LMFDB - Embedded newform 230.2.l.a.227.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	230.227
Dual form			230.2.l.a.153.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.599278 + 0.800541i) q^{2} +(-1.05014 - 2.81554i) q^{3} +(-0.281733 - 0.959493i) q^{4} +(1.82975 - 1.28531i) q^{5} +(2.88328 + 0.846609i) q^{6} +(0.193807 - 0.890918i) q^{7} +(0.936950 + 0.349464i) q^{8} +(-4.55723 + 3.94886i) q^{9} +(-0.0675806 + 2.23505i) q^{10} +(-4.85200 - 0.697612i) q^{11} +(-2.40563 + 1.80083i) q^{12} +(0.517727 - 0.112625i) q^{13} +(0.597072 + 0.689058i) q^{14} +(-5.54035 - 3.80197i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(5.49341 - 2.99963i) q^{17} +(-0.430181 - 6.01471i) q^{18} +(-3.07061 + 0.901613i) q^{19} +(-1.74875 - 1.39351i) q^{20} +(-2.71194 + 0.389918i) q^{21} +(3.46616 - 3.46616i) q^{22} +(-3.86197 - 2.84345i) q^{23} -3.00501i q^{24} +(1.69594 - 4.70359i) q^{25} +(-0.220101 + 0.481955i) q^{26} +(7.99162 + 4.36376i) q^{27} +(-0.909432 + 0.0650438i) q^{28} +(0.421780 - 1.43645i) q^{29} +(6.36384 - 2.15684i) q^{30} +(3.23025 + 7.07325i) q^{31} +(0.0713392 - 0.997452i) q^{32} +(3.13113 + 14.3936i) q^{33} +(-0.890751 + 6.19531i) q^{34} +(-0.790490 - 1.87926i) q^{35} +(5.07282 + 3.26011i) q^{36} +(-5.80254 - 0.415006i) q^{37} +(1.11837 - 2.99847i) q^{38} +(-0.860786 - 1.33941i) q^{39} +(2.16355 - 0.564842i) q^{40} +(0.940286 - 1.08515i) q^{41} +(1.31306 - 2.40469i) q^{42} +(11.1534 - 4.16001i) q^{43} +(0.697612 + 4.85200i) q^{44} +(-3.26305 + 13.0829i) q^{45} +(4.59069 - 1.38765i) q^{46} +(-0.416132 - 0.416132i) q^{47} +(2.40563 + 1.80083i) q^{48} +(5.61125 + 2.56257i) q^{49} +(2.74908 + 4.17643i) q^{50} +(-14.2144 - 12.3169i) q^{51} +(-0.253923 - 0.465025i) q^{52} +(-1.49093 - 0.324331i) q^{53} +(-8.28257 + 3.78252i) q^{54} +(-9.77457 + 4.95988i) q^{55} +(0.492932 - 0.767017i) q^{56} +(5.76311 + 7.69861i) q^{57} +(0.897174 + 1.19848i) q^{58} +(7.41732 - 11.5416i) q^{59} +(-2.08706 + 6.38706i) q^{60} +(5.26049 - 2.40239i) q^{61} +(-7.59825 - 1.65290i) q^{62} +(2.63489 + 4.82543i) q^{63} +(0.755750 + 0.654861i) q^{64} +(0.802551 - 0.871515i) q^{65} +(-13.3991 - 6.11915i) q^{66} +(3.09240 + 2.31494i) q^{67} +(-4.42579 - 4.42579i) q^{68} +(-3.95023 + 13.8596i) q^{69} +(1.97815 + 0.493377i) q^{70} +(0.108388 + 0.753855i) q^{71} +(-5.64988 + 2.10730i) q^{72} +(0.0284134 - 0.0520352i) q^{73} +(3.80956 - 4.39647i) q^{74} +(-15.0241 + 0.164441i) q^{75} +(1.73018 + 2.69222i) q^{76} +(-1.56187 + 4.18753i) q^{77} +(1.58810 + 0.113583i) q^{78} +(13.7011 + 8.80519i) q^{79} +(-0.844388 + 2.07051i) q^{80} +(1.31948 - 9.17722i) q^{81} +(0.305213 + 1.40304i) q^{82} +(0.417094 - 5.83173i) q^{83} +(1.13817 + 2.49224i) q^{84} +(6.19609 - 12.5493i) q^{85} +(-3.35373 + 11.4218i) q^{86} +(-4.48731 + 0.320939i) q^{87} +(-4.30229 - 2.34923i) q^{88} +(-2.73698 + 5.99315i) q^{89} +(-8.51791 - 10.4525i) q^{90} -0.483079i q^{91} +(-1.64023 + 4.50662i) q^{92} +(16.5228 - 16.5228i) q^{93} +(0.582509 - 0.0837522i) q^{94} +(-4.45959 + 5.59642i) q^{95} +(-2.88328 + 0.846609i) q^{96} +(0.457698 + 6.39945i) q^{97} +(-5.41414 + 2.95634i) q^{98} +(24.8664 - 15.9807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.599278	+	0.800541i	−0.423753	+	0.566068i
$2$	−0.599278	+	0.800541i	−0.423753	+	0.566068i
$3$	−1.05014	−	2.81554i	−0.606300	−	1.62555i	−0.769271	−	0.638923i	$-0.779380\pi$
$3$	−1.05014	−	2.81554i	−0.606300	−	1.62555i	0.162971	−	0.986631i	$-0.447892\pi$
$4$	−0.281733	−	0.959493i	−0.140866	−	0.479746i
$5$	1.82975	−	1.28531i	0.818287	−	0.574809i
$5$	1.82975	−	1.28531i	0.818287	−	0.574809i
$6$	2.88328	+	0.846609i	1.17710	+	0.345627i
$7$	0.193807	−	0.890918i	0.0732523	−	0.336735i	−0.925906	−	0.377754i	$-0.876697\pi$
$7$	0.193807	−	0.890918i	0.0732523	−	0.336735i	0.999158	+	0.0410184i	$0.0130602\pi$
$8$	0.936950	+	0.349464i	0.331262	+	0.123554i
$9$	−4.55723	+	3.94886i	−1.51908	+	1.31629i
$10$	−0.0675806	+	2.23505i	−0.0213709	+	0.706784i
$11$	−4.85200	−	0.697612i	−1.46293	−	0.210338i	−0.635586	−	0.772030i	$-0.719241\pi$
$11$	−4.85200	−	0.697612i	−1.46293	−	0.210338i	−0.827346	+	0.561693i	$0.810150\pi$
$12$	−2.40563	+	1.80083i	−0.694446	+	0.519856i
$13$	0.517727	−	0.112625i	0.143592	−	0.0312364i	−0.140195	−	0.990124i	$-0.544773\pi$
$13$	0.517727	−	0.112625i	0.143592	−	0.0312364i	0.283787	+	0.958887i	$0.408409\pi$
$14$	0.597072	+	0.689058i	0.159574	+	0.184159i
$15$	−5.54035	−	3.80197i	−1.43051	−	0.981663i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	5.49341	−	2.99963i	1.33235	−	0.727517i	0.354149	−	0.935189i	$-0.384771\pi$
$17$	5.49341	−	2.99963i	1.33235	−	0.727517i	0.978198	+	0.207672i	$0.0665888\pi$
$18$	−0.430181	−	6.01471i	−0.101395	−	1.41768i
$19$	−3.07061	+	0.901613i	−0.704447	+	0.206844i	−0.614286	−	0.789083i	$-0.710556\pi$
$19$	−3.07061	+	0.901613i	−0.704447	+	0.206844i	−0.0901601	+	0.995927i	$0.528738\pi$
$20$	−1.74875	−	1.39351i	−0.391032	−	0.311599i
$21$	−2.71194	+	0.389918i	−0.591794	+	0.0850872i
$22$	3.46616	−	3.46616i	0.738988	−	0.738988i
$23$	−3.86197	−	2.84345i	−0.805276	−	0.592900i
$23$	−3.86197	−	2.84345i	−0.805276	−	0.592900i
$24$		−	3.00501i		−	0.613395i
$25$	1.69594	−	4.70359i	0.339189	−	0.940718i
$26$	−0.220101	+	0.481955i	−0.0431654	+	0.0945191i
$27$	7.99162	+	4.36376i	1.53799	+	0.839805i
$28$	−0.909432	+	0.0650438i	−0.171866	+	0.0122921i
$29$	0.421780	−	1.43645i	0.0783225	−	0.266742i	−0.911017	−	0.412369i	$-0.864702\pi$
$29$	0.421780	−	1.43645i	0.0783225	−	0.266742i	0.989340	+	0.145627i	$0.0465198\pi$
$30$	6.36384	−	2.15684i	1.16187	−	0.393784i
$31$	3.23025	+	7.07325i	0.580170	+	1.27039i	0.941203	+	0.337841i	$0.109697\pi$
$31$	3.23025	+	7.07325i	0.580170	+	1.27039i	−0.361034	+	0.932553i	$0.617576\pi$
$32$	0.0713392	−	0.997452i	0.0126111	−	0.176326i
$33$	3.13113	+	14.3936i	0.545060	+	2.50560i
$34$	−0.890751	+	6.19531i	−0.152763	+	1.06249i
$35$	−0.790490	−	1.87926i	−0.133617	−	0.317652i
$36$	5.07282	+	3.26011i	0.845470	+	0.543351i
$37$	−5.80254	−	0.415006i	−0.953932	−	0.0682265i	−0.414312	−	0.910135i	$-0.635978\pi$
$37$	−5.80254	−	0.415006i	−0.953932	−	0.0682265i	−0.539620	+	0.841909i	$0.681432\pi$
$38$	1.11837	−	2.99847i	0.181424	−	0.486416i
$39$	−0.860786	−	1.33941i	−0.137836	−	0.214477i
$40$	2.16355	−	0.564842i	0.342087	−	0.0893094i
$41$	0.940286	−	1.08515i	0.146848	−	0.169472i	−0.677560	−	0.735467i	$-0.736963\pi$
$41$	0.940286	−	1.08515i	0.146848	−	0.169472i	0.824408	+	0.565996i	$0.191508\pi$
$42$	1.31306	−	2.40469i	0.202610	−	0.371052i
$43$	11.1534	−	4.16001i	1.70088	−	0.634395i	0.703774	−	0.710424i	$-0.251497\pi$
$43$	11.1534	−	4.16001i	1.70088	−	0.634395i	0.997106	+	0.0760291i	$0.0242242\pi$
$44$	0.697612	+	4.85200i	0.105169	+	0.731466i
$45$	−3.26305	+	13.0829i	−0.486427	+	1.95028i
$46$	4.59069	−	1.38765i	0.676860	−	0.204598i
$47$	−0.416132	−	0.416132i	−0.0606991	−	0.0606991i	0.676106	−	0.736805i	$-0.263666\pi$
$47$	−0.416132	−	0.416132i	−0.0606991	−	0.0606991i	−0.736805	+	0.676106i	$0.763666\pi$
$48$	2.40563	+	1.80083i	0.347223	+	0.259928i
$49$	5.61125	+	2.56257i	0.801607	+	0.366082i
$50$	2.74908	+	4.17643i	0.388778	+	0.590636i
$51$	−14.2144	−	12.3169i	−1.99042	−	1.72471i
$52$	−0.253923	−	0.465025i	−0.0352128	−	0.0644874i
$53$	−1.49093	−	0.324331i	−0.204795	−	0.0445503i	0.108998	−	0.994042i	$-0.465236\pi$
$53$	−1.49093	−	0.324331i	−0.204795	−	0.0445503i	−0.313792	+	0.949492i	$0.601600\pi$
$54$	−8.28257	+	3.78252i	−1.12711	+	0.514736i
$55$	−9.77457	+	4.95988i	−1.31800	+	0.668790i
$56$	0.492932	−	0.767017i	0.0658708	−	0.102497i
$57$	5.76311	+	7.69861i	0.763342	+	1.01971i
$58$	0.897174	+	1.19848i	0.117805	+	0.157369i
$59$	7.41732	−	11.5416i	0.965653	−	1.50259i	0.104321	−	0.994544i	$-0.466733\pi$
$59$	7.41732	−	11.5416i	0.965653	−	1.50259i	0.861332	−	0.508042i	$-0.169631\pi$
$60$	−2.08706	+	6.38706i	−0.269439	+	0.824566i
$61$	5.26049	−	2.40239i	0.673537	−	0.307594i	−0.0491281	−	0.998792i	$-0.515644\pi$
$61$	5.26049	−	2.40239i	0.673537	−	0.307594i	0.722665	+	0.691199i	$0.242917\pi$
$62$	−7.59825	−	1.65290i	−0.964978	−	0.209918i
$63$	2.63489	+	4.82543i	0.331965	+	0.607948i
$64$	0.755750	+	0.654861i	0.0944687	+	0.0818576i
$65$	0.802551	−	0.871515i	0.0995442	−	0.108098i
$66$	−13.3991	−	6.11915i	−1.64931	−	0.753216i
$67$	3.09240	+	2.31494i	0.377797	+	0.282815i	0.771254	−	0.636528i	$-0.219630\pi$
$67$	3.09240	+	2.31494i	0.377797	+	0.282815i	−0.393457	+	0.919343i	$0.628721\pi$
$68$	−4.42579	−	4.42579i	−0.536706	−	0.536706i
$69$	−3.95023	+	13.8596i	−0.475552	+	1.66850i
$70$	1.97815	+	0.493377i	0.236434	+	0.0589699i
$71$	0.108388	+	0.753855i	0.0128633	+	0.0894661i	0.995242	−	0.0974364i	$-0.0310643\pi$
$71$	0.108388	+	0.753855i	0.0128633	+	0.0894661i	−0.982378	+	0.186902i	$0.940155\pi$
$72$	−5.64988	+	2.10730i	−0.665845	+	0.248347i
$73$	0.0284134	−	0.0520352i	0.00332553	−	0.00609026i	−0.876011	−	0.482291i	$-0.839805\pi$
$73$	0.0284134	−	0.0520352i	0.00332553	−	0.00609026i	0.879336	+	0.476201i	$0.157987\pi$
$74$	3.80956	−	4.39647i	0.442853	−	0.511079i
$75$	−15.0241	+	0.164441i	−1.73484	+	0.0189880i
$76$	1.73018	+	2.69222i	0.198466	+	0.308818i
$77$	−1.56187	+	4.18753i	−0.177991	+	0.477213i
$78$	1.58810	+	0.113583i	0.179817	+	0.0128608i
$79$	13.7011	+	8.80519i	1.54150	+	0.990661i	0.987406	+	0.158206i	$0.0505711\pi$
$79$	13.7011	+	8.80519i	1.54150	+	0.990661i	0.554093	+	0.832455i	$0.313065\pi$
$80$	−0.844388	+	2.07051i	−0.0944055	+	0.231490i
$81$	1.31948	−	9.17722i	0.146609	−	1.01969i
$82$	0.305213	+	1.40304i	0.0337052	+	0.154940i
$83$	0.417094	−	5.83173i	0.0457820	−	0.640116i	−0.921817	−	0.387625i	$-0.873296\pi$
$83$	0.417094	−	5.83173i	0.0457820	−	0.640116i	0.967599	−	0.252491i	$-0.0812498\pi$
$84$	1.13817	+	2.49224i	0.124184	+	0.271925i
$85$	6.19609	−	12.5493i	0.672060	−	1.36116i
$86$	−3.35373	+	11.4218i	−0.361642	+	1.23164i
$87$	−4.48731	+	0.320939i	−0.481090	+	0.0344083i
$88$	−4.30229	−	2.34923i	−0.458625	−	0.250428i
$89$	−2.73698	+	5.99315i	−0.290119	+	0.635273i	−0.997431	−	0.0716289i	$-0.977180\pi$
$89$	−2.73698	+	5.99315i	−0.290119	+	0.635273i	0.707312	+	0.706901i	$0.249908\pi$
$90$	−8.51791	−	10.4525i	−0.897866	−	1.10179i
$91$		−	0.483079i		−	0.0506405i
$92$	−1.64023	+	4.50662i	−0.171005	+	0.469848i
$93$	16.5228	−	16.5228i	1.71334	−	1.71334i
$94$	0.582509	−	0.0837522i	0.0600813	−	0.00863838i
$95$	−4.45959	+	5.59642i	−0.457544	+	0.574180i
$96$	−2.88328	+	0.846609i	−0.294274	+	0.0864066i
$97$	0.457698	+	6.39945i	0.0464722	+	0.649766i	0.966296	+	0.257434i	$0.0828770\pi$
$97$	0.457698	+	6.39945i	0.0464722	+	0.649766i	−0.919824	+	0.392332i	$0.871668\pi$
$98$	−5.41414	+	2.95634i	−0.546911	+	0.298636i
$99$	24.8664	−	15.9807i	2.49917	−	1.60612i
$100$	−4.99087	−	0.302092i	−0.499087	−	0.0302092i
$101$	−11.3538	−	13.1030i	−1.12974	−	1.30379i	−0.947217	−	0.320592i	$-0.896118\pi$
$101$	−11.3538	−	13.1030i	−1.12974	−	1.30379i	−0.182526	−	0.983201i	$-0.558427\pi$
$102$	18.3786	−	3.99801i	1.81975	−	0.395862i
$103$	14.5300	−	10.8770i	1.43168	−	1.07174i	0.447555	−	0.894256i	$-0.352295\pi$
$103$	14.5300	−	10.8770i	1.43168	−	1.07174i	0.984124	−	0.177485i	$-0.0567961\pi$
$104$	0.524442	+	0.0754034i	0.0514258	+	0.00739391i
$105$	−4.46100	+	4.19915i	−0.435349	+	0.409795i
$106$	1.15312	−	0.999184i	0.112001	−	0.0970493i
$107$	−5.11616	−	1.90823i	−0.494598	−	0.184475i	0.0897731	−	0.995962i	$-0.471386\pi$
$107$	−5.11616	−	1.90823i	−0.494598	−	0.184475i	−0.584371	+	0.811487i	$0.698659\pi$
$108$	1.93549	−	8.89732i	0.186243	−	0.856145i
$109$	−1.94333	−	0.570612i	−0.186137	−	0.0546547i	0.187336	−	0.982296i	$-0.440015\pi$
$109$	−1.94333	−	0.570612i	−0.186137	−	0.0546547i	−0.373473	+	0.927641i	$0.621833\pi$
$110$	1.88710	−	10.7973i	0.179927	−	1.02948i
$111$	4.92503	+	16.7731i	0.467463	+	1.59203i
$112$	0.318626	+	0.854268i	0.0301073	+	0.0807208i
$113$	1.28189	−	1.71240i	0.120590	−	0.161089i	−0.736184	−	0.676781i	$-0.763374\pi$
$113$	1.28189	−	1.71240i	0.120590	−	0.161089i	0.856774	+	0.515692i	$0.172465\pi$
$114$	−9.61676			−0.900692
$115$	−10.7211	−	0.238955i	−0.999752	−	0.0222826i
$116$	−1.49709			−0.139002
$117$	−1.91466	+	2.55769i	−0.177010	+	0.236458i
$118$	4.79447	+	12.8545i	0.441367	+	1.18335i
$119$	−1.60776	−	5.47553i	−0.147383	−	0.501941i
$120$	−3.86237	−	5.49840i	−0.352585	−	0.501933i
$121$	12.5008	+	3.67056i	1.13643	+	0.333687i
$122$	−1.22929	+	5.65094i	−0.111294	+	0.511612i
$123$	−4.04271	−	1.50785i	−0.364519	−	0.135959i
$124$	5.87667	−	5.09217i	0.527741	−	0.457290i
$125$	−2.94244	−	10.7862i	−0.263179	−	0.964747i
$126$	−5.44199	−	0.782440i	−0.484811	−	0.0697053i
$127$	−4.76314	+	3.56565i	−0.422661	+	0.316400i	−0.789350	−	0.613944i	$-0.789582\pi$
$127$	−4.76314	+	3.56565i	−0.422661	+	0.316400i	0.366689	+	0.930344i	$0.380491\pi$
$128$	−0.977147	+	0.212565i	−0.0863684	+	0.0187883i
$129$	−23.4253	−	27.0343i	−2.06249	−	2.38024i
$130$	0.216733	+	1.16475i	0.0190087	+	0.102156i
$131$	−3.32964	+	2.13983i	−0.290912	+	0.186958i	−0.677954	−	0.735104i	$-0.737133\pi$
$131$	−3.32964	+	2.13983i	−0.290912	+	0.186958i	0.387042	+	0.922062i	$0.373497\pi$
$132$	12.9284	−	7.05944i	1.12527	−	0.614446i
$133$	0.208156	+	2.91040i	0.0180494	+	0.252364i
$134$	−3.70641	+	1.08830i	−0.320185	+	0.0940149i
$135$	20.2314	−	2.28716i	1.74124	−	0.196848i
$136$	6.19531	−	0.890751i	0.531244	−	0.0763813i
$137$	0.539311	−	0.539311i	0.0460764	−	0.0460764i	−0.683693	−	0.729770i	$-0.739627\pi$
$137$	0.539311	−	0.539311i	0.0460764	−	0.0460764i	0.729770	+	0.683693i	$0.239627\pi$
$138$	−8.72787	−	11.4680i	−0.742965	−	0.976225i
$139$			20.8398i			1.76761i	0.467856	+	0.883805i	$0.345027\pi$
$139$			20.8398i			1.76761i	−0.467856	+	0.883805i	$0.654973\pi$
$140$	−1.58043	+	1.28792i	−0.133571	+	0.108849i
$141$	−0.734639	+	1.60864i	−0.0618678	+	0.135472i
$142$	−0.668446	−	0.364999i	−0.0560947	−	0.0306301i
$143$	−2.59058	+	0.185282i	−0.216635	+	0.0154940i
$144$	1.69887	−	5.78582i	0.141572	−	0.482151i
$145$	−1.07454	−	3.17046i	−0.0892354	−	0.263292i
$146$	0.0246288	+	0.0539296i	0.00203830	+	0.00446324i
$147$	1.32241	−	18.4898i	0.109071	−	1.52501i
$148$	1.23657	+	5.68442i	0.101645	+	0.467256i
$149$	−0.412638	+	2.86996i	−0.0338046	+	0.235116i	−0.999718	−	0.0237495i	$-0.992440\pi$
$149$	−0.412638	+	2.86996i	−0.0338046	+	0.235116i	0.965913	+	0.258866i	$0.0833487\pi$
$150$	8.87199	−	12.1260i	0.724395	−	0.990083i
$151$	−9.27930	−	5.96345i	−0.755139	−	0.485298i	0.105560	−	0.994413i	$-0.466337\pi$
$151$	−9.27930	−	5.96345i	−0.755139	−	0.485298i	−0.860699	+	0.509115i	$0.829973\pi$
$152$	−3.19209	−	0.228303i	−0.258913	−	0.0185178i
$153$	−13.1896	+	35.3627i	−1.06632	+	2.85890i
$154$	−2.41630	−	3.75983i	−0.194711	−	0.302976i
$155$	15.0019	+	8.79039i	1.20498	+	0.706061i
$156$	−1.04264	+	1.20327i	−0.0834782	+	0.0963390i
$157$	−1.85653	+	3.39999i	−0.148168	+	0.271349i	−0.941213	−	0.337814i	$-0.890313\pi$
$157$	−1.85653	+	3.39999i	−0.148168	+	0.271349i	0.793045	+	0.609163i	$0.208494\pi$
$158$	−15.2597	+	5.69158i	−1.21400	+	0.452797i
$159$	0.652518	+	4.53836i	0.0517480	+	0.359915i
$160$	−1.15150	−	1.91678i	−0.0910345	−	0.151535i
$161$	−3.28176	+	2.88962i	−0.258639	+	0.227734i
$162$	6.55600	+	6.55600i	0.515088	+	0.515088i
$163$	−12.0028	−	8.98517i	−0.940131	−	0.703773i	0.0150219	−	0.999887i	$-0.495218\pi$
$163$	−12.0028	−	8.98517i	−0.940131	−	0.703773i	−0.955153	+	0.296114i	$0.904309\pi$
$164$	−1.30610	−	0.596476i	−0.101989	−	0.0465770i
$165$	24.2294	+	22.3121i	1.88626	+	1.73700i
$166$	4.41859	+	3.82873i	0.342949	+	0.297167i
$167$	0.943274	+	1.72748i	0.0729928	+	0.133676i	0.911627	−	0.411019i	$-0.134827\pi$
$167$	0.943274	+	1.72748i	0.0729928	+	0.133676i	−0.838634	+	0.544695i	$0.816645\pi$
$168$	−2.67722	−	0.582393i	−0.206552	−	0.0449326i
$169$	−11.5699	+	5.28378i	−0.889989	+	0.406444i
$170$	6.33306	+	12.4807i	0.485724	+	0.957229i
$171$	10.4331	−	16.2343i	0.797841	−	1.24147i
$172$	−7.13378	−	9.52961i	−0.543945	−	0.726626i
$173$	8.32071	+	11.1152i	0.632612	+	0.845071i	0.996255	−	0.0864679i	$-0.0275580\pi$
$173$	8.32071	+	11.1152i	0.632612	+	0.845071i	−0.363643	+	0.931539i	$0.618467\pi$
$174$	2.43222	−	3.78461i	0.184386	−	0.286911i
$175$	−3.86183	−	2.42254i	−0.291927	−	0.183127i
$176$	4.45892	−	2.03632i	0.336103	−	0.153493i
$177$	−40.2851	−	8.76348i	−3.02801	−	0.658703i
$178$	−3.15755	−	5.78263i	−0.236669	−	0.433426i
$179$	9.16986	+	7.94573i	0.685388	+	0.593892i	0.926360	−	0.376640i	$-0.122921\pi$
$179$	9.16986	+	7.94573i	0.685388	+	0.593892i	−0.240972	+	0.970532i	$0.577466\pi$
$180$	13.4722	−	0.554996i	1.00416	−	0.0413669i
$181$	5.81577	+	2.65597i	0.432283	+	0.197417i	0.619659	−	0.784871i	$-0.287271\pi$
$181$	5.81577	+	2.65597i	0.432283	+	0.197417i	−0.187376	+	0.982288i	$0.559998\pi$
$182$	0.386725	+	0.289499i	0.0286660	+	0.0214591i
$183$	−12.2883	−	12.2883i	−0.908376	−	0.908376i
$184$	−2.62479	−	4.01379i	−0.193502	−	0.295900i
$185$	−11.1506	+	6.69872i	−0.819808	+	0.492500i
$186$	3.32544	+	23.1290i	0.243833	+	1.69590i
$187$	−28.7466	+	10.7219i	−2.10216	+	0.784064i
$188$	−0.282038	+	0.516514i	−0.0205697	+	0.0376706i
$189$	5.43658	−	6.27415i	0.395453	−	0.456377i
$190$	−1.80763	−	6.92389i	−0.131139	−	0.502312i
$191$	11.6591	+	18.1419i	0.843621	+	1.31270i	0.948035	+	0.318166i	$0.103067\pi$
$191$	11.6591	+	18.1419i	0.843621	+	1.31270i	−0.104414	+	0.994534i	$0.533297\pi$
$192$	1.05014	−	2.81554i	0.0757875	−	0.203194i
$193$	−19.8560	−	1.42013i	−1.42927	−	0.102223i	−0.664865	−	0.746963i	$-0.731511\pi$
$193$	−19.8560	−	1.42013i	−1.42927	−	0.102223i	−0.764402	+	0.644740i	$0.776966\pi$
$194$	−5.39731	−	3.46864i	−0.387504	−	0.249034i
$195$	−3.29658	−	1.34440i	−0.236073	−	0.0962745i
$196$	0.877898	−	6.10592i	0.0627070	−	0.436137i
$197$	3.58225	+	16.4673i	0.255224	+	1.17325i	0.909078	+	0.416626i	$0.136788\pi$
$197$	3.58225	+	16.4673i	0.255224	+	1.17325i	−0.653853	+	0.756621i	$0.726849\pi$
$198$	−2.10870	+	29.4835i	−0.149859	+	2.09530i
$199$	−0.726464	−	1.59073i	−0.0514976	−	0.112764i	0.882134	−	0.470998i	$-0.156106\pi$
$199$	−0.726464	−	1.59073i	−0.0514976	−	0.112764i	−0.933632	+	0.358234i	$0.883379\pi$
$200$	3.23275	−	3.81436i	0.228590	−	0.269716i
$201$	3.27035	−	11.1378i	0.230673	−	0.785600i
$202$	17.2935	−	1.23686i	1.21677	−	0.0870250i
$203$	−1.19802	−	0.654166i	−0.0840842	−	0.0459134i
$204$	−7.81329	+	17.1087i	−0.547040	+	1.19785i
$205$	0.325731	−	3.19411i	0.0227500	−	0.223086i
$206$			18.1502i			1.26458i
$207$	28.8282	−	2.29213i	2.00370	−	0.159314i
$208$	−0.374650	+	0.374650i	−0.0259773	+	0.0259773i
$209$	15.5276	−	2.23253i	1.07406	−	0.154427i
$210$	−0.688211	−	6.08767i	−0.0474911	−	0.420089i
$211$	20.1638	−	5.92064i	1.38814	−	0.407594i	0.499543	−	0.866289i	$-0.333501\pi$
$211$	20.1638	−	5.92064i	1.38814	−	0.407594i	0.888593	+	0.458696i	$0.151683\pi$
$212$	0.108849	+	1.52191i	0.00747578	+	0.104525i
$213$	2.00869	−	1.09683i	0.137633	−	0.0751533i
$214$	4.59361	−	2.95214i	0.314013	−	0.201804i
$215$	15.0610	−	21.9474i	1.02715	−	1.49680i
$216$	5.96277	+	6.88141i	0.405715	+	0.468220i
$217$	6.92774	−	1.50704i	0.470285	−	0.102304i
$218$	1.62139	−	1.21376i	0.109814	−	0.0822061i
$219$	−0.176345	−	0.0253546i	−0.0119163	−	0.00171331i
$220$	7.51278	+	7.98127i	0.506512	+	0.538097i
$221$	2.50625	−	2.17168i	0.168589	−	0.146083i
$222$	−16.3790	−	6.10906i	−1.09929	−	0.410013i
$223$	−3.94503	+	18.1350i	−0.264179	+	1.21441i	0.633494	+	0.773747i	$0.281620\pi$
$223$	−3.94503	+	18.1350i	−0.264179	+	1.21441i	−0.897673	+	0.440662i	$0.854744\pi$
$224$	−0.874822	−	0.256871i	−0.0584515	−	0.0171629i
$225$	10.8450	+	28.1324i	0.723001	+	1.87549i
$226$	0.602642	+	2.05241i	0.0400871	+	0.136524i
$227$	−2.91212	−	7.80769i	−0.193284	−	0.518215i	0.803768	−	0.594943i	$-0.202825\pi$
$227$	−2.91212	−	7.80769i	−0.193284	−	0.518215i	−0.997052	+	0.0767281i	$0.975553\pi$
$228$	5.76311	−	7.69861i	0.381671	−	0.509853i
$229$	11.3403			0.749388			0.374694	−	0.927148i	$-0.377748\pi$
$229$	11.3403			0.749388			0.374694	+	0.927148i	$0.377748\pi$
$230$	6.61623	−	8.43952i	0.436262	−	0.556485i
$231$	13.4303			0.883652
$232$	0.897174	−	1.19848i	0.0589024	−	0.0786843i
$233$	−6.03235	−	16.1734i	−0.395192	−	1.05955i	−0.970391	−	0.241538i	$-0.922348\pi$
$233$	−6.03235	−	16.1734i	−0.395192	−	1.05955i	0.575199	−	0.818014i	$-0.304925\pi$
$234$	−0.900120	−	3.06553i	−0.0588427	−	0.200400i
$235$	−1.29628	−	0.226556i	−0.0845597	−	0.0147789i
$236$	−13.1638	−	3.86523i	−0.856888	−	0.251605i
$237$	10.4032	−	47.8228i	0.675762	−	3.10643i
$238$	5.34688	+	1.99428i	0.346587	+	0.129270i
$239$	9.97290	−	8.64156i	0.645093	−	0.558976i	−0.269677	−	0.962951i	$-0.586917\pi$
$239$	9.97290	−	8.64156i	0.645093	−	0.558976i	0.914770	+	0.403974i	$0.132372\pi$
$240$	6.71633	+	0.203080i	0.433537	+	0.0131088i
$241$	−20.6338	−	2.96669i	−1.32914	−	0.191102i	−0.559102	−	0.829099i	$-0.688854\pi$
$241$	−20.6338	−	2.96669i	−1.32914	−	0.191102i	−0.770039	+	0.637997i	$0.779763\pi$
$242$	−10.4299	+	7.80770i	−0.670458	+	0.501898i
$243$	−0.532537	+	0.115846i	−0.0341623	+	0.00743155i
$244$	−3.78712	−	4.37057i	−0.242446	−	0.279797i
$245$	13.5609	−	2.52335i	0.866372	−	0.161211i
$246$	3.62981	−	2.33274i	0.231428	−	0.148730i
$247$	−1.48819	+	0.812615i	−0.0946915	+	0.0517055i
$248$	0.554730	+	7.75614i	0.0352254	+	0.492515i
$249$	−16.8575	+	4.94981i	−1.06830	+	0.313681i
$250$	10.3981	+	4.10839i	0.657636	+	0.259837i
$251$	−14.1648	+	2.03659i	−0.894074	+	0.128548i	−0.574011	−	0.818848i	$-0.694613\pi$
$251$	−14.1648	+	2.03659i	−0.894074	+	0.128548i	−0.320063	+	0.947396i	$0.603704\pi$
$252$	3.88764	−	3.88764i	0.244898	−	0.244898i
$253$	16.7546	+	16.4906i	1.05335	+	1.03675i
$254$		−	5.94990i		−	0.373330i
$255$	−41.8399	−	4.26678i	−2.62011	−	0.267196i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	11.8981	+	6.49684i	0.742182	+	0.405262i	0.805395	−	0.592738i	$-0.201953\pi$
$257$	11.8981	+	6.49684i	0.742182	+	0.405262i	−0.0632136	+	0.998000i	$0.520135\pi$
$258$	35.6804	−	2.55191i	2.22136	−	0.158875i
$259$	−1.49431	+	5.08916i	−0.0928520	+	0.316225i
$260$	−1.06232	−	0.524508i	−0.0658821	−	0.0325286i
$261$	3.75019	+	8.21178i	0.232131	+	0.508296i
$262$	0.282357	−	3.94786i	0.0174440	−	0.243900i
$263$	2.93011	+	13.4695i	0.180679	+	0.830566i	0.974848	+	0.222870i	$0.0715424\pi$
$263$	2.93011	+	13.4695i	0.180679	+	0.830566i	−0.794170	+	0.607696i	$0.792094\pi$
$264$	−2.09633	+	14.5803i	−0.129020	+	0.897355i
$265$	−3.14488	+	1.32286i	−0.193189	+	0.0812628i
$266$	−2.45464	−	1.57750i	−0.150504	−	0.0967228i
$267$	19.7482	+	1.41242i	1.20857	+	0.0864386i
$268$	1.34994	−	3.61933i	0.0824607	−	0.221086i
$269$	10.0072	+	15.5715i	0.610150	+	0.949412i	0.999598	+	0.0283632i	$0.00902951\pi$
$269$	10.0072	+	15.5715i	0.610150	+	0.949412i	−0.389448	+	0.921049i	$0.627334\pi$
$270$	−10.2933	+	17.5667i	−0.626429	+	1.06908i
$271$	−8.74529	+	10.0926i	−0.531239	+	0.613082i	−0.956409	−	0.292031i	$-0.905669\pi$
$271$	−8.74529	+	10.0926i	−0.531239	+	0.613082i	0.425170	+	0.905113i	$0.360214\pi$
$272$	−2.99963	+	5.49341i	−0.181879	+	0.333087i
$273$	−1.36013	+	0.507302i	−0.0823188	+	0.0307033i
$274$	0.108544	+	0.754937i	0.00655736	+	0.0456074i
$275$	−11.5100	+	21.6387i	−0.694079	+	1.30486i
$276$	14.4111	−	0.114471i	0.867444	−	0.00689034i
$277$	2.52900	+	2.52900i	0.151953	+	0.151953i	0.778990	−	0.627037i	$-0.215732\pi$
$277$	2.52900	+	2.52900i	0.151953	+	0.151953i	−0.627037	+	0.778990i	$0.715732\pi$
$278$	−16.6831	−	12.4888i	−1.00059	−	0.749030i
$279$	−42.6523	−	19.4786i	−2.55352	−	1.16616i
$280$	−0.0839160	−	2.03702i	−0.00501494	−	0.121735i
$281$	−9.73232	−	8.43310i	−0.580581	−	0.503077i	0.314334	−	0.949312i	$-0.398219\pi$
$281$	−9.73232	−	8.43310i	−0.580581	−	0.503077i	−0.894915	+	0.446236i	$0.852764\pi$
$282$	−0.847526	−	1.55213i	−0.0504694	−	0.0924279i
$283$	−22.6493	−	4.92706i	−1.34636	−	0.292883i	−0.519106	−	0.854710i	$-0.673735\pi$
$283$	−22.6493	−	4.92706i	−1.34636	−	0.292883i	−0.827255	+	0.561827i	$0.810099\pi$
$284$	0.692782	−	0.316383i	0.0411090	−	0.0187739i
$285$	20.4401	+	6.67911i	1.21077	+	0.395637i
$286$	1.40415	−	2.18490i	0.0830290	−	0.129196i
$287$	−0.784544	−	1.04803i	−0.0463101	−	0.0618631i
$288$	3.61369	+	4.82732i	0.212939	+	0.284453i
$289$	11.9889	−	18.6551i	0.705228	−	1.09736i
$290$	3.18203	+	1.03977i	0.186855	+	0.0610576i
$291$	17.5373	−	8.00901i	1.02805	−	0.469496i
$292$	−0.0579324	−	0.0126024i	−0.00339023	−	0.000737500i
$293$	−4.79522	−	8.78180i	−0.280140	−	0.513038i	0.699286	−	0.714842i	$-0.253501\pi$
$293$	−4.79522	−	8.78180i	−0.280140	−	0.513038i	−0.979426	+	0.201804i	$0.935320\pi$
$294$	14.0093	+	12.1392i	0.817041	+	0.707970i
$295$	−1.26271	−	30.6517i	−0.0735181	−	1.78461i
$296$	−5.29166	−	2.41662i	−0.307571	−	0.140463i
$297$	−35.7311	−	26.7480i	−2.07333	−	1.55207i
$298$	−2.05024	−	2.05024i	−0.118767	−	0.118767i
$299$	−2.31969	−	1.03718i	−0.134151	−	0.0599815i
$300$	4.39057	+	14.3692i	0.253490	+	0.829608i
$301$	−1.54461	−	10.7430i	−0.0890300	−	0.619217i
$302$	10.3349	−	3.85470i	0.594705	−	0.221813i
$303$	−24.9688	+	45.7270i	−1.43442	+	2.62695i
$304$	2.09571	−	2.41858i	0.120197	−	0.138715i
$305$	6.53755	−	11.1571i	0.374339	−	0.638855i
$306$	−20.4051	−	31.7509i	−1.16648	−	1.81508i
$307$	−1.32251	+	3.54578i	−0.0754795	+	0.202368i	−0.969210	−	0.246236i	$-0.920806\pi$
$307$	−1.32251	+	3.54578i	−0.0754795	+	0.202368i	0.893730	+	0.448605i	$0.148079\pi$
$308$	4.45793	+	0.318838i	0.254014	+	0.0181675i
$309$	−45.8831	−	29.4873i	−2.61020	−	1.67747i
$310$	−16.0274	+	6.74174i	−0.910293	+	0.382905i
$311$	−2.68182	+	18.6525i	−0.152072	+	1.05768i	0.760667	+	0.649142i	$0.224872\pi$
$311$	−2.68182	+	18.6525i	−0.152072	+	1.05768i	−0.912739	+	0.408542i	$0.866037\pi$
$312$	−0.338438	−	1.55577i	−0.0191603	−	0.0880783i
$313$	0.133883	−	1.87192i	0.00756749	−	0.105807i	−0.992264	−	0.124142i	$-0.960382\pi$
$313$	0.133883	−	1.87192i	0.00756749	−	0.105807i	0.999832	+	0.0183351i	$0.00583657\pi$
$314$	−1.60925	−	3.52377i	−0.0908153	−	0.198858i
$315$	11.0234	+	5.44267i	0.621096	+	0.306660i
$316$	4.58846	−	15.6269i	0.258121	−	0.879079i
$317$	5.79689	−	0.414602i	0.325586	−	0.0232863i	0.0924102	−	0.995721i	$-0.470543\pi$
$317$	5.79689	−	0.414602i	0.325586	−	0.0232863i	0.233175	+	0.972435i	$0.425088\pi$
$318$	−4.02418	−	2.19737i	−0.225665	−	0.123222i
$319$	−3.04856	+	6.67541i	−0.170686	+	0.373751i
$320$	2.22453	+	0.226855i	0.124355	+	0.0126816i
$321$			16.4087i			0.915842i
$322$	−0.346573	−	4.35886i	−0.0193137	−	0.242910i
$323$	−14.1636	+	14.1636i	−0.788085	+	0.788085i
$324$	−9.17722	+	1.31948i	−0.509845	+	0.0733047i
$325$	0.348296	−	2.62618i	0.0193200	−	0.145674i
$326$	14.3860	−	4.22411i	0.796767	−	0.233952i
$327$	0.434188	+	6.07074i	0.0240107	+	0.335713i
$328$	1.26022	−	0.688133i	0.0695841	−	0.0379958i
$329$	−0.451389	+	0.290090i	−0.0248859	+	0.0159932i
$330$	−32.3819	+	6.02550i	−1.78257	+	0.331693i
$331$	7.58992	+	8.75923i	0.417180	+	0.481451i	0.924976	−	0.380026i	$-0.124085\pi$
$331$	7.58992	+	8.75923i	0.417180	+	0.481451i	−0.507796	+	0.861477i	$0.669540\pi$
$332$	−5.71301	+	1.24279i	−0.313542	+	0.0682070i
$333$	28.0823	−	21.0221i	1.53890	−	1.15201i
$334$	−1.94820	−	0.280109i	−0.106601	−	0.0153269i
$335$	8.63373	+	0.261056i	0.471711	+	0.0142630i
$336$	2.07063	−	1.79421i	0.112962	−	0.0978820i
$337$	14.2296	+	5.30737i	0.775137	+	0.289111i	0.705733	−	0.708478i	$-0.250618\pi$
$337$	14.2296	+	5.30737i	0.775137	+	0.289111i	0.0694034	+	0.997589i	$0.477890\pi$
$338$	2.70368	−	12.4286i	0.147061	−	0.676027i
$339$	−6.16751	−	1.81094i	−0.334973	−	0.0983569i
$340$	−13.7866	−	2.40955i	−0.747684	−	0.130676i
$341$	−10.7388	−	36.5729i	−0.581536	−	1.98053i
$342$	6.74386	+	18.0810i	0.364666	+	0.977708i
$343$	7.19530	−	9.61180i	0.388510	−	0.518988i
$344$	11.9040			0.641818
$345$	10.5859	+	30.4368i	0.569928	+	1.63866i
$346$	−13.8846			−0.746439
$347$	−17.7670	+	23.7340i	−0.953783	+	1.27411i	0.00790725	+	0.999969i	$0.497483\pi$
$347$	−17.7670	+	23.7340i	−0.953783	+	1.27411i	−0.961691	+	0.274137i	$0.911608\pi$
$348$	1.57216	+	4.21513i	0.0842767	+	0.225954i
$349$	0.612171	+	2.08486i	0.0327688	+	0.111600i	0.974253	−	0.225456i	$-0.0723871\pi$
$349$	0.612171	+	2.08486i	0.0327688	+	0.111600i	−0.941485	+	0.337056i	$0.890569\pi$
$350$	4.25365	−	1.63978i	0.227367	−	0.0876499i
$351$	4.62894	+	1.35918i	0.247075	+	0.0725477i
$352$	−1.04197	+	4.78987i	−0.0555373	+	0.255301i
$353$	24.7543	+	9.23286i	1.31754	+	0.491416i	0.907269	−	0.420550i	$-0.138163\pi$
$353$	24.7543	+	9.23286i	1.31754	+	0.491416i	0.410267	+	0.911966i	$0.365436\pi$
$354$	31.1575	−	26.9981i	1.65600	−	1.43493i
$355$	1.16726	+	1.24005i	0.0619518	+	0.0658150i
$356$	6.52148	+	0.937647i	0.345638	+	0.0496952i
$357$	−13.7282	+	10.2768i	−0.726573	+	0.543906i
$358$	−11.8562	+	2.57915i	−0.626619	+	0.136313i
$359$	10.9116	+	12.5926i	0.575891	+	0.664614i	0.966716	−	0.255851i	$-0.0823557\pi$
$359$	10.9116	+	12.5926i	0.575891	+	0.664614i	−0.390825	+	0.920465i	$0.627810\pi$
$360$	−7.62931	+	11.1177i	−0.402100	+	0.585953i
$361$	−7.36807	+	4.73517i	−0.387793	+	0.249220i
$362$	−5.61147	+	3.06410i	−0.294933	+	0.161045i
$363$	−2.79299	−	39.0511i	−0.146594	−	2.04965i
$364$	−0.463511	+	0.136099i	−0.0242946	+	0.00713354i
$365$	−0.0148922	−	0.131731i	−0.000779494	−	0.00689513i
$366$	17.2014	−	2.47318i	0.899130	−	0.129275i
$367$	21.0752	−	21.0752i	1.10012	−	1.10012i	0.105720	−	0.994396i	$-0.466285\pi$
$367$	21.0752	−	21.0752i	1.10012	−	1.10012i	0.994396	−	0.105720i	$-0.0337146\pi$
$368$	4.78618	+	0.304124i	0.249497	+	0.0158535i
$369$			8.65832i			0.450734i
$370$	1.31970	−	12.9409i	0.0686078	−	0.672765i
$371$	−0.577905	+	1.26544i	−0.0300033	+	0.0656981i
$372$	−20.5086	−	11.1985i	−1.06332	−	0.580616i
$373$	14.0789	−	1.00695i	0.728980	−	0.0521377i	0.298084	−	0.954540i	$-0.403652\pi$
$373$	14.0789	−	1.00695i	0.728980	−	0.0521377i	0.430895	+	0.902402i	$0.358198\pi$
$374$	8.64384	−	29.4382i	0.446962	−	1.52221i
$375$	−27.2790	+	19.6116i	−1.40868	+	1.01274i
$376$	−0.244472	−	0.535318i	−0.0126077	−	0.0276069i
$377$	0.0565871	−	0.791191i	0.00291438	−	0.0407484i
$378$	1.76469	+	8.11217i	0.0907661	+	0.417245i
$379$	1.62209	−	11.2819i	0.0833209	−	0.579510i	−0.904801	−	0.425835i	$-0.859980\pi$
$379$	1.62209	−	11.2819i	0.0833209	−	0.579510i	0.988122	−	0.153674i	$-0.0491107\pi$
$380$	6.62613	+	2.70225i	0.339913	+	0.138622i
$381$	15.0412	+	9.66640i	0.770584	+	0.495224i
$382$	−21.5103	−	1.53845i	−1.10056	−	0.0787140i
$383$	3.10517	−	8.32529i	0.158667	−	0.425402i	−0.833154	−	0.553041i	$-0.813467\pi$
$383$	3.10517	−	8.32529i	0.158667	−	0.425402i	0.991821	+	0.127639i	$0.0407399\pi$
$384$	1.62463	+	2.52797i	0.0829066	+	0.129005i
$385$	2.52446	+	9.66960i	0.128658	+	0.492809i
$386$	13.0361	−	15.0445i	0.663522	−	0.765745i
$387$	−34.4013	+	63.0014i	−1.74872	+	3.20254i
$388$	6.01128	−	2.24209i	0.305177	−	0.113825i
$389$	−3.06001	−	21.2829i	−0.155149	−	1.07908i	−0.907418	−	0.420228i	$-0.861950\pi$
$389$	−3.06001	−	21.2829i	−0.155149	−	1.07908i	0.752270	−	0.658855i	$-0.228959\pi$
$390$	3.05181	−	1.83338i	0.154535	−	0.0928367i
$391$	−29.7447	−	4.03576i	−1.50425	−	0.204097i
$392$	4.36193	+	4.36193i	0.220311	+	0.220311i
$393$	9.52136	+	7.12760i	0.480289	+	0.359540i
$394$	−15.3295	−	7.00076i	−0.772290	−	0.352693i
$395$	36.3870	−	1.49898i	1.83083	−	0.0754220i
$396$	−22.3390	−	19.3569i	−1.12258	−	0.972720i
$397$	−18.5975	−	34.0588i	−0.933383	−	1.70936i	−0.666291	−	0.745692i	$-0.732119\pi$
$397$	−18.5975	−	34.0588i	−0.933383	−	1.70936i	−0.267092	−	0.963671i	$-0.586063\pi$
$398$	1.70880	+	0.371727i	0.0856545	+	0.0186330i
$399$	7.97577	−	3.64241i	0.399288	−	0.182349i
$400$	1.11623	+	4.87381i	0.0558117	+	0.243690i
$401$	16.2340	−	25.2606i	0.810687	−	1.26145i	−0.151335	−	0.988483i	$-0.548357\pi$
$401$	16.2340	−	25.2606i	0.810687	−	1.26145i	0.962022	−	0.272972i	$-0.0880066\pi$
$402$	6.95642	+	9.29269i	0.346955	+	0.463477i
$403$	2.46901	+	3.29821i	0.122990	+	0.164295i
$404$	−9.37347	+	14.5854i	−0.466347	+	0.725651i
$405$	−9.38127	−	18.4879i	−0.466159	−	0.918673i
$406$	1.24163	−	0.567034i	0.0616211	−	0.0281414i
$407$	27.8644	+	6.06153i	1.38119	+	0.300459i
$408$	−9.01391	−	16.5077i	−0.446255	−	0.817255i
$409$	17.0511	+	14.7749i	0.843125	+	0.730572i	0.965078	−	0.261964i	$-0.0843702\pi$
$409$	17.0511	+	14.7749i	0.843125	+	0.730572i	−0.121953	+	0.992536i	$0.538916\pi$
$410$	2.36181	+	2.17492i	0.116642	+	0.107412i
$411$	−2.08480	−	0.952098i	−0.102836	−	0.0469635i
$412$	−14.5300	−	10.8770i	−0.715839	−	0.535871i
$413$	−8.84507	−	8.84507i	−0.435237	−	0.435237i
$414$	−15.4412	+	24.4518i	−0.758893	+	1.20174i
$415$	−6.73242	−	11.2067i	−0.330481	−	0.550114i
$416$	−0.0754034	−	0.524442i	−0.00369696	−	0.0257129i
$417$	58.6754	−	21.8848i	2.87334	−	1.07170i
$418$	−7.51809	+	13.7684i	−0.367722	+	0.673433i
$419$	7.25412	−	8.37170i	0.354387	−	0.408984i	−0.550364	−	0.834925i	$-0.685511\pi$
$419$	7.25412	−	8.37170i	0.354387	−	0.408984i	0.904751	+	0.425940i	$0.140057\pi$
$420$	5.28586	+	3.09726i	0.257924	+	0.151131i
$421$	12.4338	+	19.3473i	0.605985	+	0.942931i	0.999719	+	0.0237068i	$0.00754682\pi$
$421$	12.4338	+	19.3473i	0.605985	+	0.942931i	−0.393734	+	0.919225i	$0.628817\pi$
$422$	−7.34402	+	19.6901i	−0.357502	+	0.958499i
$423$	3.53966	+	0.253161i	0.172104	+	0.0123091i
$424$	−1.28358	−	0.824907i	−0.0623362	−	0.0400610i
$425$	−4.79251	−	30.9260i	−0.232471	−	1.50013i
$426$	−0.325707	+	2.26534i	−0.0157805	+	0.109756i
$427$	−1.12081	−	5.15227i	−0.0542397	−	0.249336i
$428$	−0.389543	+	5.44653i	−0.0188293	+	0.263268i
$429$	3.24214	+	7.09930i	0.156532	+	0.342758i
$430$	8.54405	+	25.2095i	0.412031	+	1.21571i
$431$	3.51925	−	11.9855i	0.169516	−	0.577319i	−0.830284	−	0.557340i	$-0.811822\pi$
$431$	3.51925	−	11.9855i	0.169516	−	0.577319i	0.999800	−	0.0199789i	$-0.00635991\pi$
$432$	−9.08220	+	0.649572i	−0.436968	+	0.0312526i
$433$	14.8113	+	8.08756i	0.711784	+	0.388663i	0.793973	−	0.607953i	$-0.208009\pi$
$433$	14.8113	+	8.08756i	0.711784	+	0.388663i	−0.0821889	+	0.996617i	$0.526191\pi$
$434$	−2.94519	+	6.44907i	−0.141374	+	0.309565i
$435$	−7.79814	+	6.35484i	−0.373892	+	0.304691i
$436$			2.02537i			0.0969976i
$437$	14.4223	+	5.24913i	0.689912	+	0.251100i
$438$	0.125977	−	0.125977i	0.00601942	−	0.00601942i
$439$	−9.58365	+	1.37792i	−0.457403	+	0.0657646i	−0.367165	−	0.930156i	$-0.619672\pi$
$439$	−9.58365	+	1.37792i	−0.457403	+	0.0657646i	−0.0902374	+	0.995920i	$0.528763\pi$
$440$	−10.8916	+	1.23129i	−0.519236	+	0.0586996i
$441$	−35.6910	+	10.4798i	−1.69957	+	0.499039i
$442$	0.236578	+	3.30780i	0.0112529	+	0.157336i
$443$	22.0369	−	12.0331i	1.04701	−	0.571708i	0.138838	−	0.990315i	$-0.455663\pi$
$443$	22.0369	−	12.0331i	1.04701	−	0.571708i	0.908168	+	0.418607i	$0.137481\pi$
$444$	14.7061	−	9.45106i	0.697923	−	0.448528i
$445$	2.69509	+	14.4838i	0.127760	+	0.686599i
$446$	−12.1537	−	14.0261i	−0.575492	−	0.664153i
$447$	8.51381	−	1.85207i	0.402690	−	0.0875998i
$448$	0.729897	−	0.546394i	0.0344844	−	0.0258147i
$449$	−26.6011	−	3.82466i	−1.25538	−	0.180497i	−0.517652	−	0.855591i	$-0.673194\pi$
$449$	−26.6011	−	3.82466i	−1.25538	−	0.180497i	−0.737731	+	0.675094i	$0.764103\pi$
$450$	−29.0203	−	8.17722i	−1.36803	−	0.385478i
$451$	−5.31928	+	4.60918i	−0.250475	+	0.217038i
$452$	−2.00419	−	0.747523i	−0.0942691	−	0.0351605i
$453$	−7.04574	+	32.3887i	−0.331038	+	1.52176i
$454$	7.99555	+	2.34771i	0.375250	+	0.110183i
$455$	−0.620908	−	0.883913i	−0.0291086	−	0.0414385i
$456$	2.70935	+	9.22721i	0.126877	+	0.432104i
$457$	−6.20136	−	16.6265i	−0.290087	−	0.777755i	−0.997481	−	0.0709347i	$-0.977402\pi$
$457$	−6.20136	−	16.6265i	−0.290087	−	0.777755i	0.707393	−	0.706820i	$-0.249871\pi$
$458$	−6.79599	+	9.07838i	−0.317556	+	0.424205i
$459$	56.9909			2.66011
$460$	2.79122	+	10.3542i	0.130141	+	0.482766i
$461$	−17.7750			−0.827863			−0.413932	−	0.910308i	$-0.635845\pi$
$461$	−17.7750			−0.827863			−0.413932	+	0.910308i	$0.635845\pi$
$462$	−8.04851	+	10.7515i	−0.374450	+	0.500207i
$463$	4.47656	+	12.0021i	0.208043	+	0.557786i	0.998501	−	0.0547308i	$-0.0174301\pi$
$463$	4.47656	+	12.0021i	0.208043	+	0.557786i	−0.790458	+	0.612516i	$0.790157\pi$
$464$	0.421780	+	1.43645i	0.0195806	+	0.0666855i
$465$	8.99559	−	51.4696i	0.417160	−	2.38684i
$466$	16.5625	+	4.86319i	0.767243	+	0.225283i
$467$	−1.48091	+	6.80762i	−0.0685282	+	0.315019i	−0.998633	−	0.0522760i	$-0.983352\pi$
$467$	−1.48091	+	6.80762i	−0.0685282	+	0.315019i	0.930104	+	0.367295i	$0.119716\pi$
$468$	2.99350	+	1.11652i	0.138375	+	0.0516111i
$469$	2.66175	−	2.30642i	0.122908	−	0.106501i
$470$	0.958197	−	0.901952i	0.0441983	−	0.0416039i
$471$	11.5224	+	1.65668i	0.530926	+	0.0763356i
$472$	10.9830	−	8.22179i	0.505535	−	0.378439i
$473$	−57.0184	+	12.4036i	−2.62171	+	0.570318i
$474$	32.0497	+	36.9874i	1.47209	+	1.69889i
$475$	−0.966767	+	15.9720i	−0.0443583	+	0.732845i
$476$	−4.80077	+	3.08527i	−0.220043	+	0.141413i
$477$	8.07523	−	4.40941i	0.369739	−	0.201893i
$478$	0.941394	+	13.1624i	0.0430584	+	0.602035i
$479$	−16.1425	+	4.73988i	−0.737572	+	0.216571i	−0.628877	−	0.777505i	$-0.716485\pi$
$479$	−16.1425	+	4.73988i	−0.737572	+	0.216571i	−0.108695	+	0.994075i	$0.534667\pi$
$480$	−4.18752	+	5.25500i	−0.191133	+	0.239857i
$481$	−3.05087	+	0.438649i	−0.139108	+	0.0200007i
$482$	14.7403	−	14.7403i	0.671404	−	0.671404i
$483$	11.5821	+	6.20542i	0.527006	+	0.282356i
$484$		−	13.0285i		−	0.592206i
$485$	9.06276	+	11.1211i	0.411519	+	0.504983i
$486$	0.226398	−	0.495742i	0.0102696	−	0.0224873i
$487$	−17.3154	−	9.45494i	−0.784637	−	0.428444i	0.0363872	−	0.999338i	$-0.488415\pi$
$487$	−17.3154	−	9.45494i	−0.784637	−	0.428444i	−0.821024	+	0.570894i	$0.806597\pi$
$488$	5.76836	−	0.412561i	0.261122	−	0.0186758i
$489$	−12.6935	+	43.2301i	−0.574019	+	1.95493i
$490$	−6.10668	+	12.3682i	−0.275872	+	0.558739i
$491$	3.66479	+	8.02476i	0.165389	+	0.362152i	0.974122	−	0.226025i	$-0.0725730\pi$
$491$	3.66479	+	8.02476i	0.165389	+	0.362152i	−0.808732	+	0.588177i	$0.799846\pi$
$492$	−0.307811	+	4.30377i	−0.0138772	+	0.194029i
$493$	−1.99181	−	9.15619i	−0.0897065	−	0.412374i
$494$	0.241309	−	1.67834i	0.0108570	−	0.0755122i
$495$	24.9591	−	61.2017i	1.12183	−	2.75081i
$496$	−6.54155	−	4.20400i	−0.293724	−	0.188765i
$497$	0.692629	+	0.0495378i	0.0310687	+	0.00222207i
$498$	6.13979	−	16.4614i	0.275131	−	0.737654i
$499$	−2.69017	−	4.18599i	−0.120429	−	0.187390i	0.775805	−	0.630972i	$-0.217344\pi$
$499$	−2.69017	−	4.18599i	−0.120429	−	0.187390i	−0.896234	+	0.443582i	$0.853708\pi$
$500$	−9.52030	+	5.86207i	−0.425761	+	0.262160i
$501$	3.87321	−	4.46993i	0.173042	−	0.199702i
$502$	6.85827	−	12.5600i	0.306100	−	0.560580i
$503$	−10.0563	+	3.75081i	−0.448389	+	0.167240i	−0.563507	−	0.826111i	$-0.690548\pi$
$503$	−10.0563	+	3.75081i	−0.448389	+	0.167240i	0.115118	+	0.993352i	$0.463275\pi$
$504$	0.782440	+	5.44199i	0.0348526	+	0.242405i
$505$	−37.6159	−	9.38194i	−1.67389	−	0.417491i
$506$	−23.2420	+	3.53035i	−1.03323	+	0.156943i
$507$	27.0267	+	27.0267i	1.20030	+	1.20030i
$508$	4.76314	+	3.56565i	0.211330	+	0.158200i
$509$	1.47240	+	0.672421i	0.0652628	+	0.0298045i	0.447779	−	0.894144i	$-0.352215\pi$
$509$	1.47240	+	0.672421i	0.0652628	+	0.0298045i	−0.382516	+	0.923949i	$0.624942\pi$
$510$	28.4894	−	30.9376i	1.26153	−	1.36994i
$511$	−0.0408524	−	0.0353988i	−0.00180720	−	0.00156595i
$512$	0.479249	+	0.877679i	0.0211800	+	0.0387883i
$513$	−28.4736	−	6.19405i	−1.25714	−	0.273474i
$514$	−12.3312	+	5.63149i	−0.543908	+	0.248394i
$515$	12.6058	−	38.5777i	0.555478	−	1.69993i
$516$	−19.3395	+	30.0929i	−0.851375	+	1.32477i
$517$	1.72877	+	2.30937i	0.0760313	+	0.101566i
$518$	−3.17857	−	4.24608i	−0.139658	−	0.186562i
$519$	22.5573	−	35.0998i	0.990155	−	1.54071i
$520$	1.05651	−	0.536103i	0.0463312	−	0.0235097i
$521$	−17.0200	+	7.77279i	−0.745661	+	0.340532i	−0.751749	−	0.659449i	$-0.770789\pi$
$521$	−17.0200	+	7.77279i	−0.745661	+	0.340532i	0.00608768	+	0.999981i	$0.498062\pi$
$522$	−8.82127	−	1.91895i	−0.386097	−	0.0839902i
$523$	0.0346361	+	0.0634313i	0.00151453	+	0.00277366i	0.878435	−	0.477862i	$-0.158588\pi$
$523$	0.0346361	+	0.0634313i	0.00151453	+	0.00277366i	−0.876921	+	0.480635i	$0.840406\pi$
$524$	2.99122	+	2.59190i	0.130672	+	0.113228i
$525$	−2.76529	+	13.4172i	−0.120687	+	0.585572i
$526$	−12.5389	−	5.72630i	−0.546720	−	0.249679i
$527$	38.9622	+	29.1667i	1.69722	+	1.27052i
$528$	−10.4158	−	10.4158i	−0.453291	−	0.453291i
$529$	6.82960	+	21.9626i	0.296939	+	0.954896i
$530$	0.825653	−	3.31037i	0.0358641	−	0.143793i
$531$	11.7737	+	81.8876i	0.510933	+	3.55362i
$532$	2.73387	−	1.01968i	0.118528	−	0.0442087i
$533$	0.364597	−	0.667709i	0.0157924	−	0.0289217i
$534$	−12.9653	+	14.9628i	−0.561065	+	0.647504i
$535$	−11.8139	+	3.08429i	−0.510761	+	0.133345i
$536$	2.08843	+	3.24967i	0.0902066	+	0.140364i
$537$	12.7419	−	34.1623i	0.549852	−	1.47421i
$538$	−18.4627	−	1.32048i	−0.795985	−	0.0569300i
$539$	−25.4381	−	16.3481i	−1.09570	−	0.704161i
$540$	−7.89437	−	18.7675i	−0.339720	−	0.807627i
$541$	−3.62220	+	25.1929i	−0.155730	+	1.08313i	0.750660	+	0.660688i	$0.229735\pi$
$541$	−3.62220	+	25.1929i	−0.155730	+	1.08313i	−0.906391	+	0.422440i	$0.861174\pi$
$542$	−2.83869	−	13.0492i	−0.121932	−	0.560513i
$543$	1.37061	−	19.1637i	0.0588187	−	0.822392i
$544$	−2.60009	−	5.69340i	−0.111478	−	0.244103i
$545$	−4.28921	+	1.45371i	−0.183730	+	0.0622699i
$546$	0.408979	−	1.39286i	0.0175027	−	0.0596087i
$547$	−15.8755	+	1.13544i	−0.678788	+	0.0485479i	−0.406477	−	0.913661i	$-0.633243\pi$
$547$	−15.8755	+	1.13544i	−0.678788	+	0.0485479i	−0.272312	+	0.962209i	$0.587788\pi$
$548$	−0.669406	−	0.365523i	−0.0285956	−	0.0156144i
$549$	−14.4866	+	31.7212i	−0.618272	+	1.35383i
$550$	−10.4250	−	22.1818i	−0.444523	−	0.945836i
$551$			4.79106i			0.204106i
$552$	−8.54459	+	11.6052i	−0.363682	+	0.493952i
$553$	10.5001	−	10.5001i	0.446509	−	0.446509i
$554$	−3.54014	+	0.508996i	−0.150406	+	0.0216252i
$555$	30.5702	+	24.3603i	1.29763	+	1.03404i
$556$	19.9957	−	5.87125i	0.848004	−	0.248997i
$557$	2.70385	+	37.8048i	0.114566	+	1.60184i	0.651789	+	0.758401i	$0.274019\pi$
$557$	2.70385	+	37.8048i	0.114566	+	1.60184i	−0.537223	+	0.843440i	$0.680527\pi$
$558$	41.1540	−	22.4718i	1.74219	−	0.951306i
$559$	5.30590	−	3.40989i	0.224416	−	0.144223i
$560$	1.68101	+	1.15356i	0.0710354	+	0.0487468i
$561$	60.3760	+	69.6776i	2.54908	+	2.94179i
$562$	12.5834	−	2.73735i	0.530799	−	0.115468i
$563$	2.69350	−	2.01633i	0.113518	−	0.0849783i	−0.541011	−	0.841016i	$-0.681958\pi$
$563$	2.69350	−	2.01633i	0.113518	−	0.0849783i	0.654528	+	0.756037i	$0.272867\pi$
$564$	1.75045	+	0.251676i	0.0737071	+	0.0105975i
$565$	0.144559	−	4.78089i	0.00608163	−	0.201134i
$566$	17.5175	−	15.1790i	0.736317	−	0.638022i
$567$	−7.92042	−	2.95417i	−0.332627	−	0.124063i
$568$	−0.161891	+	0.744201i	−0.00679280	+	0.0312260i
$569$	19.6448	+	5.76822i	0.823551	+	0.241817i	0.666245	−	0.745733i	$-0.267901\pi$
$569$	19.6448	+	5.76822i	0.823551	+	0.241817i	0.157307	+	0.987550i	$0.449719\pi$
$570$	−17.5962	+	12.3605i	−0.737025	+	0.517726i
$571$	−1.00427	−	3.42023i	−0.0420274	−	0.143132i	0.935807	−	0.352514i	$-0.114673\pi$
$571$	−1.00427	−	3.42023i	−0.0420274	−	0.143132i	−0.977834	+	0.209382i	$0.932855\pi$
$572$	0.907626	+	2.43344i	0.0379497	+	0.101747i
$573$	38.8355	−	51.8782i	1.62238	−	2.16724i
$574$	1.30915			0.0546428
$575$	−19.9241	+	13.3428i	−0.830893	+	0.556433i
$576$	−6.03008			−0.251253
$577$	−4.19224	+	5.60018i	−0.174525	+	0.233138i	−0.879271	−	0.476321i	$-0.841970\pi$
$577$	−4.19224	+	5.60018i	−0.174525	+	0.233138i	0.704746	+	0.709460i	$0.251061\pi$
$578$	7.74948	+	20.7772i	0.322336	+	0.864216i
$579$	16.8532	+	57.3968i	0.700396	+	2.38533i
$580$	−2.73930	+	1.92423i	−0.113743	+	0.0798994i
$581$	−5.11476	−	1.50183i	−0.212196	−	0.0623064i
$582$	−4.09816	+	18.8389i	−0.169874	+	0.780899i
$583$	7.00771	+	2.61374i	0.290230	+	0.108250i
$584$	0.0448063	−	0.0388249i	0.00185410	−	0.00160659i
$585$	−0.215916	+	7.14085i	−0.00892705	+	0.295238i
$586$	9.90386	+	1.42396i	0.409125	+	0.0588233i
$587$	−31.3092	+	23.4378i	−1.29227	+	0.967381i	−0.292330	+	0.956317i	$0.594431\pi$
$587$	−31.3092	+	23.4378i	−1.29227	+	0.967381i	−0.999939	+	0.0110633i	$0.996478\pi$
$588$	−18.1134	+	3.94032i	−0.746983	+	0.162496i
$589$	−16.2962	−	18.8068i	−0.671472	−	0.774920i
$590$	25.2947	+	17.3580i	1.04137	+	0.714620i
$591$	42.6026	−	27.3790i	1.75243	−	1.12622i
$592$	5.10578	−	2.78796i	0.209846	−	0.114585i
$593$	−1.50386	−	21.0267i	−0.0617561	−	0.863464i	−0.930055	−	0.367421i	$-0.880241\pi$
$593$	−1.50386	−	21.0267i	−0.0617561	−	0.863464i	0.868298	−	0.496042i	$-0.165214\pi$
$594$	42.8257	−	12.5748i	1.75716	−	0.515949i
$595$	−9.97956	−	7.95235i	−0.409122	−	0.326015i
$596$	2.86996	−	0.412638i	0.117558	−	0.0169023i
$597$	−3.71589	+	3.71589i	−0.152081	+	0.152081i
$598$	2.22044	−	1.23545i	0.0908005	−	0.0505212i
$599$			0.455876i			0.0186266i	0.999957	+	0.00931330i	$0.00296456\pi$
$599$			0.455876i			0.0186266i	−0.999957	+	0.00931330i	$0.997035\pi$
$600$	−14.1343	−	5.09633i	−0.577032	−	0.208057i
$601$	−10.1291	+	22.1796i	−0.413174	+	0.904725i	0.582589	+	0.812767i	$0.302040\pi$
$601$	−10.1291	+	22.1796i	−0.413174	+	0.904725i	−0.995763	+	0.0919576i	$0.970688\pi$
$602$	9.52588	+	5.20152i	0.388246	+	0.211998i
$603$	−23.2342	+	1.66174i	−0.946168	+	0.0676713i
$604$	−3.10760	+	10.5835i	−0.126447	+	0.430637i
$605$	27.5911	−	9.35121i	1.12174	−	0.380181i
$606$	−21.6431	−	47.3918i	−0.879191	−	1.92516i
$607$	1.24544	−	17.4135i	0.0505508	−	0.706793i	−0.907474	−	0.420108i	$-0.861992\pi$
$607$	1.24544	−	17.4135i	0.0505508	−	0.706793i	0.958025	−	0.286685i	$-0.0925533\pi$
$608$	0.680261	+	3.12711i	0.0275882	+	0.126821i
$609$	−0.583744	+	4.06003i	−0.0236545	+	0.164521i
$610$	5.01394	+	11.9198i	0.203008	+	0.482618i
$611$	−0.262309	−	0.168576i	−0.0106119	−	0.00681985i
$612$	37.6462	+	2.69251i	1.52176	+	0.108838i
$613$	10.0023	−	26.8172i	0.403988	−	1.08313i	−0.562584	−	0.826740i	$-0.690193\pi$
$613$	10.0023	−	26.8172i	0.403988	−	1.08313i	0.966572	−	0.256395i	$-0.0825347\pi$
$614$	−2.04599	−	3.18363i	−0.0825696	−	0.128481i
$615$	−9.33520	+	2.43716i	−0.376432	+	0.0982757i
$616$	−2.92678	+	3.37769i	−0.117923	+	0.136091i
$617$	1.24247	−	2.27542i	0.0500200	−	0.0916048i	−0.851473	−	0.524398i	$-0.824290\pi$
$617$	1.24247	−	2.27542i	0.0500200	−	0.0916048i	0.901493	+	0.432794i	$0.142472\pi$
$618$	51.1025	−	19.0603i	2.05565	−	0.766716i
$619$	1.69746	+	11.8061i	0.0682267	+	0.474527i	0.995078	+	0.0990978i	$0.0315957\pi$
$619$	1.69746	+	11.8061i	0.0682267	+	0.474527i	−0.926851	+	0.375429i	$0.877495\pi$
$620$	4.20780	−	16.8707i	0.168989	−	0.677545i
$621$	−18.4553	−	39.5765i	−0.740585	−	1.58815i
$622$	−13.3249	−	13.3249i	−0.534280	−	0.534280i
$623$	4.80896	+	3.59994i	0.192667	+	0.144229i
$624$	1.44828	+	0.661407i	0.0579775	+	0.0264775i
$625$	−19.2475	−	15.9541i	−0.769902	−	0.638162i
$626$	1.41832	+	1.22898i	0.0566874	+	0.0491199i
$627$	−22.5919	−	41.3740i	−0.902235	−	1.65232i
$628$	3.78531	+	0.823444i	0.151050	+	0.0328590i
$629$	−33.1206	+	15.1257i	−1.32060	+	0.603100i
$630$	−10.9631	+	5.56299i	−0.436782	+	0.221635i
$631$	−7.65917	+	11.9179i	−0.304907	+	0.474444i	−0.959568	−	0.281479i	$-0.909175\pi$
$631$	−7.65917	+	11.9179i	−0.304907	+	0.474444i	0.654661	+	0.755923i	$0.272812\pi$
$632$	9.76018	+	13.0381i	0.388239	+	0.518627i
$633$	−37.8447	−	50.5546i	−1.50419	−	2.00937i
$634$	−3.14204	+	4.88911i	−0.124786	+	0.194171i
$635$	−4.13238	+	12.6464i	−0.163988	+	0.501855i
$636$	4.17069	−	1.90469i	0.165379	−	0.0755259i
$637$	3.19370	+	0.694747i	0.126539	+	0.0275269i
$638$	−3.51701	−	6.44092i	−0.139240	−	0.254998i
$639$	−3.47081	−	3.00748i	−0.137303	−	0.118974i
$640$	−1.51472	+	1.64488i	−0.0598745	+	0.0650196i
$641$	8.79116	+	4.01479i	0.347230	+	0.158575i	0.581393	−	0.813623i	$-0.302508\pi$
$641$	8.79116	+	4.01479i	0.347230	+	0.158575i	−0.234163	+	0.972197i	$0.575235\pi$
$642$	−13.1358	−	9.83335i	−0.518429	−	0.388091i
$643$	−4.13771	−	4.13771i	−0.163175	−	0.163175i	0.620796	−	0.783972i	$-0.286809\pi$
$643$	−4.13771	−	4.13771i	−0.163175	−	0.163175i	−0.783972	+	0.620796i	$0.786809\pi$
$644$	3.69714	+	2.33472i	0.145688	+	0.0920010i
$645$	−77.6100	−	19.3570i	−3.05589	−	0.762182i
$646$	−2.85062	−	19.8265i	−0.112156	−	0.780063i
$647$	−2.35343	+	0.877784i	−0.0925229	+	0.0345093i	−0.395299	−	0.918552i	$-0.629359\pi$
$647$	−2.35343	+	0.877784i	−0.0925229	+	0.0345093i	0.302776	+	0.953062i	$0.402086\pi$
$648$	4.44340	−	8.13748i	0.174553	−	0.319670i
$649$	−44.0404	+	50.8253i	−1.72874	+	1.99507i
$650$	1.89364	+	1.85264i	0.0742746	+	0.0726664i
$651$	−11.5182	−	17.9227i	−0.451435	−	0.702447i
$652$	−5.23963	+	14.0480i	−0.205200	+	0.550162i
$653$	−38.0001	−	2.71782i	−1.48706	−	0.106357i	−0.695976	−	0.718065i	$-0.745028\pi$
$653$	−38.0001	−	2.71782i	−1.48706	−	0.106357i	−0.791083	+	0.611709i	$0.790482\pi$
$654$	−5.12008	−	3.29047i	−0.200211	−	0.128668i
$655$	−3.34204	+	8.19496i	−0.130584	+	0.320204i
$656$	−0.204344	+	1.42124i	−0.00797828	+	0.0554902i
$657$	0.0759935	+	0.349337i	0.00296479	+	0.0136289i
$658$	0.0382783	−	0.535200i	0.00149224	−	0.0208643i
$659$	−8.84239	−	19.3621i	−0.344451	−	0.754242i	0.655549	−	0.755153i	$-0.272437\pi$
$659$	−8.84239	−	19.3621i	−0.344451	−	0.754242i	−1.00000		0.000910993i	$0.999710\pi$
$660$	14.5821	−	29.5340i	0.567608	−	1.14961i
$661$	11.8137	−	40.2336i	0.459498	−	1.56491i	−0.325583	−	0.945514i	$-0.605561\pi$
$661$	11.8137	−	40.2336i	0.459498	−	1.56491i	0.785081	−	0.619393i	$-0.212621\pi$
$662$	−11.5606	+	0.826830i	−0.449315	+	0.0321357i
$663$	−8.74638	−	4.77588i	−0.339681	−	0.185480i
$664$	2.42878	−	5.31828i	0.0942548	−	0.206389i
$665$	4.12165	+	5.05775i	0.159831	+	0.196131i
$666$			35.0791i			1.35929i
$667$	−5.71337	+	4.34821i	−0.221223	+	0.168364i
$668$	1.39175	−	1.39175i	0.0538485	−	0.0538485i
$669$	55.2027	−	7.93695i	2.13426	−	0.306860i
$670$	−5.38299	+	6.75521i	−0.207963	+	0.260977i
$671$	−27.1998	+	7.98659i	−1.05004	+	0.308319i
$672$	0.195457	+	2.73285i	0.00753993	+	0.105422i
$673$	−3.92517	+	2.14331i	−0.151304	+	0.0826184i	−0.553117	−	0.833103i	$-0.686562\pi$
$673$	−3.92517	+	2.14331i	−0.151304	+	0.0826184i	0.401813	+	0.915722i	$0.368380\pi$
$674$	−12.7763	+	8.21080i	−0.492123	+	0.316268i
$675$	34.0787	−	30.1886i	1.31169	−	1.16196i
$676$	8.32935	+	9.61259i	0.320360	+	0.369715i
$677$	0.522203	−	0.113598i	0.0200699	−	0.00436593i	−0.202519	−	0.979278i	$-0.564913\pi$
$677$	0.522203	−	0.113598i	0.0200699	−	0.00436593i	0.222589	+	0.974912i	$0.428549\pi$
$678$	5.14578	−	3.85209i	0.197623	−	0.147938i
$679$	5.79009	+	0.832490i	0.222203	+	0.0319480i
$680$	10.1910	−	9.59276i	0.390805	−	0.367865i
$681$	−18.9247	+	16.3984i	−0.725198	+	0.628388i
$682$	35.7136	+	13.3205i	1.36754	+	0.510067i
$683$	3.67589	−	16.8978i	0.140654	−	0.646575i	−0.851791	−	0.523882i	$-0.824483\pi$
$683$	3.67589	−	16.8978i	0.140654	−	0.646575i	0.992445	−	0.122693i	$-0.0391531\pi$
$684$	−18.5160	−	5.43679i	−0.707978	−	0.207881i
$685$	0.293619	−	1.67998i	0.0112186	−	0.0641889i
$686$	3.38266	+	11.5203i	0.129150	+	0.439846i
$687$	−11.9089	−	31.9291i	−0.454354	−	1.21817i
$688$	−7.13378	+	9.52961i	−0.271973	+	0.363313i
$689$	−0.808420			−0.0307984
$690$	−30.7098	−	9.76559i	−1.16910	−	0.371770i
$691$	42.2991			1.60913			0.804566	−	0.593863i	$-0.202398\pi$
$691$	42.2991			1.60913			0.804566	+	0.593863i	$0.202398\pi$
$692$	8.32071	−	11.1152i	0.316306	−	0.422535i
$693$	−9.41818	−	25.2511i	−0.357767	−	0.959211i
$694$	−8.35263	−	28.4465i	−0.317062	−	1.07981i
$695$	26.7857	+	38.1316i	1.01604	+	1.44641i
$696$	−4.31654	−	1.26745i	−0.163618	−	0.0480426i
$697$	1.91034	−	8.78167i	0.0723591	−	0.332629i
$698$	−2.03588	−	0.759344i	−0.0770592	−	0.0287416i
$699$	−39.2019	+	33.9687i	−1.48275	+	1.28481i
$700$	−1.23641	+	4.38791i	−0.0467317	+	0.165847i
$701$	7.56341	+	1.08745i	0.285666	+	0.0410726i	0.283658	−	0.958925i	$-0.408452\pi$
$701$	7.56341	+	1.08745i	0.285666	+	0.0410726i	0.00200770	+	0.999998i	$0.499361\pi$
$702$	−3.86210	+	2.89113i	−0.145766	+	0.109119i
$703$	18.1915	−	3.95732i	0.686106	−	0.149253i
$704$	−3.21006	−	3.70460i	−0.120984	−	0.139622i
$705$	0.723395	+	3.88764i	0.0272446	+	0.146417i
$706$	−22.2260	+	14.2838i	−0.836485	+	0.537576i
$707$	−13.8741	+	7.57584i	−0.521790	+	0.284919i
$708$	2.94112	+	41.1222i	0.110534	+	1.54547i
$709$	42.0954	−	12.3603i	1.58093	−	0.464202i	0.630769	−	0.775971i	$-0.282740\pi$
$709$	42.0954	−	12.3603i	1.58093	−	0.464202i	0.950158	+	0.311769i	$0.100921\pi$
$710$	−1.69222	+	0.191306i	−0.0635081	+	0.00717959i
$711$	−97.2097	+	13.9766i	−3.64565	+	0.524165i
$712$	−4.65880	+	4.65880i	−0.174596	+	0.174596i
$713$	7.63732	−	36.5017i	0.286020	−	1.36700i
$714$		−	17.1486i		−	0.641772i
$715$	−4.50195	+	3.66872i	−0.168363	+	0.137202i
$716$	5.04042	−	11.0370i	0.188370	−	0.412472i
$717$	−34.8037	−	19.0042i	−1.29977	−	0.709726i
$718$	−16.6200	+	1.18869i	−0.620253	+	0.0443613i
$719$	−2.38659	+	8.12799i	−0.0890049	+	0.303123i	−0.991949	−	0.126634i	$-0.959583\pi$
$719$	−2.38659	+	8.12799i	−0.0890049	+	0.303123i	0.902945	+	0.429757i	$0.141401\pi$
$720$	−4.32808	−	12.7702i	−0.161298	−	0.475915i
$721$	−6.87449	−	15.0530i	−0.256019	−	0.560604i
$722$	0.624820	−	8.73613i	0.0232534	−	0.325125i
$723$	13.3156	+	61.2108i	0.495212	+	2.27645i
$724$	0.909895	−	6.32846i	0.0338160	−	0.235195i
$725$	−6.04116	−	4.42002i	−0.224363	−	0.164155i
$726$	32.9358	+	21.1665i	1.22236	+	0.785564i
$727$	−17.3869	−	1.24353i	−0.644844	−	0.0461201i	−0.254912	−	0.966964i	$-0.582047\pi$
$727$	−17.3869	−	1.24353i	−0.644844	−	0.0461201i	−0.389931	+	0.920844i	$0.627501\pi$
$728$	0.168819	−	0.452621i	0.00625685	−	0.0167753i
$729$	−14.1524	−	22.0215i	−0.524163	−	0.815613i
$730$	0.114381	+	0.0670217i	0.00423343	+	0.00248059i
$731$	48.7918	−	56.3087i	1.80463	−	2.08265i
$732$	−8.32851	+	15.2525i	−0.307831	+	0.563750i
$733$	−19.2558	+	7.18203i	−0.711228	+	0.265274i	−0.678929	−	0.734204i	$-0.737556\pi$
$733$	−19.2558	+	7.18203i	−0.711228	+	0.265274i	−0.0322992	+	0.999478i	$0.510283\pi$
$734$	4.24167	+	29.5014i	0.156563	+	1.08892i
$735$	−21.3455	−	35.5313i	−0.787339	−	1.31059i
$736$	−3.11171	+	3.64928i	−0.114699	+	0.134514i
$737$	−13.3894	−	13.3894i	−0.493204	−	0.493204i
$738$	−6.93134	−	5.18874i	−0.255146	−	0.191000i
$739$	−42.3232	−	19.3284i	−1.55688	−	0.711005i	−0.563530	−	0.826096i	$-0.690557\pi$
$739$	−42.3232	−	19.3284i	−1.55688	−	0.711005i	−0.993355	+	0.115090i	$0.963284\pi$
$740$	9.56886	+	8.81166i	0.351758	+	0.323923i
$741$	3.85077	+	3.33671i	0.141461	+	0.122577i
$742$	−0.666708	−	1.22098i	−0.0244756	−	0.0448237i
$743$	33.0907	+	7.19844i	1.21398	+	0.264085i	0.773569	−	0.633712i	$-0.218469\pi$
$743$	33.0907	+	7.19844i	1.21398	+	0.264085i	0.440410	+	0.897797i	$0.354833\pi$
$744$	21.2552	−	9.70692i	0.779253	−	0.355873i
$745$	2.93377	+	5.78166i	0.107485	+	0.211824i
$746$	−7.63109	+	11.8742i	−0.279394	+	0.434746i
$747$	21.1279	+	28.2236i	0.773029	+	1.03265i
$748$	18.3865	+	24.5614i	0.672275	+	0.898055i
$749$	−2.69162	+	4.18825i	−0.0983498	+	0.153035i
$750$	0.647809	−	33.5908i	0.0236546	−	1.22656i
$751$	29.1447	−	13.3100i	1.06351	−	0.485687i	0.194712	−	0.980860i	$-0.437623\pi$
$751$	29.1447	−	13.3100i	1.06351	−	0.485687i	0.868794	+	0.495173i	$0.164895\pi$
$752$	0.575050	+	0.125095i	0.0209699	+	0.00456173i
$753$	20.6092	+	37.7429i	0.751040	+	1.37543i
$754$	0.599470	+	0.519443i	0.0218314	+	0.0189170i
$755$	−24.6437	+	1.01521i	−0.896875	+	0.0369472i
$756$	−7.55167	−	3.44873i	−0.274652	−	0.125429i
$757$	27.9116	+	20.8944i	1.01446	+	0.759419i	0.970864	−	0.239630i	$-0.0770262\pi$
$757$	27.9116	+	20.8944i	1.01446	+	0.759419i	0.0436006	+	0.999049i	$0.486117\pi$
$758$	8.05951	+	8.05951i	0.292735	+	0.292735i
$759$	28.8351	−	64.4908i	1.04665	−	2.34087i
$760$	−6.13416	+	3.68510i	−0.222509	+	0.133672i
$761$	−4.16652	−	28.9788i	−0.151036	−	1.05048i	−0.914487	−	0.404614i	$-0.867406\pi$
$761$	−4.16652	−	28.9788i	−0.151036	−	1.05048i	0.763451	−	0.645865i	$-0.223503\pi$
$762$	−16.7522	+	6.24825i	−0.606868	+	0.226350i
$763$	−0.885000	+	1.62076i	−0.0320391	+	0.0586753i
$764$	14.1223	−	16.2980i	0.510925	−	0.589639i
$765$	21.3185	+	81.6575i	0.770771	+	2.95233i
$766$	4.80388	+	7.47498i	0.173571	+	0.270082i
$767$	2.54028	−	6.81076i	0.0917242	−	0.245922i
$768$	−2.99735	−	0.214375i	−0.108158	−	0.00773559i
$769$	5.98137	+	3.84399i	0.215694	+	0.138618i	0.644027	−	0.765003i	$-0.277263\pi$
$769$	5.98137	+	3.84399i	0.215694	+	0.138618i	−0.428333	+	0.903621i	$0.640899\pi$
$770$	−9.25377	−	3.77384i	−0.333483	−	0.136000i
$771$	5.79745	−	40.3221i	0.208790	−	1.45217i
$772$	4.23148	+	19.4518i	0.152294	+	0.700086i
$773$	−3.20295	+	44.7831i	−0.115202	+	1.61074i	0.530866	+	0.847456i	$0.321867\pi$
$773$	−3.20295	+	44.7831i	−0.115202	+	1.61074i	−0.646068	+	0.763280i	$0.723588\pi$
$774$	−29.8192	−	65.2950i	−1.07183	−	2.34698i
$775$	38.7480	−	3.19792i	1.39187	−	0.114873i
$776$	−1.80754	+	6.15591i	−0.0648869	+	0.220984i
$777$	15.8980	−	1.13705i	0.570337	−	0.0407913i
$778$	18.8716	+	10.3047i	0.676580	+	0.369441i
$779$	−1.90887	+	4.17984i	−0.0683923	+	0.149758i
$780$	−0.361189	+	3.54181i	−0.0129326	+	0.126817i
$781$		−	3.73331i		−	0.133588i
$782$	21.0561	−	21.3933i	0.752965	−	0.765022i
$783$	9.63902	−	9.63902i	0.344470	−	0.344470i
$784$	−6.10592	+	0.877898i	−0.218068	+	0.0313535i
$785$	0.973060	+	8.60734i	0.0347300	+	0.307209i
$786$	−11.4119	+	3.35083i	−0.407048	+	0.119520i
$787$	−1.93456	−	27.0487i	−0.0689596	−	0.964181i	−0.907692	−	0.419637i	$-0.862157\pi$
$787$	−1.93456	−	27.0487i	−0.0689596	−	0.964181i	0.838732	−	0.544544i	$-0.183297\pi$
$788$	14.7910	−	8.07652i	0.526909	−	0.287714i
$789$	34.8469	−	22.3948i	1.24058	−	0.797275i
$790$	−20.6059	+	30.0276i	−0.733126	+	1.06834i
$791$	−1.27717	−	1.47393i	−0.0454110	−	0.0524070i
$792$	28.8833	−	6.28317i	1.02632	−	0.223263i
$793$	2.45293	−	1.83624i	0.0871061	−	0.0652068i
$794$	38.4106	+	5.52261i	1.36314	+	0.195990i
$795$	7.02715	+	7.46536i	0.249227	+	0.264769i
$796$	−1.32163	+	1.14520i	−0.0468439	+	0.0405905i
$797$	30.4193	+	11.3458i	1.07751	+	0.401889i	0.824667	−	0.565619i	$-0.191363\pi$
$797$	30.4193	+	11.3458i	1.07751	+	0.401889i	0.252840	+	0.967508i	$0.418635\pi$
$798$	−1.86380	+	8.56774i	−0.0659778	+	0.303295i
$799$	−3.53422	−	1.03774i	−0.125032	−	0.0367127i
$800$	−4.57062	−	2.02717i	−0.161596	−	0.0716714i
$801$	−11.1931	−	38.1201i	−0.395488	−	1.34691i
$802$	10.4935	+	28.1341i	0.370538	+	0.993450i
$803$	−0.174162	+	0.232653i	−0.00614604	+	0.00821015i
$804$	−11.6080			−0.409383
$805$	−2.29073	+	9.50535i	−0.0807375	+	0.335020i
$806$	−4.11997			−0.145120
$807$	33.3332	−	44.5280i	1.17339	−	1.56746i
$808$	−6.05891	−	16.2446i	−0.213152	−	0.571481i
$809$	−5.12288	−	17.4469i	−0.180111	−	0.613402i	−0.999210	−	0.0397491i	$-0.987344\pi$
$809$	−5.12288	−	17.4469i	−0.180111	−	0.613402i	0.819099	−	0.573653i	$-0.194474\pi$
$810$	20.4223	+	3.56931i	0.717568	+	0.125413i
$811$	−51.8800	−	15.2333i	−1.82175	−	0.534915i	−0.822333	−	0.569006i	$-0.807328\pi$
$811$	−51.8800	−	15.2333i	−1.82175	−	0.534915i	−0.999419	+	0.0340915i	$0.989146\pi$
$812$	−0.290148	+	1.33379i	−0.0101822	+	0.0468067i
$813$	37.6000	+	14.0241i	1.31869	+	0.491845i
$814$	−21.5510	+	18.6741i	−0.755362	+	0.654525i
$815$	−33.5108	−	1.01326i	−1.17383	−	0.0354929i
$816$	18.6170	+	2.67672i	0.651724	+	0.0937038i
$817$	−30.4971	+	22.8298i	−1.06696	+	0.798714i
$818$	−22.0463	+	4.79588i	−0.770830	+	0.167684i
$819$	1.90761	+	2.20150i	0.0666574	+	0.0769267i
$820$	−3.15649	+	0.587347i	−0.110229	+	0.0205111i
$821$	−17.0378	+	10.9495i	−0.594623	+	0.382141i	−0.803063	−	0.595894i	$-0.796798\pi$
$821$	−17.0378	+	10.9495i	−0.594623	+	0.382141i	0.208440	+	0.978035i	$0.433161\pi$
$822$	2.01157	−	1.09840i	0.0701616	−	0.0383111i
$823$	−1.43531	−	20.0682i	−0.0500317	−	0.699535i	−0.959132	−	0.282958i	$-0.908684\pi$
$823$	−1.43531	−	20.0682i	−0.0500317	−	0.699535i	0.909101	−	0.416577i	$-0.136770\pi$
$824$	17.4150	−	5.11349i	0.606679	−	0.178137i
$825$	73.0118	+	9.68315i	2.54194	+	0.337124i
$826$	12.3815	−	1.78019i	0.430807	−	0.0619408i
$827$	−8.89824	+	8.89824i	−0.309422	+	0.309422i	−0.844685	−	0.535263i	$-0.820212\pi$
$827$	−8.89824	+	8.89824i	−0.309422	+	0.309422i	0.535263	+	0.844685i	$0.320212\pi$
$828$	−10.3211	−	27.0147i	−0.358684	−	0.938827i
$829$			13.7542i			0.477702i	0.971056	+	0.238851i	$0.0767707\pi$
$829$			13.7542i			0.477702i	−0.971056	+	0.238851i	$0.923229\pi$
$830$	13.0060	+	1.32634i	0.451445	+	0.0460378i
$831$	4.46470	−	9.77632i	0.154879	−	0.339137i
$832$	0.465025	+	0.253923i	0.0161218	+	0.00880319i
$833$	38.5117	−	2.75441i	1.33435	−	0.0954346i
$834$	−17.6432	+	60.0871i	−0.610933	+	2.08065i
$835$	3.94630	+	1.94844i	0.136567	+	0.0674287i
$836$	−6.51672	−	14.2696i	−0.225385	−	0.493525i
$837$	−5.05104	+	70.6228i	−0.174590	+	2.44108i
$838$	2.35466	+	10.8242i	0.0813404	+	0.373916i
$839$	−2.79755	+	19.4574i	−0.0965822	+	0.671744i	0.882803	+	0.469743i	$0.155653\pi$
$839$	−2.79755	+	19.4574i	−0.0965822	+	0.671744i	−0.979385	+	0.202001i	$0.935256\pi$
$840$	−5.64718	+	2.37543i	−0.194846	+	0.0819601i
$841$	22.5109	+	14.4669i	0.776237	+	0.498857i
$842$	−22.9396	−	1.64067i	−0.790552	−	0.0565414i
$843$	−13.5234	+	36.2577i	−0.465772	+	1.24878i
$844$	−11.3616	−	17.6790i	−0.391083	−	0.608537i
$845$	−14.3786	+	24.5389i	−0.494639	+	0.844162i
$846$	−2.32390	+	2.68193i	−0.0798974	+	0.0922065i
$847$	5.69291	−	10.4258i	0.195611	−	0.358234i
$848$	1.42959	−	0.533211i	0.0490925	−	0.0183105i
$849$	9.91268	+	68.9442i	0.340202	+	2.36616i
$850$	27.6295	+	14.6966i	0.947686	+	0.504090i
$851$	21.2292	+	18.1020i	0.727727	+	0.620527i
$852$	−1.61831	−	1.61831i	−0.0554423	−	0.0554423i
$853$	10.6625	+	7.98187i	0.365078	+	0.273294i	0.766030	−	0.642805i	$-0.222230\pi$
$853$	10.6625	+	7.98187i	0.365078	+	0.273294i	−0.400952	+	0.916099i	$0.631320\pi$
$854$	4.79628	+	2.19039i	0.164125	+	0.0749535i
$855$	−1.77612	−	43.1144i	−0.0607421	−	1.47448i
$856$	−4.12672	−	3.57583i	−0.141049	−	0.122219i
$857$	7.03949	+	12.8919i	0.240464	+	0.440378i	0.969842	−	0.243733i	$-0.0783722\pi$
$857$	7.03949	+	12.8919i	0.240464	+	0.440378i	−0.729378	+	0.684111i	$0.760190\pi$
$858$	−7.62623	−	1.65898i	−0.260355	−	0.0566368i
$859$	2.69835	−	1.23229i	0.0920665	−	0.0420454i	−0.368849	−	0.929489i	$-0.620248\pi$
$859$	2.69835	−	1.23229i	0.0920665	−	0.0420454i	0.460916	+	0.887444i	$0.347521\pi$
$860$	−25.3015	−	8.26764i	−0.862775	−	0.281924i
$861$	−2.12688	+	3.30949i	−0.0724840	+	0.112787i
$862$	7.48585	+	9.99992i	0.254969	+	0.340599i
$863$	12.0525	+	16.1002i	0.410272	+	0.548059i	0.957315	−	0.289045i	$-0.0933378\pi$
$863$	12.0525	+	16.1002i	0.410272	+	0.548059i	−0.547044	+	0.837104i	$0.684247\pi$
$864$	4.92275	−	7.65995i	0.167475	−	0.260597i
$865$	29.5113	+	9.64323i	1.00341	+	0.327880i
$866$	−15.3505	+	7.01033i	−0.521631	+	0.238221i
$867$	−65.1141	−	14.1647i	−2.21139	−	0.481059i
$868$	−3.39776	−	6.22253i	−0.115327	−	0.211207i
$869$	−60.3353	−	52.2808i	−2.04673	−	1.77351i
$870$	−0.414058	−	10.0510i	−0.0140379	−	0.340762i
$871$	1.86174	+	0.850227i	0.0630826	+	0.0288088i
$872$	−1.62139	−	1.21376i	−0.0549072	−	0.0411030i
$873$	−27.3564	−	27.3564i	−0.925873	−	0.925873i
$874$	−12.8451	+	8.39996i	−0.434492	+	0.284133i
$875$	−10.1799	+	0.531025i	−0.344143	+	0.0179519i
$876$	0.0253546	+	0.176345i	0.000856653	+	0.00595816i
$877$	30.8032	−	11.4890i	1.04015	−	0.387956i	0.229391	−	0.973334i	$-0.426327\pi$
$877$	30.8032	−	11.4890i	1.04015	−	0.387956i	0.810761	+	0.585378i	$0.199054\pi$
$878$	4.64019	−	8.49787i	0.156599	−	0.286789i
$879$	−19.6898	+	22.7233i	−0.664122	+	0.766438i
$880$	5.54138	−	9.45705i	0.186800	−	0.318797i
$881$	−15.6916	−	24.4167i	−0.528664	−	0.822618i	0.469515	−	0.882924i	$-0.344429\pi$
$881$	−15.6916	−	24.4167i	−0.528664	−	0.822618i	−0.998180	+	0.0603063i	$0.980792\pi$
$882$	12.9993	−	34.8524i	0.437709	−	1.17354i
$883$	−36.8286	−	2.63403i	−1.23938	−	0.0886423i	−0.563789	−	0.825919i	$-0.690657\pi$
$883$	−36.8286	−	2.63403i	−1.23938	−	0.0886423i	−0.675591	+	0.737276i	$0.736112\pi$
$884$	−2.78980	−	1.79290i	−0.0938313	−	0.0603017i
$885$	−84.9752	+	35.7439i	−2.85641	+	1.20152i
$886$	−3.57327	+	24.8526i	−0.120046	+	0.834940i
$887$	−3.73810	−	17.1838i	−0.125513	−	0.576974i	−0.996347	−	0.0853969i	$-0.972784\pi$
$887$	−3.73810	−	17.1838i	−0.125513	−	0.576974i	0.870834	−	0.491577i	$-0.163579\pi$
$888$	−1.24710	+	17.4367i	−0.0418498	+	0.585137i
$889$	2.25357	+	4.93462i	0.0755822	+	0.165502i
$890$	−13.2100	−	6.52230i	−0.442800	−	0.218628i
$891$	−12.8043	+	43.6073i	−0.428959	+	1.46090i
$892$	18.5119	−	1.32399i	0.619823	−	0.0443306i
$893$	1.65297	+	0.902590i	0.0553145	+	0.0302040i
$894$	−3.61948	+	7.92556i	−0.121054	+	0.265070i
$895$	26.9913	+	2.75254i	0.902219	+	0.0920071i
$896$			0.911755i			0.0304596i
$897$	−0.484213	+	7.62036i	−0.0161674	+	0.254436i
$898$	19.0032	−	19.0032i	0.634146	−	0.634146i
$899$	11.5228	−	1.65673i	0.384308	−	0.0552551i
$900$	23.9374	−	18.3315i	0.797914	−	0.611051i
$901$	−9.16314	+	2.69054i	−0.305269	+	0.0896349i
$902$	−0.502114	−	7.02048i	−0.0167186	−	0.233756i
$903$	−28.6253	+	15.6306i	−0.952592	+	0.520155i
$904$	1.79949	−	1.15646i	0.0598501	−	0.0384633i
$905$	14.0551	−	2.61532i	0.467208	−	0.0869362i
$906$	−21.7062	−	25.0502i	−0.721139	−	0.832239i
$907$	40.1942	−	8.74372i	1.33463	−	0.290330i	0.512036	−	0.858964i	$-0.328891\pi$
$907$	40.1942	−	8.74372i	1.33463	−	0.290330i	0.822591	+	0.568634i	$0.192528\pi$
$908$	−6.67099	+	4.99384i	−0.221385	+	0.165726i
$909$	103.484	+	14.8787i	3.43233	+	0.493495i
$910$	1.07971	+	0.0326468i	0.0357919	+	0.00108223i
$911$	13.2781	−	11.5055i	0.439923	−	0.381196i	−0.406549	−	0.913629i	$-0.633268\pi$
$911$	13.2781	−	11.5055i	0.439923	−	0.381196i	0.846472	+	0.532433i	$0.178722\pi$
$912$	−9.01042	−	3.36071i	−0.298365	−	0.111284i
$913$	−6.09202	+	28.0046i	−0.201616	+	0.926816i
$914$	17.0265	+	4.99944i	0.563188	+	0.165367i
$915$	−38.2787	−	6.69016i	−1.26546	−	0.221170i
$916$	−3.19493	−	10.8809i	−0.105564	−	0.359516i
$917$	1.26110	+	3.38115i	0.0416453	+	0.111655i
$918$	−34.1534	+	45.6236i	−1.12723	+	1.50580i
$919$	16.3579			0.539598			0.269799	−	0.962917i	$-0.413043\pi$
$919$	16.3579			0.539598			0.269799	+	0.962917i	$0.413043\pi$
$920$	−9.96167	−	3.97054i	−0.328426	−	0.130905i
$921$	11.3721			0.374724
$922$	10.6521	−	14.2296i	0.350810	−	0.468627i
$923$	0.141018	+	0.378083i	0.00464166	+	0.0124448i
$924$	−3.78377	−	12.8863i	−0.124477	−	0.423929i
$925$	−11.7928	+	26.5890i	−0.387745	+	0.874239i
$926$	−12.2909	−	3.60893i	−0.403904	−	0.118597i
$927$	−23.2646	+	106.946i	−0.764110	+	3.51256i
$928$	−1.40270	−	0.523180i	−0.0460459	−	0.0171742i
$929$	19.8784	−	17.2247i	0.652188	−	0.565125i	−0.264669	−	0.964339i	$-0.585263\pi$
$929$	19.8784	−	17.2247i	0.652188	−	0.565125i	0.916857	+	0.399215i	$0.130717\pi$
$930$	35.8127	+	38.0459i	1.17434	+	1.24757i
$931$	−19.5404	−	2.80949i	−0.640411	−	0.0920772i
$932$	−13.8187	+	10.3446i	−0.452647	+	0.338847i
$933$	55.3331	−	12.0370i	1.81152	−	0.394073i
$934$	−4.56231	−	5.26518i	−0.149283	−	0.172282i
$935$	−38.8179	+	56.5667i	−1.26948	+	1.84993i
$936$	−2.68776	+	1.72732i	−0.0878522	+	0.0564592i
$937$	4.70850	−	2.57104i	0.153820	−	0.0839921i	−0.400495	−	0.916299i	$-0.631162\pi$
$937$	4.70850	−	2.57104i	0.153820	−	0.0839921i	0.554315	+	0.832307i	$0.312980\pi$
$938$	0.251257	+	3.51303i	0.00820383	+	0.114705i
$939$	−5.41107	+	1.58883i	−0.176584	+	0.0518497i
$940$	0.147824	+	1.30760i	0.00482148	+	0.0426491i
$941$	−1.12646	+	0.161961i	−0.0367217	+	0.00527978i	−0.160651	−	0.987011i	$-0.551359\pi$
$941$	−1.12646	+	0.161961i	−0.0367217	+	0.00527978i	0.123929	+	0.992291i	$0.460450\pi$
$942$	−8.23138	+	8.23138i	−0.268193	+	0.268193i
$943$	−6.71692	+	1.51715i	−0.218733	+	0.0494053i
$944$			13.7195i			0.446532i
$945$	1.88332	−	18.4678i	0.0612646	−	0.600758i
$946$	24.2403	−	53.0788i	0.788119	−	1.72574i
$947$	−31.6137	−	17.2624i	−1.02731	−	0.560952i	−0.125050	−	0.992150i	$-0.539909\pi$
$947$	−31.6137	−	17.2624i	−1.02731	−	0.560952i	−0.902257	+	0.431199i	$0.858091\pi$
$948$	−48.8166	+	3.49143i	−1.58549	+	0.113396i
$949$	0.00884991	−	0.0301400i	0.000287280	−	0.000978387i
$950$	−12.2069	−	10.3456i	−0.396043	−	0.335655i
$951$	−7.25489	−	15.8860i	−0.235256	−	0.515139i
$952$	0.407111	−	5.69215i	0.0131945	−	0.184484i
$953$	3.45757	+	15.8942i	0.112002	+	0.514864i	0.998627	+	0.0523760i	$0.0166794\pi$
$953$	3.45757	+	15.8942i	0.112002	+	0.514864i	−0.886626	+	0.462488i	$0.846957\pi$
$954$	−1.30939	+	9.10702i	−0.0423931	+	0.294851i
$955$	44.6511	+	18.2095i	1.44488	+	0.589245i
$956$	−11.1012	−	7.13431i	−0.359039	−	0.230740i
$957$	21.9963	+	1.57321i	0.711040	+	0.0508546i
$958$	5.87940	−	15.7633i	0.189955	−	0.509288i
$959$	−0.375959	−	0.585004i	−0.0121404	−	0.0188908i
$960$	−1.69736	−	6.50149i	−0.0547819	−	0.209835i
$961$	−19.2958	+	22.2685i	−0.622444	+	0.718338i
$962$	1.47716	−	2.70522i	0.0476256	−	0.0872198i
$963$	30.8508	−	11.5068i	0.994154	−	0.370800i
$964$	2.96669	+	20.6338i	0.0955508	+	0.664570i
$965$	−38.1568	+	22.9227i	−1.22831	+	0.737908i
$966$	−11.9086	+	5.55322i	−0.383153	+	0.178672i
$967$	−17.7036	−	17.7036i	−0.569310	−	0.569310i	0.362625	−	0.931935i	$-0.381880\pi$
$967$	−17.7036	−	17.7036i	−0.569310	−	0.569310i	−0.931935	+	0.362625i	$0.881880\pi$
$968$	10.4299	+	7.80770i	0.335229	+	0.250949i
$969$	54.7521	+	25.0044i	1.75889	+	0.803258i
$970$	−14.3340	+	0.590497i	−0.460237	+	0.0189597i
$971$	23.7885	+	20.6128i	0.763409	+	0.661497i	0.946902	−	0.321524i	$-0.104195\pi$
$971$	23.7885	+	20.6128i	0.763409	+	0.661497i	−0.183493	+	0.983021i	$0.558740\pi$
$972$	0.261187	+	0.478328i	0.00837757	+	0.0153424i
$973$	18.5666	+	4.03891i	0.595217	+	0.129481i
$974$	17.9458	−	8.19558i	0.575021	−	0.262603i
$975$	−7.75988	+	1.77722i	−0.248515	+	0.0569167i
$976$	−3.12658	+	4.86505i	−0.100079	+	0.155727i
$977$	−24.8681	−	33.2199i	−0.795601	−	1.06280i	−0.996533	−	0.0831936i	$-0.973488\pi$
$977$	−24.8681	−	33.2199i	−0.795601	−	1.06280i	0.200932	−	0.979605i	$-0.435603\pi$
$978$	−27.0005	−	36.0685i	−0.863381	−	1.15334i
$979$	17.4607	−	27.1694i	0.558047	−	0.868337i
$980$	−6.24168	−	12.3006i	−0.199383	−	0.392930i
$981$	11.1095	−	5.07352i	0.354697	−	0.161985i
$982$	−8.62038	−	1.87525i	−0.275087	−	0.0598416i
$983$	26.9412	+	49.3391i	0.859290	+	1.57367i	0.818502	+	0.574504i	$0.194805\pi$
$983$	26.9412	+	49.3391i	0.859290	+	1.57367i	0.0407879	+	0.999168i	$0.487013\pi$
$984$	−3.26088	−	2.82557i	−0.103953	−	0.0900758i
$985$	27.7202	+	25.5267i	0.883241	+	0.813349i
$986$	8.52355	+	3.89258i	0.271445	+	0.123965i
$987$	1.29078	+	0.966269i	0.0410861	+	0.0307567i
$988$	1.19897	+	1.19897i	0.0381443	+	0.0381443i
$989$	−54.9029	−	15.6483i	−1.74581	−	0.497588i
$990$	34.0371	+	56.6576i	1.08177	+	1.80070i
$991$	1.75378	+	12.1978i	0.0557108	+	0.387477i	0.998531	+	0.0541764i	$0.0172533\pi$
$991$	1.75378	+	12.1978i	0.0557108	+	0.387477i	−0.942821	+	0.333301i	$0.891838\pi$
$992$	7.28568	−	2.71742i	0.231320	−	0.0862781i
$993$	16.6915	−	30.5682i	0.529688	−	0.970052i
$994$	−0.454734	+	0.524791i	−0.0144233	+	0.0166454i
$995$	−3.37383	−	1.97691i	−0.106958	−	0.0626721i
$996$	9.49861	+	14.7801i	0.300975	+	0.468326i
$997$	−0.203206	+	0.544818i	−0.00643561	+	0.0172545i	−0.940128	−	0.340822i	$-0.889295\pi$
$997$	−0.203206	+	0.544818i	−0.00643561	+	0.0172545i	0.933692	+	0.358077i	$0.116567\pi$
$998$	4.96321	+	0.354976i	0.157108	+	0.0112366i
$999$	−44.5607	−	28.6374i	−1.40984	−	0.906048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.227.1	yes	240
5.3	odd	4	inner	230.2.l.a.43.12	✓	240
23.15	odd	22	inner	230.2.l.a.107.12	yes	240
115.38	even	44	inner	230.2.l.a.153.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.12	✓	240	5.3	odd	4	inner
230.2.l.a.107.12	yes	240	23.15	odd	22	inner
230.2.l.a.153.1	yes	240	115.38	even	44	inner
230.2.l.a.227.1	yes	240	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 + 0.800541i) q^{2} +(-1.05014 - 2.81554i) q^{3} +(-0.281733 - 0.959493i) q^{4} +(1.82975 - 1.28531i) q^{5} +(2.88328 + 0.846609i) q^{6} +(0.193807 - 0.890918i) q^{7} +(0.936950 + 0.349464i) q^{8} +(-4.55723 + 3.94886i) q^{9} +(-0.0675806 + 2.23505i) q^{10} +(-4.85200 - 0.697612i) q^{11} +(-2.40563 + 1.80083i) q^{12} +(0.517727 - 0.112625i) q^{13} +(0.597072 + 0.689058i) q^{14} +(-5.54035 - 3.80197i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(5.49341 - 2.99963i) q^{17} +(-0.430181 - 6.01471i) q^{18} +(-3.07061 + 0.901613i) q^{19} +(-1.74875 - 1.39351i) q^{20} +(-2.71194 + 0.389918i) q^{21} +(3.46616 - 3.46616i) q^{22} +(-3.86197 - 2.84345i) q^{23} -3.00501i q^{24} +(1.69594 - 4.70359i) q^{25} +(-0.220101 + 0.481955i) q^{26} +(7.99162 + 4.36376i) q^{27} +(-0.909432 + 0.0650438i) q^{28} +(0.421780 - 1.43645i) q^{29} +(6.36384 - 2.15684i) q^{30} +(3.23025 + 7.07325i) q^{31} +(0.0713392 - 0.997452i) q^{32} +(3.13113 + 14.3936i) q^{33} +(-0.890751 + 6.19531i) q^{34} +(-0.790490 - 1.87926i) q^{35} +(5.07282 + 3.26011i) q^{36} +(-5.80254 - 0.415006i) q^{37} +(1.11837 - 2.99847i) q^{38} +(-0.860786 - 1.33941i) q^{39} +(2.16355 - 0.564842i) q^{40} +(0.940286 - 1.08515i) q^{41} +(1.31306 - 2.40469i) q^{42} +(11.1534 - 4.16001i) q^{43} +(0.697612 + 4.85200i) q^{44} +(-3.26305 + 13.0829i) q^{45} +(4.59069 - 1.38765i) q^{46} +(-0.416132 - 0.416132i) q^{47} +(2.40563 + 1.80083i) q^{48} +(5.61125 + 2.56257i) q^{49} +(2.74908 + 4.17643i) q^{50} +(-14.2144 - 12.3169i) q^{51} +(-0.253923 - 0.465025i) q^{52} +(-1.49093 - 0.324331i) q^{53} +(-8.28257 + 3.78252i) q^{54} +(-9.77457 + 4.95988i) q^{55} +(0.492932 - 0.767017i) q^{56} +(5.76311 + 7.69861i) q^{57} +(0.897174 + 1.19848i) q^{58} +(7.41732 - 11.5416i) q^{59} +(-2.08706 + 6.38706i) q^{60} +(5.26049 - 2.40239i) q^{61} +(-7.59825 - 1.65290i) q^{62} +(2.63489 + 4.82543i) q^{63} +(0.755750 + 0.654861i) q^{64} +(0.802551 - 0.871515i) q^{65} +(-13.3991 - 6.11915i) q^{66} +(3.09240 + 2.31494i) q^{67} +(-4.42579 - 4.42579i) q^{68} +(-3.95023 + 13.8596i) q^{69} +(1.97815 + 0.493377i) q^{70} +(0.108388 + 0.753855i) q^{71} +(-5.64988 + 2.10730i) q^{72} +(0.0284134 - 0.0520352i) q^{73} +(3.80956 - 4.39647i) q^{74} +(-15.0241 + 0.164441i) q^{75} +(1.73018 + 2.69222i) q^{76} +(-1.56187 + 4.18753i) q^{77} +(1.58810 + 0.113583i) q^{78} +(13.7011 + 8.80519i) q^{79} +(-0.844388 + 2.07051i) q^{80} +(1.31948 - 9.17722i) q^{81} +(0.305213 + 1.40304i) q^{82} +(0.417094 - 5.83173i) q^{83} +(1.13817 + 2.49224i) q^{84} +(6.19609 - 12.5493i) q^{85} +(-3.35373 + 11.4218i) q^{86} +(-4.48731 + 0.320939i) q^{87} +(-4.30229 - 2.34923i) q^{88} +(-2.73698 + 5.99315i) q^{89} +(-8.51791 - 10.4525i) q^{90} -0.483079i q^{91} +(-1.64023 + 4.50662i) q^{92} +(16.5228 - 16.5228i) q^{93} +(0.582509 - 0.0837522i) q^{94} +(-4.45959 + 5.59642i) q^{95} +(-2.88328 + 0.846609i) q^{96} +(0.457698 + 6.39945i) q^{97} +(-5.41414 + 2.95634i) q^{98} +(24.8664 - 15.9807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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