LMFDB - Embedded newform 220.2.r.c.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] 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("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	220.151
Dual form			220.2.r.c.51.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26745 + 0.627351i) q^{2} +(-1.88633 + 0.612906i) q^{3} +(1.21286 - 1.59027i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.00632 - 1.96022i) q^{6} +(0.668539 - 2.05755i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(0.755537 - 0.548930i) q^{9} +(-1.39414 - 0.237451i) q^{10} +(3.31496 - 0.105060i) q^{11} +(-1.31317 + 3.74315i) q^{12} +(1.85832 + 2.55775i) q^{13} +(0.443466 + 3.02725i) q^{14} +(-1.88633 - 0.612906i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(-2.62058 + 3.60691i) q^{17} +(-0.613234 + 1.16973i) q^{18} +(1.21650 + 3.74402i) q^{19} +(1.91596 - 0.573655i) q^{20} +4.29097i q^{21} +(-4.13564 + 2.21280i) q^{22} +8.67477i q^{23} +(-0.683887 - 5.56807i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-3.95993 - 2.07601i) q^{26} +(2.40870 - 3.31529i) q^{27} +(-2.46122 - 3.55868i) q^{28} +(6.12821 + 1.99118i) q^{29} +(2.77534 - 0.406563i) q^{30} +(-0.673670 - 0.927228i) q^{31} +(3.76092 + 4.22558i) q^{32} +(-6.18872 + 2.22994i) q^{33} +(1.05865 - 6.21560i) q^{34} +(1.75026 - 1.27164i) q^{35} +(0.0434146 - 1.86728i) q^{36} +(3.17897 - 9.78387i) q^{37} +(-3.89067 - 3.98218i) q^{38} +(-5.07306 - 3.68579i) q^{39} +(-2.06851 + 1.92906i) q^{40} +(-1.29856 + 0.421929i) q^{41} +(-2.69194 - 5.43859i) q^{42} -4.00994 q^{43} +(3.85352 - 5.39911i) q^{44} +0.933895 q^{45} +(-5.44212 - 10.9948i) q^{46} +(3.61139 - 1.17341i) q^{47} +(4.35993 + 6.62822i) q^{48} +(1.87655 + 1.36339i) q^{49} +(-0.988310 - 1.01156i) q^{50} +(2.73257 - 8.40999i) q^{51} +(6.32141 + 0.146974i) q^{52} +(6.21075 - 4.51237i) q^{53} +(-0.973058 + 5.71306i) q^{54} +(2.74361 + 1.86349i) q^{55} +(5.35202 + 2.96641i) q^{56} +(-4.58946 - 6.31685i) q^{57} +(-9.01637 + 1.32082i) q^{58} +(0.112673 + 0.0366097i) q^{59} +(-3.26255 + 2.25641i) q^{60} +(-7.07767 + 9.74158i) q^{61} +(1.43554 + 0.752588i) q^{62} +(-0.624345 - 1.92153i) q^{63} +(-7.41770 - 2.99629i) q^{64} +3.16156i q^{65} +(6.44494 - 6.70883i) q^{66} -6.69412i q^{67} +(2.55758 + 8.54212i) q^{68} +(-5.31681 - 16.3635i) q^{69} +(-1.42060 + 2.70976i) q^{70} +(-0.556753 + 0.766305i) q^{71} +(1.11642 + 2.39393i) q^{72} +(1.45249 + 0.471942i) q^{73} +(2.10873 + 14.3949i) q^{74} +(-1.16582 - 1.60461i) q^{75} +(7.42946 + 2.60640i) q^{76} +(2.00001 - 6.89093i) q^{77} +(8.74214 + 1.48897i) q^{78} +(-3.49460 + 2.53897i) q^{79} +(1.41153 - 3.74267i) q^{80} +(-3.37741 + 10.3946i) q^{81} +(1.38117 - 1.34943i) q^{82} +(0.790772 + 0.574530i) q^{83} +(6.82381 + 5.20435i) q^{84} +(-4.24018 + 1.37772i) q^{85} +(5.08240 - 2.51564i) q^{86} -12.7802 q^{87} +(-1.49701 + 9.26061i) q^{88} -13.2930 q^{89} +(-1.18367 + 0.585879i) q^{90} +(6.50506 - 2.11362i) q^{91} +(13.7952 + 10.5213i) q^{92} +(1.83907 + 1.33616i) q^{93} +(-3.84112 + 3.75285i) q^{94} +(-1.21650 + 3.74402i) q^{95} +(-9.68421 - 5.66574i) q^{96} +(11.7313 - 8.52327i) q^{97} +(-3.23376 - 0.550779i) q^{98} +(2.44690 - 1.89906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) $ 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$3$	−1.88633	+	0.612906i	−1.08907	+	0.353861i	−0.797888	−	0.602805i	$-0.794050\pi$
$3$	−1.88633	+	0.612906i	−1.08907	+	0.353861i	−0.291185	+	0.956667i	$0.594050\pi$
$4$	1.21286	−	1.59027i	0.606431	−	0.795136i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	2.00632	−	1.96022i	0.819078	−	0.800256i
$7$	0.668539	−	2.05755i	0.252684	−	0.777681i	−0.741593	−	0.670850i	$-0.765930\pi$
$7$	0.668539	−	2.05755i	0.252684	−	0.777681i	0.994277	−	0.106831i	$-0.0340704\pi$
$8$	−0.539585	+	2.77648i	−0.190772	+	0.981634i
$9$	0.755537	−	0.548930i	0.251846	−	0.182977i
$10$	−1.39414	−	0.237451i	−0.440865	−	0.0750887i
$11$	3.31496	−	0.105060i	0.999498	−	0.0316768i
$11$	3.31496	−	0.105060i	0.999498	−	0.0316768i
$12$	−1.31317	+	3.74315i	−0.379080	+	1.08055i
$13$	1.85832	+	2.55775i	0.515404	+	0.709393i	0.984819	−	0.173585i	$-0.0555350\pi$
$13$	1.85832	+	2.55775i	0.515404	+	0.709393i	−0.469415	+	0.882978i	$0.655535\pi$
$14$	0.443466	+	3.02725i	0.118521	+	0.809067i
$15$	−1.88633	−	0.612906i	−0.487048	−	0.158252i
$16$	−1.05793	−	3.85756i	−0.264483	−	0.964390i
$17$	−2.62058	+	3.60691i	−0.635583	+	0.874805i	−0.998370	−	0.0570671i	$-0.981825\pi$
$17$	−2.62058	+	3.60691i	−0.635583	+	0.874805i	0.362787	+	0.931872i	$0.381825\pi$
$18$	−0.613234	+	1.16973i	−0.144541	+	0.275707i
$19$	1.21650	+	3.74402i	0.279085	+	0.858936i	0.988109	+	0.153752i	$0.0491357\pi$
$19$	1.21650	+	3.74402i	0.279085	+	0.858936i	−0.709024	+	0.705184i	$0.750864\pi$
$20$	1.91596	−	0.573655i	0.428423	−	0.128273i
$21$			4.29097i			0.936366i
$22$	−4.13564	+	2.21280i	−0.881721	+	0.471771i
$23$			8.67477i			1.80881i	0.426671	+	0.904407i	$0.359686\pi$
$23$			8.67477i			1.80881i	−0.426671	+	0.904407i	$0.640314\pi$
$24$	−0.683887	−	5.56807i	−0.139598	−	1.13658i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−3.95993	−	2.07601i	−0.776607	−	0.407139i
$27$	2.40870	−	3.31529i	0.463554	−	0.638028i
$28$	−2.46122	−	3.55868i	−0.465127	−	0.672528i
$29$	6.12821	+	1.99118i	1.13798	+	0.369752i	0.816603	−	0.577199i	$-0.195854\pi$
$29$	6.12821	+	1.99118i	1.13798	+	0.369752i	0.321377	+	0.946951i	$0.395854\pi$
$30$	2.77534	−	0.406563i	0.506705	−	0.0742278i
$31$	−0.673670	−	0.927228i	−0.120995	−	0.166535i	0.744223	−	0.667931i	$-0.232820\pi$
$31$	−0.673670	−	0.927228i	−0.120995	−	0.166535i	−0.865218	+	0.501396i	$0.832820\pi$
$32$	3.76092	+	4.22558i	0.664843	+	0.746983i
$33$	−6.18872	+	2.22994i	−1.07732	+	0.388182i
$34$	1.05865	−	6.21560i	0.181557	−	1.06597i
$35$	1.75026	−	1.27164i	0.295847	−	0.214946i
$36$	0.0434146	−	1.86728i	0.00723577	−	0.311214i
$37$	3.17897	−	9.78387i	0.522620	−	1.60846i	−0.246355	−	0.969180i	$-0.579233\pi$
$37$	3.17897	−	9.78387i	0.522620	−	1.60846i	0.768975	−	0.639279i	$-0.220767\pi$
$38$	−3.89067	−	3.98218i	−0.631150	−	0.645995i
$39$	−5.07306	−	3.68579i	−0.812340	−	0.590199i
$40$	−2.06851	+	1.92906i	−0.327060	+	0.305011i
$41$	−1.29856	+	0.421929i	−0.202802	+	0.0658943i	−0.408656	−	0.912688i	$-0.634003\pi$
$41$	−1.29856	+	0.421929i	−0.202802	+	0.0658943i	0.205855	+	0.978583i	$0.434003\pi$
$42$	−2.69194	−	5.43859i	−0.415376	−	0.839193i
$43$	−4.00994			−0.611510			−0.305755	−	0.952110i	$-0.598909\pi$
$43$	−4.00994			−0.611510			−0.305755	+	0.952110i	$0.598909\pi$
$44$	3.85352	−	5.39911i	0.580939	−	0.813947i
$45$	0.933895			0.139217
$46$	−5.44212	−	10.9948i	−0.802397	−	1.62110i
$47$	3.61139	−	1.17341i	0.526776	−	0.171160i	−0.0335423	−	0.999437i	$-0.510679\pi$
$47$	3.61139	−	1.17341i	0.526776	−	0.171160i	0.560318	+	0.828277i	$0.310679\pi$
$48$	4.35993	+	6.62822i	0.629301	+	0.956702i
$49$	1.87655	+	1.36339i	0.268079	+	0.194771i
$50$	−0.988310	−	1.01156i	−0.139768	−	0.143056i
$51$	2.73257	−	8.40999i	0.382637	−	1.17763i
$52$	6.32141	+	0.146974i	0.876621	+	0.0203816i
$53$	6.21075	−	4.51237i	0.853112	−	0.619822i	−0.0728901	−	0.997340i	$-0.523222\pi$
$53$	6.21075	−	4.51237i	0.853112	−	0.619822i	0.926002	+	0.377518i	$0.123222\pi$
$54$	−0.973058	+	5.71306i	−0.132416	+	0.777450i
$55$	2.74361	+	1.86349i	0.369949	+	0.251273i
$56$	5.35202	+	2.96641i	0.715193	+	0.396403i
$57$	−4.58946	−	6.31685i	−0.607889	−	0.836687i
$58$	−9.01637	+	1.32082i	−1.18391	+	0.173432i
$59$	0.112673	+	0.0366097i	0.0146688	+	0.00476618i	0.316342	−	0.948645i	$-0.397545\pi$
$59$	0.112673	+	0.0366097i	0.0146688	+	0.00476618i	−0.301673	+	0.953411i	$0.597545\pi$
$60$	−3.26255	+	2.25641i	−0.421193	+	0.291301i
$61$	−7.07767	+	9.74158i	−0.906203	+	1.24728i	0.0622434	+	0.998061i	$0.480174\pi$
$61$	−7.07767	+	9.74158i	−0.906203	+	1.24728i	−0.968447	+	0.249221i	$0.919826\pi$
$62$	1.43554	+	0.752588i	0.182314	+	0.0955787i
$63$	−0.624345	−	1.92153i	−0.0786600	−	0.242091i
$64$	−7.41770	−	2.99629i	−0.927212	−	0.374537i
$65$			3.16156i			0.392143i
$66$	6.44494	−	6.70883i	0.793318	−	0.825800i
$67$		−	6.69412i		−	0.817817i	−0.912575	−	0.408909i	$-0.865909\pi$
$67$		−	6.69412i		−	0.817817i	0.912575	−	0.408909i	$-0.134091\pi$
$68$	2.55758	+	8.54212i	0.310152	+	1.03588i
$69$	−5.31681	−	16.3635i	−0.640069	−	1.96993i
$70$	−1.42060	+	2.70976i	−0.169794	+	0.323878i
$71$	−0.556753	+	0.766305i	−0.0660744	+	0.0909436i	−0.840775	−	0.541384i	$-0.817900\pi$
$71$	−0.556753	+	0.766305i	−0.0660744	+	0.0909436i	0.774701	+	0.632328i	$0.217900\pi$
$72$	1.11642	+	2.39393i	0.131571	+	0.282127i
$73$	1.45249	+	0.471942i	0.170001	+	0.0552366i	0.392781	−	0.919632i	$-0.371513\pi$
$73$	1.45249	+	0.471942i	0.170001	+	0.0552366i	−0.222780	+	0.974869i	$0.571513\pi$
$74$	2.10873	+	14.3949i	0.245135	+	1.67337i
$75$	−1.16582	−	1.60461i	−0.134617	−	0.185284i
$76$	7.42946	+	2.60640i	0.852217	+	0.298975i
$77$	2.00001	−	6.89093i	0.227923	−	0.785295i
$78$	8.74214	+	1.48897i	0.989852	+	0.168593i
$79$	−3.49460	+	2.53897i	−0.393173	+	0.285657i	−0.766754	−	0.641941i	$-0.778130\pi$
$79$	−3.49460	+	2.53897i	−0.393173	+	0.285657i	0.373582	+	0.927597i	$0.378130\pi$
$80$	1.41153	−	3.74267i	0.157814	−	0.418443i
$81$	−3.37741	+	10.3946i	−0.375268	+	1.15496i
$82$	1.38117	−	1.34943i	0.152525	−	0.149020i
$83$	0.790772	+	0.574530i	0.0867985	+	0.0630628i	0.630338	−	0.776321i	$-0.282916\pi$
$83$	0.790772	+	0.574530i	0.0867985	+	0.0630628i	−0.543540	+	0.839384i	$0.682916\pi$
$84$	6.82381	+	5.20435i	0.744539	+	0.567842i
$85$	−4.24018	+	1.37772i	−0.459912	+	0.149435i
$86$	5.08240	−	2.51564i	0.548049	−	0.271268i
$87$	−12.7802			−1.37018
$88$	−1.49701	+	9.26061i	−0.159581	+	0.987185i
$89$	−13.2930			−1.40905			−0.704527	−	0.709677i	$-0.748841\pi$
$89$	−13.2930			−1.40905			−0.704527	+	0.709677i	$0.748841\pi$
$90$	−1.18367	+	0.585879i	−0.124769	+	0.0617571i
$91$	6.50506	−	2.11362i	0.681916	−	0.221568i
$92$	13.7952	+	10.5213i	1.43825	+	1.09692i
$93$	1.83907	+	1.33616i	0.190702	+	0.138553i
$94$	−3.84112	+	3.75285i	−0.396181	+	0.387077i
$95$	−1.21650	+	3.74402i	−0.124811	+	0.384128i
$96$	−9.68421	−	5.66574i	−0.988391	−	0.578257i
$97$	11.7313	−	8.52327i	1.19113	−	0.865407i	0.197747	−	0.980253i	$-0.436638\pi$
$97$	11.7313	−	8.52327i	1.19113	−	0.865407i	0.993383	+	0.114846i	$0.0366375\pi$
$98$	−3.23376	−	0.550779i	−0.326659	−	0.0556371i
$99$	2.44690	−	1.89906i	0.245923	−	0.190862i
$100$	1.88723	+	0.662079i	0.188723	+	0.0662079i
$101$	−4.97379	−	6.84583i	−0.494911	−	0.681186i	0.486374	−	0.873751i	$-0.338319\pi$
$101$	−4.97379	−	6.84583i	−0.494911	−	0.681186i	−0.981284	+	0.192565i	$0.938319\pi$
$102$	1.81261	+	12.3735i	0.179476	+	1.22516i
$103$	−7.12868	−	2.31625i	−0.702410	−	0.228227i	−0.0640295	−	0.997948i	$-0.520395\pi$
$103$	−7.12868	−	2.31625i	−0.702410	−	0.228227i	−0.638380	+	0.769721i	$0.720395\pi$
$104$	−8.10427	+	3.77946i	−0.794689	+	0.370606i
$105$	−2.52217	+	3.47147i	−0.246138	+	0.338781i
$106$	−5.04098	+	9.61553i	−0.489623	+	0.933943i
$107$	3.11661	+	9.59195i	0.301294	+	0.927288i	0.981034	+	0.193835i	$0.0620927\pi$
$107$	3.11661	+	9.59195i	0.301294	+	0.927288i	−0.679740	+	0.733453i	$0.737907\pi$
$108$	−2.35079	−	7.85148i	−0.226205	−	0.755509i
$109$		−	0.409727i		−	0.0392447i	−0.999807	−	0.0196224i	$-0.993754\pi$
$109$		−	0.409727i		−	0.0392447i	0.999807	−	0.0196224i	$-0.00624639\pi$
$110$	−4.64645	−	0.640674i	−0.443022	−	0.0610859i
$111$			20.4040i			1.93666i
$112$	−8.64439	−	0.402184i	−0.816818	−	0.0380028i
$113$	−4.42188	−	13.6091i	−0.415975	−	1.28024i	−0.911376	−	0.411575i	$-0.864979\pi$
$113$	−4.42188	−	13.6091i	−0.415975	−	1.28024i	0.495400	−	0.868665i	$-0.335021\pi$
$114$	9.77979	+	5.12709i	0.915961	+	0.480196i
$115$	−5.09890	+	7.01803i	−0.475475	+	0.654435i
$116$	10.5992	−	7.33050i	0.984110	−	0.680620i
$117$	2.80805	+	0.912392i	0.259605	+	0.0843506i
$118$	−0.165775	+	0.0242845i	−0.0152608	+	0.00223557i
$119$	5.66945	+	7.80332i	0.519717	+	0.715330i
$120$	2.71956	−	4.90665i	0.248260	−	0.447913i
$121$	10.9779	−	0.696539i	0.997993	−	0.0633217i
$122$	2.85921	−	16.7872i	0.258861	−	1.51984i
$123$	2.19092	−	1.59180i	0.197548	−	0.143527i
$124$	−2.29161	−	0.0532803i	−0.205793	−	0.00478471i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	1.99680	+	2.04377i	0.177889	+	0.182073i
$127$	7.10692	+	5.16348i	0.630638	+	0.458185i	0.856621	−	0.515946i	$-0.172560\pi$
$127$	7.10692	+	5.16348i	0.630638	+	0.458185i	−0.225983	+	0.974131i	$0.572560\pi$
$128$	11.2813	−	0.855842i	0.997135	−	0.0756465i
$129$	7.56407	−	2.45772i	0.665979	−	0.216390i
$130$	−1.98340	−	4.00712i	−0.173956	−	0.351447i
$131$	0.809002			0.0706829			0.0353414	−	0.999375i	$-0.488748\pi$
$131$	0.809002			0.0706829			0.0353414	+	0.999375i	$0.488748\pi$
$132$	−3.95986	+	12.5464i	−0.344661	+	1.09202i
$133$	8.51678			0.738499
$134$	4.19956	+	8.48447i	0.362787	+	0.732947i
$135$	3.89736	−	1.26633i	0.335431	−	0.108988i
$136$	−8.60050	−	9.22221i	−0.737487	−	0.790798i
$137$	−17.1284	−	12.4445i	−1.46337	−	1.06320i	−0.982468	−	0.186431i	$-0.940308\pi$
$137$	−17.1284	−	12.4445i	−1.46337	−	1.06320i	−0.480906	−	0.876772i	$-0.659692\pi$
$138$	17.0044	+	17.4044i	1.44751	+	1.48156i
$139$	5.01958	−	15.4487i	0.425755	−	1.31034i	−0.476515	−	0.879167i	$-0.658100\pi$
$139$	5.01958	−	15.4487i	0.425755	−	1.31034i	0.902270	−	0.431172i	$-0.141900\pi$
$140$	0.100573	−	4.32570i	0.00849998	−	0.365589i
$141$	−6.09309	+	4.42689i	−0.513131	+	0.372811i
$142$	0.224915	−	1.32053i	0.0188745	−	0.110817i
$143$	6.42896	+	8.28362i	0.537617	+	0.692711i
$144$	−2.91683	−	2.33380i	−0.243070	−	0.194483i
$145$	3.78744	+	5.21297i	0.314530	+	0.432913i
$146$	−2.13703	+	0.313056i	−0.176862	+	0.0259087i
$147$	−4.37543	−	1.42166i	−0.360879	−	0.117257i
$148$	−11.7034	−	16.9219i	−0.962011	−	1.39097i
$149$	−3.71483	+	5.11302i	−0.304331	+	0.418875i	−0.933603	−	0.358310i	$-0.883353\pi$
$149$	−3.71483	+	5.11302i	−0.304331	+	0.418875i	0.629272	+	0.777185i	$0.283353\pi$
$150$	2.48427	+	1.30239i	0.202840	+	0.106339i
$151$	−4.36717	−	13.4408i	−0.355395	−	1.09379i	−0.955780	−	0.294082i	$-0.904986\pi$
$151$	−4.36717	−	13.4408i	−0.355395	−	1.09379i	0.600385	−	0.799711i	$-0.295014\pi$
$152$	−11.0516	+	1.35739i	−0.896403	+	0.110099i
$153$			4.16367i			0.336612i
$154$	1.78811	+	9.98863i	0.144090	+	0.804907i
$155$		−	1.14612i		−	0.0920583i
$156$	−12.0143	+	3.59719i	−0.961917	+	0.288005i
$157$	4.63070	+	14.2518i	0.369570	+	1.13742i	0.947070	+	0.321029i	$0.104029\pi$
$157$	4.63070	+	14.2518i	0.369570	+	1.13742i	−0.577499	+	0.816391i	$0.695971\pi$
$158$	2.83640	−	5.41036i	0.225652	−	0.430425i
$159$	−8.94987	+	12.3184i	−0.709771	+	0.976915i
$160$	0.558916	+	5.62918i	0.0441862	+	0.445025i
$161$	17.8488	+	5.79942i	1.40668	+	0.457058i
$162$	−2.24036	−	15.2935i	−0.176019	−	1.20157i
$163$	−2.27783	−	3.13516i	−0.178413	−	0.245565i	0.710439	−	0.703759i	$-0.248496\pi$
$163$	−2.27783	−	3.13516i	−0.178413	−	0.245565i	−0.888852	+	0.458194i	$0.848496\pi$
$164$	−0.903998	+	2.57681i	−0.0705903	+	0.201215i
$165$	−6.31750	−	1.83358i	−0.491817	−	0.142744i
$166$	−1.36270	−	0.232097i	−0.105766	−	0.0180142i
$167$	−17.8746	+	12.9866i	−1.38317	+	1.00494i	−0.386599	+	0.922248i	$0.626350\pi$
$167$	−17.8746	+	12.9866i	−1.38317	+	1.00494i	−0.996576	+	0.0826873i	$0.973650\pi$
$168$	−11.9138	−	2.31534i	−0.919169	−	0.178632i
$169$	0.928459	−	2.85750i	0.0714200	−	0.219808i
$170$	4.50991	−	4.40627i	0.345894	−	0.337945i
$171$	2.97432	+	2.16097i	0.227452	+	0.165253i
$172$	−4.86350	+	6.37689i	−0.370839	+	0.486234i
$173$	−7.70232	+	2.50263i	−0.585596	+	0.190272i	−0.586806	−	0.809728i	$-0.699615\pi$
$173$	−7.70232	+	2.50263i	−0.585596	+	0.190272i	0.00120986	+	0.999999i	$0.499615\pi$
$174$	16.1983	−	8.01769i	1.22799	−	0.607819i
$175$	2.16344			0.163540
$176$	−3.91227	−	12.6765i	−0.294899	−	0.955529i
$177$	−0.234977			−0.0176619
$178$	16.8482	−	8.33937i	1.26283	−	0.625062i
$179$	17.3150	−	5.62597i	1.29418	−	0.420505i	0.420627	−	0.907234i	$-0.361810\pi$
$179$	17.3150	−	5.62597i	1.29418	−	0.420505i	0.873553	+	0.486729i	$0.161810\pi$
$180$	1.13269	−	1.48515i	0.0844254	−	0.110696i
$181$	1.65843	+	1.20492i	0.123270	+	0.0895611i	0.647712	−	0.761885i	$-0.275726\pi$
$181$	1.65843	+	1.20492i	0.123270	+	0.0895611i	−0.524442	+	0.851446i	$0.675726\pi$
$182$	−6.91886	+	6.75987i	−0.512860	+	0.501075i
$183$	7.38016	−	22.7138i	0.545557	−	1.67905i
$184$	−24.0853	−	4.68077i	−1.77559	−	0.345071i
$185$	8.32266	−	6.04677i	0.611894	−	0.444567i
$186$	−3.16917	−	0.539778i	−0.232375	−	0.0395784i
$187$	−8.30816	+	12.2321i	−0.607553	+	0.894499i
$188$	2.51408	−	7.16629i	0.183358	−	0.522655i
$189$	−5.21107	−	7.17242i	−0.379049	−	0.521717i
$190$	−0.806952	−	5.50853i	−0.0585424	−	0.399631i
$191$	−21.9303	−	7.12559i	−1.58682	−	0.515589i	−0.623019	−	0.782207i	$-0.714094\pi$
$191$	−21.9303	−	7.12559i	−1.58682	−	0.515589i	−0.963802	+	0.266617i	$0.914094\pi$
$192$	15.8287	+	1.10565i	1.14234	+	0.0797934i
$193$	3.91182	−	5.38415i	0.281579	−	0.387560i	−0.644677	−	0.764455i	$-0.723008\pi$
$193$	3.91182	−	5.38415i	0.281579	−	0.387560i	0.926256	+	0.376895i	$0.123008\pi$
$194$	−9.52173	+	18.1624i	−0.683620	+	1.30399i
$195$	−1.93774	−	5.96374i	−0.138764	−	0.427072i
$196$	4.44416	−	1.33062i	0.317440	−	0.0950441i
$197$			5.72912i			0.408183i	0.978952	+	0.204092i	$0.0654240\pi$
$197$			5.72912i			0.408183i	−0.978952	+	0.204092i	$0.934576\pi$
$198$	−1.90996	+	3.94203i	−0.135735	+	0.280148i
$199$		−	9.49871i		−	0.673346i	−0.941622	−	0.336673i	$-0.890698\pi$
$199$		−	9.49871i		−	0.673346i	0.941622	−	0.336673i	$-0.109302\pi$
$200$	−2.80733	+	0.344804i	−0.198508	+	0.0243813i
$201$	4.10287	+	12.6273i	0.289394	+	0.890663i
$202$	10.5988	+	5.55645i	0.745727	+	0.390950i
$203$	8.19389	−	11.2779i	0.575098	−	0.791555i
$204$	−10.0599	−	14.5457i	−0.704337	−	1.01840i
$205$	−1.29856	−	0.421929i	−0.0906957	−	0.0294688i
$206$	10.4883	−	1.53645i	0.730758	−	0.107050i
$207$	4.76184	+	6.55410i	0.330970	+	0.455542i
$208$	7.90072	−	9.87450i	0.547816	−	0.684673i
$209$	4.42601	+	12.2835i	0.306154	+	0.849665i
$210$	1.01890	−	5.98220i	0.0703106	−	0.412811i
$211$	19.8848	−	14.4472i	1.36893	−	0.994585i	0.371109	−	0.928590i	$-0.378978\pi$
$211$	19.8848	−	14.4472i	1.36893	−	0.994585i	0.997820	−	0.0659952i	$-0.0210222\pi$
$212$	0.356882	−	15.3497i	0.0245108	−	1.05422i
$213$	0.580547	−	1.78674i	0.0397784	−	0.122425i
$214$	−9.96767	−	10.2021i	−0.681376	−	0.697402i
$215$	−3.24411	−	2.35698i	−0.221246	−	0.160745i
$216$	7.90514	+	8.47659i	0.537877	+	0.576759i
$217$	−2.35819	+	0.766223i	−0.160085	+	0.0520146i
$218$	0.257042	+	0.519309i	0.0174091	+	0.0351720i
$219$	−3.02913			−0.204689
$220$	6.29108	−	2.10293i	0.424144	−	0.141780i
$221$	−14.0955			−0.948163
$222$	−12.8005	−	25.8611i	−0.859112	−	1.73568i
$223$	5.05248	−	1.64165i	0.338339	−	0.109933i	−0.134920	−	0.990857i	$-0.543078\pi$
$223$	5.05248	−	1.64165i	0.338339	−	0.109933i	0.473259	+	0.880924i	$0.343078\pi$
$224$	11.2087	−	4.91332i	0.748910	−	0.328285i
$225$	0.755537	+	0.548930i	0.0503691	+	0.0365953i
$226$	14.1422	+	14.4748i	0.940726	+	0.962852i
$227$	7.14832	−	22.0003i	0.474451	−	1.46021i	−0.372247	−	0.928134i	$-0.621412\pi$
$227$	7.14832	−	22.0003i	0.474451	−	1.46021i	0.846697	−	0.532075i	$-0.178588\pi$
$228$	−15.6119	−	0.362978i	−1.03392	−	0.0240388i
$229$	−3.45085	+	2.50719i	−0.228038	+	0.165680i	−0.695938	−	0.718102i	$-0.745011\pi$
$229$	−3.45085	+	2.50719i	−0.228038	+	0.165680i	0.467899	+	0.883782i	$0.345011\pi$
$230$	2.05984	−	12.0938i	0.135822	−	0.797442i
$231$	0.450809	+	14.2244i	0.0296611	+	0.935896i
$232$	−8.83515	+	15.9405i	−0.580056	+	1.04654i
$233$	−3.63198	−	4.99899i	−0.237939	−	0.327495i	0.673303	−	0.739367i	$-0.264875\pi$
$233$	−3.63198	−	4.99899i	−0.237939	−	0.327495i	−0.911242	+	0.411872i	$0.864875\pi$
$234$	−4.13146	+	0.605222i	−0.270082	+	0.0395646i
$235$	3.61139	+	1.17341i	0.235581	+	0.0765450i
$236$	0.194876	−	0.134778i	0.0126854	−	0.00877332i
$237$	5.03581	−	6.93120i	0.327111	−	0.450230i
$238$	−12.0812	−	6.33360i	−0.783106	−	0.410546i
$239$	−2.43080	−	7.48124i	−0.157236	−	0.483921i	0.841145	−	0.540810i	$-0.181882\pi$
$239$	−2.43080	−	7.48124i	−0.157236	−	0.483921i	−0.998381	+	0.0568884i	$0.981882\pi$
$240$	−0.368716	+	7.92505i	−0.0238005	+	0.511560i
$241$			7.93127i			0.510898i	0.966822	+	0.255449i	$0.0822233\pi$
$241$			7.93127i			0.510898i	−0.966822	+	0.255449i	$0.917777\pi$
$242$	−13.4770	+	7.76984i	−0.866335	+	0.499464i
$243$		−	9.38390i		−	0.601978i
$244$	6.90752	+	23.0706i	0.442209	+	1.47695i
$245$	0.716779	+	2.20602i	0.0457933	+	0.140937i
$246$	−1.77827	+	3.39200i	−0.113378	+	0.216266i
$247$	−7.31562	+	10.0691i	−0.465482	+	0.640681i
$248$	2.93793	−	1.37012i	0.186559	−	0.0870024i
$249$	−1.84379	−	0.599084i	−0.116845	−	0.0379654i
$250$	−0.204982	−	1.39928i	−0.0129642	−	0.0884982i
$251$	−2.01865	−	2.77843i	−0.127416	−	0.175373i	0.740543	−	0.672009i	$-0.234568\pi$
$251$	−2.01865	−	2.77843i	−0.127416	−	0.175373i	−0.867959	+	0.496636i	$0.834568\pi$
$252$	−3.81301	−	1.33768i	−0.240197	−	0.0842659i
$253$	0.911371	+	28.7565i	0.0572974	+	1.80791i
$254$	−12.2470	−	2.08593i	−0.768444	−	0.130883i
$255$	7.15397	−	5.19766i	0.447999	−	0.325490i
$256$	−13.7616	+	8.16206i	−0.860098	+	0.510129i
$257$	−4.96642	+	15.2851i	−0.309797	+	0.953457i	0.668047	+	0.744119i	$0.267131\pi$
$257$	−4.96642	+	15.2851i	−0.309797	+	0.953457i	−0.977843	+	0.209337i	$0.932869\pi$
$258$	−8.04523	+	7.86036i	−0.500874	+	0.489364i
$259$	−18.0055	−	13.0818i	−1.11881	−	0.812863i
$260$	5.02774	+	3.83453i	0.311807	+	0.237808i
$261$	5.72310	−	1.85955i	0.354251	−	0.115103i
$262$	−1.02537	+	0.507528i	−0.0633476	+	0.0313552i
$263$	−2.73012			−0.168347			−0.0841733	−	0.996451i	$-0.526825\pi$
$263$	−2.73012			−0.168347			−0.0841733	+	0.996451i	$0.526825\pi$
$264$	−2.85204	−	18.3861i	−0.175531	−	1.13159i
$265$	7.67691			0.471589
$266$	−10.7946	+	5.34301i	−0.661859	+	0.327601i
$267$	25.0750	−	8.14736i	1.53456	−	0.498610i
$268$	−10.6455	−	8.11905i	−0.650276	−	0.495950i
$269$	19.8056	+	14.3896i	1.20757	+	0.877350i	0.995008	−	0.0997979i	$-0.0318196\pi$
$269$	19.8056	+	14.3896i	1.20757	+	0.877350i	0.212561	+	0.977148i	$0.431820\pi$
$270$	−4.14528	+	4.05002i	−0.252273	+	0.246476i
$271$	−6.26330	+	19.2765i	−0.380469	+	1.17096i	0.559246	+	0.829002i	$0.311091\pi$
$271$	−6.26330	+	19.2765i	−0.380469	+	1.17096i	−0.939714	+	0.341960i	$0.888909\pi$
$272$	16.6863	+	6.29317i	1.01175	+	0.381579i
$273$	−10.9752	+	7.97398i	−0.664252	+	0.482607i
$274$	29.5164	+	5.02728i	1.78315	+	0.303709i
$275$	1.12430	+	3.12025i	0.0677977	+	0.188158i
$276$	−32.4709	−	11.3915i	−1.95452	−	0.685685i
$277$	17.0989	+	23.5346i	1.02737	+	1.41406i	0.906903	+	0.421339i	$0.138440\pi$
$277$	17.0989	+	23.5346i	1.02737	+	1.41406i	0.120468	+	0.992717i	$0.461560\pi$
$278$	3.32967	+	22.7295i	0.199700	+	1.36322i
$279$	−1.01797	−	0.330757i	−0.0609440	−	0.0198019i
$280$	2.58626	+	5.54571i	0.154559	+	0.331420i
$281$	15.4637	−	21.2840i	0.922488	−	1.26970i	−0.0402301	−	0.999190i	$-0.512809\pi$
$281$	15.4637	−	21.2840i	0.922488	−	1.26970i	0.962718	−	0.270506i	$-0.0871909\pi$
$282$	4.94548	−	9.43337i	0.294499	−	0.561749i
$283$	7.24916	+	22.3106i	0.430918	+	1.32623i	0.897213	+	0.441599i	$0.145589\pi$
$283$	7.24916	+	22.3106i	0.430918	+	1.32623i	−0.466295	+	0.884629i	$0.654411\pi$
$284$	0.543368	+	1.81481i	0.0322430	+	0.107689i
$285$		−	7.80805i		−	0.462509i
$286$	−13.3451	−	6.46586i	−0.789114	−	0.382334i
$287$			2.95394i			0.174365i
$288$	5.16106	+	1.12810i	0.304118	+	0.0664738i
$289$	−0.889114	−	2.73641i	−0.0523008	−	0.160965i
$290$	−8.07075	−	4.23112i	−0.473931	−	0.248460i
$291$	−16.9051	+	23.2679i	−0.990994	+	1.36399i
$292$	2.51218	−	1.73745i	0.147014	−	0.101677i
$293$	−31.9767	−	10.3899i	−1.86810	−	0.606983i	−0.992227	−	0.124443i	$-0.960286\pi$
$293$	−31.9767	−	10.3899i	−1.86810	−	0.606983i	−0.875874	−	0.482540i	$-0.839714\pi$
$294$	6.43752	−	0.943040i	0.375444	−	0.0549992i
$295$	0.0696358	+	0.0958454i	0.00405435	+	0.00558033i
$296$	25.4494	+	14.1056i	1.47922	+	0.819871i
$297$	7.63644	−	11.2431i	0.443111	−	0.652391i
$298$	1.50070	−	8.81100i	0.0869334	−	0.510408i
$299$	−22.1879	+	16.1205i	−1.28316	+	0.932270i
$300$	−3.96574	−	0.0922039i	−0.228962	−	0.00532340i
$301$	−2.68080	+	8.25065i	−0.154519	+	0.475560i
$302$	13.9672	+	14.2958i	0.803724	+	0.822628i
$303$	13.5781	+	9.86504i	0.780039	+	0.566732i
$304$	13.1558	−	8.65365i	0.754537	−	0.496321i
$305$	−11.4519	+	3.72095i	−0.655735	+	0.213061i
$306$	−2.61208	−	5.27724i	−0.149323	−	0.301680i
$307$	9.76104			0.557092			0.278546	−	0.960423i	$-0.410148\pi$
$307$	9.76104			0.557092			0.278546	+	0.960423i	$0.410148\pi$
$308$	−8.53272	−	11.5383i	−0.486197	−	0.657457i
$309$	14.8667			0.845736
$310$	0.719017	+	1.45265i	0.0408374	+	0.0825048i
$311$	−12.1346	+	3.94278i	−0.688092	+	0.223574i	−0.632134	−	0.774859i	$-0.717821\pi$
$311$	−12.1346	+	3.94278i	−0.688092	+	0.223574i	−0.0559570	+	0.998433i	$0.517821\pi$
$312$	12.9709	−	12.0965i	0.734332	−	0.684827i
$313$	10.5101	+	7.63602i	0.594065	+	0.431613i	0.843767	−	0.536709i	$-0.180333\pi$
$313$	10.5101	+	7.63602i	0.594065	+	0.431613i	−0.249702	+	0.968323i	$0.580333\pi$
$314$	−14.8101	−	15.1584i	−0.835781	−	0.855439i
$315$	0.624345	−	1.92153i	0.0351778	−	0.108266i
$316$	−0.200806	+	8.63679i	−0.0112962	+	0.485857i
$317$	12.6756	−	9.20938i	0.711934	−	0.517250i	−0.171863	−	0.985121i	$-0.554979\pi$
$317$	12.6756	−	9.20938i	0.711934	−	0.517250i	0.883797	+	0.467871i	$0.154979\pi$
$318$	3.61554	−	21.2277i	0.202749	−	1.19039i
$319$	20.5240	+	5.95684i	1.14912	+	0.333519i
$320$	−4.23987	−	6.78407i	−0.237016	−	0.379241i
$321$	−11.7579	−	16.1834i	−0.656263	−	0.903269i
$322$	−26.2607	+	3.84696i	−1.46345	+	0.214383i
$323$	−16.6923	−	5.42365i	−0.928783	−	0.301780i
$324$	12.4339	+	17.9782i	0.690772	+	0.998790i
$325$	−1.85832	+	2.55775i	−0.103081	+	0.141879i
$326$	4.85388	+	2.54466i	0.268831	+	0.140936i
$327$	0.251124	+	0.772880i	0.0138872	+	0.0427404i
$328$	−0.470793	−	3.83311i	−0.0259952	−	0.211648i
$329$		−	8.21509i		−	0.452913i
$330$	9.15742	−	1.63932i	0.504099	−	0.0902414i
$331$			20.7468i			1.14035i	0.821523	+	0.570175i	$0.193125\pi$
$331$			20.7468i			1.14035i	−0.821523	+	0.570175i	$0.806875\pi$
$332$	1.87276	−	0.560718i	0.102781	−	0.0307734i
$333$	−2.96883	−	9.13711i	−0.162691	−	0.500710i
$334$	14.5079	−	27.6735i	0.793840	−	1.51423i
$335$	3.93471	−	5.41566i	0.214976	−	0.295889i
$336$	16.5527	−	4.53955i	0.903023	−	0.247653i
$337$	−24.5682	−	7.98269i	−1.33831	−	0.434845i	−0.449569	−	0.893245i	$-0.648423\pi$
$337$	−24.5682	−	7.98269i	−1.33831	−	0.434845i	−0.888746	+	0.458401i	$0.848423\pi$
$338$	0.615881	+	4.20422i	0.0334995	+	0.228679i
$339$	16.6822	+	22.9611i	0.906055	+	1.24708i
$340$	−2.95181	+	8.41402i	−0.160084	+	0.456314i
$341$	−2.33061	−	3.00295i	−0.126209	−	0.162619i
$342$	−5.12548	−	0.872980i	−0.277154	−	0.0472053i
$343$	16.3116	−	11.8511i	0.880743	−	0.639897i
$344$	2.16370	−	11.1335i	0.116659	−	0.600279i
$345$	5.31681	−	16.3635i	0.286248	−	0.880980i
$346$	8.19228	−	8.00402i	0.440419	−	0.430299i
$347$	−12.2474	−	8.89825i	−0.657474	−	0.477683i	0.208335	−	0.978058i	$-0.433196\pi$
$347$	−12.2474	−	8.89825i	−0.657474	−	0.477683i	−0.865809	+	0.500375i	$0.833196\pi$
$348$	−15.5007	+	20.3240i	−0.830923	+	1.08948i
$349$	16.7168	−	5.43162i	0.894831	−	0.290748i	0.174729	−	0.984617i	$-0.444095\pi$
$349$	16.7168	−	5.43162i	0.894831	−	0.290748i	0.720102	+	0.693868i	$0.244095\pi$
$350$	−2.74205	+	1.35723i	−0.146569	+	0.0725472i
$351$	12.9558			0.691530
$352$	12.9112	+	13.6125i	0.688171	+	0.725548i
$353$	27.7541			1.47720			0.738602	−	0.674142i	$-0.235486\pi$
$353$	27.7541			1.47720			0.738602	+	0.674142i	$0.235486\pi$
$354$	0.297821	−	0.147413i	0.0158290	−	0.00783490i
$355$	−0.900845	+	0.292702i	−0.0478119	+	0.0155350i
$356$	−16.1226	+	21.1395i	−0.854495	+	1.12039i
$357$	−15.4772	−	11.2448i	−0.819138	−	0.595138i
$358$	−18.4164	+	17.9932i	−0.973337	+	0.950970i
$359$	−4.23768	+	13.0422i	−0.223656	+	0.688344i	0.774769	+	0.632245i	$0.217866\pi$
$359$	−4.23768	+	13.0422i	−0.223656	+	0.688344i	−0.998425	+	0.0560990i	$0.982134\pi$
$360$	−0.503915	+	2.59294i	−0.0265587	+	0.136660i
$361$	2.83355	−	2.05869i	0.149134	−	0.108352i
$362$	−2.85789	−	0.486760i	−0.150207	−	0.0255835i
$363$	−20.2811	+	8.04234i	−1.06448	+	0.422113i
$364$	4.52851	−	12.9084i	0.237358	−	0.676581i
$365$	0.897686	+	1.23556i	0.0469870	+	0.0646721i
$366$	4.89553	+	33.4185i	0.255893	+	1.74682i
$367$	−26.9913	−	8.77001i	−1.40893	−	0.457791i	−0.496866	−	0.867827i	$-0.665516\pi$
$367$	−26.9913	−	8.77001i	−1.40893	−	0.457791i	−0.912069	+	0.410037i	$0.865516\pi$
$368$	33.4634	−	9.17730i	1.74440	−	0.478400i
$369$	−0.749504	+	1.03160i	−0.0390176	+	0.0537031i
$370$	−6.75512	+	12.8852i	−0.351182	+	0.669870i
$371$	−5.13231	−	15.7956i	−0.266456	−	0.820068i
$372$	4.35540	−	1.30404i	0.225817	−	0.0676113i
$373$		−	36.8629i		−	1.90869i	−0.298708	−	0.954345i	$-0.596556\pi$
$373$		−	36.8629i		−	1.90869i	0.298708	−	0.954345i	$-0.403444\pi$
$374$	2.85637	−	20.7157i	0.147700	−	1.07118i
$375$		−	1.98340i		−	0.102423i
$376$	1.30931	+	10.6601i	0.0675223	+	0.549754i
$377$	6.29522	+	19.3747i	0.324220	+	0.997847i
$378$	11.1044	+	5.82152i	0.571148	+	0.299427i
$379$	7.95643	−	10.9511i	0.408695	−	0.562520i	−0.554205	−	0.832380i	$-0.686978\pi$
$379$	7.95643	−	10.9511i	0.408695	−	0.562520i	0.962899	+	0.269861i	$0.0869776\pi$
$380$	4.47855	+	6.47555i	0.229745	+	0.332189i
$381$	−16.5707	−	5.38416i	−0.848944	−	0.275839i
$382$	32.2658	−	4.72666i	1.65086	−	0.241837i
$383$	15.0329	+	20.6910i	0.768143	+	1.05726i	0.996493	+	0.0836790i	$0.0266671\pi$
$383$	15.0329	+	20.6910i	0.768143	+	1.05726i	−0.228350	+	0.973579i	$0.573333\pi$
$384$	−20.7557	+	8.52877i	−1.05918	+	0.435232i
$385$	5.66843	−	4.39930i	0.288890	−	0.224209i
$386$	−1.58028	+	9.27823i	−0.0804342	+	0.472249i
$387$	−3.02966	+	2.20117i	−0.154006	+	0.111892i
$388$	0.674102	−	28.9935i	0.0342223	−	1.47192i
$389$	−7.70500	+	23.7135i	−0.390659	+	1.20232i	0.541632	+	0.840616i	$0.317807\pi$
$389$	−7.70500	+	23.7135i	−0.390659	+	1.20232i	−0.932291	+	0.361709i	$0.882193\pi$
$390$	6.19734	+	6.34311i	0.313815	+	0.321196i
$391$	−31.2891	−	22.7329i	−1.58236	−	1.14965i
$392$	−4.79800	+	4.47454i	−0.242335	+	0.225998i
$393$	−1.52605	+	0.495842i	−0.0769788	+	0.0250119i
$394$	−3.59417	−	7.26138i	−0.181072	−	0.365823i
$395$	−4.31956			−0.217341
$396$	−0.0522591	−	6.19454i	−0.00262612	−	0.311287i
$397$	5.97091			0.299671			0.149836	−	0.988711i	$-0.452126\pi$
$397$	5.97091			0.299671			0.149836	+	0.988711i	$0.452126\pi$
$398$	5.95902	+	12.0391i	0.298699	+	0.603468i
$399$	−16.0655	+	5.21998i	−0.804279	+	0.261326i
$400$	3.34184	−	2.19820i	0.167092	−	0.109910i
$401$	−20.7320	−	15.0627i	−1.03531	−	0.752195i	−0.0659435	−	0.997823i	$-0.521006\pi$
$401$	−20.7320	−	15.0627i	−1.03531	−	0.752195i	−0.969364	+	0.245628i	$0.921006\pi$
$402$	−13.1219	−	13.4306i	−0.654463	−	0.669856i
$403$	1.11973	−	3.44617i	0.0557776	−	0.171666i
$404$	−16.9193	−	0.393375i	−0.841765	−	0.0195711i
$405$	−8.84217	+	6.42421i	−0.439371	+	0.319222i
$406$	−3.31014	+	19.4347i	−0.164279	+	0.964526i
$407$	9.51028	−	32.7671i	0.471407	−	1.62421i
$408$	21.8757	+	12.1248i	1.08301	+	0.600269i
$409$	−7.03003	−	9.67600i	−0.347612	−	0.478447i	0.599033	−	0.800724i	$-0.295552\pi$
$409$	−7.03003	−	9.67600i	−0.347612	−	0.478447i	−0.946645	+	0.322277i	$0.895552\pi$
$410$	1.91056	−	0.279881i	0.0943560	−	0.0138223i
$411$	39.9370	+	12.9763i	1.96995	+	0.640075i
$412$	−12.3296	+	8.52725i	−0.607434	+	0.420107i
$413$	0.150653	−	0.207355i	0.00741313	−	0.0102033i
$414$	−10.1471	−	5.31966i	−0.498703	−	0.261447i
$415$	0.302048	+	0.929609i	0.0148270	+	0.0456327i
$416$	−3.81900	+	17.4720i	−0.187242	+	0.856633i
$417$			32.2178i			1.57771i
$418$	−13.3158	−	12.7920i	−0.651296	−	0.625678i
$419$		−	13.1418i		−	0.642018i	−0.947076	−	0.321009i	$-0.895978\pi$
$419$		−	13.1418i		−	0.642018i	0.947076	−	0.321009i	$-0.104022\pi$
$420$	2.46153	+	8.22135i	0.120111	+	0.401161i
$421$	−2.76091	−	8.49720i	−0.134558	−	0.414128i	0.860963	−	0.508668i	$-0.169862\pi$
$421$	−2.76091	−	8.49720i	−0.134558	−	0.414128i	−0.995521	+	0.0945400i	$0.969862\pi$
$422$	−16.1396	+	30.7858i	−0.785663	+	1.49863i
$423$	2.08442	−	2.86896i	0.101348	−	0.139493i
$424$	9.17730	+	19.6788i	0.445689	+	0.955689i
$425$	−4.24018	−	1.37772i	−0.205679	−	0.0668291i
$426$	0.385098	+	2.62881i	0.0186581	+	0.127366i
$427$	15.3121	+	21.0753i	0.741004	+	1.01990i
$428$	19.0338	+	6.67745i	0.920035	+	0.322767i
$429$	−17.2042	−	11.6853i	−0.830628	−	0.564171i
$430$	5.59040	+	0.952166i	0.269593	+	0.0459175i
$431$	19.1954	−	13.9462i	0.924608	−	0.671767i	−0.0200586	−	0.999799i	$-0.506385\pi$
$431$	19.1954	−	13.9462i	0.924608	−	0.671767i	0.944667	+	0.328032i	$0.106385\pi$
$432$	−15.3372	−	5.78436i	−0.737910	−	0.278300i
$433$	1.25353	−	3.85797i	0.0602408	−	0.185402i	−0.916407	−	0.400247i	$-0.868924\pi$
$433$	1.25353	−	3.85797i	0.0602408	−	0.185402i	0.976648	+	0.214844i	$0.0689245\pi$
$434$	2.50820	−	2.45056i	0.120398	−	0.117631i
$435$	−10.3394	−	7.51203i	−0.495737	−	0.360174i
$436$	−0.651577	−	0.496942i	−0.0312049	−	0.0237992i
$437$	−32.4785	+	10.5529i	−1.55366	+	0.504813i
$438$	3.83927	−	1.90032i	0.183447	−	0.0908010i
$439$	−15.9976			−0.763526			−0.381763	−	0.924260i	$-0.624683\pi$
$439$	−15.9976			−0.763526			−0.381763	+	0.924260i	$0.624683\pi$
$440$	−6.65436	+	6.61208i	−0.317234	+	0.315218i
$441$	2.16621			0.103153
$442$	17.8653	−	8.84279i	0.849765	−	0.420609i
$443$	−18.5635	+	6.03163i	−0.881976	+	0.286572i	−0.714778	−	0.699352i	$-0.753472\pi$
$443$	−18.5635	+	6.03163i	−0.881976	+	0.286572i	−0.167199	+	0.985923i	$0.553472\pi$
$444$	32.4480	+	24.7473i	1.53991	+	1.17445i
$445$	−10.7543	−	7.81343i	−0.509801	−	0.370392i
$446$	−5.37388	+	5.25039i	−0.254460	+	0.248613i
$447$	3.87359	−	11.9217i	0.183215	−	0.563876i
$448$	−11.1240	+	13.2591i	−0.525562	+	0.626436i
$449$	−9.22004	+	6.69875i	−0.435121	+	0.316134i	−0.783693	−	0.621148i	$-0.786667\pi$
$449$	−9.22004	+	6.69875i	−0.435121	+	0.316134i	0.348572	+	0.937282i	$0.386667\pi$
$450$	−1.30198	−	0.221755i	−0.0613758	−	0.0104536i
$451$	−4.26036	+	1.53511i	−0.200613	+	0.0722853i
$452$	−27.0054	−	9.47402i	−1.27023	−	0.445621i
$453$	16.4758	+	22.6770i	0.774102	+	1.06546i
$454$	4.74174	+	32.3688i	0.222541	+	1.51914i
$455$	6.50506	+	2.11362i	0.304962	+	0.0990882i
$456$	20.0150	−	9.33407i	0.937289	−	0.437108i
$457$	2.44913	−	3.37094i	0.114566	−	0.157686i	−0.747883	−	0.663830i	$-0.768930\pi$
$457$	2.44913	−	3.37094i	0.114566	−	0.157686i	0.862449	+	0.506144i	$0.168930\pi$
$458$	2.80089	−	5.34263i	0.130877	−	0.249645i
$459$	5.64578	+	17.3759i	0.263523	+	0.811039i
$460$	4.97632	+	16.6205i	0.232022	+	0.774937i
$461$		−	23.9567i		−	1.11577i	−0.829917	−	0.557887i	$-0.811612\pi$
$461$		−	23.9567i		−	1.11577i	0.829917	−	0.557887i	$-0.188388\pi$
$462$	−9.49506	−	17.7459i	−0.441750	−	0.825614i
$463$			2.35157i			0.109287i	0.998506	+	0.0546433i	$0.0174022\pi$
$463$			2.35157i			0.109287i	−0.998506	+	0.0546433i	$0.982598\pi$
$464$	1.19787	−	25.7465i	0.0556095	−	1.19525i
$465$	0.702461	+	2.16195i	0.0325759	+	0.100258i
$466$	7.73948	+	4.05745i	0.358524	+	0.187958i
$467$	18.2786	−	25.1583i	0.845833	−	1.16419i	−0.138933	−	0.990302i	$-0.544367\pi$
$467$	18.2786	−	25.1583i	0.845833	−	1.16419i	0.984766	−	0.173887i	$-0.0556329\pi$
$468$	4.85673	−	3.35896i	0.224503	−	0.155268i
$469$	−13.7735	−	4.47528i	−0.636001	−	0.206649i
$470$	−5.31340	+	0.778367i	−0.245089	+	0.0359034i
$471$	−17.4701	−	24.0455i	−0.804978	−	1.10796i
$472$	−0.162443	+	0.293081i	−0.00747703	+	0.0134901i
$473$	−13.2928	+	0.421284i	−0.611203	+	0.0193707i
$474$	−2.03435	+	11.9442i	−0.0934408	+	0.548614i
$475$	−3.18485	+	2.31393i	−0.146131	+	0.106170i
$476$	19.2857	+	0.448394i	0.883957	+	0.0205521i
$477$	2.21547	−	6.81853i	0.101440	−	0.312199i
$478$	7.77428	+	7.95714i	0.355588	+	0.363951i
$479$	13.7911	+	10.0198i	0.630133	+	0.457819i	0.856446	−	0.516236i	$-0.172667\pi$
$479$	13.7911	+	10.0198i	0.630133	+	0.457819i	−0.226313	+	0.974055i	$0.572667\pi$
$480$	−4.50445	−	10.2759i	−0.205599	−	0.469029i
$481$	30.9323	−	10.0505i	1.41039	−	0.458264i
$482$	−4.97569	−	10.0525i	−0.226636	−	0.457879i
$483$	−37.2232			−1.69371
$484$	12.2070	−	18.3027i	0.554865	−	0.831941i
$485$	14.5007			0.658441
$486$	5.88700	+	11.8936i	0.267040	+	0.539506i
$487$	3.58219	−	1.16392i	0.162324	−	0.0527424i	−0.226728	−	0.973958i	$-0.572803\pi$
$487$	3.58219	−	1.16392i	0.162324	−	0.0527424i	0.389052	+	0.921216i	$0.372803\pi$
$488$	−23.2283	−	24.9074i	−1.05150	−	1.12751i
$489$	6.21829	+	4.51785i	0.281201	+	0.204304i
$490$	−2.29243	−	2.34635i	−0.103561	−	0.105997i
$491$	11.9119	−	36.6612i	0.537579	−	1.65450i	−0.200432	−	0.979708i	$-0.564234\pi$
$491$	11.9119	−	36.6612i	0.537579	−	1.65450i	0.738010	−	0.674789i	$-0.235766\pi$
$492$	0.125894	−	5.41478i	0.00567576	−	0.244117i
$493$	−23.2414	+	16.8859i	−1.04674	+	0.760502i
$494$	2.95534	−	17.3515i	0.132967	−	0.780682i
$495$	3.09582	−	0.0981149i	0.139147	−	0.00440994i
$496$	−2.86414	+	3.57967i	−0.128604	+	0.160732i
$497$	1.20450	+	1.65785i	0.0540292	+	0.0743648i
$498$	2.71275	−	0.397394i	0.121561	−	0.0178077i
$499$	−8.45653	−	2.74769i	−0.378566	−	0.123004i	0.113552	−	0.993532i	$-0.463777\pi$
$499$	−8.45653	−	2.74769i	−0.378566	−	0.123004i	−0.492118	+	0.870528i	$0.663777\pi$
$500$	1.13764	+	1.64492i	0.0508770	+	0.0735631i
$501$	25.7577	−	35.4525i	1.15077	−	1.58390i
$502$	4.30158	+	2.25512i	0.191989	+	0.100651i
$503$	−2.67219	−	8.22415i	−0.119147	−	0.366697i	0.873642	−	0.486569i	$-0.161752\pi$
$503$	−2.67219	−	8.22415i	−0.119147	−	0.366697i	−0.992789	+	0.119872i	$0.961752\pi$
$504$	5.67199	−	0.696650i	0.252651	−	0.0310313i
$505$		−	8.46192i		−	0.376550i
$506$	−19.1955	−	35.8757i	−0.853345	−	1.59487i
$507$			5.95925i			0.264660i
$508$	16.8311	−	5.03935i	0.746758	−	0.223585i
$509$	2.61645	+	8.05261i	0.115972	+	0.356926i	0.992149	−	0.125065i	$-0.0399139\pi$
$509$	2.61645	+	8.05261i	0.115972	+	0.356926i	−0.876176	+	0.481991i	$0.839914\pi$
$510$	−5.80654	+	11.0758i	−0.257118	+	0.490446i
$511$	1.94209	−	2.67305i	0.0859129	−	0.118249i
$512$	12.3216	−	18.9783i	0.544544	−	0.838732i
$513$	15.3427	+	4.98514i	0.677396	+	0.220099i
$514$	−3.29441	−	22.4888i	−0.145310	−	0.991937i
$515$	−4.40577	−	6.06402i	−0.194141	−	0.267213i
$516$	5.26574	−	15.0098i	0.231811	−	0.660769i
$517$	11.8483	−	4.26923i	0.521090	−	0.187761i
$518$	31.0280	+	5.28474i	1.36329	+	0.232198i
$519$	12.9952	−	9.44159i	0.570427	−	0.414440i
$520$	−8.77800	−	1.70593i	−0.384941	−	0.0748099i
$521$	1.75482	−	5.40078i	0.0768801	−	0.236613i	−0.905229	−	0.424923i	$-0.860301\pi$
$521$	1.75482	−	5.40078i	0.0768801	−	0.236613i	0.982110	+	0.188311i	$0.0603011\pi$
$522$	−6.08716	+	5.94728i	−0.266428	+	0.260305i
$523$	4.73587	+	3.44081i	0.207085	+	0.150456i	0.686494	−	0.727136i	$-0.259149\pi$
$523$	4.73587	+	3.44081i	0.207085	+	0.150456i	−0.479409	+	0.877592i	$0.659149\pi$
$524$	0.981208	−	1.28653i	0.0428643	−	0.0562025i
$525$	−4.08095	+	1.32598i	−0.178107	+	0.0578706i
$526$	3.46030	−	1.71275i	0.150876	−	0.0746792i
$527$	5.10983			0.222588
$528$	15.1493	+	21.5142i	0.659291	+	0.936287i
$529$	−52.2516			−2.27181
$530$	−9.73011	+	4.81612i	−0.422649	+	0.209199i
$531$	0.105225	−	0.0341896i	0.00456636	−	0.00148370i
$532$	10.3297	−	13.5440i	0.447849	−	0.587207i
$533$	−3.49233	−	2.53733i	−0.151270	−	0.109904i
$534$	−26.6701	+	26.0572i	−1.15413	+	1.12760i
$535$	−3.11661	+	9.59195i	−0.134743	+	0.414696i
$536$	18.5861	+	3.61205i	0.802797	+	0.156017i
$537$	−29.2135	+	21.2249i	−1.26066	+	0.915921i
$538$	−34.1299	−	5.81306i	−1.47145	−	0.250619i
$539$	6.36393	+	4.32245i	0.274114	+	0.186181i
$540$	2.71315	−	7.73374i	0.116755	−	0.332807i
$541$	−8.71813	−	11.9995i	−0.374822	−	0.515898i	0.579382	−	0.815056i	$-0.303294\pi$
$541$	−8.71813	−	11.9995i	−0.374822	−	0.515898i	−0.954203	+	0.299159i	$0.903294\pi$
$542$	−4.15468	−	28.3613i	−0.178459	−	1.21822i
$543$	−3.86685	−	1.25642i	−0.165943	−	0.0539180i
$544$	−25.0971	+	2.49186i	−1.07603	+	0.106838i
$545$	0.240831	−	0.331476i	0.0103161	−	0.0141989i
$546$	8.90810	−	16.9920i	0.381231	−	0.727188i
$547$	4.35574	+	13.4056i	0.186238	+	0.573182i	0.999968	−	0.00806215i	$-0.00256629\pi$
$547$	4.35574	+	13.4056i	0.186238	+	0.573182i	−0.813730	+	0.581244i	$0.802566\pi$
$548$	−40.5644	+	12.1453i	−1.73283	+	0.518822i
$549$			11.2453i			0.479936i
$550$	−3.38248	−	3.24943i	−0.144230	−	0.138556i
$551$			25.3664i			1.08064i
$552$	48.3017	−	5.93256i	2.05586	−	0.252506i
$553$	2.88779	+	8.88771i	0.122801	+	0.377944i
$554$	−36.4364	−	19.1019i	−1.54803	−	0.811563i
$555$	−11.9932	+	16.5072i	−0.509082	+	0.700692i
$556$	−18.4795	−	26.7196i	−0.783707	−	1.13316i
$557$	16.3059	+	5.29811i	0.690904	+	0.224488i	0.633363	−	0.773855i	$-0.281674\pi$
$557$	16.3059	+	5.29811i	0.690904	+	0.224488i	0.0575410	+	0.998343i	$0.481674\pi$
$558$	1.49772	−	0.219403i	0.0634036	−	0.00928807i
$559$	−7.45174	−	10.2564i	−0.315175	−	0.433801i
$560$	−6.75706	−	5.40642i	−0.285538	−	0.228463i
$561$	8.17482	−	28.1659i	0.345141	−	1.18916i
$562$	−6.24698	+	36.6776i	−0.263513	+	1.54715i
$563$	−28.3227	+	20.5777i	−1.19366	+	0.867245i	−0.993646	−	0.112548i	$-0.964099\pi$
$563$	−28.3227	+	20.5777i	−1.19366	+	0.867245i	−0.200014	+	0.979793i	$0.564099\pi$
$564$	−0.350121	+	15.0589i	−0.0147427	+	0.634093i
$565$	4.42188	−	13.6091i	0.186030	−	0.572541i
$566$	−23.1845	−	23.7298i	−0.974518	−	0.997439i
$567$	19.1295	+	13.8984i	0.803362	+	0.583677i
$568$	−1.82722	−	1.95930i	−0.0766682	−	0.0822104i
$569$	24.8973	−	8.08962i	1.04375	−	0.339135i	0.263537	−	0.964649i	$-0.415111\pi$
$569$	24.8973	−	8.08962i	1.04375	−	0.339135i	0.780212	+	0.625515i	$0.215111\pi$
$570$	4.89839	+	9.89632i	0.205171	+	0.414511i
$571$	0.540313			0.0226114			0.0113057	−	0.999936i	$-0.496401\pi$
$571$	0.540313			0.0226114			0.0113057	+	0.999936i	$0.496401\pi$
$572$	20.9706	−	0.176915i	0.876827	−	0.00739720i
$573$	45.7351			1.91061
$574$	−1.85315	−	3.74397i	−0.0773492	−	0.156270i
$575$	−8.25019	+	2.68065i	−0.344057	+	0.111791i
$576$	−7.24910	+	1.80798i	−0.302046	+	0.0753326i
$577$	17.1276	+	12.4439i	0.713031	+	0.518047i	0.884150	−	0.467203i	$-0.154738\pi$
$577$	17.1276	+	12.4439i	0.713031	+	0.518047i	−0.171119	+	0.985250i	$0.554738\pi$
$578$	2.84360	+	2.91048i	0.118278	+	0.121060i
$579$	−4.07900	+	12.5539i	−0.169517	+	0.521721i
$580$	12.8837	+	0.299547i	0.534966	+	0.0124380i
$581$	1.71079	−	1.24296i	0.0709753	−	0.0515666i
$582$	6.82926	−	40.0963i	0.283082	−	1.66204i
$583$	20.1143	−	15.6108i	0.833050	−	0.646535i
$584$	−2.09408	+	3.77815i	−0.0866535	+	0.156341i
$585$	1.73547	+	2.38867i	0.0717529	+	0.0987594i
$586$	47.0470	−	6.89198i	1.94349	−	0.284705i
$587$	6.33408	+	2.05807i	0.261435	+	0.0849455i	0.436802	−	0.899558i	$-0.356111\pi$
$587$	6.33408	+	2.05807i	0.261435	+	0.0849455i	−0.175367	+	0.984503i	$0.556111\pi$
$588$	−7.56762	+	5.23384i	−0.312083	+	0.215840i
$589$	2.65203	−	3.65021i	0.109275	−	0.150404i
$590$	−0.148389	−	0.0777933i	−0.00610906	−	0.00320270i
$591$	−3.51141	−	10.8070i	−0.144440	−	0.444541i
$592$	−41.1050	−	1.91243i	−1.68941	−	0.0786003i
$593$		−	17.3655i		−	0.713114i	−0.934274	−	0.356557i	$-0.883951\pi$
$593$		−	17.3655i		−	0.713114i	0.934274	−	0.356557i	$-0.116049\pi$
$594$	−2.62543	+	19.0408i	−0.107723	+	0.781254i
$595$			9.64544i			0.395424i
$596$	3.62552	+	12.1090i	0.148507	+	0.496003i
$597$	5.82181	+	17.9177i	0.238271	+	0.733323i
$598$	18.0089	−	34.3515i	0.736439	−	1.40474i
$599$	10.2918	−	14.1655i	0.420512	−	0.578785i	−0.545231	−	0.838286i	$-0.683558\pi$
$599$	10.2918	−	14.1655i	0.420512	−	0.578785i	0.965743	+	0.259501i	$0.0835581\pi$
$600$	5.08422	−	2.37104i	0.207562	−	0.0967975i
$601$	−16.4987	−	5.36075i	−0.672995	−	0.218669i	−0.0474692	−	0.998873i	$-0.515116\pi$
$601$	−16.4987	−	5.36075i	−0.672995	−	0.218669i	−0.625526	+	0.780203i	$0.715116\pi$
$602$	−1.77827	−	12.1391i	−0.0724769	−	0.494753i
$603$	−3.67460	−	5.05765i	−0.149641	−	0.205964i
$604$	−26.6712	−	9.35680i	−1.08524	−	0.380723i
$605$	9.29074	+	5.88915i	0.377722	+	0.239428i
$606$	−23.3984	−	3.98524i	−0.950493	−	0.161889i
$607$	−13.4664	+	9.78390i	−0.546583	+	0.397116i	−0.826524	−	0.562901i	$-0.809685\pi$
$607$	−13.4664	+	9.78390i	−0.546583	+	0.397116i	0.279941	+	0.960017i	$0.409685\pi$
$608$	−11.2455	+	19.2214i	−0.456063	+	0.779530i
$609$	−8.54408	+	26.2960i	−0.346223	+	1.06557i
$610$	12.1804	−	11.9005i	0.493170	−	0.481837i
$611$	9.71241	+	7.05648i	0.392922	+	0.285475i
$612$	6.62136	+	5.04995i	0.267653	+	0.204132i
$613$	20.1537	−	6.54833i	0.814000	−	0.264485i	0.127709	−	0.991812i	$-0.459238\pi$
$613$	20.1537	−	6.54833i	0.814000	−	0.264485i	0.686291	+	0.727327i	$0.259238\pi$
$614$	−12.3716	+	6.12360i	−0.499279	+	0.247128i
$615$	2.70812			0.109202
$616$	18.0534	+	9.27124i	0.727391	+	0.373549i
$617$	−25.8431			−1.04040			−0.520202	−	0.854043i	$-0.674143\pi$
$617$	−25.8431			−1.04040			−0.520202	+	0.854043i	$0.674143\pi$
$618$	−18.8428	+	9.32662i	−0.757968	+	0.375172i
$619$	34.2763	−	11.1371i	1.37768	−	0.447636i	0.475775	−	0.879567i	$-0.342168\pi$
$619$	34.2763	−	11.1371i	1.37768	−	0.447636i	0.901907	+	0.431931i	$0.142168\pi$
$620$	−1.82264	−	1.39008i	−0.0731989	−	0.0558270i
$621$	28.7594	+	20.8949i	1.15407	+	0.838483i
$622$	12.9065	−	12.6099i	0.517505	−	0.505613i
$623$	−8.88688	+	27.3510i	−0.356045	+	1.09579i
$624$	−8.85123	+	23.4690i	−0.354333	+	0.939510i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−18.1115	−	3.08477i	−0.723880	−	0.123292i
$627$	−15.8775	−	20.4579i	−0.634087	−	0.817011i
$628$	28.2807	+	9.92143i	1.12852	+	0.395908i
$629$	26.9588	+	37.1057i	1.07492	+	1.47950i
$630$	0.414150	+	2.82713i	0.0165001	+	0.112636i
$631$	27.4535	+	8.92019i	1.09291	+	0.355107i	0.799369	−	0.600840i	$-0.205167\pi$
$631$	27.4535	+	8.92019i	1.09291	+	0.355107i	0.293539	+	0.955947i	$0.405167\pi$
$632$	−5.16378	−	11.0727i	−0.205404	−	0.440447i
$633$	−28.6546	+	39.4397i	−1.13892	+	1.56759i
$634$	−10.2882	+	19.6245i	−0.408597	+	0.779388i
$635$	2.71460	+	8.35469i	0.107726	+	0.331546i
$636$	8.73471	+	29.1733i	0.346354	+	1.15680i
$637$			7.33337i			0.290559i
$638$	−29.7501	+	5.32572i	−1.17782	+	0.210847i
$639$			0.884589i			0.0349938i
$640$	9.62981	+	5.93859i	0.380652	+	0.234743i
$641$	6.10563	+	18.7912i	0.241158	+	0.742207i	0.996245	+	0.0865825i	$0.0275946\pi$
$641$	6.10563	+	18.7912i	0.241158	+	0.742207i	−0.755087	+	0.655625i	$0.772405\pi$
$642$	25.0552	+	13.1353i	0.988852	+	0.518409i
$643$	−14.1640	+	19.4951i	−0.558576	+	0.768813i	−0.991145	−	0.132788i	$-0.957607\pi$
$643$	−14.1640	+	19.4951i	−0.558576	+	0.768813i	0.432569	+	0.901601i	$0.357607\pi$
$644$	30.8707	−	21.3505i	1.21648	−	0.841328i
$645$	7.56407	+	2.45772i	0.297835	+	0.0967724i
$646$	24.5592	−	3.59770i	0.966268	−	0.141550i
$647$	10.4606	+	14.3978i	0.411250	+	0.566038i	0.963523	−	0.267626i	$-0.0862392\pi$
$647$	10.4606	+	14.3978i	0.411250	+	0.566038i	−0.552272	+	0.833664i	$0.686239\pi$
$648$	−27.0380	−	14.9861i	−1.06215	−	0.588709i
$649$	0.377353	+	0.109522i	0.0148124	+	0.00429912i
$650$	0.750716	−	4.40764i	0.0294455	−	0.172882i
$651$	3.97871	−	2.89070i	0.155938	−	0.113295i
$652$	−7.74844	−	0.180152i	−0.303453	−	0.00705531i
$653$	−2.84702	+	8.76222i	−0.111412	+	0.342892i	−0.991182	−	0.132508i	$-0.957697\pi$
$653$	−2.84702	+	8.76222i	−0.111412	+	0.342892i	0.879769	+	0.475401i	$0.157697\pi$
$654$	−0.803154	−	0.822045i	−0.0314058	−	0.0321445i
$655$	0.654497	+	0.475520i	0.0255733	+	0.0185801i
$656$	3.00141	+	4.56292i	0.117185	+	0.178152i
$657$	1.35647	−	0.440744i	0.0529209	−	0.0171951i
$658$	5.15375	+	10.4122i	0.200914	+	0.405911i
$659$	−23.7876			−0.926633			−0.463317	−	0.886193i	$-0.653341\pi$
$659$	−23.7876			−0.926633			−0.463317	+	0.886193i	$0.653341\pi$
$660$	−10.5782	+	7.82267i	−0.411754	+	0.304497i
$661$	−30.7116			−1.19454			−0.597272	−	0.802038i	$-0.703749\pi$
$661$	−30.7116			−1.19454			−0.597272	+	0.802038i	$0.703749\pi$
$662$	−13.0155	−	26.2956i	−0.505864	−	1.02201i
$663$	26.5887	−	8.63918i	1.03262	−	0.335518i
$664$	−2.02186	+	1.88556i	−0.0784634	+	0.0731738i
$665$	6.89022	+	5.00604i	0.267191	+	0.194126i
$666$	9.49501	+	9.71834i	0.367924	+	0.376578i
$667$	−17.2730	+	53.1608i	−0.668813	+	2.05839i
$668$	−1.02711	+	44.1764i	−0.0397400	+	1.70924i
$669$	−8.52447	+	6.19339i	−0.329575	+	0.239450i
$670$	−1.58953	+	9.33252i	−0.0614089	+	0.360547i
$671$	−22.4388	+	33.0365i	−0.866239	+	1.27536i
$672$	−18.1318	+	16.1380i	−0.699450	+	0.622536i
$673$	6.35951	+	8.75312i	0.245141	+	0.337408i	0.913802	−	0.406159i	$-0.133132\pi$
$673$	6.35951	+	8.75312i	0.245141	+	0.337408i	−0.668661	+	0.743567i	$0.733132\pi$
$674$	36.1469	−	5.29521i	1.39233	−	0.203964i
$675$	3.89736	+	1.26633i	0.150009	+	0.0487410i
$676$	−3.41812	−	4.94226i	−0.131466	−	0.190087i
$677$	4.03856	−	5.55860i	0.155214	−	0.213634i	−0.724327	−	0.689457i	$-0.757849\pi$
$677$	4.03856	−	5.55860i	0.155214	−	0.213634i	0.879542	+	0.475822i	$0.157849\pi$
$678$	−35.5486	−	18.6365i	−1.36524	−	0.715730i
$679$	−9.69424	−	29.8358i	−0.372031	−	1.14499i
$680$	−1.53727	−	12.5162i	−0.0589517	−	0.479973i
$681$			45.8810i			1.75816i
$682$	4.83783	+	2.34398i	0.185250	+	0.0897557i
$683$		−	10.6775i		−	0.408562i	−0.978912	−	0.204281i	$-0.934514\pi$
$683$		−	10.6775i		−	0.408562i	0.978912	−	0.204281i	$-0.0654857\pi$
$684$	7.04396	−	2.10902i	0.269332	−	0.0806402i
$685$	−6.54245	−	20.1356i	−0.249974	−	0.769341i
$686$	−13.2394	+	25.2537i	−0.505481	+	0.964192i
$687$	4.97277	−	6.84443i	0.189723	−	0.261131i
$688$	4.24224	+	15.4686i	0.161734	+	0.589734i
$689$	23.0831	+	7.50015i	0.879395	+	0.285733i
$690$	3.52684	+	24.0754i	0.134264	+	0.916535i
$691$	−27.8181	−	38.2883i	−1.05825	−	1.45656i	−0.881431	−	0.472313i	$-0.843419\pi$
$691$	−27.8181	−	38.2883i	−1.05825	−	1.45656i	−0.176819	−	0.984243i	$-0.556581\pi$
$692$	−5.36198	+	15.2841i	−0.203832	+	0.581015i
$693$	−2.27155	−	6.30422i	−0.0862892	−	0.239477i
$694$	21.1053	+	3.59468i	0.801146	+	0.136452i
$695$	13.1414	−	9.54780i	0.498483	−	0.362169i
$696$	6.89602	−	35.4841i	0.261393	−	1.34502i
$697$	1.88112	−	5.78951i	0.0712527	−	0.219293i
$698$	−17.7802	+	17.3716i	−0.672991	+	0.657526i
$699$	9.91503	+	7.20369i	0.375021	+	0.272469i
$700$	2.62395	−	3.44045i	0.0991760	−	0.130037i
$701$	0.689187	−	0.223930i	0.0260302	−	0.00845774i	−0.295973	−	0.955196i	$-0.595644\pi$
$701$	0.689187	−	0.223930i	0.0260302	−	0.00845774i	0.322003	+	0.946739i	$0.395644\pi$
$702$	−16.4209	+	8.12784i	−0.619765	+	0.306766i
$703$	40.4982			1.52742
$704$	−24.9042	−	9.15329i	−0.938611	−	0.344978i
$705$	−7.53147			−0.283652
$706$	−35.1770	+	17.4116i	−1.32390	+	0.655293i
$707$	−17.4108	+	5.65712i	−0.654801	+	0.212758i
$708$	−0.284994	+	0.373677i	−0.0107107	+	0.0140436i
$709$	−12.6604	−	9.19829i	−0.475470	−	0.345449i	0.324099	−	0.946023i	$-0.394939\pi$
$709$	−12.6604	−	9.19829i	−0.475470	−	0.345449i	−0.799569	+	0.600574i	$0.794939\pi$
$710$	0.958150	−	0.936132i	0.0359587	−	0.0351324i
$711$	−1.24658	+	3.83658i	−0.0467504	+	0.143883i
$712$	7.17270	−	36.9078i	0.268808	−	1.38318i
$713$	8.04348	−	5.84393i	0.301231	−	0.218857i
$714$	26.6710	+	4.54264i	0.998136	+	0.170004i
$715$	0.332153	+	10.4804i	0.0124218	+	0.391946i
$716$	12.0538	−	34.3590i	0.450473	−	1.28406i
$717$	9.17059	+	12.6222i	0.342482	+	0.471386i
$718$	−2.81101	−	19.1889i	−0.104906	−	0.716124i
$719$	10.4581	+	3.39806i	0.390023	+	0.126726i	0.497463	−	0.867485i	$-0.334265\pi$
$719$	10.4581	+	3.39806i	0.390023	+	0.126726i	−0.107440	+	0.994212i	$0.534265\pi$
$720$	−0.987996	−	3.60256i	−0.0368204	−	0.134259i
$721$	−9.53159	+	13.1191i	−0.354975	+	0.488581i
$722$	−2.29986	+	4.38692i	−0.0855919	+	0.163264i
$723$	−4.86112	−	14.9610i	−0.180787	−	0.556406i
$724$	3.92760	−	1.17595i	0.145968	−	0.0437040i
$725$			6.44358i			0.239309i
$726$	20.6599	−	22.9166i	0.766761	−	0.850515i
$727$		−	7.80710i		−	0.289549i	−0.989465	−	0.144775i	$-0.953754\pi$
$727$		−	7.80710i		−	0.289549i	0.989465	−	0.144775i	$-0.0462457\pi$
$728$	2.35840	+	19.2017i	0.0874082	+	0.711661i
$729$	−4.38078	−	13.4827i	−0.162251	−	0.499357i
$730$	−1.91290	−	1.00285i	−0.0707997	−	0.0371170i
$731$	10.5083	−	14.4635i	0.388665	−	0.534952i
$732$	−27.1700	−	39.2852i	−1.00423	−	1.45202i
$733$	0.776549	+	0.252316i	0.0286825	+	0.00931951i	0.323323	−	0.946289i	$-0.395200\pi$
$733$	0.776549	+	0.252316i	0.0286825	+	0.00931951i	−0.294641	+	0.955608i	$0.595200\pi$
$734$	39.7120	−	5.81746i	1.46580	−	0.214727i
$735$	−2.70416	−	3.72196i	−0.0997445	−	0.137287i
$736$	−36.6559	+	32.6251i	−1.35115	+	1.20258i
$737$	−0.703284	−	22.1908i	−0.0259058	−	0.817407i
$738$	0.302782	−	1.77771i	0.0111456	−	0.0654383i
$739$	−6.06980	+	4.40997i	−0.223281	+	0.162223i	−0.693802	−	0.720165i	$-0.744066\pi$
$739$	−6.06980	+	4.40997i	−0.223281	+	0.162223i	0.470521	+	0.882389i	$0.344066\pi$
$740$	0.478236	−	20.5692i	0.0175803	−	0.756138i
$741$	7.62827	−	23.4774i	0.280232	−	0.862464i
$742$	16.4143	+	16.8004i	0.602590	+	0.616763i
$743$	8.89011	+	6.45904i	0.326147	+	0.236959i	0.738794	−	0.673932i	$-0.235396\pi$
$743$	8.89011	+	6.45904i	0.326147	+	0.236959i	−0.412647	+	0.910891i	$0.635396\pi$
$744$	−4.70216	+	4.38517i	−0.172390	+	0.160768i
$745$	−6.01072	+	1.95300i	−0.220216	+	0.0715524i
$746$	23.1260	+	46.7219i	0.846702	+	1.71061i
$747$	0.912834			0.0333988
$748$	9.37570	+	28.0481i	0.342809	+	1.02554i
$749$	21.8195			0.797267
$750$	1.24429	+	2.51387i	0.0454351	+	0.0917935i
$751$	11.1966	−	3.63801i	0.408571	−	0.132753i	−0.0975185	−	0.995234i	$-0.531091\pi$
$751$	11.1966	−	3.63801i	0.408571	−	0.132753i	0.506090	+	0.862481i	$0.331091\pi$
$752$	−8.34712	−	12.6898i	−0.304388	−	0.462749i
$753$	5.51075	+	4.00379i	0.200823	+	0.145906i
$754$	−20.1336	−	20.6071i	−0.733222	−	0.750468i
$755$	4.36717	−	13.4408i	0.158937	−	0.489159i
$756$	−17.7264	−	0.412141i	−0.644703	−	0.0149894i
$757$	0.669234	−	0.486227i	0.0243237	−	0.0176722i	−0.575557	−	0.817762i	$-0.695215\pi$
$757$	0.669234	−	0.486227i	0.0243237	−	0.0176722i	0.599881	+	0.800089i	$0.295215\pi$
$758$	−3.21421	+	18.8714i	−0.116745	+	0.685442i
$759$	−19.3442	−	53.6857i	−0.702149	−	1.94867i
$760$	−9.73878	−	5.39782i	−0.353263	−	0.195799i
$761$	−8.42620	−	11.5977i	−0.305449	−	0.420415i	0.628506	−	0.777805i	$-0.283667\pi$
$761$	−8.42620	−	11.5977i	−0.305449	−	0.420415i	−0.933955	+	0.357390i	$0.883667\pi$
$762$	24.3803	−	3.57151i	0.883207	−	0.129382i
$763$	−0.843034	−	0.273918i	−0.0305199	−	0.00991651i
$764$	−37.9301	+	26.2328i	−1.37226	+	0.949069i
$765$	−2.44734	+	3.36848i	−0.0884838	+	0.121788i
$766$	−32.0339	−	16.7939i	−1.15743	−	0.606788i
$767$	0.115744	+	0.356222i	0.00417926	+	0.0128624i
$768$	20.9563	−	23.8309i	0.756195	−	0.859923i
$769$		−	2.50888i		−	0.0904725i	−0.998976	−	0.0452362i	$-0.985596\pi$
$769$		−	2.50888i		−	0.0904725i	0.998976	−	0.0452362i	$-0.0144041\pi$
$770$	−4.42455	+	9.13200i	−0.159450	+	0.329094i
$771$		−	31.8766i		−	1.14801i
$772$	−3.81777	−	12.7511i	−0.137405	−	0.458922i
$773$	−4.73441	−	14.5710i	−0.170285	−	0.524083i	0.829102	−	0.559097i	$-0.188852\pi$
$773$	−4.73441	−	14.5710i	−0.170285	−	0.524083i	−0.999387	+	0.0350147i	$0.988852\pi$
$774$	2.45903	−	4.69054i	0.0883881	−	0.168598i
$775$	0.673670	−	0.927228i	0.0241990	−	0.0333070i
$776$	17.3347	+	37.1707i	0.622279	+	1.33435i
$777$	41.9823	+	13.6409i	1.50611	+	0.489364i
$778$	−5.11100	−	34.8895i	−0.183238	−	1.25085i
$779$	−3.15942	−	4.34857i	−0.113198	−	0.155804i
$780$	−11.8342	−	4.15167i	−0.423731	−	0.148654i
$781$	−1.76511	+	2.59876i	−0.0631605	+	0.0929910i
$782$	53.9189	+	9.18355i	1.92814	+	0.328403i
$783$	21.3623	−	15.5206i	0.763428	−	0.554663i
$784$	3.27412	−	8.68129i	0.116933	−	0.310046i
$785$	−4.63070	+	14.2518i	−0.165277	+	0.508670i
$786$	1.62312	−	1.58582i	0.0578948	−	0.0565644i
$787$	10.8975	+	7.91747i	0.388453	+	0.282227i	0.764821	−	0.644243i	$-0.222827\pi$
$787$	10.8975	+	7.91747i	0.388453	+	0.282227i	−0.376368	+	0.926470i	$0.622827\pi$
$788$	9.11086	+	6.94864i	0.324561	+	0.247535i
$789$	5.14992	−	1.67331i	0.183342	−	0.0595714i
$790$	5.47483	−	2.70988i	0.194786	−	0.0964132i
$791$	−30.9577			−1.10073
$792$	3.95238	+	7.81848i	0.140442	+	0.277818i
$793$	−38.0691			−1.35187
$794$	−7.56784	+	3.74586i	−0.268572	+	0.132935i
$795$	−14.4812	+	4.70522i	−0.513595	+	0.166877i
$796$	−15.1055	−	11.5206i	−0.535401	−	0.408338i
$797$	2.14733	+	1.56012i	0.0760622	+	0.0552624i	0.625167	−	0.780491i	$-0.285031\pi$
$797$	2.14733	+	1.56012i	0.0760622	+	0.0552624i	−0.549104	+	0.835754i	$0.685031\pi$
$798$	17.0874	−	16.6948i	0.604888	−	0.590988i
$799$	−5.23153	+	16.1010i	−0.185078	+	0.569612i
$800$	−2.85657	+	4.88262i	−0.100995	+	0.172627i
$801$	−10.0433	+	7.29692i	−0.354864	+	0.257824i
$802$	35.7264	+	6.08497i	1.26154	+	0.214868i
$803$	4.86452	+	1.41187i	0.171665	+	0.0498238i
$804$	25.0571	+	8.79053i	0.883696	+	0.310018i
$805$	11.0311	+	15.1831i	0.388797	+	0.535133i
$806$	0.742755	+	5.07031i	0.0261624	+	0.178594i
$807$	−46.1794	−	15.0046i	−1.62559	−	0.528186i
$808$	21.6911	−	10.1157i	0.763091	−	0.355870i
$809$	8.10115	−	11.1503i	0.284821	−	0.392023i	−0.642502	−	0.766284i	$-0.722104\pi$
$809$	8.10115	−	11.1503i	0.284821	−	0.392023i	0.927323	+	0.374261i	$0.122104\pi$
$810$	7.17678	−	13.6895i	0.252166	−	0.481001i
$811$	12.3429	+	37.9876i	0.433418	+	1.33392i	0.894699	+	0.446670i	$0.147390\pi$
$811$	12.3429	+	37.9876i	0.433418	+	1.33392i	−0.461280	+	0.887255i	$0.652610\pi$
$812$	−7.99690	−	26.7091i	−0.280636	−	0.937305i
$813$		−	40.2006i		−	1.40990i
$814$	8.50268	+	47.4970i	0.298019	+	1.66477i
$815$		−	3.87527i		−	0.135745i
$816$	−35.3329	−	1.64388i	−1.23690	−	0.0575473i
$817$	−4.87811	−	15.0133i	−0.170663	−	0.525248i
$818$	14.9805	+	7.85356i	0.523779	+	0.274593i
$819$	3.75458	−	5.16774i	0.131196	−	0.180575i
$820$	−2.24596	+	1.55333i	−0.0784324	+	0.0542446i
$821$	2.79822	+	0.909197i	0.0976586	+	0.0317312i	0.357439	−	0.933937i	$-0.383650\pi$
$821$	2.79822	+	0.909197i	0.0976586	+	0.0317312i	−0.259780	+	0.965668i	$0.583650\pi$
$822$	−58.7589	+	8.60767i	−2.04945	+	0.300227i
$823$	−17.5777	−	24.1937i	−0.612721	−	0.843338i	0.384077	−	0.923301i	$-0.374520\pi$
$823$	−17.5777	−	24.1937i	−0.612721	−	0.843338i	−0.996798	+	0.0799631i	$0.974520\pi$
$824$	10.2775	−	18.5428i	0.358035	−	0.645970i
$825$	−4.03321	−	5.19673i	−0.140418	−	0.180927i
$826$	−0.0608601	+	0.357325i	−0.00211759	+	0.0124329i
$827$	−14.4618	+	10.5071i	−0.502886	+	0.365368i	−0.810118	−	0.586267i	$-0.800597\pi$
$827$	−14.4618	+	10.5071i	−0.502886	+	0.365368i	0.307232	+	0.951635i	$0.400597\pi$
$828$	16.1983	+	0.376612i	0.562928	+	0.0130882i
$829$	16.1777	−	49.7899i	0.561876	−	1.72928i	−0.115180	−	0.993345i	$-0.536745\pi$
$829$	16.1777	−	49.7899i	0.561876	−	1.72928i	0.677056	−	0.735931i	$-0.263255\pi$
$830$	−0.966022	−	0.988743i	−0.0335311	−	0.0343198i
$831$	−46.6786	−	33.9140i	−1.61926	−	1.17646i
$832$	−6.12065	−	24.5407i	−0.212195	−	0.850796i
$833$	−9.83529	+	3.19568i	−0.340772	+	0.110724i
$834$	−20.2119	−	40.8345i	−0.699880	−	1.41398i
$835$	−22.0942			−0.764600
$836$	24.9022	+	7.85958i	0.861260	+	0.271829i
$837$	−4.69670			−0.162342
$838$	8.24451	+	16.6566i	0.284802	+	0.575391i
$839$	5.94199	−	1.93067i	0.205140	−	0.0666541i	−0.204644	−	0.978836i	$-0.565604\pi$
$839$	5.94199	−	1.93067i	0.205140	−	0.0666541i	0.409785	+	0.912182i	$0.365604\pi$
$840$	−8.27754	−	8.87590i	−0.285602	−	0.306248i
$841$	10.1287	+	7.35892i	0.349265	+	0.253756i
$842$	8.83004	+	9.03772i	0.304303	+	0.311461i
$843$	−16.1246	+	49.6264i	−0.555361	+	1.70922i
$844$	1.14262	−	49.1447i	0.0393307	−	1.69163i
$845$	2.43074	−	1.76603i	0.0836199	−	0.0607534i
$846$	−0.842056	+	4.94392i	−0.0289505	+	0.169976i
$847$	5.90600	−	23.0533i	0.202933	−	0.792121i
$848$	−23.9773	−	19.1846i	−0.823384	−	0.658801i
$849$	−27.3486	−	37.6421i	−0.938602	−	1.29187i
$850$	6.23853	−	0.913890i	0.213980	−	0.0313462i
$851$	84.8728	+	27.5768i	2.90940	+	0.945322i
$852$	−2.13728	−	3.09030i	−0.0732220	−	0.105872i
$853$	−25.2147	+	34.7051i	−0.863335	+	1.18828i	0.117429	+	0.993081i	$0.462535\pi$
$853$	−25.2147	+	34.7051i	−0.863335	+	1.18828i	−0.980764	+	0.195198i	$0.937465\pi$
$854$	−32.6289	−	17.1058i	−1.11654	−	0.585350i
$855$	1.13609	+	3.49652i	0.0388534	+	0.119578i
$856$	−28.3135	+	3.47755i	−0.967737	+	0.118860i
$857$		−	1.34505i		−	0.0459459i	−0.999736	−	0.0229729i	$-0.992687\pi$
$857$		−	1.34505i		−	0.0459459i	0.999736	−	0.0229729i	$-0.00731316\pi$
$858$	29.1363	+	4.01744i	0.994696	+	0.137153i
$859$			8.64868i			0.295089i	0.989055	+	0.147545i	$0.0471370\pi$
$859$			8.64868i			0.295089i	−0.989055	+	0.147545i	$0.952863\pi$
$860$	−7.68290	+	2.30032i	−0.261985	+	0.0784403i
$861$	−1.81049	−	5.57210i	−0.0617012	−	0.189897i
$862$	−15.5800	+	29.7184i	−0.530656	+	1.01221i
$863$	23.9258	−	32.9311i	0.814445	−	1.12099i	−0.176178	−	0.984358i	$-0.556373\pi$
$863$	23.9258	−	32.9311i	0.814445	−	1.12099i	0.990622	−	0.136629i	$-0.0436267\pi$
$864$	23.0679	−	2.29039i	0.784787	−	0.0779208i
$865$	−7.70232	−	2.50263i	−0.261887	−	0.0850921i
$866$	0.831512	+	5.67619i	0.0282559	+	0.192885i
$867$	3.35433	+	4.61683i	0.113919	+	0.156796i
$868$	−1.64166	+	4.67949i	−0.0557215	+	0.158832i
$869$	−11.3177	+	8.78374i	−0.383927	+	0.297968i
$870$	17.8174	+	3.03468i	0.604066	+	0.102885i
$871$	17.1219	−	12.4398i	0.580154	−	0.421506i
$872$	1.13760	+	0.221082i	0.0385240	+	0.00748680i
$873$	4.18473	−	12.8793i	0.141632	−	0.435898i
$874$	34.5445	−	33.7507i	1.16848	−	1.14163i
$875$	1.75026	+	1.27164i	0.0591695	+	0.0429891i
$876$	−3.67391	+	4.81713i	−0.124130	+	0.162756i
$877$	−26.7095	+	8.67845i	−0.901916	+	0.293050i	−0.723028	−	0.690819i	$-0.757250\pi$
$877$	−26.7095	+	8.67845i	−0.901916	+	0.293050i	−0.178889	+	0.983869i	$0.557250\pi$
$878$	20.2762	−	10.0361i	0.684289	−	0.338703i
$879$	66.6867			2.24929
$880$	4.28598	−	12.5551i	0.144480	−	0.423232i
$881$	−42.5103			−1.43221			−0.716105	−	0.697993i	$-0.754077\pi$
$881$	−42.5103			−1.43221			−0.716105	+	0.697993i	$0.754077\pi$
$882$	−2.74556	+	1.35897i	−0.0924480	+	0.0457590i
$883$	−48.5687	+	15.7809i	−1.63447	+	0.531070i	−0.975292	−	0.220920i	$-0.929094\pi$
$883$	−48.5687	+	15.7809i	−1.63447	+	0.531070i	−0.659174	+	0.751990i	$0.729094\pi$
$884$	−17.0958	+	22.4156i	−0.574995	+	0.753918i
$885$	−0.190100	−	0.138116i	−0.00639015	−	0.00464272i
$886$	19.7443	−	19.2906i	0.663323	−	0.648080i
$887$	−4.42344	+	13.6139i	−0.148525	+	0.457111i	−0.997447	−	0.0714053i	$-0.977252\pi$
$887$	−4.42344	+	13.6139i	−0.148525	+	0.457111i	0.848923	+	0.528517i	$0.177252\pi$
$888$	−56.6514	−	11.0097i	−1.90110	−	0.369461i
$889$	15.3754	−	11.1709i	0.515674	−	0.374659i
$890$	18.5323	+	3.15644i	0.621203	+	0.105804i
$891$	−10.1039	+	34.8125i	−0.338494	+	1.16626i
$892$	3.51729	−	10.0259i	0.117768	−	0.335692i
$893$	8.78655	+	12.0937i	0.294031	+	0.404699i
$894$	2.56949	+	17.5403i	0.0859367	+	0.586634i
$895$	17.3150	+	5.62597i	0.578775	+	0.188055i
$896$	5.78104	−	23.7840i	0.193131	−	0.794567i
$897$	31.9734	−	44.0076i	1.06756	−	1.46937i
$898$	7.48348	−	14.2745i	0.249727	−	0.476347i
$899$	−2.28212	−	7.02364i	−0.0761130	−	0.234252i
$900$	1.78931	−	0.535733i	0.0596436	−	0.0178578i
$901$			34.2267i			1.14026i
$902$	4.43675	−	4.61841i	0.147728	−	0.153776i
$903$		−	17.2065i		−	0.572597i
$904$	40.1715	−	4.93398i	1.33608	−	0.164102i
$905$	0.633465	+	1.94960i	0.0210571	+	0.0648070i
$906$	−35.1088	−	18.4059i	−1.16641	−	0.611495i
$907$	9.79869	−	13.4867i	0.325360	−	0.447820i	−0.614734	−	0.788734i	$-0.710737\pi$
$907$	9.79869	−	13.4867i	0.325360	−	0.447820i	0.940094	+	0.340915i	$0.110737\pi$
$908$	−26.3165	−	38.0511i	−0.873343	−	1.26277i
$909$	−7.51576	−	2.44202i	−0.249282	−	0.0809966i
$910$	−9.57083	+	1.40204i	−0.317270	+	0.0464773i
$911$	14.6953	+	20.2263i	0.486876	+	0.670128i	0.979808	−	0.199940i	$-0.0640747\pi$
$911$	14.6953	+	20.2263i	0.486876	+	0.670128i	−0.492932	+	0.870068i	$0.664075\pi$
$912$	−19.5123	+	24.3869i	−0.646117	+	0.807531i
$913$	2.68174	+	1.82146i	0.0887526	+	0.0602817i
$914$	−0.989393	+	5.80897i	−0.0327262	+	0.192144i
$915$	19.3215	−	14.0379i	0.638749	−	0.464078i
$916$	−0.198293	+	8.52866i	−0.00655177	+	0.281795i
$917$	0.540849	−	1.66456i	0.0178604	−	0.0549687i
$918$	−18.0566	−	18.4813i	−0.595955	−	0.609972i
$919$	37.0121	+	26.8909i	1.22092	+	0.887048i	0.996176	−	0.0873709i	$-0.0278465\pi$
$919$	37.0121	+	26.8909i	1.22092	+	0.887048i	0.224741	+	0.974419i	$0.427847\pi$
$920$	−16.7341	−	17.9438i	−0.551709	−	0.591590i
$921$	−18.4125	+	5.98260i	−0.606714	+	0.197133i
$922$	15.0292	+	30.3639i	0.494962	+	0.999983i
$923$	−2.99464			−0.0985698
$924$	23.1674	+	16.5353i	0.762152	+	0.543972i
$925$	10.2874			0.338247
$926$	−1.47526	−	2.98049i	−0.0484799	−	0.0979451i
$927$	−6.65744	+	2.16313i	−0.218659	+	0.0710466i
$928$	14.6338	+	33.3839i	0.480379	+	1.09588i
$929$	34.1164	+	24.7870i	1.11932	+	0.813236i	0.984106	−	0.177580i	$-0.0568269\pi$
$929$	34.1164	+	24.7870i	1.11932	+	0.813236i	0.135217	+	0.990816i	$0.456827\pi$
$930$	−2.24664	−	2.29948i	−0.0736702	−	0.0754029i
$931$	−2.82174	+	8.68441i	−0.0924787	+	0.284620i
$932$	−12.3549	−	0.287252i	−0.404697	−	0.00940925i
$933$	20.4734	−	14.8748i	0.670268	−	0.486978i
$934$	−7.38413	+	43.3541i	−0.241616	+	1.41859i
$935$	−13.9113	+	5.01255i	−0.454948	+	0.163928i
$936$	−4.04842	+	7.30419i	−0.132327	+	0.238745i
$937$	−6.67224	−	9.18355i	−0.217973	−	0.300014i	0.686002	−	0.727600i	$-0.259364\pi$
$937$	−6.67224	−	9.18355i	−0.217973	−	0.300014i	−0.903975	+	0.427586i	$0.859364\pi$
$938$	20.2648	−	2.96861i	0.661669	−	0.0969287i
$939$	−24.5056	−	7.96236i	−0.799711	−	0.259842i
$940$	6.24617	−	4.31991i	0.203728	−	0.140900i
$941$	−33.8939	+	46.6510i	−1.10491	+	1.52078i	−0.276199	+	0.961100i	$0.589075\pi$
$941$	−33.8939	+	46.6510i	−1.10491	+	1.52078i	−0.828710	+	0.559678i	$0.810925\pi$
$942$	37.2274	+	19.5166i	1.21293	+	0.635885i
$943$	−3.66014	−	11.2647i	−0.119190	−	0.366830i
$944$	0.0220239	−	0.473374i	0.000716817	−	0.0154070i
$945$		−	8.86560i		−	0.288398i
$946$	16.5837	−	8.87320i	0.539181	−	0.288493i
$947$		−	40.2825i		−	1.30900i	−0.756060	−	0.654502i	$-0.772878\pi$
$947$		−	40.2825i		−	1.30900i	0.756060	−	0.654502i	$-0.227122\pi$
$948$	−4.91475	−	16.4149i	−0.159624	−	0.533131i
$949$	1.49207	+	4.59212i	0.0484347	+	0.149067i
$950$	2.58500	−	4.93081i	0.0838683	−	0.159977i
$951$	−18.2659	+	25.1409i	−0.592313	+	0.815249i
$952$	−24.7249	+	11.5306i	−0.801340	+	0.373708i
$953$	−19.1705	−	6.22886i	−0.620992	−	0.201773i	−0.0184114	−	0.999830i	$-0.505861\pi$
$953$	−19.1705	−	6.22886i	−0.620992	−	0.201773i	−0.602581	+	0.798058i	$0.705861\pi$
$954$	1.46960	+	10.0320i	0.0475802	+	0.324799i
$955$	−13.5537	−	18.6550i	−0.438587	−	0.603663i
$956$	−14.8454	−	5.20808i	−0.480136	−	0.168441i
$957$	−42.3660	+	1.34269i	−1.36950	+	0.0434030i
$958$	−23.7655	−	4.04778i	−0.767830	−	0.130778i
$959$	−37.0561	+	26.9228i	−1.19660	+	0.869384i
$960$	12.1558	+	10.1983i	0.392326	+	0.329150i
$961$	9.17361	−	28.2335i	0.295923	−	0.910757i
$962$	−32.8999	+	32.1439i	−1.06074	+	1.03636i
$963$	7.62002	+	5.53627i	0.245552	+	0.178404i
$964$	12.6129	+	9.61954i	0.406234	+	0.309825i
$965$	6.32945	−	2.05656i	0.203752	−	0.0662031i
$966$	47.1785	−	23.3520i	1.51794	−	0.751337i
$967$	36.5643			1.17583			0.587915	−	0.808923i	$-0.299949\pi$
$967$	36.5643			1.17583			0.587915	+	0.808923i	$0.299949\pi$
$968$	−3.98959	+	30.8558i	−0.128230	+	0.991744i
$969$	34.8113			1.11830
$970$	−18.3789	+	9.09699i	−0.590110	+	0.292087i
$971$	−53.3853	+	17.3459i	−1.71322	+	0.556658i	−0.990864	−	0.134867i	$-0.956939\pi$
$971$	−53.3853	+	17.3459i	−1.71322	+	0.556658i	−0.722353	+	0.691524i	$0.756939\pi$
$972$	−14.9230	−	11.3814i	−0.478654	−	0.365058i
$973$	−28.4306	−	20.6561i	−0.911444	−	0.662203i
$974$	−3.81006	+	3.72250i	−0.122082	+	0.119277i
$975$	1.93774	−	5.96374i	0.0620572	−	0.190993i
$976$	45.0664	+	16.9966i	1.44254	+	0.544049i
$977$	37.3247	−	27.1180i	1.19412	−	0.867581i	0.200428	−	0.979708i	$-0.435767\pi$
$977$	37.3247	−	27.1180i	1.19412	−	0.867581i	0.993694	+	0.112128i	$0.0357666\pi$
$978$	−10.7157	−	1.82511i	−0.342649	−	0.0583604i
$979$	−44.0658	+	1.39656i	−1.40835	+	0.0446343i
$980$	4.37752	+	1.53572i	0.139835	+	0.0490569i
$981$	−0.224911	−	0.309564i	−0.00718086	−	0.00988361i
$982$	7.90163	+	53.9392i	0.252151	+	1.72127i
$983$	17.4194	+	5.65990i	0.555592	+	0.180523i	0.573337	−	0.819320i	$-0.305649\pi$
$983$	17.4194	+	5.65990i	0.555592	+	0.180523i	−0.0177449	+	0.999843i	$0.505649\pi$
$984$	3.23740	+	6.94195i	0.103205	+	0.221301i
$985$	−3.36749	+	4.63496i	−0.107297	+	0.147682i
$986$	18.8640	−	35.9826i	0.600752	−	1.14592i
$987$	5.03508	+	15.4964i	0.160268	+	0.493255i
$988$	7.13975	+	23.8462i	0.227146	+	0.758650i
$989$		−	34.7853i		−	1.10611i
$990$	−3.86225	+	2.06652i	−0.122750	+	0.0656784i
$991$			15.4087i			0.489473i	0.969590	+	0.244737i	$0.0787015\pi$
$991$			15.4087i			0.489473i	−0.969590	+	0.244737i	$0.921298\pi$
$992$	1.38445	−	6.33387i	0.0439564	−	0.201101i
$993$	−12.7159	−	39.1354i	−0.403526	−	1.24192i
$994$	−2.56670	−	1.34560i	−0.0814107	−	0.0426799i
$995$	5.58320	−	7.68462i	0.176999	−	0.243619i
$996$	−3.18897	+	2.20552i	−0.101046	+	0.0698846i
$997$	−33.2801	−	10.8134i	−1.05399	−	0.342463i	−0.269759	−	0.962928i	$-0.586944\pi$
$997$	−33.2801	−	10.8134i	−1.05399	−	0.342463i	−0.784234	+	0.620465i	$0.786944\pi$
$998$	12.4420	−	1.82264i	0.393845	−	0.0576948i
$999$	−24.7792	−	34.1056i	−0.783979	−	1.07905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.c.151.1	yes	32
4.3	odd	2	inner	220.2.r.c.151.8	yes	32
11.7	odd	10	inner	220.2.r.c.51.8	yes	32
44.7	even	10	inner	220.2.r.c.51.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.c.51.1	✓	32	44.7	even	10	inner
220.2.r.c.51.8	yes	32	11.7	odd	10	inner
220.2.r.c.151.1	yes	32	1.1	even	1	trivial
220.2.r.c.151.8	yes	32	4.3	odd	2	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26745 + 0.627351i) q^{2} +(-1.88633 + 0.612906i) q^{3} +(1.21286 - 1.59027i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.00632 - 1.96022i) q^{6} +(0.668539 - 2.05755i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(0.755537 - 0.548930i) q^{9} +(-1.39414 - 0.237451i) q^{10} +(3.31496 - 0.105060i) q^{11} +(-1.31317 + 3.74315i) q^{12} +(1.85832 + 2.55775i) q^{13} +(0.443466 + 3.02725i) q^{14} +(-1.88633 - 0.612906i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(-2.62058 + 3.60691i) q^{17} +(-0.613234 + 1.16973i) q^{18} +(1.21650 + 3.74402i) q^{19} +(1.91596 - 0.573655i) q^{20} +4.29097i q^{21} +(-4.13564 + 2.21280i) q^{22} +8.67477i q^{23} +(-0.683887 - 5.56807i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-3.95993 - 2.07601i) q^{26} +(2.40870 - 3.31529i) q^{27} +(-2.46122 - 3.55868i) q^{28} +(6.12821 + 1.99118i) q^{29} +(2.77534 - 0.406563i) q^{30} +(-0.673670 - 0.927228i) q^{31} +(3.76092 + 4.22558i) q^{32} +(-6.18872 + 2.22994i) q^{33} +(1.05865 - 6.21560i) q^{34} +(1.75026 - 1.27164i) q^{35} +(0.0434146 - 1.86728i) q^{36} +(3.17897 - 9.78387i) q^{37} +(-3.89067 - 3.98218i) q^{38} +(-5.07306 - 3.68579i) q^{39} +(-2.06851 + 1.92906i) q^{40} +(-1.29856 + 0.421929i) q^{41} +(-2.69194 - 5.43859i) q^{42} -4.00994 q^{43} +(3.85352 - 5.39911i) q^{44} +0.933895 q^{45} +(-5.44212 - 10.9948i) q^{46} +(3.61139 - 1.17341i) q^{47} +(4.35993 + 6.62822i) q^{48} +(1.87655 + 1.36339i) q^{49} +(-0.988310 - 1.01156i) q^{50} +(2.73257 - 8.40999i) q^{51} +(6.32141 + 0.146974i) q^{52} +(6.21075 - 4.51237i) q^{53} +(-0.973058 + 5.71306i) q^{54} +(2.74361 + 1.86349i) q^{55} +(5.35202 + 2.96641i) q^{56} +(-4.58946 - 6.31685i) q^{57} +(-9.01637 + 1.32082i) q^{58} +(0.112673 + 0.0366097i) q^{59} +(-3.26255 + 2.25641i) q^{60} +(-7.07767 + 9.74158i) q^{61} +(1.43554 + 0.752588i) q^{62} +(-0.624345 - 1.92153i) q^{63} +(-7.41770 - 2.99629i) q^{64} +3.16156i q^{65} +(6.44494 - 6.70883i) q^{66} -6.69412i q^{67} +(2.55758 + 8.54212i) q^{68} +(-5.31681 - 16.3635i) q^{69} +(-1.42060 + 2.70976i) q^{70} +(-0.556753 + 0.766305i) q^{71} +(1.11642 + 2.39393i) q^{72} +(1.45249 + 0.471942i) q^{73} +(2.10873 + 14.3949i) q^{74} +(-1.16582 - 1.60461i) q^{75} +(7.42946 + 2.60640i) q^{76} +(2.00001 - 6.89093i) q^{77} +(8.74214 + 1.48897i) q^{78} +(-3.49460 + 2.53897i) q^{79} +(1.41153 - 3.74267i) q^{80} +(-3.37741 + 10.3946i) q^{81} +(1.38117 - 1.34943i) q^{82} +(0.790772 + 0.574530i) q^{83} +(6.82381 + 5.20435i) q^{84} +(-4.24018 + 1.37772i) q^{85} +(5.08240 - 2.51564i) q^{86} -12.7802 q^{87} +(-1.49701 + 9.26061i) q^{88} -13.2930 q^{89} +(-1.18367 + 0.585879i) q^{90} +(6.50506 - 2.11362i) q^{91} +(13.7952 + 10.5213i) q^{92} +(1.83907 + 1.33616i) q^{93} +(-3.84112 + 3.75285i) q^{94} +(-1.21650 + 3.74402i) q^{95} +(-9.68421 - 5.66574i) q^{96} +(11.7313 - 8.52327i) q^{97} +(-3.23376 - 0.550779i) q^{98} +(2.44690 - 1.89906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) \) 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Introduction

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