LMFDB - Embedded newform 234.2.y.a.11.4

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			11.4
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.0694742 - 1.73066i) q^{3} -1.00000i q^{4} +(0.339151 + 0.0908752i) q^{5} +(1.17463 + 1.27288i) q^{6} +(2.97685 + 0.797644i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99035 - 0.240472i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0694742 - 1.73066i) q^{3} -1.00000i q^{4} +(0.339151 + 0.0908752i) q^{5} +(1.17463 + 1.27288i) q^{6} +(2.97685 + 0.797644i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99035 - 0.240472i) q^{9} +(-0.304074 + 0.175557i) q^{10} +(-2.35360 - 2.35360i) q^{11} +(-1.73066 - 0.0694742i) q^{12} +(2.60734 - 2.49034i) q^{13} +(-2.66897 + 1.54093i) q^{14} +(0.180836 - 0.580640i) q^{15} -1.00000 q^{16} +(3.87756 - 6.71613i) q^{17} +(2.28453 - 1.94445i) q^{18} +(3.67410 - 0.984473i) q^{19} +(0.0908752 - 0.339151i) q^{20} +(1.58726 - 5.09649i) q^{21} +3.32849 q^{22} +(-3.34250 + 5.78938i) q^{23} +(1.27288 - 1.17463i) q^{24} +(-4.22336 - 2.43836i) q^{25} +(-0.0827293 + 3.60460i) q^{26} +(-0.623927 + 5.15856i) q^{27} +(0.797644 - 2.97685i) q^{28} +5.68973i q^{29} +(0.282704 + 0.538445i) q^{30} +(0.293661 - 1.09596i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.23679 + 3.90976i) q^{33} +(2.00717 + 7.49087i) q^{34} +(0.937115 + 0.541044i) q^{35} +(-0.240472 + 2.99035i) q^{36} +(8.90068 + 2.38493i) q^{37} +(-1.90186 + 3.29411i) q^{38} +(-4.12878 - 4.68542i) q^{39} +(0.175557 + 0.304074i) q^{40} +(-0.678577 - 2.53248i) q^{41} +(2.48140 + 4.72613i) q^{42} +(-3.68906 + 2.12988i) q^{43} +(-2.35360 + 2.35360i) q^{44} +(-0.992326 - 0.353305i) q^{45} +(-1.73021 - 6.45722i) q^{46} +(-4.17527 + 1.11876i) q^{47} +(-0.0694742 + 1.73066i) q^{48} +(2.16322 + 1.24894i) q^{49} +(4.71055 - 1.26219i) q^{50} +(-11.3539 - 7.17732i) q^{51} +(-2.49034 - 2.60734i) q^{52} +5.65439i q^{53} +(-3.20647 - 4.08883i) q^{54} +(-0.584342 - 1.01211i) q^{55} +(1.54093 + 2.66897i) q^{56} +(-1.44853 - 6.42701i) q^{57} +(-4.02325 - 4.02325i) q^{58} +(7.75962 + 7.75962i) q^{59} +(-0.580640 - 0.180836i) q^{60} +(5.01742 + 8.69042i) q^{61} +(0.567309 + 0.982608i) q^{62} +(-8.71000 - 3.10108i) q^{63} +1.00000i q^{64} +(1.11059 - 0.607659i) q^{65} +(0.231245 - 5.76048i) q^{66} +(-13.3180 + 3.56856i) q^{67} +(-6.71613 - 3.87756i) q^{68} +(9.78722 + 6.18694i) q^{69} +(-1.04522 + 0.280065i) q^{70} +(-0.343507 - 1.28199i) q^{71} +(-1.94445 - 2.28453i) q^{72} +(-2.19140 + 2.19140i) q^{73} +(-7.98013 + 4.60733i) q^{74} +(-4.51338 + 7.13979i) q^{75} +(-0.984473 - 3.67410i) q^{76} +(-5.12898 - 8.88365i) q^{77} +(6.23258 + 0.393603i) q^{78} +(-6.22990 + 10.7905i) q^{79} +(-0.339151 - 0.0908752i) q^{80} +(8.88435 + 1.43819i) q^{81} +(2.27056 + 1.31091i) q^{82} +(-1.05166 - 3.92483i) q^{83} +(-5.09649 - 1.58726i) q^{84} +(1.92541 - 1.92541i) q^{85} +(1.10251 - 4.11462i) q^{86} +(9.84697 + 0.395290i) q^{87} -3.32849i q^{88} +(1.43929 - 5.37149i) q^{89} +(0.951504 - 0.451856i) q^{90} +(9.74806 - 5.33364i) q^{91} +(5.78938 + 3.34250i) q^{92} +(-1.87632 - 0.584367i) q^{93} +(2.16128 - 3.74344i) q^{94} +1.33554 q^{95} +(-1.17463 - 1.27288i) q^{96} +(-0.218799 + 0.816569i) q^{97} +(-2.41276 + 0.646496i) q^{98} +(6.47211 + 7.60406i) 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
$3$	0.0694742	−	1.73066i	0.0401110	−	0.999195i
$3$	0.0694742	−	1.73066i	0.0401110	−	0.999195i
$4$		−	1.00000i		−	0.500000i
$5$	0.339151	+	0.0908752i	0.151673	+	0.0406406i	0.333857	−	0.942624i	$-0.391650\pi$
$5$	0.339151	+	0.0908752i	0.151673	+	0.0406406i	−0.182184	+	0.983265i	$0.558317\pi$
$6$	1.17463	+	1.27288i	0.479542	+	0.519653i
$7$	2.97685	+	0.797644i	1.12514	+	0.301481i	0.772963	−	0.634451i	$-0.218774\pi$
$7$	2.97685	+	0.797644i	1.12514	+	0.301481i	0.352180	+	0.935932i	$0.385440\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.99035	−	0.240472i	−0.996782	−	0.0801574i
$10$	−0.304074	+	0.175557i	−0.0961568	+	0.0555161i
$11$	−2.35360	−	2.35360i	−0.709637	−	0.709637i	0.256821	−	0.966459i	$-0.417325\pi$
$11$	−2.35360	−	2.35360i	−0.709637	−	0.709637i	−0.966459	+	0.256821i	$0.917325\pi$
$12$	−1.73066	−	0.0694742i	−0.499598	−	0.0200555i
$13$	2.60734	−	2.49034i	0.723145	−	0.690696i
$13$	2.60734	−	2.49034i	0.723145	−	0.690696i
$14$	−2.66897	+	1.54093i	−0.713312	+	0.411831i
$15$	0.180836	−	0.580640i	0.0466917	−	0.149921i
$16$	−1.00000			−0.250000
$17$	3.87756	−	6.71613i	0.940446	−	1.62890i	0.175824	−	0.984422i	$-0.443741\pi$
$17$	3.87756	−	6.71613i	0.940446	−	1.62890i	0.764622	−	0.644479i	$-0.222926\pi$
$18$	2.28453	−	1.94445i	0.538470	−	0.458312i
$19$	3.67410	−	0.984473i	0.842897	−	0.225854i	0.188565	−	0.982061i	$-0.439616\pi$
$19$	3.67410	−	0.984473i	0.842897	−	0.225854i	0.654332	+	0.756207i	$0.272950\pi$
$20$	0.0908752	−	0.339151i	0.0203203	−	0.0758364i
$21$	1.58726	−	5.09649i	0.346369	−	1.11215i
$22$	3.32849			0.709637
$23$	−3.34250	+	5.78938i	−0.696960	+	1.20717i	0.272556	+	0.962140i	$0.412131\pi$
$23$	−3.34250	+	5.78938i	−0.696960	+	1.20717i	−0.969515	+	0.245030i	$0.921202\pi$
$24$	1.27288	−	1.17463i	0.259827	−	0.239771i
$25$	−4.22336	−	2.43836i	−0.844672	−	0.487672i
$26$	−0.0827293	+	3.60460i	−0.0162246	+	0.706921i
$27$	−0.623927	+	5.15856i	−0.120075	+	0.992765i
$28$	0.797644	−	2.97685i	0.150741	−	0.562572i
$29$			5.68973i			1.05656i	0.849071	+	0.528278i	$0.177162\pi$
$29$			5.68973i			1.05656i	−0.849071	+	0.528278i	$0.822838\pi$
$30$	0.282704	+	0.538445i	0.0516145	+	0.0983062i
$31$	0.293661	−	1.09596i	0.0527430	−	0.196840i	−0.934527	−	0.355892i	$-0.884177\pi$
$31$	0.293661	−	1.09596i	0.0527430	−	0.196840i	0.987270	+	0.159052i	$0.0508438\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.23679	+	3.90976i	−0.737531	+	0.680602i
$34$	2.00717	+	7.49087i	0.344227	+	1.28467i
$35$	0.937115	+	0.541044i	0.158401	+	0.0914531i
$36$	−0.240472	+	2.99035i	−0.0400787	+	0.498391i
$37$	8.90068	+	2.38493i	1.46326	+	0.392080i	0.900615	−	0.434617i	$-0.143116\pi$
$37$	8.90068	+	2.38493i	1.46326	+	0.392080i	0.562647	+	0.826697i	$0.309783\pi$
$38$	−1.90186	+	3.29411i	−0.308522	+	0.534375i
$39$	−4.12878	−	4.68542i	−0.661134	−	0.750268i
$40$	0.175557	+	0.304074i	0.0277581	+	0.0480784i
$41$	−0.678577	−	2.53248i	−0.105976	−	0.395508i	0.892478	−	0.451091i	$-0.148965\pi$
$41$	−0.678577	−	2.53248i	−0.105976	−	0.395508i	−0.998454	+	0.0555831i	$0.982298\pi$
$42$	2.48140	+	4.72613i	0.382888	+	0.729257i
$43$	−3.68906	+	2.12988i	−0.562577	+	0.324804i	−0.754179	−	0.656669i	$-0.771965\pi$
$43$	−3.68906	+	2.12988i	−0.562577	+	0.324804i	0.191602	+	0.981473i	$0.438632\pi$
$44$	−2.35360	+	2.35360i	−0.354819	+	0.354819i
$45$	−0.992326	−	0.353305i	−0.147927	−	0.0526676i
$46$	−1.73021	−	6.45722i	−0.255105	−	0.952065i
$47$	−4.17527	+	1.11876i	−0.609026	+	0.163188i	−0.550134	−	0.835076i	$-0.685423\pi$
$47$	−4.17527	+	1.11876i	−0.609026	+	0.163188i	−0.0588917	+	0.998264i	$0.518757\pi$
$48$	−0.0694742	+	1.73066i	−0.0100277	+	0.249799i
$49$	2.16322	+	1.24894i	0.309031	+	0.178419i
$50$	4.71055	−	1.26219i	0.666172	−	0.178500i
$51$	−11.3539	−	7.17732i	−1.58987	−	1.00503i
$52$	−2.49034	−	2.60734i	−0.345348	−	0.361573i
$53$			5.65439i			0.776690i	0.921514	+	0.388345i	$0.126953\pi$
$53$			5.65439i			0.776690i	−0.921514	+	0.388345i	$0.873047\pi$
$54$	−3.20647	−	4.08883i	−0.436345	−	0.556420i
$55$	−0.584342	−	1.01211i	−0.0787927	−	0.136473i
$56$	1.54093	+	2.66897i	0.205916	+	0.356656i
$57$	−1.44853	−	6.42701i	−0.191862	−	0.851278i
$58$	−4.02325	−	4.02325i	−0.528278	−	0.528278i
$59$	7.75962	+	7.75962i	1.01022	+	1.01022i	0.999947	+	0.0102689i	$0.00326875\pi$
$59$	7.75962	+	7.75962i	1.01022	+	1.01022i	0.0102689	+	0.999947i	$0.496731\pi$
$60$	−0.580640	−	0.180836i	−0.0749603	−	0.0233458i
$61$	5.01742	+	8.69042i	0.642415	+	1.11269i	0.984892	+	0.173169i	$0.0554006\pi$
$61$	5.01742	+	8.69042i	0.642415	+	1.11269i	−0.342478	+	0.939526i	$0.611266\pi$
$62$	0.567309	+	0.982608i	0.0720483	+	0.124791i
$63$	−8.71000	−	3.10108i	−1.09736	−	0.390700i
$64$			1.00000i			0.125000i
$65$	1.11059	−	0.607659i	0.137752	−	0.0753708i
$66$	0.231245	−	5.76048i	0.0284642	−	0.709066i
$67$	−13.3180	+	3.56856i	−1.62706	+	0.435969i	−0.953064	−	0.302768i	$-0.902089\pi$
$67$	−13.3180	+	3.56856i	−1.62706	+	0.435969i	−0.673994	+	0.738737i	$0.735423\pi$
$68$	−6.71613	−	3.87756i	−0.814450	−	0.470223i
$69$	9.78722	+	6.18694i	1.17824	+	0.744820i
$70$	−1.04522	+	0.280065i	−0.124927	+	0.0334741i
$71$	−0.343507	−	1.28199i	−0.0407668	−	0.152144i	0.942542	−	0.334087i	$-0.108428\pi$
$71$	−0.343507	−	1.28199i	−0.0407668	−	0.152144i	−0.983309	+	0.181943i	$0.941761\pi$
$72$	−1.94445	−	2.28453i	−0.229156	−	0.269235i
$73$	−2.19140	+	2.19140i	−0.256484	+	0.256484i	−0.823622	−	0.567138i	$-0.808050\pi$
$73$	−2.19140	+	2.19140i	−0.256484	+	0.256484i	0.567138	+	0.823622i	$0.308050\pi$
$74$	−7.98013	+	4.60733i	−0.927671	+	0.535591i
$75$	−4.51338	+	7.13979i	−0.521160	+	0.824432i
$76$	−0.984473	−	3.67410i	−0.112927	−	0.421448i
$77$	−5.12898	−	8.88365i	−0.584502	−	1.01239i
$78$	6.23258	+	0.393603i	0.705701	+	0.0445668i
$79$	−6.22990	+	10.7905i	−0.700919	+	1.21403i	0.267225	+	0.963634i	$0.413893\pi$
$79$	−6.22990	+	10.7905i	−0.700919	+	1.21403i	−0.968144	+	0.250393i	$0.919440\pi$
$80$	−0.339151	−	0.0908752i	−0.0379182	−	0.0101602i
$81$	8.88435	+	1.43819i	0.987150	+	0.159799i
$82$	2.27056	+	1.31091i	0.250742	+	0.144766i
$83$	−1.05166	−	3.92483i	−0.115434	−	0.430806i	0.883885	−	0.467705i	$-0.154919\pi$
$83$	−1.05166	−	3.92483i	−0.115434	−	0.430806i	−0.999319	+	0.0368984i	$0.988252\pi$
$84$	−5.09649	−	1.58726i	−0.556073	−	0.173185i
$85$	1.92541	−	1.92541i	0.208840	−	0.208840i
$86$	1.10251	−	4.11462i	0.118887	−	0.443691i
$87$	9.84697	+	0.395290i	1.05571	+	0.0423795i
$88$		−	3.32849i		−	0.354819i
$89$	1.43929	−	5.37149i	0.152564	−	0.569377i	−0.846737	−	0.532011i	$-0.821437\pi$
$89$	1.43929	−	5.37149i	0.152564	−	0.569377i	0.999302	−	0.0373662i	$-0.0118968\pi$
$90$	0.951504	−	0.451856i	0.100297	−	0.0476298i
$91$	9.74806	−	5.33364i	1.02187	−	0.559117i
$92$	5.78938	+	3.34250i	0.603585	+	0.348480i
$93$	−1.87632	−	0.584367i	−0.194566	−	0.0605960i
$94$	2.16128	−	3.74344i	0.222919	−	0.386107i
$95$	1.33554			0.137023
$96$	−1.17463	−	1.27288i	−0.119886	−	0.129913i
$97$	−0.218799	+	0.816569i	−0.0222157	+	0.0829101i	−0.976144	−	0.217126i	$-0.930332\pi$
$97$	−0.218799	+	0.816569i	−0.0222157	+	0.0829101i	0.953928	+	0.300036i	$0.0969986\pi$
$98$	−2.41276	+	0.646496i	−0.243725	+	0.0653060i
$99$	6.47211	+	7.60406i	0.650471	+	0.764237i
$100$	−2.43836	+	4.22336i	−0.243836	+	0.422336i
$101$	10.5139			1.04617			0.523087	−	0.852279i	$-0.324780\pi$
$101$	10.5139			1.04617			0.523087	+	0.852279i	$0.324780\pi$
$102$	13.1036	−	2.95330i	1.29745	−	0.292421i
$103$	−1.30284	+	0.752193i	−0.128372	+	0.0741158i	−0.562811	−	0.826586i	$-0.690280\pi$
$103$	−1.30284	+	0.752193i	−0.128372	+	0.0741158i	0.434439	+	0.900701i	$0.356947\pi$
$104$	3.60460	+	0.0827293i	0.353460	+	0.00811228i
$105$	1.00147	−	1.58424i	0.0977331	−	0.154606i
$106$	−3.99826	−	3.99826i	−0.388345	−	0.388345i
$107$	4.75429	−	2.74489i	0.459615	−	0.265359i	−0.252267	−	0.967658i	$-0.581176\pi$
$107$	4.75429	−	2.74489i	0.459615	−	0.265359i	0.711882	+	0.702299i	$0.247843\pi$
$108$	5.15856	+	0.623927i	0.496382	+	0.0600374i
$109$	2.22967	+	2.22967i	0.213564	+	0.213564i	0.805780	−	0.592216i	$-0.201747\pi$
$109$	2.22967	+	2.22967i	0.213564	+	0.213564i	−0.592216	+	0.805780i	$0.701747\pi$
$110$	1.12886	+	0.302478i	0.107633	+	0.0288401i
$111$	4.74586	−	15.2383i	0.450457	−	1.44636i
$112$	−2.97685	−	0.797644i	−0.281286	−	0.0753703i
$113$			6.68745i			0.629102i	0.949241	+	0.314551i	$0.101854\pi$
$113$			6.68745i			0.629102i	−0.949241	+	0.314551i	$0.898146\pi$
$114$	5.56884	+	3.52032i	0.521570	+	0.329708i
$115$	−1.65972	+	1.65972i	−0.154770	+	0.154770i
$116$	5.68973			0.528278
$117$	−8.39570	+	6.81999i	−0.776183	+	0.630508i
$118$	−10.9738			−1.01022
$119$	16.9000	−	16.9000i	1.54922	−	1.54922i
$120$	0.538445	−	0.282704i	0.0491531	−	0.0258073i
$121$			0.0788774i			0.00717067i
$122$	−9.69291	−	2.59721i	−0.877555	−	0.235140i
$123$	−4.43001	+	0.998442i	−0.399440	+	0.0900265i
$124$	−1.09596	−	0.293661i	−0.0984199	−	0.0263715i
$125$	−2.45215	−	2.45215i	−0.219327	−	0.219327i
$126$	8.35170	−	3.96610i	0.744028	−	0.353329i
$127$	−10.6922	+	6.17316i	−0.948782	+	0.547780i	−0.892702	−	0.450647i	$-0.851193\pi$
$127$	−10.6922	+	6.17316i	−0.948782	+	0.547780i	−0.0560797	+	0.998426i	$0.517860\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.42980	+	6.53248i	0.301977	+	0.575153i
$130$	−0.355627	+	1.21499i	−0.0311905	+	0.106561i
$131$	4.12094	−	2.37922i	0.360048	−	0.207874i	−0.309054	−	0.951045i	$-0.600012\pi$
$131$	4.12094	−	2.37922i	0.360048	−	0.207874i	0.669102	+	0.743171i	$0.266679\pi$
$132$	3.90976	+	4.23679i	0.340301	+	0.368765i
$133$	11.7225			1.01647
$134$	6.89393	−	11.9406i	0.595545	−	1.03151i
$135$	−0.680390	+	1.69283i	−0.0585587	+	0.145696i
$136$	7.49087	−	2.00717i	0.642337	−	0.172114i
$137$	−1.27487	+	4.75789i	−0.108920	+	0.406494i	−0.998760	−	0.0497773i	$-0.984149\pi$
$137$	−1.27487	+	4.75789i	−0.108920	+	0.406494i	0.889840	+	0.456272i	$0.150815\pi$
$138$	−11.2954	+	2.54578i	−0.961531	+	0.216711i
$139$	4.10037			0.347789			0.173894	−	0.984764i	$-0.444365\pi$
$139$	4.10037			0.347789			0.173894	+	0.984764i	$0.444365\pi$
$140$	0.541044	−	0.937115i	0.0457265	−	0.0792007i
$141$	1.64612	+	7.30368i	0.138628	+	0.615081i
$142$	1.14940	+	0.663605i	0.0964553	+	0.0556885i
$143$	−11.9979	−	0.275364i	−1.00331	−	0.0230271i
$144$	2.99035	+	0.240472i	0.249196	+	0.0200393i
$145$	−0.517055	+	1.92968i	−0.0429391	+	0.160251i
$146$		−	3.09911i		−	0.256484i
$147$	2.31177	−	3.65702i	0.190671	−	0.301626i
$148$	2.38493	−	8.90068i	0.196040	−	0.731631i
$149$	5.36748	−	5.36748i	0.439721	−	0.439721i	−0.452197	−	0.891918i	$-0.649360\pi$
$149$	5.36748	−	5.36748i	0.439721	−	0.439721i	0.891918	+	0.452197i	$0.149360\pi$
$150$	−1.85715	−	8.24003i	−0.151636	−	0.672796i
$151$	−3.77372	−	14.0837i	−0.307101	−	1.14612i	−0.931122	−	0.364709i	$-0.881169\pi$
$151$	−3.77372	−	14.0837i	−0.307101	−	1.14612i	0.624021	−	0.781408i	$-0.285498\pi$
$152$	3.29411	+	1.90186i	0.267188	+	0.154261i
$153$	−13.2103	+	19.1511i	−1.06799	+	1.54828i
$154$	9.90843	+	2.65496i	0.798444	+	0.213942i
$155$	0.199191	−	0.345008i	0.0159994	−	0.0277117i
$156$	−4.68542	+	4.12878i	−0.375134	+	0.330567i
$157$	−8.20325	−	14.2085i	−0.654691	−	1.13396i	−0.981971	−	0.189031i	$-0.939465\pi$
$157$	−8.20325	−	14.2085i	−0.654691	−	1.13396i	0.327280	−	0.944927i	$-0.393868\pi$
$158$	−3.22484	−	12.0353i	−0.256554	−	0.957473i
$159$	9.78581	+	0.392834i	0.776065	+	0.0311538i
$160$	0.304074	−	0.175557i	0.0240392	−	0.0138790i
$161$	−14.5680	+	14.5680i	−1.14812	+	1.14812i
$162$	−7.29914	+	5.26523i	−0.573474	+	0.413675i
$163$	4.81720	+	17.9780i	0.377312	+	1.40815i	0.849937	+	0.526884i	$0.176640\pi$
$163$	4.81720	+	17.9780i	0.377312	+	1.40815i	−0.472625	+	0.881263i	$0.656694\pi$
$164$	−2.53248	+	0.678577i	−0.197754	+	0.0529880i
$165$	−1.79221	+	0.940980i	−0.139523	+	0.0732552i
$166$	3.51891	+	2.03164i	0.273120	+	0.157686i
$167$	−0.832317	+	0.223019i	−0.0644066	+	0.0172577i	−0.290878	−	0.956760i	$-0.593948\pi$
$167$	−0.832317	+	0.223019i	−0.0644066	+	0.0172577i	0.226472	+	0.974018i	$0.427281\pi$
$168$	4.72613	−	2.48140i	0.364629	−	0.191444i
$169$	0.596413	−	12.9863i	0.0458779	−	0.998947i
$170$			2.72294i			0.208840i
$171$	−11.2236	+	2.06040i	−0.858289	+	0.157562i
$172$	2.12988	+	3.68906i	0.162402	+	0.281289i
$173$	−11.9390	−	20.6789i	−0.907702	−	1.57219i	−0.817248	−	0.576286i	$-0.804501\pi$
$173$	−11.9390	−	20.6789i	−0.907702	−	1.57219i	−0.0904542	−	0.995901i	$-0.528832\pi$
$174$	−7.24237	+	6.68335i	−0.549043	+	0.506663i
$175$	−10.6274	−	10.6274i	−0.803354	−	0.803354i
$176$	2.35360	+	2.35360i	0.177409	+	0.177409i
$177$	13.9683	−	12.8901i	1.04992	−	0.968882i
$178$	2.78049	+	4.81595i	0.208407	+	0.360971i
$179$	−5.19785	−	9.00294i	−0.388506	−	0.672912i	0.603743	−	0.797179i	$-0.293675\pi$
$179$	−5.19785	−	9.00294i	−0.388506	−	0.672912i	−0.992249	+	0.124267i	$0.960342\pi$
$180$	−0.353305	+	0.992326i	−0.0263338	+	0.0739636i
$181$		−	0.635701i		−	0.0472513i	−0.999721	−	0.0236256i	$-0.992479\pi$
$181$		−	0.635701i		−	0.0472513i	0.999721	−	0.0236256i	$-0.00752097\pi$
$182$	−3.12146	+	10.6644i	−0.231378	+	0.790496i
$183$	15.3887	−	8.07967i	1.13757	−	0.597266i
$184$	−6.45722	+	1.73021i	−0.476033	+	0.127553i
$185$	2.80194	+	1.61770i	0.206003	+	0.118936i
$186$	1.73997	−	0.913552i	0.127581	−	0.0669848i
$187$	−24.9333	+	6.68086i	−1.82330	+	0.488553i
$188$	1.11876	+	4.17527i	0.0815940	+	0.304513i
$189$	−5.97203	+	14.8586i	−0.434401	+	1.08080i
$190$	−0.944369	+	0.944369i	−0.0685117	+	0.0685117i
$191$	0.129112	−	0.0745427i	0.00934220	−	0.00539372i	−0.495322	−	0.868710i	$-0.664950\pi$
$191$	0.129112	−	0.0745427i	0.00934220	−	0.00539372i	0.504664	+	0.863316i	$0.331616\pi$
$192$	1.73066	+	0.0694742i	0.124899	+	0.00501387i
$193$	−1.10422	−	4.12101i	−0.0794837	−	0.296637i	0.914729	−	0.404068i	$-0.132404\pi$
$193$	−1.10422	−	4.12101i	−0.0794837	−	0.296637i	−0.994213	+	0.107431i	$0.965737\pi$
$194$	−0.422687	−	0.732116i	−0.0303472	−	0.0525629i
$195$	−0.974491	−	1.96427i	−0.0697848	−	0.140664i
$196$	1.24894	−	2.16322i	0.0892097	−	0.154516i
$197$	18.4733	+	4.94991i	1.31617	+	0.352667i	0.847542	−	0.530729i	$-0.178082\pi$
$197$	18.4733	+	4.94991i	1.31617	+	0.352667i	0.468629	+	0.883395i	$0.344748\pi$
$198$	−9.95335	−	0.800410i	−0.707354	−	0.0568827i
$199$	−4.55185	−	2.62801i	−0.322672	−	0.186295i	0.329911	−	0.944012i	$-0.392981\pi$
$199$	−4.55185	−	2.62801i	−0.322672	−	0.186295i	−0.652583	+	0.757717i	$0.726315\pi$
$200$	−1.26219	−	4.71055i	−0.0892501	−	0.333086i
$201$	5.25069	+	23.2969i	0.370355	+	1.64324i
$202$	−7.43446	+	7.43446i	−0.523087	+	0.523087i
$203$	−4.53838	+	16.9375i	−0.318532	+	1.18878i
$204$	−7.17732	+	11.3539i	−0.502513	+	0.794934i
$205$		−	0.920560i		−	0.0642947i
$206$	0.389364	−	1.45313i	0.0271283	−	0.101244i
$207$	11.3874	−	16.5085i	0.791481	−	1.14742i
$208$	−2.60734	+	2.49034i	−0.180786	+	0.172674i
$209$	−10.9644	−	6.33032i	−0.758425	−	0.437877i
$210$	0.412080	+	1.82837i	0.0284363	+	0.126169i
$211$	−11.9338	+	20.6699i	−0.821556	+	1.42298i	0.0829678	+	0.996552i	$0.473560\pi$
$211$	−11.9338	+	20.6699i	−0.821556	+	1.42298i	−0.904523	+	0.426424i	$0.859773\pi$
$212$	5.65439			0.388345
$213$	−2.24254	+	0.505428i	−0.153657	+	0.0346314i
$214$	−1.42086	+	5.30272i	−0.0971280	+	0.362487i
$215$	−1.44470	+	0.387107i	−0.0985279	+	0.0264005i
$216$	−4.08883	+	3.20647i	−0.278210	+	0.218173i
$217$	1.74837	−	3.02826i	0.118687	−	0.205572i
$218$	−3.15324			−0.213564
$219$	3.64032	+	3.94481i	0.245990	+	0.266565i
$220$	−1.01211	+	0.584342i	−0.0682364	+	0.0393963i
$221$	−6.61534	−	27.1677i	−0.444996	−	1.82749i
$222$	7.41929	+	14.1310i	0.497950	+	0.948408i
$223$	−15.6524	−	15.6524i	−1.04816	−	1.04816i	−0.998780	−	0.0493797i	$-0.984276\pi$
$223$	−15.6524	−	15.6524i	−1.04816	−	1.04816i	−0.0493797	−	0.998780i	$-0.515724\pi$
$224$	2.66897	−	1.54093i	0.178328	−	0.102958i
$225$	12.0430	+	8.30714i	0.802864	+	0.553809i
$226$	−4.72874	−	4.72874i	−0.314551	−	0.314551i
$227$	21.5776	+	5.78170i	1.43216	+	0.383745i	0.889780	−	0.456390i	$-0.150858\pi$
$227$	21.5776	+	5.78170i	1.43216	+	0.383745i	0.542377	+	0.840135i	$0.317525\pi$
$228$	−6.42701	+	1.44853i	−0.425639	+	0.0959312i
$229$	8.99230	+	2.40948i	0.594228	+	0.159223i	0.543385	−	0.839484i	$-0.317142\pi$
$229$	8.99230	+	2.40948i	0.594228	+	0.159223i	0.0508431	+	0.998707i	$0.483809\pi$
$230$		−	2.34720i		−	0.154770i
$231$	−15.7309	+	8.25932i	−1.03502	+	0.543423i
$232$	−4.02325	+	4.02325i	−0.264139	+	0.264139i
$233$	−28.4945			−1.86674			−0.933370	−	0.358917i	$-0.883146\pi$
$233$	−28.4945			−1.86674			−0.933370	+	0.358917i	$0.883146\pi$
$234$	1.11420	−	10.7591i	0.0728373	−	0.703345i
$235$	−1.51771			−0.0990047
$236$	7.75962	−	7.75962i	0.505108	−	0.505108i
$237$	18.2419	+	11.5315i	1.18494	+	0.749051i
$238$			23.9002i			1.54922i
$239$	13.9526	+	3.73860i	0.902521	+	0.241830i	0.680099	−	0.733121i	$-0.261937\pi$
$239$	13.9526	+	3.73860i	0.902521	+	0.241830i	0.222422	+	0.974950i	$0.428604\pi$
$240$	−0.180836	+	0.580640i	−0.0116729	+	0.0374802i
$241$	29.4794	+	7.89898i	1.89894	+	0.508818i	0.997042	+	0.0768587i	$0.0244890\pi$
$241$	29.4794	+	7.89898i	1.89894	+	0.508818i	0.901893	+	0.431959i	$0.142178\pi$
$242$	−0.0557747	−	0.0557747i	−0.00358534	−	0.00358534i
$243$	3.10625	−	15.2758i	0.199266	−	0.979945i
$244$	8.69042	−	5.01742i	0.556347	−	0.321207i
$245$	0.620160	+	0.620160i	0.0396206	+	0.0396206i
$246$	2.42648	−	3.83849i	0.154707	−	0.244733i
$247$	7.12795	−	11.7166i	0.453541	−	0.745511i
$248$	0.982608	−	0.567309i	0.0623957	−	0.0360242i
$249$	−6.86560	+	1.54738i	−0.435090	+	0.0980612i
$250$	3.46786			0.219327
$251$	−8.22674	+	14.2491i	−0.519267	+	0.899397i	0.480482	+	0.877005i	$0.340462\pi$
$251$	−8.22674	+	14.2491i	−0.519267	+	0.899397i	−0.999749	+	0.0223928i	$0.992872\pi$
$252$	−3.10108	+	8.71000i	−0.195350	+	0.548678i
$253$	21.4928	−	5.75898i	1.35124	−	0.362064i
$254$	3.19546	−	11.9256i	0.200501	−	0.748281i
$255$	−3.19845	−	3.46599i	−0.200295	−	0.217048i
$256$	1.00000			0.0625000
$257$	−6.07726	+	10.5261i	−0.379089	+	0.656601i	−0.990930	−	0.134380i	$-0.957096\pi$
$257$	−6.07726	+	10.5261i	−0.379089	+	0.656601i	0.611841	+	0.790981i	$0.290429\pi$
$258$	−7.04439	−	2.19392i	−0.438565	−	0.136588i
$259$	24.5936	+	14.1991i	1.52818	+	0.882292i
$260$	−0.607659	−	1.11059i	−0.0376854	−	0.0688759i
$261$	1.36822	−	17.0143i	0.0846908	−	1.05316i
$262$	−1.23158	+	4.59631i	−0.0760871	+	0.283961i
$263$			8.30088i			0.511854i	0.966696	+	0.255927i	$0.0823808\pi$
$263$			8.30088i			0.511854i	−0.966696	+	0.255927i	$0.917619\pi$
$264$	−5.76048	−	0.231245i	−0.354533	−	0.0142321i
$265$	−0.513844	+	1.91769i	−0.0315652	+	0.117803i
$266$	−8.28907	+	8.28907i	−0.508235	+	0.508235i
$267$	−9.19622	−	2.86409i	−0.562799	−	0.175280i
$268$	3.56856	+	13.3180i	0.217985	+	0.813529i
$269$	−15.3432	−	8.85839i	−0.935490	−	0.540105i	−0.0469463	−	0.998897i	$-0.514949\pi$
$269$	−15.3432	−	8.85839i	−0.935490	−	0.540105i	−0.888544	+	0.458792i	$0.848282\pi$
$270$	−0.715903	−	1.67812i	−0.0435685	−	0.102127i
$271$	−6.44584	−	1.72716i	−0.391557	−	0.104917i	0.0576685	−	0.998336i	$-0.481633\pi$
$271$	−6.44584	−	1.72716i	−0.391557	−	0.104917i	−0.449226	+	0.893418i	$0.648300\pi$
$272$	−3.87756	+	6.71613i	−0.235112	+	0.407225i
$273$	−8.55346	−	17.2411i	−0.517679	−	1.04348i
$274$	−2.46287	−	4.26581i	−0.148787	−	0.257707i
$275$	4.20118	+	15.6790i	0.253341	+	0.945481i
$276$	6.18694	−	9.78722i	0.372410	−	0.589121i
$277$	−15.1301	+	8.73535i	−0.909077	+	0.524856i	−0.880134	−	0.474725i	$-0.842548\pi$
$277$	−15.1301	+	8.73535i	−0.909077	+	0.524856i	−0.0289433	+	0.999581i	$0.509214\pi$
$278$	−2.89940	+	2.89940i	−0.173894	+	0.173894i
$279$	−1.14169	+	3.20667i	−0.0683515	+	0.191979i
$280$	0.280065	+	1.04522i	0.0167371	+	0.0624636i
$281$	13.9665	−	3.74231i	0.833172	−	0.223248i	0.183075	−	0.983099i	$-0.441395\pi$
$281$	13.9665	−	3.74231i	0.833172	−	0.223248i	0.650097	+	0.759851i	$0.274728\pi$
$282$	−6.32846	−	4.00050i	−0.376855	−	0.238227i
$283$	3.09306	+	1.78578i	0.183863	+	0.106154i	0.589107	−	0.808055i	$-0.299480\pi$
$283$	3.09306	+	1.78578i	0.183863	+	0.106154i	−0.405243	+	0.914209i	$0.632813\pi$
$284$	−1.28199	+	0.343507i	−0.0760719	+	0.0203834i
$285$	0.0927856	−	2.31136i	0.00549614	−	0.136913i
$286$	8.67851	−	8.28908i	0.513171	−	0.490144i
$287$		−	8.08009i		−	0.476953i
$288$	−2.28453	+	1.94445i	−0.134617	+	0.114578i
$289$	−21.5709	−	37.3619i	−1.26888	−	2.19776i
$290$	−0.998874	−	1.73010i	−0.0586559	−	0.101595i
$291$	1.39800	+	0.435397i	0.0819522	+	0.0255234i
$292$	2.19140	+	2.19140i	0.128242	+	0.128242i
$293$	−4.84724	−	4.84724i	−0.283179	−	0.283179i	0.551197	−	0.834375i	$-0.314171\pi$
$293$	−4.84724	−	4.84724i	−0.283179	−	0.283179i	−0.834375	+	0.551197i	$0.814171\pi$
$294$	0.951239	+	4.22057i	0.0554774	+	0.246149i
$295$	1.92652	+	3.33684i	0.112167	+	0.194278i
$296$	4.60733	+	7.98013i	0.267796	+	0.463836i
$297$	13.6097	−	10.6727i	0.789713	−	0.619294i
$298$			7.59077i			0.439721i
$299$	5.70251	+	23.4188i	0.329784	+	1.35435i
$300$	7.13979	+	4.51338i	0.412216	+	0.260580i
$301$	−12.6807	+	3.39778i	−0.730902	+	0.195845i
$302$	12.6271	+	7.29027i	0.726609	+	0.419508i
$303$	0.730447	−	18.1960i	0.0419631	−	1.04533i
$304$	−3.67410	+	0.984473i	−0.210724	+	0.0564634i
$305$	0.911918	+	3.40332i	0.0522163	+	0.194874i
$306$	−4.20080	−	22.8830i	−0.240143	−	1.30813i
$307$	2.89643	−	2.89643i	0.165308	−	0.165308i	−0.619605	−	0.784913i	$-0.712707\pi$
$307$	2.89643	−	2.89643i	0.165308	−	0.165308i	0.784913	+	0.619605i	$0.212707\pi$
$308$	−8.88365	+	5.12898i	−0.506193	+	0.292251i
$309$	1.21127	+	2.30702i	0.0689070	+	0.131242i
$310$	0.103109	+	0.384807i	0.00585618	+	0.0218556i
$311$	14.2341	+	24.6543i	0.807144	+	1.39801i	0.914834	+	0.403830i	$0.132321\pi$
$311$	14.2341	+	24.6543i	0.807144	+	1.39801i	−0.107690	+	0.994185i	$0.534345\pi$
$312$	0.393603	−	6.23258i	0.0222834	−	0.352850i
$313$	−2.79680	+	4.84421i	−0.158085	+	0.273811i	−0.934178	−	0.356807i	$-0.883865\pi$
$313$	−2.79680	+	4.84421i	−0.158085	+	0.273811i	0.776093	+	0.630618i	$0.217199\pi$
$314$	15.8475	+	4.24632i	0.894324	+	0.239634i
$315$	−2.67219	−	1.84326i	−0.150561	−	0.103856i
$316$	10.7905	+	6.22990i	0.607014	+	0.350459i
$317$	0.535423	+	1.99822i	0.0300723	+	0.112231i	0.979331	−	0.202266i	$-0.0648306\pi$
$317$	0.535423	+	1.99822i	0.0300723	+	0.112231i	−0.949258	+	0.314498i	$0.898164\pi$
$318$	−7.19739	+	6.64183i	−0.403609	+	0.372456i
$319$	13.3914	−	13.3914i	0.749772	−	0.749772i
$320$	−0.0908752	+	0.339151i	−0.00508008	+	0.0189591i
$321$	−4.42017	−	8.41875i	−0.246710	−	0.469889i
$322$		−	20.6023i		−	1.14812i
$323$	7.63470	−	28.4931i	0.424806	−	1.58540i
$324$	1.43819	−	8.88435i	0.0798995	−	0.493575i
$325$	−17.0841	+	4.15998i	−0.947654	+	0.230754i
$326$	−16.1187	−	9.30611i	−0.892730	−	0.515418i
$327$	4.01371	−	3.70390i	0.221959	−	0.204826i
$328$	1.31091	−	2.27056i	0.0723829	−	0.125371i
$329$	−13.3215			−0.734439
$330$	0.601912	−	1.93266i	0.0331342	−	0.106389i
$331$	6.28560	−	23.4582i	0.345488	−	1.28938i	−0.546554	−	0.837424i	$-0.684061\pi$
$331$	6.28560	−	23.4582i	0.345488	−	1.28938i	0.892042	−	0.451953i	$-0.149273\pi$
$332$	−3.92483	+	1.05166i	−0.215403	+	0.0577171i
$333$	−26.0426	−	9.27213i	−1.42713	−	0.508110i
$334$	0.430839	−	0.746235i	0.0235745	−	0.0408322i
$335$	−4.84112			−0.264499
$336$	−1.58726	+	5.09649i	−0.0865923	+	0.278036i
$337$	23.9772	−	13.8433i	1.30612	−	0.754090i	0.324676	−	0.945825i	$-0.394745\pi$
$337$	23.9772	−	13.8433i	1.30612	−	0.754090i	0.981447	+	0.191735i	$0.0614113\pi$
$338$	8.76098	+	9.60444i	0.476535	+	0.522412i
$339$	11.5737	+	0.464605i	0.628596	+	0.0252339i
$340$	−1.92541	−	1.92541i	−0.104420	−	0.104420i
$341$	−3.27061	+	1.88829i	−0.177113	+	0.102256i
$342$	6.47935	−	9.39319i	0.350363	−	0.507925i
$343$	−9.81106	−	9.81106i	−0.529748	−	0.529748i
$344$	−4.11462	−	1.10251i	−0.221845	−	0.0594433i
$345$	2.75711	+	2.98772i	0.148438	+	0.160854i
$346$	23.0643	+	6.18006i	1.23994	+	0.332242i
$347$		−	2.18710i		−	0.117410i	−0.998275	−	0.0587049i	$-0.981303\pi$
$347$		−	2.18710i		−	0.117410i	0.998275	−	0.0587049i	$-0.0186971\pi$
$348$	0.395290	−	9.84697i	0.0211897	−	0.527853i
$349$	−20.5657	+	20.5657i	−1.10086	+	1.10086i	−0.106552	+	0.994307i	$0.533981\pi$
$349$	−20.5657	+	20.5657i	−1.10086	+	1.10086i	−0.994307	+	0.106552i	$0.966019\pi$
$350$	15.0294			0.803354
$351$	11.2198	+	15.0039i	0.598867	+	0.800848i
$352$	−3.32849			−0.177409
$353$	−5.13936	+	5.13936i	−0.273541	+	0.273541i	−0.830524	−	0.556983i	$-0.811959\pi$
$353$	−5.13936	+	5.13936i	−0.273541	+	0.273541i	0.556983	+	0.830524i	$0.311959\pi$
$354$	−0.762393	+	18.9918i	−0.0405208	+	1.00940i
$355$		−	0.466003i		−	0.0247329i
$356$	−5.37149	−	1.43929i	−0.284689	−	0.0762821i
$357$	−28.0740	−	30.4222i	−1.48583	−	1.61011i
$358$	10.0415	+	2.69061i	0.530709	+	0.142203i
$359$	5.00179	+	5.00179i	0.263985	+	0.263985i	0.826671	−	0.562686i	$-0.190232\pi$
$359$	5.00179	+	5.00179i	0.263985	+	0.263985i	−0.562686	+	0.826671i	$0.690232\pi$
$360$	−0.451856	−	0.951504i	−0.0238149	−	0.0501487i
$361$	−3.92464	+	2.26589i	−0.206560	+	0.119257i
$362$	0.449508	+	0.449508i	0.0236256	+	0.0236256i
$363$	0.136510	+	0.00547995i	0.00716490	+	0.000287623i
$364$	−5.33364	−	9.74806i	−0.279559	−	0.510937i
$365$	−0.942359	+	0.544071i	−0.0493253	+	0.0284780i
$366$	−5.16828	+	16.5947i	−0.270150	+	0.867417i
$367$	17.5261			0.914857			0.457428	−	0.889246i	$-0.348771\pi$
$367$	17.5261			0.914857			0.457428	+	0.889246i	$0.348771\pi$
$368$	3.34250	−	5.78938i	0.174240	−	0.301793i
$369$	1.42019	+	7.73619i	0.0739321	+	0.402730i
$370$	−3.12516	+	0.837384i	−0.162469	+	0.0435335i
$371$	−4.51019	+	16.8323i	−0.234157	+	0.873888i
$372$	−0.584367	+	1.87632i	−0.0302980	+	0.0972829i
$373$	12.1273			0.627927			0.313963	−	0.949435i	$-0.398343\pi$
$373$	12.1273			0.627927			0.313963	+	0.949435i	$0.398343\pi$
$374$	12.9064	−	22.3546i	0.667376	−	1.15593i
$375$	−4.41419	+	4.07347i	−0.227948	+	0.210353i
$376$	−3.74344	−	2.16128i	−0.193053	−	0.111459i
$377$	14.1694	+	14.8350i	0.729759	+	0.764044i
$378$	−6.28374	−	14.7295i	−0.323201	−	0.757602i
$379$	1.59520	−	5.95337i	0.0819399	−	0.305804i	−0.912777	−	0.408458i	$-0.866067\pi$
$379$	1.59520	−	5.95337i	0.0819399	−	0.305804i	0.994717	+	0.102654i	$0.0327334\pi$
$380$		−	1.33554i		−	0.0685117i
$381$	9.94079	+	18.9335i	0.509282	+	0.969990i
$382$	−0.0385862	+	0.144006i	−0.00197424	+	0.00736796i
$383$	−10.3289	+	10.3289i	−0.527785	+	0.527785i	−0.919911	−	0.392127i	$-0.871740\pi$
$383$	−10.3289	+	10.3289i	−0.527785	+	0.527785i	0.392127	+	0.919911i	$0.371740\pi$
$384$	−1.27288	+	1.17463i	−0.0649566	+	0.0599428i
$385$	−0.932194	−	3.47900i	−0.0475090	−	0.177306i
$386$	3.69480	+	2.13319i	0.188060	+	0.108577i
$387$	11.5438	−	5.48197i	0.586802	−	0.278664i
$388$	0.816569	+	0.218799i	0.0414550	+	0.0111078i
$389$	2.49669	−	4.32440i	0.126587	−	0.219256i	−0.795765	−	0.605606i	$-0.792931\pi$
$389$	2.49669	−	4.32440i	0.126587	−	0.219256i	0.922352	+	0.386350i	$0.126264\pi$
$390$	2.07802	+	0.699878i	0.105224	+	0.0354397i
$391$	25.9215	+	44.8974i	1.31091	+	2.27056i
$392$	0.646496	+	2.41276i	0.0326530	+	0.121863i
$393$	−3.83132	−	7.29722i	−0.193265	−	0.368096i
$394$	−16.5627	+	9.56250i	−0.834419	+	0.481752i
$395$	−3.09347	+	3.09347i	−0.155649	+	0.155649i
$396$	7.60406	−	6.47211i	0.382118	−	0.325236i
$397$	−1.56112	−	5.82617i	−0.0783503	−	0.292407i	0.915622	−	0.402041i	$-0.131699\pi$
$397$	−1.56112	−	5.82617i	−0.0783503	−	0.292407i	−0.993972	+	0.109634i	$0.965032\pi$
$398$	5.07693	−	1.36036i	0.254483	−	0.0681886i
$399$	0.814413	−	20.2876i	0.0407716	−	1.01565i
$400$	4.22336	+	2.43836i	0.211168	+	0.121918i
$401$	7.37085	−	1.97501i	0.368083	−	0.0986274i	−0.0700364	−	0.997544i	$-0.522312\pi$
$401$	7.37085	−	1.97501i	0.368083	−	0.0986274i	0.438119	+	0.898917i	$0.355645\pi$
$402$	−20.1862	−	12.7606i	−1.00680	−	0.636441i
$403$	−1.96363	−	3.58884i	−0.0978155	−	0.178773i
$404$		−	10.5139i		−	0.523087i
$405$	2.88244	+	1.29513i	0.143230	+	0.0643555i
$406$	−8.76748	−	15.1857i	−0.435123	−	0.753655i
$407$	−15.3355	−	26.5618i	−0.760151	−	1.31662i
$408$	−2.95330	−	13.1036i	−0.146210	−	0.648723i
$409$	−3.33008	−	3.33008i	−0.164662	−	0.164662i	0.619966	−	0.784628i	$-0.287146\pi$
$409$	−3.33008	−	3.33008i	−0.164662	−	0.164662i	−0.784628	+	0.619966i	$0.787146\pi$
$410$	0.650934	+	0.650934i	0.0321474	+	0.0321474i
$411$	8.14571	+	2.53692i	0.401798	+	0.125137i
$412$	0.752193	+	1.30284i	0.0370579	+	0.0641862i
$413$	16.9098	+	29.2886i	0.832077	+	1.44120i
$414$	3.62114	+	19.7254i	0.177969	+	0.969450i
$415$		−	1.42668i		−	0.0700329i
$416$	0.0827293	−	3.60460i	0.00405614	−	0.176730i
$417$	0.284870	−	7.09633i	0.0139501	−	0.347509i
$418$	12.2292	−	3.27681i	0.598151	−	0.160274i
$419$	−12.1816	−	7.03305i	−0.595110	−	0.343587i	0.172005	−	0.985096i	$-0.444975\pi$
$419$	−12.1816	−	7.03305i	−0.595110	−	0.343587i	−0.767116	+	0.641509i	$0.778309\pi$
$420$	−1.58424	−	1.00147i	−0.0773028	−	0.0488666i
$421$	29.6767	−	7.95186i	1.44636	−	0.387550i	0.551601	−	0.834108i	$-0.314017\pi$
$421$	29.6767	−	7.95186i	1.44636	−	0.387550i	0.894755	+	0.446558i	$0.147350\pi$
$422$	−6.17738	−	23.0543i	−0.300710	−	1.12227i
$423$	12.7545	−	2.34144i	0.620147	−	0.113845i
$424$	−3.99826	+	3.99826i	−0.194172	+	0.194172i
$425$	−32.7527	+	18.9098i	−1.58874	+	0.917258i
$426$	1.22833	−	1.94311i	0.0595126	−	0.0941440i
$427$	8.00423	+	29.8722i	0.387352	+	1.44562i
$428$	−2.74489	−	4.75429i	−0.132679	−	0.229807i
$429$	−1.31011	+	20.7451i	−0.0632525	+	1.00158i
$430$	0.747833	−	1.29529i	0.0360637	−	0.0624642i
$431$	37.7065	+	10.1034i	1.81626	+	0.486665i	0.996314	−	0.0857790i	$-0.0273379\pi$
$431$	37.7065	+	10.1034i	1.81626	+	0.486665i	0.819944	+	0.572444i	$0.194005\pi$
$432$	0.623927	−	5.15856i	0.0300187	−	0.248191i
$433$	−1.12288	−	0.648297i	−0.0539623	−	0.0311552i	0.472776	−	0.881183i	$-0.343252\pi$
$433$	−1.12288	−	0.648297i	−0.0539623	−	0.0311552i	−0.526738	+	0.850027i	$0.676585\pi$
$434$	0.905022	+	3.37759i	0.0434424	+	0.162129i
$435$	3.30369	+	1.02891i	0.158400	+	0.0493324i
$436$	2.22967	−	2.22967i	0.106782	−	0.106782i
$437$	−6.58121	+	24.5614i	−0.314822	+	1.17493i
$438$	−5.36349	−	0.215308i	−0.256278	−	0.0102878i
$439$		−	18.8010i		−	0.897321i	−0.893702	−	0.448660i	$-0.851901\pi$
$439$		−	18.8010i		−	0.897321i	0.893702	−	0.448660i	$-0.148099\pi$
$440$	0.302478	−	1.12886i	0.0144201	−	0.0538164i
$441$	−6.16844	−	4.25494i	−0.293735	−	0.202616i
$442$	23.8882	+	14.5327i	1.13625	+	0.691249i
$443$	18.8039	+	10.8564i	0.893400	+	0.515805i	0.875053	−	0.484027i	$-0.160826\pi$
$443$	18.8039	+	10.8564i	0.893400	+	0.515805i	0.0183470	+	0.999832i	$0.494160\pi$
$444$	−15.2383	−	4.74586i	−0.723179	−	0.225229i
$445$	0.976271	−	1.69095i	0.0462797	−	0.0801588i
$446$	22.1358			1.04816
$447$	−8.91637	−	9.66217i	−0.421730	−	0.457005i
$448$	−0.797644	+	2.97685i	−0.0376852	+	0.140643i
$449$	−21.9490	+	5.88123i	−1.03584	+	0.277552i	−0.736388	−	0.676559i	$-0.763470\pi$
$449$	−21.9490	+	5.88123i	−1.03584	+	0.277552i	−0.299451	+	0.954112i	$0.596804\pi$
$450$	−14.3897	+	2.64162i	−0.678337	+	0.124527i
$451$	−4.36336	+	7.55756i	−0.205463	+	0.355872i
$452$	6.68745			0.314551
$453$	−24.6363	+	5.55256i	−1.15751	+	0.260882i
$454$	−19.3460	+	11.1694i	−0.907951	+	0.524206i
$455$	3.79076	−	0.923052i	0.177713	−	0.0432734i
$456$	3.52032	−	5.56884i	0.164854	−	0.260785i
$457$	−20.5331	−	20.5331i	−0.960498	−	0.960498i	0.0387513	−	0.999249i	$-0.487662\pi$
$457$	−20.5331	−	20.5331i	−0.960498	−	0.960498i	−0.999249	+	0.0387513i	$0.987662\pi$
$458$	−8.06228	+	4.65476i	−0.376725	+	0.217503i
$459$	32.2262	+	24.1930i	1.50419	+	1.12923i
$460$	1.65972	+	1.65972i	0.0773850	+	0.0773850i
$461$	11.3082	+	3.03004i	0.526678	+	0.141123i	0.512354	−	0.858775i	$-0.328774\pi$
$461$	11.3082	+	3.03004i	0.526678	+	0.141123i	0.0143239	+	0.999897i	$0.495440\pi$
$462$	5.28320	−	16.9636i	0.245797	−	0.789220i
$463$	−17.8104	−	4.77229i	−0.827722	−	0.221787i	−0.180002	−	0.983666i	$-0.557610\pi$
$463$	−17.8104	−	4.77229i	−0.827722	−	0.221787i	−0.647720	+	0.761879i	$0.724277\pi$
$464$		−	5.68973i		−	0.264139i
$465$	−0.583252	−	0.368700i	−0.0270477	−	0.0170980i
$466$	20.1487	−	20.1487i	0.933370	−	0.933370i
$467$	−15.3781			−0.711613			−0.355807	−	0.934560i	$-0.615794\pi$
$467$	−15.3781			−0.711613			−0.355807	+	0.934560i	$0.615794\pi$
$468$	6.81999	+	8.39570i	0.315254	+	0.388091i
$469$	−42.4923			−1.96211
$470$	1.07319	−	1.07319i	0.0495024	−	0.0495024i
$471$	−25.1599	+	13.2099i	−1.15931	+	0.608680i
$472$			10.9738i			0.505108i
$473$	13.6955	+	3.66969i	0.629719	+	0.168733i
$474$	−21.0529	+	4.74494i	−0.966993	+	0.217943i
$475$	−17.9176	−	4.80100i	−0.822114	−	0.220285i
$476$	−16.9000	−	16.9000i	−0.774610	−	0.774610i
$477$	1.35972	−	16.9086i	0.0622574	−	0.774191i
$478$	−12.5096	+	7.22241i	−0.572175	+	0.330346i
$479$	−10.9954	−	10.9954i	−0.502391	−	0.502391i	0.409789	−	0.912180i	$-0.365602\pi$
$479$	−10.9954	−	10.9954i	−0.502391	−	0.502391i	−0.912180	+	0.409789i	$0.865602\pi$
$480$	−0.282704	−	0.538445i	−0.0129036	−	0.0245765i
$481$	29.1463	−	15.9474i	1.32896	−	0.727139i
$482$	−26.4305	+	15.2597i	−1.20388	+	0.695058i
$483$	24.2001	+	26.2243i	1.10114	+	1.19325i
$484$	0.0788774			0.00358534
$485$	−0.148412	+	0.257057i	−0.00673903	+	0.0116723i
$486$	8.60520	+	12.9981i	0.390340	+	0.589606i
$487$	16.7862	−	4.49786i	0.760656	−	0.203817i	0.142417	−	0.989807i	$-0.454513\pi$
$487$	16.7862	−	4.49786i	0.760656	−	0.203817i	0.618240	+	0.785990i	$0.287846\pi$
$488$	−2.59721	+	9.69291i	−0.117570	+	0.438777i
$489$	31.4485	−	7.08790i	1.42215	−	0.320526i
$490$	−0.877039			−0.0396206
$491$	4.04041	−	6.99820i	0.182341	−	0.315824i	−0.760336	−	0.649530i	$-0.774966\pi$
$491$	4.04041	−	6.99820i	0.182341	−	0.315824i	0.942677	+	0.333706i	$0.108299\pi$
$492$	0.998442	+	4.43001i	0.0450132	+	0.199720i
$493$	38.2130	+	22.0623i	1.72103	+	0.993634i
$494$	3.24468	+	13.3251i	0.145985	+	0.599526i
$495$	1.50400	+	3.16708i	0.0675998	+	0.142350i
$496$	−0.293661	+	1.09596i	−0.0131858	+	0.0492099i
$497$		−	4.09028i		−	0.183474i
$498$	3.76055	−	5.94887i	0.168514	−	0.266575i
$499$	3.39501	−	12.6704i	0.151982	−	0.567203i	−0.847363	−	0.531014i	$-0.821811\pi$
$499$	3.39501	−	12.6704i	0.151982	−	0.567203i	0.999345	−	0.0361895i	$-0.0115220\pi$
$500$	−2.45215	+	2.45215i	−0.109663	+	0.109663i
$501$	0.328144	+	1.45595i	0.0146604	+	0.0650470i
$502$	−4.25847	−	15.8928i	−0.190065	−	0.709332i
$503$	−17.8854	−	10.3261i	−0.797470	−	0.460419i	0.0451158	−	0.998982i	$-0.485634\pi$
$503$	−17.8854	−	10.3261i	−0.797470	−	0.460419i	−0.842586	+	0.538562i	$0.818968\pi$
$504$	−3.96610	−	8.35170i	−0.176664	−	0.372014i
$505$	3.56580	+	0.955455i	0.158676	+	0.0425172i
$506$	−11.1255	+	19.2699i	−0.494589	+	0.856653i
$507$	−22.4334	−	1.93440i	−0.996303	−	0.0859097i
$508$	6.17316	+	10.6922i	0.273890	+	0.474391i
$509$	−8.90280	−	33.2257i	−0.394610	−	1.47270i	−0.822444	−	0.568846i	$-0.807390\pi$
$509$	−8.90280	−	33.2257i	−0.394610	−	1.47270i	0.427834	−	0.903857i	$-0.359277\pi$
$510$	4.71247	+	0.189174i	0.208672	+	0.00837676i
$511$	−8.27143	+	4.77551i	−0.365906	+	0.211256i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.78609	+	19.5673i	0.123009	+	0.863918i
$514$	−3.14582	−	11.7404i	−0.138756	−	0.517845i
$515$	−0.510214	+	0.136711i	−0.0224827	+	0.00602423i
$516$	6.53248	−	3.42980i	0.287576	−	0.150989i
$517$	12.4600	+	7.19380i	0.547992	+	0.316383i
$518$	−27.4307	+	7.35002i	−1.20523	+	0.322941i
$519$	−36.6175	+	19.2256i	−1.60733	+	0.843910i
$520$	1.21499	+	0.355627i	0.0532807	+	0.0155953i
$521$		−	10.8135i		−	0.473747i	−0.971540	−	0.236874i	$-0.923877\pi$
$521$		−	10.8135i		−	0.473747i	0.971540	−	0.236874i	$-0.0761227\pi$
$522$	11.0634	+	12.9984i	0.484233	+	0.568924i
$523$	12.9411	+	22.4147i	0.565876	+	0.980126i	0.996968	+	0.0778180i	$0.0247953\pi$
$523$	12.9411	+	22.4147i	0.565876	+	0.980126i	−0.431091	+	0.902308i	$0.641871\pi$
$524$	−2.37922	−	4.12094i	−0.103937	−	0.180024i
$525$	−19.1307	+	17.6540i	−0.834930	+	0.770484i
$526$	−5.86961	−	5.86961i	−0.255927	−	0.255927i
$527$	−6.22190	−	6.22190i	−0.271030	−	0.271030i
$528$	4.23679	−	3.90976i	0.184383	−	0.170151i
$529$	−10.8446	−	18.7835i	−0.471506	−	0.816673i
$530$	−0.992670	−	1.71935i	−0.0431188	−	0.0746840i
$531$	−21.3380	−	25.0699i	−0.925989	−	1.08794i
$532$		−	11.7225i		−	0.508235i
$533$	−8.07603	−	4.91315i	−0.349812	−	0.212812i
$534$	8.52793	−	4.47749i	0.369040	−	0.193760i
$535$	1.86187	−	0.498885i	0.0804954	−	0.0215687i
$536$	−11.9406	−	6.89393i	−0.515757	−	0.297772i
$537$	−15.9421	+	8.37023i	−0.687953	+	0.361202i
$538$	17.1131	−	4.58544i	0.737798	−	0.197692i
$539$	−2.15186	−	8.03085i	−0.0926872	−	0.345913i
$540$	1.69283	+	0.680390i	0.0728478	+	0.0292793i
$541$	−20.8711	+	20.8711i	−0.897318	+	0.897318i	−0.995198	−	0.0978806i	$-0.968794\pi$
$541$	−20.8711	+	20.8711i	−0.897318	+	0.897318i	0.0978806	+	0.995198i	$0.468794\pi$
$542$	5.77918	−	3.33661i	0.248237	−	0.143320i
$543$	−1.10018	−	0.0441648i	−0.0472132	−	0.00189529i
$544$	−2.00717	−	7.49087i	−0.0860568	−	0.321168i
$545$	0.553574	+	0.958818i	0.0237125	+	0.0410713i
$546$	18.2395	+	6.14308i	0.780579	+	0.262900i
$547$	8.21466	−	14.2282i	0.351233	−	0.608354i	−0.635233	−	0.772321i	$-0.719096\pi$
$547$	8.21466	−	14.2282i	0.351233	−	0.608354i	0.986466	+	0.163967i	$0.0524291\pi$
$548$	4.75789	+	1.27487i	0.203247	+	0.0544599i
$549$	−12.9140	−	27.1939i	−0.551157	−	1.16061i
$550$	−14.0574	−	8.11607i	−0.599411	−	0.346070i
$551$	5.60138	+	20.9047i	0.238627	+	0.890568i
$552$	2.54578	+	11.2954i	0.108356	+	0.480766i
$553$	−27.1525	+	27.1525i	−1.15464	+	1.15464i
$554$	4.52175	−	16.8754i	0.192111	−	0.716967i
$555$	2.99435	−	4.73681i	0.127103	−	0.201066i
$556$		−	4.10037i		−	0.173894i
$557$	−6.82819	+	25.4831i	−0.289320	+	1.07976i	0.656305	+	0.754496i	$0.272118\pi$
$557$	−6.82819	+	25.4831i	−0.289320	+	1.07976i	−0.945625	+	0.325260i	$0.894548\pi$
$558$	−1.46016	−	3.07476i	−0.0618135	−	0.130165i
$559$	−4.31450	+	14.7403i	−0.182484	+	0.623450i
$560$	−0.937115	−	0.541044i	−0.0396003	−	0.0228633i
$561$	9.83006	+	43.6152i	0.415025	+	1.84143i
$562$	−7.22960	+	12.5220i	−0.304962	+	0.528210i
$563$	−27.8900			−1.17542			−0.587712	−	0.809070i	$-0.699971\pi$
$563$	−27.8900			−1.17542			−0.587712	+	0.809070i	$0.699971\pi$
$564$	7.30368	−	1.64612i	0.307541	−	0.0693140i
$565$	−0.607723	+	2.26805i	−0.0255671	+	0.0954177i
$566$	−3.44986	+	0.924387i	−0.145008	+	0.0388549i
$567$	25.3002	+	11.3678i	1.06251	+	0.477404i
$568$	0.663605	−	1.14940i	0.0278442	−	0.0482277i
$569$	−0.402831			−0.0168875			−0.00844377	−	0.999964i	$-0.502688\pi$
$569$	−0.402831			−0.0168875			−0.00844377	+	0.999964i	$0.502688\pi$
$570$	1.56877	+	1.69999i	0.0657085	+	0.0712047i
$571$	−30.8570	+	17.8153i	−1.29133	+	0.745548i	−0.978889	−	0.204390i	$-0.934479\pi$
$571$	−30.8570	+	17.8153i	−1.29133	+	0.745548i	−0.312437	+	0.949938i	$0.601145\pi$
$572$	−0.275364	+	11.9979i	−0.0115136	+	0.501657i
$573$	−0.120038	−	0.228627i	−0.00501466	−	0.00955103i
$574$	5.71349	+	5.71349i	0.238476	+	0.238476i
$575$	28.2332	−	16.3004i	1.17741	−	0.679775i
$576$	0.240472	−	2.99035i	0.0100197	−	0.124598i
$577$	33.2996	+	33.2996i	1.38628	+	1.38628i	0.832986	+	0.553294i	$0.186629\pi$
$577$	33.2996	+	33.2996i	1.38628	+	1.38628i	0.553294	+	0.832986i	$0.313371\pi$
$578$	41.6718	+	11.1659i	1.73332	+	0.464442i
$579$	−7.20878	+	1.62473i	−0.299587	+	0.0675213i
$580$	1.92968	+	0.517055i	0.0801255	+	0.0214696i
$581$		−	12.5225i		−	0.519520i
$582$	−1.29641	+	0.680664i	−0.0537378	+	0.0282144i
$583$	13.3082	−	13.3082i	0.551168	−	0.551168i
$584$	−3.09911			−0.128242
$585$	−3.46718	+	1.55004i	−0.143350	+	0.0640864i
$586$	6.85503			0.283179
$587$	4.31874	−	4.31874i	0.178253	−	0.178253i	−0.612341	−	0.790594i	$-0.709772\pi$
$587$	4.31874	−	4.31874i	0.178253	−	0.178253i	0.790594	+	0.612341i	$0.209772\pi$
$588$	−3.65702	−	2.31177i	−0.150813	−	0.0953356i
$589$		−	4.31576i		−	0.177828i
$590$	−3.72176	−	0.997242i	−0.153222	−	0.0410558i
$591$	9.85002	−	31.6271i	0.405176	−	1.30097i
$592$	−8.90068	−	2.38493i	−0.365816	−	0.0980200i
$593$	−5.57423	−	5.57423i	−0.228906	−	0.228906i	0.583329	−	0.812236i	$-0.301750\pi$
$593$	−5.57423	−	5.57423i	−0.228906	−	0.228906i	−0.812236	+	0.583329i	$0.801750\pi$
$594$	−2.07674	+	17.1702i	−0.0852096	+	0.704503i
$595$	7.26744	−	4.19586i	0.297936	−	0.172013i
$596$	−5.36748	−	5.36748i	−0.219861	−	0.219861i
$597$	−4.86442	+	7.69511i	−0.199088	+	0.314940i
$598$	−20.5919	−	12.5273i	−0.842066	−	0.512281i
$599$	12.2562	−	7.07612i	0.500775	−	0.289122i	−0.228259	−	0.973601i	$-0.573303\pi$
$599$	12.2562	−	7.07612i	0.500775	−	0.289122i	0.729033	+	0.684478i	$0.239970\pi$
$600$	−8.24003	+	1.85715i	−0.336398	+	0.0758179i
$601$	−39.6189			−1.61609			−0.808044	−	0.589121i	$-0.799474\pi$
$601$	−39.6189			−1.61609			−0.808044	+	0.589121i	$0.799474\pi$
$602$	6.56400	−	11.3692i	0.267529	−	0.463373i
$603$	40.6837	−	7.46861i	1.65677	−	0.304145i
$604$	−14.0837	+	3.77372i	−0.573058	+	0.153550i
$605$	−0.00716800	+	0.0267513i	−0.000291421	+	0.00108760i
$606$	12.3500	+	13.3830i	0.501685	+	0.543648i
$607$	−6.85360			−0.278179			−0.139090	−	0.990280i	$-0.544418\pi$
$607$	−6.85360			−0.278179			−0.139090	+	0.990280i	$0.544418\pi$
$608$	1.90186	−	3.29411i	0.0771304	−	0.133594i
$609$	28.9976	+	9.03110i	1.17504	+	0.365959i
$610$	−3.05134	−	1.76169i	−0.123545	−	0.0713288i
$611$	−8.10024	+	13.3148i	−0.327701	+	0.538660i
$612$	19.1511	+	13.2103i	0.774138	+	0.533994i
$613$	−5.58884	+	20.8578i	−0.225731	+	0.842440i	0.756379	+	0.654134i	$0.226967\pi$
$613$	−5.58884	+	20.8578i	−0.225731	+	0.842440i	−0.982110	+	0.188307i	$0.939700\pi$
$614$			4.09617i			0.165308i
$615$	−1.59317	−	0.0639552i	−0.0642430	−	0.00257892i
$616$	2.65496	−	9.90843i	0.106971	−	0.399222i
$617$	19.7634	−	19.7634i	0.795644	−	0.795644i	−0.186761	−	0.982405i	$-0.559799\pi$
$617$	19.7634	−	19.7634i	0.795644	−	0.795644i	0.982405	+	0.186761i	$0.0597991\pi$
$618$	−2.48781	−	0.774810i	−0.100074	−	0.0311674i
$619$	4.70742	+	17.5683i	0.189207	+	0.706130i	0.993691	+	0.112155i	$0.0357754\pi$
$619$	4.70742	+	17.5683i	0.189207	+	0.706130i	−0.804484	+	0.593975i	$0.797558\pi$
$620$	−0.345008	−	0.199191i	−0.0138559	−	0.00799969i
$621$	−27.7794	−	20.8546i	−1.11475	−	0.836868i
$622$	−27.4983	−	7.36814i	−1.10258	−	0.295435i
$623$	8.56908	−	14.8421i	0.343313	−	0.594636i
$624$	4.12878	+	4.68542i	0.165284	+	0.187567i
$625$	11.5830	+	20.0623i	0.463319	+	0.802493i
$626$	−1.44773	−	5.40301i	−0.0578630	−	0.215948i
$627$	−11.7174	+	18.5359i	−0.467946	+	0.740251i
$628$	−14.2085	+	8.20325i	−0.566979	+	0.327345i
$629$	50.5304	−	50.5304i	2.01478	−	2.01478i
$630$	3.19291	−	0.586145i	0.127208	−	0.0233526i
$631$	−2.24267	−	8.36975i	−0.0892792	−	0.333195i	0.906811	−	0.421538i	$-0.138509\pi$
$631$	−2.24267	−	8.36975i	−0.0892792	−	0.333195i	−0.996090	+	0.0883431i	$0.971843\pi$
$632$	−12.0353	+	3.22484i	−0.478737	+	0.128277i
$633$	34.9435	+	22.0893i	1.38888	+	0.877971i
$634$	−1.79156	−	1.03436i	−0.0711519	−	0.0410796i
$635$	−4.18727	+	1.12197i	−0.166167	+	0.0445242i
$636$	0.392834	−	9.78581i	0.0155769	−	0.388032i
$637$	8.75051	−	2.13076i	0.346708	−	0.0844236i
$638$			18.9382i			0.749772i
$639$	0.718924	+	3.91619i	0.0284402	+	0.154922i
$640$	−0.175557	−	0.304074i	−0.00693952	−	0.0120196i
$641$	−13.2773	−	22.9970i	−0.524424	−	0.908329i	−0.999596	−	0.0284355i	$-0.990947\pi$
$641$	−13.2773	−	22.9970i	−0.524424	−	0.908329i	0.475172	−	0.879893i	$-0.342386\pi$
$642$	9.07848	+	2.82742i	0.358299	+	0.111590i
$643$	−23.6006	−	23.6006i	−0.930715	−	0.930715i	0.0670354	−	0.997751i	$-0.478646\pi$
$643$	−23.6006	−	23.6006i	−0.930715	−	0.930715i	−0.997751	+	0.0670354i	$0.978646\pi$
$644$	14.5680	+	14.5680i	0.574060	+	0.574060i
$645$	0.569580	+	2.52718i	0.0224272	+	0.0995076i
$646$	14.7491	+	25.5462i	0.580296	+	1.00510i
$647$	−11.9267	−	20.6576i	−0.468886	−	0.812134i	0.530482	−	0.847696i	$-0.322011\pi$
$647$	−11.9267	−	20.6576i	−0.468886	−	0.812134i	−0.999367	+	0.0355623i	$0.988678\pi$
$648$	5.26523	+	7.29914i	0.206838	+	0.286737i
$649$		−	36.5261i		−	1.43377i
$650$	9.13871	−	15.0218i	0.358450	−	0.589204i
$651$	−5.11942	−	3.23621i	−0.200646	−	0.126837i
$652$	17.9780	−	4.81720i	0.704074	−	0.188656i
$653$	−25.8931	−	14.9494i	−1.01327	−	0.585014i	−0.101126	−	0.994874i	$-0.532244\pi$
$653$	−25.8931	−	14.9494i	−1.01327	−	0.585014i	−0.912149	+	0.409859i	$0.865578\pi$
$654$	−0.219069	+	5.45717i	−0.00856626	+	0.213392i
$655$	1.61383	−	0.432425i	0.0630576	−	0.0168962i
$656$	0.678577	+	2.53248i	0.0264940	+	0.0988769i
$657$	7.08002	−	6.02608i	0.276218	−	0.235100i
$658$	9.41974	−	9.41974i	0.367220	−	0.367220i
$659$	20.6263	−	11.9086i	0.803487	−	0.463893i	−0.0412023	−	0.999151i	$-0.513119\pi$
$659$	20.6263	−	11.9086i	0.803487	−	0.463893i	0.844689	+	0.535258i	$0.179785\pi$
$660$	0.940980	+	1.79221i	0.0366276	+	0.0697617i
$661$	3.35543	+	12.5226i	0.130511	+	0.487074i	0.999976	−	0.00692047i	$-0.00220287\pi$
$661$	3.35543	+	12.5226i	0.130511	+	0.487074i	−0.869465	+	0.493995i	$0.835536\pi$
$662$	12.1428	+	21.0320i	0.471945	+	0.817432i
$663$	−47.4775	+	9.56144i	−1.84387	+	0.371335i
$664$	2.03164	−	3.51891i	0.0788430	−	0.136560i
$665$	3.97570	+	1.06529i	0.154171	+	0.0413100i
$666$	24.9713	−	11.8585i	0.967618	−	0.459508i
$667$	−32.9400	−	19.0179i	−1.27544	−	0.736377i
$668$	0.223019	+	0.832317i	0.00862885	+	0.0322033i
$669$	−28.1763	+	26.0014i	−1.08936	+	1.00527i
$670$	3.42319	−	3.42319i	0.132249	−	0.132249i
$671$	8.64479	−	32.2628i	0.333728	−	1.24549i
$672$	−2.48140	−	4.72613i	−0.0957220	−	0.182314i
$673$		−	46.4053i		−	1.78879i	−0.447276	−	0.894396i	$-0.647606\pi$
$673$		−	46.4053i		−	1.78879i	0.447276	−	0.894396i	$-0.352394\pi$
$674$	−7.16580	+	26.7431i	−0.276016	+	1.03011i
$675$	15.2135	−	20.2651i	0.585567	−	0.780004i
$676$	−12.9863	−	0.596413i	−0.499474	−	0.0229389i
$677$	−28.9400	−	16.7085i	−1.11225	−	0.642159i	−0.172841	−	0.984950i	$-0.555295\pi$
$677$	−28.9400	−	16.7085i	−1.11225	−	0.642159i	−0.939412	+	0.342790i	$0.888628\pi$
$678$	−8.51235	+	7.85530i	−0.326915	+	0.301681i
$679$	−1.30266	+	2.25628i	−0.0499917	+	0.0865881i
$680$	2.72294			0.104420
$681$	11.5052	−	36.9418i	0.440882	−	1.41561i
$682$	0.977449	−	3.64789i	0.0374284	−	0.139685i
$683$	−4.57669	+	1.22632i	−0.175122	+	0.0469238i	−0.345314	−	0.938487i	$-0.612228\pi$
$683$	−4.57669	+	1.22632i	−0.175122	+	0.0469238i	0.170192	+	0.985411i	$0.445561\pi$
$684$	2.06040	+	11.2236i	0.0787812	+	0.429144i
$685$	−0.864749	+	1.49779i	−0.0330404	+	0.0572276i
$686$	13.8749			0.529748
$687$	4.79472	−	15.3952i	0.182930	−	0.587363i
$688$	3.68906	−	2.12988i	0.140644	−	0.0812010i
$689$	14.0813	+	14.7429i	0.536457	+	0.561660i
$690$	−4.06221	−	0.163070i	−0.154646	−	0.00620798i
$691$	3.43143	+	3.43143i	0.130538	+	0.130538i	0.769357	−	0.638819i	$-0.220577\pi$
$691$	3.43143	+	3.43143i	0.130538	+	0.130538i	−0.638819	+	0.769357i	$0.720577\pi$
$692$	−20.6789	+	11.9390i	−0.786093	+	0.453851i
$693$	13.2012	+	27.7986i	0.501470	+	1.05598i
$694$	1.54652	+	1.54652i	0.0587049	+	0.0587049i
$695$	1.39064	+	0.372622i	0.0527501	+	0.0141344i
$696$	6.68335	+	7.24237i	0.253332	+	0.274521i
$697$	−19.6397	−	5.26245i	−0.743907	−	0.199329i
$698$		−	29.0844i		−	1.10086i
$699$	−1.97964	+	49.3143i	−0.0748767	+	1.86524i
$700$	−10.6274	+	10.6274i	−0.401677	+	0.401677i
$701$	1.76335			0.0666009			0.0333004	−	0.999445i	$-0.489398\pi$
$701$	1.76335			0.0666009			0.0333004	+	0.999445i	$0.489398\pi$
$702$	−18.5429	−	2.67577i	−0.699858	−	0.100991i
$703$	35.0499			1.32193
$704$	2.35360	−	2.35360i	0.0887047	−	0.0887047i
$705$	−0.105442	+	2.62664i	−0.00397118	+	0.0989251i
$706$		−	7.26816i		−	0.273541i
$707$	31.2984	+	8.38637i	1.17710	+	0.315402i
$708$	−12.8901	−	13.9683i	−0.484441	−	0.524962i
$709$	33.1400	+	8.87983i	1.24460	+	0.333489i	0.820247	−	0.572009i	$-0.193836\pi$
$709$	33.1400	+	8.87983i	1.24460	+	0.333489i	0.424350	+	0.905498i	$0.360502\pi$
$710$	0.329514	+	0.329514i	0.0123664	+	0.0123664i
$711$	21.2244	−	30.7692i	0.795977	−	1.15394i
$712$	4.81595	−	2.78049i	0.180485	−	0.104203i
$713$	5.36335	+	5.36335i	0.200859	+	0.200859i
$714$	41.3630	+	1.66045i	1.54797	+	0.0621407i
$715$	−4.04407	−	1.18370i	−0.151240	−	0.0442679i
$716$	−9.00294	+	5.19785i	−0.336456	+	0.194253i
$717$	7.43958	−	23.8875i	0.277836	−	0.892094i
$718$	−7.07360			−0.263985
$719$	15.1571	−	26.2528i	0.565264	−	0.979065i	−0.431762	−	0.901988i	$-0.642108\pi$
$719$	15.1571	−	26.2528i	0.565264	−	0.979065i	0.997025	−	0.0770774i	$-0.0245588\pi$
$720$	0.992326	+	0.353305i	0.0369818	+	0.0131669i
$721$	−4.47833	+	1.19997i	−0.166782	+	0.0446891i
$722$	1.17291	−	4.37737i	0.0436513	−	0.162909i
$723$	15.7185	−	50.4700i	0.584577	−	1.87700i
$724$	−0.635701			−0.0236256
$725$	13.8736	−	24.0298i	0.515253	−	0.892444i
$726$	−0.100402	+	0.0926520i	−0.00372626	+	0.00343864i
$727$	19.2180	+	11.0955i	0.712758	+	0.411511i	0.812081	−	0.583544i	$-0.198335\pi$
$727$	19.2180	+	11.0955i	0.712758	+	0.411511i	−0.0993236	+	0.995055i	$0.531668\pi$
$728$	10.6644	+	3.12146i	0.395248	+	0.115689i
$729$	−26.2214	−	6.43713i	−0.971164	−	0.238412i
$730$	0.281632	−	1.05107i	0.0104237	−	0.0389017i
$731$			33.0350i			1.22184i
$732$	−8.07967	−	15.3887i	−0.298633	−	0.568784i
$733$	0.276984	−	1.03372i	0.0102306	−	0.0381813i	−0.960622	−	0.277859i	$-0.910375\pi$
$733$	0.276984	−	1.03372i	0.0102306	−	0.0381813i	0.970852	+	0.239678i	$0.0770418\pi$
$734$	−12.3928	+	12.3928i	−0.457428	+	0.457428i
$735$	1.11637	−	1.03020i	0.0411779	−	0.0379995i
$736$	1.73021	+	6.45722i	0.0637763	+	0.238016i
$737$	39.7443	+	22.9464i	1.46400	+	0.845242i
$738$	−6.47453	−	4.46608i	−0.238331	−	0.164399i
$739$	−44.6085	−	11.9528i	−1.64095	−	0.439691i	−0.683890	−	0.729585i	$-0.739713\pi$
$739$	−44.6085	−	11.9528i	−1.64095	−	0.439691i	−0.957059	+	0.289894i	$0.906380\pi$
$740$	1.61770	−	2.80194i	0.0594679	−	0.103001i
$741$	−19.7822	−	13.1500i	−0.726719	−	0.483079i
$742$	−8.71302	−	15.0914i	−0.319865	−	0.554022i
$743$	0.837432	+	3.12534i	0.0307224	+	0.114658i	0.979584	−	0.201034i	$-0.0644302\pi$
$743$	0.837432	+	3.12534i	0.0307224	+	0.114658i	−0.948862	+	0.315692i	$0.897764\pi$
$744$	−0.913552	−	1.73997i	−0.0334924	−	0.0637904i
$745$	2.30816	−	1.33262i	0.0845643	−	0.0488232i
$746$	−8.57528	+	8.57528i	−0.313963	+	0.313963i
$747$	2.20100	+	11.9895i	0.0805304	+	0.438673i
$748$	6.68086	+	24.9333i	0.244277	+	0.911652i
$749$	16.3423	−	4.37890i	0.597133	−	0.160001i
$750$	0.240927	−	6.00168i	0.00879741	−	0.219150i
$751$	−19.1224	−	11.0403i	−0.697785	−	0.402866i	0.108737	−	0.994071i	$-0.465319\pi$
$751$	−19.1224	−	11.0403i	−0.697785	−	0.402866i	−0.806522	+	0.591204i	$0.798653\pi$
$752$	4.17527	−	1.11876i	0.152256	−	0.0407970i
$753$	24.0888	+	15.2276i	0.877845	+	0.554925i
$754$	−20.5092	−	0.470707i	−0.746901	−	0.0171422i
$755$		−	5.11944i		−	0.186316i
$756$	14.8586	+	5.97203i	0.540401	+	0.217201i
$757$	7.92964	+	13.7345i	0.288208	+	0.499190i	0.973382	−	0.229189i	$-0.0736074\pi$
$757$	7.92964	+	13.7345i	0.288208	+	0.499190i	−0.685174	+	0.728379i	$0.740274\pi$
$758$	3.08169	+	5.33764i	0.111932	+	0.193872i
$759$	−8.47363	−	37.5968i	−0.307573	−	1.36468i
$760$	0.944369	+	0.944369i	0.0342559	+	0.0342559i
$761$	−9.46921	−	9.46921i	−0.343259	−	0.343259i	0.514332	−	0.857591i	$-0.328040\pi$
$761$	−9.46921	−	9.46921i	−0.343259	−	0.343259i	−0.857591	+	0.514332i	$0.828040\pi$
$762$	−20.4172	−	6.35878i	−0.739636	−	0.230354i
$763$	4.85892	+	8.41589i	0.175905	+	0.304676i
$764$	−0.0745427	−	0.129112i	−0.00269686	−	0.00467110i
$765$	−6.22064	+	5.29463i	−0.224908	+	0.191428i
$766$		−	14.6073i		−	0.527785i
$767$	39.5560	+	0.907851i	1.42829	+	0.0327806i
$768$	0.0694742	−	1.73066i	0.00250694	−	0.0624497i
$769$	−40.5584	+	10.8676i	−1.46257	+	0.391896i

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0694742 - 1.73066i) q^{3} -1.00000i q^{4} +(0.339151 + 0.0908752i) q^{5} +(1.17463 + 1.27288i) q^{6} +(2.97685 + 0.797644i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99035 - 0.240472i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.0694742 - 1.73066i) q^{3} -1.00000i q^{4} +(0.339151 + 0.0908752i) q^{5} +(1.17463 + 1.27288i) q^{6} +(2.97685 + 0.797644i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99035 - 0.240472i) q^{9} +(-0.304074 + 0.175557i) q^{10} +(-2.35360 - 2.35360i) q^{11} +(-1.73066 - 0.0694742i) q^{12} +(2.60734 - 2.49034i) q^{13} +(-2.66897 + 1.54093i) q^{14} +(0.180836 - 0.580640i) q^{15} -1.00000 q^{16} +(3.87756 - 6.71613i) q^{17} +(2.28453 - 1.94445i) q^{18} +(3.67410 - 0.984473i) q^{19} +(0.0908752 - 0.339151i) q^{20} +(1.58726 - 5.09649i) q^{21} +3.32849 q^{22} +(-3.34250 + 5.78938i) q^{23} +(1.27288 - 1.17463i) q^{24} +(-4.22336 - 2.43836i) q^{25} +(-0.0827293 + 3.60460i) q^{26} +(-0.623927 + 5.15856i) q^{27} +(0.797644 - 2.97685i) q^{28} +5.68973i q^{29} +(0.282704 + 0.538445i) q^{30} +(0.293661 - 1.09596i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.23679 + 3.90976i) q^{33} +(2.00717 + 7.49087i) q^{34} +(0.937115 + 0.541044i) q^{35} +(-0.240472 + 2.99035i) q^{36} +(8.90068 + 2.38493i) q^{37} +(-1.90186 + 3.29411i) q^{38} +(-4.12878 - 4.68542i) q^{39} +(0.175557 + 0.304074i) q^{40} +(-0.678577 - 2.53248i) q^{41} +(2.48140 + 4.72613i) q^{42} +(-3.68906 + 2.12988i) q^{43} +(-2.35360 + 2.35360i) q^{44} +(-0.992326 - 0.353305i) q^{45} +(-1.73021 - 6.45722i) q^{46} +(-4.17527 + 1.11876i) q^{47} +(-0.0694742 + 1.73066i) q^{48} +(2.16322 + 1.24894i) q^{49} +(4.71055 - 1.26219i) q^{50} +(-11.3539 - 7.17732i) q^{51} +(-2.49034 - 2.60734i) q^{52} +5.65439i q^{53} +(-3.20647 - 4.08883i) q^{54} +(-0.584342 - 1.01211i) q^{55} +(1.54093 + 2.66897i) q^{56} +(-1.44853 - 6.42701i) q^{57} +(-4.02325 - 4.02325i) q^{58} +(7.75962 + 7.75962i) q^{59} +(-0.580640 - 0.180836i) q^{60} +(5.01742 + 8.69042i) q^{61} +(0.567309 + 0.982608i) q^{62} +(-8.71000 - 3.10108i) q^{63} +1.00000i q^{64} +(1.11059 - 0.607659i) q^{65} +(0.231245 - 5.76048i) q^{66} +(-13.3180 + 3.56856i) q^{67} +(-6.71613 - 3.87756i) q^{68} +(9.78722 + 6.18694i) q^{69} +(-1.04522 + 0.280065i) q^{70} +(-0.343507 - 1.28199i) q^{71} +(-1.94445 - 2.28453i) q^{72} +(-2.19140 + 2.19140i) q^{73} +(-7.98013 + 4.60733i) q^{74} +(-4.51338 + 7.13979i) q^{75} +(-0.984473 - 3.67410i) q^{76} +(-5.12898 - 8.88365i) q^{77} +(6.23258 + 0.393603i) q^{78} +(-6.22990 + 10.7905i) q^{79} +(-0.339151 - 0.0908752i) q^{80} +(8.88435 + 1.43819i) q^{81} +(2.27056 + 1.31091i) q^{82} +(-1.05166 - 3.92483i) q^{83} +(-5.09649 - 1.58726i) q^{84} +(1.92541 - 1.92541i) q^{85} +(1.10251 - 4.11462i) q^{86} +(9.84697 + 0.395290i) q^{87} -3.32849i q^{88} +(1.43929 - 5.37149i) q^{89} +(0.951504 - 0.451856i) q^{90} +(9.74806 - 5.33364i) q^{91} +(5.78938 + 3.34250i) q^{92} +(-1.87632 - 0.584367i) q^{93} +(2.16128 - 3.74344i) q^{94} +1.33554 q^{95} +(-1.17463 - 1.27288i) q^{96} +(-0.218799 + 0.816569i) q^{97} +(-2.41276 + 0.646496i) q^{98} +(6.47211 + 7.60406i) 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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