	−	0.933730i	0.459864	−	0.887989i	$-0.347898\pi$
$648$		0			0
$649$			3.07576i			0.120734i
$650$	17.9483	−	18.0377i	0.703991	−	0.707498i
$651$		0			0
$652$	3.57125	+	3.46535i	0.139861	+	0.135713i
$653$	−15.1849	+	8.76701i	−0.594232	+	0.343080i	−0.766769	−	0.641923i	$-0.778137\pi$
$653$	−15.1849	+	8.76701i	−0.594232	+	0.343080i	0.172537	+	0.985003i	$0.444803\pi$
$654$		0			0
$655$	−0.942016	+	0.942016i	−0.0368076	+	0.0368076i
$656$	20.8375	+	19.6195i	0.813567	+	0.766012i
$657$		0			0
$658$	10.7968	−	41.5419i	0.420901	−	1.61947i
$659$	1.44190	−	2.49744i	0.0561684	−	0.0972865i	−0.836574	−	0.547854i	$-0.815445\pi$
$659$	1.44190	−	2.49744i	0.0561684	−	0.0972865i	0.892742	+	0.450567i	$0.148778\pi$
$660$		0			0
$661$	−10.3684	+	38.6953i	−0.403283	+	1.50507i	0.403917	+	0.914796i	$0.367649\pi$
$661$	−10.3684	+	38.6953i	−0.403283	+	1.50507i	−0.807200	+	0.590278i	$0.799018\pi$
$662$	6.54657	+	11.1445i	0.254440	+	0.433143i
$663$		0			0
$664$	0.229115	+	10.1482i	0.00889141	+	0.393828i
$665$	0.0363752	−	0.135754i	0.00141057	−	0.00526431i
$666$		0			0
$667$	23.3606	+	13.4872i	0.904525	+	0.522228i
$668$	−5.07838	−	17.8725i	−0.196488	−	0.691508i
$669$		0			0
$670$	1.19164	−	1.20971i	0.0460371	−	0.0467351i
$671$	−3.08184	−	3.08184i	−0.118973	−	0.118973i
$672$		0			0
$673$	6.34609	−	3.66391i	0.244624	−	0.141234i	−0.372676	−	0.927961i	$-0.621560\pi$
$673$	6.34609	−	3.66391i	0.244624	−	0.141234i	0.617300	+	0.786728i	$0.288226\pi$
$674$	11.4374	−	3.15707i	0.440553	−	0.121606i
$675$		0			0
$676$	0.129187	+	25.9997i	0.00496875	+	0.999988i
$677$			45.6313i			1.75376i	0.480714	+	0.876878i	$0.340378\pi$
$677$			45.6313i			1.75376i	−0.480714	+	0.876878i	$0.659622\pi$
$678$		0			0
$679$	19.6484	−	11.3440i	0.754035	−	0.435342i
$680$	1.54181	+	0.844349i	0.0591257	+	0.0323793i
$681$		0			0
$682$	0.505537	+	0.497986i	0.0193580	+	0.0190689i
$683$	−5.80580	−	21.6676i	−0.222153	−	0.829086i	−0.983525	−	0.180771i	$-0.942141\pi$
$683$	−5.80580	−	21.6676i	−0.222153	−	0.829086i	0.761372	−	0.648315i	$-0.224526\pi$
$684$		0			0
$685$	1.04744	+	0.604742i	0.0400208	+	0.0231060i
$686$	−7.97192	−	4.52295i	−0.304369	−	0.172687i
$687$		0			0
$688$	19.2012	−	11.8702i	0.732039	−	0.452548i
$689$	6.95836	+	12.1937i	0.265092	+	0.464545i
$690$		0			0
$691$	−1.10893	+	4.13859i	−0.0421857	+	0.157439i	−0.983806	−	0.179238i	$-0.942637\pi$
$691$	−1.10893	+	4.13859i	−0.0421857	+	0.157439i	0.941620	+	0.336678i	$0.109303\pi$
$692$	−0.0892447	−	5.92995i	−0.00339257	−	0.225423i
$693$		0			0
$694$	−4.22884	−	1.09908i	−0.160524	−	0.0417204i
$695$	0.272168	+	1.01575i	0.0103239	+	0.0385294i
$696$		0			0
$697$	−32.0667	+	32.0667i	−1.21461	+	1.21461i
$698$	42.3722	−	0.318829i	1.60381	−	0.0120679i
$699$		0			0
$700$	−24.9571	−	24.2171i	−0.943291	−	0.915319i
$701$	36.4870			1.37810			0.689048	−	0.724716i	$-0.258029\pi$
$701$	36.4870			1.37810			0.689048	+	0.724716i	$0.258029\pi$
$702$		0			0
$703$			1.27936i			0.0482521i
$704$	−0.544402	+	2.47334i	−0.0205179	+	0.0932176i
$705$		0			0
$706$	35.6711	−	0.268407i	1.34250	−	0.0101016i
$707$	−15.8676	−	15.8676i	−0.596761	−	0.596761i
$708$		0			0
$709$	−14.8664	+	3.98345i	−0.558321	+	0.149602i	−0.526935	−	0.849906i	$-0.676659\pi$
$709$	−14.8664	+	3.98345i	−0.558321	+	0.149602i	−0.0313862	+	0.999507i	$0.509992\pi$
$710$	−0.244978	+	0.942584i	−0.00919387	+	0.0353745i
$711$		0			0
$712$	0.168122	+	0.276584i	0.00630064	+	0.0103654i
$713$	11.2857	+	3.02398i	0.422651	+	0.113249i
$714$		0			0
$715$	0.0564503	−	0.0966466i	0.00211112	−	0.00361438i
$716$	6.09873	−	10.9403i	0.227920	−	0.408858i
$717$		0			0
$718$	−9.65575	+	17.0187i	−0.360350	+	0.635133i
$719$	−11.9512	+	20.7000i	−0.445703	+	0.771980i	−0.998101	−	0.0616005i	$-0.980380\pi$
$719$	−11.9512	+	20.7000i	−0.445703	+	0.771980i	0.552398	+	0.833580i	$0.313713\pi$
$720$		0			0
$721$	52.3002	−	14.0138i	1.94776	−	0.521902i
$722$	−18.9719	−	18.6886i	−0.706063	−	0.695517i
$723$		0			0
$724$	33.7756	−	20.1840i	1.25526	−	0.750134i
$725$	9.13095	+	15.8153i	0.339115	+	0.587364i
$726$		0			0
$727$	21.0545			0.780868			0.390434	−	0.920631i	$-0.372325\pi$
$727$	21.0545			0.780868			0.390434	+	0.920631i	$0.372325\pi$
$728$	35.5269	−	0.622959i	1.31671	−	0.0230884i
$729$		0			0
$730$	−0.282782	+	0.0780564i	−0.0104662	+	0.00288900i
$731$	17.8844	+	30.9766i	0.661477	+	1.14571i
$732$		0			0
$733$	2.18046	−	2.18046i	0.0805370	−	0.0805370i	−0.665691	−	0.746228i	$-0.731863\pi$
$733$	2.18046	−	2.18046i	0.0805370	−	0.0805370i	0.746228	+	0.665691i	$0.231863\pi$
$734$	8.52080	+	8.39352i	0.314508	+	0.309811i
$735$		0			0
$736$	12.2996	+	39.8428i	0.453368	+	1.46863i
$737$	−1.93815	+	3.35697i	−0.0713926	+	0.123656i
$738$		0			0
$739$	45.3273	+	12.1454i	1.66739	+	0.446776i	0.964405	−	0.264429i	$-0.0851833\pi$
$739$	45.3273	+	12.1454i	1.66739	+	0.446776i	0.702985	+	0.711204i	$0.251850\pi$
$740$	−0.532767	−	0.296994i	−0.0195849	−	0.0109177i
$741$		0			0
$742$	16.5435	−	9.71812i	0.607332	−	0.356763i
$743$	41.4704	+	11.1120i	1.52140	+	0.407658i	0.920203	−	0.391442i	$-0.128024\pi$
$743$	41.4704	+	11.1120i	1.52140	+	0.407658i	0.601198	+	0.799100i	$0.294690\pi$
$744$		0			0
$745$	0.973548	+	0.562078i	0.0356680	+	0.0205929i
$746$	−3.69173	+	14.2044i	−0.135164	+	0.520060i
$747$		0			0
$748$	−3.89129	−	0.980152i	−0.142280	−	0.0358379i
$749$	4.26305	+	4.26305i	0.155768	+	0.155768i
$750$		0			0
$751$	−3.78589	−	6.55735i	−0.138149	−	0.239281i	0.788647	−	0.614846i	$-0.210782\pi$
$751$	−3.78589	−	6.55735i	−0.138149	−	0.239281i	−0.926796	+	0.375565i	$0.877449\pi$
$752$	−33.3693	+	10.0268i	−1.21685	+	0.365639i
$753$		0			0
$754$	−18.0356	−	4.78463i	−0.656817	−	0.174246i
$755$	1.05926			0.0385505
$756$		0			0
$757$	18.5122	−	10.6880i	0.672836	−	0.388462i	−0.124314	−	0.992243i	$-0.539673\pi$
$757$	18.5122	−	10.6880i	0.672836	−	0.388462i	0.797151	+	0.603781i	$0.206340\pi$
$758$	6.65657	−	0.0500872i	0.241777	−	0.00181925i
$759$		0			0
$760$	−0.109508	+	0.0320084i	−0.00397226	+	0.00116107i
$761$	−0.991139	−	3.69898i	−0.0359288	−	0.134088i	0.945632	−	0.325239i	$-0.105445\pi$
$761$	−0.991139	−	3.69898i	−0.0359288	−	0.134088i	−0.981561	+	0.191151i	$0.938778\pi$
$762$		0			0
$763$	32.5639	−	56.4024i	1.17889	−	2.04190i
$764$	16.1396	−	0.242898i	0.583910	−	0.00878773i
$765$		0			0
$766$	27.3436	−	16.0624i	0.987965	−	0.580357i
$767$	−24.6457	−	24.8954i	−0.889906	−	0.898922i
$768$		0			0
$769$	4.33512	−	16.1789i	0.156329	−	0.583426i	−0.842659	−	0.538447i	$-0.819011\pi$
$769$	4.33512	−	16.1789i	0.156329	−	0.583426i	0.998988	−	0.0449792i	$-0.0143221\pi$
$770$	−0.133039	−	0.0754811i	−0.00479439	−	0.00272015i
$771$		0			0
$772$	−7.55201	+	2.14586i	−0.271803	+	0.0772313i
$773$	−6.29416	−	23.4901i	−0.226385	−	0.844882i	−0.981845	−	0.189686i	$-0.939253\pi$
$773$	−6.29416	−	23.4901i	−0.226385	−	0.844882i	0.755459	−	0.655195i	$-0.227414\pi$
$774$		0			0
$775$	5.59321	+	5.59321i	0.200914	+	0.200914i
$776$	−16.1539	−	8.84645i	−0.579892	−	0.317569i
$777$		0			0
$778$	−0.0963214	−	0.348952i	−0.00345329	−	0.0125105i
$779$		−	2.94326i		−	0.105453i
$780$		0			0
$781$		−	2.22320i		−	0.0795523i
$782$	−63.6890	+	17.5801i	−2.27751	+	0.628663i
$783$		0			0
$784$	−0.618695	−	20.5502i	−0.0220962	−	0.733937i
$785$	0.0204986	+	0.0204986i	0.000731625	+	0.000731625i
$786$		0			0
$787$	−9.30815	−	34.7385i	−0.331800	−	1.23829i	−0.907297	−	0.420490i	$-0.861858\pi$
$787$	−9.30815	−	34.7385i	−0.331800	−	1.23829i	0.575498	−	0.817803i	$-0.304808\pi$
$788$	−35.7302	+	10.1526i	−1.27284	+	0.361670i
$789$		0			0
$790$	0.705156	−	1.24287i	0.0250883	−	0.0442193i
$791$	12.4144	−	46.3312i	0.441405	−	1.64735i
$792$		0			0
$793$	49.6390	+	0.250181i	1.76273	+	0.00888417i
$794$	−22.2129	−	37.8138i	−0.788305	−	1.34196i
$795$		0			0
$796$	0.0449957	+	2.98979i	0.00159483	+	0.105970i
$797$	−5.36008	+	9.28393i	−0.189864	+	0.328854i	−0.945205	−	0.326478i	$-0.894138\pi$
$797$	−5.36008	+	9.28393i	−0.189864	+	0.328854i	0.755341	+	0.655332i	$0.227471\pi$
$798$		0			0
$799$	−14.2892	−	53.3280i	−0.505515	−	1.88661i
$800$	−6.27563	+	27.5235i	−0.221877	+	0.973102i
$801$		0			0
$802$	−0.227715	−	30.2632i	−0.00804089	−	1.06863i
$803$	0.579952	−	0.334836i	0.0204661	−	0.0118161i
$804$		0			0
$805$	−2.51847			−0.0887642
$806$	−8.08216	+	0.0200792i	−0.284682	+	0.000707261i
$807$		0			0
$808$	−4.31640	+	17.6976i	−0.151850	+	0.622600i
$809$	19.6641	+	34.0593i	0.691355	+	1.19746i	0.971394	+	0.237473i	$0.0763191\pi$
$809$	19.6641	+	34.0593i	0.691355	+	1.19746i	−0.280040	+	0.959988i	$0.590348\pi$
$810$		0			0
$811$	−38.2641	−	38.2641i	−1.34364	−	1.34364i	−0.892410	−	0.451226i	$-0.850987\pi$
$811$	−38.2641	−	38.2641i	−1.34364	−	1.34364i	−0.451226	−	0.892410i	$-0.649013\pi$
$812$	−6.22862	+	24.7282i	−0.218582	+	0.867788i
$813$		0			0
$814$	1.34762	+	0.350249i	0.0472342	+	0.0122762i
$815$	0.211293	+	0.121990i	0.00740127	+	0.00427312i
$816$		0			0
$817$	−2.24237	−	0.600841i	−0.0784506	−	0.0210208i
$818$	−23.1854	−	39.4694i	−0.810658	−	1.38002i
$819$		0			0
$820$	1.22566	+	0.683255i	0.0428021	+	0.0238603i
$821$	19.9781	+	5.35310i	0.697239	+	0.186825i	0.589993	−	0.807408i	$-0.299130\pi$
$821$	19.9781	+	5.35310i	0.697239	+	0.186825i	0.107245	+	0.994233i	$0.465797\pi$
$822$		0			0
$823$	−11.8141	+	20.4626i	−0.411813	+	0.713281i	−0.995088	−	0.0989937i	$-0.968438\pi$
$823$	−11.8141	+	20.4626i	−0.411813	+	0.713281i	0.583275	+	0.812275i	$0.301771\pi$
$824$	−31.7737	−	30.3707i	−1.10689	−	1.05801i
$825$		0			0
$826$	−33.5970	+	34.1064i	−1.16899	+	1.18671i
$827$	17.7598	−	17.7598i	0.617568	−	0.617568i	−0.327339	−	0.944907i	$-0.606152\pi$
$827$	17.7598	−	17.7598i	0.617568	−	0.617568i	0.944907	+	0.327339i	$0.106152\pi$
$828$		0			0
$829$	16.4735	+	28.5329i	0.572147	+	0.990988i	0.996345	+	0.0854184i	$0.0272227\pi$
$829$	16.4735	+	28.5329i	0.572147	+	0.990988i	−0.424198	+	0.905569i	$0.639444\pi$
$830$	0.132425	+	0.479749i	0.00459655	+	0.0166523i
$831$		0			0
$832$	−15.4122	−	24.3816i	−0.534322	−	0.845281i
$833$	32.5767			1.12872
$834$		0			0
$835$	−0.455484	−	0.788922i	−0.0157627	−	0.0273018i
$836$	0.223564	−	0.133600i	0.00773213	−	0.00462066i
$837$		0			0
$838$	−20.7472	+	21.0618i	−0.716700	+	0.727567i
$839$	42.5633	−	11.4048i	1.46945	−	0.393737i	0.566706	−	0.823920i	$-0.308218\pi$
$839$	42.5633	−	11.4048i	1.46945	−	0.393737i	0.902742	+	0.430183i	$0.141551\pi$
$840$		0			0
$841$	−7.80433	+	13.5175i	−0.269115	+	0.466121i
$842$	14.6542	+	8.31423i	0.505018	+	0.286527i
$843$		0			0
$844$	17.9446	+	10.0034i	0.617680	+	0.344330i
$845$	0.317506	+	1.23459i	0.0109225	+	0.0424713i
$846$		0			0
$847$	−36.6834	−	9.82927i	−1.26045	−	0.337738i
$848$	−13.7169	−	7.37825i	−0.471041	−	0.253370i
$849$		0			0
$850$	−43.2921	−	11.2517i	−1.48491	−	0.385929i
$851$	22.1445	−	5.93359i	0.759102	−	0.203401i
$852$		0			0
$853$	0.463907	+	0.463907i	0.0158839	+	0.0158839i	0.715004	−	0.699120i	$-0.246425\pi$
$853$	0.463907	+	0.463907i	0.0158839	+	0.0158839i	−0.699120	+	0.715004i	$0.746425\pi$
$854$	−0.510439	−	67.8371i	−0.0174669	−	2.32134i
$855$		0			0
$856$	1.15966	−	4.75473i	0.0396365	−	0.162513i
$857$			33.1382i			1.13198i	0.824412	+	0.565990i	$0.191506\pi$
$857$			33.1382i			1.13198i	−0.824412	+	0.565990i	$0.808494\pi$
$858$		0			0
$859$	21.3046			0.726903			0.363451	−	0.931613i	$-0.381598\pi$
$859$	21.3046			0.726903			0.363451	+	0.931613i	$0.381598\pi$
$860$	0.770757	−	0.794311i	0.0262826	−	0.0270858i
$861$		0			0
$862$	−0.237859	−	31.6114i	−0.00810151	−	1.07669i
$863$	−27.2032	+	27.2032i	−0.926008	+	0.926008i	−0.997445	−	0.0714372i	$-0.977241\pi$
$863$	−27.2032	+	27.2032i	−0.926008	+	0.926008i	0.0714372	+	0.997445i	$0.477241\pi$
$864$		0			0
$865$	−0.0752583	−	0.280868i	−0.00255886	−	0.00954979i
$866$	5.07679	−	19.5336i	0.172516	−	0.663777i
$867$		0			0
$868$	0.166212	+	11.0441i	0.00564159	+	0.374861i
$869$	−0.844278	+	3.15089i	−0.0286402	+	0.106887i
$870$		0			0
$871$	−11.2115	−	42.7018i	−0.379889	−	1.44689i
$872$	−52.8560	+	1.19332i	−1.78993	+	0.0404110i
$873$		0			0
$874$	2.11607	−	3.72967i	0.0715771	−	0.126158i
$875$	−2.95602	−	1.70666i	−0.0999318	−	0.0576957i
$876$		0			0
$877$	4.86299	+	18.1489i	0.164212	+	0.612846i	0.998139	+	0.0609726i	$0.0194202\pi$
$877$	4.86299	+	18.1489i	0.164212	+	0.612846i	−0.833928	+	0.551874i	$0.813913\pi$
$878$	−3.54512	+	3.59887i	−0.119642	+	0.121456i
$879$		0			0
$880$	0.00373661	+	0.124113i	0.000125961	+	0.00418386i
$881$	10.8962	−	6.29091i	0.367101	−	0.211946i	−0.305090	−	0.952324i	$-0.598687\pi$
$881$	10.8962	−	6.29091i	0.367101	−	0.211946i	0.672191	+	0.740377i	$0.265353\pi$
$882$		0			0
$883$		−	44.2186i		−	1.48807i	−0.668139	−	0.744036i	$-0.732909\pi$
$883$		−	44.2186i		−	1.48807i	0.668139	−	0.744036i	$-0.267091\pi$
$884$	39.3502	−	23.2471i	1.32349	−	0.781884i
$885$		0			0
$886$	−3.28852	−	11.9136i	−0.110480	−	0.400246i
$887$	5.54684	−	3.20247i	0.186245	−	0.107528i	−0.403979	−	0.914768i	$-0.632373\pi$
$887$	5.54684	−	3.20247i	0.186245	−	0.107528i	0.590223	+	0.807240i	$0.299040\pi$
$888$		0			0
$889$	20.8545	+	20.8545i	0.699437	+	0.699437i
$890$	0.0113056	+	0.0111367i	0.000378963	+	0.000373303i
$891$		0			0
$892$	8.14563	−	2.31454i	0.272736	−	0.0774965i
$893$	3.10314	+	1.79160i	0.103843	+	0.0599536i
$894$		0			0
$895$	0.158944	−	0.593187i	0.00531291	−	0.0198280i
$896$	−33.0534	+	21.4797i	−1.10424	+	0.717587i
$897$		0			0
$898$	−31.9539	+	18.7706i	−1.06632	+	0.626383i
$899$	1.50124	−	5.60271i	0.0500692	−	0.186861i
$900$		0			0
$901$	12.3396	−	21.3729i	0.411093	−	0.712034i
$902$	−3.10030	−	0.805770i	−0.103229	−	0.0268292i
$903$		0			0
$904$	−37.3736	+	10.9241i	−1.24303	+	0.363330i
$905$	1.36413	−	1.36413i	0.0453451	−	0.0453451i
$906$		0			0
$907$	11.0865	−	6.40082i	0.368123	−	0.212536i	−0.304515	−	0.952507i	$-0.598494\pi$
$907$	11.0865	−	6.40082i	0.368123	−	0.212536i	0.672638	+	0.739972i	$0.265161\pi$
$908$	29.5938	−	30.4982i	0.982105	−	1.01212i
$909$		0			0
$910$	1.68165	−	0.455077i	0.0557461	−	0.0150857i
$911$			4.52483i			0.149914i	0.997187	+	0.0749572i	$0.0238820\pi$
$911$			4.52483i			0.149914i	−0.997187	+	0.0749572i	$0.976118\pi$
$912$		0			0
$913$	−0.568060	−	0.983909i	−0.0188000	−	0.0325626i
$914$	45.7507	−	0.344251i	1.51330	−	0.0113868i
$915$		0			0
$916$	7.29426	+	1.83730i	0.241009	+	0.0607063i
$917$	45.7232	−	12.2515i	1.50991	−	0.404580i
$918$		0			0
$919$	44.0101	+	25.4093i	1.45176	+	0.838174i	0.998581	−	0.0532452i	$-0.0169565\pi$
$919$	44.0101	+	25.4093i	1.45176	+	0.838174i	0.453179	+	0.891420i	$0.350290\pi$
$920$	1.06192	+	1.74701i	0.0350105	+	0.0575972i
$921$		0			0
$922$	−19.8664	+	11.6700i	−0.654264	+	0.384332i
$923$	17.8143	+	17.9947i	0.586363	+	0.592304i
$924$		0			0
$925$	14.9920	+	4.01708i	0.492932	+	0.132081i
$926$	24.4936	−	43.1712i	0.804911	−	1.41869i
$927$		0			0
$928$	19.7798	−	6.10605i	0.649303	−	0.200441i
$929$	−58.1272	+	15.5751i	−1.90709	+	0.511003i	−0.912240	+	0.409657i	$0.865649\pi$
$929$	−58.1272	+	15.5751i	−1.90709	+	0.511003i	−0.994851	+	0.101347i	$0.967685\pi$
$930$		0			0
$931$	−1.49504	+	1.49504i	−0.0489979	+	0.0489979i
$932$	13.3023	+	22.2599i	0.435733	+	0.729147i
$933$		0			0
$934$	14.3756	−	3.96811i	0.470385	−	0.129841i
$935$	−0.196747			−0.00643433
$936$		0			0
$937$	−31.3424			−1.02391			−0.511956	−	0.859012i	$-0.671079\pi$
$937$	−31.3424			−1.02391			−0.511956	+	0.859012i	$0.671079\pi$
$938$	−58.1604	+	16.0540i	−1.89900	+	0.524182i
$939$		0			0
$940$	−1.46645	+	0.876338i	−0.0478302	+	0.0285830i
$941$	−22.8653	+	22.8653i	−0.745387	+	0.745387i	−0.973609	−	0.228222i	$-0.926709\pi$
$941$	−22.8653	+	22.8653i	−0.745387	+	0.745387i	0.228222	+	0.973609i	$0.426709\pi$
$942$		0			0
$943$	−50.9448	+	13.6506i	−1.65899	+	0.444525i
$944$	37.8252	+	8.92446i	1.23111	+	0.290466i
$945$		0			0
$946$	−1.24679	+	2.19752i	−0.0405366	+	0.0714476i
$947$	20.0408	+	5.36992i	0.651239	+	0.174499i	0.569289	−	0.822138i	$-0.307219\pi$
$947$	20.0408	+	5.36992i	0.651239	+	0.174499i	0.0819499	+	0.996636i	$0.473885\pi$
$948$		0			0
$949$	−2.01117	+	7.35728i	−0.0652855	+	0.238827i
$950$	2.50317	−	1.47043i	0.0812135	−	0.0477070i
$951$		0			0
$952$	−32.4433	−	53.3738i	−1.05149	−	1.72985i
$953$	−2.83553	−	1.63710i	−0.0918520	−	0.0530308i	0.453370	−	0.891322i	$-0.350221\pi$
$953$	−2.83553	−	1.63710i	−0.0918520	−	0.0530308i	−0.545222	+	0.838291i	$0.683555\pi$
$954$		0			0
$955$	0.764439	−	0.204831i	0.0247367	−	0.00662817i
$956$	−1.38663	+	5.50503i	−0.0448467	+	0.178045i
$957$		0			0
$958$	−14.6453	+	0.110198i	−0.473167	+	0.00356034i
$959$	−21.4877	−	37.2178i	−0.693874	−	1.20182i
$960$		0			0
$961$			28.4876i			0.918956i
$962$	−13.7143	+	7.96344i	−0.442166	+	0.256752i
$963$		0			0
$964$	11.1895	+	10.8577i	0.360389	+	0.349702i
$965$	−0.333358	+	0.192464i	−0.0107312	+	0.00619565i
$966$		0			0
$967$	15.9826	−	15.9826i	0.513966	−	0.513966i	−0.401773	−	0.915739i	$-0.631606\pi$
$967$	15.9826	−	15.9826i	0.513966	−	0.513966i	0.915739	+	0.401773i	$0.131606\pi$
$968$	8.64930	+	29.5911i	0.277999	+	0.951093i
$969$		0			0
$970$	−0.873972	−	0.227146i	−0.0280616	−	0.00729322i
$971$	−12.5870	+	21.8014i	−0.403938	+	0.699640i	−0.994197	−	0.107573i	$-0.965692\pi$
$971$	−12.5870	+	21.8014i	−0.403938	+	0.699640i	0.590260	+	0.807213i	$0.299025\pi$
$972$		0			0
$973$	9.67068	−	36.0915i	0.310028	−	1.15704i
$974$	29.6687	−	17.4282i	0.950645	−	0.558435i
$975$		0			0
$976$	−46.8420	+	28.9578i	−1.49938	+	0.926918i
$977$	5.42229	−	20.2363i	0.173475	−	0.647416i	−0.823332	−	0.567560i	$-0.807887\pi$
$977$	5.42229	−	20.2363i	0.173475	−	0.647416i	0.996806	−	0.0798556i	$-0.0254459\pi$
$978$		0			0
$979$	−0.0313732	−	0.0181133i	−0.00100269	−	0.000578905i
$980$	−0.275519	−	0.969641i	−0.00880112	−	0.0309740i
$981$		0			0
$982$	−32.7960	−	32.3061i	−1.04656	−	1.03093i
$983$	−14.2586	−	14.2586i	−0.454777	−	0.454777i	0.442159	−	0.896937i	$-0.354213\pi$
$983$	−14.2586	−	14.2586i	−0.454777	−	0.454777i	−0.896937	+	0.442159i	$0.854213\pi$
$984$		0			0
$985$	−1.57719	+	0.910592i	−0.0502535	+	0.0290139i
$986$	8.72755	+	31.6181i	0.277942	+	1.00693i
$987$		0			0
$988$	−0.739020	+	2.87277i	−0.0235114	+	0.0913949i
$989$			41.5997i			1.32280i
$990$		0			0
$991$	−23.1803	+	13.3832i	−0.736348	+	0.425131i	−0.820740	−	0.571302i	$-0.806439\pi$
$991$	−23.1803	+	13.3832i	−0.736348	+	0.425131i	0.0843920	+	0.996433i	$0.473105\pi$
$992$	7.59100	−	4.77209i	0.241014	−	0.151514i
$993$		0			0
$994$	24.2843	−	24.6525i	0.770251	−	0.781931i
$995$	0.0379440	+	0.141609i	0.00120291	+	0.00448931i
$996$		0			0
$997$	−31.1545	−	17.9870i	−0.986672	−	0.569655i	−0.0823942	−	0.996600i	$-0.526257\pi$
$997$	−31.1545	−	17.9870i	−0.986672	−	0.569655i	−0.904278	+	0.426944i	$0.859590\pi$
$998$	−20.1870	+	35.5805i	−0.639008	+	1.12628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.d.739.8		48
3.2	odd	2		104.2.u.a.11.5	✓	48
8.3	odd	2	inner	936.2.ed.d.739.2		48
12.11	even	2		416.2.bk.a.271.2		48
13.6	odd	12	inner	936.2.ed.d.19.2		48
24.5	odd	2		416.2.bk.a.271.1		48
24.11	even	2		104.2.u.a.11.11	yes	48
39.32	even	12		104.2.u.a.19.11	yes	48
104.19	even	12	inner	936.2.ed.d.19.8		48
156.71	odd	12		416.2.bk.a.175.1		48
312.149	even	12		416.2.bk.a.175.2		48
312.227	odd	12		104.2.u.a.19.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.5	✓	48	3.2	odd	2
104.2.u.a.11.11	yes	48	24.11	even	2
104.2.u.a.19.5	yes	48	312.227	odd	12
104.2.u.a.19.11	yes	48	39.32	even	12
416.2.bk.a.175.1		48	156.71	odd	12
416.2.bk.a.175.2		48	312.149	even	12
416.2.bk.a.271.1		48	24.5	odd	2
416.2.bk.a.271.2		48	12.11	even	2
936.2.ed.d.19.2		48	13.6	odd	12	inner
936.2.ed.d.19.8		48	104.19	even	12	inner
936.2.ed.d.739.2		48	8.3	odd	2	inner
936.2.ed.d.739.8		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.376293 + 1.36323i) q^{2} +(-1.71681 + 1.02595i) q^{4} +(-0.0693382 + 0.0693382i) q^{5} +(3.36551 - 0.901786i) q^{7} +(-2.04463 - 1.95435i) q^{8} +(-0.120616 - 0.0684326i) q^{10} +(0.305781 + 0.0819339i) q^{11} +(-3.13155 + 1.78702i) q^{13} +(2.49576 + 4.24864i) q^{14} +(1.89485 - 3.52272i) q^{16} +(5.48889 + 3.16901i) q^{17} +(-0.397336 + 0.106466i) q^{19} +(0.0479027 - 0.190178i) q^{20} +(0.00336858 + 0.447683i) q^{22} +(3.68562 + 6.38369i) q^{23} +4.99038i q^{25} +(-3.61450 - 3.59658i) q^{26} +(-4.85274 + 5.00104i) q^{28} +(3.16915 - 1.82971i) q^{29} +(1.12080 - 1.12080i) q^{31} +(5.51530 + 1.25755i) q^{32} +(-2.25467 + 8.67511i) q^{34} +(-0.170830 + 0.295887i) q^{35} +(0.804964 - 3.00417i) q^{37} +(-0.294652 - 0.501598i) q^{38} +(0.277282 - 0.00626016i) q^{40} +(-1.85187 + 6.91129i) q^{41} +(4.88743 + 2.82176i) q^{43} +(-0.609028 + 0.173052i) q^{44} +(-7.31557 + 7.42650i) q^{46} +(-6.15946 - 6.15946i) q^{47} +(4.45127 - 2.56994i) q^{49} +(-6.80306 + 1.87785i) q^{50} +(3.54287 - 6.28077i) q^{52} -3.89384i q^{53} +(-0.0268835 + 0.0155212i) q^{55} +(-8.64364 - 4.73356i) q^{56} +(3.68685 + 3.63178i) q^{58} +(2.51467 + 9.38488i) q^{59} +(-11.9231 - 6.88378i) q^{61} +(1.94966 + 1.10616i) q^{62} +(0.361046 + 7.99185i) q^{64} +(0.0932273 - 0.341044i) q^{65} +(-3.16917 + 11.8275i) q^{67} +(-12.6746 + 0.190751i) q^{68} +(-0.467645 - 0.121541i) q^{70} +(-1.81764 - 6.78351i) q^{71} +(1.49582 - 1.49582i) q^{73} +(4.39828 - 0.0330948i) q^{74} +(0.572920 - 0.590428i) q^{76} +1.10300 q^{77} +10.3044i q^{79} +(0.112874 + 0.375645i) q^{80} +(-10.1185 + 0.0761368i) q^{82} +(-2.53771 - 2.53771i) q^{83} +(-0.600323 + 0.160856i) q^{85} +(-2.00761 + 7.72451i) q^{86} +(-0.465083 - 0.765128i) q^{88} +(-0.110536 - 0.0296181i) q^{89} +(-8.92775 + 8.83821i) q^{91} +(-12.8768 - 7.17829i) q^{92} +(6.07901 - 10.7145i) q^{94} +(0.0201684 - 0.0349327i) q^{95} +(6.28973 - 1.68533i) q^{97} +(5.17841 + 5.10107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more