LMFDB - Embedded newform 234.2.y.a.11.1

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			11.1
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.69503 - 0.356189i) q^{3} -1.00000i q^{4} +(-3.71422 - 0.995221i) q^{5} +(1.45043 - 0.946704i) q^{6} +(2.11355 + 0.566325i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.74626 + 1.20750i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.69503 - 0.356189i) q^{3} -1.00000i q^{4} +(-3.71422 - 0.995221i) q^{5} +(1.45043 - 0.946704i) q^{6} +(2.11355 + 0.566325i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.74626 + 1.20750i) q^{9} +(3.33007 - 1.92262i) q^{10} +(2.96155 + 2.96155i) q^{11} +(-0.356189 + 1.69503i) q^{12} +(3.17583 + 1.70707i) q^{13} +(-1.89496 + 1.09406i) q^{14} +(5.94122 + 3.00989i) q^{15} -1.00000 q^{16} +(0.465866 - 0.806903i) q^{17} +(-2.79573 + 1.08807i) q^{18} +(-1.86997 + 0.501056i) q^{19} +(-0.995221 + 3.71422i) q^{20} +(-3.38082 - 1.71276i) q^{21} -4.18826 q^{22} +(3.91493 - 6.78085i) q^{23} +(-0.946704 - 1.45043i) 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} +7.40705i q^{29} +(-6.32939 + 2.07276i) q^{30} +(-0.333283 + 1.24383i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.96504 - 6.07478i) q^{33} +(0.241150 + 0.899984i) q^{34} +(-7.28657 - 4.20690i) q^{35} +(1.20750 - 2.74626i) q^{36} +(4.93092 + 1.32124i) q^{37} +(0.967965 - 1.67657i) q^{38} +(-4.77510 - 4.02473i) q^{39} +(-1.92262 - 3.33007i) q^{40} +(2.83325 + 10.5738i) q^{41} +(3.60170 - 1.17949i) q^{42} +(1.70588 - 0.984890i) q^{43} +(2.96155 - 2.96155i) q^{44} +(-8.99846 - 7.21806i) q^{45} +(2.02652 + 7.56306i) q^{46} +(9.40830 - 2.52095i) q^{47} +(1.69503 + 0.356189i) q^{48} +(-1.91580 - 1.10609i) q^{49} +(-9.45241 + 2.53277i) q^{50} +(-1.07707 + 1.20179i) q^{51} +(1.70707 - 3.17583i) q^{52} +2.04197i q^{53} +(5.12641 - 0.848495i) q^{54} +(-8.05243 - 13.9472i) q^{55} +(1.09406 + 1.89496i) q^{56} +(3.34812 - 0.183244i) q^{57} +(-5.23757 - 5.23757i) q^{58} +(-4.46186 - 4.46186i) q^{59} +(3.00989 - 5.94122i) q^{60} +(-0.430522 - 0.745686i) q^{61} +(-0.643854 - 1.11519i) q^{62} +(5.12052 + 4.10739i) q^{63} +1.00000i q^{64} +(-10.0968 - 9.50108i) q^{65} +(7.09923 + 1.49181i) q^{66} +(-3.23147 + 0.865869i) q^{67} +(-0.806903 - 0.465866i) q^{68} +(-9.05119 + 10.0993i) q^{69} +(8.12711 - 2.17765i) q^{70} +(2.90450 + 10.8397i) q^{71} +(1.08807 + 2.79573i) q^{72} +(-2.45316 + 2.45316i) q^{73} +(-4.42095 + 2.55243i) q^{74} +(-12.6222 - 11.3123i) q^{75} +(0.501056 + 1.86997i) q^{76} +(4.58218 + 7.93658i) q^{77} +(6.22242 - 0.530587i) q^{78} +(6.38240 - 11.0546i) q^{79} +(3.71422 + 0.995221i) q^{80} +(6.08388 + 6.63223i) q^{81} +(-9.48023 - 5.47341i) q^{82} +(-1.45546 - 5.43185i) q^{83} +(-1.71276 + 3.38082i) q^{84} +(-2.53337 + 2.53337i) q^{85} +(-0.509817 + 1.90266i) q^{86} +(2.63831 - 12.5552i) q^{87} +4.18826i 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} +(1.00796 - 1.98962i) q^{93} +(-4.87009 + 8.43525i) q^{94} +7.44412 q^{95} +(-1.45043 + 0.946704i) q^{96} +(-4.55884 + 17.0138i) q^{97} +(2.13680 - 0.572553i) q^{98} +(4.55710 + 11.7092i) 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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.69503	−	0.356189i	−0.978626	−	0.205646i
$3$	−1.69503	−	0.356189i	−0.978626	−	0.205646i
$4$		−	1.00000i		−	0.500000i
$5$	−3.71422	−	0.995221i	−1.66105	−	0.445076i	−0.698372	−	0.715735i	$-0.746092\pi$
$5$	−3.71422	−	0.995221i	−1.66105	−	0.445076i	−0.962675	+	0.270659i	$0.912759\pi$
$6$	1.45043	−	0.946704i	0.592136	−	0.386490i
$7$	2.11355	+	0.566325i	0.798848	+	0.214051i	0.635078	−	0.772448i	$-0.280968\pi$
$7$	2.11355	+	0.566325i	0.798848	+	0.214051i	0.163770	+	0.986499i	$0.447635\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.74626	+	1.20750i	0.915420	+	0.402501i
$10$	3.33007	−	1.92262i	1.05306	−	0.607986i
$11$	2.96155	+	2.96155i	0.892940	+	0.892940i	0.994799	−	0.101859i	$-0.0324791\pi$
$11$	2.96155	+	2.96155i	0.892940	+	0.892940i	−0.101859	+	0.994799i	$0.532479\pi$
$12$	−0.356189	+	1.69503i	−0.102823	+	0.489313i
$13$	3.17583	+	1.70707i	0.880818	+	0.473456i
$13$	3.17583	+	1.70707i	0.880818	+	0.473456i
$14$	−1.89496	+	1.09406i	−0.506449	+	0.292399i
$15$	5.94122	+	3.00989i	1.53402	+	0.777151i
$16$	−1.00000			−0.250000
$17$	0.465866	−	0.806903i	0.112989	−	0.195703i	−0.803985	−	0.594649i	$-0.797291\pi$
$17$	0.465866	−	0.806903i	0.112989	−	0.195703i	0.916974	+	0.398947i	$0.130624\pi$
$18$	−2.79573	+	1.08807i	−0.658960	+	0.256459i
$19$	−1.86997	+	0.501056i	−0.429000	+	0.114950i	−0.466857	−	0.884333i	$-0.654614\pi$
$19$	−1.86997	+	0.501056i	−0.429000	+	0.114950i	0.0378569	+	0.999283i	$0.487947\pi$
$20$	−0.995221	+	3.71422i	−0.222538	+	0.830524i
$21$	−3.38082	−	1.71276i	−0.737755	−	0.373755i
$22$	−4.18826			−0.892940
$23$	3.91493	−	6.78085i	0.816319	−	1.41391i	−0.0920584	−	0.995754i	$-0.529345\pi$
$23$	3.91493	−	6.78085i	0.816319	−	1.41391i	0.908377	−	0.418152i	$-0.137322\pi$
$24$	−0.946704	−	1.45043i	−0.193245	−	0.296068i
$25$	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
$29$			7.40705i			1.37545i	0.725969	+	0.687727i	$0.241391\pi$
$29$			7.40705i			1.37545i	−0.725969	+	0.687727i	$0.758609\pi$
$30$	−6.32939	+	2.07276i	−1.15558	+	0.378433i
$31$	−0.333283	+	1.24383i	−0.0598595	+	0.223399i	−0.989375	−	0.145383i	$-0.953558\pi$
$31$	−0.333283	+	1.24383i	−0.0598595	+	0.223399i	0.929516	+	0.368782i	$0.120225\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.96504	−	6.07478i	−0.690225	−	1.05748i
$34$	0.241150	+	0.899984i	0.0413569	+	0.154346i
$35$	−7.28657	−	4.20690i	−1.23165	−	0.711096i
$36$	1.20750	−	2.74626i	0.201250	−	0.457710i
$37$	4.93092	+	1.32124i	0.810639	+	0.217210i	0.640250	−	0.768167i	$-0.278831\pi$
$37$	4.93092	+	1.32124i	0.810639	+	0.217210i	0.170389	+	0.985377i	$0.445498\pi$
$38$	0.967965	−	1.67657i	0.157025	−	0.271975i
$39$	−4.77510	−	4.02473i	−0.764627	−	0.644473i
$40$	−1.92262	−	3.33007i	−0.303993	−	0.526531i
$41$	2.83325	+	10.5738i	0.442479	+	1.65135i	0.722508	+	0.691362i	$0.242989\pi$
$41$	2.83325	+	10.5738i	0.442479	+	1.65135i	−0.280029	+	0.959991i	$0.590344\pi$
$42$	3.60170	−	1.17949i	0.555755	−	0.182000i
$43$	1.70588	−	0.984890i	0.260144	−	0.150194i	−0.364256	−	0.931299i	$-0.618677\pi$
$43$	1.70588	−	0.984890i	0.260144	−	0.150194i	0.624400	+	0.781104i	$0.285343\pi$
$44$	2.96155	−	2.96155i	0.446470	−	0.446470i
$45$	−8.99846	−	7.21806i	−1.34141	−	1.07600i
$46$	2.02652	+	7.56306i	0.298793	+	1.11511i
$47$	9.40830	−	2.52095i	1.37234	−	0.367718i	0.504008	−	0.863699i	$-0.331858\pi$
$47$	9.40830	−	2.52095i	1.37234	−	0.367718i	0.868333	+	0.495981i	$0.165191\pi$
$48$	1.69503	+	0.356189i	0.244657	+	0.0514114i
$49$	−1.91580	−	1.10609i	−0.273686	−	0.158012i
$50$	−9.45241	+	2.53277i	−1.33677	+	0.358187i
$51$	−1.07707	+	1.20179i	−0.150820	+	0.168284i
$52$	1.70707	−	3.17583i	0.236728	−	0.440409i
$53$			2.04197i			0.280486i	0.990117	+	0.140243i	$0.0447883\pi$
$53$			2.04197i			0.280486i	−0.990117	+	0.140243i	$0.955212\pi$
$54$	5.12641	−	0.848495i	0.697616	−	0.115466i
$55$	−8.05243	−	13.9472i	−1.08579	−	1.88064i
$56$	1.09406	+	1.89496i	0.146199	+	0.253225i
$57$	3.34812	−	0.183244i	0.443469	−	0.0242712i
$58$	−5.23757	−	5.23757i	−0.687727	−	0.687727i
$59$	−4.46186	−	4.46186i	−0.580884	−	0.580884i	0.354262	−	0.935146i	$-0.384732\pi$
$59$	−4.46186	−	4.46186i	−0.580884	−	0.580884i	−0.935146	+	0.354262i	$0.884732\pi$
$60$	3.00989	−	5.94122i	0.388575	−	0.767009i
$61$	−0.430522	−	0.745686i	−0.0551227	−	0.0954753i	0.837147	−	0.546977i	$-0.184222\pi$
$61$	−0.430522	−	0.745686i	−0.0551227	−	0.0954753i	−0.892270	+	0.451502i	$0.850888\pi$
$62$	−0.643854	−	1.11519i	−0.0817696	−	0.141629i
$63$	5.12052	+	4.10739i	0.645125	+	0.517483i
$64$			1.00000i			0.125000i
$65$	−10.0968	−	9.50108i	−1.25236	−	1.17846i
$66$	7.09923	+	1.49181i	0.873854	+	0.183629i
$67$	−3.23147	+	0.865869i	−0.394786	+	0.105783i	−0.450750	−	0.892650i	$-0.648843\pi$
$67$	−3.23147	+	0.865869i	−0.394786	+	0.105783i	0.0559639	+	0.998433i	$0.482177\pi$
$68$	−0.806903	−	0.465866i	−0.0978514	−	0.0564945i
$69$	−9.05119	+	10.0993i	−1.08963	+	1.21581i
$70$	8.12711	−	2.17765i	0.971376	−	0.260279i
$71$	2.90450	+	10.8397i	0.344700	+	1.28644i	0.892962	+	0.450132i	$0.148623\pi$
$71$	2.90450	+	10.8397i	0.344700	+	1.28644i	−0.548262	+	0.836307i	$0.684710\pi$
$72$	1.08807	+	2.79573i	0.128230	+	0.329480i
$73$	−2.45316	+	2.45316i	−0.287121	+	0.287121i	−0.835941	−	0.548820i	$-0.815077\pi$
$73$	−2.45316	+	2.45316i	−0.287121	+	0.287121i	0.548820	+	0.835941i	$0.315077\pi$
$74$	−4.42095	+	2.55243i	−0.513925	+	0.296714i
$75$	−12.6222	−	11.3123i	−1.45749	−	1.30623i
$76$	0.501056	+	1.86997i	0.0574750	+	0.214500i
$77$	4.58218	+	7.93658i	0.522188	+	0.904457i
$78$	6.22242	−	0.530587i	0.704550	−	0.0600771i
$79$	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
$81$	6.08388	+	6.63223i	0.675986	+	0.736914i
$82$	−9.48023	−	5.47341i	−1.04692	−	0.604437i
$83$	−1.45546	−	5.43185i	−0.159757	−	0.596223i	−0.998651	−	0.0519272i	$-0.983464\pi$
$83$	−1.45546	−	5.43185i	−0.159757	−	0.596223i	0.838893	−	0.544296i	$-0.183203\pi$
$84$	−1.71276	+	3.38082i	−0.186878	+	0.368877i
$85$	−2.53337	+	2.53337i	−0.274783	+	0.274783i
$86$	−0.509817	+	1.90266i	−0.0549749	+	0.205169i
$87$	2.63831	−	12.5552i	0.282856	−	1.34606i
$88$			4.18826i			0.446470i
$89$	0.522663	−	1.95060i	0.0554022	−	0.206764i	−0.932676	−	0.360714i	$-0.882533\pi$
$89$	0.522663	−	1.95060i	0.0554022	−	0.206764i	0.988079	+	0.153951i	$0.0491996\pi$
$90$	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
$93$	1.00796	−	1.98962i	0.104521	−	0.206314i
$94$	−4.87009	+	8.43525i	−0.502312	+	0.870030i
$95$	7.44412			0.763750
$96$	−1.45043	+	0.946704i	−0.148034	+	0.0966226i
$97$	−4.55884	+	17.0138i	−0.462880	+	1.72749i	0.200945	+	0.979603i	$0.435599\pi$
$97$	−4.55884	+	17.0138i	−0.462880	+	1.72749i	−0.663825	+	0.747888i	$0.731068\pi$
$98$	2.13680	−	0.572553i	0.215849	−	0.0578366i
$99$	4.55710	+	11.7092i	0.458005	+	1.17682i
$100$	4.89293	−	8.47480i	0.489293	−	0.847480i
$101$	5.95775			0.592818			0.296409	−	0.955061i	$-0.404211\pi$
$101$	5.95775			0.592818			0.296409	+	0.955061i	$0.404211\pi$
$102$	−0.0881922	−	1.61139i	−0.00873233	−	0.159552i
$103$	−3.14153	+	1.81377i	−0.309544	+	0.178716i	−0.646723	−	0.762725i	$-0.723861\pi$
$103$	−3.14153	+	1.81377i	−0.309544	+	0.178716i	0.337178	+	0.941441i	$0.390528\pi$
$104$	1.03857	+	3.45273i	0.101840	+	0.338568i
$105$	10.8525	+	9.72622i	1.05910	+	0.949182i
$106$	−1.44389	−	1.44389i	−0.140243	−	0.140243i
$107$	−3.85034	+	2.22300i	−0.372227	+	0.214905i	−0.674431	−	0.738338i	$-0.735611\pi$
$107$	−3.85034	+	2.22300i	−0.372227	+	0.214905i	0.302204	+	0.953243i	$0.402278\pi$
$108$	−3.02494	+	4.22489i	−0.291075	+	0.406541i
$109$	5.79714	+	5.79714i	0.555266	+	0.555266i	0.927956	−	0.372690i	$-0.121565\pi$
$109$	5.79714	+	5.79714i	0.555266	+	0.555266i	−0.372690	+	0.927956i	$0.621565\pi$
$110$	15.5561	+	4.16824i	1.48322	+	0.397426i
$111$	−7.88746	−	3.99588i	−0.748644	−	0.379272i
$112$	−2.11355	−	0.566325i	−0.199712	−	0.0535126i
$113$		−	12.5666i		−	1.18217i	−0.806610	−	0.591084i	$-0.798700\pi$
$113$		−	12.5666i		−	1.18217i	0.806610	−	0.591084i	$-0.201300\pi$
$114$	−2.23791	+	2.49705i	−0.209599	+	0.233870i
$115$	−21.2893	+	21.2893i	−1.98524	+	1.98524i
$116$	7.40705			0.687727
$117$	6.66037	+	8.52288i	0.615751	+	0.787941i
$118$	6.31002			0.580884
$119$	1.44160	−	1.44160i	0.132151	−	0.132151i
$120$	2.07276	+	6.32939i	0.189217	+	0.577792i
$121$			6.54150i			0.594682i
$122$	0.831705	+	0.222855i	0.0752990	+	0.0201763i
$123$	−1.03616	−	18.9321i	−0.0934276	−	1.70705i
$124$	1.24383	+	0.333283i	0.111699	+	0.0299297i
$125$	−13.0127	−	13.0127i	−1.16389	−	1.16389i
$126$	−6.52512	+	0.716391i	−0.581304	+	0.0638211i
$127$	0.0921603	−	0.0532087i	0.00817790	−	0.00472151i	−0.495905	−	0.868377i	$-0.665164\pi$
$127$	0.0921603	−	0.0532087i	0.00817790	−	0.00472151i	0.504083	+	0.863655i	$0.331830\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−3.24232	+	1.06180i	−0.285471	+	0.0934866i
$130$	13.8578	−	0.421249i	1.21541	−	0.0369460i
$131$	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	$0.151442\pi$
$132$	−6.07478	+	3.96504i	−0.528742	+	0.345113i
$133$	−4.23603			−0.367310
$134$	1.67273	−	2.89725i	0.144502	−	0.250284i
$135$	12.6817	+	15.4400i	1.09147	+	1.32886i
$136$	0.899984	−	0.241150i	0.0771729	−	0.0206784i
$137$	0.681728	−	2.54424i	0.0582439	−	0.217369i	−0.930670	−	0.365860i	$-0.880775\pi$
$137$	0.681728	−	2.54424i	0.0582439	−	0.217369i	0.988914	+	0.148491i	$0.0474415\pi$
$138$	−0.741128	−	13.5414i	−0.0630890	−	1.15272i
$139$	−14.6578			−1.24326			−0.621629	−	0.783312i	$-0.713529\pi$
$139$	−14.6578			−1.24326			−0.621629	+	0.783312i	$0.713529\pi$
$140$	−4.20690	+	7.28657i	−0.355548	+	0.615827i
$141$	−16.8453	+	0.921949i	−1.41863	+	0.0776421i
$142$	−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
$146$		−	3.46929i		−	0.287121i
$147$	2.85336	+	2.55724i	0.235341	+	0.210917i
$148$	1.32124	−	4.93092i	0.108605	−	0.405320i
$149$	−4.33712	+	4.33712i	−0.355311	+	0.355311i	−0.862081	−	0.506770i	$-0.830839\pi$
$149$	−4.33712	+	4.33712i	−0.355311	+	0.355311i	0.506770	+	0.862081i	$0.330839\pi$
$150$	16.9243	−	0.926272i	1.38186	−	0.0756298i
$151$	1.02381	+	3.82090i	0.0833163	+	0.310941i	0.994990	−	0.0999742i	$-0.0318760\pi$
$151$	1.02381	+	3.82090i	0.0833163	+	0.310941i	−0.911674	+	0.410915i	$0.865209\pi$
$152$	−1.67657	−	0.967965i	−0.135987	−	0.0785124i
$153$	2.25373	−	1.65343i	0.182203	−	0.133672i
$154$	−8.85210	−	2.37191i	−0.713323	−	0.191134i
$155$	2.47577	−	4.28816i	0.198859	−	0.344434i
$156$	−4.02473	+	4.77510i	−0.322236	+	0.382314i
$157$	−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	$0.943054\pi$
$158$	3.30377	+	12.3298i	0.262834	+	0.980910i
$159$	0.727326	−	3.46119i	0.0576807	−	0.274491i
$160$	−3.33007	+	1.92262i	−0.263265	+	0.151996i
$161$	12.1146	−	12.1146i	0.954761	−	0.954761i
$162$	−8.99164	−	0.387745i	−0.706450	−	0.0304641i
$163$	−0.512492	−	1.91264i	−0.0401414	−	0.149810i	0.942946	−	0.332945i	$-0.108042\pi$
$163$	−0.512492	−	1.91264i	−0.0401414	−	0.149810i	−0.983088	+	0.183135i	$0.941376\pi$
$164$	10.5738	−	2.83325i	0.825677	−	0.221239i
$165$	8.68127	+	26.5091i	0.675836	+	2.06373i
$166$	4.87006	+	2.81173i	0.377990	+	0.218233i
$167$	21.6497	−	5.80101i	1.67530	−	0.448896i	0.708770	−	0.705440i	$-0.249250\pi$
$167$	21.6497	−	5.80101i	1.67530	−	0.448896i	0.966533	+	0.256544i	$0.0825838\pi$
$168$	−1.17949	−	3.60170i	−0.0909999	−	0.277878i
$169$	7.17183	+	10.8427i	0.551679	+	0.834056i
$170$		−	3.58273i		−	0.274783i
$171$	−5.74044	−	0.881959i	−0.438982	−	0.0674451i
$172$	−0.984890	−	1.70588i	−0.0750971	−	0.130072i
$173$	−9.52249	−	16.4934i	−0.723981	−	1.25397i	−0.959392	−	0.282076i	$-0.908977\pi$
$173$	−9.52249	−	16.4934i	−0.723981	−	1.25397i	0.235411	−	0.971896i	$-0.424356\pi$
$174$	7.01228	+	10.7434i	0.531600	+	0.814456i
$175$	15.1409	+	15.1409i	1.14455	+	1.14455i
$176$	−2.96155	−	2.96155i	−0.223235	−	0.223235i
$177$	5.97372	+	9.15225i	0.449012	+	0.687925i
$178$	1.00971	+	1.74886i	0.0756808	+	0.131083i
$179$	−0.255705	−	0.442894i	−0.0191123	−	0.0331035i	0.856311	−	0.516460i	$-0.172751\pi$
$179$	−0.255705	−	0.442894i	−0.0191123	−	0.0331035i	−0.875423	+	0.483357i	$0.839417\pi$
$180$	−7.21806	+	8.99846i	−0.538002	+	0.670706i
$181$			2.38215i			0.177064i	0.996073	+	0.0885319i	$0.0282175\pi$
$181$			2.38215i			0.177064i	−0.996073	+	0.0885319i	$0.971782\pi$
$182$	−7.88570	+	0.239709i	−0.584527	+	0.0177684i
$183$	0.464143	+	1.41731i	0.0343104	+	0.104770i
$184$	7.56306	−	2.02652i	0.557556	−	0.149397i
$185$	−16.9996	−	9.81472i	−1.24983	−	0.721592i
$186$	0.694135	+	2.11961i	0.0508965	+	0.155418i
$187$	3.76936	−	1.01000i	0.275643	−	0.0738584i
$188$	−2.52095	−	9.40830i	−0.183859	−	0.686171i
$189$	−7.21644	−	8.78603i	−0.524918	−	0.639090i
$190$	−5.26379	+	5.26379i	−0.381875	+	0.381875i
$191$	−20.4524	+	11.8082i	−1.47989	+	0.854412i	−0.999741	−	0.0227772i	$-0.992749\pi$
$191$	−20.4524	+	11.8082i	−1.47989	+	0.854412i	−0.480145	+	0.877189i	$0.659416\pi$
$192$	0.356189	−	1.69503i	0.0257057	−	0.122328i
$193$	−4.08516	−	15.2460i	−0.294056	−	1.09743i	−0.941964	−	0.335714i	$-0.891022\pi$
$193$	−4.08516	−	15.2460i	−0.294056	−	1.09743i	0.647908	−	0.761719i	$-0.275644\pi$
$194$	−8.80700	−	15.2542i	−0.632306	−	1.09519i
$195$	13.7302	+	19.7010i	0.983242	+	1.41082i
$196$	−1.10609	+	1.91580i	−0.0790062	+	0.136843i
$197$	18.2302	+	4.88476i	1.29885	+	0.348025i	0.841014	−	0.541014i	$-0.181959\pi$
$197$	18.2302	+	4.88476i	1.29885	+	0.348025i	0.457833	+	0.889038i	$0.348626\pi$
$198$	−11.5020	−	5.05733i	−0.817414	−	0.359409i
$199$	−4.30172	−	2.48360i	−0.304941	−	0.176058i	0.339719	−	0.940527i	$-0.389668\pi$
$199$	−4.30172	−	2.48360i	−0.304941	−	0.176058i	−0.644660	+	0.764469i	$0.723001\pi$
$200$	2.53277	+	9.45241i	0.179094	+	0.668387i
$201$	5.78585	−	0.316662i	0.408102	−	0.0223356i
$202$	−4.21276	+	4.21276i	−0.296409	+	0.296409i
$203$	−4.19479	+	15.6552i	−0.294417	+	1.09878i
$204$	1.20179	+	1.07707i	0.0841421	+	0.0754098i
$205$		−	42.0932i		−	2.93991i
$206$	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
$210$	−14.5514	+	0.796401i	−1.00414	+	0.0549569i
$211$	6.62163	−	11.4690i	0.455852	−	0.789559i	−0.542885	−	0.839807i	$-0.682668\pi$
$211$	6.62163	−	11.4690i	0.455852	−	0.789559i	0.998737	+	0.0502484i	$0.0160013\pi$
$212$	2.04197			0.140243
$213$	−1.06222	−	19.4082i	−0.0727820	−	1.32983i
$214$	1.15071	−	4.29450i	0.0786607	−	0.293566i
$215$	−7.31619	+	1.96037i	−0.498960	+	0.133696i
$216$	−0.848495	−	5.12641i	−0.0577328	−	0.348808i
$217$	−1.40882	+	2.44015i	−0.0956372	+	0.165648i
$218$	−8.19840			−0.555266
$219$	5.03197	−	3.28439i	0.340029	−	0.221939i
$220$	−13.9472	+	8.05243i	−0.940321	+	0.542894i
$221$	2.85695	−	1.76732i	0.192179	−	0.118883i
$222$	8.40279	−	2.75176i	0.563958	−	0.184686i
$223$	−5.75133	−	5.75133i	−0.385137	−	0.385137i	0.487812	−	0.872949i	$-0.337795\pi$
$223$	−5.75133	−	5.75133i	−0.385137	−	0.385137i	−0.872949	+	0.487812i	$0.837795\pi$
$224$	1.89496	−	1.09406i	0.126612	−	0.0730996i
$225$	17.3658	+	23.6706i	1.15772	+	1.57804i
$226$	8.88595	+	8.88595i	0.591084	+	0.591084i
$227$	−10.1846	−	2.72896i	−0.675977	−	0.181128i	−0.0955315	−	0.995426i	$-0.530455\pi$
$227$	−10.1846	−	2.72896i	−0.675977	−	0.181128i	−0.580446	+	0.814299i	$0.697122\pi$
$228$	−0.183244	−	3.34812i	−0.0121356	−	0.221735i
$229$	−14.1016	−	3.77851i	−0.931859	−	0.249691i	−0.239212	−	0.970967i	$-0.576889\pi$
$229$	−14.1016	−	3.77851i	−0.931859	−	0.249691i	−0.692647	+	0.721276i	$0.743556\pi$
$230$		−	30.1077i		−	1.98524i
$231$	−4.94002	−	15.0849i	−0.325030	−	0.992511i
$232$	−5.23757	+	5.23757i	−0.343864	+	0.343864i
$233$	−17.7535			−1.16307			−0.581536	−	0.813521i	$-0.697548\pi$
$233$	−17.7535			−1.16307			−0.581536	+	0.813521i	$0.697548\pi$
$234$	−10.7362	−	1.31700i	−0.701846	−	0.0860947i
$235$	−37.4533			−2.44319
$236$	−4.46186	+	4.46186i	−0.290442	+	0.290442i
$237$	−14.7559	+	16.4646i	−0.958498	+	1.06949i
$238$			2.03873i			0.132151i
$239$	−10.7752	−	2.88720i	−0.696988	−	0.186757i	−0.107107	−	0.994247i	$-0.534159\pi$
$239$	−10.7752	−	2.88720i	−0.696988	−	0.186757i	−0.589881	+	0.807490i	$0.700825\pi$
$240$	−5.94122	−	3.00989i	−0.383504	−	0.194288i
$241$	2.55136	+	0.683636i	0.164348	+	0.0440368i	0.340055	−	0.940406i	$-0.389554\pi$
$241$	2.55136	+	0.683636i	0.164348	+	0.0440368i	−0.175707	+	0.984443i	$0.556221\pi$
$242$	−4.62554	−	4.62554i	−0.297341	−	0.297341i
$243$	−7.95003	−	13.4088i	−0.509995	−	0.860178i
$244$	−0.745686	+	0.430522i	−0.0477377	+	0.0275614i
$245$	6.01489	+	6.01489i	0.384277	+	0.384277i
$246$	14.1197	+	12.6544i	0.900240	+	0.806812i
$247$	−6.79404	−	1.60089i	−0.432294	−	0.101862i
$248$	−1.11519	+	0.643854i	−0.0708145	+	0.0408848i
$249$	0.532284	+	9.72557i	0.0337321	+	0.616333i
$250$	18.4028			1.16389
$251$	3.16017	−	5.47357i	0.199468	−	0.345489i	−0.748888	−	0.662697i	$-0.769412\pi$
$251$	3.16017	−	5.47357i	0.199468	−	0.345489i	0.948356	+	0.317208i	$0.102745\pi$
$252$	4.10739	−	5.12052i	0.258741	−	0.322563i
$253$	31.6760	−	8.48757i	1.99146	−	0.533609i
$254$	−0.0275429	+	0.102791i	−0.00172819	+	0.00644971i
$255$	5.19650	−	3.39179i	0.325418	−	0.212402i
$256$	1.00000			0.0625000
$257$	0.511580	−	0.886083i	0.0319115	−	0.0552723i	−0.849629	−	0.527382i	$-0.823174\pi$
$257$	0.511580	−	0.886083i	0.0319115	−	0.0552723i	0.881540	+	0.472109i	$0.156507\pi$
$258$	1.54186	−	3.04348i	0.0959921	−	0.189479i
$259$	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
$263$		−	11.6474i		−	0.718209i	−0.933297	−	0.359105i	$-0.883082\pi$
$263$		−	11.6474i		−	0.718209i	0.933297	−	0.359105i	$-0.116918\pi$
$264$	1.49181	−	7.09923i	0.0918146	−	0.436927i
$265$	2.03221	−	7.58430i	0.124837	−	0.465900i
$266$	2.99533	−	2.99533i	0.183655	−	0.183655i
$267$	−1.58071	+	3.12017i	−0.0967381	+	0.190951i
$268$	0.865869	+	3.23147i	0.0528913	+	0.197393i
$269$	24.3789	+	14.0752i	1.48641	+	0.858178i	0.999880	−	0.0154875i	$-0.00493003\pi$
$269$	24.3789	+	14.0752i	1.48641	+	0.858178i	0.486527	+	0.873665i	$0.338263\pi$
$270$	−19.8850	−	1.95042i	−1.21016	−	0.118699i
$271$	1.95393	+	0.523554i	0.118693	+	0.0318037i	0.317677	−	0.948199i	$-0.397097\pi$
$271$	1.95393	+	0.523554i	0.118693	+	0.0318037i	−0.198984	+	0.980003i	$0.563764\pi$
$272$	−0.465866	+	0.806903i	−0.0282473	+	0.0489257i
$273$	−7.81311	−	11.2107i	−0.472871	−	0.678504i
$274$	1.31700	+	2.28111i	0.0795627	+	0.137807i
$275$	10.6079	+	39.5891i	0.639679	+	2.38732i
$276$	10.0993	+	9.05119i	0.607906	+	0.544817i
$277$	−13.6892	+	7.90346i	−0.822504	+	0.474873i	−0.851279	−	0.524713i	$-0.824173\pi$
$277$	−13.6892	+	7.90346i	−0.822504	+	0.474873i	0.0287755	+	0.999586i	$0.490839\pi$
$278$	10.3646	−	10.3646i	0.621629	−	0.621629i
$279$	−2.41721	+	3.01344i	−0.144715	+	0.180410i
$280$	−2.17765	−	8.12711i	−0.130140	−	0.485688i
$281$	−18.9089	+	5.06663i	−1.12801	+	0.302250i	−0.774122	−	0.633037i	$-0.781808\pi$
$281$	−18.9089	+	5.06663i	−1.12801	+	0.302250i	−0.353891	+	0.935287i	$0.615142\pi$
$282$	11.2595	−	12.5633i	0.670494	−	0.748136i
$283$	28.1378	+	16.2454i	1.67262	+	0.965687i	0.966164	+	0.257930i	$0.0830403\pi$
$283$	28.1378	+	16.2454i	1.67262	+	0.965687i	0.706456	+	0.707757i	$0.250293\pi$
$284$	10.8397	−	2.90450i	0.643219	−	0.172350i
$285$	−12.6180	−	2.65151i	−0.747426	−	0.157062i
$286$	−13.3012	−	7.14965i	−0.786517	−	0.422767i
$287$			23.9529i			1.41389i
$288$	2.79573	−	1.08807i	0.164740	−	0.0641148i
$289$	8.06594	+	13.9706i	0.474467	+	0.821801i
$290$	14.2409	+	24.6660i	0.836256	+	1.44844i
$291$	13.7875	−	27.2151i	0.808238	−	1.59538i
$292$	2.45316	+	2.45316i	0.143560	+	0.143560i
$293$	−10.2821	−	10.2821i	−0.600684	−	0.600684i	0.339810	−	0.940494i	$-0.389637\pi$
$293$	−10.2821	−	10.2821i	−0.600684	−	0.600684i	−0.940494	+	0.339810i	$0.889637\pi$
$294$	−3.82587	+	0.209391i	−0.223129	+	0.0122120i
$295$	12.1318	+	21.0128i	0.706338	+	1.22341i
$296$	2.55243	+	4.42095i	0.148357	+	0.256962i
$297$	−3.55372	−	21.4707i	−0.206208	−	1.24586i
$298$		−	6.13362i		−	0.355311i
$299$	24.0085	−	14.8518i	1.38845	−	0.858902i
$300$	−11.3123	+	12.6222i	−0.653116	+	0.728746i
$301$	4.16323	−	1.11553i	0.239965	−	0.0642983i
$302$	−3.42573	−	1.97784i	−0.197128	−	0.113812i
$303$	−10.0986	−	2.12208i	−0.580147	−	0.121911i
$304$	1.86997	−	0.501056i	0.107250	−	0.0287375i
$305$	0.856929	+	3.19810i	0.0490676	+	0.183123i
$306$	−0.424472	+	2.76278i	−0.0242655	+	0.157937i
$307$	6.00502	−	6.00502i	0.342724	−	0.342724i	−0.514666	−	0.857391i	$-0.672084\pi$
$307$	6.00502	−	6.00502i	0.342724	−	0.342724i	0.857391	+	0.514666i	$0.172084\pi$
$308$	7.93658	−	4.58218i	0.452228	−	0.261094i
$309$	5.97104	−	1.95541i	0.339681	−	0.111239i
$310$	1.28155	+	4.78283i	0.0727874	+	0.271646i
$311$	7.13805	+	12.3635i	0.404762	+	0.701068i	0.994294	−	0.106677i	$-0.0340212\pi$
$311$	7.13805	+	12.3635i	0.404762	+	0.701068i	−0.589532	+	0.807745i	$0.700688\pi$
$312$	−0.530587	−	6.22242i	−0.0300386	−	0.352275i
$313$	−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
$315$	−14.9310	−	20.3518i	−0.841264	−	1.14669i
$316$	−11.0546	−	6.38240i	−0.621872	−	0.359038i
$317$	5.12627	+	19.1315i	0.287920	+	1.07453i	0.946679	+	0.322178i	$0.104415\pi$
$317$	5.12627	+	19.1315i	0.287920	+	1.07453i	−0.658759	+	0.752354i	$0.728918\pi$
$318$	1.93314	+	2.96173i	0.108405	+	0.166086i
$319$	−21.9363	+	21.9363i	−1.22820	+	1.22820i
$320$	0.995221	−	3.71422i	0.0556345	−	0.207631i
$321$	7.31826	−	2.39660i	0.408465	−	0.133765i
$322$			17.1326i			0.954761i
$323$	−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
$327$	−7.76146	−	11.8912i	−0.429210	−	0.657586i
$328$	−5.47341	+	9.48023i	−0.302219	+	0.523458i
$329$	21.3126			1.17500
$330$	−24.8834	−	12.6062i	−1.36978	−	0.693949i
$331$	6.29719	−	23.5014i	0.346125	−	1.29176i	−0.545167	−	0.838327i	$-0.683534\pi$
$331$	6.29719	−	23.5014i	0.346125	−	1.29176i	0.891292	−	0.453429i	$-0.149799\pi$
$332$	−5.43185	+	1.45546i	−0.298111	+	0.0798787i
$333$	11.9462	+	9.58256i	0.654648	+	0.525121i
$334$	−11.2067	+	19.4106i	−0.613203	+	1.06210i
$335$	12.8641			0.702840
$336$	3.38082	+	1.71276i	0.184439	+	0.0934388i
$337$	−8.81745	+	5.09076i	−0.480317	+	0.277311i	−0.720549	−	0.693404i	$-0.756110\pi$
$337$	−8.81745	+	5.09076i	−0.480317	+	0.277311i	0.240232	+	0.970716i	$0.422777\pi$
$338$	−12.7382	−	2.59572i	−0.692868	−	0.141189i
$339$	−4.47609	+	21.3008i	−0.243108	+	1.15690i
$340$	2.53337	+	2.53337i	0.137391	+	0.137391i
$341$	−4.67070	+	2.69663i	−0.252932	+	0.146031i
$342$	4.68274	−	3.43546i	0.253214	−	0.185768i
$343$	−14.2533	−	14.2533i	−0.769607	−	0.769607i
$344$	1.90266	+	0.509817i	0.102585	+	0.0274875i
$345$	43.6691	−	28.5030i	2.35106	−	1.53455i
$346$	18.3960	+	4.92920i	0.988977	+	0.264996i
$347$		−	16.1265i		−	0.865715i	−0.901462	−	0.432857i	$-0.857505\pi$
$347$		−	16.1265i		−	0.865715i	0.901462	−	0.432857i	$-0.142495\pi$
$348$	−12.5552	−	2.63831i	−0.673028	−	0.141428i
$349$	20.7759	−	20.7759i	1.11211	−	1.11211i	0.119243	−	0.992865i	$-0.461953\pi$
$349$	20.7759	−	20.7759i	1.11211	−	1.11211i	0.992865	−	0.119243i	$-0.0380466\pi$
$350$	−21.4125			−1.14455
$351$	−8.25377	−	16.8189i	−0.440554	−	0.897726i
$352$	4.18826			0.223235
$353$	−15.0529	+	15.0529i	−0.801184	+	0.801184i	−0.983281	−	0.182096i	$-0.941712\pi$
$353$	−15.0529	+	15.0529i	−0.801184	+	0.801184i	0.182096	+	0.983281i	$0.441712\pi$
$354$	−10.6957	−	2.24756i	−0.568469	−	0.119456i
$355$		−	43.1517i		−	2.29025i
$356$	−1.95060	−	0.522663i	−0.103382	−	0.0277011i
$357$	−2.95704	+	1.93008i	−0.156503	+	0.102150i
$358$	0.493984	+	0.132363i	0.0261079	+	0.00699558i
$359$	−11.8574	−	11.8574i	−0.625809	−	0.625809i	0.321202	−	0.947011i	$-0.395913\pi$
$359$	−11.8574	−	11.8574i	−0.625809	−	0.625809i	−0.947011	+	0.321202i	$0.895913\pi$
$360$	−1.25894	−	11.4668i	−0.0663518	−	0.604354i
$361$	−13.2088	+	7.62609i	−0.695198	+	0.401373i
$362$	−1.68443	−	1.68443i	−0.0885319	−	0.0885319i
$363$	2.33001	−	11.0881i	0.122294	−	0.581972i
$364$	5.40653	−	5.74553i	0.283379	−	0.301148i
$365$	11.5530	−	6.67013i	0.604712	−	0.349131i
$366$	−1.33039	−	0.673990i	−0.0695404	−	0.0352300i
$367$	9.73112			0.507960			0.253980	−	0.967209i	$-0.418260\pi$
$367$	9.73112			0.507960			0.253980	+	0.967209i	$0.418260\pi$
$368$	−3.91493	+	6.78085i	−0.204080	+	0.353476i
$369$	−4.98709	+	32.4596i	−0.259617	+	1.68978i
$370$	18.9606	−	5.08047i	0.985714	−	0.264121i
$371$	−1.15642	+	4.31580i	−0.0600381	+	0.224065i
$372$	−1.98962	−	1.00796i	−0.103157	−	0.0522605i
$373$	23.7302			1.22870			0.614351	−	0.789032i	$-0.289418\pi$
$373$	23.7302			1.22870			0.614351	+	0.789032i	$0.289418\pi$
$374$	−1.95117	+	3.37952i	−0.100892	+	0.174751i
$375$	17.4220	+	26.6920i	0.899667	+	1.37837i
$376$	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	−0.966896	−	0.255170i	$-0.917869\pi$
$379$	−0.0380534	+	0.142017i	−0.00195467	+	0.00729493i	0.964942	+	0.262465i	$0.0845353\pi$
$380$		−	7.44412i		−	0.381875i
$381$	−0.175167	+	0.0573640i	−0.00897407	+	0.00293885i
$382$	6.11238	−	22.8117i	0.312737	−	1.16715i
$383$	−16.2995	+	16.2995i	−0.832867	+	0.832867i	−0.987908	−	0.155041i	$-0.950449\pi$
$383$	−16.2995	+	16.2995i	−0.832867	+	0.832867i	0.155041	+	0.987908i	$0.450449\pi$
$384$	0.946704	+	1.45043i	0.0483113	+	0.0740170i
$385$	−9.12057	−	34.0384i	−0.464827	−	1.73476i
$386$	13.6692	+	7.89192i	0.695744	+	0.401688i
$387$	5.87404	−	0.644909i	0.298594	−	0.0327826i
$388$	17.0138	+	4.55884i	0.863745	+	0.231440i
$389$	16.4933	−	28.5672i	0.836243	−	1.44841i	−0.0567717	−	0.998387i	$-0.518081\pi$
$389$	16.4933	−	28.5672i	0.836243	−	1.44841i	0.893015	−	0.450028i	$-0.148586\pi$
$390$	−23.6394	−	4.22197i	−1.19703	−	0.213788i
$391$	−3.64766	−	6.31793i	−0.184470	−	0.319512i
$392$	−0.572553	−	2.13680i	−0.0289183	−	0.107925i
$393$	−20.3783	+	6.67353i	−1.02795	+	0.336635i
$394$	−16.3447	+	9.43664i	−0.823436	+	0.475411i
$395$	−34.7074	+	34.7074i	−1.74632	+	1.74632i
$396$	11.7092	−	4.55710i	0.588412	−	0.229003i
$397$	5.53019	+	20.6390i	0.277552	+	1.03584i	0.954112	+	0.299451i	$0.0968037\pi$
$397$	5.53019	+	20.6390i	0.277552	+	1.03584i	−0.676559	+	0.736388i	$0.736530\pi$
$398$	4.79795	−	1.28561i	0.240499	−	0.0644416i
$399$	7.18020	+	1.50883i	0.359460	+	0.0755358i
$400$	−8.47480	−	4.89293i	−0.423740	−	0.244646i
$401$	−26.3984	+	7.07343i	−1.31827	+	0.353230i	−0.848331	−	0.529467i	$-0.822392\pi$
$401$	−26.3984	+	7.07343i	−1.31827	+	0.353230i	−0.469943	+	0.882697i	$0.655725\pi$
$402$	−3.86730	+	4.31512i	−0.192883	+	0.215219i
$403$	−3.18176	+	3.38126i	−0.158495	+	0.168433i
$404$		−	5.95775i		−	0.296409i
$405$	−15.9963	−	30.6883i	−0.794862	−	1.52492i
$406$	−8.10372	−	14.0361i	−0.402181	−	0.696598i
$407$	10.6903	+	18.5161i	0.529896	+	0.917807i
$408$	−1.61139	+	0.0881922i	−0.0797759	+	0.00436617i
$409$	−12.3294	−	12.3294i	−0.609648	−	0.609648i	0.333206	−	0.942854i	$-0.391869\pi$
$409$	−12.3294	−	12.3294i	−0.609648	−	0.609648i	−0.942854	+	0.333206i	$0.891869\pi$
$410$	29.7644	+	29.7644i	1.46996	+	1.46996i
$411$	−2.06178	+	4.06975i	−0.101700	+	0.200746i
$412$	1.81377	+	3.14153i	0.0893578	+	0.154772i
$413$	−6.90351	−	11.9572i	−0.339699	−	0.588377i
$414$	−3.56708	+	23.2171i	−0.175312	+	1.14106i
$415$			21.6236i			1.06146i
$416$	3.45273	−	1.03857i	0.169284	−	0.0509202i
$417$	24.8454	+	5.22094i	1.21669	+	0.255671i
$418$	7.83190	−	2.09855i	0.383071	−	0.102643i
$419$	17.0583	+	9.84862i	0.833353	+	0.481137i	0.854999	−	0.518629i	$-0.173557\pi$
$419$	17.0583	+	9.84862i	0.833353	+	0.481137i	−0.0216462	+	0.999766i	$0.506891\pi$
$420$	9.72622	−	10.8525i	0.474591	−	0.529548i
$421$	−4.34449	+	1.16410i	−0.211737	+	0.0567348i	−0.363128	−	0.931739i	$-0.618291\pi$
$421$	−4.34449	+	1.16410i	−0.211737	+	0.0567348i	0.151391	+	0.988474i	$0.451625\pi$
$422$	3.42761	+	12.7920i	0.166853	+	0.622705i
$423$	28.8817	+	4.43737i	1.40428	+	0.215753i
$424$	−1.44389	+	1.44389i	−0.0701214	+	0.0701214i
$425$	7.89624	−	4.55890i	0.383024	−	0.221139i
$426$	14.4748	+	12.9726i	0.701306	+	0.628524i
$427$	−0.487630	−	1.81986i	−0.0235981	−	0.0880693i
$428$	2.22300	+	3.85034i	0.107453	+	0.186113i
$429$	−2.22223	−	26.0611i	−0.107291	−	1.25824i
$430$	3.78714	−	6.55951i	0.182632	−	0.316328i
$431$	−0.579994	−	0.155409i	−0.0279373	−	0.00748579i	0.244823	−	0.969568i	$-0.421270\pi$
$431$	−0.579994	−	0.155409i	−0.0279373	−	0.00748579i	−0.272761	+	0.962082i	$0.587937\pi$
$432$	4.22489	+	3.02494i	0.203270	+	0.145538i
$433$	−7.94515	−	4.58713i	−0.381819	−	0.220444i	0.296790	−	0.954943i	$-0.404084\pi$
$433$	−7.94515	−	4.58713i	−0.381819	−	0.220444i	−0.678610	+	0.734499i	$0.737417\pi$
$434$	−0.729261	−	2.72164i	−0.0350056	−	0.130643i
$435$	−22.2944	+	44.0069i	−1.06894	+	2.10997i
$436$	5.79714	−	5.79714i	0.277633	−	0.277633i
$437$	−3.92319	+	14.6416i	−0.187672	+	0.700401i
$438$	−1.23572	+	5.88056i	−0.0590452	+	0.280984i
$439$		−	15.4681i		−	0.738252i	−0.929379	−	0.369126i	$-0.879657\pi$
$439$		−	15.4681i		−	0.738252i	0.929379	−	0.369126i	$-0.120343\pi$
$440$	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	$0.804400\pi$
$444$	−3.99588	+	7.88746i	−0.189636	+	0.374322i
$445$	−3.88257	+	6.72480i	−0.184051	+	0.318786i
$446$	8.13360			0.385137
$447$	8.89639	−	5.80672i	0.420785	−	0.274649i
$448$	−0.566325	+	2.11355i	−0.0267563	+	0.0998559i
$449$	−17.1746	+	4.60193i	−0.810521	+	0.217178i	−0.640198	−	0.768210i	$-0.721148\pi$
$449$	−17.1746	+	4.60193i	−0.810521	+	0.217178i	−0.170323	+	0.985388i	$0.554481\pi$
$450$	−29.0171	−	4.45818i	−1.36788	−	0.210161i
$451$	−22.9241	+	39.7056i	−1.07945	+	1.86967i
$452$	−12.5666			−0.591084
$453$	−0.374422	−	6.84122i	−0.0175919	−	0.321428i
$454$	9.13129	−	5.27195i	0.428552	−	0.247425i
$455$	−15.9594	−	25.7991i	−0.748191	−	1.20948i
$456$	2.49705	+	2.23791i	0.116935	+	0.104800i
$457$	−18.5795	−	18.5795i	−0.869111	−	0.869111i	0.123263	−	0.992374i	$-0.460664\pi$
$457$	−18.5795	−	18.5795i	−0.869111	−	0.869111i	−0.992374	+	0.123263i	$0.960664\pi$
$458$	12.6431	−	7.29952i	0.590775	−	0.341084i
$459$	−4.40907	+	1.99986i	−0.205798	+	0.0933457i
$460$	21.2893	+	21.2893i	0.992620	+	0.992620i
$461$	−35.3774	−	9.47934i	−1.64769	−	0.441497i	−0.688725	−	0.725023i	$-0.741829\pi$
$461$	−35.3774	−	9.47934i	−1.64769	−	0.441497i	−0.958965	+	0.283526i	$0.908496\pi$
$462$	14.1597	+	7.17349i	0.658770	+	0.333741i
$463$	27.7142	+	7.42600i	1.28799	+	0.345115i	0.836896	−	0.547362i	$-0.184368\pi$
$463$	27.7142	+	7.42600i	1.28799	+	0.345115i	0.451092	+	0.892477i	$0.351035\pi$
$464$		−	7.40705i		−	0.343864i
$465$	−5.72391	+	6.38673i	−0.265440	+	0.296177i
$466$	12.5536	−	12.5536i	0.581536	−	0.581536i
$467$	−30.1627			−1.39576			−0.697881	−	0.716214i	$-0.745874\pi$
$467$	−30.1627			−1.39576			−0.697881	+	0.716214i	$0.745874\pi$
$468$	8.52288	−	6.66037i	0.393970	−	0.307876i
$469$	−7.32023			−0.338017
$470$	26.4835	−	26.4835i	1.22159	−	1.22159i
$471$	4.56468	+	13.9387i	0.210329	+	0.642262i
$472$		−	6.31002i		−	0.290442i
$473$	7.96884	+	2.13524i	0.366407	+	0.0981786i
$474$	−1.20824	−	22.0762i	−0.0554963	−	1.01399i
$475$	−18.2992	−	4.90326i	−0.839626	−	0.224977i
$476$	−1.44160	−	1.44160i	−0.0660757	−	0.0660757i
$477$	−2.46568	+	5.60777i	−0.112896	+	0.256762i
$478$	9.66076	−	5.57764i	0.441873	−	0.255115i
$479$	8.40895	+	8.40895i	0.384215	+	0.384215i	0.872618	−	0.488403i	$-0.162420\pi$
$479$	8.40895	+	8.40895i	0.384215	+	0.384215i	−0.488403	+	0.872618i	$0.662420\pi$
$480$	6.32939	−	2.07276i	0.288896	−	0.0946083i
$481$	13.4043	+	12.6135i	0.611186	+	0.575124i
$482$	−2.28749	+	1.32068i	−0.104192	+	0.0601554i
$483$	−24.8496	+	16.2195i	−1.13070	+	0.738012i
$484$	6.54150			0.297341
$485$	33.8650	−	58.6559i	1.53773	−	2.66343i
$486$	15.1030	+	3.85996i	0.685086	+	0.175091i
$487$	20.6057	−	5.52129i	0.933735	−	0.250194i	0.240288	−	0.970702i	$-0.422758\pi$
$487$	20.6057	−	5.52129i	0.933735	−	0.250194i	0.693447	+	0.720508i	$0.256091\pi$
$488$	0.222855	−	0.831705i	0.0100882	−	0.0376495i
$489$	0.187426	+	3.42453i	0.00847570	+	0.154863i
$490$	−8.50634			−0.384277
$491$	−9.99582	+	17.3133i	−0.451105	+	0.781337i	−0.998455	−	0.0555669i	$-0.982303\pi$
$491$	−9.99582	+	17.3133i	−0.451105	+	0.781337i	0.547350	+	0.836904i	$0.315637\pi$
$492$	−18.9321	+	1.03616i	−0.853526	+	0.0467138i
$493$	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
$497$			24.5552i			1.10145i
$498$	−7.25340	−	6.50063i	−0.325033	−	0.291300i
$499$	−0.0739605	+	0.276024i	−0.00331093	+	0.0123565i	−0.967562	−	0.252635i	$-0.918703\pi$
$499$	−0.0739605	+	0.276024i	−0.00331093	+	0.0123565i	0.964251	+	0.264992i	$0.0853693\pi$
$500$	−13.0127	+	13.0127i	−0.581947	+	0.581947i
$501$	−38.7631	+	2.12152i	−1.73181	+	0.0947826i
$502$	1.63582	+	6.10498i	0.0730104	+	0.272478i
$503$	−6.95762	−	4.01698i	−0.310225	−	0.179108i	0.336802	−	0.941575i	$-0.390655\pi$
$503$	−6.95762	−	4.01698i	−0.310225	−	0.179108i	−0.647027	+	0.762467i	$0.723988\pi$
$504$	0.716391	+	6.52512i	0.0319106	+	0.290652i
$505$	−22.1284	−	5.92927i	−0.984699	−	0.263849i
$506$	−16.3967	+	28.4000i	−0.728923	+	1.26253i
$507$	−8.29441	−	20.9333i	−0.368368	−	0.929680i
$508$	−0.0532087	−	0.0921603i	−0.00236076	−	0.00408895i
$509$	−7.97104	−	29.7483i	−0.353310	−	1.31857i	−0.882598	−	0.470129i	$-0.844208\pi$
$509$	−7.97104	−	29.7483i	−0.353310	−	1.31857i	0.529288	−	0.848442i	$-0.322459\pi$
$510$	−1.27613	+	6.07284i	−0.0565079	+	0.268910i
$511$	−6.57417	+	3.79560i	−0.290824	+	0.167907i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	9.41607	+	3.53963i	0.415730	+	0.156278i
$514$	0.264813	+	0.988297i	0.0116804	+	0.0435919i
$515$	13.4734	−	3.61019i	0.593710	−	0.159084i
$516$	1.06180	+	3.24232i	0.0467433	+	0.142735i
$517$	35.3290	+	20.3972i	1.55377	+	0.897068i
$518$	−10.7894	+	2.89101i	−0.474059	+	0.127024i
$519$	10.2661	+	31.3487i	0.450633	+	1.37605i
$520$	−0.421249	−	13.8578i	−0.0184730	−	0.607705i
$521$		−	5.90138i		−	0.258544i	−0.991609	−	0.129272i	$-0.958736\pi$
$521$		−	5.90138i		−	0.258544i	0.991609	−	0.129272i	$-0.0412640\pi$
$522$	−8.05935	−	20.7081i	−0.352748	−	0.906370i
$523$	5.66854	+	9.81820i	0.247868	+	0.429320i	0.962934	−	0.269737i	$-0.0869368\pi$
$523$	5.66854	+	9.81820i	0.247868	+	0.429320i	−0.715066	+	0.699057i	$0.753603\pi$
$524$	−6.19013	−	10.7216i	−0.270417	−	0.468376i
$525$	−20.2713	−	31.0574i	−0.884714	−	1.35546i
$526$	8.23595	+	8.23595i	0.359105	+	0.359105i
$527$	0.848386	+	0.848386i	0.0369563	+	0.0369563i
$528$	3.96504	+	6.07478i	0.172556	+	0.264371i
$529$	−19.1533	−	33.1745i	−0.832752	−	1.44237i
$530$	3.92592	+	6.79990i	0.170531	+	0.295369i
$531$	−6.86571	−	17.6411i	−0.297946	−	0.765559i
$532$			4.23603i			0.183655i
$533$	−9.05233	+	38.4172i	−0.392100	+	1.66404i
$534$	−1.08856	−	3.32403i	−0.0471066	−	0.143845i
$535$	16.5134	−	4.42474i	0.713935	−	0.191298i
$536$	−2.89725	−	1.67273i	−0.125142	−	0.0722509i
$537$	0.275674	+	0.841798i	0.0118962	+	0.0363263i
$538$	−27.1911	+	7.28584i	−1.17229	+	0.314115i
$539$	−2.39800	−	8.94945i	−0.103289	−	0.385480i
$540$	15.4400	−	12.6817i	0.664431	−	0.545733i
$541$	1.72650	−	1.72650i	0.0742279	−	0.0742279i	−0.669018	−	0.743246i	$-0.733285\pi$
$541$	1.72650	−	1.72650i	0.0742279	−	0.0742279i	0.743246	+	0.669018i	$0.233285\pi$
$542$	−1.75185	+	1.01143i	−0.0752483	+	0.0434446i
$543$	0.848496	−	4.03782i	0.0364124	−	0.173279i
$544$	−0.241150	−	0.899984i	−0.0103392	−	0.0385865i
$545$	−15.7624	−	27.3013i	−0.675187	−	1.16946i
$546$	13.4519	+	2.40248i	0.575688	+	0.102817i
$547$	−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
$549$	−0.281907	−	2.56770i	−0.0120315	−	0.109587i
$550$	−35.4947	−	20.4929i	−1.51350	−	0.873818i
$551$	−3.71134	−	13.8509i	−0.158109	−	0.590069i
$552$	−13.5414	+	0.741128i	−0.576362	+	0.0315445i
$553$	19.7500	−	19.7500i	0.839857	−	0.839857i
$554$	4.09113	−	15.2683i	0.173815	−	0.648688i
$555$	25.3189	+	22.6913i	1.07473	+	0.963193i
$556$			14.6578i			0.621629i
$557$	5.72596	−	21.3696i	0.242617	−	0.905457i	−0.731950	−	0.681359i	$-0.761389\pi$
$557$	5.72596	−	21.3696i	0.242617	−	0.905457i	0.974566	−	0.224099i	$-0.0719439\pi$
$558$	−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
$561$	−6.74894	+	0.369372i	−0.284940	+	0.0155949i
$562$	9.78798	−	16.9533i	0.412881	−	0.715131i
$563$	16.2778			0.686026			0.343013	−	0.939331i	$-0.388552\pi$
$563$	16.2778			0.686026			0.343013	+	0.939331i	$0.388552\pi$
$564$	0.921949	+	16.8453i	0.0388211	+	0.709315i
$565$	−12.5066	+	46.6752i	−0.526155	+	1.96364i
$566$	−31.3837	+	8.40922i	−1.31915	+	0.353466i
$567$	9.10259	+	17.4630i	0.382273	+	0.733377i
$568$	−5.61105	+	9.71863i	−0.235435	+	0.407785i
$569$	14.6047			0.612260			0.306130	−	0.951990i	$-0.400966\pi$
$569$	14.6047			0.612260			0.306130	+	0.951990i	$0.400966\pi$
$570$	10.7972	−	7.04738i	0.452244	−	0.295182i
$571$	−17.7611	+	10.2544i	−0.743278	+	0.429132i	−0.823260	−	0.567664i	$-0.807847\pi$
$571$	−17.7611	+	10.2544i	−0.743278	+	0.429132i	0.0799818	+	0.996796i	$0.474514\pi$
$572$	14.4609	−	4.34981i	0.604642	−	0.181875i
$573$	38.8734	−	12.7304i	1.62396	−	0.531818i
$574$	−16.9372	−	16.9372i	−0.706946	−	0.706946i
$575$	66.3565	−	38.3109i	2.76726	−	1.59768i
$576$	−1.20750	+	2.74626i	−0.0503126	+	0.114427i
$577$	−21.6621	−	21.6621i	−0.901806	−	0.901806i	0.0937859	−	0.995592i	$-0.470103\pi$
$577$	−21.6621	−	21.6621i	−0.901806	−	0.901806i	−0.995592	+	0.0937859i	$0.970103\pi$
$578$	−15.5822	−	4.17524i	−0.648134	−	0.173667i
$579$	1.49401	+	27.2976i	0.0620888	+	1.13445i
$580$	−27.5114	−	7.37165i	−1.14235	−	0.306091i
$581$		−	12.3048i		−	0.510487i
$582$	9.49477	+	28.9932i	0.393571	+	1.20181i
$583$	−6.04737	+	6.04737i	−0.250457	+	0.250457i
$584$	−3.46929			−0.143560
$585$	−16.2559	−	38.2844i	−0.672098	−	1.58286i
$586$	14.5410			0.600684
$587$	−10.9465	+	10.9465i	−0.451811	+	0.451811i	−0.895955	−	0.444144i	$-0.853508\pi$
$587$	−10.9465	+	10.9465i	−0.451811	+	0.451811i	0.444144	+	0.895955i	$0.353508\pi$
$588$	2.55724	−	2.85336i	0.105459	−	0.117671i
$589$		−	2.49291i		−	0.102719i
$590$	−23.4368	−	6.27986i	−0.964876	−	0.258538i
$591$	−29.1608	−	14.7732i	−1.19952	−	0.607689i
$592$	−4.93092	−	1.32124i	−0.202660	−	0.0543025i
$593$	15.6420	+	15.6420i	0.642338	+	0.642338i	0.951130	−	0.308791i	$-0.0999245\pi$
$593$	15.6420	+	15.6420i	0.642338	+	0.642338i	−0.308791	+	0.951130i	$0.599925\pi$
$594$	17.6949	+	12.6692i	0.726032	+	0.519825i
$595$	−6.78913	+	3.91970i	−0.278327	+	0.160692i
$596$	4.33712	+	4.33712i	0.177655	+	0.177655i
$597$	6.40692	+	5.74200i	0.262218	+	0.235005i
$598$	−6.47479	+	27.4784i	−0.264774	+	1.12368i
$599$	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	$0.141815\pi$
$600$	−0.926272	−	16.9243i	−0.0378149	−	0.690931i
$601$	46.3112			1.88907			0.944536	−	0.328407i	$-0.106512\pi$
$601$	46.3112			1.88907			0.944536	+	0.328407i	$0.106512\pi$
$602$	−2.15505	+	3.73265i	−0.0878332	+	0.152132i
$603$	−9.91998	−	1.52410i	−0.403973	−	0.0620663i
$604$	3.82090	−	1.02381i	0.155470	−	0.0416581i
$605$	6.51024	−	24.2966i	0.264679	−	0.987795i
$606$	8.64130	−	5.64022i	0.351029	−	0.229118i
$607$	−0.676366			−0.0274528			−0.0137264	−	0.999906i	$-0.504369\pi$
$607$	−0.676366			−0.0274528			−0.0137264	+	0.999906i	$0.504369\pi$
$608$	−0.967965	+	1.67657i	−0.0392562	+	0.0679937i
$609$	12.6865	−	25.0419i	0.514083	−	1.01475i
$610$	−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	−0.688543	−	0.725196i	$-0.741749\pi$
$613$	6.69356	−	24.9807i	0.270351	−	1.00896i	0.958893	−	0.283766i	$-0.0915840\pi$
$614$			8.49238i			0.342724i
$615$	−14.9931	+	71.3492i	−0.604581	+	2.87708i
$616$	−2.37191	+	8.85210i	−0.0955671	+	0.356661i
$617$	−16.4300	+	16.4300i	−0.661445	+	0.661445i	−0.955721	−	0.294275i	$-0.904922\pi$
$617$	−16.4300	+	16.4300i	−0.661445	+	0.661445i	0.294275	+	0.955721i	$0.404922\pi$
$618$	−2.83948	+	5.60484i	−0.114221	+	0.225460i
$619$	−2.71346	−	10.1268i	−0.109063	−	0.407029i	0.889711	−	0.456524i	$-0.150906\pi$
$619$	−2.71346	−	10.1268i	−0.109063	−	0.407029i	−0.998774	+	0.0494944i	$0.984239\pi$
$620$	−4.28816	−	2.47577i	−0.172217	−	0.0994294i
$621$	−37.0518	+	16.8060i	−1.48684	+	0.674400i
$622$	−13.7896	−	3.69493i	−0.552915	−	0.148153i
$623$	2.20935	−	3.82671i	0.0885158	−	0.153314i
$624$	4.77510	+	4.02473i	0.191157	+	0.161118i
$625$	10.9169	+	18.9086i	0.436675	+	0.756343i
$626$	−0.0443588	−	0.165549i	−0.00177293	−	0.00661668i
$627$	10.4583	+	9.37292i	0.417664	+	0.374319i
$628$	−7.33355	+	4.23403i	−0.292640	+	0.168956i
$629$	3.36326	−	3.36326i	0.134102	−	0.134102i
$630$	24.9487	+	3.83311i	0.993979	+	0.152715i
$631$	−6.92325	−	25.8379i	−0.275610	−	1.02859i	−0.955431	−	0.295213i	$-0.904609\pi$
$631$	−6.92325	−	25.8379i	−0.275610	−	1.02859i	0.679821	−	0.733378i	$-0.262057\pi$
$632$	12.3298	−	3.30377i	0.490455	−	0.131417i
$633$	−15.3090	+	17.0818i	−0.608478	+	0.678939i
$634$	−17.1528	−	9.90320i	−0.681226	−	0.393306i
$635$	−0.395257	+	0.105909i	−0.0156853	+	0.00420287i
$636$	−3.46119	−	0.727326i	−0.137245	−	0.0288403i
$637$	−4.19609	−	6.78315i	−0.166255	−	0.268758i
$638$		−	31.0226i		−	1.22820i
$639$	−5.11250	+	33.2759i	−0.202247	+	1.31637i
$640$	1.92262	+	3.33007i	0.0759982	+	0.131633i
$641$	−8.11862	−	14.0619i	−0.320666	−	0.555410i	0.659959	−	0.751301i	$-0.270573\pi$
$641$	−8.11862	−	14.0619i	−0.320666	−	0.555410i	−0.980626	+	0.195891i	$0.937240\pi$
$642$	−3.48014	+	6.86944i	−0.137350	+	0.271115i
$643$	−28.2088	−	28.2088i	−1.11245	−	1.11245i	−0.992819	−	0.119629i	$-0.961830\pi$
$643$	−28.2088	−	28.2088i	−1.11245	−	1.11245i	−0.119629	−	0.992819i	$-0.538170\pi$
$644$	−12.1146	−	12.1146i	−0.477381	−	0.477381i
$645$	13.0994	−	0.716936i	0.515789	−	0.0282293i
$646$	−0.901884	−	1.56211i	−0.0354841	−	0.0614603i
$647$	−1.17726	−	2.03908i	−0.0462830	−	0.0801645i	0.841956	−	0.539546i	$-0.181404\pi$
$647$	−1.17726	−	2.03908i	−0.0462830	−	0.0801645i	−0.888239	+	0.459382i	$0.848071\pi$
$648$	−0.387745	+	8.99164i	−0.0152321	+	0.353225i
$649$		−	26.4280i		−	1.03739i
$650$	−34.3429	−	8.09228i	−1.34704	−	0.317405i
$651$	3.25716	−	3.63433i	0.127658	−	0.142441i
$652$	−1.91264	+	0.512492i	−0.0749049	+	0.0200707i
$653$	−12.6180	−	7.28502i	−0.493782	−	0.285085i	0.232360	−	0.972630i	$-0.425355\pi$
$653$	−12.6180	−	7.28502i	−0.493782	−	0.285085i	−0.726142	+	0.687545i	$0.758688\pi$
$654$	13.8965	+	2.92018i	0.543398	+	0.114188i
$655$	−45.9829	+	12.3211i	−1.79670	+	0.481425i
$656$	−2.83325	−	10.5738i	−0.110620	−	0.412838i
$657$	−9.69921	+	3.77482i	−0.378402	+	0.147270i
$658$	−15.0703	+	15.0703i	−0.587501	+	0.587501i
$659$	3.83999	−	2.21702i	0.149585	−	0.0863628i	−0.423339	−	0.905971i	$-0.639142\pi$
$659$	3.83999	−	2.21702i	0.149585	−	0.0863628i	0.572924	+	0.819608i	$0.305809\pi$
$660$	26.5091	−	8.68127i	1.03187	−	0.337918i
$661$	5.45199	+	20.3471i	0.212058	+	0.791411i	0.987182	+	0.159601i	$0.0510208\pi$
$661$	5.45199	+	20.3471i	0.212058	+	0.791411i	−0.775124	+	0.631809i	$0.782313\pi$
$662$	12.1652	+	21.0708i	0.472816	+	0.818941i
$663$	−5.47212	+	1.97805i	−0.212520	+	0.0768213i
$664$	2.81173	−	4.87006i	0.109116	−	0.188995i
$665$	15.7335	+	4.21579i	0.610120	+	0.163481i
$666$	−15.2231	+	1.67134i	−0.589884	+	0.0647632i
$667$	50.2261	+	28.9981i	1.94476	+	1.12281i
$668$	−5.80101	−	21.6497i	−0.224448	−	0.837651i
$669$	7.70012	+	11.7972i	0.297704	+	0.456107i
$670$	−9.09628	+	9.09628i	−0.351420	+	0.351420i
$671$	0.933373	−	3.48339i	0.0360325	−	0.134475i
$672$	−3.60170	+	1.17949i	−0.138939	+	0.0455000i
$673$			32.8052i			1.26455i	0.774745	+	0.632274i	$0.217878\pi$
$673$			32.8052i			1.26455i	−0.774745	+	0.632274i	$0.782122\pi$
$674$	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	$0.523435\pi$
$678$	−11.8969	−	18.2270i	−0.456897	−	0.700005i
$679$	−19.2707	+	33.3778i	−0.739541	+	1.28092i
$680$	−3.58273			−0.137391
$681$	16.2912	+	8.25333i	0.624281	+	0.316268i
$682$	1.39588	−	5.20948i	0.0534509	−	0.199481i
$683$	11.5934	−	3.10645i	0.443611	−	0.118865i	−0.0300976	−	0.999547i	$-0.509582\pi$
$683$	11.5934	−	3.10645i	0.443611	−	0.118865i	0.473708	+	0.880682i	$0.342915\pi$
$684$	−0.881959	+	5.74044i	−0.0337226	+	0.219491i
$685$	−5.06417	+	8.77140i	−0.193492	+	0.335138i
$686$	20.1573			0.769607
$687$	22.5568	+	11.4275i	0.860594	+	0.435987i
$688$	−1.70588	+	0.984890i	−0.0650360	+	0.0375486i
$689$	−3.48578	+	6.48494i	−0.132798	+	0.247057i
$690$	−10.7240	+	51.0334i	−0.408256	+	1.94281i
$691$	−15.6544	−	15.6544i	−0.595522	−	0.595522i	0.343596	−	0.939118i	$-0.388355\pi$
$691$	−15.6544	−	15.6544i	−0.595522	−	0.595522i	−0.939118	+	0.343596i	$0.888355\pi$
$692$	−16.4934	+	9.52249i	−0.626986	+	0.361991i
$693$	3.00043	+	27.3289i	0.113977	+	1.03814i
$694$	11.4031	+	11.4031i	0.432857	+	0.432857i
$695$	54.4422	+	14.5877i	2.06511	+	0.553345i
$696$	10.7434	−	7.01228i	0.407228	−	0.265800i
$697$	9.85196	+	2.63983i	0.373170	+	0.0999905i
$698$			29.3815i			1.11211i
$699$	30.0928	+	6.32361i	1.13821	+	0.239181i
$700$	15.1409	−	15.1409i	0.572274	−	0.572274i
$701$	26.8651			1.01468			0.507341	−	0.861746i	$-0.330629\pi$
$701$	26.8651			1.01468			0.507341	+	0.861746i	$0.330629\pi$
$702$	17.7291	+	6.05646i	0.669140	+	0.228586i
$703$	−9.88267			−0.372732
$704$	−2.96155	+	2.96155i	−0.111617	+	0.111617i
$705$	63.4846	+	13.3405i	2.39097	+	0.502431i
$706$		−	21.2880i		−	0.801184i
$707$	12.5920	+	3.37402i	0.473571	+	0.126893i
$708$	9.15225	−	5.97372i	0.343963	−	0.224506i
$709$	18.0428	+	4.83455i	0.677611	+	0.181565i	0.581181	−	0.813774i	$-0.302591\pi$
$709$	18.0428	+	4.83455i	0.677611	+	0.181565i	0.0964301	+	0.995340i	$0.469258\pi$
$710$	30.5128	+	30.5128i	1.14513	+	1.14513i
$711$	30.8762	−	22.6521i	1.15795	−	0.849521i
$712$	1.74886	−	1.00971i	0.0655415	−	0.0378404i
$713$	7.12945	+	7.12945i	0.267000	+	0.267000i
$714$	0.726174	−	3.45571i	0.0271764	−	0.129327i
$715$	−1.76430	−	58.0401i	−0.0659811	−	2.17057i
$716$	−0.442894	+	0.255705i	−0.0165517	+	0.00955615i
$717$	17.2359	+	8.73189i	0.643685	+	0.326099i
$718$	16.7689			0.625809
$719$	−14.5977	+	25.2840i	−0.544404	+	0.942936i	0.454240	+	0.890879i	$0.349911\pi$
$719$	−14.5977	+	25.2840i	−0.544404	+	0.942936i	−0.998644	+	0.0520563i	$0.983422\pi$
$720$	8.99846	+	7.21806i	0.335353	+	0.269001i
$721$	−7.66697	+	2.05436i	−0.285533	+	0.0765083i
$722$	3.94755	−	14.7325i	0.146913	−	0.548286i
$723$	−4.08114	−	2.06755i	−0.151779	−	0.0768930i
$724$	2.38215			0.0885319
$725$	−36.2422	+	62.7733i	−1.34600	+	2.33134i
$726$	6.19287	+	9.48800i	0.229839	+	0.352133i
$727$	36.4712	+	21.0566i	1.35264	+	0.780948i	0.988619	−	0.150443i	$-0.0480699\pi$
$727$	36.4712	+	21.0566i	1.35264	+	0.780948i	0.364022	+	0.931390i	$0.381403\pi$
$728$	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
$731$		−	1.83531i		−	0.0678812i
$732$	1.41731	−	0.464143i	0.0523852	−	0.0171552i
$733$	−10.0518	+	37.5139i	−0.371272	+	1.38561i	0.487444	+	0.873154i	$0.337929\pi$
$733$	−10.0518	+	37.5139i	−0.371272	+	1.38561i	−0.858716	+	0.512452i	$0.828737\pi$
$734$	−6.88094	+	6.88094i	−0.253980	+	0.253980i
$735$	−8.05299	−	12.3379i	−0.297039	−	0.455089i
$736$	−2.02652	−	7.56306i	−0.0746983	−	0.278778i
$737$	−12.1344	−	7.00582i	−0.446978	−	0.258063i
$738$	−19.4260	−	26.4788i	−0.715081	−	0.974699i
$739$	−13.9922	−	3.74921i	−0.514713	−	0.137917i	−0.00789285	−	0.999969i	$-0.502512\pi$
$739$	−13.9922	−	3.74921i	−0.514713	−	0.137917i	−0.506820	+	0.862052i	$0.669179\pi$
$740$	−9.81472	+	16.9996i	−0.360796	+	0.624917i
$741$	10.9459	+	5.13352i	0.402107	+	0.188585i
$742$	−2.23402	−	3.86944i	−0.0820135	−	0.142052i
$743$	−3.45307	−	12.8870i	−0.126681	−	0.472780i	0.873213	−	0.487339i	$-0.162032\pi$
$743$	−3.45307	−	12.8870i	−0.126681	−	0.472780i	−0.999894	+	0.0145589i	$0.995366\pi$
$744$	2.11961	−	0.694135i	0.0777088	−	0.0254482i
$745$	20.4254	−	11.7926i	0.748329	−	0.432048i
$746$	−16.7798	+	16.7798i	−0.614351	+	0.614351i
$747$	2.56190	−	16.6747i	0.0937351	−	0.610097i
$748$	−1.01000	−	3.76936i	−0.0369292	−	0.137822i
$749$	−9.39684	+	2.51787i	−0.343353	+	0.0920011i
$750$	−31.1933	−	6.55486i	−1.13902	−	0.239350i
$751$	26.4563	+	15.2745i	0.965402	+	0.557375i	0.897832	−	0.440339i	$-0.145142\pi$
$751$	26.4563	+	15.2745i	0.965402	+	0.557375i	0.0675709	+	0.997714i	$0.478475\pi$
$752$	−9.40830	+	2.52095i	−0.343085	+	0.0919295i
$753$	−7.30621	+	8.15226i	−0.266253	+	0.297085i
$754$	−7.69276	−	25.5746i	−0.280154	−	0.931371i
$755$		−	15.2106i		−	0.553569i
$756$	−8.78603	+	7.21644i	−0.319545	+	0.262459i
$757$	−22.0323	−	38.1611i	−0.800778	−	1.38699i	−0.919105	−	0.394014i	$-0.871086\pi$
$757$	−22.0323	−	38.1611i	−0.800778	−	1.38699i	0.118326	−	0.992975i	$-0.462247\pi$
$758$	−0.0735135	−	0.127329i	−0.00267013	−	0.00462480i
$759$	−56.7150	+	3.10404i	−2.05863	+	0.112669i
$760$	5.26379	+	5.26379i	0.190938	+	0.190938i
$761$	−16.2670	−	16.2670i	−0.589680	−	0.589680i	0.347865	−	0.937545i	$-0.386907\pi$
$761$	−16.2670	−	16.2670i	−0.589680	−	0.589680i	−0.937545	+	0.347865i	$0.886907\pi$
$762$	0.0832992	−	0.164424i	0.00301761	−	0.00595646i
$763$	8.96950	+	15.5356i	0.324718	+	0.562427i
$764$	11.8082	+	20.4524i	0.427206	+	0.739943i
$765$	−10.0164	+	3.89824i	−0.362142	+	0.140941i
$766$		−	23.0510i		−	0.832867i
$767$	−6.55341	−	21.7868i	−0.236630	−	0.786676i
$768$	−1.69503	−	0.356189i	−0.0611642	−	0.0128529i
$769$	35.2148	−	9.43577i	1.26988	−	0.340262i

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.69503 - 0.356189i) q^{3} -1.00000i q^{4} +(-3.71422 - 0.995221i) q^{5} +(1.45043 - 0.946704i) q^{6} +(2.11355 + 0.566325i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.74626 + 1.20750i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.69503 - 0.356189i) q^{3} -1.00000i q^{4} +(-3.71422 - 0.995221i) q^{5} +(1.45043 - 0.946704i) q^{6} +(2.11355 + 0.566325i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.74626 + 1.20750i) q^{9} +(3.33007 - 1.92262i) q^{10} +(2.96155 + 2.96155i) q^{11} +(-0.356189 + 1.69503i) q^{12} +(3.17583 + 1.70707i) q^{13} +(-1.89496 + 1.09406i) q^{14} +(5.94122 + 3.00989i) q^{15} -1.00000 q^{16} +(0.465866 - 0.806903i) q^{17} +(-2.79573 + 1.08807i) q^{18} +(-1.86997 + 0.501056i) q^{19} +(-0.995221 + 3.71422i) q^{20} +(-3.38082 - 1.71276i) q^{21} -4.18826 q^{22} +(3.91493 - 6.78085i) q^{23} +(-0.946704 - 1.45043i) 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} +7.40705i q^{29} +(-6.32939 + 2.07276i) q^{30} +(-0.333283 + 1.24383i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.96504 - 6.07478i) q^{33} +(0.241150 + 0.899984i) q^{34} +(-7.28657 - 4.20690i) q^{35} +(1.20750 - 2.74626i) q^{36} +(4.93092 + 1.32124i) q^{37} +(0.967965 - 1.67657i) q^{38} +(-4.77510 - 4.02473i) q^{39} +(-1.92262 - 3.33007i) q^{40} +(2.83325 + 10.5738i) q^{41} +(3.60170 - 1.17949i) q^{42} +(1.70588 - 0.984890i) q^{43} +(2.96155 - 2.96155i) q^{44} +(-8.99846 - 7.21806i) q^{45} +(2.02652 + 7.56306i) q^{46} +(9.40830 - 2.52095i) q^{47} +(1.69503 + 0.356189i) q^{48} +(-1.91580 - 1.10609i) q^{49} +(-9.45241 + 2.53277i) q^{50} +(-1.07707 + 1.20179i) q^{51} +(1.70707 - 3.17583i) q^{52} +2.04197i q^{53} +(5.12641 - 0.848495i) q^{54} +(-8.05243 - 13.9472i) q^{55} +(1.09406 + 1.89496i) q^{56} +(3.34812 - 0.183244i) q^{57} +(-5.23757 - 5.23757i) q^{58} +(-4.46186 - 4.46186i) q^{59} +(3.00989 - 5.94122i) q^{60} +(-0.430522 - 0.745686i) q^{61} +(-0.643854 - 1.11519i) q^{62} +(5.12052 + 4.10739i) q^{63} +1.00000i q^{64} +(-10.0968 - 9.50108i) q^{65} +(7.09923 + 1.49181i) q^{66} +(-3.23147 + 0.865869i) q^{67} +(-0.806903 - 0.465866i) q^{68} +(-9.05119 + 10.0993i) q^{69} +(8.12711 - 2.17765i) q^{70} +(2.90450 + 10.8397i) q^{71} +(1.08807 + 2.79573i) q^{72} +(-2.45316 + 2.45316i) q^{73} +(-4.42095 + 2.55243i) q^{74} +(-12.6222 - 11.3123i) q^{75} +(0.501056 + 1.86997i) q^{76} +(4.58218 + 7.93658i) q^{77} +(6.22242 - 0.530587i) q^{78} +(6.38240 - 11.0546i) q^{79} +(3.71422 + 0.995221i) q^{80} +(6.08388 + 6.63223i) q^{81} +(-9.48023 - 5.47341i) q^{82} +(-1.45546 - 5.43185i) q^{83} +(-1.71276 + 3.38082i) q^{84} +(-2.53337 + 2.53337i) q^{85} +(-0.509817 + 1.90266i) q^{86} +(2.63831 - 12.5552i) q^{87} +4.18826i 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} +(1.00796 - 1.98962i) q^{93} +(-4.87009 + 8.43525i) q^{94} +7.44412 q^{95} +(-1.45043 + 0.946704i) q^{96} +(-4.55884 + 17.0138i) q^{97} +(2.13680 - 0.572553i) q^{98} +(4.55710 + 11.7092i) 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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