LMFDB - Embedded newform 114.2.l.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Root			$1.69944 + 0.334495i$ of defining polynomial
Character	$\chi$	$=$	114.71
Dual form			114.2.l.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(0.560041 + 1.63901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.343148 + 0.408948i) q^{5} +(1.08684 + 1.34862i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.37271 + 1.83583i) q^{9} +(-0.182585 + 0.501649i) q^{10} +(-1.25645 - 0.725411i) q^{11} +(1.48255 + 0.895567i) q^{12} +(2.94737 - 0.519701i) q^{13} +(-1.09775 - 0.921124i) q^{14} +(-0.862447 - 0.333396i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.89590 - 5.20894i) q^{17} +(-1.60173 + 2.53663i) q^{18} +(-4.35653 + 0.143752i) q^{19} +0.533844i q^{20} +(1.63278 - 1.86939i) q^{21} +(-1.42878 - 0.251933i) q^{22} +(-0.396438 - 0.472456i) q^{23} +(1.69944 + 0.334495i) q^{24} +(0.818753 + 4.64338i) q^{25} +(2.59188 - 1.49642i) q^{26} +(-4.33775 - 2.86075i) q^{27} +(-1.34659 - 0.490120i) q^{28} +(4.97822 + 1.81193i) q^{29} +(-0.924463 - 0.0183150i) q^{30} +(-4.28601 + 2.47453i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.485293 - 2.46559i) q^{33} +(-3.56312 - 4.24636i) q^{34} +(0.753384 + 0.132842i) q^{35} +(-0.637553 + 2.93147i) q^{36} +6.41883i q^{37} +(-4.04463 + 1.62510i) q^{38} +(2.50245 + 4.53972i) q^{39} +(0.182585 + 0.501649i) q^{40} +(1.37347 - 7.78933i) q^{41} +(0.894945 - 2.31510i) q^{42} +(4.88757 + 4.10116i) q^{43} +(-1.42878 + 0.251933i) q^{44} +(0.0634325 - 1.60027i) q^{45} +(-0.534119 - 0.308374i) q^{46} +(-4.37381 + 12.0169i) q^{47} +(1.71136 - 0.266922i) q^{48} +(2.47323 - 4.28377i) q^{49} +(2.35751 + 4.08332i) q^{50} +(7.47572 - 6.02462i) q^{51} +(1.92376 - 2.29265i) q^{52} +(1.41439 - 1.18682i) q^{53} +(-5.05459 - 1.20463i) q^{54} +(0.727804 - 0.264899i) q^{55} -1.43301 q^{56} +(-2.67545 - 7.05989i) q^{57} +5.29771 q^{58} +(1.75650 - 0.639313i) q^{59} +(-0.874975 + 0.298975i) q^{60} +(9.02625 - 7.57392i) q^{61} +(-3.18119 + 3.79120i) q^{62} +(3.97837 + 1.62921i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.798855 + 1.38366i) q^{65} +(-0.387256 - 2.48288i) q^{66} +(3.17216 - 8.71543i) q^{67} +(-4.80058 - 2.77162i) q^{68} +(0.552339 - 0.914360i) q^{69} +(0.753384 - 0.132842i) q^{70} +(9.59384 + 8.05019i) q^{71} +(0.403519 + 2.97274i) q^{72} +(-2.80621 + 15.9148i) q^{73} +(2.19537 + 6.03173i) q^{74} +(-7.15201 + 3.94243i) q^{75} +(-3.24489 + 2.91044i) q^{76} +2.07905i q^{77} +(3.90420 + 3.41005i) q^{78} +(-7.87896 - 1.38927i) q^{79} +(0.343148 + 0.408948i) q^{80} +(2.25948 - 8.71176i) q^{81} +(-1.37347 - 7.78933i) q^{82} +(-4.29627 + 2.48045i) q^{83} +(0.0491635 - 2.48157i) q^{84} +(2.78076 + 1.01211i) q^{85} +(5.99550 + 2.18218i) q^{86} +(-0.181753 + 9.17411i) q^{87} +(-1.25645 + 0.725411i) q^{88} +(0.832120 + 4.71919i) q^{89} +(-0.487719 - 1.52546i) q^{90} +(-2.75678 - 3.28540i) q^{91} +(-0.607378 - 0.107097i) q^{92} +(-6.45612 - 5.63897i) q^{93} +12.7882i q^{94} +(1.43615 - 1.83092i) q^{95} +(1.51686 - 0.836144i) q^{96} +(-2.83601 - 7.79188i) q^{97} +(0.858945 - 4.87132i) q^{98} +(4.31291 - 0.585434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.560041	+	1.63901i	0.323340	+	0.946283i
$3$	0.560041	+	1.63901i	0.323340	+	0.946283i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.343148	+	0.408948i	−0.153461	+	0.182887i	−0.837297	−	0.546748i	$-0.815866\pi$
$5$	−0.343148	+	0.408948i	−0.153461	+	0.182887i	0.683837	+	0.729635i	$0.260310\pi$
$6$	1.08684	+	1.34862i	0.443701	+	0.550572i
$7$	−0.716507	−	1.24103i	−0.270814	−	0.469064i	0.698256	−	0.715848i	$-0.253960\pi$
$7$	−0.716507	−	1.24103i	−0.270814	−	0.469064i	−0.969071	+	0.246784i	$0.920626\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.37271	+	1.83583i	−0.790902	+	0.611942i
$10$	−0.182585	+	0.501649i	−0.0577386	+	0.158635i
$11$	−1.25645	−	0.725411i	−0.378834	−	0.218720i	0.298477	−	0.954417i	$-0.403521\pi$
$11$	−1.25645	−	0.725411i	−0.378834	−	0.218720i	−0.677311	+	0.735697i	$0.736855\pi$
$12$	1.48255	+	0.895567i	0.427976	+	0.258528i
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.250741	−	0.968054i	$-0.419326\pi$
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.566713	+	0.823915i	$0.308215\pi$
$14$	−1.09775	−	0.921124i	−0.293387	−	0.246181i
$15$	−0.862447	−	0.333396i	−0.222683	−	0.0860824i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.89590	−	5.20894i	−0.459823	−	1.26335i	−0.925618	−	0.378460i	$-0.876454\pi$
$17$	−1.89590	−	5.20894i	−0.459823	−	1.26335i	0.465795	−	0.884893i	$-0.345768\pi$
$18$	−1.60173	+	2.53663i	−0.377530	+	0.597889i
$19$	−4.35653	+	0.143752i	−0.999456	+	0.0329790i
$19$	−4.35653	+	0.143752i	−0.999456	+	0.0329790i
$20$			0.533844i			0.119371i
$21$	1.63278	−	1.86939i	0.356302	−	0.407934i
$22$	−1.42878	−	0.251933i	−0.304617	−	0.0537122i
$23$	−0.396438	−	0.472456i	−0.0826630	−	0.0985139i	0.723128	−	0.690714i	$-0.242704\pi$
$23$	−0.396438	−	0.472456i	−0.0826630	−	0.0985139i	−0.805791	+	0.592200i	$0.798259\pi$
$24$	1.69944	+	0.334495i	0.346898	+	0.0682785i
$25$	0.818753	+	4.64338i	0.163751	+	0.928676i
$26$	2.59188	−	1.49642i	0.508309	−	0.293472i
$27$	−4.33775	−	2.86075i	−0.834801	−	0.550552i
$28$	−1.34659	−	0.490120i	−0.254482	−	0.0926240i
$29$	4.97822	+	1.81193i	0.924433	+	0.336466i	0.760001	−	0.649922i	$-0.225199\pi$
$29$	4.97822	+	1.81193i	0.924433	+	0.336466i	0.164432	+	0.986388i	$0.447421\pi$
$30$	−0.924463	−	0.0183150i	−0.168783	−	0.00334384i
$31$	−4.28601	+	2.47453i	−0.769790	+	0.444439i	−0.832800	−	0.553574i	$-0.813263\pi$
$31$	−4.28601	+	2.47453i	−0.769790	+	0.444439i	0.0630096	+	0.998013i	$0.479930\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.485293	−	2.46559i	0.0844786	−	0.429204i
$34$	−3.56312	−	4.24636i	−0.611071	−	0.728245i
$35$	0.753384	+	0.132842i	0.127345	+	0.0224544i
$36$	−0.637553	+	2.93147i	−0.106259	+	0.488579i
$37$			6.41883i			1.05525i	0.849478	+	0.527625i	$0.176917\pi$
$37$			6.41883i			1.05525i	−0.849478	+	0.527625i	$0.823083\pi$
$38$	−4.04463	+	1.62510i	−0.656126	+	0.263627i
$39$	2.50245	+	4.53972i	0.400712	+	0.726937i
$40$	0.182585	+	0.501649i	0.0288693	+	0.0793177i
$41$	1.37347	−	7.78933i	0.214500	−	1.21649i	−0.667273	−	0.744814i	$-0.732538\pi$
$41$	1.37347	−	7.78933i	0.214500	−	1.21649i	0.881772	−	0.471675i	$-0.156350\pi$
$42$	0.894945	−	2.31510i	0.138093	−	0.357227i
$43$	4.88757	+	4.10116i	0.745348	+	0.625421i	0.934268	−	0.356571i	$-0.116054\pi$
$43$	4.88757	+	4.10116i	0.745348	+	0.625421i	−0.188920	+	0.981992i	$0.560499\pi$
$44$	−1.42878	+	0.251933i	−0.215397	+	0.0379803i
$45$	0.0634325	−	1.60027i	0.00945596	−	0.238555i
$46$	−0.534119	−	0.308374i	−0.0787516	−	0.0454672i
$47$	−4.37381	+	12.0169i	−0.637985	+	1.75285i	0.0199780	+	0.999800i	$0.493640\pi$
$47$	−4.37381	+	12.0169i	−0.637985	+	1.75285i	−0.657963	+	0.753050i	$0.728582\pi$
$48$	1.71136	−	0.266922i	0.247014	−	0.0385269i
$49$	2.47323	−	4.28377i	0.353319	−	0.611967i
$50$	2.35751	+	4.08332i	0.333402	+	0.577469i
$51$	7.47572	−	6.02462i	1.04681	−	0.843615i
$52$	1.92376	−	2.29265i	0.266778	−	0.317933i
$53$	1.41439	−	1.18682i	0.194282	−	0.163022i	−0.540458	−	0.841371i	$-0.681749\pi$
$53$	1.41439	−	1.18682i	0.194282	−	0.163022i	0.734739	+	0.678349i	$0.237304\pi$
$54$	−5.05459	−	1.20463i	−0.687842	−	0.163929i
$55$	0.727804	−	0.264899i	0.0981370	−	0.0357190i
$56$	−1.43301			−0.191495
$57$	−2.67545	−	7.05989i	−0.354372	−	0.935105i
$58$	5.29771			0.695624
$59$	1.75650	−	0.639313i	0.228676	−	0.0832314i	−0.225141	−	0.974326i	$-0.572284\pi$
$59$	1.75650	−	0.639313i	0.228676	−	0.0832314i	0.453817	+	0.891095i	$0.350062\pi$
$60$	−0.874975	+	0.298975i	−0.112959	+	0.0385975i
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.155856	−	0.987780i	$-0.450186\pi$
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.999837	+	0.0180382i	$0.00574206\pi$
$62$	−3.18119	+	3.79120i	−0.404012	+	0.481483i
$63$	3.97837	+	1.62921i	0.501228	+	0.205261i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.798855	+	1.38366i	−0.0990857	+	0.171622i
$66$	−0.387256	−	2.48288i	−0.0476679	−	0.305621i
$67$	3.17216	−	8.71543i	0.387541	−	1.06476i	−0.580564	−	0.814215i	$-0.697168\pi$
$67$	3.17216	−	8.71543i	0.387541	−	1.06476i	0.968105	−	0.250545i	$-0.0806099\pi$
$68$	−4.80058	−	2.77162i	−0.582156	−	0.336108i
$69$	0.552339	−	0.914360i	0.0664938	−	0.110076i
$70$	0.753384	−	0.132842i	0.0900466	−	0.0158776i
$71$	9.59384	+	8.05019i	1.13858	+	0.955382i	0.999391	−	0.0348843i	$-0.0111063\pi$
$71$	9.59384	+	8.05019i	1.13858	+	0.955382i	0.139188	+	0.990266i	$0.455551\pi$
$72$	0.403519	+	2.97274i	0.0475551	+	0.350341i
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	0.155852	+	0.987780i	$0.450188\pi$
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	−0.484294	+	0.874905i	$0.660923\pi$
$74$	2.19537	+	6.03173i	0.255207	+	0.701174i
$75$	−7.15201	+	3.94243i	−0.825843	+	0.455232i
$76$	−3.24489	+	2.91044i	−0.372215	+	0.333851i
$77$			2.07905i			0.236930i
$78$	3.90420	+	3.41005i	0.442064	+	0.386112i
$79$	−7.87896	−	1.38927i	−0.886452	−	0.156305i	−0.288159	−	0.957583i	$-0.593043\pi$
$79$	−7.87896	−	1.38927i	−0.886452	−	0.156305i	−0.598293	+	0.801277i	$0.704154\pi$
$80$	0.343148	+	0.408948i	0.0383651	+	0.0457218i
$81$	2.25948	−	8.71176i	0.251053	−	0.967973i
$82$	−1.37347	−	7.78933i	−0.151674	−	0.860187i
$83$	−4.29627	+	2.48045i	−0.471577	+	0.272265i	−0.716900	−	0.697176i	$-0.754439\pi$
$83$	−4.29627	+	2.48045i	−0.471577	+	0.272265i	0.245323	+	0.969442i	$0.421106\pi$
$84$	0.0491635	−	2.48157i	0.00536418	−	0.270761i
$85$	2.78076	+	1.01211i	0.301616	+	0.109779i
$86$	5.99550	+	2.18218i	0.646511	+	0.235311i
$87$	−0.181753	+	9.17411i	−0.0194859	+	0.983568i
$88$	−1.25645	+	0.725411i	−0.133938	+	0.0773291i
$89$	0.832120	+	4.71919i	0.0882046	+	0.500233i	0.996619	+	0.0821621i	$0.0261825\pi$
$89$	0.832120	+	4.71919i	0.0882046	+	0.500233i	−0.908414	+	0.418071i	$0.862706\pi$
$90$	−0.487719	−	1.52546i	−0.0514101	−	0.160798i
$91$	−2.75678	−	3.28540i	−0.288989	−	0.344403i
$92$	−0.607378	−	0.107097i	−0.0633235	−	0.0111656i
$93$	−6.45612	−	5.63897i	−0.669468	−	0.584734i
$94$			12.7882i			1.31900i
$95$	1.43615	−	1.83092i	0.147346	−	0.187849i
$96$	1.51686	−	0.836144i	0.154814	−	0.0853386i
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	−0.996352	−	0.0853335i	$-0.972804\pi$
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	0.708399	−	0.705812i	$-0.249418\pi$
$98$	0.858945	−	4.87132i	0.0867666	−	0.492078i
$99$	4.31291	−	0.585434i	0.433464	−	0.0588383i
$100$	3.61191	+	3.03075i	0.361191	+	0.303075i
$101$	−3.10192	+	0.546953i	−0.308653	+	0.0544238i	−0.325829	−	0.945429i	$-0.605643\pi$
$101$	−3.10192	+	0.546953i	−0.308653	+	0.0544238i	0.0171763	+	0.999852i	$0.494532\pi$
$102$	4.96434	−	8.21813i	0.491543	−	0.813716i
$103$	−8.85438	−	5.11208i	−0.872448	−	0.503708i	−0.00428731	−	0.999991i	$-0.501365\pi$
$103$	−8.85438	−	5.11208i	−0.872448	−	0.503708i	−0.868161	+	0.496282i	$0.834698\pi$
$104$	1.02361	−	2.81235i	0.100373	−	0.275774i
$105$	0.204197	+	1.30920i	0.0199276	+	0.127765i
$106$	0.923180	−	1.59899i	0.0896672	−	0.155308i
$107$	−5.80970	−	10.0627i	−0.561645	−	0.972798i	−0.997353	−	0.0727101i	$-0.976835\pi$
$107$	−5.80970	−	10.0627i	−0.561645	−	0.972798i	0.435708	−	0.900088i	$-0.356498\pi$
$108$	−5.16177	+	0.596790i	−0.496691	+	0.0574261i
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	−0.767026	−	0.641616i	$-0.778264\pi$
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	0.765061	+	0.643958i	$0.222709\pi$
$110$	0.593311	−	0.497847i	0.0565700	−	0.0474678i
$111$	−10.5205	+	3.59481i	−0.998565	+	0.341204i
$112$	−1.34659	+	0.490120i	−0.127241	+	0.0463120i
$113$	−10.3475			−0.973413			−0.486706	−	0.873566i	$-0.661802\pi$
$113$	−10.3475			−0.973413			−0.486706	+	0.873566i	$0.661802\pi$
$114$	−4.92872	−	5.71907i	−0.461617	−	0.535640i
$115$	0.329247			0.0307024
$116$	4.97822	−	1.81193i	0.462216	−	0.168233i
$117$	−6.03917	+	6.64396i	−0.558321	+	0.614235i
$118$	1.43191	−	1.20152i	0.131818	−	0.110608i
$119$	−5.10601	+	6.08510i	−0.468067	+	0.557820i
$120$	−0.719953	+	0.580203i	−0.0657224	+	0.0529651i
$121$	−4.44756	−	7.70340i	−0.404323	−	0.700309i
$122$	5.89147	−	10.2043i	0.533388	−	0.923856i
$123$	13.5360	−	2.11122i	1.22050	−	0.190362i
$124$	−1.69268	+	4.65059i	−0.152007	+	0.417636i
$125$	−4.49147	−	2.59315i	−0.401729	−	0.231938i
$126$	4.29567	+	0.170274i	0.382689	+	0.0151692i
$127$	−0.772141	+	0.136149i	−0.0685165	+	0.0120813i	−0.207801	−	0.978171i	$-0.566631\pi$
$127$	−0.772141	+	0.136149i	−0.0685165	+	0.0120813i	0.139285	+	0.990252i	$0.455520\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−3.98460	+	10.3076i	−0.350825	+	0.907534i
$130$	−0.277439	+	1.57344i	−0.0243330	+	0.138000i
$131$	−3.93973	−	10.8243i	−0.344216	−	0.945726i	−0.984157	−	0.177301i	$-0.943263\pi$
$131$	−3.93973	−	10.8243i	−0.344216	−	0.945726i	0.639941	−	0.768424i	$-0.278959\pi$
$132$	−1.21310	−	2.20069i	−0.105586	−	0.191546i
$133$	3.29988	+	5.30357i	0.286136	+	0.459878i
$134$		−	9.27477i		−	0.801218i
$135$	2.65839	−	0.792254i	0.228798	−	0.0681863i
$136$	−5.45902	−	0.962573i	−0.468107	−	0.0825399i
$137$	8.70595	+	10.3754i	0.743800	+	0.886426i	0.996709	−	0.0810638i	$-0.0258318\pi$
$137$	8.70595	+	10.3754i	0.743800	+	0.886426i	−0.252909	+	0.967490i	$0.581387\pi$
$138$	0.206299	−	1.04813i	0.0175613	−	0.0892226i
$139$	−1.25656	−	7.12628i	−0.106580	−	0.604444i	−0.990578	−	0.136953i	$-0.956269\pi$
$139$	−1.25656	−	7.12628i	−0.106580	−	0.604444i	0.883998	−	0.467491i	$-0.154842\pi$
$140$	0.662515	−	0.382503i	0.0559927	−	0.0323274i
$141$	−22.1454	−	0.438733i	−1.86498	−	0.0369480i
$142$	11.7686	+	4.28342i	0.987598	+	0.359456i
$143$	−4.08022	−	1.48508i	−0.341205	−	0.124188i
$144$	1.39592	+	2.65545i	0.116327	+	0.221287i
$145$	−2.44925	+	1.41408i	−0.203399	+	0.117433i
$146$	2.80621	+	15.9148i	0.232243	+	1.31712i
$147$	8.40625	+	1.65457i	0.693336	+	0.136467i
$148$	4.12595	+	4.91711i	0.339151	+	0.404184i
$149$	19.4195	+	3.42419i	1.59091	+	0.280520i	0.897831	−	0.440341i	$-0.145142\pi$
$149$	19.4195	+	3.42419i	1.59091	+	0.280520i	0.693079	+	0.720861i	$0.256254\pi$
$150$	−5.37230	+	6.15080i	−0.438646	+	0.502211i
$151$		−	4.23079i		−	0.344297i	−0.985071	−	0.172148i	$-0.944929\pi$
$151$		−	4.23079i		−	0.344297i	0.985071	−	0.172148i	$-0.0550709\pi$
$152$	−2.05377	+	3.84474i	−0.166583	+	0.311850i
$153$	14.0611	+	8.87874i	1.13677	+	0.717804i
$154$	0.711077	+	1.95367i	0.0573002	+	0.157431i
$155$	0.458783	−	2.60189i	0.0368503	−	0.208989i
$156$	4.83506	+	1.86908i	0.387115	+	0.149647i
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	0.898211	−	0.439565i	$-0.144867\pi$
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	−0.276914	+	0.960895i	$0.589312\pi$
$158$	−7.87896	+	1.38927i	−0.626817	+	0.110525i
$159$	2.73732	+	1.65354i	0.217084	+	0.131134i
$160$	0.462322	+	0.266922i	0.0365498	+	0.0211020i
$161$	−0.302280	+	0.830508i	−0.0238230	+	0.0654532i
$162$	−0.856379	−	8.95916i	−0.0672835	−	0.703898i
$163$	−5.20216	+	9.01041i	−0.407465	+	0.705750i	−0.994605	−	0.103735i	$-0.966920\pi$
$163$	−5.20216	+	9.01041i	−0.407465	+	0.705750i	0.587140	+	0.809485i	$0.300254\pi$
$164$	−3.95475	−	6.84982i	−0.308814	−	0.534881i
$165$	0.841772	+	1.04452i	0.0655319	+	0.0813160i
$166$	−3.18881	+	3.80028i	−0.247500	+	0.294959i
$167$	18.2265	−	15.2939i	1.41041	−	1.18347i	0.454162	−	0.890919i	$-0.349939\pi$
$167$	18.2265	−	15.2939i	1.41041	−	1.18347i	0.956249	−	0.292555i	$-0.0945056\pi$
$168$	−0.802548	−	2.34873i	−0.0619179	−	0.181208i
$169$	−3.79909	+	1.38276i	−0.292238	+	0.106366i
$170$	2.95922			0.226962
$171$	10.0729	−	8.33891i	0.770291	−	0.637692i
$172$	6.38027			0.486491
$173$	−23.5435	+	8.56912i	−1.78998	+	0.651498i	−0.790752	+	0.612137i	$0.790310\pi$
$173$	−23.5435	+	8.56912i	−1.78998	+	0.651498i	−0.999225	+	0.0393612i	$0.987468\pi$
$174$	2.96694	+	8.68301i	0.224923	+	0.658257i
$175$	5.17592	−	4.34311i	0.391263	−	0.328308i
$176$	−0.932570	+	1.11139i	−0.0702951	+	0.0837745i
$177$	2.03155	+	2.52088i	0.152701	+	0.189481i
$178$	2.39599	+	4.14998i	0.179587	+	0.311054i
$179$	7.77173	−	13.4610i	0.580886	−	1.00612i	−0.414488	−	0.910055i	$-0.636039\pi$
$179$	7.77173	−	13.4610i	0.580886	−	1.00612i	0.995375	−	0.0960699i	$-0.0306272\pi$
$180$	−0.980045	−	1.26666i	−0.0730482	−	0.0944109i
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	−0.322506	−	0.946567i	$-0.604525\pi$
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	0.855496	−	0.517810i	$-0.173252\pi$
$182$	−3.71420	−	2.14439i	−0.275315	−	0.158953i
$183$	17.4688	+	10.5524i	1.29133	+	0.780056i
$184$	−0.607378	+	0.107097i	−0.0447765	+	0.00789530i
$185$	−2.62497	−	2.20261i	−0.192992	−	0.161939i
$186$	−7.99541	−	3.09078i	−0.586252	−	0.226627i
$187$	−1.39652	+	7.92007i	−0.102124	+	0.579173i
$188$	4.37381	+	12.0169i	0.318993	+	0.876425i
$189$	−0.442240	+	7.43302i	−0.0321682	+	0.540673i
$190$	0.723325	−	2.21170i	0.0524755	−	0.160453i
$191$			1.59398i			0.115336i	0.998336	+	0.0576682i	$0.0183665\pi$
$191$			1.59398i			0.115336i	−0.998336	+	0.0576682i	$0.981633\pi$
$192$	1.13940	−	1.30452i	0.0822294	−	0.0941453i
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	0.325898	−	0.945405i	$-0.394333\pi$
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	−0.0171035	+	0.999854i	$0.505444\pi$
$194$	−5.32996	−	6.35200i	−0.382669	−	0.456047i
$195$	−2.71522	−	0.534426i	−0.194441	−	0.0382710i
$196$	−0.858945	−	4.87132i	−0.0613532	−	0.347951i
$197$	5.69700	−	3.28916i	0.405894	−	0.234343i	−0.283130	−	0.959082i	$-0.591373\pi$
$197$	5.69700	−	3.28916i	0.405894	−	0.234343i	0.689024	+	0.724738i	$0.258039\pi$
$198$	3.85258	−	2.02523i	0.273791	−	0.143927i
$199$	10.2412	+	3.72750i	0.725981	+	0.264235i	0.678463	−	0.734635i	$-0.262647\pi$
$199$	10.2412	+	3.72750i	0.725981	+	0.264235i	0.0475182	+	0.998870i	$0.484869\pi$
$200$	4.43066	+	1.61263i	0.313295	+	0.114030i
$201$	16.0612	+	0.318196i	1.13287	+	0.0224438i
$202$	−2.72779	+	1.57489i	−0.191926	+	0.110809i
$203$	−1.31829	−	7.47637i	−0.0925255	−	0.524738i
$204$	1.85418	−	9.42042i	0.129819	−	0.659562i
$205$	2.71413	+	3.23457i	0.189563	+	0.225912i
$206$	−10.0688	−	1.77541i	−0.701529	−	0.123698i
$207$	1.80798	+	0.393209i	0.125663	+	0.0273299i
$208$		−	2.99284i		−	0.207516i
$209$	5.57803	+	2.97966i	0.385841	+	0.206107i
$210$	0.639655	+	1.16041i	0.0441404	+	0.0800757i
$211$	−2.58901	−	7.11324i	−0.178235	−	0.489695i	0.818116	−	0.575054i	$-0.195019\pi$
$211$	−2.58901	−	7.11324i	−0.178235	−	0.489695i	−0.996350	+	0.0853581i	$0.972797\pi$
$212$	0.320617	−	1.81831i	0.0220201	−	0.124882i
$213$	−7.82139	+	20.2328i	−0.535913	+	1.38633i
$214$	−8.90098	−	7.46881i	−0.608459	−	0.510558i
$215$	−3.35432	+	0.591458i	−0.228763	+	0.0403371i
$216$	−4.64636	+	2.32623i	−0.316145	+	0.158280i
$217$	6.14192	+	3.54604i	0.416940	+	0.240721i
$218$	−0.0109159	+	0.0299912i	−0.000739318	+	0.00203126i
$219$	−27.6561	+	4.31354i	−1.86883	+	0.291482i
$220$	0.387256	−	0.670747i	0.0261088	−	0.0452218i
$221$	−8.29501	−	14.3674i	−0.557983	−	0.966454i
$222$	−8.65657	+	6.97625i	−0.580991	+	0.468215i
$223$	−7.40150	+	8.82076i	−0.495641	+	0.590682i	−0.954643	−	0.297753i	$-0.903763\pi$
$223$	−7.40150	+	8.82076i	−0.495641	+	0.590682i	0.459002	+	0.888435i	$0.348207\pi$
$224$	−1.09775	+	0.921124i	−0.0733467	+	0.0615452i
$225$	−10.4671	−	9.51429i	−0.697807	−	0.634286i
$226$	−9.72349	+	3.53906i	−0.646797	+	0.235415i
$227$	−1.54291			−0.102407			−0.0512033	−	0.998688i	$-0.516306\pi$
$227$	−1.54291			−0.102407			−0.0512033	+	0.998688i	$0.516306\pi$
$228$	−6.58752	−	3.68844i	−0.436269	−	0.244273i
$229$	−8.17334			−0.540110			−0.270055	−	0.962845i	$-0.587042\pi$
$229$	−8.17334			−0.540110			−0.270055	+	0.962845i	$0.587042\pi$
$230$	0.309391	−	0.112609i	0.0204006	−	0.00742522i
$231$	−3.40758	+	1.16435i	−0.224202	+	0.0766088i
$232$	4.05828	−	3.40531i	0.266439	−	0.223569i
$233$	−5.39612	+	6.43084i	−0.353511	+	0.421298i	−0.913268	−	0.407358i	$-0.866450\pi$
$233$	−5.39612	+	6.43084i	−0.353511	+	0.421298i	0.559757	+	0.828657i	$0.310894\pi$
$234$	−3.40259	+	8.30880i	−0.222435	+	0.543163i
$235$	−3.41344	−	5.91225i	−0.222668	−	0.385673i
$236$	0.934613	−	1.61880i	0.0608381	−	0.105375i
$237$	−2.13551	−	13.6917i	−0.138716	−	0.889375i
$238$	−2.71685	+	7.46448i	−0.176107	+	0.483851i
$239$	7.60840	+	4.39271i	0.492147	+	0.284141i	0.725465	−	0.688260i	$-0.241625\pi$
$239$	7.60840	+	4.39271i	0.492147	+	0.284141i	−0.233318	+	0.972401i	$0.574958\pi$
$240$	−0.478093	+	0.791451i	−0.0308608	+	0.0510880i
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.582806	−	0.812611i	$-0.698045\pi$
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.269730	+	0.962936i	$0.586934\pi$
$242$	−6.81405	−	5.71767i	−0.438024	−	0.367546i
$243$	15.5441	−	1.17563i	0.997152	−	0.0754169i
$244$	2.04609	−	11.6039i	0.130987	−	0.742865i
$245$	0.903153	+	2.48139i	0.0577003	+	0.158530i
$246$	11.9976	−	6.61347i	0.764938	−	0.421660i
$247$	−12.7656	+	2.68778i	−0.812256	+	0.171020i
$248$			4.94906i			0.314265i
$249$	−6.47158	−	5.65248i	−0.410120	−	0.358211i
$250$	−5.10751	−	0.900591i	−0.323027	−	0.0569584i
$251$	−5.05003	−	6.01839i	−0.318755	−	0.379877i	0.582746	−	0.812654i	$-0.301978\pi$
$251$	−5.05003	−	6.01839i	−0.318755	−	0.379877i	−0.901501	+	0.432777i	$0.857534\pi$
$252$	4.09485	−	1.30920i	0.257951	−	0.0824719i
$253$	0.155379	+	0.881197i	0.00976858	+	0.0554004i
$254$	−0.679010	+	0.392026i	−0.0426049	+	0.0245979i
$255$	−0.101524	+	5.12452i	−0.00635769	+	0.320910i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	11.5445	+	4.20184i	0.720123	+	0.262103i	0.675978	−	0.736922i	$-0.263721\pi$
$257$	11.5445	+	4.20184i	0.720123	+	0.262103i	0.0441451	+	0.999025i	$0.485944\pi$
$258$	−0.218893	+	11.0488i	−0.0136277	+	0.687868i
$259$	7.96595	−	4.59914i	0.494980	−	0.285777i
$260$	0.277439	+	1.57344i	0.0172061	+	0.0975804i
$261$	−15.1382	+	4.83999i	−0.937034	+	0.299588i
$262$	−7.40427	−	8.82407i	−0.457438	−	0.545153i
$263$	23.4707	+	4.13852i	1.44727	+	0.255192i	0.841416	−	0.540387i	$-0.181722\pi$
$263$	23.4707	+	4.13852i	1.44727	+	0.255192i	0.605849	+	0.795579i	$0.292833\pi$
$264$	−1.89262	−	1.65307i	−0.116483	−	0.101740i
$265$			0.985668i			0.0605491i
$266$	4.91481	+	3.85510i	0.301346	+	0.236371i
$267$	−7.26877	+	4.00679i	−0.444842	+	0.245212i
$268$	−3.17216	−	8.71543i	−0.193770	−	0.532380i
$269$	3.30229	−	18.7282i	0.201344	−	1.14188i	−0.701745	−	0.712428i	$-0.747596\pi$
$269$	3.30229	−	18.7282i	0.201344	−	1.14188i	0.903090	−	0.429452i	$-0.141293\pi$
$270$	2.22710	−	1.65370i	0.135537	−	0.100641i
$271$	4.13554	+	3.47013i	0.251216	+	0.210795i	0.759696	−	0.650279i	$-0.225348\pi$
$271$	4.13554	+	3.47013i	0.251216	+	0.210795i	−0.508480	+	0.861074i	$0.669792\pi$
$272$	−5.45902	+	0.962573i	−0.331002	+	0.0583645i
$273$	3.84089	−	6.35834i	0.232461	−	0.384825i
$274$	11.7295	+	6.77203i	0.708605	+	0.409113i
$275$	2.33964	−	6.42810i	0.141085	−	0.387629i
$276$	−0.164623	−	1.05548i	−0.00990917	−	0.0635323i
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	−0.864619	−	0.502428i	$-0.832440\pi$
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	0.867425	+	0.497568i	$0.165774\pi$
$278$	−3.61811	−	6.26675i	−0.217000	−	0.375855i
$279$	5.62664	−	13.7397i	0.336858	−	0.822575i
$280$	0.491736	−	0.586029i	0.0293869	−	0.0350219i
$281$	−7.81505	+	6.55760i	−0.466207	+	0.391194i	−0.845409	−	0.534120i	$-0.820643\pi$
$281$	−7.81505	+	6.55760i	−0.466207	+	0.391194i	0.379202	+	0.925314i	$0.376199\pi$
$282$	−20.9599	+	7.16190i	−1.24814	+	0.426485i
$283$	18.1732	−	6.61449i	1.08028	−	0.393190i	0.260269	−	0.965536i	$-0.416189\pi$
$283$	18.1732	−	6.61449i	1.08028	−	0.393190i	0.820013	+	0.572346i	$0.193966\pi$
$284$	12.5239			0.743155
$285$	3.80520	+	1.32847i	0.225401	+	0.0786917i
$286$	−4.34208			−0.256752
$287$	−10.6509	+	3.87660i	−0.628701	+	0.228828i
$288$	2.21995	+	2.01787i	0.130812	+	0.118904i
$289$	−10.5158	+	8.82384i	−0.618579	+	0.519049i
$290$	−1.81790	+	2.16649i	−0.106751	+	0.127221i
$291$	11.1827	−	9.01203i	0.655541	−	0.528295i
$292$	8.08015	+	13.9952i	0.472855	+	0.819009i
$293$	−8.09268	+	14.0169i	−0.472780	+	0.818878i	−0.999515	−	0.0311512i	$-0.990083\pi$
$293$	−8.09268	+	14.0169i	−0.472780	+	0.818878i	0.526735	+	0.850030i	$0.323416\pi$
$294$	8.46519	−	1.32032i	0.493700	−	0.0770027i
$295$	−0.341293	+	0.937695i	−0.0198709	+	0.0545947i
$296$	5.55887	+	3.20942i	0.323103	+	0.186544i
$297$	3.37494	+	6.74104i	0.195834	+	0.391155i
$298$	19.4195	−	3.42419i	1.12494	−	0.198358i
$299$	−1.41399	−	1.18647i	−0.0817729	−	0.0686156i
$300$	−2.94461	+	7.61730i	−0.170007	+	0.439785i
$301$	1.58767	−	9.00413i	0.0915118	−	0.518989i
$302$	−1.44702	−	3.97564i	−0.0832664	−	0.228772i
$303$	−2.63367	−	4.77777i	−0.151300	−	0.274476i
$304$	−0.614935	+	4.31530i	−0.0352689	+	0.247500i
$305$			6.29025i			0.360179i
$306$	16.2498	+	3.53410i	0.928941	+	0.202031i
$307$	17.5661	+	3.09738i	1.00255	+	0.176777i	0.650745	−	0.759296i	$-0.274457\pi$
$307$	17.5661	+	3.09738i	1.00255	+	0.176777i	0.351806	+	0.936073i	$0.385568\pi$
$308$	1.33639	+	1.59264i	0.0761477	+	0.0907493i
$309$	3.41993	−	17.3754i	0.194553	−	0.988452i
$310$	−0.458783	−	2.60189i	−0.0260571	−	0.147777i
$311$	−28.3493	+	16.3675i	−1.60754	+	0.928114i	−0.617622	+	0.786475i	$0.711904\pi$
$311$	−28.3493	+	16.3675i	−1.60754	+	0.928114i	−0.989918	+	0.141639i	$0.954763\pi$
$312$	5.18273	+	0.102678i	0.293415	+	0.00581297i
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.474208	−	0.880413i	$-0.657265\pi$
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.929183	+	0.369621i	$0.879488\pi$
$314$	9.54950	+	3.47573i	0.538909	+	0.196147i
$315$	−2.03143	+	1.06789i	−0.114458	+	0.0601686i
$316$	−6.92864	+	4.00025i	−0.389767	+	0.225032i
$317$	2.32840	+	13.2050i	0.130776	+	0.741669i	0.977708	+	0.209968i	$0.0673359\pi$
$317$	2.32840	+	13.2050i	0.130776	+	0.741669i	−0.846932	+	0.531701i	$0.821553\pi$
$318$	3.13779	+	0.617598i	0.175958	+	0.0346332i
$319$	−4.94049	−	5.88785i	−0.276614	−	0.329656i
$320$	0.525734	+	0.0927010i	0.0293894	+	0.00518214i
$321$	13.2392	−	15.1577i	0.738940	−	0.846020i
$322$			0.883809i			0.0492527i
$323$	9.00833	+	22.4203i	0.501237	+	1.24750i
$324$	−3.86895	−	8.12596i	−0.214942	−	0.451442i
$325$	4.82634	+	13.2603i	0.267717	+	0.735547i
$326$	−1.80669	+	10.2463i	−0.100063	+	0.567488i
$327$	−0.0515616	−	0.0199321i	−0.00285136	−	0.00110225i
$328$	−6.05902	−	5.08412i	−0.334554	−	0.280724i
$329$	18.0472	−	3.18221i	0.994975	−	0.175441i
$330$	1.14825	+	0.693628i	0.0632093	+	0.0381829i
$331$	21.6450	+	12.4967i	1.18971	+	0.686882i	0.958242	−	0.285959i	$-0.0923121\pi$
$331$	21.6450	+	12.4967i	1.18971	+	0.686882i	0.231473	+	0.972841i	$0.425645\pi$
$332$	−1.69673	+	4.66173i	−0.0931202	+	0.255846i
$333$	−11.7839	−	15.2300i	−0.645752	−	0.834600i
$334$	11.8965	−	20.6054i	0.650948	−	1.12748i
$335$	2.47564	+	4.28793i	0.135259	+	0.234275i
$336$	−1.55746	−	1.93259i	−0.0849664	−	0.105432i
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	−0.390589	−	0.920565i	$-0.627729\pi$
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	0.974405	+	0.224801i	$0.0721732\pi$
$338$	−3.09705	+	2.59873i	−0.168457	+	0.141352i
$339$	−5.79504	−	16.9597i	−0.314743	−	0.921124i
$340$	2.78076	−	1.01211i	0.150808	−	0.0548896i
$341$	7.18020			0.388830
$342$	6.61332	−	11.2811i	0.357607	−	0.610014i
$343$	−17.1195			−0.924364
$344$	5.99550	−	2.18218i	0.323256	−	0.117655i
$345$	0.184392	+	0.539639i	0.00992733	+	0.0290532i
$346$	−19.1928	+	16.1047i	−1.03181	+	0.865793i
$347$	−23.0175	+	27.4312i	−1.23564	+	1.47258i	−0.406399	+	0.913696i	$0.633216\pi$
$347$	−23.0175	+	27.4312i	−1.23564	+	1.47258i	−0.829244	+	0.558886i	$0.811229\pi$
$348$	5.75777	+	7.14460i	0.308649	+	0.382991i
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	0.999627	+	0.0273031i	$0.00869193\pi$
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	−0.476168	+	0.879354i	$0.657975\pi$
$350$	3.37834	−	5.85146i	0.180580	−	0.312774i
$351$	−14.2717	−	6.17737i	−0.761767	−	0.329723i
$352$	−0.496210	+	1.36333i	−0.0264481	+	0.0726656i
$353$	−27.9356	−	16.1286i	−1.48686	−	0.858441i	−0.486976	−	0.873416i	$-0.661900\pi$
$353$	−27.9356	−	16.1286i	−1.48686	−	0.858441i	−0.999888	+	0.0149745i	$0.995233\pi$
$354$	2.77122	+	1.67402i	0.147289	+	0.0889730i
$355$	−6.58422	+	1.16098i	−0.349454	+	0.0616182i
$356$	3.67088	+	3.08023i	0.194556	+	0.163252i
$357$	−12.8331	−	4.96089i	−0.679201	−	0.262558i
$358$	2.69909	−	15.3073i	0.142651	−	0.809017i
$359$	5.99057	+	16.4590i	0.316170	+	0.868671i	0.991377	+	0.131042i	$0.0418323\pi$
$359$	5.99057	+	16.4590i	0.316170	+	0.868671i	−0.675206	+	0.737629i	$0.735945\pi$
$360$	−1.35416	−	0.855072i	−0.0713706	−	0.0450662i
$361$	18.9587	−	1.25252i	0.997825	−	0.0659220i
$362$		−	20.9656i		−	1.10193i
$363$	10.1351	−	11.6038i	0.531956	−	0.609042i
$364$	−4.22363	−	0.744740i	−0.221378	−	0.0390350i
$365$	−5.54538	−	6.60873i	−0.290258	−	0.345917i
$366$	20.0244	+	3.94133i	1.04669	+	0.206017i
$367$	3.59236	+	20.3733i	0.187520	+	1.06348i	0.922675	+	0.385578i	$0.125998\pi$
$367$	3.59236	+	20.3733i	0.187520	+	1.06348i	−0.735155	+	0.677899i	$0.762891\pi$
$368$	−0.534119	+	0.308374i	−0.0278429	+	0.0160751i
$369$	11.0410	+	21.0032i	0.574772	+	1.09339i
$370$	−3.22000	−	1.17198i	−0.167400	−	0.0609286i
$371$	−2.48630	−	0.904938i	−0.129082	−	0.0469820i
$372$	−8.57034	−	0.169791i	−0.444351	−	0.00880325i
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	−0.434738	−	0.900557i	$-0.643159\pi$
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	0.562536	+	0.826773i	$0.309826\pi$
$374$	1.39652	+	7.92007i	0.0722124	+	0.409537i
$375$	1.73479	−	8.81383i	0.0895842	−	0.455144i
$376$	8.22007	+	9.79630i	0.423918	+	0.505205i
$377$	15.6143	+	2.75323i	0.804179	+	0.141798i
$378$	2.12667	+	7.13601i	0.109384	+	0.367037i
$379$		−	15.1648i		−	0.778963i	−0.921034	−	0.389482i	$-0.872654\pi$
$379$		−	15.1648i		−	0.778963i	0.921034	−	0.389482i	$-0.127346\pi$
$380$	−0.0767411	−	2.32571i	−0.00393673	−	0.119306i
$381$	−0.655581	−	1.18930i	−0.0335864	−	0.0609296i
$382$	0.545173	+	1.49785i	0.0278935	+	0.0766368i
$383$	−0.366876	+	2.08066i	−0.0187465	+	0.106317i	−0.992745	−	0.120237i	$-0.961635\pi$
$383$	−0.366876	+	2.08066i	−0.0187465	+	0.106317i	0.973999	+	0.226553i	$0.0727458\pi$
$384$	0.624519	−	1.61554i	0.0318698	−	0.0824428i
$385$	−0.850223	−	0.713422i	−0.0433314	−	0.0363594i
$386$	4.28991	−	0.756427i	0.218351	−	0.0385011i
$387$	−19.1258	−	0.758118i	−0.972219	−	0.0385373i
$388$	−7.18104	−	4.14597i	−0.364562	−	0.210480i
$389$	−1.43738	+	3.94918i	−0.0728783	+	0.200231i	−0.970783	−	0.239958i	$-0.922866\pi$
$389$	−1.43738	+	3.94918i	−0.0728783	+	0.200231i	0.897905	+	0.440189i	$0.145089\pi$
$390$	−2.73426	+	0.426464i	−0.138454	+	0.0215948i
$391$	−1.70939	+	2.96075i	−0.0864475	+	0.149731i
$392$	−2.47323	−	4.28377i	−0.124917	−	0.216363i
$393$	15.5348	−	12.5193i	0.783625	−	0.631517i
$394$	4.22847	−	5.03929i	0.213027	−	0.253876i
$395$	3.27179	−	2.74536i	0.164622	−	0.138134i
$396$	2.92757	−	3.22076i	0.147116	−	0.161849i
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	−0.334860	−	0.942268i	$-0.608689\pi$
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	0.349161	+	0.937063i	$0.386467\pi$
$398$	10.8985			0.546291
$399$	−6.84453	+	8.37876i	−0.342655	+	0.419463i
$400$	4.71501			0.235751
$401$	−11.8640	+	4.31814i	−0.592460	+	0.215638i	−0.620811	−	0.783960i	$-0.713197\pi$
$401$	−11.8640	+	4.31814i	−0.592460	+	0.215638i	0.0283512	+	0.999598i	$0.490974\pi$
$402$	15.2014	−	5.19426i	0.758179	−	0.259066i
$403$	−11.3464	+	9.52080i	−0.565207	+	0.474265i
$404$	−2.02464	+	2.41287i	−0.100729	+	0.120045i
$405$	2.78732	+	3.91344i	0.138503	+	0.194460i
$406$	−3.79585	−	6.57461i	−0.188385	−	0.326292i
$407$	4.65629	−	8.06493i	0.230804	−	0.399764i
$408$	−1.47961	−	9.48647i	−0.0732517	−	0.469650i
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	0.660515	+	0.750813i	$0.270338\pi$
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	−0.988597	+	0.150585i	$0.951884\pi$
$410$	3.65673	+	2.11122i	0.180593	+	0.104266i
$411$	−12.1296	+	20.0798i	−0.598310	+	0.990462i
$412$	−10.0688	+	1.77541i	−0.496056	+	0.0874680i
$413$	−2.05195	−	1.72179i	−0.100970	−	0.0847237i
$414$	1.83343	−	0.248869i	0.0901081	−	0.0122313i
$415$	0.459881	−	2.60812i	0.0225747	−	0.128027i
$416$	−1.02361	−	2.81235i	−0.0501867	−	0.137887i
$417$	10.9763	−	6.05052i	0.537513	−	0.296295i
$418$	6.26074	+	0.892161i	0.306223	+	0.0436370i
$419$		−	15.4879i		−	0.756633i	−0.925676	−	0.378316i	$-0.876503\pi$
$419$		−	15.4879i		−	0.756633i	0.925676	−	0.378316i	$-0.123497\pi$
$420$	0.997962	+	0.871651i	0.0486956	+	0.0425322i
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.498962	−	0.866624i	$-0.333715\pi$
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.172468	+	0.985015i	$0.444826\pi$
$422$	−4.86574	−	5.79876i	−0.236861	−	0.282279i
$423$	−11.6832	−	36.5422i	−0.568059	−	1.77674i
$424$	−0.320617	−	1.81831i	−0.0155705	−	0.0883049i
$425$	22.6348	−	13.0682i	1.09795	−	0.633901i
$426$	−0.429666	+	21.6877i	−0.0208174	+	1.05077i
$427$	−15.8668	−	5.77505i	−0.767849	−	0.279474i
$428$	−10.9187	−	3.97407i	−0.527774	−	0.192094i
$429$	0.148967	−	7.51922i	0.00719219	−	0.363032i
$430$	−2.94974	+	1.70304i	−0.142249	+	0.0821277i
$431$	−4.86245	−	27.5763i	−0.234216	−	1.32831i	−0.844258	−	0.535936i	$-0.819959\pi$
$431$	−4.86245	−	27.5763i	−0.234216	−	1.32831i	0.610042	−	0.792369i	$-0.291152\pi$
$432$	−3.57053	+	3.77509i	−0.171787	+	0.181629i
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	0.667488	−	0.744621i	$-0.267370\pi$
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	−0.849216	+	0.528045i	$0.822925\pi$
$434$	6.98433	+	1.23153i	0.335259	+	0.0591151i
$435$	−3.68937	−	3.22241i	−0.176892	−	0.154503i
$436$			0.0319160i			0.00152850i
$437$	1.79501	+	2.00128i	0.0858669	+	0.0957342i
$438$	−24.5129	+	13.5123i	−1.17127	+	0.645645i
$439$	7.65568	+	21.0338i	0.365386	+	1.00389i	0.977094	+	0.212806i	$0.0682602\pi$
$439$	7.65568	+	21.0338i	0.365386	+	1.00389i	−0.611709	+	0.791083i	$0.709518\pi$
$440$	0.134493	−	0.762746i	0.00641169	−	0.0363625i
$441$	1.99599	+	14.7046i	0.0950473	+	0.700217i
$442$	−12.7087	−	10.6639i	−0.604491	−	0.507228i
$443$	14.6859	−	2.58952i	0.697748	−	0.123032i	0.186487	−	0.982457i	$-0.440290\pi$
$443$	14.6859	−	2.58952i	0.697748	−	0.123032i	0.511261	+	0.859426i	$0.329179\pi$
$444$	−5.74849	+	9.51625i	−0.272811	+	0.451621i
$445$	−2.21544	−	1.27909i	−0.105022	−	0.0606345i
$446$	−3.93825	+	10.8203i	−0.186482	+	0.512354i
$447$	5.26346	+	33.7465i	0.248953	+	1.59615i
$448$	−0.716507	+	1.24103i	−0.0338518	+	0.0586330i
$449$	−2.44541	−	4.23557i	−0.115406	−	0.199889i	0.802536	−	0.596604i	$-0.203484\pi$
$449$	−2.44541	−	4.23557i	−0.115406	−	0.199889i	−0.917942	+	0.396715i	$0.870150\pi$
$450$	−13.0899	−	5.36055i	−0.617066	−	0.252699i
$451$	−7.37616	+	8.79056i	−0.347330	+	0.413931i
$452$	−7.92666	+	6.65126i	−0.372839	+	0.312849i
$453$	6.93431	−	2.36942i	0.325802	−	0.111325i
$454$	−1.44986	+	0.527706i	−0.0680453	+	0.0247665i
$455$	2.28954			0.107335
$456$	−7.45176	−	1.21294i	−0.348961	−	0.0568010i
$457$	−30.3578			−1.42008			−0.710039	−	0.704162i	$-0.751323\pi$
$457$	−30.3578			−1.42008			−0.710039	+	0.704162i	$0.751323\pi$
$458$	−7.68043	+	2.79545i	−0.358883	+	0.130623i
$459$	−6.67754	+	28.0188i	−0.311681	+	1.30780i
$460$	0.252218	−	0.211636i	0.0117597	−	0.00986757i
$461$	16.0576	−	19.1367i	0.747879	−	0.891287i	−0.249138	−	0.968468i	$-0.580147\pi$
$461$	16.0576	−	19.1367i	0.747879	−	0.891287i	0.997017	+	0.0771808i	$0.0245919\pi$
$462$	−2.80385	+	2.25960i	−0.130447	+	0.105126i
$463$	−2.94958	−	5.10883i	−0.137079	−	0.237427i	0.789311	−	0.613994i	$-0.210438\pi$
$463$	−2.94958	−	5.10883i	−0.137079	−	0.237427i	−0.926390	+	0.376566i	$0.877105\pi$
$464$	2.64886	−	4.58796i	0.122970	−	0.212990i
$465$	4.52145	−	0.705214i	0.209677	−	0.0327035i
$466$	−2.87121	+	7.88859i	−0.133006	+	0.365432i
$467$	4.76849	+	2.75309i	0.220659	+	0.127398i	0.606256	−	0.795270i	$-0.292671\pi$
$467$	4.76849	+	2.75309i	0.220659	+	0.127398i	−0.385596	+	0.922668i	$0.626004\pi$
$468$	−0.355616	+	8.97147i	−0.0164383	+	0.414707i
$469$	−13.0890	+	2.30794i	−0.604392	+	0.106571i
$470$	−5.22969	−	4.38823i	−0.241228	−	0.202414i
$471$	−6.34659	+	16.4177i	−0.292435	+	0.756489i
$472$	0.324588	−	1.84083i	0.0149404	−	0.0847310i
$473$	−3.16596	−	8.69840i	−0.145571	−	0.399953i
$474$	−6.68958	−	12.1356i	−0.307262	−	0.557409i
$475$	−4.23442	−	20.1113i	−0.194288	−	0.922770i
$476$			7.94354i			0.364091i
$477$	−1.17715	+	5.41255i	−0.0538981	+	0.247824i
$478$	8.65196	+	1.52557i	0.395731	+	0.0697781i
$479$	−21.4896	−	25.6103i	−0.981884	−	1.17016i	−0.985415	−	0.170170i	$-0.945568\pi$
$479$	−21.4896	−	25.6103i	−0.981884	−	1.17016i	0.00353081	−	0.999994i	$-0.498876\pi$
$480$	−0.178568	+	0.907238i	−0.00815048	+	0.0414096i
$481$	3.33588	+	18.9187i	0.152103	+	0.862618i
$482$	−11.6386	+	6.71954i	−0.530123	+	0.306067i
$483$	−1.53050	−	0.0303215i	−0.0696402	−	0.00137967i
$484$	−8.35867	−	3.04231i	−0.379940	−	0.138287i
$485$	4.15965	+	1.51399i	0.188880	+	0.0687467i
$486$	14.2046	−	6.42112i	0.644332	−	0.291268i
$487$	21.9456	−	12.6703i	0.994448	−	0.574145i	0.0878470	−	0.996134i	$-0.472001\pi$
$487$	21.9456	−	12.6703i	0.994448	−	0.574145i	0.906601	+	0.421989i	$0.138668\pi$
$488$	−2.04609	−	11.6039i	−0.0926219	−	0.525285i
$489$	−17.6816	−	3.48020i	−0.799589	−	0.157380i
$490$	1.69737	+	2.02285i	0.0766794	+	0.0913830i
$491$	7.76474	+	1.36913i	0.350418	+	0.0617881i	0.346087	−	0.938202i	$-0.387510\pi$
$491$	7.76474	+	1.36913i	0.350418	+	0.0617881i	0.00433112	+	0.999991i	$0.498621\pi$
$492$	9.01210	−	10.3180i	0.406297	−	0.465174i
$493$		−	29.3665i		−	1.32260i
$494$	−11.0765	+	6.89178i	−0.498354	+	0.310076i
$495$	−1.24056	+	1.96465i	−0.0557589	+	0.0883044i
$496$	1.69268	+	4.65059i	0.0760035	+	0.208818i
$497$	3.11645	−	17.6742i	0.139792	−	0.792798i
$498$	−8.01456	−	3.09818i	−0.359141	−	0.138833i
$499$	−9.89069	−	8.29927i	−0.442768	−	0.371526i	0.393976	−	0.919121i	$-0.371099\pi$
$499$	−9.89069	−	8.29927i	−0.442768	−	0.371526i	−0.836744	+	0.547594i	$0.815544\pi$
$500$	−5.10751	+	0.900591i	−0.228415	+	0.0402757i
$501$	35.2744	+	21.3082i	1.57594	+	0.951982i
$502$	−6.80388	−	3.92822i	−0.303672	−	0.175325i
$503$	−2.85952	+	7.85647i	−0.127500	+	0.350303i	−0.986975	−	0.160875i	$-0.948568\pi$
$503$	−2.85952	+	7.85647i	−0.127500	+	0.350303i	0.859475	+	0.511178i	$0.170791\pi$
$504$	3.40012	−	2.63077i	0.151454	−	0.117184i
$505$	0.840744	−	1.45621i	0.0374126	−	0.0648006i
$506$	0.447396	+	0.774912i	0.0198892	+	0.0344490i
$507$	−4.39400	−	5.45235i	−0.195144	−	0.242147i
$508$	−0.503979	+	0.600619i	−0.0223605	+	0.0266482i
$509$	−5.11088	+	4.28853i	−0.226536	+	0.190086i	−0.748990	−	0.662581i	$-0.769461\pi$
$509$	−5.11088	+	4.28853i	−0.226536	+	0.190086i	0.522454	+	0.852667i	$0.325016\pi$
$510$	1.65729	+	4.85019i	0.0733859	+	0.214770i
$511$	21.7614	−	7.92049i	0.962666	−	0.350382i
$512$	−1.00000			−0.0441942
$513$	19.3088	+	11.8394i	0.852503	+	0.522722i
$514$	12.2853			0.541884
$515$	5.12894	−	1.86678i	0.226008	−	0.0822603i
$516$	3.57322	+	10.4573i	0.157302	+	0.460358i
$517$	14.2127	−	11.9259i	0.625073	−	0.524499i
$518$	5.91254	−	7.04629i	0.259782	−	0.309596i
$519$	−27.2302	−	33.7889i	−1.19527	−	1.48317i
$520$	0.798855	+	1.38366i	0.0350321	+	0.0606774i
$521$	−7.75609	+	13.4339i	−0.339800	+	0.588552i	−0.984395	−	0.175973i	$-0.943693\pi$
$521$	−7.75609	+	13.4339i	−0.339800	+	0.588552i	0.644595	+	0.764525i	$0.277026\pi$
$522$	−12.5699	+	9.72569i	−0.550171	+	0.425682i
$523$	−7.60779	+	20.9022i	−0.332666	+	0.913991i	0.654750	+	0.755845i	$0.272774\pi$
$523$	−7.60779	+	20.9022i	−0.332666	+	0.913991i	−0.987416	+	0.158146i	$0.949448\pi$
$524$	−9.97575	−	5.75950i	−0.435793	−	0.251605i
$525$	10.0171	+	6.05106i	0.437183	+	0.264090i
$526$	23.4707	−	4.13852i	1.02337	−	0.180448i
$527$	21.0155	+	17.6341i	0.915450	+	0.768154i
$528$	−2.34386	−	0.906066i	−0.102004	−	0.0394314i
$529$	3.92786	−	22.2760i	0.170776	−	0.968521i
$530$	0.337118	+	0.926225i	0.0146435	+	0.0402326i
$531$	−2.99399	+	4.74153i	−0.129928	+	0.205765i
$532$	5.93693	+	1.94165i	0.257398	+	0.0841810i
$533$		−	23.6718i		−	1.02534i
$534$	−5.46001	+	6.25122i	−0.236278	+	0.270517i
$535$	6.10871	+	1.07713i	0.264103	+	0.0465684i
$536$	−5.96171	−	7.10489i	−0.257507	−	0.306884i
$537$	26.4152	+	5.19921i	1.13990	+	0.224362i
$538$	−3.30229	−	18.7282i	−0.142372	−	0.807431i
$539$	−6.21498	+	3.58822i	−0.267698	+	0.154556i
$540$	1.52720	−	2.31568i	0.0657200	−	0.0996511i
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	0.493008	−	0.870025i	$-0.335897\pi$
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	−0.181575	+	0.983377i	$0.558119\pi$
$542$	5.07299	+	1.84642i	0.217904	+	0.0793104i
$543$	36.3063	+	0.719281i	1.55805	+	0.0308673i
$544$	−4.80058	+	2.77162i	−0.205823	+	0.118832i
$545$	−0.00295864	−	0.0167793i	−0.000126734	−	0.000718746i
$546$	1.43458	−	7.28855i	0.0613942	−	0.311921i
$547$	18.1301	+	21.6066i	0.775188	+	0.923833i	0.998705	−	0.0508673i	$-0.0161986\pi$
$547$	18.1301	+	21.6066i	0.775188	+	0.923833i	−0.223518	+	0.974700i	$0.571754\pi$
$548$	13.3383	+	2.35190i	0.569784	+	0.100468i
$549$	−7.51224	+	34.5413i	−0.320615	+	1.47419i
$550$		−	6.84064i		−	0.291686i
$551$	−21.9482	−	7.17807i	−0.935026	−	0.305796i
$552$	−0.515690	−	0.935520i	−0.0219492	−	0.0398184i
$553$	3.92121	+	10.7734i	0.166747	+	0.458133i
$554$	0.0162172	−	0.0919724i	0.000689003	−	0.00390753i
$555$	2.14001	−	5.53590i	0.0908384	−	0.234986i
$556$	−5.54326	−	4.65135i	−0.235087	−	0.197261i
$557$	−30.7949	+	5.42997i	−1.30482	+	0.230075i	−0.782487	−	0.622666i	$-0.786049\pi$
$557$	−30.7949	+	5.42997i	−1.30482	+	0.230075i	−0.522333	+	0.852741i	$0.674938\pi$
$558$	0.588058	−	14.8355i	0.0248945	−	0.628038i
$559$	16.5369	+	9.54757i	0.699435	+	0.403819i
$560$	0.261648	−	0.718871i	0.0110566	−	0.0303778i
$561$	−13.7632	+	2.14665i	−0.581082	+	0.0906317i
$562$	−5.10091	+	8.83503i	−0.215169	+	0.372683i
$563$	4.37942	+	7.58538i	0.184571	+	0.319686i	0.943432	−	0.331567i	$-0.107577\pi$
$563$	4.37942	+	7.58538i	0.184571	+	0.319686i	−0.758861	+	0.651252i	$0.774244\pi$
$564$	−17.2464	+	13.8987i	−0.726203	+	0.585241i
$565$	3.55073	−	4.23160i	0.149380	−	0.178025i
$566$	14.8149	−	12.4312i	0.622716	−	0.522521i
$567$	−12.4305	+	3.43796i	−0.522030	+	0.144381i
$568$	11.7686	−	4.28342i	0.493799	−	0.179728i
$569$	39.4950			1.65572			0.827859	−	0.560936i	$-0.189559\pi$
$569$	39.4950			1.65572			0.827859	+	0.560936i	$0.189559\pi$
$570$	4.03008	−	0.0531037i	0.168802	−	0.00222427i
$571$	−1.49689			−0.0626431			−0.0313215	−	0.999509i	$-0.509972\pi$
$571$	−1.49689			−0.0626431			−0.0313215	+	0.999509i	$0.509972\pi$
$572$	−4.08022	+	1.48508i	−0.170603	+	0.0620942i
$573$	−2.61255	+	0.892695i	−0.109141	+	0.0372929i
$574$	−8.68267	+	7.28562i	−0.362408	+	0.304096i
$575$	1.86921	−	2.22764i	0.0779514	−	0.0928988i
$576$	2.77623	+	1.13691i	0.115676	+	0.0473713i
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	0.733551	−	0.679634i	$-0.237861\pi$
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	−0.955356	+	0.295457i	$0.904528\pi$
$578$	−6.86373	+	11.8883i	−0.285493	+	0.494489i
$579$	1.16274	+	7.45484i	0.0483217	+	0.309813i
$580$	−0.967285	+	2.65759i	−0.0401643	+	0.110351i
$581$	6.15662	+	3.55453i	0.255420	+	0.147467i
$582$	7.42599	−	12.2932i	0.307817	−	0.509571i
$583$	−2.63804	+	0.465158i	−0.109257	+	0.0192649i
$584$	12.3795	+	10.3876i	0.512268	+	0.429844i
$585$	−0.644706	−	4.74957i	−0.0266553	−	0.196371i
$586$	−2.81056	+	15.9395i	−0.116103	+	0.658454i
$587$	−0.0214414	−	0.0589098i	−0.000884983	−	0.00243147i	0.939249	−	0.343236i	$-0.111523\pi$
$587$	−0.0214414	−	0.0589098i	−0.000884983	−	0.00243147i	−0.940134	+	0.340804i	$0.889301\pi$
$588$	7.50310	−	4.13596i	0.309423	−	0.170564i
$589$	18.3164	−	11.3965i	0.754714	−	0.469584i
$590$			0.997875i			0.0410818i
$591$	8.58152	+	7.49537i	0.352997	+	0.308318i
$592$	6.32132	+	1.11462i	0.259804	+	0.0458105i
$593$	−10.0616	−	11.9910i	−0.413181	−	0.492409i	0.518811	−	0.854889i	$-0.326375\pi$
$593$	−10.0616	−	11.9910i	−0.413181	−	0.492409i	−0.931992	+	0.362479i	$0.881930\pi$
$594$	5.47698	+	5.18021i	0.224723	+	0.212547i
$595$	−0.736374	−	4.17618i	−0.0301884	−	0.171207i
$596$	17.0772	−	9.85955i	0.699511	−	0.403863i
$597$	−0.373902	+	18.8730i	−0.0153028	+	0.772421i
$598$	−1.73451	−	0.631310i	−0.0709294	−	0.0258162i
$599$	2.10138	+	0.764839i	0.0858600	+	0.0312505i	0.384593	−	0.923086i	$-0.374342\pi$
$599$	2.10138	+	0.764839i	0.0858600	+	0.0312505i	−0.298733	+	0.954337i	$0.596564\pi$
$600$	−0.161761	+	8.16504i	−0.00660388	+	0.333336i
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	−0.792197	−	0.610266i	$-0.791063\pi$
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	0.132407	+	0.991195i	$0.457729\pi$
$602$	−1.58767	−	9.00413i	−0.0647086	−	0.366981i
$603$	8.47342	+	26.5027i	0.345064	+	1.07927i
$604$	−2.71950	−	3.24097i	−0.110655	−	0.131873i
$605$	4.67646	+	0.824586i	0.190125	+	0.0335242i
$606$	−4.10893	−	3.58887i	−0.166914	−	0.145788i
$607$		−	43.2872i		−	1.75697i	−0.477766	−	0.878487i	$-0.658553\pi$
$607$		−	43.2872i		−	1.75697i	0.477766	−	0.878487i	$-0.341447\pi$
$608$	0.898071	+	4.26538i	0.0364216	+	0.172984i
$609$	11.5155	−	6.34776i	0.466634	−	0.257224i
$610$	2.15139	+	5.91090i	0.0871073	+	0.239325i
$611$	−6.64602	+	37.6915i	−0.268869	+	1.52483i
$612$	16.4786	−	2.23680i	0.666107	−	0.0904173i
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	0.493902	−	0.869518i	$-0.335570\pi$
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	−0.770542	+	0.637389i	$0.780015\pi$
$614$	17.5661	−	3.09738i	0.708911	−	0.125000i
$615$	−3.78147	+	6.25998i	−0.152484	+	0.252427i
$616$	1.80051	+	1.03952i	0.0725446	+	0.0418836i
$617$	−8.89796	+	24.4469i	−0.358218	+	0.984197i	0.621429	+	0.783470i	$0.286552\pi$
$617$	−8.89796	+	24.4469i	−0.358218	+	0.984197i	−0.979647	+	0.200726i	$0.935670\pi$
$618$	−2.72905	−	17.4972i	−0.109779	−	0.703841i
$619$	−9.72654	+	16.8469i	−0.390943	+	0.677133i	−0.992574	−	0.121641i	$-0.961184\pi$
$619$	−9.72654	+	16.8469i	−0.390943	+	0.677133i	0.601631	+	0.798774i	$0.294518\pi$
$620$	−1.32101	−	2.28806i	−0.0530531	−	0.0918907i
$621$	0.368069	+	3.18351i	0.0147701	+	0.127750i
$622$	−21.0416	+	25.0764i	−0.843692	+	1.00547i
$623$	5.26042	−	4.41402i	0.210754	−	0.176844i
$624$	4.90529	−	1.67611i	0.196369	−	0.0670983i
$625$	−19.5516	+	7.11620i	−0.782064	+	0.284648i
$626$	−26.4219			−1.05603
$627$	−1.75976	+	10.8112i	−0.0702779	+	0.431757i
$628$	10.1624			0.405522
$629$	33.4353	−	12.1695i	1.33315	−	0.485228i
$630$	−1.54369	+	1.69828i	−0.0615019	+	0.0676610i
$631$	−11.6007	+	9.73414i	−0.461816	+	0.387510i	−0.843799	−	0.536660i	$-0.819686\pi$
$631$	−11.6007	+	9.73414i	−0.461816	+	0.387510i	0.381982	+	0.924170i	$0.375241\pi$
$632$	−5.14263	+	6.12874i	−0.204563	+	0.243788i
$633$	10.2087	−	8.22711i	0.405760	−	0.326998i
$634$	6.70437	+	11.6123i	0.266265	+	0.461184i
$635$	0.209281	−	0.362485i	0.00830506	−	0.0143848i
$636$	3.15979	−	0.492834i	0.125294	−	0.0195421i
$637$	5.06326	−	13.9112i	0.200614	−	0.551182i
$638$	−6.65631	−	3.84302i	−0.263526	−	0.152147i
$639$	−37.5421	−	1.48811i	−1.48514	−	0.0588688i
$640$	0.525734	−	0.0927010i	0.0207814	−	0.00366433i
$641$	−28.6682	−	24.0555i	−1.13233	−	0.950135i	−0.133166	−	0.991094i	$-0.542514\pi$
$641$	−28.6682	−	24.0555i	−1.13233	−	0.950135i	−0.999161	+	0.0409586i	$0.986959\pi$
$642$	7.25654	−	18.7716i	0.286393	−	0.740858i
$643$	1.81700	−	10.3047i	0.0716554	−	0.406378i	−0.927791	−	0.373101i	$-0.878295\pi$
$643$	1.81700	−	10.3047i	0.0716554	−	0.406378i	0.999446	−	0.0332769i	$-0.0105943\pi$
$644$	0.302280	+	0.830508i	0.0119115	+	0.0327266i
$645$	−2.84797	−	5.16653i	−0.112139	−	0.203432i
$646$	16.1333	+	17.9872i	0.634755	+	0.707697i
$647$		−	15.2706i		−	0.600348i	−0.953884	−	0.300174i	$-0.902955\pi$
$647$		−	15.2706i		−	0.600348i	0.953884	−	0.300174i	$-0.0970448\pi$
$648$	−6.41486	−	6.31265i	−0.252000	−	0.247984i
$649$	−2.67071	−	0.470919i	−0.104835	−	0.0184852i
$650$	9.07055	+	10.8099i	0.355776	+	0.423998i
$651$	−2.37226	+	12.0526i	−0.0929763	+	0.472378i
$652$	1.80669	+	10.2463i	0.0707555	+	0.401275i
$653$	−2.32583	+	1.34282i	−0.0910168	+	0.0525486i	−0.544818	−	0.838555i	$-0.683401\pi$
$653$	−2.32583	+	1.34282i	−0.0910168	+	0.0525486i	0.453801	+	0.891103i	$0.350068\pi$
$654$	−0.0552692	−	0.00109496i	−0.00216120	−	4.28165e-5i
$655$	5.77850	+	2.10320i	0.225785	+	0.0821789i
$656$	−7.43249	−	2.70521i	−0.290190	−	0.105621i
$657$	−22.5585	−	42.9129i	−0.880091	−	1.67419i
$658$	15.8705	−	9.16281i	0.618695	−	0.357203i
$659$	5.97002	+	33.8577i	0.232559	+	1.31891i	0.847694	+	0.530486i	$0.177991\pi$
$659$	5.97002	+	33.8577i	0.232559	+	1.31891i	−0.615134	+	0.788422i	$0.710898\pi$
$660$	1.31624	+	0.259071i	0.0512346	+	0.0100843i
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	0.938799	−	0.344465i	$-0.111940\pi$
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	−0.502253	+	0.864721i	$0.667495\pi$
$662$	24.6137	+	4.34007i	0.956640	+	0.168682i
$663$	18.9027	−	21.6419i	0.734121	−	0.840503i
$664$			4.96091i			0.192521i
$665$	−3.30123	−	0.470429i	−0.128016	−	0.0182425i
$666$	−16.2822	−	10.2812i	−0.630922	−	0.398389i
$667$	−1.11750	−	3.07031i	−0.0432698	−	0.118883i
$668$	4.13162	−	23.4316i	0.159857	−	0.906594i
$669$	−18.6025	−	7.19114i	−0.719213	−	0.278025i
$670$	3.79290	+	3.18262i	0.146533	+	0.122955i
$671$	−16.8352	+	2.96851i	−0.649917	+	0.114598i
$672$	−2.12452	−	1.28336i	−0.0819551	−	0.0495067i
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.474863	−	0.880060i	$-0.657502\pi$
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.999586	+	0.0287864i	$0.990836\pi$
$674$	5.70262	−	15.6678i	0.219657	−	0.603502i
$675$	9.73201	−	22.4841i	0.374585	−	0.865413i
$676$	−2.02145	+	3.50126i	−0.0777483	+	0.134664i
$677$	−9.28464	−	16.0815i	−0.356838	−	0.618061i	0.630593	−	0.776114i	$-0.282812\pi$
$677$	−9.28464	−	16.0815i	−0.356838	−	0.618061i	−0.987431	+	0.158053i	$0.949478\pi$
$678$	−11.2461	−	13.9549i	−0.431904	−	0.535934i
$679$	−7.63791	+	9.10251i	−0.293116	+	0.349322i
$680$	2.26690	−	1.90215i	0.0869315	−	0.0729442i
$681$	−0.864093	−	2.52884i	−0.0331121	−	0.0969055i
$682$	6.74718	−	2.45577i	0.258363	−	0.0940364i
$683$	−18.9873			−0.726527			−0.363264	−	0.931686i	$-0.618338\pi$
$683$	−18.9873			−0.726527			−0.363264	+	0.931686i	$0.618338\pi$
$684$	2.35611	−	12.8627i	0.0900882	−	0.491817i
$685$	−7.23041			−0.276260
$686$	−16.0870	+	5.85520i	−0.614206	+	0.223553i
$687$	−4.57741	−	13.3962i	−0.174639	−	0.511096i
$688$	4.88757	−	4.10116i	0.186337	−	0.156355i
$689$	3.55195	−	4.23305i	0.135319	−	0.161266i
$690$	0.357839	+	0.444029i	0.0136227	+	0.0169039i
$691$	7.53839	+	13.0569i	0.286774	+	0.496707i	0.973038	−	0.230646i	$-0.0740839\pi$
$691$	7.53839	+	13.0569i	0.286774	+	0.496707i	−0.686264	+	0.727352i	$0.740751\pi$
$692$	−12.5272	+	21.6978i	−0.476213	+	0.824826i
$693$	−3.81677	−	4.93298i	−0.144987	−	0.187388i
$694$	−12.2473	+	33.6493i	−0.464903	+	1.27731i
$695$	3.34547	+	1.93151i	0.126901	+	0.0732662i
$696$	7.85414	+	4.74446i	0.297710	+	0.179838i
$697$	−43.1781	+	7.61346i	−1.63549	+	0.288380i
$698$	14.9823	+	12.5717i	0.567089	+	0.475844i
$699$	−13.5623	−	5.24275i	−0.512972	−	0.198299i
$700$	1.17329	−	6.65403i	0.0443460	−	0.251499i
$701$	4.16179	+	11.4344i	0.157189	+	0.431872i	0.993140	−	0.116931i	$-0.0373057\pi$
$701$	4.16179	+	11.4344i	0.157189	+	0.431872i	−0.835951	+	0.548804i	$0.815083\pi$
$702$	−15.5238	−	0.923615i	−0.585908	−	0.0348596i
$703$	−0.922720	−	27.9638i	−0.0348010	−	1.05468i
$704$			1.45082i			0.0546799i
$705$	7.77857	−	8.90577i	0.292958	−	0.335411i
$706$	−31.7672	−	5.60142i	−1.19558	−	0.210812i
$707$	2.90133	+	3.45768i	0.109116	+	0.130039i
$708$	3.17665	+	0.625247i	0.119386	+	0.0234982i
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	−0.803369	−	0.595481i	$-0.796961\pi$
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	0.551253	−	0.834338i	$-0.314150\pi$
$710$	−5.79007	+	3.34290i	−0.217297	+	0.125457i
$711$	21.2449	−	11.1681i	0.796747	−	0.418835i
$712$	4.50300	+	1.63896i	0.168757	+	0.0614225i
$713$	2.86824	+	1.04395i	0.107417	+	0.0390964i
$714$	−13.7559	−	0.272525i	−0.514802	−	0.0101990i
$715$	2.00744	−	1.15900i	0.0750740	−	0.0433440i
$716$	−2.69909	−	15.3073i	−0.100870	−	0.572061i
$717$	−2.93868	+	14.9303i	−0.109747	+	0.557584i
$718$	11.2586	+	13.4175i	0.420167	+	0.500736i
$719$	−26.0696	−	4.59678i	−0.972233	−	0.171431i	−0.335098	−	0.942183i	$-0.608769\pi$
$719$	−26.0696	−	4.59678i	−0.972233	−	0.171431i	−0.637135	+	0.770752i	$0.719881\pi$
$720$	−1.56495	−	0.340354i	−0.0583222	−	0.0126842i
$721$			14.6514i			0.545646i
$722$	17.3869	−	7.66123i	0.647075	−	0.285121i
$723$	−11.2370	−	20.3852i	−0.417909	−	0.758134i
$724$	−7.17064	−	19.7012i	−0.266495	−	0.732188i
$725$	−4.33752	+	24.5993i	−0.161091	+	0.913595i
$726$	5.55517	−	14.3704i	0.206172	−	0.533337i
$727$	23.0429	+	19.3353i	0.854614	+	0.717107i	0.960801	−	0.277240i	$-0.0894196\pi$
$727$	23.0429	+	19.3353i	0.854614	+	0.717107i	−0.106187	+	0.994346i	$0.533864\pi$
$728$	−4.22363	+	0.744740i	−0.156538	+	0.0276019i
$729$	10.6322	+	24.8185i	0.393785	+	0.919203i
$730$	−7.47127	−	4.31354i	−0.276524	−	0.159651i
$731$	12.0964	−	33.2345i	0.447400	−	1.22922i
$732$	20.1648	−	3.14512i	0.745314	−	0.116247i
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	−0.762339	−	0.647178i	$-0.775949\pi$
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	0.941642	+	0.336616i	$0.109282\pi$
$734$	10.3438	+	17.9160i	0.381796	+	0.661291i
$735$	−3.56122	+	2.86996i	−0.131358	+	0.105860i
$736$	−0.396438	+	0.472456i	−0.0146129	+	0.0174150i
$737$	−10.3079	+	8.64938i	−0.379697	+	0.318604i
$738$	17.5587	+	15.9603i	0.646345	+	0.587508i
$739$	−46.3353	+	16.8647i	−1.70447	+	0.620377i	−0.996322	−	0.0856846i	$-0.972692\pi$
$739$	−46.3353	+	16.8647i	−1.70447	+	0.620377i	−0.708150	+	0.706062i	$0.750470\pi$
$740$	−3.42665			−0.125966
$741$	−11.5546	−	19.4177i	−0.424468	−	0.713326i
$742$	−2.64586			−0.0971326
$743$	6.36036	−	2.31498i	0.233339	−	0.0849285i	−0.222704	−	0.974886i	$-0.571488\pi$
$743$	6.36036	−	2.31498i	0.233339	−	0.0849285i	0.456043	+	0.889958i	$0.349266\pi$
$744$	−8.11156	+	2.77168i	−0.297384	+	0.101615i
$745$	−8.06409	+	6.76658i	−0.295445	+	0.247908i
$746$	1.83196	−	2.18324i	0.0670728	−	0.0799342i
$747$	5.64011	−	13.7726i	0.206361	−	0.503913i
$748$	4.02112	+	6.96479i	0.147027	+	0.254658i
$749$	−8.32539	+	14.4200i	−0.304203	+	0.526895i
$750$	−1.38434	−	8.87562i	−0.0505488	−	0.324092i
$751$	7.71871	−	21.2070i	0.281660	−	0.773853i	−0.715505	−	0.698607i	$-0.753804\pi$
$751$	7.71871	−	21.2070i	0.281660	−	0.773853i	0.997165	−	0.0752462i	$-0.0239743\pi$
$752$	11.0749	+	6.39408i	0.403859	+	0.233168i
$753$	7.03597	−	11.6476i	0.256405	−	0.424462i
$754$	15.6143	−	2.75323i	0.568641	−	0.100267i
$755$	1.73017	+	1.45179i	0.0629675	+	0.0528360i
$756$	4.43908	+	5.97829i	0.161448	+	0.217428i
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	0.142523	+	0.989791i	$0.454478\pi$
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	−0.472457	+	0.881354i	$0.656633\pi$
$758$	−5.18667	−	14.2502i	−0.188388	−	0.517592i
$759$	−1.35727	+	0.748174i	−0.0492659	+	0.0271570i
$760$	−0.867551	−	2.15920i	−0.0314694	−	0.0783225i
$761$			16.8329i			0.610193i	0.952321	+	0.305097i	$0.0986888\pi$
$761$			16.8329i			0.610193i	−0.952321	+	0.305097i	$0.901311\pi$
$762$	−1.02281	−	0.893353i	−0.0370524	−	0.0323627i
$763$	0.0450412	+	0.00794198i	0.00163060	+	0.000287519i
$764$	1.02459	+	1.22106i	0.0370684	+	0.0441764i
$765$	−8.45599	+	2.70354i	−0.305727	+	0.0977468i
$766$

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.560041 + 1.63901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.343148 + 0.408948i) q^{5} +(1.08684 + 1.34862i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.37271 + 1.83583i) q^{9} +(-0.182585 + 0.501649i) q^{10} +(-1.25645 - 0.725411i) q^{11} +(1.48255 + 0.895567i) q^{12} +(2.94737 - 0.519701i) q^{13} +(-1.09775 - 0.921124i) q^{14} +(-0.862447 - 0.333396i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.89590 - 5.20894i) q^{17} +(-1.60173 + 2.53663i) q^{18} +(-4.35653 + 0.143752i) q^{19} +0.533844i q^{20} +(1.63278 - 1.86939i) q^{21} +(-1.42878 - 0.251933i) q^{22} +(-0.396438 - 0.472456i) q^{23} +(1.69944 + 0.334495i) q^{24} +(0.818753 + 4.64338i) q^{25} +(2.59188 - 1.49642i) q^{26} +(-4.33775 - 2.86075i) q^{27} +(-1.34659 - 0.490120i) q^{28} +(4.97822 + 1.81193i) q^{29} +(-0.924463 - 0.0183150i) q^{30} +(-4.28601 + 2.47453i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.485293 - 2.46559i) q^{33} +(-3.56312 - 4.24636i) q^{34} +(0.753384 + 0.132842i) q^{35} +(-0.637553 + 2.93147i) q^{36} +6.41883i q^{37} +(-4.04463 + 1.62510i) q^{38} +(2.50245 + 4.53972i) q^{39} +(0.182585 + 0.501649i) q^{40} +(1.37347 - 7.78933i) q^{41} +(0.894945 - 2.31510i) q^{42} +(4.88757 + 4.10116i) q^{43} +(-1.42878 + 0.251933i) q^{44} +(0.0634325 - 1.60027i) q^{45} +(-0.534119 - 0.308374i) q^{46} +(-4.37381 + 12.0169i) q^{47} +(1.71136 - 0.266922i) q^{48} +(2.47323 - 4.28377i) q^{49} +(2.35751 + 4.08332i) q^{50} +(7.47572 - 6.02462i) q^{51} +(1.92376 - 2.29265i) q^{52} +(1.41439 - 1.18682i) q^{53} +(-5.05459 - 1.20463i) q^{54} +(0.727804 - 0.264899i) q^{55} -1.43301 q^{56} +(-2.67545 - 7.05989i) q^{57} +5.29771 q^{58} +(1.75650 - 0.639313i) q^{59} +(-0.874975 + 0.298975i) q^{60} +(9.02625 - 7.57392i) q^{61} +(-3.18119 + 3.79120i) q^{62} +(3.97837 + 1.62921i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.798855 + 1.38366i) q^{65} +(-0.387256 - 2.48288i) q^{66} +(3.17216 - 8.71543i) q^{67} +(-4.80058 - 2.77162i) q^{68} +(0.552339 - 0.914360i) q^{69} +(0.753384 - 0.132842i) q^{70} +(9.59384 + 8.05019i) q^{71} +(0.403519 + 2.97274i) q^{72} +(-2.80621 + 15.9148i) q^{73} +(2.19537 + 6.03173i) q^{74} +(-7.15201 + 3.94243i) q^{75} +(-3.24489 + 2.91044i) q^{76} +2.07905i q^{77} +(3.90420 + 3.41005i) q^{78} +(-7.87896 - 1.38927i) q^{79} +(0.343148 + 0.408948i) q^{80} +(2.25948 - 8.71176i) q^{81} +(-1.37347 - 7.78933i) q^{82} +(-4.29627 + 2.48045i) q^{83} +(0.0491635 - 2.48157i) q^{84} +(2.78076 + 1.01211i) q^{85} +(5.99550 + 2.18218i) q^{86} +(-0.181753 + 9.17411i) q^{87} +(-1.25645 + 0.725411i) q^{88} +(0.832120 + 4.71919i) q^{89} +(-0.487719 - 1.52546i) q^{90} +(-2.75678 - 3.28540i) q^{91} +(-0.607378 - 0.107097i) q^{92} +(-6.45612 - 5.63897i) q^{93} +12.7882i q^{94} +(1.43615 - 1.83092i) q^{95} +(1.51686 - 0.836144i) q^{96} +(-2.83601 - 7.79188i) q^{97} +(0.858945 - 4.87132i) q^{98} +(4.31291 - 0.585434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Introduction

L-functions

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