LMFDB - Embedded newform 234.2.z.a.227.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (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			227.11
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.539047 + 1.64603i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.995221 + 3.71422i) q^{5} +(1.72946 - 0.0946541i) q^{6} +(-1.54723 - 1.54723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.41886 + 1.77458i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.539047 + 1.64603i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.995221 + 3.71422i) q^{5} +(1.72946 - 0.0946541i) q^{6} +(-1.54723 - 1.54723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.41886 + 1.77458i) q^{9} +(3.33007 + 1.92262i) q^{10} +(4.04555 + 1.08400i) q^{11} +(0.356189 - 1.69503i) q^{12} +(-0.109551 + 3.60389i) q^{13} +(-1.89496 + 1.09406i) q^{14} +(-6.65020 + 0.363968i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.465866 - 0.806903i) q^{17} +(1.08807 + 2.79573i) q^{18} +(-1.86997 - 0.501056i) q^{19} +(2.71899 - 2.71899i) q^{20} +(1.71276 - 3.38082i) q^{21} +(2.09413 - 3.62714i) q^{22} +7.82985 q^{23} +(-1.54509 - 0.782758i) q^{24} +(-8.47480 - 4.89293i) q^{25} +(3.45273 + 1.03857i) q^{26} +(-4.22489 - 3.02494i) q^{27} +(0.566325 + 2.11355i) q^{28} +(6.41469 - 3.70352i) q^{29} +(-1.36963 + 6.51780i) q^{30} +(1.24383 + 0.333283i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.396436 + 7.24344i) q^{33} +(-0.899984 + 0.241150i) q^{34} +(7.28657 - 4.20690i) q^{35} +(2.98208 - 0.327402i) q^{36} +(4.93092 - 1.32124i) q^{37} +(-0.967965 + 1.67657i) q^{38} +(-5.99117 + 1.76234i) q^{39} +(-1.92262 - 3.33007i) q^{40} +(-7.74058 - 7.74058i) q^{41} +(-2.82232 - 2.52942i) q^{42} -1.96978i q^{43} +(-2.96155 - 2.96155i) q^{44} +(-4.18387 - 10.7503i) q^{45} +(2.02652 - 7.56306i) q^{46} +(2.52095 + 9.40830i) q^{47} +(-1.15598 + 1.28985i) q^{48} -2.21217i q^{49} +(-6.91965 + 6.91965i) q^{50} +(1.07707 - 1.20179i) q^{51} +(1.89682 - 3.06628i) q^{52} +2.04197i q^{53} +(-4.01535 + 3.29802i) q^{54} +(-8.05243 + 13.9472i) q^{55} +2.18811 q^{56} +(-0.183244 - 3.34812i) q^{57} +(-1.91709 - 7.15466i) q^{58} +(1.63315 + 6.09501i) q^{59} +(5.94122 + 3.00989i) q^{60} +0.861044 q^{61} +(0.643854 - 1.11519i) q^{62} +(6.48820 + 0.996846i) q^{63} -1.00000i q^{64} +(-13.2766 - 3.99356i) q^{65} +(7.09923 + 1.49181i) q^{66} +(2.36560 - 2.36560i) q^{67} +0.931731i q^{68} +(4.22066 + 12.8882i) q^{69} +(-2.17765 - 8.12711i) q^{70} +(-2.90450 + 10.8397i) q^{71} +(0.455574 - 2.96521i) q^{72} +(-2.45316 - 2.45316i) q^{73} -5.10487i q^{74} +(3.48561 - 16.5873i) q^{75} +(1.36891 + 1.36891i) q^{76} +(-4.58218 - 7.93658i) q^{77} +(0.151659 + 6.24316i) q^{78} +(6.38240 - 11.0546i) q^{79} +(-3.71422 + 0.995221i) q^{80} +(2.70174 - 8.58491i) q^{81} +(-9.48023 + 5.47341i) q^{82} +(-5.43185 + 1.45546i) q^{83} +(-3.17370 + 2.07149i) q^{84} +(3.46065 - 0.927279i) q^{85} +(-1.90266 - 0.509817i) q^{86} +(9.55395 + 8.56243i) q^{87} +(-3.62714 + 2.09413i) q^{88} +(-0.522663 - 1.95060i) q^{89} +(-11.4668 + 1.25894i) q^{90} +(5.74553 - 5.40653i) q^{91} +(-6.78085 - 3.91493i) q^{92} +(0.121887 + 2.22704i) q^{93} +9.74019 q^{94} +(3.72206 - 6.44679i) q^{95} +(0.946704 + 1.45043i) q^{96} +(-12.4550 + 12.4550i) q^{97} +(-2.13680 - 0.572553i) q^{98} +(-11.7092 + 4.55710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.539047	+	1.64603i	0.311219	+	0.950338i
$3$	0.539047	+	1.64603i	0.311219	+	0.950338i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.995221	+	3.71422i	−0.445076	+	1.66105i	0.270659	+	0.962675i	$0.412759\pi$
$5$	−0.995221	+	3.71422i	−0.445076	+	1.66105i	−0.715735	+	0.698372i	$0.753908\pi$
$6$	1.72946	−	0.0946541i	0.706050	−	0.0386424i
$7$	−1.54723	−	1.54723i	−0.584797	−	0.584797i	0.351421	−	0.936218i	$-0.385699\pi$
$7$	−1.54723	−	1.54723i	−0.584797	−	0.584797i	−0.936218	+	0.351421i	$0.885699\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.41886	+	1.77458i	−0.806286	+	0.591526i
$10$	3.33007	+	1.92262i	1.05306	+	0.607986i
$11$	4.04555	+	1.08400i	1.21978	+	0.326839i	0.810591	−	0.585612i	$-0.199146\pi$
$11$	4.04555	+	1.08400i	1.21978	+	0.326839i	0.409187	+	0.912451i	$0.365812\pi$
$12$	0.356189	−	1.69503i	0.102823	−	0.489313i
$13$	−0.109551	+	3.60389i	−0.0303839	+	0.999538i
$13$	−0.109551	+	3.60389i	−0.0303839	+	0.999538i
$14$	−1.89496	+	1.09406i	−0.506449	+	0.292399i
$15$	−6.65020	+	0.363968i	−1.71707	+	0.0939761i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.465866	−	0.806903i	−0.112989	−	0.195703i	0.803985	−	0.594649i	$-0.202709\pi$
$17$	−0.465866	−	0.806903i	−0.112989	−	0.195703i	−0.916974	+	0.398947i	$0.869376\pi$
$18$	1.08807	+	2.79573i	0.256459	+	0.658960i
$19$	−1.86997	−	0.501056i	−0.429000	−	0.114950i	0.0378569	−	0.999283i	$-0.487947\pi$
$19$	−1.86997	−	0.501056i	−0.429000	−	0.114950i	−0.466857	+	0.884333i	$0.654614\pi$
$20$	2.71899	−	2.71899i	0.607986	−	0.607986i
$21$	1.71276	−	3.38082i	0.373755	−	0.737755i
$22$	2.09413	−	3.62714i	0.446470	−	0.773308i
$23$	7.82985			1.63264			0.816319	−	0.577602i	$-0.196011\pi$
$23$	7.82985			1.63264			0.816319	+	0.577602i	$0.196011\pi$
$24$	−1.54509	−	0.782758i	−0.315389	−	0.159780i
$25$	−8.47480	−	4.89293i	−1.69496	−	0.978586i
$26$	3.45273	+	1.03857i	0.677137	+	0.203681i
$27$	−4.22489	−	3.02494i	−0.813081	−	0.582150i
$28$	0.566325	+	2.11355i	0.107025	+	0.399424i
$29$	6.41469	−	3.70352i	1.19118	−	0.687727i	0.232605	−	0.972571i	$-0.425275\pi$
$29$	6.41469	−	3.70352i	1.19118	−	0.687727i	0.958574	+	0.284844i	$0.0919419\pi$
$30$	−1.36963	+	6.51780i	−0.250059	+	1.18998i
$31$	1.24383	+	0.333283i	0.223399	+	0.0598595i	0.368782	−	0.929516i	$-0.379775\pi$
$31$	1.24383	+	0.333283i	0.223399	+	0.0598595i	−0.145383	+	0.989375i	$0.546442\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	0.396436	+	7.24344i	0.0690106	+	1.26092i
$34$	−0.899984	+	0.241150i	−0.154346	+	0.0413569i
$35$	7.28657	−	4.20690i	1.23165	−	0.711096i
$36$	2.98208	−	0.327402i	0.497014	−	0.0545669i
$37$	4.93092	−	1.32124i	0.810639	−	0.217210i	0.170389	−	0.985377i	$-0.445498\pi$
$37$	4.93092	−	1.32124i	0.810639	−	0.217210i	0.640250	+	0.768167i	$0.278831\pi$
$38$	−0.967965	+	1.67657i	−0.157025	+	0.271975i
$39$	−5.99117	+	1.76234i	−0.959356	+	0.282200i
$40$	−1.92262	−	3.33007i	−0.303993	−	0.526531i
$41$	−7.74058	−	7.74058i	−1.20887	−	1.20887i	−0.971392	−	0.237483i	$-0.923678\pi$
$41$	−7.74058	−	7.74058i	−1.20887	−	1.20887i	−0.237483	−	0.971392i	$-0.576322\pi$
$42$	−2.82232	−	2.52942i	−0.435494	−	0.390298i
$43$		−	1.96978i		−	0.300389i	−0.988656	−	0.150194i	$-0.952010\pi$
$43$		−	1.96978i		−	0.300389i	0.988656	−	0.150194i	$-0.0479899\pi$
$44$	−2.96155	−	2.96155i	−0.446470	−	0.446470i
$45$	−4.18387	−	10.7503i	−0.623694	−	1.60255i
$46$	2.02652	−	7.56306i	0.298793	−	1.11511i
$47$	2.52095	+	9.40830i	0.367718	+	1.37234i	0.863699	+	0.504008i	$0.168142\pi$
$47$	2.52095	+	9.40830i	0.367718	+	1.37234i	−0.495981	+	0.868333i	$0.665191\pi$
$48$	−1.15598	+	1.28985i	−0.166852	+	0.186173i
$49$		−	2.21217i		−	0.316025i
$50$	−6.91965	+	6.91965i	−0.978586	+	0.978586i
$51$	1.07707	−	1.20179i	0.150820	−	0.168284i
$52$	1.89682	−	3.06628i	0.263041	−	0.425217i
$53$			2.04197i			0.280486i	0.990117	+	0.140243i	$0.0447883\pi$
$53$			2.04197i			0.280486i	−0.990117	+	0.140243i	$0.955212\pi$
$54$	−4.01535	+	3.29802i	−0.546420	+	0.448804i
$55$	−8.05243	+	13.9472i	−1.08579	+	1.88064i
$56$	2.18811			0.292399
$57$	−0.183244	−	3.34812i	−0.0242712	−	0.443469i
$58$	−1.91709	−	7.15466i	−0.251726	−	0.939453i
$59$	1.63315	+	6.09501i	0.212618	+	0.793503i	0.986991	+	0.160773i	$0.0513988\pi$
$59$	1.63315	+	6.09501i	0.212618	+	0.793503i	−0.774373	+	0.632729i	$0.781935\pi$
$60$	5.94122	+	3.00989i	0.767009	+	0.388575i
$61$	0.861044			0.110245			0.0551227	−	0.998480i	$-0.482445\pi$
$61$	0.861044			0.110245			0.0551227	+	0.998480i	$0.482445\pi$
$62$	0.643854	−	1.11519i	0.0817696	−	0.141629i
$63$	6.48820	+	0.996846i	0.817436	+	0.125591i
$64$		−	1.00000i		−	0.125000i
$65$	−13.2766	−	3.99356i	−1.64676	−	0.495340i
$66$	7.09923	+	1.49181i	0.873854	+	0.183629i
$67$	2.36560	−	2.36560i	0.289004	−	0.289004i	−0.547683	−	0.836686i	$-0.684490\pi$
$67$	2.36560	−	2.36560i	0.289004	−	0.289004i	0.836686	+	0.547683i	$0.184490\pi$
$68$			0.931731i			0.112989i
$69$	4.22066	+	12.8882i	0.508107	+	1.55156i
$70$	−2.17765	−	8.12711i	−0.260279	−	0.971376i
$71$	−2.90450	+	10.8397i	−0.344700	+	1.28644i	0.548262	+	0.836307i	$0.315290\pi$
$71$	−2.90450	+	10.8397i	−0.344700	+	1.28644i	−0.892962	+	0.450132i	$0.851377\pi$
$72$	0.455574	−	2.96521i	0.0536899	−	0.349453i
$73$	−2.45316	−	2.45316i	−0.287121	−	0.287121i	0.548820	−	0.835941i	$-0.315077\pi$
$73$	−2.45316	−	2.45316i	−0.287121	−	0.287121i	−0.835941	+	0.548820i	$0.815077\pi$
$74$		−	5.10487i		−	0.593429i
$75$	3.48561	−	16.5873i	0.402484	−	1.91534i
$76$	1.36891	+	1.36891i	0.157025	+	0.157025i
$77$	−4.58218	−	7.93658i	−0.522188	−	0.904457i
$78$	0.151659	+	6.24316i	0.0171720	+	0.706898i
$79$	6.38240	−	11.0546i	0.718076	−	1.24374i	−0.243686	−	0.969854i	$-0.578357\pi$
$79$	6.38240	−	11.0546i	0.718076	−	1.24374i	0.961761	−	0.273889i	$-0.0883102\pi$
$80$	−3.71422	+	0.995221i	−0.415262	+	0.111269i
$81$	2.70174	−	8.58491i	0.300193	−	0.953878i
$82$	−9.48023	+	5.47341i	−1.04692	+	0.604437i
$83$	−5.43185	+	1.45546i	−0.596223	+	0.159757i	−0.544296	−	0.838893i	$-0.683203\pi$
$83$	−5.43185	+	1.45546i	−0.596223	+	0.159757i	−0.0519272	+	0.998651i	$0.516536\pi$
$84$	−3.17370	+	2.07149i	−0.346279	+	0.226018i
$85$	3.46065	−	0.927279i	0.375360	−	0.100577i
$86$	−1.90266	−	0.509817i	−0.205169	−	0.0549749i
$87$	9.55395	+	8.56243i	1.02429	+	0.917989i
$88$	−3.62714	+	2.09413i	−0.386654	+	0.223235i
$89$	−0.522663	−	1.95060i	−0.0554022	−	0.206764i	0.932676	−	0.360714i	$-0.117467\pi$
$89$	−0.522663	−	1.95060i	−0.0554022	−	0.206764i	−0.988079	+	0.153951i	$0.950800\pi$
$90$	−11.4668	+	1.25894i	−1.20871	+	0.132704i
$91$	5.74553	−	5.40653i	0.602295	−	0.566759i
$92$	−6.78085	−	3.91493i	−0.706953	−	0.408159i
$93$	0.121887	+	2.22704i	0.0126391	+	0.230934i
$94$	9.74019			1.00462
$95$	3.72206	−	6.44679i	0.381875	−	0.661427i
$96$	0.946704	+	1.45043i	0.0966226	+	0.148034i
$97$	−12.4550	+	12.4550i	−1.26461	+	1.26461i	−0.315778	+	0.948833i	$0.602265\pi$
$97$	−12.4550	+	12.4550i	−1.26461	+	1.26461i	−0.948833	+	0.315778i	$0.897735\pi$
$98$	−2.13680	−	0.572553i	−0.215849	−	0.0578366i
$99$	−11.7092	+	4.55710i	−1.17682	+	0.458005i
$100$	4.89293	+	8.47480i	0.489293	+	0.847480i
$101$	2.97887	+	5.15956i	0.296409	+	0.513395i	0.975312	−	0.220833i	$-0.0708775\pi$
$101$	2.97887	+	5.15956i	0.296409	+	0.513395i	−0.678903	+	0.734228i	$0.737544\pi$
$102$	−0.882074	−	1.35141i	−0.0873383	−	0.133810i
$103$	3.14153	−	1.81377i	0.309544	−	0.178716i	−0.337178	−	0.941441i	$-0.609472\pi$
$103$	3.14153	−	1.81377i	0.309544	−	0.178716i	0.646723	+	0.762725i	$0.276139\pi$
$104$	−2.47087	−	2.62580i	−0.242289	−	0.257481i
$105$	10.8525	+	9.72622i	1.05910	+	0.949182i
$106$	1.97239	+	0.528500i	0.191575	+	0.0513324i
$107$	3.85034	+	2.22300i	0.372227	+	0.214905i	0.674431	−	0.738338i	$-0.264389\pi$
$107$	3.85034	+	2.22300i	0.372227	+	0.214905i	−0.302204	+	0.953243i	$0.597722\pi$
$108$	2.14640	+	4.73212i	0.206537	+	0.455349i
$109$	5.79714	−	5.79714i	0.555266	−	0.555266i	−0.372690	−	0.927956i	$-0.621565\pi$
$109$	5.79714	−	5.79714i	0.555266	−	0.555266i	0.927956	+	0.372690i	$0.121565\pi$
$110$	11.3878	+	11.3878i	1.08579	+	1.08579i
$111$	4.83280	+	7.40426i	0.458709	+	0.702781i
$112$	0.566325	−	2.11355i	0.0535126	−	0.199712i
$113$	10.8830	+	6.28331i	1.02379	+	0.591084i	0.915199	−	0.403002i	$-0.132033\pi$
$113$	10.8830	+	6.28331i	1.02379	+	0.591084i	0.108589	+	0.994087i	$0.465367\pi$
$114$	−3.28146	−	0.689557i	−0.307337	−	0.0645830i
$115$	−7.79243	+	29.0818i	−0.726648	+	2.71189i
$116$	−7.40705			−0.687727
$117$	−6.13039	−	8.91169i	−0.566755	−	0.823886i
$118$	6.31002			0.580884
$119$	−0.527662	+	1.96926i	−0.0483707	+	0.180522i
$120$	4.44503	−	4.95976i	0.405774	−	0.452762i
$121$	5.66511	+	3.27075i	0.515010	+	0.297341i
$122$	0.222855	−	0.831705i	0.0201763	−	0.0752990i
$123$	8.56872	−	16.9138i	0.772616	−	1.52506i
$124$	−0.910547	−	0.910547i	−0.0817696	−	0.0817696i
$125$	13.0127	−	13.0127i	1.16389	−	1.16389i
$126$	2.64215	−	6.00912i	0.235381	−	0.535335i
$127$	0.0921603	+	0.0532087i	0.00817790	+	0.00472151i	0.504083	−	0.863655i	$-0.331830\pi$
$127$	0.0921603	+	0.0532087i	0.00817790	+	0.00472151i	−0.495905	+	0.868377i	$0.665164\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	3.24232	−	1.06180i	0.285471	−	0.0934866i
$130$	−7.29371	+	11.7906i	−0.639701	+	1.03410i
$131$	10.7216	−	6.19013i	0.936752	−	0.540834i	0.0478111	−	0.998856i	$-0.484775\pi$
$131$	10.7216	−	6.19013i	0.936752	−	0.540834i	0.888941	+	0.458023i	$0.151442\pi$
$132$	3.27839	−	6.47122i	0.285348	−	0.563247i
$133$	2.11802	+	3.66851i	0.183655	+	0.318100i
$134$	−1.67273	−	2.89725i	−0.144502	−	0.250284i
$135$	15.4400	−	12.6817i	1.32886	−	1.09147i
$136$	0.899984	+	0.241150i	0.0771729	+	0.0206784i
$137$	−1.86252	+	1.86252i	−0.159125	+	0.159125i	−0.782179	−	0.623054i	$-0.785892\pi$
$137$	−1.86252	+	1.86252i	−0.159125	+	0.159125i	0.623054	+	0.782179i	$0.285892\pi$
$138$	13.5414	−	0.741128i	1.15272	−	0.0630890i
$139$	7.32890	−	12.6940i	0.621629	−	1.07669i	−0.367554	−	0.930002i	$-0.619805\pi$
$139$	7.32890	−	12.6940i	0.621629	−	1.07669i	0.989182	−	0.146690i	$-0.0468621\pi$
$140$	−8.41380			−0.711096
$141$	−14.1275	+	9.22108i	−1.18975	+	0.776555i
$142$	9.71863	+	5.61105i	0.815569	+	0.470869i
$143$	−4.34981	+	14.4609i	−0.363749	+	1.20928i
$144$	−2.74626	−	1.20750i	−0.228855	−	0.100625i
$145$	7.37165	+	27.5114i	0.612182	+	2.28470i
$146$	−3.00450	+	1.73465i	−0.248654	+	0.143560i
$147$	3.64131	−	1.19247i	0.300331	−	0.0983529i
$148$	−4.93092	−	1.32124i	−0.405320	−	0.108605i
$149$	−5.92462	+	1.58750i	−0.485364	+	0.130053i	−0.493199	−	0.869916i	$-0.664173\pi$
$149$	−5.92462	+	1.58750i	−0.485364	+	0.130053i	0.00783529	+	0.999969i	$0.497506\pi$
$150$	−15.1200	−	7.65996i	−1.23454	−	0.625433i
$151$	−3.82090	+	1.02381i	−0.310941	+	0.0833163i	−0.410915	−	0.911674i	$-0.634791\pi$
$151$	−3.82090	+	1.02381i	−0.310941	+	0.0833163i	0.0999742	+	0.994990i	$0.468124\pi$
$152$	1.67657	−	0.967965i	0.135987	−	0.0785124i
$153$	2.55878	+	1.12507i	0.206865	+	0.0909564i
$154$	−8.85210	+	2.37191i	−0.713323	+	0.191134i
$155$	−2.47577	+	4.28816i	−0.198859	+	0.344434i
$156$	6.06968	+	1.46936i	0.485963	+	0.117643i
$157$	−4.23403	−	7.33355i	−0.337912	−	0.585281i	0.646128	−	0.763229i	$-0.276387\pi$
$157$	−4.23403	−	7.33355i	−0.337912	−	0.585281i	−0.984040	+	0.177948i	$0.943054\pi$
$158$	−9.02607	−	9.02607i	−0.718076	−	0.718076i
$159$	−3.36114	+	1.10071i	−0.266556	+	0.0872924i
$160$			3.84524i			0.303993i
$161$	−12.1146	−	12.1146i	−0.954761	−	0.954761i
$162$	−7.59312	−	4.83162i	−0.596572	−	0.379608i
$163$	−0.512492	+	1.91264i	−0.0401414	+	0.149810i	−0.983088	−	0.183135i	$-0.941376\pi$
$163$	−0.512492	+	1.91264i	−0.0401414	+	0.149810i	0.942946	+	0.332945i	$0.108042\pi$
$164$	2.83325	+	10.5738i	0.221239	+	0.825677i
$165$	−27.2982	−	5.73637i	−2.12516	−	0.446576i
$166$			5.62346i			0.436465i
$167$	15.8487	−	15.8487i	1.22641	−	1.22641i	0.261093	−	0.965314i	$-0.415917\pi$
$167$	15.8487	−	15.8487i	1.22641	−	1.22641i	0.965314	−	0.261093i	$-0.0840829\pi$
$168$	1.17949	+	3.60170i	0.0909999	+	0.277878i
$169$	−12.9760	−	0.789618i	−0.998154	−	0.0607398i
$170$		−	3.58273i		−	0.274783i
$171$	5.41234	−	2.10642i	0.413892	−	0.161082i
$172$	−0.984890	+	1.70588i	−0.0750971	+	0.130072i
$173$	−19.0450			−1.44796			−0.723981	−	0.689820i	$-0.757690\pi$
$173$	−19.0450			−1.44796			−0.723981	+	0.689820i	$0.757690\pi$
$174$	10.7434	−	7.01228i	0.814456	−	0.531600i
$175$	5.54197	+	20.6829i	0.418934	+	1.56348i
$176$	1.08400	+	4.04555i	0.0817096	+	0.304945i
$177$	−9.15225	+	5.97372i	−0.687925	+	0.449012i
$178$	−2.01941			−0.151362
$179$	0.255705	−	0.442894i	0.0191123	−	0.0331035i	−0.856311	−	0.516460i	$-0.827249\pi$
$179$	0.255705	−	0.442894i	0.0191123	−	0.0331035i	0.875423	+	0.483357i	$0.160583\pi$
$180$	−1.75179	+	11.4019i	−0.130571	+	0.849850i
$181$		−	2.38215i		−	0.177064i	−0.996073	−	0.0885319i	$-0.971782\pi$
$181$		−	2.38215i		−	0.177064i	0.996073	−	0.0885319i	$-0.0282175\pi$
$182$	−3.73526	−	6.94907i	−0.276876	−	0.515099i
$183$	0.464143	+	1.41731i	0.0343104	+	0.104770i
$184$	−5.53654	+	5.53654i	−0.408159	+	0.408159i
$185$			19.6294i			1.44318i
$186$	2.18271	+	0.458668i	0.160044	+	0.0336311i
$187$	−1.01000	−	3.76936i	−0.0738584	−	0.275643i
$188$	2.52095	−	9.40830i	0.183859	−	0.686171i
$189$	1.85660	+	11.2171i	0.135048	+	0.815927i
$190$	−5.26379	−	5.26379i	−0.381875	−	0.381875i
$191$		−	23.6164i		−	1.70882i	−0.519596	−	0.854412i	$-0.673918\pi$
$191$		−	23.6164i		−	1.70882i	0.519596	−	0.854412i	$-0.326082\pi$
$192$	1.64603	−	0.539047i	0.118792	−	0.0389023i
$193$	−11.1609	−	11.1609i	−0.803376	−	0.803376i	0.180245	−	0.983622i	$-0.442311\pi$
$193$	−11.1609	−	11.1609i	−0.803376	−	0.803376i	−0.983622	+	0.180245i	$0.942311\pi$
$194$	8.80700	+	15.2542i	0.632306	+	1.09519i
$195$	−0.583163	−	24.0064i	−0.0417612	−	1.71914i
$196$	−1.10609	+	1.91580i	−0.0790062	+	0.136843i
$197$	−18.2302	+	4.88476i	−1.29885	+	0.348025i	−0.841014	−	0.541014i	$-0.818041\pi$
$197$	−18.2302	+	4.88476i	−1.29885	+	0.348025i	−0.457833	+	0.889038i	$0.651374\pi$
$198$	1.37124	+	12.4897i	0.0974499	+	0.887606i
$199$	−4.30172	+	2.48360i	−0.304941	+	0.176058i	−0.644660	−	0.764469i	$-0.723001\pi$
$199$	−4.30172	+	2.48360i	−0.304941	+	0.176058i	0.339719	+	0.940527i	$0.389668\pi$
$200$	9.45241	−	2.53277i	0.668387	−	0.179094i
$201$	5.16902	+	2.61869i	0.364595	+	0.184708i
$202$	5.75474	−	1.54198i	0.404902	−	0.108493i
$203$	−15.6552	−	4.19479i	−1.09878	−	0.294417i
$204$	−1.53366	+	0.502247i	−0.107378	+	0.0351643i
$205$	36.4537	−	21.0466i	2.54604	−	1.46996i
$206$	−0.938874	−	3.50392i	−0.0654144	−	0.244130i
$207$	−18.9393	+	13.8947i	−1.31637	+	0.965748i
$208$	−3.17583	+	1.70707i	−0.220204	+	0.118364i
$209$	−7.02189	−	4.05409i	−0.485714	−	0.280427i
$210$	12.2036	−	7.96538i	0.842132	−	0.549664i
$211$	−13.2433			−0.911704			−0.455852	−	0.890056i	$-0.650665\pi$
$211$	−13.2433			−0.911704			−0.455852	+	0.890056i	$0.650665\pi$
$212$	1.02098	−	1.76839i	0.0701214	−	0.121454i
$213$	−19.4082	+	1.06222i	−1.32983	+	0.0727820i
$214$	3.14379	−	3.14379i	0.214905	−	0.214905i
$215$	7.31619	+	1.96037i	0.498960	+	0.133696i
$216$	5.12641	−	0.848495i	0.348808	−	0.0577328i
$217$	−1.40882	−	2.44015i	−0.0956372	−	0.165648i
$218$	−4.09920	−	7.10002i	−0.277633	−	0.480874i
$219$	2.71562	−	5.36035i	0.183504	−	0.362219i
$220$	13.9472	−	8.05243i	0.940321	−	0.542894i
$221$	2.95902	−	1.59053i	0.199045	−	0.106991i
$222$	8.40279	−	2.75176i	0.563958	−	0.184686i
$223$	7.85646	+	2.10513i	0.526107	+	0.140970i	0.512090	−	0.858932i	$-0.328871\pi$
$223$	7.85646	+	2.10513i	0.526107	+	0.140970i	0.0140172	+	0.999902i	$0.495538\pi$
$224$	−1.89496	−	1.09406i	−0.126612	−	0.0730996i
$225$	29.1822	−	3.20391i	1.94548	−	0.213594i
$226$	8.88595	−	8.88595i	0.591084	−	0.591084i
$227$	−7.45566	−	7.45566i	−0.494850	−	0.494850i	0.414981	−	0.909830i	$-0.363788\pi$
$227$	−7.45566	−	7.45566i	−0.494850	−	0.494850i	−0.909830	+	0.414981i	$0.863788\pi$
$228$	−1.51537	+	2.99118i	−0.100358	+	0.198096i
$229$	3.77851	−	14.1016i	0.249691	−	0.931859i	−0.721276	−	0.692647i	$-0.756444\pi$
$229$	3.77851	−	14.1016i	0.249691	−	0.931859i	0.970967	−	0.239212i	$-0.0768891\pi$
$230$	26.0740	+	15.0538i	1.71927	+	0.992620i
$231$	10.5939	−	11.8206i	0.697025	−	0.777740i
$232$	−1.91709	+	7.15466i	−0.125863	+	0.469726i
$233$	17.7535			1.16307			0.581536	−	0.813521i	$-0.302452\pi$
$233$	17.7535			1.16307			0.581536	+	0.813521i	$0.302452\pi$
$234$	−10.1947	+	3.61499i	−0.666448	+	0.236319i
$235$	−37.4533			−2.44319
$236$	1.63315	−	6.09501i	0.106309	−	0.396751i
$237$	21.6367	+	4.54668i	1.40546	+	0.295338i
$238$	1.76559	+	1.01937i	0.114446	+	0.0660757i
$239$	−2.88720	+	10.7752i	−0.186757	+	0.696988i	0.807490	+	0.589881i	$0.200825\pi$
$239$	−2.88720	+	10.7752i	−0.186757	+	0.696988i	−0.994247	+	0.107107i	$0.965841\pi$
$240$	−3.64030	−	5.57725i	−0.234981	−	0.360010i
$241$	−1.86773	−	1.86773i	−0.120311	−	0.120311i	0.644388	−	0.764699i	$-0.277112\pi$
$241$	−1.86773	−	1.86773i	−0.120311	−	0.120311i	−0.764699	+	0.644388i	$0.777112\pi$
$242$	4.62554	−	4.62554i	0.297341	−	0.297341i
$243$	15.5874	−	0.180506i	0.999933	−	0.0115795i
$244$	−0.745686	−	0.430522i	−0.0477377	−	0.0275614i
$245$	8.21649	+	2.20160i	0.524932	+	0.140655i
$246$	−14.1197	−	12.6544i	−0.900240	−	0.806812i
$247$	2.01060	−	6.68425i	0.127932	−	0.425309i
$248$	−1.11519	+	0.643854i	−0.0708145	+	0.0408848i
$249$	−5.32376	−	8.15645i	−0.337379	−	0.516894i
$250$	−9.20138	−	15.9373i	−0.581947	−	1.00796i
$251$	−3.16017	−	5.47357i	−0.199468	−	0.345489i	0.748888	−	0.662697i	$-0.230588\pi$
$251$	−3.16017	−	5.47357i	−0.199468	−	0.345489i	−0.948356	+	0.317208i	$0.897255\pi$
$252$	−5.12052	−	4.10739i	−0.322563	−	0.258741i
$253$	31.6760	+	8.48757i	1.99146	+	0.533609i
$254$	0.0752485	−	0.0752485i	0.00472151	−	0.00472151i
$255$	3.39179	+	5.19650i	0.212402	+	0.325418i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.02316			0.0638230			0.0319115	−	0.999491i	$-0.489841\pi$
$257$	1.02316			0.0638230			0.0319115	+	0.999491i	$0.489841\pi$
$258$	−0.186448	−	3.40666i	−0.0116077	−	0.212089i
$259$	−9.67352	−	5.58501i	−0.601083	−	0.347035i
$260$	9.50108	+	10.0968i	0.589232	+	0.626178i
$261$	−8.94403	+	20.3417i	−0.553622	+	1.25912i
$262$	−3.20424	−	11.9584i	−0.197959	−	0.738793i
$263$	−10.0869	+	5.82370i	−0.621987	+	0.359105i	−0.777642	−	0.628707i	$-0.783585\pi$
$263$	−10.0869	+	5.82370i	−0.621987	+	0.359105i	0.155655	+	0.987811i	$0.450251\pi$
$264$	−5.40220	−	4.84156i	−0.332483	−	0.297977i
$265$	−7.58430	−	2.03221i	−0.465900	−	0.124837i
$266$	4.09169	−	1.09637i	0.250878	−	0.0672225i
$267$	2.92902	−	1.91179i	0.179253	−	0.117000i
$268$	−3.23147	+	0.865869i	−0.197393	+	0.0528913i
$269$	−24.3789	+	14.0752i	−1.48641	+	0.858178i	−0.999880	−	0.0154875i	$-0.995070\pi$
$269$	−24.3789	+	14.0752i	−1.48641	+	0.858178i	−0.486527	+	0.873665i	$0.661737\pi$
$270$	−8.25340	−	18.1961i	−0.502286	−	1.10738i
$271$	1.95393	−	0.523554i	0.118693	−	0.0318037i	−0.198984	−	0.980003i	$-0.563764\pi$
$271$	1.95393	−	0.523554i	0.118693	−	0.0318037i	0.317677	+	0.948199i	$0.397097\pi$
$272$	0.465866	−	0.806903i	0.0282473	−	0.0489257i
$273$	11.9964	+	6.54297i	0.726058	+	0.395999i
$274$	1.31700	+	2.28111i	0.0795627	+	0.137807i
$275$	−28.9813	−	28.9813i	−1.74764	−	1.74764i
$276$	2.78891	−	13.2718i	0.167873	−	0.798871i
$277$			15.8069i			0.949745i	0.880055	+	0.474873i	$0.157506\pi$
$277$			15.8069i			0.949745i	−0.880055	+	0.474873i	$0.842494\pi$
$278$	−10.3646	−	10.3646i	−0.621629	−	0.621629i
$279$	−3.60009	+	1.40111i	−0.215532	+	0.0838823i
$280$	−2.17765	+	8.12711i	−0.130140	+	0.485688i
$281$	−5.06663	−	18.9089i	−0.302250	−	1.12801i	−0.935287	−	0.353891i	$-0.884858\pi$
$281$	−5.06663	−	18.9089i	−0.302250	−	1.12801i	0.633037	−	0.774122i	$-0.281808\pi$
$282$	5.25042	+	16.0327i	0.312658	+	0.954732i
$283$			32.4907i			1.93137i	0.259708	+	0.965687i	$0.416374\pi$
$283$			32.4907i			1.93137i	−0.259708	+	0.965687i	$0.583626\pi$
$284$	7.93523	−	7.93523i	0.470869	−	0.470869i
$285$	12.6180	+	2.65151i	0.747426	+	0.157062i
$286$	12.8424	+	7.94436i	0.759386	+	0.469760i
$287$			23.9529i			1.41389i
$288$	−1.87714	+	2.34016i	−0.110612	+	0.137895i
$289$	8.06594	−	13.9706i	0.474467	−	0.821801i
$290$	28.4819			1.67251
$291$	−27.2151	−	13.7875i	−1.59538	−	0.808238i
$292$	0.897919	+	3.35108i	0.0525467	+	0.196107i
$293$	3.76349	+	14.0455i	0.219866	+	0.820550i	0.984397	+	0.175963i	$0.0563039\pi$
$293$	3.76349	+	14.0455i	0.219866	+	0.820550i	−0.764531	+	0.644587i	$0.777029\pi$
$294$	−0.209391	−	3.82587i	−0.0122120	−	0.223129i
$295$	−24.2635			−1.41268
$296$	−2.55243	+	4.42095i	−0.148357	+	0.256962i
$297$	−13.8130	−	16.8173i	−0.801510	−	0.975840i
$298$			6.13362i			0.355311i
$299$	−0.857767	+	28.2179i	−0.0496060	+	1.63188i
$300$	−11.3123	+	12.6222i	−0.653116	+	0.728746i
$301$	−3.04770	+	3.04770i	−0.175666	+	0.175666i
$302$			3.95569i			0.227624i
$303$	−6.88706	+	7.68457i	−0.395651	+	0.441467i
$304$	−0.501056	−	1.86997i	−0.0287375	−	0.107250i
$305$	−0.856929	+	3.19810i	−0.0490676	+	0.183123i
$306$	1.74899	−	2.18040i	0.0999832	−	0.124645i
$307$	6.00502	+	6.00502i	0.342724	+	0.342724i	0.857391	−	0.514666i	$-0.172084\pi$
$307$	6.00502	+	6.00502i	0.342724	+	0.342724i	−0.514666	+	0.857391i	$0.672084\pi$
$308$			9.16437i			0.522188i
$309$	4.67895	+	4.19337i	0.266176	+	0.238552i
$310$	3.50127	+	3.50127i	0.198859	+	0.198859i
$311$	−7.13805	−	12.3635i	−0.404762	−	0.701068i	0.589532	−	0.807745i	$-0.299312\pi$
$311$	−7.13805	−	12.3635i	−0.404762	−	0.701068i	−0.994294	+	0.106677i	$0.965979\pi$
$312$	2.99024	−	5.48256i	0.169289	−	0.310389i
$313$	−0.0856946	+	0.148427i	−0.00484375	+	0.00838962i	−0.868437	−	0.495799i	$-0.834875\pi$
$313$	−0.0856946	+	0.148427i	−0.00484375	+	0.00838962i	0.863593	+	0.504189i	$0.168208\pi$
$314$	−8.17951	+	2.19169i	−0.461597	+	0.123684i
$315$	−10.1597	+	23.1065i	−0.572434	+	1.30190i
$316$	−11.0546	+	6.38240i	−0.621872	+	0.359038i
$317$	19.1315	−	5.12627i	1.07453	−	0.287920i	0.322178	−	0.946679i	$-0.395585\pi$
$317$	19.1315	−	5.12627i	1.07453	−	0.287920i	0.752354	+	0.658759i	$0.228918\pi$
$318$	0.193280	+	3.53150i	0.0108386	+	0.198037i
$319$	29.9656	−	8.02925i	1.67775	−	0.449552i
$320$	3.71422	+	0.995221i	0.207631	+	0.0556345i
$321$	−1.58361	+	7.53609i	−0.0883887	+	0.420624i
$322$	−14.8373	+	8.56629i	−0.826848	+	0.477381i
$323$	0.466849	+	1.74231i	0.0259762	+	0.0969445i
$324$	−6.63223	+	6.08388i	−0.368457	+	0.337993i
$325$	18.5620	−	30.0062i	1.02963	−	1.66444i
$326$	1.71483	+	0.990058i	0.0949757	+	0.0548342i
$327$	12.6672	+	6.41736i	0.700499	+	0.354881i
$328$	10.9468			0.604437
$329$	10.6563	−	18.4573i	0.587501	−	1.01758i
$330$	−12.6062	+	24.8834i	−0.693949	+	1.36978i
$331$	17.2043	−	17.2043i	0.945631	−	0.945631i	−0.0529651	−	0.998596i	$-0.516867\pi$
$331$	17.2043	−	17.2043i	0.945631	−	0.945631i	0.998596	+	0.0529651i	$0.0168672\pi$
$332$	5.43185	+	1.45546i	0.298111	+	0.0798787i
$333$	−9.58256	+	11.9462i	−0.525121	+	0.654648i
$334$	−11.2067	−	19.4106i	−0.613203	−	1.06210i
$335$	6.43204	+	11.1406i	0.351420	+	0.608677i
$336$	3.78425	−	0.207114i	0.206448	−	0.0112990i
$337$	8.81745	−	5.09076i	0.480317	−	0.277311i	−0.240232	−	0.970716i	$-0.577223\pi$
$337$	8.81745	−	5.09076i	0.480317	−	0.277311i	0.720549	+	0.693404i	$0.243890\pi$
$338$	−4.12115	+	12.3295i	−0.224161	+	0.670635i
$339$	−4.47609	+	21.3008i	−0.243108	+	1.15690i
$340$	−3.46065	−	0.927279i	−0.187680	−	0.0502887i
$341$	4.67070	+	2.69663i	0.252932	+	0.146031i
$342$	−0.633827	−	5.77310i	−0.0342734	−	0.312174i
$343$	−14.2533	+	14.2533i	−0.769607	+	0.769607i
$344$	1.39284	+	1.39284i	0.0750971	+	0.0750971i
$345$	−52.0701	+	2.84981i	−2.80336	+	0.153429i
$346$	−4.92920	+	18.3960i	−0.264996	+	0.988977i
$347$	13.9659	+	8.06324i	0.749731	+	0.432857i	0.825597	−	0.564261i	$-0.190839\pi$
$347$	13.9659	+	8.06324i	0.749731	+	0.432857i	−0.0758657	+	0.997118i	$0.524172\pi$
$348$	−3.99275	−	12.1923i	−0.214034	−	0.653573i
$349$	7.60450	−	28.3804i	0.407060	−	1.51917i	−0.393166	−	0.919468i	$-0.628620\pi$
$349$	7.60450	−	28.3804i	0.407060	−	1.51917i	0.800225	−	0.599700i	$-0.204713\pi$
$350$	21.4125			1.14455
$351$	11.3644	−	14.8947i	0.606586	−	0.795018i
$352$	4.18826			0.223235
$353$	5.50974	−	20.5626i	0.293254	−	1.09444i	−0.649340	−	0.760498i	$-0.724955\pi$
$353$	5.50974	−	20.5626i	0.293254	−	1.09444i	0.942594	−	0.333940i	$-0.108378\pi$
$354$	3.40139	+	10.3865i	0.180782	+	0.552037i
$355$	−37.3705	−	21.5758i	−1.98342	−	1.14513i
$356$	−0.522663	+	1.95060i	−0.0277011	+	0.103382i
$357$	−3.52591	+	0.192974i	−0.186611	+	0.0102133i
$358$	−0.361622	−	0.361622i	−0.0191123	−	0.0191123i
$359$	11.8574	−	11.8574i	0.625809	−	0.625809i	−0.321202	−	0.947011i	$-0.604087\pi$
$359$	11.8574	−	11.8574i	0.625809	−	0.625809i	0.947011	+	0.321202i	$0.104087\pi$
$360$	10.5600	+	4.64314i	0.556562	+	0.244715i
$361$	−13.2088	−	7.62609i	−0.695198	−	0.401373i
$362$	−2.30098	−	0.616546i	−0.120937	−	0.0324049i
$363$	−2.33001	+	11.0881i	−0.122294	+	0.581972i
$364$	−7.67904	+	1.80943i	−0.402491	+	0.0948398i
$365$	11.5530	−	6.67013i	0.604712	−	0.349131i
$366$	1.48914	−	0.0815014i	0.0778388	−	0.00426015i
$367$	−4.86556	−	8.42740i	−0.253980	−	0.439907i	0.710638	−	0.703558i	$-0.248406\pi$
$367$	−4.86556	−	8.42740i	−0.253980	−	0.439907i	−0.964618	+	0.263651i	$0.915073\pi$
$368$	3.91493	+	6.78085i	0.204080	+	0.353476i
$369$	32.4596	+	4.98709i	1.68978	+	0.259617i
$370$	18.9606	+	5.08047i	0.985714	+	0.264121i
$371$	3.15938	−	3.15938i	0.164027	−	0.164027i
$372$	1.00796	−	1.98962i	0.0522605	−	0.103157i
$373$	−11.8651	+	20.5510i	−0.614351	+	1.06409i	0.376146	+	0.926560i	$0.377249\pi$
$373$	−11.8651	+	20.5510i	−0.614351	+	1.06409i	−0.990498	+	0.137528i	$0.956084\pi$
$374$	−3.90233			−0.201785
$375$	28.4339	+	14.4049i	1.46832	+	0.743867i
$376$	−8.43525	−	4.87009i	−0.435015	−	0.251156i
$377$	12.6443	+	23.5235i	0.651217	+	1.21152i
$378$	11.3155	+	1.10987i	0.582004	+	0.0570857i
$379$	−0.0380534	−	0.142017i	−0.00195467	−	0.00729493i	0.964942	−	0.262465i	$-0.0845353\pi$
$379$	−0.0380534	−	0.142017i	−0.00195467	−	0.00729493i	−0.966896	+	0.255170i	$0.917869\pi$
$380$	−6.44679	+	3.72206i	−0.330714	+	0.190938i
$381$	−0.0379047	+	0.180381i	−0.00194192	+	0.00924120i
$382$	−22.8117	−	6.11238i	−1.16715	−	0.312737i
$383$	−22.2656	+	5.96604i	−1.13772	+	0.304851i	−0.778033	−	0.628223i	$-0.783782\pi$
$383$	−22.2656	+	5.96604i	−1.13772	+	0.304851i	−0.359685	+	0.933074i	$0.617116\pi$
$384$	−0.0946541	−	1.72946i	−0.00483030	−	0.0882563i
$385$	34.0384	−	9.12057i	1.73476	−	0.464827i
$386$	−13.6692	+	7.89192i	−0.695744	+	0.401688i
$387$	3.49553	+	4.76462i	0.177688	+	0.242199i
$388$	17.0138	−	4.55884i	0.863745	−	0.231440i
$389$	−16.4933	+	28.5672i	−0.836243	+	1.44841i	0.0567717	+	0.998387i	$0.481919\pi$
$389$	−16.4933	+	28.5672i	−0.836243	+	1.44841i	−0.893015	+	0.450028i	$0.851414\pi$
$390$	−23.3394	−	5.65003i	−1.18183	−	0.286100i
$391$	−3.64766	−	6.31793i	−0.184470	−	0.319512i
$392$	1.56424	+	1.56424i	0.0790062	+	0.0790062i
$393$	15.9686	+	14.3114i	0.805510	+	0.721913i
$394$			18.8733i			0.950822i
$395$	34.7074	+	34.7074i	1.74632	+	1.74632i
$396$	12.4191	+	1.90806i	0.624081	+	0.0958837i
$397$	5.53019	−	20.6390i	0.277552	−	1.03584i	−0.676559	−	0.736388i	$-0.736530\pi$
$397$	5.53019	−	20.6390i	0.277552	−	1.03584i	0.954112	−	0.299451i	$-0.0968037\pi$
$398$	1.28561	+	4.79795i	0.0644416	+	0.240499i
$399$	−4.89678	+	5.46382i	−0.245146	+	0.273533i
$400$		−	9.78586i		−	0.489293i
$401$	−19.3250	+	19.3250i	−0.965043	+	0.965043i	−0.999409	−	0.0343661i	$-0.989059\pi$
$401$	−19.3250	+	19.3250i	−0.965043	+	0.965043i	0.0343661	+	0.999409i	$0.489059\pi$
$402$	3.86730	−	4.31512i	0.192883	−	0.215219i
$403$	−1.33738	+	4.44611i	−0.0666196	+	0.221477i
$404$		−	5.95775i		−	0.296409i
$405$	29.1974	+	18.5787i	1.45083	+	0.923184i
$406$	−8.10372	+	14.0361i	−0.402181	+	0.696598i
$407$	21.3805			1.05979
$408$	0.0881922	+	1.61139i	0.00436617	+	0.0797759i
$409$	−4.51286	−	16.8422i	−0.223146	−	0.832794i	−0.983139	−	0.182862i	$-0.941464\pi$
$409$	−4.51286	−	16.8422i	−0.223146	−	0.832794i	0.759992	−	0.649932i	$-0.225203\pi$
$410$	−10.8945	−	40.6589i	−0.538042	−	2.00800i
$411$	−4.06975	−	2.06178i	−0.200746	−	0.101700i
$412$	−3.62753			−0.178716
$413$	6.90351	−	11.9572i	0.339699	−	0.588377i
$414$	8.51939	+	21.8902i	0.418705	+	1.07584i
$415$		−	21.6236i		−	1.06146i
$416$	0.826936	+	3.50944i	0.0405439	+	0.172065i
$417$	24.8454	+	5.22094i	1.21669	+	0.255671i
$418$	−5.73335	+	5.73335i	−0.280427	+	0.280427i
$419$		−	19.6972i		−	0.962273i	−0.876646	−	0.481137i	$-0.840224\pi$
$419$		−	19.6972i		−	0.962273i	0.876646	−	0.481137i	$-0.159776\pi$
$420$	−4.53543	−	13.8494i	−0.221307	−	0.675782i
$421$	1.16410	+	4.34449i	0.0567348	+	0.211737i	0.988474	−	0.151391i	$-0.0483753\pi$
$421$	1.16410	+	4.34449i	0.0567348	+	0.211737i	−0.931739	+	0.363128i	$0.881709\pi$
$422$	−3.42761	+	12.7920i	−0.166853	+	0.622705i
$423$	−22.7936	−	18.2837i	−1.10826	−	0.888985i
$424$	−1.44389	−	1.44389i	−0.0701214	−	0.0701214i
$425$			9.11779i			0.442278i
$426$	−3.99719	+	19.0218i	−0.193665	+	0.921610i
$427$	−1.33223	−	1.33223i	−0.0644712	−	0.0644712i
$428$	−2.22300	−	3.85034i	−0.107453	−	0.186113i
$429$	−26.1479	+	0.635185i	−1.26243	+	0.0306670i
$430$	3.78714	−	6.55951i	0.182632	−	0.316328i
$431$	0.579994	−	0.155409i	0.0279373	−	0.00748579i	−0.244823	−	0.969568i	$-0.578730\pi$
$431$	0.579994	−	0.155409i	0.0279373	−	0.00748579i	0.272761	+	0.962082i	$0.412063\pi$
$432$	0.507229	−	5.17134i	0.0244041	−	0.248806i
$433$	−7.94515	+	4.58713i	−0.381819	+	0.220444i	−0.678610	−	0.734499i	$-0.737417\pi$
$433$	−7.94515	+	4.58713i	−0.381819	+	0.220444i	0.296790	+	0.954943i	$0.404084\pi$
$434$	−2.72164	+	0.729261i	−0.130643	+	0.0350056i
$435$	−41.3110	+	26.9639i	−1.98071	+	1.29282i
$436$	−7.91904	+	2.12190i	−0.379253	+	0.101621i
$437$	−14.6416	−	3.92319i	−0.700401	−	0.187672i
$438$	−4.47485	−	4.01045i	−0.213817	−	0.191627i
$439$	13.3958	−	7.73405i	0.639345	−	0.369126i	−0.145017	−	0.989429i	$-0.546324\pi$
$439$	13.3958	−	7.73405i	0.639345	−	0.369126i	0.784362	+	0.620303i	$0.212990\pi$
$440$	−4.16824	−	15.5561i	−0.198713	−	0.741608i
$441$	3.92568	+	5.35093i	0.186937	+	0.254806i
$442$	−0.770483	−	3.26986i	−0.0366481	−	0.155531i
$443$	−15.2867	−	8.82576i	−0.726292	−	0.419325i	0.0907723	−	0.995872i	$-0.471066\pi$
$443$	−15.2867	−	8.82576i	−0.726292	−	0.419325i	−0.817064	+	0.576547i	$0.804400\pi$
$444$	−0.483197	−	8.82868i	−0.0229315	−	0.418991i
$445$	7.76513			0.368103
$446$	4.06680	−	7.04391i	0.192569	−	0.333539i
$447$	−5.80672	−	8.89639i	−0.274649	−	0.420785i
$448$	−1.54723	+	1.54723i	−0.0730996	+	0.0730996i
$449$	17.1746	+	4.60193i	0.810521	+	0.217178i	0.640198	−	0.768210i	$-0.278852\pi$
$449$	17.1746	+	4.60193i	0.810521	+	0.217178i	0.170323	+	0.985388i	$0.445519\pi$
$450$	4.45818	−	29.0171i	0.210161	−	1.36788i
$451$	−22.9241	−	39.7056i	−1.07945	−	1.86967i
$452$	−6.28331	−	10.8830i	−0.295542	−	0.511894i
$453$	−3.74487	−	5.73746i	−0.175949	−	0.269569i
$454$	−9.13129	+	5.27195i	−0.428552	+	0.247425i
$455$	14.3629	+	26.7208i	0.673345	+	1.25269i
$456$	2.49705	+	2.23791i	0.116935	+	0.104800i
$457$	25.3800	+	6.80056i	1.18723	+	0.318117i	0.797790	−	0.602936i	$-0.206002\pi$
$457$	25.3800	+	6.80056i	1.18723	+	0.318117i	0.389438	+	0.921053i	$0.372669\pi$
$458$	−12.6431	−	7.29952i	−0.590775	−	0.341084i
$459$	−0.472601	+	4.81830i	−0.0220591	+	0.224899i
$460$	21.2893	−	21.2893i	0.992620	−	0.992620i
$461$	−25.8981	−	25.8981i	−1.20619	−	1.20619i	−0.972251	−	0.233942i	$-0.924837\pi$
$461$	−25.8981	−	25.8981i	−1.20619	−	1.20619i	−0.233942	−	0.972251i	$-0.575163\pi$
$462$	−8.67595	−	13.2923i	−0.403642	−	0.618413i
$463$	−7.42600	+	27.7142i	−0.345115	+	1.28799i	0.547362	+	0.836896i	$0.315632\pi$
$463$	−7.42600	+	27.7142i	−0.345115	+	1.28799i	−0.892477	+	0.451092i	$0.851035\pi$
$464$	6.41469	+	3.70352i	0.297795	+	0.171932i
$465$	−8.39302	−	1.76369i	−0.389217	−	0.0817890i
$466$	4.59495	−	17.1486i	0.212857	−	0.794393i
$467$	30.1627			1.39576			0.697881	−	0.716214i	$-0.254126\pi$
$467$	30.1627			1.39576			0.697881	+	0.716214i	$0.254126\pi$
$468$	0.853228	+	10.7829i	0.0394405	+	0.498442i
$469$	−7.32023			−0.338017
$470$	−9.69364	+	36.1772i	−0.447134	+	1.66873i
$471$	9.78893	−	10.9225i	0.451050	−	0.503281i
$472$	−5.46464	−	3.15501i	−0.251530	−	0.145221i
$473$	2.13524	−	7.96884i	0.0981786	−	0.366407i
$474$	9.99175	−	19.7227i	0.458936	−	0.905893i
$475$	13.3960	+	13.3960i	0.614649	+	0.614649i
$476$	1.44160	−	1.44160i	0.0660757	−	0.0660757i
$477$	−3.62363	−	4.93922i	−0.165915	−	0.226151i
$478$	9.66076	+	5.57764i	0.441873	+	0.255115i
$479$	11.4868	+	3.07789i	0.524847	+	0.140632i	0.511508	−	0.859279i	$-0.329087\pi$
$479$	11.4868	+	3.07789i	0.524847	+	0.140632i	0.0133394	+	0.999911i	$0.495754\pi$
$480$	−6.32939	+	2.07276i	−0.288896	+	0.0946083i
$481$	4.22140	+	17.9152i	0.192479	+	0.816864i
$482$	−2.28749	+	1.32068i	−0.104192	+	0.0601554i
$483$	13.4107	−	26.4713i	0.610207	−	1.20449i
$484$	−3.27075	−	5.66511i	−0.148671	−	0.257505i
$485$	−33.8650	−	58.6559i	−1.53773	−	2.66343i
$486$	3.85996	−	15.1030i	0.175091	−	0.685086i
$487$	20.6057	+	5.52129i	0.933735	+	0.250194i	0.693447	−	0.720508i	$-0.256091\pi$
$487$	20.6057	+	5.52129i	0.933735	+	0.250194i	0.240288	+	0.970702i	$0.422758\pi$
$488$	−0.608850	+	0.608850i	−0.0275614	+	0.0275614i
$489$	−3.42453	+	0.187426i	−0.154863	+	0.00847570i
$490$	4.25317	−	7.36670i	0.192139	−	0.332794i
$491$	−19.9916			−0.902210			−0.451105	−	0.892471i	$-0.648970\pi$
$491$	−19.9916			−0.902210			−0.451105	+	0.892471i	$0.648970\pi$
$492$	−15.8776	+	10.3634i	−0.715818	+	0.467218i
$493$	−5.97677	−	3.45069i	−0.269180	−	0.155411i
$494$	−5.93611	−	3.67211i	−0.267078	−	0.165216i
$495$	−5.27275	−	48.0260i	−0.236993	−	2.15861i
$496$	0.333283	+	1.24383i	0.0149649	+	0.0558497i
$497$	21.2654	−	12.2776i	0.953885	−	0.550726i
$498$	−9.25641	+	3.03131i	−0.414790	+	0.135836i
$499$	0.276024	+	0.0739605i	0.0123565	+	0.00331093i	0.264992	−	0.964251i	$-0.414631\pi$
$499$	0.276024	+	0.0739605i	0.0123565	+	0.00331093i	−0.252635	+	0.967562i	$0.581297\pi$
$500$	−17.7757	+	4.76299i	−0.794954	+	0.213007i
$501$	34.6306	+	17.5443i	1.54718	+	0.783820i
$502$	−6.10498	+	1.63582i	−0.272478	+	0.0730104i
$503$	6.95762	−	4.01698i	0.310225	−	0.179108i	−0.336802	−	0.941575i	$-0.609345\pi$
$503$	6.95762	−	4.01698i	0.310225	−	0.179108i	0.647027	+	0.762467i	$0.276012\pi$
$504$	−5.29273	+	3.88297i	−0.235757	+	0.172961i
$505$	−22.1284	+	5.92927i	−0.984699	+	0.263849i
$506$	16.3967	−	28.4000i	0.728923	−	1.26253i
$507$	−5.69493	−	21.7846i	−0.252921	−	0.967487i
$508$	−0.0532087	−	0.0921603i	−0.00236076	−	0.00408895i
$509$	21.7773	+	21.7773i	0.965261	+	0.965261i	0.999417	−	0.0341557i	$-0.0108742\pi$
$509$	21.7773	+	21.7773i	0.965261	+	0.965261i	−0.0341557	+	0.999417i	$0.510874\pi$
$510$	5.89730	−	1.93126i	0.261137	−	0.0855176i
$511$			7.59120i			0.335815i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	6.38474	+	7.77344i	0.281893	+	0.343206i
$514$	0.264813	−	0.988297i	0.0116804	−	0.0435919i
$515$	3.61019	+	13.4734i	0.159084	+	0.593710i
$516$	−3.33884	−	0.701614i	−0.146984	−	0.0308868i
$517$			40.7944i			1.79414i
$518$	−7.89839	+	7.89839i	−0.347035	+	0.347035i
$519$	−10.2661	−	31.3487i	−0.450633	−	1.37605i
$520$	12.2118	−	6.56409i	0.535524	−	0.287854i
$521$		−	5.90138i		−	0.258544i	−0.991609	−	0.129272i	$-0.958736\pi$
$521$		−	5.90138i		−	0.258544i	0.991609	−	0.129272i	$-0.0412640\pi$
$522$	17.3337	+	13.9041i	0.758674	+	0.608565i
$523$	5.66854	−	9.81820i	0.247868	−	0.429320i	−0.715066	−	0.699057i	$-0.753603\pi$
$523$	5.66854	−	9.81820i	0.247868	−	0.429320i	0.962934	+	0.269737i	$0.0869368\pi$
$524$	−12.3803			−0.540834
$525$	−31.0574	+	20.2713i	−1.35546	+	0.884714i
$526$	3.01457	+	11.2505i	0.131441	+	0.490546i
$527$	−0.310531	−	1.15892i	−0.0135269	−	0.0504832i
$528$	−6.07478	+	3.96504i	−0.264371	+	0.172556i
$529$	38.3066			1.66550
$530$	−3.92592	+	6.79990i	−0.170531	+	0.295369i
$531$	−14.7664	−	11.8448i	−0.640809	−	0.514021i
$532$		−	4.23603i		−	0.183655i
$533$	28.7441	−	27.0482i	1.24505	−	1.17159i
$534$	−1.08856	−	3.32403i	−0.0471066	−	0.143845i
$535$	−12.0886	+	12.0886i	−0.522637	+	0.522637i
$536$			3.34546i			0.144502i
$537$	0.866856	+	0.182159i	0.0374076	+	0.00786072i
$538$	7.28584	+	27.1911i	0.314115	+	1.17229i
$539$	2.39800	−	8.94945i	0.103289	−	0.385480i
$540$	−19.7123	+	3.26267i	−0.848281	+	0.140403i
$541$	1.72650	+	1.72650i	0.0742279	+	0.0742279i	0.743246	−	0.669018i	$-0.233285\pi$
$541$	1.72650	+	1.72650i	0.0742279	+	0.0742279i	−0.669018	+	0.743246i	$0.733285\pi$
$542$		−	2.02286i		−	0.0868892i
$543$	3.92110	−	1.28409i	0.168271	−	0.0551056i
$544$	−0.658834	−	0.658834i	−0.0282473	−	0.0282473i
$545$	15.7624	+	27.3013i	0.675187	+	1.16946i
$546$	9.42493	−	9.89423i	0.403350	−	0.423434i
$547$	−9.56787	+	16.5720i	−0.409092	+	0.708569i	−0.994788	−	0.101962i	$-0.967488\pi$
$547$	−9.56787	+	16.5720i	−0.409092	+	0.708569i	0.585696	+	0.810531i	$0.300821\pi$
$548$	2.54424	−	0.681728i	0.108685	−	0.0291220i
$549$	−2.08274	+	1.52799i	−0.0888893	+	0.0652130i
$550$	−35.4947	+	20.4929i	−1.51350	+	0.873818i
$551$	−13.8509	+	3.71134i	−0.590069	+	0.158109i
$552$	−12.0978	−	6.12888i	−0.514916	−	0.260863i
$553$	−26.9791	+	7.22901i	−1.14727	+	0.307409i
$554$	15.2683	+	4.09113i	0.648688	+	0.173815i
$555$	−32.3107	+	10.5812i	−1.37151	+	0.449146i
$556$	−12.6940	+	7.32890i	−0.538346	+	0.310814i
$557$	−5.72596	−	21.3696i	−0.242617	−	0.905457i	−0.974566	−	0.224099i	$-0.928056\pi$
$557$	−5.72596	−	21.3696i	−0.242617	−	0.905457i	0.731950	−	0.681359i	$-0.238611\pi$
$558$	0.421598	+	3.84005i	0.0178477	+	0.162562i
$559$	7.09886	+	0.215791i	0.300250	+	0.00912699i
$560$	7.28657	+	4.20690i	0.307914	+	0.177774i
$561$	5.66006	−	3.69435i	0.238968	−	0.155976i
$562$	−19.5760			−0.825762
$563$	8.13888	−	14.0970i	0.343013	−	0.594116i	−0.641978	−	0.766723i	$-0.721886\pi$
$563$	8.13888	−	14.0970i	0.343013	−	0.594116i	0.984991	+	0.172607i	$0.0552191\pi$
$564$	16.8453	−	0.921949i	0.709315	−	0.0388211i
$565$	−34.1686	+	34.1686i	−1.43748	+	1.43748i
$566$	31.3837	+	8.40922i	1.31915	+	0.353466i
$567$	−17.4630	+	9.10259i	−0.733377	+	0.382273i
$568$	−5.61105	−	9.71863i	−0.235435	−	0.407785i
$569$	7.30234	+	12.6480i	0.306130	+	0.530233i	0.977512	−	0.210878i	$-0.0676324\pi$
$569$	7.30234	+	12.6480i	0.306130	+	0.530233i	−0.671382	+	0.741111i	$0.734299\pi$
$570$	5.82694	−	11.5018i	0.244064	−	0.481757i
$571$	17.7611	−	10.2544i	0.743278	−	0.429132i	−0.0799818	−	0.996796i	$-0.525486\pi$
$571$	17.7611	−	10.2544i	0.743278	−	0.429132i	0.823260	+	0.567664i	$0.192153\pi$
$572$	10.9975	−	10.3486i	0.459829	−	0.432698i
$573$	38.8734	−	12.7304i	1.62396	−	0.531818i
$574$	23.1367	+	6.19946i	0.965707	+	0.258760i
$575$	−66.3565	−	38.3109i	−2.76726	−	1.59768i
$576$	1.77458	+	2.41886i	0.0739408	+	0.100786i
$577$	−21.6621	+	21.6621i	−0.901806	+	0.901806i	−0.995592	−	0.0937859i	$-0.970103\pi$
$577$	−21.6621	+	21.6621i	−0.901806	+	0.901806i	0.0937859	+	0.995592i	$0.470103\pi$
$578$	−11.4070	−	11.4070i	−0.474467	−	0.474467i
$579$	12.3549	−	24.3874i	0.513454	−	1.01351i
$580$	7.37165	−	27.5114i	0.306091	−	1.14235i
$581$	10.6562	+	6.15238i	0.442095	+	0.255244i
$582$	−20.3615	+	22.7193i	−0.844011	+	0.941746i
$583$	−2.21349	+	8.26087i	−0.0916735	+	0.342130i
$584$	3.46929			0.143560
$585$	39.2010	−	13.9005i	1.62076	−	0.574715i
$586$	14.5410			0.600684
$587$	4.00670	−	14.9532i	0.165374	−	0.617186i	−0.832618	−	0.553848i	$-0.813159\pi$
$587$	4.00670	−	14.9532i	0.165374	−	0.617186i	0.997992	−	0.0633375i	$-0.0201745\pi$
$588$	−3.74970	−	0.787952i	−0.154635	−	0.0324946i
$589$	−2.15893	−	1.24646i	−0.0889571	−	0.0513594i
$590$	−6.27986	+	23.4368i	−0.258538	+	0.964876i
$591$	−17.8674	−	27.3744i	−0.734967	−	1.12603i
$592$	3.60969	+	3.60969i	0.148357	+	0.148357i
$593$	−15.6420	+	15.6420i	−0.642338	+	0.642338i	−0.951130	−	0.308791i	$-0.900075\pi$
$593$	−15.6420	+	15.6420i	−0.642338	+	0.642338i	0.308791	+	0.951130i	$0.400075\pi$
$594$	−19.8194	+	8.98966i	−0.813198	+	0.368850i
$595$	−6.78913	−	3.91970i	−0.278327	−	0.160692i
$596$	5.92462	+	1.58750i	0.242682	+	0.0650264i
$597$	−6.40692	−	5.74200i	−0.262218	−	0.235005i
$598$	27.0344	+	8.13187i	1.10552	+	0.332537i
$599$	23.9942	−	13.8531i	0.980378	−	0.566022i	0.0779938	−	0.996954i	$-0.475149\pi$
$599$	23.9942	−	13.8531i	0.980378	−	0.566022i	0.902384	+	0.430932i	$0.141815\pi$
$600$	9.26431	+	14.1937i	0.378214	+	0.579456i
$601$	−23.1556	−	40.1067i	−0.944536	−	1.63599i	−0.756677	−	0.653789i	$-0.773178\pi$
$601$	−23.1556	−	40.1067i	−0.944536	−	1.63599i	−0.187860	−	0.982196i	$-0.560155\pi$
$602$	2.15505	+	3.73265i	0.0878332	+	0.152132i
$603$	−1.52410	+	9.91998i	−0.0620663	+	0.403973i
$604$	3.82090	+	1.02381i	0.155470	+	0.0416581i
$605$	−17.7863	+	17.7863i	−0.723116	+	0.723116i
$606$	5.64022	+	8.64130i	0.229118	+	0.351029i
$607$	0.338183	−	0.585750i	0.0137264	−	0.0237749i	−0.859081	−	0.511840i	$-0.828964\pi$
$607$	0.338183	−	0.585750i	0.0137264	−	0.0237749i	0.872807	+	0.488065i	$0.162297\pi$
$608$	−1.93593			−0.0785124
$609$	−1.53410	−	28.0302i	−0.0621649	−	1.13584i
$610$	2.86734	+	1.65546i	0.116095	+	0.0670276i
$611$	−34.1826	+	8.05452i	−1.38288	+	0.325851i
$612$	−1.65343	−	2.25373i	−0.0668360	−	0.0911015i
$613$	6.69356	+	24.9807i	0.270351	+	1.00896i	0.958893	+	0.283766i	$0.0915840\pi$
$613$	6.69356	+	24.9807i	0.270351	+	1.00896i	−0.688543	+	0.725196i	$0.741749\pi$
$614$	7.35461	−	4.24619i	0.296808	−	0.171362i
$615$	54.2937	+	48.6590i	2.18933	+	1.96212i
$616$	8.85210	+	2.37191i	0.356661	+	0.0955671i
$617$	−22.4437	+	6.01378i	−0.903551	+	0.242106i	−0.680541	−	0.732710i	$-0.738255\pi$
$617$	−22.4437	+	6.01378i	−0.903551	+	0.242106i	−0.223010	+	0.974816i	$0.571588\pi$
$618$	5.26148	−	3.43420i	0.211648	−	0.138144i
$619$	10.1268	−	2.71346i	0.407029	−	0.109063i	−0.0494944	−	0.998774i	$-0.515761\pi$
$619$	10.1268	−	2.71346i	0.407029	−	0.109063i	0.456524	+	0.889711i	$0.349094\pi$
$620$	4.28816	−	2.47577i	0.172217	−	0.0994294i
$621$	−33.0803	−	23.6848i	−1.32747	−	0.950440i
$622$	−13.7896	+	3.69493i	−0.552915	+	0.148153i
$623$	−2.20935	+	3.82671i	−0.0885158	+	0.153314i
$624$	−4.52182	−	4.30734i	−0.181018	−	0.172432i
$625$	10.9169	+	18.9086i	0.436675	+	0.756343i
$626$	0.121191	+	0.121191i	0.00484375	+	0.00484375i
$627$	2.88804	−	13.7436i	0.115337	−	0.548867i
$628$			8.46805i			0.337912i
$629$	−3.36326	−	3.36326i	−0.134102	−	0.134102i
$630$	19.6896	+	15.7939i	0.784454	+	0.629244i
$631$	−6.92325	+	25.8379i	−0.275610	+	1.02859i	0.679821	+	0.733378i	$0.262057\pi$
$631$	−6.92325	+	25.8379i	−0.275610	+	1.02859i	−0.955431	+	0.295213i	$0.904609\pi$
$632$	3.30377	+	12.3298i	0.131417	+	0.490455i
$633$	−7.13874	−	21.7989i	−0.283739	−	0.866427i
$634$		−	19.8064i		−	0.786612i
$635$	−0.289349	+	0.289349i	−0.0114824	+	0.0114824i
$636$	3.46119	+	0.727326i	0.137245	+	0.0288403i
$637$	7.97243	+	0.242346i	0.315879	+	0.00960208i
$638$		−	31.0226i		−	1.22820i
$639$	−12.2104	−	31.3740i	−0.483035	−	1.24114i
$640$	1.92262	−	3.33007i	0.0759982	−	0.131633i
$641$	−16.2372			−0.641333			−0.320666	−	0.947192i	$-0.603907\pi$
$641$	−16.2372			−0.641333			−0.320666	+	0.947192i	$0.603907\pi$
$642$	6.86944	+	3.48014i	0.271115	+	0.137350i
$643$	−10.3251	−	38.5340i	−0.407184	−	1.51963i	−0.799992	−	0.600011i	$-0.795163\pi$
$643$	−10.3251	−	38.5340i	−0.407184	−	1.51963i	0.392808	−	0.919621i	$-0.371504\pi$
$644$	4.43424	+	16.5488i	0.174733	+	0.652114i
$645$	0.716936	+	13.0994i	0.0282293	+	0.515789i
$646$	1.80377			0.0709683
$647$	1.17726	−	2.03908i	0.0462830	−	0.0801645i	−0.841956	−	0.539546i	$-0.818596\pi$
$647$	1.17726	−	2.03908i	0.0462830	−	0.0801645i	0.888239	+	0.459382i	$0.151929\pi$
$648$	4.16003	+	7.98086i	0.163421	+	0.313518i
$649$			26.4280i			1.03739i
$650$	−24.1796	−	25.6957i	−0.948401	−	1.00787i
$651$	3.25716	−	3.63433i	0.127658	−	0.142441i
$652$	1.40015	−	1.40015i	0.0548342	−	0.0548342i
$653$			14.5700i			0.570170i	0.958502	+	0.285085i	$0.0920218\pi$
$653$			14.5700i			0.570170i	−0.958502	+	0.285085i	$0.907978\pi$
$654$	9.47722	−	10.5747i	0.370589	−	0.413502i
$655$	12.3211	+	45.9829i	0.481425	+	1.79670i
$656$	2.83325	−	10.5738i	0.110620	−	0.412838i
$657$	10.2872	+	1.58052i	0.401341	+	0.0616619i
$658$	−15.0703	−	15.0703i	−0.587501	−	0.587501i
$659$			4.43404i			0.172726i	0.996264	+	0.0863628i	$0.0275244\pi$
$659$			4.43404i			0.172726i	−0.996264	+	0.0863628i	$0.972476\pi$
$660$	20.7728	+	18.6170i	0.808579	+	0.724664i
$661$	14.8951	+	14.8951i	0.579353	+	0.579353i	0.934725	−	0.355372i	$-0.115646\pi$
$661$	14.8951	+	14.8951i	0.579353	+	0.579353i	−0.355372	+	0.934725i	$0.615646\pi$
$662$	−12.1652	−	21.0708i	−0.472816	−	0.818941i
$663$	4.21312	+	4.01328i	0.163624	+	0.155863i
$664$	2.81173	−	4.87006i	0.109116	−	0.188995i
$665$	−15.7335	+	4.21579i	−0.610120	+	0.163481i
$666$	9.05899	+	12.3479i	0.351029	+	0.478473i
$667$	50.2261	−	28.9981i	1.94476	−	1.12281i
$668$	−21.6497	+	5.80101i	−0.837651	+	0.224448i
$669$	0.769879	+	14.0668i	0.0297652	+	0.543852i
$670$	12.4258	−	3.32947i	0.480049	−	0.128629i
$671$	3.48339	+	0.933373i	0.134475	+	0.0360325i
$672$	0.779381	−	3.70891i	0.0300653	−	0.143074i
$673$	−28.4102	+	16.4026i	−1.09513	+	0.632274i	−0.934938	−	0.354811i	$-0.884545\pi$
$673$	−28.4102	+	16.4026i	−1.09513	+	0.632274i	−0.160193	+	0.987086i	$0.551212\pi$
$674$	−2.63517	−	9.83459i	−0.101503	−	0.378814i
$675$	21.0043	+	46.3079i	0.808457	+	1.78239i
$676$	10.8427	+	7.17183i	0.417028	+	0.275840i
$677$	19.6014	+	11.3169i	0.753344	+	0.434944i	0.826901	−	0.562347i	$-0.190102\pi$
$677$	19.6014	+	11.3169i	0.753344	+	0.434944i	−0.0735566	+	0.997291i	$0.523435\pi$
$678$	19.4165	+	9.83663i	0.745687	+	0.377774i
$679$	38.5414			1.47908
$680$	−1.79136	+	3.10273i	−0.0686957	+	0.118984i
$681$	8.25333	−	16.2912i	0.316268	−	0.624281i
$682$	3.81361	−	3.81361i	0.146031	−	0.146031i
$683$	−11.5934	−	3.10645i	−0.443611	−	0.118865i	0.0300976	−	0.999547i	$-0.490418\pi$
$683$	−11.5934	−	3.10645i	−0.443611	−	0.118865i	−0.473708	+	0.880682i	$0.657085\pi$
$684$	−5.74044	−	0.881959i	−0.219491	−	0.0337226i
$685$	−5.06417	−	8.77140i	−0.193492	−	0.335138i
$686$	10.0786	+	17.4567i	0.384804	+	0.666500i
$687$	25.2485	−	1.38186i	0.963290	−	0.0527212i
$688$	1.70588	−	0.984890i	0.0650360	−	0.0375486i
$689$	−7.35901	−	0.223699i	−0.280356	−	0.00852226i
$690$	−10.7240	+	51.0334i	−0.408256	+	1.94281i
$691$	21.3843	+	5.72991i	0.813498	+	0.217976i	0.641502	−	0.767121i	$-0.278312\pi$
$691$	21.3843	+	5.72991i	0.813498	+	0.217976i	0.171996	+	0.985098i	$0.444978\pi$
$692$	16.4934	+	9.52249i	0.626986	+	0.361991i
$693$	25.1677	+	11.0660i	0.956043	+	0.420363i
$694$	11.4031	−	11.4031i	0.432857	−	0.432857i
$695$	39.8545	+	39.8545i	1.51177	+	1.51177i
$696$	−12.8102	+	0.701108i	−0.485570	+	0.0265754i
$697$	−2.63983	+	9.85196i	−0.0999905	+	0.373170i
$698$	−25.4452	−	14.6908i	−0.963113	−	0.556054i
$699$	9.56998	+	29.2229i	0.361970	+	1.10531i
$700$	5.54197	−	20.6829i	0.209467	−	0.781741i
$701$	−26.8651			−1.01468			−0.507341	−	0.861746i	$-0.669371\pi$
$701$	−26.8651			−1.01468			−0.507341	+	0.861746i	$0.669371\pi$
$702$	−11.4458	−	14.8322i	−0.431994	−	0.559804i
$703$	−9.88267			−0.372732
$704$	1.08400	−	4.04555i	0.0408548	−	0.152472i
$705$	−20.1891	−	61.6495i	−0.760366	−	2.32185i
$706$	−18.4359	−	10.6440i	−0.693846	−	0.400592i
$707$	3.37402	−	12.5920i	0.126893	−	0.473571i
$708$	10.9129	−	0.597269i	0.410133	−	0.0224468i
$709$	−13.2082	−	13.2082i	−0.496046	−	0.496046i	0.414159	−	0.910205i	$-0.364076\pi$
$709$	−13.2082	−	13.2082i	−0.496046	−	0.496046i	−0.910205	+	0.414159i	$0.864076\pi$
$710$	−30.5128	+	30.5128i	−1.14513	+	1.14513i
$711$	4.17921	+	38.0656i	0.156733	+	1.42757i
$712$	1.74886	+	1.00971i	0.0655415	+	0.0378404i
$713$	9.73901	+	2.60956i	0.364729	+	0.0977288i
$714$	−0.726174	+	3.45571i	−0.0271764	+	0.129327i
$715$	−49.3820	−	30.5480i	−1.84678	−	1.14243i
$716$	−0.442894	+	0.255705i	−0.0165517	+	0.00955615i
$717$	−19.2926	+	1.05589i	−0.720497	+	0.0394331i
$718$	−8.38444	−	14.5223i	−0.312904	−	0.541966i
$719$	14.5977	+	25.2840i	0.544404	+	0.942936i	0.998644	+	0.0520563i	$0.0165775\pi$
$719$	14.5977	+	25.2840i	0.544404	+	0.942936i	−0.454240	+	0.890879i	$0.650089\pi$
$720$	7.21806	−	8.99846i	0.269001	−	0.335353i
$721$	−7.66697	−	2.05436i	−0.285533	−	0.0765083i
$722$	−10.7849	+	10.7849i	−0.401373	+	0.401373i
$723$	2.06755	−	4.08114i	0.0768930	−	0.151779i
$724$	−1.19108	+	2.06300i	−0.0442660	+	0.0766709i
$725$	−72.4843			−2.69200
$726$	10.1072	+	5.12042i	0.375113	+	0.190037i
$727$	−36.4712	−	21.0566i	−1.35264	−	0.780948i	−0.364022	−	0.931390i	$-0.618597\pi$
$727$	−36.4712	−	21.0566i	−1.35264	−	0.780948i	−0.988619	+	0.150443i	$0.951930\pi$
$728$	−0.239709	+	7.88570i	−0.00888422	+	0.292264i
$729$	8.69946	+	25.5601i	0.322202	+	0.946671i
$730$	−3.45271	−	12.8857i	−0.127791	−	0.476921i
$731$	−1.58942	+	0.917653i	−0.0587869	+	0.0339406i
$732$	0.306694	−	1.45950i	0.0113358	−	0.0539445i
$733$	37.5139	+	10.0518i	1.38561	+	0.371272i	0.873154	−	0.487444i	$-0.162071\pi$
$733$	37.5139	+	10.0518i	1.38561	+	0.371272i	0.512452	+	0.858716i	$0.328737\pi$
$734$	−9.39954	+	2.51860i	−0.346943	+	0.0929632i
$735$	0.805160	+	14.7114i	0.0296988	+	0.542638i
$736$	7.56306	−	2.02652i	0.278778	−	0.0746983i
$737$	12.1344	−	7.00582i	0.446978	−	0.258063i
$738$	13.2183	−	30.0628i	0.486573	−	1.10663i
$739$	−13.9922	+	3.74921i	−0.514713	+	0.137917i	−0.506820	−	0.862052i	$-0.669179\pi$
$739$	−13.9922	+	3.74921i	−0.514713	+	0.137917i	−0.00789285	+	0.999969i	$0.502512\pi$
$740$	9.81472	−	16.9996i	0.360796	−	0.624917i
$741$	12.0863	−	0.293601i	0.444002	−	0.0107857i
$742$	−2.23402	−	3.86944i	−0.0820135	−	0.142052i
$743$	9.43397	+	9.43397i	0.346099	+	0.346099i	0.858654	−	0.512555i	$-0.171301\pi$
$743$	9.43397	+	9.43397i	0.346099	+	0.346099i	−0.512555	+	0.858654i	$0.671301\pi$
$744$	−1.66094	−	1.48857i	−0.0608932	−	0.0545736i
$745$		−	23.5852i		−	0.864096i
$746$	16.7798	+	16.7798i	0.614351	+	0.614351i
$747$	10.5560	−	13.1598i	0.386225	−	0.481492i
$748$	−1.01000	+	3.76936i	−0.0369292	+	0.137822i
$749$	−2.51787	−	9.39684i	−0.0920011	−	0.343353i
$750$	21.2733	−	23.7367i	0.776791	−	0.866743i
$751$			30.5491i			1.11475i	0.830261	+	0.557375i	$0.188192\pi$
$751$			30.5491i			1.11475i	−0.830261	+	0.557375i	$0.811808\pi$
$752$	−6.88735	+	6.88735i	−0.251156	+	0.251156i
$753$	7.30621	−	8.15226i	0.266253	−	0.297085i
$754$	25.9946	−	6.12516i	0.946667	−	0.223065i
$755$		−	15.2106i		−	0.553569i
$756$	4.00071	−	10.6426i	0.145504	−	0.387069i
$757$	−22.0323	+	38.1611i	−0.800778	+	1.38699i	0.118326	+	0.992975i	$0.462247\pi$
$757$	−22.0323	+	38.1611i	−0.800778	+	1.38699i	−0.919105	+	0.394014i	$0.871086\pi$
$758$	−0.147027			−0.00534026
$759$	3.10404	+	56.7150i	0.112669	+	2.05863i
$760$	1.92668	+	7.19046i	0.0698880	+	0.260826i
$761$	5.95415	+	22.2212i	0.215838	+	0.805517i	0.985870	+	0.167512i	$0.0535734\pi$
$761$	5.95415	+	22.2212i	0.215838	+	0.805517i	−0.770032	+	0.638005i	$0.779760\pi$
$762$	0.164424	+	0.0832992i	0.00595646	+	0.00301761i
$763$	−17.9390			−0.649435
$764$	−11.8082	+	20.4524i	−0.427206	+	0.739943i
$765$	−6.72529	+	8.38415i	−0.243153	+	0.303130i
$766$			23.0510i			0.832867i
$767$	−22.1446	+	5.21798i	−0.799596	+	0.188410i
$768$	−1.69503	−	0.356189i	−0.0611642	−	0.0128529i
$769$	−25.7790	+	25.7790i	−0.929614	+	0.929614i	−0.997681	−

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.539047 + 1.64603i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.995221 + 3.71422i) q^{5} +(1.72946 - 0.0946541i) q^{6} +(-1.54723 - 1.54723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.41886 + 1.77458i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.539047 + 1.64603i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.995221 + 3.71422i) q^{5} +(1.72946 - 0.0946541i) q^{6} +(-1.54723 - 1.54723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.41886 + 1.77458i) q^{9} +(3.33007 + 1.92262i) q^{10} +(4.04555 + 1.08400i) q^{11} +(0.356189 - 1.69503i) q^{12} +(-0.109551 + 3.60389i) q^{13} +(-1.89496 + 1.09406i) q^{14} +(-6.65020 + 0.363968i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.465866 - 0.806903i) q^{17} +(1.08807 + 2.79573i) q^{18} +(-1.86997 - 0.501056i) q^{19} +(2.71899 - 2.71899i) q^{20} +(1.71276 - 3.38082i) q^{21} +(2.09413 - 3.62714i) q^{22} +7.82985 q^{23} +(-1.54509 - 0.782758i) q^{24} +(-8.47480 - 4.89293i) q^{25} +(3.45273 + 1.03857i) q^{26} +(-4.22489 - 3.02494i) q^{27} +(0.566325 + 2.11355i) q^{28} +(6.41469 - 3.70352i) q^{29} +(-1.36963 + 6.51780i) q^{30} +(1.24383 + 0.333283i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.396436 + 7.24344i) q^{33} +(-0.899984 + 0.241150i) q^{34} +(7.28657 - 4.20690i) q^{35} +(2.98208 - 0.327402i) q^{36} +(4.93092 - 1.32124i) q^{37} +(-0.967965 + 1.67657i) q^{38} +(-5.99117 + 1.76234i) q^{39} +(-1.92262 - 3.33007i) q^{40} +(-7.74058 - 7.74058i) q^{41} +(-2.82232 - 2.52942i) q^{42} -1.96978i q^{43} +(-2.96155 - 2.96155i) q^{44} +(-4.18387 - 10.7503i) q^{45} +(2.02652 - 7.56306i) q^{46} +(2.52095 + 9.40830i) q^{47} +(-1.15598 + 1.28985i) q^{48} -2.21217i q^{49} +(-6.91965 + 6.91965i) q^{50} +(1.07707 - 1.20179i) q^{51} +(1.89682 - 3.06628i) q^{52} +2.04197i q^{53} +(-4.01535 + 3.29802i) q^{54} +(-8.05243 + 13.9472i) q^{55} +2.18811 q^{56} +(-0.183244 - 3.34812i) q^{57} +(-1.91709 - 7.15466i) q^{58} +(1.63315 + 6.09501i) q^{59} +(5.94122 + 3.00989i) q^{60} +0.861044 q^{61} +(0.643854 - 1.11519i) q^{62} +(6.48820 + 0.996846i) q^{63} -1.00000i q^{64} +(-13.2766 - 3.99356i) q^{65} +(7.09923 + 1.49181i) q^{66} +(2.36560 - 2.36560i) q^{67} +0.931731i q^{68} +(4.22066 + 12.8882i) q^{69} +(-2.17765 - 8.12711i) q^{70} +(-2.90450 + 10.8397i) q^{71} +(0.455574 - 2.96521i) q^{72} +(-2.45316 - 2.45316i) q^{73} -5.10487i q^{74} +(3.48561 - 16.5873i) q^{75} +(1.36891 + 1.36891i) q^{76} +(-4.58218 - 7.93658i) q^{77} +(0.151659 + 6.24316i) q^{78} +(6.38240 - 11.0546i) q^{79} +(-3.71422 + 0.995221i) q^{80} +(2.70174 - 8.58491i) q^{81} +(-9.48023 + 5.47341i) q^{82} +(-5.43185 + 1.45546i) q^{83} +(-3.17370 + 2.07149i) q^{84} +(3.46065 - 0.927279i) q^{85} +(-1.90266 - 0.509817i) q^{86} +(9.55395 + 8.56243i) q^{87} +(-3.62714 + 2.09413i) q^{88} +(-0.522663 - 1.95060i) q^{89} +(-11.4668 + 1.25894i) q^{90} +(5.74553 - 5.40653i) q^{91} +(-6.78085 - 3.91493i) q^{92} +(0.121887 + 2.22704i) q^{93} +9.74019 q^{94} +(3.72206 - 6.44679i) q^{95} +(0.946704 + 1.45043i) q^{96} +(-12.4550 + 12.4550i) q^{97} +(-2.13680 - 0.572553i) q^{98} +(-11.7092 + 4.55710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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