LMFDB - Embedded newform 234.2.t.a.103.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("234.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.14
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.66410 + 0.480381i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.515076 + 0.297379i) q^{5} +(1.68134 - 0.416029i) q^{6} +(-1.45217 + 0.838409i) q^{7} -1.00000i q^{8} +(2.53847 + 1.59880i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.66410 + 0.480381i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.515076 + 0.297379i) q^{5} +(1.68134 - 0.416029i) q^{6} +(-1.45217 + 0.838409i) q^{7} -1.00000i q^{8} +(2.53847 + 1.59880i) q^{9} +0.594758 q^{10} +(-0.416337 + 0.240372i) q^{11} +(1.24807 - 1.20096i) q^{12} +(-2.27160 - 2.79997i) q^{13} +(-0.838409 + 1.45217i) q^{14} +(0.714283 + 0.742302i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.09349 q^{17} +(2.99778 + 0.115371i) q^{18} -0.480744i q^{19} +(0.515076 - 0.297379i) q^{20} +(-2.81931 + 0.697605i) q^{21} +(-0.240372 + 0.416337i) q^{22} +(-1.83339 + 3.17553i) q^{23} +(0.480381 - 1.66410i) q^{24} +(-2.32313 - 4.02378i) q^{25} +(-3.36725 - 1.28905i) q^{26} +(3.45624 + 3.88001i) q^{27} +1.67682i q^{28} +(1.23339 + 2.13629i) q^{29} +(0.989738 + 0.285710i) q^{30} +(-0.993791 - 0.573765i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.808297 + 0.200004i) q^{33} +(-1.81302 + 1.04675i) q^{34} -0.997301 q^{35} +(2.65384 - 1.39898i) q^{36} -3.65012i q^{37} +(-0.240372 - 0.416337i) q^{38} +(-2.43512 - 5.75067i) q^{39} +(0.297379 - 0.515076i) q^{40} +(8.58235 + 4.95502i) q^{41} +(-2.09279 + 2.01380i) q^{42} +(-3.45822 - 5.98981i) q^{43} +0.480744i q^{44} +(0.832053 + 1.57839i) q^{45} +3.66679i q^{46} +(-5.40488 + 3.12051i) q^{47} +(-0.416029 - 1.68134i) q^{48} +(-2.09414 + 3.62716i) q^{49} +(-4.02378 - 2.32313i) q^{50} +(-3.48378 - 1.00567i) q^{51} +(-3.56065 + 0.567277i) q^{52} -5.08592 q^{53} +(4.93319 + 1.63207i) q^{54} -0.285927 q^{55} +(0.838409 + 1.45217i) q^{56} +(0.230940 - 0.800008i) q^{57} +(2.13629 + 1.23339i) q^{58} +(8.13185 + 4.69493i) q^{59} +(0.999994 - 0.247437i) q^{60} +(-3.90635 - 6.76599i) q^{61} -1.14753 q^{62} +(-5.02673 - 0.193456i) q^{63} -1.00000 q^{64} +(-0.337393 - 2.11772i) q^{65} +(-0.600004 + 0.577357i) q^{66} +(12.4551 + 7.19096i) q^{67} +(-1.04675 + 1.81302i) q^{68} +(-4.57642 + 4.40368i) q^{69} +(-0.863688 + 0.498651i) q^{70} +6.51028i q^{71} +(1.59880 - 2.53847i) q^{72} -5.91514i q^{73} +(-1.82506 - 3.16110i) q^{74} +(-1.93298 - 7.81197i) q^{75} +(-0.416337 - 0.240372i) q^{76} +(0.403061 - 0.698121i) q^{77} +(-4.98421 - 3.76267i) q^{78} +(1.02895 + 1.78219i) q^{79} -0.594758i q^{80} +(3.88765 + 8.11703i) q^{81} +9.91005 q^{82} +(-9.57834 + 5.53006i) q^{83} +(-0.805511 + 2.79040i) q^{84} +(-1.07831 - 0.622560i) q^{85} +(-5.98981 - 3.45822i) q^{86} +(1.02625 + 4.14750i) q^{87} +(0.240372 + 0.416337i) q^{88} -9.48720i q^{89} +(1.50978 + 0.950902i) q^{90} +(5.64626 + 2.16150i) q^{91} +(1.83339 + 3.17553i) q^{92} +(-1.37814 - 1.43220i) q^{93} +(-3.12051 + 5.40488i) q^{94} +(0.142963 - 0.247620i) q^{95} +(-1.20096 - 1.24807i) q^{96} +(8.41374 - 4.85767i) q^{97} +4.18828i q^{98} +(-1.44117 - 0.0554640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.66410	+	0.480381i	0.960770	+	0.277348i
$3$	1.66410	+	0.480381i	0.960770	+	0.277348i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.515076	+	0.297379i	0.230349	+	0.132992i	0.610733	−	0.791837i	$-0.290875\pi$
$5$	0.515076	+	0.297379i	0.230349	+	0.132992i	−0.380384	+	0.924829i	$0.624208\pi$
$6$	1.68134	−	0.416029i	0.686406	−	0.169843i
$7$	−1.45217	+	0.838409i	−0.548868	+	0.316889i	−0.748665	−	0.662948i	$-0.769305\pi$
$7$	−1.45217	+	0.838409i	−0.548868	+	0.316889i	0.199798	+	0.979837i	$0.435972\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.53847	+	1.59880i	0.846156	+	0.532935i
$10$	0.594758			0.188079
$11$	−0.416337	+	0.240372i	−0.125530	+	0.0724750i	−0.561450	−	0.827510i	$-0.689756\pi$
$11$	−0.416337	+	0.240372i	−0.125530	+	0.0724750i	0.435920	+	0.899985i	$0.356423\pi$
$12$	1.24807	−	1.20096i	0.360288	−	0.346688i
$13$	−2.27160	−	2.79997i	−0.630028	−	0.776572i
$13$	−2.27160	−	2.79997i	−0.630028	−	0.776572i
$14$	−0.838409	+	1.45217i	−0.224074	+	0.388108i
$15$	0.714283	+	0.742302i	0.184427	+	0.191661i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.09349			−0.507746			−0.253873	−	0.967238i	$-0.581705\pi$
$17$	−2.09349			−0.507746			−0.253873	+	0.967238i	$0.581705\pi$
$18$	2.99778	+	0.115371i	0.706584	+	0.0271932i
$19$		−	0.480744i		−	0.110290i	−0.998478	−	0.0551452i	$-0.982438\pi$
$19$		−	0.480744i		−	0.110290i	0.998478	−	0.0551452i	$-0.0175622\pi$
$20$	0.515076	−	0.297379i	0.115174	−	0.0664960i
$21$	−2.81931	+	0.697605i	−0.615224	+	0.152230i
$22$	−0.240372	+	0.416337i	−0.0512475	+	0.0887633i
$23$	−1.83339	+	3.17553i	−0.382289	+	0.662144i	−0.991389	−	0.130950i	$-0.958197\pi$
$23$	−1.83339	+	3.17553i	−0.382289	+	0.662144i	0.609100	+	0.793093i	$0.291531\pi$
$24$	0.480381	−	1.66410i	0.0980573	−	0.339683i
$25$	−2.32313	−	4.02378i	−0.464626	−	0.804756i
$26$	−3.36725	−	1.28905i	−0.660372	−	0.252803i
$27$	3.45624	+	3.88001i	0.665153	+	0.746707i
$28$			1.67682i			0.316889i
$29$	1.23339	+	2.13629i	0.229035	+	0.396700i	0.957522	−	0.288359i	$-0.0931098\pi$
$29$	1.23339	+	2.13629i	0.229035	+	0.396700i	−0.728488	+	0.685059i	$0.759776\pi$
$30$	0.989738	+	0.285710i	0.180701	+	0.0521633i
$31$	−0.993791	−	0.573765i	−0.178490	−	0.103051i	0.408093	−	0.912940i	$-0.366194\pi$
$31$	−0.993791	−	0.573765i	−0.178490	−	0.103051i	−0.586583	+	0.809889i	$0.699527\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.808297	+	0.200004i	−0.140706	+	0.0348162i
$34$	−1.81302	+	1.04675i	−0.310930	+	0.179515i
$35$	−0.997301			−0.168575
$36$	2.65384	−	1.39898i	0.442307	−	0.233163i
$37$		−	3.65012i		−	0.600076i	−0.953927	−	0.300038i	$-0.903001\pi$
$37$		−	3.65012i		−	0.600076i	0.953927	−	0.300038i	$-0.0969994\pi$
$38$	−0.240372	−	0.416337i	−0.0389935	−	0.0675388i
$39$	−2.43512	−	5.75067i	−0.389931	−	0.920844i
$40$	0.297379	−	0.515076i	0.0470198	−	0.0814406i
$41$	8.58235	+	4.95502i	1.34034	+	0.773845i	0.986857	−	0.161597i	$-0.0516645\pi$
$41$	8.58235	+	4.95502i	1.34034	+	0.773845i	0.353481	+	0.935442i	$0.384998\pi$
$42$	−2.09279	+	2.01380i	−0.322925	+	0.310736i
$43$	−3.45822	−	5.98981i	−0.527374	−	0.913438i	−0.999491	−	0.0319023i	$-0.989843\pi$
$43$	−3.45822	−	5.98981i	−0.527374	−	0.913438i	0.472117	−	0.881536i	$-0.343490\pi$
$44$			0.480744i			0.0724750i
$45$	0.832053	+	1.57839i	0.124035	+	0.235293i
$46$			3.66679i			0.540638i
$47$	−5.40488	+	3.12051i	−0.788383	+	0.455173i	−0.839393	−	0.543525i	$-0.817089\pi$
$47$	−5.40488	+	3.12051i	−0.788383	+	0.455173i	0.0510099	+	0.998698i	$0.483756\pi$
$48$	−0.416029	−	1.68134i	−0.0600486	−	0.242681i
$49$	−2.09414	+	3.62716i	−0.299163	+	0.518165i
$50$	−4.02378	−	2.32313i	−0.569049	−	0.328540i
$51$	−3.48378	−	1.00567i	−0.487827	−	0.140822i
$52$	−3.56065	+	0.567277i	−0.493773	+	0.0786671i
$53$	−5.08592			−0.698605			−0.349302	−	0.937010i	$-0.613581\pi$
$53$	−5.08592			−0.698605			−0.349302	+	0.937010i	$0.613581\pi$
$54$	4.93319	+	1.63207i	0.671322	+	0.222096i
$55$	−0.285927			−0.0385544
$56$	0.838409	+	1.45217i	0.112037	+	0.194054i
$57$	0.230940	−	0.800008i	0.0305888	−	0.105964i
$58$	2.13629	+	1.23339i	0.280509	+	0.161952i
$59$	8.13185	+	4.69493i	1.05868	+	0.611227i	0.925066	−	0.379807i	$-0.124009\pi$
$59$	8.13185	+	4.69493i	1.05868	+	0.611227i	0.133611	+	0.991034i	$0.457343\pi$
$60$	0.999994	−	0.247437i	0.129099	−	0.0319439i
$61$	−3.90635	−	6.76599i	−0.500157	−	0.866297i	−1.00000		0.000180927i	$-0.999942\pi$
$61$	−3.90635	−	6.76599i	−0.500157	−	0.866297i	0.499843	−	0.866116i	$-0.333391\pi$
$62$	−1.14753			−0.145737
$63$	−5.02673	−	0.193456i	−0.633309	−	0.0243732i
$64$	−1.00000			−0.125000
$65$	−0.337393	−	2.11772i	−0.0418484	−	0.262671i
$66$	−0.600004	+	0.577357i	−0.0738554	+	0.0710677i
$67$	12.4551	+	7.19096i	1.52163	+	0.878516i	0.999674	+	0.0255454i	$0.00813225\pi$
$67$	12.4551	+	7.19096i	1.52163	+	0.878516i	0.521960	+	0.852970i	$0.325201\pi$
$68$	−1.04675	+	1.81302i	−0.126936	+	0.219860i
$69$	−4.57642	+	4.40368i	−0.550936	+	0.530141i
$70$	−0.863688	+	0.498651i	−0.103231	+	0.0596002i
$71$			6.51028i			0.772628i	0.922367	+	0.386314i	$0.126252\pi$
$71$			6.51028i			0.772628i	−0.922367	+	0.386314i	$0.873748\pi$
$72$	1.59880	−	2.53847i	0.188421	−	0.299161i
$73$		−	5.91514i		−	0.692315i	−0.938176	−	0.346157i	$-0.887486\pi$
$73$		−	5.91514i		−	0.692315i	0.938176	−	0.346157i	$-0.112514\pi$
$74$	−1.82506	−	3.16110i	−0.212159	−	0.367470i
$75$	−1.93298	−	7.81197i	−0.223201	−	0.902048i
$76$	−0.416337	−	0.240372i	−0.0477571	−	0.0275726i
$77$	0.403061	−	0.698121i	0.0459330	−	0.0795583i
$78$	−4.98421	−	3.76267i	−0.564351	−	0.426038i
$79$	1.02895	+	1.78219i	0.115766	+	0.200512i	0.918086	−	0.396382i	$-0.129734\pi$
$79$	1.02895	+	1.78219i	0.115766	+	0.200512i	−0.802320	+	0.596894i	$0.796401\pi$
$80$		−	0.594758i		−	0.0664960i
$81$	3.88765	+	8.11703i	0.431961	+	0.901892i
$82$	9.91005			1.09438
$83$	−9.57834	+	5.53006i	−1.05136	+	0.607003i	−0.923030	−	0.384729i	$-0.874295\pi$
$83$	−9.57834	+	5.53006i	−1.05136	+	0.607003i	−0.128330	+	0.991732i	$0.540962\pi$
$84$	−0.805511	+	2.79040i	−0.0878885	+	0.304457i
$85$	−1.07831	−	0.622560i	−0.116959	−	0.0675261i
$86$	−5.98981	−	3.45822i	−0.645898	−	0.372909i
$87$	1.02625	+	4.14750i	0.110026	+	0.444659i
$88$	0.240372	+	0.416337i	0.0256238	+	0.0443817i
$89$		−	9.48720i		−	1.00564i	−0.864391	−	0.502821i	$-0.832296\pi$
$89$		−	9.48720i		−	1.00564i	0.864391	−	0.502821i	$-0.167704\pi$
$90$	1.50978	+	0.950902i	0.159144	+	0.100234i
$91$	5.64626	+	2.16150i	0.591889	+	0.226586i
$92$	1.83339	+	3.17553i	0.191144	+	0.331072i
$93$	−1.37814	−	1.43220i	−0.142907	−	0.148512i
$94$	−3.12051	+	5.40488i	−0.321856	+	0.557471i
$95$	0.142963	−	0.247620i	0.0146677	−	0.0254053i
$96$	−1.20096	−	1.24807i	−0.122573	−	0.127381i
$97$	8.41374	−	4.85767i	0.854286	−	0.493222i	−0.00780887	−	0.999970i	$-0.502486\pi$
$97$	8.41374	−	4.85767i	0.854286	−	0.493222i	0.862095	+	0.506747i	$0.169152\pi$
$98$			4.18828i			0.423080i
$99$	−1.44117	−	0.0554640i	−0.144843	−	0.00557435i
$100$	−4.64626			−0.464626
$101$	2.89748	+	5.01858i	0.288310	+	0.499367i	0.973406	−	0.229085i	$-0.0735734\pi$
$101$	2.89748	+	5.01858i	0.288310	+	0.499367i	−0.685097	+	0.728452i	$0.740240\pi$
$102$	−3.51988	+	0.870952i	−0.348520	+	0.0862371i
$103$	−0.857037	+	1.48443i	−0.0844463	+	0.146265i	−0.905155	−	0.425081i	$-0.860245\pi$
$103$	−0.857037	+	1.48443i	−0.0844463	+	0.146265i	0.820709	+	0.571347i	$0.193579\pi$
$104$	−2.79997	+	2.27160i	−0.274560	+	0.222749i
$105$	−1.65961	−	0.479084i	−0.161961	−	0.0467539i
$106$	−4.40453	+	2.54296i	−0.427806	+	0.246994i
$107$	14.1021			1.36330			0.681651	−	0.731678i	$-0.261262\pi$
$107$	14.1021			1.36330			0.681651	+	0.731678i	$0.261262\pi$
$108$	5.08830	−	1.05318i	0.489622	−	0.101343i
$109$		−	18.3474i		−	1.75736i	−0.477413	−	0.878679i	$-0.658425\pi$
$109$		−	18.3474i		−	1.75736i	0.477413	−	0.878679i	$-0.341575\pi$
$110$	−0.247620	+	0.142963i	−0.0236096	+	0.0136310i
$111$	1.75345	−	6.07417i	0.166430	−	0.576535i
$112$	1.45217	+	0.838409i	0.137217	+	0.0792222i
$113$	10.1390	−	17.5612i	0.953793	−	1.65202i	0.216686	−	0.976241i	$-0.430475\pi$
$113$	10.1390	−	17.5612i	0.953793	−	1.65202i	0.737107	−	0.675776i	$-0.236191\pi$
$114$	−0.200004	−	0.808297i	−0.0187321	−	0.0757040i
$115$	−1.88867	+	1.09043i	−0.176120	+	0.101683i
$116$	2.46678			0.229035
$117$	−1.28978	−	10.7395i	−0.119240	−	0.992865i
$118$	9.38985			0.864406
$119$	3.04010	−	1.75520i	0.278685	−	0.160899i
$120$	0.742302	−	0.714283i	0.0677626	−	0.0652048i
$121$	−5.38444	+	9.32613i	−0.489495	+	0.847830i
$122$	−6.76599	−	3.90635i	−0.612564	−	0.353664i
$123$	11.9016	+	12.3685i	1.07313	+	1.11523i
$124$	−0.993791	+	0.573765i	−0.0892450	+	0.0515256i
$125$		−	5.73719i		−	0.513150i
$126$	−4.45001	+	2.34583i	−0.396438	+	0.208983i
$127$	18.5473			1.64581			0.822904	−	0.568180i	$-0.192352\pi$
$127$	18.5473			1.64581			0.822904	+	0.568180i	$0.192352\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.87744	−	11.6289i	−0.253344	−	1.02387i
$130$	−1.35105	−	1.66531i	−0.118495	−	0.146057i
$131$	2.32256	−	4.02280i	0.202923	−	0.351474i	−0.746546	−	0.665334i	$-0.768289\pi$
$131$	2.32256	−	4.02280i	0.202923	−	0.351474i	0.949469	+	0.313861i	$0.101622\pi$
$132$	−0.230940	+	0.800008i	−0.0201008	+	0.0696317i
$133$	0.403061	+	0.698121i	0.0349498	+	0.0605348i
$134$	14.3819			1.24241
$135$	0.626390	+	3.02631i	0.0539111	+	0.260463i
$136$			2.09349i			0.179515i
$137$	11.2762	−	6.51034i	0.963395	−	0.556216i	0.0661784	−	0.997808i	$-0.478919\pi$
$137$	11.2762	−	6.51034i	0.963395	−	0.556216i	0.897216	+	0.441592i	$0.145586\pi$
$138$	−1.76145	+	6.10190i	−0.149945	+	0.519429i
$139$	−5.09027	+	8.81661i	−0.431751	+	0.747815i	−0.997024	−	0.0770888i	$-0.975437\pi$
$139$	−5.09027	+	8.81661i	−0.431751	+	0.747815i	0.565273	+	0.824904i	$0.308771\pi$
$140$	−0.498651	+	0.863688i	−0.0421437	+	0.0729950i
$141$	−10.4933	+	2.59645i	−0.883696	+	0.218660i
$142$	3.25514	+	5.63807i	0.273165	+	0.473136i
$143$	1.61879	+	0.619702i	0.135370	+	0.0518221i
$144$	0.115371	−	2.99778i	0.00961426	−	0.249815i
$145$			1.46714i			0.121839i
$146$	−2.95757	−	5.12266i	−0.244770	−	0.423955i
$147$	−5.22728	+	5.02997i	−0.431139	+	0.414865i
$148$	−3.16110	−	1.82506i	−0.259841	−	0.150019i
$149$	4.54901	+	2.62637i	0.372669	+	0.215161i	0.674624	−	0.738162i	$-0.264306\pi$
$149$	4.54901	+	2.62637i	0.372669	+	0.215161i	−0.301955	+	0.953322i	$0.597639\pi$
$150$	−5.57999	−	5.79887i	−0.455605	−	0.473476i
$151$	10.3258	−	5.96162i	0.840304	−	0.485150i	−0.0170637	−	0.999854i	$-0.505432\pi$
$151$	10.3258	−	5.96162i	0.840304	−	0.485150i	0.857367	+	0.514705i	$0.172098\pi$
$152$	−0.480744			−0.0389935
$153$	−5.31426	−	3.34708i	−0.429632	−	0.270596i
$154$		−	0.806121i		−	0.0649591i
$155$	−0.341252	−	0.591065i	−0.0274100	−	0.0474755i
$156$	−6.19779	−	0.766459i	−0.496220	−	0.0613659i
$157$	−6.19540	+	10.7307i	−0.494446	+	0.856406i	−0.999980	−	0.00640095i	$-0.997962\pi$
$157$	−6.19540	+	10.7307i	−0.494446	+	0.856406i	0.505533	+	0.862807i	$0.331296\pi$
$158$	1.78219	+	1.02895i	0.141784	+	0.0818588i
$159$	−8.46349	−	2.44318i	−0.671198	−	0.193757i
$160$	−0.297379	−	0.515076i	−0.0235099	−	0.0407203i
$161$		−	6.14853i		−	0.484572i
$162$	7.42532	+	5.08573i	0.583388	+	0.399573i
$163$			21.3629i			1.67327i	0.547760	+	0.836635i	$0.315481\pi$
$163$			21.3629i			1.67327i	−0.547760	+	0.836635i	$0.684519\pi$
$164$	8.58235	−	4.95502i	0.670169	−	0.386922i
$165$	−0.475811	−	0.137354i	−0.0370418	−	0.0106930i
$166$	−5.53006	+	9.57834i	−0.429216	+	0.743423i
$167$	−12.7614	−	7.36778i	−0.987504	−	0.570136i	−0.0829768	−	0.996551i	$-0.526443\pi$
$167$	−12.7614	−	7.36778i	−0.987504	−	0.570136i	−0.904527	+	0.426416i	$0.859776\pi$
$168$	0.697605	+	2.81931i	0.0538214	+	0.217514i
$169$	−2.67968	+	12.7208i	−0.206129	+	0.978525i
$170$	−1.24512			−0.0954964
$171$	0.768616	−	1.22035i	0.0587776	−	0.0933229i
$172$	−6.91644			−0.527374
$173$	−5.82435	−	10.0881i	−0.442817	−	0.766982i	0.555080	−	0.831797i	$-0.312688\pi$
$173$	−5.82435	−	10.0881i	−0.442817	−	0.766982i	−0.997897	+	0.0648152i	$0.979354\pi$
$174$	2.96251	+	3.07872i	0.224587	+	0.233397i
$175$	6.74715	+	3.89547i	0.510037	+	0.294470i
$176$	0.416337	+	0.240372i	0.0313826	+	0.0181187i
$177$	11.2769	+	11.7192i	0.847622	+	0.880870i
$178$	−4.74360	−	8.21616i	−0.355548	−	0.615827i
$179$	−0.896158			−0.0669820			−0.0334910	−	0.999439i	$-0.510663\pi$
$179$	−0.896158			−0.0669820			−0.0334910	+	0.999439i	$0.510663\pi$
$180$	1.78295	+	0.0686180i	0.132894	+	0.00511448i
$181$	1.42191			0.105689			0.0528447	−	0.998603i	$-0.483171\pi$
$181$	1.42191			0.105689			0.0528447	+	0.998603i	$0.483171\pi$
$182$	5.97056	−	0.951220i	0.442567	−	0.0705091i
$183$	−3.25031	−	13.1358i	−0.240270	−	0.971029i
$184$	3.17553	+	1.83339i	0.234103	+	0.135160i
$185$	1.08547	−	1.88009i	0.0798053	−	0.138227i
$186$	−1.90961	−	0.551252i	−0.140019	−	0.0404197i
$187$	0.871597	−	0.503217i	0.0637375	−	0.0367989i
$188$			6.24102i			0.455173i
$189$	−8.27206	−	2.73668i	−0.601704	−	0.199064i
$190$		−	0.285927i		−	0.0207433i
$191$	7.42036	+	12.8524i	0.536918	+	0.929970i	0.999068	+	0.0431677i	$0.0137450\pi$
$191$	7.42036	+	12.8524i	0.536918	+	0.929970i	−0.462150	+	0.886802i	$0.652922\pi$
$192$	−1.66410	−	0.480381i	−0.120096	−	0.0346685i
$193$	−12.2175	−	7.05376i	−0.879433	−	0.507741i	−0.00896136	−	0.999960i	$-0.502853\pi$
$193$	−12.2175	−	7.05376i	−0.879433	−	0.507741i	−0.870471	+	0.492219i	$0.836186\pi$
$194$	4.85767	−	8.41374i	0.348761	−	0.604071i
$195$	0.455858	−	3.68618i	0.0326447	−	0.263973i
$196$	2.09414	+	3.62716i	0.149581	+	0.259083i
$197$			0.442517i			0.0315280i	0.999876	+	0.0157640i	$0.00501805\pi$
$197$			0.442517i			0.0315280i	−0.999876	+	0.0157640i	$0.994982\pi$
$198$	−1.27582	+	0.672550i	−0.0906685	+	0.0477960i
$199$	−13.2925			−0.942282			−0.471141	−	0.882058i	$-0.656158\pi$
$199$	−13.2925			−0.942282			−0.471141	+	0.882058i	$0.656158\pi$
$200$	−4.02378	+	2.32313i	−0.284524	+	0.164270i
$201$	17.2722	+	17.9497i	1.21828	+	1.26607i
$202$	5.01858	+	2.89748i	0.353106	+	0.203866i
$203$	−3.58217	−	2.06817i	−0.251419	−	0.145157i
$204$	−2.61283	+	2.51421i	−0.182935	+	0.176030i
$205$	2.94704	+	5.10442i	0.205830	+	0.356508i
$206$			1.71407i			0.119425i
$207$	−9.73106	+	5.12975i	−0.676356	+	0.356542i
$208$	−1.28905	+	3.36725i	−0.0893793	+	0.233477i
$209$	0.115558	+	0.200152i	0.00799329	+	0.0138448i
$210$	−1.67681	+	0.414906i	−0.115711	+	0.0286313i
$211$	4.82032	−	8.34904i	0.331845	−	0.574772i	−0.651029	−	0.759053i	$-0.725662\pi$
$211$	4.82032	−	8.34904i	0.331845	−	0.574772i	0.982874	+	0.184281i	$0.0589957\pi$
$212$	−2.54296	+	4.40453i	−0.174651	+	0.302505i
$213$	−3.12741	+	10.8338i	−0.214287	+	0.742318i
$214$	12.2128	−	7.05105i	0.834848	−	0.482000i
$215$		−	4.11361i		−	0.280546i
$216$	3.88001	−	3.45624i	0.264001	−	0.235167i
$217$	1.92420			0.130623
$218$	−9.17368	−	15.8893i	−0.621320	−	1.07616i
$219$	2.84152	−	9.84340i	0.192012	−	0.665155i
$220$	−0.142963	+	0.247620i	−0.00963859	+	0.0166945i
$221$	4.75557	+	5.86171i	0.319894	+	0.394301i
$222$	−1.51856	−	6.13711i	−0.101919	−	0.411896i
$223$	−20.0340	+	11.5666i	−1.34158	+	0.774559i	−0.987039	−	0.160482i	$-0.948695\pi$
$223$	−20.0340	+	11.5666i	−1.34158	+	0.774559i	−0.354537	+	0.935042i	$0.615362\pi$
$224$	1.67682			0.112037
$225$	0.536045	−	13.9285i	0.0357363	−	0.928565i
$226$		−	20.2779i		−	1.34887i
$227$	−11.5239	+	6.65331i	−0.764866	+	0.441595i	−0.831040	−	0.556213i	$-0.812254\pi$
$227$	−11.5239	+	6.65331i	−0.764866	+	0.441595i	0.0661743	+	0.997808i	$0.478921\pi$
$228$	−0.577357	−	0.600004i	−0.0382364	−	0.0397362i
$229$	−0.700965	−	0.404702i	−0.0463211	−	0.0267435i	0.476661	−	0.879087i	$-0.341847\pi$
$229$	−0.700965	−	0.404702i	−0.0463211	−	0.0267435i	−0.522982	+	0.852344i	$0.675180\pi$
$230$	−1.09043	+	1.88867i	−0.0719005	+	0.124535i
$231$	1.00610	−	0.968122i	0.0661964	−	0.0636978i
$232$	2.13629	−	1.23339i	0.140254	−	0.0809760i
$233$	−15.4712			−1.01355			−0.506776	−	0.862078i	$-0.669163\pi$
$233$	−15.4712			−1.01355			−0.506776	+	0.862078i	$0.669163\pi$
$234$	−6.48672	−	8.65578i	−0.424050	−	0.565846i
$235$	−3.71190			−0.242138
$236$	8.13185	−	4.69493i	0.529338	−	0.305614i
$237$	0.856146	+	3.46004i	0.0556126	+	0.224754i
$238$	1.75520	−	3.04010i	0.113773	−	0.197060i
$239$	−25.2511	−	14.5788i	−1.63336	−	0.943021i	−0.983047	−	0.183355i	$-0.941304\pi$
$239$	−25.2511	−	14.5788i	−1.63336	−	0.943021i	−0.650313	−	0.759666i	$-0.725362\pi$
$240$	0.285710	−	0.989738i	0.0184425	−	0.0638873i
$241$	−13.5054	+	7.79735i	−0.869959	+	0.502271i	−0.867335	−	0.497725i	$-0.834169\pi$
$241$	−13.5054	+	7.79735i	−0.869959	+	0.502271i	−0.00262472	+	0.999997i	$0.500835\pi$
$242$			10.7689i			0.692250i
$243$	2.57017	+	15.3751i	0.164877	+	0.986314i
$244$	−7.81270			−0.500157
$245$	−2.15728	+	1.24551i	−0.137824	+	0.0795725i
$246$	16.4913	+	4.76060i	1.05145	+	0.303524i
$247$	−1.34607	+	1.09206i	−0.0856484	+	0.0694860i
$248$	−0.573765	+	0.993791i	−0.0364341	+	0.0631058i
$249$	−18.5959	+	4.60133i	−1.17846	+	0.291597i
$250$	−2.86860	−	4.96856i	−0.181426	−	0.314239i
$251$	−2.79495			−0.176416			−0.0882079	−	0.996102i	$-0.528114\pi$
$251$	−2.79495			−0.176416			−0.0882079	+	0.996102i	$0.528114\pi$
$252$	−2.68090	+	4.25655i	−0.168881	+	0.268137i
$253$		−	1.76279i		−	0.110825i
$254$	16.0624	−	9.27366i	1.00785	−	0.581881i
$255$	−1.49534	−	1.55400i	−0.0936421	−	0.0973153i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.4798	+	18.1515i	−0.653712	+	1.13226i	0.328503	+	0.944503i	$0.393456\pi$
$257$	−10.4798	+	18.1515i	−0.653712	+	1.13226i	−0.982215	+	0.187759i	$0.939877\pi$
$258$	−8.30640	−	8.63222i	−0.517134	−	0.537419i
$259$	3.06029	+	5.30059i	0.190157	+	0.329362i
$260$	−2.00270	−	0.766671i	−0.124202	−	0.0475469i
$261$	−0.284595	+	7.39486i	−0.0176160	+	0.457730i
$262$		−	4.64513i		−	0.286977i
$263$	−7.92418	−	13.7251i	−0.488626	−	0.846325i	0.511288	−	0.859409i	$-0.329168\pi$
$263$	−7.92418	−	13.7251i	−0.488626	−	0.846325i	−0.999914	+	0.0130839i	$0.995835\pi$
$264$	0.200004	+	0.808297i	0.0123094	+	0.0497472i
$265$	−2.61963	−	1.51245i	−0.160923	−	0.0929088i
$266$	0.698121	+	0.403061i	0.0428046	+	0.0247132i
$267$	4.55747	−	15.7877i	0.278913	−	0.966189i
$268$	12.4551	−	7.19096i	0.760817	−	0.439258i
$269$	18.9028			1.15252			0.576261	−	0.817266i	$-0.304511\pi$
$269$	18.9028			1.15252			0.576261	+	0.817266i	$0.304511\pi$
$270$	2.05562	+	2.30767i	0.125101	+	0.140440i
$271$			9.63804i			0.585469i	0.956194	+	0.292735i	$0.0945653\pi$
$271$			9.63804i			0.585469i	−0.956194	+	0.292735i	$0.905435\pi$
$272$	1.04675	+	1.81302i	0.0634682	+	0.109930i
$273$	8.35761	+	6.30931i	0.505826	+	0.381857i
$274$	6.51034	−	11.2762i	0.393304	−	0.681223i
$275$	1.93441	+	1.11683i	0.116649	+	0.0673475i
$276$	1.52549	+	6.16513i	0.0918237	+	0.371097i
$277$	−1.35010	−	2.33844i	−0.0811197	−	0.140503i	0.822611	−	0.568604i	$-0.192516\pi$
$277$	−1.35010	−	2.33844i	−0.0811197	−	0.140503i	−0.903731	+	0.428100i	$0.859183\pi$
$278$			10.1805i			0.610588i
$279$	−1.60537	−	3.04536i	−0.0961109	−	0.182321i
$280$			0.997301i			0.0596002i
$281$	−9.34820	+	5.39719i	−0.557667	+	0.321969i	−0.752208	−	0.658925i	$-0.771011\pi$
$281$	−9.34820	+	5.39719i	−0.557667	+	0.321969i	0.194542	+	0.980894i	$0.437678\pi$
$282$	−7.78925	+	7.49524i	−0.463843	+	0.446335i
$283$	14.6088	−	25.3032i	0.868403	−	1.50412i	0.00477479	−	0.999989i	$-0.498480\pi$
$283$	14.6088	−	25.3032i	0.868403	−	1.50412i	0.863628	−	0.504129i	$-0.168187\pi$
$284$	5.63807	+	3.25514i	0.334558	+	0.193157i
$285$	0.356857	−	0.343388i	0.0211384	−	0.0203405i
$286$	1.71176	−	0.272715i	0.101219	−	0.0161260i
$287$	−16.6173			−0.980891
$288$	−1.39898	−	2.65384i	−0.0824355	−	0.156379i
$289$	−12.6173			−0.742194
$290$	0.733568	+	1.27058i	0.0430766	+	0.0746109i
$291$	16.3348	−	4.04187i	0.957566	−	0.236938i
$292$	−5.12266	−	2.95757i	−0.299781	−	0.173079i
$293$	20.5199	+	11.8472i	1.19879	+	0.692120i	0.960285	−	0.279022i	$-0.0900104\pi$
$293$	20.5199	+	11.8472i	1.19879	+	0.692120i	0.238502	+	0.971142i	$0.423344\pi$
$294$	−2.01197	+	6.96972i	−0.117340	+	0.406483i
$295$	2.79235	+	4.83649i	0.162577	+	0.281591i
$296$	−3.65012			−0.212159
$297$	−2.37160	−	0.784606i	−0.137614	−	0.0455275i
$298$	5.25274			0.304283
$299$	13.0561	−	2.08008i	0.755055	−	0.120294i
$300$	−7.73185	−	2.23198i	−0.446399	−	0.128863i
$301$	10.0438	+	5.79881i	0.578917	+	0.334238i
$302$	5.96162	−	10.3258i	0.343053	−	0.594184i
$303$	2.41087	+	9.74331i	0.138501	+	0.559739i
$304$	−0.416337	+	0.240372i	−0.0238786	+	0.0137863i
$305$		−	4.64667i		−	0.266067i
$306$	−6.27582	−	0.241528i	−0.358765	−	0.0138073i
$307$			6.55237i			0.373963i	0.982363	+	0.186982i	$0.0598705\pi$
$307$			6.55237i			0.373963i	−0.982363	+	0.186982i	$0.940129\pi$
$308$	−0.403061	−	0.698121i	−0.0229665	−	0.0397792i
$309$	−2.13929	+	2.05854i	−0.121700	+	0.117106i
$310$	−0.591065	−	0.341252i	−0.0335702	−	0.0193818i
$311$	−12.7115	+	22.0169i	−0.720802	+	1.24847i	0.239876	+	0.970803i	$0.422893\pi$
$311$	−12.7115	+	22.0169i	−0.720802	+	1.24847i	−0.960679	+	0.277663i	$0.910440\pi$
$312$	−5.75067	+	2.43512i	−0.325568	+	0.137861i
$313$	−0.590728	−	1.02317i	−0.0333899	−	0.0578331i	0.848848	−	0.528638i	$-0.177297\pi$
$313$	−0.590728	−	1.02317i	−0.0333899	−	0.0578331i	−0.882237	+	0.470805i	$0.843964\pi$
$314$			12.3908i			0.699253i
$315$	−2.53162	−	1.59449i	−0.142641	−	0.0898394i
$316$	2.05790			0.115766
$317$	−24.2009	+	13.9724i	−1.35926	+	0.784769i	−0.989524	−	0.144368i	$-0.953885\pi$
$317$	−24.2009	+	13.9724i	−1.35926	+	0.784769i	−0.369735	+	0.929137i	$0.620552\pi$
$318$	−8.55118	+	2.11589i	−0.479526	+	0.118653i
$319$	−1.02701	−	0.592945i	−0.0575016	−	0.0331985i
$320$	−0.515076	−	0.297379i	−0.0287936	−	0.0166240i
$321$	23.4673	+	6.77438i	1.30982	+	0.378109i
$322$	−3.07427	−	5.32479i	−0.171322	−	0.296739i
$323$			1.00643i			0.0559995i
$324$	8.97338	+	0.691715i	0.498521	+	0.0384286i
$325$	−5.98925	+	15.6451i	−0.332224	+	0.867835i
$326$	10.6814	+	18.5008i	0.591591	+	1.02466i
$327$	8.81372	−	30.5319i	0.487400	−	1.68842i
$328$	4.95502	−	8.58235i	0.273595	−	0.473881i
$329$	5.23253	−	9.06301i	0.288479	−	0.499660i
$330$	−0.480741	+	0.118954i	−0.0264639	+	0.00654819i
$331$	21.3503	−	12.3266i	1.17352	−	0.677530i	0.219010	−	0.975723i	$-0.429717\pi$
$331$	21.3503	−	12.3266i	1.17352	−	0.677530i	0.954506	+	0.298193i	$0.0963838\pi$
$332$			11.0601i			0.607003i
$333$	5.83583	−	9.26572i	0.319802	−	0.507758i
$334$	−14.7356			−0.806294
$335$	4.27688	+	7.40778i	0.233671	+	0.404730i
$336$	2.01380	+	2.09279i	0.109862	+	0.114171i
$337$	7.63940	−	13.2318i	0.416145	−	0.720784i	−0.579403	−	0.815041i	$-0.696714\pi$
$337$	7.63940	−	13.2318i	0.416145	−	0.720784i	0.995548	+	0.0942571i	$0.0300476\pi$
$338$	4.03974	+	12.3564i	0.219733	+	0.672099i
$339$	25.3083	−	24.3530i	1.37456	−	1.32268i
$340$	−1.07831	+	0.622560i	−0.0584794	+	0.0337631i
$341$	0.551669			0.0298745
$342$	0.0554640	−	1.44117i	0.00299915	−	0.0779294i
$343$		−	18.7607i		−	1.01298i
$344$	−5.98981	+	3.45822i	−0.322949	+	0.186455i
$345$	−3.66676	+	0.907297i	−0.197412	+	0.0488472i
$346$	−10.0881	−	5.82435i	−0.542338	−	0.313119i
$347$	0.607688	−	1.05255i	0.0326224	−	0.0565036i	−0.849253	−	0.527986i	$-0.822947\pi$
$347$	0.607688	−	1.05255i	0.0326224	−	0.0565036i	0.881876	+	0.471482i	$0.156281\pi$
$348$	4.10497	+	1.18499i	0.220049	+	0.0635223i
$349$	−3.30094	+	1.90580i	−0.176695	+	0.102015i	−0.585739	−	0.810500i	$-0.699196\pi$
$349$	−3.30094	+	1.90580i	−0.176695	+	0.102015i	0.409044	+	0.912515i	$0.365862\pi$
$350$	7.79094			0.416443
$351$	3.01272	−	18.4912i	0.160807	−	0.986986i
$352$	0.480744			0.0256238
$353$	17.3353	−	10.0086i	0.922667	−	0.532702i	0.0381819	−	0.999271i	$-0.487843\pi$
$353$	17.3353	−	10.0086i	0.922667	−	0.532702i	0.884485	+	0.466569i	$0.154510\pi$
$354$	15.6257	+	4.51070i	0.830495	+	0.239741i
$355$	−1.93602	+	3.35329i	−0.102753	+	0.177974i
$356$	−8.21616	−	4.74360i	−0.435455	−	0.251410i
$357$	5.90220	−	1.46043i	0.312377	−	0.0772941i
$358$	−0.776096	+	0.448079i	−0.0410179	+	0.0236817i
$359$			9.96717i			0.526047i	0.964789	+	0.263024i	$0.0847197\pi$
$359$			9.96717i			0.526047i	−0.964789	+	0.263024i	$0.915280\pi$
$360$	1.57839	−	0.832053i	0.0831886	−	0.0438530i
$361$	18.7689			0.987836
$362$	1.23141	−	0.710953i	0.0647213	−	0.0373669i
$363$	−13.4404	+	12.9330i	−0.705436	+	0.678809i
$364$	4.69504	−	3.80906i	0.246087	−	0.199649i
$365$	1.75904	−	3.04675i	0.0920723	−	0.159474i
$366$	−9.38277	−	9.75081i	−0.490445	−	0.509683i
$367$	−7.16334	−	12.4073i	−0.373923	−	0.647654i	0.616242	−	0.787557i	$-0.288654\pi$
$367$	−7.16334	−	12.4073i	−0.373923	−	0.647654i	−0.990165	+	0.139903i	$0.955321\pi$
$368$	3.66679			0.191144
$369$	13.8639	+	26.2997i	0.721727	+	1.36911i
$370$		−	2.17094i		−	0.112862i
$371$	7.38560	−	4.26408i	0.383441	−	0.221380i
$372$	−1.92939	+	0.477406i	−0.100034	+	0.0247523i
$373$	13.9877	−	24.2275i	0.724257	−	1.25445i	−0.235022	−	0.971990i	$-0.575516\pi$
$373$	13.9877	−	24.2275i	0.724257	−	1.25445i	0.959279	−	0.282460i	$-0.0911505\pi$
$374$	0.503217	−	0.871597i	0.0260207	−	0.0450692i
$375$	2.75604	−	9.54727i	0.142321	−	0.493019i
$376$	3.12051	+	5.40488i	0.160928	+	0.278736i
$377$	3.17979	−	8.30625i	0.163768	−	0.427794i
$378$	−8.53215	+	1.76600i	−0.438847	+	0.0908332i
$379$			4.05068i			0.208069i	0.994574	+	0.104035i	$0.0331753\pi$
$379$			4.05068i			0.208069i	−0.994574	+	0.104035i	$0.966825\pi$
$380$	−0.142963	−	0.247620i	−0.00733387	−	0.0127026i
$381$	30.8646	+	8.90977i	1.58124	+	0.456461i
$382$	12.8524	+	7.42036i	0.657588	+	0.379659i
$383$	−27.1033	−	15.6481i	−1.38492	−	0.799581i	−0.392179	−	0.919889i	$-0.628279\pi$
$383$	−27.1033	−	15.6481i	−1.38492	−	0.799581i	−0.992737	+	0.120308i	$0.961612\pi$
$384$	−1.68134	+	0.416029i	−0.0858008	+	0.0212304i
$385$	0.415213	−	0.239724i	0.0211612	−	0.0122174i
$386$	−14.1075			−0.718054
$387$	0.797958	−	20.7340i	0.0405625	−	1.05397i
$388$		−	9.71535i		−	0.493222i
$389$	7.66964	+	13.2842i	0.388866	+	0.673536i	0.992297	−	0.123879i	$-0.0395335\pi$
$389$	7.66964	+	13.2842i	0.388866	+	0.673536i	−0.603431	+	0.797415i	$0.706200\pi$
$390$	−1.44831	−	3.42026i	−0.0733379	−	0.173191i
$391$	3.83819	−	6.64794i	0.194106	−	0.336201i
$392$	3.62716	+	2.09414i	0.183199	+	0.105770i
$393$	5.79746	−	5.57863i	0.292443	−	0.281405i
$394$	0.221259	+	0.383231i	0.0111468	+	0.0193069i
$395$			1.22395i			0.0615837i
$396$	−0.768616	+	1.22035i	−0.0386244	+	0.0613251i
$397$			24.1832i			1.21372i	0.794808	+	0.606860i	$0.207571\pi$
$397$			24.1832i			1.21372i	−0.794808	+	0.606860i	$0.792429\pi$
$398$	−11.5117	+	6.64626i	−0.577028	+	0.333147i
$399$	0.335370	+	1.35537i	0.0167895	+	0.0678532i
$400$	−2.32313	+	4.02378i	−0.116157	+	0.201189i
$401$	24.8876	+	14.3689i	1.24283	+	0.717548i	0.969669	−	0.244421i	$-0.0785978\pi$
$401$	24.8876	+	14.3689i	1.24283	+	0.717548i	0.273160	+	0.961969i	$0.411931\pi$
$402$	23.9330	+	6.90880i	1.19367	+	0.344579i
$403$	0.650967	+	4.08595i	0.0324270	+	0.203536i
$404$	5.79495			0.288310
$405$	−0.411403	+	5.33699i	−0.0204428	+	0.265197i
$406$	−4.13634			−0.205283
$407$	0.877388	+	1.51968i	0.0434905	+	0.0753278i
$408$	−1.00567	+	3.48378i	−0.0497882	+	0.172473i
$409$	−25.9100	−	14.9591i	−1.28117	−	0.739682i	−0.304105	−	0.952638i	$-0.598357\pi$
$409$	−25.9100	−	14.9591i	−1.28117	−	0.739682i	−0.977062	+	0.212956i	$0.931691\pi$
$410$	5.10442	+	2.94704i	0.252090	+	0.145544i
$411$	21.8923	−	5.41698i	1.07987	−	0.267200i
$412$	0.857037	+	1.48443i	0.0422232	+	0.0731327i
$413$	−15.7451			−0.774764
$414$	−5.86248	+	9.30802i	−0.288125	+	0.457464i
$415$	−6.57809			−0.322906
$416$	0.567277	+	3.56065i	0.0278130	+	0.174575i
$417$	−12.7061	+	12.2265i	−0.622218	+	0.598733i
$418$	0.200152	+	0.115558i	0.00978974	+	0.00565211i
$419$	−12.2858	+	21.2796i	−0.600200	+	1.03958i	0.392590	+	0.919713i	$0.371579\pi$
$419$	−12.2858	+	21.2796i	−0.600200	+	1.03958i	−0.992790	+	0.119863i	$0.961754\pi$
$420$	−1.24470	+	1.19772i	−0.0607354	+	0.0584429i
$421$	24.6735	−	14.2452i	1.20251	−	0.694271i	0.241399	−	0.970426i	$-0.422394\pi$
$421$	24.6735	−	14.2452i	1.20251	−	0.694271i	0.961113	+	0.276155i	$0.0890603\pi$
$422$		−	9.64064i		−	0.469299i
$423$	−18.7092	−	0.720034i	−0.909673	−	0.0350092i
$424$			5.08592i			0.246994i
$425$	4.86345	+	8.42375i	0.235912	+	0.408612i
$426$	2.70847	+	10.9460i	0.131226	+	0.530337i
$427$	11.3453	+	6.55024i	0.549040	+	0.316988i
$428$	7.05105	−	12.2128i	0.340825	−	0.590327i
$429$	2.39613	+	1.80888i	0.115686	+	0.0873336i
$430$	−2.05681	−	3.56249i	−0.0991880	−	0.171799i
$431$		−	7.13767i		−	0.343809i	−0.985114	−	0.171905i	$-0.945008\pi$
$431$		−	7.13767i		−	0.343809i	0.985114	−	0.171905i	$-0.0549921\pi$
$432$	1.63207	−	4.93319i	0.0785228	−	0.237348i
$433$	−7.85282			−0.377382			−0.188691	−	0.982036i	$-0.560424\pi$
$433$	−7.85282			−0.377382			−0.188691	+	0.982036i	$0.560424\pi$
$434$	1.66641	−	0.962100i	0.0799901	−	0.0461823i
$435$	−0.704784	+	2.44146i	−0.0337918	+	0.117059i
$436$	−15.8893	−	9.17368i	−0.760959	−	0.439340i
$437$	1.52662	+	0.881394i	0.0730281	+	0.0421628i
$438$	−2.46087	−	9.94539i	−0.117585	−	0.475209i
$439$	2.07427	+	3.59274i	0.0989994	+	0.171472i	0.911271	−	0.411808i	$-0.135102\pi$
$439$	2.07427	+	3.59274i	0.0989994	+	0.171472i	−0.812271	+	0.583280i	$0.801769\pi$
$440$			0.285927i			0.0136310i
$441$	−11.1150	+	5.85930i	−0.529287	+	0.279014i
$442$	7.04930	+	2.69861i	0.335301	+	0.128360i
$443$	−8.92349	−	15.4559i	−0.423968	−	0.734334i	0.572356	−	0.820006i	$-0.306030\pi$
$443$	−8.92349	−	15.4559i	−0.423968	−	0.734334i	−0.996323	+	0.0856716i	$0.972696\pi$
$444$	−4.38366	−	4.55562i	−0.208039	−	0.216200i
$445$	2.82130	−	4.88663i	0.133742	−	0.231648i
$446$	−11.5666	+	20.0340i	−0.547696	+	0.948638i
$447$	6.30835	+	6.55580i	0.298375	+	0.310079i
$448$	1.45217	−	0.838409i	0.0686084	−	0.0396111i
$449$		−	19.7308i		−	0.931152i	−0.885008	−	0.465576i	$-0.845847\pi$
$449$		−	19.7308i		−	0.931152i	0.885008	−	0.465576i	$-0.154153\pi$
$450$	−6.50001	−	12.3304i	−0.306413	−	0.581262i
$451$	−4.76420			−0.224337
$452$	−10.1390	−	17.5612i	−0.476896	−	0.826009i
$453$	20.0471	−	4.96041i	0.941893	−	0.233060i
$454$	−6.65331	+	11.5239i	−0.312255	+	0.540842i
$455$	2.26547	+	2.79242i	0.106207	+	0.130910i
$456$	−0.800008	−	0.230940i	−0.0374638	−	0.0108148i
$457$	−31.4762	+	18.1728i	−1.47240	+	0.850088i	−0.999518	−	0.0310408i	$-0.990118\pi$
$457$	−31.4762	+	18.1728i	−1.47240	+	0.850088i	−0.472877	+	0.881128i	$0.656784\pi$
$458$	−0.809405			−0.0378210
$459$	−7.23559	−	8.12275i	−0.337729	−	0.379138i
$460$			2.18085i			0.101683i
$461$	−19.8630	+	11.4679i	−0.925112	+	0.534114i	−0.885262	−	0.465092i	$-0.846021\pi$
$461$	−19.8630	+	11.4679i	−0.925112	+	0.534114i	−0.0398498	+	0.999206i	$0.512688\pi$
$462$	0.387245	−	1.34147i	0.0180163	−	0.0624107i
$463$	−25.6143	−	14.7884i	−1.19040	−	0.687277i	−0.232002	−	0.972715i	$-0.574528\pi$
$463$	−25.6143	−	14.7884i	−1.19040	−	0.687277i	−0.958397	+	0.285438i	$0.907861\pi$
$464$	1.23339	−	2.13629i	0.0572586	−	0.0991749i
$465$	−0.283941	−	1.14752i	−0.0131675	−	0.0532151i
$466$	−13.3984	+	7.73559i	−0.620671	+	0.358344i
$467$	−12.5970			−0.582920			−0.291460	−	0.956583i	$-0.594141\pi$
$467$	−12.5970			−0.582920			−0.291460	+	0.956583i	$0.594141\pi$
$468$	−9.94555	−	4.25276i	−0.459733	−	0.196584i
$469$	−24.1159			−1.11357
$470$	−3.21460	+	1.85595i	−0.148278	+	0.0856086i
$471$	−15.4646	+	14.8809i	−0.712572	+	0.685675i
$472$	4.69493	−	8.13185i	0.216101	−	0.374299i
$473$	2.87957	+	1.66252i	0.132403	+	0.0764428i
$474$	2.47146	+	2.56841i	0.113518	+	0.117971i
$475$	−1.93441	+	1.11683i	−0.0887568	+	0.0512438i
$476$		−	3.51040i		−	0.160899i
$477$	−12.9104	−	8.13139i	−0.591129	−	0.372311i
$478$	−29.1575			−1.33363
$479$	11.0404	−	6.37417i	0.504448	−	0.291243i	−0.226101	−	0.974104i	$-0.572598\pi$
$479$	11.0404	−	6.37417i	0.504448	−	0.291243i	0.730549	+	0.682861i	$0.239264\pi$
$480$	−0.247437	−	0.999994i	−0.0112939	−	0.0456433i
$481$	−10.2202	+	8.29161i	−0.466003	+	0.378065i
$482$	−7.79735	+	13.5054i	−0.355159	+	0.615154i
$483$	2.95364	−	10.2318i	0.134395	−	0.465562i
$484$	5.38444	+	9.32613i	0.244747	+	0.423915i
$485$	5.77828			0.262378
$486$	9.91339	+	12.0302i	0.449681	+	0.545699i
$487$		−	20.8054i		−	0.942782i	−0.881924	−	0.471391i	$-0.843752\pi$
$487$		−	20.8054i		−	0.942782i	0.881924	−	0.471391i	$-0.156248\pi$
$488$	−6.76599	+	3.90635i	−0.306282	+	0.176832i
$489$	−10.2623	+	35.5500i	−0.464078	+	1.60763i
$490$	−1.24551	+	2.15728i	−0.0562663	+	0.0974561i
$491$	7.37362	−	12.7715i	0.332767	−	0.576369i	−0.650286	−	0.759689i	$-0.725351\pi$
$491$	7.37362	−	12.7715i	0.332767	−	0.576369i	0.983053	+	0.183320i	$0.0586844\pi$
$492$	16.6622	−	4.12287i	0.751190	−	0.185873i
$493$	−2.58209	−	4.47231i	−0.116291	−	0.201423i
$494$	−0.619702	+	1.61879i	−0.0278817	+	0.0728326i
$495$	−0.725816	−	0.457141i	−0.0326230	−	0.0205470i
$496$			1.14753i			0.0515256i
$497$	−5.45828	−	9.45402i	−0.244837	−	0.424071i
$498$	−13.8038	+	13.2828i	−0.618564	+	0.595216i
$499$	25.7627	+	14.8741i	1.15330	+	0.665856i	0.949688	−	0.313197i	$-0.101400\pi$
$499$	25.7627	+	14.8741i	1.15330	+	0.665856i	0.203608	+	0.979053i	$0.434733\pi$
$500$	−4.96856	−	2.86860i	−0.222201	−	0.128288i
$501$	−17.6969	−	18.3910i	−0.790638	−	0.821651i
$502$	−2.42050	+	1.39748i	−0.108032	+	0.0623724i
$503$	−26.1270			−1.16495			−0.582473	−	0.812850i	$-0.697915\pi$
$503$	−26.1270			−1.16495			−0.582473	+	0.812850i	$0.697915\pi$
$504$	−0.193456	+	5.02673i	−0.00861724	+	0.223908i
$505$			3.44660i			0.153372i
$506$	−0.881394	−	1.52662i	−0.0391827	−	0.0678665i
$507$	−10.5701	+	19.8815i	−0.469434	+	0.882967i
$508$	9.27366	−	16.0624i	0.411452	−	0.712656i
$509$	15.4810	+	8.93795i	0.686182	+	0.396168i	0.802180	−	0.597082i	$-0.203673\pi$
$509$	15.4810	+	8.93795i	0.686182	+	0.396168i	−0.115998	+	0.993249i	$0.537007\pi$
$510$	−2.07201	−	0.598132i	−0.0917500	−	0.0264857i
$511$	4.95931	+	8.58977i	0.219387	+	0.379989i
$512$			1.00000i			0.0441942i
$513$	1.86529	−	1.66157i	0.0823546	−	0.0733599i
$514$			20.9596i			0.924488i
$515$	−0.882878	+	0.509730i	−0.0389042	+	0.0224614i
$516$	−11.5097	−	3.32252i	−0.506685	−	0.146266i
$517$	1.50017	−	2.59837i	0.0659773	−	0.114276i
$518$	5.30059	+	3.06029i	0.232894	+	0.134462i
$519$	−4.84620	−	19.5855i	−0.212724	−	0.859707i
$520$	−2.11772	+	0.337393i	−0.0928683	+	0.0147956i
$521$	−13.7904			−0.604168			−0.302084	−	0.953281i	$-0.597682\pi$
$521$	−13.7904			−0.604168			−0.302084	+	0.953281i	$0.597682\pi$
$522$	3.45096	+	6.54643i	0.151045	+	0.286530i
$523$	−0.523640			−0.0228972			−0.0114486	−	0.999934i	$-0.503644\pi$
$523$	−0.523640			−0.0228972			−0.0114486	+	0.999934i	$0.503644\pi$
$524$	−2.32256	−	4.02280i	−0.101462	−	0.175737i
$525$	9.35664	+	9.72366i	0.408357	+	0.424375i
$526$	−13.7251	−	7.92418i	−0.598442	−	0.345511i
$527$	2.08049	+	1.20117i	0.0906276	+	0.0523239i
$528$	0.577357	+	0.600004i	0.0251262	+	0.0261118i
$529$	4.77734	+	8.27459i	0.207710	+	0.359765i
$530$	−3.02489			−0.131393
$531$	13.1362	+	24.9192i	0.570062	+	1.08140i
$532$	0.806121			0.0349498
$533$	−5.62174	−	35.2862i	−0.243505	−	1.52841i
$534$	−3.94695	−	15.9513i	−0.170801	−	0.690278i
$535$	7.26365	+	4.19367i	0.314035	+	0.181308i
$536$	7.19096	−	12.4551i	0.310602	−	0.537979i
$537$	−1.49130	−	0.430497i	−0.0643543	−	0.0185773i
$538$	16.3703	−	9.45139i	0.705773	−	0.407478i
$539$		−	2.01349i		−	0.0867273i
$540$	2.93406	+	0.970684i	0.126262	+	0.0417716i
$541$			11.3636i			0.488558i	0.969705	+	0.244279i	$0.0785513\pi$
$541$			11.3636i			0.488558i	−0.969705	+	0.244279i	$0.921449\pi$
$542$	4.81902	+	8.34679i	0.206995	+	0.358525i
$543$	2.36620	+	0.683057i	0.101543	+	0.0293128i
$544$	1.81302	+	1.04675i	0.0777324	+	0.0448788i
$545$	5.45612	−	9.45028i	0.233715	−	0.404806i
$546$	10.3926	+	1.28521i	0.444760	+	0.0550020i
$547$	4.14239	+	7.17484i	0.177116	+	0.306774i	0.940892	−	0.338708i	$-0.109990\pi$
$547$	4.14239	+	7.17484i	0.177116	+	0.306774i	−0.763776	+	0.645482i	$0.776657\pi$
$548$		−	13.0207i		−	0.556216i
$549$	0.901360	−	23.4208i	0.0384691	−	0.999573i
$550$	2.23366			0.0952438
$551$	1.02701	−	0.592945i	0.0437521	−	0.0252603i
$552$	4.40368	+	4.57642i	0.187433	+	0.194785i
$553$	−2.98841	−	1.72536i	−0.127080	−	0.0733698i
$554$	−2.33844	−	1.35010i	−0.0993510	−	0.0573603i
$555$	2.70949	−	2.60722i	0.115011	−	0.110670i
$556$	5.09027	+	8.81661i	0.215876	+	0.373908i
$557$			26.7334i			1.13273i	0.824154	+	0.566365i	$0.191651\pi$
$557$			26.7334i			1.13273i	−0.824154	+	0.566365i	$0.808349\pi$
$558$	−2.91297	−	1.83468i	−0.123316	−	0.0776681i
$559$	−8.91562	+	23.2894i	−0.377090	+	0.985035i
$560$	0.498651	+	0.863688i	0.0210718	+	0.0364975i
$561$	1.69216	−	0.418706i	0.0714431	−	0.0176778i
$562$	−5.39719	+	9.34820i	−0.227667	+	0.394330i
$563$	−2.36071	+	4.08888i	−0.0994922	+	0.172326i	−0.911475	−	0.411356i	$-0.865055\pi$
$563$	−2.36071	+	4.08888i	−0.0994922	+	0.172326i	0.811982	+	0.583682i	$0.198389\pi$
$564$	−2.99807	+	10.3857i	−0.126241	+	0.437317i
$565$	10.4447	−	6.03023i	0.439410	−	0.253694i
$566$		−	29.2176i		−	1.22811i
$567$	−12.4509	−	8.52785i	−0.522889	−	0.358136i
$568$	6.51028			0.273165
$569$	21.0546	+	36.4676i	0.882653	+	1.52880i	0.848380	+	0.529388i	$0.177578\pi$
$569$	21.0546	+	36.4676i	0.882653	+	1.52880i	0.0342730	+	0.999413i	$0.489088\pi$
$570$	0.137354	−	0.475811i	0.00575311	−	0.0199295i
$571$	5.89219	−	10.2056i	0.246581	−	0.427090i	−0.715994	−	0.698106i	$-0.754026\pi$
$571$	5.89219	−	10.2056i	0.246581	−	0.427090i	0.962575	+	0.271016i	$0.0873597\pi$
$572$	1.34607	−	1.09206i	0.0562820	−	0.0456613i
$573$	6.17417	+	24.9524i	0.257930	+	1.04240i
$574$	−14.3910	+	8.30867i	−0.600671	+	0.346797i
$575$	17.0369			0.710486
$576$	−2.53847	−	1.59880i	−0.105770	−	0.0666169i
$577$		−	21.5466i		−	0.896997i	−0.893784	−	0.448498i	$-0.851959\pi$
$577$		−	21.5466i		−	0.896997i	0.893784	−	0.448498i	$-0.148041\pi$
$578$	−10.9269	+	6.30865i	−0.454499	+	0.262405i
$579$	−16.9426	−	17.6072i	−0.704111	−	0.731731i
$580$	1.27058	+	0.733568i	0.0527579	+	0.0304598i
$581$	9.27290	−	16.0611i	0.384705	−	0.666328i
$582$	12.1255	−	11.6678i	0.502617	−	0.483645i
$583$	2.11746	−	1.22251i	0.0876961	−	0.0506313i
$584$	−5.91514			−0.244770
$585$	2.52937	−	5.91520i	0.104576	−	0.244563i
$586$	23.6944			0.978805
$587$	7.62960	−	4.40495i	0.314907	−	0.181812i	−0.334213	−	0.942498i	$-0.608470\pi$
$587$	7.62960	−	4.40495i	0.314907	−	0.181812i	0.649120	+	0.760686i	$0.275137\pi$
$588$	1.74245	+	7.04194i	0.0718573	+	0.290405i
$589$	−0.275834	+	0.477759i	−0.0113656	+	0.0196857i
$590$	4.83649	+	2.79235i	0.199115	+	0.114959i
$591$	−0.212577	+	0.736393i	−0.00874424	+	0.0302912i
$592$	−3.16110	+	1.82506i	−0.129920	+	0.0750095i
$593$		−	26.7483i		−	1.09842i	−0.835685	−	0.549210i	$-0.814929\pi$
$593$		−	26.7483i		−	1.09842i	0.835685	−	0.549210i	$-0.185071\pi$
$594$	−2.44617	+	0.506313i	−0.100368	+	0.0207743i
$595$	2.08784			0.0855931
$596$	4.54901	−	2.62637i	0.186335	−	0.107580i
$597$	−22.1201	−	6.38547i	−0.905316	−	0.261340i
$598$	10.2669	−	8.32947i	0.419845	−	0.340617i
$599$	23.9224	−	41.4349i	0.977445	−	1.69298i	0.305825	−	0.952088i	$-0.401068\pi$
$599$	23.9224	−	41.4349i	0.977445	−	1.69298i	0.671620	−	0.740896i	$-0.265599\pi$
$600$	−7.81197	+	1.93298i	−0.318922	+	0.0789136i
$601$	10.5193	+	18.2199i	0.429091	+	0.743207i	0.996793	−	0.0800273i	$-0.0255008\pi$
$601$	10.5193	+	18.2199i	0.429091	+	0.743207i	−0.567702	+	0.823234i	$0.692167\pi$
$602$	11.5976			0.472683
$603$	20.1200	+	38.1673i	0.819348	+	1.55429i
$604$		−	11.9232i		−	0.485150i
$605$	−5.54679	+	3.20244i	−0.225509	+	0.130198i
$606$	6.95953	+	7.23252i	0.282712	+	0.293801i
$607$	−11.7683	+	20.3833i	−0.477662	+	0.827334i	−0.999672	−	0.0256049i	$-0.991849\pi$
$607$	−11.7683	+	20.3833i	−0.477662	+	0.827334i	0.522011	+	0.852939i	$0.325182\pi$
$608$	−0.240372	+	0.416337i	−0.00974838	+	0.0168847i
$609$	−4.96759	−	5.16245i	−0.201297	−	0.209193i
$610$	−2.32333	−	4.02413i	−0.0940690	−	0.162932i
$611$	21.0151	+	8.04497i	0.850179	+	0.325465i
$612$	−5.55579	+	2.92874i	−0.224579	+	0.118387i
$613$		−	40.7009i		−	1.64390i	−0.569563	−	0.821948i	$-0.692888\pi$
$613$		−	40.7009i		−	1.64390i	0.569563	−	0.821948i	$-0.307112\pi$
$614$	3.27618	+	5.67452i	0.132216	+	0.229005i
$615$	2.45211	+	9.90998i	0.0988786	+	0.399609i
$616$	−0.698121	−	0.403061i	−0.0281281	−	0.0162398i
$617$	−34.0924	−	19.6832i	−1.37251	−	0.792417i	−0.381264	−	0.924466i	$-0.624511\pi$
$617$	−34.0924	−	19.6832i	−1.37251	−	0.792417i	−0.991243	+	0.132049i	$0.957844\pi$
$618$	−0.823408	+	2.85239i	−0.0331223	+	0.114740i
$619$	21.1669	−	12.2207i	0.850770	−	0.491192i	−0.0101406	−	0.999949i	$-0.503228\pi$
$619$	21.1669	−	12.2207i	0.850770	−	0.491192i	0.860911	+	0.508756i	$0.169895\pi$
$620$	−0.682503			−0.0274100
$621$	−18.6577	+	3.86180i	−0.748708	+	0.154969i
$622$			25.4230i			1.01937i
$623$	7.95416	+	13.7770i	0.318677	+	0.551964i
$624$	−3.76267	+	4.98421i	−0.150627	+	0.199528i
$625$	−9.90953	+	17.1638i	−0.396381	+	0.686553i
$626$	−1.02317	−	0.590728i	−0.0408942	−	0.0236103i
$627$	0.0961506	+	0.388584i	0.00383989	+	0.0155186i
$628$	6.19540	+	10.7307i	0.247223	+	0.428203i
$629$			7.64149i			0.304686i
$630$	−2.98969	−	0.115060i	−0.119112	−	0.00458409i
$631$			5.70930i			0.227284i	0.993522	+	0.113642i	$0.0362516\pi$
$631$			5.70930i			0.227284i	−0.993522	+	0.113642i	$0.963748\pi$
$632$	1.78219	−	1.02895i	0.0708918	−	0.0409294i
$633$	12.0322	−	11.5781i	0.478238	−	0.460187i
$634$	−13.9724	+	24.2009i	−0.554915	+	0.961141i
$635$	9.55327	+	5.51558i	0.379110	+	0.218879i
$636$	−6.34760	+	6.10800i	−0.251699	+	0.242198i
$637$	14.9130	−	2.37591i	0.590874	−	0.0941372i
$638$	−1.18589			−0.0469498
$639$	−10.4087	+	16.5261i	−0.411761	+	0.653764i
$640$	−0.594758			−0.0235099
$641$	−19.7411	−	34.1925i	−0.779725	−	1.35052i	−0.932100	−	0.362201i	$-0.882026\pi$
$641$	−19.7411	−	34.1925i	−0.779725	−	1.35052i	0.152375	−	0.988323i	$-0.451308\pi$
$642$	23.7105	−	5.86688i	0.935778	−	0.231547i
$643$	−25.5467	−	14.7494i	−1.00747	−	0.581660i	−0.0970167	−	0.995283i	$-0.530930\pi$
$643$	−25.5467	−	14.7494i	−1.00747	−	0.581660i	−0.910449	+	0.413622i	$0.864263\pi$
$644$	−5.32479	−	3.07427i	−0.209826	−	0.121143i
$645$	1.97610	−	6.84547i	0.0778088	−	0.269540i
$646$	0.503217	+	0.871597i	0.0197988	+	0.0342925i
$647$	47.5940			1.87111			0.935556	−	0.353178i	$-0.114899\pi$
$647$	47.5940			1.87111			0.935556	+	0.353178i	$0.114899\pi$
$648$	8.11703	−	3.88765i	0.318867	−	0.152721i
$649$	−4.51412			−0.177195
$650$	2.63572	+	16.5437i	0.103381	+	0.648897i
$651$	3.20206	+	0.924349i	0.125499	+	0.0362281i
$652$	18.5008	+	10.6814i	0.724548	+	0.418318i
$653$	−6.23738	+	10.8035i	−0.244088	+	0.422772i	−0.961875	−	0.273490i	$-0.911822\pi$
$653$	−6.23738	+	10.8035i	−0.244088	+	0.422772i	0.717787	+	0.696263i	$0.245155\pi$
$654$	−7.63303	−	30.8482i	−0.298475	−	1.20626i
$655$	2.39259	−	1.38136i	0.0934863	−	0.0539744i
$656$		−	9.91005i		−	0.386922i
$657$	9.45715	−	15.0154i	0.368959	−	0.585807i
$658$		−	10.4651i		−	0.407970i
$659$	−1.87306	−	3.24423i	−0.0729639	−	0.126377i	0.827235	−	0.561856i	$-0.189912\pi$
$659$	−1.87306	−	3.24423i	−0.0729639	−	0.126377i	−0.900199	+	0.435479i	$0.856579\pi$
$660$	−0.356857	+	0.343388i	−0.0138907	+	0.0133663i
$661$	28.6397	+	16.5352i	1.11396	+	0.643143i	0.939851	−	0.341584i	$-0.110963\pi$
$661$	28.6397	+	16.5352i	1.11396	+	0.643143i	0.174105	+	0.984727i	$0.444297\pi$
$662$	12.3266	−	21.3503i	0.479086	−	0.829801i
$663$	5.09790	+	12.0390i	0.197986	+	0.467555i
$664$	5.53006	+	9.57834i	0.214608	+	0.371712i
$665$			0.479447i			0.0185922i
$666$	0.421119	−	10.9423i	0.0163180	−	0.424004i
$667$	−9.04515			−0.350230
$668$	−12.7614	+	7.36778i	−0.493752	+	0.285068i
$669$	−38.8950	+	9.62411i	−1.50377	+	0.372090i
$670$	7.40778	+	4.27688i	0.286187	+	0.165230i
$671$	3.25271	+	1.87796i	0.125570	+	0.0724977i
$672$	2.79040	+	0.805511i	0.107642	+	0.0310733i
$673$	7.07178	+	12.2487i	0.272597	+	0.472152i	0.969526	−	0.244988i	$-0.0787840\pi$
$673$	7.07178	+	12.2487i	0.272597	+	0.472152i	−0.696929	+	0.717140i	$0.745451\pi$
$674$		−	15.2788i		−	0.588518i
$675$	7.58300	−	22.9209i	0.291870	−	0.882226i
$676$	9.67672	+	8.68108i	0.372181	+	0.333888i
$677$	17.1064	+	29.6291i	0.657451	+	1.13874i	0.981273	+	0.192620i	$0.0616986\pi$
$677$	17.1064	+	29.6291i	0.657451	+	1.13874i	−0.323823	+	0.946118i	$0.604968\pi$
$678$	9.74112	−	33.7445i	0.374105	−	1.29595i
$679$	−8.14544	+	14.1083i	−0.312593	+	0.541427i
$680$	−0.622560	+	1.07831i	−0.0238741	+	0.0413512i
$681$	−22.3730	+	5.53594i	−0.857335	+	0.212138i
$682$	0.477759	−	0.275834i	0.0182944	−	0.0105622i
$683$			16.3144i			0.624255i	0.950040	+	0.312127i	$0.101042\pi$
$683$			16.3144i			0.624255i	−0.950040	+	0.312127i	$0.898958\pi$
$684$	−0.672550	−	1.27582i	−0.0257156	−	0.0487822i
$685$	7.74416			0.295889
$686$	−9.38036	−	16.2473i	−0.358144	−	0.620323i
$687$	−0.972066	−	1.01020i	−0.0370866	−	0.0385414i
$688$	−3.45822	+	5.98981i	−0.131843	+	0.228359i
$689$	11.5532	+	14.2404i	0.440141	+	0.542517i
$690$	−2.72186	+	2.61912i	−0.103619	+	0.0997083i
$691$	−21.9516	+	12.6738i	−0.835078	+	0.482132i	−0.855588	−	0.517657i	$-0.826804\pi$
$691$	−21.9516	+	12.6738i	−0.835078	+	0.482132i	0.0205104	+	0.999790i	$0.493471\pi$
$692$	−11.6487			−0.442817
$693$	2.13932	−	1.12774i	0.0812659	−	0.0428395i
$694$		−	1.21538i		−	0.0461350i
$695$	−5.24375	+	3.02748i	−0.198907	+	0.114839i
$696$	4.14750	−	1.02625i	0.157211	−	0.0388999i
$697$	−17.9671	−	10.3733i	−0.680551	−	0.392916i
$698$	−1.90580	+	3.30094i	−0.0721355	+	0.124942i
$699$	−25.7456	−	7.43206i	−0.973789	−	0.281106i
$700$	6.74715	−	3.89547i	0.255018	−	0.147235i
$701$	35.4651			1.33950			0.669750	−	0.742587i	$-0.266401\pi$
$701$	35.4651			1.33950			0.669750	+	0.742587i	$0.266401\pi$
$702$	−6.63649	−	17.5202i	−0.250478	−	0.661257i
$703$	−1.75478			−0.0661826
$704$	0.416337	−	0.240372i	0.0156913	−	0.00905937i
$705$	−6.17698	−	1.78312i	−0.232638	−	0.0671564i
$706$	10.0086	−	17.3353i	0.376677	−	0.652424i
$707$	−8.41524	−	4.85854i	−0.316488	−	0.182724i
$708$	15.7876	−	3.90645i	0.593333	−	0.146813i
$709$	18.7687	−	10.8361i	0.704874	−	0.406959i	−0.104286	−	0.994547i	$-0.533256\pi$
$709$	18.7687	−	10.8361i	0.704874	−	0.406959i	0.809160	+	0.587588i	$0.199923\pi$
$710$			3.87204i			0.145315i
$711$	−0.237422	+	6.16913i	−0.00890403	+	0.231360i
$712$	−9.48720			−0.355548
$713$	3.64402	−	2.10387i	0.136470	−	0.0787907i
$714$	4.38124	−	4.21587i	0.163964	−	0.157775i
$715$	0.649511	+	0.800587i	0.0242903	+	0.0299402i
$716$	−0.448079	+	0.776096i	−0.0167455	+	0.0290041i
$717$	−35.0171	−	36.3907i	−1.30774	−	1.35903i
$718$	4.98359	+	8.63182i	0.185986	+	0.322137i
$719$	15.4819			0.577378			0.288689	−	0.957423i	$-0.406781\pi$
$719$	15.4819			0.577378			0.288689	+	0.957423i	$0.406781\pi$
$720$	0.950902	−	1.50978i	0.0354380	−	0.0562660i
$721$		−	2.87419i		−	0.107040i
$722$	16.2543	−	9.38444i	0.604924	−	0.349253i
$723$	−26.2201	+	6.48784i	−0.975135	+	0.241286i
$724$	0.710953	−	1.23141i	0.0264224	−	0.0457649i
$725$	5.73065	−	9.92578i	0.212831	−	0.368634i
$726$	−5.17316	+	17.9205i	−0.191994	+	0.665093i
$727$	2.73280	+	4.73335i	0.101354	+	0.175550i	0.912243	−	0.409650i	$-0.134349\pi$
$727$	2.73280	+	4.73335i	0.101354	+	0.175550i	−0.810889	+	0.585200i	$0.801016\pi$
$728$	2.16150	−	5.64626i	0.0801104	−	0.209264i
$729$	−3.10888	+	26.8204i	−0.115144	+	0.993349i
$730$		−	3.51808i		−	0.130210i
$731$	7.23975	+	12.5396i	0.267772	+	0.463794i
$732$	−13.0011	−	3.75307i	−0.480535	−	0.138717i
$733$	16.5705	+	9.56700i	0.612046	+	0.353365i	0.773766	−	0.633472i	$-0.218371\pi$
$733$	16.5705	+	9.56700i	0.612046	+	0.353365i	−0.161720	+	0.986837i	$0.551704\pi$
$734$	−12.4073	−	7.16334i	−0.457960	−	0.264404i
$735$	−4.18825	+	1.03633i	−0.154486	+	0.0382258i
$736$	3.17553	−	1.83339i	0.117052	−	0.0675798i
$737$	−6.91403			−0.254681
$738$	25.1563	+	15.8442i	0.926018	+	0.583234i
$739$		−	3.40317i		−	0.125188i	−0.998039	−	0.0625938i	$-0.980063\pi$
$739$		−	3.40317i		−	0.125188i	0.998039	−	0.0625938i	$-0.0199373\pi$
$740$	−1.08547	−	1.88009i	−0.0399027	−	0.0691134i
$741$	−2.76460	+	1.17067i	−0.101560	+	0.0430056i
$742$	4.26408	−	7.38560i	0.156539	−	0.271134i
$743$	−19.8454	−	11.4578i	−0.728058	−	0.420345i	0.0896532	−	0.995973i	$-0.471424\pi$
$743$	−19.8454	−	11.4578i	−0.728058	−	0.420345i	−0.817711	+	0.575628i	$0.804757\pi$
$744$	−1.43220	+	1.37814i	−0.0525071	+	0.0505252i
$745$	1.56206	+	2.70556i	0.0572293	+	0.0991240i
$746$		−	27.9755i		−	1.02425i
$747$	−33.1558	−	1.27602i	−1.21311	−	0.0466871i
$748$		−	1.00643i		−	0.0367989i
$749$	−20.4786	+	11.8233i	−0.748272	+	0.432015i
$750$	−2.38684	−	9.64620i	−0.0871550	−	0.352229i
$751$	7.68694	−	13.3142i	0.280500	−	0.485841i	−0.691008	−	0.722847i	$-0.742833\pi$
$751$	7.68694	−	13.3142i	0.280500	−	0.485841i	0.971508	+	0.237006i	$0.0761663\pi$
$752$	5.40488	+	3.12051i	0.197096	+	0.113793i
$753$	−4.65109	−	1.34264i	−0.169495	−	0.0489286i
$754$	−1.39935	−	8.78332i	−0.0509612	−	0.319870i
$755$	7.09144			0.258084
$756$	−6.50606	+	5.79548i	−0.236623	+	0.210779i
$757$	41.9292			1.52394			0.761971	−	0.647611i	$-0.224232\pi$
$757$	41.9292			1.52394			0.761971	+	0.647611i	$0.224232\pi$
$758$	2.02534	+	3.50799i	0.0735637	+	0.127416i
$759$	0.846809	−	2.93346i	0.0307372	−	0.106478i
$760$	−0.247620	−	0.142963i	−0.00898211	−	0.00518583i
$761$	−2.20005	−	1.27020i	−0.0797518	−	0.0460447i	0.459594	−	0.888129i	$-0.347995\pi$
$761$	−2.20005	−	1.27020i	−0.0797518	−	0.0460447i	−0.539346	+	0.842085i	$0.681328\pi$
$762$	31.1844	−	7.71622i	1.12969	−	0.279529i
$763$	15.3826	+	26.6434i	0.556887	+	0.964557i
$764$	14.8407			0.536918
$765$	−1.74189	−	3.30435i	−0.0629783	−	0.119469i
$766$	−31.2962			−1.13078
$767$	−5.32664	−	33.4339i	−0.192334	−	1.20723i
$768$	−1.24807	+	1.20096i	−0.0450359	+	0.0433361i
$769$	8.65130	+	4.99483i	0.311974	+	0.180118i	0.647809	−	0.761802i	$-0.275685\pi$
$769$	8.65130	+	4.99483i	0.311974	+	0.180118i	−0.335836	+	0.941921i	$0.609019\pi$
$770$	0.239724	−	0.415213i	0.00863904	−

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.66410 + 0.480381i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.515076 + 0.297379i) q^{5} +(1.68134 - 0.416029i) q^{6} +(-1.45217 + 0.838409i) q^{7} -1.00000i q^{8} +(2.53847 + 1.59880i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.66410 + 0.480381i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.515076 + 0.297379i) q^{5} +(1.68134 - 0.416029i) q^{6} +(-1.45217 + 0.838409i) q^{7} -1.00000i q^{8} +(2.53847 + 1.59880i) q^{9} +0.594758 q^{10} +(-0.416337 + 0.240372i) q^{11} +(1.24807 - 1.20096i) q^{12} +(-2.27160 - 2.79997i) q^{13} +(-0.838409 + 1.45217i) q^{14} +(0.714283 + 0.742302i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.09349 q^{17} +(2.99778 + 0.115371i) q^{18} -0.480744i q^{19} +(0.515076 - 0.297379i) q^{20} +(-2.81931 + 0.697605i) q^{21} +(-0.240372 + 0.416337i) q^{22} +(-1.83339 + 3.17553i) q^{23} +(0.480381 - 1.66410i) q^{24} +(-2.32313 - 4.02378i) q^{25} +(-3.36725 - 1.28905i) q^{26} +(3.45624 + 3.88001i) q^{27} +1.67682i q^{28} +(1.23339 + 2.13629i) q^{29} +(0.989738 + 0.285710i) q^{30} +(-0.993791 - 0.573765i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.808297 + 0.200004i) q^{33} +(-1.81302 + 1.04675i) q^{34} -0.997301 q^{35} +(2.65384 - 1.39898i) q^{36} -3.65012i q^{37} +(-0.240372 - 0.416337i) q^{38} +(-2.43512 - 5.75067i) q^{39} +(0.297379 - 0.515076i) q^{40} +(8.58235 + 4.95502i) q^{41} +(-2.09279 + 2.01380i) q^{42} +(-3.45822 - 5.98981i) q^{43} +0.480744i q^{44} +(0.832053 + 1.57839i) q^{45} +3.66679i q^{46} +(-5.40488 + 3.12051i) q^{47} +(-0.416029 - 1.68134i) q^{48} +(-2.09414 + 3.62716i) q^{49} +(-4.02378 - 2.32313i) q^{50} +(-3.48378 - 1.00567i) q^{51} +(-3.56065 + 0.567277i) q^{52} -5.08592 q^{53} +(4.93319 + 1.63207i) q^{54} -0.285927 q^{55} +(0.838409 + 1.45217i) q^{56} +(0.230940 - 0.800008i) q^{57} +(2.13629 + 1.23339i) q^{58} +(8.13185 + 4.69493i) q^{59} +(0.999994 - 0.247437i) q^{60} +(-3.90635 - 6.76599i) q^{61} -1.14753 q^{62} +(-5.02673 - 0.193456i) q^{63} -1.00000 q^{64} +(-0.337393 - 2.11772i) q^{65} +(-0.600004 + 0.577357i) q^{66} +(12.4551 + 7.19096i) q^{67} +(-1.04675 + 1.81302i) q^{68} +(-4.57642 + 4.40368i) q^{69} +(-0.863688 + 0.498651i) q^{70} +6.51028i q^{71} +(1.59880 - 2.53847i) q^{72} -5.91514i q^{73} +(-1.82506 - 3.16110i) q^{74} +(-1.93298 - 7.81197i) q^{75} +(-0.416337 - 0.240372i) q^{76} +(0.403061 - 0.698121i) q^{77} +(-4.98421 - 3.76267i) q^{78} +(1.02895 + 1.78219i) q^{79} -0.594758i q^{80} +(3.88765 + 8.11703i) q^{81} +9.91005 q^{82} +(-9.57834 + 5.53006i) q^{83} +(-0.805511 + 2.79040i) q^{84} +(-1.07831 - 0.622560i) q^{85} +(-5.98981 - 3.45822i) q^{86} +(1.02625 + 4.14750i) q^{87} +(0.240372 + 0.416337i) q^{88} -9.48720i q^{89} +(1.50978 + 0.950902i) q^{90} +(5.64626 + 2.16150i) q^{91} +(1.83339 + 3.17553i) q^{92} +(-1.37814 - 1.43220i) q^{93} +(-3.12051 + 5.40488i) q^{94} +(0.142963 - 0.247620i) q^{95} +(-1.20096 - 1.24807i) q^{96} +(8.41374 - 4.85767i) q^{97} +4.18828i q^{98} +(-1.44117 - 0.0554640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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