LMFDB - Embedded newform 230.2.l.a.43.12

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			43.12
Character	$\chi$	$=$	230.43
Dual form			230.2.l.a.107.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.800541 + 0.599278i) q^{2} +(2.81554 - 1.05014i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-1.01183 + 1.99404i) q^{5} +(2.88328 + 0.846609i) q^{6} +(-0.890918 - 0.193807i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(4.55723 - 3.94886i) q^{9} +(-2.00500 + 0.989945i) q^{10} +(-4.85200 - 0.697612i) q^{11} +(1.80083 + 2.40563i) q^{12} +(0.112625 + 0.517727i) q^{13} +(-0.597072 - 0.689058i) q^{14} +(-0.754821 + 6.67687i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-2.99963 - 5.49341i) q^{17} +(6.01471 - 0.430181i) q^{18} +(3.07061 - 0.901613i) q^{19} +(-2.19833 - 0.409057i) q^{20} +(-2.71194 + 0.389918i) q^{21} +(-3.46616 - 3.46616i) q^{22} +(2.84345 - 3.86197i) q^{23} +3.00501i q^{24} +(-2.95240 - 4.03526i) q^{25} +(-0.220101 + 0.481955i) q^{26} +(4.36376 - 7.99162i) q^{27} +(-0.0650438 - 0.909432i) q^{28} +(-0.421780 + 1.43645i) q^{29} +(-4.60557 + 4.89276i) q^{30} +(3.23025 + 7.07325i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(-14.3936 + 3.13113i) q^{33} +(0.890751 - 6.19531i) q^{34} +(1.28792 - 1.58043i) q^{35} +(5.07282 + 3.26011i) q^{36} +(-0.415006 + 5.80254i) q^{37} +(2.99847 + 1.11837i) q^{38} +(0.860786 + 1.33941i) q^{39} +(-1.51472 - 1.64488i) q^{40} +(0.940286 - 1.08515i) q^{41} +(-2.40469 - 1.31306i) q^{42} +(4.16001 + 11.1534i) 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} +(-1.80083 + 2.40563i) q^{48} +(-5.61125 - 2.56257i) q^{49} +(0.0547222 - 4.99970i) q^{50} +(-14.2144 - 12.3169i) q^{51} +(-0.465025 + 0.253923i) q^{52} +(0.324331 - 1.49093i) q^{53} +(8.28257 - 3.78252i) q^{54} +(6.30046 - 8.96922i) q^{55} +(0.492932 - 0.767017i) q^{56} +(7.69861 - 5.76311i) q^{57} +(-1.19848 + 0.897174i) q^{58} +(-7.41732 + 11.5416i) q^{59} +(-6.61907 + 1.15685i) q^{60} +(5.26049 - 2.40239i) q^{61} +(-1.65290 + 7.59825i) q^{62} +(-4.82543 + 2.63489i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(-1.14633 - 0.299273i) q^{65} +(-13.3991 - 6.11915i) q^{66} +(2.31494 - 3.09240i) 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} +(2.10730 + 5.64988i) q^{72} +(0.0520352 + 0.0284134i) q^{73} +(-3.80956 + 4.39647i) q^{74} +(-12.5502 - 8.26100i) q^{75} +(1.73018 + 2.69222i) q^{76} +(4.18753 + 1.56187i) q^{77} +(-0.113583 + 1.58810i) q^{78} +(-13.7011 - 8.80519i) q^{79} +(-0.226855 - 2.22453i) q^{80} +(1.31948 - 9.17722i) q^{81} +(1.40304 - 0.305213i) q^{82} +(5.83173 + 0.417094i) q^{83} +(-1.13817 - 2.49224i) q^{84} +(13.9892 - 0.422989i) q^{85} +(-3.35373 + 11.4218i) q^{86} +(0.320939 + 4.48731i) q^{87} +(2.34923 - 4.30229i) q^{88} +(2.73698 - 5.99315i) q^{89} +(-5.22807 + 12.4289i) q^{90} -0.483079i q^{91} +(4.50662 + 1.64023i) q^{92} +(16.5228 + 16.5228i) q^{93} +(-0.582509 + 0.0837522i) q^{94} +(-1.30908 + 7.03520i) q^{95} +(-2.88328 + 0.846609i) q^{96} +(6.39945 - 0.457698i) q^{97} +(-2.95634 - 5.41414i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$3$	2.81554	−	1.05014i	1.62555	−	0.606300i	0.638923	−	0.769271i	$-0.279380\pi$
$3$	2.81554	−	1.05014i	1.62555	−	0.606300i	0.986631	+	0.162971i	$0.0521075\pi$
$4$	0.281733	+	0.959493i	0.140866	+	0.479746i
$5$	−1.01183	+	1.99404i	−0.452504	+	0.891762i
$5$	−1.01183	+	1.99404i	−0.452504	+	0.891762i
$6$	2.88328	+	0.846609i	1.17710	+	0.345627i
$7$	−0.890918	−	0.193807i	−0.336735	−	0.0732523i	0.0410184	−	0.999158i	$-0.486940\pi$
$7$	−0.890918	−	0.193807i	−0.336735	−	0.0732523i	−0.377754	+	0.925906i	$0.623303\pi$
$8$	−0.349464	+	0.936950i	−0.123554	+	0.331262i
$9$	4.55723	−	3.94886i	1.51908	−	1.31629i
$10$	−2.00500	+	0.989945i	−0.634035	+	0.313048i
$11$	−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	$0.810150\pi$
$12$	1.80083	+	2.40563i	0.519856	+	0.694446i
$13$	0.112625	+	0.517727i	0.0312364	+	0.143592i	0.990124	−	0.140195i	$-0.0447729\pi$
$13$	0.112625	+	0.517727i	0.0312364	+	0.143592i	−0.958887	+	0.283787i	$0.908409\pi$
$14$	−0.597072	−	0.689058i	−0.159574	−	0.184159i
$15$	−0.754821	+	6.67687i	−0.194894	+	1.72396i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	−2.99963	−	5.49341i	−0.727517	−	1.33235i	−0.935189	−	0.354149i	$-0.884771\pi$
$17$	−2.99963	−	5.49341i	−0.727517	−	1.33235i	0.207672	−	0.978198i	$-0.433411\pi$
$18$	6.01471	−	0.430181i	1.41768	−	0.101395i
$19$	3.07061	−	0.901613i	0.704447	−	0.206844i	0.0901601	−	0.995927i	$-0.471262\pi$
$19$	3.07061	−	0.901613i	0.704447	−	0.206844i	0.614286	+	0.789083i	$0.289444\pi$
$20$	−2.19833	−	0.409057i	−0.491562	−	0.0914679i
$21$	−2.71194	+	0.389918i	−0.591794	+	0.0850872i
$22$	−3.46616	−	3.46616i	−0.738988	−	0.738988i
$23$	2.84345	−	3.86197i	0.592900	−	0.805276i
$23$	2.84345	−	3.86197i	0.592900	−	0.805276i
$24$			3.00501i			0.613395i
$25$	−2.95240	−	4.03526i	−0.590480	−	0.807052i
$26$	−0.220101	+	0.481955i	−0.0431654	+	0.0945191i
$27$	4.36376	−	7.99162i	0.839805	−	1.53799i
$28$	−0.0650438	−	0.909432i	−0.0122921	−	0.171866i
$29$	−0.421780	+	1.43645i	−0.0783225	+	0.266742i	−0.989340	−	0.145627i	$-0.953480\pi$
$29$	−0.421780	+	1.43645i	−0.0783225	+	0.266742i	0.911017	+	0.412369i	$0.135298\pi$
$30$	−4.60557	+	4.89276i	−0.840857	+	0.893293i
$31$	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	$0.617576\pi$
$32$	−0.997452	−	0.0713392i	−0.176326	−	0.0126111i
$33$	−14.3936	+	3.13113i	−2.50560	+	0.545060i
$34$	0.890751	−	6.19531i	0.152763	−	1.06249i
$35$	1.28792	−	1.58043i	0.217698	−	0.267141i
$36$	5.07282	+	3.26011i	0.845470	+	0.543351i
$37$	−0.415006	+	5.80254i	−0.0682265	+	0.953932i	0.841909	+	0.539620i	$0.181432\pi$
$37$	−0.415006	+	5.80254i	−0.0682265	+	0.953932i	−0.910135	+	0.414312i	$0.864022\pi$
$38$	2.99847	+	1.11837i	0.486416	+	0.181424i
$39$	0.860786	+	1.33941i	0.137836	+	0.214477i
$40$	−1.51472	−	1.64488i	−0.239498	−	0.260078i
$41$	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	$0.191508\pi$
$42$	−2.40469	−	1.31306i	−0.371052	−	0.202610i
$43$	4.16001	+	11.1534i	0.634395	+	1.70088i	0.710424	+	0.703774i	$0.248503\pi$
$43$	4.16001	+	11.1534i	0.634395	+	1.70088i	−0.0760291	+	0.997106i	$0.524224\pi$
$44$	−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	−0.736805	−	0.676106i	$-0.763666\pi$
$47$	−0.416132	+	0.416132i	−0.0606991	+	0.0606991i	0.676106	+	0.736805i	$0.263666\pi$
$48$	−1.80083	+	2.40563i	−0.259928	+	0.347223i
$49$	−5.61125	−	2.56257i	−0.801607	−	0.366082i
$50$	0.0547222	−	4.99970i	0.00773889	−	0.707064i
$51$	−14.2144	−	12.3169i	−1.99042	−	1.72471i
$52$	−0.465025	+	0.253923i	−0.0644874	+	0.0352128i
$53$	0.324331	−	1.49093i	0.0445503	−	0.204795i	−0.949492	−	0.313792i	$-0.898400\pi$
$53$	0.324331	−	1.49093i	0.0445503	−	0.204795i	0.994042	+	0.108998i	$0.0347641\pi$
$54$	8.28257	−	3.78252i	1.12711	−	0.514736i
$55$	6.30046	−	8.96922i	0.849554	−	1.20941i
$56$	0.492932	−	0.767017i	0.0658708	−	0.102497i
$57$	7.69861	−	5.76311i	1.01971	−	0.763342i
$58$	−1.19848	+	0.897174i	−0.157369	+	0.117805i
$59$	−7.41732	+	11.5416i	−0.965653	+	1.50259i	−0.104321	+	0.994544i	$0.533267\pi$
$59$	−7.41732	+	11.5416i	−0.965653	+	1.50259i	−0.861332	+	0.508042i	$0.830369\pi$
$60$	−6.61907	+	1.15685i	−0.854518	+	0.149348i
$61$	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	$0.242917\pi$
$62$	−1.65290	+	7.59825i	−0.209918	+	0.964978i
$63$	−4.82543	+	2.63489i	−0.607948	+	0.331965i
$64$	−0.755750	−	0.654861i	−0.0944687	−	0.0818576i
$65$	−1.14633	−	0.299273i	−0.142184	−	0.0371203i
$66$	−13.3991	−	6.11915i	−1.64931	−	0.753216i
$67$	2.31494	−	3.09240i	0.282815	−	0.377797i	−0.636528	−	0.771254i	$-0.719630\pi$
$67$	2.31494	−	3.09240i	0.282815	−	0.377797i	0.919343	+	0.393457i	$0.128721\pi$
$68$	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	$0.940155\pi$
$72$	2.10730	+	5.64988i	0.248347	+	0.665845i
$73$	0.0520352	+	0.0284134i	0.00609026	+	0.00332553i	0.482291	−	0.876011i	$-0.339805\pi$
$73$	0.0520352	+	0.0284134i	0.00609026	+	0.00332553i	−0.476201	+	0.879336i	$0.657987\pi$
$74$	−3.80956	+	4.39647i	−0.442853	+	0.511079i
$75$	−12.5502	−	8.26100i	−1.44917	−	0.953898i
$76$	1.73018	+	2.69222i	0.198466	+	0.308818i
$77$	4.18753	+	1.56187i	0.477213	+	0.177991i
$78$	−0.113583	+	1.58810i	−0.0128608	+	0.179817i
$79$	−13.7011	−	8.80519i	−1.54150	−	0.990661i	−0.987406	−	0.158206i	$-0.949429\pi$
$79$	−13.7011	−	8.80519i	−1.54150	−	0.990661i	−0.554093	−	0.832455i	$-0.686935\pi$
$80$	−0.226855	−	2.22453i	−0.0253631	−	0.248710i
$81$	1.31948	−	9.17722i	0.146609	−	1.01969i
$82$	1.40304	−	0.305213i	0.154940	−	0.0337052i
$83$	5.83173	+	0.417094i	0.640116	+	0.0457820i	0.387625	−	0.921817i	$-0.373296\pi$
$83$	5.83173	+	0.417094i	0.640116	+	0.0457820i	0.252491	+	0.967599i	$0.418750\pi$
$84$	−1.13817	−	2.49224i	−0.124184	−	0.271925i
$85$	13.9892	−	0.422989i	1.51734	−	0.0458795i
$86$	−3.35373	+	11.4218i	−0.361642	+	1.23164i
$87$	0.320939	+	4.48731i	0.0344083	+	0.481090i
$88$	2.34923	−	4.30229i	0.250428	−	0.458625i
$89$	2.73698	−	5.99315i	0.290119	−	0.635273i	−0.707312	−	0.706901i	$-0.750092\pi$
$89$	2.73698	−	5.99315i	0.290119	−	0.635273i	0.997431	+	0.0716289i	$0.0228197\pi$
$90$	−5.22807	+	12.4289i	−0.551087	+	1.31012i
$91$		−	0.483079i		−	0.0506405i
$92$	4.50662	+	1.64023i	0.469848	+	0.171005i
$93$	16.5228	+	16.5228i	1.71334	+	1.71334i
$94$	−0.582509	+	0.0837522i	−0.0600813	+	0.00863838i
$95$	−1.30908	+	7.03520i	−0.134309	+	0.721797i
$96$	−2.88328	+	0.846609i	−0.294274	+	0.0864066i
$97$	6.39945	−	0.457698i	0.649766	−	0.0464722i	0.257434	−	0.966296i	$-0.417123\pi$
$97$	6.39945	−	0.457698i	0.649766	−	0.0464722i	0.392332	+	0.919824i	$0.371668\pi$
$98$	−2.95634	−	5.41414i	−0.298636	−	0.546911i
$99$	−24.8664	+	15.9807i	−2.49917	+	1.60612i
$100$	3.04002	−	3.96967i	0.304002	−	0.396967i
$101$	−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	$-0.558427\pi$
$102$	−3.99801	−	18.3786i	−0.395862	−	1.81975i
$103$	10.8770	+	14.5300i	1.07174	+	1.43168i	0.894256	+	0.447555i	$0.147705\pi$
$103$	10.8770	+	14.5300i	1.07174	+	1.43168i	0.177485	+	0.984124i	$0.443204\pi$
$104$	−0.524442	−	0.0754034i	−0.0514258	−	0.00739391i
$105$	1.96651	−	5.80226i	0.191912	−	0.566242i
$106$	1.15312	−	0.999184i	0.112001	−	0.0970493i
$107$	−1.90823	+	5.11616i	−0.184475	+	0.494598i	−0.995962	−	0.0897731i	$-0.971386\pi$
$107$	−1.90823	+	5.11616i	−0.184475	+	0.494598i	0.811487	+	0.584371i	$0.198659\pi$
$108$	8.89732	+	1.93549i	0.856145	+	0.186243i
$109$	1.94333	+	0.570612i	0.186137	+	0.0546547i	0.373473	−	0.927641i	$-0.378167\pi$
$109$	1.94333	+	0.570612i	0.186137	+	0.0546547i	−0.187336	+	0.982296i	$0.559985\pi$
$110$	10.4188	−	3.40450i	0.993396	−	0.324607i
$111$	4.92503	+	16.7731i	0.467463	+	1.59203i
$112$	0.854268	−	0.318626i	0.0807208	−	0.0301073i
$113$	1.71240	+	1.28189i	0.161089	+	0.120590i	0.676781	−	0.736184i	$-0.263374\pi$
$113$	1.71240	+	1.28189i	0.161089	+	0.120590i	−0.515692	+	0.856774i	$0.672465\pi$
$114$	9.61676			0.900692
$115$	4.82384	+	9.57761i	0.449825	+	0.893117i
$116$	−1.49709			−0.139002
$117$	2.55769	+	1.91466i	0.236458	+	0.177010i
$118$	−12.8545	+	4.79447i	−1.18335	+	0.441367i
$119$	1.60776	+	5.47553i	0.147383	+	0.501941i
$120$	−5.99211	−	3.04056i	−0.547002	−	0.277564i
$121$	12.5008	+	3.67056i	1.13643	+	0.333687i
$122$	5.65094	+	1.22929i	0.511612	+	0.111294i
$123$	1.50785	−	4.04271i	0.135959	−	0.364519i
$124$	−5.87667	+	5.09217i	−0.527741	+	0.457290i
$125$	11.0338	−	1.80421i	0.986893	−	0.161374i
$126$	−5.44199	−	0.782440i	−0.484811	−	0.0697053i
$127$	3.56565	+	4.76314i	0.316400	+	0.422661i	0.930344	−	0.366689i	$-0.119509\pi$
$127$	3.56565	+	4.76314i	0.316400	+	0.422661i	−0.613944	+	0.789350i	$0.710418\pi$
$128$	−0.212565	−	0.977147i	−0.0187883	−	0.0863684i
$129$	23.4253	+	27.0343i	2.06249	+	2.38024i
$130$	−0.738333	−	0.926548i	−0.0647561	−	0.0812636i
$131$	−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	$0.373497\pi$
$132$	−7.05944	−	12.9284i	−0.614446	−	1.12527i
$133$	−2.91040	+	0.208156i	−0.252364	+	0.0180494i
$134$	3.70641	−	1.08830i	0.320185	−	0.0940149i
$135$	11.5202	+	16.7877i	0.991505	+	1.44485i
$136$	6.19531	−	0.890751i	0.531244	−	0.0763813i
$137$	−0.539311	−	0.539311i	−0.0460764	−	0.0460764i	0.683693	−	0.729770i	$-0.260373\pi$
$137$	−0.539311	−	0.539311i	−0.0460764	−	0.0460764i	−0.729770	+	0.683693i	$0.760373\pi$
$138$	11.4680	−	8.72787i	0.976225	−	0.742965i
$139$		−	20.8398i		−	1.76761i	−0.467856	−	0.883805i	$-0.654973\pi$
$139$		−	20.8398i		−	1.76761i	0.467856	−	0.883805i	$-0.345027\pi$
$140$	1.87926	+	0.790490i	0.158826	+	0.0668086i
$141$	−0.734639	+	1.60864i	−0.0618678	+	0.135472i
$142$	−0.364999	+	0.668446i	−0.0306301	+	0.0560947i
$143$	−0.185282	−	2.59058i	−0.0154940	−	0.216635i
$144$	−1.69887	+	5.78582i	−0.141572	+	0.482151i
$145$	−2.43757	−	2.29449i	−0.202429	−	0.190547i
$146$	0.0246288	+	0.0539296i	0.00203830	+	0.00446324i
$147$	−18.4898	−	1.32241i	−1.52501	−	0.109071i
$148$	−5.68442	+	1.23657i	−0.467256	+	0.101645i
$149$	0.412638	−	2.86996i	0.0338046	−	0.235116i	−0.965913	−	0.258866i	$-0.916651\pi$
$149$	0.412638	−	2.86996i	0.0338046	−	0.235116i	0.999718	+	0.0237495i	$0.00756041\pi$
$150$	−5.09633	−	14.1343i	−0.416113	−	1.15406i
$151$	−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	$0.829973\pi$
$152$	−0.228303	+	3.19209i	−0.0185178	+	0.258913i
$153$	−35.3627	−	13.1896i	−2.85890	−	1.06632i
$154$	2.41630	+	3.75983i	0.194711	+	0.302976i
$155$	−17.3728	−	0.715683i	−1.39542	−	0.0574850i
$156$	−1.04264	+	1.20327i	−0.0834782	+	0.0963390i
$157$	3.39999	+	1.85653i	0.271349	+	0.148168i	0.609163	−	0.793045i	$-0.291506\pi$
$157$	3.39999	+	1.85653i	0.271349	+	0.148168i	−0.337814	+	0.941213i	$0.609687\pi$
$158$	−5.69158	−	15.2597i	−0.452797	−	1.21400i
$159$	−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
$163$	8.98517	−	12.0028i	0.703773	−	0.940131i	−0.296114	−	0.955153i	$-0.595691\pi$
$163$	8.98517	−	12.0028i	0.703773	−	0.940131i	0.999887	+	0.0150219i	$0.00478179\pi$
$164$	1.30610	+	0.596476i	0.101989	+	0.0465770i
$165$	8.32025	−	31.8696i	0.647731	−	2.48104i
$166$	4.41859	+	3.82873i	0.342949	+	0.297167i
$167$	1.72748	−	0.943274i	0.133676	−	0.0729928i	−0.411019	−	0.911627i	$-0.634827\pi$
$167$	1.72748	−	0.943274i	0.133676	−	0.0729928i	0.544695	+	0.838634i	$0.316645\pi$
$168$	0.582393	−	2.67722i	0.0449326	−	0.206552i
$169$	11.5699	−	5.28378i	0.889989	−	0.406444i
$170$	11.4524	+	8.04479i	0.878360	+	0.617008i
$171$	10.4331	−	16.2343i	0.797841	−	1.24147i
$172$	−9.52961	+	7.13378i	−0.726626	+	0.543945i
$173$	−11.1152	+	8.32071i	−0.845071	+	0.632612i	−0.931539	−	0.363643i	$-0.881533\pi$
$173$	−11.1152	+	8.32071i	−0.845071	+	0.632612i	0.0864679	+	0.996255i	$0.472442\pi$
$174$	−2.43222	+	3.78461i	−0.184386	+	0.286911i
$175$	1.84828	+	4.16728i	0.139717	+	0.315017i
$176$	4.45892	−	2.03632i	0.336103	−	0.153493i
$177$	−8.76348	+	40.2851i	−0.658703	+	3.02801i
$178$	5.78263	−	3.15755i	0.433426	−	0.236669i
$179$	−9.16986	−	7.94573i	−0.685388	−	0.593892i	0.240972	−	0.970532i	$-0.422534\pi$
$179$	−9.16986	−	7.94573i	−0.685388	−	0.593892i	−0.926360	+	0.376640i	$0.877079\pi$
$180$	−11.6336	+	6.81675i	−0.867119	+	0.508090i
$181$	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	$0.559998\pi$
$182$	0.289499	−	0.386725i	0.0214591	−	0.0286660i
$183$	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
$187$	10.7219	+	28.7466i	0.784064	+	2.10216i
$188$	−0.516514	−	0.282038i	−0.0376706	−	0.0205697i
$189$	−5.43658	+	6.27415i	−0.395453	+	0.456377i
$190$	−5.26402	+	4.84747i	−0.381892	+	0.351672i
$191$	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	$0.533297\pi$
$192$	−2.81554	−	1.05014i	−0.203194	−	0.0757875i
$193$	1.42013	−	19.8560i	0.102223	−	1.42927i	−0.644740	−	0.764402i	$-0.723034\pi$
$193$	1.42013	−	19.8560i	0.102223	−	1.42927i	0.746963	−	0.664865i	$-0.231511\pi$
$194$	5.39731	+	3.46864i	0.387504	+	0.249034i
$195$	−3.54181	+	0.361189i	−0.253634	+	0.0258653i
$196$	0.877898	−	6.10592i	0.0627070	−	0.436137i
$197$	16.4673	−	3.58225i	1.17325	−	0.255224i	0.416626	−	0.909078i	$-0.363212\pi$
$197$	16.4673	−	3.58225i	1.17325	−	0.255224i	0.756621	+	0.653853i	$0.226849\pi$
$198$	−29.4835	−	2.10870i	−2.09530	−	0.149859i
$199$	0.726464	+	1.59073i	0.0514976	+	0.112764i	0.933632	−	0.358234i	$-0.116621\pi$
$199$	0.726464	+	1.59073i	0.0514976	+	0.112764i	−0.882134	+	0.470998i	$0.843894\pi$
$200$	4.81259	−	1.35607i	0.340302	−	0.0958888i
$201$	3.27035	−	11.1378i	0.230673	−	0.785600i
$202$	−1.23686	−	17.2935i	−0.0870250	−	1.21677i
$203$	0.654166	−	1.19802i	0.0459134	−	0.0840842i
$204$	7.81329	−	17.1087i	0.547040	−	1.19785i
$205$	1.21242	+	2.97295i	0.0846791	+	0.207640i
$206$			18.1502i			1.26458i
$207$	−2.29213	−	28.8282i	−0.159314	−	2.00370i
$208$	−0.374650	−	0.374650i	−0.0259773	−	0.0259773i
$209$	−15.5276	+	2.23253i	−1.07406	+	0.154427i
$210$	5.05144	−	3.46646i	0.348582	−	0.239208i
$211$	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	$0.151683\pi$
$212$	1.52191	−	0.108849i	0.104525	−	0.00747578i
$213$	1.09683	+	2.00869i	0.0751533	+	0.137633i
$214$	−4.59361	+	2.95214i	−0.314013	+	0.201804i
$215$	−26.4496	−	2.99013i	−1.80385	−	0.203925i
$216$	5.96277	+	6.88141i	0.405715	+	0.468220i
$217$	−1.50704	−	6.92774i	−0.102304	−	0.470285i
$218$	1.21376	+	1.62139i	0.0822061	+	0.109814i
$219$	0.176345	+	0.0253546i	0.0119163	+	0.00171331i
$220$	10.3809	+	3.51833i	0.699883	+	0.237206i
$221$	2.50625	−	2.17168i	0.168589	−	0.146083i
$222$	−6.10906	+	16.3790i	−0.410013	+	1.09929i
$223$	−18.1350	−	3.94503i	−1.21441	−	0.264179i	−0.440662	−	0.897673i	$-0.645256\pi$
$223$	−18.1350	−	3.94503i	−1.21441	−	0.264179i	−0.773747	+	0.633494i	$0.781620\pi$
$224$	0.874822	+	0.256871i	0.0584515	+	0.0171629i
$225$	−29.3894	−	6.73098i	−1.95930	−	0.448732i
$226$	0.602642	+	2.05241i	0.0400871	+	0.136524i
$227$	−7.80769	+	2.91212i	−0.518215	+	0.193284i	−0.594943	−	0.803768i	$-0.702825\pi$
$227$	−7.80769	+	2.91212i	−0.518215	+	0.193284i	0.0767281	+	0.997052i	$0.475553\pi$
$228$	7.69861	+	5.76311i	0.509853	+	0.381671i
$229$	−11.3403			−0.749388			−0.374694	−	0.927148i	$-0.622252\pi$
$229$	−11.3403			−0.749388			−0.374694	+	0.927148i	$0.622252\pi$
$230$	−1.87797	+	10.5581i	−0.123829	+	0.696180i
$231$	13.4303			0.883652
$232$	−1.19848	−	0.897174i	−0.0786843	−	0.0589024i
$233$	16.1734	−	6.03235i	1.05955	−	0.395192i	0.241538	−	0.970391i	$-0.422348\pi$
$233$	16.1734	−	6.03235i	1.05955	−	0.395192i	0.818014	+	0.575199i	$0.195075\pi$
$234$	0.900120	+	3.06553i	0.0588427	+	0.200400i
$235$	−0.408730	−	1.25084i	−0.0266626	−	0.0815958i
$236$	−13.1638	−	3.86523i	−0.856888	−	0.251605i
$237$	−47.8228	−	10.4032i	−3.10643	−	0.675762i
$238$	−1.99428	+	5.34688i	−0.129270	+	0.346587i
$239$	−9.97290	+	8.64156i	−0.645093	+	0.558976i	−0.914770	−	0.403974i	$-0.867628\pi$
$239$	−9.97290	+	8.64156i	−0.645093	+	0.558976i	0.269677	+	0.962951i	$0.413083\pi$
$240$	−2.97479	−	6.02503i	−0.192022	−	0.388914i
$241$	−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	$0.779763\pi$
$242$	7.80770	+	10.4299i	0.501898	+	0.670458i
$243$	−0.115846	−	0.532537i	−0.00743155	−	0.0341623i
$244$	3.78712	+	4.37057i	0.242446	+	0.279797i
$245$	10.7875	−	8.59618i	0.689188	−	0.549190i
$246$	3.62981	−	2.33274i	0.231428	−	0.148730i
$247$	0.812615	+	1.48819i	0.0517055	+	0.0946915i
$248$	−7.75614	+	0.554730i	−0.492515	+	0.0352254i
$249$	16.8575	−	4.94981i	1.06830	−	0.313681i
$250$	9.91424	+	5.16796i	0.627032	+	0.326851i
$251$	−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
$253$	−16.4906	+	16.7546i	−1.03675	+	1.05335i
$254$			5.94990i			0.373330i
$255$	38.9430	−	15.8816i	2.43870	−	0.994544i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	6.49684	−	11.8981i	0.405262	−	0.742182i	−0.592738	−	0.805395i	$-0.701953\pi$
$257$	6.49684	−	11.8981i	0.405262	−	0.742182i	0.998000	+	0.0632136i	$0.0201349\pi$
$258$	2.55191	+	35.6804i	0.158875	+	2.22136i
$259$	1.49431	−	5.08916i	0.0928520	−	0.316225i
$260$	−0.0358066	−	1.18421i	−0.00222063	−	0.0734413i
$261$	3.75019	+	8.21178i	0.232131	+	0.508296i
$262$	−3.94786	−	0.282357i	−0.243900	−	0.0174440i
$263$	−13.4695	+	2.93011i	−0.830566	+	0.180679i	−0.607696	−	0.794170i	$-0.707906\pi$
$263$	−13.4695	+	2.93011i	−0.830566	+	0.180679i	−0.222870	+	0.974848i	$0.571542\pi$
$264$	2.09633	−	14.5803i	0.129020	−	0.897355i
$265$	2.64480	+	2.15529i	0.162469	+	0.132399i
$266$	−2.45464	−	1.57750i	−0.150504	−	0.0967228i
$267$	1.41242	−	19.7482i	0.0864386	−	1.20857i
$268$	3.61933	+	1.34994i	0.221086	+	0.0824607i
$269$	−10.0072	−	15.5715i	−0.610150	−	0.949412i	−0.999598	−	0.0283632i	$-0.990970\pi$
$269$	−10.0072	−	15.5715i	−0.610150	−	0.949412i	0.389448	−	0.921049i	$-0.372666\pi$
$270$	−0.838043	+	20.3430i	−0.0510016	+	1.23804i
$271$	−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	$0.360214\pi$
$272$	5.49341	+	2.99963i	0.333087	+	0.181879i
$273$	−0.507302	−	1.36013i	−0.0307033	−	0.0823188i
$274$	−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	−0.627037	−	0.778990i	$-0.715732\pi$
$277$	2.52900	−	2.52900i	0.151953	−	0.151953i	0.778990	+	0.627037i	$0.215732\pi$
$278$	12.4888	−	16.6831i	0.749030	−	1.00059i
$279$	42.6523	+	19.4786i	2.55352	+	1.16616i
$280$	1.03070	+	1.75902i	0.0615961	+	0.105121i
$281$	−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	$0.852764\pi$
$282$	−1.55213	+	0.847526i	−0.0924279	+	0.0504694i
$283$	4.92706	−	22.6493i	0.292883	−	1.34636i	−0.561827	−	0.827255i	$-0.689901\pi$
$283$	4.92706	−	22.6493i	0.292883	−	1.34636i	0.854710	−	0.519106i	$-0.173735\pi$
$284$	−0.692782	+	0.316383i	−0.0411090	+	0.0187739i
$285$	3.70219	+	21.1826i	0.219299	+	1.25475i
$286$	1.40415	−	2.18490i	0.0830290	−	0.129196i
$287$	−1.04803	+	0.784544i	−0.0618631	+	0.0463101i
$288$	−4.82732	+	3.61369i	−0.284453	+	0.212939i
$289$	−11.9889	+	18.6551i	−0.705228	+	1.09736i
$290$	−0.576340	−	3.29761i	−0.0338439	−	0.193643i
$291$	17.5373	−	8.00901i	1.02805	−	0.469496i
$292$	−0.0126024	+	0.0579324i	−0.000737500	+	0.00339023i
$293$	8.78180	−	4.79522i	0.513038	−	0.280140i	−0.201804	−	0.979426i	$-0.564680\pi$
$293$	8.78180	−	4.79522i	0.513038	−	0.280140i	0.714842	+	0.699286i	$0.246499\pi$
$294$	−14.0093	−	12.1392i	−0.817041	−	0.707970i
$295$	−15.5093	−	26.4686i	−0.902988	−	1.54106i
$296$	−5.29166	−	2.41662i	−0.307571	−	0.140463i
$297$	−26.7480	+	35.7311i	−1.55207	+	2.07333i
$298$	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
$302$	−3.85470	−	10.3349i	−0.221813	−	0.594705i
$303$	−45.7270	−	24.9688i	−2.62695	−	1.43442i
$304$	−2.09571	+	2.41858i	−0.120197	+	0.138715i
$305$	−0.532264	+	12.9204i	−0.0304774	+	0.739822i
$306$	−20.4051	−	31.7509i	−1.16648	−	1.81508i
$307$	3.54578	+	1.32251i	0.202368	+	0.0754795i	0.448605	−	0.893730i	$-0.351921\pi$
$307$	3.54578	+	1.32251i	0.202368	+	0.0754795i	−0.246236	+	0.969210i	$0.579194\pi$
$308$	−0.318838	+	4.45793i	−0.0181675	+	0.254014i
$309$	45.8831	+	29.4873i	2.61020	+	1.67747i
$310$	−13.4788	−	10.9841i	−0.765543	−	0.623854i
$311$	−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	$0.866037\pi$
$312$	−1.55577	+	0.338438i	−0.0880783	+	0.0191603i
$313$	1.87192	+	0.133883i	0.105807	+	0.00756749i	0.124142	−	0.992264i	$-0.460382\pi$
$313$	1.87192	+	0.133883i	0.105807	+	0.00756749i	−0.0183351	+	0.999832i	$0.505837\pi$
$314$	1.60925	+	3.52377i	0.0908153	+	0.198858i
$315$	−0.371555	−	12.2882i	−0.0209348	−	0.692360i
$316$	4.58846	−	15.6269i	0.258121	−	0.879079i
$317$	−0.414602	−	5.79689i	−0.0232863	−	0.325586i	−0.995721	−	0.0924102i	$-0.970543\pi$
$317$	−0.414602	−	5.79689i	−0.0232863	−	0.325586i	0.972435	−	0.233175i	$-0.0749117\pi$
$318$	2.19737	−	4.02418i	0.123222	−	0.225665i
$319$	3.04856	−	6.67541i	0.170686	−	0.373751i
$320$	2.07051	−	0.844388i	0.115745	−	0.0472027i
$321$			16.4087i			0.915842i
$322$	−4.35886	+	0.346573i	−0.242910	+	0.0193137i
$323$	−14.1636	−	14.1636i	−0.788085	−	0.788085i
$324$	9.17722	−	1.31948i	0.509845	−	0.0733047i
$325$	1.75665	−	1.98301i	0.0974413	−	0.109997i
$326$	14.3860	−	4.22411i	0.796767	−	0.233952i
$327$	6.07074	−	0.434188i	0.335713	−	0.0240107i
$328$	0.688133	+	1.26022i	0.0379958	+	0.0695841i
$329$	0.451389	−	0.290090i	0.0248859	−	0.0159932i
$330$	25.7594	−	20.5268i	1.41801	−	1.12996i
$331$	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	$0.669540\pi$
$332$	1.24279	+	5.71301i	0.0682070	+	0.313542i
$333$	21.0221	+	28.0823i	1.15201	+	1.53890i
$334$	1.94820	+	0.280109i	0.106601	+	0.0153269i
$335$	3.82405	+	7.74507i	0.208930	+	0.423158i
$336$	2.07063	−	1.79421i	0.112962	−	0.0978820i
$337$	5.30737	−	14.2296i	0.289111	−	0.775137i	−0.708478	−	0.705733i	$-0.750618\pi$
$337$	5.30737	−	14.2296i	0.289111	−	0.775137i	0.997589	−	0.0694034i	$-0.0221096\pi$
$338$	12.4286	+	2.70368i	0.676027	+	0.147061i
$339$	6.16751	+	1.81094i	0.334973	+	0.0983569i
$340$	4.34707	+	13.3034i	0.235753	+	0.721476i
$341$	−10.7388	−	36.5729i	−0.581536	−	1.98053i
$342$	18.0810	−	6.74386i	0.977708	−	0.364666i
$343$	9.61180	+	7.19530i	0.518988	+	0.388510i
$344$	−11.9040			−0.641818
$345$	23.6396	+	21.9004i	1.27271	+	1.17908i
$346$	−13.8846			−0.746439
$347$	23.7340	+	17.7670i	1.27411	+	0.953783i	0.999969	−	0.00790725i	$-0.00251698\pi$
$347$	23.7340	+	17.7670i	1.27411	+	0.953783i	0.274137	+	0.961691i	$0.411608\pi$
$348$	−4.21513	+	1.57216i	−0.225954	+	0.0842767i
$349$	−0.612171	−	2.08486i	−0.0327688	−	0.111600i	0.941485	−	0.337056i	$-0.109431\pi$
$349$	−0.612171	−	2.08486i	−0.0327688	−	0.111600i	−0.974253	+	0.225456i	$0.927613\pi$
$350$	−1.01773	+	4.44372i	−0.0544001	+	0.237527i
$351$	4.62894	+	1.35918i	0.247075	+	0.0725477i
$352$	4.78987	+	1.04197i	0.255301	+	0.0555373i
$353$	−9.23286	+	24.7543i	−0.491416	+	1.31754i	0.420550	+	0.907269i	$0.361837\pi$
$353$	−9.23286	+	24.7543i	−0.491416	+	1.31754i	−0.911966	+	0.410267i	$0.865436\pi$
$354$	−31.1575	+	26.9981i	−1.65600	+	1.43493i
$355$	−1.61289	−	0.546642i	−0.0856032	−	0.0290128i
$356$	6.52148	+	0.937647i	0.345638	+	0.0496952i
$357$	10.2768	+	13.7282i	0.543906	+	0.726573i
$358$	−2.57915	−	11.8562i	−0.136313	−	0.626619i
$359$	−10.9116	−	12.5926i	−0.575891	−	0.664614i	0.390825	−	0.920465i	$-0.372190\pi$
$359$	−10.9116	−	12.5926i	−0.575891	−	0.664614i	−0.966716	+	0.255851i	$0.917644\pi$
$360$	−13.3983	−	1.51468i	−0.706153	−	0.0798306i
$361$	−7.36807	+	4.73517i	−0.387793	+	0.249220i
$362$	3.06410	+	5.61147i	0.161045	+	0.294933i
$363$	39.0511	−	2.79299i	2.04965	−	0.146594i
$364$	0.463511	−	0.136099i	0.0242946	−	0.00713354i
$365$	−0.109308	+	0.0750108i	−0.00572145	+	0.00392625i
$366$	17.2014	−	2.47318i	0.899130	−	0.129275i
$367$	−21.0752	−	21.0752i	−1.10012	−	1.10012i	−0.994396	−	0.105720i	$-0.966285\pi$
$367$	−21.0752	−	21.0752i	−1.10012	−	1.10012i	−0.105720	−	0.994396i	$-0.533715\pi$
$368$	−0.304124	+	4.78618i	−0.0158535	+	0.249497i
$369$		−	8.65832i		−	0.450734i
$370$	−4.91211	−	12.0449i	−0.255369	−	0.626185i
$371$	−0.577905	+	1.26544i	−0.0300033	+	0.0656981i
$372$	−11.1985	+	20.5086i	−0.580616	+	1.06332i
$373$	1.00695	+	14.0789i	0.0521377	+	0.728980i	0.954540	+	0.298084i	$0.0963477\pi$
$373$	1.00695	+	14.0789i	0.0521377	+	0.728980i	−0.902402	+	0.430895i	$0.858198\pi$
$374$	−8.64384	+	29.4382i	−0.446962	+	1.52221i
$375$	29.1715	−	16.6669i	1.50641	−	0.860676i
$376$	−0.244472	−	0.535318i	−0.0126077	−	0.0276069i
$377$	−0.791191	−	0.0565871i	−0.0407484	−	0.00291438i
$378$	−8.11217	+	1.76469i	−0.417245	+	0.0907661i
$379$	−1.62209	+	11.2819i	−0.0833209	+	0.579510i	0.904801	+	0.425835i	$0.140020\pi$
$379$	−1.62209	+	11.2819i	−0.0833209	+	0.579510i	−0.988122	+	0.153674i	$0.950889\pi$
$380$	−7.11904	+	0.725991i	−0.365199	+	0.0372425i
$381$	15.0412	+	9.66640i	0.770584	+	0.495224i
$382$	−1.53845	+	21.5103i	−0.0787140	+	1.10056i
$383$	8.32529	+	3.10517i	0.425402	+	0.158667i	0.553041	−	0.833154i	$-0.313467\pi$
$383$	8.32529	+	3.10517i	0.425402	+	0.158667i	−0.127639	+	0.991821i	$0.540740\pi$
$384$	−1.62463	−	2.52797i	−0.0829066	−	0.129005i
$385$	−7.35149	+	6.76976i	−0.374667	+	0.345019i
$386$	13.0361	−	15.0445i	0.663522	−	0.765745i
$387$	63.0014	+	34.4013i	3.20254	+	1.74872i
$388$	2.24209	+	6.01128i	0.113825	+	0.305177i
$389$	3.06001	+	21.2829i	0.155149	+	1.07908i	0.907418	+	0.420228i	$0.138050\pi$
$389$	3.06001	+	21.2829i	0.155149	+	1.07908i	−0.752270	+	0.658855i	$0.771041\pi$
$390$	−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
$393$	−7.12760	+	9.52136i	−0.359540	+	0.480289i
$394$	15.3295	+	7.00076i	0.772290	+	0.352693i
$395$	31.4211	−	18.4113i	1.58097	−	0.926373i
$396$	−22.3390	−	19.3569i	−1.12258	−	0.972720i
$397$	−34.0588	+	18.5975i	−1.70936	+	0.933383i	−0.745692	+	0.666291i	$0.767881\pi$
$397$	−34.0588	+	18.5975i	−1.70936	+	0.933383i	−0.963671	+	0.267092i	$0.913937\pi$
$398$	−0.371727	+	1.70880i	−0.0186330	+	0.0856545i
$399$	−7.97577	+	3.64241i	−0.399288	+	0.182349i
$400$	4.66534	+	1.79849i	0.233267	+	0.0899244i
$401$	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	$-0.0880066\pi$
$402$	9.29269	−	6.95642i	0.463477	−	0.346955i
$403$	−3.29821	+	2.46901i	−0.164295	+	0.122990i
$404$	9.37347	−	14.5854i	0.466347	−	0.725651i
$405$	16.9647	+	11.9169i	0.842981	+	0.592155i
$406$	1.24163	−	0.567034i	0.0616211	−	0.0281414i
$407$	6.06153	−	27.8644i	0.300459	−	1.38119i
$408$	16.5077	−	9.01391i	0.817255	−	0.446255i
$409$	−17.0511	−	14.7749i	−0.843125	−	0.730572i	0.121953	−	0.992536i	$-0.461084\pi$
$409$	−17.0511	−	14.7749i	−0.843125	−	0.730572i	−0.965078	+	0.261964i	$0.915630\pi$
$410$	−0.811032	+	3.10655i	−0.0400540	+	0.153421i
$411$	−2.08480	−	0.952098i	−0.102836	−	0.0469635i
$412$	−10.8770	+	14.5300i	−0.535871	+	0.715839i
$413$	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
$417$	−21.8848	−	58.6754i	−1.07170	−	2.87334i
$418$	−13.7684	−	7.51809i	−0.673433	−	0.367722i
$419$	−7.25412	+	8.37170i	−0.354387	+	0.408984i	−0.904751	−	0.425940i	$-0.859943\pi$
$419$	−7.25412	+	8.37170i	−0.354387	+	0.408984i	0.550364	+	0.834925i	$0.314489\pi$
$420$	6.12125	+	0.252168i	0.298687	+	0.0123046i
$421$	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	$0.628817\pi$
$422$	19.6901	+	7.34402i	0.958499	+	0.357502i
$423$	−0.253161	+	3.53966i	−0.0123091	+	0.172104i
$424$	1.28358	+	0.824907i	0.0623362	+	0.0400610i
$425$	−13.3112	+	28.3230i	−0.645689	+	1.37387i
$426$	−0.325707	+	2.26534i	−0.0157805	+	0.109756i
$427$	−5.15227	+	1.12081i	−0.249336	+	0.0542397i
$428$	−5.44653	−	0.389543i	−0.263268	−	0.0188293i
$429$	−3.24214	−	7.09930i	−0.156532	−	0.342758i
$430$	−19.3821	−	18.2444i	−0.934686	−	0.879821i
$431$	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	$-0.00635991\pi$
$432$	0.649572	+	9.08220i	0.0312526	+	0.436968i
$433$	−8.08756	+	14.8113i	−0.388663	+	0.711784i	−0.996617	−	0.0821889i	$-0.973809\pi$
$433$	−8.08756	+	14.8113i	−0.388663	+	0.711784i	0.607953	+	0.793973i	$0.291991\pi$
$434$	2.94519	−	6.44907i	0.141374	−	0.309565i
$435$	−9.27262	−	3.90043i	−0.444588	−	0.187011i
$436$			2.02537i			0.0969976i
$437$	5.24913	−	14.4223i	0.251100	−	0.689912i
$438$	0.125977	+	0.125977i	0.00601942	+	0.00601942i
$439$	9.58365	−	1.37792i	0.457403	−	0.0657646i	0.0902374	−	0.995920i	$-0.471237\pi$
$439$	9.58365	−	1.37792i	0.457403	−	0.0657646i	0.367165	+	0.930156i	$0.380328\pi$
$440$	6.20192	+	9.03763i	0.295665	+	0.430852i
$441$	−35.6910	+	10.4798i	−1.69957	+	0.499039i
$442$	3.30780	−	0.236578i	0.157336	−	0.0112529i
$443$	12.0331	+	22.0369i	0.571708	+	1.04701i	0.990315	+	0.138838i	$0.0443367\pi$
$443$	12.0331	+	22.0369i	0.571708	+	1.04701i	−0.418607	+	0.908168i	$0.637481\pi$
$444$	−14.7061	+	9.45106i	−0.697923	+	0.448528i
$445$	9.18123	+	11.5217i	0.435232	+	0.546181i
$446$	−12.1537	−	14.0261i	−0.575492	−	0.664153i
$447$	−1.85207	−	8.51381i	−0.0875998	−	0.402690i
$448$	0.546394	+	0.729897i	0.0258147	+	0.0344844i
$449$	26.6011	+	3.82466i	1.25538	+	0.180497i	0.737731	−	0.675094i	$-0.235897\pi$
$449$	26.6011	+	3.82466i	1.25538	+	0.180497i	0.517652	+	0.855591i	$0.326806\pi$
$450$	−19.4937	−	23.0009i	−0.918944	−	1.08427i
$451$	−5.31928	+	4.60918i	−0.250475	+	0.217038i
$452$	−0.747523	+	2.00419i	−0.0351605	+	0.0942691i
$453$	−32.3887	−	7.04574i	−1.52176	−	0.331038i
$454$	−7.99555	−	2.34771i	−0.375250	−	0.110183i
$455$	0.963280	+	0.488794i	0.0451593	+	0.0229150i
$456$	2.70935	+	9.22721i	0.126877	+	0.432104i
$457$	−16.6265	+	6.20136i	−0.777755	+	0.290087i	−0.706820	−	0.707393i	$-0.749871\pi$
$457$	−16.6265	+	6.20136i	−0.777755	+	0.290087i	−0.0709347	+	0.997481i	$0.522598\pi$
$458$	−9.07838	−	6.79599i	−0.424205	−	0.317556i
$459$	−56.9909			−2.66011
$460$	−7.83062	+	7.32676i	−0.365104	+	0.341612i
$461$	−17.7750			−0.827863			−0.413932	−	0.910308i	$-0.635845\pi$
$461$	−17.7750			−0.827863			−0.413932	+	0.910308i	$0.635845\pi$
$462$	10.7515	+	8.04851i	0.500207	+	0.374450i
$463$	−12.0021	+	4.47656i	−0.557786	+	0.208043i	−0.612516	−	0.790458i	$-0.709843\pi$
$463$	−12.0021	+	4.47656i	−0.557786	+	0.208043i	0.0547308	+	0.998501i	$0.482570\pi$
$464$	−0.421780	−	1.43645i	−0.0195806	−	0.0666855i
$465$	−49.6655	+	16.2289i	−2.30318	+	0.752598i
$466$	16.5625	+	4.86319i	0.767243	+	0.225283i
$467$	6.80762	+	1.48091i	0.315019	+	0.0685282i	0.367295	−	0.930104i	$-0.380284\pi$
$467$	6.80762	+	1.48091i	0.315019	+	0.0685282i	−0.0522760	+	0.998633i	$0.516648\pi$
$468$	−1.11652	+	2.99350i	−0.0516111	+	0.138375i
$469$	−2.66175	+	2.30642i	−0.122908	+	0.106501i
$470$	0.422395	−	1.24629i	0.0194836	−	0.0574871i
$471$	11.5224	+	1.65668i	0.530926	+	0.0763356i
$472$	−8.22179	−	10.9830i	−0.378439	−	0.505535i
$473$	−12.4036	−	57.0184i	−0.570318	−	2.62171i
$474$	−32.0497	−	36.9874i	−1.47209	−	1.69889i
$475$	−12.7039	−	9.72879i	−0.582896	−	0.446388i
$476$	−4.80077	+	3.08527i	−0.220043	+	0.141413i
$477$	−4.40941	−	8.07523i	−0.201893	−	0.369739i
$478$	−13.1624	+	0.941394i	−0.602035	+	0.0430584i
$479$	16.1425	−	4.73988i	0.737572	−	0.216571i	0.108695	−	0.994075i	$-0.465333\pi$
$479$	16.1425	−	4.73988i	0.737572	−	0.216571i	0.628877	+	0.777505i	$0.283515\pi$
$480$	1.22922	−	6.60601i	0.0561060	−	0.301522i
$481$	−3.05087	+	0.438649i	−0.139108	+	0.0200007i
$482$	−14.7403	−	14.7403i	−0.671404	−	0.671404i
$483$	−6.20542	+	11.5821i	−0.282356	+	0.527006i
$484$			13.0285i			0.592206i
$485$	−5.56249	+	13.2239i	−0.252579	+	0.600466i
$486$	0.226398	−	0.495742i	0.0102696	−	0.0224873i
$487$	−9.45494	+	17.3154i	−0.428444	+	0.784637i	−0.999338	−	0.0363872i	$-0.988415\pi$
$487$	−9.45494	+	17.3154i	−0.428444	+	0.784637i	0.570894	+	0.821024i	$0.306597\pi$
$488$	0.412561	+	5.76836i	0.0186758	+	0.261122i
$489$	12.6935	−	43.2301i	0.574019	−	1.95493i
$490$	13.7873	−	0.416885i	0.622849	−	0.0188329i
$491$	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	$0.799846\pi$
$492$	4.30377	+	0.307811i	0.194029	+	0.0138772i
$493$	9.15619	−	1.99181i	0.412374	−	0.0897065i
$494$	−0.241309	+	1.67834i	−0.0108570	+	0.0755122i
$495$	−6.70555	−	65.7544i	−0.301392	−	2.95544i
$496$	−6.54155	−	4.20400i	−0.293724	−	0.188765i
$497$	0.0495378	−	0.692629i	0.00222207	−	0.0310687i
$498$	16.4614	+	6.13979i	0.737654	+	0.275131i
$499$	2.69017	+	4.18599i	0.120429	+	0.187390i	0.896234	−	0.443582i	$-0.146292\pi$
$499$	2.69017	+	4.18599i	0.120429	+	0.187390i	−0.775805	+	0.630972i	$0.782656\pi$
$500$	4.83971	+	10.0786i	0.216439	+	0.450726i
$501$	3.87321	−	4.46993i	0.173042	−	0.199702i
$502$	−12.5600	−	6.85827i	−0.560580	−	0.306100i
$503$	−3.75081	−	10.0563i	−0.167240	−	0.448389i	0.826111	−	0.563507i	$-0.190548\pi$
$503$	−3.75081	−	10.0563i	−0.167240	−	0.448389i	−0.993352	+	0.115118i	$0.963275\pi$
$504$	−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
$508$	−3.56565	+	4.76314i	−0.158200	+	0.211330i
$509$	−1.47240	−	0.672421i	−0.0652628	−	0.0298045i	0.382516	−	0.923949i	$-0.375058\pi$
$509$	−1.47240	−	0.672421i	−0.0652628	−	0.0298045i	−0.447779	+	0.894144i	$0.647785\pi$
$510$	40.6929	+	10.6238i	1.80191	+	0.470429i
$511$	−0.0408524	−	0.0353988i	−0.00180720	−	0.00156595i
$512$	0.877679	−	0.479249i	0.0387883	−	0.0211800i
$513$	6.19405	−	28.4736i	0.273474	−	1.25714i
$514$	12.3312	−	5.63149i	0.543908	−	0.248394i
$515$	−39.9790	+	6.98732i	−1.76168	+	0.307898i
$516$	−19.3395	+	30.0929i	−0.851375	+	1.32477i
$517$	2.30937	−	1.72877i	0.101566	−	0.0760313i
$518$	4.24608	−	3.17857i	0.186562	−	0.139658i
$519$	−22.5573	+	35.0998i	−0.990155	+	1.54071i
$520$	0.681003	−	0.969464i	0.0298640	−	0.0425138i
$521$	−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	$0.498062\pi$
$522$	−1.91895	+	8.82127i	−0.0839902	+	0.386097i
$523$	−0.0634313	+	0.0346361i	−0.00277366	+	0.00151453i	−0.480635	−	0.876921i	$-0.659594\pi$
$523$	−0.0634313	+	0.0346361i	−0.00277366	+	0.00151453i	0.477862	+	0.878435i	$0.341412\pi$
$524$	−2.99122	−	2.59190i	−0.130672	−	0.113228i
$525$	9.58017	+	9.79220i	0.418113	+	0.427367i
$526$	−12.5389	−	5.72630i	−0.546720	−	0.249679i
$527$	29.1667	−	38.9622i	1.27052	−	1.69722i
$528$	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
$532$	−1.01968	−	2.73387i	−0.0442087	−	0.118528i
$533$	0.667709	+	0.364597i	0.0289217	+	0.0157924i
$534$	12.9653	−	14.9628i	0.561065	−	0.647504i
$535$	−8.27103	−	8.98176i	−0.357588	−	0.388316i
$536$	2.08843	+	3.24967i	0.0902066	+	0.140364i
$537$	−34.1623	−	12.7419i	−1.47421	−	0.549852i
$538$	1.32048	−	18.4627i	0.0569300	−	0.795985i
$539$	25.4381	+	16.3481i	1.09570	+	0.704161i
$540$	−12.8620	+	15.7832i	−0.553493	+	0.679202i
$541$	−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	$0.861174\pi$
$542$	−13.0492	+	2.83869i	−0.560513	+	0.121932i
$543$	19.1637	+	1.37061i	0.822392	+	0.0588187i
$544$	2.60009	+	5.69340i	0.111478	+	0.244103i
$545$	−3.10414	+	3.29771i	−0.132967	+	0.141258i
$546$	0.408979	−	1.39286i	0.0175027	−	0.0596087i
$547$	1.13544	+	15.8755i	0.0485479	+	0.678788i	0.962209	+	0.272312i	$0.0877882\pi$
$547$	1.13544	+	15.8755i	0.0485479	+	0.678788i	−0.913661	+	0.406477i	$0.866757\pi$
$548$	0.365523	−	0.669406i	0.0156144	−	0.0285956i
$549$	14.4866	−	31.7212i	0.618272	−	1.35383i
$550$	−3.75336	+	24.2204i	−0.160044	+	1.03276i
$551$			4.79106i			0.204106i
$552$	11.6052	+	8.54459i	0.493952	+	0.363682i
$553$	10.5001	+	10.5001i	0.446509	+	0.446509i
$554$	3.54014	−	0.508996i	0.150406	−	0.0216252i
$555$	−38.4296	−	7.15082i	−1.63124	−	0.303535i
$556$	19.9957	−	5.87125i	0.848004	−	0.248997i
$557$	37.8048	−	2.70385i	1.60184	−	0.114566i	0.758401	−	0.651789i	$-0.225981\pi$
$557$	37.8048	−	2.70385i	1.60184	−	0.114566i	0.843440	+	0.537223i	$0.180527\pi$
$558$	22.4718	+	41.1540i	0.951306	+	1.74219i
$559$	−5.30590	+	3.40989i	−0.224416	+	0.144223i
$560$	−0.229021	+	2.02584i	−0.00967792	+	0.0856074i
$561$	60.3760	+	69.6776i	2.54908	+	2.94179i
$562$	−2.73735	−	12.5834i	−0.115468	−	0.530799i
$563$	2.01633	+	2.69350i	0.0849783	+	0.113518i	0.841016	−	0.541011i	$-0.181958\pi$
$563$	2.01633	+	2.69350i	0.0849783	+	0.113518i	−0.756037	+	0.654528i	$0.772867\pi$
$564$	−1.75045	−	0.251676i	−0.0737071	−	0.0105975i
$565$	−4.28880	+	2.11755i	−0.180431	+	0.0890859i
$566$	17.5175	−	15.1790i	0.736317	−	0.638022i
$567$	−2.95417	+	7.92042i	−0.124063	+	0.332627i
$568$	−0.744201	−	0.161891i	−0.0312260	−	0.00679280i
$569$	−19.6448	−	5.76822i	−0.823551	−	0.241817i	−0.157307	−	0.987550i	$-0.550281\pi$
$569$	−19.6448	−	5.76822i	−0.823551	−	0.241817i	−0.666245	+	0.745733i	$0.732099\pi$
$570$	−9.73052	+	19.1762i	−0.407567	+	0.803203i
$571$	−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	$0.932855\pi$
$572$	2.43344	−	0.907626i	0.101747	−	0.0379497i
$573$	51.8782	+	38.8355i	2.16724	+	1.62238i
$574$	−1.30915			−0.0546428
$575$	−23.9790	−	0.0719746i	−0.999995	−	0.00300155i
$576$	−6.03008			−0.251253
$577$	5.60018	+	4.19224i	0.233138	+	0.174525i	0.709460	−	0.704746i	$-0.248939\pi$
$577$	5.60018	+	4.19224i	0.233138	+	0.174525i	−0.476321	+	0.879271i	$0.658030\pi$
$578$	−20.7772	+	7.74948i	−0.864216	+	0.322336i
$579$	−16.8532	−	57.3968i	−0.700396	−	2.38533i
$580$	1.51480	−	2.98526i	0.0628988	−	0.123956i
$581$	−5.11476	−	1.50183i	−0.212196	−	0.0623064i
$582$	18.8389	+	4.09816i	0.780899	+	0.169874i
$583$	−2.61374	+	7.00771i	−0.108250	+	0.290230i
$584$	−0.0448063	+	0.0388249i	−0.00185410	+	0.00160659i
$585$	−6.40585	+	3.16282i	−0.264849	+	0.130767i
$586$	9.90386	+	1.42396i	0.409125	+	0.0588233i
$587$	23.4378	+	31.3092i	0.967381	+	1.29227i	0.956317	+	0.292330i	$0.0944307\pi$
$587$	23.4378	+	31.3092i	0.967381	+	1.29227i	0.0110633	+	0.999939i	$0.496478\pi$
$588$	−3.94032	−	18.1134i	−0.162496	−	0.746983i
$589$	16.2962	+	18.8068i	0.671472	+	0.774920i
$590$	3.44617	−	30.4836i	0.141876	−	1.25499i
$591$	42.6026	−	27.3790i	1.75243	−	1.12622i
$592$	−2.78796	−	5.10578i	−0.114585	−	0.209846i
$593$	21.0267	−	1.50386i	0.863464	−	0.0617561i	0.367421	−	0.930055i	$-0.380241\pi$
$593$	21.0267	−	1.50386i	0.863464	−	0.0617561i	0.496042	+	0.868298i	$0.334786\pi$
$594$	−42.8257	+	12.5748i	−1.75716	+	0.515949i
$595$	−12.5452	−	2.33436i	−0.514303	−	0.0956995i
$596$	2.86996	−	0.412638i	0.117558	−	0.0169023i
$597$	3.71589	+	3.71589i	0.152081	+	0.152081i
$598$	1.23545	+	2.22044i	0.0505212	+	0.0908005i
$599$		−	0.455876i		−	0.0186266i	−0.999957	−	0.00931330i	$-0.997035\pi$
$599$		−	0.455876i		−	0.0186266i	0.999957	−	0.00931330i	$-0.00296456\pi$
$600$	12.1260	−	8.87199i	0.495042	−	0.362198i
$601$	−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	$0.970688\pi$
$602$	5.20152	−	9.52588i	0.211998	−	0.388246i
$603$	−1.66174	−	23.2342i	−0.0676713	−	0.946168i
$604$	3.10760	−	10.5835i	0.126447	−	0.430637i
$605$	−19.9679	+	21.2131i	−0.811811	+	0.862435i
$606$	−21.6431	−	47.3918i	−0.879191	−	1.92516i
$607$	−17.4135	−	1.24544i	−0.706793	−	0.0505508i	−0.286685	−	0.958025i	$-0.592553\pi$
$607$	−17.4135	−	1.24544i	−0.706793	−	0.0505508i	−0.420108	+	0.907474i	$0.638008\pi$
$608$	−3.12711	+	0.680261i	−0.126821	+	0.0275882i
$609$	0.583744	−	4.06003i	0.0236545	−	0.164521i
$610$	−8.16903	+	10.0244i	−0.330754	+	0.405875i
$611$	−0.262309	−	0.168576i	−0.0106119	−	0.00681985i
$612$	2.69251	−	37.6462i	0.108838	−	1.52176i
$613$	26.8172	+	10.0023i	1.08313	+	0.403988i	0.826740	−	0.562584i	$-0.190193\pi$
$613$	26.8172	+	10.0023i	1.08313	+	0.403988i	0.256395	+	0.966572i	$0.417465\pi$
$614$	2.04599	+	3.18363i	0.0825696	+	0.128481i
$615$	6.53565	+	7.09726i	0.263543	+	0.286189i
$616$	−2.92678	+	3.37769i	−0.117923	+	0.136091i
$617$	−2.27542	−	1.24247i	−0.0916048	−	0.0500200i	0.432794	−	0.901493i	$-0.357528\pi$
$617$	−2.27542	−	1.24247i	−0.0916048	−	0.0500200i	−0.524398	+	0.851473i	$0.675710\pi$
$618$	19.0603	+	51.1025i	0.766716	+	2.05565i
$619$	−1.69746	−	11.8061i	−0.0682267	−	0.474527i	−0.995078	−	0.0990978i	$-0.968404\pi$
$619$	−1.69746	−	11.8061i	−0.0682267	−	0.474527i	0.926851	−	0.375429i	$-0.122505\pi$
$620$	−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
$623$	−3.59994	+	4.80896i	−0.144229	+	0.192667i
$624$	−1.44828	−	0.661407i	−0.0579775	−	0.0264775i
$625$	−7.56665	+	23.8274i	−0.302666	+	0.953097i
$626$	1.41832	+	1.22898i	0.0566874	+	0.0491199i
$627$	−41.3740	+	22.5919i	−1.65232	+	0.902235i
$628$	−0.823444	+	3.78531i	−0.0328590	+	0.151050i
$629$	33.1206	−	15.1257i	1.32060	−	0.603100i
$630$	7.06658	−	10.0599i	0.281539	−	0.400794i
$631$	−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	$0.272812\pi$
$632$	13.0381	−	9.76018i	0.518627	−	0.388239i
$633$	50.5546	−	37.8447i	2.00937	−	1.50419i
$634$	3.14204	−	4.88911i	0.124786	−	0.194171i
$635$	−13.1057	+	2.29055i	−0.520085	+	0.0908978i
$636$	4.17069	−	1.90469i	0.165379	−	0.0755259i
$637$	0.694747	−	3.19370i	0.0275269	−	0.126539i
$638$	6.44092	−	3.51701i	0.254998	−	0.139240i
$639$	3.47081	+	3.00748i	0.137303	+	0.118974i
$640$	2.16355	+	0.564842i	0.0855219	+	0.0223273i
$641$	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	$0.575235\pi$
$642$	−9.83335	+	13.1358i	−0.388091	+	0.518429i
$643$	4.13771	−	4.13771i	0.163175	−	0.163175i	−0.620796	−	0.783972i	$-0.713191\pi$
$643$	4.13771	−	4.13771i	0.163175	−	0.163175i	0.783972	+	0.620796i	$0.213191\pi$
$644$	−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
$647$	0.877784	+	2.35343i	0.0345093	+	0.0925229i	0.953062	−	0.302776i	$-0.0979136\pi$
$647$	0.877784	+	2.35343i	0.0345093	+	0.0925229i	−0.918552	+	0.395299i	$0.870641\pi$
$648$	8.13748	+	4.44340i	0.319670	+	0.174553i
$649$	44.0404	−	50.8253i	1.72874	−	1.99507i
$650$	2.59464	−	0.534758i	0.101770	−	0.0209749i
$651$	−11.5182	−	17.9227i	−0.451435	−	0.702447i
$652$	14.0480	+	5.23963i	0.550162	+	0.205200i
$653$	2.71782	−	38.0001i	0.106357	−	1.48706i	−0.611709	−	0.791083i	$-0.709518\pi$
$653$	2.71782	−	38.0001i	0.106357	−	1.48706i	0.718065	−	0.695976i	$-0.245028\pi$
$654$	5.12008	+	3.29047i	0.200211	+	0.128668i
$655$	−0.897879	−	8.80457i	−0.0350830	−	0.344023i
$656$	−0.204344	+	1.42124i	−0.00797828	+	0.0554902i
$657$	0.349337	−	0.0759935i	0.0136289	−	0.00296479i
$658$	0.535200	+	0.0382783i	0.0208643	+	0.00149224i
$659$	8.84239	+	19.3621i	0.344451	+	0.754242i	1.00000		0.000910993i	$-0.000289978\pi$
$659$	8.84239	+	19.3621i	0.344451	+	0.754242i	−0.655549	+	0.755153i	$0.727563\pi$
$660$	32.9227	−	0.995478i	1.28152	−	0.0387489i
$661$	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	$-0.212621\pi$
$662$	0.826830	+	11.5606i	0.0321357	+	0.449315i
$663$	4.77588	−	8.74638i	0.185480	−	0.339681i
$664$	−2.42878	+	5.31828i	−0.0942548	+	0.206389i
$665$	2.52976	−	6.01408i	0.0980999	−	0.233216i
$666$			35.0791i			1.35929i
$667$	4.34821	+	5.71337i	0.168364	+	0.221223i
$668$	1.39175	+	1.39175i	0.0538485	+	0.0538485i
$669$	−55.2027	+	7.93695i	−2.13426	+	0.306860i
$670$	−1.58014	+	8.49192i	−0.0610462	+	0.328071i
$671$	−27.1998	+	7.98659i	−1.05004	+	0.308319i
$672$	2.73285	−	0.195457i	0.105422	−	0.00753993i
$673$	−2.14331	−	3.92517i	−0.0826184	−	0.151304i	0.833103	−	0.553117i	$-0.186562\pi$
$673$	−2.14331	−	3.92517i	−0.0826184	−	0.151304i	−0.915722	+	0.401813i	$0.868380\pi$
$674$	12.7763	−	8.21080i	0.492123	−	0.316268i
$675$	−45.1318	+	5.98559i	−1.73713	+	0.230385i
$676$	8.32935	+	9.61259i	0.320360	+	0.369715i
$677$	−0.113598	−	0.522203i	−0.00436593	−	0.0200699i	0.974912	−	0.222589i	$-0.0714508\pi$
$677$	−0.113598	−	0.522203i	−0.00436593	−	0.0200699i	−0.979278	+	0.202519i	$0.935087\pi$
$678$	3.85209	+	5.14578i	0.147938	+	0.197623i
$679$	−5.79009	−	0.832490i	−0.222203	−	0.0319480i
$680$	−4.49240	+	13.2550i	−0.172276	+	0.508306i
$681$	−18.9247	+	16.3984i	−0.725198	+	0.628388i
$682$	13.3205	−	35.7136i	0.510067	−	1.36754i
$683$	16.8978	+	3.67589i	0.646575	+	0.140654i	0.523882	−	0.851791i	$-0.324483\pi$
$683$	16.8978	+	3.67589i	0.646575	+	0.140654i	0.122693	+	0.992445i	$0.460847\pi$
$684$	18.5160	+	5.43679i	0.707978	+	0.207881i
$685$	1.62110	−	0.529717i	0.0619390	−	0.0202394i
$686$	3.38266	+	11.5203i	0.129150	+	0.439846i
$687$	−31.9291	+	11.9089i	−1.21817	+	0.454354i
$688$	−9.52961	−	7.13378i	−0.363313	−	0.271973i
$689$	0.808420			0.0307984
$690$	5.80001	+	31.6989i	0.220803	+	1.20676i
$691$	42.2991			1.60913			0.804566	−	0.593863i	$-0.202398\pi$
$691$	42.2991			1.60913			0.804566	+	0.593863i	$0.202398\pi$
$692$	−11.1152	−	8.32071i	−0.422535	−	0.316306i
$693$	25.2511	−	9.41818i	0.959211	−	0.357767i
$694$	8.35263	+	28.4465i	0.317062	+	1.07981i
$695$	41.5554	+	21.0863i	1.57629	+	0.799850i
$696$	−4.31654	−	1.26745i	−0.163618	−	0.0480426i
$697$	−8.78167	−	1.91034i	−0.332629	−	0.0723591i
$698$	0.759344	−	2.03588i	0.0287416	−	0.0770592i
$699$	39.2019	−	33.9687i	1.48275	−	1.28481i
$700$	−3.47776	+	2.94748i	−0.131447	+	0.111404i
$701$	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	$0.499361\pi$
$702$	2.89113	+	3.86210i	0.109119	+	0.145766i
$703$	3.95732	+	18.1915i	0.149253	+	0.686106i
$704$	3.21006	+	3.70460i	0.120984	+	0.139622i
$705$	−2.46436	−	3.09257i	−0.0928130	−	0.116473i
$706$	−22.2260	+	14.2838i	−0.836485	+	0.537576i
$707$	7.57584	+	13.8741i	0.284919	+	0.521790i
$708$	−41.1222	+	2.94112i	−1.54547	+	0.110534i
$709$	−42.0954	+	12.3603i	−1.58093	+	0.464202i	−0.950158	−	0.311769i	$-0.899079\pi$
$709$	−42.0954	+	12.3603i	−1.58093	+	0.464202i	−0.630769	+	0.775971i	$0.717260\pi$
$710$	−0.963592	−	1.40418i	−0.0361630	−	0.0526978i
$711$	−97.2097	+	13.9766i	−3.64565	+	0.524165i
$712$	4.65880	+	4.65880i	0.174596	+	0.174596i
$713$	36.5017	+	7.63732i	1.36700	+	0.286020i
$714$			17.1486i			0.641772i
$715$	5.35319	+	2.25176i	0.200198	+	0.0842111i
$716$	5.04042	−	11.0370i	0.188370	−	0.412472i
$717$	−19.0042	+	34.8037i	−0.709726	+	1.29977i
$718$	−1.18869	−	16.6200i	−0.0443613	−	0.620253i
$719$	2.38659	−	8.12799i	0.0890049	−	0.303123i	−0.902945	−	0.429757i	$-0.858599\pi$
$719$	2.38659	−	8.12799i	0.0890049	−	0.303123i	0.991949	+	0.126634i	$0.0404174\pi$
$720$	−9.81819	−	9.24187i	−0.365902	−	0.344424i
$721$	−6.87449	−	15.0530i	−0.256019	−	0.560604i
$722$	−8.73613	−	0.624820i	−0.325125	−	0.0232534i
$723$	−61.2108	+	13.3156i	−2.27645	+	0.495212i
$724$	−0.909895	+	6.32846i	−0.0338160	+	0.235195i
$725$	7.04171	−	2.53899i	0.261523	−	0.0942955i
$726$	32.9358	+	21.1665i	1.22236	+	0.785564i
$727$	−1.24353	+	17.3869i	−0.0461201	+	0.644844i	0.920844	+	0.389931i	$0.127501\pi$
$727$	−1.24353	+	17.3869i	−0.0461201	+	0.644844i	−0.966964	+	0.254912i	$0.917953\pi$
$728$	0.452621	+	0.168819i	0.0167753	+	0.00625685i
$729$	14.1524	+	22.0215i	0.524163	+	0.815613i
$730$	−0.132458	−	0.00545668i	−0.00490249	−	0.000201961i
$731$	48.7918	−	56.3087i	1.80463	−	2.08265i
$732$	15.2525	+	8.32851i	0.563750	+	0.307831i
$733$	−7.18203	−	19.2558i	−0.265274	−	0.711228i	−0.999478	−	0.0322992i	$-0.989717\pi$
$733$	−7.18203	−	19.2558i	−0.265274	−	0.711228i	0.734204	−	0.678929i	$-0.237556\pi$
$734$	−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
$738$	5.18874	−	6.93134i	0.191000	−	0.255146i
$739$	42.3232	+	19.3284i	1.55688	+	0.711005i	0.993355	−	0.115090i	$-0.0367158\pi$
$739$	42.3232	+	19.3284i	1.55688	+	0.711005i	0.563530	+	0.826096i	$0.309443\pi$
$740$	3.28589	−	12.5862i	0.120792	−	0.462676i
$741$	3.85077	+	3.33671i	0.141461	+	0.122577i
$742$	−1.22098	+	0.666708i	−0.0448237	+	0.0244756i
$743$	−7.19844	+	33.0907i	−0.264085	+	1.21398i	0.633712	+	0.773569i	$0.281531\pi$
$743$	−7.19844	+	33.0907i	−0.264085	+	1.21398i	−0.897797	+	0.440410i	$0.854833\pi$
$744$	−21.2552	+	9.70692i	−0.779253	+	0.355873i
$745$	5.30530	+	3.72672i	0.194371	+	0.136537i
$746$	−7.63109	+	11.8742i	−0.279394	+	0.434746i
$747$	28.2236	−	21.1279i	1.03265	−	0.773029i
$748$	−24.5614	+	18.3865i	−0.898055	+	0.672275i
$749$	2.69162	−	4.18825i	0.0983498	−	0.153035i
$750$	33.3411	+	4.13925i	1.21744	+	0.151144i
$751$	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	$0.164895\pi$
$752$	0.125095	−	0.575050i	0.00456173	−	0.0209699i
$753$	−37.7429	+	20.6092i	−1.37543	+	0.751040i
$754$	−0.599470	−	0.519443i	−0.0218314	−	0.0189170i
$755$	21.2804	−	12.4693i	0.774474	−	0.453805i
$756$	−7.55167	−	3.44873i	−0.274652	−	0.125429i
$757$	20.8944	−	27.9116i	0.759419	−	1.01446i	−0.239630	−	0.970864i	$-0.577026\pi$
$757$	20.8944	−	27.9116i	0.759419	−	1.01446i	0.999049	−	0.0436006i	$-0.0138829\pi$
$758$	−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	$-0.223503\pi$
$762$	6.24825	+	16.7522i	0.226350	+	0.606868i
$763$	−1.62076	−	0.885000i	−0.0586753	−	0.0320391i
$764$	−14.1223	+	16.2980i	−0.510925	+	0.589639i
$765$	62.0816	−	57.1690i	2.24457	−	2.06695i
$766$	4.80388	+	7.47498i	0.173571	+	0.270082i
$767$	−6.81076	−	2.54028i	−0.245922	−	0.0917242i
$768$	0.214375	−	2.99735i	0.00773559	−	0.108158i
$769$	−5.98137	−	3.84399i	−0.215694	−	0.138618i	0.428333	−	0.903621i	$-0.359101\pi$
$769$	−5.98137	−	3.84399i	−0.215694	−	0.138618i	−0.644027	+	0.765003i	$0.722737\pi$
$770$	−9.94214	+	1.01389i	−0.358290	+	0.0365380i
$771$	5.79745	−	40.3221i	0.208790	−	1.45217i
$772$	19.4518	−	4.23148i	0.700086	−	0.152294i
$773$	−44.7831	−	3.20295i	−1.61074	−	0.115202i	−0.763280	−	0.646068i	$-0.776412\pi$
$773$	−44.7831	−	3.20295i	−1.61074	−	0.115202i	−0.847456	+	0.530866i	$0.821867\pi$
$774$	29.8192	+	65.2950i	1.07183	+	2.34698i
$775$	19.0054	−	33.9180i	0.682695	−	1.21837i
$776$	−1.80754	+	6.15591i	−0.0648869	+	0.220984i
$777$	−1.13705	−	15.8980i	−0.0407913	−	0.570337i
$778$	−10.3047	+	18.8716i	−0.369441	+	0.676580i
$779$	1.90887	−	4.17984i	0.0683923	−	0.149758i
$780$	−1.34440	−	3.29658i	−0.0481373	−	0.118036i
$781$		−	3.73331i		−	0.133588i
$782$	−21.3933	−	21.0561i	−0.765022	−	0.752965i
$783$	9.63902	+	9.63902i	0.344470	+	0.344470i
$784$	6.10592	−	0.877898i	0.218068	−	0.0313535i
$785$	−7.14222	+	4.90122i	−0.254917	+	0.174932i
$786$	−11.4119	+	3.35083i	−0.407048	+	0.119520i
$787$	−27.0487	+	1.93456i	−0.964181	+	0.0689596i	−0.544544	−	0.838732i	$-0.683297\pi$
$787$	−27.0487	+	1.93456i	−0.964181	+	0.0689596i	−0.419637	+	0.907692i	$0.637843\pi$
$788$	8.07652	+	14.7910i	0.287714	+	0.526909i
$789$	−34.8469	+	22.3948i	−1.24058	+	0.797275i
$790$	36.1874	+	4.09099i	1.28749	+	0.145551i
$791$	−1.27717	−	1.47393i	−0.0454110	−	0.0524070i
$792$	−6.28317	−	28.8833i	−0.223263	−	1.02632i
$793$	1.83624	+	2.45293i	0.0652068	+	0.0871061i
$794$	−38.4106	−	5.52261i	−1.36314	−	0.195990i
$795$	9.70991	+	3.29090i	0.344375	+	0.116716i
$796$	−1.32163	+	1.14520i	−0.0468439	+	0.0405905i
$797$	11.3458	−	30.4193i	0.401889	−	1.07751i	−0.565619	−	0.824667i	$-0.691363\pi$
$797$	11.3458	−	30.4193i	0.401889	−	1.07751i	0.967508	−	0.252840i	$-0.0813646\pi$
$798$	−8.56774	−	1.86380i	−0.303295	−	0.0659778i
$799$	3.53422	+	1.03774i	0.125032	+	0.0367127i
$800$	2.65701	+	4.23560i	0.0939394	+	0.149751i
$801$	−11.1931	−	38.1201i	−0.395488	−	1.34691i
$802$	28.1341	−	10.4935i	0.993450	−	0.370538i
$803$	−0.232653	−	0.174162i	−0.00821015	−	0.00614604i
$804$	11.6080			0.409383
$805$	−2.44143	−	9.46776i	−0.0860492	−	0.333695i
$806$	−4.11997			−0.145120
$807$	−44.5280	−	33.3332i	−1.56746	−	1.17339i
$808$	16.2446	−	6.05891i	0.571481	−	0.213152i
$809$	5.12288	+	17.4469i	0.180111	+	0.613402i	0.999210	+	0.0397491i	$0.0126559\pi$
$809$	5.12288	+	17.4469i	0.180111	+	0.613402i	−0.819099	+	0.573653i	$0.805526\pi$
$810$	6.43938	+	19.7065i	0.226257	+	0.692416i
$811$	−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	$0.989146\pi$
$812$	1.33379	+	0.290148i	0.0468067	+	0.0101822i
$813$	−14.0241	+	37.6000i	−0.491845	+	1.31869i
$814$	21.5510	−	18.6741i	0.755362	−	0.654525i
$815$	14.8426	+	30.0616i	0.519913	+	1.05301i
$816$	18.6170	+	2.67672i	0.651724	+	0.0937038i
$817$	22.8298	+	30.4971i	0.798714	+	1.06696i
$818$	−4.79588	−	22.0463i	−0.167684	−	0.770830i
$819$	−1.90761	−	2.20150i	−0.0666574	−	0.0769267i
$820$	−2.51095	+	2.00089i	−0.0876862	+	0.0698740i
$821$	−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	$0.433161\pi$
$822$	−1.09840	−	2.01157i	−0.0383111	−	0.0701616i
$823$	20.0682	−	1.43531i	0.699535	−	0.0500317i	0.282958	−	0.959132i	$-0.408684\pi$
$823$	20.0682	−	1.43531i	0.699535	−	0.0500317i	0.416577	+	0.909101i	$0.363230\pi$
$824$	−17.4150	+	5.11349i	−0.606679	+	0.178137i
$825$	55.1306	+	48.8375i	1.91940	+	1.70030i
$826$	12.3815	−	1.78019i	0.430807	−	0.0619408i
$827$	8.89824	+	8.89824i	0.309422	+	0.309422i	0.844685	−	0.535263i	$-0.179788\pi$
$827$	8.89824	+	8.89824i	0.309422	+	0.309422i	−0.535263	+	0.844685i	$0.679788\pi$
$828$	27.0147	−	10.3211i	0.938827	−	0.358684i
$829$		−	13.7542i		−	0.477702i	−0.971056	−	0.238851i	$-0.923229\pi$
$829$		−	13.7542i		−	0.477702i	0.971056	−	0.238851i	$-0.0767707\pi$
$830$	−12.1055	+	4.93682i	−0.420188	+	0.171360i
$831$	4.46470	−	9.77632i	0.154879	−	0.339137i
$832$	0.253923	−	0.465025i	0.00880319	−	0.0161218i
$833$	2.75441	+	38.5117i	0.0954346	+	1.33435i
$834$	17.6432	−	60.0871i	0.610933	−	2.08065i
$835$	0.133015	+	4.39910i	0.00460316	+	0.152237i
$836$	−6.51672	−	14.2696i	−0.225385	−	0.493525i
$837$	70.6228	+	5.05104i	2.44108	+	0.174590i
$838$	−10.8242	+	2.35466i	−0.373916	+	0.0813404i
$839$	2.79755	−	19.4574i	0.0965822	−	0.671744i	−0.882803	−	0.469743i	$-0.844347\pi$
$839$	2.79755	−	19.4574i	0.0965822	−	0.671744i	0.979385	−	0.202001i	$-0.0647444\pi$
$840$	4.74920	+	3.87020i	0.163863	+	0.133535i
$841$	22.5109	+	14.4669i	0.776237	+	0.498857i
$842$	−1.64067	+	22.9396i	−0.0565414	+	0.790552i
$843$	−36.2577	−	13.5234i	−1.24878	−	0.465772i
$844$	11.3616	+	17.6790i	0.391083	+	0.608537i
$845$	−1.17066	+	28.4171i	−0.0402718	+	0.977577i
$846$	−2.32390	+	2.68193i	−0.0798974	+	0.0922065i
$847$	−10.4258	−	5.69291i	−0.358234	−	0.195611i
$848$	0.533211	+	1.42959i	0.0183105	+	0.0490925i
$849$	−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
$853$	−7.98187	+	10.6625i	−0.273294	+	0.365078i	−0.916099	−	0.400952i	$-0.868680\pi$
$853$	−7.98187	+	10.6625i	−0.273294	+	0.365078i	0.642805	+	0.766030i	$0.277770\pi$
$854$	−4.79628	−	2.19039i	−0.164125	−	0.0749535i
$855$	21.8153	+	37.2304i	0.746066	+	1.27325i
$856$	−4.12672	−	3.57583i	−0.141049	−	0.122219i
$857$	12.8919	−	7.03949i	0.440378	−	0.240464i	−0.243733	−	0.969842i	$-0.578372\pi$
$857$	12.8919	−	7.03949i	0.440378	−	0.240464i	0.684111	+	0.729378i	$0.260190\pi$
$858$	1.65898	−	7.62623i	0.0566368	−	0.260355i
$859$	−2.69835	+	1.23229i	−0.0920665	+	0.0420454i	−0.460916	−	0.887444i	$-0.652479\pi$
$859$	−2.69835	+	1.23229i	−0.0920665	+	0.0420454i	0.368849	+	0.929489i	$0.379752\pi$
$860$	−4.58270	−	26.2206i	−0.156269	−	0.894115i
$861$	−2.12688	+	3.30949i	−0.0724840	+	0.112787i
$862$	9.99992	−	7.48585i	0.340599	−	0.254969i
$863$	−16.1002	+	12.0525i	−0.548059	+	0.410272i	−0.837104	−	0.547044i	$-0.815753\pi$
$863$	−16.1002	+	12.0525i	−0.548059	+	0.410272i	0.289045	+	0.957315i	$0.406662\pi$
$864$	−4.92275	+	7.65995i	−0.167475	+	0.260597i
$865$	−5.34518	−	30.5832i	−0.181742	−	1.03986i
$866$	−15.3505	+	7.01033i	−0.521631	+	0.238221i
$867$	−14.1647	+	65.1141i	−0.481059	+	2.21139i
$868$	6.22253	−	3.39776i	0.211207	−	0.115327i
$869$	60.3353	+	52.2808i	2.04673	+	1.77351i
$870$	−5.08568	−	8.67933i	−0.172421	−	0.294257i
$871$	1.86174	+	0.850227i	0.0630826	+	0.0288088i
$872$	−1.21376	+	1.62139i	−0.0411030	+	0.0549072i
$873$	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
$877$	−11.4890	−	30.8032i	−0.387956	−	1.04015i	−0.973334	−	0.229391i	$-0.926327\pi$
$877$	−11.4890	−	30.8032i	−0.387956	−	1.04015i	0.585378	−	0.810761i	$-0.300946\pi$
$878$	8.49787	+	4.64019i	0.286789	+	0.156599i
$879$	19.6898	−	22.7233i	0.664122	−	0.766438i
$880$	−0.451160	+	10.9517i	−0.0152086	+	0.369181i
$881$	−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	$0.980792\pi$
$882$	−34.8524	−	12.9993i	−1.17354	−	0.437709i
$883$	2.63403	−	36.8286i	0.0886423	−	1.23938i	−0.737276	−	0.675591i	$-0.763888\pi$
$883$	2.63403	−	36.8286i	0.0886423	−	1.23938i	0.825919	−	0.563789i	$-0.190657\pi$
$884$	2.78980	+	1.79290i	0.0938313	+	0.0603017i
$885$	−71.4629	−	58.2363i	−2.40220	−	1.95759i
$886$	−3.57327	+	24.8526i	−0.120046	+	0.834940i
$887$	−17.1838	+	3.73810i	−0.576974	+	0.125513i	−0.491577	−	0.870834i	$-0.663579\pi$
$887$	−17.1838	+	3.73810i	−0.576974	+	0.125513i	−0.0853969	+	0.996347i	$0.527216\pi$
$888$	−17.4367	−	1.24710i	−0.585137	−	0.0418498i
$889$	−2.25357	−	4.93462i	−0.0755822	−	0.165502i
$890$	0.445258	+	14.7257i	0.0149251	+	0.493607i
$891$	−12.8043	+	43.6073i	−0.428959	+	1.46090i
$892$	−1.32399	−	18.5119i	−0.0443306	−	0.619823i
$893$	−0.902590	+	1.65297i	−0.0302040	+	0.0553145i
$894$	3.61948	−	7.92556i	0.121054	−	0.265070i
$895$	25.1225	−	10.2454i	0.839751	−	0.342465i
$896$			0.911755i			0.0304596i
$897$	7.62036	+	0.484213i	0.254436	+	0.0161674i
$898$	19.0032	+	19.0032i	0.634146	+	0.634146i
$899$	−11.5228	+	1.65673i	−0.384308	+	0.0552551i
$900$	−1.82164	−	30.0953i	−0.0607212	−	1.00318i
$901$	−9.16314	+	2.69054i	−0.305269	+	0.0896349i
$902$	−7.02048	+	0.502114i	−0.233756	+	0.0167186i
$903$	−15.6306	−	28.6253i	−0.520155	−	0.952592i
$904$	−1.79949	+	1.15646i	−0.0598501	+	0.0384633i
$905$	−11.1807	+	8.90949i	−0.371658	+	0.296161i
$906$	−21.7062	−	25.0502i	−0.721139	−	0.832239i
$907$	−8.74372	−	40.1942i	−0.290330	−	1.33463i	−0.858964	−	0.512036i	$-0.828891\pi$
$907$	−8.74372	−	40.1942i	−0.290330	−	1.33463i	0.568634	−	0.822591i	$-0.307472\pi$
$908$	−4.99384	−	6.67099i	−0.165726	−	0.221385i
$909$	−103.484	−	14.8787i	−3.43233	−	0.493495i
$910$	0.478222	+	0.968572i	0.0158529	+	0.0321079i
$911$	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	$0.178722\pi$
$912$	−3.36071	+	9.01042i	−0.111284	+	0.298365i
$913$	−28.0046	−	6.09202i	−0.926816	−	0.201616i
$914$	−17.0265	−	4.99944i	−0.563188	−	0.165367i
$915$	12.0697	+	36.9370i	0.399012	+	1.22110i
$916$	−3.19493	−	10.8809i	−0.105564	−	0.359516i
$917$	3.38115	−	1.26110i	0.111655	−	0.0416453i
$918$	−45.6236	−	34.1534i	−1.50580	−	1.12723i
$919$	−16.3579			−0.539598			−0.269799	−	0.962917i	$-0.586957\pi$
$919$	−16.3579			−0.539598			−0.269799	+	0.962917i	$0.586957\pi$
$920$	−10.6595	+	1.17266i	−0.351433	+	0.0386616i
$921$	11.3721			0.374724
$922$	−14.2296	−	10.6521i	−0.468627	−	0.350810i
$923$	−0.378083	+	0.141018i	−0.0124448	+	0.00464166i
$924$	3.78377	+	12.8863i	0.124477	+	0.423929i
$925$	24.6400	−	15.4568i	0.810159	−	0.508216i
$926$	−12.2909	−	3.60893i	−0.403904	−	0.118597i
$927$	106.946	+	23.2646i	3.51256	+	0.764110i
$928$	0.523180	−	1.40270i	0.0171742	−	0.0460459i
$929$	−19.8784	+	17.2247i	−0.652188	+	0.565125i	−0.916857	−	0.399215i	$-0.869283\pi$
$929$	−19.8784	+	17.2247i	−0.652188	+	0.565125i	0.264669	+	0.964339i	$0.414737\pi$
$930$	−49.4849	−	16.7715i	−1.62267	−	0.549959i
$931$	−19.5404	−	2.80949i	−0.640411	−	0.0920772i
$932$	10.3446	+	13.8187i	0.338847	+	0.452647i
$933$	12.0370	+	55.3331i	0.394073	+	1.81152i
$934$	4.56231	+	5.26518i	0.149283	+	0.172282i
$935$	−68.1706	−	7.70669i	−2.22942	−	0.252036i
$936$	−2.68776	+	1.72732i	−0.0878522	+	0.0564592i
$937$	−2.57104	−	4.70850i	−0.0839921	−	0.153820i	0.832307	−	0.554315i	$-0.187020\pi$
$937$	−2.57104	−	4.70850i	−0.0839921	−	0.153820i	−0.916299	+	0.400495i	$0.868838\pi$
$938$	−3.51303	+	0.251257i	−0.114705	+	0.00820383i
$939$	5.41107	−	1.58883i	0.176584	−	0.0518497i
$940$	1.08502	−	0.744575i	0.0353894	−	0.0242854i
$941$	−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
$943$	−1.51715	−	6.71692i	−0.0494053	−	0.218733i
$944$		−	13.7195i		−	0.446532i
$945$	−7.01002	−	17.1891i	−0.228036	−	0.559163i
$946$	24.2403	−	53.0788i	0.788119	−	1.72574i
$947$	−17.2624	+	31.6137i	−0.560952	+	1.02731i	0.431199	+	0.902257i	$0.358091\pi$
$947$	−17.2624	+	31.6137i	−0.560952	+	1.02731i	−0.992150	+	0.125050i	$0.960091\pi$
$948$	−3.49143	−	48.8166i	−0.113396	−	1.58549i
$949$	−0.00884991	+	0.0301400i	−0.000287280	+	0.000978387i
$950$	−4.33976	−	15.4015i	−0.140801	−	0.499690i
$951$	−7.25489	−	15.8860i	−0.235256	−	0.515139i
$952$	−5.69215	−	0.407111i	−0.184484	−	0.0131945i
$953$	−15.8942	+	3.45757i	−0.514864	+	0.112002i	−0.462488	−	0.886626i	$-0.653043\pi$
$953$	−15.8942	+	3.45757i	−0.514864	+	0.112002i	−0.0523760	+	0.998627i	$0.516679\pi$
$954$	1.30939	−	9.10702i	0.0423931	−	0.294851i
$955$	−47.9727	+	4.89219i	−1.55236	+	0.158308i
$956$	−11.1012	−	7.13431i	−0.359039	−	0.230740i
$957$	1.57321	−	21.9963i	0.0508546	−	0.711040i
$958$	15.7633	+	5.87940i	0.509288	+	0.189955i
$959$	0.375959	+	0.585004i	0.0121404	+	0.0188908i
$960$	4.94288	−	4.55174i	0.159531	−	0.146907i
$961$	−19.2958	+	22.2685i	−0.622444	+	0.718338i
$962$	−2.70522	−	1.47716i	−0.0872198	−	0.0476256i
$963$	11.5068	+	30.8508i	0.370800	+	0.994154i
$964$	−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	−0.931935	−	0.362625i	$-0.881880\pi$
$967$	−17.7036	+	17.7036i	−0.569310	+	0.569310i	0.362625	+	0.931935i	$0.381880\pi$
$968$	−7.80770	+	10.4299i	−0.250949	+	0.335229i
$969$	−54.7521	−	25.0044i	−1.75889	−	0.803258i
$970$	−12.3778	+	7.25279i	−0.397426	+	0.232873i
$971$	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	$0.558740\pi$
$972$	0.478328	−	0.261187i	0.0153424	−	0.00837757i
$973$	−4.03891	+	18.5666i	−0.129481	+	0.595217i
$974$	−17.9458	+	8.19558i	−0.575021	+	0.262603i
$975$	2.86348	−	7.42797i	0.0917047	−	0.237885i
$976$	−3.12658	+	4.86505i	−0.100079	+	0.155727i
$977$	−33.2199	+	24.8681i	−1.06280	+	0.795601i	−0.979605	−	0.200932i	$-0.935603\pi$
$977$	−33.2199	+	24.8681i	−1.06280	+	0.795601i	−0.0831936	+	0.996533i	$0.526512\pi$
$978$	36.0685	−	27.0005i	1.15334	−	0.863381i
$979$	−17.4607	+	27.1694i	−0.558047	+	0.868337i
$980$	11.2872	+	7.92871i	0.360555	+	0.253273i
$981$	11.1095	−	5.07352i	0.354697	−	0.161985i
$982$	−1.87525	+	8.62038i	−0.0598416	+	0.275087i
$983$	−49.3391	+	26.9412i	−1.57367	+	0.859290i	−0.574504	+	0.818502i	$0.694805\pi$
$983$	−49.3391	+	26.9412i	−1.57367	+	0.859290i	−0.999168	+	0.0407879i	$0.987013\pi$
$984$	3.26088	+	2.82557i	0.103953	+	0.0900758i
$985$	−9.51897	+	36.4611i	−0.303300	+	1.16175i
$986$	8.52355	+	3.89258i	0.271445	+	0.123965i
$987$	0.966269	−	1.29078i	0.0307567	−	0.0410861i
$988$	−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	$0.891838\pi$
$992$	−2.71742	−	7.28568i	−0.0862781	−	0.231320i
$993$	30.5682	+	16.6915i	0.970052	+	0.529688i
$994$	0.454734	−	0.524791i	0.0144233	−	0.0166454i
$995$	−3.90705	−	0.160953i	−0.123862	−	0.00510255i
$996$	9.49861	+	14.7801i	0.300975	+	0.468326i
$997$	0.544818	+	0.203206i	0.0172545	+	0.00643561i	0.358077	−	0.933692i	$-0.383433\pi$
$997$	0.544818	+	0.203206i	0.0172545	+	0.00643561i	−0.340822	+	0.940128i	$0.610705\pi$
$998$	−0.354976	+	4.96321i	−0.0112366	+	0.157108i
$999$	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.43.12	✓	240
5.2	odd	4	inner	230.2.l.a.227.1	yes	240
23.15	odd	22	inner	230.2.l.a.153.1	yes	240
115.107	even	44	inner	230.2.l.a.107.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.12	✓	240	1.1	even	1	trivial
230.2.l.a.107.12	yes	240	115.107	even	44	inner
230.2.l.a.153.1	yes	240	23.15	odd	22	inner
230.2.l.a.227.1	yes	240	5.2	odd	4	inner

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+(0.800541 + 0.599278i) q^{2} +(2.81554 - 1.05014i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-1.01183 + 1.99404i) q^{5} +(2.88328 + 0.846609i) q^{6} +(-0.890918 - 0.193807i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(4.55723 - 3.94886i) q^{9} +(-2.00500 + 0.989945i) q^{10} +(-4.85200 - 0.697612i) q^{11} +(1.80083 + 2.40563i) q^{12} +(0.112625 + 0.517727i) q^{13} +(-0.597072 - 0.689058i) q^{14} +(-0.754821 + 6.67687i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-2.99963 - 5.49341i) q^{17} +(6.01471 - 0.430181i) q^{18} +(3.07061 - 0.901613i) q^{19} +(-2.19833 - 0.409057i) q^{20} +(-2.71194 + 0.389918i) q^{21} +(-3.46616 - 3.46616i) q^{22} +(2.84345 - 3.86197i) q^{23} +3.00501i q^{24} +(-2.95240 - 4.03526i) q^{25} +(-0.220101 + 0.481955i) q^{26} +(4.36376 - 7.99162i) q^{27} +(-0.0650438 - 0.909432i) q^{28} +(-0.421780 + 1.43645i) q^{29} +(-4.60557 + 4.89276i) q^{30} +(3.23025 + 7.07325i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(-14.3936 + 3.13113i) q^{33} +(0.890751 - 6.19531i) q^{34} +(1.28792 - 1.58043i) q^{35} +(5.07282 + 3.26011i) q^{36} +(-0.415006 + 5.80254i) q^{37} +(2.99847 + 1.11837i) q^{38} +(0.860786 + 1.33941i) q^{39} +(-1.51472 - 1.64488i) q^{40} +(0.940286 - 1.08515i) q^{41} +(-2.40469 - 1.31306i) q^{42} +(4.16001 + 11.1534i) 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} +(-1.80083 + 2.40563i) q^{48} +(-5.61125 - 2.56257i) q^{49} +(0.0547222 - 4.99970i) q^{50} +(-14.2144 - 12.3169i) q^{51} +(-0.465025 + 0.253923i) q^{52} +(0.324331 - 1.49093i) q^{53} +(8.28257 - 3.78252i) q^{54} +(6.30046 - 8.96922i) q^{55} +(0.492932 - 0.767017i) q^{56} +(7.69861 - 5.76311i) q^{57} +(-1.19848 + 0.897174i) q^{58} +(-7.41732 + 11.5416i) q^{59} +(-6.61907 + 1.15685i) q^{60} +(5.26049 - 2.40239i) q^{61} +(-1.65290 + 7.59825i) q^{62} +(-4.82543 + 2.63489i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(-1.14633 - 0.299273i) q^{65} +(-13.3991 - 6.11915i) q^{66} +(2.31494 - 3.09240i) 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} +(2.10730 + 5.64988i) q^{72} +(0.0520352 + 0.0284134i) q^{73} +(-3.80956 + 4.39647i) q^{74} +(-12.5502 - 8.26100i) q^{75} +(1.73018 + 2.69222i) q^{76} +(4.18753 + 1.56187i) q^{77} +(-0.113583 + 1.58810i) q^{78} +(-13.7011 - 8.80519i) q^{79} +(-0.226855 - 2.22453i) q^{80} +(1.31948 - 9.17722i) q^{81} +(1.40304 - 0.305213i) q^{82} +(5.83173 + 0.417094i) q^{83} +(-1.13817 - 2.49224i) q^{84} +(13.9892 - 0.422989i) q^{85} +(-3.35373 + 11.4218i) q^{86} +(0.320939 + 4.48731i) q^{87} +(2.34923 - 4.30229i) q^{88} +(2.73698 - 5.99315i) q^{89} +(-5.22807 + 12.4289i) q^{90} -0.483079i q^{91} +(4.50662 + 1.64023i) q^{92} +(16.5228 + 16.5228i) q^{93} +(-0.582509 + 0.0837522i) q^{94} +(-1.30908 + 7.03520i) q^{95} +(-2.88328 + 0.846609i) q^{96} +(6.39945 - 0.457698i) q^{97} +(-2.95634 - 5.41414i) 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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