LMFDB - Embedded newform 912.2.bb.c.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.31
Dual form			912.2.bb.c.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +1.09638i q^{7} +(-0.500000 + 0.866025i) q^{9} -5.65685i q^{11} +(-0.949490 - 0.548188i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.00000 + 1.73205i) q^{17} +(4.00000 - 1.73205i) q^{19} +(0.949490 - 0.548188i) q^{21} +(4.89898 + 2.82843i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(7.89898 + 4.56048i) q^{29} -1.89898 q^{31} +(-4.89898 + 2.82843i) q^{33} +(-1.89898 + 1.09638i) q^{35} +4.56048i q^{37} +1.09638i q^{39} +(4.50000 - 2.59808i) q^{43} -2.00000 q^{45} +(-1.89898 - 1.09638i) q^{47} +5.79796 q^{49} +(1.00000 - 1.73205i) q^{51} +(1.10102 + 0.635674i) q^{53} +(9.79796 - 5.65685i) q^{55} +(-3.50000 - 2.59808i) q^{57} +(3.89898 + 6.75323i) q^{59} +(0.0505103 - 0.0874863i) q^{61} +(-0.949490 - 0.548188i) q^{63} -2.19275i q^{65} +(5.39898 - 9.35131i) q^{67} -5.65685i q^{69} +(2.00000 + 3.46410i) q^{71} +(-6.39898 - 11.0834i) q^{73} -1.00000 q^{75} +6.20204 q^{77} +(-4.94949 - 8.57277i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.46410i q^{83} +(-2.00000 + 3.46410i) q^{85} -9.12096i q^{87} +(7.89898 + 4.56048i) q^{89} +(0.601021 - 1.04100i) q^{91} +(0.949490 + 1.64456i) q^{93} +(7.00000 + 5.19615i) q^{95} +(-15.7980 + 9.12096i) q^{97} +(4.89898 + 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9} + 6 q^{13} + 4 q^{15} + 4 q^{17} + 16 q^{19} - 6 q^{21} + 2 q^{25} + 4 q^{27} + 12 q^{29} + 12 q^{31} + 12 q^{35} + 18 q^{43} - 8 q^{45} + 12 q^{47} - 16 q^{49} + 4 q^{51}+ \cdots - 24 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9 + 6 * q^13 + 4 * q^15 + 4 * q^17 + 16 * q^19 - 6 * q^21 + 2 * q^25 + 4 * q^27 + 12 * q^29 + 12 * q^31 + 12 * q^35 + 18 * q^43 - 8 * q^45 + 12 * q^47 - 16 * q^49 + 4 * q^51 + 24 * q^53 - 14 * q^57 - 4 * q^59 + 10 * q^61 + 6 * q^63 + 2 * q^67 + 8 * q^71 - 6 * q^73 - 4 * q^75 + 64 * q^77 - 10 * q^79 - 2 * q^81 - 8 * q^85 + 12 * q^89 + 22 * q^91 - 6 * q^93 + 28 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$			1.09638i			0.414391i	0.978300	+	0.207196i	$0.0664337\pi$
$7$			1.09638i			0.414391i	−0.978300	+	0.207196i	$0.933566\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		−	5.65685i		−	1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$		−	5.65685i		−	1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$		0			0
$13$	−0.949490	−	0.548188i	−0.263341	−	0.152040i	0.362517	−	0.931977i	$-0.381918\pi$
$13$	−0.949490	−	0.548188i	−0.263341	−	0.152040i	−0.625858	+	0.779937i	$0.715251\pi$
$14$		0			0
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$		0			0
$21$	0.949490	−	0.548188i	0.207196	−	0.119624i
$22$		0			0
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.914540	−	0.404495i	$-0.132553\pi$
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.106967	+	0.994263i	$0.465886\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	7.89898	+	4.56048i	1.46680	+	0.846859i	0.999310	−	0.0371370i	$-0.0118238\pi$
$29$	7.89898	+	4.56048i	1.46680	+	0.846859i	0.467493	+	0.883997i	$0.345157\pi$
$30$		0			0
$31$	−1.89898			−0.341067			−0.170533	−	0.985352i	$-0.554549\pi$
$31$	−1.89898			−0.341067			−0.170533	+	0.985352i	$0.554549\pi$
$32$		0			0
$33$	−4.89898	+	2.82843i	−0.852803	+	0.492366i
$34$		0			0
$35$	−1.89898	+	1.09638i	−0.320986	+	0.185321i
$36$		0			0
$37$			4.56048i			0.749738i	0.927078	+	0.374869i	$0.122312\pi$
$37$			4.56048i			0.749738i	−0.927078	+	0.374869i	$0.877688\pi$
$38$		0			0
$39$			1.09638i			0.175561i
$40$		0			0
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$		0			0
$43$	4.50000	−	2.59808i	0.686244	−	0.396203i	−0.115960	−	0.993254i	$-0.536994\pi$
$43$	4.50000	−	2.59808i	0.686244	−	0.396203i	0.802203	+	0.597051i	$0.203661\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	−1.89898	−	1.09638i	−0.276995	−	0.159923i	0.355067	−	0.934841i	$-0.384458\pi$
$47$	−1.89898	−	1.09638i	−0.276995	−	0.159923i	−0.632062	+	0.774918i	$0.717791\pi$
$48$		0			0
$49$	5.79796			0.828280
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$		0			0
$53$	1.10102	+	0.635674i	0.151237	+	0.0873166i	0.573709	−	0.819059i	$-0.305504\pi$
$53$	1.10102	+	0.635674i	0.151237	+	0.0873166i	−0.422472	+	0.906376i	$0.638837\pi$
$54$		0			0
$55$	9.79796	−	5.65685i	1.32116	−	0.762770i
$56$		0			0
$57$	−3.50000	−	2.59808i	−0.463586	−	0.344124i
$58$		0			0
$59$	3.89898	+	6.75323i	0.507604	+	0.879196i	0.999961	+	0.00880259i	$0.00280199\pi$
$59$	3.89898	+	6.75323i	0.507604	+	0.879196i	−0.492357	+	0.870393i	$0.663865\pi$
$60$		0			0
$61$	0.0505103	−	0.0874863i	0.00646718	−	0.0112015i	−0.862774	−	0.505590i	$-0.831275\pi$
$61$	0.0505103	−	0.0874863i	0.00646718	−	0.0112015i	0.869241	+	0.494389i	$0.164608\pi$
$62$		0			0
$63$	−0.949490	−	0.548188i	−0.119624	−	0.0690652i
$64$		0			0
$65$		−	2.19275i		−	0.271977i
$66$		0			0
$67$	5.39898	−	9.35131i	0.659590	−	1.14244i	−0.321131	−	0.947035i	$-0.604063\pi$
$67$	5.39898	−	9.35131i	0.659590	−	1.14244i	0.980722	−	0.195409i	$-0.0626035\pi$
$68$		0			0
$69$		−	5.65685i		−	0.681005i
$70$		0			0
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	0.959955	−	0.280155i	$-0.0903858\pi$
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	−0.722599	+	0.691268i	$0.757052\pi$
$72$		0			0
$73$	−6.39898	−	11.0834i	−0.748944	−	1.29721i	−0.948329	−	0.317288i	$-0.897228\pi$
$73$	−6.39898	−	11.0834i	−0.748944	−	1.29721i	0.199385	−	0.979921i	$-0.436105\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	6.20204			0.706788
$78$		0			0
$79$	−4.94949	−	8.57277i	−0.556861	−	0.964512i	−0.997756	−	0.0669530i	$-0.978672\pi$
$79$	−4.94949	−	8.57277i	−0.556861	−	0.964512i	0.440895	−	0.897559i	$-0.354661\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$		0			0
$87$		−	9.12096i		−	0.977869i
$88$		0			0
$89$	7.89898	+	4.56048i	0.837290	+	0.483410i	0.856342	−	0.516409i	$-0.172731\pi$
$89$	7.89898	+	4.56048i	0.837290	+	0.483410i	−0.0190520	+	0.999818i	$0.506065\pi$
$90$		0			0
$91$	0.601021	−	1.04100i	0.0630041	−	0.109126i
$92$		0			0
$93$	0.949490	+	1.64456i	0.0984575	+	0.170533i
$94$		0			0
$95$	7.00000	+	5.19615i	0.718185	+	0.533114i
$96$		0			0
$97$	−15.7980	+	9.12096i	−1.60404	+	0.926093i	−0.613372	+	0.789794i	$0.710187\pi$
$97$	−15.7980	+	9.12096i	−1.60404	+	0.926093i	−0.990668	+	0.136299i	$0.956479\pi$
$98$		0			0
$99$	4.89898	+	2.82843i	0.492366	+	0.284268i
$100$		0			0
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−11.8990			−1.17244			−0.586221	−	0.810151i	$-0.699385\pi$
$103$	−11.8990			−1.17244			−0.586221	+	0.810151i	$0.699385\pi$
$104$		0			0
$105$	1.89898	+	1.09638i	0.185321	+	0.106995i
$106$		0			0
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$		0			0
$109$	14.6969	−	8.48528i	1.40771	−	0.812743i	0.412544	−	0.910938i	$-0.364640\pi$
$109$	14.6969	−	8.48528i	1.40771	−	0.812743i	0.995167	+	0.0981950i	$0.0313069\pi$
$110$		0			0
$111$	3.94949	−	2.28024i	0.374869	−	0.216431i
$112$		0			0
$113$			16.0492i			1.50978i	0.655853	+	0.754889i	$0.272309\pi$
$113$			16.0492i			1.50978i	−0.655853	+	0.754889i	$0.727691\pi$
$114$		0			0
$115$			11.3137i			1.05501i
$116$		0			0
$117$	0.949490	−	0.548188i	0.0877804	−	0.0506800i
$118$		0			0
$119$	−1.89898	+	1.09638i	−0.174079	+	0.100505i
$120$		0			0
$121$	−21.0000			−1.90909
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−6.89898	+	11.9494i	−0.612185	+	1.06034i	0.378686	+	0.925525i	$0.376376\pi$
$127$	−6.89898	+	11.9494i	−0.612185	+	1.06034i	−0.990871	+	0.134811i	$0.956957\pi$
$128$		0			0
$129$	−4.50000	−	2.59808i	−0.396203	−	0.228748i
$130$		0			0
$131$	−12.0000	+	6.92820i	−1.04844	+	0.605320i	−0.922214	−	0.386681i	$-0.873621\pi$
$131$	−12.0000	+	6.92820i	−1.04844	+	0.605320i	−0.126231	+	0.992001i	$0.540288\pi$
$132$		0			0
$133$	1.89898	+	4.38551i	0.164662	+	0.380272i
$134$		0			0
$135$	1.00000	+	1.73205i	0.0860663	+	0.149071i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−6.39898	−	3.69445i	−0.542754	−	0.313359i	0.203440	−	0.979087i	$-0.434788\pi$
$139$	−6.39898	−	3.69445i	−0.542754	−	0.313359i	−0.746194	+	0.665728i	$0.768121\pi$
$140$		0			0
$141$			2.19275i			0.184663i
$142$		0			0
$143$	−3.10102	+	5.37113i	−0.259320	+	0.449156i
$144$		0			0
$145$			18.2419i			1.51491i
$146$		0			0
$147$	−2.89898	−	5.02118i	−0.239104	−	0.414140i
$148$		0			0
$149$	2.89898	+	5.02118i	0.237494	+	0.411351i	0.959994	−	0.280019i	$-0.0903408\pi$
$149$	2.89898	+	5.02118i	0.237494	+	0.411351i	−0.722501	+	0.691370i	$0.757007\pi$
$150$		0			0
$151$	−2.20204			−0.179200			−0.0895998	−	0.995978i	$-0.528559\pi$
$151$	−2.20204			−0.179200			−0.0895998	+	0.995978i	$0.528559\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−1.89898	−	3.28913i	−0.152530	−	0.264189i
$156$		0			0
$157$	−6.84847	−	11.8619i	−0.546567	−	0.946682i	−0.998506	−	0.0546336i	$-0.982601\pi$
$157$	−6.84847	−	11.8619i	−0.546567	−	0.946682i	0.451939	−	0.892049i	$-0.350732\pi$
$158$		0			0
$159$		−	1.27135i		−	0.100825i
$160$		0			0
$161$	−3.10102	+	5.37113i	−0.244395	+	0.423304i
$162$		0			0
$163$			15.5885i			1.22098i	0.792023	+	0.610491i	$0.209028\pi$
$163$			15.5885i			1.22098i	−0.792023	+	0.610491i	$0.790972\pi$
$164$		0			0
$165$	−9.79796	−	5.65685i	−0.762770	−	0.440386i
$166$		0			0
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$		0			0
$169$	−5.89898	−	10.2173i	−0.453768	−	0.785949i
$170$		0			0
$171$	−0.500000	+	4.33013i	−0.0382360	+	0.331133i
$172$		0			0
$173$	7.89898	−	4.56048i	0.600548	−	0.346727i	−0.168709	−	0.985666i	$-0.553960\pi$
$173$	7.89898	−	4.56048i	0.600548	−	0.346727i	0.769257	+	0.638939i	$0.220626\pi$
$174$		0			0
$175$	0.949490	+	0.548188i	0.0717747	+	0.0414391i
$176$		0			0
$177$	3.89898	−	6.75323i	0.293065	−	0.507604i
$178$		0			0
$179$	−6.20204			−0.463562			−0.231781	−	0.972768i	$-0.574455\pi$
$179$	−6.20204			−0.463562			−0.231781	+	0.972768i	$0.574455\pi$
$180$		0			0
$181$	−14.6969	−	8.48528i	−1.09241	−	0.630706i	−0.158196	−	0.987408i	$-0.550568\pi$
$181$	−14.6969	−	8.48528i	−1.09241	−	0.630706i	−0.934218	+	0.356702i	$0.883901\pi$
$182$		0			0
$183$	−0.101021			−0.00746765
$184$		0			0
$185$	−7.89898	+	4.56048i	−0.580745	+	0.335293i
$186$		0			0
$187$	9.79796	−	5.65685i	0.716498	−	0.413670i
$188$		0			0
$189$			1.09638i			0.0797496i
$190$		0			0
$191$			24.2487i			1.75458i	0.479965	+	0.877288i	$0.340649\pi$
$191$			24.2487i			1.75458i	−0.479965	+	0.877288i	$0.659351\pi$
$192$		0			0
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$	−1.89898	+	1.09638i	−0.135989	+	0.0785131i
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−15.9495	−	9.20844i	−1.13063	−	0.652769i	−0.186536	−	0.982448i	$-0.559726\pi$
$199$	−15.9495	−	9.20844i	−1.13063	−	0.652769i	−0.944093	+	0.329679i	$0.893060\pi$
$200$		0			0
$201$	−10.7980			−0.761629
$202$		0			0
$203$	−5.00000	+	8.66025i	−0.350931	+	0.607831i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.89898	+	2.82843i	−0.340503	+	0.196589i
$208$		0			0
$209$	−9.79796	−	22.6274i	−0.677739	−	1.56517i
$210$		0			0
$211$	0.601021	+	1.04100i	0.0413760	+	0.0716653i	0.885972	−	0.463739i	$-0.153493\pi$
$211$	0.601021	+	1.04100i	0.0413760	+	0.0716653i	−0.844596	+	0.535404i	$0.820159\pi$
$212$		0			0
$213$	2.00000	−	3.46410i	0.137038	−	0.237356i
$214$		0			0
$215$	9.00000	+	5.19615i	0.613795	+	0.354375i
$216$		0			0
$217$		−	2.08200i		−	0.141335i
$218$		0			0
$219$	−6.39898	+	11.0834i	−0.432403	+	0.748944i
$220$		0			0
$221$		−	2.19275i		−	0.147501i
$222$		0			0
$223$	1.94949	+	3.37662i	0.130547	+	0.226115i	0.923888	−	0.382664i	$-0.124993\pi$
$223$	1.94949	+	3.37662i	0.130547	+	0.226115i	−0.793340	+	0.608778i	$0.791660\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$		0			0
$227$	3.79796			0.252079			0.126040	−	0.992025i	$-0.459773\pi$
$227$	3.79796			0.252079			0.126040	+	0.992025i	$0.459773\pi$
$228$		0			0
$229$	21.6969			1.43377			0.716887	−	0.697189i	$-0.245566\pi$
$229$	21.6969			1.43377			0.716887	+	0.697189i	$0.245566\pi$
$230$		0			0
$231$	−3.10102	−	5.37113i	−0.204032	−	0.353394i
$232$		0			0
$233$	9.79796	+	16.9706i	0.641886	+	1.11178i	0.985011	+	0.172489i	$0.0551809\pi$
$233$	9.79796	+	16.9706i	0.641886	+	1.11178i	−0.343126	+	0.939289i	$0.611486\pi$
$234$		0			0
$235$		−	4.38551i		−	0.286079i
$236$		0			0
$237$	−4.94949	+	8.57277i	−0.321504	+	0.556861i
$238$		0			0
$239$			0.921404i			0.0596006i	0.999556	+	0.0298003i	$0.00948714\pi$
$239$			0.921404i			0.0596006i	−0.999556	+	0.0298003i	$0.990513\pi$
$240$		0			0
$241$	5.29796	+	3.05878i	0.341272	+	0.197033i	0.660834	−	0.750532i	$-0.270203\pi$
$241$	5.29796	+	3.05878i	0.341272	+	0.197033i	−0.319563	+	0.947565i	$0.603536\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	5.79796	+	10.0424i	0.370418	+	0.641583i
$246$		0			0
$247$	−4.74745	−	0.548188i	−0.302073	−	0.0348804i
$248$		0			0
$249$	−3.00000	+	1.73205i	−0.190117	+	0.109764i
$250$		0			0
$251$	−18.7980	−	10.8530i	−1.18652	−	0.685036i	−0.229004	−	0.973426i	$-0.573547\pi$
$251$	−18.7980	−	10.8530i	−1.18652	−	0.685036i	−0.957513	+	0.288390i	$0.906880\pi$
$252$		0			0
$253$	16.0000	−	27.7128i	1.00591	−	1.74229i
$254$		0			0
$255$	4.00000			0.250490
$256$		0			0
$257$	−1.10102	−	0.635674i	−0.0686798	−	0.0396523i	0.465267	−	0.885170i	$-0.345958\pi$
$257$	−1.10102	−	0.635674i	−0.0686798	−	0.0396523i	−0.533947	+	0.845518i	$0.679292\pi$
$258$		0			0
$259$	−5.00000			−0.310685
$260$		0			0
$261$	−7.89898	+	4.56048i	−0.488935	+	0.282286i
$262$		0			0
$263$	−3.79796	+	2.19275i	−0.234192	+	0.135211i	−0.612505	−	0.790467i	$-0.709838\pi$
$263$	−3.79796	+	2.19275i	−0.234192	+	0.135211i	0.378312	+	0.925678i	$0.376505\pi$
$264$		0			0
$265$			2.54270i			0.156197i
$266$		0			0
$267$		−	9.12096i		−	0.558193i
$268$		0			0
$269$	−0.797959	+	0.460702i	−0.0486524	+	0.0280895i	−0.524129	−	0.851639i	$-0.675609\pi$
$269$	−0.797959	+	0.460702i	−0.0486524	+	0.0280895i	0.475476	+	0.879728i	$0.342276\pi$
$270$		0			0
$271$	12.7980	−	7.38891i	0.777421	−	0.448844i	−0.0580947	−	0.998311i	$-0.518503\pi$
$271$	12.7980	−	7.38891i	0.777421	−	0.448844i	0.835515	+	0.549467i	$0.185169\pi$
$272$		0			0
$273$	−1.20204			−0.0727508
$274$		0			0
$275$	−4.89898	−	2.82843i	−0.295420	−	0.170561i
$276$		0			0
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$		0			0
$279$	0.949490	−	1.64456i	0.0568445	−	0.0984575i
$280$		0			0
$281$	−16.1010	−	9.29593i	−0.960506	−	0.554549i	−0.0641775	−	0.997938i	$-0.520442\pi$
$281$	−16.1010	−	9.29593i	−0.960506	−	0.554549i	−0.896329	+	0.443390i	$0.853776\pi$
$282$		0			0
$283$	−12.7980	+	7.38891i	−0.760760	+	0.439225i	−0.829568	−	0.558405i	$-0.811414\pi$
$283$	−12.7980	+	7.38891i	−0.760760	+	0.439225i	0.0688087	+	0.997630i	$0.478080\pi$
$284$		0			0
$285$	1.00000	−	8.66025i	0.0592349	−	0.512989i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	15.7980	+	9.12096i	0.926093	+	0.534680i
$292$		0			0
$293$		−	6.57826i		−	0.384306i	−0.981365	−	0.192153i	$-0.938453\pi$
$293$		−	6.57826i		−	0.384306i	0.981365	−	0.192153i	$-0.0615470\pi$
$294$		0			0
$295$	−7.79796	+	13.5065i	−0.454015	+	0.786377i
$296$		0			0
$297$		−	5.65685i		−	0.328244i
$298$		0			0
$299$	−3.10102	−	5.37113i	−0.179337	−	0.310620i
$300$		0			0
$301$	2.84847	+	4.93369i	0.164183	+	0.284373i
$302$		0			0
$303$	−12.0000			−0.689382
$304$		0			0
$305$	0.202041			0.0115688
$306$		0			0
$307$	15.7980	+	27.3629i	0.901637	+	1.56168i	0.825369	+	0.564594i	$0.190967\pi$
$307$	15.7980	+	27.3629i	0.901637	+	1.56168i	0.0762684	+	0.997087i	$0.475699\pi$
$308$		0			0
$309$	5.94949	+	10.3048i	0.338455	+	0.586221i
$310$		0			0
$311$		−	33.0197i		−	1.87238i	−0.351499	−	0.936188i	$-0.614328\pi$
$311$		−	33.0197i		−	1.87238i	0.351499	−	0.936188i	$-0.385672\pi$
$312$		0			0
$313$	8.79796	−	15.2385i	0.497290	−	0.861332i	−0.502705	−	0.864458i	$-0.667662\pi$
$313$	8.79796	−	15.2385i	0.497290	−	0.861332i	0.999995	+	0.00312637i	$0.000995155\pi$
$314$		0			0
$315$		−	2.19275i		−	0.123548i
$316$		0			0
$317$	−12.7980	−	7.38891i	−0.718805	−	0.415002i	0.0955077	−	0.995429i	$-0.469553\pi$
$317$	−12.7980	−	7.38891i	−0.718805	−	0.415002i	−0.814313	+	0.580426i	$0.802886\pi$
$318$		0			0
$319$	25.7980	−	44.6834i	1.44441	−	2.50179i
$320$		0			0
$321$	4.00000	+	6.92820i	0.223258	+	0.386695i
$322$		0			0
$323$	7.00000	+	5.19615i	0.389490	+	0.289122i
$324$		0			0
$325$	−0.949490	+	0.548188i	−0.0526682	+	0.0304080i
$326$		0			0
$327$	−14.6969	−	8.48528i	−0.812743	−	0.469237i
$328$		0			0
$329$	1.20204	−	2.08200i	0.0662707	−	0.114784i
$330$		0			0
$331$	−1.20204			−0.0660702			−0.0330351	−	0.999454i	$-0.510517\pi$
$331$	−1.20204			−0.0660702			−0.0330351	+	0.999454i	$0.510517\pi$
$332$		0			0
$333$	−3.94949	−	2.28024i	−0.216431	−	0.124956i
$334$		0			0
$335$	21.5959			1.17991
$336$		0			0
$337$	−22.1969	+	12.8154i	−1.20914	+	0.698100i	−0.962572	−	0.271025i	$-0.912637\pi$
$337$	−22.1969	+	12.8154i	−1.20914	+	0.698100i	−0.246572	+	0.969125i	$0.579304\pi$
$338$		0			0
$339$	13.8990	−	8.02458i	0.754889	−	0.435835i
$340$		0			0
$341$			10.7423i			0.581725i
$342$		0			0
$343$			14.0314i			0.757623i
$344$		0			0
$345$	9.79796	−	5.65685i	0.527504	−	0.304555i
$346$		0			0
$347$	−1.89898	+	1.09638i	−0.101943	+	0.0588566i	−0.550105	−	0.835096i	$-0.685412\pi$
$347$	−1.89898	+	1.09638i	−0.101943	+	0.0588566i	0.448162	+	0.893952i	$0.352079\pi$
$348$		0			0
$349$	−21.6969			−1.16141			−0.580705	−	0.814114i	$-0.697223\pi$
$349$	−21.6969			−1.16141			−0.580705	+	0.814114i	$0.697223\pi$
$350$		0			0
$351$	−0.949490	−	0.548188i	−0.0506800	−	0.0292601i
$352$		0			0
$353$	−3.79796			−0.202145			−0.101072	−	0.994879i	$-0.532227\pi$
$353$	−3.79796			−0.202145			−0.101072	+	0.994879i	$0.532227\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$		0			0
$357$	1.89898	+	1.09638i	0.100505	+	0.0580264i
$358$		0			0
$359$	−9.79796	+	5.65685i	−0.517116	+	0.298557i	−0.735754	−	0.677249i	$-0.763172\pi$
$359$	−9.79796	+	5.65685i	−0.517116	+	0.298557i	0.218638	+	0.975806i	$0.429839\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$		0			0
$363$	10.5000	+	18.1865i	0.551107	+	0.954545i
$364$		0			0
$365$	12.7980	−	22.1667i	0.669876	−	1.16026i
$366$		0			0
$367$	5.84847	+	3.37662i	0.305288	+	0.176258i	0.644816	−	0.764338i	$-0.276934\pi$
$367$	5.84847	+	3.37662i	0.305288	+	0.176258i	−0.339528	+	0.940596i	$0.610267\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.696938	+	1.20713i	−0.0361832	+	0.0626712i
$372$		0			0
$373$			33.3697i			1.72782i	0.503650	+	0.863908i	$0.331990\pi$
$373$			33.3697i			1.72782i	−0.503650	+	0.863908i	$0.668010\pi$
$374$		0			0
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$		0			0
$377$	−5.00000	−	8.66025i	−0.257513	−	0.446026i
$378$		0			0
$379$	−6.59592			−0.338810			−0.169405	−	0.985547i	$-0.554185\pi$
$379$	−6.59592			−0.338810			−0.169405	+	0.985547i	$0.554185\pi$
$380$		0			0
$381$	13.7980			0.706891
$382$		0			0
$383$	6.89898	+	11.9494i	0.352521	+	0.610585i	0.986691	−	0.162609i	$-0.0519910\pi$
$383$	6.89898	+	11.9494i	0.352521	+	0.610585i	−0.634169	+	0.773194i	$0.718658\pi$
$384$		0			0
$385$	6.20204	+	10.7423i	0.316085	+	0.547476i
$386$		0			0
$387$			5.19615i			0.264135i
$388$		0			0
$389$	−18.6969	+	32.3840i	−0.947972	+	1.64194i	−0.198285	+	0.980144i	$0.563537\pi$
$389$	−18.6969	+	32.3840i	−0.947972	+	1.64194i	−0.749688	+	0.661792i	$0.769796\pi$
$390$		0			0
$391$			11.3137i			0.572159i
$392$		0			0
$393$	12.0000	+	6.92820i	0.605320	+	0.349482i
$394$		0			0
$395$	9.89898	−	17.1455i	0.498072	−	0.862686i
$396$		0			0
$397$	3.05051	+	5.28364i	0.153101	+	0.265178i	0.932366	−	0.361516i	$-0.117741\pi$
$397$	3.05051	+	5.28364i	0.153101	+	0.265178i	−0.779265	+	0.626694i	$0.784407\pi$
$398$		0			0
$399$	2.84847	−	3.83732i	0.142602	−	0.192106i
$400$		0			0
$401$	−4.10102	+	2.36773i	−0.204795	+	0.118239i	−0.598890	−	0.800831i	$-0.704391\pi$
$401$	−4.10102	+	2.36773i	−0.204795	+	0.118239i	0.394095	+	0.919070i	$0.371058\pi$
$402$		0			0
$403$	1.80306	+	1.04100i	0.0898169	+	0.0518558i
$404$		0			0
$405$	1.00000	−	1.73205i	0.0496904	−	0.0860663i
$406$		0			0
$407$	25.7980			1.27876
$408$		0			0
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$		0			0
$413$	−7.40408	+	4.27475i	−0.364331	+	0.210347i
$414$		0			0
$415$	6.00000	−	3.46410i	0.294528	−	0.170046i
$416$		0			0
$417$			7.38891i			0.361836i
$418$		0			0
$419$		−	35.2125i		−	1.72024i	−0.510090	−	0.860121i	$-0.670388\pi$
$419$		−	35.2125i		−	1.72024i	0.510090	−	0.860121i	$-0.329612\pi$
$420$		0			0
$421$	4.89898	−	2.82843i	0.238762	−	0.137849i	−0.375846	−	0.926682i	$-0.622648\pi$
$421$	4.89898	−	2.82843i	0.238762	−	0.137849i	0.614607	+	0.788833i	$0.289314\pi$
$422$		0			0
$423$	1.89898	−	1.09638i	0.0923315	−	0.0533076i
$424$		0			0
$425$	2.00000			0.0970143
$426$		0			0
$427$	0.0959179	+	0.0553782i	0.00464179	+	0.00267994i
$428$		0			0
$429$	6.20204			0.299437
$430$		0			0
$431$	−7.89898	+	13.6814i	−0.380480	+	0.659011i	−0.991131	−	0.132889i	$-0.957575\pi$
$431$	−7.89898	+	13.6814i	−0.380480	+	0.659011i	0.610651	+	0.791900i	$0.290908\pi$
$432$		0			0
$433$	10.1969	+	5.88721i	0.490034	+	0.282921i	0.724588	−	0.689182i	$-0.242030\pi$
$433$	10.1969	+	5.88721i	0.490034	+	0.282921i	−0.234555	+	0.972103i	$0.575363\pi$
$434$		0			0
$435$	15.7980	−	9.12096i	0.757454	−	0.437316i
$436$		0			0
$437$	24.4949	+	2.82843i	1.17175	+	0.135302i
$438$		0			0
$439$	−10.8485	−	18.7901i	−0.517769	−	0.896803i	−0.999787	−	0.0206411i	$-0.993429\pi$
$439$	−10.8485	−	18.7901i	−0.517769	−	0.896803i	0.482018	−	0.876161i	$-0.339904\pi$
$440$		0			0
$441$	−2.89898	+	5.02118i	−0.138047	+	0.239104i
$442$		0			0
$443$	18.7980	+	10.8530i	0.893118	+	0.515642i	0.874961	−	0.484193i	$-0.160887\pi$
$443$	18.7980	+	10.8530i	0.893118	+	0.515642i	0.0181569	+	0.999835i	$0.494220\pi$
$444$		0			0
$445$			18.2419i			0.864750i
$446$		0			0
$447$	2.89898	−	5.02118i	0.137117	−	0.237494i
$448$		0			0
$449$			28.6342i			1.35133i	0.737208	+	0.675666i	$0.236144\pi$
$449$			28.6342i			1.35133i	−0.737208	+	0.675666i	$0.763856\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	1.10102	+	1.90702i	0.0517305	+	0.0895998i
$454$		0			0
$455$	2.40408			0.112705
$456$		0			0
$457$	20.7980			0.972887			0.486444	−	0.873712i	$-0.338294\pi$
$457$	20.7980			0.972887			0.486444	+	0.873712i	$0.338294\pi$
$458$		0			0
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	10.7980	+	18.7026i	0.502911	+	0.871068i	0.999994	+	0.00336470i	$0.00107102\pi$
$461$	10.7980	+	18.7026i	0.502911	+	0.871068i	−0.497083	+	0.867703i	$0.665596\pi$
$462$		0			0
$463$			3.28913i			0.152859i	0.997075	+	0.0764294i	$0.0243520\pi$
$463$			3.28913i			0.152859i	−0.997075	+	0.0764294i	$0.975648\pi$
$464$		0			0
$465$	−1.89898	+	3.28913i	−0.0880631	+	0.152530i
$466$		0			0
$467$		−	16.3991i		−	0.758860i	−0.925220	−	0.379430i	$-0.876120\pi$
$467$		−	16.3991i		−	0.758860i	0.925220	−	0.379430i	$-0.123880\pi$
$468$		0			0
$469$	10.2526	+	5.91931i	0.473419	+	0.273328i
$470$		0			0
$471$	−6.84847	+	11.8619i	−0.315561	+	0.546567i
$472$		0			0
$473$	−14.6969	−	25.4558i	−0.675766	−	1.17046i
$474$		0			0
$475$	0.500000	−	4.33013i	0.0229416	−	0.198680i
$476$		0			0
$477$	−1.10102	+	0.635674i	−0.0504123	+	0.0291055i
$478$		0			0
$479$	−21.7980	−	12.5851i	−0.995974	−	0.575026i	−0.0889195	−	0.996039i	$-0.528341\pi$
$479$	−21.7980	−	12.5851i	−0.995974	−	0.575026i	−0.907055	+	0.421013i	$0.861675\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$		0			0
$483$	6.20204			0.282203
$484$		0			0
$485$	−31.5959	−	18.2419i	−1.43470	−	0.828323i
$486$		0			0
$487$	−1.79796			−0.0814733			−0.0407366	−	0.999170i	$-0.512970\pi$
$487$	−1.79796			−0.0814733			−0.0407366	+	0.999170i	$0.512970\pi$
$488$		0			0
$489$	13.5000	−	7.79423i	0.610491	−	0.352467i
$490$		0			0
$491$	21.7980	−	12.5851i	0.983728	−	0.567956i	0.0803345	−	0.996768i	$-0.474401\pi$
$491$	21.7980	−	12.5851i	0.983728	−	0.567956i	0.903394	+	0.428812i	$0.141068\pi$
$492$		0			0
$493$			18.2419i			0.821574i
$494$		0			0
$495$			11.3137i			0.508513i
$496$		0			0
$497$	−3.79796	+	2.19275i	−0.170362	+	0.0983584i
$498$		0			0
$499$	−1.80306	+	1.04100i	−0.0807161	+	0.0466015i	−0.539815	−	0.841784i	$-0.681506\pi$
$499$	−1.80306	+	1.04100i	−0.0807161	+	0.0466015i	0.459099	+	0.888385i	$0.348172\pi$
$500$		0			0
$501$	6.00000			0.268060
$502$		0			0
$503$	23.6969	+	13.6814i	1.05659	+	0.610025i	0.924488	−	0.381211i	$-0.124493\pi$
$503$	23.6969	+	13.6814i	1.05659	+	0.610025i	0.132106	+	0.991236i	$0.457826\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$		0			0
$507$	−5.89898	+	10.2173i	−0.261983	+	0.453768i
$508$		0			0
$509$	−31.8990	−	18.4169i	−1.41390	−	0.816314i	−0.418145	−	0.908381i	$-0.637319\pi$
$509$	−31.8990	−	18.4169i	−1.41390	−	0.816314i	−0.995753	+	0.0920665i	$0.970653\pi$
$510$		0			0
$511$	12.1515	−	7.01569i	0.537552	−	0.310356i
$512$		0			0
$513$	4.00000	−	1.73205i	0.176604	−	0.0764719i
$514$		0			0
$515$	−11.8990	−	20.6096i	−0.524332	−	0.908169i
$516$		0			0
$517$	−6.20204	+	10.7423i	−0.272765	+	0.472444i
$518$		0			0
$519$	−7.89898	−	4.56048i	−0.346727	−	0.200183i
$520$		0			0
$521$		−	1.27135i		−	0.0556988i	−0.999612	−	0.0278494i	$-0.991134\pi$
$521$		−	1.27135i		−	0.0556988i	0.999612	−	0.0278494i	$-0.00886589\pi$
$522$		0			0
$523$	13.2980	−	23.0327i	0.581479	−	1.00715i	−0.413825	−	0.910356i	$-0.635808\pi$
$523$	13.2980	−	23.0327i	0.581479	−	1.00715i	0.995304	−	0.0967951i	$-0.0308591\pi$
$524$		0			0
$525$		−	1.09638i		−	0.0478498i
$526$		0			0
$527$	−1.89898	−	3.28913i	−0.0827208	−	0.143277i
$528$		0			0
$529$	4.50000	+	7.79423i	0.195652	+	0.338880i
$530$		0			0
$531$	−7.79796			−0.338403
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−8.00000	−	13.8564i	−0.345870	−	0.599065i
$536$		0			0
$537$	3.10102	+	5.37113i	0.133819	+	0.231781i
$538$		0			0
$539$		−	32.7982i		−	1.41272i
$540$		0			0
$541$	11.0505	−	19.1400i	0.475099	−	0.822895i	−0.524495	−	0.851414i	$-0.675746\pi$
$541$	11.0505	−	19.1400i	0.475099	−	0.822895i	0.999593	+	0.0285189i	$0.00907908\pi$
$542$		0			0
$543$			16.9706i			0.728277i
$544$		0			0
$545$	29.3939	+	16.9706i	1.25910	+	0.726939i
$546$		0			0
$547$	19.5000	−	33.7750i	0.833760	−	1.44411i	−0.0612764	−	0.998121i	$-0.519517\pi$
$547$	19.5000	−	33.7750i	0.833760	−	1.44411i	0.895036	−	0.445993i	$-0.147150\pi$
$548$		0			0
$549$	0.0505103	+	0.0874863i	0.00215573	+	0.00373383i
$550$		0			0
$551$	39.4949	+	4.56048i	1.68254	+	0.194283i
$552$		0			0
$553$	9.39898	−	5.42650i	0.399685	−	0.230758i
$554$		0			0
$555$	7.89898	+	4.56048i	0.335293	+	0.193582i
$556$		0			0
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$		0			0
$559$	−5.69694			−0.240955
$560$		0			0
$561$	−9.79796	−	5.65685i	−0.413670	−	0.238833i
$562$		0			0
$563$	−43.5959			−1.83735			−0.918674	−	0.395016i	$-0.870739\pi$
$563$	−43.5959			−1.83735			−0.918674	+	0.395016i	$0.870739\pi$
$564$		0			0
$565$	−27.7980	+	16.0492i	−1.16947	+	0.675193i
$566$		0			0
$567$	0.949490	−	0.548188i	0.0398748	−	0.0230217i
$568$		0			0
$569$			2.54270i			0.106595i	0.998579	+	0.0532977i	$0.0169732\pi$
$569$			2.54270i			0.106595i	−0.998579	+	0.0532977i	$0.983027\pi$
$570$		0			0
$571$		−	9.93160i		−	0.415625i	−0.978169	−	0.207812i	$-0.933366\pi$
$571$		−	9.93160i		−	0.415625i	0.978169	−	0.207812i	$-0.0666343\pi$
$572$		0			0
$573$	21.0000	−	12.1244i	0.877288	−	0.506502i
$574$		0			0
$575$	4.89898	−	2.82843i	0.204302	−	0.117954i
$576$		0			0
$577$	−2.40408			−0.100083			−0.0500416	−	0.998747i	$-0.515935\pi$
$577$	−2.40408			−0.100083			−0.0500416	+	0.998747i	$0.515935\pi$
$578$		0			0
$579$	10.5000	+	6.06218i	0.436365	+	0.251936i
$580$		0			0
$581$	3.79796			0.157566
$582$		0			0
$583$	3.59592	−	6.22831i	0.148928	−	0.257950i
$584$		0			0
$585$	1.89898	+	1.09638i	0.0785131	+	0.0453296i
$586$		0			0
$587$	−4.10102	+	2.36773i	−0.169267	+	0.0977265i	−0.582240	−	0.813017i	$-0.697824\pi$
$587$	−4.10102	+	2.36773i	−0.169267	+	0.0977265i	0.412973	+	0.910743i	$0.364490\pi$
$588$		0			0
$589$	−7.59592	+	3.28913i	−0.312984	+	0.135526i
$590$		0			0
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$		0			0
$593$	−1.89898	+	3.28913i	−0.0779817	+	0.135068i	−0.902379	−	0.430943i	$-0.858181\pi$
$593$	−1.89898	+	3.28913i	−0.0779817	+	0.135068i	0.824397	+	0.566012i	$0.191514\pi$
$594$		0			0
$595$	−3.79796	−	2.19275i	−0.155701	−	0.0898941i
$596$		0			0
$597$			18.4169i			0.753753i
$598$		0			0
$599$	20.8990	−	36.1981i	0.853909	−	1.47901i	−0.0237442	−	0.999718i	$-0.507559\pi$
$599$	20.8990	−	36.1981i	0.853909	−	1.47901i	0.877653	−	0.479296i	$-0.159108\pi$
$600$		0			0
$601$			27.2521i			1.11164i	0.831304	+	0.555818i	$0.187595\pi$
$601$			27.2521i			1.11164i	−0.831304	+	0.555818i	$0.812405\pi$
$602$		0			0
$603$	5.39898	+	9.35131i	0.219863	+	0.380815i
$604$		0			0
$605$	−21.0000	−	36.3731i	−0.853771	−	1.47878i
$606$		0			0
$607$	−12.1010			−0.491165			−0.245583	−	0.969376i	$-0.578979\pi$
$607$	−12.1010			−0.491165			−0.245583	+	0.969376i	$0.578979\pi$
$608$		0			0
$609$	10.0000			0.405220
$610$		0			0
$611$	1.20204	+	2.08200i	0.0486294	+	0.0842285i
$612$		0			0
$613$	16.7980	+	29.0949i	0.678463	+	1.17513i	0.975444	+	0.220249i	$0.0706870\pi$
$613$	16.7980	+	29.0949i	0.678463	+	1.17513i	−0.296980	+	0.954884i	$0.595980\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.89898	−	11.9494i	0.277742	−	0.481064i	−0.693081	−	0.720860i	$-0.743747\pi$
$617$	6.89898	−	11.9494i	0.277742	−	0.481064i	0.970823	+	0.239796i	$0.0770805\pi$
$618$		0			0
$619$			32.5590i			1.30866i	0.756210	+	0.654329i	$0.227049\pi$
$619$			32.5590i			1.30866i	−0.756210	+	0.654329i	$0.772951\pi$
$620$		0			0
$621$	4.89898	+	2.82843i	0.196589	+	0.113501i
$622$		0			0
$623$	−5.00000	+	8.66025i	−0.200321	+	0.346966i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	−14.6969	+	19.7990i	−0.586939	+	0.790695i
$628$		0			0
$629$	−7.89898	+	4.56048i	−0.314953	+	0.181838i
$630$		0			0
$631$	36.6464	+	21.1578i	1.45887	+	0.842280i	0.998956	−	0.0456831i	$-0.0145464\pi$
$631$	36.6464	+	21.1578i	1.45887	+	0.842280i	0.459915	+	0.887963i	$0.347880\pi$
$632$		0			0
$633$	0.601021	−	1.04100i	0.0238884	−	0.0413760i
$634$		0			0
$635$	−27.5959			−1.09511
$636$		0			0
$637$	−5.50510	−	3.17837i	−0.218120	−	0.125932i
$638$		0			0
$639$	−4.00000			−0.158238
$640$		0			0
$641$	−11.2020	+	6.46750i	−0.442454	+	0.255451i	−0.704638	−	0.709567i	$-0.748891\pi$
$641$	−11.2020	+	6.46750i	−0.442454	+	0.255451i	0.262184	+	0.965018i	$0.415557\pi$
$642$		0			0
$643$	−15.0959	+	8.71563i	−0.595325	+	0.343711i	−0.767200	−	0.641408i	$-0.778351\pi$
$643$	−15.0959	+	8.71563i	−0.595325	+	0.343711i	0.171875	+	0.985119i	$0.445017\pi$
$644$		0			0
$645$		−	10.3923i		−	0.409197i
$646$		0			0
$647$			39.3765i			1.54805i	0.633156	+	0.774024i	$0.281759\pi$
$647$			39.3765i			1.54805i	−0.633156	+	0.774024i	$0.718241\pi$
$648$		0			0
$649$	38.2020	−	22.0560i	1.49956	−	0.865772i
$650$		0			0
$651$	−1.80306	+	1.04100i	−0.0706676	+	0.0407999i
$652$		0			0
$653$	−43.5959			−1.70604			−0.853020	−	0.521878i	$-0.825232\pi$
$653$	−43.5959			−1.70604			−0.853020	+	0.521878i	$0.825232\pi$
$654$		0			0
$655$	−24.0000	−	13.8564i	−0.937758	−	0.541415i
$656$		0			0
$657$	12.7980			0.499296
$658$		0			0
$659$	18.6969	−	32.3840i	0.728329	−	1.26150i	−0.229260	−	0.973365i	$-0.573630\pi$
$659$	18.6969	−	32.3840i	0.728329	−	1.26150i	0.957589	−	0.288138i	$-0.0930362\pi$
$660$		0			0
$661$	−42.4949	−	24.5344i	−1.65286	−	0.954279i	−0.975888	−	0.218270i	$-0.929959\pi$
$661$	−42.4949	−	24.5344i	−1.65286	−	0.954279i	−0.676972	−	0.736009i	$-0.736708\pi$
$662$		0			0
$663$	−1.89898	+	1.09638i	−0.0737503	+	0.0425797i
$664$		0			0
$665$	−5.69694	+	7.67463i	−0.220918	+	0.297610i
$666$		0			0
$667$	25.7980	+	44.6834i	0.998901	+	1.73015i
$668$		0			0
$669$	1.94949	−	3.37662i	0.0753716	−	0.130547i
$670$		0			0
$671$	−0.494897	−	0.285729i	−0.0191053	−	0.0110305i
$672$		0			0
$673$		−	41.3300i		−	1.59316i	−0.604536	−	0.796578i	$-0.706641\pi$
$673$		−	41.3300i		−	1.59316i	0.604536	−	0.796578i	$-0.293359\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$			36.8338i			1.41564i	0.706394	+	0.707818i	$0.250320\pi$
$677$			36.8338i			1.41564i	−0.706394	+	0.707818i	$0.749680\pi$
$678$		0			0
$679$	−10.0000	−	17.3205i	−0.383765	−	0.664700i
$680$		0			0
$681$	−1.89898	−	3.28913i	−0.0727691	−	0.126040i
$682$		0			0
$683$	35.7980			1.36977			0.684885	−	0.728651i	$-0.259852\pi$
$683$	35.7980			1.36977			0.684885	+	0.728651i	$0.259852\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$		0			0
$687$	−10.8485	−	18.7901i	−0.413895	−	0.716887i
$688$		0			0
$689$	−0.696938	−	1.20713i	−0.0265512	−	0.0459881i
$690$		0			0
$691$			24.2487i			0.922464i	0.887279	+	0.461232i	$0.152592\pi$
$691$			24.2487i			0.922464i	−0.887279	+	0.461232i	$0.847408\pi$
$692$		0			0
$693$	−3.10102	+	5.37113i	−0.117798	+	0.204032i
$694$		0			0
$695$		−	14.7778i		−	0.560554i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	9.79796	−	16.9706i	0.370593	−	0.641886i
$700$		0			0
$701$	−21.0000	−	36.3731i	−0.793159	−	1.37379i	−0.924002	−	0.382389i	$-0.875102\pi$
$701$	−21.0000	−	36.3731i	−0.793159	−	1.37379i	0.130843	−	0.991403i	$-0.458232\pi$
$702$		0			0
$703$	7.89898	+	18.2419i	0.297916	+	0.688007i
$704$		0			0
$705$	−3.79796	+	2.19275i	−0.143039	+	0.0825838i
$706$		0			0
$707$	11.3939	+	6.57826i	0.428511	+	0.247401i
$708$		0			0
$709$	18.8485	−	32.6465i	0.707869	−	1.22607i	−0.257777	−	0.966204i	$-0.582990\pi$
$709$	18.8485	−	32.6465i	0.707869	−	1.22607i	0.965646	−	0.259861i	$-0.0836767\pi$
$710$		0			0
$711$	9.89898			0.371241
$712$		0			0
$713$	−9.30306	−	5.37113i	−0.348402	−	0.201150i
$714$		0			0
$715$	−12.4041			−0.463886
$716$		0			0
$717$	0.797959	−	0.460702i	0.0298003	−	0.0172052i
$718$		0			0
$719$	−13.1010	+	7.56388i	−0.488586	+	0.282085i	−0.723988	−	0.689813i	$-0.757693\pi$
$719$	−13.1010	+	7.56388i	−0.488586	+	0.282085i	0.235402	+	0.971898i	$0.424359\pi$
$720$		0			0
$721$		−	13.0458i		−	0.485849i
$722$		0			0
$723$		−	6.11756i		−	0.227514i
$724$		0			0
$725$	7.89898	−	4.56048i	0.293361	−	0.169372i
$726$		0			0
$727$	−42.3434	+	24.4470i	−1.57043	+	0.906687i	−0.574313	+	0.818636i	$0.694731\pi$
$727$	−42.3434	+	24.4470i	−1.57043	+	0.906687i	−0.996116	+	0.0880513i	$0.971936\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.00000	+	5.19615i	0.332877	+	0.192187i
$732$		0			0
$733$	−41.5959			−1.53638			−0.768190	−	0.640222i	$-0.778842\pi$
$733$	−41.5959			−1.53638			−0.768190	+	0.640222i	$0.778842\pi$
$734$		0			0
$735$	5.79796	−	10.0424i	0.213861	−	0.370418i
$736$		0			0
$737$	−52.8990	−	30.5412i	−1.94856	−	1.12500i
$738$		0			0
$739$	8.60102	−	4.96580i	0.316394	−	0.182670i	−0.333390	−	0.942789i	$-0.608193\pi$
$739$	8.60102	−	4.96580i	0.316394	−	0.182670i	0.649784	+	0.760119i	$0.274859\pi$
$740$		0			0
$741$	1.89898	+	4.38551i	0.0697608	+	0.161106i
$742$		0			0
$743$	−1.10102	−	1.90702i	−0.0403925	−	0.0699619i	0.845122	−	0.534573i	$-0.179528\pi$
$743$	−1.10102	−	1.90702i	−0.0403925	−	0.0699619i	−0.885515	+	0.464611i	$0.846194\pi$
$744$		0			0
$745$	−5.79796	+	10.0424i	−0.212421	+	0.367924i
$746$		0			0
$747$	3.00000	+	1.73205i	0.109764	+	0.0633724i
$748$		0			0
$749$		−	8.77101i		−	0.320486i
$750$		0			0
$751$	−20.7474	+	35.9356i	−0.757085	+	1.31131i	0.187246	+	0.982313i	$0.440044\pi$
$751$	−20.7474	+	35.9356i	−0.757085	+	1.31131i	−0.944331	+	0.328997i	$0.893289\pi$
$752$		0			0
$753$			21.7060i			0.791011i
$754$		0			0
$755$	−2.20204	−	3.81405i	−0.0801405	−	0.138807i
$756$		0			0
$757$	−15.7474	−	27.2754i	−0.572351	−	0.991341i	−0.996324	−	0.0856658i	$-0.972698\pi$
$757$	−15.7474	−	27.2754i	−0.572351	−	0.991341i	0.423973	−	0.905675i	$-0.360635\pi$
$758$		0			0
$759$	−32.0000			−1.16153
$760$		0			0
$761$	−15.7980			−0.572676			−0.286338	−	0.958129i	$-0.592438\pi$
$761$	−15.7980			−0.572676			−0.286338	+	0.958129i	$0.592438\pi$
$762$		0			0
$763$	9.30306	+	16.1134i	0.336793	+	0.583343i
$764$		0			0
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$		0			0
$767$		−	8.54950i		−	0.308704i
$768$		0			0
$769$	−16.0959	+	27.8789i	−0.580434	+	1.00534i	0.414994	+	0.909824i	$0.363784\pi$
$769$	−16.0959	+	27.8789i	−0.580434	+	1.00534i	−0.995428	+	0.0955165i	$0.969550\pi$
$770$		0			0
$771$			1.27135i			0.0457865i
$772$		0			0
$773$	−6.30306	−	3.63907i	−0.226705	−	0.130888i	0.382346	−	0.924019i	$-0.375116\pi$
$773$	−6.30306	−	3.63907i	−0.226705	−	0.130888i	−0.609051	+	0.793131i	$0.708450\pi$
$774$		0			0
$775$	−0.949490	+	1.64456i	−0.0341067	+	0.0590745i
$776$		0			0
$777$	2.50000	+	4.33013i	0.0896870	+	0.155342i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	19.5959	−	11.3137i	0.701197	−	0.404836i
$782$		0			0
$783$	7.89898	+	4.56048i	0.282286	+	0.162978i
$784$		0			0
$785$	13.6969	−	23.7238i	0.488865	−	0.846738i
$786$		0			0
$787$	−34.5959			−1.23321			−0.616606	−	0.787272i	$-0.711493\pi$
$787$	−34.5959			−1.23321			−0.616606	+	0.787272i	$0.711493\pi$
$788$		0			0
$789$	3.79796	+	2.19275i	0.135211	+	0.0780641i
$790$		0			0
$791$	−17.5959			−0.625639
$792$		0			0
$793$	−0.0959179	+	0.0553782i	−0.00340615	+	0.00196654i
$794$		0			0
$795$	2.20204	−	1.27135i	0.0780983	−	0.0450901i
$796$		0			0
$797$			52.1830i			1.84842i	0.381887	+	0.924209i	$0.375274\pi$
$797$			52.1830i			1.84842i	−0.381887	+	0.924209i	$0.624726\pi$
$798$		0			0
$799$		−	4.38551i		−	0.155148i
$800$		0			0
$801$	−7.89898	+	4.56048i	−0.279097	+	0.161137i
$802$		0			0
$803$	−62.6969	+	36.1981i	−2.21253	+	1.27740i
$804$		0			0
$805$	−12.4041			−0.437186
$806$		0			0
$807$	0.797959	+	0.460702i	0.0280895	+	0.0162175i
$808$		0			0
$809$	43.3939			1.52565			0.762824	−	0.646606i	$-0.223812\pi$
$809$	43.3939			1.52565			0.762824	+	0.646606i	$0.223812\pi$
$810$		0			0
$811$	−4.00000	+	6.92820i	−0.140459	+	0.243282i	−0.927670	−	0.373402i	$-0.878191\pi$
$811$	−4.00000	+	6.92820i	−0.140459	+	0.243282i	0.787211	+	0.616684i	$0.211524\pi$
$812$		0			0
$813$	−12.7980	−	7.38891i	−0.448844	−	0.259140i
$814$		0			0
$815$	−27.0000	+	15.5885i	−0.945769	+	0.546040i
$816$		0			0
$817$	13.5000	−	18.1865i	0.472305	−	0.636266i
$818$		0			0
$819$	0.601021	+	1.04100i	0.0210014	+	0.0363754i
$820$		0			0
$821$	−23.6969	+	41.0443i	−0.827029	+	1.43246i	0.0733300	+	0.997308i	$0.476637\pi$
$821$	−23.6969	+	41.0443i	−0.827029	+	1.43246i	−0.900359	+	0.435148i	$0.856696\pi$
$822$		0			0
$823$	38.3939	+	22.1667i	1.33833	+	0.772683i	0.986559	−	0.163404i	$-0.0522475\pi$
$823$	38.3939	+	22.1667i	1.33833	+	0.772683i	0.351767	+	0.936088i	$0.385581\pi$
$824$		0			0
$825$			5.65685i			0.196946i
$826$		0			0
$827$	22.7980	−	39.4872i	0.792763	−	1.37311i	−0.131487	−	0.991318i	$-0.541975\pi$
$827$	22.7980	−	39.4872i	0.792763	−	1.37311i	0.924250	−	0.381787i	$-0.124691\pi$
$828$		0			0
$829$		−	42.3157i		−	1.46968i	−0.678239	−	0.734842i	$-0.737256\pi$
$829$		−	42.3157i		−	1.46968i	0.678239	−	0.734842i	$-0.262744\pi$
$830$		0			0
$831$	−1.00000	−	1.73205i	−0.0346896	−	0.0600842i
$832$		0			0
$833$	5.79796	+	10.0424i	0.200887	+	0.347947i
$834$		0			0
$835$	−12.0000			−0.415277
$836$		0			0
$837$	−1.89898			−0.0656383
$838$		0			0
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	0.913154	−	0.407615i	$-0.133640\pi$
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	−0.809582	+	0.587007i	$0.800306\pi$
$840$		0			0
$841$	27.0959	+	46.9315i	0.934342	+	1.61833i
$842$		0			0
$843$			18.5919i			0.640338i
$844$		0			0
$845$	11.7980	−	20.4347i	0.405862	−	0.702974i
$846$		0			0
$847$		−	23.0239i		−	0.791111i
$848$		0			0
$849$	12.7980	+	7.38891i	0.439225	+	0.253587i
$850$		0			0
$851$	−12.8990	+	22.3417i	−0.442171	+	0.765863i
$852$		0			0
$853$	22.6464	+	39.2248i	0.775399	+	1.34303i	0.934570	+	0.355779i	$0.115785\pi$
$853$	22.6464	+	39.2248i	0.775399	+	1.34303i	−0.159171	+	0.987251i	$0.550882\pi$
$854$		0			0
$855$	−8.00000	+	3.46410i	−0.273594	+	0.118470i
$856$		0			0
$857$	46.5959	−	26.9022i	1.59169	−	0.918960i	0.598668	−	0.800997i	$-0.295697\pi$
$857$	46.5959	−	26.9022i	1.59169	−	0.918960i	0.993018	−	0.117963i	$-0.0376366\pi$
$858$		0			0
$859$	−3.70204	−	2.13737i	−0.126312	−	0.0729263i	0.435513	−	0.900183i	$-0.356567\pi$
$859$	−3.70204	−	2.13737i	−0.126312	−	0.0729263i	−0.561825	+	0.827256i	$0.689900\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.79796			−0.265446			−0.132723	−	0.991153i	$-0.542372\pi$
$863$	−7.79796			−0.265446			−0.132723	+	0.991153i	$0.542372\pi$
$864$		0			0
$865$	15.7980	+	9.12096i	0.537147	+	0.310122i
$866$		0			0
$867$	−13.0000			−0.441503
$868$		0			0
$869$	−48.4949	+	27.9985i	−1.64508	+	0.949785i
$870$		0			0
$871$	−10.2526	+	5.91931i	−0.347394	+	0.200568i
$872$		0			0
$873$		−	18.2419i		−	0.617395i
$874$		0			0
$875$			13.1565i			0.444771i
$876$		0			0
$877$	20.5454	−	11.8619i	0.693769	−	0.400548i	−0.111253	−	0.993792i	$-0.535487\pi$
$877$	20.5454	−	11.8619i	0.693769	−	0.400548i	0.805022	+	0.593244i	$0.202153\pi$
$878$		0			0
$879$	−5.69694	+	3.28913i	−0.192153	+	0.110940i
$880$		0			0
$881$	−3.79796			−0.127956			−0.0639782	−	0.997951i	$-0.520379\pi$
$881$	−3.79796			−0.127956			−0.0639782	+	0.997951i	$0.520379\pi$
$882$		0			0
$883$	18.7020	+	10.7976i	0.629374	+	0.363369i	0.780510	−	0.625144i	$-0.214960\pi$
$883$	18.7020	+	10.7976i	0.629374	+	0.363369i	−0.151136	+	0.988513i	$0.548293\pi$
$884$		0			0
$885$	15.5959			0.524251
$886$		0			0
$887$	−12.5959	+	21.8168i	−0.422930	+	0.732535i	−0.996225	−	0.0868136i	$-0.972332\pi$
$887$	−12.5959	+	21.8168i	−0.422930	+	0.732535i	0.573295	+	0.819349i	$0.305665\pi$
$888$		0			0
$889$	−13.1010	−	7.56388i	−0.439394	−	0.253684i
$890$		0			0
$891$	−4.89898	+	2.82843i	−0.164122	+	0.0947559i
$892$		0			0
$893$	−9.49490	−	1.09638i	−0.317735	−	0.0366888i
$894$		0			0
$895$	−6.20204	−	10.7423i	−0.207311	−	0.359074i
$896$		0			0
$897$	−3.10102	+	5.37113i	−0.103540	+	0.179337i
$898$		0			0
$899$	−15.0000	−	8.66025i	−0.500278	−	0.288836i
$900$		0			0
$901$			2.54270i			0.0847096i
$902$		0			0
$903$	2.84847	−	4.93369i	0.0947911	−	0.164183i
$904$		0			0
$905$		−	33.9411i		−	1.12824i
$906$		0			0
$907$	−27.5959	−	47.7975i	−0.916307	−	1.58709i	−0.804976	−	0.593308i	$-0.797822\pi$
$907$	−27.5959	−	47.7975i	−0.916307	−	1.58709i	−0.111332	−	0.993783i	$-0.535512\pi$
$908$		0			0
$909$	6.00000	+	10.3923i	0.199007	+	0.344691i
$910$		0			0
$911$	−23.5959			−0.781768			−0.390884	−	0.920440i	$-0.627831\pi$
$911$	−23.5959			−0.781768			−0.390884	+	0.920440i	$0.627831\pi$
$912$		0			0
$913$	−19.5959			−0.648530
$914$		0			0
$915$	−0.101021	−	0.174973i	−0.00333964	−	0.00578442i
$916$		0			0
$917$	−7.59592	−	13.1565i	−0.250839	−	0.434466i
$918$		0			0
$919$			36.3089i			1.19772i	0.800854	+	0.598859i	$0.204379\pi$
$919$			36.3089i			1.19772i	−0.800854	+	0.598859i	$0.795621\pi$
$920$		0			0
$921$	15.7980	−	27.3629i	0.520560	−	0.901637i
$922$		0			0
$923$		−	4.38551i		−	0.144351i
$924$		0			0
$925$	3.94949	+	2.28024i	0.129858	+	0.0749738i
$926$		0			0
$927$	5.94949	−	10.3048i	0.195407	−	0.338455i
$928$		0			0
$929$	5.89898	+	10.2173i	0.193539	+	0.335220i	0.946421	−	0.322936i	$-0.104670\pi$
$929$	5.89898	+	10.2173i	0.193539	+	0.335220i	−0.752881	+	0.658156i	$0.771337\pi$
$930$		0			0
$931$	23.1918	−	10.0424i	0.760082	−	0.329125i
$932$		0			0
$933$	−28.5959	+	16.5099i	−0.936188	+	0.540509i
$934$		0			0
$935$	19.5959	+	11.3137i	0.640855	+	0.369998i
$936$		0			0
$937$	14.5000	−	25.1147i	0.473694	−	0.820463i	−0.525852	−	0.850576i	$-0.676253\pi$
$937$	14.5000	−	25.1147i	0.473694	−	0.820463i	0.999546	+	0.0301133i	$0.00958681\pi$
$938$		0			0
$939$	−17.5959			−0.574221
$940$		0			0
$941$	−9.79796	−	5.65685i	−0.319404	−	0.184408i	0.331723	−	0.943377i	$-0.392370\pi$
$941$	−9.79796	−	5.65685i	−0.319404	−	0.184408i	−0.651127	+	0.758969i	$0.725703\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−1.89898	+	1.09638i	−0.0617738	+	0.0356651i
$946$		0			0
$947$	−42.0000	+	24.2487i	−1.36482	+	0.787977i	−0.990260	−	0.139227i	$-0.955538\pi$
$947$	−42.0000	+	24.2487i	−1.36482	+	0.787977i	−0.374556	+	0.927204i	$0.622205\pi$
$948$		0			0
$949$			14.0314i			0.455478i
$950$		0			0
$951$			14.7778i			0.479203i
$952$		0			0
$953$	−10.8990	+	6.29253i	−0.353053	+	0.203835i	−0.666029	−	0.745926i	$-0.732007\pi$
$953$	−10.8990	+	6.29253i	−0.353053	+	0.203835i	0.312976	+	0.949761i	$0.398674\pi$
$954$		0			0
$955$	−42.0000	+	24.2487i	−1.35909	+	0.784670i
$956$		0			0
$957$	−51.5959			−1.66786
$958$		0			0
$959$	11.3939	+	6.57826i	0.367927	+	0.212423i
$960$		0			0
$961$	−27.3939			−0.883673
$962$		0			0
$963$	4.00000	−	6.92820i	0.128898	−	0.223258i
$964$		0			0
$965$	−21.0000	−	12.1244i	−0.676014	−	0.390297i
$966$		0			0
$967$	42.3434	−	24.4470i	1.36167	−	0.786161i	0.371825	−	0.928303i	$-0.378732\pi$
$967$	42.3434	−	24.4470i	1.36167	−	0.786161i	0.989846	+	0.142142i	$0.0453990\pi$
$968$		0			0
$969$	1.00000	−	8.66025i	0.0321246	−	0.278207i
$970$		0			0
$971$	−12.5959	−	21.8168i	−0.404222	−	0.700133i	0.590008	−	0.807397i	$-0.299124\pi$
$971$	−12.5959	−	21.8168i	−0.404222	−	0.700133i	−0.994231	+	0.107264i	$0.965791\pi$
$972$		0			0
$973$	4.05051	−	7.01569i	0.129853	−	0.224913i
$974$		0			0
$975$	0.949490	+	0.548188i	0.0304080	+	0.0175561i
$976$		0			0
$977$			12.2351i			0.391436i	0.980660	+	0.195718i	$0.0627037\pi$
$977$			12.2351i			0.391436i	−0.980660	+	0.195718i	$0.937296\pi$
$978$		0			0
$979$	25.7980	−	44.6834i	0.824506	−	1.42809i
$980$		0			0
$981$			16.9706i			0.541828i
$982$		0			0
$983$	9.10102	+	15.7634i	0.290277	+	0.502775i	0.973875	−	0.227084i	$-0.0729191\pi$
$983$	9.10102	+	15.7634i	0.290277	+	0.502775i	−0.683598	+	0.729859i	$0.739586\pi$
$984$		0			0
$985$	−2.00000	−	3.46410i	−0.0637253	−	0.110375i
$986$		0			0
$987$	−2.40408			−0.0765228
$988$		0			0
$989$	29.3939			0.934671
$990$		0			0
$991$	−11.8485	−	20.5222i	−0.376379	−	0.651908i	0.614153	−	0.789187i	$-0.289498\pi$
$991$	−11.8485	−	20.5222i	−0.376379	−	0.651908i	−0.990532	+	0.137279i	$0.956164\pi$
$992$		0			0
$993$	0.601021	+	1.04100i	0.0190728	+	0.0330351i
$994$		0			0
$995$		−	36.8338i		−	1.16771i
$996$		0			0
$997$	−11.9495	+	20.6971i	−0.378444	+	0.655484i	−0.990836	−	0.135070i	$-0.956874\pi$
$997$	−11.9495	+	20.6971i	−0.378444	+	0.655484i	0.612392	+	0.790554i	$0.290207\pi$
$998$		0			0
$999$			4.56048i			0.144287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.c.31.2	✓	4
3.2	odd	2		2736.2.bm.j.1855.2		4
4.3	odd	2		912.2.bb.d.31.1	yes	4
12.11	even	2		2736.2.bm.i.1855.1		4
19.8	odd	6		912.2.bb.d.559.2	yes	4
57.8	even	6		2736.2.bm.i.559.2		4
76.27	even	6	inner	912.2.bb.c.559.1	yes	4
228.179	odd	6		2736.2.bm.j.559.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.c.31.2	✓	4	1.1	even	1	trivial
912.2.bb.c.559.1	yes	4	76.27	even	6	inner
912.2.bb.d.31.1	yes	4	4.3	odd	2
912.2.bb.d.559.2	yes	4	19.8	odd	6
2736.2.bm.i.559.2		4	57.8	even	6
2736.2.bm.i.1855.1		4	12.11	even	2
2736.2.bm.j.559.1		4	228.179	odd	6
2736.2.bm.j.1855.2		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +1.09638i q^{7} +(-0.500000 + 0.866025i) q^{9} -5.65685i q^{11} +(-0.949490 - 0.548188i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.00000 + 1.73205i) q^{17} +(4.00000 - 1.73205i) q^{19} +(0.949490 - 0.548188i) q^{21} +(4.89898 + 2.82843i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(7.89898 + 4.56048i) q^{29} -1.89898 q^{31} +(-4.89898 + 2.82843i) q^{33} +(-1.89898 + 1.09638i) q^{35} +4.56048i q^{37} +1.09638i q^{39} +(4.50000 - 2.59808i) q^{43} -2.00000 q^{45} +(-1.89898 - 1.09638i) q^{47} +5.79796 q^{49} +(1.00000 - 1.73205i) q^{51} +(1.10102 + 0.635674i) q^{53} +(9.79796 - 5.65685i) q^{55} +(-3.50000 - 2.59808i) q^{57} +(3.89898 + 6.75323i) q^{59} +(0.0505103 - 0.0874863i) q^{61} +(-0.949490 - 0.548188i) q^{63} -2.19275i q^{65} +(5.39898 - 9.35131i) q^{67} -5.65685i q^{69} +(2.00000 + 3.46410i) q^{71} +(-6.39898 - 11.0834i) q^{73} -1.00000 q^{75} +6.20204 q^{77} +(-4.94949 - 8.57277i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.46410i q^{83} +(-2.00000 + 3.46410i) q^{85} -9.12096i q^{87} +(7.89898 + 4.56048i) q^{89} +(0.601021 - 1.04100i) q^{91} +(0.949490 + 1.64456i) q^{93} +(7.00000 + 5.19615i) q^{95} +(-15.7980 + 9.12096i) q^{97} +(4.89898 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{5} - 2 q^{9} + 6 q^{13} + 4 q^{15} + 4 q^{17} + 16 q^{19} - 6 q^{21} + 2 q^{25} + 4 q^{27} + 12 q^{29} + 12 q^{31} + 12 q^{35} + 18 q^{43} - 8 q^{45} + 12 q^{47} - 16 q^{49} + 4 q^{51}+ \cdots - 24 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^5 - 2 * q^9 + 6 * q^13 + 4 * q^15 + 4 * q^17 + 16 * q^19 - 6 * q^21 + 2 * q^25 + 4 * q^27 + 12 * q^29 + 12 * q^31 + 12 * q^35 + 18 * q^43 - 8 * q^45 + 12 * q^47 - 16 * q^49 + 4 * q^51 + 24 * q^53 - 14 * q^57 - 4 * q^59 + 10 * q^61 + 6 * q^63 + 2 * q^67 + 8 * q^71 - 6 * q^73 - 4 * q^75 + 64 * q^77 - 10 * q^79 - 2 * q^81 - 8 * q^85 + 12 * q^89 + 22 * q^91 - 6 * q^93 + 28 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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