LMFDB - Embedded newform 756.2.bo.a.169.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.8
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.a.85.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48997 + 0.883169i) q^{3} +(-0.192063 - 1.08924i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.44003 + 2.63179i) q^{9} +O(q^{10})$	\(q+(1.48997 + 0.883169i) q^{3} +(-0.192063 - 1.08924i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.44003 + 2.63179i) q^{9} +(-0.363128 + 2.05940i) q^{11} +(0.435813 + 0.158623i) q^{13} +(0.675817 - 1.79256i) q^{15} +(2.42280 + 4.19641i) q^{17} +(-0.100033 + 0.173262i) q^{19} +(0.573694 + 1.63428i) q^{21} +(0.756139 - 0.634476i) q^{23} +(3.54890 - 1.29169i) q^{25} +(-0.178718 + 5.19308i) q^{27} +(-3.65999 + 1.33213i) q^{29} +(6.93676 - 5.82063i) q^{31} +(-2.35985 + 2.74774i) q^{33} +(0.553023 - 0.957864i) q^{35} +(1.94112 + 3.36212i) q^{37} +(0.509258 + 0.621240i) q^{39} +(1.81516 + 0.660663i) q^{41} +(0.927544 - 5.26036i) q^{43} +(2.59008 - 2.07401i) q^{45} +(-2.52213 - 2.11632i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-0.0962385 + 8.39226i) q^{51} -4.18839 q^{53} +2.31293 q^{55} +(-0.302065 + 0.169809i) q^{57} +(0.461820 + 2.61911i) q^{59} +(-0.396649 - 0.332828i) q^{61} +(-0.588559 + 2.94170i) q^{63} +(0.0890754 - 0.505171i) q^{65} +(-2.70746 - 0.985435i) q^{67} +(1.68697 - 0.277552i) q^{69} +(-6.57991 - 11.3967i) q^{71} +(-3.85105 + 6.67021i) q^{73} +(6.42854 + 1.20969i) q^{75} +(-1.60193 + 1.34418i) q^{77} +(-6.19535 + 2.25492i) q^{79} +(-4.85265 + 7.57970i) q^{81} +(-9.11894 + 3.31902i) q^{83} +(4.10557 - 3.44499i) q^{85} +(-6.62976 - 1.24756i) q^{87} +(-0.185672 + 0.321594i) q^{89} +(0.231891 + 0.401647i) q^{91} +(15.4762 - 2.54624i) q^{93} +(0.207937 + 0.0756828i) q^{95} +(0.500292 - 2.83730i) q^{97} +(-5.94282 + 2.00991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	1.48997	+	0.883169i	0.860235	+	0.509898i
$3$	1.48997	+	0.883169i	0.860235	+	0.509898i
$4$		0			0
$5$	−0.192063	−	1.08924i	−0.0858931	−	0.487124i	−0.997160	−	0.0753084i	$-0.976006\pi$
$5$	−0.192063	−	1.08924i	−0.0858931	−	0.487124i	0.911267	−	0.411816i	$-0.135105\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$		0			0
$9$	1.44003	+	2.63179i	0.480009	+	0.877264i
$10$		0			0
$11$	−0.363128	+	2.05940i	−0.109487	+	0.620932i	0.879846	+	0.475259i	$0.157646\pi$
$11$	−0.363128	+	2.05940i	−0.109487	+	0.620932i	−0.989333	+	0.145673i	$0.953465\pi$
$12$		0			0
$13$	0.435813	+	0.158623i	0.120873	+	0.0439941i	0.401748	−	0.915750i	$-0.368403\pi$
$13$	0.435813	+	0.158623i	0.120873	+	0.0439941i	−0.280876	+	0.959744i	$0.590625\pi$
$14$		0			0
$15$	0.675817	−	1.79256i	0.174495	−	0.462838i
$16$		0			0
$17$	2.42280	+	4.19641i	0.587614	+	1.01778i	0.994544	+	0.104318i	$0.0332661\pi$
$17$	2.42280	+	4.19641i	0.587614	+	1.01778i	−0.406930	+	0.913460i	$0.633401\pi$
$18$		0			0
$19$	−0.100033	+	0.173262i	−0.0229491	+	0.0397490i	−0.877272	−	0.479994i	$-0.840639\pi$
$19$	−0.100033	+	0.173262i	−0.0229491	+	0.0397490i	0.854323	+	0.519743i	$0.173972\pi$
$20$		0			0
$21$	0.573694	+	1.63428i	0.125190	+	0.356629i
$22$		0			0
$23$	0.756139	−	0.634476i	0.157666	−	0.132297i	−0.560542	−	0.828126i	$-0.689407\pi$
$23$	0.756139	−	0.634476i	0.157666	−	0.132297i	0.718208	+	0.695829i	$0.244963\pi$
$24$		0			0
$25$	3.54890	−	1.29169i	0.709780	−	0.258339i
$26$		0			0
$27$	−0.178718	+	5.19308i	−0.0343943	+	0.999408i
$28$		0			0
$29$	−3.65999	+	1.33213i	−0.679642	+	0.247370i	−0.658694	−	0.752411i	$-0.728891\pi$
$29$	−3.65999	+	1.33213i	−0.679642	+	0.247370i	−0.0209484	+	0.999781i	$0.506669\pi$
$30$		0			0
$31$	6.93676	−	5.82063i	1.24588	−	1.04542i	0.248838	−	0.968545i	$-0.419951\pi$
$31$	6.93676	−	5.82063i	1.24588	−	1.04542i	0.997041	−	0.0768712i	$-0.0244930\pi$
$32$		0			0
$33$	−2.35985	+	2.74774i	−0.410797	+	0.478320i
$34$		0			0
$35$	0.553023	−	0.957864i	0.0934779	−	0.161909i
$36$		0			0
$37$	1.94112	+	3.36212i	0.319118	+	0.552729i	0.980304	−	0.197493i	$-0.0632799\pi$
$37$	1.94112	+	3.36212i	0.319118	+	0.552729i	−0.661186	+	0.750222i	$0.729947\pi$
$38$		0			0
$39$	0.509258	+	0.621240i	0.0815465	+	0.0994780i
$40$		0			0
$41$	1.81516	+	0.660663i	0.283480	+	0.103178i	0.479847	−	0.877352i	$-0.340692\pi$
$41$	1.81516	+	0.660663i	0.283480	+	0.103178i	−0.196367	+	0.980530i	$0.562914\pi$
$42$		0			0
$43$	0.927544	−	5.26036i	0.141449	−	0.802198i	−0.828701	−	0.559692i	$-0.810919\pi$
$43$	0.927544	−	5.26036i	0.141449	−	0.802198i	0.970150	−	0.242506i	$-0.0779694\pi$
$44$		0			0
$45$	2.59008	−	2.07401i	0.386107	−	0.309175i
$46$		0			0
$47$	−2.52213	−	2.11632i	−0.367890	−	0.308697i	0.440036	−	0.897980i	$-0.354966\pi$
$47$	−2.52213	−	2.11632i	−0.367890	−	0.308697i	−0.807926	+	0.589283i	$0.799410\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−0.0962385	+	8.39226i	−0.0134761	+	1.17515i
$52$		0			0
$53$	−4.18839			−0.575320			−0.287660	−	0.957733i	$-0.592877\pi$
$53$	−4.18839			−0.575320			−0.287660	+	0.957733i	$0.592877\pi$
$54$		0			0
$55$	2.31293			0.311875
$56$		0			0
$57$	−0.302065	+	0.169809i	−0.0400095	+	0.0224918i
$58$		0			0
$59$	0.461820	+	2.61911i	0.0601238	+	0.340979i	1.00000		0.000536745i	$-0.000170851\pi$
$59$	0.461820	+	2.61911i	0.0601238	+	0.340979i	−0.939876	+	0.341516i	$0.889060\pi$
$60$		0			0
$61$	−0.396649	−	0.332828i	−0.0507857	−	0.0426143i	0.617042	−	0.786931i	$-0.288331\pi$
$61$	−0.396649	−	0.332828i	−0.0507857	−	0.0426143i	−0.667827	+	0.744316i	$0.732776\pi$
$62$		0			0
$63$	−0.588559	+	2.94170i	−0.0741514	+	0.370619i
$64$		0			0
$65$	0.0890754	−	0.505171i	0.0110484	−	0.0626588i
$66$		0			0
$67$	−2.70746	−	0.985435i	−0.330769	−	0.120390i	0.171297	−	0.985219i	$-0.445204\pi$
$67$	−2.70746	−	0.985435i	−0.330769	−	0.120390i	−0.502066	+	0.864829i	$0.667427\pi$
$68$		0			0
$69$	1.68697	−	0.277552i	0.203088	−	0.0334134i
$70$		0			0
$71$	−6.57991	−	11.3967i	−0.780892	−	1.35254i	−0.931423	−	0.363939i	$-0.881432\pi$
$71$	−6.57991	−	11.3967i	−0.780892	−	1.35254i	0.150531	−	0.988605i	$-0.451902\pi$
$72$		0			0
$73$	−3.85105	+	6.67021i	−0.450731	+	0.780689i	−0.998432	−	0.0559853i	$-0.982170\pi$
$73$	−3.85105	+	6.67021i	−0.450731	+	0.780689i	0.547701	+	0.836674i	$0.315503\pi$
$74$		0			0
$75$	6.42854	+	1.20969i	0.742304	+	0.139683i
$76$		0			0
$77$	−1.60193	+	1.34418i	−0.182557	+	0.153183i
$78$		0			0
$79$	−6.19535	+	2.25492i	−0.697031	+	0.253699i	−0.666143	−	0.745824i	$-0.732056\pi$
$79$	−6.19535	+	2.25492i	−0.697031	+	0.253699i	−0.0308884	+	0.999523i	$0.509834\pi$
$80$		0			0
$81$	−4.85265	+	7.57970i	−0.539183	+	0.842189i
$82$		0			0
$83$	−9.11894	+	3.31902i	−1.00093	+	0.364310i	−0.789944	−	0.613178i	$-0.789891\pi$
$83$	−9.11894	+	3.31902i	−1.00093	+	0.364310i	−0.210989	+	0.977488i	$0.567668\pi$
$84$		0			0
$85$	4.10557	−	3.44499i	0.445312	−	0.373661i
$86$		0			0
$87$	−6.62976	−	1.24756i	−0.710785	−	0.133752i
$88$		0			0
$89$	−0.185672	+	0.321594i	−0.0196812	+	0.0340889i	−0.875698	−	0.482859i	$-0.839598\pi$
$89$	−0.185672	+	0.321594i	−0.0196812	+	0.0340889i	0.856017	+	0.516948i	$0.172932\pi$
$90$		0			0
$91$	0.231891	+	0.401647i	0.0243088	+	0.0421041i
$92$		0			0
$93$	15.4762	−	2.54624i	1.60480	−	0.264033i
$94$		0			0
$95$	0.207937	+	0.0756828i	0.0213339	+	0.00776489i
$96$		0			0
$97$	0.500292	−	2.83730i	0.0507970	−	0.288084i	−0.948818	−	0.315823i	$-0.897720\pi$
$97$	0.500292	−	2.83730i	0.0507970	−	0.288084i	0.999615	+	0.0277387i	$0.00883063\pi$
$98$		0			0
$99$	−5.94282	+	2.00991i	−0.597276	+	0.202004i
$100$		0			0
$101$	−6.65531	−	5.58447i	−0.662228	−	0.555675i	0.248526	−	0.968625i	$-0.420054\pi$
$101$	−6.65531	−	5.58447i	−0.662228	−	0.555675i	−0.910754	+	0.412950i	$0.864498\pi$
$102$		0			0
$103$	−1.50688	−	8.54597i	−0.148478	−	0.842059i	−0.964509	−	0.264051i	$-0.914941\pi$
$103$	−1.50688	−	8.54597i	−0.148478	−	0.842059i	0.816031	−	0.578008i	$-0.196170\pi$
$104$		0			0
$105$	1.66994	−	0.938777i	0.162970	−	0.0916152i
$106$		0			0
$107$	−2.64816			−0.256007			−0.128004	−	0.991774i	$-0.540857\pi$
$107$	−2.64816			−0.256007			−0.128004	+	0.991774i	$0.540857\pi$
$108$		0			0
$109$	17.6476			1.69033			0.845167	−	0.534502i	$-0.179501\pi$
$109$	17.6476			1.69033			0.845167	+	0.534502i	$0.179501\pi$
$110$		0			0
$111$	−0.0771054	+	6.72380i	−0.00731852	+	0.638195i
$112$		0			0
$113$	−2.65215	−	15.0411i	−0.249493	−	1.41495i	−0.809822	−	0.586676i	$-0.800436\pi$
$113$	−2.65215	−	15.0411i	−0.249493	−	1.41495i	0.560329	−	0.828270i	$-0.310675\pi$
$114$		0			0
$115$	−0.836324	−	0.701759i	−0.0779876	−	0.0654394i
$116$		0			0
$117$	0.210120	+	1.37539i	0.0194256	+	0.127155i
$118$		0			0
$119$	−0.841428	+	4.77198i	−0.0771336	+	0.437446i
$120$		0			0
$121$	6.22735	+	2.26657i	0.566123	+	0.206052i
$122$		0			0
$123$	2.12105	+	2.58746i	0.191249	+	0.233303i
$124$		0			0
$125$	−4.85370	−	8.40685i	−0.434128	−	0.751931i
$126$		0			0
$127$	5.02965	−	8.71161i	0.446309	−	0.773030i	−0.551833	−	0.833954i	$-0.686072\pi$
$127$	5.02965	−	8.71161i	0.446309	−	0.773030i	0.998142	+	0.0609243i	$0.0194048\pi$
$128$		0			0
$129$	6.02780	−	7.01861i	0.530718	−	0.617954i
$130$		0			0
$131$	−9.92788	+	8.33048i	−0.867403	+	0.727837i	−0.963550	−	0.267530i	$-0.913793\pi$
$131$	−9.92788	+	8.33048i	−0.867403	+	0.727837i	0.0961467	+	0.995367i	$0.469348\pi$
$132$		0			0
$133$	−0.188000	+	0.0684265i	−0.0163017	+	0.00593333i
$134$		0			0
$135$	5.69085	−	0.802730i	0.489790	−	0.0690880i
$136$		0			0
$137$	4.41894	−	1.60836i	0.377535	−	0.137412i	−0.146281	−	0.989243i	$-0.546730\pi$
$137$	4.41894	−	1.60836i	0.377535	−	0.137412i	0.523816	+	0.851832i	$0.324508\pi$
$138$		0			0
$139$	7.52327	−	6.31277i	0.638115	−	0.535442i	−0.265324	−	0.964159i	$-0.585479\pi$
$139$	7.52327	−	6.31277i	0.638115	−	0.535442i	0.903439	+	0.428717i	$0.141034\pi$
$140$		0			0
$141$	−1.88883	−	5.38072i	−0.159068	−	0.453138i
$142$		0			0
$143$	−0.484924	+	0.839912i	−0.0405513	+	0.0702370i
$144$		0			0
$145$	2.15396	+	3.73076i	0.178876	+	0.309823i
$146$		0			0
$147$	−0.611021	+	1.62070i	−0.0503961	+	0.133673i
$148$		0			0
$149$	13.2401	+	4.81900i	1.08467	+	0.394788i	0.821644	−	0.570001i	$-0.193057\pi$
$149$	13.2401	+	4.81900i	1.08467	+	0.394788i	0.263026	+	0.964789i	$0.415279\pi$
$150$		0			0
$151$	0.830050	−	4.70745i	0.0675485	−	0.383087i	−0.932227	−	0.361875i	$-0.882137\pi$
$151$	0.830050	−	4.70745i	0.0675485	−	0.383087i	0.999775	−	0.0212113i	$-0.00675226\pi$
$152$		0			0
$153$	−7.55517	+	12.4192i	−0.610800	+	1.00404i
$154$		0			0
$155$	−7.67237	−	6.43789i	−0.616260	−	0.517103i
$156$		0			0
$157$	−2.25778	−	12.8045i	−0.180190	−	1.02191i	−0.931981	−	0.362507i	$-0.881921\pi$
$157$	−2.25778	−	12.8045i	−0.180190	−	1.02191i	0.751791	−	0.659402i	$-0.229190\pi$
$158$		0			0
$159$	−6.24058	−	3.69905i	−0.494910	−	0.293354i
$160$		0			0
$161$	0.987069			0.0777919
$162$		0			0
$163$	−14.0837			−1.10312			−0.551560	−	0.834135i	$-0.685967\pi$
$163$	−14.0837			−1.10312			−0.551560	+	0.834135i	$0.685967\pi$
$164$		0			0
$165$	3.44620	+	2.04271i	0.268286	+	0.159024i
$166$		0			0
$167$	0.533420	+	3.02517i	0.0412773	+	0.234095i	0.998466	−	0.0553698i	$-0.0176338\pi$
$167$	0.533420	+	3.02517i	0.0412773	+	0.234095i	−0.957189	+	0.289465i	$0.906523\pi$
$168$		0			0
$169$	−9.79381	−	8.21798i	−0.753370	−	0.632152i
$170$		0			0
$171$	−0.600039	−	0.0137637i	−0.0458861	−	0.00105254i
$172$		0			0
$173$	−2.10861	+	11.9585i	−0.160315	+	0.909190i	0.793450	+	0.608635i	$0.208283\pi$
$173$	−2.10861	+	11.9585i	−0.160315	+	0.909190i	−0.953765	+	0.300554i	$0.902828\pi$
$174$		0			0
$175$	3.54890	+	1.29169i	0.268272	+	0.0976429i
$176$		0			0
$177$	−1.62502	+	4.31026i	−0.122144	+	0.323979i
$178$		0			0
$179$	−9.36887	−	16.2274i	−0.700262	−	1.21289i	−0.968374	−	0.249502i	$-0.919733\pi$
$179$	−9.36887	−	16.2274i	−0.700262	−	1.21289i	0.268112	−	0.963388i	$-0.413600\pi$
$180$		0			0
$181$	−5.35808	+	9.28047i	−0.398263	+	0.689812i	−0.993512	−	0.113730i	$-0.963720\pi$
$181$	−5.35808	+	9.28047i	−0.398263	+	0.689812i	0.595249	+	0.803541i	$0.297054\pi$
$182$		0			0
$183$	−0.297052	−	0.846213i	−0.0219587	−	0.0625538i
$184$		0			0
$185$	3.28935	−	2.76009i	0.241838	−	0.202926i
$186$		0			0
$187$	−9.52186	+	3.46567i	−0.696307	+	0.253435i
$188$		0			0
$189$	−3.47495	+	3.86325i	−0.252766	+	0.281010i
$190$		0			0
$191$	−21.6314	+	7.87318i	−1.56519	+	0.569684i	−0.971919	−	0.235317i	$-0.924387\pi$
$191$	−21.6314	+	7.87318i	−1.56519	+	0.569684i	−0.593274	+	0.805001i	$0.702165\pi$
$192$		0			0
$193$	6.34786	−	5.32648i	0.456929	−	0.383409i	−0.385071	−	0.922887i	$-0.625823\pi$
$193$	6.34786	−	5.32648i	0.456929	−	0.383409i	0.842000	+	0.539478i	$0.181379\pi$
$194$		0			0
$195$	0.578871	−	0.674022i	0.0414538	−	0.0482677i
$196$		0			0
$197$	11.6593	−	20.1945i	0.830689	−	1.43880i	−0.0668028	−	0.997766i	$-0.521280\pi$
$197$	11.6593	−	20.1945i	0.830689	−	1.43880i	0.897492	−	0.441030i	$-0.145387\pi$
$198$		0			0
$199$	−7.29719	−	12.6391i	−0.517284	−	0.895963i	−0.999798	−	0.0200745i	$-0.993610\pi$
$199$	−7.29719	−	12.6391i	−0.517284	−	0.895963i	0.482514	−	0.875888i	$-0.339724\pi$
$200$		0			0
$201$	−3.16373	−	3.85942i	−0.223153	−	0.272222i
$202$		0			0
$203$	−3.65999	−	1.33213i	−0.256881	−	0.0934969i
$204$		0			0
$205$	0.370998	−	2.10403i	0.0259116	−	0.146952i
$206$		0			0
$207$	2.75867	+	1.07634i	0.191741	+	0.0748106i
$208$		0			0
$209$	−0.320491	−	0.268924i	−0.0221688	−	0.0186018i
$210$		0			0
$211$	−2.57639	−	14.6115i	−0.177366	−	1.00589i	−0.935377	−	0.353652i	$-0.884940\pi$
$211$	−2.57639	−	14.6115i	−0.177366	−	1.00589i	0.758011	−	0.652242i	$-0.226171\pi$
$212$		0			0
$213$	0.261368	−	22.7920i	0.0179086	−	1.56168i
$214$		0			0
$215$	−5.90796			−0.402919
$216$		0			0
$217$	9.05530			0.614714
$218$		0			0
$219$	−11.6289	+	6.53729i	−0.785806	+	0.441749i
$220$		0			0
$221$	0.390240	+	2.21316i	0.0262504	+	0.148873i
$222$		0			0
$223$	4.16835	+	3.49766i	0.279133	+	0.234221i	0.771596	−	0.636113i	$-0.219459\pi$
$223$	4.16835	+	3.49766i	0.279133	+	0.234221i	−0.492463	+	0.870334i	$0.663903\pi$
$224$		0			0
$225$	8.50998	+	7.47989i	0.567332	+	0.498660i
$226$		0			0
$227$	−2.68213	+	15.2111i	−0.178019	+	1.00960i	0.756582	+	0.653899i	$0.226868\pi$
$227$	−2.68213	+	15.2111i	−0.178019	+	1.00960i	−0.934601	+	0.355697i	$0.884243\pi$
$228$		0			0
$229$	10.6713	+	3.88403i	0.705178	+	0.256664i	0.669620	−	0.742704i	$-0.266457\pi$
$229$	10.6713	+	3.88403i	0.705178	+	0.256664i	0.0355580	+	0.999368i	$0.488679\pi$
$230$		0			0
$231$	−3.57396	+	0.588012i	−0.235149	+	0.0386884i
$232$		0			0
$233$	−3.01368	−	5.21984i	−0.197433	−	0.341963i	0.750263	−	0.661140i	$-0.229927\pi$
$233$	−3.01368	−	5.21984i	−0.197433	−	0.341963i	−0.947695	+	0.319177i	$0.896594\pi$
$234$		0			0
$235$	−1.82078	+	3.15368i	−0.118774	+	0.205723i
$236$		0			0
$237$	−11.2224	−	2.11177i	−0.728971	−	0.137174i
$238$		0			0
$239$	−5.27074	+	4.42267i	−0.340936	+	0.286079i	−0.797138	−	0.603797i	$-0.793654\pi$
$239$	−5.27074	+	4.42267i	−0.340936	+	0.286079i	0.456202	+	0.889876i	$0.349209\pi$
$240$		0			0
$241$	−19.5209	+	7.10502i	−1.25745	+	0.457675i	−0.882913	−	0.469537i	$-0.844421\pi$
$241$	−19.5209	+	7.10502i	−1.25745	+	0.457675i	−0.374538	+	0.927212i	$0.622199\pi$
$242$		0			0
$243$	−13.9245	+	7.00782i	−0.893254	+	0.449552i
$244$		0			0
$245$	1.03934	−	0.378290i	0.0664012	−	0.0241681i
$246$		0			0
$247$	−0.0710789	+	0.0596423i	−0.00452264	+	0.00379495i
$248$		0			0
$249$	−16.5182	−	3.10831i	−1.04680	−	0.196981i
$250$		0			0
$251$	0.0467296	−	0.0809381i	0.00294955	−	0.00510877i	−0.864547	−	0.502552i	$-0.832394\pi$
$251$	0.0467296	−	0.0809381i	0.00294955	−	0.00510877i	0.867496	+	0.497443i	$0.165728\pi$
$252$		0			0
$253$	1.03206	+	1.78759i	0.0648853	+	0.112385i
$254$		0			0
$255$	9.15969	−	1.50701i	0.573602	−	0.0943729i
$256$		0			0
$257$	26.7137	+	9.72298i	1.66635	+	0.606503i	0.991342	−	0.131305i	$-0.0419167\pi$
$257$	26.7137	+	9.72298i	1.66635	+	0.606503i	0.675011	+	0.737808i	$0.264139\pi$
$258$		0			0
$259$	−0.674144	+	3.82326i	−0.0418893	+	0.237566i
$260$		0			0
$261$	−8.77635	−	7.71402i	−0.543243	−	0.477486i
$262$		0			0
$263$	−15.2341	−	12.7830i	−0.939377	−	0.788231i	0.0380995	−	0.999274i	$-0.487870\pi$
$263$	−15.2341	−	12.7830i	−0.939377	−	0.788231i	−0.977477	+	0.211043i	$0.932314\pi$
$264$		0			0
$265$	0.804434	+	4.56217i	0.0494160	+	0.280252i
$266$		0			0
$267$	−0.560668	+	0.315185i	−0.0343123	+	0.0192890i
$268$		0			0
$269$	3.11110			0.189687			0.0948437	−	0.995492i	$-0.469765\pi$
$269$	3.11110			0.189687			0.0948437	+	0.995492i	$0.469765\pi$
$270$		0			0
$271$	22.3654			1.35860			0.679302	−	0.733859i	$-0.262283\pi$
$271$	22.3654			1.35860			0.679302	+	0.733859i	$0.262283\pi$
$272$		0			0
$273$	−0.00921120	+	0.803242i	−0.000557487	+	0.0486144i
$274$		0			0
$275$	1.37141	+	7.77766i	0.0826992	+	0.469010i
$276$		0			0
$277$	−11.9417	−	10.0202i	−0.717505	−	0.602058i	0.209189	−	0.977875i	$-0.432918\pi$
$277$	−11.9417	−	10.0202i	−0.717505	−	0.602058i	−0.926694	+	0.375817i	$0.877362\pi$
$278$		0			0
$279$	25.3078	+	9.87424i	1.51514	+	0.591155i
$280$		0			0
$281$	0.935918	−	5.30785i	0.0558322	−	0.316640i	−0.944082	−	0.329710i	$-0.893049\pi$
$281$	0.935918	−	5.30785i	0.0558322	−	0.316640i	0.999915	+	0.0130696i	$0.00416030\pi$
$282$		0			0
$283$	−22.3869	−	8.14815i	−1.33076	−	0.484357i	−0.423870	−	0.905723i	$-0.639329\pi$
$283$	−22.3869	−	8.14815i	−1.33076	−	0.484357i	−0.906891	+	0.421366i	$0.861551\pi$
$284$		0			0
$285$	0.242979	+	0.296408i	0.0143928	+	0.0175577i
$286$		0			0
$287$	0.965824	+	1.67286i	0.0570108	+	0.0987456i
$288$		0			0
$289$	−3.23988	+	5.61164i	−0.190581	+	0.330096i
$290$		0			0
$291$	3.25123	−	3.78565i	0.190591	−	0.221919i
$292$		0			0
$293$	0.0674487	−	0.0565961i	0.00394039	−	0.00330638i	−0.640815	−	0.767695i	$-0.721404\pi$
$293$	0.0674487	−	0.0565961i	0.00394039	−	0.00330638i	0.644756	+	0.764389i	$0.276959\pi$
$294$		0			0
$295$	2.76415	−	1.00607i	0.160935	−	0.0585755i
$296$		0			0
$297$	−10.6297	−	2.25380i	−0.616799	−	0.130779i
$298$		0			0
$299$	0.430177	−	0.156572i	0.0248778	−	0.00905478i
$300$		0			0
$301$	4.09184	−	3.43346i	0.235850	−	0.197901i
$302$		0			0
$303$	−4.98419	−	14.1984i	−0.286334	−	0.815680i
$304$		0			0
$305$	−0.286349	+	0.495971i	−0.0163963	+	0.0283992i
$306$		0			0
$307$	15.0984	+	26.1513i	0.861713	+	1.49253i	0.870274	+	0.492568i	$0.163942\pi$
$307$	15.0984	+	26.1513i	0.861713	+	1.49253i	−0.00856112	+	0.999963i	$0.502725\pi$
$308$		0			0
$309$	5.30232	−	14.0641i	0.301638	−	0.800077i
$310$		0			0
$311$	26.5081	+	9.64817i	1.50314	+	0.547097i	0.956871	−	0.290514i	$-0.0938261\pi$
$311$	26.5081	+	9.64817i	1.50314	+	0.547097i	0.546267	+	0.837611i	$0.316048\pi$
$312$		0			0
$313$	−3.26399	+	18.5110i	−0.184492	+	1.04631i	0.742115	+	0.670273i	$0.233823\pi$
$313$	−3.26399	+	18.5110i	−0.184492	+	1.04631i	−0.926607	+	0.376032i	$0.877288\pi$
$314$		0			0
$315$	3.31727	+	0.0760917i	0.186907	+	0.00428728i
$316$		0			0
$317$	22.9979	+	19.2975i	1.29169	+	1.08386i	0.991517	+	0.129974i	$0.0414893\pi$
$317$	22.9979	+	19.2975i	1.29169	+	1.08386i	0.300174	+	0.953884i	$0.402955\pi$
$318$		0			0
$319$	−1.41434	−	8.02110i	−0.0791877	−	0.449096i
$320$		0			0
$321$	−3.94568	−	2.33877i	−0.220227	−	0.130538i
$322$		0			0
$323$	−0.969436			−0.0539409
$324$		0			0
$325$	1.75155			0.0971585
$326$		0			0
$327$	26.2944	+	15.5858i	1.45408	+	0.861897i
$328$		0			0
$329$	−0.571720	−	3.24239i	−0.0315200	−	0.178759i
$330$		0			0
$331$	−17.3749	−	14.5793i	−0.955013	−	0.801351i	0.0251219	−	0.999684i	$-0.492003\pi$
$331$	−17.3749	−	14.5793i	−0.955013	−	0.801351i	−0.980135	+	0.198334i	$0.936447\pi$
$332$		0			0
$333$	−6.05313	+	9.95017i	−0.331710	+	0.545266i
$334$		0			0
$335$	−0.553375	+	3.13835i	−0.0302341	+	0.171466i
$336$		0			0
$337$	28.5196	+	10.3803i	1.55356	+	0.565451i	0.969250	−	0.246078i	$-0.0791419\pi$
$337$	28.5196	+	10.3803i	1.55356	+	0.565451i	0.584313	+	0.811528i	$0.301364\pi$
$338$		0			0
$339$	9.33219	−	24.7531i	0.506855	−	1.34440i
$340$		0			0
$341$	9.46808	+	16.3992i	0.512725	+	0.888066i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$		0			0
$345$	−0.626327	−	1.78422i	−0.0337203	−	0.0960589i
$346$		0			0
$347$	−2.14545	+	1.80024i	−0.115174	+	0.0966422i	−0.698556	−	0.715556i	$-0.746174\pi$
$347$	−2.14545	+	1.80024i	−0.115174	+	0.0966422i	0.583382	+	0.812198i	$0.301729\pi$
$348$		0			0
$349$	−2.13485	+	0.777020i	−0.114276	+	0.0415929i	−0.398525	−	0.917157i	$-0.630478\pi$
$349$	−2.13485	+	0.777020i	−0.114276	+	0.0415929i	0.284249	+	0.958750i	$0.408256\pi$
$350$		0			0
$351$	−0.901629	+	2.23486i	−0.0481254	+	0.119288i
$352$		0			0
$353$	9.20857	−	3.35165i	0.490123	−	0.178390i	−0.0851235	−	0.996370i	$-0.527128\pi$
$353$	9.20857	−	3.35165i	0.490123	−	0.178390i	0.575246	+	0.817980i	$0.304906\pi$
$354$		0			0
$355$	−11.1501	+	9.35601i	−0.591784	+	0.496565i
$356$		0			0
$357$	−5.46816	+	6.36698i	−0.289406	+	0.336976i
$358$		0			0
$359$	14.4634	−	25.0514i	0.763350	−	1.32216i	−0.177765	−	0.984073i	$-0.556887\pi$
$359$	14.4634	−	25.0514i	0.763350	−	1.32216i	0.941115	−	0.338088i	$-0.109780\pi$
$360$		0			0
$361$	9.47999	+	16.4198i	0.498947	+	0.864201i
$362$		0			0
$363$	7.27681	+	8.87693i	0.381934	+	0.465918i
$364$		0			0
$365$	8.00512	+	2.91363i	0.419007	+	0.152506i
$366$		0			0
$367$	−2.16187	+	12.2606i	−0.112849	+	0.639997i	0.874944	+	0.484224i	$0.160898\pi$
$367$	−2.16187	+	12.2606i	−0.112849	+	0.639997i	−0.987793	+	0.155773i	$0.950213\pi$
$368$		0			0
$369$	0.875146	+	5.72848i	0.0455583	+	0.298213i
$370$		0			0
$371$	−3.20849	−	2.69224i	−0.166577	−	0.139774i
$372$		0			0
$373$	3.29574	+	18.6911i	0.170647	+	0.967788i	0.943049	+	0.332654i	$0.107944\pi$
$373$	3.29574	+	18.6911i	0.170647	+	0.967788i	−0.772402	+	0.635134i	$0.780945\pi$
$374$		0			0
$375$	0.192799	−	16.8126i	0.00995609	−	0.868198i
$376$		0			0
$377$	−1.80637			−0.0930330
$378$		0			0
$379$	13.0785			0.671799			0.335899	−	0.941898i	$-0.390960\pi$
$379$	13.0785			0.671799			0.335899	+	0.941898i	$0.390960\pi$
$380$		0			0
$381$	15.1878	−	8.53801i	0.778097	−	0.437416i
$382$		0			0
$383$	0.878747	+	4.98362i	0.0449019	+	0.254651i	0.998993	−	0.0448651i	$-0.0142858\pi$
$383$	0.878747	+	4.98362i	0.0449019	+	0.254651i	−0.954091	+	0.299516i	$0.903175\pi$
$384$		0			0
$385$	1.77181	+	1.48672i	0.0902996	+	0.0757704i
$386$		0			0
$387$	15.1799	−	5.13396i	0.771636	−	0.260974i
$388$		0			0
$389$	4.15713	−	23.5762i	0.210775	−	1.19536i	−0.677315	−	0.735693i	$-0.736857\pi$
$389$	4.15713	−	23.5762i	0.210775	−	1.19536i	0.888090	−	0.459670i	$-0.152032\pi$
$390$		0			0
$391$	4.49449	+	1.63586i	0.227296	+	0.0827290i
$392$		0			0
$393$	−22.1495	+	3.64418i	−1.11729	+	0.183825i
$394$		0			0
$395$	3.64605	+	6.31515i	0.183453	+	0.317750i
$396$		0			0
$397$	−13.3981	+	23.2061i	−0.672429	+	1.16468i	0.304784	+	0.952422i	$0.401416\pi$
$397$	−13.3981	+	23.2061i	−0.672429	+	1.16468i	−0.977213	+	0.212260i	$0.931918\pi$
$398$		0			0
$399$	−0.340547	−	0.0640824i	−0.0170487	−	0.00320813i
$400$		0			0
$401$	0.620597	−	0.520743i	0.0309911	−	0.0260046i	−0.627161	−	0.778890i	$-0.715783\pi$
$401$	0.620597	−	0.520743i	0.0309911	−	0.0260046i	0.658152	+	0.752885i	$0.271339\pi$
$402$		0			0
$403$	3.94641	−	1.43638i	0.196585	−	0.0715511i
$404$		0			0
$405$	9.18814	+	3.82993i	0.456562	+	0.190311i
$406$		0			0
$407$	−7.62882	+	2.77666i	−0.378147	+	0.137634i
$408$		0			0
$409$	−17.1810	+	14.4166i	−0.849545	+	0.712853i	−0.959689	−	0.281062i	$-0.909313\pi$
$409$	−17.1810	+	14.4166i	−0.849545	+	0.712853i	0.110144	+	0.993916i	$0.464869\pi$
$410$		0			0
$411$	8.00454	+	1.50626i	0.394835	+	0.0742981i
$412$		0			0
$413$	−1.32976	+	2.30321i	−0.0654330	+	0.113333i
$414$		0			0
$415$	5.36663	+	9.29528i	0.263437	+	0.456287i
$416$		0			0
$417$	16.7847	−	2.76153i	0.821950	−	0.135233i
$418$		0			0
$419$	36.1461	+	13.1561i	1.76585	+	0.642717i	1.00000		0.000300706i	$-9.57177e-5\pi$
$419$	36.1461	+	13.1561i	1.76585	+	0.642717i	0.765851	+	0.643018i	$0.222318\pi$
$420$		0			0
$421$	0.217194	−	1.23177i	0.0105854	−	0.0600326i	−0.979058	−	0.203584i	$-0.934741\pi$
$421$	0.217194	−	1.23177i	0.0105854	−	0.0600326i	0.989643	+	0.143551i	$0.0458522\pi$
$422$		0			0
$423$	1.93777	−	9.68527i	0.0942178	−	0.470914i
$424$		0			0
$425$	14.0187	+	11.7631i	0.680009	+	0.570595i
$426$		0			0
$427$	−0.0899131	−	0.509922i	−0.00435120	−	0.0246769i
$428$		0			0
$429$	−1.46431	+	0.823176i	−0.0706974	+	0.0397433i
$430$		0			0
$431$	6.57381			0.316649			0.158325	−	0.987387i	$-0.449391\pi$
$431$	6.57381			0.316649			0.158325	+	0.987387i	$0.449391\pi$
$432$		0			0
$433$	−23.5134			−1.12998			−0.564990	−	0.825098i	$-0.691120\pi$
$433$	−23.5134			−1.12998			−0.564990	+	0.825098i	$0.691120\pi$
$434$		0			0
$435$	−0.0855596	+	7.46103i	−0.00410227	+	0.357729i
$436$		0			0
$437$	0.0342918	+	0.194478i	0.00164040	+	0.00930316i
$438$		0			0
$439$	−10.8379	−	9.09409i	−0.517265	−	0.434037i	0.346412	−	0.938083i	$-0.387400\pi$
$439$	−10.8379	−	9.09409i	−0.517265	−	0.434037i	−0.863677	+	0.504045i	$0.831844\pi$
$440$		0			0
$441$	−2.34175	+	1.87515i	−0.111512	+	0.0892931i
$442$		0			0
$443$	−6.37088	+	36.1310i	−0.302689	+	1.71664i	0.331496	+	0.943457i	$0.392447\pi$
$443$	−6.37088	+	36.1310i	−0.302689	+	1.71664i	−0.634186	+	0.773181i	$0.718664\pi$
$444$		0			0
$445$	0.385954	+	0.140476i	0.0182960	+	0.00665919i
$446$		0			0
$447$	15.4714	+	18.8734i	0.731770	+	0.892681i
$448$		0			0
$449$	−4.49019	−	7.77724i	−0.211905	−	0.367031i	0.740405	−	0.672161i	$-0.234634\pi$
$449$	−4.49019	−	7.77724i	−0.211905	−	0.367031i	−0.952311	+	0.305130i	$0.901300\pi$
$450$		0			0
$451$	−2.01970	+	3.49823i	−0.0951040	+	0.164725i
$452$		0			0
$453$	5.39422	−	6.28088i	0.253442	−	0.295102i
$454$		0			0
$455$	0.392954	−	0.329727i	0.0184220	−	0.0154579i
$456$		0			0
$457$	−1.96948	+	0.716832i	−0.0921284	+	0.0335320i	−0.387673	−	0.921797i	$-0.626721\pi$
$457$	−1.96948	+	0.716832i	−0.0921284	+	0.0335320i	0.295545	+	0.955329i	$0.404499\pi$
$458$		0			0
$459$	−22.2253	+	11.8318i	−1.03739	+	0.552261i
$460$		0			0
$461$	−6.27791	+	2.28497i	−0.292391	+	0.106422i	−0.484051	−	0.875040i	$-0.660835\pi$
$461$	−6.27791	+	2.28497i	−0.292391	+	0.106422i	0.191660	+	0.981461i	$0.438613\pi$
$462$		0			0
$463$	14.1355	−	11.8611i	0.656932	−	0.551231i	−0.252234	−	0.967666i	$-0.581165\pi$
$463$	14.1355	−	11.8611i	0.656932	−	0.551231i	0.909165	+	0.416435i	$0.136721\pi$
$464$		0			0
$465$	−5.74587	−	16.3683i	−0.266459	−	0.759060i
$466$		0			0
$467$	2.26744	−	3.92733i	0.104925	−	0.181735i	−0.808783	−	0.588108i	$-0.799873\pi$
$467$	2.26744	−	3.92733i	0.104925	−	0.181735i	0.913707	+	0.406373i	$0.133206\pi$
$468$		0			0
$469$	−1.44061	−	2.49521i	−0.0665212	−	0.115218i
$470$		0			0
$471$	7.94450	−	21.0723i	0.366063	−	0.970961i
$472$		0			0
$473$	10.4964	+	3.82037i	0.482624	+	0.175661i
$474$		0			0
$475$	−0.131205	+	0.744101i	−0.00602010	+	0.0341417i
$476$		0			0
$477$	−6.03139	−	11.0230i	−0.276158	−	0.504707i
$478$		0			0
$479$	25.6834	+	21.5509i	1.17350	+	0.984686i	1.00000		0.000147702i	$-4.70151e-5\pi$
$479$	25.6834	+	21.5509i	1.17350	+	0.984686i	0.173503	+	0.984833i	$0.444491\pi$
$480$		0			0
$481$	0.312656	+	1.77316i	0.0142559	+	0.0808492i
$482$		0			0
$483$	1.47070	+	0.871748i	0.0669193	+	0.0396659i
$484$		0			0
$485$	−3.18659			−0.144696
$486$		0			0
$487$	−0.913860			−0.0414109			−0.0207055	−	0.999786i	$-0.506591\pi$
$487$	−0.913860			−0.0414109			−0.0207055	+	0.999786i	$0.506591\pi$
$488$		0			0
$489$	−20.9843	−	12.4383i	−0.948942	−	0.562478i
$490$		0			0
$491$	−2.85399	−	16.1858i	−0.128799	−	0.730453i	−0.978979	−	0.203961i	$-0.934618\pi$
$491$	−2.85399	−	16.1858i	−0.128799	−	0.730453i	0.850180	−	0.526492i	$-0.176493\pi$
$492$		0			0
$493$	−14.4575	−	12.1313i	−0.651135	−	0.546367i
$494$		0			0
$495$	3.33068	+	6.08715i	0.149703	+	0.273597i
$496$		0			0
$497$	2.28518	−	12.9599i	0.102504	−	0.581331i
$498$		0			0
$499$	−3.91683	−	1.42561i	−0.175341	−	0.0638190i	0.252858	−	0.967503i	$-0.418630\pi$
$499$	−3.91683	−	1.42561i	−0.175341	−	0.0638190i	−0.428199	+	0.903684i	$0.640852\pi$
$500$		0			0
$501$	−1.87696	+	4.97852i	−0.0838563	+	0.222424i
$502$		0			0
$503$	−9.03507	−	15.6492i	−0.402854	−	0.697764i	0.591215	−	0.806514i	$-0.298648\pi$
$503$	−9.03507	−	15.6492i	−0.402854	−	0.697764i	−0.994069	+	0.108750i	$0.965315\pi$
$504$		0			0
$505$	−4.80460	+	8.32181i	−0.213802	+	0.370316i
$506$		0			0
$507$	−7.33462	−	20.8941i	−0.325742	−	0.927941i
$508$		0			0
$509$	−12.1482	+	10.1936i	−0.538461	+	0.451823i	−0.871011	−	0.491263i	$-0.836535\pi$
$509$	−12.1482	+	10.1936i	−0.538461	+	0.451823i	0.332550	+	0.943086i	$0.392091\pi$
$510$		0			0
$511$	−7.23760	+	2.63427i	−0.320173	+	0.116533i
$512$		0			0
$513$	−0.881885	−	0.550443i	−0.0389362	−	0.0243027i
$514$		0			0
$515$	−9.01922	+	3.28273i	−0.397434	+	0.144654i
$516$		0			0
$517$	5.27420	−	4.42558i	0.231959	−	0.194637i
$518$		0			0
$519$	−13.7032	+	15.9556i	−0.601502	+	0.700373i
$520$		0			0
$521$	−2.79716	+	4.84482i	−0.122546	+	0.212255i	−0.920771	−	0.390104i	$-0.872439\pi$
$521$	−2.79716	+	4.84482i	−0.122546	+	0.212255i	0.798225	+	0.602359i	$0.205772\pi$
$522$		0			0
$523$	−0.511325	−	0.885641i	−0.0223587	−	0.0387264i	0.854630	−	0.519238i	$-0.173784\pi$
$523$	−0.511325	−	0.885641i	−0.0223587	−	0.0387264i	−0.876988	+	0.480512i	$0.840451\pi$
$524$		0			0
$525$	4.14698	+	5.05887i	0.180989	+	0.220787i
$526$		0			0
$527$	41.2321	+	15.0073i	1.79610	+	0.653726i
$528$		0			0
$529$	−3.82472	+	21.6911i	−0.166292	+	0.943090i
$530$		0			0
$531$	−6.22792	+	4.98700i	−0.270269	+	0.216417i
$532$		0			0
$533$	0.686272	+	0.575851i	0.0297257	+	0.0249429i
$534$		0			0
$535$	0.508613	+	2.88449i	0.0219893	+	0.124707i
$536$		0			0
$537$	0.372151	−	32.4526i	0.0160595	−	1.40043i
$538$		0			0
$539$	−2.09117			−0.0900730
$540$		0			0
$541$	−38.5035			−1.65540			−0.827698	−	0.561174i	$-0.810350\pi$
$541$	−38.5035			−1.65540			−0.827698	+	0.561174i	$0.810350\pi$
$542$		0			0
$543$	−16.1796	+	9.09554i	−0.694333	+	0.390327i
$544$		0			0
$545$	−3.38945	−	19.2225i	−0.145188	−	0.823403i
$546$		0			0
$547$	16.2088	+	13.6008i	0.693039	+	0.581529i	0.919784	−	0.392425i	$-0.128364\pi$
$547$	16.2088	+	13.6008i	0.693039	+	0.581529i	−0.226745	+	0.973954i	$0.572808\pi$
$548$		0			0
$549$	0.304749	−	1.52318i	0.0130064	−	0.0650077i
$550$		0			0
$551$	0.135312	−	0.767392i	0.00576448	−	0.0326920i
$552$		0			0
$553$	−6.19535	−	2.25492i	−0.263453	−	0.0958891i
$554$		0			0
$555$	7.33866	−	1.20741i	0.311509	−	0.0512515i
$556$		0			0
$557$	1.72316	+	2.98460i	0.0730127	+	0.126462i	0.900220	−	0.435435i	$-0.143405\pi$
$557$	1.72316	+	2.98460i	0.0730127	+	0.126462i	−0.827208	+	0.561896i	$0.810072\pi$
$558$		0			0
$559$	1.23865	−	2.14540i	0.0523893	−	0.0907409i
$560$		0			0
$561$	−17.2481	−	3.24566i	−0.728214	−	0.137032i
$562$		0			0
$563$	−28.5252	+	23.9355i	−1.20219	+	1.00876i	−0.202629	+	0.979255i	$0.564949\pi$
$563$	−28.5252	+	23.9355i	−1.20219	+	1.00876i	−0.999565	+	0.0295051i	$0.990607\pi$
$564$		0			0
$565$	−15.8740	+	5.77767i	−0.667825	+	0.243068i
$566$		0			0
$567$	−8.58948	+	2.68716i	−0.360724	+	0.112850i
$568$		0			0
$569$	−8.64395	+	3.14614i	−0.362373	+	0.131893i	−0.516789	−	0.856113i	$-0.672873\pi$
$569$	−8.64395	+	3.14614i	−0.362373	+	0.131893i	0.154416	+	0.988006i	$0.450651\pi$
$570$		0			0
$571$	25.7207	−	21.5822i	1.07638	−	0.903187i	0.0807610	−	0.996733i	$-0.474265\pi$
$571$	25.7207	−	21.5822i	1.07638	−	0.903187i	0.995615	+	0.0935469i	$0.0298205\pi$
$572$		0			0
$573$	−39.1835	−	7.37335i	−1.63691	−	0.308026i
$574$		0			0
$575$	1.86391	−	3.22839i	0.0777305	−	0.134633i
$576$		0			0
$577$	5.34159	+	9.25190i	0.222373	+	0.385162i	0.955528	−	0.294900i	$-0.0952863\pi$
$577$	5.34159	+	9.25190i	0.222373	+	0.385162i	−0.733155	+	0.680062i	$0.761953\pi$
$578$		0			0
$579$	14.1623	−	2.33008i	0.588565	−	0.0968348i
$580$		0			0
$581$	−9.11894	−	3.31902i	−0.378317	−	0.137696i
$582$		0			0
$583$	1.52092	−	8.62557i	0.0629901	−	0.357234i
$584$		0			0
$585$	1.45778	−	0.493032i	0.0602716	−	0.0203844i
$586$		0			0
$587$	−11.0923	−	9.30757i	−0.457830	−	0.384165i	0.384502	−	0.923124i	$-0.374373\pi$
$587$	−11.0923	−	9.30757i	−0.457830	−	0.384165i	−0.842332	+	0.538960i	$0.818818\pi$
$588$		0			0
$589$	0.314590	+	1.78413i	0.0129625	+	0.0735138i
$590$		0			0
$591$	35.2071	−	19.7921i	1.44823	−	0.814136i
$592$		0			0
$593$	44.0027			1.80697			0.903486	−	0.428617i	$-0.140999\pi$
$593$	44.0027			1.80697			0.903486	+	0.428617i	$0.140999\pi$
$594$		0			0
$595$	5.35945			0.219716
$596$		0			0
$597$	0.289860	−	25.2766i	0.0118632	−	1.03450i
$598$		0			0
$599$	−5.25696	−	29.8137i	−0.214793	−	1.21815i	−0.881265	−	0.472623i	$-0.843307\pi$
$599$	−5.25696	−	29.8137i	−0.214793	−	1.21815i	0.666471	−	0.745531i	$-0.267804\pi$
$600$		0			0
$601$	6.38407	+	5.35687i	0.260412	+	0.218511i	0.763640	−	0.645642i	$-0.223410\pi$
$601$	6.38407	+	5.35687i	0.260412	+	0.218511i	−0.503228	+	0.864153i	$0.667855\pi$
$602$		0			0
$603$	−1.30536	−	8.54453i	−0.0531582	−	0.347960i
$604$		0			0
$605$	1.27280	−	7.21842i	0.0517468	−	0.293471i
$606$		0			0
$607$	−15.3057	−	5.57082i	−0.621239	−	0.226112i	0.0121747	−	0.999926i	$-0.496125\pi$
$607$	−15.3057	−	5.57082i	−0.621239	−	0.226112i	−0.633414	+	0.773813i	$0.718347\pi$
$608$		0			0
$609$	−4.27678	−	5.21721i	−0.173304	−	0.211412i
$610$		0			0
$611$	−0.763480	−	1.32239i	−0.0308871	−	0.0534980i
$612$		0			0
$613$	−2.45717	+	4.25594i	−0.0992442	+	0.171896i	−0.911372	−	0.411584i	$-0.864976\pi$
$613$	−2.45717	+	4.25594i	−0.0992442	+	0.171896i	0.812128	+	0.583480i	$0.198309\pi$
$614$		0			0
$615$	2.41099	−	2.80730i	0.0972206	−	0.113201i
$616$		0			0
$617$	8.98171	−	7.53655i	0.361590	−	0.303410i	−0.443834	−	0.896109i	$-0.646382\pi$
$617$	8.98171	−	7.53655i	0.361590	−	0.303410i	0.805424	+	0.592699i	$0.201938\pi$
$618$		0			0
$619$	−40.6741	+	14.8041i	−1.63483	+	0.595029i	−0.986124	−	0.166011i	$-0.946911\pi$
$619$	−40.6741	+	14.8041i	−1.63483	+	0.595029i	−0.648705	+	0.761040i	$0.724689\pi$
$620$		0			0
$621$	3.15975	+	4.04008i	0.126796	+	0.162123i
$622$		0			0
$623$	−0.348950	+	0.127007i	−0.0139804	+	0.00508844i
$624$		0			0
$625$	6.24058	−	5.23646i	0.249623	−	0.209459i
$626$		0			0
$627$	−0.240017	−	0.683736i	−0.00958535	−	0.0273058i
$628$		0			0
$629$	−9.40588	+	16.2915i	−0.375037	+	0.649583i
$630$		0			0
$631$	0.0152526	+	0.0264183i	0.000607197	+	0.00105170i	0.866329	−	0.499474i	$-0.166473\pi$
$631$	0.0152526	+	0.0264183i	0.000607197	+	0.00105170i	−0.865722	+	0.500526i	$0.833140\pi$
$632$		0			0
$633$	9.06563	−	24.0460i	0.360326	−	0.955744i
$634$		0			0
$635$	−10.4551	−	3.80533i	−0.414896	−	0.151010i
$636$		0			0
$637$	−0.0805350	+	0.456736i	−0.00319091	+	0.0180966i
$638$		0			0
$639$	20.5186	−	33.7286i	0.811703	−	1.33428i
$640$		0			0
$641$	−3.99631	−	3.35331i	−0.157845	−	0.132448i	0.560445	−	0.828192i	$-0.310630\pi$
$641$	−3.99631	−	3.35331i	−0.157845	−	0.132448i	−0.718290	+	0.695744i	$0.755075\pi$
$642$		0			0
$643$	−2.42967	−	13.7793i	−0.0958166	−	0.543403i	−0.994494	−	0.104793i	$-0.966582\pi$
$643$	−2.42967	−	13.7793i	−0.0958166	−	0.543403i	0.898677	−	0.438610i	$-0.144529\pi$
$644$		0			0
$645$	−8.80269	−	5.21772i	−0.346605	−	0.205448i
$646$		0			0
$647$	42.1271			1.65619			0.828094	−	0.560590i	$-0.189425\pi$
$647$	42.1271			1.65619			0.828094	+	0.560590i	$0.189425\pi$
$648$		0			0
$649$	−5.56149			−0.218308
$650$		0			0
$651$	13.4921	+	7.99735i	0.528798	+	0.313441i
$652$		0			0
$653$	0.961768	+	5.45446i	0.0376369	+	0.213449i	0.997826	−	0.0659008i	$-0.0209921\pi$
$653$	0.961768	+	5.45446i	0.0376369	+	0.213449i	−0.960189	+	0.279350i	$0.909881\pi$
$654$		0			0
$655$	10.9807	+	9.21389i	0.429051	+	0.360017i
$656$		0			0
$657$	−23.1002	−	0.529874i	−0.901225	−	0.0206724i
$658$		0			0
$659$	−2.32733	+	13.1990i	−0.0906601	+	0.514159i	0.905331	+	0.424707i	$0.139623\pi$
$659$	−2.32733	+	13.1990i	−0.0906601	+	0.514159i	−0.995991	+	0.0894522i	$0.971488\pi$
$660$		0			0
$661$	−34.4019	−	12.5213i	−1.33808	−	0.487021i	−0.428873	−	0.903365i	$-0.641089\pi$
$661$	−34.4019	−	12.5213i	−1.33808	−	0.487021i	−0.909207	+	0.416343i	$0.863311\pi$
$662$		0			0
$663$	−1.37315	+	3.64219i	−0.0533286	+	0.141451i
$664$		0			0
$665$	0.110641	+	0.191636i	0.00429047	+	0.00743131i
$666$		0			0
$667$	−1.92226	+	3.32944i	−0.0744300	+	0.128917i
$668$		0			0
$669$	3.12169	+	8.89276i	0.120692	+	0.343814i
$670$		0			0
$671$	0.829461	−	0.696000i	0.0320210	−	0.0268688i
$672$		0			0
$673$	−7.31470	+	2.66233i	−0.281961	+	0.102625i	−0.479129	−	0.877744i	$-0.659048\pi$
$673$	−7.31470	+	2.66233i	−0.281961	+	0.102625i	0.197169	+	0.980370i	$0.436825\pi$
$674$		0			0
$675$	6.07362	+	18.6606i	0.233774	+	0.718246i
$676$		0			0
$677$	14.0468	−	5.11260i	0.539861	−	0.196493i	−0.0576750	−	0.998335i	$-0.518369\pi$
$677$	14.0468	−	5.11260i	0.539861	−	0.196493i	0.597536	+	0.801842i	$0.296146\pi$
$678$		0			0
$679$	2.20703	−	1.85192i	0.0846979	−	0.0710700i
$680$		0			0
$681$	−17.4303	+	20.2953i	−0.667929	+	0.777718i
$682$		0			0
$683$	0.683169	−	1.18328i	0.0261407	−	0.0452771i	−0.852659	−	0.522468i	$-0.825012\pi$
$683$	0.683169	−	1.18328i	0.0261407	−	0.0452771i	0.878800	+	0.477191i	$0.158345\pi$
$684$		0			0
$685$	−2.60061	−	4.50439i	−0.0993642	−	0.172104i
$686$		0			0
$687$	12.4696	+	15.2116i	0.475747	+	0.580360i
$688$		0			0
$689$	−1.82535	−	0.664374i	−0.0695404	−	0.0253107i
$690$		0			0
$691$	−1.85765	+	10.5353i	−0.0706684	+	0.400781i	0.928870	+	0.370406i	$0.120781\pi$
$691$	−1.85765	+	10.5353i	−0.0706684	+	0.400781i	−0.999539	+	0.0303751i	$0.990330\pi$
$692$		0			0
$693$	−5.84441	−	2.28029i	−0.222011	−	0.0866210i
$694$		0			0
$695$	−8.32108	−	6.98221i	−0.315636	−	0.264850i
$696$		0			0
$697$	1.62534	+	9.21778i	0.0615643	+	0.349148i
$698$		0			0
$699$	0.119710	−	10.4390i	0.00452783	−	0.394839i
$700$		0			0
$701$	−36.8787			−1.39289			−0.696444	−	0.717611i	$-0.745236\pi$
$701$	−36.8787			−1.39289			−0.696444	+	0.717611i	$0.745236\pi$
$702$		0			0
$703$	−0.776703			−0.0292939
$704$		0			0
$705$	−5.49813	+	3.09083i	−0.207072	+	0.116408i
$706$		0			0
$707$	−1.50864	−	8.55590i	−0.0567381	−	0.321778i
$708$		0			0
$709$	−16.9790	−	14.2470i	−0.637658	−	0.535059i	0.265640	−	0.964072i	$-0.414417\pi$
$709$	−16.9790	−	14.2470i	−0.637658	−	0.535059i	−0.903298	+	0.429013i	$0.858861\pi$
$710$		0			0
$711$	−14.8559	−	13.0577i	−0.557142	−	0.489703i
$712$		0			0
$713$	1.55210	−	8.80241i	0.0581267	−	0.329653i
$714$		0			0
$715$	1.00800	+	0.366883i	0.0376972	+	0.0137207i
$716$		0			0
$717$	−11.7592	+	1.93470i	−0.439156	+	0.0722529i
$718$		0			0
$719$	−4.37232	−	7.57308i	−0.163060	−	0.282428i	0.772905	−	0.634522i	$-0.218803\pi$
$719$	−4.37232	−	7.57308i	−0.163060	−	0.282428i	−0.935965	+	0.352094i	$0.885470\pi$
$720$		0			0
$721$	4.33890	−	7.51520i	0.161589	−	0.279881i
$722$		0			0
$723$	−35.3605	−	6.65396i	−1.31507	−	0.247463i
$724$		0			0
$725$	−11.2682	+	9.45517i	−0.418492	+	0.351156i
$726$		0			0
$727$	35.0357	−	12.7519i	1.29940	−	0.472943i	0.402600	−	0.915376i	$-0.368107\pi$
$727$	35.0357	−	12.7519i	1.29940	−	0.472943i	0.896802	+	0.442433i	$0.145884\pi$
$728$		0			0
$729$	−26.9361	−	1.85619i	−0.997634	−	0.0687479i
$730$		0			0
$731$	24.3219	−	8.85244i	0.899577	−	0.327419i
$732$		0			0
$733$	−8.60263	+	7.21846i	−0.317745	+	0.266620i	−0.787685	−	0.616079i	$-0.788720\pi$
$733$	−8.60263	+	7.21846i	−0.317745	+	0.266620i	0.469939	+	0.882699i	$0.344276\pi$
$734$		0			0
$735$	1.88268	+	0.354274i	0.0694439	+	0.0130676i
$736$		0			0
$737$	3.01256	−	5.21791i	0.110969	−	0.192204i
$738$		0			0
$739$	−7.94372	−	13.7589i	−0.292214	−	0.506130i	0.682119	−	0.731242i	$-0.261059\pi$
$739$	−7.94372	−	13.7589i	−0.292214	−	0.506130i	−0.974333	+	0.225111i	$0.927725\pi$
$740$		0			0
$741$	−0.158580	+	0.0260906i	−0.00582557	+	0.000958462i
$742$		0			0
$743$	15.1175	+	5.50232i	0.554607	+	0.201860i	0.604092	−	0.796914i	$-0.293536\pi$
$743$	15.1175	+	5.50232i	0.554607	+	0.201860i	−0.0494852	+	0.998775i	$0.515758\pi$
$744$		0			0
$745$	2.70613	−	15.3472i	0.0991448	−	0.562278i
$746$		0			0
$747$	−21.8665	−	19.2197i	−0.800053	−	0.703211i
$748$		0			0
$749$	−2.02861	−	1.70220i	−0.0741238	−	0.0621972i
$750$		0			0
$751$	3.78360	+	21.4579i	0.138066	+	0.783009i	0.972676	+	0.232168i	$0.0745819\pi$
$751$	3.78360	+	21.4579i	0.138066	+	0.783009i	−0.834610	+	0.550841i	$0.814307\pi$
$752$		0			0
$753$	0.141108	−	0.0793253i	0.00514225	−	0.00289077i
$754$		0			0
$755$	−5.28697			−0.192413
$756$		0			0
$757$	−17.7315			−0.644463			−0.322232	−	0.946661i	$-0.604433\pi$
$757$	−17.7315			−0.644463			−0.322232	+	0.946661i	$0.604433\pi$
$758$		0			0
$759$	−0.0409957	+	3.57494i	−0.00148805	+	0.129762i
$760$		0			0
$761$	−7.12352	−	40.3995i	−0.258228	−	1.46448i	−0.787650	−	0.616123i	$-0.788702\pi$
$761$	−7.12352	−	40.3995i	−0.258228	−	1.46448i	0.529422	−	0.848358i	$-0.322409\pi$
$762$		0			0
$763$	13.5189	+	11.3437i	0.489415	+	0.410668i
$764$		0			0
$765$	14.9786	+	5.84414i	0.541553	+	0.211295i
$766$		0			0
$767$	−0.214184	+	1.21470i	−0.00773373	+	0.0438602i
$768$		0			0
$769$	22.1502	+	8.06201i	0.798756	+	0.290724i	0.708971	−	0.705238i	$-0.249160\pi$
$769$	22.1502	+	8.06201i	0.798756	+	0.290724i	0.0897853	+	0.995961i	$0.471382\pi$
$770$		0			0
$771$	31.2156	+	38.0796i	1.12420	+	1.37140i
$772$		0			0
$773$	19.3772	+	33.5622i	0.696948	+	1.20715i	0.969520	+	0.245013i	$0.0787924\pi$
$773$	19.3772	+	33.5622i	0.696948	+	1.20715i	−0.272572	+	0.962135i	$0.587874\pi$
$774$		0			0
$775$	17.0994	−	29.6170i	0.614229	−	1.06388i
$776$		0			0
$777$	−4.38104	+	5.10117i	−0.157169	+	0.183003i
$778$		0			0
$779$	−0.296043	+	0.248409i	−0.0106068	+	0.00890019i
$780$		0			0
$781$	25.8598	−	9.41219i	0.925336	−	0.336795i
$782$		0			0
$783$	−6.26373	−	19.2447i	−0.223847	−	0.687748i
$784$		0			0
$785$	−13.5136	+	4.91853i	−0.482319	+	0.175550i
$786$		0			0
$787$	−13.4296	+	11.2688i	−0.478714	+	0.401689i	−0.849961	−	0.526845i	$-0.823375\pi$
$787$	−13.4296	+	11.2688i	−0.478714	+	0.401689i	0.371247	+	0.928534i	$0.378930\pi$
$788$		0			0
$789$	−11.4089	−	32.5006i	−0.406168	−	1.15705i
$790$		0			0
$791$	7.63656	−	13.2269i	0.271525	−	0.470295i
$792$		0			0
$793$	−0.120071	−	0.207968i	−0.00426383	−	0.00738518i
$794$		0			0
$795$	−2.83058	+	7.50795i	−0.100390	+	0.266280i
$796$		0			0
$797$	26.1306	+	9.51078i	0.925595	+	0.336889i	0.760462	−	0.649382i	$-0.224972\pi$
$797$	26.1306	+	9.51078i	0.925595	+	0.336889i	0.165133	+	0.986271i	$0.447195\pi$
$798$		0			0
$799$	2.77032	−	15.7113i	0.0980070	−	0.555825i
$800$		0			0
$801$	−1.11374	−	0.0255471i	−0.0393521	−	0.000902661i
$802$		0			0
$803$	−12.3382	−	10.3530i	−0.435406	−	0.365349i
$804$		0			0
$805$	−0.189579	−	1.07516i	−0.00668179	−	0.0378943i
$806$		0			0
$807$	4.63546	+	2.74763i	0.163176	+	0.0967212i
$808$		0			0
$809$	−8.66229			−0.304550			−0.152275	−	0.988338i	$-0.548660\pi$
$809$	−8.66229			−0.304550			−0.152275	+	0.988338i	$0.548660\pi$
$810$		0			0
$811$	17.6672			0.620378			0.310189	−	0.950675i	$-0.399608\pi$
$811$	17.6672			0.620378			0.310189	+	0.950675i	$0.399608\pi$
$812$		0			0
$813$	33.3239	+	19.7525i	1.16872	+	0.692749i
$814$		0			0
$815$	2.70495	+	15.3405i	0.0947504	+	0.537356i
$816$		0			0
$817$	0.818636	+	0.686917i	0.0286404	+	0.0240322i
$818$		0			0
$819$	−0.723122	+	1.18867i	−0.0252679	+	0.0415356i
$820$		0			0
$821$	−6.35371	+	36.0337i	−0.221746	+	1.25758i	0.647063	+	0.762437i	$0.275997\pi$
$821$	−6.35371	+	36.0337i	−0.221746	+	1.25758i	−0.868809	+	0.495147i	$0.835114\pi$
$822$		0			0
$823$	−28.6698	−	10.4349i	−0.999365	−	0.363739i	−0.210025	−	0.977696i	$-0.567355\pi$
$823$	−28.6698	−	10.4349i	−0.999365	−	0.363739i	−0.789340	+	0.613957i	$0.789577\pi$
$824$		0			0
$825$	−4.82562	+	12.7997i	−0.168007	+	0.445627i
$826$		0			0
$827$	0.504803	+	0.874345i	0.0175537	+	0.0304040i	0.874669	−	0.484721i	$-0.161079\pi$
$827$	0.504803	+	0.874345i	0.0175537	+	0.0304040i	−0.857115	+	0.515125i	$0.827746\pi$
$828$		0			0
$829$	−15.6749	+	27.1498i	−0.544413	+	0.942952i	0.454230	+	0.890884i	$0.349914\pi$
$829$	−15.6749	+	27.1498i	−0.544413	+	0.942952i	−0.998644	+	0.0520674i	$0.983419\pi$
$830$		0			0
$831$	−8.94316	−	25.4764i	−0.310235	−	0.883766i
$832$		0			0
$833$	−3.71194	+	3.11469i	−0.128611	+	0.107917i
$834$		0			0
$835$	3.19270	−	1.16205i	0.110488	−	0.0402143i
$836$		0			0
$837$	28.9873	+	37.0634i	1.00195	+	1.28110i
$838$		0			0
$839$	−18.9614	+	6.90138i	−0.654619	+	0.238262i	−0.647912	−	0.761716i	$-0.724357\pi$
$839$	−18.9614	+	6.90138i	−0.654619	+	0.238262i	−0.00670773	+	0.999978i	$0.502135\pi$
$840$		0			0
$841$	−10.5944	+	8.88972i	−0.365322	+	0.306542i
$842$		0			0
$843$	6.08222	−	7.08197i	0.209483	−	0.243916i
$844$		0			0
$845$	−7.07035	+	12.2462i	−0.243227	+	0.421282i
$846$		0			0
$847$	3.31351	+	5.73916i	0.113853	+	0.197200i
$848$		0			0
$849$	−26.1596	−	31.9119i	−0.897794	−	1.09521i
$850$		0			0
$851$	3.60094	+	1.31063i	0.123439	+	0.0449280i
$852$		0			0
$853$	9.16916	−	52.0009i	0.313946	−	1.78048i	−0.264123	−	0.964489i	$-0.585083\pi$
$853$	9.16916	−	52.0009i	0.313946	−	1.78048i	0.578069	−	0.815988i	$-0.303806\pi$
$854$		0			0
$855$	0.100253	+	0.656232i	0.00342859	+	0.0224426i
$856$		0			0
$857$	20.7983	+	17.4518i	0.710455	+	0.596142i	0.924727	−	0.380632i	$-0.124293\pi$
$857$	20.7983	+	17.4518i	0.710455	+	0.596142i	−0.214272	+	0.976774i	$0.568738\pi$
$858$		0			0
$859$	−8.61704	−	48.8696i	−0.294010	−	1.66741i	−0.671201	−	0.741276i	$-0.734221\pi$
$859$	−8.61704	−	48.8696i	−0.294010	−	1.66741i	0.377191	−	0.926135i	$-0.376890\pi$
$860$		0			0
$861$	−0.0383645	+	3.34549i	−0.00130746	+	0.114014i
$862$		0			0
$863$	−1.22203			−0.0415985			−0.0207992	−	0.999784i	$-0.506621\pi$
$863$	−1.22203			−0.0415985			−0.0207992	+	0.999784i	$0.506621\pi$
$864$		0			0
$865$	13.4307			0.456658
$866$		0			0
$867$	−9.78335	+	5.49981i	−0.332260	+	0.186783i
$868$		0			0
$869$	−2.39408	−	13.5775i	−0.0812137	−	0.460586i
$870$		0			0
$871$	−1.02363	−	0.858931i	−0.0346845	−	0.0291038i
$872$		0			0
$873$	8.18761	−	2.76912i	0.277109	−	0.0937205i
$874$		0			0
$875$	1.68567	−	9.55991i	0.0569861	−	0.323184i
$876$		0			0
$877$	34.5948	+	12.5915i	1.16818	+	0.425185i	0.852015	−	0.523518i	$-0.175381\pi$
$877$	34.5948	+	12.5915i	1.16818	+	0.425185i	0.316170	+	0.948702i	$0.397603\pi$
$878$		0			0
$879$	0.150480	−	0.0247581i	0.00507558	−	0.000835069i
$880$		0			0
$881$	−21.3297	−	36.9442i	−0.718616	−	1.24468i	−0.961548	−	0.274637i	$-0.911442\pi$
$881$	−21.3297	−	36.9442i	−0.718616	−	1.24468i	0.242932	−	0.970043i	$-0.421891\pi$
$882$		0			0
$883$	8.60116	−	14.8976i	0.289452	−	0.501346i	−0.684227	−	0.729269i	$-0.739860\pi$
$883$	8.60116	−	14.8976i	0.289452	−	0.501346i	0.973679	+	0.227923i	$0.0731936\pi$
$884$		0			0
$885$	5.00703	+	0.942197i	0.168309	+	0.0316716i
$886$		0			0
$887$	−10.1131	+	8.48590i	−0.339565	+	0.284929i	−0.796584	−	0.604528i	$-0.793362\pi$
$887$	−10.1131	+	8.48590i	−0.339565	+	0.284929i	0.457019	+	0.889457i	$0.348917\pi$
$888$		0			0
$889$	9.45265	−	3.44048i	0.317032	−	0.115390i
$890$		0			0
$891$	−13.8475	−	12.7459i	−0.463908	−	0.427005i
$892$		0			0
$893$	0.618973	−	0.225288i	0.0207131	−	0.00753897i
$894$		0			0
$895$	−15.8761	+	13.3216i	−0.530680	+	0.445293i
$896$		0			0
$897$	0.779231	+	0.146632i	0.0260178	+	0.00489589i
$898$		0			0
$899$	−17.6346	+	30.5441i	−0.588148	+	1.01870i
$900$		0			0
$901$	−10.1476	−	17.5762i	−0.338066	−	0.585547i
$902$		0			0
$903$	9.12904	−	1.50197i	0.303795	−	0.0499825i
$904$		0			0
$905$	11.1378	+	4.05382i	0.370232	+	0.134753i
$906$		0			0
$907$	−8.32024	+	47.1864i	−0.276269	+	1.56680i	0.458633	+	0.888626i	$0.348339\pi$
$907$	−8.32024	+	47.1864i	−0.276269	+	1.56680i	−0.734902	+	0.678174i	$0.762772\pi$
$908$		0			0
$909$	5.11333	−	25.5572i	0.169598	−	0.847677i
$910$		0			0
$911$	−27.0429	−	22.6917i	−0.895970	−	0.751808i	0.0734286	−	0.997300i	$-0.476606\pi$
$911$	−27.0429	−	22.6917i	−0.895970	−	0.751808i	−0.969398	+	0.245492i	$0.921050\pi$
$912$		0			0
$913$	−3.52385	−	19.9848i	−0.116623	−	0.661399i
$914$		0			0
$915$	−0.864678	+	0.486088i	−0.0285854	+	0.0160696i
$916$		0			0
$917$	−12.9599			−0.427974
$918$		0			0
$919$	−17.6688			−0.582840			−0.291420	−	0.956595i	$-0.594128\pi$
$919$	−17.6688			−0.582840			−0.291420	+	0.956595i	$0.594128\pi$
$920$		0			0
$921$	−0.599741	+	52.2991i	−0.0197621	+	1.72331i
$922$		0			0
$923$	−1.05983	−	6.01057i	−0.0348846	−	0.197840i
$924$		0			0
$925$	11.2317	+	9.42450i	0.369295	+	0.309876i
$926$		0			0
$927$	20.3212	−	16.2722i	0.667437	−	0.534450i
$928$		0			0
$929$	9.17497	−	52.0338i	0.301021	−	1.70717i	−0.340646	−	0.940191i	$-0.610646\pi$
$929$	9.17497	−	52.0338i	0.301021	−	1.70717i	0.641667	−	0.766983i	$-0.278243\pi$
$930$		0			0
$931$	−0.188000	−	0.0684265i	−0.00616146	−	0.00224259i
$932$		0			0
$933$	30.9754	+	37.7866i	1.01409	+	1.23708i
$934$		0			0
$935$	5.60375	+	9.70599i	0.183262	+	0.317420i
$936$		0			0
$937$	3.84621	−	6.66183i	0.125650	−	0.217633i	−0.796337	−	0.604854i	$-0.793232\pi$
$937$	3.84621	−	6.66183i	0.125650	−	0.217633i	0.921987	+	0.387221i	$0.126565\pi$
$938$		0			0
$939$	−21.2116	+	24.6982i	−0.692215	+	0.805996i
$940$		0			0
$941$	−27.2686	+	22.8811i	−0.888931	+	0.745902i	−0.967995	−	0.250968i	$-0.919251\pi$
$941$	−27.2686	+	22.8811i	−0.888931	+	0.745902i	0.0790642	+	0.996870i	$0.474807\pi$
$942$		0			0
$943$	1.79168	−	0.652120i	0.0583452	−	0.0212359i
$944$		0			0
$945$	4.87543	+	3.04308i	0.158598	+	0.0989914i
$946$		0			0
$947$	9.06040	−	3.29772i	0.294423	−	0.107161i	−0.190585	−	0.981671i	$-0.561039\pi$
$947$	9.06040	−	3.29772i	0.294423	−	0.107161i	0.485009	+	0.874509i	$0.338816\pi$
$948$		0			0
$949$	−2.73638	+	2.29610i	−0.0888268	+	0.0745345i
$950$		0			0
$951$	17.2232	+	49.0638i	0.558502	+	1.59100i
$952$		0			0
$953$	11.3987	−	19.7431i	0.369240	−	0.639543i	−0.620207	−	0.784438i	$-0.712951\pi$
$953$	11.3987	−	19.7431i	0.369240	−	0.639543i	0.989447	+	0.144895i	$0.0462846\pi$
$954$		0			0
$955$	12.7304	+	22.0497i	0.411946	+	0.713511i
$956$		0			0
$957$	4.97667	−	13.2003i	0.160873	−	0.426705i
$958$		0			0
$959$	4.41894	+	1.60836i	0.142695	+	0.0519367i
$960$		0			0
$961$	8.85578	−	50.2236i	0.285670	−	1.62012i
$962$		0			0
$963$	−3.81342	−	6.96941i	−0.122886	−	0.224586i
$964$		0			0
$965$	−7.02102	−	5.89134i	−0.226015	−	0.189649i
$966$		0			0
$967$	9.12799	+	51.7674i	0.293536	+	1.66473i	0.673092	+	0.739559i	$0.264966\pi$
$967$	9.12799	+	51.7674i	0.293536	+	1.66473i	−0.379555	+	0.925169i	$0.623923\pi$
$968$		0			0
$969$	−1.44443	−	0.856176i	−0.0464018	−	0.0275043i
$970$		0			0
$971$	−53.7088			−1.72360			−0.861799	−	0.507250i	$-0.830662\pi$
$971$	−53.7088			−1.72360			−0.861799	+	0.507250i	$0.830662\pi$
$972$		0			0
$973$	9.82093			0.314844
$974$		0			0
$975$	2.60976	+	1.54691i	0.0835791	+	0.0495409i
$976$		0			0
$977$	−8.28368	−	46.9791i	−0.265018	−	1.50299i	−0.768983	−	0.639269i	$-0.779237\pi$
$977$	−8.28368	−	46.9791i	−0.265018	−	1.50299i	0.503965	−	0.863724i	$-0.331874\pi$
$978$		0			0
$979$	−0.594867	−	0.499153i	−0.0190120	−	0.0159530i
$980$		0			0
$981$	25.4130	+	46.4448i	0.811375	+	1.48287i
$982$		0			0
$983$	4.86221	−	27.5749i	0.155080	−	0.879504i	−0.803632	−	0.595126i	$-0.797102\pi$
$983$	4.86221	−	27.5749i	0.155080	−	0.879504i	0.958712	−	0.284378i	$-0.0917869\pi$
$984$		0			0
$985$	−24.2360	−	8.82118i	−0.772223	−	0.281066i
$986$		0			0
$987$	2.01173	−	5.33599i	0.0640340	−	0.169846i
$988$		0			0
$989$	−2.63622	−	4.56607i	−0.0838269	−	0.145192i
$990$		0			0
$991$	20.5919	−	35.6662i	0.654122	−	1.13297i	−0.327991	−	0.944681i	$-0.606372\pi$
$991$	20.5919	−	35.6662i	0.654122	−	1.13297i	0.982113	−	0.188292i	$-0.0602951\pi$
$992$		0			0
$993$	−13.0122	−	37.0677i	−0.412929	−	1.17631i
$994$		0			0
$995$	−12.3655	+	10.3759i	−0.392014	+	0.328939i
$996$		0			0
$997$	−20.4989	+	7.46100i	−0.649208	+	0.236292i	−0.645570	−	0.763701i	$-0.723380\pi$
$997$	−20.4989	+	7.46100i	−0.649208	+	0.236292i	−0.00363768	+	0.999993i	$0.501158\pi$
$998$		0			0
$999$	−17.8067	+	9.47952i	−0.563378	+	0.299919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.169.8	yes	54
27.4	even	9	inner	756.2.bo.a.85.8	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.8	✓	54	27.4	even	9	inner
756.2.bo.a.169.8	yes	54	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48997 + 0.883169i) q^{3} +(-0.192063 - 1.08924i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.44003 + 2.63179i) q^{9} +O(q^{10})\)	\(q+(1.48997 + 0.883169i) q^{3} +(-0.192063 - 1.08924i) q^{5} +(0.766044 + 0.642788i) q^{7} +(1.44003 + 2.63179i) q^{9} +(-0.363128 + 2.05940i) q^{11} +(0.435813 + 0.158623i) q^{13} +(0.675817 - 1.79256i) q^{15} +(2.42280 + 4.19641i) q^{17} +(-0.100033 + 0.173262i) q^{19} +(0.573694 + 1.63428i) q^{21} +(0.756139 - 0.634476i) q^{23} +(3.54890 - 1.29169i) q^{25} +(-0.178718 + 5.19308i) q^{27} +(-3.65999 + 1.33213i) q^{29} +(6.93676 - 5.82063i) q^{31} +(-2.35985 + 2.74774i) q^{33} +(0.553023 - 0.957864i) q^{35} +(1.94112 + 3.36212i) q^{37} +(0.509258 + 0.621240i) q^{39} +(1.81516 + 0.660663i) q^{41} +(0.927544 - 5.26036i) q^{43} +(2.59008 - 2.07401i) q^{45} +(-2.52213 - 2.11632i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-0.0962385 + 8.39226i) q^{51} -4.18839 q^{53} +2.31293 q^{55} +(-0.302065 + 0.169809i) q^{57} +(0.461820 + 2.61911i) q^{59} +(-0.396649 - 0.332828i) q^{61} +(-0.588559 + 2.94170i) q^{63} +(0.0890754 - 0.505171i) q^{65} +(-2.70746 - 0.985435i) q^{67} +(1.68697 - 0.277552i) q^{69} +(-6.57991 - 11.3967i) q^{71} +(-3.85105 + 6.67021i) q^{73} +(6.42854 + 1.20969i) q^{75} +(-1.60193 + 1.34418i) q^{77} +(-6.19535 + 2.25492i) q^{79} +(-4.85265 + 7.57970i) q^{81} +(-9.11894 + 3.31902i) q^{83} +(4.10557 - 3.44499i) q^{85} +(-6.62976 - 1.24756i) q^{87} +(-0.185672 + 0.321594i) q^{89} +(0.231891 + 0.401647i) q^{91} +(15.4762 - 2.54624i) q^{93} +(0.207937 + 0.0756828i) q^{95} +(0.500292 - 2.83730i) q^{97} +(-5.94282 + 2.00991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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