LMFDB - Embedded newform 912.2.cc.d.257.2

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 = [18,0,0,0,0,0,0,0,0,0,0,0,-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			257.2
Root			$1.47158 + 0.913487i$ of defining polynomial
Character	$\chi$	$=$	912.257
Dual form			912.2.cc.d.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0553136 + 1.73117i) q^{3} +(0.882820 - 2.42553i) q^{5} +(1.58376 - 2.74316i) q^{7} +(-2.99388 + 0.191514i) q^{9} +(-2.16590 + 1.25049i) q^{11} +(2.71907 - 3.24046i) q^{13} +(4.24783 + 1.39414i) q^{15} +(-1.32278 + 0.233243i) q^{17} +(-3.14841 - 3.01455i) q^{19} +(4.83647 + 2.59003i) q^{21} +(-1.30503 - 3.58554i) q^{23} +(-1.27359 - 1.06867i) q^{25} +(-0.497145 - 5.17232i) q^{27} +(1.32242 - 7.49981i) q^{29} +(-6.89193 - 3.97906i) q^{31} +(-2.28460 - 3.68037i) q^{33} +(-5.25543 - 6.26318i) q^{35} +4.10469i q^{37} +(5.76019 + 4.52793i) q^{39} +(-4.95792 + 4.16019i) q^{41} +(11.7465 + 4.27537i) q^{43} +(-2.17853 + 7.43081i) q^{45} +(6.16940 + 1.08783i) q^{47} +(-1.51662 - 2.62686i) q^{49} +(-0.476950 - 2.27706i) q^{51} +(3.46508 - 1.26118i) q^{53} +(1.12098 + 6.35742i) q^{55} +(5.04455 - 5.61716i) q^{57} +(-1.54335 - 8.75275i) q^{59} +(-0.133301 + 0.0485177i) q^{61} +(-4.21625 + 8.51601i) q^{63} +(-5.45938 - 9.45593i) q^{65} +(4.48795 + 0.791347i) q^{67} +(6.13498 - 2.45755i) q^{69} +(8.59275 + 3.12750i) q^{71} +(-1.67672 + 1.40694i) q^{73} +(1.77960 - 2.26391i) q^{75} +7.92190i q^{77} +(-6.41515 - 7.64528i) q^{79} +(8.92664 - 1.14674i) q^{81} +(12.3308 + 7.11920i) q^{83} +(-0.602044 + 3.41436i) q^{85} +(13.0566 + 1.87449i) q^{87} +(12.7492 + 10.6978i) q^{89} +(-4.58274 - 12.5910i) q^{91} +(6.50720 - 12.1512i) q^{93} +(-10.0914 + 4.97524i) q^{95} +(0.538573 - 0.0949649i) q^{97} +(6.24498 - 4.15861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * 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
$3$	0.0553136	+	1.73117i	0.0319353	+	0.999490i
$3$	0.0553136	+	1.73117i	0.0319353	+	0.999490i
$4$		0			0
$5$	0.882820	−	2.42553i	0.394809	−	1.08473i	−0.569970	−	0.821666i	$-0.693045\pi$
$5$	0.882820	−	2.42553i	0.394809	−	1.08473i	0.964779	−	0.263063i	$-0.0847327\pi$
$6$		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
$9$	−2.99388	+	0.191514i	−0.997960	+	0.0638380i
$10$		0			0
$11$	−2.16590	+	1.25049i	−0.653045	+	0.377036i	−0.789622	−	0.613594i	$-0.789723\pi$
$11$	−2.16590	+	1.25049i	−0.653045	+	0.377036i	0.136577	+	0.990629i	$0.456390\pi$
$12$		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
$15$	4.24783	+	1.39414i	1.09678	+	0.359966i
$16$		0			0
$17$	−1.32278	+	0.233243i	−0.320822	+	0.0565696i	−0.331740	−	0.943371i	$-0.607636\pi$
$17$	−1.32278	+	0.233243i	−0.320822	+	0.0565696i	0.0109180	+	0.999940i	$0.496525\pi$
$18$		0			0
$19$	−3.14841	−	3.01455i	−0.722294	−	0.691586i
$19$	−3.14841	−	3.01455i	−0.722294	−	0.691586i
$20$		0			0
$21$	4.83647	+	2.59003i	1.05541	+	0.565190i
$22$		0			0
$23$	−1.30503	−	3.58554i	−0.272117	−	0.747636i	−0.998197	−	0.0600255i	$-0.980882\pi$
$23$	−1.30503	−	3.58554i	−0.272117	−	0.747636i	0.726080	−	0.687611i	$-0.241340\pi$
$24$		0			0
$25$	−1.27359	−	1.06867i	−0.254718	−	0.213734i
$26$		0			0
$27$	−0.497145	−	5.17232i	−0.0956757	−	0.995413i
$28$		0			0
$29$	1.32242	−	7.49981i	0.245567	−	1.39268i	−0.573606	−	0.819132i	$-0.694456\pi$
$29$	1.32242	−	7.49981i	0.245567	−	1.39268i	0.819172	−	0.573547i	$-0.194433\pi$
$30$		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
$33$	−2.28460	−	3.68037i	−0.397699	−	0.640671i
$34$		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	−0.941805	−	0.336158i	$-0.890872\pi$
$41$	−4.95792	+	4.16019i	−0.774297	+	0.649712i	0.167509	+	0.985871i	$0.446428\pi$
$42$		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
$45$	−2.17853	+	7.43081i	−0.324757	+	1.10772i
$46$		0			0
$47$	6.16940	+	1.08783i	0.899899	+	0.158676i	0.604414	−	0.796671i	$-0.293407\pi$
$47$	6.16940	+	1.08783i	0.899899	+	0.158676i	0.295486	+	0.955347i	$0.404519\pi$
$48$		0			0
$49$	−1.51662	−	2.62686i	−0.216660	−	0.375266i
$50$		0			0
$51$	−0.476950	−	2.27706i	−0.0667863	−	0.318852i
$52$		0			0
$53$	3.46508	−	1.26118i	0.475965	−	0.173237i	−0.0928877	−	0.995677i	$-0.529610\pi$
$53$	3.46508	−	1.26118i	0.475965	−	0.173237i	0.568853	+	0.822440i	$0.307388\pi$
$54$		0			0
$55$	1.12098	+	6.35742i	0.151153	+	0.857234i
$56$		0			0
$57$	5.04455	−	5.61716i	0.668167	−	0.744011i
$58$		0			0
$59$	−1.54335	−	8.75275i	−0.200927	−	1.13951i	−0.903722	−	0.428119i	$-0.859176\pi$
$59$	−1.54335	−	8.75275i	−0.200927	−	1.13951i	0.702796	−	0.711392i	$-0.251935\pi$
$60$		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
$63$	−4.21625	+	8.51601i	−0.531197	+	1.07292i
$64$		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
$69$	6.13498	−	2.45755i	0.738565	−	0.295855i
$70$		0			0
$71$	8.59275	+	3.12750i	1.01977	+	0.371166i	0.797178	−	0.603745i	$-0.206325\pi$
$71$	8.59275	+	3.12750i	1.01977	+	0.371166i	0.222594	+	0.974911i	$0.428548\pi$
$72$		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
$81$	8.92664	−	1.14674i	0.991849	−	0.127416i
$82$		0			0
$83$	12.3308	+	7.11920i	1.35348	+	0.781433i	0.988735	−	0.149673i	$-0.0478222\pi$
$83$	12.3308	+	7.11920i	1.35348	+	0.781433i	0.364747	+	0.931107i	$0.381156\pi$
$84$		0			0
$85$	−0.602044	+	3.41436i	−0.0653008	+	0.370339i
$86$		0			0
$87$	13.0566	+	1.87449i	1.39981	+	0.200966i
$88$		0			0
$89$	12.7492	+	10.6978i	1.35141	+	1.13397i	0.978533	+	0.206089i	$0.0660737\pi$
$89$	12.7492	+	10.6978i	1.35141	+	1.13397i	0.372879	+	0.927880i	$0.378371\pi$
$90$		0			0
$91$	−4.58274	−	12.5910i	−0.480402	−	1.31989i
$92$		0			0
$93$	6.50720	−	12.1512i	0.674765	−	1.26002i
$94$		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
$99$	6.24498	−	4.15861i	0.627644	−	0.417956i
$100$		0			0
$101$	−7.56338	+	9.01368i	−0.752584	+	0.896895i	−0.997355	−	0.0726860i	$-0.976843\pi$
$101$	−7.56338	+	9.01368i	−0.752584	+	0.896895i	0.244771	+	0.969581i	$0.421287\pi$
$102$		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
$105$	10.5519	−	9.44447i	1.02976	−	0.921686i
$106$		0			0
$107$	2.82951	−	4.90085i	0.273539	−	0.473783i	−0.696227	−	0.717822i	$-0.745139\pi$
$107$	2.82951	−	4.90085i	0.273539	−	0.473783i	0.969765	+	0.244039i	$0.0784725\pi$
$108$		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
$111$	−7.10590	+	0.227045i	−0.674462	+	0.0215502i
$112$		0			0
$113$	−5.15697			−0.485127			−0.242564	−	0.970136i	$-0.577988\pi$
$113$	−5.15697			−0.485127			−0.242564	+	0.970136i	$0.577988\pi$
$114$		0			0
$115$	−9.84893			−0.918417
$116$		0			0
$117$	−7.51998	+	10.2223i	−0.695223	+	0.945052i
$118$		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
$123$	−7.47622	−	8.35287i	−0.674108	−	0.753153i
$124$		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
$129$	−6.75164	+	20.5716i	−0.594448	+	1.81123i
$130$		0			0
$131$	−4.43285	+	0.781631i	−0.387300	+	0.0682914i	−0.363908	−	0.931435i	$-0.618558\pi$
$131$	−4.43285	+	0.781631i	−0.387300	+	0.0682914i	−0.0233919	+	0.999726i	$0.507447\pi$
$132$		0			0
$133$	−13.2557	+	3.86224i	−1.14942	+	0.334898i
$134$		0			0
$135$	−12.9845	−	3.36038i	−1.11753	−	0.289216i
$136$		0			0
$137$	2.69063	+	7.39245i	0.229876	+	0.631580i	0.999980	−	0.00633905i	$-0.00201780\pi$
$137$	2.69063	+	7.39245i	0.229876	+	0.631580i	−0.770104	+	0.637919i	$0.779796\pi$
$138$		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
$141$	−1.54197	+	10.7404i	−0.129857	+	0.904507i
$142$		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
$147$	4.46365	−	2.77082i	0.368156	−	0.228534i
$148$		0			0
$149$	−8.79633	−	10.4831i	−0.720624	−	0.858806i	0.274068	−	0.961710i	$-0.411631\pi$
$149$	−8.79633	−	10.4831i	−0.720624	−	0.858806i	−0.994691	+	0.102905i	$0.967186\pi$
$150$		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
$159$	2.37499	+	5.92887i	0.188349	+	0.470190i
$160$		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
$165$	−10.9437	+	2.29226i	−0.851969	+	0.178452i
$166$		0			0
$167$	−2.20429	+	0.802294i	−0.170573	+	0.0620834i	−0.425895	−	0.904773i	$-0.640041\pi$
$167$	−2.20429	+	0.802294i	−0.170573	+	0.0620834i	0.255322	+	0.966856i	$0.417818\pi$
$168$		0			0
$169$	−0.849826	−	4.81960i	−0.0653712	−	0.370739i
$170$		0			0
$171$	10.0033	+	8.42225i	0.764970	+	0.644066i
$172$		0			0
$173$	−2.59056	−	14.6918i	−0.196956	−	1.11700i	−0.909605	−	0.415474i	$-0.863616\pi$
$173$	−2.59056	−	14.6918i	−0.196956	−	1.11700i	0.712649	−	0.701521i	$-0.247495\pi$
$174$		0			0
$175$	−4.94860	+	1.80114i	−0.374079	+	0.136154i
$176$		0			0
$177$	15.0671	−	3.15594i	1.13251	−	0.237215i
$178$		0			0
$179$	−0.0974666	−	0.168817i	−0.00728500	−	0.0126180i	0.862360	−	0.506296i	$-0.168986\pi$
$179$	−0.0974666	−	0.168817i	−0.00728500	−	0.0126180i	−0.869645	+	0.493678i	$0.835652\pi$
$180$		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
$183$	−0.0913657	−	0.228083i	−0.00675395	−	0.0168604i
$184$		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	$0.133404\pi$
$191$			11.2480i			0.813878i	−0.913455	+	0.406939i	$0.866596\pi$
$192$		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
$195$	16.0678	−	9.97415i	1.15064	−	0.714263i
$196$		0			0
$197$	19.7987	+	11.4308i	1.41060	+	0.814411i	0.995445	−	0.0953383i	$-0.0303933\pi$
$197$	19.7987	+	11.4308i	1.41060	+	0.814411i	0.415157	+	0.909750i	$0.363727\pi$
$198$		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
$201$	−1.12171	+	7.81317i	−0.0791193	+	0.551098i
$202$		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
$207$	4.59378	+	10.4847i	0.319290	+	0.728740i
$208$		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
$213$	−4.93894	+	15.0485i	−0.338410	+	1.03110i
$214$		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
$219$	−2.52839	−	2.82486i	−0.170853	−	0.190887i
$220$		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
$225$	4.01764	+	2.95556i	0.267843	+	0.197037i
$226$		0			0
$227$	20.0547			1.33108			0.665539	−	0.746363i	$-0.268202\pi$
$227$	20.0547			1.33108			0.665539	+	0.746363i	$0.268202\pi$
$228$		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
$231$	−13.7141	+	0.438189i	−0.902324	+	0.0288307i
$232$		0			0
$233$	2.12137	−	5.82843i	0.138976	−	0.381833i	−0.850606	−	0.525803i	$-0.823765\pi$
$233$	2.12137	−	5.82843i	0.138976	−	0.381833i	0.989582	+	0.143970i	$0.0459870\pi$
$234$		0			0
$235$	8.08503	−	14.0037i	0.527409	−	0.913500i
$236$		0			0
$237$	12.8804	−	11.5286i	0.836672	−	0.748862i
$238$		0			0
$239$	−0.498666	+	0.287905i	−0.0322560	+	0.0186230i	−0.516041	−	0.856564i	$-0.672595\pi$
$239$	−0.498666	+	0.287905i	−0.0322560	+	0.0186230i	0.483785	+	0.875187i	$0.339262\pi$
$240$		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
$243$	2.47897	+	15.3901i	0.159026	+	0.987274i
$244$		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
$249$	−11.6425	+	21.7405i	−0.737811	+	1.37775i
$250$		0			0
$251$	2.05161	+	5.63675i	0.129496	+	0.355789i	0.987449	−	0.157941i	$-0.0504856\pi$
$251$	2.05161	+	5.63675i	0.129496	+	0.355789i	−0.857952	+	0.513730i	$0.828263\pi$
$252$		0			0
$253$	7.31023	+	6.13401i	0.459590	+	0.385642i
$254$		0			0
$255$	−5.94413	−	0.853378i	−0.372236	−	0.0534406i
$256$		0			0
$257$	−3.23144	+	18.3264i	−0.201572	+	1.14317i	0.701172	+	0.712992i	$0.252660\pi$
$257$	−3.23144	+	18.3264i	−0.201572	+	1.14317i	−0.902744	+	0.430178i	$0.858451\pi$
$258$		0			0
$259$	11.2598	+	6.50086i	0.699651	+	0.403944i
$260$		0			0
$261$	−2.52284	+	22.7068i	−0.156160	+	1.40551i
$262$		0			0
$263$	−1.37946	−	1.64398i	−0.0850614	−	0.101372i	0.721835	−	0.692065i	$-0.243299\pi$
$263$	−1.37946	−	1.64398i	−0.0850614	−	0.101372i	−0.806896	+	0.590693i	$0.798854\pi$
$264$		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	$0.569220\pi$
$269$	−19.9247	+	16.7188i	−1.21483	+	1.01936i	−0.999079	+	0.0429154i	$0.986335\pi$
$270$		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
$273$	21.5436	−	8.62995i	1.30388	−	0.522308i
$274$		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
$279$	21.3957	+	10.5929i	1.28092	+	0.634182i
$280$		0			0
$281$	28.0317	−	10.2027i	1.67223	−	0.608642i	0.680017	−	0.733196i	$-0.261972\pi$
$281$	28.0317	−	10.2027i	1.67223	−	0.608642i	0.992213	+	0.124555i	$0.0397502\pi$
$282$		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
$285$	−9.17116	−	17.1946i	−0.543252	−	1.01852i
$286$		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
$291$	0.194191	+	0.927107i	0.0113837	+	0.0543480i
$292$		0			0
$293$	−4.63502	−	8.02810i	−0.270781	−	0.469006i	0.698281	−	0.715824i	$-0.253949\pi$
$293$	−4.63502	−	8.02810i	−0.270781	−	0.469006i	−0.969062	+	0.246817i	$0.920615\pi$
$294$		0			0
$295$	−22.5925	−	3.98367i	−1.31539	−	0.231938i
$296$		0			0
$297$	7.54468	+	10.5811i	0.437787	+	0.613976i
$298$		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
$309$	−7.14658	−	11.5128i	−0.406555	−	0.654938i
$310$		0			0
$311$	19.8290	+	11.4483i	1.12440	+	0.649172i	0.942520	−	0.334148i	$-0.108449\pi$
$311$	19.8290	+	11.4483i	1.12440	+	0.649172i	0.181879	+	0.983321i	$0.441782\pi$
$312$		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
$315$	16.9336	+	17.7447i	0.954102	+	0.999802i
$316$		0			0
$317$	−15.9117	−	13.3515i	−0.893689	−	0.749894i	0.0752579	−	0.997164i	$-0.476022\pi$
$317$	−15.9117	−	13.3515i	−0.893689	−	0.749894i	−0.968947	+	0.247270i	$0.920466\pi$
$318$		0			0
$319$	6.51417	+	17.8975i	0.364723	+	1.00207i
$320$		0			0
$321$	8.64070	+	4.62727i	0.482277	+	0.258269i
$322$		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
$327$	27.1618	+	8.91456i	1.50205	+	0.492977i
$328$		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
$333$	−0.786106	−	12.2889i	−0.0430783	−	0.673430i
$334$		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
$339$	−0.285251	−	8.92758i	−0.0154927	−	0.484880i
$340$		0			0
$341$	19.9030			1.07781
$342$		0			0
$343$	12.5648			0.678437
$344$		0			0
$345$	−0.544779	−	17.0501i	−0.0293299	−	0.917949i
$346$		0			0
$347$	4.73541	−	13.0104i	0.254210	−	0.698436i	−0.745288	−	0.666743i	$-0.767688\pi$
$347$	4.73541	−	13.0104i	0.254210	−	0.698436i	0.999498	−	0.0316932i	$-0.0100899\pi$
$348$		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
$351$	−18.1125	−	12.4529i	−0.966772	−	0.664687i
$352$		0			0
$353$	−19.7460	+	11.4004i	−1.05098	+	0.606781i	−0.922922	−	0.384987i	$-0.874206\pi$
$353$	−19.7460	+	11.4004i	−1.05098	+	0.606781i	−0.128053	+	0.991767i	$0.540873\pi$
$354$		0			0
$355$	15.1717	−	18.0809i	0.805230	−	0.959636i
$356$		0			0
$357$	−7.00172	−	2.29798i	−0.370570	−	0.121622i
$358$		0			0
$359$	7.31056	−	1.28905i	0.385837	−	0.0680334i	0.0226346	−	0.999744i	$-0.492795\pi$
$359$	7.31056	−	1.28905i	0.385837	−	0.0680334i	0.363202	+	0.931710i	$0.381683\pi$
$360$		0			0
$361$	0.824917	+	18.9821i	0.0434167	+	0.999057i
$362$		0			0
$363$	−7.24532	−	3.88001i	−0.380281	−	0.203648i
$364$		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
$369$	14.0467	−	13.4046i	0.731241	−	0.697817i
$370$		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
$375$	7.86931	+	12.6770i	0.406370	+	0.654640i
$376$		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	−0.752750	−	0.658307i	$-0.771273\pi$
$383$	−4.60213	+	3.86165i	−0.235158	+	0.197321i	0.517592	+	0.855628i	$0.326829\pi$
$384$		0			0
$385$	19.2148	+	6.99361i	0.979276	+	0.356427i
$386$		0			0
$387$	−35.9863	−	10.5503i	−1.82929	−	0.536303i
$388$		0			0
$389$	20.4701	+	3.60942i	1.03787	+	0.183005i	0.666520	−	0.745487i	$-0.267783\pi$
$389$	20.4701	+	3.60942i	1.03787	+	0.183005i	0.371353	+	0.928492i	$0.378894\pi$
$390$		0			0
$391$	2.56257	+	4.43850i	0.129595	+	0.224465i
$392$		0			0
$393$	−1.59833	−	7.63076i	−0.0806251	−	0.384921i
$394$		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
$399$	−7.41940	−	22.7343i	−0.371435	−	1.13814i
$400$		0			0
$401$	−1.59795	−	9.06241i	−0.0797977	−	0.452555i	−0.998358	−	0.0572753i	$-0.981759\pi$
$401$	−1.59795	−	9.06241i	−0.0797977	−	0.452555i	0.918561	−	0.395280i	$-0.129352\pi$
$402$		0			0
$403$	−31.6336	+	11.5137i	−1.57578	+	0.573538i
$404$		0			0
$405$	5.09917	−	22.6642i	0.253380	−	1.12619i
$406$		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
$411$	−12.6487	+	5.06684i	−0.623916	+	0.249929i
$412$		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	$-0.833744\pi$
$419$		−	20.4238i		−	0.997766i	0.866669	−	0.498883i	$-0.166256\pi$
$420$		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
$423$	−18.6788	−	2.07531i	−0.908193	−	0.100905i
$424$		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
$429$	−18.1381	−	2.60403i	−0.875717	−	0.125724i
$430$		0			0
$431$	−7.15165	−	6.00095i	−0.344483	−	0.289055i	0.454087	−	0.890957i	$-0.349965\pi$
$431$	−7.15165	−	6.00095i	−0.344483	−	0.289055i	−0.798570	+	0.601902i	$0.794410\pi$
$432$		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
$435$	16.0732	−	30.0142i	0.770652	−	1.43907i
$436$		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
$441$	5.04366	+	7.57406i	0.240174	+	0.360670i
$442$		0			0
$443$	17.0745	−	20.3486i	0.811235	−	0.966792i	−0.188649	−	0.982045i	$-0.560411\pi$
$443$	17.0745	−	20.3486i	0.811235	−	0.966792i	0.999884	+	0.0152527i	$0.00485526\pi$
$444$		0			0
$445$	37.2032	−	21.4793i	1.76360	−	1.01821i
$446$		0			0
$447$	17.6614	−	15.8078i	0.835354	−	0.747682i
$448$		0			0
$449$	5.66925	−	9.81944i	0.267549	−	0.463408i	−0.700680	−	0.713476i	$-0.747120\pi$
$449$	5.66925	−	9.81944i	0.267549	−	0.463408i	0.968228	+	0.250068i	$0.0804531\pi$
$450$		0			0
$451$	5.53612	−	15.2104i	0.260686	−	0.716229i
$452$		0			0
$453$	−14.9513	+	0.477717i	−0.702472	+	0.0224451i
$454$		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
$459$	1.86402	+	6.72590i	0.0870050	+	0.313938i
$460$		0			0
$461$	−9.40832	+	25.8492i	−0.438189	+	1.20392i	0.502480	+	0.864589i	$0.332421\pi$
$461$	−9.40832	+	25.8492i	−0.438189	+	1.20392i	−0.940669	+	0.339326i	$0.889801\pi$
$462$		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
$465$	−23.7283	−	26.5107i	−1.10038	−	1.22940i
$466$		0			0
$467$	−17.7092	+	10.2244i	−0.819486	+	0.473130i	−0.850239	−	0.526397i	$-0.823543\pi$
$467$	−17.7092	+	10.2244i	−0.819486	+	0.473130i	0.0307535	+	0.999527i	$0.490209\pi$
$468$		0			0
$469$	9.27865	−	11.0579i	0.428448	−	0.510605i
$470$		0			0
$471$	1.85530	−	5.65293i	0.0854878	−	0.260473i
$472$		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
$477$	−10.1325	+	4.43945i	−0.463935	+	0.203268i
$478$		0			0
$479$	−3.36367	−	9.24160i	−0.153690	−	0.422259i	0.838822	−	0.544405i	$-0.183245\pi$
$479$	−3.36367	−	9.24160i	−0.153690	−	0.422259i	−0.992512	+	0.122146i	$0.961022\pi$
$480$		0			0
$481$	13.3011	+	11.1609i	0.606477	+	0.508895i
$482$		0			0
$483$	2.97490	−	20.7214i	0.135363	−	0.942857i
$484$		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
$489$	11.2814	−	7.00294i	0.510161	−	0.316684i
$490$		0			0
$491$	18.0754	+	21.5414i	0.815729	+	0.972148i	0.999942	−	0.0107379i	$-0.00341805\pi$
$491$	18.0754	+	21.5414i	0.815729	+	0.972148i	−0.184213	+	0.982886i	$0.558974\pi$
$492$		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
$501$	−1.51083	−	3.77161i	−0.0674990	−	0.168503i
$502$		0			0
$503$	−25.8762	−	4.56267i	−1.15376	−	0.203439i	−0.436144	−	0.899877i	$-0.643656\pi$
$503$	−25.8762	−	4.56267i	−1.15376	−	0.203439i	−0.717618	+	0.696437i	$0.754767\pi$
$504$		0			0
$505$	15.1858	+	26.3026i	0.675761	+	1.17045i
$506$		0			0
$507$	8.29653	−	1.73778i	0.368462	−	0.0771775i
$508$		0			0
$509$	25.0043	−	9.10082i	1.10830	−	0.403387i	0.277928	−	0.960602i	$-0.410352\pi$
$509$	25.0043	−	9.10082i	1.10830	−	0.403387i	0.830368	+	0.557215i	$0.188130\pi$
$510$		0			0
$511$	1.20392	+	6.82777i	0.0532583	+	0.302043i
$512$		0			0
$513$	−14.0270	+	17.7832i	−0.619308	+	0.785148i
$514$		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
$519$	25.2906	−	5.29734i	1.11014	−	0.232528i
$520$		0			0
$521$	10.2977	+	17.8362i	0.451151	+	0.781417i	0.998458	−	0.0555154i	$-0.0176802\pi$
$521$	10.2977	+	17.8362i	0.451151	+	0.781417i	−0.547307	+	0.836932i	$0.684347\pi$
$522$		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
$525$	−3.39180	−	8.46723i	−0.148031	−	0.369540i
$526$		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
$537$	0.286860	−	0.178069i	0.0123789	−	0.00768424i
$538$		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
$543$	1.75083	−	12.1953i	0.0751354	−	0.523349i
$544$		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
$549$	0.389797	−	0.170785i	0.0166361	−	0.00728894i
$550$		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
$555$	−5.72253	+	17.4360i	−0.242908	+	0.740117i
$556$		0			0
$557$	13.8808	−	16.5425i	0.588147	−	0.700927i	−0.387101	−	0.922037i	$-0.626524\pi$
$557$	13.8808	−	16.5425i	0.588147	−	0.700927i	0.975249	+	0.221110i	$0.0709681\pi$
$558$		0			0
$559$	45.7937	−	26.4390i	1.93687	−	1.11825i
$560$		0			0
$561$	3.88046	+	4.33547i	0.163833	+	0.183044i
$562$		0			0
$563$	−13.0149	+	22.5424i	−0.548512	+	0.950051i	0.449865	+	0.893097i	$0.351472\pi$
$563$	−13.0149	+	22.5424i	−0.548512	+	0.950051i	−0.998377	+	0.0569541i	$0.981861\pi$
$564$		0			0
$565$	−4.55268	+	12.5084i	−0.191533	+	0.526231i
$566$		0			0
$567$	10.9920	−	26.3034i	0.461621	−	1.10464i
$568$		0			0
$569$	4.80544			0.201455			0.100727	−	0.994914i	$-0.467883\pi$
$569$	4.80544			0.201455			0.100727	+	0.994914i	$0.467883\pi$
$570$		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
$573$	−19.4722	+	0.622168i	−0.813462	+	0.0259914i
$574$		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
$579$	20.8137	−	18.6293i	0.864987	−	0.774205i
$580$		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
$585$	18.1557	+	27.2644i	0.750645	+	1.12724i
$586$		0			0
$587$	−14.9298	+	2.63253i	−0.616220	+	0.108656i	−0.473041	−	0.881040i	$-0.656844\pi$
$587$	−14.9298	+	2.63253i	−0.616220	+	0.108656i	−0.143180	+	0.989697i	$0.545733\pi$
$588$		0			0
$589$	9.70350	+	33.3038i	0.399826	+	1.37226i
$590$		0			0
$591$	−18.6935	+	34.9072i	−0.768948	+	1.43589i
$592$		0			0
$593$	−0.398860	−	1.09586i	−0.0163792	−	0.0450015i	0.931234	−	0.364423i	$-0.118734\pi$
$593$	−0.398860	−	1.09586i	−0.0163792	−	0.0450015i	−0.947613	+	0.319421i	$0.896511\pi$
$594$		0			0
$595$	8.41264	+	7.05905i	0.344885	+	0.289393i
$596$		0			0
$597$	−0.572431	−	0.0821819i	−0.0234280	−	0.00336348i
$598$		0			0
$599$	4.45202	−	25.2486i	0.181905	−	1.03163i	−0.747964	−	0.663739i	$-0.768968\pi$
$599$	4.45202	−	25.2486i	0.181905	−	1.03163i	0.929868	−	0.367892i	$-0.119921\pi$
$600$		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
$603$	−13.5879	−	1.50969i	−0.553344	−	0.0614794i
$604$		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
$615$	−26.8603	+	10.7597i	−1.08311	+	0.433873i
$616$		0			0
$617$	−24.5040	−	4.32072i	−0.986495	−	0.173946i	−0.342950	−	0.939354i	$-0.611426\pi$
$617$	−24.5040	−	4.32072i	−0.986495	−	0.173946i	−0.643545	+	0.765408i	$0.722537\pi$
$618$		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
$621$	−17.8967	+	8.53255i	−0.718171	+	0.342400i
$622$		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
$627$	−3.90183	+	18.4744i	−0.155824	+	0.737796i
$628$		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
$633$	−0.910797	−	4.34834i	−0.0362009	−	0.172831i
$634$		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
$639$	−26.3246	−	7.71774i	−1.04139	−	0.305309i
$640$		0			0
$641$	8.36361	+	3.04411i	0.330343	+	0.120235i	0.501867	−	0.864945i	$-0.332647\pi$
$641$	8.36361	+	3.04411i	0.330343	+	0.120235i	−0.171524	+	0.985180i	$0.554869\pi$
$642$		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	$-0.950546\pi$
$647$		−	7.87198i		−	0.309479i	0.987955	−	0.154740i	$-0.0494539\pi$
$648$		0			0
$649$	14.2879	+	17.0277i	0.560850	+	0.668395i
$650$		0			0
$651$	−23.0268	−	37.0949i	−0.902490	−	1.45386i
$652$		0			0
$653$	1.40402	+	0.810613i	0.0549437	+	0.0317217i	0.527220	−	0.849729i	$-0.323234\pi$
$653$	1.40402	+	0.810613i	0.0549437	+	0.0317217i	−0.472277	+	0.881450i	$0.656568\pi$
$654$		0			0
$655$	−2.01754	+	11.4420i	−0.0788318	+	0.447077i
$656$		0			0
$657$	4.75046	−	4.53332i	0.185333	−	0.176862i
$658$		0			0
$659$	−9.29693	−	7.80105i	−0.362157	−	0.303886i	0.443493	−	0.896278i	$-0.353739\pi$
$659$	−9.29693	−	7.80105i	−0.362157	−	0.303886i	−0.805650	+	0.592392i	$0.798184\pi$
$660$		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
$663$	−8.67559	−	4.64595i	−0.336932	−	0.180434i
$664$		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
$669$	−10.9847	−	3.60520i	−0.424694	−	0.139385i
$670$		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
$675$	−4.89434	+	7.11870i	−0.188383	+	0.273999i
$676$		0			0
$677$	−0.610403	+	1.05725i	−0.0234597	+	0.0406334i	−0.877517	−	0.479546i	$-0.840801\pi$
$677$	−0.610403	+	1.05725i	−0.0234597	+	0.0406334i	0.854057	+	0.520179i	$0.174135\pi$
$678$		0			0
$679$	0.592469	−	1.62779i	0.0227369	−	0.0624690i
$680$		0			0
$681$	1.10930	+	34.7181i	0.0425084	+	1.33040i
$682$		0			0
$683$	40.7336			1.55863			0.779313	−	0.626635i	$-0.215568\pi$
$683$	40.7336			1.55863			0.779313	+	0.626635i	$0.215568\pi$
$684$		0			0
$685$	20.3059			0.775850
$686$		0			0
$687$	0.913051	+	28.5760i	0.0348351	+	1.09024i
$688$		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
$693$	−1.51716	−	23.7172i	−0.0576320	−	0.900943i
$694$		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
$699$	10.2073	+	3.35006i	0.386077	+	0.126711i
$700$		0			0
$701$	−23.1182	+	4.07636i	−0.873162	+	0.153962i	−0.592233	−	0.805767i	$-0.701754\pi$
$701$	−23.1182	+	4.07636i	−0.873162	+	0.153962i	−0.280929	+	0.959729i	$0.590642\pi$
$702$		0			0
$703$	12.3738	−	12.9232i	0.466687	−	0.487408i
$704$		0			0
$705$	24.6899	+	13.2219i	0.929877	+	0.497967i
$706$		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
$711$	20.6704	+	21.6605i	0.775199	+	0.812330i
$712$		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
$717$	−0.525995	−	0.847349i	−0.0196436	−	0.0316448i
$718$		0			0
$719$	−26.4940	−	31.5743i	−0.988060	−	1.17752i	−0.984115	−	0.177532i	$-0.943189\pi$
$719$	−26.4940	−	31.5743i	−0.988060	−	1.17752i	−0.00394505	−	0.999992i	$-0.501256\pi$
$720$		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
$729$	−26.5057	+	5.14278i	−0.981692	+	0.190474i
$730$		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
$735$	−2.78011	−	13.2728i	−0.102546	−	0.489576i
$736$		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
$741$	−4.48572	−	31.6201i	−0.164787	−	1.16160i
$742$		0			0
$743$	−0.154876	−	0.878343i	−0.00568183	−	0.0322233i	0.981835	−	0.189737i	$-0.0607634\pi$
$743$	−0.154876	−	0.878343i	−0.00568183	−	0.0322233i	−0.987517	+	0.157513i	$0.949652\pi$
$744$		0			0
$745$	−33.1925	+	12.0811i	−1.21608	+	0.442617i
$746$		0			0
$747$	−38.2804	−	18.9525i	−1.40061	−	0.693436i
$748$		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
$753$	−9.64468	+	3.86347i	−0.351472	+	0.140793i
$754$		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	$-0.857209\pi$
$761$		−	23.9282i		−	0.867396i	0.901058	−	0.433698i	$-0.142791\pi$
$762$		0			0
$763$	−33.6048	−	40.0486i	−1.21657	−	1.44986i
$764$		0			0
$765$	1.14855	−	10.3375i	0.0415259	−	0.373753i
$766$		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
$771$	−31.9048	−	4.58047i	−1.14902	−	0.164961i
$772$		0			0
$773$	27.0855	+	22.7275i	0.974199	+	0.817450i	0.983204	−	0.182509i	$-0.0584219\pi$
$773$	27.0855	+	22.7275i	0.974199	+	0.817450i	−0.00900488	+	0.999959i	$0.502866\pi$
$774$		0			0
$775$	4.52520	+	12.4329i	0.162550	+	0.446602i
$776$		0			0
$777$	−10.6313	+	19.8522i	−0.381394	+	0.712194i
$778$		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
$783$	−39.4488	−	3.11147i	−1.40978	−	0.111195i
$784$		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
$789$	2.76970	−	2.47902i	0.0986041	−	0.0882554i
$790$		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
$795$	16.4773	−	0.526477i	0.584390	−	0.0186722i
$796$		0			0
$797$	13.5711			0.480714			0.240357	−	0.970685i	$-0.422735\pi$
$797$	13.5711			0.480714			0.240357	+	0.970685i	$0.422735\pi$
$798$		0			0
$799$	−8.41451			−0.297684
$800$		0			0
$801$	−40.2184	−	29.5864i	−1.42105	−	1.04538i
$802$		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
$807$	−30.0452	−	33.5682i	−1.05764	−	1.18166i
$808$		0			0
$809$	7.06352	−	4.07812i	0.248340	−	0.143379i	−0.370664	−	0.928767i	$-0.620870\pi$
$809$	7.06352	−	4.07812i	0.248340	−	0.143379i	0.619004	+	0.785388i	$0.287536\pi$
$810$		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
$813$	2.66041	−	8.10601i	0.0933046	−	0.284290i
$814$		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
$819$	16.1315	+	36.8182i	0.563681	+	1.28653i
$820$		0			0
$821$	−1.32613	−	3.64350i	−0.0462821	−	0.127159i	0.914398	−	0.404816i	$-0.132664\pi$
$821$	−1.32613	−	3.64350i	−0.0462821	−	0.127159i	−0.960680	+	0.277657i	$0.910442\pi$
$822$		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
$825$	−1.02345	+	7.12878i	−0.0356321	+	0.248192i
$826$		0			0
$827$	−5.27611	+	29.9223i	−0.183468	+	1.04050i	0.744439	+	0.667690i	$0.232717\pi$
$827$	−5.27611	+	29.9223i	−0.183468	+	1.04050i	−0.927908	+	0.372810i	$0.878394\pi$
$828$		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
$831$	2.48962	−	1.54544i	0.0863639	−	0.0536106i
$832$		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	−0.813759	−	0.581203i	$-0.802582\pi$
$839$	−11.0849	+	9.30133i	−0.382693	+	0.321118i	0.431066	+	0.902321i	$0.358138\pi$
$840$		0			0
$841$	−27.2472	−	9.91717i	−0.939559	−	0.341971i
$842$		0			0
$843$	19.2131	+	47.9632i	0.661735	+	1.65194i
$844$		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
$849$	40.0486	−	8.38852i	1.37446	−	0.287893i
$850$		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
$855$	29.2595	−	16.8279i	1.00065	−	0.575502i
$856$		0			0
$857$	3.26971	+	18.5435i	0.111691	+	0.633433i	0.988335	+	0.152293i	$0.0486658\pi$
$857$	3.26971	+	18.5435i	0.111691	+	0.633433i	−0.876644	+	0.481139i	$0.840223\pi$
$858$		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
$861$	−34.7538	+	7.27949i	−1.18441	+	0.248084i
$862$		0			0
$863$	9.85277	+	17.0655i	0.335392	+	0.580916i	0.983560	−	0.180581i	$-0.0577979\pi$
$863$	9.85277	+	17.0655i	0.335392	+	0.580916i	−0.648168	+	0.761497i	$0.724465\pi$
$864$		0			0
$865$	−37.9223	−	6.68673i	−1.28940	−	0.227356i
$866$		0			0
$867$	−9.78721	−	24.4326i	−0.332391	−	0.829774i
$868$		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
$879$	13.6416	−	8.46806i	0.460120	−	0.285621i
$880$		0			0
$881$	−26.6755	−	15.4011i	−0.898719	−	0.518876i	−0.0219346	−	0.999759i	$-0.506983\pi$
$881$	−26.6755	−	15.4011i	−0.898719	−	0.518876i	−0.876784	+	0.480884i	$0.840316\pi$
$882$		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
$885$	5.64673	−	39.3318i	0.189813	−	1.32212i
$886$		0			0
$887$	14.6182	+	12.2661i	0.490831	+	0.411856i	0.854324	−	0.519741i	$-0.173972\pi$
$887$	14.6182	+	12.2661i	0.490831	+	0.411856i	−0.363493	+	0.931597i	$0.618416\pi$
$888$		0			0
$889$	8.49015	+	23.3265i	0.284751	+	0.782346i
$890$		0			0
$891$	−17.9003	+	13.6464i	−0.599682	+	0.457171i
$892$		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
$897$	8.71784	−	26.5624i	0.291080	−	0.886894i
$898$		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
$903$	45.7382	+	51.1014i	1.52207	+	1.70055i
$904$		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
$909$	20.9176	−	28.4344i	0.693793	−	0.943109i
$910$		0			0
$911$	32.6294			1.08106			0.540530	−	0.841325i	$-0.318224\pi$
$911$	32.6294			1.08106			0.540530	+	0.841325i	$0.318224\pi$
$912$		0			0
$913$	−35.6098			−1.17851
$914$		0			0
$915$	−0.633882	+	0.0202535i	−0.0209555	+	0.000669561i
$916$		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
$921$	3.54205	−	3.17031i	0.116715	−	0.104465i
$922$		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
$927$	19.5352	−	13.0087i	0.641621	−	0.427263i
$928$		0			0
$929$	26.6622	−	4.70127i	0.874760	−	0.154244i	0.281798	−	0.959474i	$-0.409069\pi$
$929$	26.6622	−	4.70127i	0.874760	−	0.154244i	0.592962	+	0.805230i	$0.297958\pi$
$930$		0			0
$931$	−3.14389	+	12.8424i	−0.103037	+	0.420891i
$932$		0			0
$933$	−18.7221	+	34.9606i	−0.612933	+	1.14456i
$934$		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
$939$	−23.0284	−	3.30610i	−0.751502	−	0.107891i
$940$		0			0
$941$	3.32233	−	18.8419i	0.108305	−	0.614227i	−0.881544	−	0.472102i	$-0.843495\pi$
$941$	3.32233	−	18.8419i	0.108305	−	0.614227i	0.989849	−	0.142125i	$-0.0453935\pi$
$942$		0			0
$943$	21.3867	+	12.3476i	0.696448	+	0.402094i
$944$		0			0
$945$	−29.7824	+	30.2965i	−0.968823	+	0.985544i
$946$		0			0
$947$	−26.2400	−	31.2716i	−0.852684	−	1.01619i	−0.999634	−	0.0270453i	$-0.991390\pi$
$947$	−26.2400	−	31.2716i	−0.852684	−	1.01619i	0.146950	−	0.989144i	$-0.453054\pi$
$948$		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	−0.0505382	−	0.998722i	$-0.516094\pi$
$953$	28.5318	−	23.9410i	0.924235	−	0.775525i	0.974773	+	0.223197i	$0.0716492\pi$
$954$		0			0
$955$	27.2824	+	9.92997i	0.882837	+	0.321326i
$956$		0			0
$957$	−30.6233	+	12.2671i	−0.989911	+	0.396539i
$958$		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
$963$	−7.53263	+	15.2145i	−0.242735	+	0.490279i
$964$		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
$969$	−5.36269	+	8.60690i	−0.172274	+	0.276493i
$970$		0			0
$971$	−7.41064	−	42.0279i	−0.237819	−	1.34874i	−0.836595	−	0.547822i	$-0.815457\pi$
$971$	−7.41064	−	42.0279i	−0.237819	−	1.34874i	0.598776	−	0.800916i	$-0.295654\pi$
$972$		0			0
$973$	22.4111	−	8.15697i	0.718466	−	0.261500i
$974$		0			0
$975$	−2.49726	−	11.9225i	−0.0799764	−	0.381824i
$976$		0			0
$977$	18.1173	+	31.3801i	0.579623	+	1.00394i	0.995522	+	0.0945264i	$0.0301337\pi$
$977$	18.1173	+	31.3801i	0.579623	+	1.00394i	−0.415899	+	0.909411i	$0.636533\pi$
$978$		0			0
$979$	−40.9910	−	7.22783i	−1.31008	−	0.231002i
$980$		0			0
$981$	−13.9302	+	47.5148i	−0.444757	+	1.51703i
$982$		0			0
$983$	−51.2605	−	18.6573i	−1.63496	−	0.595075i	−0.648809	−	0.760951i	$-0.724733\pi$
$983$	−51.2605	−	18.6573i	−1.63496	−	0.595075i	−0.986147	+	0.165876i	$0.946955\pi$
$984$		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
$993$	−8.22056	−	13.2429i	−0.260872	−	0.420250i
$994$		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
$999$	21.2307	−	2.04063i	0.671711	−	0.0645625i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.0553136 + 1.73117i) q^{3} +(0.882820 - 2.42553i) q^{5} +(1.58376 - 2.74316i) q^{7} +(-2.99388 + 0.191514i) q^{9} +(-2.16590 + 1.25049i) q^{11} +(2.71907 - 3.24046i) q^{13} +(4.24783 + 1.39414i) q^{15} +(-1.32278 + 0.233243i) q^{17} +(-3.14841 - 3.01455i) q^{19} +(4.83647 + 2.59003i) q^{21} +(-1.30503 - 3.58554i) q^{23} +(-1.27359 - 1.06867i) q^{25} +(-0.497145 - 5.17232i) q^{27} +(1.32242 - 7.49981i) q^{29} +(-6.89193 - 3.97906i) q^{31} +(-2.28460 - 3.68037i) q^{33} +(-5.25543 - 6.26318i) q^{35} +4.10469i q^{37} +(5.76019 + 4.52793i) q^{39} +(-4.95792 + 4.16019i) q^{41} +(11.7465 + 4.27537i) q^{43} +(-2.17853 + 7.43081i) q^{45} +(6.16940 + 1.08783i) q^{47} +(-1.51662 - 2.62686i) q^{49} +(-0.476950 - 2.27706i) q^{51} +(3.46508 - 1.26118i) q^{53} +(1.12098 + 6.35742i) q^{55} +(5.04455 - 5.61716i) q^{57} +(-1.54335 - 8.75275i) q^{59} +(-0.133301 + 0.0485177i) q^{61} +(-4.21625 + 8.51601i) q^{63} +(-5.45938 - 9.45593i) q^{65} +(4.48795 + 0.791347i) q^{67} +(6.13498 - 2.45755i) q^{69} +(8.59275 + 3.12750i) q^{71} +(-1.67672 + 1.40694i) q^{73} +(1.77960 - 2.26391i) q^{75} +7.92190i q^{77} +(-6.41515 - 7.64528i) q^{79} +(8.92664 - 1.14674i) q^{81} +(12.3308 + 7.11920i) q^{83} +(-0.602044 + 3.41436i) q^{85} +(13.0566 + 1.87449i) q^{87} +(12.7492 + 10.6978i) q^{89} +(-4.58274 - 12.5910i) q^{91} +(6.50720 - 12.1512i) q^{93} +(-10.0914 + 4.97524i) q^{95} +(0.538573 - 0.0949649i) q^{97} +(6.24498 - 4.15861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more