LMFDB - Embedded newform 234.2.y.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.1
Character	$\chi$	$=$	234.59
Dual form			234.2.y.a.119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.36368 - 1.06788i) q^{3} -1.00000i q^{4} +(0.763001 + 2.84756i) q^{5} +(1.71938 - 0.209163i) q^{6} +(-0.504962 - 1.88454i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.719258 + 2.91250i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36368 - 1.06788i) q^{3} -1.00000i q^{4} +(0.763001 + 2.84756i) q^{5} +(1.71938 - 0.209163i) q^{6} +(-0.504962 - 1.88454i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.719258 + 2.91250i) q^{9} +(-2.55305 - 1.47400i) q^{10} +(-0.566782 - 0.566782i) q^{11} +(-1.06788 + 1.36368i) q^{12} +(2.11327 + 2.92131i) q^{13} +(1.68964 + 0.975511i) q^{14} +(2.00036 - 4.69796i) q^{15} -1.00000 q^{16} +(4.02058 + 6.96385i) q^{17} +(-2.56804 - 1.55086i) q^{18} +(-1.18319 + 4.41574i) q^{19} +(2.84756 - 0.763001i) q^{20} +(-1.32386 + 3.10916i) q^{21} +0.801550 q^{22} +(3.49688 + 6.05678i) q^{23} +(-0.209163 - 1.71938i) q^{24} +(-3.19629 + 1.84538i) q^{25} +(-3.55999 - 0.571370i) q^{26} +(2.12937 - 4.73981i) q^{27} +(-1.88454 + 0.504962i) q^{28} -7.87674i q^{29} +(1.90749 + 4.73643i) q^{30} +(-2.31031 + 0.619046i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.167654 + 1.37817i) q^{33} +(-7.76717 - 2.08121i) q^{34} +(4.98106 - 2.87582i) q^{35} +(2.91250 - 0.719258i) q^{36} +(-2.09658 - 7.82455i) q^{37} +(-2.28576 - 3.95904i) q^{38} +(0.237782 - 6.24047i) q^{39} +(-1.47400 + 2.55305i) q^{40} +(-5.00455 - 1.34097i) q^{41} +(-1.26239 - 3.13462i) q^{42} +(2.02114 + 1.16691i) q^{43} +(-0.566782 + 0.566782i) q^{44} +(-7.74472 + 4.27037i) q^{45} +(-6.75546 - 1.81012i) q^{46} +(-1.37959 + 5.14869i) q^{47} +(1.36368 + 1.06788i) q^{48} +(2.76566 - 1.59676i) q^{49} +(0.955238 - 3.56500i) q^{50} +(1.95377 - 13.7900i) q^{51} +(2.92131 - 2.11327i) q^{52} +8.27924i q^{53} +(1.84586 + 4.85724i) q^{54} +(1.18149 - 2.04640i) q^{55} +(0.975511 - 1.68964i) q^{56} +(6.32899 - 4.75815i) q^{57} +(5.56970 + 5.56970i) q^{58} +(-6.24226 - 6.24226i) q^{59} +(-4.69796 - 2.00036i) q^{60} +(2.46959 - 4.27745i) q^{61} +(1.19590 - 2.07137i) q^{62} +(5.12554 - 2.82617i) q^{63} +1.00000i q^{64} +(-6.70618 + 8.24664i) q^{65} +(-1.09306 - 0.855961i) q^{66} +(0.200953 - 0.749969i) q^{67} +(6.96385 - 4.02058i) q^{68} +(1.69929 - 11.9938i) q^{69} +(-1.48863 + 5.55565i) q^{70} +(2.57304 + 0.689443i) q^{71} +(-1.55086 + 2.56804i) q^{72} +(5.68293 - 5.68293i) q^{73} +(7.01530 + 4.05028i) q^{74} +(6.32937 + 0.896749i) q^{75} +(4.41574 + 1.18319i) q^{76} +(-0.781921 + 1.35433i) q^{77} +(4.24454 + 4.58082i) q^{78} +(0.554497 + 0.960416i) q^{79} +(-0.763001 - 2.84756i) q^{80} +(-7.96534 + 4.18968i) q^{81} +(4.48696 - 2.59055i) q^{82} +(2.29264 + 0.614312i) q^{83} +(3.10916 + 1.32386i) q^{84} +(-16.7623 + 16.7623i) q^{85} +(-2.25429 + 0.604036i) q^{86} +(-8.41143 + 10.7414i) q^{87} -0.801550i q^{88} +(2.84070 - 0.761164i) q^{89} +(2.45674 - 8.49595i) q^{90} +(4.43822 - 5.45771i) q^{91} +(6.05678 - 3.49688i) q^{92} +(3.81160 + 1.62296i) q^{93} +(-2.66516 - 4.61619i) q^{94} -13.4769 q^{95} +(-1.71938 + 0.209163i) q^{96} +(-3.54866 + 0.950861i) q^{97} +(-0.826542 + 3.08469i) q^{98} +(1.24309 - 2.05842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.36368	−	1.06788i	−0.787322	−	0.616542i
$3$	−1.36368	−	1.06788i	−0.787322	−	0.616542i
$4$		−	1.00000i		−	0.500000i
$5$	0.763001	+	2.84756i	0.341224	+	1.27347i	0.896962	+	0.442109i	$0.145769\pi$
$5$	0.763001	+	2.84756i	0.341224	+	1.27347i	−0.555737	+	0.831358i	$0.687564\pi$
$6$	1.71938	−	0.209163i	0.701932	−	0.0853903i
$7$	−0.504962	−	1.88454i	−0.190858	−	0.712290i	−0.993300	−	0.115561i	$-0.963133\pi$
$7$	−0.504962	−	1.88454i	−0.190858	−	0.712290i	0.802443	−	0.596729i	$-0.203533\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.719258	+	2.91250i	0.239753	+	0.970834i
$10$	−2.55305	−	1.47400i	−0.807345	−	0.466121i
$11$	−0.566782	−	0.566782i	−0.170891	−	0.170891i	0.616480	−	0.787371i	$-0.288558\pi$
$11$	−0.566782	−	0.566782i	−0.170891	−	0.170891i	−0.787371	+	0.616480i	$0.788558\pi$
$12$	−1.06788	+	1.36368i	−0.308271	+	0.393661i
$13$	2.11327	+	2.92131i	0.586117	+	0.810226i
$13$	2.11327	+	2.92131i	0.586117	+	0.810226i
$14$	1.68964	+	0.975511i	0.451574	+	0.260716i
$15$	2.00036	−	4.69796i	0.516492	−	1.21301i
$16$	−1.00000			−0.250000
$17$	4.02058	+	6.96385i	0.975135	+	1.68898i	0.679490	+	0.733685i	$0.262201\pi$
$17$	4.02058	+	6.96385i	0.975135	+	1.68898i	0.295645	+	0.955298i	$0.404465\pi$
$18$	−2.56804	−	1.55086i	−0.605293	−	0.365541i
$19$	−1.18319	+	4.41574i	−0.271443	+	1.01304i	0.686744	+	0.726899i	$0.259039\pi$
$19$	−1.18319	+	4.41574i	−0.271443	+	1.01304i	−0.958188	+	0.286141i	$0.907627\pi$
$20$	2.84756	−	0.763001i	0.636733	−	0.170612i
$21$	−1.32386	+	3.10916i	−0.288890	+	0.678474i
$22$	0.801550			0.170891
$23$	3.49688	+	6.05678i	0.729150	+	1.26293i	0.957243	+	0.289286i	$0.0934177\pi$
$23$	3.49688	+	6.05678i	0.729150	+	1.26293i	−0.228093	+	0.973639i	$0.573249\pi$
$24$	−0.209163	−	1.71938i	−0.0426951	−	0.350966i
$25$	−3.19629	+	1.84538i	−0.639258	+	0.369076i
$26$	−3.55999	−	0.571370i	−0.698172	−	0.112055i
$27$	2.12937	−	4.73981i	0.409797	−	0.912177i
$28$	−1.88454	+	0.504962i	−0.356145	+	0.0954288i
$29$		−	7.87674i		−	1.46267i	−0.682016	−	0.731337i	$-0.738897\pi$
$29$		−	7.87674i		−	1.46267i	0.682016	−	0.731337i	$-0.261103\pi$
$30$	1.90749	+	4.73643i	0.348258	+	0.864750i
$31$	−2.31031	+	0.619046i	−0.414944	+	0.111184i	−0.460250	−	0.887789i	$-0.652240\pi$
$31$	−2.31031	+	0.619046i	−0.414944	+	0.111184i	0.0453062	+	0.998973i	$0.485574\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.167654	+	1.37817i	0.0291849	+	0.239908i
$34$	−7.76717	−	2.08121i	−1.33206	−	0.356924i
$35$	4.98106	−	2.87582i	0.841953	−	0.486102i
$36$	2.91250	−	0.719258i	0.485417	−	0.119876i
$37$	−2.09658	−	7.82455i	−0.344676	−	1.28635i	−0.892990	−	0.450076i	$-0.851397\pi$
$37$	−2.09658	−	7.82455i	−0.344676	−	1.28635i	0.548314	−	0.836272i	$-0.315270\pi$
$38$	−2.28576	−	3.95904i	−0.370798	−	0.642242i
$39$	0.237782	−	6.24047i	0.0380756	−	0.999275i
$40$	−1.47400	+	2.55305i	−0.233061	+	0.403673i
$41$	−5.00455	−	1.34097i	−0.781580	−	0.209424i	−0.154099	−	0.988055i	$-0.549247\pi$
$41$	−5.00455	−	1.34097i	−0.781580	−	0.209424i	−0.627481	+	0.778632i	$0.715914\pi$
$42$	−1.26239	−	3.13462i	−0.194792	−	0.483682i
$43$	2.02114	+	1.16691i	0.308222	+	0.177952i	0.646130	−	0.763227i	$-0.276386\pi$
$43$	2.02114	+	1.16691i	0.308222	+	0.177952i	−0.337909	+	0.941179i	$0.609720\pi$
$44$	−0.566782	+	0.566782i	−0.0854456	+	0.0854456i
$45$	−7.74472	+	4.27037i	−1.15452	+	0.636589i
$46$	−6.75546	−	1.81012i	−0.996038	−	0.266887i
$47$	−1.37959	+	5.14869i	−0.201233	+	0.751013i	0.789331	+	0.613968i	$0.210427\pi$
$47$	−1.37959	+	5.14869i	−0.201233	+	0.751013i	−0.990565	+	0.137046i	$0.956239\pi$
$48$	1.36368	+	1.06788i	0.196831	+	0.154135i
$49$	2.76566	−	1.59676i	0.395095	−	0.228108i
$50$	0.955238	−	3.56500i	0.135091	−	0.504167i
$51$	1.95377	−	13.7900i	0.273583	−	1.93099i
$52$	2.92131	−	2.11327i	0.405113	−	0.293058i
$53$			8.27924i			1.13724i	0.822600	+	0.568620i	$0.192523\pi$
$53$			8.27924i			1.13724i	−0.822600	+	0.568620i	$0.807477\pi$
$54$	1.84586	+	4.85724i	0.251190	+	0.660987i
$55$	1.18149	−	2.04640i	0.159312	−	0.275936i
$56$	0.975511	−	1.68964i	0.130358	−	0.225787i
$57$	6.32899	−	4.75815i	0.838295	−	0.630233i
$58$	5.56970	+	5.56970i	0.731337	+	0.731337i
$59$	−6.24226	−	6.24226i	−0.812673	−	0.812673i	0.172361	−	0.985034i	$-0.444861\pi$
$59$	−6.24226	−	6.24226i	−0.812673	−	0.812673i	−0.985034	+	0.172361i	$0.944861\pi$
$60$	−4.69796	−	2.00036i	−0.606504	−	0.258246i
$61$	2.46959	−	4.27745i	0.316198	−	0.547671i	−0.663493	−	0.748182i	$-0.730927\pi$
$61$	2.46959	−	4.27745i	0.316198	−	0.547671i	0.979691	+	0.200511i	$0.0642603\pi$
$62$	1.19590	−	2.07137i	0.151880	−	0.263064i
$63$	5.12554	−	2.82617i	0.645757	−	0.356065i
$64$			1.00000i			0.125000i
$65$	−6.70618	+	8.24664i	−0.831799	+	1.02287i
$66$	−1.09306	−	0.855961i	−0.134546	−	0.105362i
$67$	0.200953	−	0.749969i	0.0245504	−	0.0916232i	−0.952564	−	0.304339i	$-0.901564\pi$
$67$	0.200953	−	0.749969i	0.0245504	−	0.0916232i	0.977114	+	0.212716i	$0.0682310\pi$
$68$	6.96385	−	4.02058i	0.844491	−	0.487567i
$69$	1.69929	−	11.9938i	0.204570	−	1.44388i
$70$	−1.48863	+	5.55565i	−0.177926	+	0.664027i
$71$	2.57304	+	0.689443i	0.305363	+	0.0818218i	0.408247	−	0.912872i	$-0.366140\pi$
$71$	2.57304	+	0.689443i	0.305363	+	0.0818218i	−0.102884	+	0.994693i	$0.532807\pi$
$72$	−1.55086	+	2.56804i	−0.182770	+	0.302647i
$73$	5.68293	−	5.68293i	0.665137	−	0.665137i	−0.291449	−	0.956586i	$-0.594137\pi$
$73$	5.68293	−	5.68293i	0.665137	−	0.665137i	0.956586	+	0.291449i	$0.0941375\pi$
$74$	7.01530	+	4.05028i	0.815512	+	0.470836i
$75$	6.32937	+	0.896749i	0.730852	+	0.103548i
$76$	4.41574	+	1.18319i	0.506520	+	0.135722i
$77$	−0.781921	+	1.35433i	−0.0891082	+	0.154340i
$78$	4.24454	+	4.58082i	0.480600	+	0.518675i
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	0.895531	−	0.444998i	$-0.146796\pi$
$79$	0.554497	+	0.960416i	0.0623857	+	0.108055i	−0.833146	+	0.553054i	$0.813462\pi$
$80$	−0.763001	−	2.84756i	−0.0853061	−	0.318367i
$81$	−7.96534	+	4.18968i	−0.885037	+	0.465520i
$82$	4.48696	−	2.59055i	0.495502	−	0.286078i
$83$	2.29264	+	0.614312i	0.251650	+	0.0674295i	0.382439	−	0.923981i	$-0.375084\pi$
$83$	2.29264	+	0.614312i	0.251650	+	0.0674295i	−0.130789	+	0.991410i	$0.541751\pi$
$84$	3.10916	+	1.32386i	0.339237	+	0.144445i
$85$	−16.7623	+	16.7623i	−1.81812	+	1.81812i
$86$	−2.25429	+	0.604036i	−0.243087	+	0.0651349i
$87$	−8.41143	+	10.7414i	−0.901800	+	1.15160i
$88$		−	0.801550i		−	0.0854456i
$89$	2.84070	−	0.761164i	0.301114	−	0.0806832i	−0.105099	−	0.994462i	$-0.533516\pi$
$89$	2.84070	−	0.761164i	0.301114	−	0.0806832i	0.406213	+	0.913779i	$0.366849\pi$
$90$	2.45674	−	8.49595i	0.258963	−	0.895552i
$91$	4.43822	−	5.45771i	0.465252	−	0.572123i
$92$	6.05678	−	3.49688i	0.631463	−	0.364575i
$93$	3.81160	+	1.62296i	0.395244	+	0.168293i
$94$	−2.66516	−	4.61619i	−0.274890	−	0.476123i
$95$	−13.4769			−1.38270
$96$	−1.71938	+	0.209163i	−0.175483	+	0.0213476i
$97$	−3.54866	+	0.950861i	−0.360312	+	0.0965453i	−0.434433	−	0.900704i	$-0.643051\pi$
$97$	−3.54866	+	0.950861i	−0.360312	+	0.0965453i	0.0741216	+	0.997249i	$0.476385\pi$
$98$	−0.826542	+	3.08469i	−0.0834933	+	0.311601i
$99$	1.24309	−	2.05842i	0.124935	−	0.206878i
$100$	1.84538	+	3.19629i	0.184538	+	0.319629i
$101$	−13.6438			−1.35761			−0.678804	−	0.734319i	$-0.737502\pi$
$101$	−13.6438			−1.35761			−0.678804	+	0.734319i	$0.737502\pi$
$102$	8.36947	+	11.1325i	0.828701	+	1.10228i
$103$	11.6669	+	6.73592i	1.14958	+	0.663710i	0.948785	−	0.315924i	$-0.102314\pi$
$103$	11.6669	+	6.73592i	1.14958	+	0.663710i	0.200794	+	0.979633i	$0.435648\pi$
$104$	−0.571370	+	3.55999i	−0.0560274	+	0.349086i
$105$	−9.86361	−	1.39748i	−0.962590	−	0.136380i
$106$	−5.85430	−	5.85430i	−0.568620	−	0.568620i
$107$	−16.0522	−	9.26775i	−1.55183	−	0.895947i	−0.997993	−	0.0633192i	$-0.979831\pi$
$107$	−16.0522	−	9.26775i	−1.55183	−	0.895947i	−0.553833	−	0.832628i	$-0.686835\pi$
$108$	−4.73981	−	2.12937i	−0.456088	−	0.204899i
$109$	4.23071	+	4.23071i	0.405229	+	0.405229i	0.880071	−	0.474842i	$-0.157495\pi$
$109$	4.23071	+	4.23071i	0.405229	+	0.405229i	−0.474842	+	0.880071i	$0.657495\pi$
$110$	0.611584	+	2.28246i	0.0583122	+	0.217624i
$111$	−5.49662	+	12.9091i	−0.521716	+	1.22528i
$112$	0.504962	+	1.88454i	0.0477144	+	0.178073i
$113$		−	5.97917i		−	0.562473i	−0.959639	−	0.281236i	$-0.909256\pi$
$113$		−	5.97917i		−	0.562473i	0.959639	−	0.281236i	$-0.0907445\pi$
$114$	−1.11075	+	7.83979i	−0.104031	+	0.734264i
$115$	−14.5789	+	14.5789i	−1.35949	+	1.35949i
$116$	−7.87674			−0.731337
$117$	−6.98834	+	8.25609i	−0.646072	+	0.763276i
$118$	8.82789			0.812673
$119$	11.0934	−	11.0934i	1.01693	−	1.01693i
$120$	4.73643	−	1.90749i	0.432375	−	0.174129i
$121$		−	10.3575i		−	0.941592i
$122$	1.27835	+	4.77087i	0.115737	+	0.431935i
$123$	5.39263	+	7.17292i	0.486237	+	0.646760i
$124$	0.619046	+	2.31031i	0.0555920	+	0.207472i
$125$	2.72919	+	2.72919i	0.244106	+	0.244106i
$126$	−1.62590	+	5.62271i	−0.144846	+	0.500911i
$127$	1.93815	+	1.11899i	0.171983	+	0.0992946i	0.583521	−	0.812098i	$-0.301675\pi$
$127$	1.93815	+	1.11899i	0.171983	+	0.0992946i	−0.411537	+	0.911393i	$0.635008\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.51008	−	3.74963i	−0.132955	−	0.330137i
$130$	−1.08927	−	10.5732i	−0.0955352	−	0.927334i
$131$	7.37842	+	4.25993i	0.644656	+	0.372192i	0.786406	−	0.617710i	$-0.211940\pi$
$131$	7.37842	+	4.25993i	0.644656	+	0.372192i	−0.141750	+	0.989903i	$0.545273\pi$
$132$	1.37817	−	0.167654i	0.119954	−	0.0145924i
$133$	8.91912			0.773386
$134$	0.388212	+	0.672403i	0.0335364	+	0.0580868i
$135$	15.1216	+	2.44702i	1.30146	+	0.210606i
$136$	−2.08121	+	7.76717i	−0.178462	+	0.666029i
$137$	11.2268	−	3.00821i	0.959170	−	0.257009i	0.254921	−	0.966962i	$-0.417951\pi$
$137$	11.2268	−	3.00821i	0.959170	−	0.257009i	0.704249	+	0.709953i	$0.251284\pi$
$138$	7.27930	+	9.68245i	0.619655	+	0.824225i
$139$	22.8286			1.93629			0.968147	−	0.250381i	$-0.0805558\pi$
$139$	22.8286			1.93629			0.968147	+	0.250381i	$0.0805558\pi$
$140$	−2.87582	−	4.98106i	−0.243051	−	0.420976i
$141$	7.37951	−	5.54794i	0.621467	−	0.467221i
$142$	−2.30692	+	1.33190i	−0.193593	+	0.111771i
$143$	0.457981	−	2.85351i	0.0382983	−	0.238623i
$144$	−0.719258	−	2.91250i	−0.0599381	−	0.242709i
$145$	22.4295	−	6.00996i	1.86267	−	0.499100i
$146$			8.03688i			0.665137i
$147$	−5.47663	−	0.775932i	−0.451705	−	0.0639978i
$148$	−7.82455	+	2.09658i	−0.643174	+	0.172338i
$149$	−5.50303	+	5.50303i	−0.450826	+	0.450826i	−0.895629	−	0.444803i	$-0.853274\pi$
$149$	−5.50303	+	5.50303i	−0.450826	+	0.450826i	0.444803	+	0.895629i	$0.353274\pi$
$150$	−5.10964	+	3.84144i	−0.417200	+	0.313652i
$151$	−7.67704	−	2.05706i	−0.624748	−	0.167401i	−0.0674629	−	0.997722i	$-0.521490\pi$
$151$	−7.67704	−	2.05706i	−0.624748	−	0.167401i	−0.557285	+	0.830321i	$0.688157\pi$
$152$	−3.95904	+	2.28576i	−0.321121	+	0.185399i
$153$	−17.3904	+	16.7188i	−1.40593	+	1.35163i
$154$	−0.404752	−	1.51056i	−0.0326159	−	0.121724i
$155$	−3.52554	−	6.10641i	−0.283178	−	0.490479i
$156$	−6.24047	−	0.237782i	−0.499637	−	0.0190378i
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	−0.776632	−	0.629954i	$-0.783074\pi$
$157$	1.97021	−	3.41251i	0.157240	−	0.272348i	0.933872	+	0.357606i	$0.116407\pi$
$158$	−1.07121	−	0.287029i	−0.0852205	−	0.0228348i
$159$	8.84124	−	11.2902i	0.701156	−	0.895375i
$160$	2.55305	+	1.47400i	0.201836	+	0.116530i
$161$	9.64846	−	9.64846i	0.760405	−	0.760405i
$162$	2.66979	−	8.59489i	0.209759	−	0.675279i
$163$	−19.9290	−	5.33996i	−1.56096	−	0.418258i	−0.627992	−	0.778220i	$-0.716123\pi$
$163$	−19.9290	−	5.33996i	−1.56096	−	0.418258i	−0.932967	+	0.359962i	$0.882790\pi$
$164$	−1.34097	+	5.00455i	−0.104712	+	0.390790i
$165$	−3.79649	+	1.52895i	−0.295556	+	0.119028i
$166$	−2.05553	+	1.18676i	−0.159540	+	0.0921103i
$167$	1.46059	−	5.45101i	0.113024	−	0.421811i	−0.886107	−	0.463480i	$-0.846601\pi$
$167$	1.46059	−	5.45101i	0.113024	−	0.421811i	0.999131	+	0.0416684i	$0.0132673\pi$
$168$	−3.13462	+	1.26239i	−0.241841	+	0.0973959i
$169$	−4.06814	+	12.3471i	−0.312934	+	0.949775i
$170$		−	23.7054i		−	1.81812i
$171$	−13.7119	−	0.270000i	−1.04857	−	0.0206474i
$172$	1.16691	−	2.02114i	0.0889759	−	0.154111i
$173$	−8.21647	+	14.2313i	−0.624687	+	1.08199i	0.363915	+	0.931432i	$0.381440\pi$
$173$	−8.21647	+	14.2313i	−0.624687	+	1.08199i	−0.988601	+	0.150557i	$0.951893\pi$
$174$	−1.64752	−	13.5431i	−0.124898	−	1.02670i
$175$	5.09170	+	5.09170i	0.384896	+	0.384896i
$176$	0.566782	+	0.566782i	0.0427228	+	0.0427228i
$177$	1.84646	+	15.1785i	0.138789	+	1.14088i
$178$	−1.47046	+	2.54690i	−0.110215	+	0.190898i
$179$	3.02863	−	5.24575i	0.226371	−	0.392085i	−0.730359	−	0.683063i	$-0.760647\pi$
$179$	3.02863	−	5.24575i	0.226371	−	0.392085i	0.956730	+	0.290978i	$0.0939806\pi$
$180$	4.27037	+	7.74472i	0.318295	+	0.577258i
$181$		−	12.2487i		−	0.910436i	−0.890380	−	0.455218i	$-0.849561\pi$
$181$		−	12.2487i		−	0.910436i	0.890380	−	0.455218i	$-0.150439\pi$
$182$	0.720889	+	6.99748i	0.0534358	+	0.518687i
$183$	−7.93554	+	3.19585i	−0.586612	+	0.236244i
$184$	−1.81012	+	6.75546i	−0.133444	+	0.498019i
$185$	20.6812	−	11.9403i	1.52051	−	0.877867i
$186$	−3.84281	+	1.54760i	−0.281769	+	0.113476i
$187$	1.66819	−	6.22578i	0.121990	−	0.455274i
$188$	5.14869	+	1.37959i	0.375507	+	0.100617i
$189$	−10.0076	−	1.61946i	−0.727948	−	0.117799i
$190$	9.52957	−	9.52957i	0.691348	−	0.691348i
$191$	−0.364345	−	0.210355i	−0.0263631	−	0.0152207i	0.486761	−	0.873535i	$-0.338178\pi$
$191$	−0.364345	−	0.210355i	−0.0263631	−	0.0152207i	−0.513124	+	0.858315i	$0.671512\pi$
$192$	1.06788	−	1.36368i	0.0770677	−	0.0984153i
$193$	13.1262	+	3.51716i	0.944847	+	0.253171i	0.698174	−	0.715928i	$-0.253996\pi$
$193$	13.1262	+	3.51716i	0.944847	+	0.253171i	0.246673	+	0.969099i	$0.420663\pi$
$194$	1.83692	−	3.18164i	0.131883	−	0.228429i
$195$	17.9515	−	4.08439i	1.28554	−	0.292489i
$196$	−1.59676	−	2.76566i	−0.114054	−	0.197547i
$197$	−0.239457	−	0.893667i	−0.0170606	−	0.0636712i	0.956871	−	0.290514i	$-0.0938263\pi$
$197$	−0.239457	−	0.893667i	−0.0170606	−	0.0636712i	−0.973931	+	0.226843i	$0.927160\pi$
$198$	0.576521	+	2.33452i	0.0409716	+	0.165907i
$199$	11.1074	−	6.41286i	0.787382	−	0.454595i	−0.0516579	−	0.998665i	$-0.516451\pi$
$199$	11.1074	−	6.41286i	0.787382	−	0.454595i	0.839040	+	0.544070i	$0.183117\pi$
$200$	−3.56500	−	0.955238i	−0.252083	−	0.0675455i
$201$	−1.07491	+	0.808124i	−0.0758186	+	0.0570007i
$202$	9.64762	−	9.64762i	0.678804	−	0.678804i
$203$	−14.8441	+	3.97745i	−1.04185	+	0.279162i
$204$	−13.7900	−	1.95377i	−0.965493	−	0.136792i
$205$		−	15.2739i		−	1.06678i
$206$	−13.0128	+	3.48677i	−0.906644	+	0.242935i
$207$	−15.1252	+	14.5411i	−1.05127	+	1.01067i
$208$	−2.11327	−	2.92131i	−0.146529	−	0.202557i
$209$	3.17337	−	1.83215i	0.219507	−	0.126732i
$210$	7.96280	−	5.98646i	0.549485	−	0.413105i
$211$	−3.42303	−	5.92886i	−0.235651	−	0.408159i	0.723811	−	0.689999i	$-0.242389\pi$
$211$	−3.42303	−	5.92886i	−0.235651	−	0.408159i	−0.959462	+	0.281839i	$0.909056\pi$
$212$	8.27924			0.568620
$213$	−2.77256	−	3.68788i	−0.189973	−	0.252689i
$214$	17.9039	−	4.79734i	1.22389	−	0.327939i
$215$	−1.78070	+	6.64568i	−0.121443	+	0.453231i
$216$	4.85724	−	1.84586i	0.330493	−	0.125595i
$217$	2.33324	+	4.04129i	0.158390	+	0.274340i
$218$	−5.98313			−0.405229
$219$	−13.8184	+	1.68101i	−0.933762	+	0.113592i
$220$	−2.04640	−	1.18149i	−0.137968	−	0.0796560i
$221$	−11.8470	+	26.4619i	−0.796916	+	1.78002i
$222$	−5.24141	−	13.0148i	−0.351781	−	0.873497i
$223$	12.5100	+	12.5100i	0.837733	+	0.837733i	0.988560	−	0.150827i	$-0.0481937\pi$
$223$	12.5100	+	12.5100i	0.837733	+	0.837733i	−0.150827	+	0.988560i	$0.548194\pi$
$224$	−1.68964	−	0.975511i	−0.112893	−	0.0651791i
$225$	−7.67362	−	7.98190i	−0.511575	−	0.532126i
$226$	4.22791	+	4.22791i	0.281236	+	0.281236i
$227$	−5.01242	−	18.7066i	−0.332686	−	1.24160i	−0.906356	−	0.422515i	$-0.861147\pi$
$227$	−5.01242	−	18.7066i	−0.332686	−	1.24160i	0.573669	−	0.819087i	$-0.305519\pi$
$228$	−4.75815	−	6.32899i	−0.315116	−	0.419147i
$229$	−6.72179	−	25.0861i	−0.444188	−	1.65773i	−0.718070	−	0.695971i	$-0.754974\pi$
$229$	−6.72179	−	25.0861i	−0.444188	−	1.65773i	0.273882	−	0.961763i	$-0.411692\pi$
$230$		−	20.6177i		−	1.35949i
$231$	2.51255	−	1.01187i	0.165314	−	0.0665763i
$232$	5.56970	−	5.56970i	0.365669	−	0.365669i
$233$	11.9090			0.780184			0.390092	−	0.920776i	$-0.372443\pi$
$233$	11.9090			0.780184			0.390092	+	0.920776i	$0.372443\pi$
$234$	−0.896436	−	10.7794i	−0.0586019	−	0.704674i
$235$	−15.7138			−1.02506
$236$	−6.24226	+	6.24226i	−0.406337	+	0.406337i
$237$	0.269454	−	1.90184i	0.0175029	−	0.123538i
$238$			15.6885i			1.01693i
$239$	2.40211	+	8.96480i	0.155380	+	0.579885i	0.999073	+	0.0430587i	$0.0137102\pi$
$239$	2.40211	+	8.96480i	0.155380	+	0.579885i	−0.843693	+	0.536826i	$0.819623\pi$
$240$	−2.00036	+	4.69796i	−0.129123	+	0.303252i
$241$	−2.53446	−	9.45875i	−0.163259	−	0.609292i	−0.998256	−	0.0590365i	$-0.981197\pi$
$241$	−2.53446	−	9.45875i	−0.163259	−	0.609292i	0.834997	−	0.550255i	$-0.185470\pi$
$242$	7.32387	+	7.32387i	0.470796	+	0.470796i
$243$	15.3363	+	2.79265i	0.983822	+	0.179148i
$244$	−4.27745	−	2.46959i	−0.273836	−	0.158099i
$245$	6.65706	+	6.65706i	0.425304	+	0.425304i
$246$	−8.88518	−	1.25886i	−0.566499	−	0.0802619i
$247$	−15.4002	+	5.87519i	−0.979890	+	0.373829i
$248$	−2.07137	−	1.19590i	−0.131532	−	0.0759400i
$249$	−2.47042	−	3.28600i	−0.156557	−	0.208242i
$250$	−3.85966			−0.244106
$251$	−7.05445	−	12.2187i	−0.445273	−	0.771235i	0.552798	−	0.833315i	$-0.313560\pi$
$251$	−7.05445	−	12.2187i	−0.445273	−	0.771235i	−0.998071	+	0.0620799i	$0.980227\pi$
$252$	−2.82617	−	5.12554i	−0.178032	−	0.322879i
$253$	1.45090	−	5.41484i	0.0912174	−	0.340428i
$254$	−2.16173	+	0.579234i	−0.135639	+	0.0363444i
$255$	40.7585	−	4.95829i	2.55240	−	0.310500i
$256$	1.00000			0.0625000
$257$	−2.55988	−	4.43384i	−0.159681	−	0.276575i	0.775073	−	0.631872i	$-0.217713\pi$
$257$	−2.55988	−	4.43384i	−0.159681	−	0.276575i	−0.934754	+	0.355297i	$0.884380\pi$
$258$	3.71918	+	1.58361i	0.231546	+	0.0985910i
$259$	−13.6870	+	7.90220i	−0.850469	+	0.491019i
$260$	8.24664	+	6.70618i	0.511435	+	0.415900i
$261$	22.9410	−	5.66541i	1.42001	−	0.350680i
$262$	−8.22956	+	2.20510i	−0.508424	+	0.136232i
$263$		−	14.4227i		−	0.889343i	−0.895694	−	0.444671i	$-0.853320\pi$
$263$		−	14.4227i		−	0.889343i	0.895694	−	0.444671i	$-0.146680\pi$
$264$	−0.855961	+	1.09306i	−0.0526808	+	0.0672732i
$265$	−23.5756	+	6.31706i	−1.44824	+	0.388054i
$266$	−6.30677	+	6.30677i	−0.386693	+	0.386693i
$267$	−4.68665	−	1.99555i	−0.286818	−	0.122126i
$268$	−0.749969	−	0.200953i	−0.0458116	−	0.0122752i
$269$	10.3656	−	5.98459i	0.632002	−	0.364887i	−0.149525	−	0.988758i	$-0.547774\pi$
$269$	10.3656	−	5.98459i	0.632002	−	0.364887i	0.781527	+	0.623871i	$0.214441\pi$
$270$	−12.4229	+	8.96227i	−0.756033	+	0.545427i
$271$	6.16812	+	23.0197i	0.374687	+	1.39835i	0.853802	+	0.520598i	$0.174291\pi$
$271$	6.16812	+	23.0197i	0.374687	+	1.39835i	−0.479115	+	0.877752i	$0.659042\pi$
$272$	−4.02058	−	6.96385i	−0.243784	−	0.422246i
$273$	−11.8805	+	2.70309i	−0.719041	+	0.163598i
$274$	−5.81141	+	10.0657i	−0.351080	+	0.608089i
$275$	2.85752	+	0.765671i	0.172315	+	0.0461717i
$276$	−11.9938	−	1.69929i	−0.721940	−	0.102285i
$277$	−8.17883	−	4.72205i	−0.491419	−	0.283721i	0.233744	−	0.972298i	$-0.424902\pi$
$277$	−8.17883	−	4.72205i	−0.491419	−	0.283721i	−0.725163	+	0.688577i	$0.758235\pi$
$278$	−16.1422	+	16.1422i	−0.968147	+	0.968147i
$279$	−3.46468	−	6.28353i	−0.207425	−	0.376185i
$280$	5.55565	+	1.48863i	0.332014	+	0.0889628i
$281$	5.04768	−	18.8382i	0.301119	−	1.12379i	−0.635115	−	0.772417i	$-0.719047\pi$
$281$	5.04768	−	18.8382i	0.301119	−	1.12379i	0.936235	−	0.351376i	$-0.114286\pi$
$282$	−1.29511	+	9.14109i	−0.0771230	+	0.544344i
$283$	17.9472	−	10.3618i	1.06685	−	0.615946i	0.139530	−	0.990218i	$-0.455441\pi$
$283$	17.9472	−	10.3618i	1.06685	−	0.615946i	0.927319	+	0.374272i	$0.122107\pi$
$284$	0.689443	−	2.57304i	0.0409109	−	0.152682i
$285$	18.3781	+	14.3917i	1.08863	+	0.852490i
$286$	1.69390	+	2.34158i	0.100162	+	0.138461i
$287$			10.1084i			0.596682i
$288$	2.56804	+	1.55086i	0.151323	+	0.0913852i
$289$	−23.8302	+	41.2751i	−1.40178	+	2.42795i
$290$	−11.6104	+	20.1097i	−0.681783	+	1.18088i
$291$	5.85465	+	2.49288i	0.343206	+	0.146135i
$292$	−5.68293	−	5.68293i	−0.332568	−	0.332568i
$293$	13.6517	+	13.6517i	0.797542	+	0.797542i	0.982707	−	0.185165i	$-0.0592820\pi$
$293$	13.6517	+	13.6517i	0.797542	+	0.797542i	−0.185165	+	0.982707i	$0.559282\pi$
$294$	4.42123	−	3.32389i	0.257851	−	0.193853i
$295$	13.0123	−	22.5380i	0.757608	−	1.31222i
$296$	4.05028	−	7.01530i	0.235418	−	0.407756i
$297$	−3.89332	+	1.47955i	−0.225914	+	0.0858522i
$298$		−	7.78247i		−	0.450826i
$299$	−10.3039	+	23.0151i	−0.595888	+	1.33100i
$300$	0.896749	−	6.32937i	0.0517738	−	0.365426i
$301$	1.17849	−	4.39818i	0.0679269	−	0.253507i
$302$	6.88304	−	3.97393i	0.396075	−	0.228674i
$303$	18.6058	+	14.5700i	1.06888	+	0.837023i
$304$	1.18319	−	4.41574i	0.0678608	−	0.253260i
$305$	14.0646	+	3.76859i	0.805335	+	0.215789i
$306$	0.474922	−	24.1188i	0.0271495	−	1.37878i
$307$	−15.5762	+	15.5762i	−0.888978	+	0.888978i	−0.994425	−	0.105447i	$-0.966373\pi$
$307$	−15.5762	+	15.5762i	−0.888978	+	0.888978i	0.105447	+	0.994425i	$0.466373\pi$
$308$	1.35433	+	0.781921i	0.0771700	+	0.0445541i
$309$	−8.71685	−	21.6446i	−0.495884	−	1.23132i
$310$	6.81082	+	1.82495i	0.386828	+	0.103650i
$311$	4.85889	−	8.41584i	0.275522	−	0.477218i	−0.694745	−	0.719257i	$-0.744483\pi$
$311$	4.85889	−	8.41584i	0.275522	−	0.477218i	0.970267	+	0.242038i	$0.0778159\pi$
$312$	4.58082	−	4.24454i	0.259338	−	0.240300i
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	0.933202	−	0.359353i	$-0.117003\pi$
$313$	2.74916	+	4.76168i	0.155392	+	0.269146i	−0.777810	+	0.628500i	$0.783669\pi$
$314$	1.01986	+	3.80616i	0.0575539	+	0.214794i
$315$	11.9585	+	12.4389i	0.673784	+	0.700852i
$316$	0.960416	−	0.554497i	0.0540276	−	0.0311929i
$317$	1.01082	+	0.270848i	0.0567731	+	0.0152123i	0.287094	−	0.957902i	$-0.407311\pi$
$317$	1.01082	+	0.270848i	0.0567731	+	0.0152123i	−0.230321	+	0.973115i	$0.573978\pi$
$318$	1.73171	+	14.2351i	0.0971093	+	0.798266i
$319$	−4.46439	+	4.46439i	−0.249958	+	0.249958i
$320$	−2.84756	+	0.763001i	−0.159183	+	0.0426530i
$321$	11.9933	+	29.7801i	0.669398	+	1.66216i
$322$			13.6450i			0.760405i
$323$	−35.5077	+	9.51426i	−1.97570	+	0.529388i
$324$	4.18968	+	7.96534i	0.232760	+	0.442519i
$325$	−12.1456	−	5.43757i	−0.673715	−	0.301622i
$326$	17.8678	−	10.3160i	0.989609	−	0.571351i
$327$	−1.25145	−	10.2872i	−0.0692051	−	0.568886i
$328$	−2.59055	−	4.48696i	−0.143039	−	0.247751i
$329$	10.3996			0.573346
$330$	1.60339	−	3.76565i	0.0882639	−	0.207292i
$331$	11.9246	−	3.19520i	0.655438	−	0.175624i	0.0842515	−	0.996445i	$-0.473150\pi$
$331$	11.9246	−	3.19520i	0.655438	−	0.175624i	0.571186	+	0.820821i	$0.306483\pi$
$332$	0.614312	−	2.29264i	0.0337147	−	0.125825i
$333$	21.2810	−	11.7342i	1.16619	−	0.643028i
$334$	2.82165	+	4.88724i	0.154394	+	0.267418i
$335$	2.28891			0.125056
$336$	1.32386	−	3.10916i	0.0722226	−	0.169618i
$337$	−18.3428	−	10.5902i	−0.999195	−	0.576886i	−0.0911852	−	0.995834i	$-0.529066\pi$
$337$	−18.3428	−	10.5902i	−0.999195	−	0.576886i	−0.908010	+	0.418948i	$0.862399\pi$
$338$	−5.85409	−	11.6073i	−0.318420	−	0.631354i
$339$	−6.38504	+	8.15368i	−0.346788	+	0.442847i
$340$	16.7623	+	16.7623i	0.909062	+	0.909062i
$341$	1.66031	+	0.958578i	0.0899106	+	0.0519099i
$342$	9.88668	−	9.50484i	0.534610	−	0.513963i
$343$	−14.0628	−	14.0628i	−0.759319	−	0.759319i
$344$	0.604036	+	2.25429i	0.0325674	+	0.121543i
$345$	35.4495	−	4.31244i	1.90854	−	0.232174i
$346$	−4.25316	−	15.8730i	−0.228651	−	0.853338i
$347$		−	2.51714i		−	0.135127i	−0.997715	−	0.0675636i	$-0.978477\pi$
$347$		−	2.51714i		−	0.135127i	0.997715	−	0.0675636i	$-0.0215226\pi$
$348$	10.7414	+	8.41143i	0.575798	+	0.450900i
$349$	−12.5807	+	12.5807i	−0.673429	+	0.673429i	−0.958505	−	0.285076i	$-0.907981\pi$
$349$	−12.5807	+	12.5807i	−0.673429	+	0.673429i	0.285076	+	0.958505i	$0.407981\pi$
$350$	−7.20075			−0.384896
$351$	18.3464	−	3.79597i	0.979259	−	0.202614i
$352$	−0.801550			−0.0427228
$353$	−2.20712	+	2.20712i	−0.117473	+	0.117473i	−0.763400	−	0.645927i	$-0.776471\pi$
$353$	−2.20712	+	2.20712i	−0.117473	+	0.117473i	0.645927	+	0.763400i	$0.276471\pi$
$354$	−12.0384	−	9.42714i	−0.639836	−	0.501047i
$355$			7.85291i			0.416789i
$356$	−0.761164	−	2.84070i	−0.0403416	−	0.150557i
$357$	−26.9744	+	3.28145i	−1.42764	+	0.173673i
$358$	1.56774	+	5.85087i	0.0828574	+	0.309228i
$359$	−14.3618	−	14.3618i	−0.757986	−	0.757986i	0.217970	−	0.975956i	$-0.430057\pi$
$359$	−14.3618	−	14.3618i	−0.757986	−	0.757986i	−0.975956	+	0.217970i	$0.930057\pi$
$360$	−8.49595	−	2.45674i	−0.447776	−	0.129482i
$361$	−1.64433	−	0.949354i	−0.0865436	−	0.0499660i
$362$	8.66111	+	8.66111i	0.455218	+	0.455218i
$363$	−11.0606	+	14.1244i	−0.580531	+	0.741337i
$364$	−5.45771	−	4.43822i	−0.286062	−	0.232626i
$365$	20.5186	+	11.8464i	1.07399	+	0.620069i
$366$	3.35146	−	7.87108i	0.175184	−	0.411428i
$367$	23.2205			1.21210			0.606049	−	0.795427i	$-0.292753\pi$
$367$	23.2205			1.21210			0.606049	+	0.795427i	$0.292753\pi$
$368$	−3.49688	−	6.05678i	−0.182288	−	0.315731i
$369$	0.306002	−	15.5403i	0.0159298	−	0.808994i
$370$	−6.18074	+	23.0668i	−0.321321	+	1.19919i
$371$	15.6026	−	4.18070i	0.810045	−	0.217051i
$372$	1.62296	−	3.81160i	0.0841464	−	0.197622i
$373$	25.3140			1.31071			0.655355	−	0.755321i	$-0.272519\pi$
$373$	25.3140			1.31071			0.655355	+	0.755321i	$0.272519\pi$
$374$	3.22270	+	5.58188i	0.166642	+	0.288632i
$375$	−0.807297	−	6.63621i	−0.0416886	−	0.342692i
$376$	−4.61619	+	2.66516i	−0.238062	+	0.137445i
$377$	23.0104	−	16.6457i	1.18510	−	0.857298i
$378$	8.22159	−	5.93132i	0.422873	−	0.305074i
$379$	−22.2862	+	5.97156i	−1.14476	+	0.306738i	−0.780865	−	0.624700i	$-0.785221\pi$
$379$	−22.2862	+	5.97156i	−1.14476	+	0.306738i	−0.363898	+	0.931439i	$0.618554\pi$
$380$			13.4769i			0.691348i
$381$	−1.44807	−	3.59567i	−0.0741870	−	0.184212i
$382$	0.406374	−	0.108888i	0.0207919	−	0.00557117i
$383$	16.8662	−	16.8662i	0.861821	−	0.861821i	−0.129729	−	0.991550i	$-0.541411\pi$
$383$	16.8662	−	16.8662i	0.861821	−	0.861821i	0.991550	+	0.129729i	$0.0414106\pi$
$384$	0.209163	+	1.71938i	0.0106738	+	0.0877415i
$385$	−4.45313	−	1.19321i	−0.226953	−	0.0608118i
$386$	−11.7687	+	6.79464i	−0.599009	+	0.345838i
$387$	−1.94490	+	6.72589i	−0.0988648	+	0.341896i
$388$	0.950861	+	3.54866i	0.0482726	+	0.180156i
$389$	12.4984	+	21.6479i	0.633694	+	1.09759i	0.986790	+	0.162004i	$0.0517957\pi$
$389$	12.4984	+	21.6479i	0.633694	+	1.09759i	−0.353096	+	0.935587i	$0.614871\pi$
$390$	−9.80555	+	15.5817i	−0.496523	+	0.789012i
$391$	−28.1190	+	48.7035i	−1.42204	+	2.46304i
$392$	3.08469	+	0.826542i	0.155801	+	0.0417467i
$393$	−5.51272	−	13.6885i	−0.278080	−	0.690492i
$394$	0.801240	+	0.462596i	0.0403659	+	0.0233053i
$395$	−2.31176	+	2.31176i	−0.116317	+	0.116317i
$396$	−2.05842	−	1.24309i	−0.103439	−	0.0624677i
$397$	20.3908	+	5.46370i	1.02338	+	0.274215i	0.731212	−	0.682150i	$-0.238955\pi$
$397$	20.3908	+	5.46370i	1.02338	+	0.274215i	0.292173	+	0.956366i	$0.405622\pi$
$398$	−3.31954	+	12.3887i	−0.166393	+	0.620989i
$399$	−12.1628	−	9.52456i	−0.608904	−	0.476825i
$400$	3.19629	−	1.84538i	0.159814	−	0.0922689i
$401$	4.57548	−	17.0759i	0.228488	−	0.852730i	−0.752488	−	0.658606i	$-0.771147\pi$
$401$	4.57548	−	17.0759i	0.228488	−	0.852730i	0.980977	−	0.194125i	$-0.0621867\pi$
$402$	0.188649	−	1.33151i	0.00940896	−	0.0664096i
$403$	−6.69075	−	5.44093i	−0.333290	−	0.271032i
$404$			13.6438i			0.678804i
$405$	−18.0079	−	19.4850i	−0.894820	−	0.968219i
$406$	7.68385	−	13.3088i	0.381343	−	0.660506i
$407$	−3.24651	+	5.62312i	−0.160923	+	0.278727i
$408$	11.1325	−	8.36947i	0.551142	−	0.414350i
$409$	−14.7908	−	14.7908i	−0.731359	−	0.731359i	0.239530	−	0.970889i	$-0.423007\pi$
$409$	−14.7908	−	14.7908i	−0.731359	−	0.731359i	−0.970889	+	0.239530i	$0.923007\pi$
$410$	10.8003	+	10.8003i	0.533388	+	0.533388i
$411$	−18.5222	−	7.88664i	−0.913632	−	0.389019i
$412$	6.73592	−	11.6669i	0.331855	−	0.574789i
$413$	−8.61171	+	14.9159i	−0.423754	+	0.733964i
$414$	0.413061	−	20.9772i	0.0203008	−	1.03097i
$415$			6.99715i			0.343477i
$416$	3.55999	+	0.571370i	0.174543	+	0.0280137i
$417$	−31.1309	−	24.3782i	−1.52449	−	1.19381i
$418$	−0.948390	+	3.53944i	−0.0463872	+	0.173120i
$419$	−15.5017	+	8.94990i	−0.757306	+	0.437231i	−0.828328	−	0.560244i	$-0.810707\pi$
$419$	−15.5017	+	8.94990i	−0.757306	+	0.437231i	0.0710214	+	0.997475i	$0.477374\pi$
$420$	−1.39748	+	9.86361i	−0.0681902	+	0.481295i
$421$	−0.247286	+	0.922884i	−0.0120520	+	0.0449786i	−0.971690	−	0.236260i	$-0.924078\pi$
$421$	−0.247286	+	0.922884i	−0.0120520	+	0.0449786i	0.959638	+	0.281238i	$0.0907451\pi$
$422$	6.61278	+	1.77189i	0.321905	+	0.0862542i
$423$	−15.9878	−	0.314815i	−0.777356	−	0.0153069i
$424$	−5.85430	+	5.85430i	−0.284310	+	0.284310i
$425$	−25.7019	−	14.8390i	−1.24672	−	0.719797i
$426$	4.56822	+	0.647228i	0.221331	+	0.0313583i
$427$	−9.30808	−	2.49409i	−0.450450	−	0.120698i
$428$	−9.26775	+	16.0522i	−0.447974	+	0.775913i
$429$	−3.67175	+	3.40221i	−0.177274	+	0.164260i
$430$	−3.44006	−	5.95835i	−0.165894	−	0.287337i
$431$	10.1624	+	37.9267i	0.489507	+	1.82687i	0.558845	+	0.829272i	$0.311245\pi$
$431$	10.1624	+	37.9267i	0.489507	+	1.82687i	−0.0693375	+	0.997593i	$0.522089\pi$
$432$	−2.12937	+	4.73981i	−0.102449	+	0.228044i
$433$	9.53436	−	5.50467i	0.458192	−	0.264537i	−0.253092	−	0.967442i	$-0.581447\pi$
$433$	9.53436	−	5.50467i	0.458192	−	0.264537i	0.711284	+	0.702905i	$0.248114\pi$
$434$	−4.50747	−	1.20777i	−0.216365	−	0.0579749i
$435$	−37.0046	−	15.7564i	−1.77423	−	0.755459i
$436$	4.23071	−	4.23071i	0.202614	−	0.202614i
$437$	−30.8826	+	8.27498i	−1.47732	+	0.395846i
$438$	8.58244	−	10.9598i	0.410085	−	0.523677i
$439$			4.26304i			0.203464i	0.994812	+	0.101732i	$0.0324384\pi$
$439$			4.26304i			0.203464i	−0.994812	+	0.101732i	$0.967562\pi$
$440$	2.28246	−	0.611584i	0.108812	−	0.0291561i
$441$	6.63978	+	6.90652i	0.316180	+	0.328882i
$442$	−10.3343	−	27.0885i	−0.491553	−	1.28847i
$443$	24.9846	−	14.4249i	1.18705	−	0.685346i	0.229419	−	0.973328i	$-0.426317\pi$
$443$	24.9846	−	14.4249i	1.18705	−	0.685346i	0.957636	+	0.287981i	$0.0929841\pi$
$444$	12.9091	+	5.49662i	0.612639	+	0.260858i
$445$	4.33492	+	7.50829i	0.205495	+	0.355927i
$446$	−17.6918			−0.837733
$447$	13.3810	−	1.62780i	0.632899	−	0.0769923i
$448$	1.88454	−	0.504962i	0.0890363	−	0.0238572i
$449$	−6.56424	+	24.4981i	−0.309786	+	1.15614i	0.618961	+	0.785421i	$0.287554\pi$
$449$	−6.56424	+	24.4981i	−0.309786	+	1.15614i	−0.928747	+	0.370714i	$0.879113\pi$
$450$	11.0701	+	0.217981i	0.521851	+	0.0102757i
$451$	2.07645	+	3.59652i	0.0977764	+	0.169354i
$452$	−5.97917			−0.281236
$453$	8.27234	+	11.0033i	0.388669	+	0.516982i
$454$	16.7719	+	9.68326i	0.787144	+	0.454458i
$455$	18.9275	+	8.47384i	0.887335	+	0.397260i
$456$	7.83979	+	1.11075i	0.367132	+	0.0520155i
$457$	−20.3409	−	20.3409i	−0.951506	−	0.951506i	0.0473712	−	0.998877i	$-0.484916\pi$
$457$	−20.3409	−	20.3409i	−0.951506	−	0.951506i	−0.998877	+	0.0473712i	$0.984916\pi$
$458$	22.4916	+	12.9855i	1.05096	+	0.606773i
$459$	41.5686	−	4.22819i	1.94026	−	0.197355i
$460$	14.5789	+	14.5789i	0.679745	+	0.679745i
$461$	−9.57678	−	35.7410i	−0.446035	−	1.66462i	−0.713190	−	0.700971i	$-0.752750\pi$
$461$	−9.57678	−	35.7410i	−0.446035	−	1.66462i	0.267155	−	0.963654i	$-0.413917\pi$
$462$	−1.06114	+	2.49215i	−0.0493688	+	0.115945i
$463$	0.644720	+	2.40613i	0.0299627	+	0.111822i	0.979288	−	0.202474i	$-0.0648981\pi$
$463$	0.644720	+	2.40613i	0.0299627	+	0.111822i	−0.949325	+	0.314296i	$0.898231\pi$
$464$			7.87674i			0.365669i
$465$	−1.71321	+	12.0921i	−0.0794483	+	0.560756i
$466$	−8.42093	+	8.42093i	−0.390092	+	0.390092i
$467$	31.2741			1.44719			0.723596	−	0.690223i	$-0.242488\pi$
$467$	31.2741			1.44719			0.723596	+	0.690223i	$0.242488\pi$
$468$	8.25609	+	6.98834i	0.381638	+	0.323036i
$469$	−1.51482			−0.0699480
$470$	11.1113	−	11.1113i	0.512528	−	0.512528i
$471$	−6.33090	+	2.54962i	−0.291713	+	0.117480i
$472$		−	8.82789i		−	0.406337i
$473$	−0.484165	−	1.80693i	−0.0222619	−	0.0830827i
$474$	1.15427	+	1.53534i	0.0530174	+	0.0705203i
$475$	−4.36688	−	16.2974i	−0.200366	−	0.747777i
$476$	−11.0934	−	11.0934i	−0.508467	−	0.508467i
$477$	−24.1133	+	5.95491i	−1.10407	+	0.272656i
$478$	−8.03762	−	4.64052i	−0.367632	−	0.212253i
$479$	−3.91612	−	3.91612i	−0.178932	−	0.178932i	0.611958	−	0.790890i	$-0.290382\pi$
$479$	−3.91612	−	3.91612i	−0.178932	−	0.178932i	−0.790890	+	0.611958i	$0.790382\pi$
$480$	−1.90749	−	4.73643i	−0.0870645	−	0.216187i
$481$	18.4273	−	22.6602i	0.840213	−	1.03322i
$482$	8.48048	+	4.89621i	0.386275	+	0.223016i
$483$	−23.4609	+	2.85402i	−1.06751	+	0.129862i
$484$	−10.3575			−0.470796
$485$	−5.41526	−	9.37951i	−0.245894	−	0.425902i
$486$	−12.8191	+	8.86968i	−0.581485	+	0.402337i
$487$	−0.759319	+	2.83382i	−0.0344080	+	0.128412i	−0.980994	−	0.194040i	$-0.937841\pi$
$487$	−0.759319	+	2.83382i	−0.0344080	+	0.128412i	0.946586	+	0.322453i	$0.104507\pi$
$488$	4.77087	−	1.27835i	0.215967	−	0.0578683i
$489$	21.4744	+	28.5638i	0.971105	+	1.29170i
$490$	−9.41450			−0.425304
$491$	−17.8494	−	30.9160i	−0.805531	−	1.39522i	−0.915932	−	0.401334i	$-0.868547\pi$
$491$	−17.8494	−	30.9160i	−0.805531	−	1.39522i	0.110400	−	0.993887i	$-0.464787\pi$
$492$	7.17292	−	5.39263i	0.323380	−	0.243118i
$493$	54.8525	−	31.6691i	2.47043	−	1.42630i
$494$	6.73518	−	15.0440i	0.303030	−	0.676860i
$495$	6.80994	+	1.96920i	0.306084	+	0.0885090i
$496$	2.31031	−	0.619046i	0.103736	−	0.0277960i
$497$		−	5.19714i		−	0.233124i
$498$	4.07040	+	0.576697i	0.182399	+	0.0258424i
$499$	−17.6124	+	4.71922i	−0.788438	+	0.211261i	−0.630502	−	0.776188i	$-0.717151\pi$
$499$	−17.6124	+	4.71922i	−0.788438	+	0.211261i	−0.157936	+	0.987449i	$0.550484\pi$
$500$	2.72919	−	2.72919i	0.122053	−	0.122053i
$501$	−7.81281	+	5.87370i	−0.349051	+	0.262418i
$502$	13.6281	+	3.65165i	0.608254	+	0.162981i
$503$	−20.2816	+	11.7096i	−0.904310	+	0.522104i	−0.878596	−	0.477565i	$-0.841519\pi$
$503$	−20.2816	+	11.7096i	−0.904310	+	0.522104i	−0.0257142	+	0.999669i	$0.508186\pi$
$504$	5.62271	+	1.62590i	0.250455	+	0.0724231i
$505$	−10.4102	−	38.8515i	−0.463249	−	1.72887i
$506$	2.80293	+	4.85481i	0.124605	+	0.215823i
$507$	18.7329	−	12.4932i	0.831956	−	0.554842i
$508$	1.11899	−	1.93815i	0.0496473	−	0.0859917i
$509$	3.19606	+	0.856383i	0.141663	+	0.0379585i	0.328954	−	0.944346i	$-0.393304\pi$
$509$	3.19606	+	0.856383i	0.141663	+	0.0379585i	−0.187291	+	0.982305i	$0.559971\pi$
$510$	−25.3146	+	32.3267i	−1.12095	+	1.43145i
$511$	−13.5794	−	7.84007i	−0.600717	−	0.346824i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	18.4103	+	15.0109i	0.812835	+	0.662745i
$514$	4.94531	+	1.32509i	0.218128	+	0.0584473i
$515$	−10.2790	+	38.3618i	−0.452948	+	1.69042i
$516$	−3.74963	+	1.51008i	−0.165068	+	0.0664775i
$517$	3.70011	−	2.13626i	0.162731	−	0.0939525i
$518$	4.09048	−	15.2659i	0.179725	−	0.670744i
$519$	26.4020	−	10.6328i	1.15892	−	0.466729i
$520$	−10.5732	+	1.08927i	−0.463667	+	0.0477676i
$521$		−	7.00178i		−	0.306754i	−0.988168	−	0.153377i	$-0.950985\pi$
$521$		−	7.00178i		−	0.306754i	0.988168	−	0.153377i	$-0.0490148\pi$
$522$	−12.2157	+	20.2278i	−0.534667	+	0.885347i
$523$	−21.4957	+	37.2316i	−0.939940	+	1.62802i	−0.174360	+	0.984682i	$0.555786\pi$
$523$	−21.4957	+	37.2316i	−0.939940	+	1.62802i	−0.765580	+	0.643341i	$0.777548\pi$
$524$	4.25993	−	7.37842i	0.186096	−	0.322328i
$525$	−1.50613	−	12.3808i	−0.0657328	−	0.540342i
$526$	10.1984	+	10.1984i	0.444671	+	0.444671i
$527$	−13.5997	−	13.5997i	−0.592414	−	0.592414i
$528$	−0.167654	−	1.37817i	−0.00729622	−	0.0599770i
$529$	−12.9564	+	22.4411i	−0.563320	+	0.975698i
$530$	12.2036	−	21.1373i	0.530092	−	0.918146i
$531$	13.6908	−	22.6704i	0.594130	−	0.983811i
$532$		−	8.91912i		−	0.386693i
$533$	−6.65861	−	17.4537i	−0.288417	−	0.756003i
$534$	4.72503	−	1.90289i	0.204472	−	0.0823463i
$535$	14.1426	−	52.7809i	0.611438	−	2.28192i
$536$	0.672403	−	0.388212i	0.0290434	−	0.0167682i
$537$	−9.73193	+	3.91931i	−0.419964	+	0.169131i
$538$	−3.09785	+	11.5613i	−0.133558	+	0.498445i
$539$	−2.47254	−	0.662515i	−0.106500	−	0.0285365i
$540$	2.44702	−	15.1216i	0.105303	−	0.650730i
$541$	8.12664	−	8.12664i	0.349391	−	0.349391i	−0.510491	−	0.859883i	$-0.670536\pi$
$541$	8.12664	−	8.12664i	0.349391	−	0.349391i	0.859883	+	0.510491i	$0.170536\pi$
$542$	−20.6389	−	11.9159i	−0.886518	−	0.511832i
$543$	−13.0801	+	16.7033i	−0.561322	+	0.716806i
$544$	7.76717	+	2.08121i	0.333015	+	0.0892310i
$545$	−8.81916	+	15.2752i	−0.377771	+	0.654319i
$546$	6.48941	−	10.3122i	0.277721	−	0.441320i
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	0.905969	−	0.423345i	$-0.139144\pi$
$547$	2.01972	+	3.49826i	0.0863570	+	0.149575i	−0.819612	+	0.572919i	$0.805811\pi$
$548$	−3.00821	−	11.2268i	−0.128504	−	0.479585i
$549$	14.2343	+	4.11609i	0.607507	+	0.175670i
$550$	−2.56199	+	1.47916i	−0.109243	+	0.0630717i
$551$	34.7816	+	9.31971i	1.48175	+	0.397033i
$552$	9.68245	−	7.27930i	0.412113	−	0.309828i
$553$	1.52995	−	1.52995i	0.0650599	−	0.0650599i
$554$	9.12230	−	2.44431i	0.387570	−	0.103849i
$555$	−40.9533	−	5.80229i	−1.73837	−	0.246294i
$556$		−	22.8286i		−	0.968147i
$557$	22.2275	−	5.95584i	0.941810	−	0.252357i	0.244926	−	0.969542i	$-0.421236\pi$
$557$	22.2275	−	5.95584i	0.941810	−	0.252357i	0.696883	+	0.717185i	$0.254570\pi$
$558$	6.89303	+	1.99323i	0.291805	+	0.0843801i
$559$	0.862329	+	8.37039i	0.0364726	+	0.354030i
$560$	−4.98106	+	2.87582i	−0.210488	+	0.121525i
$561$	−8.92328	+	6.70855i	−0.376741	+	0.283235i
$562$	9.75137	+	16.8899i	0.411337	+	0.712456i
$563$	4.88910			0.206051			0.103025	−	0.994679i	$-0.467148\pi$
$563$	4.88910			0.206051			0.103025	+	0.994679i	$0.467148\pi$
$564$	−5.54794	−	7.37951i	−0.233610	−	0.310733i
$565$	17.0260	−	4.56211i	0.716290	−	0.191929i
$566$	−5.36367	+	20.0175i	−0.225452	+	0.841397i
$567$	11.9178	+	12.8954i	0.500501	+	0.541556i
$568$	1.33190	+	2.30692i	0.0558853	+	0.0967963i
$569$	−21.3664			−0.895725			−0.447863	−	0.894102i	$-0.647815\pi$
$569$	−21.3664			−0.895725			−0.447863	+	0.894102i	$0.647815\pi$
$570$	−23.1718	+	2.81885i	−0.970559	+	0.118069i
$571$	−21.5820	−	12.4604i	−0.903179	−	0.521451i	−0.0249486	−	0.999689i	$-0.507942\pi$
$571$	−21.5820	−	12.4604i	−0.903179	−	0.521451i	−0.878230	+	0.478238i	$0.841276\pi$
$572$	−2.85351	−	0.457981i	−0.119311	−	0.0191492i
$573$	0.272217	+	0.675934i	0.0113720	+	0.0282376i
$574$	−7.14774	−	7.14774i	−0.298341	−	0.298341i
$575$	−22.3541	−	12.9061i	−0.932230	−	0.538223i
$576$	−2.91250	+	0.719258i	−0.121354	+	0.0299691i
$577$	−4.11164	−	4.11164i	−0.171170	−	0.171170i	0.616323	−	0.787493i	$-0.288621\pi$
$577$	−4.11164	−	4.11164i	−0.171170	−	0.171170i	−0.787493	+	0.616323i	$0.788621\pi$
$578$	−12.3354	−	46.0364i	−0.513085	−	1.91486i
$579$	−14.1441	−	18.8136i	−0.587809	−	0.781865i
$580$	−6.00996	−	22.4295i	−0.249550	−	0.931333i
$581$		−	4.63079i		−	0.192117i
$582$	−5.90259	+	2.37713i	−0.244670	+	0.0985353i
$583$	4.69252	−	4.69252i	0.194344	−	0.194344i
$584$	8.03688			0.332568
$585$	−28.8418	−	13.6003i	−1.19246	−	0.562303i
$586$	−19.3065			−0.797542
$587$	−12.7350	+	12.7350i	−0.525630	+	0.525630i	−0.919266	−	0.393636i	$-0.871217\pi$
$587$	−12.7350	+	12.7350i	−0.525630	+	0.525630i	0.393636	+	0.919266i	$0.371217\pi$
$588$	−0.775932	+	5.47663i	−0.0319989	+	0.225852i
$589$		−	10.9342i		−	0.450535i
$590$	6.73569	+	25.1379i	0.277304	+	1.03491i
$591$	−0.627787	+	1.47439i	−0.0258237	+	0.0606483i
$592$	2.09658	+	7.82455i	0.0861690	+	0.321587i
$593$	−8.08152	−	8.08152i	−0.331868	−	0.331868i	0.521427	−	0.853296i	$-0.325400\pi$
$593$	−8.08152	−	8.08152i	−0.331868	−	0.331868i	−0.853296	+	0.521427i	$0.825400\pi$
$594$	1.70680	−	3.79920i	0.0700307	−	0.155883i
$595$	40.0535	+	23.1249i	1.64203	+	0.948029i
$596$	5.50303	+	5.50303i	0.225413	+	0.225413i
$597$	−21.9951	−	3.11628i	−0.900201	−	0.127541i
$598$	−8.98821	−	23.5601i	−0.367555	−	0.963443i
$599$	−0.103217	−	0.0595921i	−0.00421731	−	0.00243487i	0.497890	−	0.867240i	$-0.334108\pi$
$599$	−0.103217	−	0.0595921i	−0.00421731	−	0.00243487i	−0.502107	+	0.864805i	$0.667442\pi$
$600$	3.84144	+	5.10964i	0.156826	+	0.208600i
$601$	27.0871			1.10490			0.552452	−	0.833545i	$-0.313692\pi$
$601$	27.0871			1.10490			0.552452	+	0.833545i	$0.313692\pi$
$602$	2.27666	+	3.94330i	0.0927899	+	0.160717i
$603$	2.32882	+	0.0458567i	0.0948370	+	0.00186743i
$604$	−2.05706	+	7.67704i	−0.0837004	+	0.312374i
$605$	29.4936	−	7.90279i	1.19909	−	0.321294i
$606$	−23.4588	+	2.85377i	−0.952949	+	0.115927i
$607$	−18.4983			−0.750823			−0.375412	−	0.926858i	$-0.622499\pi$
$607$	−18.4983			−0.750823			−0.375412	+	0.926858i	$0.622499\pi$
$608$	2.28576	+	3.95904i	0.0926996	+	0.160560i
$609$	24.4900	+	10.4277i	0.992386	+	0.422552i
$610$	−12.6100	+	7.28036i	−0.510562	+	0.294773i
$611$	−17.9564	+	6.85039i	−0.726437	+	0.277137i
$612$	16.7188	+	17.3904i	0.675816	+	0.702965i
$613$	−21.0392	+	5.63743i	−0.849764	+	0.227694i	−0.657317	−	0.753614i	$-0.728309\pi$
$613$	−21.0392	+	5.63743i	−0.849764	+	0.227694i	−0.192447	+	0.981307i	$0.561642\pi$
$614$		−	22.0280i		−	0.888978i
$615$	−16.3107	+	20.8288i	−0.657712	+	0.839897i
$616$	−1.51056	+	0.404752i	−0.0608620	+	0.0163079i
$617$	−1.85763	+	1.85763i	−0.0747856	+	0.0747856i	−0.743510	−	0.668725i	$-0.766841\pi$
$617$	−1.85763	+	1.85763i	−0.0747856	+	0.0747856i	0.668725	+	0.743510i	$0.266841\pi$
$618$	21.4688	+	9.14128i	0.863600	+	0.367716i
$619$	13.7714	+	3.69004i	0.553520	+	0.148315i	0.524728	−	0.851270i	$-0.324167\pi$
$619$	13.7714	+	3.69004i	0.553520	+	0.148315i	0.0287923	+	0.999585i	$0.490834\pi$
$620$	−6.10641	+	3.52554i	−0.245239	+	0.141589i
$621$	36.1541	−	3.67744i	1.45081	−	0.147571i
$622$	2.51514	+	9.38665i	0.100848	+	0.376370i
$623$	−2.86889	−	4.96907i	−0.114940	−	0.199081i
$624$	−0.237782	+	6.24047i	−0.00951889	+	0.249819i
$625$	−14.9160	+	25.8354i	−0.596642	+	1.03341i
$626$	−5.31097	−	1.42307i	−0.212269	−	0.0568773i
$627$	−6.28399	−	0.890320i	−0.250958	−	0.0355559i
$628$	−3.41251	−	1.97021i	−0.136174	−	0.0786201i
$629$	46.0595	−	46.0595i	1.83651	−	1.83651i
$630$	−17.2516	−	0.339699i	−0.687318	−	0.0135339i
$631$	34.0030	+	9.11109i	1.35364	+	0.362707i	0.861477	−	0.507797i	$-0.169540\pi$
$631$	34.0030	+	9.11109i	1.35364	+	0.362707i	0.492163	+	0.870503i	$0.336206\pi$
$632$	−0.287029	+	1.07121i	−0.0114174	+	0.0426103i
$633$	−1.66340	+	11.7405i	−0.0661141	+	0.466642i
$634$	−0.906274	+	0.523237i	−0.0359927	+	0.0207804i
$635$	−1.70759	+	6.37280i	−0.0677635	+	0.252897i
$636$	−11.2902	−	8.84124i	−0.447687	−	0.350578i
$637$	10.5092	+	4.70498i	0.416391	+	0.186418i
$638$		−	6.31360i		−	0.249958i
$639$	−0.157328	+	7.98986i	−0.00622379	+	0.316074i
$640$	1.47400	−	2.55305i	0.0582651	−	0.100918i
$641$	2.90958	−	5.03954i	0.114922	−	0.199050i	−0.802827	−	0.596212i	$-0.796672\pi$
$641$	2.90958	−	5.03954i	0.114922	−	0.199050i	0.917748	+	0.397162i	$0.130005\pi$
$642$	−29.5382	−	12.5772i	−1.16578	−	0.496383i
$643$	−4.20333	−	4.20333i	−0.165763	−	0.165763i	0.619351	−	0.785114i	$-0.287396\pi$
$643$	−4.20333	−	4.20333i	−0.165763	−	0.165763i	−0.785114	+	0.619351i	$0.787396\pi$
$644$	−9.64846	−	9.64846i	−0.380203	−	0.380203i
$645$	9.52511	−	7.16101i	0.375051	−	0.281964i
$646$	18.3801	−	31.8353i	0.723157	−	1.25254i
$647$	2.47586	−	4.28832i	0.0973362	−	0.168591i	−0.813245	−	0.581921i	$-0.802301\pi$
$647$	2.47586	−	4.28832i	0.0973362	−	0.168591i	0.910581	+	0.413330i	$0.135634\pi$
$648$	−8.59489	−	2.66979i	−0.337639	−	0.104879i
$649$			7.07600i			0.277757i
$650$	12.4332	−	4.74327i	0.487668	−	0.186046i
$651$	1.13382	−	8.00265i	0.0444379	−	0.313649i
$652$	−5.33996	+	19.9290i	−0.209129	+	0.780480i
$653$	−17.7446	+	10.2448i	−0.694400	+	0.400912i	−0.805258	−	0.592924i	$-0.797973\pi$
$653$	−17.7446	+	10.2448i	−0.694400	+	0.400912i	0.110859	+	0.993836i	$0.464640\pi$
$654$	8.15908	+	6.38927i	0.319045	+	0.249840i
$655$	−6.50067	+	24.2608i	−0.254002	+	0.947949i
$656$	5.00455	+	1.34097i	0.195395	+	0.0523559i
$657$	20.6390	+	12.4641i	0.805206	+	0.486269i
$658$	−7.35360	+	7.35360i	−0.286673	+	0.286673i
$659$	−4.16393	−	2.40405i	−0.162204	−	0.0936484i	0.416701	−	0.909044i	$-0.363186\pi$
$659$	−4.16393	−	2.40405i	−0.162204	−	0.0936484i	−0.578905	+	0.815395i	$0.696520\pi$
$660$	1.52895	+	3.79649i	0.0595142	+	0.147778i
$661$	39.4745	+	10.5772i	1.53538	+	0.411404i	0.924770	−	0.380527i	$-0.124257\pi$
$661$	39.4745	+	10.5772i	1.53538	+	0.411404i	0.610611	+	0.791931i	$0.290924\pi$
$662$	−6.17265	+	10.6913i	−0.239907	+	0.415531i
$663$	44.4137	−	23.4345i	1.72489	−	0.910119i
$664$	1.18676	+	2.05553i	0.0460552	+	0.0797699i
$665$	6.80530	+	25.3977i	0.263898	+	0.984881i
$666$	−6.75065	+	23.3453i	−0.261583	+	0.904611i
$667$	47.7077	−	27.5440i	1.84725	−	1.06651i
$668$	−5.45101	−	1.46059i	−0.210906	−	0.0565120i
$669$	−3.70047	−	30.4189i	−0.143068	−	1.17606i
$670$	−1.61850	+	1.61850i	−0.0625282	+	0.0625282i
$671$	−3.82410	+	1.02466i	−0.147628	+	0.0395567i
$672$	1.26239	+	3.13462i	0.0486979	+	0.120920i
$673$			26.1416i			1.00768i	0.863796	+	0.503842i	$0.168081\pi$
$673$			26.1416i			1.00768i	−0.863796	+	0.503842i	$0.831919\pi$
$674$	20.4587	−	5.48190i	0.788040	−	0.211155i
$675$	1.94066	+	19.0793i	0.0746962	+	0.734362i
$676$	12.3471	+	4.06814i	0.474887	+	0.156467i
$677$	−34.5645	+	19.9558i	−1.32842	+	0.766964i	−0.985055	−	0.172238i	$-0.944900\pi$
$677$	−34.5645	+	19.9558i	−1.32842	+	0.766964i	−0.343365	+	0.939202i	$0.611567\pi$
$678$	−1.25062	−	10.2804i	−0.0480297	−	0.394818i
$679$	3.58388	+	6.20745i	0.137537	+	0.238220i
$680$	−23.7054			−0.909062
$681$	−13.1411	+	30.8626i	−0.503568	+	1.18266i
$682$	−1.85183	+	0.496197i	−0.0709103	+	0.0190003i
$683$	9.69531	−	36.1834i	0.370981	−	1.38452i	−0.488148	−	0.872761i	$-0.662327\pi$
$683$	9.69531	−	36.1834i	0.370981	−	1.38452i	0.859129	−	0.511759i	$-0.171006\pi$
$684$	−0.270000	+	13.7119i	−0.0103237	+	0.524287i
$685$	17.1321	+	29.6737i	0.654584	+	1.13377i
$686$	19.8878			0.759319
$687$	−17.6226	+	41.3875i	−0.672343	+	1.57903i
$688$	−2.02114	−	1.16691i	−0.0770554	−	0.0444880i
$689$	−24.1862	+	17.4963i	−0.921422	+	0.666556i
$690$	−22.0172	+	28.1160i	−0.838182	+	1.07036i
$691$	32.8832	+	32.8832i	1.25094	+	1.25094i	0.955300	+	0.295637i	$0.0955319\pi$
$691$	32.8832	+	32.8832i	1.25094	+	1.25094i	0.295637	+	0.955300i	$0.404468\pi$
$692$	14.2313	+	8.21647i	0.540994	+	0.312343i
$693$	−4.50689	−	1.30324i	−0.171202	−	0.0495059i
$694$	1.77989	+	1.77989i	0.0675636	+	0.0675636i
$695$	17.4182	+	65.0057i	0.660711	+	2.46581i
$696$	−13.5431	+	1.64752i	−0.513349	+	0.0624491i
$697$	−10.7829	−	40.2424i	−0.408433	−	1.52429i
$698$		−	17.7918i		−	0.673429i
$699$	−16.2401	−	12.7174i	−0.614256	−	0.481016i
$700$	5.09170	−	5.09170i	0.192448	−	0.192448i
$701$	−27.1053			−1.02375			−0.511876	−	0.859059i	$-0.671049\pi$
$701$	−27.1053			−1.02375			−0.511876	+	0.859059i	$0.671049\pi$
$702$	−10.2887	+	15.6570i	−0.388323	+	0.590936i
$703$	37.0318			1.39668
$704$	0.566782	−	0.566782i	0.0213614	−	0.0213614i
$705$	21.4286	+	16.7805i	0.807050	+	0.631990i
$706$		−	3.12134i		−	0.117473i
$707$	6.88960	+	25.7123i	0.259110	+	0.967012i
$708$	15.1785	−	1.84646i	0.570441	−	0.0693944i
$709$	11.7626	+	43.8986i	0.441753	+	1.64865i	0.724369	+	0.689413i	$0.242131\pi$
$709$	11.7626	+	43.8986i	0.441753	+	1.64865i	−0.282615	+	0.959233i	$0.591202\pi$
$710$	−5.55285	−	5.55285i	−0.208395	−	0.208395i
$711$	−2.39839	+	2.30576i	−0.0899466	+	0.0864727i
$712$	2.54690	+	1.47046i	0.0954492	+	0.0551076i
$713$	−11.8283	−	11.8283i	−0.442974	−	0.442974i
$714$	16.7535	−	21.3941i	0.626982	−	0.800655i
$715$	8.47498	−	0.873104i	0.316946	−	0.0326522i
$716$	−5.24575	−	3.02863i	−0.196043	−	0.113185i
$717$	6.29763	−	14.7903i	0.235189	−	0.552354i
$718$	20.3106			0.757986
$719$	10.2199	+	17.7014i	0.381138	+	0.660150i	0.991225	−	0.132184i	$-0.0421990\pi$
$719$	10.2199	+	17.7014i	0.381138	+	0.660150i	−0.610087	+	0.792334i	$0.708866\pi$
$720$	7.74472	−	4.27037i	0.288629	−	0.159147i
$721$	6.80276	−	25.3882i	0.253348	−	0.945508i
$722$	1.83401	−	0.491422i	0.0682548	−	0.0182888i
$723$	−6.64462	+	15.6052i	−0.247116	+	0.580365i
$724$	−12.2487			−0.455218
$725$	14.5356	+	25.1763i	0.539837	+	0.935026i
$726$	−2.16640	−	17.8085i	−0.0804028	−	0.660934i
$727$	−25.7087	+	14.8430i	−0.953485	+	0.550495i	−0.894162	−	0.447744i	$-0.852227\pi$
$727$	−25.7087	+	14.8430i	−0.953485	+	0.550495i	−0.0593229	+	0.998239i	$0.518894\pi$
$728$	6.99748	−	0.720889i	0.259344	−	0.0267179i
$729$	−17.9316	−	20.1856i	−0.664133	−	0.747615i
$730$	−22.8855	+	6.13215i	−0.847030	+	0.226961i
$731$			18.7666i			0.694108i
$732$	3.19585	+	7.93554i	0.118122	+	0.293306i
$733$	1.64769	−	0.441496i	0.0608587	−	0.0163070i	−0.228261	−	0.973600i	$-0.573304\pi$
$733$	1.64769	−	0.441496i	0.0608587	−	0.0163070i	0.289120	+	0.957293i	$0.406637\pi$
$734$	−16.4194	+	16.4194i	−0.606049	+	0.606049i
$735$	−1.96916	−	16.1871i	−0.0726336	−	0.597069i
$736$	6.75546	+	1.81012i	0.249009	+	0.0667219i
$737$	−0.538965	+	0.311172i	−0.0198530	+	0.0114622i
$738$	10.7723	+	11.2050i	0.396532	+	0.412462i
$739$	−12.2243	−	45.6218i	−0.449679	−	1.67822i	−0.703279	−	0.710914i	$-0.748281\pi$
$739$	−12.2243	−	45.6218i	−0.449679	−	1.67822i	0.253600	−	0.967309i	$-0.418385\pi$
$740$	−11.9403	−	20.6812i	−0.438933	−	0.760255i
$741$	27.2749	+	8.43367i	1.00197	+	0.309819i
$742$	−8.07649	+	13.9889i	−0.296497	+	0.513548i
$743$	−31.1963	−	8.35903i	−1.14448	−	0.306663i	−0.363730	−	0.931504i	$-0.618497\pi$
$743$	−31.1963	−	8.35903i	−1.14448	−	0.306663i	−0.780752	+	0.624842i	$0.785164\pi$
$744$	1.54760	+	3.84281i	0.0567379	+	0.140884i
$745$	−19.8690	−	11.4714i	−0.727945	−	0.420279i
$746$	−17.8997	+	17.8997i	−0.655355	+	0.655355i
$747$	−0.140183	+	7.11917i	−0.00512903	+	0.260477i
$748$	−6.22578	−	1.66819i	−0.227637	−	0.0609952i
$749$	−9.35972	+	34.9309i	−0.341997	+	1.27635i
$750$	5.26335	+	4.12166i	0.192190	+	0.150502i
$751$	31.9440	−	18.4429i	1.16565	−	0.672991i	0.213002	−	0.977052i	$-0.431676\pi$
$751$	31.9440	−	18.4429i	1.16565	−	0.672991i	0.952653	+	0.304061i	$0.0983427\pi$
$752$	1.37959	−	5.14869i	0.0503084	−	0.187753i
$753$	−3.42806	+	24.1957i	−0.124925	+	0.881740i
$754$	−4.50053	+	28.0411i	−0.163900	+	1.02120i
$755$		−	23.4303i		−	0.852717i
$756$	−1.61946	+	10.0076i	−0.0588993	+	0.363974i
$757$	−6.73813	+	11.6708i	−0.244902	+	0.424182i	−0.962104	−	0.272683i	$-0.912089\pi$
$757$	−6.73813	+	11.6708i	−0.244902	+	0.424182i	0.717202	+	0.696865i	$0.245422\pi$
$758$	11.5362	−	19.9812i	0.419012	−	0.725751i
$759$	−7.76097	+	5.83473i	−0.281706	+	0.211787i
$760$	−9.52957	−	9.52957i	−0.345674	−	0.345674i
$761$	−28.9718	−	28.9718i	−1.05023	−	1.05023i	−0.998670	−	0.0515555i	$-0.983582\pi$
$761$	−28.9718	−	28.9718i	−1.05023	−	1.05023i	−0.0515555	−	0.998670i	$-0.516418\pi$
$762$	3.56647	+	1.51858i	0.129199	+	0.0550124i
$763$	5.83661	−	10.1093i	0.211299	−	0.365981i
$764$	−0.210355	+	0.364345i	−0.00761037	+	0.0131815i
$765$	−60.8765	−	36.7638i	−2.20100	−	1.32920i
$766$			23.8524i			0.861821i
$767$	5.04399	−	31.4272i	0.182128	−	1.13477i
$768$	−1.36368	−	1.06788i	−0.0492076	−	0.0385339i
$769$	−5.66777	+	21.1524i	−0.204385	+	0.762775i	0.785251	+

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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36368 - 1.06788i) q^{3} -1.00000i q^{4} +(0.763001 + 2.84756i) q^{5} +(1.71938 - 0.209163i) q^{6} +(-0.504962 - 1.88454i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.719258 + 2.91250i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36368 - 1.06788i) q^{3} -1.00000i q^{4} +(0.763001 + 2.84756i) q^{5} +(1.71938 - 0.209163i) q^{6} +(-0.504962 - 1.88454i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.719258 + 2.91250i) q^{9} +(-2.55305 - 1.47400i) q^{10} +(-0.566782 - 0.566782i) q^{11} +(-1.06788 + 1.36368i) q^{12} +(2.11327 + 2.92131i) q^{13} +(1.68964 + 0.975511i) q^{14} +(2.00036 - 4.69796i) q^{15} -1.00000 q^{16} +(4.02058 + 6.96385i) q^{17} +(-2.56804 - 1.55086i) q^{18} +(-1.18319 + 4.41574i) q^{19} +(2.84756 - 0.763001i) q^{20} +(-1.32386 + 3.10916i) q^{21} +0.801550 q^{22} +(3.49688 + 6.05678i) q^{23} +(-0.209163 - 1.71938i) q^{24} +(-3.19629 + 1.84538i) q^{25} +(-3.55999 - 0.571370i) q^{26} +(2.12937 - 4.73981i) q^{27} +(-1.88454 + 0.504962i) q^{28} -7.87674i q^{29} +(1.90749 + 4.73643i) q^{30} +(-2.31031 + 0.619046i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.167654 + 1.37817i) q^{33} +(-7.76717 - 2.08121i) q^{34} +(4.98106 - 2.87582i) q^{35} +(2.91250 - 0.719258i) q^{36} +(-2.09658 - 7.82455i) q^{37} +(-2.28576 - 3.95904i) q^{38} +(0.237782 - 6.24047i) q^{39} +(-1.47400 + 2.55305i) q^{40} +(-5.00455 - 1.34097i) q^{41} +(-1.26239 - 3.13462i) q^{42} +(2.02114 + 1.16691i) q^{43} +(-0.566782 + 0.566782i) q^{44} +(-7.74472 + 4.27037i) q^{45} +(-6.75546 - 1.81012i) q^{46} +(-1.37959 + 5.14869i) q^{47} +(1.36368 + 1.06788i) q^{48} +(2.76566 - 1.59676i) q^{49} +(0.955238 - 3.56500i) q^{50} +(1.95377 - 13.7900i) q^{51} +(2.92131 - 2.11327i) q^{52} +8.27924i q^{53} +(1.84586 + 4.85724i) q^{54} +(1.18149 - 2.04640i) q^{55} +(0.975511 - 1.68964i) q^{56} +(6.32899 - 4.75815i) q^{57} +(5.56970 + 5.56970i) q^{58} +(-6.24226 - 6.24226i) q^{59} +(-4.69796 - 2.00036i) q^{60} +(2.46959 - 4.27745i) q^{61} +(1.19590 - 2.07137i) q^{62} +(5.12554 - 2.82617i) q^{63} +1.00000i q^{64} +(-6.70618 + 8.24664i) q^{65} +(-1.09306 - 0.855961i) q^{66} +(0.200953 - 0.749969i) q^{67} +(6.96385 - 4.02058i) q^{68} +(1.69929 - 11.9938i) q^{69} +(-1.48863 + 5.55565i) q^{70} +(2.57304 + 0.689443i) q^{71} +(-1.55086 + 2.56804i) q^{72} +(5.68293 - 5.68293i) q^{73} +(7.01530 + 4.05028i) q^{74} +(6.32937 + 0.896749i) q^{75} +(4.41574 + 1.18319i) q^{76} +(-0.781921 + 1.35433i) q^{77} +(4.24454 + 4.58082i) q^{78} +(0.554497 + 0.960416i) q^{79} +(-0.763001 - 2.84756i) q^{80} +(-7.96534 + 4.18968i) q^{81} +(4.48696 - 2.59055i) q^{82} +(2.29264 + 0.614312i) q^{83} +(3.10916 + 1.32386i) q^{84} +(-16.7623 + 16.7623i) q^{85} +(-2.25429 + 0.604036i) q^{86} +(-8.41143 + 10.7414i) q^{87} -0.801550i q^{88} +(2.84070 - 0.761164i) q^{89} +(2.45674 - 8.49595i) q^{90} +(4.43822 - 5.45771i) q^{91} +(6.05678 - 3.49688i) q^{92} +(3.81160 + 1.62296i) q^{93} +(-2.66516 - 4.61619i) q^{94} -13.4769 q^{95} +(-1.71938 + 0.209163i) q^{96} +(-3.54866 + 0.950861i) q^{97} +(-0.826542 + 3.08469i) q^{98} +(1.24309 - 2.05842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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