LMFDB - Embedded newform 357.2.bh.a.151.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(25,357)] 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("357.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			151.15
Character	$\chi$	$=$	357.151
Dual form			357.2.bh.a.331.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.200803 - 0.749407i) q^{2} +(0.991445 + 0.130526i) q^{3} +(1.21076 + 0.699034i) q^{4} +(-3.40086 - 2.60957i) q^{5} +(0.296902 - 0.716785i) q^{6} +(-0.149664 - 2.64151i) q^{7} +(1.86419 - 1.86419i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-2.63853 + 2.02461i) q^{10} +(0.722180 + 0.941163i) q^{11} +(1.10916 + 0.851090i) q^{12} -1.32321i q^{13} +(-2.00962 - 0.418265i) q^{14} +(-3.03114 - 3.03114i) q^{15} +(0.375365 + 0.650151i) q^{16} +(-2.45497 - 3.31257i) q^{17} +(0.387921 - 0.671900i) q^{18} +(-0.330997 + 1.23530i) q^{19} +(-2.29345 - 5.53688i) q^{20} +(0.196403 - 2.63845i) q^{21} +(0.850330 - 0.352218i) q^{22} +(-0.774302 + 0.101939i) q^{23} +(2.09157 - 1.60492i) q^{24} +(3.46188 + 12.9199i) q^{25} +(-0.991626 - 0.265705i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.66530 - 3.30287i) q^{28} +(4.66396 - 1.93188i) q^{29} +(-2.88022 + 1.66290i) q^{30} +(7.43193 + 0.978433i) q^{31} +(5.65567 - 1.51543i) q^{32} +(0.593155 + 1.02737i) q^{33} +(-2.97543 + 1.17459i) q^{34} +(-6.38423 + 9.37397i) q^{35} +(0.988583 + 0.988583i) q^{36} +(5.02840 - 6.55314i) q^{37} +(0.859274 + 0.496102i) q^{38} +(0.172714 - 1.31189i) q^{39} +(-11.2046 + 1.47511i) q^{40} +(3.55444 + 1.47230i) q^{41} +(-1.93783 - 0.676995i) q^{42} +(-7.00164 + 7.00164i) q^{43} +(0.216483 + 1.64435i) q^{44} +(-2.60957 - 3.40086i) q^{45} +(-0.0790885 + 0.600737i) q^{46} +(-4.97122 + 2.87014i) q^{47} +(0.287292 + 0.693583i) q^{48} +(-6.95520 + 0.790680i) q^{49} +10.3774 q^{50} +(-2.00159 - 3.60467i) q^{51} +(0.924972 - 1.60210i) q^{52} +(-5.30700 + 1.42201i) q^{53} +(0.472303 - 0.615518i) q^{54} -5.08534i q^{55} +(-5.20330 - 4.64529i) q^{56} +(-0.489403 + 1.18152i) q^{57} +(-0.511224 - 3.88313i) q^{58} +(3.77450 + 14.0866i) q^{59} +(-1.55112 - 5.78887i) q^{60} +(0.974697 + 7.40356i) q^{61} +(2.22560 - 5.37307i) q^{62} +(0.539110 - 2.59024i) q^{63} -3.04124i q^{64} +(-3.45302 + 4.50006i) q^{65} +(0.889029 - 0.238214i) q^{66} +(0.874010 - 1.51383i) q^{67} +(-0.656780 - 5.72684i) q^{68} -0.780984 q^{69} +(5.74294 + 6.66670i) q^{70} +(2.55867 + 6.17717i) q^{71} +(2.28316 - 1.31818i) q^{72} +(1.10767 - 8.41361i) q^{73} +(-3.90125 - 5.08421i) q^{74} +(1.74587 + 13.2612i) q^{75} +(-1.26427 + 1.26427i) q^{76} +(2.37801 - 2.04851i) q^{77} +(-0.948461 - 0.392865i) q^{78} +(3.35584 - 0.441805i) q^{79} +(0.420051 - 3.19061i) q^{80} +(0.866025 + 0.500000i) q^{81} +(1.81709 - 2.36808i) q^{82} +(1.79946 + 1.79946i) q^{83} +(2.08216 - 3.05724i) q^{84} +(-0.295398 + 17.6720i) q^{85} +(3.84113 + 6.65303i) q^{86} +(4.87622 - 1.30658i) q^{87} +(3.10079 + 0.408227i) q^{88} +(8.86973 - 5.12094i) q^{89} +(-3.07263 + 1.27273i) q^{90} +(-3.49529 + 0.198038i) q^{91} +(-1.00875 - 0.417840i) q^{92} +(7.24064 + 1.94012i) q^{93} +(1.15266 + 4.30180i) q^{94} +(4.34926 - 3.33731i) q^{95} +(5.80509 - 0.764255i) q^{96} +(-9.30496 + 3.85424i) q^{97} +(-0.804084 + 5.37105i) q^{98} +(0.453981 + 1.09601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	0.200803	−	0.749407i	0.141989	−	0.529911i	−0.857882	−	0.513847i	$-0.828220\pi$
$2$	0.200803	−	0.749407i	0.141989	−	0.529911i	0.999871	−	0.0160636i	$-0.00511342\pi$
$3$	0.991445	+	0.130526i	0.572411	+	0.0753593i
$3$	0.991445	+	0.130526i	0.572411	+	0.0753593i
$4$	1.21076	+	0.699034i	0.605381	+	0.349517i
$5$	−3.40086	−	2.60957i	−1.52091	−	1.16703i	−0.933943	−	0.357423i	$-0.883655\pi$
$5$	−3.40086	−	2.60957i	−1.52091	−	1.16703i	−0.586966	−	0.809611i	$-0.699678\pi$
$6$	0.296902	−	0.716785i	0.121210	−	0.292626i
$7$	−0.149664	−	2.64151i	−0.0565677	−	0.998399i
$7$	−0.149664	−	2.64151i	−0.0565677	−	0.998399i
$8$	1.86419	−	1.86419i	0.659092	−	0.659092i
$9$	0.965926	+	0.258819i	0.321975	+	0.0862730i
$10$	−2.63853	+	2.02461i	−0.834376	+	0.640239i
$11$	0.722180	+	0.941163i	0.217745	+	0.283771i	0.889435	−	0.457061i	$-0.151098\pi$
$11$	0.722180	+	0.941163i	0.217745	+	0.283771i	−0.671690	+	0.740832i	$0.734431\pi$
$12$	1.10916	+	0.851090i	0.320187	+	0.245688i
$13$		−	1.32321i		−	0.366994i	−0.983020	−	0.183497i	$-0.941258\pi$
$13$		−	1.32321i		−	0.366994i	0.983020	−	0.183497i	$-0.0587417\pi$
$14$	−2.00962	−	0.418265i	−0.537094	−	0.111786i
$15$	−3.03114	−	3.03114i	−0.782638	−	0.782638i
$16$	0.375365	+	0.650151i	0.0938411	+	0.162538i
$17$	−2.45497	−	3.31257i	−0.595417	−	0.803417i
$17$	−2.45497	−	3.31257i	−0.595417	−	0.803417i
$18$	0.387921	−	0.671900i	0.0914340	−	0.158368i
$19$	−0.330997	+	1.23530i	−0.0759358	+	0.283396i	−0.993444	−	0.114321i	$-0.963531\pi$
$19$	−0.330997	+	1.23530i	−0.0759358	+	0.283396i	0.917508	+	0.397717i	$0.130197\pi$
$20$	−2.29345	−	5.53688i	−0.512831	−	1.23808i
$21$	0.196403	−	2.63845i	0.0428587	−	0.575757i
$22$	0.850330	−	0.352218i	0.181291	−	0.0750931i
$23$	−0.774302	+	0.101939i	−0.161453	+	0.0212557i	−0.210819	−	0.977525i	$-0.567613\pi$
$23$	−0.774302	+	0.101939i	−0.161453	+	0.0212557i	0.0493662	+	0.998781i	$0.484280\pi$
$24$	2.09157	−	1.60492i	0.426940	−	0.327603i
$25$	3.46188	+	12.9199i	0.692375	+	2.58398i
$26$	−0.991626	−	0.265705i	−0.194474	−	0.0521091i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	1.66530	−	3.30287i	0.314712	−	0.624183i
$29$	4.66396	−	1.93188i	0.866076	−	0.358741i	0.0949954	−	0.995478i	$-0.469716\pi$
$29$	4.66396	−	1.93188i	0.866076	−	0.358741i	0.771081	+	0.636737i	$0.219716\pi$
$30$	−2.88022	+	1.66290i	−0.525854	+	0.303602i
$31$	7.43193	+	0.978433i	1.33481	+	0.175732i	0.763930	−	0.645299i	$-0.223267\pi$
$31$	7.43193	+	0.978433i	1.33481	+	0.175732i	0.570885	+	0.821030i	$0.306600\pi$
$32$	5.65567	−	1.51543i	0.999791	−	0.267893i
$33$	0.593155	+	1.02737i	0.103255	+	0.178843i
$34$	−2.97543	+	1.17459i	−0.510282	+	0.201441i
$35$	−6.38423	+	9.37397i	−1.07913	+	1.58449i
$36$	0.988583	+	0.988583i	0.164764	+	0.164764i
$37$	5.02840	−	6.55314i	0.826664	−	1.07733i	−0.169120	−	0.985596i	$-0.554092\pi$
$37$	5.02840	−	6.55314i	0.826664	−	1.07733i	0.995784	−	0.0917337i	$-0.0292409\pi$
$38$	0.859274	+	0.496102i	0.139393	+	0.0804784i
$39$	0.172714	−	1.31189i	0.0276564	−	0.210071i
$40$	−11.2046	+	1.47511i	−1.77160	+	0.233236i
$41$	3.55444	+	1.47230i	0.555110	+	0.229934i	0.642561	−	0.766235i	$-0.277872\pi$
$41$	3.55444	+	1.47230i	0.555110	+	0.229934i	−0.0874505	+	0.996169i	$0.527872\pi$
$42$	−1.93783	−	0.676995i	−0.299014	−	0.104463i
$43$	−7.00164	+	7.00164i	−1.06774	+	1.06774i	−0.0702083	+	0.997532i	$0.522366\pi$
$43$	−7.00164	+	7.00164i	−1.06774	+	1.06774i	−0.997532	+	0.0702083i	$0.977634\pi$
$44$	0.216483	+	1.64435i	0.0326361	+	0.247895i
$45$	−2.60957	−	3.40086i	−0.389011	−	0.506970i
$46$	−0.0790885	+	0.600737i	−0.0116610	+	0.0885738i
$47$	−4.97122	+	2.87014i	−0.725128	+	0.418653i	−0.816637	−	0.577152i	$-0.804164\pi$
$47$	−4.97122	+	2.87014i	−0.725128	+	0.418653i	0.0915094	+	0.995804i	$0.470831\pi$
$48$	0.287292	+	0.693583i	0.0414670	+	0.100110i
$49$	−6.95520	+	0.790680i	−0.993600	+	0.112954i
$50$	10.3774			1.46759
$51$	−2.00159	−	3.60467i	−0.280278	−	0.504755i
$52$	0.924972	−	1.60210i	0.128271	−	0.222171i
$53$	−5.30700	+	1.42201i	−0.728972	+	0.195327i	−0.604171	−	0.796854i	$-0.706496\pi$
$53$	−5.30700	+	1.42201i	−0.728972	+	0.195327i	−0.124801	+	0.992182i	$0.539829\pi$
$54$	0.472303	−	0.615518i	0.0642723	−	0.0837613i
$55$		−	5.08534i		−	0.685707i
$56$	−5.20330	−	4.64529i	−0.695320	−	0.620753i
$57$	−0.489403	+	1.18152i	−0.0648231	+	0.156497i
$58$	−0.511224	−	3.88313i	−0.0671270	−	0.509880i
$59$	3.77450	+	14.0866i	0.491398	+	1.83392i	0.549334	+	0.835603i	$0.314882\pi$
$59$	3.77450	+	14.0866i	0.491398	+	1.83392i	−0.0579356	+	0.998320i	$0.518452\pi$
$60$	−1.55112	−	5.78887i	−0.200249	−	0.747339i
$61$	0.974697	+	7.40356i	0.124797	+	0.947929i	0.933215	+	0.359319i	$0.116991\pi$
$61$	0.974697	+	7.40356i	0.124797	+	0.947929i	−0.808418	+	0.588609i	$0.799676\pi$
$62$	2.22560	−	5.37307i	0.282651	−	0.682381i
$63$	0.539110	−	2.59024i	0.0679215	−	0.326340i
$64$		−	3.04124i		−	0.380155i
$65$	−3.45302	+	4.50006i	−0.428294	+	0.558164i
$66$	0.889029	−	0.238214i	0.109432	−	0.0293222i
$67$	0.874010	−	1.51383i	0.106777	−	0.184944i	−0.807686	−	0.589613i	$-0.799280\pi$
$67$	0.874010	−	1.51383i	0.106777	−	0.184944i	0.914463	+	0.404670i	$0.132613\pi$
$68$	−0.656780	−	5.72684i	−0.0796463	−	0.694482i
$69$	−0.780984			−0.0940194
$70$	5.74294	+	6.66670i	0.686413	+	0.796823i
$71$	2.55867	+	6.17717i	0.303658	+	0.733095i	0.999883	+	0.0152721i	$0.00486146\pi$
$71$	2.55867	+	6.17717i	0.303658	+	0.733095i	−0.696225	+	0.717823i	$0.745139\pi$
$72$	2.28316	−	1.31818i	0.269073	−	0.155349i
$73$	1.10767	−	8.41361i	0.129643	−	0.984738i	−0.795722	−	0.605662i	$-0.792908\pi$
$73$	1.10767	−	8.41361i	0.129643	−	0.984738i	0.925365	−	0.379076i	$-0.123758\pi$
$74$	−3.90125	−	5.08421i	−0.453511	−	0.591027i
$75$	1.74587	+	13.2612i	0.201596	+	1.53128i
$76$	−1.26427	+	1.26427i	−0.145022	+	0.145022i
$77$	2.37801	−	2.04851i	0.271000	−	0.233449i
$78$	−0.948461	−	0.392865i	−0.107392	−	0.0444833i
$79$	3.35584	−	0.441805i	0.377562	−	0.0497069i	0.0606427	−	0.998160i	$-0.480685\pi$
$79$	3.35584	−	0.441805i	0.377562	−	0.0497069i	0.316919	+	0.948453i	$0.397352\pi$
$80$	0.420051	−	3.19061i	0.0469632	−	0.356721i
$81$	0.866025	+	0.500000i	0.0962250	+	0.0555556i
$82$	1.81709	−	2.36808i	0.200664	−	0.261511i
$83$	1.79946	+	1.79946i	0.197516	+	0.197516i	0.798934	−	0.601418i	$-0.205397\pi$
$83$	1.79946	+	1.79946i	0.197516	+	0.197516i	−0.601418	+	0.798934i	$0.705397\pi$
$84$	2.08216	−	3.05724i	0.227183	−	0.333573i
$85$	−0.295398	+	17.6720i	−0.0320404	+	1.91680i
$86$	3.84113	+	6.65303i	0.414200	+	0.717415i
$87$	4.87622	−	1.30658i	0.522786	−	0.140080i
$88$	3.10079	+	0.408227i	0.330545	+	0.0435171i
$89$	8.86973	−	5.12094i	0.940190	−	0.542819i	0.0501701	−	0.998741i	$-0.484024\pi$
$89$	8.86973	−	5.12094i	0.940190	−	0.542819i	0.890020	+	0.455922i	$0.150690\pi$
$90$	−3.07263	+	1.27273i	−0.323884	+	0.134157i
$91$	−3.49529	+	0.198038i	−0.366406	+	0.0207600i
$92$	−1.00875	−	0.417840i	−0.105170	−	0.0435628i
$93$	7.24064	+	1.94012i	0.750820	+	0.201182i
$94$	1.15266	+	4.30180i	0.118888	+	0.443697i
$95$	4.34926	−	3.33731i	0.446225	−	0.342400i
$96$	5.80509	−	0.764255i	0.592479	−	0.0780014i
$97$	−9.30496	+	3.85424i	−0.944776	+	0.391339i	−0.801265	−	0.598310i	$-0.795839\pi$
$97$	−9.30496	+	3.85424i	−0.944776	+	0.391339i	−0.143511	+	0.989649i	$0.545839\pi$
$98$	−0.804084	+	5.37105i	−0.0812247	+	0.542558i
$99$	0.453981	+	1.09601i	0.0456268	+	0.110153i
$100$	−4.83994	+	18.0629i	−0.483994	+	1.80629i
$101$	3.59173	−	6.22106i	0.357391	−	0.619019i	−0.630133	−	0.776487i	$-0.717000\pi$
$101$	3.59173	−	6.22106i	0.357391	−	0.619019i	0.987524	+	0.157468i	$0.0503331\pi$
$102$	−3.10329	+	0.776174i	−0.307271	+	0.0768527i
$103$	3.37528	+	5.84615i	0.332576	+	0.576039i	0.983016	−	0.183519i	$-0.0587489\pi$
$103$	3.37528	+	5.84615i	0.332576	+	0.576039i	−0.650440	+	0.759558i	$0.725416\pi$
$104$	−2.46673	−	2.46673i	−0.241883	−	0.241883i
$105$	−7.55316	+	8.46046i	−0.737113	+	0.825657i
$106$			4.26264i			0.414024i
$107$	−9.54771	−	7.32622i	−0.923012	−	0.708252i	0.0336558	−	0.999433i	$-0.489285\pi$
$107$	−9.54771	−	7.32622i	−0.923012	−	0.708252i	−0.956668	+	0.291181i	$0.905952\pi$
$108$	0.851090	+	1.10916i	0.0818961	+	0.106729i
$109$	−7.08427	+	5.43595i	−0.678550	+	0.520670i	−0.889562	−	0.456814i	$-0.848991\pi$
$109$	−7.08427	+	5.43595i	−0.678550	+	0.520670i	0.211012	+	0.977483i	$0.432324\pi$
$110$	−3.81098	−	1.02115i	−0.363363	−	0.0973629i
$111$	5.84074	−	5.84074i	0.554378	−	0.554378i
$112$	1.66120	−	1.08884i	0.156969	−	0.102885i
$113$	−7.39748	+	17.8591i	−0.695896	+	1.68004i	0.0366528	+	0.999328i	$0.488330\pi$
$113$	−7.39748	+	17.8591i	−0.695896	+	1.68004i	−0.732549	+	0.680714i	$0.761670\pi$
$114$	0.787168	+	0.604016i	0.0737251	+	0.0565712i
$115$	2.89931	+	1.67392i	0.270362	+	0.156093i
$116$	6.99740	+	0.921225i	0.649692	+	0.0855336i
$117$	0.342473	−	1.27813i	0.0316617	−	0.118163i
$118$	11.3145			1.04159
$119$	−8.38279	+	6.98060i	−0.768449	+	0.639911i
$120$	−11.3013			−1.03166
$121$	2.48277	−	9.26581i	0.225706	−	0.842346i
$122$	5.74400	+	0.756212i	0.520037	+	0.0684642i
$123$	3.33186	+	1.92365i	0.300424	+	0.173450i
$124$	8.31435	+	6.37982i	0.746651	+	0.572925i
$125$	13.7398	−	33.1708i	1.22893	−	2.96689i
$126$	−1.83289	−	0.924141i	−0.163287	−	0.0823290i
$127$	7.45558	−	7.45558i	0.661575	−	0.661575i	−0.294176	−	0.955751i	$-0.595045\pi$
$127$	7.45558	−	7.45558i	0.661575	−	0.661575i	0.955751	+	0.294176i	$0.0950452\pi$
$128$	9.03221	+	2.42017i	0.798343	+	0.213915i
$129$	−7.85564	+	6.02785i	−0.691651	+	0.530722i
$130$	2.67900	+	3.49134i	0.234964	+	0.306211i
$131$	−1.99523	−	1.53099i	−0.174324	−	0.133764i	0.517914	−	0.855433i	$-0.326709\pi$
$131$	−1.99523	−	1.53099i	−0.174324	−	0.133764i	−0.692238	+	0.721669i	$0.743375\pi$
$132$			1.65854i			0.144358i
$133$	3.31259	+	0.689453i	0.287238	+	0.0597831i
$134$	−0.958970	−	0.958970i	−0.0828424	−	0.0828424i
$135$	−2.14334	−	3.71238i	−0.184470	−	0.319511i
$136$	−10.7518	−	1.59874i	−0.921960	−	0.137091i
$137$	7.99908	−	13.8548i	0.683408	−	1.18370i	−0.290527	−	0.956867i	$-0.593831\pi$
$137$	7.99908	−	13.8548i	0.683408	−	1.18370i	0.973934	−	0.226830i	$-0.0728361\pi$
$138$	−0.156824	+	0.585274i	−0.0133497	+	0.0498219i
$139$	−7.87499	−	19.0119i	−0.667948	−	1.61257i	−0.785038	−	0.619448i	$-0.787356\pi$
$139$	−7.87499	−	19.0119i	−0.667948	−	1.61257i	0.117089	−	0.993121i	$-0.462644\pi$
$140$	−14.2825	+	6.88686i	−1.20709	+	0.582046i
$141$	−5.30332	+	2.19671i	−0.446620	+	0.184996i
$142$	5.14300	−	0.677089i	0.431591	−	0.0568201i
$143$	1.24536	−	0.955599i	0.104142	−	0.0799112i
$144$	0.194303	+	0.725149i	0.0161919	+	0.0604291i
$145$	−20.9028	−	5.60090i	−1.73589	−	0.465129i
$146$	−6.08279	−	2.51957i	−0.503415	−	0.208521i
$147$	−6.99890	−	0.123920i	−0.577260	−	0.0102208i
$148$	10.6691	−	4.41927i	0.876991	−	0.363262i
$149$	−0.128364	+	0.0741108i	−0.0105160	+	0.00607139i	−0.505249	−	0.862974i	$-0.668599\pi$
$149$	−0.128364	+	0.0741108i	−0.0105160	+	0.00607139i	0.494733	+	0.869045i	$0.335266\pi$
$150$	10.2886	+	1.35452i	0.840063	+	0.110596i
$151$	1.70482	−	0.456805i	0.138736	−	0.0371742i	−0.188783	−	0.982019i	$-0.560454\pi$
$151$	1.70482	−	0.456805i	0.138736	−	0.0371742i	0.327519	+	0.944845i	$0.393788\pi$
$152$	1.68579	+	2.91987i	0.136736	+	0.236833i
$153$	−1.51396	−	3.83509i	−0.122396	−	0.310049i
$154$	−1.05765	−	2.19344i	−0.0852281	−	0.176753i
$155$	−22.7216	−	22.7216i	−1.82505	−	1.82505i
$156$	1.12617	−	1.46766i	0.0901661	−	0.117507i
$157$	3.07327	+	1.77435i	0.245273	+	0.141609i	0.617598	−	0.786494i	$-0.288106\pi$
$157$	3.07327	+	1.77435i	0.245273	+	0.141609i	−0.372325	+	0.928103i	$0.621439\pi$
$158$	0.342771	−	2.60361i	0.0272694	−	0.207132i
$159$	−5.44720	+	0.717138i	−0.431991	+	0.0568727i
$160$	−23.1887	−	9.60509i	−1.83323	−	0.759349i
$161$	0.385158	+	2.03007i	0.0303547	+	0.159992i
$162$	0.548604	−	0.548604i	0.0431024	−	0.0431024i
$163$	−2.47166	−	18.7741i	−0.193595	−	1.47050i	−0.761906	−	0.647688i	$-0.775736\pi$
$163$	−2.47166	−	18.7741i	−0.193595	−	1.47050i	0.568310	−	0.822814i	$-0.307597\pi$
$164$	3.27440	+	4.26728i	0.255687	+	0.333218i
$165$	0.663770	−	5.04183i	0.0516744	−	0.392506i
$166$	1.70986	−	0.987190i	0.132711	−	0.0766208i
$167$	3.00830	+	7.26269i	0.232790	+	0.562004i	0.996503	−	0.0835511i	$-0.0266262\pi$
$167$	3.00830	+	7.26269i	0.232790	+	0.562004i	−0.763714	+	0.645555i	$0.776626\pi$
$168$	−4.55245	−	5.28472i	−0.351229	−	0.407725i
$169$	11.2491			0.865316
$170$	13.1842	+	3.76996i	1.01118	+	0.289143i
$171$	−0.639436	+	1.10754i	−0.0488989	+	0.0846954i
$172$	−13.3717	+	3.58294i	−1.01958	+	0.273197i
$173$	−4.43794	+	5.78364i	−0.337411	+	0.439722i	−0.930985	−	0.365057i	$-0.881050\pi$
$173$	−4.43794	+	5.78364i	−0.337411	+	0.439722i	0.593575	+	0.804779i	$0.297716\pi$
$174$		−	3.91664i		−	0.296920i
$175$	33.6100	−	11.0782i	2.54068	−	0.837437i
$176$	−0.340817	+	0.822805i	−0.0256900	+	0.0620212i
$177$	1.90354	+	14.4588i	0.143079	+	1.08679i
$178$	−2.05660	−	7.67534i	−0.154149	−	0.575291i
$179$	5.82458	+	21.7376i	0.435349	+	1.62475i	0.740229	+	0.672355i	$0.234717\pi$
$179$	5.82458	+	21.7376i	0.435349	+	1.62475i	−0.304880	+	0.952391i	$0.598616\pi$
$180$	−0.782253	−	5.94180i	−0.0583057	−	0.442876i
$181$	−1.78187	+	4.30181i	−0.132445	+	0.319751i	−0.976164	−	0.217035i	$-0.930362\pi$
$181$	−1.78187	+	4.30181i	−0.132445	+	0.319751i	0.843719	+	0.536785i	$0.180362\pi$
$182$	−0.553454	+	2.65916i	−0.0410247	+	0.197110i
$183$			7.46744i			0.552009i
$184$	−1.25342	+	1.63348i	−0.0924030	+	0.120422i
$185$	−34.2017	+	9.16432i	−2.51456	+	0.673774i
$186$	2.90788	−	5.03660i	0.213216	−	0.369302i
$187$	1.34474	−	4.70280i	0.0983374	−	0.343903i
$188$	−8.02529			−0.585305
$189$	0.872592	−	2.49772i	0.0634718	−	0.181682i
$190$	−1.62765	−	3.92951i	−0.118082	−	0.285076i
$191$	5.51588	−	3.18460i	0.399115	−	0.230429i	−0.286987	−	0.957935i	$-0.592654\pi$
$191$	5.51588	−	3.18460i	0.399115	−	0.230429i	0.686102	+	0.727505i	$0.259320\pi$
$192$	0.396962	−	3.01522i	0.0286483	−	0.217605i
$193$	0.412229	+	0.537227i	0.0296729	+	0.0386705i	0.807954	−	0.589245i	$-0.200575\pi$
$193$	0.412229	+	0.537227i	0.0296729	+	0.0386705i	−0.778281	+	0.627916i	$0.783908\pi$
$194$	1.01993	+	7.74714i	0.0732268	+	0.556213i
$195$	−4.01085	+	4.01085i	−0.287223	+	0.287223i
$196$	−8.97381	−	3.90460i	−0.640986	−	0.278900i
$197$	−8.52845	−	3.53260i	−0.607627	−	0.251687i	0.0575865	−	0.998341i	$-0.481660\pi$
$197$	−8.52845	−	3.53260i	−0.607627	−	0.251687i	−0.665214	+	0.746653i	$0.731660\pi$
$198$	0.912516	−	0.120135i	0.0648497	−	0.00853762i
$199$	0.956189	−	7.26297i	0.0677824	−	0.514859i	−0.923550	−	0.383479i	$-0.874726\pi$
$199$	0.956189	−	7.26297i	0.0677824	−	0.514859i	0.991332	−	0.131380i	$-0.0419407\pi$
$200$	30.5388	+	17.6316i	2.15942	+	1.24674i
$201$	1.06413	−	1.38680i	0.0750577	−	0.0978172i
$202$	−3.94088	−	3.94088i	−0.277279	−	0.277279i
$203$	−5.80111	−	12.0308i	−0.407158	−	0.844396i
$204$	0.0963418	−	5.76358i	0.00674527	−	0.403531i
$205$	−8.24608	−	14.2826i	−0.575931	−	0.997542i
$206$	5.05891	−	1.35553i	0.352471	−	0.0944443i
$207$	−0.774302	−	0.101939i	−0.0538177	−	0.00708524i
$208$	0.860289	−	0.496688i	0.0596503	−	0.0344391i
$209$	−1.40165	+	0.580584i	−0.0969544	+	0.0401598i
$210$	4.82363	+	7.35927i	0.332862	+	0.507838i
$211$	−0.0104845	−	0.00434281i	−0.000721781	−	0.000298972i	0.382323	−	0.924029i	$-0.375124\pi$
$211$	−0.0104845	−	0.00434281i	−0.000721781	−	0.000298972i	−0.383044	+	0.923730i	$0.625124\pi$
$212$	−7.41954	−	1.98806i	−0.509576	−	0.136541i
$213$	1.73050	+	6.45830i	0.118572	+	0.442515i
$214$	−7.40752	+	5.68399i	−0.506368	+	0.388550i
$215$	42.0828	−	5.54031i	2.87003	−	0.377846i
$216$	2.43569	−	1.00889i	0.165727	−	0.0686465i
$217$	1.47225	−	19.7780i	0.0999429	−	1.34262i
$218$	2.65120	+	6.40055i	0.179562	+	0.433500i
$219$	2.19639	−	8.19705i	0.148418	−	0.553905i
$220$	3.55482	−	6.15713i	0.239666	−	0.415114i
$221$	−4.38325	+	3.24845i	−0.294849	+	0.218514i
$222$	−3.20425	−	5.54992i	−0.215055	−	0.372487i
$223$	12.8999	+	12.8999i	0.863843	+	0.863843i	0.991782	−	0.127939i	$-0.0408363\pi$
$223$	12.8999	+	12.8999i	0.863843	+	0.863843i	−0.127939	+	0.991782i	$0.540836\pi$
$224$	−4.84949	−	14.7127i	−0.324020	−	0.983036i
$225$			13.3757i			0.891711i
$226$	11.8983	+	9.12988i	0.791462	+	0.607310i
$227$	6.85052	+	8.92777i	0.454685	+	0.592557i	0.963297	−	0.268439i	$-0.0865078\pi$
$227$	6.85052	+	8.92777i	0.454685	+	0.592557i	−0.508612	+	0.860996i	$0.669841\pi$
$228$	−1.41848	+	1.08844i	−0.0939409	+	0.0720834i
$229$	−26.7775	−	7.17501i	−1.76951	−	0.474138i	−0.780899	−	0.624657i	$-0.785239\pi$
$229$	−26.7775	−	7.17501i	−1.76951	−	0.474138i	−0.988607	+	0.150519i	$0.951905\pi$
$230$	1.83663	−	1.83663i	0.121104	−	0.121104i
$231$	2.62505	−	1.72059i	0.172716	−	0.113206i
$232$	5.09314	−	12.2959i	0.334381	−	0.807267i
$233$	−2.54356	−	1.95174i	−0.166634	−	0.127863i	0.522078	−	0.852898i	$-0.325157\pi$
$233$	−2.54356	−	1.95174i	−0.166634	−	0.127863i	−0.688712	+	0.725035i	$0.741824\pi$
$234$	−0.889068	−	0.513303i	−0.0581202	−	0.0335557i
$235$	24.3962	+	3.21183i	1.59144	+	0.209516i
$236$	−5.27701	+	19.6941i	−0.343504	+	1.28197i
$237$	3.38480			0.219866
$238$	3.54802	+	7.68384i	0.229984	+	0.498070i
$239$	−4.85520			−0.314057			−0.157028	−	0.987594i	$-0.550191\pi$
$239$	−4.85520			−0.314057			−0.157028	+	0.987594i	$0.550191\pi$
$240$	0.832916	−	3.10848i	0.0537645	−	0.200652i
$241$	−20.7901	−	2.73707i	−1.33921	−	0.176310i	−0.573346	−	0.819314i	$-0.694355\pi$
$241$	−20.7901	−	2.73707i	−1.33921	−	0.176310i	−0.765863	+	0.643003i	$0.777688\pi$
$242$	−6.44531	−	3.72120i	−0.414320	−	0.239208i
$243$	0.793353	+	0.608761i	0.0508936	+	0.0390521i
$244$	−3.99521	+	9.64530i	−0.255767	+	0.617477i
$245$	25.7170	+	15.4611i	1.64300	+	0.987772i
$246$	2.11064	−	2.11064i	0.134570	−	0.134570i
$247$	1.63456	+	0.437980i	0.104005	+	0.0278680i
$248$	15.6785	−	12.0306i	0.995589	−	0.763942i
$249$	1.54919	+	2.01894i	0.0981758	+	0.127945i
$250$	−22.0994	−	16.9575i	−1.39769	−	1.07249i
$251$			10.6261i			0.670713i	0.942091	+	0.335356i	$0.108857\pi$
$251$			10.6261i			0.670713i	−0.942091	+	0.335356i	$0.891143\pi$
$252$	2.46340	−	2.75931i	0.155180	−	0.173820i
$253$	−0.655126	−	0.655126i	−0.0411875	−	0.0411875i
$254$	−4.09016	−	7.08436i	−0.256639	−	0.444512i
$255$	−2.59953	+	17.4822i	−0.162789	+	1.09478i
$256$	6.66863	−	11.5504i	0.416790	−	0.721901i
$257$	−5.88309	+	21.9560i	−0.366977	+	1.36958i	0.497744	+	0.867324i	$0.334162\pi$
$257$	−5.88309	+	21.9560i	−0.366977	+	1.36958i	−0.864721	+	0.502253i	$0.832505\pi$
$258$	2.93987	+	7.09748i	0.183028	+	0.441870i
$259$	−18.0628	−	12.3018i	−1.12237	−	0.764398i
$260$	−7.32648	+	3.03473i	−0.454369	+	0.188206i
$261$	5.00505	−	0.658927i	0.309805	−	0.0407866i
$262$	−1.54798	+	1.18781i	−0.0956348	+	0.0733832i
$263$	−5.26380	−	19.6448i	−0.324580	−	1.21135i	−0.914734	−	0.404057i	$-0.867600\pi$
$263$	−5.26380	−	19.6448i	−0.324580	−	1.21135i	0.590154	−	0.807291i	$-0.299067\pi$
$264$	3.02098	+	0.809469i	0.185928	+	0.0498194i
$265$	21.7591	+	9.01293i	1.33665	+	0.553660i
$266$	1.18186	−	2.34403i	0.0724644	−	0.143722i
$267$	9.46227	−	3.91940i	0.579082	−	0.239863i
$268$	2.11644	−	1.22193i	0.129282	−	0.0746410i
$269$	−20.4856	−	2.69698i	−1.24903	−	0.164438i	−0.523138	−	0.852248i	$-0.675239\pi$
$269$	−20.4856	−	2.69698i	−1.24903	−	0.164438i	−0.725891	+	0.687810i	$0.758572\pi$
$270$	−3.21247	+	0.860779i	−0.195505	+	0.0523853i
$271$	−10.9450	−	18.9573i	−0.664862	−	1.15157i	−0.979323	−	0.202304i	$-0.935157\pi$
$271$	−10.9450	−	18.9573i	−0.664862	−	1.15157i	0.314461	−	0.949270i	$-0.398176\pi$
$272$	1.23216	−	2.83952i	0.0747109	−	0.172171i
$273$	−3.49124	−	0.259884i	−0.211299	−	0.0157289i
$274$	−8.77665	−	8.77665i	−0.530217	−	0.530217i
$275$	−9.65963	+	12.5887i	−0.582498	+	0.759126i
$276$	−0.945586	−	0.545934i	−0.0569176	−	0.0328614i
$277$	−1.16759	+	8.86875i	−0.0701539	+	0.532872i	0.919897	+	0.392160i	$0.128272\pi$
$277$	−1.16759	+	8.86875i	−0.0701539	+	0.532872i	−0.990051	+	0.140711i	$0.955061\pi$
$278$	−15.8290	+	2.08392i	−0.949359	+	0.124985i
$279$	6.92546	+	2.86862i	0.414616	+	0.171740i
$280$	5.57346	+	29.3763i	0.333078	+	1.75557i
$281$	5.34624	−	5.34624i	0.318930	−	0.318930i	−0.529426	−	0.848356i	$-0.677593\pi$
$281$	5.34624	−	5.34624i	0.318930	−	0.318930i	0.848356	+	0.529426i	$0.177593\pi$
$282$	0.581305	+	4.41545i	0.0346162	+	0.262936i
$283$	1.51408	+	1.97319i	0.0900029	+	0.117294i	0.836184	−	0.548449i	$-0.184781\pi$
$283$	1.51408	+	1.97319i	0.0900029	+	0.117294i	−0.746181	+	0.665743i	$0.768115\pi$
$284$	−1.22011	+	9.26768i	−0.0724004	+	0.549936i
$285$	4.74766	−	2.74106i	0.281227	−	0.162366i
$286$	−0.466060	−	1.12517i	−0.0275587	−	0.0665326i
$287$	3.35712	−	9.60946i	0.198165	−	0.567228i
$288$	5.85518			0.345020
$289$	−4.94628	+	16.2645i	−0.290958	+	0.956736i
$290$	−8.39470	+	14.5400i	−0.492954	+	0.853821i
$291$	−9.72844	+	2.60673i	−0.570291	+	0.152809i
$292$	7.22253	−	9.41258i	0.422666	−	0.550829i
$293$			21.4483i			1.25302i	0.779412	+	0.626511i	$0.215518\pi$
$293$			21.4483i			1.25302i	−0.779412	+	0.626511i	$0.784482\pi$
$294$	−1.49827	+	5.22014i	−0.0873807	+	0.304445i
$295$	23.9235	−	57.7564i	1.39288	−	3.36271i
$296$	−2.84241	−	21.5902i	−0.165212	−	1.25491i
$297$	0.307040	+	1.14589i	0.0178162	+	0.0664911i
$298$	0.0297633	+	0.111078i	0.00172414	+	0.00643459i
$299$	0.134887	+	1.02457i	0.00780072	+	0.0592523i
$300$	−7.15621	+	17.2766i	−0.413164	+	0.997466i
$301$	19.5428	+	17.4471i	1.12643	+	1.00563i
$302$		−	1.36933i		−	0.0787961i
$303$	4.37302	−	5.69903i	0.251223	−	0.327401i
$304$	−0.927373	+	0.248489i	−0.0531885	+	0.0142518i
$305$	16.0053	−	27.7220i	0.916460	−	1.58736i
$306$	−3.17805	+	0.364473i	−0.181677	+	0.0208355i
$307$	−4.61821			−0.263575			−0.131787	−	0.991278i	$-0.542072\pi$
$307$	−4.61821			−0.263575			−0.131787	+	0.991278i	$0.542072\pi$
$308$	4.31118	−	0.817944i	0.245652	−	0.0466067i
$309$	2.58333	+	6.23670i	0.146960	+	0.354793i
$310$	−21.5903	+	12.4652i	−1.22625	+	0.707975i
$311$	4.03512	−	30.6497i	0.228810	−	1.73799i	−0.362892	−	0.931831i	$-0.618211\pi$
$311$	4.03512	−	30.6497i	0.228810	−	1.73799i	0.591703	−	0.806156i	$-0.298456\pi$
$312$	−2.12365	−	2.76760i	−0.120228	−	0.156684i
$313$	0.617087	+	4.68724i	0.0348798	+	0.264938i	0.999995	+	0.00311337i	$0.000991020\pi$
$313$	0.617087	+	4.68724i	0.0348798	+	0.264938i	−0.965115	+	0.261825i	$0.915676\pi$
$314$	1.94683	−	1.94683i	0.109866	−	0.109866i
$315$	−8.59285	+	7.40220i	−0.484152	+	0.417067i
$316$	4.37196	+	1.81093i	0.245942	+	0.101873i
$317$	−32.9359	+	4.33610i	−1.84987	+	0.243539i	−0.971935	−	0.235248i	$-0.924410\pi$
$317$	−32.9359	+	4.33610i	−1.84987	+	0.243539i	−0.877931	+	0.478788i	$0.841076\pi$
$318$	−0.556386	+	4.22617i	−0.0312006	+	0.236992i
$319$	5.18643	+	2.99439i	0.290384	+	0.167654i
$320$	−7.93633	+	10.3428i	−0.443654	+	0.578182i
$321$	−8.50977	−	8.50977i	−0.474969	−	0.474969i
$322$	1.59869	+	0.119005i	0.0890916	+	0.00663187i
$323$	4.90459	−	1.93616i	0.272899	−	0.107731i
$324$	0.699034	+	1.21076i	0.0388352	+	0.0672646i
$325$	17.0958	−	4.58081i	0.948305	−	0.254097i
$326$	−14.5658	−	1.91762i	−0.806723	−	0.106207i
$327$	−7.73320	+	4.46476i	−0.427647	+	0.246902i
$328$	9.37081	−	3.88152i	0.517416	−	0.214321i
$329$	8.32553	+	12.7020i	0.459001	+	0.700284i
$330$	−3.64509	−	1.50985i	−0.200656	−	0.0831144i
$331$	22.3895	+	5.99925i	1.23064	+	0.329748i	0.814828	−	0.579703i	$-0.196831\pi$
$331$	22.3895	+	5.99925i	1.23064	+	0.329748i	0.415810	+	0.909451i	$0.363498\pi$
$332$	0.920834	+	3.43660i	0.0505374	+	0.188608i
$333$	6.55314	−	5.02840i	0.359110	−	0.275555i
$334$	6.04678	−	0.796074i	0.330865	−	0.0435592i
$335$	−6.92282	+	2.86753i	−0.378234	+	0.156670i
$336$	1.78911	−	0.862690i	0.0976041	−	0.0470636i
$337$	12.5264	+	30.2415i	0.682358	+	1.64736i	0.759636	+	0.650349i	$0.225377\pi$
$337$	12.5264	+	30.2415i	0.682358	+	1.64736i	−0.0772772	+	0.997010i	$0.524623\pi$
$338$	2.25885	−	8.43015i	0.122865	−	0.458540i
$339$	−9.66527	+	16.7407i	−0.524946	+	0.909232i
$340$	−12.7110	+	21.1901i	−0.689349	+	1.14919i
$341$	4.44633	+	7.70127i	0.240782	+	0.417047i
$342$	0.701594	+	0.701594i	0.0379379	+	0.0379379i
$343$	3.12954	+	18.2539i	0.168979	+	0.985620i
$344$			26.1048i			1.40748i
$345$	2.65601	+	2.03803i	0.142995	+	0.109724i
$346$	3.44315	+	4.48720i	0.185105	+	0.241233i
$347$	−9.84497	+	7.55431i	−0.528506	+	0.405537i	−0.838252	−	0.545282i	$-0.816422\pi$
$347$	−9.84497	+	7.55431i	−0.528506	+	0.405537i	0.309747	+	0.950819i	$0.399756\pi$
$348$	6.81729	+	1.82669i	0.365445	+	0.0979207i
$349$	−6.87040	+	6.87040i	−0.367764	+	0.367764i	−0.866661	−	0.498897i	$-0.833738\pi$
$349$	−6.87040	+	6.87040i	−0.367764	+	0.367764i	0.498897	+	0.866661i	$0.333738\pi$
$350$	−1.55313	−	27.4121i	−0.0830181	−	1.46524i
$351$	0.506372	−	1.22249i	0.0270282	−	0.0652517i
$352$	5.51068	+	4.22849i	0.293720	+	0.225379i
$353$	10.8138	+	6.24333i	0.575558	+	0.332299i	0.759366	−	0.650663i	$-0.225509\pi$
$353$	10.8138	+	6.24333i	0.575558	+	0.332299i	−0.183808	+	0.982962i	$0.558842\pi$
$354$	11.2177	+	1.47684i	0.596217	+	0.0784934i
$355$	7.41809	−	27.6847i	0.393711	−	1.46935i
$356$	14.3189			0.758898
$357$	−9.22223	+	5.82671i	−0.488092	+	0.308382i
$358$	17.4599			0.922785
$359$	−1.33688	+	4.98932i	−0.0705580	+	0.263326i	−0.992189	−	0.124740i	$-0.960190\pi$
$359$	−1.33688	+	4.98932i	−0.0705580	+	0.263326i	0.921631	+	0.388066i	$0.126857\pi$
$360$	−11.2046	−	1.47511i	−0.590534	−	0.0777452i
$361$	15.0381	+	8.68224i	0.791478	+	0.456960i
$362$	2.86600	+	2.19916i	0.150634	+	0.115585i
$363$	3.67096	−	8.86247i	0.192675	−	0.465159i
$364$	−4.37040	−	2.20355i	−0.229071	−	0.115497i
$365$	−25.7229	+	25.7229i	−1.34640	+	1.34640i
$366$	5.59615	+	1.49948i	0.292516	+	0.0783793i
$367$	0.877281	−	0.673161i	0.0457937	−	0.0351387i	−0.585611	−	0.810592i	$-0.699145\pi$
$367$	0.877281	−	0.673161i	0.0457937	−	0.0351387i	0.631405	+	0.775453i	$0.282479\pi$
$368$	−0.356921	−	0.465149i	−0.0186058	−	0.0242476i
$369$	3.05227	+	2.34209i	0.158895	+	0.121924i
$370$			27.4712i			1.42816i
$371$	4.55051	+	13.8057i	0.236251	+	0.716755i
$372$	7.41048	+	7.41048i	0.384216	+	0.384216i
$373$	−9.44236	−	16.3547i	−0.488907	−	0.846812i	0.511012	−	0.859574i	$-0.329271\pi$
$373$	−9.44236	−	16.3547i	−0.488907	−	0.846812i	−0.999919	+	0.0127620i	$0.995938\pi$
$374$	−3.25428	−	1.95210i	−0.168275	−	0.100940i
$375$	17.9519	−	31.0936i	0.927033	−	1.60567i
$376$	−3.91683	+	14.6178i	−0.201995	+	0.753856i
$377$	−2.55629	−	6.17143i	−0.131656	−	0.317845i
$378$	−1.69659	−	1.15548i	−0.0872629	−	0.0594312i
$379$	−11.9069	+	4.93198i	−0.611614	+	0.253339i	−0.666918	−	0.745131i	$-0.732387\pi$
$379$	−11.9069	+	4.93198i	−0.611614	+	0.253339i	0.0553045	+	0.998470i	$0.482387\pi$
$380$	7.59881	−	1.00040i	0.389811	−	0.0513196i
$381$	8.36494	−	6.41864i	0.428549	−	0.328837i
$382$	−1.27895	−	4.77312i	−0.0654369	−	0.244214i
$383$	17.1093	+	4.58441i	0.874242	+	0.234252i	0.667921	−	0.744232i	$-0.267184\pi$
$383$	17.1093	+	4.58441i	0.874242	+	0.234252i	0.206321	+	0.978484i	$0.433851\pi$
$384$	8.63905	+	3.57841i	0.440859	+	0.182610i
$385$	−13.4330	+	0.761092i	−0.684609	+	0.0387889i
$386$	0.485379	−	0.201050i	0.0247051	−	0.0102332i
$387$	−8.57523	+	4.95091i	−0.435903	+	0.251669i
$388$	−13.9603	−	1.83791i	−0.708729	−	0.0933059i
$389$	−18.7341	+	5.01979i	−0.949857	+	0.254513i	−0.700302	−	0.713847i	$-0.746951\pi$
$389$	−18.7341	+	5.01979i	−0.949857	+	0.254513i	−0.249556	+	0.968360i	$0.580285\pi$
$390$	2.20037	+	3.81115i	0.111420	+	0.192985i
$391$	2.23857	+	2.31468i	0.113209	+	0.117058i
$392$	−11.4919	+	14.4398i	−0.580426	+	0.729321i
$393$	−1.77833	−	1.77833i	−0.0897047	−	0.0897047i
$394$	−4.35989	+	5.68192i	−0.219648	+	0.286251i
$395$	−12.5657	−	7.25478i	−0.632247	−	0.365028i
$396$	−0.216483	+	1.64435i	−0.0108787	+	0.0826318i
$397$	−16.9394	+	2.23012i	−0.850166	+	0.111926i	−0.543003	−	0.839731i	$-0.682713\pi$
$397$	−16.9394	+	2.23012i	−0.850166	+	0.111926i	−0.307162	+	0.951657i	$0.599380\pi$
$398$	−5.25092	−	2.17500i	−0.263205	−	0.109023i
$399$	3.19426	+	1.11593i	0.159913	+	0.0558666i
$400$	−7.10041	+	7.10041i	−0.355021	+	0.355021i
$401$	0.570663	+	4.33462i	0.0284976	+	0.216461i	0.999769	−	0.0215159i	$-0.00684924\pi$
$401$	0.570663	+	4.33462i	0.0284976	+	0.216461i	−0.971271	+	0.237976i	$0.923516\pi$
$402$	−0.825596	−	1.07594i	−0.0411770	−	0.0536629i
$403$	1.29468	−	9.83405i	0.0644924	−	0.489869i
$404$	8.69747	−	5.02149i	0.432715	−	0.249828i
$405$	−1.64044	−	3.96038i	−0.0815143	−	0.196793i
$406$	−10.1808	+	1.93157i	−0.505267	+	0.0958623i
$407$	9.79898			0.485717
$408$	−10.4511	−	2.98846i	−0.517409	−	0.147951i
$409$	−16.5337	+	28.6372i	−0.817537	+	1.41602i	0.0899541	+	0.995946i	$0.471328\pi$
$409$	−16.5337	+	28.6372i	−0.817537	+	1.41602i	−0.907492	+	0.420070i	$0.862005\pi$
$410$	−12.3593	+	3.31167i	−0.610384	+	0.163552i
$411$	9.73906	−	12.6922i	0.480393	−	0.626060i
$412$			9.43773i			0.464964i
$413$	36.6451	−	12.0787i	1.80319	−	0.594352i
$414$	−0.231876	+	0.559798i	−0.0113961	+	0.0275126i
$415$	−1.42389	−	10.8155i	−0.0698960	−	0.530913i
$416$	−2.00524	−	7.48367i	−0.0983151	−	0.366917i
$417$	−5.32607	−	19.8772i	−0.260819	−	0.973389i
$418$	0.153637	+	1.16699i	0.00751465	+	0.0570794i
$419$	0.882085	−	2.12954i	0.0430927	−	0.104035i	−0.900868	−	0.434094i	$-0.857069\pi$
$419$	0.882085	−	2.12954i	0.0430927	−	0.104035i	0.943960	+	0.330059i	$0.107069\pi$
$420$	−15.0592	+	4.96370i	−0.734815	+	0.242204i
$421$		−	4.68883i		−	0.228519i	−0.993451	−	0.114260i	$-0.963550\pi$
$421$		−	4.68883i		−	0.228519i	0.993451	−	0.114260i	$-0.0364496\pi$
$422$	−0.00535985	+	0.00698509i	−0.000260913	+	0.000340029i
$423$	−5.54468	+	1.48569i	−0.269592	+	0.0722369i
$424$	−7.24237	+	12.5442i	−0.351721	+	0.609198i
$425$	34.2993	−	43.1856i	1.66376	−	2.09481i
$426$	5.18738			0.251329
$427$	19.4107	−	3.68272i	0.939351	−	0.178220i
$428$	−6.43873	−	15.5445i	−0.311228	−	0.751371i
$429$	1.35944	−	0.784871i	0.0656342	−	0.0378939i
$430$	4.29841	−	32.6497i	0.207288	−	1.57451i
$431$	−5.19642	−	6.77210i	−0.250303	−	0.326201i	0.651256	−	0.758858i	$-0.274243\pi$
$431$	−5.19642	−	6.77210i	−0.250303	−	0.326201i	−0.901558	+	0.432658i	$0.857576\pi$
$432$	0.0979898	+	0.744307i	0.00471454	+	0.0358105i
$433$	11.8775	−	11.8775i	0.570794	−	0.570794i	−0.361556	−	0.932350i	$-0.617754\pi$
$433$	11.8775	−	11.8775i	0.570794	−	0.570794i	0.932350	+	0.361556i	$0.117754\pi$
$434$	−14.5261	−	5.07480i	−0.697277	−	0.243598i
$435$	−19.9929	−	8.28135i	−0.958588	−	0.397060i
$436$	−12.3773	+	1.62950i	−0.592764	+	0.0780389i
$437$	0.130367	−	0.990234i	0.00623629	−	0.0473693i
$438$	−5.70188	−	3.29198i	−0.272446	−	0.157297i
$439$	−2.85832	+	3.72503i	−0.136420	+	0.177786i	−0.856568	−	0.516035i	$-0.827407\pi$
$439$	−2.85832	+	3.72503i	−0.136420	+	0.177786i	0.720147	+	0.693821i	$0.244074\pi$
$440$	−9.48005	−	9.48005i	−0.451943	−	0.451943i
$441$	−6.92285	−	1.03640i	−0.329660	−	0.0493524i
$442$	1.55424	+	3.93713i	0.0739277	+	0.187270i
$443$	5.49805	+	9.52290i	0.261220	+	0.452446i	0.966566	−	0.256416i	$-0.0825418\pi$
$443$	5.49805	+	9.52290i	0.261220	+	0.452446i	−0.705346	+	0.708863i	$0.749209\pi$
$444$	11.1546	−	2.98887i	0.529375	−	0.141846i
$445$	−43.5281	−	5.73059i	−2.06343	−	0.271656i
$446$	12.2576	−	7.07694i	0.580415	−	0.335103i
$447$	−0.136939	+	0.0567219i	−0.00647698	+	0.00268285i
$448$	−8.03349	+	0.455165i	−0.379547	+	0.0215045i
$449$	−24.5208	−	10.1569i	−1.15721	−	0.479332i	−0.280264	−	0.959923i	$-0.590422\pi$
$449$	−24.5208	−	10.1569i	−1.15721	−	0.479332i	−0.876945	+	0.480591i	$0.840422\pi$
$450$	10.0238	+	2.68587i	0.472527	+	0.126613i
$451$	1.18127	+	4.40857i	0.0556240	+	0.207591i
$452$	−21.4407	+	16.4520i	−1.00849	+	0.773838i
$453$	1.74986	−	0.230373i	0.0822155	−	0.0108239i
$454$	8.06613	−	3.34110i	0.378562	−	0.156806i
$455$	12.4038	+	8.44770i	0.581498	+	0.396034i
$456$	1.29025	+	3.11493i	0.0604213	+	0.145870i
$457$	1.46464	−	5.46610i	0.0685128	−	0.255693i	−0.923171	−	0.384389i	$-0.874412\pi$
$457$	1.46464	−	5.46610i	0.0685128	−	0.255693i	0.991684	+	0.128695i	$0.0410789\pi$
$458$	−10.7540	+	18.6265i	−0.502501	+	0.870358i
$459$	−1.00043	−	3.99989i	−0.0466959	−	0.186699i
$460$	2.34025	+	4.05343i	0.109115	+	0.188992i
$461$	19.0285	+	19.0285i	0.886246	+	0.886246i	0.994160	−	0.107914i	$-0.0344171\pi$
$461$	19.0285	+	19.0285i	0.886246	+	0.886246i	−0.107914	+	0.994160i	$0.534417\pi$
$462$	−0.762303	−	2.31273i	−0.0354655	−	0.107598i
$463$		−	18.0406i		−	0.838416i	−0.907890	−	0.419208i	$-0.862308\pi$
$463$		−	18.0406i		−	0.838416i	0.907890	−	0.419208i	$-0.137692\pi$
$464$	3.00670	+	2.30712i	0.139582	+	0.107105i
$465$	−19.5615	−	25.4930i	−0.907142	−	1.18221i
$466$	−1.97341	+	1.51425i	−0.0914162	+	0.0701461i
$467$	−7.45364	−	1.99720i	−0.344914	−	0.0924193i	0.0822037	−	0.996616i	$-0.473804\pi$
$467$	−7.45364	−	1.99720i	−0.344914	−	0.0924193i	−0.427117	+	0.904196i	$0.640471\pi$
$468$	1.30811	−	1.30811i	0.0604673	−	0.0604673i
$469$	−4.12961	−	2.08214i	−0.190688	−	0.0961445i
$470$	7.30580	−	17.6378i	0.336991	−	0.813569i
$471$	2.81538	+	2.16031i	0.129726	+	0.0995420i
$472$	33.2966	+	19.2238i	1.53260	+	0.884847i
$473$	−11.6461	−	1.53324i	−0.535490	−	0.0704986i
$474$	0.679678	−	2.53659i	0.0312186	−	0.116510i
$475$	−17.1058			−0.784867
$476$	−15.0292	+	2.59200i	−0.688864	+	0.118804i
$477$	−5.49421			−0.251562
$478$	−0.974938	+	3.63852i	−0.0445926	+	0.166422i
$479$	23.3568	+	3.07499i	1.06720	+	0.140500i	0.643610	−	0.765354i	$-0.277436\pi$
$479$	23.3568	+	3.07499i	1.06720	+	0.140500i	0.423591	+	0.905853i	$0.360769\pi$
$480$	−21.7366	−	12.5497i	−0.992138	−	0.572811i
$481$	−8.67121	−	6.65365i	−0.395373	−	0.303380i
$482$	−6.22589	+	15.0306i	−0.283582	+	0.684627i
$483$	0.116885	+	2.06298i	0.00531846	+	0.0938689i
$484$	9.48315	−	9.48315i	0.431052	−	0.431052i
$485$	41.7027	+	11.1742i	1.89362	+	0.507395i
$486$	0.615518	−	0.472303i	0.0279204	−	0.0214241i
$487$	6.52170	+	8.49925i	0.295527	+	0.385138i	0.917391	−	0.397987i	$-0.130291\pi$
$487$	6.52170	+	8.49925i	0.295527	+	0.385138i	−0.621864	+	0.783125i	$0.713624\pi$
$488$	15.6187	+	11.9846i	0.707025	+	0.542519i
$489$		−	18.9361i		−	0.856321i
$490$	16.7507	−	16.1678i	0.756719	−	0.730388i
$491$	8.52592	+	8.52592i	0.384770	+	0.384770i	0.872817	−	0.488048i	$-0.162291\pi$
$491$	8.52592	+	8.52592i	0.384770	+	0.384770i	−0.488048	+	0.872817i	$0.662291\pi$
$492$	2.68939	+	4.65816i	0.121247	+	0.210006i
$493$	−17.8494	−	10.7070i	−0.803895	−	0.482220i
$494$	0.656450	−	1.13700i	0.0295351	−	0.0511562i
$495$	1.31618	−	4.91206i	0.0591580	−	0.220781i
$496$	2.15356	+	5.19915i	0.0966975	+	0.233449i
$497$	15.9342	−	7.68326i	0.714744	−	0.344641i
$498$	1.82409	−	0.755563i	0.0817394	−	0.0338576i
$499$	−3.73741	+	0.492039i	−0.167309	+	0.0220267i	−0.213715	−	0.976896i	$-0.568557\pi$
$499$	−3.73741	+	0.492039i	−0.167309	+	0.0220267i	0.0464060	+	0.998923i	$0.485223\pi$
$500$	39.8232	−	30.5574i	1.78095	−	1.36657i
$501$	2.03460	+	7.59322i	0.0908991	+	0.339240i
$502$	7.96326	+	2.13375i	0.355418	+	0.0952339i
$503$	8.45588	+	3.50254i	0.377029	+	0.156171i	0.563147	−	0.826357i	$-0.309591\pi$
$503$	8.45588	+	3.50254i	0.377029	+	0.156171i	−0.186118	+	0.982527i	$0.559591\pi$
$504$	−3.82371	−	5.83372i	−0.170322	−	0.259854i
$505$	−28.4493	+	11.7841i	−1.26598	+	0.524384i
$506$	−0.622507	+	0.359405i	−0.0276738	+	0.0159775i
$507$	11.1529	+	1.46830i	0.495316	+	0.0652096i
$508$	14.2386	−	3.81523i	0.631737	−	0.169273i
$509$	5.84590	+	10.1254i	0.259115	+	0.448800i	0.966005	−	0.258523i	$-0.0832359\pi$
$509$	5.84590	+	10.1254i	0.259115	+	0.448800i	−0.706890	+	0.707323i	$0.749903\pi$
$510$	12.5793	+	5.45859i	0.557021	+	0.241710i
$511$	−22.3904	−	1.66672i	−0.990495	−	0.0737313i
$512$	5.90721	+	5.90721i	0.261064	+	0.261064i
$513$	−0.778528	+	1.01460i	−0.0343729	+	0.0447956i
$514$	15.2726	+	8.81765i	0.673646	+	0.388930i
$515$	3.77710	−	28.6899i	0.166439	−	1.26423i
$516$	−13.7250	+	1.80693i	−0.604209	+	0.0795456i
$517$	−6.29138	−	2.60598i	−0.276695	−	0.114611i
$518$	−12.8461	+	11.0661i	−0.564426	+	0.486218i
$519$	−5.15489	+	5.15489i	−0.226275	+	0.226275i
$520$	1.95189	+	14.8261i	0.0855960	+	0.650167i
$521$	4.74166	+	6.17945i	0.207736	+	0.270727i	0.885588	−	0.464472i	$-0.153756\pi$
$521$	4.74166	+	6.17945i	0.207736	+	0.270727i	−0.677852	+	0.735198i	$0.737089\pi$
$522$	0.511224	−	3.88313i	0.0223757	−	0.169960i
$523$	−3.42295	+	1.97624i	−0.149675	+	0.0864151i	−0.572967	−	0.819578i	$-0.694208\pi$
$523$	−3.42295	+	1.97624i	−0.149675	+	0.0864151i	0.423292	+	0.905993i	$0.360874\pi$
$524$	−1.34553	−	3.24840i	−0.0587799	−	0.141907i
$525$	34.7684	−	6.59648i	1.51742	−	0.287894i
$526$	−15.7789			−0.687993
$527$	−15.0040	−	27.0208i	−0.653585	−	1.17705i
$528$	−0.445299	+	0.771280i	−0.0193791	+	0.0335657i
$529$	−21.6271	+	5.79498i	−0.940310	+	0.251955i
$530$	11.1237	−	14.4966i	0.483181	−	0.629693i
$531$			14.5836i			0.632872i
$532$	3.52881	+	3.15038i	0.152993	+	0.136586i
$533$	1.94817	−	4.70329i	0.0843844	−	0.203722i
$534$	−1.03717	−	7.87812i	−0.0448829	−	0.340919i
$535$	13.3521	+	49.8308i	0.577263	+	2.15437i
$536$	−1.19275	−	4.45139i	−0.0515188	−	0.192271i
$537$	2.93742	+	22.3119i	0.126759	+	0.962830i
$538$	−6.13470	+	14.8105i	−0.264486	+	0.638525i
$539$	−5.76706	−	5.97496i	−0.248405	−	0.257360i
$540$		−	5.99308i		−	0.257901i
$541$	16.7575	−	21.8388i	0.720462	−	0.938925i	−0.279311	−	0.960201i	$-0.590106\pi$
$541$	16.7575	−	21.8388i	0.720462	−	0.938925i	0.999774	+	0.0212758i	$0.00677279\pi$
$542$	−16.4045	+	4.39558i	−0.704634	+	0.188806i
$543$	−2.32812	+	4.03242i	−0.0999092	+	0.173048i
$544$	−18.9045	−	15.0145i	−0.810522	−	0.643741i
$545$	38.2781			1.63965
$546$	−0.895809	+	2.56417i	−0.0383371	+	0.109736i
$547$	10.2144	+	24.6596i	0.436734	+	1.05437i	0.977070	+	0.212920i	$0.0682975\pi$
$547$	10.2144	+	24.6596i	0.436734	+	1.05437i	−0.540335	+	0.841450i	$0.681703\pi$
$548$	19.3700	−	11.1833i	0.827444	−	0.477725i
$549$	−0.974697	+	7.40356i	−0.0415991	+	0.315976i
$550$	7.49436	+	9.76684i	0.319560	+	0.416459i
$551$	0.842684	+	6.40082i	0.0358995	+	0.272684i
$552$	−1.45590	+	1.45590i	−0.0619674	+	0.0619674i
$553$	−1.66928	−	8.79838i	−0.0709852	−	0.374145i
$554$	6.41185	+	2.65587i	0.272413	+	0.112837i
$555$	−35.1053	+	4.62170i	−1.49014	+	0.196180i
$556$	3.75523	−	28.5238i	0.159257	−	1.20968i
$557$	−27.9679	−	16.1473i	−1.18504	−	0.684183i	−0.227865	−	0.973693i	$-0.573174\pi$
$557$	−27.9679	−	16.1473i	−1.18504	−	0.684183i	−0.957175	+	0.289510i	$0.906508\pi$
$558$	3.54042	−	4.61396i	0.149878	−	0.195324i
$559$	9.26468	+	9.26468i	0.391854	+	0.391854i
$560$	−8.49090	−	0.632053i	−0.358806	−	0.0267091i
$561$	1.94708	−	4.48704i	0.0822057	−	0.189443i
$562$	−2.93296	−	5.08004i	−0.123720	−	0.214289i
$563$	7.42647	−	1.98992i	0.312988	−	0.0838650i	−0.0989055	−	0.995097i	$-0.531534\pi$
$563$	7.42647	−	1.98992i	0.312988	−	0.0838650i	0.411894	+	0.911232i	$0.364867\pi$
$564$	−7.95664	−	1.04751i	−0.335035	−	0.0441082i
$565$	71.7623	−	41.4320i	3.01906	−	1.74306i
$566$	1.78275	−	0.738441i	0.0749348	−	0.0310390i
$567$	1.19114	−	2.36245i	0.0500234	−	0.0992136i
$568$	16.2853	+	6.74559i	0.683316	+	0.283039i
$569$	1.96084	+	0.525405i	0.0822026	+	0.0220261i	0.299686	−	0.954038i	$-0.403118\pi$
$569$	1.96084	+	0.525405i	0.0822026	+	0.0220261i	−0.217483	+	0.976064i	$0.569785\pi$
$570$	−1.10083	−	4.10834i	−0.0461085	−	0.172079i
$571$	−14.3501	+	11.0112i	−0.600535	+	0.460806i	−0.863743	−	0.503933i	$-0.831886\pi$
$571$	−14.3501	+	11.0112i	−0.600535	+	0.460806i	0.263208	+	0.964739i	$0.415219\pi$
$572$	2.17583	−	0.286454i	0.0909761	−	0.0119772i
$573$	5.88437	−	2.43739i	0.245823	−	0.101823i
$574$	−6.52727	−	4.44546i	−0.272443	−	0.185550i
$575$	−3.99758	−	9.65101i	−0.166711	−	0.402475i
$576$	0.787131	−	2.93761i	0.0327971	−	0.122401i
$577$	16.6347	−	28.8121i	0.692511	−	1.19946i	−0.278502	−	0.960436i	$-0.589838\pi$
$577$	16.6347	−	28.8121i	0.692511	−	1.19946i	0.971013	−	0.239028i	$-0.0768288\pi$
$578$	11.1955	+	6.97274i	0.465672	+	0.290028i
$579$	0.338580	+	0.586438i	0.0140709	+	0.0243715i
$580$	−21.3931	−	21.3931i	−0.888302	−	0.888302i
$581$	4.48398	−	5.02261i	0.186027	−	0.208373i
$582$			7.81399i			0.323900i
$583$	−5.17094	−	3.96780i	−0.214159	−	0.164330i
$584$	−13.6197	−	17.7495i	−0.563586	−	0.734480i
$585$	−4.50006	+	3.45302i	−0.186055	+	0.142765i
$586$	16.0735	+	4.30688i	0.663990	+	0.177916i
$587$	−14.2535	+	14.2535i	−0.588303	+	0.588303i	−0.937172	−	0.348869i	$-0.886566\pi$
$587$	−14.2535	+	14.2535i	−0.588303	+	0.588303i	0.348869	+	0.937172i	$0.386566\pi$
$588$	−8.38738	−	5.04251i	−0.345890	−	0.207950i
$589$	−3.66860	+	8.85678i	−0.151162	+	0.364937i
$590$	−38.4791	−	29.5261i	−1.58416	−	1.21557i
$591$	−7.99439	−	4.61557i	−0.328845	−	0.189859i
$592$	6.14801	+	0.809401i	0.252682	+	0.0332662i
$593$	5.96817	−	22.2735i	0.245083	−	0.914664i	−0.728258	−	0.685303i	$-0.759670\pi$
$593$	5.96817	−	22.2735i	0.245083	−	0.914664i	0.973341	−	0.229361i	$-0.0736636\pi$
$594$	0.920390			0.0377641
$595$	46.7250	−	1.86456i	1.91554	−	0.0764396i
$596$	−0.207224			−0.00848821
$597$	1.89602	−	7.07603i	0.0775988	−	0.289603i
$598$	0.794904	+	0.104651i	0.0325060	+	0.00427950i
$599$	−20.6267	−	11.9088i	−0.842784	−	0.486582i	0.0154255	−	0.999881i	$-0.495090\pi$
$599$	−20.6267	−	11.9088i	−0.842784	−	0.486582i	−0.858210	+	0.513299i	$0.828423\pi$
$600$	27.9761	+	21.4668i	1.14212	+	0.876380i
$601$	−2.33160	+	5.62898i	−0.0951079	+	0.229611i	−0.964273	−	0.264912i	$-0.914657\pi$
$601$	−2.33160	+	5.62898i	−0.0951079	+	0.229611i	0.869165	+	0.494523i	$0.164657\pi$
$602$	16.9992	−	11.1421i	0.692836	−	0.454119i
$603$	1.23604	−	1.23604i	0.0503353	−	0.0503353i
$604$	2.38345	+	0.638644i	0.0969813	+	0.0259860i
$605$	−32.6233	+	25.0327i	−1.32632	+	1.01772i
$606$	−3.39277	−	4.42155i	−0.137822	−	0.179613i
$607$	30.9059	+	23.7149i	1.25443	+	0.962559i	0.999990	−	0.00452894i	$-0.00144161\pi$
$607$	30.9059	+	23.7149i	1.25443	+	0.962559i	0.254442	+	0.967088i	$0.418108\pi$
$608$			7.48803i			0.303680i
$609$	−4.18115	−	12.6851i	−0.169429	−	0.514025i
$610$	−17.5611	−	17.5611i	−0.711029	−	0.711029i
$611$	3.79781	+	6.57800i	0.153643	+	0.266117i
$612$	0.847815	−	5.70169i	0.0342709	−	0.230477i
$613$	−6.81062	+	11.7963i	−0.275078	+	0.476450i	−0.970155	−	0.242486i	$-0.922037\pi$
$613$	−6.81062	+	11.7963i	−0.275078	+	0.476450i	0.695076	+	0.718936i	$0.255371\pi$
$614$	−0.927349	+	3.46091i	−0.0374248	+	0.139671i
$615$	−6.31127	−	15.2368i	−0.254495	−	0.614406i
$616$	0.614260	−	8.25188i	0.0247492	−	0.332478i
$617$	0.265133	−	0.109822i	0.0106739	−	0.00442126i	−0.377340	−	0.926075i	$-0.623161\pi$
$617$	0.265133	−	0.109822i	0.0106739	−	0.00442126i	0.388014	+	0.921653i	$0.373161\pi$
$618$	5.19256	−	0.683614i	0.208876	−	0.0274990i
$619$	−13.8240	+	10.6075i	−0.555633	+	0.426352i	−0.848033	−	0.529944i	$-0.822213\pi$
$619$	−13.8240	+	10.6075i	−0.555633	+	0.426352i	0.292400	+	0.956296i	$0.405546\pi$
$620$	−11.6273	−	43.3937i	−0.466964	−	1.74273i
$621$	−0.754372	−	0.202133i	−0.0302719	−	0.00811134i
$622$	−22.1589	−	9.17850i	−0.888489	−	0.368024i
$623$	−14.8545	−	22.6631i	−0.595134	−	0.907978i
$624$	0.917760	−	0.380149i	0.0367398	−	0.0152181i
$625$	−75.3702	+	43.5150i	−3.01481	+	1.74060i
$626$	3.63656	+	0.478762i	0.145346	+	0.0191352i
$627$	−1.46544	+	0.392664i	−0.0585242	+	0.0156815i
$628$	2.48066	+	4.29664i	0.0989893	+	0.171454i
$629$	−34.0523	−	0.569205i	−1.35775	−	0.0226957i
$630$	3.82179	+	7.92592i	0.152264	+	0.315776i
$631$	−14.7533	−	14.7533i	−0.587321	−	0.587321i	0.349584	−	0.936905i	$-0.386323\pi$
$631$	−14.7533	−	14.7533i	−0.587321	−	0.587321i	−0.936905	+	0.349584i	$0.886323\pi$
$632$	5.43233	−	7.07955i	0.216086	−	0.281609i
$633$	−0.00982793	−	0.00567416i	−0.000390625	−	0.000225528i
$634$	−3.36413	+	25.5531i	−0.133607	+	1.01484i
$635$	−44.8112	+	5.89950i	−1.77828	+	0.234115i
$636$	−7.09657	−	2.93950i	−0.281397	−	0.116559i
$637$	1.04624	+	9.20323i	0.0414535	+	0.364645i
$638$	3.28546	−	3.28546i	0.130073	−	0.130073i
$639$	0.872714	+	6.62892i	0.0345240	+	0.262236i
$640$	−24.4016	−	31.8008i	−0.964560	−	1.25704i
$641$	−0.630589	+	4.78980i	−0.0249068	+	0.189186i	−0.999375	−	0.0353379i	$-0.988749\pi$
$641$	−0.630589	+	4.78980i	−0.0249068	+	0.189186i	0.974469	+	0.224524i	$0.0720826\pi$
$642$	−8.08606	+	4.66849i	−0.319131	+	0.184251i
$643$	11.3284	+	27.3491i	0.446747	+	1.07854i	0.973533	+	0.228544i	$0.0733966\pi$
$643$	11.3284	+	27.3491i	0.446747	+	1.07854i	−0.526787	+	0.849997i	$0.676603\pi$
$644$	−0.952756	+	2.72718i	−0.0375438	+	0.107466i
$645$	42.4460			1.67131
$646$	−0.466115	−	4.06432i	−0.0183390	−	0.159909i
$647$	3.04283	−	5.27033i	0.119626	−	0.207198i	−0.799994	−	0.600009i	$-0.795164\pi$
$647$	3.04283	−	5.27033i	0.119626	−	0.207198i	0.919619	+	0.392810i	$0.128497\pi$
$648$	2.54653	−	0.682342i	0.100037	−	0.0268049i
$649$	−10.5319	+	13.7255i	−0.413415	+	0.538773i
$650$		−	13.7315i		−	0.538596i
$651$	4.04120	−	19.4166i	0.158387	−	0.760998i
$652$	10.1312	−	24.4588i	0.396767	−	0.957879i
$653$	−2.52144	−	19.1522i	−0.0986716	−	0.749485i	−0.967231	−	0.253899i	$-0.918287\pi$
$653$	−2.52144	−	19.1522i	−0.0986716	−	0.749485i	0.868559	−	0.495586i	$-0.165047\pi$
$654$	1.79308	+	6.69185i	0.0701148	+	0.261672i
$655$	2.79026	+	10.4134i	0.109024	+	0.406884i
$656$	0.376996	+	2.86357i	0.0147192	+	0.111804i
$657$	3.24753	−	7.84023i	0.126698	−	0.305877i
$658$	11.1908	−	3.68860i	0.436261	−	0.143797i
$659$		−	41.8725i		−	1.63112i	−0.578673	−	0.815560i	$-0.696429\pi$
$659$		−	41.8725i		−	1.63112i	0.578673	−	0.815560i	$-0.303571\pi$
$660$	4.32808	−	5.64046i	0.168470	−	0.219555i
$661$	25.8963	−	6.93888i	1.00725	−	0.269891i	0.282769	−	0.959188i	$-0.408747\pi$
$661$	25.8963	−	6.93888i	1.00725	−	0.269891i	0.724479	+	0.689297i	$0.242080\pi$
$662$	8.99175	−	15.5742i	0.349474	−	0.605307i
$663$	−4.76975	+	2.64853i	−0.185242	+	0.102860i
$664$	6.70908			0.260363
$665$	−9.46647	−	10.9892i	−0.367094	−	0.426141i
$666$	−2.45243	−	5.92068i	−0.0950296	−	0.229422i
$667$	−3.41439	+	1.97130i	−0.132206	+	0.0763289i
$668$	−1.43452	+	10.8963i	−0.0555034	+	0.421590i
$669$	11.1058	+	14.4733i	0.429374	+	0.559572i
$670$	0.758821	+	5.76382i	0.0293158	+	0.222676i
$671$	−6.26405	+	6.26405i	−0.241821	+	0.241821i
$672$	−2.88760	−	15.2198i	−0.111392	−	0.587118i
$673$	−20.6316	−	8.54588i	−0.795289	−	0.329420i	−0.0522212	−	0.998636i	$-0.516630\pi$
$673$	−20.6316	−	8.54588i	−0.795289	−	0.329420i	−0.743068	+	0.669216i	$0.766630\pi$
$674$	25.1785	−	3.31481i	0.969840	−	0.127682i
$675$	−1.74587	+	13.2612i	−0.0671987	+	0.510425i
$676$	13.6200	+	7.86350i	0.523846	+	0.302442i
$677$	−4.42623	+	5.76838i	−0.170114	+	0.221697i	−0.870628	−	0.491942i	$-0.836287\pi$
$677$	−4.42623	+	5.76838i	−0.170114	+	0.221697i	0.700514	+	0.713638i	$0.252954\pi$
$678$	10.6048	+	10.6048i	0.407275	+	0.407275i
$679$	11.5737	+	24.0024i	0.444156	+	0.921126i
$680$	32.3933	+	33.4947i	1.24223	+	1.28446i
$681$	5.62660	+	9.74556i	0.215612	+	0.373451i
$682$	6.66422	−	1.78567i	0.255186	−	0.0683769i
$683$	22.0958	+	2.90897i	0.845474	+	0.111309i	0.540803	−	0.841149i	$-0.318120\pi$
$683$	22.0958	+	2.90897i	0.845474	+	0.111309i	0.304670	+	0.952458i	$0.401454\pi$
$684$	−1.54841	+	0.893975i	−0.0592050	+	0.0341820i
$685$	−63.3588	+	26.2441i	−2.42082	+	1.00273i
$686$	14.3080	+	1.32015i	0.546283	+	0.0504034i
$687$	−25.6119	−	10.6088i	−0.977154	−	0.404750i
$688$	−7.18029	−	1.92395i	−0.273746	−	0.0733500i
$689$	1.88162	+	7.02230i	0.0716840	+	0.267528i
$690$	2.06065	−	1.58119i	0.0784476	−	0.0601949i
$691$	−48.2729	+	6.35525i	−1.83639	+	0.241765i	−0.967433	−	0.253127i	$-0.918541\pi$
$691$	−48.2729	+	6.35525i	−1.83639	+	0.241765i	−0.868954	+	0.494892i	$0.835208\pi$
$692$	−9.41626	+	3.90034i	−0.357952	+	0.148269i
$693$	2.82718	−	1.36323i	0.107395	−	0.0517849i
$694$	3.68435	+	8.89481i	0.139856	+	0.337643i
$695$	−22.8312	+	85.2071i	−0.866036	+	3.23209i
$696$	6.65450	−	11.5259i	0.252238	−	0.436890i
$697$	−3.84894	−	15.3888i	−0.145789	−	0.582892i
$698$	3.76912	+	6.52832i	0.142663	+	0.247100i
$699$	−2.26705	−	2.26705i	−0.0857477	−	0.0857477i
$700$	48.4378	+	10.0814i	1.83078	+	0.381041i
$701$			29.5994i			1.11795i	0.829183	+	0.558977i	$0.188806\pi$
$701$			29.5994i			1.11795i	−0.829183	+	0.558977i	$0.811194\pi$
$702$	−0.814462	−	0.624959i	−0.0307399	−	0.0235875i
$703$	6.43068	+	8.38063i	0.242538	+	0.316081i
$704$	2.86230	−	2.19632i	0.107877	−	0.0827771i
$705$	23.7683	+	6.36870i	0.895166	+	0.239859i
$706$	6.85023	−	6.85023i	0.257812	−	0.257812i
$707$	−16.9706	−	8.55655i	−0.638245	−	0.321802i
$708$	−7.80246	+	18.8368i	−0.293234	+	0.707930i
$709$	25.0259	+	19.2030i	0.939867	+	0.721186i	0.960406	−	0.278603i	$-0.0898715\pi$
$709$	25.0259	+	19.2030i	0.939867	+	0.721186i	−0.0205388	+	0.999789i	$0.506538\pi$
$710$	−19.2575	−	11.1183i	−0.722722	−	0.417264i
$711$	3.35584	+	0.441805i	0.125854	+	0.0165690i
$712$	6.98847	−	26.0813i	0.261904	−	0.977439i
$713$	−5.85431			−0.219245
$714$	2.51473	+	8.08122i	0.0941113	+	0.302432i
$715$	−6.72899			−0.251650
$716$	−8.14315	+	30.3907i	−0.304324	+	1.13575i
$717$	−4.81366	−	0.633731i	−0.179770	−	0.0236671i
$718$	3.47058	+	2.00374i	0.129521	+	0.0747789i
$719$	−35.1873	−	27.0002i	−1.31227	−	1.00694i	−0.998346	−	0.0574866i	$-0.981691\pi$
$719$	−35.1873	−	27.0002i	−1.31227	−	1.00694i	−0.313919	−	0.949450i	$-0.601642\pi$
$720$	1.23153	−	2.97317i	0.0458964	−	0.110804i
$721$	14.9375	−	9.79081i	0.556303	−	0.364629i
$722$	9.52622	−	9.52622i	0.354529	−	0.354529i
$723$	−20.2550	−	5.42731i	−0.753291	−	0.201844i
$724$	−5.16452	+	3.96288i	−0.191938	+	0.147279i
$725$	41.1057	+	53.5700i	1.52663	+	1.98954i
$726$	−5.90446	−	4.53065i	−0.219135	−	0.168148i
$727$			51.0202i			1.89224i	0.323823	+	0.946118i	$0.395032\pi$
$727$			51.0202i			1.89224i	−0.323823	+	0.946118i	$0.604968\pi$
$728$	−6.14672	+	6.88508i	−0.227812	+	0.255178i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	14.1117	+	24.4422i	0.522297	+	0.904645i
$731$	40.3823	+	6.00465i	1.49359	+	0.222090i
$732$	−5.22000	+	9.04130i	−0.192937	+	0.334176i
$733$	4.51086	−	16.8348i	0.166613	−	0.621806i	−0.831216	−	0.555949i	$-0.812355\pi$
$733$	4.51086	−	16.8348i	0.166613	−	0.621806i	0.997829	−	0.0658576i	$-0.0209783\pi$
$734$	−0.328311	−	0.792613i	−0.0121182	−	0.0292559i
$735$	23.4789	+	18.6855i	0.866032	+	0.689227i
$736$	−4.22472	+	1.74994i	−0.155725	+	0.0645035i
$737$	2.05595	−	0.270671i	0.0757320	−	0.00997031i
$738$	2.36808	−	1.81709i	0.0871702	−	0.0668881i
$739$	−12.2077	−	45.5599i	−0.449069	−	1.67595i	−0.704965	−	0.709242i	$-0.749037\pi$
$739$	−12.2077	−	45.5599i	−0.449069	−	1.67595i	0.255896	−	0.966704i	$-0.417630\pi$
$740$	−47.8163	−	12.8123i	−1.75776	−	0.470991i
$741$	1.56341	+	0.647586i	0.0574333	+	0.0237897i
$742$	11.2598	−	0.637964i	0.413361	−	0.0234204i
$743$	32.0223	−	13.2641i	1.17479	−	0.486612i	0.292014	−	0.956414i	$-0.405675\pi$
$743$	32.0223	−	13.2641i	1.17479	−	0.486612i	0.882772	+	0.469802i	$0.155675\pi$
$744$	17.1147	−	9.88119i	0.627456	−	0.362262i
$745$	0.629943	+	0.0829336i	0.0230793	+	0.00303845i
$746$	−14.1523	+	3.79211i	−0.518154	+	0.138839i
$747$	1.27241	+	2.20388i	0.0465550	+	0.0806357i
$748$	4.91558	−	4.75395i	0.179731	−	0.173822i
$749$	−17.9234	+	26.3169i	−0.654905	+	0.961598i
$750$	−19.6970	−	19.6970i	−0.719232	−	0.719232i
$751$	−8.63610	+	11.2548i	−0.315136	+	0.410693i	−0.923885	−	0.382669i	$-0.875005\pi$
$751$	−8.63610	+	11.2548i	−0.315136	+	0.410693i	0.608749	+	0.793363i	$0.291671\pi$
$752$	−3.73204	−	2.15470i	−0.136094	−	0.0785737i
$753$	−1.38698	+	10.5352i	−0.0505445	+	0.383923i
$754$	−5.13822	+	0.676459i	−0.187123	+	0.0246352i
$755$	−6.98990	−	2.89531i	−0.254389	−	0.105371i
$756$	2.80249	−	2.41417i	0.101926	−	0.0878024i
$757$	20.1749	−	20.1749i	0.733271	−	0.733271i	−0.237996	−	0.971266i	$-0.576490\pi$
$757$	20.1749	−	20.1749i	0.733271	−	0.733271i	0.971266	+	0.237996i	$0.0764904\pi$
$758$	1.30513	+	9.91343i	0.0474044	+	0.360072i
$759$	−0.564011	−	0.735033i	−0.0204723	−	0.0266800i
$760$	1.88648	−	14.3292i	0.0684298	−	0.519776i
$761$	−4.04237	+	2.33386i	−0.146536	+	0.0846025i	−0.571475	−	0.820619i	$-0.693629\pi$
$761$	−4.04237	+	2.33386i	−0.146536	+	0.0846025i	0.424940	+	0.905222i	$0.360295\pi$
$762$	−3.13047	−	7.55762i	−0.113405	−	0.273784i
$763$	15.4194	+	17.8996i	0.558220	+	0.648010i
$764$	8.90457			0.322156
$765$	−4.85918	+	16.9934i	−0.175684	+	0.614397i
$766$	6.87117	−	11.9012i	0.248266	−	0.430009i
$767$	18.6396	−	4.99448i	0.673038	−	0.180340i
$768$	8.11921	−	10.5812i	0.292977	−	0.381815i
$769$			37.5728i			1.35491i	0.735565	+	0.677455i	$0.236917\pi$
$769$			37.5728i			1.35491i	−0.735565	+	0.677455i	$0.763083\pi$
$770$	−2.12702	+	10.2196i	−0.0766523	+	0.368289i
$771$	−8.69859	+	21.0002i	−0.313272	+	0.756306i
$772$	0.123571	+	0.938617i	0.00444743	+	0.0337816i
$773$	−4.07832	−	15.2205i	−0.146687	−	0.547443i	−0.999675	−	0.0255120i	$-0.991878\pi$
$773$	−4.07832	−	15.2205i	−0.146687	−	0.547443i	0.852988	−	0.521931i	$-0.174788\pi$
$774$	1.98831	+	7.42049i	0.0714685	+	0.266724i
$775$	13.0872	+	99.4071i	0.470106	+	3.57081i
$776$	−10.1612	+	24.5313i	−0.364766	+	0.880622i
$777$	−16.3025	−	14.5542i	−0.584850	−	0.522131i
$778$			15.0475i			0.539478i
$779$	−2.99523	+	3.90346i	−0.107315	+	0.139856i
$780$	−7.65991	+	2.05247i	−0.274269	+	0.0734901i
$781$	−3.96591	+	6.86915i	−0.141911	+	0.245798i
$782$	2.18414	−	1.21280i	0.0781049	−	0.0433697i
$783$	5.04824			0.180409
$784$	−3.12480	−	4.22513i	−0.111600	−	0.150898i
$785$	−5.82145	−	14.0542i	−0.207776	−	0.501616i
$786$	−1.68978	+	0.975596i	−0.0602725	+	0.0347984i
$787$	−2.93312	+	22.2793i	−0.104554	+	0.794170i	0.856176	+	0.516685i	$0.172834\pi$
$787$	−2.93312	+	22.2793i	−0.104554	+	0.794170i	−0.960730	+	0.277485i	$0.910499\pi$
$788$	−7.85652	−	10.2388i	−0.279877	−	0.364743i
$789$	−2.65461	−	20.1638i	−0.0945066	−	0.717849i
$790$	−7.96000	+	7.96000i	−0.283204	+	0.283204i
$791$	48.2822	+	16.8677i	1.71672	+	0.599746i
$792$	2.88948	+	1.19686i	0.102673	+	0.0425286i
$793$	9.79650	−	1.28973i	0.347884	−	0.0457998i
$794$	−1.73022	+	13.1423i	−0.0614033	+	0.466404i
$795$	20.3966	+	11.7760i	0.723392	+	0.417650i
$796$	6.23478	−	8.12533i	0.220986	−	0.287995i
$797$	8.68173	+	8.68173i	0.307523	+	0.307523i	0.843948	−	0.536425i	$-0.180226\pi$
$797$	8.68173	+	8.68173i	0.307523	+	0.307523i	−0.536425	+	0.843948i	$0.680226\pi$
$798$	1.47771	−	2.16972i	0.0523102	−	0.0768071i
$799$	21.7117	+	9.42145i	0.768106	+	0.333307i
$800$	39.1585	+	67.8245i	1.38446	+	2.39796i
$801$	9.89290	−	2.65080i	0.349549	−	0.0936613i
$802$	3.36298	+	0.442745i	0.118751	+	0.0156339i
$803$	8.71851	−	5.03364i	0.307670	−	0.177633i
$804$	2.25782	−	0.935221i	0.0796273	−	0.0329827i
$805$	3.98775	−	7.90909i	0.140550	−	0.278759i
$806$	−7.10973	−	2.94494i	−0.250429	−	0.103731i
$807$	−19.9583	−	5.34781i	−0.702566	−	0.188252i
$808$	−4.90158	−	18.2929i	−0.172437	−	0.643544i
$809$	33.1728	−	25.4544i	1.16629	−	0.894928i	0.170392	−	0.985376i	$-0.445497\pi$
$809$	33.1728	−	25.4544i	1.16629	−	0.894928i	0.995901	+	0.0904485i	$0.0288301\pi$
$810$	−3.29734	+	0.434103i	−0.115857	+	0.0152528i
$811$	40.6543	−	16.8396i	1.42757	−	0.591318i	0.470817	−	0.882231i	$-0.343959\pi$
$811$	40.6543	−	16.8396i	1.42757	−	0.591318i	0.956749	+	0.290913i	$0.0939591\pi$
$812$	1.38617	−	18.6216i	0.0486450	−	0.653490i
$813$	−8.37694	−	20.2237i	−0.293792	−	0.709277i
$814$	1.96766	−	7.34342i	0.0689666	−	0.257387i
$815$	−40.5866	+	70.2980i	−1.42169	+	2.46243i
$816$	1.59225	−	2.65440i	0.0557400	−	0.0929225i
$817$	−6.33158	−	10.9666i	−0.221514	−	0.383674i
$818$	18.1409	+	18.1409i	0.634281	+	0.634281i
$819$	−3.42745	−	0.713358i	−0.119765	−	0.0249268i
$820$		−	23.0572i		−	0.805191i
$821$	−18.5521	−	14.2355i	−0.647473	−	0.496824i	0.232035	−	0.972707i	$-0.425462\pi$
$821$	−18.5521	−	14.2355i	−0.647473	−	0.496824i	−0.879508	+	0.475884i	$0.842128\pi$
$822$	−7.55598	−	9.84715i	−0.263545	−	0.343459i
$823$	−29.6377	+	22.7418i	−1.03311	+	0.792730i	−0.978598	−	0.205784i	$-0.934026\pi$
$823$	−29.6377	+	22.7418i	−1.03311	+	0.792730i	−0.0545080	+	0.998513i	$0.517359\pi$
$824$	17.1905	+	4.60619i	0.598860	+	0.160464i
$825$	−11.2201	+	11.2201i	−0.390635	+	0.390635i
$826$	−1.69338	−	29.8875i	−0.0589203	−	1.03992i
$827$	3.81891	−	9.21967i	0.132797	−	0.320599i	−0.843468	−	0.537179i	$-0.819490\pi$
$827$	3.81891	−	9.21967i	0.132797	−	0.320599i	0.976265	+	0.216580i	$0.0694901\pi$
$828$	−0.866237	−	0.664687i	−0.0301038	−	0.0230995i
$829$	−46.8304	−	27.0375i	−1.62649	−	0.939052i	−0.985130	−	0.171808i	$-0.945039\pi$
$829$	−46.8304	−	27.0375i	−1.62649	−	0.939052i	−0.641355	−	0.767244i	$-0.721628\pi$
$830$	−8.39114	−	1.10471i	−0.291261	−	0.0383452i
$831$	−2.31521	+	8.64048i	−0.0803137	+	0.299735i
$832$	−4.02422			−0.139515
$833$	19.6940	+	21.0985i	0.682356	+	0.731020i
$834$	−15.9656			−0.552842
$835$	8.72167	−	32.5497i	0.301826	−	1.12643i
$836$	−2.10292	−	0.276854i	−0.0727309	−	0.00957521i
$837$	6.49178	+	3.74803i	0.224389	+	0.129551i
$838$	−1.41877	−	1.08866i	−0.0490105	−	0.0376071i
$839$	2.12687	−	5.13472i	0.0734278	−	0.177270i	−0.882904	−	0.469553i	$-0.844415\pi$
$839$	2.12687	−	5.13472i	0.0734278	−	0.177270i	0.956332	+	0.292283i	$0.0944149\pi$
$840$	1.69140	+	29.8525i	0.0583587	+	1.03001i
$841$	−2.48569	+	2.48569i	−0.0857133	+	0.0857133i
$842$	−3.51384	−	0.941530i	−0.121095	−	0.0324473i
$843$	5.99832	−	4.60267i	0.206593	−	0.158525i
$844$	−0.00965844	−	0.0125871i	−0.000332457	−	0.000433266i
$845$	−38.2566	−	29.3553i	−1.31607	−	1.00985i
$846$			4.45355i			0.153116i
$847$	−24.8473	−	5.17150i	−0.853765	−	0.177695i
$848$	−2.91658	−	2.91658i	−0.100156	−	0.100156i
$849$	1.24358	+	2.15394i	0.0426794	+	0.0739229i
$850$	−25.4762	−	34.3759i	−0.873827	−	1.17909i
$851$	−3.22548	+	5.58670i	−0.110568	+	0.191510i
$852$	−2.41935	+	9.02914i	−0.0828856	+	0.309333i
$853$	−5.11050	−	12.3378i	−0.174980	−	0.422440i	0.811921	−	0.583768i	$-0.198422\pi$
$853$	−5.11050	−	12.3378i	−0.174980	−	0.422440i	−0.986901	+	0.161328i	$0.948422\pi$
$854$	1.13787	−	15.2860i	0.0389373	−	0.523077i
$855$	5.06482	−	2.09792i	0.173213	−	0.0717473i
$856$	−31.4563	+	4.14129i	−1.07515	+	0.141547i
$857$	12.5172	−	9.60475i	0.427578	−	0.328092i	−0.372453	−	0.928051i	$-0.621483\pi$
$857$	12.5172	−	9.60475i	0.427578	−	0.328092i	0.800031	+	0.599959i	$0.204817\pi$
$858$	−0.315209	−	1.17638i	−0.0107611	−	0.0401608i
$859$	−42.0890	−	11.2777i	−1.43606	−	0.384791i	−0.544907	−	0.838496i	$-0.683435\pi$
$859$	−42.0890	−	11.2777i	−1.43606	−	0.384791i	−0.891152	+	0.453706i	$0.850102\pi$
$860$	54.8252	+	22.7093i	1.86952	+	0.774382i
$861$	4.58269	−	9.08906i	0.156178	−	0.309754i
$862$	−6.11851	+	2.53437i	−0.208397	+	0.0863210i
$863$	18.3638	−	10.6023i	0.625110	−	0.360907i	−0.153746	−	0.988110i	$-0.549134\pi$
$863$	18.3638	−	10.6023i	0.625110	−	0.360907i	0.778856	+	0.627203i	$0.215800\pi$
$864$	5.80509	+	0.764255i	0.197493	+	0.0260005i
$865$	30.1856	−	8.08821i	1.02634	−	0.275007i
$866$	−6.51602	−	11.2861i	−0.221423	−	0.383516i
$867$	−7.02691	+	15.4797i	−0.238646	+	0.525720i
$868$	15.6080	−	22.9173i	0.529771	−	0.777864i
$869$	2.83933	+	2.83933i	0.0963177	+	0.0963177i
$870$	−10.2207	+	13.3199i	−0.346515	+	0.451588i
$871$	−2.00312	−	1.15650i	−0.0678732	−	0.0391866i
$872$	−3.07278	+	23.3401i	−0.104058	+	0.790396i
$873$	−9.98545	+	1.31461i	−0.337956	+	0.0444928i
$874$	−0.715910	−	0.296540i	−0.0242160	−	0.0100306i
$875$	−89.6775	−	31.3294i	−3.03165	−	1.05913i
$876$	8.38932	−	8.38932i	0.283449	−	0.283449i
$877$	−4.63330	−	35.1934i	−0.156455	−	1.18840i	−0.871884	−	0.489712i	$-0.837102\pi$
$877$	−4.63330	−	35.1934i	−0.156455	−	1.18840i	0.715429	−	0.698686i	$-0.246231\pi$
$878$	2.21761	+	2.89004i	0.0748406	+	0.0975341i
$879$	−2.79956	+	21.2648i	−0.0944270	+	0.717244i
$880$	3.30623	−	1.90886i	0.111453	−	0.0643475i
$881$	−14.1607	−	34.1869i	−0.477085	−	1.15179i	−0.960970	−	0.276654i	$-0.910774\pi$
$881$	−14.1607	−	34.1869i	−0.477085	−	1.15179i	0.483884	−	0.875132i	$-0.339226\pi$
$882$	−2.16681	+	4.97992i	−0.0729604	+	0.167683i
$883$	−30.0219			−1.01032			−0.505159	−	0.863026i	$-0.668566\pi$
$883$	−30.0219			−1.01032			−0.505159	+	0.863026i	$0.668566\pi$
$884$	−7.57784	+	0.869061i	−0.254870	+	0.0292297i
$885$	31.2575	−	54.1397i	1.05071	−	1.81988i
$886$	8.24055	−	2.20805i	0.276847	−	0.0741808i
$887$	−0.371974	+	0.484766i	−0.0124897	+	0.0162768i	−0.799556	−	0.600591i	$-0.794932\pi$
$887$	−0.371974	+	0.484766i	−0.0124897	+	0.0162768i	0.787067	+	0.616868i	$0.211599\pi$
$888$		−	21.7765i		−	0.730772i
$889$	−20.8098	−	18.5782i	−0.697940	−	0.623092i
$890$	−13.0351	+	31.4696i	−0.436938	+	1.05486i
$891$	0.154845	+	1.17616i	0.00518749	+	0.0394029i
$892$	6.60125	+	24.6362i	0.221026	+	0.824882i
$893$	−1.90001	−	7.09094i	−0.0635815	−	0.237289i
$894$	0.0150101	+	0.114013i	0.000502012	+	0.00381316i
$895$	36.9172	−	89.1261i	1.23401	−	2.97916i
$896$	5.04113	−	24.2209i	0.168412	−	0.809165i
$897$			1.03341i			0.0345045i
$898$	−12.5355	+	16.3365i	−0.418314	+	0.545157i
$899$	36.5525	−	9.79421i	1.21909	−	0.326655i
$900$	−9.35004	+	16.1947i	−0.311668	+	0.539825i
$901$	17.7390	+	14.0888i	0.590972	+	0.469367i
$902$	3.54102			0.117903
$903$	17.0984	+	19.8486i	0.568998	+	0.660521i
$904$	19.5025	+	47.0831i	0.648642	+	1.56596i
$905$	17.2857	−	9.97992i	0.574597	−	0.331744i
$906$	0.178733	−	1.35761i	0.00593802	−	0.0451037i
$907$	27.1983	+	35.4455i	0.903105	+	1.17695i	0.983631	+	0.180196i	$0.0576733\pi$
$907$	27.1983	+	35.4455i	0.903105	+	1.17695i	−0.0805261	+	0.996752i	$0.525660\pi$
$908$	2.05354	+	15.5982i	0.0681490	+	0.517643i
$909$	5.07948	−	5.07948i	0.168476	−	0.168476i
$910$	8.82148	−	7.59915i	0.292429	−	0.251909i
$911$	12.0099	+	4.97465i	0.397904	+	0.164817i	0.572657	−	0.819795i	$-0.305913\pi$
$911$	12.0099	+	4.97465i	0.397904	+	0.164817i	−0.174753	+	0.984612i	$0.555913\pi$
$912$	−0.951873	+	0.125316i	−0.0315197	+	0.00414964i
$913$	−0.394051	+	2.99312i	−0.0130412	+	0.0990577i
$914$	−3.80223	−	2.19522i	−0.125767	−	0.0726114i
$915$	19.4868	−	25.3957i	0.644214	−	0.839556i
$916$	−27.4056	−	27.4056i	−0.905507	−	0.905507i
$917$	−3.74553	+	5.49956i	−0.123688	+	0.181612i
$918$	−3.19844	−	0.0534638i	−0.105564	−	0.00176457i
$919$	−27.6667	−	47.9201i	−0.912640	−	1.58074i	−0.810320	−	0.585988i	$-0.800707\pi$
$919$	−27.6667	−	47.9201i	−0.912640	−	1.58074i	−0.102320	−	0.994752i	$-0.532627\pi$
$920$	8.52537	−	2.28437i	0.281073	−	0.0753133i
$921$	−4.57870	−	0.602797i	−0.150873	−	0.0198628i
$922$	18.0811	−	10.4391i	0.595469	−	0.343794i
$923$	8.17373	−	3.38567i	0.269041	−	0.111441i
$924$	4.38106	−	0.248224i	0.144126	−	0.00816598i
$925$	102.074	+	42.2803i	3.35616	+	1.39017i
$926$	−13.5197	−	3.62260i	−0.444286	−	0.119046i
$927$	1.74717	+	6.52054i	0.0573847	+	0.214163i
$928$	23.4502	−	17.9940i	0.769791	−	0.590681i
$929$	−9.63543	+	1.26853i	−0.316128	+	0.0416191i	−0.286921	−	0.957954i	$-0.592632\pi$
$929$	−9.63543	+	1.26853i	−0.316128	+	0.0416191i	−0.0292075	+	0.999573i	$0.509298\pi$
$930$	−23.0327	+	9.54044i	−0.755270	+	0.312843i
$931$	1.32542	−	8.85344i	0.0434390	−	0.290160i
$932$	−1.71531	−	4.14114i	−0.0561870	−	0.135647i
$933$	8.00119	−	29.8608i	0.261947	−	0.977600i
$934$	−2.99343	+	5.18477i	−0.0979479	+	0.169651i
$935$	−16.8455	+	12.4843i	−0.550908	+	0.408281i
$936$	−1.74424	−	3.02111i	−0.0570123	−	0.0987481i
$937$	28.1203	+	28.1203i	0.918650	+	0.918650i	0.996931	−	0.0782815i	$-0.0249433\pi$
$937$	28.1203	+	28.1203i	0.918650	+	0.918650i	−0.0782815	+	0.996931i	$0.524943\pi$
$938$	−2.38961	+	2.67666i	−0.0780236	+	0.0873960i
$939$			4.72769i			0.154282i
$940$	27.2929	+	20.9426i	0.890195	+	0.683071i
$941$	14.0272	+	18.2806i	0.457273	+	0.595930i	0.963910	−	0.266230i	$-0.0857780\pi$
$941$	14.0272	+	18.2806i	0.457273	+	0.595930i	−0.506636	+	0.862160i	$0.669111\pi$
$942$	2.18429	−	1.67606i	0.0711680	−	0.0546091i
$943$	−2.90230	−	0.777668i	−0.0945118	−	0.0253244i
$944$	−7.74162	+	7.74162i	−0.251968	+	0.251968i
$945$	−9.48552	+	6.21728i	−0.308564	+	0.202248i
$946$	−3.48760	+	8.41981i	−0.113392	+	0.273752i
$947$	24.2364	+	18.5972i	0.787576	+	0.604328i	0.922264	−	0.386560i	$-0.126337\pi$
$947$	24.2364	+	18.5972i	0.787576	+	0.604328i	−0.134689	+	0.990888i	$0.543003\pi$
$948$	4.09819	+	2.36609i	0.133103	+	0.0768470i
$949$	−11.1330	−	1.46569i	−0.361393	−	0.0475783i
$950$	−3.43489	+	12.8192i	−0.111442	+	0.415909i
$951$	−33.2201			−1.07724
$952$	−2.61394	+	28.6403i	−0.0847184	+	0.928238i
$953$	−35.4458			−1.14820			−0.574102	−	0.818784i	$-0.694649\pi$
$953$	−35.4458			−1.14820			−0.574102	+	0.818784i	$0.694649\pi$
$954$	−1.10325	+	4.11739i	−0.0357191	+	0.133306i
$955$	−27.0692	−	3.56372i	−0.875937	−	0.115319i
$956$	−5.87849	−	3.39395i	−0.190124	−	0.109768i
$957$	4.75121	+	3.64574i	0.153585	+	0.117850i
$958$	6.99454	−	16.8863i	0.225983	−	0.545572i
$959$	−37.7949	−	19.0561i	−1.22046	−	0.615354i
$960$	−9.21844	+	9.21844i	−0.297524	+	0.297524i
$961$	24.3326	+	6.51991i	0.784923	+	0.210320i
$962$	−6.72750	+	5.16219i	−0.216903	+	0.166436i
$963$	−7.32622	−	9.54771i	−0.236084	−	0.307671i
$964$	−23.2586	−	17.8469i	−0.749108	−	0.574811i
$965$		−	2.90277i		−	0.0934436i
$966$	1.56948	+	0.326658i	0.0504973	+	0.0105100i
$967$	−26.9810	−	26.9810i	−0.867649	−	0.867649i	0.124563	−	0.992212i	$-0.460247\pi$
$967$	−26.9810	−	26.9810i	−0.867649	−	0.867649i	−0.992212	+	0.124563i	$0.960247\pi$
$968$	−12.6449	−	21.9016i	−0.406422	−	0.703944i
$969$	5.11535	−	1.27942i	0.164329	−	0.0411008i
$970$	16.7481	−	29.0085i	0.537748	−	0.931407i
$971$	−2.94170	+	10.9786i	−0.0944037	+	0.352319i	−0.996928	−	0.0783188i	$-0.975045\pi$
$971$	−2.94170	+	10.9786i	−0.0944037	+	0.352319i	0.902525	+	0.430638i	$0.141711\pi$
$972$	0.535017	+	1.29165i	0.0171607	+	0.0414296i
$973$	−49.0416	+	23.6473i	−1.57220	+	0.758098i
$974$	7.67897	−	3.18073i	0.246050	−	0.101917i
$975$	17.5475	−	2.31017i	0.561969	−	0.0739846i
$976$	−4.44756	+	3.41273i	−0.142363	+	0.109239i
$977$	−9.74063	−	36.3525i	−0.311630	−	1.16302i	−0.927086	−	0.374849i	$-0.877695\pi$
$977$	−9.74063	−	36.3525i	−0.311630	−	1.16302i	0.615456	−	0.788172i	$-0.288972\pi$
$978$	−14.1909	−	3.80243i	−0.453774	−	0.121588i
$979$	11.2252	+	4.64962i	0.358758	+	0.148603i
$980$	20.3293	+	36.6967i	0.649396	+	1.17223i
$981$	−8.24981	+	3.41718i	−0.263396	+	0.109102i
$982$	8.10141	−	4.67735i	0.258527	−	0.149260i
$983$	−2.55860	−	0.336846i	−0.0816067	−	0.0107437i	0.0896122	−	0.995977i	$-0.471437\pi$
$983$	−2.55860	−	0.336846i	−0.0816067	−	0.0107437i	−0.171219	+	0.985233i	$0.554771\pi$
$984$	9.79728	−	2.62517i	0.312326	−	0.0836875i
$985$	19.7855	+	34.2694i	0.630418	+	1.09192i
$986$	−11.6081	+	11.2264i	−0.369678	+	0.357522i
$987$	6.59636	+	13.6800i	0.209964	+	0.435440i
$988$	1.67290	+	1.67290i	0.0532221	+	0.0532221i
$989$	4.70765	−	6.13513i	0.149695	−	0.195086i
$990$	−3.41684	−	1.97271i	−0.108594	−	0.0626969i
$991$	1.18978	−	9.03728i	0.0377946	−	0.287079i	−0.962102	−	0.272690i	$-0.912087\pi$
$991$	1.18978	−	9.03728i	0.0377946	−	0.287079i	0.999896	−	0.0143883i	$-0.00458011\pi$
$992$	43.5153	−	5.72890i	1.38161	−	0.181893i
$993$	21.4149	+	8.87034i	0.679581	+	0.281492i
$994$	−2.55826	−	13.4840i	−0.0811432	−	0.427686i
$995$	−22.2051	+	22.2051i	−0.703949	+	0.703949i
$996$	0.464390	+	3.52739i	0.0147148	+	0.111770i
$997$	6.23255	+	8.12242i	0.197387	+	0.257239i	0.881551	−	0.472088i	$-0.156500\pi$
$997$	6.23255	+	8.12242i	0.197387	+	0.257239i	−0.684164	+	0.729328i	$0.739833\pi$
$998$	−0.381745	+	2.89964i	−0.0120839	+	0.0917866i
$999$	7.15341	−	4.13002i	0.226324	−	0.130668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.151.15	yes	192
7.2	even	3	inner	357.2.bh.a.100.10	yes	192
17.8	even	8	inner	357.2.bh.a.25.10	✓	192
119.93	even	24	inner	357.2.bh.a.331.15	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.10	✓	192	17.8	even	8	inner
357.2.bh.a.100.10	yes	192	7.2	even	3	inner
357.2.bh.a.151.15	yes	192	1.1	even	1	trivial
357.2.bh.a.331.15	yes	192	119.93	even	24	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.200803 - 0.749407i) q^{2} +(0.991445 + 0.130526i) q^{3} +(1.21076 + 0.699034i) q^{4} +(-3.40086 - 2.60957i) q^{5} +(0.296902 - 0.716785i) q^{6} +(-0.149664 - 2.64151i) q^{7} +(1.86419 - 1.86419i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-2.63853 + 2.02461i) q^{10} +(0.722180 + 0.941163i) q^{11} +(1.10916 + 0.851090i) q^{12} -1.32321i q^{13} +(-2.00962 - 0.418265i) q^{14} +(-3.03114 - 3.03114i) q^{15} +(0.375365 + 0.650151i) q^{16} +(-2.45497 - 3.31257i) q^{17} +(0.387921 - 0.671900i) q^{18} +(-0.330997 + 1.23530i) q^{19} +(-2.29345 - 5.53688i) q^{20} +(0.196403 - 2.63845i) q^{21} +(0.850330 - 0.352218i) q^{22} +(-0.774302 + 0.101939i) q^{23} +(2.09157 - 1.60492i) q^{24} +(3.46188 + 12.9199i) q^{25} +(-0.991626 - 0.265705i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.66530 - 3.30287i) q^{28} +(4.66396 - 1.93188i) q^{29} +(-2.88022 + 1.66290i) q^{30} +(7.43193 + 0.978433i) q^{31} +(5.65567 - 1.51543i) q^{32} +(0.593155 + 1.02737i) q^{33} +(-2.97543 + 1.17459i) q^{34} +(-6.38423 + 9.37397i) q^{35} +(0.988583 + 0.988583i) q^{36} +(5.02840 - 6.55314i) q^{37} +(0.859274 + 0.496102i) q^{38} +(0.172714 - 1.31189i) q^{39} +(-11.2046 + 1.47511i) q^{40} +(3.55444 + 1.47230i) q^{41} +(-1.93783 - 0.676995i) q^{42} +(-7.00164 + 7.00164i) q^{43} +(0.216483 + 1.64435i) q^{44} +(-2.60957 - 3.40086i) q^{45} +(-0.0790885 + 0.600737i) q^{46} +(-4.97122 + 2.87014i) q^{47} +(0.287292 + 0.693583i) q^{48} +(-6.95520 + 0.790680i) q^{49} +10.3774 q^{50} +(-2.00159 - 3.60467i) q^{51} +(0.924972 - 1.60210i) q^{52} +(-5.30700 + 1.42201i) q^{53} +(0.472303 - 0.615518i) q^{54} -5.08534i q^{55} +(-5.20330 - 4.64529i) q^{56} +(-0.489403 + 1.18152i) q^{57} +(-0.511224 - 3.88313i) q^{58} +(3.77450 + 14.0866i) q^{59} +(-1.55112 - 5.78887i) q^{60} +(0.974697 + 7.40356i) q^{61} +(2.22560 - 5.37307i) q^{62} +(0.539110 - 2.59024i) q^{63} -3.04124i q^{64} +(-3.45302 + 4.50006i) q^{65} +(0.889029 - 0.238214i) q^{66} +(0.874010 - 1.51383i) q^{67} +(-0.656780 - 5.72684i) q^{68} -0.780984 q^{69} +(5.74294 + 6.66670i) q^{70} +(2.55867 + 6.17717i) q^{71} +(2.28316 - 1.31818i) q^{72} +(1.10767 - 8.41361i) q^{73} +(-3.90125 - 5.08421i) q^{74} +(1.74587 + 13.2612i) q^{75} +(-1.26427 + 1.26427i) q^{76} +(2.37801 - 2.04851i) q^{77} +(-0.948461 - 0.392865i) q^{78} +(3.35584 - 0.441805i) q^{79} +(0.420051 - 3.19061i) q^{80} +(0.866025 + 0.500000i) q^{81} +(1.81709 - 2.36808i) q^{82} +(1.79946 + 1.79946i) q^{83} +(2.08216 - 3.05724i) q^{84} +(-0.295398 + 17.6720i) q^{85} +(3.84113 + 6.65303i) q^{86} +(4.87622 - 1.30658i) q^{87} +(3.10079 + 0.408227i) q^{88} +(8.86973 - 5.12094i) q^{89} +(-3.07263 + 1.27273i) q^{90} +(-3.49529 + 0.198038i) q^{91} +(-1.00875 - 0.417840i) q^{92} +(7.24064 + 1.94012i) q^{93} +(1.15266 + 4.30180i) q^{94} +(4.34926 - 3.33731i) q^{95} +(5.80509 - 0.764255i) q^{96} +(-9.30496 + 3.85424i) q^{97} +(-0.804084 + 5.37105i) q^{98} +(0.453981 + 1.09601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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