LMFDB - Embedded newform 912.2.cc.c.257.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(257,912)] 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("912.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,-3,0,0,0,0,0,-3,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.3
Root			$1.47158 - 0.913487i$ of defining polynomial
Character	$\chi$	$=$	912.257
Dual form			912.2.cc.c.401.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.69526 + 0.355087i) q^{3} +(-0.882820 + 2.42553i) q^{5} +(1.58376 - 2.74316i) q^{7} +(2.74783 + 1.20393i) q^{9} +(2.16590 - 1.25049i) q^{11} +(2.71907 - 3.24046i) q^{13} +(-2.35788 + 3.79843i) q^{15} +(1.32278 - 0.233243i) q^{17} +(-3.14841 - 3.01455i) q^{19} +(3.65896 - 4.08800i) q^{21} +(1.30503 + 3.58554i) q^{23} +(-1.27359 - 1.06867i) q^{25} +(4.23078 + 3.01670i) q^{27} +(-1.32242 + 7.49981i) q^{29} +(-6.89193 - 3.97906i) q^{31} +(4.11581 - 1.35082i) q^{33} +(5.25543 + 6.26318i) q^{35} +4.10469i q^{37} +(5.76019 - 4.52793i) q^{39} +(4.95792 - 4.16019i) q^{41} +(11.7465 + 4.27537i) q^{43} +(-5.34601 + 5.60207i) q^{45} +(-6.16940 - 1.08783i) q^{47} +(-1.51662 - 2.62686i) q^{49} +(2.32529 + 0.0742967i) q^{51} +(-3.46508 + 1.26118i) q^{53} +(1.12098 + 6.35742i) q^{55} +(-4.26694 - 6.22842i) q^{57} +(1.54335 + 8.75275i) q^{59} +(-0.133301 + 0.0485177i) q^{61} +(7.65449 - 5.63098i) q^{63} +(5.45938 + 9.45593i) q^{65} +(4.48795 + 0.791347i) q^{67} +(0.939187 + 6.54182i) q^{69} +(-8.59275 - 3.12750i) q^{71} +(-1.67672 + 1.40694i) q^{73} +(-1.77960 - 2.26391i) q^{75} -7.92190i q^{77} +(-6.41515 - 7.64528i) q^{79} +(6.10110 + 6.61639i) q^{81} +(-12.3308 - 7.11920i) q^{83} +(-0.602044 + 3.41436i) q^{85} +(-4.90493 + 12.2446i) q^{87} +(-12.7492 - 10.6978i) q^{89} +(-4.58274 - 12.5910i) q^{91} +(-10.2707 - 9.19278i) q^{93} +(10.0914 - 4.97524i) q^{95} +(0.538573 - 0.0949649i) q^{97} +(7.45703 - 0.828515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51}+ \cdots + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$-1$	$1$

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
$3$	1.69526	+	0.355087i	0.978760	+	0.205010i
$3$	1.69526	+	0.355087i	0.978760	+	0.205010i
$4$		0			0
$5$	−0.882820	+	2.42553i	−0.394809	+	1.08473i	0.569970	+	0.821666i	$0.306955\pi$
$5$	−0.882820	+	2.42553i	−0.394809	+	1.08473i	−0.964779	+	0.263063i	$0.915267\pi$
$6$		0			0
$7$	1.58376	−	2.74316i	0.598607	−	1.03682i	−0.394420	−	0.918930i	$-0.629055\pi$
$7$	1.58376	−	2.74316i	0.598607	−	1.03682i	0.993027	−	0.117887i	$-0.0376121\pi$
$8$		0			0
$9$	2.74783	+	1.20393i	0.915942	+	0.401311i
$10$		0			0
$11$	2.16590	−	1.25049i	0.653045	−	0.377036i	−0.136577	−	0.990629i	$-0.543610\pi$
$11$	2.16590	−	1.25049i	0.653045	−	0.377036i	0.789622	+	0.613594i	$0.210277\pi$
$12$		0			0
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	−0.243327	−	0.969944i	$-0.578239\pi$
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	0.997462	+	0.0712015i	$0.0226833\pi$
$14$		0			0
$15$	−2.35788	+	3.79843i	−0.608803	+	0.980749i
$16$		0			0
$17$	1.32278	−	0.233243i	0.320822	−	0.0565696i	−0.0109180	−	0.999940i	$-0.503475\pi$
$17$	1.32278	−	0.233243i	0.320822	−	0.0565696i	0.331740	+	0.943371i	$0.392364\pi$
$18$		0			0
$19$	−3.14841	−	3.01455i	−0.722294	−	0.691586i
$19$	−3.14841	−	3.01455i	−0.722294	−	0.691586i
$20$		0			0
$21$	3.65896	−	4.08800i	0.798450	−	0.892075i
$22$		0			0
$23$	1.30503	+	3.58554i	0.272117	+	0.747636i	0.998197	+	0.0600255i	$0.0191182\pi$
$23$	1.30503	+	3.58554i	0.272117	+	0.747636i	−0.726080	+	0.687611i	$0.758660\pi$
$24$		0			0
$25$	−1.27359	−	1.06867i	−0.254718	−	0.213734i
$26$		0			0
$27$	4.23078	+	3.01670i	0.814215	+	0.580564i
$28$		0			0
$29$	−1.32242	+	7.49981i	−0.245567	+	1.39268i	0.573606	+	0.819132i	$0.305544\pi$
$29$	−1.32242	+	7.49981i	−0.245567	+	1.39268i	−0.819172	+	0.573547i	$0.805567\pi$
$30$		0			0
$31$	−6.89193	−	3.97906i	−1.23783	−	0.714660i	−0.269177	−	0.963091i	$-0.586752\pi$
$31$	−6.89193	−	3.97906i	−1.23783	−	0.714660i	−0.968650	+	0.248431i	$0.920085\pi$
$32$		0			0
$33$	4.11581	−	1.35082i	0.716470	−	0.235147i
$34$		0			0
$35$	5.25543	+	6.26318i	0.888330	+	1.05867i
$36$		0			0
$37$			4.10469i			0.674806i	0.941360	+	0.337403i	$0.109549\pi$
$37$			4.10469i			0.674806i	−0.941360	+	0.337403i	$0.890451\pi$
$38$		0			0
$39$	5.76019	−	4.52793i	0.922368	−	0.725048i
$40$		0			0
$41$	4.95792	−	4.16019i	0.774297	−	0.649712i	−0.167509	−	0.985871i	$-0.553572\pi$
$41$	4.95792	−	4.16019i	0.774297	−	0.649712i	0.941805	+	0.336158i	$0.109128\pi$
$42$		0			0
$43$	11.7465	+	4.27537i	1.79132	+	0.651987i	0.999130	+	0.0417144i	$0.0132820\pi$
$43$	11.7465	+	4.27537i	1.79132	+	0.651987i	0.792191	+	0.610273i	$0.208940\pi$
$44$		0			0
$45$	−5.34601	+	5.60207i	−0.796935	+	0.835108i
$46$		0			0
$47$	−6.16940	−	1.08783i	−0.899899	−	0.158676i	−0.295486	−	0.955347i	$-0.595481\pi$
$47$	−6.16940	−	1.08783i	−0.899899	−	0.158676i	−0.604414	+	0.796671i	$0.706593\pi$
$48$		0			0
$49$	−1.51662	−	2.62686i	−0.216660	−	0.375266i
$50$		0			0
$51$	2.32529	+	0.0742967i	0.325605	+	0.0104036i
$52$		0			0
$53$	−3.46508	+	1.26118i	−0.475965	+	0.173237i	−0.568853	−	0.822440i	$-0.692612\pi$
$53$	−3.46508	+	1.26118i	−0.475965	+	0.173237i	0.0928877	+	0.995677i	$0.470390\pi$
$54$		0			0
$55$	1.12098	+	6.35742i	0.151153	+	0.857234i
$56$		0			0
$57$	−4.26694	−	6.22842i	−0.565170	−	0.824974i
$58$		0			0
$59$	1.54335	+	8.75275i	0.200927	+	1.13951i	0.903722	+	0.428119i	$0.140824\pi$
$59$	1.54335	+	8.75275i	0.200927	+	1.13951i	−0.702796	+	0.711392i	$0.748065\pi$
$60$		0			0
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	−0.350540	−	0.936548i	$-0.614002\pi$
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	0.333472	+	0.942760i	$0.391780\pi$
$62$		0			0
$63$	7.65449	−	5.63098i	0.964375	−	0.709437i
$64$		0			0
$65$	5.45938	+	9.45593i	0.677153	+	1.17286i
$66$		0			0
$67$	4.48795	+	0.791347i	0.548291	+	0.0966784i	0.440930	−	0.897542i	$-0.354649\pi$
$67$	4.48795	+	0.791347i	0.548291	+	0.0966784i	0.107361	+	0.994220i	$0.465760\pi$
$68$		0			0
$69$	0.939187	+	6.54182i	0.113065	+	0.787543i
$70$		0			0
$71$	−8.59275	−	3.12750i	−1.01977	−	0.371166i	−0.222594	−	0.974911i	$-0.571452\pi$
$71$	−8.59275	−	3.12750i	−1.01977	−	0.371166i	−0.797178	+	0.603745i	$0.793675\pi$
$72$		0			0
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	−0.735615	−	0.677399i	$-0.763107\pi$
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	0.539370	+	0.842069i	$0.318662\pi$
$74$		0			0
$75$	−1.77960	−	2.26391i	−0.205490	−	0.261414i
$76$		0			0
$77$		−	7.92190i		−	0.902784i
$78$		0			0
$79$	−6.41515	−	7.64528i	−0.721760	−	0.860161i	0.273040	−	0.962003i	$-0.411971\pi$
$79$	−6.41515	−	7.64528i	−0.721760	−	0.860161i	−0.994801	+	0.101842i	$0.967526\pi$
$80$		0			0
$81$	6.10110	+	6.61639i	0.677900	+	0.735155i
$82$		0			0
$83$	−12.3308	−	7.11920i	−1.35348	−	0.781433i	−0.364747	−	0.931107i	$-0.618844\pi$
$83$	−12.3308	−	7.11920i	−1.35348	−	0.781433i	−0.988735	+	0.149673i	$0.952178\pi$
$84$		0			0
$85$	−0.602044	+	3.41436i	−0.0653008	+	0.370339i
$86$		0			0
$87$	−4.90493	+	12.2446i	−0.525864	+	1.31275i
$88$		0			0
$89$	−12.7492	−	10.6978i	−1.35141	−	1.13397i	−0.978533	−	0.206089i	$-0.933926\pi$
$89$	−12.7492	−	10.6978i	−1.35141	−	1.13397i	−0.372879	−	0.927880i	$-0.621629\pi$
$90$		0			0
$91$	−4.58274	−	12.5910i	−0.480402	−	1.31989i
$92$		0			0
$93$	−10.2707	−	9.19278i	−1.06502	−	0.953247i
$94$		0			0
$95$	10.0914	−	4.97524i	1.03535	−	0.510448i
$96$		0			0
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	−0.146239	−	0.989249i	$-0.546717\pi$
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	0.200923	+	0.979607i	$0.435606\pi$
$98$		0			0
$99$	7.45703	−	0.828515i	0.749460	−	0.0832689i
$100$		0			0
$101$	7.56338	−	9.01368i	0.752584	−	0.896895i	−0.244771	−	0.969581i	$-0.578713\pi$
$101$	7.56338	−	9.01368i	0.752584	−	0.896895i	0.997355	+	0.0726860i	$0.0231571\pi$
$102$		0			0
$103$	−6.77528	+	3.91171i	−0.667588	+	0.385432i	−0.795162	−	0.606397i	$-0.792614\pi$
$103$	−6.77528	+	3.91171i	−0.667588	+	0.385432i	0.127574	+	0.991829i	$0.459281\pi$
$104$		0			0
$105$	6.68536	+	12.4839i	0.652424	+	1.21830i
$106$		0			0
$107$	−2.82951	+	4.90085i	−0.273539	+	0.473783i	−0.969765	−	0.244039i	$-0.921528\pi$
$107$	−2.82951	+	4.90085i	−0.273539	+	0.473783i	0.696227	+	0.717822i	$0.254861\pi$
$108$		0			0
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	−0.305251	−	0.952272i	$-0.598740\pi$
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	0.845944	−	0.533271i	$-0.179038\pi$
$110$		0			0
$111$	−1.45752	+	6.95852i	−0.138342	+	0.660473i
$112$		0			0
$113$	5.15697			0.485127			0.242564	−	0.970136i	$-0.422012\pi$
$113$	5.15697			0.485127			0.242564	+	0.970136i	$0.422012\pi$
$114$		0			0
$115$	−9.84893			−0.918417
$116$		0			0
$117$	11.3728	−	5.63065i	1.05142	−	0.520554i
$118$		0			0
$119$	1.45516	−	3.99801i	0.133394	−	0.366497i
$120$		0			0
$121$	−2.37257	+	4.10941i	−0.215688	+	0.373583i
$122$		0			0
$123$	9.88220	−	5.29211i	0.891048	−	0.477174i
$124$		0			0
$125$	−7.46045	+	4.30729i	−0.667283	+	0.385256i
$126$		0			0
$127$	−5.03745	+	6.00340i	−0.447001	+	0.532715i	−0.941747	−	0.336322i	$-0.890817\pi$
$127$	−5.03745	+	6.00340i	−0.447001	+	0.532715i	0.494746	+	0.869038i	$0.335261\pi$
$128$		0			0
$129$	18.3952	+	11.4189i	1.61961	+	1.00538i
$130$		0			0
$131$	4.43285	−	0.781631i	0.387300	−	0.0682914i	0.0233919	−	0.999726i	$-0.492553\pi$
$131$	4.43285	−	0.781631i	0.387300	−	0.0682914i	0.363908	+	0.931435i	$0.381442\pi$
$132$		0			0
$133$	−13.2557	+	3.86224i	−1.14942	+	0.334898i
$134$		0			0
$135$	−11.0521	+	7.59868i	−0.951214	+	0.653990i
$136$		0			0
$137$	−2.69063	−	7.39245i	−0.229876	−	0.631580i	0.770104	−	0.637919i	$-0.220204\pi$
$137$	−2.69063	−	7.39245i	−0.229876	−	0.631580i	−0.999980	+	0.00633905i	$0.997982\pi$
$138$		0			0
$139$	5.76780	+	4.83976i	0.489219	+	0.410503i	0.853746	−	0.520689i	$-0.174325\pi$
$139$	5.76780	+	4.83976i	0.489219	+	0.410503i	−0.364528	+	0.931193i	$0.618770\pi$
$140$		0			0
$141$	−10.0725	−	4.03483i	−0.848255	−	0.339794i
$142$		0			0
$143$	1.83710	−	10.4187i	0.153626	−	0.871255i
$144$		0			0
$145$	−17.0235	−	9.82854i	−1.41373	−	0.816216i
$146$		0			0
$147$	−1.63830	−	4.99175i	−0.135125	−	0.411713i
$148$		0			0
$149$	8.79633	+	10.4831i	0.720624	+	0.858806i	0.994691	−	0.102905i	$-0.0328137\pi$
$149$	8.79633	+	10.4831i	0.720624	+	0.858806i	−0.274068	+	0.961710i	$0.588369\pi$
$150$		0			0
$151$			8.63653i			0.702831i	0.936220	+	0.351415i	$0.114300\pi$
$151$			8.63653i			0.702831i	−0.936220	+	0.351415i	$0.885700\pi$
$152$		0			0
$153$	3.91559	+	0.951632i	0.316557	+	0.0769349i
$154$		0			0
$155$	15.7356	−	13.2038i	1.26392	−	1.06055i
$156$		0			0
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	0.209987	−	0.977704i	$-0.432658\pi$
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	−0.467597	+	0.883942i	$0.654880\pi$
$158$		0			0
$159$	−6.32204	+	0.907634i	−0.501371	+	0.0719800i
$160$		0			0
$161$	11.9026	+	2.09874i	0.938053	+	0.165404i
$162$		0			0
$163$	−3.83308	−	6.63909i	−0.300230	−	0.520014i	0.675958	−	0.736940i	$-0.263730\pi$
$163$	−3.83308	−	6.63909i	−0.300230	−	0.520014i	−0.976188	+	0.216926i	$0.930397\pi$
$164$		0			0
$165$	−0.357076	+	11.1755i	−0.0277983	+	0.870014i
$166$		0			0
$167$	2.20429	−	0.802294i	0.170573	−	0.0620834i	−0.255322	−	0.966856i	$-0.582182\pi$
$167$	2.20429	−	0.802294i	0.170573	−	0.0620834i	0.425895	+	0.904773i	$0.359959\pi$
$168$		0			0
$169$	−0.849826	−	4.81960i	−0.0653712	−	0.370739i
$170$		0			0
$171$	−5.02195	−	12.0739i	−0.384038	−	0.923317i
$172$		0			0
$173$	2.59056	+	14.6918i	0.196956	+	1.11700i	0.909605	+	0.415474i	$0.136384\pi$
$173$	2.59056	+	14.6918i	0.196956	+	1.11700i	−0.712649	+	0.701521i	$0.752505\pi$
$174$		0			0
$175$	−4.94860	+	1.80114i	−0.374079	+	0.136154i
$176$		0			0
$177$	−0.491615	+	15.3862i	−0.0369520	+	1.15650i
$178$		0			0
$179$	0.0974666	+	0.168817i	0.00728500	+	0.0126180i	0.869645	−	0.493678i	$-0.164348\pi$
$179$	0.0974666	+	0.168817i	0.00728500	+	0.0126180i	−0.862360	+	0.506296i	$0.831014\pi$
$180$		0			0
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.0928709	−	0.995678i	$-0.529604\pi$
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.427812	+	0.903868i	$0.640715\pi$
$182$		0			0
$183$	−0.243209	+	0.0349166i	−0.0179785	+	0.00258111i
$184$		0			0
$185$	−9.95603	−	3.62370i	−0.731982	−	0.266420i
$186$		0			0
$187$	2.57336	−	2.15930i	0.188183	−	0.157904i
$188$		0			0
$189$	14.9759	−	6.82798i	1.08933	−	0.496662i
$190$		0			0
$191$		−	11.2480i		−	0.813878i	−0.913455	−	0.406939i	$-0.866596\pi$
$191$		−	11.2480i		−	0.813878i	0.913455	−	0.406939i	$-0.133404\pi$
$192$		0			0
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	0.250704	−	0.968064i	$-0.419338\pi$
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	−0.996891	+	0.0787930i	$0.974893\pi$
$194$		0			0
$195$	5.89740	+	17.9688i	0.422322	+	1.28677i
$196$		0			0
$197$	−19.7987	−	11.4308i	−1.41060	−	0.814411i	−0.415157	−	0.909750i	$-0.636273\pi$
$197$	−19.7987	−	11.4308i	−1.41060	−	0.814411i	−0.995445	+	0.0953383i	$0.969607\pi$
$198$		0			0
$199$	−0.0579780	+	0.328809i	−0.00410995	+	0.0233087i	−0.986794	−	0.161982i	$-0.948211\pi$
$199$	−0.0579780	+	0.328809i	−0.00410995	+	0.0233087i	0.982684	+	0.185290i	$0.0593226\pi$
$200$		0			0
$201$	7.32726	+	2.93516i	0.516825	+	0.207030i
$202$		0			0
$203$	18.4788	+	15.5055i	1.29696	+	1.08827i
$204$		0			0
$205$	5.71370	+	15.6983i	0.399062	+	1.09641i
$206$		0			0
$207$	−0.730751	+	11.4236i	−0.0507907	+	0.793995i
$208$		0			0
$209$	−10.5888	−	2.59220i	−0.732443	−	0.179306i
$210$		0			0
$211$	−2.52603	+	0.445407i	−0.173899	+	0.0306631i	−0.259919	−	0.965630i	$-0.583696\pi$
$211$	−2.52603	+	0.445407i	−0.173899	+	0.0306631i	0.0860206	+	0.996293i	$0.472585\pi$
$212$		0			0
$213$	−13.4564	−	8.35311i	−0.922019	−	0.572346i
$214$		0			0
$215$	−20.7400	+	24.7170i	−1.41446	+	1.68569i
$216$		0			0
$217$	−21.8304	+	12.6038i	−1.48194	+	0.855600i
$218$		0			0
$219$	−3.34207	+	1.78974i	−0.225836	+	0.120940i
$220$		0			0
$221$	2.84093	−	4.92064i	0.191102	−	0.330998i
$222$		0			0
$223$	−2.28294	+	6.27232i	−0.152877	+	0.420026i	−0.992362	−	0.123356i	$-0.960634\pi$
$223$	−2.28294	+	6.27232i	−0.152877	+	0.420026i	0.839486	+	0.543382i	$0.182856\pi$
$224$		0			0
$225$	−2.21300	−	4.46983i	−0.147533	−	0.297989i
$226$		0			0
$227$	−20.0547			−1.33108			−0.665539	−	0.746363i	$-0.731798\pi$
$227$	−20.0547			−1.33108			−0.665539	+	0.746363i	$0.731798\pi$
$228$		0			0
$229$	16.5068			1.09080			0.545400	−	0.838176i	$-0.316378\pi$
$229$	16.5068			1.09080			0.545400	+	0.838176i	$0.316378\pi$
$230$		0			0
$231$	2.81297	−	13.4297i	0.185080	−	0.883609i
$232$		0			0
$233$	−2.12137	+	5.82843i	−0.138976	+	0.381833i	−0.989582	−	0.143970i	$-0.954013\pi$
$233$	−2.12137	+	5.82843i	−0.138976	+	0.381833i	0.850606	+	0.525803i	$0.176235\pi$
$234$		0			0
$235$	8.08503	−	14.0037i	0.527409	−	0.913500i
$236$		0			0
$237$	−8.16062	−	15.2387i	−0.530089	−	0.989859i
$238$		0			0
$239$	0.498666	−	0.287905i	0.0322560	−	0.0186230i	−0.483785	−	0.875187i	$-0.660738\pi$
$239$	0.498666	−	0.287905i	0.0322560	−	0.0186230i	0.516041	+	0.856564i	$0.327405\pi$
$240$		0			0
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	−0.800058	−	0.599923i	$-0.795198\pi$
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	0.729738	+	0.683727i	$0.239642\pi$
$242$		0			0
$243$	7.99356	+	13.3829i	0.512787	+	0.858516i
$244$		0			0
$245$	7.71043	−	1.35956i	0.492601	−	0.0868589i
$246$		0			0
$247$	−18.3293	+	2.00550i	−1.16627	+	0.127607i
$248$		0			0
$249$	−18.3760	−	16.4474i	−1.16453	−	1.04231i
$250$		0			0
$251$	−2.05161	−	5.63675i	−0.129496	−	0.355789i	0.857952	−	0.513730i	$-0.171737\pi$
$251$	−2.05161	−	5.63675i	−0.129496	−	0.355789i	−0.987449	+	0.157941i	$0.949514\pi$
$252$		0			0
$253$	7.31023	+	6.13401i	0.459590	+	0.385642i
$254$		0			0
$255$	−2.23302	+	5.57446i	−0.139837	+	0.349086i
$256$		0			0
$257$	3.23144	−	18.3264i	0.201572	−	1.14317i	−0.701172	−	0.712992i	$-0.747340\pi$
$257$	3.23144	−	18.3264i	0.201572	−	1.14317i	0.902744	−	0.430178i	$-0.141549\pi$
$258$		0			0
$259$	11.2598	+	6.50086i	0.699651	+	0.403944i
$260$		0			0
$261$	−12.6630	+	19.0161i	−0.783822	+	1.17706i
$262$		0			0
$263$	1.37946	+	1.64398i	0.0850614	+	0.101372i	0.806896	−	0.590693i	$-0.201146\pi$
$263$	1.37946	+	1.64398i	0.0850614	+	0.101372i	−0.721835	+	0.692065i	$0.756701\pi$
$264$		0			0
$265$		−	9.51804i		−	0.584688i
$266$		0			0
$267$	−17.8146	−	22.6627i	−1.09023	−	1.38694i
$268$		0			0
$269$	19.9247	−	16.7188i	1.21483	−	1.01936i	0.215752	−	0.976448i	$-0.430780\pi$
$269$	19.9247	−	16.7188i	1.21483	−	1.01936i	0.999079	−	0.0429154i	$-0.0136646\pi$
$270$		0			0
$271$	−4.62857	−	1.68466i	−0.281166	−	0.102336i	0.197588	−	0.980285i	$-0.436689\pi$
$271$	−4.62857	−	1.68466i	−0.281166	−	0.102336i	−0.478754	+	0.877949i	$0.658911\pi$
$272$		0			0
$273$	−3.29805	−	22.9723i	−0.199607	−	1.39035i
$274$		0			0
$275$	−4.09483	−	0.722029i	−0.246928	−	0.0435400i
$276$		0			0
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	0.839493	−	0.543370i	$-0.182852\pi$
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	−0.890319	+	0.455338i	$0.849518\pi$
$278$		0			0
$279$	−14.1473	−	19.2312i	−0.846977	−	1.15134i
$280$		0			0
$281$	−28.0317	+	10.2027i	−1.67223	+	0.608642i	−0.992213	−	0.124555i	$-0.960250\pi$
$281$	−28.0317	+	10.2027i	−1.67223	+	0.608642i	−0.680017	+	0.733196i	$0.738028\pi$
$282$		0			0
$283$	−4.10223	−	23.2649i	−0.243852	−	1.38296i	−0.823143	−	0.567834i	$-0.807781\pi$
$283$	−4.10223	−	23.2649i	−0.243852	−	1.38296i	0.579290	−	0.815121i	$-0.303330\pi$
$284$		0			0
$285$	18.8741	−	4.85101i	1.11801	−	0.287349i
$286$		0			0
$287$	−3.55989	−	20.1891i	−0.210134	−	1.19173i
$288$		0			0
$289$	−14.2794	+	5.19728i	−0.839966	+	0.305723i
$290$		0			0
$291$	0.946743	+	0.0302500i	0.0554991	+	0.00177328i
$292$		0			0
$293$	4.63502	+	8.02810i	0.270781	+	0.469006i	0.969062	−	0.246817i	$-0.0793847\pi$
$293$	4.63502	+	8.02810i	0.270781	+	0.469006i	−0.698281	+	0.715824i	$0.746051\pi$
$294$		0			0
$295$	−22.5925	−	3.98367i	−1.31539	−	0.231938i
$296$		0			0
$297$	12.9358	+	1.24335i	0.750612	+	0.0721463i
$298$		0			0
$299$	15.1673	+	5.52043i	0.877146	+	0.319255i
$300$		0			0
$301$	30.3317	−	25.4513i	1.74829	−	1.46699i
$302$		0			0
$303$	16.0226	−	12.5949i	0.920472	−	0.723558i
$304$		0			0
$305$		−	0.366159i		−	0.0209662i
$306$		0			0
$307$	−1.76414	−	2.10242i	−0.100685	−	0.119991i	0.713349	−	0.700809i	$-0.247177\pi$
$307$	−1.76414	−	2.10242i	−0.100685	−	0.119991i	−0.814034	+	0.580818i	$0.802733\pi$
$308$		0			0
$309$	−12.8749	+	4.22555i	−0.732425	+	0.240383i
$310$		0			0
$311$	−19.8290	−	11.4483i	−1.12440	−	0.649172i	−0.181879	−	0.983321i	$-0.558218\pi$
$311$	−19.8290	−	11.4483i	−1.12440	−	0.649172i	−0.942520	+	0.334148i	$0.891551\pi$
$312$		0			0
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	0.845177	+	0.534487i	$0.179495\pi$
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	−0.977012	+	0.213186i	$0.931616\pi$
$314$		0			0
$315$	6.90057	+	23.5373i	0.388803	+	1.32618i
$316$		0			0
$317$	15.9117	+	13.3515i	0.893689	+	0.749894i	0.968947	−	0.247270i	$-0.0795336\pi$
$317$	15.9117	+	13.3515i	0.893689	+	0.749894i	−0.0752579	+	0.997164i	$0.523978\pi$
$318$		0			0
$319$	6.51417	+	17.8975i	0.364723	+	1.00207i
$320$		0			0
$321$	−6.53699	+	7.30350i	−0.364859	+	0.407642i
$322$		0			0
$323$	−4.86778	−	3.25326i	−0.270851	−	0.181016i
$324$		0			0
$325$	−6.92597	+	1.22124i	−0.384184	+	0.0677419i
$326$		0			0
$327$	15.0770	−	24.2882i	0.833760	−	1.34314i
$328$		0			0
$329$	−12.7550	+	15.2008i	−0.703204	+	0.838046i
$330$		0			0
$331$	−7.79345	+	4.49955i	−0.428367	+	0.247318i	−0.698651	−	0.715463i	$-0.746216\pi$
$331$	−7.79345	+	4.49955i	−0.428367	+	0.247318i	0.270284	+	0.962781i	$0.412882\pi$
$332$		0			0
$333$	−4.94176	+	11.2790i	−0.270807	+	0.618083i
$334$		0			0
$335$	−5.88149	+	10.1870i	−0.321340	+	0.556577i
$336$		0			0
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	−0.760819	−	0.648964i	$-0.775203\pi$
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	0.999967	−	0.00808963i	$-0.00257504\pi$
$338$		0			0
$339$	8.74242	+	1.83117i	0.474823	+	0.0994558i
$340$		0			0
$341$	−19.9030			−1.07781
$342$		0			0
$343$	12.5648			0.678437
$344$		0			0
$345$	−16.6965	−	3.49723i	−0.898910	−	0.188284i
$346$		0			0
$347$	−4.73541	+	13.0104i	−0.254210	+	0.698436i	0.745288	+	0.666743i	$0.232312\pi$
$347$	−4.73541	+	13.0104i	−0.254210	+	0.698436i	−0.999498	+	0.0316932i	$0.989910\pi$
$348$		0			0
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	0.445926	+	0.895070i	$0.352874\pi$
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	−0.998116	+	0.0613514i	$0.980459\pi$
$350$		0			0
$351$	21.2793	−	5.50708i	1.13581	−	0.293946i
$352$		0			0
$353$	19.7460	−	11.4004i	1.05098	−	0.606781i	0.128053	−	0.991767i	$-0.459127\pi$
$353$	19.7460	−	11.4004i	1.05098	−	0.606781i	0.922922	+	0.384987i	$0.125794\pi$
$354$		0			0
$355$	15.1717	−	18.0809i	0.805230	−	0.959636i
$356$		0			0
$357$	3.88651	−	6.26097i	0.205696	−	0.331366i
$358$		0			0
$359$	−7.31056	+	1.28905i	−0.385837	+	0.0680334i	−0.363202	−	0.931710i	$-0.618317\pi$
$359$	−7.31056	+	1.28905i	−0.385837	+	0.0680334i	−0.0226346	+	0.999744i	$0.507205\pi$
$360$		0			0
$361$	0.824917	+	18.9821i	0.0434167	+	0.999057i
$362$		0			0
$363$	−5.48133	+	6.12406i	−0.287695	+	0.321430i
$364$		0			0
$365$	−1.93232	−	5.30901i	−0.101142	−	0.277886i
$366$		0			0
$367$	15.2065	+	12.7597i	0.793771	+	0.666053i	0.946676	−	0.322188i	$-0.104418\pi$
$367$	15.2065	+	12.7597i	0.793771	+	0.666053i	−0.152904	+	0.988241i	$0.548863\pi$
$368$		0			0
$369$	18.6321	−	5.46248i	0.969947	−	0.284365i
$370$		0			0
$371$	−2.02823	+	11.5027i	−0.105301	+	0.597189i
$372$		0			0
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	0.862365	−	0.506287i	$-0.168982\pi$
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	−0.00727484	+	0.999974i	$0.502316\pi$
$374$		0			0
$375$	−14.1769	+	4.65288i	−0.732091	+	0.240274i
$376$		0			0
$377$	20.7071	+	24.6778i	1.06647	+	1.27097i
$378$		0			0
$379$			30.0894i			1.54559i	0.634656	+	0.772795i	$0.281142\pi$
$379$			30.0894i			1.54559i	−0.634656	+	0.772795i	$0.718858\pi$
$380$		0			0
$381$	−10.6715	+	8.38860i	−0.546719	+	0.429761i
$382$		0			0
$383$	4.60213	−	3.86165i	0.235158	−	0.197321i	−0.517592	−	0.855628i	$-0.673171\pi$
$383$	4.60213	−	3.86165i	0.235158	−	0.197321i	0.752750	+	0.658307i	$0.228727\pi$
$384$		0			0
$385$	19.2148	+	6.99361i	0.979276	+	0.356427i
$386$		0			0
$387$	27.1300	+	25.8899i	1.37910	+	1.31606i
$388$		0			0
$389$	−20.4701	−	3.60942i	−1.03787	−	0.183005i	−0.371353	−	0.928492i	$-0.621106\pi$
$389$	−20.4701	−	3.60942i	−1.03787	−	0.183005i	−0.666520	+	0.745487i	$0.732217\pi$
$390$		0			0
$391$	2.56257	+	4.43850i	0.129595	+	0.224465i
$392$		0			0
$393$	7.79238	+	0.248979i	0.393074	+	0.0125593i
$394$		0			0
$395$	24.2072	−	8.81072i	1.21800	−	0.443315i
$396$		0			0
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	0.995691	+	0.0927316i	$0.0295599\pi$
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	−0.903928	+	0.427686i	$0.859329\pi$
$398$		0			0
$399$	−23.8434	+	1.84056i	−1.19366	+	0.0921432i
$400$		0			0
$401$	1.59795	+	9.06241i	0.0797977	+	0.452555i	0.998358	+	0.0572753i	$0.0182413\pi$
$401$	1.59795	+	9.06241i	0.0797977	+	0.452555i	−0.918561	+	0.395280i	$0.870648\pi$
$402$		0			0
$403$	−31.6336	+	11.5137i	−1.57578	+	0.573538i
$404$		0			0
$405$	−21.4344	+	8.95729i	−1.06508	+	0.445092i
$406$		0			0
$407$	5.13285	+	8.89036i	0.254426	+	0.440679i
$408$		0			0
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.714911	−	0.699215i	$-0.246467\pi$
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.432651	+	0.901561i	$0.357578\pi$
$410$		0			0
$411$	−1.93636	−	13.4875i	−0.0955136	−	0.665292i
$412$		0			0
$413$	26.4545	+	9.62865i	1.30174	+	0.473795i
$414$		0			0
$415$	28.1537	−	23.6238i	1.38201	−	1.15964i
$416$		0			0
$417$	8.05940	+	10.2527i	0.394670	+	0.502079i
$418$		0			0
$419$			20.4238i			0.997766i	0.866669	+	0.498883i	$0.166256\pi$
$419$			20.4238i			0.997766i	−0.866669	+	0.498883i	$0.833744\pi$
$420$		0			0
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	0.759695	−	0.650279i	$-0.225348\pi$
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	−0.772320	+	0.635234i	$0.780904\pi$
$422$		0			0
$423$	−15.6428	−	10.4167i	−0.760577	−	0.506478i
$424$		0			0
$425$	−1.93394	−	1.11656i	−0.0938101	−	0.0541613i
$426$		0			0
$427$	−0.0780261	+	0.442508i	−0.00377595	+	0.0214144i
$428$		0			0
$429$	6.81391	−	17.0101i	0.328979	−	0.821255i
$430$		0			0
$431$	7.15165	+	6.00095i	0.344483	+	0.289055i	0.798570	−	0.601902i	$-0.205590\pi$
$431$	7.15165	+	6.00095i	0.344483	+	0.289055i	−0.454087	+	0.890957i	$0.650035\pi$
$432$		0			0
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	−0.985949	−	0.167045i	$-0.946577\pi$
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	0.647907	−	0.761720i	$-0.275645\pi$
$434$		0			0
$435$	−25.3694	−	22.7068i	−1.21637	−	1.08871i
$436$		0			0
$437$	6.70004	−	15.2228i	0.320506	−	0.728206i
$438$		0			0
$439$	25.2438	−	4.45116i	1.20482	−	0.212442i	0.465040	−	0.885290i	$-0.346040\pi$
$439$	25.2438	−	4.45116i	1.20482	−	0.212442i	0.739781	+	0.672847i	$0.234929\pi$
$440$		0			0
$441$	−1.00484	−	9.04407i	−0.0478497	−	0.430670i
$442$		0			0
$443$	−17.0745	+	20.3486i	−0.811235	+	0.966792i	−0.999884	−	0.0152527i	$-0.995145\pi$
$443$	−17.0745	+	20.3486i	−0.811235	+	0.966792i	0.188649	+	0.982045i	$0.439589\pi$
$444$		0			0
$445$	37.2032	−	21.4793i	1.76360	−	1.01821i
$446$		0			0
$447$	11.1897	+	20.8950i	0.529254	+	0.988300i
$448$		0			0
$449$	−5.66925	+	9.81944i	−0.267549	+	0.463408i	−0.968228	−	0.250068i	$-0.919547\pi$
$449$	−5.66925	+	9.81944i	−0.267549	+	0.463408i	0.700680	+	0.713476i	$0.252880\pi$
$450$		0			0
$451$	5.53612	−	15.2104i	0.260686	−	0.716229i
$452$		0			0
$453$	−3.06672	+	14.6412i	−0.144087	+	0.687903i
$454$		0			0
$455$	34.5855			1.62139
$456$		0			0
$457$	−21.3688			−0.999591			−0.499796	−	0.866143i	$-0.666592\pi$
$457$	−21.3688			−0.999591			−0.499796	+	0.866143i	$0.666592\pi$
$458$		0			0
$459$	6.30004	+	3.00364i	0.294061	+	0.140198i
$460$		0			0
$461$	9.40832	−	25.8492i	0.438189	−	1.20392i	−0.502480	−	0.864589i	$-0.667579\pi$
$461$	9.40832	−	25.8492i	0.438189	−	1.20392i	0.940669	−	0.339326i	$-0.110199\pi$
$462$		0			0
$463$	4.52654	−	7.84019i	0.210366	−	0.364365i	−0.741463	−	0.670994i	$-0.765868\pi$
$463$	4.52654	−	7.84019i	0.210366	−	0.364365i	0.951829	+	0.306629i	$0.0992011\pi$
$464$		0			0
$465$	31.3645	−	16.7963i	1.45450	−	0.778911i
$466$		0			0
$467$	17.7092	−	10.2244i	0.819486	−	0.473130i	−0.0307535	−	0.999527i	$-0.509791\pi$
$467$	17.7092	−	10.2244i	0.819486	−	0.473130i	0.850239	+	0.526397i	$0.176457\pi$
$468$		0			0
$469$	9.27865	−	11.0579i	0.428448	−	0.510605i
$470$		0			0
$471$	−5.05488	−	3.13783i	−0.232916	−	0.144584i
$472$		0			0
$473$	30.7880	−	5.42876i	1.41564	−	0.249615i
$474$		0			0
$475$	0.788217	+	7.20391i	0.0361659	+	0.330538i
$476$		0			0
$477$	−11.0398	−	0.706200i	−0.505478	−	0.0323347i
$478$		0			0
$479$	3.36367	+	9.24160i	0.153690	+	0.422259i	0.992512	−	0.122146i	$-0.0389776\pi$
$479$	3.36367	+	9.24160i	0.153690	+	0.422259i	−0.838822	+	0.544405i	$0.816755\pi$
$480$		0			0
$481$	13.3011	+	11.1609i	0.606477	+	0.508895i
$482$		0			0
$483$	19.4327	+	7.78437i	0.884220	+	0.354201i
$484$		0			0
$485$	−0.245123	+	1.39016i	−0.0111305	+	0.0631239i
$486$		0			0
$487$	6.75564	+	3.90037i	0.306127	+	0.176743i	0.645192	−	0.764020i	$-0.276777\pi$
$487$	6.75564	+	3.90037i	0.306127	+	0.176743i	−0.339065	+	0.940763i	$0.610111\pi$
$488$		0			0
$489$	−4.14062	−	12.6161i	−0.187245	−	0.570519i
$490$		0			0
$491$	−18.0754	−	21.5414i	−0.815729	−	0.972148i	0.184213	−	0.982886i	$-0.441026\pi$
$491$	−18.0754	−	21.5414i	−0.815729	−	0.972148i	−0.999942	+	0.0107379i	$0.996582\pi$
$492$		0			0
$493$			10.2291i			0.460694i
$494$		0			0
$495$	−4.57363	+	18.8187i	−0.205569	+	0.845836i
$496$		0			0
$497$	−22.1881	+	18.6181i	−0.995274	+	0.835134i
$498$		0			0
$499$	12.8477	+	4.67618i	0.575142	+	0.209334i	0.613182	−	0.789942i	$-0.289889\pi$
$499$	12.8477	+	4.67618i	0.575142	+	0.209334i	−0.0380402	+	0.999276i	$0.512112\pi$
$500$		0			0
$501$	4.02173	−	0.577385i	0.179677	−	0.0257957i
$502$		0			0
$503$	25.8762	+	4.56267i	1.15376	+	0.203439i	0.717618	−	0.696437i	$-0.245233\pi$
$503$	25.8762	+	4.56267i	1.15376	+	0.203439i	0.436144	+	0.899877i	$0.356344\pi$
$504$		0			0
$505$	15.1858	+	26.3026i	0.675761	+	1.17045i
$506$		0			0
$507$	0.270702	−	8.47225i	0.0120223	−	0.376266i
$508$		0			0
$509$	−25.0043	+	9.10082i	−1.10830	+	0.403387i	−0.830368	−	0.557215i	$-0.811870\pi$
$509$	−25.0043	+	9.10082i	−1.10830	+	0.403387i	−0.277928	+	0.960602i	$0.589648\pi$
$510$		0			0
$511$	1.20392	+	6.82777i	0.0532583	+	0.302043i
$512$		0			0
$513$	−4.22622	−	22.2517i	−0.186592	−	0.982437i
$514$		0			0
$515$	−3.50661	−	19.8869i	−0.154520	−	0.876324i
$516$		0			0
$517$	−14.7226	+	5.35860i	−0.647501	+	0.235671i
$518$		0			0
$519$	−0.825191	+	25.8263i	−0.0362219	+	1.13365i
$520$		0			0
$521$	−10.2977	−	17.8362i	−0.451151	−	0.781417i	0.547307	−	0.836932i	$-0.315653\pi$
$521$	−10.2977	−	17.8362i	−0.451151	−	0.781417i	−0.998458	+	0.0555154i	$0.982320\pi$
$522$		0			0
$523$	−7.47024	−	1.31720i	−0.326651	−	0.0575973i	0.00791816	−	0.999969i	$-0.497480\pi$
$523$	−7.47024	−	1.31720i	−0.326651	−	0.0575973i	−0.334569	+	0.942371i	$0.608591\pi$
$524$		0			0
$525$	−9.02874	+	1.29622i	−0.394046	+	0.0565719i
$526$		0			0
$527$	−10.0446	−	3.65594i	−0.437550	−	0.159255i
$528$		0			0
$529$	6.46604	−	5.42566i	0.281132	−	0.235898i
$530$		0			0
$531$	−6.29687	+	25.9091i	−0.273261	+	1.12436i
$532$		0			0
$533$		−	27.3778i		−	1.18586i
$534$		0			0
$535$	−9.38920	−	11.1896i	−0.405931	−	0.483769i
$536$		0			0
$537$	0.105287	+	0.320799i	0.00454345	+	0.0138435i
$538$		0			0
$539$	−6.56971	−	3.79302i	−0.282977	−	0.163377i
$540$		0			0
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	−0.238148	−	0.971229i	$-0.576540\pi$
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	0.555966	−	0.831205i	$-0.312349\pi$
$542$		0			0
$543$	−11.4368	−	4.58137i	−0.490802	−	0.196605i
$544$		0			0
$545$	32.6353	+	27.3842i	1.39794	+	1.17301i
$546$		0			0
$547$	0.418676	+	1.15030i	0.0179013	+	0.0491833i	0.948321	−	0.317311i	$-0.102780\pi$
$547$	0.418676	+	1.15030i	0.0179013	+	0.0491833i	−0.930420	+	0.366495i	$0.880558\pi$
$548$		0			0
$549$	−0.424701	−	0.0271675i	−0.0181258	−	0.00115948i
$550$		0			0
$551$	26.7721	−	19.6259i	1.14053	−	0.836093i
$552$		0			0
$553$	−31.1323	+	5.48946i	−1.32388	+	0.233436i
$554$		0			0
$555$	−15.5914	−	9.67838i	−0.661816	−	0.410824i
$556$		0			0
$557$	−13.8808	+	16.5425i	−0.588147	+	0.700927i	−0.975249	−	0.221110i	$-0.929032\pi$
$557$	−13.8808	+	16.5425i	−0.588147	+	0.700927i	0.387101	+	0.922037i	$0.373476\pi$
$558$		0			0
$559$	45.7937	−	26.4390i	1.93687	−	1.11825i
$560$		0			0
$561$	5.12926	−	2.74682i	0.216557	−	0.115971i
$562$		0			0
$563$	13.0149	−	22.5424i	0.548512	−	0.950051i	−0.449865	−	0.893097i	$-0.648528\pi$
$563$	13.0149	−	22.5424i	0.548512	−	0.950051i	0.998377	−	0.0569541i	$-0.0181389\pi$
$564$		0			0
$565$	−4.55268	+	12.5084i	−0.191533	+	0.526231i
$566$		0			0
$567$	27.8125	−	6.25748i	1.16802	−	0.262789i
$568$		0			0
$569$	−4.80544			−0.201455			−0.100727	−	0.994914i	$-0.532117\pi$
$569$	−4.80544			−0.201455			−0.100727	+	0.994914i	$0.532117\pi$
$570$		0			0
$571$	46.6475			1.95214			0.976068	−	0.217466i	$-0.0697792\pi$
$571$	46.6475			1.95214			0.976068	+	0.217466i	$0.0697792\pi$
$572$		0			0
$573$	3.99403	−	19.0683i	0.166853	−	0.796591i
$574$		0			0
$575$	2.16968	−	5.96115i	0.0904820	−	0.248597i
$576$		0			0
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.276125	−	0.961122i	$-0.410950\pi$
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.694293	−	0.719692i	$-0.255717\pi$
$578$		0			0
$579$	−13.1869	−	24.6245i	−0.548028	−	1.02336i
$580$		0			0
$581$	−39.0582	+	22.5503i	−1.62041	+	0.935543i
$582$		0			0
$583$	−5.92793	+	7.06463i	−0.245510	+	0.292587i
$584$		0			0
$585$	3.61714	+	32.5560i	0.149550	+	1.34602i
$586$		0			0
$587$	14.9298	−	2.63253i	0.616220	−	0.108656i	0.143180	−	0.989697i	$-0.454267\pi$
$587$	14.9298	−	2.63253i	0.616220	−	0.108656i	0.473041	+	0.881040i	$0.343156\pi$
$588$		0			0
$589$	9.70350	+	33.3038i	0.399826	+	1.37226i
$590$		0			0
$591$	−29.5051	−	26.4085i	−1.21368	−	1.08630i
$592$		0			0
$593$	0.398860	+	1.09586i	0.0163792	+	0.0450015i	0.947613	−	0.319421i	$-0.103489\pi$
$593$	0.398860	+	1.09586i	0.0163792	+	0.0450015i	−0.931234	+	0.364423i	$0.881266\pi$
$594$		0			0
$595$	8.41264	+	7.05905i	0.344885	+	0.289393i
$596$		0			0
$597$	−0.215044	+	0.536831i	−0.00880116	+	0.0219710i
$598$		0			0
$599$	−4.45202	+	25.2486i	−0.181905	+	1.03163i	0.747964	+	0.663739i	$0.231032\pi$
$599$	−4.45202	+	25.2486i	−0.181905	+	1.03163i	−0.929868	+	0.367892i	$0.880079\pi$
$600$		0			0
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.148726	−	0.988878i	$-0.547517\pi$
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.930757	+	0.365639i	$0.880851\pi$
$602$		0			0
$603$	11.3794	+	7.57767i	0.463404	+	0.308587i
$604$		0			0
$605$	−7.87294	−	9.38261i	−0.320081	−	0.381457i
$606$		0			0
$607$		−	7.82667i		−	0.317675i	−0.987305	−	0.158837i	$-0.949225\pi$
$607$		−	7.82667i		−	0.317675i	0.987305	−	0.158837i	$-0.0507745\pi$
$608$		0			0
$609$	25.8205	+	32.8475i	1.04630	+	1.33105i
$610$		0			0
$611$	−20.3001	+	17.0338i	−0.821254	+	0.689114i
$612$		0			0
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.872615	−	0.488408i	$-0.162422\pi$
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.354519	+	0.935049i	$0.384645\pi$
$614$		0			0
$615$	4.11197	+	28.6415i	0.165810	+	1.15494i
$616$		0			0
$617$	24.5040	+	4.32072i	0.986495	+	0.173946i	0.643545	−	0.765408i	$-0.277463\pi$
$617$	24.5040	+	4.32072i	0.986495	+	0.173946i	0.342950	+	0.939354i	$0.388574\pi$
$618$		0			0
$619$	3.60285	+	6.24032i	0.144811	+	0.250820i	0.929302	−	0.369320i	$-0.120409\pi$
$619$	3.60285	+	6.24032i	0.144811	+	0.250820i	−0.784492	+	0.620140i	$0.787076\pi$
$620$		0			0
$621$	−5.29519	+	19.1065i	−0.212489	+	0.766718i
$622$		0			0
$623$	−49.5376	+	18.0302i	−1.98468	+	0.722366i
$624$		0			0
$625$	−5.30472	−	30.0846i	−0.212189	−	1.20338i
$626$		0			0
$627$	−17.0303	−	8.15441i	−0.680126	−	0.325656i
$628$		0			0
$629$	0.957388	+	5.42961i	0.0381735	+	0.216493i
$630$		0			0
$631$	−23.7099	+	8.62969i	−0.943876	+	0.343543i	−0.767695	−	0.640815i	$-0.778596\pi$
$631$	−23.7099	+	8.62969i	−0.943876	+	0.343543i	−0.176180	+	0.984358i	$0.556374\pi$
$632$		0			0
$633$	−4.44044	−	0.141879i	−0.176492	−	0.00563919i
$634$		0			0
$635$	−10.1142	−	17.5184i	−0.401372	−	0.695196i
$636$		0			0
$637$	−12.6361	−	2.22808i	−0.500659	−	0.0882796i
$638$		0			0
$639$	−19.8461	−	18.9389i	−0.785099	−	0.749212i
$640$		0			0
$641$	−8.36361	−	3.04411i	−0.330343	−	0.120235i	0.171524	−	0.985180i	$-0.445131\pi$
$641$	−8.36361	−	3.04411i	−0.330343	−	0.120235i	−0.501867	+	0.864945i	$0.667353\pi$
$642$		0			0
$643$	−5.41716	+	4.54553i	−0.213632	+	0.179258i	−0.743324	−	0.668932i	$-0.766752\pi$
$643$	−5.41716	+	4.54553i	−0.213632	+	0.179258i	0.529692	+	0.848190i	$0.322307\pi$
$644$		0			0
$645$	−43.9365	+	34.5373i	−1.73000	+	1.35990i
$646$		0			0
$647$			7.87198i			0.309479i	0.987955	+	0.154740i	$0.0494539\pi$
$647$			7.87198i			0.309479i	−0.987955	+	0.154740i	$0.950546\pi$
$648$		0			0
$649$	14.2879	+	17.0277i	0.560850	+	0.668395i
$650$		0			0
$651$	−41.4837	+	13.6150i	−1.62587	+	0.533614i
$652$		0			0
$653$	−1.40402	−	0.810613i	−0.0549437	−	0.0317217i	0.472277	−	0.881450i	$-0.343432\pi$
$653$	−1.40402	−	0.810613i	−0.0549437	−	0.0317217i	−0.527220	+	0.849729i	$0.676766\pi$
$654$		0			0
$655$	−2.01754	+	11.4420i	−0.0788318	+	0.447077i
$656$		0			0
$657$	−6.30120	+	1.84736i	−0.245833	+	0.0720723i
$658$		0			0
$659$	9.29693	+	7.80105i	0.362157	+	0.303886i	0.805650	−	0.592392i	$-0.201816\pi$
$659$	9.29693	+	7.80105i	0.362157	+	0.303886i	−0.443493	+	0.896278i	$0.646261\pi$
$660$		0			0
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	−0.965759	−	0.259440i	$-0.916462\pi$
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	0.573050	−	0.819521i	$-0.305760\pi$
$662$		0			0
$663$	6.56338	−	7.33299i	0.254900	−	0.284790i
$664$		0			0
$665$	2.33447	−	35.5618i	0.0905268	−	1.37903i
$666$		0			0
$667$	−28.6166	+	5.04588i	−1.10804	+	0.195377i
$668$		0			0
$669$	−6.09740	+	9.82258i	−0.235739	+	0.379763i
$670$		0			0
$671$	−0.228047	+	0.271776i	−0.00880367	+	0.0104918i
$672$		0			0
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	−0.572257	−	0.820075i	$-0.693932\pi$
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	0.424077	+	0.905626i	$0.360599\pi$
$674$		0			0
$675$	−2.16443	−	8.36335i	−0.0833091	−	0.321905i
$676$		0			0
$677$	0.610403	−	1.05725i	0.0234597	−	0.0406334i	−0.854057	−	0.520179i	$-0.825865\pi$
$677$	0.610403	−	1.05725i	0.0234597	−	0.0406334i	0.877517	+	0.479546i	$0.159199\pi$
$678$		0			0
$679$	0.592469	−	1.62779i	0.0227369	−	0.0624690i
$680$		0			0
$681$	−33.9980	−	7.12117i	−1.30281	−	0.272884i
$682$		0			0
$683$	−40.7336			−1.55863			−0.779313	−	0.626635i	$-0.784432\pi$
$683$	−40.7336			−1.55863			−0.779313	+	0.626635i	$0.784432\pi$
$684$		0			0
$685$	20.3059			0.775850
$686$		0			0
$687$	27.9834	+	5.86136i	1.06763	+	0.223625i
$688$		0			0
$689$	−5.33497	+	14.6577i	−0.203246	+	0.558414i
$690$		0			0
$691$	−18.9023	+	32.7397i	−0.719077	+	1.24548i	0.242289	+	0.970204i	$0.422102\pi$
$691$	−18.9023	+	32.7397i	−0.719077	+	1.24548i	−0.961366	+	0.275274i	$0.911231\pi$
$692$		0			0
$693$	9.53743	−	21.7680i	0.362297	−	0.826898i
$694$		0			0
$695$	−16.8309	+	9.71733i	−0.638433	+	0.368599i
$696$		0			0
$697$	5.58792	−	6.65943i	0.211658	−	0.252244i
$698$		0			0
$699$	−5.66589	+	9.12744i	−0.214304	+	0.345231i
$700$		0			0
$701$	23.1182	−	4.07636i	0.873162	−	0.153962i	0.280929	−	0.959729i	$-0.409358\pi$
$701$	23.1182	−	4.07636i	0.873162	−	0.153962i	0.592233	+	0.805767i	$0.298246\pi$
$702$		0			0
$703$	12.3738	−	12.9232i	0.466687	−	0.487408i
$704$		0			0
$705$	18.6788	−	20.8690i	0.703483	−	0.785973i
$706$		0			0
$707$	−12.7474	−	35.0231i	−0.479414	−	1.31718i
$708$		0			0
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	0.948987	−	0.315315i	$-0.102110\pi$
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	−0.145735	+	0.989324i	$0.546555\pi$
$710$		0			0
$711$	−8.42332	−	28.7313i	−0.315899	−	1.07751i
$712$		0			0
$713$	5.27289	−	29.9041i	0.197471	−	1.11992i
$714$		0			0
$715$	23.6490	+	13.6538i	0.884423	+	0.510622i
$716$		0			0
$717$	0.947601	−	0.311004i	0.0353888	−	0.0116147i
$718$		0			0
$719$	26.4940	+	31.5743i	0.988060	+	1.17752i	0.984115	+	0.177532i	$0.0568113\pi$
$719$	26.4940	+	31.5743i	0.988060	+	1.17752i	0.00394505	+	0.999992i	$0.498744\pi$
$720$		0			0
$721$			24.7809i			0.922889i
$722$		0			0
$723$	−2.31261	+	1.81788i	−0.0860069	+	0.0676077i
$724$		0			0
$725$	9.69903	−	8.13846i	0.360213	−	0.302255i
$726$		0			0
$727$	−4.13772	−	1.50601i	−0.153460	−	0.0558548i	0.264148	−	0.964482i	$-0.414909\pi$
$727$	−4.13772	−	1.50601i	−0.153460	−	0.0558548i	−0.417608	+	0.908627i	$0.637131\pi$
$728$		0			0
$729$	8.79906	+	25.5260i	0.325891	+	0.945407i
$730$		0			0
$731$	16.5352	+	2.91561i	0.611578	+	0.107838i
$732$		0			0
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	0.996041	−	0.0888960i	$-0.0283339\pi$
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	−0.575007	+	0.818149i	$0.695001\pi$
$734$		0			0
$735$	13.5540	+	0.433071i	0.499945	+	0.0159741i
$736$		0			0
$737$	10.7100	−	3.89814i	0.394510	−	0.143590i
$738$		0			0
$739$	8.91510	+	50.5600i	0.327947	+	1.85988i	0.488098	+	0.872789i	$0.337691\pi$
$739$	8.91510	+	50.5600i	0.327947	+	1.85988i	−0.160151	+	0.987093i	$0.551198\pi$
$740$		0			0
$741$	−31.7851	−	3.10865i	−1.16765	−	0.114199i
$742$		0			0
$743$	0.154876	+	0.878343i	0.00568183	+	0.0322233i	0.987517	−	0.157513i	$-0.0503477\pi$
$743$	0.154876	+	0.878343i	0.00568183	+	0.0322233i	−0.981835	+	0.189737i	$0.939237\pi$
$744$		0			0
$745$	−33.1925	+	12.0811i	−1.21608	+	0.442617i
$746$		0			0
$747$	−25.3119	−	34.4078i	−0.926114	−	1.25891i
$748$		0			0
$749$	8.96255	+	15.5236i	0.327484	+	0.567220i
$750$		0			0
$751$	10.0009	+	1.76342i	0.364936	+	0.0643481i	0.353110	−	0.935582i	$-0.385124\pi$
$751$	10.0009	+	1.76342i	0.364936	+	0.0643481i	0.0118266	+	0.999930i	$0.496235\pi$
$752$		0			0
$753$	−1.47648	−	10.2843i	−0.0538058	−	0.374780i
$754$		0			0
$755$	−20.9481	−	7.62450i	−0.762381	−	0.277484i
$756$		0			0
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	−0.303478	−	0.952839i	$-0.598148\pi$
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	0.885664	+	0.464326i	$0.153703\pi$
$758$		0			0
$759$	10.2146	+	12.9945i	0.370768	+	0.471672i
$760$		0			0
$761$			23.9282i			0.867396i	0.901058	+	0.433698i	$0.142791\pi$
$761$			23.9282i			0.867396i	−0.901058	+	0.433698i	$0.857209\pi$
$762$		0			0
$763$	−33.6048	−	40.0486i	−1.21657	−	1.44986i
$764$		0			0
$765$	−5.76497	+	8.65725i	−0.208433	+	0.313003i
$766$		0			0
$767$	32.5594	+	18.7982i	1.17565	+	0.678764i
$768$		0			0
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	0.870124	+	0.492833i	$0.164039\pi$
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	−0.986208	+	0.165511i	$0.947073\pi$
$770$		0			0
$771$	11.9856	−	29.9206i	0.431651	−	1.07756i
$772$		0			0
$773$	−27.0855	−	22.7275i	−0.974199	−	0.817450i	0.00900488	−	0.999959i	$-0.497134\pi$
$773$	−27.0855	−	22.7275i	−0.974199	−	0.817450i	−0.983204	+	0.182509i	$0.941578\pi$
$774$		0			0
$775$	4.52520	+	12.4329i	0.162550	+	0.446602i
$776$		0			0
$777$	16.7800	+	15.0189i	0.601978	+	0.538799i
$778$		0			0
$779$	−28.1507	−	1.84796i	−1.00860	−	0.0662100i
$780$		0			0
$781$	−22.5220	+	3.97123i	−0.805900	+	0.142102i
$782$		0			0
$783$	−28.2195	+	27.7407i	−1.00848	+	0.991372i
$784$		0			0
$785$	5.69922	−	6.79206i	0.203414	−	0.242419i
$786$		0			0
$787$	−6.19829	+	3.57858i	−0.220945	+	0.127563i	−0.606388	−	0.795169i	$-0.707382\pi$
$787$	−6.19829	+	3.57858i	−0.220945	+	0.127563i	0.385443	+	0.922732i	$0.374049\pi$
$788$		0			0
$789$	1.75480	+	3.27681i	0.0624724	+	0.116658i
$790$		0			0
$791$	8.16743	−	14.1464i	0.290400	−	0.502988i
$792$		0			0
$793$	−0.205236	+	0.563881i	−0.00728815	+	0.0200240i
$794$		0			0
$795$	3.37973	−	16.1356i	0.119867	−	0.572270i
$796$		0			0
$797$	−13.5711			−0.480714			−0.240357	−	0.970685i	$-0.577265\pi$
$797$	−13.5711			−0.480714			−0.240357	+	0.970685i	$0.577265\pi$
$798$		0			0
$799$	−8.41451			−0.297684
$800$		0			0
$801$	−22.1531	−	44.7450i	−0.782741	−	1.58099i
$802$		0			0
$803$	−1.87227	+	5.14401i	−0.0660708	+	0.181528i
$804$		0			0
$805$	−15.5984	+	27.0172i	−0.549771	+	0.952231i
$806$		0			0
$807$	39.7142	−	21.2678i	1.39801	−	0.748660i
$808$		0			0
$809$	−7.06352	+	4.07812i	−0.248340	+	0.143379i	−0.619004	−	0.785388i	$-0.712464\pi$
$809$	−7.06352	+	4.07812i	−0.248340	+	0.143379i	0.370664	+	0.928767i	$0.379130\pi$
$810$		0			0
$811$	1.94231	−	2.31476i	0.0682038	−	0.0812821i	−0.730864	−	0.682523i	$-0.760883\pi$
$811$	1.94231	−	2.31476i	0.0682038	−	0.0812821i	0.799068	+	0.601241i	$0.205327\pi$
$812$		0			0
$813$	−7.24844	−	4.49949i	−0.254214	−	0.157804i
$814$		0			0
$815$	19.4872	−	3.43612i	0.682608	−	0.120362i
$816$		0			0
$817$	−24.0943	−	48.8710i	−0.842954	−	1.70978i
$818$		0			0
$819$	2.56611	−	40.1151i	0.0896670	−	1.40174i
$820$		0			0
$821$	1.32613	+	3.64350i	0.0462821	+	0.127159i	0.960680	−	0.277657i	$-0.0895578\pi$
$821$	1.32613	+	3.64350i	0.0462821	+	0.127159i	−0.914398	+	0.404816i	$0.867336\pi$
$822$		0			0
$823$	−9.67720	−	8.12014i	−0.337326	−	0.283050i	0.458351	−	0.888771i	$-0.348440\pi$
$823$	−9.67720	−	8.12014i	−0.337326	−	0.283050i	−0.795677	+	0.605721i	$0.792885\pi$
$824$		0			0
$825$	−6.68543	−	2.67805i	−0.232757	−	0.0932378i
$826$		0			0
$827$	5.27611	−	29.9223i	0.183468	−	1.04050i	−0.744439	−	0.667690i	$-0.767283\pi$
$827$	5.27611	−	29.9223i	0.183468	−	1.04050i	0.927908	−	0.372810i	$-0.121606\pi$
$828$		0			0
$829$	20.5261	+	11.8507i	0.712901	+	0.411593i	0.812134	−	0.583471i	$-0.198306\pi$
$829$	20.5261	+	11.8507i	0.712901	+	0.411593i	−0.0992334	+	0.995064i	$0.531639\pi$
$830$		0			0
$831$	−0.913769	−	2.78417i	−0.0316983	−	0.0965818i
$832$		0			0
$833$	−2.61886	−	3.12103i	−0.0907380	−	0.108137i
$834$		0			0
$835$			6.05484i			0.209536i
$836$		0			0
$837$	−17.1546	−	37.6254i	−0.592951	−	1.30052i
$838$		0			0
$839$	11.0849	−	9.30133i	0.382693	−	0.321118i	−0.431066	−	0.902321i	$-0.641862\pi$
$839$	11.0849	−	9.30133i	0.382693	−	0.321118i	0.813759	+	0.581203i	$0.197418\pi$
$840$		0			0
$841$	−27.2472	−	9.91717i	−0.939559	−	0.341971i
$842$		0			0
$843$	−51.1439	+	7.34255i	−1.76149	+	0.252891i
$844$		0			0
$845$	12.4403	+	2.19356i	0.427960	+	0.0754609i
$846$		0			0
$847$	7.51519	+	13.0167i	0.258225	+	0.447259i
$848$		0			0
$849$	1.30672	−	40.8968i	0.0448464	−	1.40357i
$850$		0			0
$851$	−14.7175	+	5.35673i	−0.504510	+	0.183627i
$852$		0			0
$853$	8.89956	+	50.4719i	0.304715	+	1.72813i	0.624842	+	0.780751i	$0.285163\pi$
$853$	8.89956	+	50.4719i	0.304715	+	1.72813i	−0.320127	+	0.947375i	$0.603725\pi$
$854$		0			0
$855$	33.7191	−	1.52177i	1.15317	−	0.0520434i
$856$		0			0
$857$	−3.26971	−	18.5435i	−0.111691	−	0.633433i	−0.988335	−	0.152293i	$-0.951334\pi$
$857$	−3.26971	−	18.5435i	−0.111691	−	0.633433i	0.876644	−	0.481139i	$-0.159777\pi$
$858$		0			0
$859$	−22.7939	+	8.29631i	−0.777719	+	0.283066i	−0.700221	−	0.713926i	$-0.746915\pi$
$859$	−22.7939	+	8.29631i	−0.777719	+	0.283066i	−0.0774977	+	0.996993i	$0.524693\pi$
$860$		0			0
$861$	1.13396	−	35.4899i	0.0386453	−	1.20949i
$862$		0			0
$863$	−9.85277	−	17.0655i	−0.335392	−	0.580916i	0.648168	−	0.761497i	$-0.275535\pi$
$863$	−9.85277	−	17.0655i	−0.335392	−	0.580916i	−0.983560	+	0.180581i	$0.942202\pi$
$864$		0			0
$865$	−37.9223	−	6.68673i	−1.28940	−	0.227356i
$866$		0			0
$867$	−26.0528	+	3.74032i	−0.884801	+	0.127028i
$868$		0			0
$869$	−23.4549	−	8.53689i	−0.795653	−	0.289594i
$870$		0			0
$871$	14.7674	−	12.3913i	0.500374	−	0.419864i
$872$		0			0
$873$	1.59424	+	0.387458i	0.0539567	+	0.0131135i
$874$		0			0
$875$			27.2870i			0.922468i
$876$		0			0
$877$	−16.3863	−	19.5284i	−0.553324	−	0.659426i	0.414795	−	0.909915i	$-0.363853\pi$
$877$	−16.3863	−	19.5284i	−0.553324	−	0.659426i	−0.968120	+	0.250488i	$0.919409\pi$
$878$		0			0
$879$	5.00690	+	15.2556i	0.168879	+	0.514557i
$880$		0			0
$881$	26.6755	+	15.4011i	0.898719	+	0.518876i	0.876784	−	0.480884i	$-0.159684\pi$
$881$	26.6755	+	15.4011i	0.898719	+	0.518876i	0.0219346	+	0.999759i	$0.493017\pi$
$882$		0			0
$883$	1.74964	−	9.92270i	0.0588801	−	0.333926i	−0.941111	−	0.338097i	$-0.890217\pi$
$883$	1.74964	−	9.92270i	0.0588801	−	0.333926i	0.999991	+	0.00417162i	$0.00132787\pi$
$884$		0			0
$885$	−36.8857	−	14.7757i	−1.23990	−	0.496679i
$886$		0			0
$887$	−14.6182	−	12.2661i	−0.490831	−	0.411856i	0.363493	−	0.931597i	$-0.381584\pi$
$887$	−14.6182	−	12.2661i	−0.490831	−	0.411856i	−0.854324	+	0.519741i	$0.826028\pi$
$888$		0			0
$889$	8.49015	+	23.3265i	0.284751	+	0.782346i
$890$		0			0
$891$	21.4881	+	6.70114i	0.719878	+	0.224497i
$892$		0			0
$893$	16.1444	+	22.0229i	0.540253	+	0.736969i
$894$		0			0
$895$	−0.495516	+	0.0873729i	−0.0165633	+	0.00292055i
$896$		0			0
$897$	23.7523	+	14.7443i	0.793065	+	0.492297i
$898$		0			0
$899$	38.9562	−	46.4261i	1.29926	−	1.54840i
$900$		0			0
$901$	−4.28939	+	2.47648i	−0.142900	+	0.0825035i
$902$		0			0
$903$	60.4576	−	32.3762i	2.01190	−	1.07741i
$904$		0			0
$905$	9.18019	−	15.9006i	0.305160	−	0.528552i
$906$		0			0
$907$	−1.42779	+	3.92281i	−0.0474089	+	0.130255i	−0.961137	−	0.276070i	$-0.910968\pi$
$907$	−1.42779	+	3.92281i	−0.0474089	+	0.130255i	0.913729	+	0.406325i	$0.133190\pi$
$908$		0			0
$909$	31.6347	−	15.6622i	1.04926	−	0.519484i
$910$		0			0
$911$	−32.6294			−1.08106			−0.540530	−	0.841325i	$-0.681776\pi$
$911$	−32.6294			−1.08106			−0.540530	+	0.841325i	$0.681776\pi$
$912$		0			0
$913$	−35.6098			−1.17851
$914$		0			0
$915$	0.130018	−	0.620735i	0.00429827	−	0.0205209i
$916$		0			0
$917$	4.87645	−	13.3979i	0.161034	−	0.442439i
$918$		0			0
$919$	11.5230	−	19.9584i	0.380108	−	0.658367i	−0.610969	−	0.791654i	$-0.709220\pi$
$919$	11.5230	−	19.9584i	0.380108	−	0.658367i	0.991077	+	0.133287i	$0.0425534\pi$
$920$		0			0
$921$	−2.24413	−	4.19057i	−0.0739467	−	0.138084i
$922$		0			0
$923$	−33.4989	+	19.3406i	−1.10263	+	0.636603i
$924$		0			0
$925$	4.38655	−	5.22769i	0.144229	−	0.171885i
$926$		0			0
$927$	−23.3267	+	2.59172i	−0.766150	+	0.0851232i
$928$		0			0
$929$	−26.6622	+	4.70127i	−0.874760	+	0.154244i	−0.592962	−	0.805230i	$-0.702042\pi$
$929$	−26.6622	+	4.70127i	−0.874760	+	0.154244i	−0.281798	+	0.959474i	$0.590931\pi$
$930$		0			0
$931$	−3.14389	+	12.8424i	−0.103037	+	0.420891i
$932$		0			0
$933$	−29.5502	−	26.4489i	−0.967431	−	0.865897i
$934$		0			0
$935$	2.96564	+	8.14803i	0.0969868	+	0.266469i
$936$		0			0
$937$	29.6774	+	24.9023i	0.969518	+	0.813523i	0.982475	−	0.186393i	$-0.0596799\pi$
$937$	29.6774	+	24.9023i	0.969518	+	0.813523i	−0.0129567	+	0.999916i	$0.504124\pi$
$938$		0			0
$939$	−8.65101	+	21.5962i	−0.282315	+	0.704765i
$940$		0			0
$941$	−3.32233	+	18.8419i	−0.108305	+	0.614227i	0.881544	+	0.472102i	$0.156505\pi$
$941$	−3.32233	+	18.8419i	−0.108305	+	0.614227i	−0.989849	+	0.142125i	$0.954607\pi$
$942$		0			0
$943$	21.3867	+	12.3476i	0.696448	+	0.402094i
$944$		0			0
$945$	3.34047	+	42.3522i	0.108666	+	1.37772i
$946$		0			0
$947$	26.2400	+	31.2716i	0.852684	+	1.01619i	0.999634	+	0.0270453i	$0.00860982\pi$
$947$	26.2400	+	31.2716i	0.852684	+	1.01619i	−0.146950	+	0.989144i	$0.546946\pi$
$948$		0			0
$949$			9.25892i			0.300557i
$950$		0			0
$951$	22.2335	+	28.2843i	0.720971	+	0.917181i
$952$		0			0
$953$	−28.5318	+	23.9410i	−0.924235	+	0.775525i	−0.974773	−	0.223197i	$-0.928351\pi$
$953$	−28.5318	+	23.9410i	−0.924235	+	0.775525i	0.0505382	+	0.998722i	$0.483906\pi$
$954$		0			0
$955$	27.2824	+	9.92997i	0.882837	+	0.321326i
$956$		0			0
$957$	4.68804	+	32.6541i	0.151543	+	1.05556i
$958$		0			0
$959$	−24.5400	−	4.32707i	−0.792438	−	0.139728i
$960$		0			0
$961$	16.1658	+	28.0000i	0.521477	+	0.903225i
$962$		0			0
$963$	−13.6753	+	10.0602i	−0.440680	+	0.324184i
$964$		0			0
$965$	39.1169	−	14.2374i	1.25922	−	0.458318i
$966$		0			0
$967$	−9.88547	−	56.0633i	−0.317895	−	1.80287i	−0.555506	−	0.831513i	$-0.687475\pi$
$967$	−9.88547	−	56.0633i	−0.317895	−	1.80287i	0.237611	−	0.971361i	$-0.423636\pi$
$968$		0			0
$969$	−7.09698	−	7.24362i	−0.227988	−	0.232699i
$970$		0			0
$971$	7.41064	+	42.0279i	0.237819	+	1.34874i	0.836595	+	0.547822i	$0.184543\pi$
$971$	7.41064	+	42.0279i	0.237819	+	1.34874i	−0.598776	+	0.800916i	$0.704346\pi$
$972$		0			0
$973$	22.4111	−	8.15697i	0.718466	−	0.261500i
$974$		0			0
$975$	−12.1750	−	0.389010i	−0.389911	−	0.0124583i
$976$		0			0
$977$	−18.1173	−	31.3801i	−0.579623	−	1.00394i	−0.995522	−	0.0945264i	$-0.969866\pi$
$977$	−18.1173	−	31.3801i	−0.579623	−	1.00394i	0.415899	−	0.909411i	$-0.363467\pi$
$978$		0			0
$979$	−40.9910	−	7.22783i	−1.31008	−	0.231002i
$980$		0			0
$981$	34.1839	−	35.8213i	1.09141	−	1.14369i
$982$		0			0
$983$	51.2605	+	18.6573i	1.63496	+	0.595075i	0.986147	−	0.165876i	$-0.0530451\pi$
$983$	51.2605	+	18.6573i	1.63496	+	0.595075i	0.648809	+	0.760951i	$0.275267\pi$
$984$		0			0
$985$	45.2045	−	37.9311i	1.44033	−	1.20858i
$986$		0			0
$987$	−27.0206	+	21.2402i	−0.860076	+	0.676082i
$988$		0			0
$989$			47.6969i			1.51667i
$990$		0			0
$991$	−8.48805	−	10.1157i	−0.269632	−	0.321335i	0.614190	−	0.789158i	$-0.289483\pi$
$991$	−8.48805	−	10.1157i	−0.269632	−	0.321335i	−0.883822	+	0.467823i	$0.845038\pi$
$992$		0			0
$993$	−14.8097	+	4.86056i	−0.469971	+	0.154245i
$994$		0			0
$995$	−0.746352	−	0.430907i	−0.0236610	−	0.0136607i
$996$		0			0
$997$	−2.70472	+	15.3392i	−0.0856593	+	0.485798i	0.911553	+	0.411182i	$0.134884\pi$
$997$	−2.70472	+	15.3392i	−0.0856593	+	0.485798i	−0.997212	+	0.0746156i	$0.976227\pi$
$998$		0			0
$999$	−12.3826	+	17.3660i	−0.391768	+	0.549437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.c.257.3		18
3.2	odd	2		912.2.cc.d.257.2		18
4.3	odd	2		114.2.l.b.29.1	yes	18
12.11	even	2		114.2.l.a.29.2	✓	18
19.2	odd	18		912.2.cc.d.401.2		18
57.2	even	18	inner	912.2.cc.c.401.3		18
76.59	even	18		114.2.l.a.59.2	yes	18
228.59	odd	18		114.2.l.b.59.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.2	✓	18	12.11	even	2
114.2.l.a.59.2	yes	18	76.59	even	18
114.2.l.b.29.1	yes	18	4.3	odd	2
114.2.l.b.59.1	yes	18	228.59	odd	18
912.2.cc.c.257.3		18	1.1	even	1	trivial
912.2.cc.c.401.3		18	57.2	even	18	inner
912.2.cc.d.257.2		18	3.2	odd	2
912.2.cc.d.401.2		18	19.2	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69526 + 0.355087i) q^{3} +(-0.882820 + 2.42553i) q^{5} +(1.58376 - 2.74316i) q^{7} +(2.74783 + 1.20393i) q^{9} +(2.16590 - 1.25049i) q^{11} +(2.71907 - 3.24046i) q^{13} +(-2.35788 + 3.79843i) q^{15} +(1.32278 - 0.233243i) q^{17} +(-3.14841 - 3.01455i) q^{19} +(3.65896 - 4.08800i) q^{21} +(1.30503 + 3.58554i) q^{23} +(-1.27359 - 1.06867i) q^{25} +(4.23078 + 3.01670i) q^{27} +(-1.32242 + 7.49981i) q^{29} +(-6.89193 - 3.97906i) q^{31} +(4.11581 - 1.35082i) q^{33} +(5.25543 + 6.26318i) q^{35} +4.10469i q^{37} +(5.76019 - 4.52793i) q^{39} +(4.95792 - 4.16019i) q^{41} +(11.7465 + 4.27537i) q^{43} +(-5.34601 + 5.60207i) q^{45} +(-6.16940 - 1.08783i) q^{47} +(-1.51662 - 2.62686i) q^{49} +(2.32529 + 0.0742967i) q^{51} +(-3.46508 + 1.26118i) q^{53} +(1.12098 + 6.35742i) q^{55} +(-4.26694 - 6.22842i) q^{57} +(1.54335 + 8.75275i) q^{59} +(-0.133301 + 0.0485177i) q^{61} +(7.65449 - 5.63098i) q^{63} +(5.45938 + 9.45593i) q^{65} +(4.48795 + 0.791347i) q^{67} +(0.939187 + 6.54182i) q^{69} +(-8.59275 - 3.12750i) q^{71} +(-1.67672 + 1.40694i) q^{73} +(-1.77960 - 2.26391i) q^{75} -7.92190i q^{77} +(-6.41515 - 7.64528i) q^{79} +(6.10110 + 6.61639i) q^{81} +(-12.3308 - 7.11920i) q^{83} +(-0.602044 + 3.41436i) q^{85} +(-4.90493 + 12.2446i) q^{87} +(-12.7492 - 10.6978i) q^{89} +(-4.58274 - 12.5910i) q^{91} +(-10.2707 - 9.19278i) q^{93} +(10.0914 - 4.97524i) q^{95} +(0.538573 - 0.0949649i) q^{97} +(7.45703 - 0.828515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51}+ \cdots + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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