LMFDB - Embedded newform 200.2.o.a.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] 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("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	200.109
Dual form			200.2.o.a.189.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41101 + 0.0951175i) q^{2} +(-0.615546 - 1.89446i) q^{3} +(1.98191 - 0.268424i) q^{4} +(-0.987308 - 2.00630i) q^{5} +(1.04874 + 2.61455i) q^{6} -1.38088i q^{7} +(-2.77096 + 0.567263i) q^{8} +(-0.783019 + 0.568896i) q^{9} +(1.58394 + 2.73700i) q^{10} +(-3.04233 + 4.18740i) q^{11} +(-1.72847 - 3.58941i) q^{12} +(2.49716 - 1.81429i) q^{13} +(0.131346 + 1.94844i) q^{14} +(-3.19311 + 3.10538i) q^{15} +(3.85590 - 1.06398i) q^{16} +(-3.63061 - 1.17966i) q^{17} +(1.05074 - 0.877198i) q^{18} +(-6.09071 - 1.97899i) q^{19} +(-2.49529 - 3.71127i) q^{20} +(-2.61602 + 0.849997i) q^{21} +(3.89446 - 6.19785i) q^{22} +(-0.168832 + 0.232378i) q^{23} +(2.78031 + 4.90029i) q^{24} +(-3.05044 + 3.96166i) q^{25} +(-3.35095 + 2.79751i) q^{26} +(-3.27483 - 2.37930i) q^{27} +(-0.370661 - 2.73678i) q^{28} +(8.75018 - 2.84311i) q^{29} +(4.21013 - 4.68545i) q^{30} +(1.38826 - 4.27263i) q^{31} +(-5.33951 + 1.86805i) q^{32} +(9.80555 + 3.18602i) q^{33} +(5.23504 + 1.31918i) q^{34} +(-2.77046 + 1.36336i) q^{35} +(-1.39916 + 1.33768i) q^{36} +(-4.07603 + 2.96141i) q^{37} +(8.78229 + 2.21305i) q^{38} +(-4.97421 - 3.61398i) q^{39} +(3.87389 + 4.99930i) q^{40} +(3.28522 - 2.38685i) q^{41} +(3.61039 - 1.44818i) q^{42} +7.54302 q^{43} +(-4.90561 + 9.11567i) q^{44} +(1.91445 + 1.00929i) q^{45} +(0.216121 - 0.343947i) q^{46} +(0.954360 - 0.310090i) q^{47} +(-4.38915 - 6.64990i) q^{48} +5.09317 q^{49} +(3.92739 - 5.88010i) q^{50} +7.60418i q^{51} +(4.46213 - 4.26605i) q^{52} +(-1.02485 - 3.15418i) q^{53} +(4.84714 + 3.04573i) q^{54} +(11.4049 + 1.96955i) q^{55} +(0.783323 + 3.82637i) q^{56} +12.7567i q^{57} +(-12.0762 + 4.84395i) q^{58} +(1.05228 + 1.44834i) q^{59} +(-5.49488 + 7.01168i) q^{60} +(1.30861 - 1.80115i) q^{61} +(-1.55245 + 6.16078i) q^{62} +(0.785578 + 1.08126i) q^{63} +(7.35643 - 3.14372i) q^{64} +(-6.10547 - 3.21877i) q^{65} +(-14.1388 - 3.56283i) q^{66} +(-0.552275 + 1.69973i) q^{67} +(-7.51218 - 1.36343i) q^{68} +(0.544154 + 0.176806i) q^{69} +(3.77947 - 2.18723i) q^{70} +(-4.68658 - 14.4238i) q^{71} +(1.84700 - 2.02057i) q^{72} +(6.88021 - 9.46979i) q^{73} +(5.46964 - 4.56628i) q^{74} +(9.38289 + 3.34035i) q^{75} +(-12.6024 - 2.28728i) q^{76} +(5.78231 + 4.20109i) q^{77} +(7.36242 + 4.62623i) q^{78} +(-0.381800 - 1.17506i) q^{79} +(-5.94162 - 6.68559i) q^{80} +(-3.38894 + 10.4301i) q^{81} +(-4.40845 + 3.68036i) q^{82} +(1.29836 - 3.99593i) q^{83} +(-4.95655 + 2.38682i) q^{84} +(1.21779 + 8.44877i) q^{85} +(-10.6433 + 0.717473i) q^{86} +(-10.7723 - 14.8268i) q^{87} +(6.05480 - 13.3289i) q^{88} +(-9.13763 - 6.63888i) q^{89} +(-2.79732 - 1.24202i) q^{90} +(-2.50532 - 3.44828i) q^{91} +(-0.272234 + 0.505870i) q^{92} -8.94886 q^{93} +(-1.31712 + 0.528317i) q^{94} +(2.04297 + 14.1736i) q^{95} +(6.82566 + 8.96560i) q^{96} +(-4.65397 + 1.51217i) q^{97} +(-7.18651 + 0.484449i) q^{98} -5.00958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.41101	+	0.0951175i	−0.997736	+	0.0672582i
$2$	−1.41101	+	0.0951175i	−0.997736	+	0.0672582i
$3$	−0.615546	−	1.89446i	−0.355386	−	1.09377i	−0.955785	−	0.294065i	$-0.904992\pi$
$3$	−0.615546	−	1.89446i	−0.355386	−	1.09377i	0.600400	−	0.799700i	$-0.295008\pi$
$4$	1.98191	−	0.268424i	0.990953	−	0.134212i
$5$	−0.987308	−	2.00630i	−0.441538	−	0.897243i
$5$	−0.987308	−	2.00630i	−0.441538	−	0.897243i
$6$	1.04874	+	2.61455i	0.428146	+	1.06739i
$7$		−	1.38088i		−	0.521924i	−0.965349	−	0.260962i	$-0.915960\pi$
$7$		−	1.38088i		−	0.521924i	0.965349	−	0.260962i	$-0.0840398\pi$
$8$	−2.77096	+	0.567263i	−0.979682	+	0.200558i
$9$	−0.783019	+	0.568896i	−0.261006	+	0.189632i
$10$	1.58394	+	2.73700i	0.500885	+	0.865514i
$11$	−3.04233	+	4.18740i	−0.917296	+	1.26255i	0.0473169	+	0.998880i	$0.484933\pi$
$11$	−3.04233	+	4.18740i	−0.917296	+	1.26255i	−0.964613	+	0.263670i	$0.915067\pi$
$12$	−1.72847	−	3.58941i	−0.498967	−	1.03617i
$13$	2.49716	−	1.81429i	0.692587	−	0.503194i	−0.184923	−	0.982753i	$-0.559203\pi$
$13$	2.49716	−	1.81429i	0.692587	−	0.503194i	0.877510	+	0.479559i	$0.159203\pi$
$14$	0.131346	+	1.94844i	0.0351037	+	0.520742i
$15$	−3.19311	+	3.10538i	−0.824457	+	0.801806i
$16$	3.85590	−	1.06398i	0.963974	−	0.265995i
$17$	−3.63061	−	1.17966i	−0.880553	−	0.286109i	−0.166366	−	0.986064i	$-0.553203\pi$
$17$	−3.63061	−	1.17966i	−0.880553	−	0.286109i	−0.714187	+	0.699955i	$0.753203\pi$
$18$	1.05074	−	0.877198i	0.247661	−	0.206758i
$19$	−6.09071	−	1.97899i	−1.39730	−	0.454012i	−0.488986	−	0.872292i	$-0.662633\pi$
$19$	−6.09071	−	1.97899i	−1.39730	−	0.454012i	−0.908318	+	0.418280i	$0.862633\pi$
$20$	−2.49529	−	3.71127i	−0.557964	−	0.829865i
$21$	−2.61602	+	0.849997i	−0.570863	+	0.185484i
$22$	3.89446	−	6.19785i	0.830302	−	1.32139i
$23$	−0.168832	+	0.232378i	−0.0352040	+	0.0484541i	−0.826256	−	0.563295i	$-0.809534\pi$
$23$	−0.168832	+	0.232378i	−0.0352040	+	0.0484541i	0.791052	+	0.611749i	$0.209534\pi$
$24$	2.78031	+	4.90029i	0.567528	+	1.00027i
$25$	−3.05044	+	3.96166i	−0.610089	+	0.792333i
$26$	−3.35095	+	2.79751i	−0.657175	+	0.548637i
$27$	−3.27483	−	2.37930i	−0.630241	−	0.457897i
$28$	−0.370661	−	2.73678i	−0.0700484	−	0.517202i
$29$	8.75018	−	2.84311i	1.62487	−	0.527952i	0.651785	−	0.758404i	$-0.274021\pi$
$29$	8.75018	−	2.84311i	1.62487	−	0.527952i	0.973084	+	0.230452i	$0.0740206\pi$
$30$	4.21013	−	4.68545i	0.768662	−	0.855442i
$31$	1.38826	−	4.27263i	0.249339	−	0.767388i	−0.745553	−	0.666446i	$-0.767815\pi$
$31$	1.38826	−	4.27263i	0.249339	−	0.767388i	0.994892	−	0.100941i	$-0.0321855\pi$
$32$	−5.33951	+	1.86805i	−0.943901	+	0.330228i
$33$	9.80555	+	3.18602i	1.70693	+	0.554614i
$34$	5.23504	+	1.31918i	0.897803	+	0.226237i
$35$	−2.77046	+	1.36336i	−0.468293	+	0.230449i
$36$	−1.39916	+	1.33768i	−0.233194	+	0.222947i
$37$	−4.07603	+	2.96141i	−0.670095	+	0.486853i	−0.870057	−	0.492951i	$-0.835918\pi$
$37$	−4.07603	+	2.96141i	−0.670095	+	0.486853i	0.199962	+	0.979804i	$0.435918\pi$
$38$	8.78229	+	2.21305i	1.42468	+	0.359003i
$39$	−4.97421	−	3.61398i	−0.796512	−	0.578700i
$40$	3.87389	+	4.99930i	0.612515	+	0.790459i
$41$	3.28522	−	2.38685i	0.513065	−	0.372764i	−0.300920	−	0.953649i	$-0.597294\pi$
$41$	3.28522	−	2.38685i	0.513065	−	0.372764i	0.813985	+	0.580886i	$0.197294\pi$
$42$	3.61039	−	1.44818i	0.557095	−	0.223460i
$43$	7.54302			1.15030			0.575150	−	0.818048i	$-0.304944\pi$
$43$	7.54302			1.15030			0.575150	+	0.818048i	$0.304944\pi$
$44$	−4.90561	+	9.11567i	−0.739548	+	1.37424i
$45$	1.91445	+	1.00929i	0.285390	+	0.150456i
$46$	0.216121	−	0.343947i	0.0318653	−	0.0507122i
$47$	0.954360	−	0.310090i	0.139208	−	0.0452313i	−0.238584	−	0.971122i	$-0.576683\pi$
$47$	0.954360	−	0.310090i	0.139208	−	0.0452313i	0.377792	+	0.925890i	$0.376683\pi$
$48$	−4.38915	−	6.64990i	−0.633519	−	0.959831i
$49$	5.09317			0.727595
$50$	3.92739	−	5.88010i	0.555416	−	0.831572i
$51$			7.60418i			1.06480i
$52$	4.46213	−	4.26605i	0.618786	−	0.591595i
$53$	−1.02485	−	3.15418i	−0.140775	−	0.433260i	0.855669	−	0.517524i	$-0.173146\pi$
$53$	−1.02485	−	3.15418i	−0.140775	−	0.433260i	−0.996443	+	0.0842641i	$0.973146\pi$
$54$	4.84714	+	3.04573i	0.659612	+	0.414471i
$55$	11.4049	+	1.96955i	1.53783	+	0.265574i
$56$	0.783323	+	3.82637i	0.104676	+	0.511320i
$57$			12.7567i			1.68967i
$58$	−12.0762	+	4.84395i	−1.58568	+	0.636042i
$59$	1.05228	+	1.44834i	0.136996	+	0.188558i	0.872003	−	0.489501i	$-0.162821\pi$
$59$	1.05228	+	1.44834i	0.136996	+	0.188558i	−0.735007	+	0.678060i	$0.762821\pi$
$60$	−5.49488	+	7.01168i	−0.709386	+	0.905204i
$61$	1.30861	−	1.80115i	0.167550	−	0.230613i	−0.716983	−	0.697091i	$-0.754477\pi$
$61$	1.30861	−	1.80115i	0.167550	−	0.230613i	0.884533	+	0.466478i	$0.154477\pi$
$62$	−1.55245	+	6.16078i	−0.197162	+	0.782420i
$63$	0.785578	+	1.08126i	0.0989736	+	0.136225i
$64$	7.35643	−	3.14372i	0.919553	−	0.392965i
$65$	−6.10547	−	3.21877i	−0.757290	−	0.399239i
$66$	−14.1388	−	3.56283i	−1.74036	−	0.438553i
$67$	−0.552275	+	1.69973i	−0.0674711	+	0.207655i	−0.979108	−	0.203343i	$-0.934819\pi$
$67$	−0.552275	+	1.69973i	−0.0674711	+	0.207655i	0.911637	+	0.410997i	$0.134819\pi$
$68$	−7.51218	−	1.36343i	−0.910986	−	0.165340i
$69$	0.544154	+	0.176806i	0.0655085	+	0.0212850i
$70$	3.77947	−	2.18723i	0.451733	−	0.261424i
$71$	−4.68658	−	14.4238i	−0.556194	−	1.71179i	−0.692768	−	0.721161i	$-0.743609\pi$
$71$	−4.68658	−	14.4238i	−0.556194	−	1.71179i	0.136574	−	0.990630i	$-0.456391\pi$
$72$	1.84700	−	2.02057i	0.217671	−	0.238126i
$73$	6.88021	−	9.46979i	0.805267	−	1.10836i	−0.186769	−	0.982404i	$-0.559802\pi$
$73$	6.88021	−	9.46979i	0.805267	−	1.10836i	0.992036	−	0.125951i	$-0.0401983\pi$
$74$	5.46964	−	4.56628i	0.635833	−	0.530820i
$75$	9.38289	+	3.34035i	1.08344	+	0.385710i
$76$	−12.6024	−	2.28728i	−1.44560	−	0.262369i
$77$	5.78231	+	4.20109i	0.658955	+	0.478759i
$78$	7.36242	+	4.62623i	0.833630	+	0.523817i
$79$	−0.381800	−	1.17506i	−0.0429559	−	0.132205i	0.927279	−	0.374372i	$-0.122142\pi$
$79$	−0.381800	−	1.17506i	−0.0429559	−	0.132205i	−0.970234	+	0.242167i	$0.922142\pi$
$80$	−5.94162	−	6.68559i	−0.664293	−	0.747472i
$81$	−3.38894	+	10.4301i	−0.376549	+	1.15890i
$82$	−4.40845	+	3.68036i	−0.486832	+	0.406428i
$83$	1.29836	−	3.99593i	0.142513	−	0.438610i	−0.854170	−	0.519994i	$-0.825934\pi$
$83$	1.29836	−	3.99593i	0.142513	−	0.438610i	0.996683	+	0.0813841i	$0.0259341\pi$
$84$	−4.95655	+	2.38682i	−0.540804	+	0.260423i
$85$	1.21779	+	8.44877i	0.132088	+	0.916398i
$86$	−10.6433	+	0.717473i	−1.14769	+	0.0773671i
$87$	−10.7723	−	14.8268i	−1.15491	−	1.58960i
$88$	6.05480	−	13.3289i	0.645444	−	1.42087i
$89$	−9.13763	−	6.63888i	−0.968587	−	0.703720i	−0.0134580	−	0.999909i	$-0.504284\pi$
$89$	−9.13763	−	6.63888i	−0.968587	−	0.703720i	−0.955129	+	0.296190i	$0.904284\pi$
$90$	−2.79732	−	1.24202i	−0.294863	−	0.130921i
$91$	−2.50532	−	3.44828i	−0.262629	−	0.361478i
$92$	−0.272234	+	0.505870i	−0.0283824	+	0.0527406i
$93$	−8.94886			−0.927954
$94$	−1.31712	+	0.528317i	−0.135850	+	0.0544918i
$95$	2.04297	+	14.1736i	0.209604	+	1.45418i
$96$	6.82566	+	8.96560i	0.696641	+	0.915048i
$97$	−4.65397	+	1.51217i	−0.472539	+	0.153537i	−0.535599	−	0.844473i	$-0.679914\pi$
$97$	−4.65397	+	1.51217i	−0.472539	+	0.153537i	0.0630600	+	0.998010i	$0.479914\pi$
$98$	−7.18651	+	0.484449i	−0.725948	+	0.0489368i
$99$		−	5.00958i		−	0.503482i
$100$	−4.98229	+	8.67046i	−0.498229	+	0.867046i
$101$		−	16.5698i		−	1.64876i	−0.566039	−	0.824378i	$-0.691525\pi$
$101$		−	16.5698i		−	1.64876i	0.566039	−	0.824378i	$-0.308475\pi$
$102$	−0.723290	−	10.7296i	−0.0716164	−	1.06239i
$103$	−3.86872	+	1.25702i	−0.381196	+	0.123858i	−0.493346	−	0.869833i	$-0.664226\pi$
$103$	−3.86872	+	1.25702i	−0.381196	+	0.123858i	0.112150	+	0.993691i	$0.464226\pi$
$104$	−5.89034	+	6.44387i	−0.577595	+	0.631874i
$105$	4.28816	+	4.40930i	0.418482	+	0.430304i
$106$	1.74610	+	4.35310i	0.169596	+	0.422810i
$107$	13.5206			1.30709			0.653545	−	0.756888i	$-0.273281\pi$
$107$	13.5206			1.30709			0.653545	+	0.756888i	$0.273281\pi$
$108$	−7.12906	−	3.83651i	−0.685995	−	0.369169i
$109$	5.89818	+	8.11815i	0.564944	+	0.777578i	0.991945	−	0.126673i	$-0.0404299\pi$
$109$	5.89818	+	8.11815i	0.564944	+	0.777578i	−0.427001	+	0.904251i	$0.640430\pi$
$110$	−16.2798	−	1.69425i	−1.55221	−	0.161540i
$111$	8.11925	+	5.89898i	0.770645	+	0.559906i
$112$	−1.46923	−	5.32454i	−0.138829	−	0.503122i
$113$	5.59149	+	7.69603i	0.526004	+	0.723982i	0.986515	−	0.163672i	$-0.0523339\pi$
$113$	5.59149	+	7.69603i	0.526004	+	0.723982i	−0.460511	+	0.887654i	$0.652334\pi$
$114$	−1.21339	−	17.9999i	−0.113644	−	1.68585i
$115$	0.632909	+	0.109299i	0.0590190	+	0.0101922i
$116$	16.5789	−	7.98353i	1.53931	−	0.741252i
$117$	−0.923177	+	2.84125i	−0.0853478	+	0.262673i
$118$	−1.62255	−	1.94354i	−0.149367	−	0.178917i
$119$	−1.62897	+	5.01345i	−0.149327	+	0.459582i
$120$	7.08640	−	10.4162i	0.646897	−	0.950866i
$121$	−4.87941	−	15.0173i	−0.443583	−	1.36521i
$122$	−1.67514	+	2.66591i	−0.151660	+	0.241360i
$123$	−6.54400	−	4.75449i	−0.590052	−	0.428698i
$124$	1.60453	−	8.84060i	0.144091	−	0.793909i
$125$	10.9600	+	2.20871i	0.980292	+	0.197553i
$126$	−1.21131	−	1.45094i	−0.107912	−	0.129260i
$127$	−4.92287	+	6.77575i	−0.436834	+	0.601251i	−0.969505	−	0.245072i	$-0.921188\pi$
$127$	−4.92287	+	6.77575i	−0.436834	+	0.601251i	0.532671	+	0.846323i	$0.321188\pi$
$128$	−10.0810	+	5.13555i	−0.891041	+	0.453923i
$129$	−4.64308	−	14.2899i	−0.408800	−	1.25816i
$130$	8.92105	+	3.96099i	0.782428	+	0.347401i
$131$	8.61583	+	2.79945i	0.752769	+	0.244589i	0.660172	−	0.751114i	$-0.270483\pi$
$131$	8.61583	+	2.79945i	0.752769	+	0.244589i	0.0925967	+	0.995704i	$0.470483\pi$
$132$	20.2889	+	3.68234i	1.76592	+	0.320507i
$133$	−2.73275	+	8.41055i	−0.236960	+	0.729287i
$134$	0.617592	−	2.45087i	0.0533519	−	0.211723i
$135$	−1.54032	+	8.91938i	−0.132570	+	0.767658i
$136$	10.7295	+	1.20927i	0.920044	+	0.103694i
$137$	−0.409034	−	0.562988i	−0.0349462	−	0.0480993i	0.791186	−	0.611575i	$-0.209464\pi$
$137$	−0.409034	−	0.562988i	−0.0349462	−	0.0480993i	−0.826133	+	0.563476i	$0.809464\pi$
$138$	−0.784625	−	0.197717i	−0.0667917	−	0.0168308i
$139$	−6.25490	+	8.60913i	−0.530533	+	0.730217i	−0.987212	−	0.159415i	$-0.949039\pi$
$139$	−6.25490	+	8.60913i	−0.530533	+	0.730217i	0.456678	+	0.889632i	$0.349039\pi$
$140$	−5.12483	+	3.44570i	−0.433127	+	0.291215i
$141$	−1.17491	−	1.61712i	−0.0989449	−	0.136186i
$142$	7.98477	+	19.9064i	0.670067	+	1.67051i
$143$			15.9763i			1.33600i
$144$	−2.41394	+	3.02672i	−0.201162	+	0.252227i
$145$	−14.3432	−	14.7484i	−1.19114	−	1.22479i
$146$	−8.80730	+	14.0164i	−0.728898	+	1.16001i
$147$	−3.13508	−	9.64878i	−0.258577	−	0.795818i
$148$	−7.28339	+	6.96334i	−0.598691	+	0.572383i
$149$			3.22211i			0.263966i	0.991252	+	0.131983i	$0.0421344\pi$
$149$			3.22211i			0.263966i	−0.991252	+	0.131983i	$0.957866\pi$
$150$	−13.5571	−	3.82079i	−1.10693	−	0.311966i
$151$	20.1976			1.64366			0.821828	−	0.569736i	$-0.192955\pi$
$151$	20.1976			1.64366			0.821828	+	0.569736i	$0.192955\pi$
$152$	17.9997	+	2.02867i	1.45997	+	0.164547i
$153$	3.51394	−	1.14175i	0.284085	−	0.0923049i
$154$	−8.55850	−	5.37779i	−0.689664	−	0.433355i
$155$	−9.94281	+	1.43314i	−0.798626	+	0.115113i
$156$	−10.8285	−	5.82736i	−0.866974	−	0.466563i
$157$	−21.3717			−1.70565			−0.852824	−	0.522198i	$-0.825112\pi$
$157$	−21.3717			−1.70565			−0.852824	+	0.522198i	$0.825112\pi$
$158$	0.650493	+	1.62171i	0.0517505	+	0.129016i
$159$	−5.34461	+	3.88309i	−0.423855	+	0.307949i
$160$	9.01961	+	8.86829i	0.713063	+	0.701100i
$161$	0.320886	+	0.233138i	0.0252894	+	0.0183738i
$162$	3.78975	−	15.0393i	0.297751	−	1.18160i
$163$	−10.2617	+	7.45556i	−0.803759	+	0.583965i	−0.912014	−	0.410158i	$-0.865473\pi$
$163$	−10.2617	+	7.45556i	−0.803759	+	0.583965i	0.108256	+	0.994123i	$0.465473\pi$
$164$	5.87031	−	5.61235i	0.458394	−	0.438251i
$165$	−3.28901	−	22.8184i	−0.256049	−	1.77641i
$166$	−1.45191	+	5.76180i	−0.112690	+	0.447202i
$167$	8.75032	+	2.84315i	0.677120	+	0.220010i	0.627334	−	0.778750i	$-0.284146\pi$
$167$	8.75032	+	2.84315i	0.677120	+	0.220010i	0.0497860	+	0.998760i	$0.484146\pi$
$168$	6.76671	−	3.83928i	0.522063	−	0.296207i
$169$	−1.07308	+	3.30259i	−0.0825444	+	0.254045i
$170$	−2.52195	−	11.8055i	−0.193424	−	0.905439i
$171$	5.89498	−	1.91539i	0.450800	−	0.146474i
$172$	14.9495	−	2.02472i	1.13989	−	0.154384i
$173$	15.7758	+	11.4618i	1.19941	+	0.871423i	0.994227	−	0.107301i	$-0.0342208\pi$
$173$	15.7758	+	11.4618i	1.19941	+	0.871423i	0.205184	+	0.978723i	$0.434221\pi$
$174$	16.6101	+	19.8961i	1.25921	+	1.50832i
$175$	5.47059	+	4.21230i	0.413538	+	0.318420i
$176$	−7.27558	+	19.3832i	−0.548418	+	1.46106i
$177$	2.09609	−	2.88503i	0.157552	−	0.216852i
$178$	13.5248	+	8.49838i	1.01372	+	0.636981i
$179$	3.15544	−	1.02527i	0.235849	−	0.0766320i	−0.188708	−	0.982033i	$-0.560430\pi$
$179$	3.15544	−	1.02527i	0.235849	−	0.0766320i	0.424557	+	0.905401i	$0.360430\pi$
$180$	4.06519	+	1.48643i	0.303001	+	0.110792i
$181$	−4.68953	−	1.52372i	−0.348570	−	0.113257i	0.129499	−	0.991580i	$-0.458663\pi$
$181$	−4.68953	−	1.52372i	−0.348570	−	0.113257i	−0.478069	+	0.878322i	$0.658663\pi$
$182$	3.86303	+	4.62726i	0.286347	+	0.342995i
$183$	−4.21771	−	1.37042i	−0.311782	−	0.101304i
$184$	0.336008	−	0.739682i	0.0247709	−	0.0545301i
$185$	9.96576	+	5.25390i	0.732697	+	0.386274i
$186$	12.6269	−	0.851193i	0.925852	−	0.0624125i
$187$	15.9852	−	11.6139i	1.16896	−	0.849296i
$188$	1.80822	−	0.870743i	0.131878	−	0.0635055i
$189$	−3.28554	+	4.52215i	−0.238988	+	0.328938i
$190$	−4.23081	−	19.8048i	−0.306935	−	1.43679i
$191$	−0.543712	+	0.395030i	−0.0393416	+	0.0285833i	−0.607282	−	0.794486i	$-0.707740\pi$
$191$	−0.543712	+	0.395030i	−0.0393416	+	0.0285833i	0.567941	+	0.823069i	$0.307740\pi$
$192$	−10.4839	−	12.0013i	−0.756608	−	0.866121i
$193$			4.75497i			0.342270i	0.985248	+	0.171135i	$0.0547434\pi$
$193$			4.75497i			0.342270i	−0.985248	+	0.171135i	$0.945257\pi$
$194$	6.42297	−	2.57636i	0.461142	−	0.184972i
$195$	−2.33962	+	13.5479i	−0.167544	+	0.970182i
$196$	10.0942	−	1.36713i	0.721012	−	0.0976519i
$197$	−1.73569	−	5.34192i	−0.123663	−	0.380596i	0.869992	−	0.493066i	$-0.164124\pi$
$197$	−1.73569	−	5.34192i	−0.123663	−	0.380596i	−0.993655	+	0.112470i	$0.964124\pi$
$198$	0.476499	+	7.06858i	0.0338633	+	0.502342i
$199$	3.56353			0.252612			0.126306	−	0.991991i	$-0.459688\pi$
$199$	3.56353			0.252612			0.126306	+	0.991991i	$0.459688\pi$
$200$	6.20535	−	12.7080i	0.438785	−	0.898592i
$201$	3.56001			0.251104
$202$	1.57608	+	23.3802i	0.110892	+	1.64502i
$203$	−3.92599	−	12.0830i	−0.275551	−	0.848058i
$204$	2.04114	+	15.0708i	0.142908	+	1.05516i
$205$	−8.03226	−	4.23457i	−0.560997	−	0.295755i
$206$	5.33924	−	2.14165i	0.372002	−	0.149216i
$207$		−	0.278004i		−	0.0193226i
$208$	7.69841	−	9.65265i	0.533789	−	0.669291i
$209$	26.8168	−	19.4835i	1.85495	−	1.34770i
$210$	−6.47005	−	5.81370i	−0.446476	−	0.401183i
$211$	16.5725	−	22.8101i	1.14090	−	1.57031i	0.375411	−	0.926859i	$-0.377502\pi$
$211$	16.5725	−	22.8101i	1.14090	−	1.57031i	0.765487	−	0.643452i	$-0.222498\pi$
$212$	−2.87782	−	5.97619i	−0.197650	−	0.410446i
$213$	−24.4405	+	17.7570i	−1.67463	+	1.21669i
$214$	−19.0778	+	1.28605i	−1.30413	+	0.0879126i
$215$	−7.44728	−	15.1335i	−0.507901	−	1.03210i
$216$	10.4241	+	4.73526i	0.709271	+	0.322194i
$217$	−5.90000	−	1.91703i	−0.400518	−	0.130136i
$218$	−9.09458	−	10.8938i	−0.615963	−	0.737820i
$219$	−22.1752	−	7.20516i	−1.49846	−	0.486879i
$220$	23.1321	+	0.842117i	1.55956	+	0.0567755i
$221$	−11.2065	+	3.64120i	−0.753828	+	0.244934i
$222$	−12.0174	−	7.55124i	−0.806558	−	0.506806i
$223$	9.72513	−	13.3855i	0.651243	−	0.896359i	−0.347909	−	0.937528i	$-0.613108\pi$
$223$	9.72513	−	13.3855i	0.651243	−	0.896359i	0.999152	+	0.0411689i	$0.0131082\pi$
$224$	2.57956	+	7.37323i	0.172354	+	0.492645i
$225$	0.134778	−	4.83744i	0.00898521	−	0.322496i
$226$	−8.62169	−	10.3273i	−0.573506	−	0.686964i
$227$	9.97209	+	7.24515i	0.661871	+	0.480878i	0.867294	−	0.497796i	$-0.165857\pi$
$227$	9.97209	+	7.24515i	0.661871	+	0.480878i	−0.205423	+	0.978673i	$0.565857\pi$
$228$	3.42421	+	25.2827i	0.226774	+	1.67438i
$229$	−10.7797	+	3.50252i	−0.712340	+	0.231453i	−0.642699	−	0.766119i	$-0.722185\pi$
$229$	−10.7797	+	3.50252i	−0.712340	+	0.231453i	−0.0696410	+	0.997572i	$0.522185\pi$
$230$	−0.903437	−	0.0940216i	−0.0595709	−	0.00619960i
$231$	4.39951	−	13.5403i	0.289467	−	0.890887i
$232$	−22.6336	+	12.8418i	−1.48597	+	0.843105i
$233$	−6.12514	−	1.99018i	−0.401271	−	0.130381i	0.101427	−	0.994843i	$-0.467659\pi$
$233$	−6.12514	−	1.99018i	−0.401271	−	0.130381i	−0.502698	+	0.864462i	$0.667659\pi$
$234$	1.03236	−	4.09684i	0.0674876	−	0.267819i
$235$	−1.56438	−	1.60857i	−0.102049	−	0.104932i
$236$	2.47429	+	2.58802i	0.161063	+	0.168466i
$237$	−1.99109	+	1.44661i	−0.129335	+	0.0939673i
$238$	1.82163	−	7.22898i	0.118078	−	0.468585i
$239$	1.70418	+	1.23816i	0.110234	+	0.0800897i	0.641537	−	0.767092i	$-0.278297\pi$
$239$	1.70418	+	1.23816i	0.110234	+	0.0800897i	−0.531303	+	0.847182i	$0.678297\pi$
$240$	−9.00822	+	15.3714i	−0.581478	+	0.992222i
$241$	−17.2054	+	12.5005i	−1.10830	+	0.805227i	−0.982395	−	0.186816i	$-0.940183\pi$
$241$	−17.2054	+	12.5005i	−1.10830	+	0.805227i	−0.125904	+	0.992042i	$0.540183\pi$
$242$	8.31331	+	20.7254i	0.534400	+	1.33228i
$243$	9.70164			0.622360
$244$	2.11007	−	3.92097i	0.135083	−	0.251014i
$245$	−5.02853	−	10.2184i	−0.321261	−	0.652829i
$246$	9.68589	+	6.08619i	0.617550	+	0.388041i
$247$	−18.7999	+	6.10847i	−1.19621	+	0.388672i
$248$	−1.42311	+	12.6268i	−0.0903678	+	0.801803i
$249$	−8.36931			−0.530384
$250$	−15.6748	−	2.07402i	−0.991360	−	0.131173i
$251$			17.4979i			1.10446i	0.833693	+	0.552229i	$0.186222\pi$
$251$			17.4979i			1.10446i	−0.833693	+	0.552229i	$0.813778\pi$
$252$	1.84718	+	1.93208i	0.116361	+	0.121710i
$253$	−0.459417	−	1.41394i	−0.0288833	−	0.0888936i
$254$	6.30173	−	10.0289i	0.395406	−	0.629270i
$255$	15.2562	−	7.50767i	0.955382	−	0.470148i
$256$	13.7359	−	8.20520i	0.858493	−	0.512825i
$257$			28.7486i			1.79329i	0.442753	+	0.896644i	$0.354002\pi$
$257$			28.7486i			1.79329i	−0.442753	+	0.896644i	$0.645998\pi$
$258$	7.91065	+	19.7216i	0.492496	+	1.22781i
$259$	4.08936	+	5.62852i	0.254100	+	0.349739i
$260$	−12.9645	−	4.74045i	−0.804022	−	0.293990i
$261$	−5.23412	+	7.20415i	−0.323984	+	0.445926i
$262$	−12.4233	−	3.13054i	−0.767515	−	0.193406i
$263$	−12.3479	−	16.9955i	−0.761407	−	1.04799i	−0.997096	−	0.0761580i	$-0.975735\pi$
$263$	−12.3479	−	16.9955i	−0.761407	−	1.04799i	0.235689	−	0.971829i	$-0.424265\pi$
$264$	−28.9781	−	3.26600i	−1.78348	−	0.201008i
$265$	−5.31637	+	5.17031i	−0.326582	+	0.317609i
$266$	3.05595	−	12.1273i	0.187373	−	0.743573i
$267$	−6.95243	+	21.3974i	−0.425482	+	1.30950i
$268$	−0.638309	+	3.51694i	−0.0389910	+	0.214831i
$269$	−15.0792	−	4.89953i	−0.919396	−	0.298730i	−0.189177	−	0.981943i	$-0.560582\pi$
$269$	−15.0792	−	4.89953i	−0.919396	−	0.298730i	−0.730219	+	0.683213i	$0.760582\pi$
$270$	1.32502	−	12.7319i	0.0806380	−	0.774836i
$271$	9.17886	+	28.2496i	0.557576	+	1.71604i	0.689041	+	0.724722i	$0.258032\pi$
$271$	9.17886	+	28.2496i	0.557576	+	1.71604i	−0.131465	+	0.991321i	$0.541968\pi$
$272$	−15.2544	−	0.685736i	−0.924934	−	0.0415789i
$273$	−4.99048	+	6.86880i	−0.302037	+	0.415719i
$274$	0.630702	+	0.755475i	0.0381021	+	0.0456399i
$275$	−7.30864	−	24.8261i	−0.440728	−	1.49707i
$276$	1.12592	+	0.204350i	0.0677725	+	0.0123004i
$277$	0.881062	+	0.640129i	0.0529379	+	0.0384616i	0.613940	−	0.789353i	$-0.289584\pi$
$277$	0.881062	+	0.640129i	0.0529379	+	0.0384616i	−0.561002	+	0.827815i	$0.689584\pi$
$278$	8.00685	−	12.7425i	0.480219	−	0.764246i
$279$	1.34365	+	4.13533i	0.0804422	+	0.247576i
$280$	6.90344	−	5.34938i	0.412560	−	0.319687i
$281$	−7.85909	+	24.1878i	−0.468834	+	1.44292i	0.385261	+	0.922808i	$0.374111\pi$
$281$	−7.85909	+	24.1878i	−0.468834	+	1.44292i	−0.854096	+	0.520116i	$0.825889\pi$
$282$	1.81162	+	2.17002i	0.107881	+	0.129223i
$283$	7.75392	−	23.8641i	0.460923	−	1.41857i	−0.403116	−	0.915149i	$-0.632073\pi$
$283$	7.75392	−	23.8641i	0.460923	−	1.41857i	0.864039	−	0.503425i	$-0.167927\pi$
$284$	−13.1600	−	27.3286i	−0.780905	−	1.62166i
$285$	25.5938	−	12.5948i	1.51605	−	0.746054i
$286$	−1.51962	−	22.5427i	−0.0898572	−	1.33298i
$287$	−3.29596	−	4.53650i	−0.194554	−	0.267781i
$288$	3.11821	−	4.50035i	0.183742	−	0.265186i
$289$	−1.96352	−	1.42658i	−0.115501	−	0.0839166i
$290$	21.6413	+	19.4459i	1.27082	+	1.14190i
$291$	5.72946	+	7.88593i	0.335867	+	0.462281i
$292$	11.0940	−	20.6150i	0.649227	−	1.20640i
$293$	31.6461			1.84879			0.924393	−	0.381440i	$-0.124572\pi$
$293$	31.6461			1.84879			0.924393	+	0.381440i	$0.124572\pi$
$294$	5.34140	+	13.3163i	0.311517	+	0.776625i
$295$	1.86688	−	3.54115i	0.108694	−	0.206174i
$296$	9.61462	−	10.5181i	0.558838	−	0.611354i
$297$	19.9262	−	6.47442i	1.15624	−	0.375684i
$298$	−0.306480	−	4.54644i	−0.0177539	−	0.263368i
$299$			0.886596i			0.0512731i
$300$	19.4926	+	4.10166i	1.12541	+	0.236809i
$301$		−	10.4160i		−	0.600369i
$302$	−28.4990	+	1.92114i	−1.63993	+	0.110549i
$303$	−31.3908	+	10.1995i	−1.80335	+	0.585945i
$304$	−25.5908	−	1.15039i	−1.46773	−	0.0659793i
$305$	−4.90564	−	0.847171i	−0.280896	−	0.0485089i
$306$	−4.84961	+	1.94526i	−0.277234	+	0.111203i
$307$	−3.74062			−0.213488			−0.106744	−	0.994287i	$-0.534043\pi$
$307$	−3.74062			−0.213488			−0.106744	+	0.994287i	$0.534043\pi$
$308$	12.5877	+	6.77406i	0.717249	+	0.385988i
$309$	4.76275	+	6.55536i	0.270943	+	0.372921i
$310$	13.8931	−	2.96791i	0.789075	−	0.168566i
$311$	−9.08998	−	6.60426i	−0.515446	−	0.374493i	0.299440	−	0.954115i	$-0.403200\pi$
$311$	−9.08998	−	6.60426i	−0.515446	−	0.374493i	−0.814885	+	0.579622i	$0.803200\pi$
$312$	15.8334	+	7.19250i	0.896391	+	0.407195i
$313$	−3.87093	−	5.32787i	−0.218798	−	0.301149i	0.685482	−	0.728089i	$-0.259591\pi$
$313$	−3.87093	−	5.32787i	−0.218798	−	0.301149i	−0.904280	+	0.426940i	$0.859591\pi$
$314$	30.1557	−	2.03282i	1.70179	−	0.114719i
$315$	1.39371	−	2.64364i	0.0785267	−	0.148952i
$316$	−1.07211	−	2.22637i	−0.0603107	−	0.125243i
$317$	6.24885	−	19.2320i	0.350970	−	1.08018i	−0.607339	−	0.794443i	$-0.707763\pi$
$317$	6.24885	−	19.2320i	0.350970	−	1.08018i	0.958309	−	0.285733i	$-0.0922370\pi$
$318$	7.17195	−	5.98744i	0.402183	−	0.335759i
$319$	−14.7157	+	45.2902i	−0.823920	+	2.53577i
$320$	−13.5703	−	11.6553i	−0.758603	−	0.651553i
$321$	−8.32258	−	25.6143i	−0.464521	−	1.42965i
$322$	−0.474950	−	0.298438i	−0.0264679	−	0.0166313i
$323$	19.7785	+	14.3699i	1.10050	+	0.799563i
$324$	−3.91687	+	21.5811i	−0.217604	+	1.19895i
$325$	−0.429827	+	15.4273i	−0.0238425	+	0.855752i
$326$	13.7702	−	11.4960i	0.762662	−	0.636702i
$327$	11.7489	−	16.1710i	0.649715	−	0.894256i
$328$	−7.74924	+	8.47746i	−0.427880	+	0.468089i
$329$	−0.428198	−	1.31786i	−0.0236073	−	0.0726559i
$330$	6.81126	+	31.8842i	0.374948	+	1.75517i
$331$	−20.2986	−	6.59541i	−1.11571	−	0.362517i	−0.307582	−	0.951522i	$-0.599520\pi$
$331$	−20.2986	−	6.59541i	−1.11571	−	0.362517i	−0.808129	+	0.589005i	$0.799520\pi$
$332$	1.50062	−	8.26806i	0.0823570	−	0.453769i
$333$	1.50687	−	4.63768i	0.0825761	−	0.254143i
$334$	−12.6172	−	3.17941i	−0.690384	−	0.173970i
$335$	3.95542	−	0.570128i	0.216108	−	0.0311494i
$336$	−9.18273	+	6.06090i	−0.500959	+	0.330649i
$337$	9.78712	+	13.4708i	0.533139	+	0.733802i	0.987605	−	0.156962i	$-0.0501700\pi$
$337$	9.78712	+	13.4708i	0.533139	+	0.733802i	−0.454466	+	0.890764i	$0.650170\pi$
$338$	1.19999	−	4.76206i	0.0652708	−	0.259022i
$339$	11.1380	−	15.3301i	0.604932	−	0.832617i
$340$	4.68140	+	16.4178i	0.253885	+	0.890379i
$341$	13.6677	+	18.8120i	0.740147	+	1.01873i
$342$	−8.13569	+	3.26336i	−0.439928	+	0.176462i
$343$		−	16.6992i		−	0.901674i
$344$	−20.9014	+	4.27887i	−1.12693	+	0.230701i
$345$	−0.182522	−	1.26630i	−0.00982666	−	0.0681751i
$346$	−23.3500	−	14.6721i	−1.25530	−	0.788779i
$347$	4.90149	+	15.0852i	0.263126	+	0.809818i	0.992119	+	0.125297i	$0.0399884\pi$
$347$	4.90149	+	15.0852i	0.263126	+	0.809818i	−0.728993	+	0.684521i	$0.760012\pi$
$348$	−25.3295	−	26.4937i	−1.35780	−	1.42021i
$349$		−	11.9445i		−	0.639375i	−0.947523	−	0.319688i	$-0.896422\pi$
$349$		−	11.9445i		−	0.639375i	0.947523	−	0.319688i	$-0.103578\pi$
$350$	−8.11973	−	5.42326i	−0.434018	−	0.289885i
$351$	−12.4945			−0.666908
$352$	8.42225	−	28.0419i	0.448907	−	1.49464i
$353$	4.78471	−	1.55465i	0.254665	−	0.0827456i	−0.178903	−	0.983867i	$-0.557255\pi$
$353$	4.78471	−	1.55465i	0.254665	−	0.0827456i	0.433567	+	0.901121i	$0.357255\pi$
$354$	−2.68320	+	4.27018i	−0.142610	+	0.226958i
$355$	−24.3113	+	23.6434i	−1.29031	+	1.25486i
$356$	−19.8920	−	10.7049i	−1.05427	−	0.567357i
$357$	10.5005			0.555744
$358$	−4.35485	+	1.74680i	−0.230161	+	0.0923212i
$359$	4.41690	−	3.20906i	0.233115	−	0.169368i	−0.465096	−	0.885260i	$-0.653980\pi$
$359$	4.41690	−	3.20906i	0.233115	−	0.169368i	0.698210	+	0.715893i	$0.253980\pi$
$360$	−5.87741	−	1.71070i	−0.309767	−	0.0901620i
$361$	17.8090	+	12.9390i	0.937315	+	0.681000i
$362$	6.76191	+	1.70393i	0.355398	+	0.0895566i
$363$	−25.4461	+	18.4877i	−1.33557	+	0.970351i
$364$	−5.89091	−	6.16168i	−0.308768	−	0.322960i
$365$	−25.7921	−	4.45412i	−1.35002	−	0.233139i
$366$	6.08158	+	1.53249i	0.317889	+	0.0801048i
$367$	14.3846	+	4.67384i	0.750871	+	0.243973i	0.659356	−	0.751831i	$-0.270829\pi$
$367$	14.3846	+	4.67384i	0.750871	+	0.243973i	0.0915149	+	0.995804i	$0.470829\pi$
$368$	−0.403755	+	1.07566i	−0.0210472	+	0.0560727i
$369$	−1.21452	+	3.73790i	−0.0632253	+	0.194587i
$370$	−14.5615	−	6.46539i	−0.757018	−	0.336120i
$371$	−4.35555	+	1.41520i	−0.226129	+	0.0734737i
$372$	−17.7358	+	2.40209i	−0.919558	+	0.124542i
$373$	26.1912	+	19.0290i	1.35613	+	0.985284i	0.998681	+	0.0513509i	$0.0163527\pi$
$373$	26.1912	+	19.0290i	1.35613	+	0.985284i	0.357447	+	0.933933i	$0.383647\pi$
$374$	−21.4506	+	17.9079i	−1.10919	+	0.925994i
$375$	−2.56209	−	22.1228i	−0.132306	−	1.14242i
$376$	−2.46859	+	1.40062i	−0.127308	+	0.0722315i
$377$	16.6924	−	22.9751i	0.859701	−	1.18328i
$378$	4.20579	−	6.69332i	0.216323	−	0.344267i
$379$	12.3752	−	4.02096i	0.635674	−	0.206543i	0.0265869	−	0.999647i	$-0.491536\pi$
$379$	12.3752	−	4.02096i	0.635674	−	0.206543i	0.609087	+	0.793104i	$0.291536\pi$
$380$	7.85351	+	27.5424i	0.402876	+	1.41290i
$381$	15.8666	+	5.15538i	0.812872	+	0.264118i
$382$	0.729609	−	0.609108i	0.0373300	−	0.0311647i
$383$	13.4131	+	4.35817i	0.685376	+	0.222692i	0.630948	−	0.775825i	$-0.282666\pi$
$383$	13.4131	+	4.35817i	0.685376	+	0.222692i	0.0544287	+	0.998518i	$0.482666\pi$
$384$	15.9344	+	15.9368i	0.813149	+	0.813272i
$385$	2.71971	−	15.7488i	0.138609	−	0.802633i
$386$	−0.452281	−	6.70931i	−0.0230205	−	0.341495i
$387$	−5.90632	+	4.29119i	−0.300235	+	0.218134i
$388$	−8.81782	+	4.24620i	−0.447657	+	0.215568i
$389$	11.6423	−	16.0243i	0.590290	−	0.812465i	−0.404486	−	0.914544i	$-0.632550\pi$
$389$	11.6423	−	16.0243i	0.590290	−	0.812465i	0.994776	+	0.102080i	$0.0325496\pi$
$390$	2.01260	−	19.3387i	0.101912	−	0.979254i
$391$	0.887092	−	0.644510i	0.0448622	−	0.0325943i
$392$	−14.1130	+	2.88916i	−0.712812	+	0.145925i
$393$		−	18.0455i		−	0.910276i
$394$	2.95719	+	7.37241i	0.148981	+	0.371417i
$395$	−1.98056	+	1.92615i	−0.0996530	+	0.0969152i
$396$	−1.34469	−	9.92852i	−0.0675733	−	0.498927i
$397$	3.25515	+	10.0183i	0.163371	+	0.502805i	0.998913	−	0.0466224i	$-0.0148457\pi$
$397$	3.25515	+	10.0183i	0.163371	+	0.502805i	−0.835541	+	0.549428i	$0.814846\pi$
$398$	−5.02818	+	0.338954i	−0.252040	+	0.0169902i
$399$	17.6156			0.881881
$400$	−7.54706	+	18.5214i	−0.377353	+	0.926069i
$401$	−14.5328			−0.725732			−0.362866	−	0.931841i	$-0.618202\pi$
$401$	−14.5328			−0.725732			−0.362866	+	0.931841i	$0.618202\pi$
$402$	−5.02322	+	0.338619i	−0.250535	+	0.0168888i
$403$	−4.28509	−	13.1882i	−0.213456	−	0.656949i
$404$	−4.44773	−	32.8398i	−0.221283	−	1.63384i
$405$	24.2717	−	3.49849i	1.20607	−	0.173841i
$406$	6.68892	+	16.6758i	0.331966	+	0.827605i
$407$		−	26.0776i		−	1.29262i
$408$	−4.31357	−	21.0709i	−0.213553	−	1.04316i
$409$	−20.3026	+	14.7507i	−1.00390	+	0.729375i	−0.962920	−	0.269785i	$-0.913047\pi$
$409$	−20.3026	+	14.7507i	−1.00390	+	0.729375i	−0.0409776	+	0.999160i	$0.513047\pi$
$410$	11.7364	+	5.21101i	0.579619	+	0.257353i
$411$	−0.814776	+	1.12144i	−0.0401899	+	0.0553167i
$412$	−7.33001	+	3.52975i	−0.361124	+	0.173898i
$413$	1.99999	−	1.45308i	0.0984131	−	0.0715013i
$414$	0.0264431	+	0.392267i	0.00129961	+	0.0192789i
$415$	−9.29889	+	1.34033i	−0.456465	+	0.0657941i
$416$	−9.94441	+	14.3523i	−0.487565	+	0.703677i
$417$	20.1598	+	6.55032i	0.987230	+	0.320770i
$418$	−35.9855	+	30.0422i	−1.76011	+	1.46941i
$419$	−0.728039	−	0.236554i	−0.0355671	−	0.0115564i	0.291179	−	0.956668i	$-0.405952\pi$
$419$	−0.728039	−	0.236554i	−0.0355671	−	0.0115564i	−0.326746	+	0.945112i	$0.605952\pi$
$420$	9.68230	+	7.58777i	0.472448	+	0.370245i
$421$	11.1284	−	3.61584i	0.542366	−	0.176225i	−0.0250056	−	0.999687i	$-0.507960\pi$
$421$	11.1284	−	3.61584i	0.542366	−	0.176225i	0.567371	+	0.823462i	$0.307960\pi$
$422$	−21.2143	+	33.7616i	−1.03270	+	1.64349i
$423$	−0.570872	+	0.785739i	−0.0277568	+	0.0382039i
$424$	4.62908	+	8.15874i	0.224808	+	0.396223i
$425$	15.7484	−	10.7848i	0.763909	−	0.523139i
$426$	32.7968	−	27.3801i	1.58901	−	1.32657i
$427$	−2.48717	−	1.80704i	−0.120363	−	0.0874486i
$428$	26.7966	−	3.62926i	1.29526	−	0.175427i
$429$	30.2664	−	9.83414i	1.46127	−	0.474797i
$430$	11.9477	+	20.6452i	0.576167	+	0.995600i
$431$	6.71966	−	20.6810i	0.323675	−	0.996169i	−0.648360	−	0.761334i	$-0.724545\pi$
$431$	6.71966	−	20.6810i	0.323675	−	0.996169i	0.972035	−	0.234835i	$-0.0754550\pi$
$432$	−15.1589	−	5.68999i	−0.729335	−	0.273760i
$433$	−3.49647	−	1.13607i	−0.168030	−	0.0545962i	0.223794	−	0.974636i	$-0.428156\pi$
$433$	−3.49647	−	1.13607i	−0.168030	−	0.0545962i	−0.391824	+	0.920040i	$0.628156\pi$
$434$	8.50731	+	2.14375i	0.408364	+	0.102903i
$435$	−19.1113	+	36.2510i	−0.916319	+	1.73810i
$436$	13.8687	+	14.5062i	0.664192	+	0.694721i
$437$	1.48818	−	1.08123i	0.0711894	−	0.0517222i
$438$	31.9748	+	8.05731i	1.52781	+	0.384993i
$439$	−1.89736	−	1.37851i	−0.0905559	−	0.0657927i	0.541586	−	0.840645i	$-0.317824\pi$
$439$	−1.89736	−	1.37851i	−0.0905559	−	0.0657927i	−0.632142	+	0.774853i	$0.717824\pi$
$440$	−32.7197	+	1.01203i	−1.55985	+	0.0482466i
$441$	−3.98804	+	2.89748i	−0.189907	+	0.137975i
$442$	15.4661	−	6.20370i	0.735647	−	0.295080i
$443$	−0.969245			−0.0460502			−0.0230251	−	0.999735i	$-0.507330\pi$
$443$	−0.969245			−0.0460502			−0.0230251	+	0.999735i	$0.507330\pi$
$444$	17.6750	+	9.51182i	0.838819	+	0.451411i
$445$	−4.29789	+	24.8874i	−0.203740	+	1.17978i
$446$	−12.4491	+	19.8121i	−0.589481	+	0.938131i
$447$	6.10416	−	1.98336i	0.288717	−	0.0938098i
$448$	−4.34111	−	10.1584i	−0.205098	−	0.479937i
$449$	34.3240			1.61985			0.809925	−	0.586533i	$-0.199508\pi$
$449$	34.3240			1.61985			0.809925	+	0.586533i	$0.199508\pi$
$450$	0.269952	+	6.83851i	0.0127257	+	0.322370i
$451$			21.0181i			0.989705i
$452$	13.1476	+	13.7519i	0.618412	+	0.646836i
$453$	−12.4325	−	38.2634i	−0.584132	−	1.79777i
$454$	−14.7599	−	9.27447i	−0.692715	−	0.435272i
$455$	−4.44474	+	8.43093i	−0.208373	+	0.395248i
$456$	−7.23643	−	35.3484i	−0.338877	−	1.65534i
$457$		−	34.4324i		−	1.61068i	−0.592812	−	0.805341i	$-0.701982\pi$
$457$		−	34.4324i		−	1.61068i	0.592812	−	0.805341i	$-0.298018\pi$
$458$	14.8771	−	5.96743i	0.695160	−	0.278840i
$459$	9.08288	+	12.5015i	0.423953	+	0.583521i
$460$	1.28370	+	0.0467328i	0.0598530	+	0.00217893i
$461$	−21.8458	+	30.0682i	−1.01746	+	1.40041i	−0.103491	+	0.994630i	$0.533001\pi$
$461$	−21.8458	+	30.0682i	−1.01746	+	1.40041i	−0.913969	+	0.405783i	$0.866999\pi$
$462$	−4.91984	+	19.5240i	−0.228892	+	0.908338i
$463$	−8.48120	−	11.6734i	−0.394155	−	0.542507i	0.565110	−	0.825015i	$-0.308834\pi$
$463$	−8.48120	−	11.6734i	−0.394155	−	0.542507i	−0.959265	+	0.282508i	$0.908834\pi$
$464$	30.7148	−	20.2728i	1.42590	−	0.941139i
$465$	8.83529	+	17.9541i	0.409727	+	0.832600i
$466$	8.83194	+	2.22556i	0.409132	+	0.103097i
$467$	3.46409	−	10.6614i	0.160299	−	0.493349i	−0.838360	−	0.545116i	$-0.816485\pi$
$467$	3.46409	−	10.6614i	0.160299	−	0.493349i	0.998659	+	0.0517673i	$0.0164854\pi$
$468$	−1.06699	+	5.87889i	−0.0493217	+	0.271752i
$469$	2.34712	+	0.762626i	0.108380	+	0.0352148i
$470$	2.36036	+	2.12092i	0.108875	+	0.0978306i
$471$	13.1553	+	40.4878i	0.606163	+	1.86558i
$472$	−3.73742	−	3.41638i	−0.172029	−	0.157252i
$473$	−22.9483	+	31.5857i	−1.05517	+	1.45231i
$474$	2.67185	−	2.23057i	0.122722	−	0.102453i
$475$	26.4195	−	18.0925i	1.21221	−	0.830143i
$476$	−1.88273	+	10.3734i	−0.0862949	+	0.475466i
$477$	2.59688	+	1.88674i	0.118903	+	0.0863881i
$478$	−2.52238	−	1.58496i	−0.115371	−	0.0724942i
$479$	1.46974	+	4.52340i	0.0671543	+	0.206680i	0.979003	−	0.203848i	$-0.0653447\pi$
$479$	1.46974	+	4.52340i	0.0671543	+	0.206680i	−0.911848	+	0.410527i	$0.865345\pi$
$480$	11.2486	−	22.5461i	0.513427	−	1.02908i
$481$	−4.80563	+	14.7902i	−0.219118	+	0.674376i
$482$	23.0880	−	19.2749i	1.05163	−	0.877946i
$483$	0.244149	−	0.751413i	0.0111092	−	0.0341905i
$484$	−13.7015	−	28.4531i	−0.622797	−	1.29332i
$485$	7.62875	+	7.84426i	0.346404	+	0.356189i
$486$	−13.6891	+	0.922796i	−0.620951	+	0.0418589i
$487$	7.81977	+	10.7630i	0.354348	+	0.487718i	0.948563	−	0.316588i	$-0.102537\pi$
$487$	7.81977	+	10.7630i	0.354348	+	0.487718i	−0.594215	+	0.804306i	$0.702537\pi$
$488$	−2.60438	+	5.73323i	−0.117895	+	0.259531i
$489$	20.4408	+	14.8511i	0.924365	+	0.671590i
$490$	8.06725	+	13.9400i	0.364441	+	0.629744i
$491$	−10.4364	−	14.3645i	−0.470990	−	0.648262i	0.505752	−	0.862679i	$-0.331215\pi$
$491$	−10.4364	−	14.3645i	−0.470990	−	0.648262i	−0.976742	+	0.214417i	$0.931215\pi$
$492$	−14.2458	−	7.66639i	−0.642250	−	0.345627i
$493$	−35.1224			−1.58184
$494$	25.9459	−	10.4073i	1.16736	−	0.468247i
$495$	−10.0507	+	4.94600i	−0.451746	+	0.222306i
$496$	0.806998	−	17.9519i	0.0362353	−	0.806065i
$497$	−19.9176	+	6.47161i	−0.893425	+	0.290291i
$498$	11.8092	−	0.796068i	0.529183	−	0.0356727i
$499$		−	15.6179i		−	0.699151i	−0.936908	−	0.349576i	$-0.886326\pi$
$499$		−	15.6179i		−	0.699151i	0.936908	−	0.349576i	$-0.113674\pi$
$500$	22.3146	+	1.43553i	0.997937	+	0.0641987i
$501$		−	18.3272i		−	0.818799i
$502$	−1.66436	−	24.6897i	−0.0742838	−	1.10196i
$503$	0.0298452	−	0.00969730i	0.00133073	−	0.000432381i	−0.308352	−	0.951272i	$-0.599777\pi$
$503$	0.0298452	−	0.00969730i	0.00133073	−	0.000432381i	0.309682	+	0.950840i	$0.399777\pi$
$504$	−2.79016	−	2.55049i	−0.124284	−	0.113608i
$505$	−33.2439	+	16.3595i	−1.47933	+	0.727988i
$506$	0.782733	+	1.95139i	0.0347967	+	0.0867497i
$507$	6.91715			0.307201
$508$	−7.93789	+	14.7503i	−0.352187	+	0.654439i
$509$	6.00479	+	8.26488i	0.266157	+	0.366334i	0.921088	−	0.389355i	$-0.127302\pi$
$509$	6.00479	+	8.26488i	0.266157	+	0.366334i	−0.654930	+	0.755689i	$0.727302\pi$
$510$	−20.8126	+	12.0445i	−0.921597	+	0.533341i
$511$	−13.0767	−	9.50075i	−0.578477	−	0.420288i
$512$	−18.6010	+	12.8842i	−0.822057	+	0.569405i
$513$	15.2374	+	20.9725i	0.672748	+	0.925959i
$514$	−2.73449	−	40.5646i	−0.120613	−	1.78923i
$515$	6.34157	+	6.52072i	0.279443	+	0.287337i
$516$	−13.0379	−	27.0750i	−0.573961	−	1.19191i
$517$	−1.60500	+	4.93969i	−0.0705879	+	0.217247i
$518$	−6.30550	−	7.55293i	−0.277048	−	0.331857i
$519$	12.0031	−	36.9418i	0.526878	−	1.62156i
$520$	18.7439	+	5.45568i	0.821974	+	0.239247i
$521$	6.03139	+	18.5627i	0.264240	+	0.813248i	0.991867	+	0.127275i	$0.0406231\pi$
$521$	6.03139	+	18.5627i	0.264240	+	0.813248i	−0.727627	+	0.685973i	$0.759377\pi$
$522$	6.70017	−	10.6630i	0.293258	−	0.466707i
$523$	−7.08464	−	5.14729i	−0.309789	−	0.225075i	0.422017	−	0.906588i	$-0.361322\pi$
$523$	−7.08464	−	5.14729i	−0.309789	−	0.225075i	−0.731806	+	0.681513i	$0.761322\pi$
$524$	17.8272	+	3.23556i	0.778785	+	0.141346i
$525$	4.61262	−	12.9567i	0.201311	−	0.565475i
$526$	19.0397	+	22.8063i	0.830168	+	0.994403i
$527$	−10.0805	+	13.8746i	−0.439113	+	0.604388i
$528$	41.1991	+	1.85203i	1.79296	+	0.0805994i
$529$	7.08190	+	21.7958i	0.307909	+	0.947645i
$530$	7.00967	−	7.80104i	0.304480	−	0.338856i
$531$	−1.64791	−	0.535440i	−0.0715134	−	0.0232361i
$532$	−3.15847	+	17.4024i	−0.136937	+	0.754492i
$533$	3.87327	−	11.9207i	0.167770	−	0.516343i
$534$	7.77469	−	30.8533i	0.336444	−	1.33515i
$535$	−13.3490	−	27.1264i	−0.577129	−	1.17278i
$536$	0.566139	−	5.02316i	0.0244535	−	0.216967i
$537$	−3.88464	−	5.34675i	−0.167635	−	0.230729i
$538$	21.7430	+	5.47900i	0.937406	+	0.236216i
$539$	−15.4951	+	21.3271i	−0.667420	+	0.918625i
$540$	−0.658592	+	18.0908i	−0.0283413	+	0.778505i
$541$	−15.5336	−	21.3802i	−0.667843	−	0.919208i	0.331866	−	0.943327i	$-0.392322\pi$
$541$	−15.5336	−	21.3802i	−0.667843	−	0.919208i	−0.999709	+	0.0241190i	$0.992322\pi$
$542$	−15.6385	−	38.9875i	−0.671732	−	1.67466i
$543$			9.82203i			0.421504i
$544$	21.5894	−	0.483380i	0.925637	−	0.0207248i
$545$	10.4641	−	19.8486i	0.448232	−	0.850221i
$546$	6.38827	−	10.1666i	0.273393	−	0.435092i
$547$	−8.93390	−	27.4957i	−0.381986	−	1.17563i	−0.938643	−	0.344890i	$-0.887916\pi$
$547$	−8.93390	−	27.4957i	−0.381986	−	1.17563i	0.556657	−	0.830742i	$-0.312084\pi$
$548$	−0.961787	−	1.00599i	−0.0410855	−	0.0429739i
$549$			2.15480i			0.0919644i
$550$	12.6740	+	34.3348i	0.540420	+	1.46404i
$551$	−58.9213			−2.51013
$552$	−1.60812	−	0.181245i	−0.0684463	−	0.00771429i
$553$	−1.62262	+	0.527221i	−0.0690008	+	0.0224197i
$554$	−1.30408	−	0.819425i	−0.0554049	−	0.0348140i
$555$	3.81889	−	22.1137i	0.162103	−	0.938675i
$556$	−10.0857	+	18.7414i	−0.427730	+	0.794814i
$557$	−33.1381			−1.40411			−0.702053	−	0.712125i	$-0.747733\pi$
$557$	−33.1381			−1.40411			−0.702053	+	0.712125i	$0.747733\pi$
$558$	−2.28925	−	5.70719i	−0.0969116	−	0.241605i
$559$	18.8361	−	13.6852i	0.796682	−	0.578824i
$560$	−9.23201	+	8.20467i	−0.390124	+	0.346711i
$561$	−31.8418	−	23.1344i	−1.34436	−	0.976735i
$562$	8.78859	−	34.8768i	0.370724	−	1.47119i
$563$	−25.4540	+	18.4934i	−1.07276	+	0.779404i	−0.976406	−	0.215943i	$-0.930717\pi$
$563$	−25.4540	+	18.4934i	−1.07276	+	0.779404i	−0.0963518	+	0.995347i	$0.530717\pi$
$564$	−2.76263	−	2.88960i	−0.116328	−	0.121674i
$565$	9.91999	−	18.8165i	0.417337	−	0.791618i
$566$	−8.67097	+	34.4101i	−0.364468	+	1.44636i
$567$	14.4027	+	4.67972i	0.604857	+	0.196530i
$568$	21.1684	+	37.3092i	0.888206	+	1.56546i
$569$	−5.66167	+	17.4248i	−0.237350	+	0.730487i	0.759451	+	0.650564i	$0.225467\pi$
$569$	−5.66167	+	17.4248i	−0.237350	+	0.730487i	−0.996801	+	0.0799229i	$0.974533\pi$
$570$	−34.9151	+	20.2059i	−1.46243	+	0.846331i
$571$	4.90965	−	1.59524i	0.205462	−	0.0667588i	−0.204478	−	0.978871i	$-0.565550\pi$
$571$	4.90965	−	1.59524i	0.205462	−	0.0667588i	0.409940	+	0.912112i	$0.365550\pi$
$572$	4.28841	+	31.6635i	0.179308	+	1.32392i
$573$	1.08305	+	0.786879i	0.0452449	+	0.0328723i
$574$	5.08214	+	6.08755i	0.212124	+	0.254089i
$575$	−0.405590	−	1.37771i	−0.0169143	−	0.0574546i
$576$	−3.97176	+	6.64664i	−0.165490	+	0.276943i
$577$	0.868662	−	1.19561i	0.0361629	−	0.0497739i	−0.790553	−	0.612394i	$-0.790207\pi$
$577$	0.868662	−	1.19561i	0.0361629	−	0.0497739i	0.826716	+	0.562620i	$0.190207\pi$
$578$	2.90624	+	1.82616i	0.120884	+	0.0759581i
$579$	9.00808	−	2.92690i	0.374363	−	0.121638i
$580$	−32.3858	−	25.3799i	−1.34475	−	1.05384i
$581$	−5.51790	−	1.79288i	−0.228921	−	0.0743810i
$582$	−8.83443	−	10.5822i	−0.366199	−	0.438645i
$583$	16.3258	+	5.30456i	0.676144	+	0.219692i
$584$	−13.6929	+	30.1433i	−0.566617	+	1.24734i
$585$	6.61184	−	0.953021i	0.273366	−	0.0394026i
$586$	−44.6531	+	3.01010i	−1.84460	+	0.124346i
$587$	−6.19025	+	4.49748i	−0.255499	+	0.185631i	−0.708160	−	0.706052i	$-0.750475\pi$
$587$	−6.19025	+	4.49748i	−0.255499	+	0.185631i	0.452662	+	0.891682i	$0.350475\pi$
$588$	−8.80339	−	18.2814i	−0.363046	−	0.753914i
$589$	−16.9110	+	23.2760i	−0.696806	+	0.959071i
$590$	−2.29736	+	5.17418i	−0.0945808	+	0.213018i
$591$	−9.05163	+	6.57640i	−0.372334	+	0.270517i
$592$	−12.5659	+	15.7557i	−0.516454	+	0.647556i
$593$		−	31.1703i		−	1.28001i	−0.768370	−	0.640006i	$-0.778932\pi$
$593$		−	31.1703i		−	1.28001i	0.768370	−	0.640006i	$-0.221068\pi$
$594$	−27.5003	+	11.0308i	−1.12835	+	0.452600i
$595$	11.6668	−	1.68163i	0.478290	−	0.0689400i
$596$	0.864892	+	6.38593i	0.0354274	+	0.261578i
$597$	−2.19352	−	6.75095i	−0.0897747	−	0.276298i
$598$	−0.0843308	−	1.25100i	−0.00344854	−	0.0511570i
$599$	−30.2376			−1.23547			−0.617737	−	0.786385i	$-0.711950\pi$
$599$	−30.2376			−1.23547			−0.617737	+	0.786385i	$0.711950\pi$
$600$	−27.8945	−	3.93340i	−1.13879	−	0.160580i
$601$	47.2925			1.92910			0.964551	−	0.263895i	$-0.0850073\pi$
$601$	47.2925			1.92910			0.964551	+	0.263895i	$0.0850073\pi$
$602$	0.990745	+	14.6971i	0.0403798	+	0.599010i
$603$	−0.534527	−	1.64511i	−0.0217676	−	0.0669939i
$604$	40.0297	−	5.42151i	1.62878	−	0.220598i
$605$	−25.3116	+	24.6162i	−1.02906	+	1.00079i
$606$	43.3226	−	17.3774i	1.75986	−	0.705908i
$607$		−	13.6800i		−	0.555252i	−0.960689	−	0.277626i	$-0.910452\pi$
$607$		−	13.6800i		−	0.555252i	0.960689	−	0.277626i	$-0.0895477\pi$
$608$	36.2183	−	0.810917i	1.46884	−	0.0328870i
$609$	−20.4740	+	14.8753i	−0.829650	+	0.602776i
$610$	7.00249	+	0.728756i	0.283522	+	0.0295065i
$611$	1.82059	−	2.50583i	0.0736533	−	0.101375i
$612$	6.65783	−	3.20606i	0.269127	−	0.129597i
$613$	−12.8625	+	9.34518i	−0.519513	+	0.377448i	−0.816420	−	0.577458i	$-0.804045\pi$
$613$	−12.8625	+	9.34518i	−0.519513	+	0.377448i	0.296907	+	0.954906i	$0.404045\pi$
$614$	5.27806	−	0.355798i	0.213005	−	0.0143589i
$615$	−3.07797	+	17.8233i	−0.124116	+	0.718706i
$616$	−18.4057	−	8.36097i	−0.741585	−	0.336873i
$617$	−10.0312	−	3.25933i	−0.403840	−	0.131216i	0.100052	−	0.994982i	$-0.468099\pi$
$617$	−10.0312	−	3.25933i	−0.403840	−	0.131216i	−0.503892	+	0.863767i	$0.668099\pi$
$618$	−7.34382	−	8.79667i	−0.295412	−	0.353854i
$619$	25.5938	+	8.31591i	1.02870	+	0.334245i	0.774276	−	0.632848i	$-0.218114\pi$
$619$	25.5938	+	8.31591i	1.02870	+	0.334245i	0.254424	+	0.967093i	$0.418114\pi$
$620$	−19.3210	+	5.50924i	−0.775951	+	0.221256i
$621$	1.10580	−	0.359295i	0.0443740	−	0.0144180i
$622$	13.4542	+	8.45407i	0.539466	+	0.338977i
$623$	−9.16751	+	12.6180i	−0.367288	+	0.505529i
$624$	−23.0253	−	8.64266i	−0.921748	−	0.345983i
$625$	−6.38958	−	24.1697i	−0.255583	−	0.966787i
$626$	5.96869	+	7.14949i	0.238557	+	0.285751i
$627$	−53.4176	−	38.8102i	−2.13330	−	1.54993i
$628$	−42.3567	+	5.73668i	−1.69022	+	0.228918i
$629$	18.2919	−	5.94341i	0.729348	−	0.236979i
$630$	−1.71509	+	3.86277i	−0.0683307	+	0.153896i
$631$	0.0360428	−	0.110928i	0.00143484	−	0.00441599i	−0.950337	−	0.311224i	$-0.899261\pi$
$631$	0.0360428	−	0.110928i	0.00143484	−	0.00441599i	0.951771	+	0.306808i	$0.0992610\pi$
$632$	1.72452	+	3.03946i	0.0685978	+	0.120903i
$633$	−53.4138	−	17.3552i	−2.12301	−	0.689808i
$634$	−6.98790	+	27.7309i	−0.277525	+	1.10134i
$635$	18.4545	+	3.18698i	0.732346	+	0.126471i
$636$	−9.55020	+	9.13053i	−0.378690	+	0.362049i
$637$	12.7184	−	9.24049i	0.503923	−	0.366121i
$638$	16.4561	−	65.3047i	0.651503	−	2.58544i
$639$	11.8753	+	8.62793i	0.469781	+	0.341316i
$640$	20.2565	+	15.1550i	0.800707	+	0.599056i
$641$	8.56388	−	6.22202i	0.338253	−	0.245755i	−0.405672	−	0.914019i	$-0.632962\pi$
$641$	8.56388	−	6.22202i	0.338253	−	0.245755i	0.743924	+	0.668264i	$0.232962\pi$
$642$	14.1796	+	35.3504i	0.559625	+	1.39517i
$643$	7.74220			0.305323			0.152661	−	0.988279i	$-0.451216\pi$
$643$	7.74220			0.305323			0.152661	+	0.988279i	$0.451216\pi$
$644$	0.698546	+	0.375923i	0.0275266	+	0.0148134i
$645$	−24.0857	+	23.4239i	−0.948372	+	0.922317i
$646$	−29.2745	−	18.3948i	−1.15179	−	0.723734i
$647$	21.5750	−	7.01014i	0.848200	−	0.275597i	0.147508	−	0.989061i	$-0.452875\pi$
$647$	21.5750	−	7.01014i	0.848200	−	0.275597i	0.700692	+	0.713464i	$0.252875\pi$
$648$	3.47401	−	30.8237i	0.136472	−	1.21087i
$649$	−9.26619			−0.363730
$650$	−0.860916	−	21.8090i	−0.0337679	−	0.855418i
$651$			12.3573i			0.484322i
$652$	−18.3365	+	17.5307i	−0.718112	+	0.686556i
$653$	−9.55959	−	29.4214i	−0.374096	−	1.15135i	−0.944087	−	0.329697i	$-0.893053\pi$
$653$	−9.55959	−	29.4214i	−0.374096	−	1.15135i	0.569991	−	0.821651i	$-0.306947\pi$
$654$	−15.0397	+	23.9349i	−0.588098	+	0.935930i
$655$	−2.88995	−	20.0498i	−0.112920	−	0.783412i
$656$	10.1279	−	12.6989i	0.395428	−	0.495808i
$657$			11.3291i			0.441992i
$658$	0.729544	+	1.81878i	0.0284406	+	0.0709036i
$659$	−13.3643	−	18.3944i	−0.520601	−	0.716545i	0.465061	−	0.885279i	$-0.346032\pi$
$659$	−13.3643	−	18.3944i	−0.520601	−	0.716545i	−0.985662	+	0.168733i	$0.946032\pi$
$660$	−12.6435	−	44.3411i	−0.492148	−	1.72597i
$661$	9.06815	−	12.4812i	0.352710	−	0.485464i	−0.595389	−	0.803437i	$-0.703002\pi$
$661$	9.06815	−	12.4812i	0.352710	−	0.485464i	0.948100	+	0.317973i	$0.103002\pi$
$662$	29.2689	+	7.37545i	1.13757	+	0.286655i
$663$	13.7962	+	18.9888i	0.535800	+	0.737465i
$664$	−1.33095	+	11.8091i	−0.0516508	+	0.458281i
$665$	19.5721	−	2.82109i	0.758974	−	0.109397i
$666$	−1.68509	+	6.68715i	−0.0652959	+	0.259122i
$667$	−0.816640	+	2.51336i	−0.0316204	+	0.0973176i
$668$	18.1055	+	3.28606i	0.700522	+	0.127142i
$669$	−31.3445	−	10.1845i	−1.21185	−	0.393754i
$670$	−5.52692	+	1.18069i	−0.213523	+	0.0456139i
$671$	3.56091	+	10.9594i	0.137467	+	0.423081i
$672$	12.3804	−	9.42543i	0.477586	−	0.363594i
$673$	13.5949	−	18.7118i	0.524046	−	0.721288i	−0.462162	−	0.886795i	$-0.652926\pi$
$673$	13.5949	−	18.7118i	0.524046	−	0.721288i	0.986209	+	0.165507i	$0.0529262\pi$
$674$	−15.0910	−	18.0765i	−0.581286	−	0.696283i
$675$	19.4157	−	5.71585i	0.747310	−	0.220003i
$676$	−1.24024	+	6.83346i	−0.0477017	+	0.262825i
$677$	2.66645	+	1.93729i	0.102480	+	0.0744561i	0.637845	−	0.770165i	$-0.279826\pi$
$677$	2.66645	+	1.93729i	0.102480	+	0.0744561i	−0.535365	+	0.844621i	$0.679826\pi$
$678$	−14.2576	+	22.6904i	−0.547562	+	0.871419i
$679$	2.08812	+	6.42658i	0.0801348	+	0.246629i
$680$	−8.16713	−	22.7204i	−0.313195	−	0.871287i
$681$	7.58734	−	23.3514i	0.290747	−	0.894829i
$682$	−21.0746	−	25.2439i	−0.806989	−	0.966637i
$683$	4.53666	−	13.9624i	0.173591	−	0.534257i	−0.825976	−	0.563706i	$-0.809375\pi$
$683$	4.53666	−	13.9624i	0.173591	−	0.534257i	0.999566	+	0.0294489i	$0.00937522\pi$
$684$	11.1692	−	5.37848i	0.427063	−	0.205651i
$685$	−0.725676	+	1.37649i	−0.0277267	+	0.0525928i
$686$	1.58839	+	23.5628i	0.0606450	+	0.899632i
$687$	13.2708	+	18.2656i	0.506311	+	0.696877i
$688$	29.0851	−	8.02563i	1.10886	−	0.305974i
$689$	−8.28182	−	6.01710i	−0.315512	−	0.229233i
$690$	0.377988	+	1.76940i	0.0143897	+	0.0673598i
$691$	0.529926	+	0.729380i	0.0201593	+	0.0277469i	0.818978	−	0.573825i	$-0.194541\pi$
$691$	0.529926	+	0.729380i	0.0201593	+	0.0277469i	−0.798818	+	0.601572i	$0.794541\pi$
$692$	34.3427	+	18.4816i	1.30551	+	0.702564i
$693$	−6.91764			−0.262779
$694$	−8.35093	−	20.8192i	−0.316997	−	0.790287i
$695$	23.4480	+	4.04931i	0.889432	+	0.153599i
$696$	38.2602	+	34.9737i	1.45025	+	1.32567i
$697$	−14.7430	+	4.79030i	−0.558433	+	0.181446i
$698$	1.13613	+	16.8538i	0.0430033	+	0.637928i
$699$			12.8289i			0.485232i
$700$	11.9729	+	6.87995i	0.452532	+	0.260038i
$701$		−	25.3479i		−	0.957379i	−0.877984	−	0.478689i	$-0.841112\pi$
$701$		−	25.3479i		−	0.957379i	0.877984	−	0.478689i	$-0.158888\pi$
$702$	17.6299	−	1.18845i	0.665398	−	0.0448551i
$703$	30.6865	−	9.97065i	1.15736	−	0.376050i
$704$	−9.21661	+	40.3686i	−0.347364	+	1.52145i
$705$	−2.08442	+	3.95380i	−0.0785040	+	0.148909i
$706$	−6.60341	+	2.64874i	−0.248523	+	0.0996865i
$707$	−22.8809			−0.860526
$708$	3.37985	−	6.28049i	0.127023	−	0.236035i
$709$	−3.03019	−	4.17070i	−0.113801	−	0.156634i	0.748317	−	0.663342i	$-0.230862\pi$
$709$	−3.03019	−	4.17070i	−0.113801	−	0.156634i	−0.862118	+	0.506708i	$0.830862\pi$
$710$	32.0546	−	35.6735i	1.20299	−	1.33880i
$711$	0.967444	+	0.702889i	0.0362820	+	0.0263604i
$712$	29.0860	+	13.2126i	1.09004	+	0.495164i
$713$	0.758482	+	1.04396i	0.0284054	+	0.0390966i
$714$	−14.8163	+	0.998778i	−0.554485	+	0.0373783i
$715$	32.0531	−	15.7735i	1.19872	−	0.589896i
$716$	5.97859	−	2.87898i	0.223430	−	0.107592i
$717$	1.29663	−	3.99063i	0.0484237	−	0.149033i
$718$	−5.92705	+	4.94815i	−0.221196	+	0.184663i
$719$	5.09933	−	15.6941i	0.190173	−	0.585292i	−0.809826	−	0.586670i	$-0.800439\pi$
$719$	5.09933	−	15.6941i	0.190173	−	0.585292i	0.999999	+	0.00137806i	$0.000438650\pi$
$720$	8.45581	+	1.85478i	0.315129	+	0.0691235i
$721$	1.73580	+	5.34224i	0.0646445	+	0.198955i
$722$	−26.3594	−	16.5631i	−0.980996	−	0.616415i
$723$	34.2724	+	24.9003i	1.27460	+	0.926053i
$724$	−9.70320	−	1.76109i	−0.360617	−	0.0654503i
$725$	−15.4285	+	43.3380i	−0.573001	+	1.60953i
$726$	34.1462	−	28.5067i	1.26729	−	1.05798i
$727$	−13.5429	+	18.6402i	−0.502278	+	0.691326i	−0.982593	−	0.185770i	$-0.940522\pi$
$727$	−13.5429	+	18.6402i	−0.502278	+	0.691326i	0.480315	+	0.877096i	$0.340522\pi$
$728$	8.89822	+	8.13386i	0.329790	+	0.301461i
$729$	4.19500	+	12.9109i	0.155370	+	0.478181i
$730$	36.8166	+	3.83154i	1.36264	+	0.141812i
$731$	−27.3858	−	8.89818i	−1.01290	−	0.329111i
$732$	−8.72695	−	1.58390i	−0.322557	−	0.0585427i
$733$	−11.8423	+	36.4467i	−0.437404	+	1.34619i	0.453200	+	0.891409i	$0.350282\pi$
$733$	−11.8423	+	36.4467i	−0.437404	+	1.34619i	−0.890603	+	0.454781i	$0.849718\pi$
$734$	−20.7414	−	5.22662i	−0.765580	−	0.192918i
$735$	−16.2630	+	15.8162i	−0.599871	+	0.583390i
$736$	0.467389	−	1.55617i	0.0172282	−	0.0573613i
$737$	−5.43724	−	7.48373i	−0.200283	−	0.275667i
$738$	1.35816	−	5.38974i	0.0499945	−	0.198399i
$739$	−5.15085	+	7.08954i	−0.189477	+	0.260793i	−0.893178	−	0.449704i	$-0.851530\pi$
$739$	−5.15085	+	7.08954i	−0.189477	+	0.260793i	0.703701	+	0.710497i	$0.251530\pi$
$740$	21.1615	+	7.73768i	0.777911	+	0.284443i
$741$	23.1444	+	31.8556i	0.850233	+	1.17024i
$742$	6.01111	−	2.41116i	0.220675	−	0.0885163i
$743$			7.97007i			0.292393i	0.989256	+	0.146197i	$0.0467032\pi$
$743$			7.97007i			0.292393i	−0.989256	+	0.146197i	$0.953297\pi$
$744$	24.7969	−	5.07636i	0.909099	−	0.186108i
$745$	6.46451	−	3.18122i	0.236841	−	0.116551i
$746$	−38.7660	−	24.3589i	−1.41933	−	0.891843i
$747$	1.25663	+	3.86752i	0.0459778	+	0.141505i
$748$	28.5637	−	27.3085i	1.04439	−	0.998499i
$749$		−	18.6704i		−	0.682202i
$750$	5.71940	+	30.9718i	0.208843	+	1.13093i
$751$	1.54105			0.0562339			0.0281169	−	0.999605i	$-0.491049\pi$
$751$	1.54105			0.0562339			0.0281169	+	0.999605i	$0.491049\pi$
$752$	3.34998	−	2.21110i	0.122161	−	0.0806305i
$753$	33.1490	−	10.7708i	1.20802	−	0.392508i
$754$	−21.3678	+	34.0058i	−0.778169	+	1.23842i
$755$	−19.9412	−	40.5223i	−0.725736	−	1.47476i
$756$	−5.29777	+	9.84440i	−0.192678	+	0.358037i
$757$	20.8270			0.756971			0.378485	−	0.925607i	$-0.376445\pi$
$757$	20.8270			0.756971			0.378485	+	0.925607i	$0.376445\pi$
$758$	−17.0791	+	6.85072i	−0.620342	+	0.248829i
$759$	−2.39585	+	1.74069i	−0.0869640	+	0.0631831i
$760$	−13.7012	−	38.1157i	−0.496993	−	1.38260i
$761$	−7.81874	−	5.68064i	−0.283429	−	0.205923i	0.436983	−	0.899470i	$-0.356047\pi$
$761$	−7.81874	−	5.68064i	−0.283429	−	0.205923i	−0.720412	+	0.693547i	$0.756047\pi$
$762$	−22.8783	−	5.76510i	−0.828795	−	0.208848i
$763$	11.2102	−	8.14469i	0.405837	−	0.294858i
$764$	−0.971549	+	0.928856i	−0.0351494	+	0.0336048i
$765$	−5.76003	−	5.92275i	−0.208254	−	0.214137i
$766$	−19.3405	−	4.87361i	−0.698802	−	0.176091i
$767$	5.25543	+	1.70759i	0.189763	+	0.0616576i
$768$	−23.9995	−	20.9714i	−0.866007	−	0.756739i
$769$	−1.06128	+	3.26628i	−0.0382706	+	0.117785i	−0.968367	−	0.249532i	$-0.919723\pi$
$769$	−1.06128	+	3.26628i	−0.0382706	+	0.117785i	0.930096	+	0.367316i	$0.119723\pi$
$770$	−2.33956	+	22.4804i	−0.0843119	+	0.810138i
$771$	54.4630	−	17.6961i	1.96144	−	0.637309i
$772$	1.27635	+	9.42389i	0.0459367	+	0.339173i
$773$	−5.52497	−	4.01412i	−0.198719	−	0.144378i	0.483976	−	0.875081i	$-0.339192\pi$
$773$	−5.52497	−	4.01412i	−0.198719	−	0.144378i	−0.682695	+	0.730703i	$0.739192\pi$
$774$	7.92572	−	6.61672i	0.284884	−	0.237833i
$775$	12.6919	+	18.5333i	0.455907	+	0.665735i
$776$	12.0382	−	6.83017i	0.432145	−	0.245189i
$777$	8.14579	−	11.2117i	0.292229	−	0.402218i
$778$	−14.9033	+	23.7179i	−0.534308	+	0.850327i
$779$	−24.7329	+	8.03620i	−0.886147	+	0.287927i
$780$	−1.00035	+	27.4786i	−0.0358183	+	0.983891i
$781$	74.6564	+	24.2573i	2.67142	+	0.867996i
$782$	−1.19039	+	0.993789i	−0.0425684	+	0.0355378i
$783$	−35.4200	−	11.5086i	−1.26581	−	0.411286i
$784$	19.6387	−	5.41903i	0.701383	−	0.193537i
$785$	21.1005	+	42.8780i	0.753108	+	1.53038i
$786$	1.71645	+	25.4624i	0.0612236	+	0.908215i
$787$	3.59275	−	2.61029i	0.128068	−	0.0930467i	−0.521907	−	0.853002i	$-0.674779\pi$
$787$	3.59275	−	2.61029i	0.128068	−	0.0930467i	0.649975	+	0.759956i	$0.274779\pi$
$788$	−4.87388	−	10.1213i	−0.173625	−	0.360556i
$789$	−24.5965	+	33.8542i	−0.875658	+	1.20524i
$790$	2.61139	−	2.90621i	0.0929090	−	0.103398i
$791$	10.6273	−	7.72119i	0.377864	−	0.274534i
$792$	2.84175	+	13.8813i	0.100977	+	0.493252i
$793$		−	6.87195i		−	0.244030i
$794$	−5.54597	−	13.8264i	−0.196819	−	0.490679i
$795$	13.0674	+	6.88906i	0.463453	+	0.244330i
$796$	7.06258	−	0.956536i	0.250326	−	0.0339035i
$797$	4.56123	+	14.0380i	0.161567	+	0.497252i	0.998767	−	0.0496450i	$-0.0158090\pi$
$797$	4.56123	+	14.0380i	0.161567	+	0.497252i	−0.837200	+	0.546897i	$0.815809\pi$
$798$	−24.8557	+	1.67555i	−0.879884	+	0.0593137i
$799$	−3.83071			−0.135521
$800$	8.88728	−	26.8517i	0.314213	−	0.949353i
$801$	10.9318			0.386255
$802$	20.5059	−	1.38232i	0.724089	−	0.0488115i
$803$	18.7220	+	57.6204i	0.660685	+	2.03338i
$804$	7.05561	−	0.955592i	0.248832	−	0.0337011i
$805$	0.150929	−	0.873972i	0.00531955	−	0.0308035i
$806$	7.30074	+	18.2010i	0.257157	+	0.641105i
$807$			31.5828i			1.11177i
$808$	9.39943	+	45.9142i	0.330671	+	1.61526i
$809$	14.9496	−	10.8616i	0.525601	−	0.381872i	−0.293108	−	0.956079i	$-0.594690\pi$
$809$	14.9496	−	10.8616i	0.525601	−	0.381872i	0.818710	+	0.574207i	$0.194690\pi$
$810$	−33.9149	+	7.24508i	−1.19165	+	0.254566i
$811$	−15.6070	+	21.4812i	−0.548036	+	0.754307i	−0.989744	−	0.142852i	$-0.954373\pi$
$811$	−15.6070	+	21.4812i	−0.548036	+	0.754307i	0.441708	+	0.897159i	$0.354373\pi$
$812$	−11.0243	−	22.8935i	−0.386877	−	0.803403i
$813$	47.8677	−	34.7779i	1.67879	−	1.21971i
$814$	2.48043	+	36.7957i	0.0869391	+	1.28969i
$815$	25.0895	+	13.2271i	0.878848	+	0.463324i
$816$	8.09070	+	29.3209i	0.283231	+	1.02644i
$817$	−45.9423	−	14.9276i	−1.60732	−	0.522249i
$818$	27.2441	−	22.7445i	0.952568	−	0.795243i
$819$	3.92343	+	1.27480i	0.137096	+	0.0445451i
$820$	−17.0558	−	6.23646i	−0.595616	−	0.217787i
$821$	−41.8393	+	13.5944i	−1.46020	+	0.474448i	−0.928132	−	0.372252i	$-0.878586\pi$
$821$	−41.8393	+	13.5944i	−1.46020	+	0.474448i	−0.532070	+	0.846700i	$0.678586\pi$
$822$	1.04299	−	1.65987i	0.0363784	−	0.0578945i
$823$	14.3603	−	19.7653i	0.500569	−	0.688975i	−0.481724	−	0.876323i	$-0.659989\pi$
$823$	14.3603	−	19.7653i	0.500569	−	0.688975i	0.982294	+	0.187348i	$0.0599893\pi$
$824$	10.0070	−	5.67774i	0.348610	−	0.197793i
$825$	−42.5332	+	29.1275i	−1.48082	+	1.01409i
$826$	−2.68380	+	2.24054i	−0.0933812	+	0.0779585i
$827$	38.6082	+	28.0505i	1.34254	+	0.975412i	0.999347	+	0.0361465i	$0.0115083\pi$
$827$	38.6082	+	28.0505i	1.34254	+	0.975412i	0.343192	+	0.939265i	$0.388492\pi$
$828$	−0.0746230	−	0.550978i	−0.00259333	−	0.0191478i
$829$	−22.8468	+	7.42337i	−0.793502	+	0.257824i	−0.677595	−	0.735436i	$-0.736978\pi$
$829$	−22.8468	+	7.42337i	−0.793502	+	0.257824i	−0.115907	+	0.993260i	$0.536978\pi$
$830$	12.9934	−	2.77571i	0.451006	−	0.0963461i
$831$	0.670362	−	2.06316i	0.0232546	−	0.0715703i
$832$	12.6665	−	21.1971i	0.439133	−	0.734876i
$833$	−18.4913	−	6.00819i	−0.640686	−	0.208172i
$834$	−29.0688	−	7.32502i	−1.00657	−	0.253645i
$835$	−2.93506	−	20.3628i	−0.101572	−	0.704684i
$836$	47.9184	−	45.8127i	1.65729	−	1.58447i
$837$	−14.7122	+	10.6891i	−0.508529	+	0.369468i
$838$	1.04977	+	0.264532i	0.0362638	+	0.00913809i
$839$	13.1474	+	9.55211i	0.453897	+	0.329776i	0.791132	−	0.611645i	$-0.209492\pi$
$839$	13.1474	+	9.55211i	0.453897	+	0.329776i	−0.337235	+	0.941420i	$0.609492\pi$
$840$	−14.3836	−	9.78548i	−0.496280	−	0.337631i
$841$	45.0210	−	32.7096i	1.55245	−	1.12792i
$842$	−15.3584	+	6.16050i	−0.529285	+	0.212305i
$843$	50.6604			1.74484
$844$	26.7223	−	49.6559i	0.919821	−	1.70923i
$845$	7.68543	−	1.10777i	0.264387	−	0.0381083i
$846$	0.730770	−	1.16299i	0.0251244	−	0.0399843i
$847$	−20.7371	+	6.73789i	−0.712535	+	0.231517i
$848$	−7.30772	−	11.0718i	−0.250948	−	0.380206i
$849$	−49.9824			−1.71539
$850$	−21.1953	+	16.7154i	−0.726994	+	0.573334i
$851$		−	1.44716i		−	0.0496081i
$852$	−43.6723	+	41.7532i	−1.49619	+	1.43044i
$853$	−14.3719	−	44.2323i	−0.492086	−	1.51449i	−0.821449	−	0.570282i	$-0.806834\pi$
$853$	−14.3719	−	44.2323i	−0.492086	−	1.51449i	0.329363	−	0.944203i	$-0.393166\pi$
$854$	3.68131	+	2.31317i	0.125972	+	0.0791552i
$855$	−9.66301	−	9.93598i	−0.330468	−	0.339803i
$856$	−37.4651	+	7.66976i	−1.28053	+	0.262147i
$857$		−	34.8114i		−	1.18913i	−0.804046	−	0.594567i	$-0.797323\pi$
$857$		−	34.8114i		−	1.18913i	0.804046	−	0.594567i	$-0.202677\pi$
$858$	−41.7708	+	16.7549i	−1.42603	+	0.572004i
$859$	23.5563	+	32.4224i	0.803730	+	1.10624i	0.992261	+	0.124172i	$0.0396275\pi$
$859$	23.5563	+	32.4224i	0.803730	+	1.10624i	−0.188531	+	0.982067i	$0.560373\pi$
$860$	−18.8220	−	27.9942i	−0.641825	−	0.954594i
$861$	−6.56539	+	9.03648i	−0.223748	+	0.307963i
$862$	−7.51440	+	29.8203i	−0.255941	+	1.01568i
$863$	30.0211	+	41.3205i	1.02193	+	1.40657i	0.910842	+	0.412755i	$0.135433\pi$
$863$	30.0211	+	41.3205i	1.02193	+	1.40657i	0.111087	+	0.993811i	$0.464567\pi$
$864$	21.9307	+	6.58676i	0.746096	+	0.224086i
$865$	7.42015	−	42.9672i	0.252293	−	1.46093i
$866$	5.04162	+	1.27044i	0.171321	+	0.0431712i
$867$	−1.49396	+	4.59793i	−0.0507375	+	0.156154i
$868$	−12.2078	−	2.21567i	−0.414360	−	0.0752046i
$869$	6.08201	+	1.97617i	0.206318	+	0.0670368i
$870$	23.5182	−	52.9684i	0.797342	−	1.79580i
$871$	1.70468	+	5.24648i	0.0577610	+	0.177770i
$872$	−20.9488	−	19.1492i	−0.709414	−	0.648475i
$873$	2.78388	−	3.83168i	0.0942200	−	0.129683i
$874$	−1.99700	+	1.66718i	−0.0675495	+	0.0563931i
$875$	3.04996	−	15.1345i	0.103108	−	0.511638i
$876$	−45.8832	−	8.32759i	−1.55025	−	0.281363i
$877$	14.2117	+	10.3254i	0.479894	+	0.348664i	0.801285	−	0.598283i	$-0.204150\pi$
$877$	14.2117	+	10.3254i	0.479894	+	0.348664i	−0.321390	+	0.946947i	$0.604150\pi$
$878$	2.80831	+	1.76462i	0.0947759	+	0.0595531i
$879$	−19.4797	−	59.9522i	−0.657033	−	2.02214i
$880$	46.0716	−	4.54020i	1.55307	−	0.153050i
$881$	2.27227	−	6.99332i	0.0765546	−	0.235611i	−0.905455	−	0.424443i	$-0.860470\pi$
$881$	2.27227	−	6.99332i	0.0765546	−	0.235611i	0.982009	+	0.188832i	$0.0604701\pi$
$882$	5.35157	−	4.46771i	0.180197	−	0.150436i
$883$	−13.8280	+	42.5583i	−0.465350	+	1.43220i	0.393191	+	0.919457i	$0.371371\pi$
$883$	−13.8280	+	42.5583i	−0.465350	+	1.43220i	−0.858541	+	0.512745i	$0.828629\pi$
$884$	−21.2328	+	10.2246i	−0.714135	+	0.343890i
$885$	−7.85771	−	1.35697i	−0.264134	−	0.0456142i
$886$	1.36762	−	0.0921922i	0.0459459	−	0.00309726i
$887$	22.0394	+	30.3347i	0.740012	+	1.01854i	0.998618	+	0.0525565i	$0.0167370\pi$
$887$	22.0394	+	30.3347i	0.740012	+	1.01854i	−0.258606	+	0.965983i	$0.583263\pi$
$888$	−25.8444	−	11.7401i	−0.867281	−	0.393971i
$889$	9.35651	+	6.79790i	0.313807	+	0.227994i
$890$	3.69715	−	35.5252i	0.123929	−	1.19081i
$891$	−33.3647	−	45.9226i	−1.11776	−	1.53846i
$892$	15.6813	−	29.1393i	0.525049	−	0.975654i
$893$	−6.42640			−0.215051
$894$	−8.42438	+	3.37916i	−0.281753	+	0.113016i
$895$	−5.17238	−	5.31850i	−0.172894	−	0.177778i
$896$	7.09159	+	13.9206i	0.236914	+	0.465056i
$897$	1.67962	−	0.545741i	0.0560808	−	0.0182218i
$898$	−48.4316	+	3.26481i	−1.61618	+	0.108948i
$899$		−	41.3333i		−	1.37854i
$900$	−1.03137	−	9.62353i	−0.0343789	−	0.320784i
$901$			12.6606i			0.421785i
$902$	−1.99919	−	29.6568i	−0.0665658	−	0.987464i
$903$	−19.7327	+	6.41154i	−0.656663	+	0.213363i
$904$	−19.8595	−	18.1535i	−0.660516	−	0.603778i
$905$	1.57298	+	10.9130i	0.0522875	+	0.362759i
$906$	21.1820	+	52.8076i	0.703724	+	1.75441i
$907$	9.10715			0.302398			0.151199	−	0.988503i	$-0.451687\pi$
$907$	9.10715			0.302398			0.151199	+	0.988503i	$0.451687\pi$
$908$	21.7085	+	11.6825i	0.720422	+	0.387696i
$909$	9.42650	+	12.9745i	0.312657	+	0.430336i
$910$	5.46965	−	12.3189i	0.181317	−	0.408368i
$911$	4.83681	+	3.51415i	0.160251	+	0.116429i	0.665021	−	0.746825i	$-0.268423\pi$
$911$	4.83681	+	3.51415i	0.160251	+	0.116429i	−0.504770	+	0.863254i	$0.668423\pi$
$912$	13.5729	+	49.1887i	0.449445	+	1.62880i
$913$	12.7825	+	17.5937i	0.423040	+	0.582265i
$914$	3.27513	+	48.5846i	0.108332	+	1.60703i
$915$	1.41472	+	9.81499i	0.0467691	+	0.324473i
$916$	−20.4241	+	9.83519i	−0.674831	+	0.324964i
$917$	3.86572	−	11.8974i	0.127657	−	0.392888i
$918$	−14.0052	−	16.7758i	−0.462239	−	0.553685i
$919$	5.41966	−	16.6800i	0.178778	−	0.550222i	−0.821008	−	0.570917i	$-0.806588\pi$
$919$	5.41966	−	16.6800i	0.178778	−	0.550222i	0.999786	+	0.0206948i	$0.00658785\pi$
$920$	−1.81576	+	0.0561621i	−0.0598640	+	0.00185161i
$921$	2.30252	+	7.08644i	0.0758708	+	0.233506i
$922$	27.9647	−	44.5044i	0.920967	−	1.46568i
$923$	−37.8721	−	27.5157i	−1.24658	−	0.905690i
$924$	5.08488	−	28.0165i	0.167280	−	0.921676i
$925$	0.701592	−	25.1815i	0.0230682	−	0.827962i
$926$	13.0774	+	15.6645i	0.429750	+	0.514769i
$927$	2.31416	−	3.18517i	0.0760070	−	0.104615i
$928$	−41.4106	+	31.5266i	−1.35937	+	1.03491i
$929$	−8.23207	−	25.3357i	−0.270085	−	0.831237i	−0.990478	−	0.137671i	$-0.956038\pi$
$929$	−8.23207	−	25.3357i	−0.270085	−	0.831237i	0.720393	−	0.693566i	$-0.243962\pi$
$930$	−14.1744	−	24.4930i	−0.464798	−	0.803157i
$931$	−31.0210	−	10.0793i	−1.01667	−	0.330337i
$932$	−12.6737	−	2.30021i	−0.415140	−	0.0753460i
$933$	−6.91618	+	21.2858i	−0.226425	+	0.696866i
$934$	−3.87378	+	15.3728i	−0.126754	+	0.503013i
$935$	−39.0833	−	20.6045i	−1.27816	−	0.673840i
$936$	0.946352	−	8.39666i	0.0309325	−	0.274454i
$937$	5.75045	+	7.91482i	0.187859	+	0.258566i	0.892550	−	0.450949i	$-0.148914\pi$
$937$	5.75045	+	7.91482i	0.187859	+	0.258566i	−0.704691	+	0.709515i	$0.748914\pi$
$938$	−3.38436	−	0.852822i	−0.110503	−	0.0278456i
$939$	−7.71069	+	10.6129i	−0.251629	+	0.346337i
$940$	−3.53223	−	2.76812i	−0.115209	−	0.0902863i
$941$	−0.184526	−	0.253979i	−0.00601539	−	0.00827947i	0.805999	−	0.591917i	$-0.201629\pi$
$941$	−0.184526	−	0.253979i	−0.00601539	−	0.00827947i	−0.812014	+	0.583638i	$0.801629\pi$
$942$	−22.4133	−	55.8774i	−0.730266	−	1.82058i
$943$			1.16639i			0.0379829i
$944$	5.59850	+	4.46505i	0.182216	+	0.145325i
$945$	12.3166	+	2.12700i	0.400659	+	0.0691913i
$946$	29.3760	−	46.7505i	0.955096	−	1.51999i
$947$	14.4398	+	44.4410i	0.469229	+	1.44414i	0.853585	+	0.520954i	$0.174424\pi$
$947$	14.4398	+	44.4410i	0.469229	+	1.44414i	−0.384356	+	0.923185i	$0.625576\pi$
$948$	−3.55784	+	3.40149i	−0.115553	+	0.110475i
$949$		−	36.1303i		−	1.17284i
$950$	−35.5572	+	28.0417i	−1.15363	+	0.909794i
$951$	−40.2806			−1.30619
$952$	1.66986	−	14.8161i	0.0541205	−	0.480193i
$953$	−31.6721	+	10.2909i	−1.02596	+	0.333354i	−0.773191	−	0.634173i	$-0.781341\pi$
$953$	−31.6721	+	10.2909i	−1.02596	+	0.333354i	−0.252768	+	0.967527i	$0.581341\pi$
$954$	−3.84369	−	2.41521i	−0.124444	−	0.0781952i
$955$	1.32936	+	0.700830i	0.0430170	+	0.0226783i
$956$	3.70987	+	1.99647i	0.119986	+	0.0645704i
$957$	94.8585			3.06634
$958$	−2.50408	−	6.24278i	−0.0809031	−	0.201695i
$959$	−0.777419	+	0.564828i	−0.0251042	+	0.0182393i
$960$	−13.7274	+	32.8828i	−0.443050	+	1.06129i
$961$	8.75140	+	6.35826i	0.282303	+	0.205105i
$962$	5.37399	−	21.3263i	0.173264	−	0.687586i
$963$	−10.5869	+	7.69184i	−0.341159	+	0.247866i
$964$	−30.7441	+	29.3931i	−0.990201	+	0.946688i
$965$	9.53987	−	4.69462i	0.307099	−	0.151125i
$966$	−0.273024	+	1.08347i	−0.00878441	+	0.0348602i
$967$	−28.5494	−	9.27626i	−0.918087	−	0.298304i	−0.188405	−	0.982091i	$-0.560332\pi$
$967$	−28.5494	−	9.27626i	−0.918087	−	0.298304i	−0.729682	+	0.683787i	$0.760332\pi$
$968$	22.0394	+	38.8444i	0.708373	+	1.24851i
$969$	15.0486	−	46.3148i	0.483431	−	1.48785i
$970$	−11.5104	−	10.3427i	−0.369576	−	0.332084i
$971$	12.0721	−	3.92245i	0.387411	−	0.125878i	−0.108834	−	0.994060i	$-0.534712\pi$
$971$	12.0721	−	3.92245i	0.387411	−	0.125878i	0.496245	+	0.868182i	$0.334712\pi$
$972$	19.2277	−	2.60415i	0.616730	−	0.0835282i
$973$	11.8882	+	8.63727i	0.381118	+	0.276898i
$974$	−12.0575	−	14.4429i	−0.386348	−	0.462781i
$975$	29.4909	−	8.68193i	0.944466	−	0.278044i
$976$	3.12948	−	8.33737i	0.100172	−	0.266873i
$977$	−29.7939	+	41.0078i	−0.953191	+	1.31196i	−0.00309631	+	0.999995i	$0.500986\pi$
$977$	−29.7939	+	41.0078i	−0.953191	+	1.31196i	−0.950095	+	0.311960i	$0.899014\pi$
$978$	−30.2548	−	19.0108i	−0.967442	−	0.607899i
$979$	55.5993	−	18.0653i	1.77696	−	0.577370i
$980$	−12.7089	−	18.9021i	−0.405972	−	0.603806i
$981$	−9.23677	−	3.00121i	−0.294907	−	0.0958213i
$982$	16.0922	+	19.2758i	0.513524	+	0.615116i
$983$	50.4346	+	16.3872i	1.60862	+	0.522671i	0.969218	−	0.246206i	$-0.0791839\pi$
$983$	50.4346	+	16.3872i	1.60862	+	0.522671i	0.639397	+	0.768876i	$0.279184\pi$
$984$	20.8302	+	9.46233i	0.664042	+	0.301648i
$985$	−9.00380	+	8.75644i	−0.286885	+	0.279003i
$986$	49.5582	−	3.34076i	1.57825	−	0.106391i
$987$	−2.23305	+	1.62241i	−0.0710788	+	0.0516418i
$988$	−35.6200	+	17.1527i	−1.13322	+	0.545702i
$989$	−1.27351	+	1.75283i	−0.0404951	+	0.0557368i
$990$	13.7112	−	7.93486i	0.435771	−	0.252187i
$991$	1.47581	−	1.07224i	0.0468808	−	0.0340609i	−0.564098	−	0.825708i	$-0.690776\pi$
$991$	1.47581	−	1.07224i	0.0468808	−	0.0340609i	0.610979	+	0.791647i	$0.290776\pi$
$992$	0.568859	+	25.4071i	0.0180613	+	0.806677i
$993$			42.5146i			1.34916i
$994$	27.4883	−	11.0260i	0.871877	−	0.349724i
$995$	−3.51830	−	7.14949i	−0.111538	−	0.226654i
$996$	−16.5872	+	2.24652i	−0.525585	+	0.0711838i
$997$	5.04048	+	15.5130i	0.159634	+	0.491302i	0.998601	−	0.0528802i	$-0.0168401\pi$
$997$	5.04048	+	15.5130i	0.159634	+	0.491302i	−0.838967	+	0.544182i	$0.816840\pi$
$998$	1.48553	+	22.0370i	0.0470237	+	0.697568i
$999$	20.3944			0.645250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.109.1	✓	112
4.3	odd	2		800.2.be.a.209.22		112
5.2	odd	4		1000.2.t.b.701.27		224
5.3	odd	4		1000.2.t.b.701.30		224
5.4	even	2		1000.2.o.a.549.28		112
8.3	odd	2		800.2.be.a.209.7		112
8.5	even	2	inner	200.2.o.a.109.18	yes	112
25.2	odd	20		1000.2.t.b.301.5		224
25.11	even	5		1000.2.o.a.949.11		112
25.14	even	10	inner	200.2.o.a.189.18	yes	112
25.23	odd	20		1000.2.t.b.301.52		224
40.13	odd	4		1000.2.t.b.701.52		224
40.29	even	2		1000.2.o.a.549.11		112
40.37	odd	4		1000.2.t.b.701.5		224
100.39	odd	10		800.2.be.a.689.7		112
200.61	even	10		1000.2.o.a.949.28		112
200.77	odd	20		1000.2.t.b.301.27		224
200.139	odd	10		800.2.be.a.689.22		112
200.173	odd	20		1000.2.t.b.301.30		224
200.189	even	10	inner	200.2.o.a.189.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.1	✓	112	1.1	even	1	trivial
200.2.o.a.109.18	yes	112	8.5	even	2	inner
200.2.o.a.189.1	yes	112	200.189	even	10	inner
200.2.o.a.189.18	yes	112	25.14	even	10	inner
800.2.be.a.209.7		112	8.3	odd	2
800.2.be.a.209.22		112	4.3	odd	2
800.2.be.a.689.7		112	100.39	odd	10
800.2.be.a.689.22		112	200.139	odd	10
1000.2.o.a.549.11		112	40.29	even	2
1000.2.o.a.549.28		112	5.4	even	2
1000.2.o.a.949.11		112	25.11	even	5
1000.2.o.a.949.28		112	200.61	even	10
1000.2.t.b.301.5		224	25.2	odd	20
1000.2.t.b.301.27		224	200.77	odd	20
1000.2.t.b.301.30		224	200.173	odd	20
1000.2.t.b.301.52		224	25.23	odd	20
1000.2.t.b.701.5		224	40.37	odd	4
1000.2.t.b.701.27		224	5.2	odd	4
1000.2.t.b.701.30		224	5.3	odd	4
1000.2.t.b.701.52		224	40.13	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41101 + 0.0951175i) q^{2} +(-0.615546 - 1.89446i) q^{3} +(1.98191 - 0.268424i) q^{4} +(-0.987308 - 2.00630i) q^{5} +(1.04874 + 2.61455i) q^{6} -1.38088i q^{7} +(-2.77096 + 0.567263i) q^{8} +(-0.783019 + 0.568896i) q^{9} +(1.58394 + 2.73700i) q^{10} +(-3.04233 + 4.18740i) q^{11} +(-1.72847 - 3.58941i) q^{12} +(2.49716 - 1.81429i) q^{13} +(0.131346 + 1.94844i) q^{14} +(-3.19311 + 3.10538i) q^{15} +(3.85590 - 1.06398i) q^{16} +(-3.63061 - 1.17966i) q^{17} +(1.05074 - 0.877198i) q^{18} +(-6.09071 - 1.97899i) q^{19} +(-2.49529 - 3.71127i) q^{20} +(-2.61602 + 0.849997i) q^{21} +(3.89446 - 6.19785i) q^{22} +(-0.168832 + 0.232378i) q^{23} +(2.78031 + 4.90029i) q^{24} +(-3.05044 + 3.96166i) q^{25} +(-3.35095 + 2.79751i) q^{26} +(-3.27483 - 2.37930i) q^{27} +(-0.370661 - 2.73678i) q^{28} +(8.75018 - 2.84311i) q^{29} +(4.21013 - 4.68545i) q^{30} +(1.38826 - 4.27263i) q^{31} +(-5.33951 + 1.86805i) q^{32} +(9.80555 + 3.18602i) q^{33} +(5.23504 + 1.31918i) q^{34} +(-2.77046 + 1.36336i) q^{35} +(-1.39916 + 1.33768i) q^{36} +(-4.07603 + 2.96141i) q^{37} +(8.78229 + 2.21305i) q^{38} +(-4.97421 - 3.61398i) q^{39} +(3.87389 + 4.99930i) q^{40} +(3.28522 - 2.38685i) q^{41} +(3.61039 - 1.44818i) q^{42} +7.54302 q^{43} +(-4.90561 + 9.11567i) q^{44} +(1.91445 + 1.00929i) q^{45} +(0.216121 - 0.343947i) q^{46} +(0.954360 - 0.310090i) q^{47} +(-4.38915 - 6.64990i) q^{48} +5.09317 q^{49} +(3.92739 - 5.88010i) q^{50} +7.60418i q^{51} +(4.46213 - 4.26605i) q^{52} +(-1.02485 - 3.15418i) q^{53} +(4.84714 + 3.04573i) q^{54} +(11.4049 + 1.96955i) q^{55} +(0.783323 + 3.82637i) q^{56} +12.7567i q^{57} +(-12.0762 + 4.84395i) q^{58} +(1.05228 + 1.44834i) q^{59} +(-5.49488 + 7.01168i) q^{60} +(1.30861 - 1.80115i) q^{61} +(-1.55245 + 6.16078i) q^{62} +(0.785578 + 1.08126i) q^{63} +(7.35643 - 3.14372i) q^{64} +(-6.10547 - 3.21877i) q^{65} +(-14.1388 - 3.56283i) q^{66} +(-0.552275 + 1.69973i) q^{67} +(-7.51218 - 1.36343i) q^{68} +(0.544154 + 0.176806i) q^{69} +(3.77947 - 2.18723i) q^{70} +(-4.68658 - 14.4238i) q^{71} +(1.84700 - 2.02057i) q^{72} +(6.88021 - 9.46979i) q^{73} +(5.46964 - 4.56628i) q^{74} +(9.38289 + 3.34035i) q^{75} +(-12.6024 - 2.28728i) q^{76} +(5.78231 + 4.20109i) q^{77} +(7.36242 + 4.62623i) q^{78} +(-0.381800 - 1.17506i) q^{79} +(-5.94162 - 6.68559i) q^{80} +(-3.38894 + 10.4301i) q^{81} +(-4.40845 + 3.68036i) q^{82} +(1.29836 - 3.99593i) q^{83} +(-4.95655 + 2.38682i) q^{84} +(1.21779 + 8.44877i) q^{85} +(-10.6433 + 0.717473i) q^{86} +(-10.7723 - 14.8268i) q^{87} +(6.05480 - 13.3289i) q^{88} +(-9.13763 - 6.63888i) q^{89} +(-2.79732 - 1.24202i) q^{90} +(-2.50532 - 3.44828i) q^{91} +(-0.272234 + 0.505870i) q^{92} -8.94886 q^{93} +(-1.31712 + 0.528317i) q^{94} +(2.04297 + 14.1736i) q^{95} +(6.82566 + 8.96560i) q^{96} +(-4.65397 + 1.51217i) q^{97} +(-7.18651 + 0.484449i) q^{98} -5.00958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

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