LMFDB - Embedded newform 504.2.cz.b.187.70

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.70
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.70

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07381 - 0.920287i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(0.306143 - 1.97643i) q^{4} -4.13478 q^{5} +(1.61332 + 1.84315i) q^{6} +(1.26742 - 2.32242i) q^{7} +(-1.49014 - 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +O(q^{10})$	\(q+(1.07381 - 0.920287i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(0.306143 - 1.97643i) q^{4} -4.13478 q^{5} +(1.61332 + 1.84315i) q^{6} +(1.26742 - 2.32242i) q^{7} +(-1.49014 - 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +(-4.43997 + 3.80518i) q^{10} -4.32492 q^{11} +(3.42863 + 0.494476i) q^{12} +(-0.641757 - 1.11156i) q^{13} +(-0.776322 - 3.66024i) q^{14} +(-0.0747925 - 7.16125i) q^{15} +(-3.81255 - 1.21014i) q^{16} +(-2.26685 + 1.30876i) q^{17} +(-3.16307 + 2.82754i) q^{18} +(1.98530 + 1.14621i) q^{19} +(-1.26583 + 8.17210i) q^{20} +(4.04526 + 2.15311i) q^{21} +(-4.64415 + 3.98017i) q^{22} -9.07493i q^{23} +(4.13676 - 2.62435i) q^{24} +12.0964 q^{25} +(-1.71208 - 0.603001i) q^{26} +(-0.162774 - 5.19360i) q^{27} +(-4.20209 - 3.21596i) q^{28} +(1.34755 + 0.778011i) q^{29} +(-6.67072 - 7.62100i) q^{30} +(-3.20286 + 5.54751i) q^{31} +(-5.20764 + 2.20918i) q^{32} +(-0.0782320 - 7.49058i) q^{33} +(-1.22973 + 3.49152i) q^{34} +(-5.24051 + 9.60269i) q^{35} +(-0.794391 + 5.94718i) q^{36} +(-3.81526 - 2.20274i) q^{37} +(3.18668 - 0.596228i) q^{38} +(1.91356 - 1.13160i) q^{39} +(6.16141 + 9.94022i) q^{40} +(0.171501 - 0.0990159i) q^{41} +(6.32533 - 1.41076i) q^{42} +(-1.95206 + 3.38106i) q^{43} +(-1.32405 + 8.54791i) q^{44} +(12.4016 - 0.259075i) q^{45} +(-8.35154 - 9.74477i) q^{46} +(1.57995 + 2.73655i) q^{47} +(2.02695 - 6.62506i) q^{48} +(-3.78728 - 5.88698i) q^{49} +(12.9892 - 11.1321i) q^{50} +(-2.30773 - 3.90241i) q^{51} +(-2.39338 + 0.928093i) q^{52} +(4.24135 - 2.44875i) q^{53} +(-4.95439 - 5.42715i) q^{54} +17.8826 q^{55} +(-7.47187 + 0.413790i) q^{56} +(-1.94928 + 3.45918i) q^{57} +(2.16301 - 0.404700i) q^{58} +(4.47816 + 2.58546i) q^{59} +(-14.1766 - 2.04455i) q^{60} +(-4.40409 - 7.62810i) q^{61} +(1.66604 + 8.90453i) q^{62} +(-3.65592 + 7.04516i) q^{63} +(-3.55895 + 7.16477i) q^{64} +(2.65352 + 4.59603i) q^{65} +(-6.97749 - 7.97147i) q^{66} +(1.06600 - 1.84636i) q^{67} +(1.89270 + 4.88093i) q^{68} +(15.7174 - 0.164153i) q^{69} +(3.20992 + 15.1343i) q^{70} +4.81184i q^{71} +(4.62009 + 7.11722i) q^{72} +(10.0900 - 5.82545i) q^{73} +(-6.12403 + 1.14581i) q^{74} +(0.218807 + 20.9504i) q^{75} +(2.87320 - 3.57290i) q^{76} +(-5.48150 + 10.0443i) q^{77} +(1.01340 - 2.97615i) q^{78} +(-7.50245 + 4.33154i) q^{79} +(15.7640 + 5.00366i) q^{80} +(8.99215 - 0.375863i) q^{81} +(0.0930362 - 0.264154i) q^{82} +(-4.89916 - 2.82853i) q^{83} +(5.49390 - 7.33601i) q^{84} +(9.37290 - 5.41145i) q^{85} +(1.01541 + 5.42707i) q^{86} +(-1.32311 + 2.34798i) q^{87} +(6.44475 + 10.3973i) q^{88} +(7.48220 + 4.31985i) q^{89} +(13.0786 - 11.6912i) q^{90} +(-3.39488 + 0.0816202i) q^{91} +(-17.9360 - 2.77823i) q^{92} +(-9.66598 - 5.44686i) q^{93} +(4.21498 + 1.48453i) q^{94} +(-8.20876 - 4.73933i) q^{95} +(-3.92040 - 8.97945i) q^{96} +(-5.28964 - 3.05398i) q^{97} +(-9.48454 - 2.83612i) q^{98} +(12.9719 - 0.270989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.07381	−	0.920287i	0.759300	−	0.650741i
$2$	1.07381	−	0.920287i	0.759300	−	0.650741i
$3$	0.0180886	+	1.73196i	0.0104435	+	0.999945i
$3$	0.0180886	+	1.73196i	0.0104435	+	0.999945i
$4$	0.306143	−	1.97643i	0.153072	−	0.988215i
$5$	−4.13478			−1.84913			−0.924564	−	0.381027i	$-0.875571\pi$
$5$	−4.13478			−1.84913			−0.924564	+	0.381027i	$0.875571\pi$
$6$	1.61332	+	1.84315i	0.658636	+	0.752462i
$7$	1.26742	−	2.32242i	0.479040	−	0.877793i
$7$	1.26742	−	2.32242i	0.479040	−	0.877793i
$8$	−1.49014	−	2.40405i	−0.526845	−	0.849961i
$9$	−2.99935	+	0.0626575i	−0.999782	+	0.0208858i
$10$	−4.43997	+	3.80518i	−1.40404	+	1.20330i
$11$	−4.32492			−1.30401			−0.652007	−	0.758213i	$-0.726073\pi$
$11$	−4.32492			−1.30401			−0.652007	+	0.758213i	$0.726073\pi$
$12$	3.42863	+	0.494476i	0.989760	+	0.142743i
$13$	−0.641757	−	1.11156i	−0.177991	−	0.308290i	0.763201	−	0.646161i	$-0.223627\pi$
$13$	−0.641757	−	1.11156i	−0.177991	−	0.308290i	−0.941192	+	0.337871i	$0.890293\pi$
$14$	−0.776322	−	3.66024i	−0.207481	−	0.978239i
$15$	−0.0747925	−	7.16125i	−0.0193113	−	1.84903i
$16$	−3.81255	−	1.21014i	−0.953138	−	0.302535i
$17$	−2.26685	+	1.30876i	−0.549791	+	0.317422i	−0.749038	−	0.662527i	$-0.769484\pi$
$17$	−2.26685	+	1.30876i	−0.549791	+	0.317422i	0.199247	+	0.979949i	$0.436151\pi$
$18$	−3.16307	+	2.82754i	−0.745543	+	0.666458i
$19$	1.98530	+	1.14621i	0.455459	+	0.262959i	0.710133	−	0.704068i	$-0.248635\pi$
$19$	1.98530	+	1.14621i	0.455459	+	0.262959i	−0.254674	+	0.967027i	$0.581968\pi$
$20$	−1.26583	+	8.17210i	−0.283049	+	1.82734i
$21$	4.04526	+	2.15311i	0.882748	+	0.469847i
$22$	−4.64415	+	3.98017i	−0.990137	+	0.848575i
$23$		−	9.07493i		−	1.89225i	−0.323796	−	0.946127i	$-0.604959\pi$
$23$		−	9.07493i		−	1.89225i	0.323796	−	0.946127i	$-0.395041\pi$
$24$	4.13676	−	2.62435i	0.844413	−	0.535693i
$25$	12.0964			2.41927
$26$	−1.71208	−	0.603001i	−0.335766	−	0.118258i
$27$	−0.162774	−	5.19360i	−0.0313259	−	0.999509i
$28$	−4.20209	−	3.21596i	−0.794121	−	0.607760i
$29$	1.34755	+	0.778011i	0.250235	+	0.144473i	0.619872	−	0.784703i	$-0.287185\pi$
$29$	1.34755	+	0.778011i	0.250235	+	0.144473i	−0.369637	+	0.929176i	$0.620518\pi$
$30$	−6.67072	−	7.62100i	−1.21790	−	1.39140i
$31$	−3.20286	+	5.54751i	−0.575250	+	0.996363i	0.420764	+	0.907170i	$0.361762\pi$
$31$	−3.20286	+	5.54751i	−0.575250	+	0.996363i	−0.996014	+	0.0891925i	$0.971571\pi$
$32$	−5.20764	+	2.20918i	−0.920590	+	0.390531i
$33$	−0.0782320	−	7.49058i	−0.0136184	−	1.30394i
$34$	−1.22973	+	3.49152i	−0.210897	+	0.598790i
$35$	−5.24051	+	9.60269i	−0.885807	+	1.62315i
$36$	−0.794391	+	5.94718i	−0.132399	+	0.991197i
$37$	−3.81526	−	2.20274i	−0.627225	−	0.362129i	0.152452	−	0.988311i	$-0.451283\pi$
$37$	−3.81526	−	2.20274i	−0.627225	−	0.362129i	−0.779677	+	0.626182i	$0.784617\pi$
$38$	3.18668	−	0.596228i	0.516948	−	0.0967210i
$39$	1.91356	−	1.13160i	0.306414	−	0.181201i
$40$	6.16141	+	9.94022i	0.974204	+	1.57169i
$41$	0.171501	−	0.0990159i	0.0267839	−	0.0154637i	−0.486548	−	0.873654i	$-0.661744\pi$
$41$	0.171501	−	0.0990159i	0.0267839	−	0.0154637i	0.513332	+	0.858190i	$0.328411\pi$
$42$	6.32533	−	1.41076i	0.976019	−	0.217686i
$43$	−1.95206	+	3.38106i	−0.297686	+	0.515607i	−0.975606	−	0.219529i	$-0.929548\pi$
$43$	−1.95206	+	3.38106i	−0.297686	+	0.515607i	0.677920	+	0.735135i	$0.262881\pi$
$44$	−1.32405	+	8.54791i	−0.199607	+	1.28865i
$45$	12.4016	−	0.259075i	1.84872	−	0.0386206i
$46$	−8.35154	−	9.74477i	−1.23137	−	1.43679i
$47$	1.57995	+	2.73655i	0.230459	+	0.399167i	0.957943	−	0.286958i	$-0.0926439\pi$
$47$	1.57995	+	2.73655i	0.230459	+	0.399167i	−0.727484	+	0.686124i	$0.759311\pi$
$48$	2.02695	−	6.62506i	0.292565	−	0.956246i
$49$	−3.78728	−	5.88698i	−0.541040	−	0.840997i
$50$	12.9892	−	11.1321i	1.83695	−	1.57432i
$51$	−2.30773	−	3.90241i	−0.323147	−	0.546446i
$52$	−2.39338	+	0.928093i	−0.331902	+	0.128703i
$53$	4.24135	−	2.44875i	0.582594	−	0.336361i	−0.179569	−	0.983745i	$-0.557470\pi$
$53$	4.24135	−	2.44875i	0.582594	−	0.336361i	0.762164	+	0.647384i	$0.224137\pi$
$54$	−4.95439	−	5.42715i	−0.674208	−	0.738542i
$55$	17.8826			2.41129
$56$	−7.47187	+	0.413790i	−0.998470	+	0.0552950i
$57$	−1.94928	+	3.45918i	−0.258188	+	0.458180i
$58$	2.16301	−	0.404700i	0.284017	−	0.0531397i
$59$	4.47816	+	2.58546i	0.583006	+	0.336599i	0.762327	−	0.647192i	$-0.224057\pi$
$59$	4.47816	+	2.58546i	0.583006	+	0.336599i	−0.179321	+	0.983791i	$0.557390\pi$
$60$	−14.1766	−	2.04455i	−1.83019	−	0.263950i
$61$	−4.40409	−	7.62810i	−0.563886	−	0.976679i	−0.997152	−	0.0754128i	$-0.975973\pi$
$61$	−4.40409	−	7.62810i	−0.563886	−	0.976679i	0.433267	−	0.901266i	$-0.357361\pi$
$62$	1.66604	+	8.90453i	0.211587	+	1.13088i
$63$	−3.65592	+	7.04516i	−0.460603	+	0.887607i
$64$	−3.55895	+	7.16477i	−0.444868	+	0.895596i
$65$	2.65352	+	4.59603i	0.329129	+	0.570068i
$66$	−6.97749	−	7.97147i	−0.858869	−	0.981221i
$67$	1.06600	−	1.84636i	0.130232	−	0.225569i	−0.793534	−	0.608526i	$-0.791761\pi$
$67$	1.06600	−	1.84636i	0.130232	−	0.225569i	0.923766	+	0.382957i	$0.125094\pi$
$68$	1.89270	+	4.88093i	0.229524	+	0.591900i
$69$	15.7174	−	0.164153i	1.89215	−	0.0197617i
$70$	3.20992	+	15.1343i	0.383659	+	1.80889i
$71$			4.81184i			0.571060i	0.958370	+	0.285530i	$0.0921696\pi$
$71$			4.81184i			0.571060i	−0.958370	+	0.285530i	$0.907830\pi$
$72$	4.62009	+	7.11722i	0.544482	+	0.838772i
$73$	10.0900	−	5.82545i	1.18094	−	0.681817i	0.224710	−	0.974426i	$-0.427857\pi$
$73$	10.0900	−	5.82545i	1.18094	−	0.681817i	0.956232	+	0.292609i	$0.0945233\pi$
$74$	−6.12403	+	1.14581i	−0.711904	+	0.133197i
$75$	0.218807	+	20.9504i	0.0252656	+	2.41914i
$76$	2.87320	−	3.57290i	0.329578	−	0.409840i
$77$	−5.48150	+	10.0443i	−0.624675	+	1.14465i
$78$	1.01340	−	2.97615i	0.114745	−	0.336983i
$79$	−7.50245	+	4.33154i	−0.844091	+	0.487336i	−0.858653	−	0.512558i	$-0.828698\pi$
$79$	−7.50245	+	4.33154i	−0.844091	+	0.487336i	0.0145616	+	0.999894i	$0.495365\pi$
$80$	15.7640	+	5.00366i	1.76247	+	0.559427i
$81$	8.99215	−	0.375863i	0.999128	−	0.0417625i
$82$	0.0930362	−	0.264154i	0.0102741	−	0.0291709i
$83$	−4.89916	−	2.82853i	−0.537753	−	0.310472i	0.206415	−	0.978465i	$-0.433820\pi$
$83$	−4.89916	−	2.82853i	−0.537753	−	0.310472i	−0.744168	+	0.667993i	$0.767154\pi$
$84$	5.49390	−	7.33601i	0.599434	−	0.800424i
$85$	9.37290	−	5.41145i	1.01663	−	0.586954i
$86$	1.01541	+	5.42707i	0.109494	+	0.585216i
$87$	−1.32311	+	2.34798i	−0.141852	+	0.251730i
$88$	6.44475	+	10.3973i	0.687013	+	1.10836i
$89$	7.48220	+	4.31985i	0.793111	+	0.457903i	0.841057	−	0.540947i	$-0.181934\pi$
$89$	7.48220	+	4.31985i	0.793111	+	0.457903i	−0.0479453	+	0.998850i	$0.515267\pi$
$90$	13.0786	−	11.6912i	1.37860	−	1.23237i
$91$	−3.39488	+	0.0816202i	−0.355880	+	0.00855612i
$92$	−17.9360	−	2.77823i	−1.86995	−	0.289650i
$93$	−9.66598	−	5.44686i	−1.00232	−	0.564813i
$94$	4.21498	+	1.48453i	0.434742	+	0.153118i
$95$	−8.20876	−	4.73933i	−0.842202	−	0.486245i
$96$	−3.92040	−	8.97945i	−0.400124	−	0.916461i
$97$	−5.28964	−	3.05398i	−0.537082	−	0.310084i	0.206814	−	0.978380i	$-0.433691\pi$
$97$	−5.28964	−	3.05398i	−0.537082	−	0.310084i	−0.743895	+	0.668296i	$0.767024\pi$
$98$	−9.48454	−	2.83612i	−0.958083	−	0.286491i
$99$	12.9719	−	0.270989i	1.30373	−	0.0272354i
$100$	3.70322	−	23.9076i	0.370322	−	2.39076i
$101$	1.77444			0.176563			0.0882816	−	0.996096i	$-0.471862\pi$
$101$	1.77444			0.176563			0.0882816	+	0.996096i	$0.471862\pi$
$102$	−6.06940	−	2.06668i	−0.600960	−	0.204632i
$103$	−13.0004			−1.28097			−0.640483	−	0.767972i	$-0.721266\pi$
$103$	−13.0004			−1.28097			−0.640483	+	0.767972i	$0.721266\pi$
$104$	−1.71593	+	3.19920i	−0.168261	+	0.313707i
$105$	−16.7262	−	8.90263i	−1.63231	−	0.868807i
$106$	2.30086	−	6.53275i	0.223480	−	0.634517i
$107$	2.20389	−	3.81725i	0.213058	−	0.369027i	−0.739612	−	0.673034i	$-0.764991\pi$
$107$	2.20389	−	3.81725i	0.213058	−	0.369027i	0.952670	+	0.304006i	$0.0983243\pi$
$108$	−10.3146	−	1.26827i	−0.992525	−	0.122040i
$109$	9.98683	−	5.76590i	0.956565	−	0.552273i	0.0614507	−	0.998110i	$-0.480427\pi$
$109$	9.98683	−	5.76590i	0.956565	−	0.552273i	0.895114	+	0.445837i	$0.147094\pi$
$110$	19.2025	−	16.4571i	1.83089	−	1.56912i
$111$	3.74604	−	6.64771i	0.355558	−	0.630973i
$112$	−7.64257	+	7.32059i	−0.722155	+	0.691731i
$113$	−4.45447	−	7.71536i	−0.419041	−	0.725800i	0.576802	−	0.816884i	$-0.304300\pi$
$113$	−4.45447	−	7.71536i	−0.419041	−	0.725800i	−0.995843	+	0.0910836i	$0.970967\pi$
$114$	1.09028	+	5.50841i	0.102114	+	0.515910i
$115$			37.5228i			3.49902i
$116$	1.95023	−	2.42516i	0.181074	−	0.225171i
$117$	1.99450	+	3.29373i	0.184391	+	0.304505i
$118$	7.18807	−	1.34489i	0.661715	−	0.123807i
$119$	0.166452	+	6.92333i	0.0152586	+	0.634661i
$120$	−17.1046	+	10.8511i	−1.56143	+	0.990565i
$121$	7.70496			0.700451
$122$	−11.7492	−	4.13812i	−1.06372	−	0.374648i
$123$	0.174593	+	0.295240i	0.0157426	+	0.0266209i
$124$	9.98374	+	8.02856i	0.896566	+	0.720986i
$125$	−29.3419			−2.62442
$126$	2.55780	+	10.9297i	0.227867	+	0.973692i
$127$			1.69119i			0.150069i	0.997181	+	0.0750343i	$0.0239066\pi$
$127$			1.69119i			0.150069i	−0.997181	+	0.0750343i	$0.976093\pi$
$128$	2.77200	+	10.9689i	0.245013	+	0.969520i
$129$	−5.89116	−	3.31972i	−0.518688	−	0.292285i
$130$	7.07905	+	2.49327i	0.620874	+	0.218675i
$131$		−	17.6471i		−	1.54184i	−0.636933	−	0.770919i	$-0.719797\pi$
$131$		−	17.6471i		−	1.54184i	0.636933	−	0.770919i	$-0.280203\pi$
$132$	−14.8286	−	2.13857i	−1.29066	−	0.186139i
$133$	5.17820	−	3.15797i	0.449007	−	0.273830i
$134$	−0.554501	−	2.96366i	−0.0479016	−	0.256021i
$135$	0.673035	+	21.4744i	0.0579256	+	1.84822i
$136$	6.52427	+	3.49938i	0.559451	+	0.300069i
$137$	3.18383			0.272013			0.136006	−	0.990708i	$-0.456573\pi$
$137$	3.18383			0.272013			0.136006	+	0.990708i	$0.456573\pi$
$138$	16.7264	−	14.6408i	1.42385	−	1.24631i
$139$	−14.1864	+	8.19051i	−1.20327	+	0.694710i	−0.961281	−	0.275568i	$-0.911134\pi$
$139$	−14.1864	+	8.19051i	−1.20327	+	0.694710i	−0.241991	+	0.970278i	$0.577801\pi$
$140$	17.3747	+	13.2973i	1.46843	+	1.12383i
$141$	−4.71101	+	2.78590i	−0.396738	+	0.234615i
$142$	4.42827	+	5.16701i	0.371612	+	0.433605i
$143$	2.77555	+	4.80739i	0.232103	+	0.402014i
$144$	11.5110	+	3.39075i	0.959249	+	0.282562i
$145$	−5.57183	−	3.21690i	−0.462716	−	0.267149i
$146$	5.47365	−	15.5411i	0.453002	−	1.28619i
$147$	10.1275	−	6.66590i	0.835300	−	0.549794i
$148$	−5.52158	+	6.86624i	−0.453871	+	0.564402i
$149$		−	5.87943i		−	0.481662i	−0.970567	−	0.240831i	$-0.922580\pi$
$149$		−	5.87943i		−	0.481662i	0.970567	−	0.240831i	$-0.0774199\pi$
$150$	19.5153	+	22.2954i	1.59342	+	1.82041i
$151$		−	10.3821i		−	0.844882i	−0.906390	−	0.422441i	$-0.861173\pi$
$151$		−	10.3821i		−	0.844882i	0.906390	−	0.422441i	$-0.138827\pi$
$152$	−0.202822	−	6.48079i	−0.0164511	−	0.525661i
$153$	6.71705	−	4.06747i	0.543042	−	0.328836i
$154$	3.35753	+	15.8302i	0.270558	+	1.27564i
$155$	13.2431	−	22.9377i	1.06371	−	1.84240i
$156$	−1.65071	−	4.12844i	−0.132162	−	0.330540i
$157$	−4.88984	+	8.46946i	−0.390252	+	0.675936i	−0.992483	−	0.122386i	$-0.960945\pi$
$157$	−4.88984	+	8.46946i	−0.390252	+	0.675936i	0.602231	+	0.798322i	$0.294279\pi$
$158$	−4.06995	+	11.5557i	−0.323788	+	0.919319i
$159$	4.31784	+	7.30154i	0.342427	+	0.579050i
$160$	21.5324	−	9.13446i	1.70229	−	0.722142i
$161$	−21.0758	−	11.5018i	−1.66101	−	0.906466i
$162$	9.30997	−	8.67896i	0.731460	−	0.681884i
$163$	6.46593	−	11.1993i	0.506451	−	0.877198i	−0.493522	−	0.869734i	$-0.664291\pi$
$163$	6.46593	−	11.1993i	0.506451	−	0.877198i	0.999972	−	0.00746457i	$-0.00237607\pi$
$164$	−0.143194	−	0.369272i	−0.0111816	−	0.0288353i
$165$	0.323472	+	30.9719i	0.0251822	+	2.41116i
$166$	−7.86384	+	1.47132i	−0.610352	+	0.114197i
$167$	−6.76297	−	11.7138i	−0.523335	−	0.906442i	−0.999631	−	0.0271574i	$-0.991354\pi$
$167$	−6.76297	−	11.7138i	−0.523335	−	0.906442i	0.476297	−	0.879285i	$-0.341979\pi$
$168$	−0.851823	−	12.9335i	−0.0657195	−	0.997838i
$169$	5.67630	−	9.83163i	0.436638	−	0.756279i
$170$	5.08465	−	14.4366i	0.389975	−	1.10724i
$171$	−6.02642	−	3.31349i	−0.460852	−	0.253389i
$172$	6.08482	+	4.89319i	0.463963	+	0.373102i
$173$	−5.43617	−	9.41572i	−0.413304	−	0.715864i	0.581945	−	0.813228i	$-0.302292\pi$
$173$	−5.43617	−	9.41572i	−0.413304	−	0.715864i	−0.995249	+	0.0973647i	$0.968959\pi$
$174$	0.740048	+	3.73892i	0.0561029	+	0.283447i
$175$	15.3312	−	28.0929i	1.15893	−	2.12362i
$176$	16.4890	+	5.23377i	1.24290	+	0.394510i
$177$	−4.39691	+	7.80274i	−0.330492	+	0.586490i
$178$	12.0100	−	2.24707i	0.900186	−	0.168425i
$179$	0.0546462	+	0.0946501i	0.00408445	+	0.00707448i	0.868060	−	0.496459i	$-0.165367\pi$
$179$	0.0546462	+	0.0946501i	0.00408445	+	0.00707448i	−0.863976	+	0.503533i	$0.832033\pi$
$180$	3.28463	−	24.5903i	0.244822	−	1.83285i
$181$	6.95290			0.516805			0.258402	−	0.966037i	$-0.416804\pi$
$181$	6.95290			0.516805			0.258402	+	0.966037i	$0.416804\pi$
$182$	−3.57035	+	3.21191i	−0.264652	+	0.238082i
$183$	13.1319	−	7.76567i	0.970736	−	0.574055i
$184$	−21.8166	+	13.5229i	−1.60834	+	0.996925i
$185$	15.7752	+	9.10784i	1.15982	+	0.669622i
$186$	−15.3921	+	3.04658i	−1.12861	+	0.223386i
$187$	9.80394	−	5.66031i	0.716935	−	0.413923i
$188$	5.89229	−	2.28488i	0.429740	−	0.166642i
$189$	−12.2680	−	6.20446i	−0.892368	−	0.451308i
$190$	−13.1762	+	2.46527i	−0.955903	+	0.178849i
$191$	−17.3398	+	10.0111i	−1.25466	+	0.724380i	−0.972032	−	0.234849i	$-0.924540\pi$
$191$	−17.3398	+	10.0111i	−1.25466	+	0.724380i	−0.282631	+	0.959229i	$0.591207\pi$
$192$	−12.4734	−	6.03434i	−0.900193	−	0.435491i
$193$	2.13070	−	3.69047i	0.153371	−	0.265646i	−0.779094	−	0.626907i	$-0.784320\pi$
$193$	2.13070	−	3.69047i	0.153371	−	0.265646i	0.932465	+	0.361261i	$0.117654\pi$
$194$	−8.49061	+	1.58859i	−0.609590	+	0.114054i
$195$	−7.91213	+	4.67892i	−0.566599	+	0.335064i
$196$	−12.7946	+	5.68304i	−0.913903	+	0.405932i
$197$			9.24136i			0.658420i	0.944257	+	0.329210i	$0.106782\pi$
$197$			9.24136i			0.658420i	−0.944257	+	0.329210i	$0.893218\pi$
$198$	13.6800	−	12.2289i	0.972198	−	0.869070i
$199$	−11.3696	−	19.6928i	−0.805971	−	1.39598i	−0.915633	−	0.402014i	$-0.868310\pi$
$199$	−11.3696	−	19.6928i	−0.805971	−	1.39598i	0.109662	−	0.993969i	$-0.465023\pi$
$200$	−18.0253	−	29.0803i	−1.27458	−	2.05629i
$201$	3.21709	+	1.81286i	0.226916	+	0.127869i
$202$	1.90541	−	1.63299i	0.134064	−	0.114897i
$203$	3.51479	−	2.14352i	0.246690	−	0.150446i
$204$	−8.41933	+	3.36637i	−0.589471	+	0.235693i
$205$	−0.709116	+	0.409408i	−0.0495268	+	0.0285943i
$206$	−13.9600	+	11.9641i	−0.972637	+	0.833577i
$207$	0.568612	+	27.2188i	0.0395213	+	1.89184i
$208$	1.10159	+	5.01448i	0.0763817	+	0.347692i
$209$	−8.58626	−	4.95728i	−0.593924	−	0.342902i
$210$	−26.1538	+	5.83320i	−1.80478	+	0.402529i
$211$	6.35436	+	11.0061i	0.437452	+	0.757689i	0.997492	−	0.0707762i	$-0.0225476\pi$
$211$	6.35436	+	11.0061i	0.437452	+	0.757689i	−0.560040	+	0.828466i	$0.689214\pi$
$212$	−3.54131	−	9.13240i	−0.243218	−	0.627216i
$213$	−8.33389	+	0.0870396i	−0.571029	+	0.00596386i
$214$	−1.14640	−	6.12722i	−0.0783665	−	0.418848i
$215$	8.07131	−	13.9799i	0.550459	−	0.953423i
$216$	−12.2431	+	8.13053i	−0.833040	+	0.553212i
$217$	8.82429	+	14.4694i	0.599032	+	0.982248i
$218$	5.41769	−	15.3822i	0.366932	−	1.04182i
$219$	10.2719	+	17.3700i	0.694113	+	1.17376i
$220$	5.47463	−	35.3437i	0.369100	−	2.38287i
$221$	2.90953	+	1.67982i	0.195716	+	0.112997i
$222$	−2.09526	−	10.5858i	−0.140625	−	0.710474i
$223$	−8.50455	+	14.7303i	−0.569507	+	0.986414i	0.427108	+	0.904201i	$0.359532\pi$
$223$	−8.50455	+	14.7303i	−0.569507	+	0.986414i	−0.996615	+	0.0822138i	$0.973801\pi$
$224$	−1.46963	+	14.8943i	−0.0981940	+	0.995167i
$225$	−36.2812	+	0.757928i	−2.41875	+	0.0505285i
$226$	−11.8836	−	4.18546i	−0.790486	−	0.278413i
$227$			10.9658i			0.727825i	0.931433	+	0.363912i	$0.118559\pi$
$227$			10.9658i			0.727825i	−0.931433	+	0.363912i	$0.881441\pi$
$228$	6.24008	+	4.91162i	0.413259	+	0.325280i
$229$	−6.00658			−0.396926			−0.198463	−	0.980108i	$-0.563595\pi$
$229$	−6.00658			−0.396926			−0.198463	+	0.980108i	$0.563595\pi$
$230$	34.5317	+	40.2924i	2.27696	+	2.65680i
$231$	−17.4954	−	9.31203i	−1.15111	−	0.612687i
$232$	−0.137669	−	4.39894i	−0.00903841	−	0.288805i
$233$	14.4408	−	25.0122i	0.946047	−	1.63860i	0.192404	−	0.981316i	$-0.438371\pi$
$233$	14.4408	−	25.0122i	0.946047	−	1.63860i	0.753642	−	0.657285i	$-0.228295\pi$
$234$	5.17289	+	1.70133i	0.338163	+	0.111220i
$235$	−6.53273	−	11.3150i	−0.426148	−	0.738111i
$236$	6.48095	−	8.05924i	0.421874	−	0.524612i
$237$	−7.63775	−	12.9156i	−0.496125	−	0.838956i
$238$	6.55019	+	7.28117i	0.424586	+	0.471968i
$239$	−1.47156	+	0.849605i	−0.0951872	+	0.0549564i	−0.546838	−	0.837238i	$-0.684169\pi$
$239$	−1.47156	+	0.849605i	−0.0951872	+	0.0549564i	0.451651	+	0.892195i	$0.350835\pi$
$240$	−8.38098	+	27.3932i	−0.540990	+	1.76822i
$241$		−	21.0026i		−	1.35290i	−0.736490	−	0.676448i	$-0.763518\pi$
$241$		−	21.0026i		−	1.35290i	0.736490	−	0.676448i	$-0.236482\pi$
$242$	8.27367	−	7.09077i	0.531852	−	0.455812i
$243$	0.813634	+	15.5672i	0.0521946	+	0.998637i
$244$	−16.4247	+	6.36908i	−1.05148	+	0.407739i
$245$	15.6596	+	24.3413i	1.00045	+	1.55511i
$246$	0.459186	+	0.156357i	0.0292766	+	0.00996893i
$247$		−	2.94236i		−	0.187218i
$248$	18.1092	−	0.566746i	1.14994	−	0.0359884i
$249$	4.81028	−	8.53630i	0.304839	−	0.540966i
$250$	−31.5077	+	27.0030i	−1.99272	+	1.70782i
$251$		−	6.69266i		−	0.422437i	−0.977439	−	0.211219i	$-0.932257\pi$
$251$		−	6.69266i		−	0.422437i	0.977439	−	0.211219i	$-0.0677432\pi$
$252$	12.8050	+	9.38250i	0.806641	+	0.591042i
$253$			39.2484i			2.46752i
$254$	1.55638	+	1.81602i	0.0976558	+	0.113947i
$255$	9.54194	+	16.1356i	0.597539	+	1.01045i
$256$	13.0711	+	9.22746i	0.816945	+	0.576716i
$257$			24.4467i			1.52494i	0.647022	+	0.762471i	$0.276014\pi$
$257$			24.4467i			1.52494i	−0.647022	+	0.762471i	$0.723986\pi$
$258$	−9.38109	+	1.85681i	−0.584041	+	0.115600i
$259$	−9.95124	+	6.06884i	−0.618340	+	0.377099i
$260$	9.89610	−	3.83745i	0.613730	−	0.237989i
$261$	−4.09053	−	2.24909i	−0.253197	−	0.139215i
$262$	−16.2404	−	18.9497i	−1.00334	−	1.17072i
$263$			2.47949i			0.152892i	0.997074	+	0.0764458i	$0.0243572\pi$
$263$			2.47949i			0.152892i	−0.997074	+	0.0764458i	$0.975643\pi$
$264$	−17.8912	+	11.3501i	−1.10113	+	0.698551i
$265$	−17.5370	+	10.1250i	−1.07729	+	0.621975i
$266$	2.65418	−	8.15649i	0.162738	−	0.500107i
$267$	−7.34645	+	13.0370i	−0.449595	+	0.797850i
$268$	−3.32285	−	2.67212i	−0.202975	−	0.163225i
$269$	−5.95410	−	10.3128i	−0.363028	−	0.628782i	0.625430	−	0.780280i	$-0.284924\pi$
$269$	−5.95410	−	10.3128i	−0.363028	−	0.628782i	−0.988458	+	0.151498i	$0.951590\pi$
$270$	20.4853	+	22.4401i	1.24670	+	1.36566i
$271$	0.560776	−	0.971293i	0.0340647	−	0.0590018i	−0.848490	−	0.529211i	$-0.822488\pi$
$271$	0.560776	−	0.971293i	0.0340647	−	0.0590018i	0.882555	+	0.470209i	$0.155821\pi$
$272$	10.2263	−	2.24653i	0.620058	−	0.136216i
$273$	−0.202771	−	5.87830i	−0.0122723	−	0.355771i
$274$	3.41883	−	2.93004i	0.206539	−	0.177010i
$275$	−52.3159			−3.15477
$276$	4.48733	−	31.1146i	0.270106	−	1.87288i
$277$			8.83901i			0.531084i	0.964099	+	0.265542i	$0.0855510\pi$
$277$			8.83901i			0.531084i	−0.964099	+	0.265542i	$0.914449\pi$
$278$	−7.69588	+	21.8506i	−0.461568	+	1.31051i
$279$	9.25888	−	16.8396i	0.554315	−	1.00816i
$280$	30.8945	−	1.71093i	1.84630	−	0.102248i
$281$	−12.6269	+	21.8704i	−0.753255	+	1.30468i	0.192982	+	0.981202i	$0.438184\pi$
$281$	−12.6269	+	21.8704i	−0.753255	+	1.30468i	−0.946237	+	0.323473i	$0.895149\pi$
$282$	−2.49490	+	7.32701i	−0.148569	+	0.436317i
$283$	−17.3279	−	10.0043i	−1.03004	−	0.594691i	−0.113040	−	0.993590i	$-0.536059\pi$
$283$	−17.3279	−	10.0043i	−1.03004	−	0.594691i	−0.916995	+	0.398899i	$0.869392\pi$
$284$	9.51026	+	1.47311i	0.564330	+	0.0874130i
$285$	8.05983	−	14.3030i	0.477423	−	0.847234i
$286$	7.40460	+	2.60793i	0.437843	+	0.154210i
$287$	−0.0125931	−	0.523791i	−0.000743345	−	0.0309184i
$288$	15.4811	−	6.95239i	0.912232	−	0.409673i
$289$	−5.07427	+	8.78889i	−0.298486	+	0.516994i
$290$	−8.94357	+	1.67334i	−0.525185	+	0.0982620i
$291$	5.19367	−	9.21667i	0.304458	−	0.540291i
$292$	−8.42462	−	21.7256i	−0.493013	−	1.27139i
$293$	−0.492008	−	0.852182i	−0.0287434	−	0.0497850i	0.851296	−	0.524686i	$-0.175817\pi$
$293$	−0.492008	−	0.852182i	−0.0287434	−	0.0497850i	−0.880039	+	0.474901i	$0.842484\pi$
$294$	4.74047	−	16.4781i	0.276470	−	0.961023i
$295$	−18.5162	−	10.6903i	−1.07805	−	0.622414i
$296$	0.389775	+	12.4545i	0.0226552	+	0.723903i
$297$	0.703986	+	22.4619i	0.0408494	+	1.30337i
$298$	−5.41077	−	6.31340i	−0.313437	−	0.365726i
$299$	−10.0873	+	5.82390i	−0.583363	+	0.336805i
$300$	41.4740	+	5.98136i	2.39450	+	0.345334i
$301$	5.37817	+	8.81872i	0.309992	+	0.508303i
$302$	−9.55450	−	11.1484i	−0.549800	−	0.641519i
$303$	0.0320972	+	3.07325i	0.00184393	+	0.176554i
$304$	−6.18198	−	6.77249i	−0.354561	−	0.388429i
$305$	18.2099	+	31.5405i	1.04270	+	1.80600i
$306$	3.46961	−	10.5493i	0.198344	−	0.603064i
$307$			6.74344i			0.384869i	0.981310	+	0.192434i	$0.0616382\pi$
$307$			6.74344i			0.384869i	−0.981310	+	0.192434i	$0.938362\pi$
$308$	18.1737	+	13.9088i	1.03554	+	0.792527i
$309$	−0.235159	−	22.5161i	−0.0133777	−	1.28090i
$310$	−6.88869	−	36.8182i	−0.391251	−	2.09114i
$311$	−15.2969	+	26.4949i	−0.867405	+	1.50239i	−0.00276682	+	0.999996i	$0.500881\pi$
$311$	−15.2969	+	26.4949i	−0.867405	+	1.50239i	−0.864639	+	0.502394i	$0.832453\pi$
$312$	−5.57191	−	2.91405i	−0.315447	−	0.164975i
$313$	10.9046	−	6.29580i	0.616367	−	0.355860i	−0.159086	−	0.987265i	$-0.550855\pi$
$313$	10.9046	−	6.29580i	0.616367	−	0.355860i	0.775453	+	0.631405i	$0.217521\pi$
$314$	2.54356	+	13.5947i	0.143541	+	0.767191i
$315$	15.1164	−	29.1301i	0.851713	−	1.64130i
$316$	6.26416	+	16.1541i	0.352387	+	0.908741i
$317$	27.2450	−	15.7299i	1.53023	−	0.883480i	0.530881	−	0.847446i	$-0.321861\pi$
$317$	27.2450	−	15.7299i	1.53023	−	0.883480i	0.999351	−	0.0360334i	$-0.0114723\pi$
$318$	11.3561	+	3.86683i	0.636816	+	0.216841i
$319$	−5.82807	−	3.36484i	−0.326309	−	0.188395i
$320$	14.7154	−	29.6247i	0.822619	−	1.65607i
$321$	6.65118	+	3.74799i	0.371232	+	0.209193i
$322$	−33.2164	+	7.04507i	−1.85108	+	0.392606i
$323$	−6.00049			−0.333876
$324$	2.01002	−	17.8874i	0.111668	−	0.993746i
$325$	−7.76293	−	13.4458i	−0.430610	−	0.745838i
$326$	−3.36340	−	17.9765i	−0.186281	−	0.995624i
$327$	10.1669	+	17.1925i	0.562233	+	0.950745i
$328$	−0.493600	−	0.264749i	−0.0272545	−	0.0146183i
$329$	8.35788	−	0.200941i	0.460785	−	0.0110783i
$330$	28.8503	+	32.9603i	1.58816	+	1.81440i
$331$	−9.02430	−	15.6306i	−0.496021	−	0.859133i	0.503969	−	0.863722i	$-0.331873\pi$
$331$	−9.02430	−	15.6306i	−0.496021	−	0.859133i	−0.999989	+	0.00458901i	$0.998539\pi$
$332$	−7.09024	+	8.81692i	−0.389128	+	0.483891i
$333$	11.5813	+	6.36773i	0.634652	+	0.348949i
$334$	−18.0422	−	6.35455i	−0.987227	−	0.347706i
$335$	−4.40765	+	7.63428i	−0.240816	+	0.417105i
$336$	−12.8172	−	13.1042i	−0.699235	−	0.714892i
$337$	14.0051	+	24.2576i	0.762908	+	1.32140i	0.941346	+	0.337444i	$0.109562\pi$
$337$	14.0051	+	24.2576i	0.762908	+	1.32140i	−0.178438	+	0.983951i	$0.557104\pi$
$338$	−2.95265	−	15.7811i	−0.160603	−	0.858381i
$339$	13.2821	−	7.85450i	0.721384	−	0.426598i
$340$	−7.82590	−	20.1816i	−0.424419	−	1.09450i
$341$	13.8521	−	23.9926i	0.750134	−	1.29927i
$342$	−9.52060	+	1.98796i	−0.514815	+	0.107497i
$343$	−18.4721	+	1.33439i	−0.997401	+	0.0720501i
$344$	11.0371	−	0.345416i	0.595080	−	0.0186236i
$345$	−64.9878	+	0.678737i	−3.49883	+	0.0365419i
$346$	−14.5026	−	5.10787i	−0.779664	−	0.274601i
$347$	16.9270	−	29.3184i	0.908689	−	1.57390i	0.0928018	−	0.995685i	$-0.470418\pi$
$347$	16.9270	−	29.3184i	0.908689	−	1.57390i	0.815887	−	0.578211i	$-0.196249\pi$
$348$	4.23556	+	3.33384i	0.227050	+	0.178713i
$349$	3.27919	−	5.67973i	0.175531	−	0.304029i	−0.764814	−	0.644251i	$-0.777169\pi$
$349$	3.27919	−	5.67973i	0.175531	−	0.304029i	0.940345	+	0.340223i	$0.110502\pi$
$350$	−9.39068	−	44.2756i	−0.501953	−	2.36663i
$351$	−5.66852	+	3.51396i	−0.302563	+	0.187561i
$352$	22.5226	−	9.55453i	1.20046	−	0.509258i
$353$			23.6201i			1.25717i	0.777740	+	0.628587i	$0.216366\pi$
$353$			23.6201i			1.25717i	−0.777740	+	0.628587i	$0.783634\pi$
$354$	2.45931	+	12.4251i	0.130711	+	0.660386i
$355$		−	19.8959i		−	1.05596i
$356$	10.8285	−	13.4656i	0.573910	−	0.713673i
$357$	−11.9879	+	0.413521i	−0.634467	+	0.0218858i
$358$	0.145785	+	0.0513461i	0.00770498	+	0.00271373i
$359$	20.1609	+	11.6399i	1.06405	+	0.614329i	0.926550	−	0.376172i	$-0.122760\pi$
$359$	20.1609	+	11.6399i	1.06405	+	0.614329i	0.137500	+	0.990502i	$0.456093\pi$
$360$	−19.1030	−	29.4281i	−1.00682	−	1.55100i
$361$	−6.87239	−	11.9033i	−0.361705	−	0.626491i
$362$	7.46610	−	6.39866i	0.392410	−	0.336306i
$363$	0.139372	+	13.3446i	0.00731515	+	0.700412i
$364$	−0.878002	+	6.73473i	−0.0460198	+	0.352996i
$365$	−41.7198	+	24.0869i	−2.18371	+	1.26077i
$366$	6.95452	−	20.4240i	0.363519	−	1.06758i
$367$	35.0257			1.82833			0.914164	−	0.405344i	$-0.132848\pi$
$367$	35.0257			1.82833			0.914164	+	0.405344i	$0.132848\pi$
$368$	−10.9819	+	34.5986i	−0.572474	+	1.80358i
$369$	−0.508185	+	0.307729i	−0.0264551	+	0.0160197i
$370$	25.3215	−	4.73765i	1.31640	−	0.246299i
$371$	−0.311437	−	12.9538i	−0.0161690	−	0.672528i
$372$	−13.7245	+	17.4366i	−0.711583	+	0.904047i
$373$		−	1.25485i		−	0.0649735i	−0.999472	−	0.0324867i	$-0.989657\pi$
$373$		−	1.25485i		−	0.0649735i	0.999472	−	0.0324867i	$-0.0103427\pi$
$374$	5.31848	−	15.1005i	0.275012	−	0.780831i
$375$	−0.530755	−	50.8189i	−0.0274081	−	2.62428i
$376$	4.22446	−	7.87613i	0.217860	−	0.406180i
$377$		−	1.99718i		−	0.102860i
$378$	−18.8834	+	4.62770i	−0.971259	+	0.238023i
$379$	−24.9135			−1.27972			−0.639861	−	0.768491i	$-0.721008\pi$
$379$	−24.9135			−1.27972			−0.639861	+	0.768491i	$0.721008\pi$
$380$	−11.8800	+	14.7731i	−0.609432	+	0.757846i
$381$	−2.92906	+	0.0305913i	−0.150060	+	0.00156724i
$382$	−9.40655	+	26.7076i	−0.481281	+	1.36648i
$383$	−1.94864			−0.0995710			−0.0497855	−	0.998760i	$-0.515854\pi$
$383$	−1.94864			−0.0995710			−0.0497855	+	0.998760i	$0.515854\pi$
$384$	−18.9475	+	4.99940i	−0.966908	+	0.255125i
$385$	22.6648	−	41.5309i	1.15510	−	2.11661i
$386$	−1.10833	−	5.92373i	−0.0564125	−	0.301510i
$387$	5.64304	−	10.2633i	0.286852	−	0.521712i
$388$	−7.65536	+	9.51965i	−0.388642	+	0.483287i
$389$			5.44098i			0.275868i	0.990441	+	0.137934i	$0.0440463\pi$
$389$			5.44098i			0.275868i	−0.990441	+	0.137934i	$0.955954\pi$
$390$	−4.19019	+	12.3057i	−0.212179	+	0.623124i
$391$	11.8769	+	20.5715i	0.600643	+	1.04034i
$392$	−8.50901	+	17.8773i	−0.429770	+	0.902938i
$393$	30.5641	−	0.319213i	1.54175	−	0.0161022i
$394$	8.50471	+	9.92348i	0.428461	+	0.499938i
$395$	31.0209	−	17.9099i	1.56083	−	0.901147i
$396$	3.43568	−	25.7211i	0.172649	−	1.29253i
$397$	12.8854	−	22.3181i	0.646698	−	1.12011i	−0.337209	−	0.941430i	$-0.609483\pi$
$397$	12.8854	−	22.3181i	0.646698	−	1.12011i	0.983907	−	0.178684i	$-0.0571839\pi$
$398$	−30.3318	−	10.6830i	−1.52040	−	0.535491i
$399$	5.56312	+	8.91129i	0.278505	+	0.446123i
$400$	−46.1180	−	14.6383i	−2.30590	−	0.731916i
$401$	26.0659			1.30167			0.650833	−	0.759221i	$-0.274420\pi$
$401$	26.0659			1.30167			0.650833	+	0.759221i	$0.274420\pi$
$402$	5.12290	−	1.01398i	0.255507	−	0.0505728i
$403$	8.22182			0.409558
$404$	0.543232	−	3.50705i	0.0270268	−	0.174482i
$405$	−37.1805	+	1.55411i	−1.84751	+	0.0772243i
$406$	1.80157	−	5.53635i	0.0894102	−	0.274765i
$407$	16.5007	+	9.52669i	0.817910	+	0.472220i
$408$	−5.94275	+	11.3630i	−0.294210	+	0.562555i
$409$	−0.474018	−	0.273674i	−0.0234387	−	0.0135323i	0.488235	−	0.872712i	$-0.337641\pi$
$409$	−0.474018	−	0.273674i	−0.0234387	−	0.0135323i	−0.511674	+	0.859180i	$0.670974\pi$
$410$	−0.384684	+	1.09222i	−0.0189982	+	0.0539408i
$411$	0.0575912	+	5.51425i	0.00284076	+	0.271998i
$412$	−3.97998	+	25.6944i	−0.196080	+	1.26587i
$413$	11.6803	−	7.12329i	0.574748	−	0.350514i
$414$	25.6597	+	28.7046i	1.26111	+	1.41076i
$415$	20.2569	+	11.6953i	0.994374	+	0.574102i
$416$	5.79767	+	4.37083i	0.284254	+	0.214297i
$417$	−14.4422	−	24.4220i	−0.707238	−	1.19595i
$418$	−13.7822	+	2.57864i	−0.674107	+	0.126125i
$419$	11.0422	−	6.37520i	0.539446	−	0.311449i	−0.205409	−	0.978676i	$-0.565852\pi$
$419$	11.0422	−	6.37520i	0.539446	−	0.311449i	0.744854	+	0.667227i	$0.232519\pi$
$420$	−22.7160	+	30.3328i	−1.10843	+	1.48009i
$421$	14.7249	+	8.50144i	0.717649	+	0.414335i	0.813887	−	0.581024i	$-0.197348\pi$
$421$	14.7249	+	8.50144i	0.717649	+	0.414335i	−0.0962379	+	0.995358i	$0.530681\pi$
$422$	16.9521	+	5.97062i	0.825217	+	0.290645i
$423$	−4.91028	−	8.10886i	−0.238746	−	0.394267i
$424$	−12.2071	−	6.54745i	−0.592831	−	0.317973i
$425$	−27.4206	+	15.8313i	−1.33010	+	0.767931i
$426$	−8.86893	+	7.76304i	−0.429701	+	0.376120i
$427$	−23.2975	+	0.560122i	−1.12745	+	0.0271062i
$428$	−6.86982	−	5.52446i	−0.332065	−	0.267035i
$429$	−8.27599	+	4.89409i	−0.399568	+	0.236289i
$430$	−4.19847	−	22.4397i	−0.202468	−	1.08214i
$431$	−15.7970	+	9.12038i	−0.760912	+	0.439313i	−0.829623	−	0.558324i	$-0.811445\pi$
$431$	−15.7970	+	9.12038i	−0.760912	+	0.439313i	0.0687108	+	0.997637i	$0.478111\pi$
$432$	−5.66441	+	19.9979i	−0.272529	+	0.962148i
$433$			0.0374331i			0.00179892i	1.00000		0.000899459i	$0.000286307\pi$
$433$			0.0374331i			0.00179892i	−1.00000		0.000899459i	$0.999714\pi$
$434$	22.7916	+	7.41656i	1.09403	+	0.356006i
$435$	5.47074	−	9.70836i	0.262302	−	0.465480i
$436$	−8.33850	−	21.5035i	−0.399342	−	1.02983i
$437$	10.4018	−	18.0164i	0.497586	−	0.861843i
$438$	27.0155	+	9.19900i	1.29085	+	0.439545i
$439$	2.88974	+	5.00518i	0.137920	+	0.238884i	0.926709	−	0.375780i	$-0.122625\pi$
$439$	2.88974	+	5.00518i	0.137920	+	0.238884i	−0.788789	+	0.614664i	$0.789292\pi$
$440$	−26.6476	−	42.9907i	−1.27037	−	2.04950i
$441$	11.7282	+	17.4198i	0.558487	+	0.829513i
$442$	4.67020	−	0.873795i	0.222139	−	0.0415622i
$443$	5.40666	+	9.36461i	0.256878	+	0.444926i	0.965404	−	0.260759i	$-0.0839728\pi$
$443$	5.40666	+	9.36461i	0.256878	+	0.444926i	−0.708526	+	0.705685i	$0.750639\pi$
$444$	−11.9919	−	9.43894i	−0.569111	−	0.447952i
$445$	−30.9372	−	17.8616i	−1.46656	−	0.846721i
$446$	4.42383	+	23.6442i	0.209474	+	1.11959i
$447$	10.1829	−	0.106351i	0.481636	−	0.00503023i
$448$	12.1289	+	17.3462i	0.573038	+	0.819529i
$449$	32.7907			1.54749			0.773744	−	0.633498i	$-0.218381\pi$
$449$	32.7907			1.54749			0.773744	+	0.633498i	$0.218381\pi$
$450$	−38.2617	+	34.2030i	−1.80367	+	1.61234i
$451$	−0.741726	+	0.428236i	−0.0349265	+	0.0201648i
$452$	−16.6126	+	6.44194i	−0.781390	+	0.303003i
$453$	17.9813	−	0.187798i	0.844836	−	0.00882351i
$454$	10.0917	+	11.7752i	0.473626	+	0.552637i
$455$	14.0371	−	0.337481i	0.658067	−	0.0158214i
$456$	11.2208	−	0.468508i	0.525461	−	0.0219399i
$457$	9.75756	+	16.9006i	0.456439	+	0.790576i	0.998770	−	0.0495893i	$-0.0157913\pi$
$457$	9.75756	+	16.9006i	0.456439	+	0.790576i	−0.542330	+	0.840165i	$0.682458\pi$
$458$	−6.44994	+	5.52778i	−0.301386	+	0.258296i
$459$	7.16619	+	11.5601i	0.334489	+	0.539578i
$460$	74.1612	+	11.4873i	3.45778	+	0.535600i
$461$	−5.74958	+	9.95857i	−0.267785	+	0.463817i	−0.968289	−	0.249831i	$-0.919625\pi$
$461$	−5.74958	+	9.95857i	−0.267785	+	0.463817i	0.700505	+	0.713648i	$0.252958\pi$
$462$	−27.3565	+	6.10145i	−1.27274	+	0.283865i
$463$	−5.14291	+	2.96926i	−0.239011	+	0.137993i	−0.614722	−	0.788744i	$-0.710732\pi$
$463$	−5.14291	+	2.96926i	−0.239011	+	0.137993i	0.375711	+	0.926737i	$0.377399\pi$
$464$	−4.19612	−	4.59694i	−0.194800	−	0.213407i
$465$	39.9667	+	22.5216i	1.85341	+	1.04441i
$466$	−7.51169	−	40.1480i	−0.347972	−	1.85982i
$467$	−32.5590	−	18.7979i	−1.50665	−	0.869865i	−0.999970	−	0.00773005i	$-0.997539\pi$
$467$	−32.5590	−	18.7979i	−1.50665	−	0.869865i	−0.506679	−	0.862135i	$-0.669127\pi$
$468$	7.12043	−	2.93363i	0.329142	−	0.135607i
$469$	−2.93696	−	4.81581i	−0.135616	−	0.222373i
$470$	−17.4280	−	6.13821i	−0.803893	−	0.283135i
$471$	−14.7572	−	8.31580i	−0.679975	−	0.383172i
$472$	−0.457498	−	14.6184i	−0.0210581	−	0.672868i
$473$	8.44249	−	14.6228i	0.388186	−	0.672358i
$474$	−20.0875	−	6.83996i	−0.922650	−	0.314170i
$475$	24.0149	+	13.8650i	1.10188	+	0.636170i
$476$	13.7344	+	1.79055i	0.629517	+	0.0820698i
$477$	−12.5678	+	7.61039i	−0.575442	+	0.348456i
$478$	−0.798297	+	2.26657i	−0.0365132	+	0.103671i
$479$	26.8661			1.22754			0.613772	−	0.789483i	$-0.289651\pi$
$479$	26.8661			1.22754			0.613772	+	0.789483i	$0.289651\pi$
$480$	16.2100	+	37.1280i	0.739881	+	1.69465i
$481$			5.65450i			0.257823i
$482$	−19.3284	−	22.5528i	−0.880386	−	1.02725i
$483$	19.5393	−	36.7104i	0.889070	−	1.67038i
$484$	2.35882	−	15.2283i	0.107219	−	0.692196i
$485$	21.8715	+	12.6275i	0.993133	+	0.573385i
$486$	15.2000	+	15.9675i	0.689486	+	0.724299i
$487$	2.83137	−	1.63469i	0.128301	−	0.0740749i	−0.434476	−	0.900684i	$-0.643066\pi$
$487$	2.83137	−	1.63469i	0.128301	−	0.0740749i	0.562777	+	0.826609i	$0.309733\pi$
$488$	−11.7756	+	21.9546i	−0.533059	+	0.993839i
$489$	19.5137	+	10.9961i	0.882439	+	0.497262i
$490$	39.2164	+	11.7267i	1.77162	+	0.529758i
$491$	6.51562	+	11.2854i	0.294046	+	0.509302i	0.974762	−	0.223245i	$-0.0716648\pi$
$491$	6.51562	+	11.2854i	0.294046	+	0.509302i	−0.680717	+	0.732547i	$0.738332\pi$
$492$	0.636972	−	0.254686i	0.0287169	−	0.0114821i
$493$	−4.07293			−0.183436
$494$	−2.70782	−	3.15954i	−0.121830	−	0.142154i
$495$	−53.6361	+	1.12048i	−2.41076	+	0.0503617i
$496$	18.9243	−	17.2743i	0.849728	−	0.775638i
$497$	11.1751	+	6.09863i	0.501272	+	0.273561i
$498$	−2.69052	−	13.5932i	−0.120565	−	0.609126i
$499$	23.0415			1.03148			0.515740	−	0.856745i	$-0.327517\pi$
$499$	23.0415			1.03148			0.515740	+	0.856745i	$0.327517\pi$
$500$	−8.98282	+	57.9922i	−0.401724	+	2.59349i
$501$	20.1655	−	11.9251i	0.900927	−	0.532772i
$502$	−6.15917	−	7.18666i	−0.274897	−	0.320756i
$503$	12.1910			0.543570			0.271785	−	0.962358i	$-0.412386\pi$
$503$	12.1910			0.543570			0.271785	+	0.962358i	$0.412386\pi$
$504$	22.3848	−	1.70927i	0.997097	−	0.0761369i
$505$	−7.33690			−0.326488
$506$	36.1198	+	42.1454i	1.60572	+	1.87359i
$507$	17.1306	+	9.65326i	0.760798	+	0.428716i
$508$	3.34251	+	0.517746i	0.148300	+	0.0229712i
$509$	3.13469			0.138943			0.0694714	−	0.997584i	$-0.477869\pi$
$509$	3.13469			0.138943			0.0694714	+	0.997584i	$0.477869\pi$
$510$	25.0956	+	8.54525i	1.11125	+	0.378390i
$511$	−0.740894	−	30.8165i	−0.0327752	−	1.36324i
$512$	22.5278	−	2.12063i	0.995599	−	0.0937195i
$513$	5.62982	−	10.4974i	0.248563	−	0.463473i
$514$	22.4980	+	26.2511i	0.992343	+	1.15789i
$515$	53.7537			2.36867
$516$	−8.36473	+	10.6272i	−0.368237	+	0.467834i
$517$	−6.83315	−	11.8354i	−0.300522	−	0.520519i
$518$	−5.10068	+	15.6748i	−0.224111	+	0.688711i
$519$	16.2093	−	9.58552i	0.711508	−	0.420758i
$520$	7.09498	−	13.2280i	0.311136	−	0.580084i
$521$	−17.1860	+	9.92234i	−0.752932	+	0.434706i	−0.826752	−	0.562566i	$-0.809814\pi$
$521$	−17.1860	+	9.92234i	−0.752932	+	0.434706i	0.0738202	+	0.997272i	$0.476481\pi$
$522$	−6.46227	+	1.34936i	−0.282846	+	0.0590600i
$523$	8.62552	+	4.97995i	0.377168	+	0.217758i	0.676585	−	0.736364i	$-0.263459\pi$
$523$	8.62552	+	4.97995i	0.377168	+	0.217758i	−0.299418	+	0.954122i	$0.596792\pi$
$524$	−34.8783	−	5.40255i	−1.52367	−	0.236012i
$525$	48.9329	+	26.0448i	2.13561	+	1.13669i
$526$	2.28184	+	2.66250i	0.0994929	+	0.116091i
$527$		−	16.7671i		−	0.730389i
$528$	−8.76639	+	28.6529i	−0.381508	+	1.24696i
$529$	−59.3543			−2.58062
$530$	−9.51356	+	27.0115i	−0.413242	+	1.17330i
$531$	−13.5935	−	7.47411i	−0.589909	−	0.324349i
$532$	−4.65623	−	11.2011i	−0.201873	−	0.485631i
$533$	−0.220123	−	0.127088i	−0.00953460	−	0.00550480i
$534$	4.10906	+	20.7601i	0.177817	+	0.898378i
$535$	−9.11259	+	15.7835i	−0.393972	+	0.682379i
$536$	−6.02723	+	0.188628i	−0.260337	+	0.00814748i
$537$	−0.162941	+	0.0963570i	−0.00703144	+	0.00415811i
$538$	−15.8843	−	5.59452i	−0.684821	−	0.241197i
$539$	16.3797	+	25.4607i	0.705524	+	1.09667i
$540$	42.6487	+	5.24403i	1.83531	+	0.225667i
$541$	−21.5113	−	12.4195i	−0.924841	−	0.533957i	−0.0396649	−	0.999213i	$-0.512629\pi$
$541$	−21.5113	−	12.4195i	−0.924841	−	0.533957i	−0.885176	+	0.465256i	$0.845962\pi$
$542$	−0.291700	−	1.55906i	−0.0125296	−	0.0669674i
$543$	0.125768	+	12.0421i	0.00539724	+	0.516776i
$544$	8.91363	−	11.8234i	0.382169	−	0.506926i
$545$	−41.2933	+	23.8407i	−1.76881	+	1.02122i
$546$	−5.62747	−	6.12558i	−0.240833	−	0.262151i
$547$	−15.1654	+	26.2672i	−0.648426	+	1.12311i	0.335073	+	0.942192i	$0.391239\pi$
$547$	−15.1654	+	26.2672i	−0.648426	+	1.12311i	−0.983499	+	0.180914i	$0.942094\pi$
$548$	0.974708	−	6.29262i	0.0416374	−	0.268807i
$549$	13.6873	+	22.6034i	0.584161	+	0.964688i
$550$	−56.1774	+	48.1456i	−2.39541	+	2.05294i
$551$	1.78353	+	3.08917i	0.0759810	+	0.131603i
$552$	−23.8158	−	37.5408i	−1.01367	−	1.59784i
$553$	0.550895	+	22.9137i	0.0234265	+	0.974391i
$554$	8.13442	+	9.49143i	0.345599	+	0.403252i
$555$	−15.4890	+	27.4868i	−0.657473	+	1.16675i
$556$	11.8449	+	30.5459i	0.502336	+	1.29543i
$557$	33.0650	−	19.0901i	1.40101	−	0.808872i	0.406511	−	0.913646i	$-0.366745\pi$
$557$	33.0650	−	19.0901i	1.40101	−	0.808872i	0.994496	+	0.104774i	$0.0334120\pi$
$558$	−5.55496	−	26.6034i	−0.235160	−	1.12621i
$559$	5.01098			0.211942
$560$	31.6003	−	30.2690i	1.33536	−	1.27910i
$561$	9.98074	+	16.8776i	0.421387	+	0.712573i
$562$	6.56814	+	35.1050i	0.277060	+	1.48081i
$563$	−20.1650	−	11.6423i	−0.849855	−	0.490664i	0.0107468	−	0.999942i	$-0.496579\pi$
$563$	−20.1650	−	11.6423i	−0.849855	−	0.490664i	−0.860602	+	0.509278i	$0.829912\pi$
$564$	4.06390	+	10.1639i	0.171121	+	0.427976i
$565$	18.4182	+	31.9013i	0.774860	+	1.34210i
$566$	−27.8137	+	5.20393i	−1.16910	+	0.218738i
$567$	10.5239	−	21.3599i	0.441964	−	0.897033i
$568$	11.5679	−	7.17032i	0.485379	−	0.300860i
$569$	−20.4075	−	35.3468i	−0.855526	−	1.48181i	−0.876156	−	0.482027i	$-0.839901\pi$
$569$	−20.4075	−	35.3468i	−0.855526	−	1.48181i	0.0206305	−	0.999787i	$-0.493433\pi$
$570$	−4.50808	−	22.7760i	−0.188823	−	0.953983i
$571$	−4.34151	+	7.51971i	−0.181687	+	0.314690i	−0.942455	−	0.334333i	$-0.891489\pi$
$571$	−4.34151	+	7.51971i	−0.181687	+	0.314690i	0.760768	+	0.649023i	$0.224822\pi$
$572$	10.3512	−	4.01393i	0.432805	−	0.167831i
$573$	−17.6525	−	29.8507i	−0.737443	−	1.24703i
$574$	−0.495561	−	0.550864i	−0.0206843	−	0.0229926i
$575$		−	109.774i		−	4.57788i
$576$	10.2256	−	21.7126i	0.426066	−	0.904692i
$577$	−2.25486	+	1.30185i	−0.0938712	+	0.0541965i	−0.546201	−	0.837654i	$-0.683926\pi$
$577$	−2.25486	+	1.30185i	−0.0938712	+	0.0541965i	0.452330	+	0.891851i	$0.350593\pi$
$578$	2.63949	+	14.1074i	0.109788	+	0.586790i
$579$	6.43028	+	3.62352i	0.267233	+	0.150588i
$580$	−8.06376	+	10.0275i	−0.334829	+	0.416370i
$581$	−12.7783	+	7.79297i	−0.530135	+	0.323307i
$582$	−2.90496	−	14.6766i	−0.120414	−	0.608366i
$583$	−18.3435	+	10.5906i	−0.759711	+	0.438619i
$584$	−29.0402	−	15.5761i	−1.20169	−	0.644543i
$585$	−8.24680	−	13.6188i	−0.340963	−	0.563069i
$586$	−1.31258	−	0.462295i	−0.0542220	−	0.0190972i
$587$	−22.9961	−	13.2768i	−0.949152	−	0.547993i	−0.0563344	−	0.998412i	$-0.517941\pi$
$587$	−22.9961	−	13.2768i	−0.949152	−	0.547993i	−0.892817	+	0.450419i	$0.851275\pi$
$588$	−10.0742	−	22.0570i	−0.415454	−	0.909614i
$589$	−12.7173	+	7.34231i	−0.524005	+	0.302535i
$590$	−29.7210	+	5.56081i	−1.22360	+	0.228935i
$591$	−16.0056	+	0.167164i	−0.658384	+	0.00687620i
$592$	11.8803	+	13.0151i	0.488276	+	0.534916i
$593$	6.26385	+	3.61643i	0.257225	+	0.148509i	0.623068	−	0.782168i	$-0.285886\pi$
$593$	6.26385	+	3.61643i	0.257225	+	0.148509i	−0.365843	+	0.930677i	$0.619219\pi$
$594$	21.4274	+	23.4720i	0.879176	+	0.963068i
$595$	−0.688241	−	28.6264i	−0.0282151	−	1.17357i
$596$	−11.6203	−	1.79995i	−0.475986	−	0.0737288i
$597$	33.9014	−	20.0479i	1.38749	−	0.820506i
$598$	−5.47219	+	15.5370i	−0.223774	+	0.635354i
$599$	−0.237738	−	0.137258i	−0.00971370	−	0.00560821i	0.495135	−	0.868816i	$-0.335118\pi$
$599$	−0.237738	−	0.137258i	−0.00971370	−	0.00560821i	−0.504849	+	0.863208i	$0.668452\pi$
$600$	50.0398	−	31.7451i	2.04287	−	1.29599i
$601$	−25.9289	−	14.9701i	−1.05766	−	0.610642i	−0.132878	−	0.991132i	$-0.542422\pi$
$601$	−25.9289	−	14.9701i	−1.05766	−	0.610642i	−0.924785	+	0.380491i	$0.875755\pi$
$602$	13.8909	+	4.52019i	0.566151	+	0.184229i
$603$	−3.08160	+	5.60466i	−0.125492	+	0.228239i
$604$	−20.5195	−	3.17841i	−0.834925	−	0.129327i
$605$	−31.8583			−1.29522
$606$	2.86274	+	3.27055i	0.116291	+	0.132857i
$607$	22.9565			0.931777			0.465889	−	0.884843i	$-0.345735\pi$
$607$	22.9565			0.931777			0.465889	+	0.884843i	$0.345735\pi$
$608$	−12.8709	−	1.58318i	−0.521984	−	0.0642066i
$609$	3.77606	+	6.04869i	0.153014	+	0.245105i
$610$	48.5803	+	17.1102i	1.96696	+	0.692772i
$611$	2.02789	−	3.51240i	0.0820395	−	0.142097i
$612$	−5.98270	−	14.5210i	−0.241836	−	0.586977i
$613$	0.368525	−	0.212768i	0.0148846	−	0.00859363i	−0.492539	−	0.870290i	$-0.663931\pi$
$613$	0.368525	−	0.212768i	0.0148846	−	0.00859363i	0.507424	+	0.861697i	$0.330598\pi$
$614$	6.20590	+	7.24119i	0.250450	+	0.292231i
$615$	−0.721904	−	1.22075i	−0.0291100	−	0.0492255i
$616$	32.3152	−	1.78961i	1.30202	−	0.0721055i
$617$	−12.0934	−	20.9465i	−0.486864	−	0.843273i	0.513022	−	0.858375i	$-0.328526\pi$
$617$	−12.0934	−	20.9465i	−0.486864	−	0.843273i	−0.999886	+	0.0151024i	$0.995193\pi$
$618$	−20.9738	−	23.9616i	−0.843690	−	0.963878i
$619$			23.6089i			0.948924i	0.880276	+	0.474462i	$0.157357\pi$
$619$			23.6089i			0.948924i	−0.880276	+	0.474462i	$0.842643\pi$
$620$	−41.2805	−	33.1963i	−1.65787	−	1.33319i
$621$	−47.1316	+	1.47716i	−1.89132	+	0.0592765i
$622$	7.95700	+	42.5281i	0.319047	+	1.70522i
$623$	19.5156	−	11.9017i	0.781877	−	0.476833i
$624$	−8.66494	+	1.99862i	−0.346875	+	0.0800087i
$625$	60.8403			2.43361
$626$	5.91559	−	16.7959i	0.236435	−	0.671299i
$627$	8.43048	−	14.9607i	0.336681	−	0.597473i
$628$	15.2423	+	12.2573i	0.608234	+	0.489120i
$629$	11.5315			0.459790
$630$	−10.5759	−	45.1917i	−0.421355	−	1.80048i
$631$			21.0121i			0.836479i	0.908337	+	0.418240i	$0.137353\pi$
$631$			21.0121i			0.836479i	−0.908337	+	0.418240i	$0.862647\pi$
$632$	21.5930	+	11.5817i	0.858922	+	0.460694i
$633$	−18.9471	+	11.2046i	−0.753079	+	0.445341i
$634$	14.7800	−	41.9642i	0.586988	−	1.66661i
$635$		−	6.99268i		−	0.277496i
$636$	15.7529	−	6.29859i	0.624642	−	0.249755i
$637$	−4.11319	+	7.98778i	−0.162970	+	0.316488i
$638$	−9.35486	+	1.75029i	−0.370363	+	0.0692948i
$639$	−0.301498	−	14.4324i	−0.0119271	−	0.570935i
$640$	−11.4616	−	45.3538i	−0.453060	−	1.79277i
$641$	−15.7767			−0.623140			−0.311570	−	0.950223i	$-0.600855\pi$
$641$	−15.7767			−0.623140			−0.311570	+	0.950223i	$0.600855\pi$
$642$	10.5913	−	2.09635i	0.418007	−	0.0827364i
$643$	−18.5270	+	10.6966i	−0.730634	+	0.421832i	−0.818654	−	0.574287i	$-0.805279\pi$
$643$	−18.5270	+	10.6966i	−0.730634	+	0.421832i	0.0880203	+	0.996119i	$0.471946\pi$
$644$	−29.1847	+	38.1337i	−1.15004	+	1.50268i
$645$	24.3586	+	13.7263i	0.959120	+	0.540472i
$646$	−6.44340	+	5.52218i	−0.253512	+	0.217267i
$647$	0.659843	+	1.14288i	0.0259411	+	0.0449313i	0.878705	−	0.477366i	$-0.158408\pi$
$647$	0.659843	+	1.14288i	0.0259411	+	0.0449313i	−0.852763	+	0.522297i	$0.825075\pi$
$648$	−14.3032	−	21.0575i	−0.561882	−	0.827217i
$649$	−19.3677	−	11.1819i	−0.760248	−	0.438929i
$650$	−20.7099	−	7.29412i	−0.812309	−	0.286099i
$651$	−24.9008	+	15.5450i	−0.975939	+	0.609257i
$652$	−20.1552	−	16.2081i	−0.789337	−	0.634756i
$653$			17.1849i			0.672498i	0.941773	+	0.336249i	$0.109158\pi$
$653$			17.1849i			0.672498i	−0.941773	+	0.336249i	$0.890842\pi$
$654$	26.7394	+	9.10496i	1.04559	+	0.356032i
$655$			72.9670i			2.85106i
$656$	−0.773678	+	0.169963i	−0.0302070	+	0.00663595i
$657$	−29.8983	+	18.1047i	−1.16644	+	0.706333i
$658$	8.78987	−	7.90743i	0.342665	−	0.308264i
$659$	10.3636	−	17.9502i	0.403707	−	0.699241i	−0.590463	−	0.807065i	$-0.701055\pi$
$659$	10.3636	−	17.9502i	0.403707	−	0.699241i	0.994170	+	0.107824i	$0.0343882\pi$
$660$	61.3127	+	8.84250i	2.38660	+	0.344194i
$661$	−4.44476	+	7.69856i	−0.172881	+	0.299439i	−0.939426	−	0.342752i	$-0.888641\pi$
$661$	−4.44476	+	7.69856i	−0.172881	+	0.299439i	0.766545	+	0.642191i	$0.221974\pi$
$662$	−24.0750	−	8.47932i	−0.935701	−	0.329558i
$663$	−2.85674	+	5.06956i	−0.110947	+	0.196886i
$664$	0.500509	+	15.9928i	0.0194235	+	0.620640i
$665$	−21.4107	+	13.0575i	−0.830271	+	0.506347i
$666$	18.2963	−	3.82038i	0.708967	−	0.148037i
$667$	7.06039	−	12.2290i	0.273379	−	0.473507i
$668$	−25.2220	+	9.78044i	−0.975867	+	0.378417i
$669$	−25.6661	−	14.4631i	−0.992308	−	0.559174i
$670$	2.29274	+	12.2541i	0.0885762	+	0.473416i
$671$	19.0473	+	32.9910i	0.735314	+	1.27360i
$672$	−25.8229	−	2.27592i	−0.996139	−	0.0877956i
$673$	7.82591	−	13.5549i	0.301667	−	0.522502i	−0.674847	−	0.737958i	$-0.735790\pi$
$673$	7.82591	−	13.5549i	0.301667	−	0.522502i	0.976514	+	0.215456i	$0.0691236\pi$
$674$	37.3628	+	13.1593i	1.43916	+	0.506879i
$675$	−1.96898	−	62.8237i	−0.0757859	−	2.41809i
$676$	−17.6938	−	14.2287i	−0.680530	−	0.547257i
$677$	2.57124	+	4.45352i	0.0988209	+	0.171163i	0.911197	−	0.411971i	$-0.135160\pi$
$677$	2.57124	+	4.45352i	0.0988209	+	0.171163i	−0.812376	+	0.583134i	$0.801826\pi$
$678$	7.03407	−	20.6576i	0.270142	−	0.793350i
$679$	−13.7968	+	8.41410i	−0.529474	+	0.322903i
$680$	−26.9764	−	14.4691i	−1.03450	−	0.554866i
$681$	−18.9923	+	0.198356i	−0.727785	+	0.00760103i
$682$	−7.20549	−	38.5114i	−0.275912	−	1.47468i
$683$	15.9748	+	27.6691i	0.611258	+	1.05873i	0.991029	+	0.133649i	$0.0426694\pi$
$683$	15.9748	+	27.6691i	0.611258	+	1.05873i	−0.379771	+	0.925080i	$0.623997\pi$
$684$	−8.39384	+	10.8964i	−0.320946	+	0.416634i
$685$	−13.1644			−0.502987
$686$	−18.6076	+	18.4325i	−0.710440	+	0.703758i
$687$	−0.108651	−	10.4031i	−0.00414529	−	0.396905i
$688$	11.5339	−	10.5282i	0.439725	−	0.401384i
$689$	−5.44383	−	3.14300i	−0.207394	−	0.119739i
$690$	−69.1601	+	60.5363i	−2.63288	+	2.30458i
$691$	3.67189	−	2.11997i	0.139685	−	0.0806474i	−0.428529	−	0.903528i	$-0.640968\pi$
$691$	3.67189	−	2.11997i	0.139685	−	0.0806474i	0.568214	+	0.822881i	$0.307635\pi$
$692$	−20.2738	+	7.86165i	−0.770692	+	0.298855i
$693$	15.8116	−	30.4698i	0.600632	−	1.15745i
$694$	−8.80496	−	47.0602i	−0.334232	−	1.78638i
$695$	58.6575	−	33.8659i	2.22501	−	1.28461i
$696$	7.61628	−	0.318008i	0.288694	−	0.0120540i
$697$	−0.259177	+	0.448908i	−0.00981703	+	0.0170036i
$698$	−1.70574	−	9.11675i	−0.0645634	−	0.345074i
$699$	43.5812	+	24.5584i	1.64839	+	0.928882i
$700$	−50.8300	−	38.9015i	−1.92120	−	1.47034i
$701$		−	8.66802i		−	0.327387i	−0.986511	−	0.163693i	$-0.947659\pi$
$701$		−	8.66802i		−	0.327387i	0.986511	−	0.163693i	$-0.0523408\pi$
$702$	−2.85306	+	8.99000i	−0.107682	+	0.339306i
$703$	−5.04962	−	8.74620i	−0.190450	−	0.329869i
$704$	15.3922	−	30.9871i	0.580114	−	1.16787i
$705$	19.4790	−	11.5191i	0.733620	−	0.433834i
$706$	21.7373	+	25.3636i	0.818094	+	0.954571i
$707$	2.24896	−	4.12099i	0.0845809	−	0.154986i
$708$	14.0755	+	11.0789i	0.528989	+	0.416372i
$709$	4.60956	−	2.66133i	0.173116	−	0.0999484i	−0.410938	−	0.911663i	$-0.634799\pi$
$709$	4.60956	−	2.66133i	0.173116	−	0.0999484i	0.584054	+	0.811715i	$0.301466\pi$
$710$	−18.3099	−	21.3644i	−0.687159	−	0.801792i
$711$	22.2310	−	13.4619i	0.833729	−	0.504859i
$712$	−0.764397	−	24.4248i	−0.0286470	−	0.915358i
$713$	50.3433	+	29.0657i	1.88537	+	1.08852i
$714$	−12.4922	+	11.4764i	−0.467508	+	0.429492i
$715$	−11.4763	−	19.8775i	−0.429188	−	0.743376i
$716$	0.203799	−	0.0790280i	0.00761632	−	0.00295341i
$717$	−1.49810	−	2.53331i	−0.0559475	−	0.0946081i
$718$	32.3610	−	6.05474i	1.20770	−	0.225961i
$719$	−4.34250	+	7.52143i	−0.161948	+	0.280502i	−0.935567	−	0.353149i	$-0.885111\pi$
$719$	−4.34250	+	7.52143i	−0.161948	+	0.280502i	0.773619	+	0.633651i	$0.218444\pi$
$720$	−47.5953	−	14.0200i	−1.77377	−	0.522494i
$721$	−16.4770	+	30.1924i	−0.613635	+	1.12442i
$722$	−18.3341	−	6.45736i	−0.682326	−	0.240318i
$723$	36.3756	−	0.379909i	1.35282	−	0.0141290i
$724$	2.12858	−	13.7419i	0.0791081	−	0.510714i
$725$	16.3005	+	9.41111i	0.605386	+	0.349520i
$726$	12.4306	+	14.2014i	0.461342	+	0.527063i
$727$	18.3777	−	31.8311i	0.681590	−	1.18055i	−0.292905	−	0.956141i	$-0.594622\pi$
$727$	18.3777	−	31.8311i	0.681590	−	1.18055i	0.974495	−	0.224407i	$-0.0720446\pi$
$728$	5.25507	+	8.03984i	0.194766	+	0.297976i
$729$	−26.9470	+	1.69077i	−0.998037	+	0.0626210i
$730$	−22.6323	+	64.2590i	−0.837659	+	2.37833i
$731$		−	10.2191i		−	0.377968i
$732$	−11.3281	−	28.3316i	−0.418697	−	1.04717i
$733$	24.0020			0.886535			0.443267	−	0.896389i	$-0.353819\pi$
$733$	24.0020			0.886535			0.443267	+	0.896389i	$0.353819\pi$
$734$	37.6110	−	32.2337i	1.38825	−	1.18977i
$735$	−41.8749	+	27.5620i	−1.54458	+	1.01664i
$736$	20.0481	+	47.2590i	0.738984	+	1.74199i
$737$	−4.61035	+	7.98536i	−0.169824	+	0.294144i
$738$	−0.262497	+	0.798119i	−0.00966263	+	0.0293792i
$739$	5.42035	+	9.38831i	0.199391	+	0.345355i	0.948331	−	0.317283i	$-0.102770\pi$
$739$	5.42035	+	9.38831i	0.199391	+	0.345355i	−0.748940	+	0.662637i	$0.769437\pi$
$740$	22.8305	−	28.3904i	0.839266	−	1.04365i
$741$	5.09604	−	0.0532233i	0.187208	−	0.00195521i
$742$	−12.2556	−	13.6233i	−0.449919	−	0.500128i
$743$	23.6520	−	13.6555i	0.867709	−	0.500972i	0.00112274	−	0.999999i	$-0.499643\pi$
$743$	23.6520	−	13.6555i	0.867709	−	0.500972i	0.866586	+	0.499027i	$0.166309\pi$
$744$	1.30915	+	31.3541i	0.0479958	+	1.14950i
$745$			24.3101i			0.890654i
$746$	−1.15482	−	1.34747i	−0.0422809	−	0.0493343i
$747$	14.8715	+	8.17678i	0.544120	+	0.299173i
$748$	−8.18579	−	21.1097i	−0.299302	−	0.771846i
$749$	−6.07200	−	9.95643i	−0.221866	−	0.363800i
$750$	−47.3379	−	54.0815i	−1.72854	−	1.97478i
$751$		−	18.6076i		−	0.679002i	−0.940606	−	0.339501i	$-0.889742\pi$
$751$		−	18.6076i		−	0.679002i	0.940606	−	0.339501i	$-0.110258\pi$
$752$	−2.71202	−	12.3452i	−0.0988973	−	0.450183i
$753$	11.5914	−	0.121061i	0.422414	−	0.00441172i
$754$	−1.83797	−	2.14459i	−0.0669351	−	0.0781014i
$755$			42.9276i			1.56230i
$756$	−16.0184	+	22.3475i	−0.582585	+	0.812770i
$757$			2.81436i			0.102290i	0.998691	+	0.0511449i	$0.0162870\pi$
$757$			2.81436i			0.102290i	−0.998691	+	0.0511449i	$0.983713\pi$
$758$	−26.7524	+	22.9276i	−0.971693	+	0.832768i
$759$	−67.9765	+	0.709950i	−2.46739	+	0.0257695i
$760$	0.838625	+	26.7966i	0.0304201	+	0.972015i
$761$			4.83042i			0.175103i	0.996160	+	0.0875513i	$0.0279042\pi$
$761$			4.83042i			0.175103i	−0.996160	+	0.0875513i	$0.972096\pi$
$762$	−3.11711	+	2.72843i	−0.112921	+	0.0988405i
$763$	−0.733320	−	30.5015i	−0.0265480	−	1.10423i
$764$	14.4778	+	37.3357i	0.523790	+	1.35076i
$765$	−27.7735	+	16.8181i	−1.00415	+	0.608059i
$766$	−2.09247	+	1.79331i	−0.0756042	+	0.0647949i
$767$		−	6.63696i		−	0.239647i
$768$	−15.7451	+	22.8055i	−0.568153	+	0.822923i
$769$	36.9610	−	21.3394i	1.33285	−	0.769520i	0.347113	−	0.937823i	$-0.387162\pi$
$769$	36.9610	−	21.3394i	1.33285	−	0.769520i	0.985735	+	0.168303i	$0.0538287\pi$
$770$	−13.8826	−	65.4545i	−0.500296	−	2.35882i
$771$	−42.3406	+	0.442208i	−1.52486	+	0.0159257i
$772$	−6.64167	−	5.34099i	−0.239039	−	0.192226i
$773$	−6.93491	−	12.0116i	−0.249431	−	0.432028i	0.713937	−	0.700210i	$-0.246910\pi$
$773$	−6.93491	−	12.0116i	−0.249431	−	0.432028i	−0.963368	+	0.268182i	$0.913577\pi$
$774$	−3.38560	−	16.2140i	−0.121693	−	0.582802i
$775$	−38.7429	+	67.1048i	−1.39169	+	2.41047i
$776$	0.540401	+	17.2674i	0.0193993	+	0.619865i
$777$	−10.6910	−	17.1253i	−0.383537	−	0.614368i
$778$	5.00726	+	5.84259i	0.179519	+	0.209467i
$779$	0.453973			0.0162653
$780$	6.82531	+	17.0702i	0.244385	+	0.611211i
$781$		−	20.8108i		−	0.744670i
$782$	31.6853	+	11.1597i	1.13306	+	0.399070i
$783$	3.82133	−	7.12530i	0.136563	−	0.254637i
$784$	7.31514	+	27.0276i	0.261255	+	0.965270i
$785$	20.2184	−	35.0193i	0.721626	−	1.24989i
$786$	32.5263	−	28.4705i	1.16017	−	1.01551i
$787$	13.5726	+	7.83613i	0.483810	+	0.279328i	0.722003	−	0.691890i	$-0.243222\pi$
$787$	13.5726	+	7.83613i	0.483810	+	0.279328i	−0.238193	+	0.971218i	$0.576555\pi$
$788$	18.2649	+	2.82918i	0.650660	+	0.100785i
$789$	−4.29436	+	0.0448505i	−0.152883	+	0.00159672i
$790$	16.8283	−	47.7801i	0.598726	−	1.69994i
$791$	−23.5640	+	0.566529i	−0.837840	+	0.0201435i
$792$	−19.9815	−	30.7814i	−0.710012	−	1.09377i
$793$	−5.65271	+	9.79078i	−0.200734	+	0.347681i
$794$	−6.70261	−	35.8237i	−0.237867	−	1.27133i
$795$	−17.8533	−	30.1902i	−0.633191	−	1.07074i
$796$	−42.4021	+	16.4425i	−1.50290	+	0.582788i
$797$	−14.7425	−	25.5348i	−0.522208	−	0.904490i	−0.999666	−	0.0258360i	$-0.991775\pi$
$797$	−14.7425	−	25.5348i	−0.522208	−	0.904490i	0.477458	−	0.878654i	$-0.341558\pi$
$798$	14.1747	+	4.44938i	0.501779	+	0.157506i
$799$	−7.16300	−	4.13556i	−0.253409	−	0.146306i
$800$	−62.9936	+	26.7230i	−2.22716	+	0.944802i
$801$	−22.7124	−	12.4879i	−0.802502	−	0.441238i
$802$	27.9898	−	23.9881i	0.988355	−	0.847048i
$803$	−43.6384	+	25.1946i	−1.53996	+	0.889099i
$804$	4.56788	−	5.80337i	0.161097	−	0.204669i
$805$	87.1437	+	47.5572i	3.07141	+	1.67617i
$806$	8.82869	−	7.56644i	0.310977	−	0.266516i
$807$	17.7536	−	10.4988i	0.624957	−	0.369575i
$808$	−2.64417	−	4.26584i	−0.0930215	−	0.150072i
$809$	6.94512	+	12.0293i	0.244177	+	0.422928i	0.961900	−	0.273401i	$-0.0881487\pi$
$809$	6.94512	+	12.0293i	0.244177	+	0.422928i	−0.717723	+	0.696329i	$0.754815\pi$
$810$	−38.4946	+	35.8856i	−1.35256	+	1.26089i
$811$			6.98818i			0.245388i	0.992445	+	0.122694i	$0.0391534\pi$
$811$			6.98818i			0.245388i	−0.992445	+	0.122694i	$0.960847\pi$
$812$	−3.16049	−	7.60296i	−0.110911	−	0.266812i
$813$	1.69238	+	0.953671i	0.0593544	+	0.0334467i
$814$	26.4859	−	4.95552i	0.928332	−	0.173691i
$815$	−26.7352	+	46.3067i	−0.936492	+	1.62205i
$816$	4.07587	+	17.6708i	0.142684	+	0.618602i
$817$	−7.75083	+	4.47494i	−0.271167	+	0.156558i
$818$	−0.760865	+	0.142358i	−0.0266030	+	0.00497743i
$819$	10.1773	−	0.457522i	0.355624	−	0.0159871i
$820$	0.592076	+	1.52686i	0.0206762	+	0.0533201i
$821$	−46.7385	+	26.9845i	−1.63119	+	0.941765i	−0.647458	+	0.762102i	$0.724168\pi$
$821$	−46.7385	+	26.9845i	−1.63119	+	0.941765i	−0.983728	+	0.179664i	$0.942499\pi$
$822$	5.13654	+	5.86827i	0.179157	+	0.204679i
$823$	24.9917	+	14.4289i	0.871155	+	0.502962i	0.867732	−	0.497033i	$-0.165577\pi$
$823$	24.9917	+	14.4289i	0.871155	+	0.502962i	0.00342303	+	0.999994i	$0.498910\pi$
$824$	19.3724	+	31.2536i	0.674871	+	1.08877i
$825$	−0.946323	−	90.6088i	−0.0329467	−	3.15459i
$826$	5.98692	−	18.3983i	0.208312	−	0.640157i
$827$	−4.23478			−0.147258			−0.0736288	−	0.997286i	$-0.523458\pi$
$827$	−4.23478			−0.147258			−0.0736288	+	0.997286i	$0.523458\pi$
$828$	53.9702	+	7.20904i	1.87560	+	0.250532i
$829$	−11.3908	−	19.7294i	−0.395617	−	0.685229i	0.597562	−	0.801822i	$-0.296136\pi$
$829$	−11.3908	−	19.7294i	−0.395617	−	0.685229i	−0.993180	+	0.116593i	$0.962803\pi$
$830$	32.5152	−	6.08360i	1.12862	−	0.211165i
$831$	−15.3088	+	0.159886i	−0.531056	+	0.00554637i
$832$	10.2480	−	0.642072i	0.355286	−	0.0222598i
$833$	16.2899	+	8.38821i	0.564410	+	0.290634i
$834$	−37.9835	−	12.9337i	−1.31526	−	0.447857i
$835$	27.9634	+	48.4340i	0.967712	+	1.67613i
$836$	−12.4263	+	15.4525i	−0.429774	+	0.534436i
$837$	29.3329	+	15.7314i	1.01389	+	0.543756i
$838$	5.99020	−	17.0077i	0.206928	−	0.587523i
$839$	−18.1968	+	31.5177i	−0.628222	+	1.08811i	0.359686	+	0.933073i	$0.382884\pi$
$839$	−18.1968	+	31.5177i	−0.628222	+	1.08811i	−0.987908	+	0.155040i	$0.950449\pi$
$840$	3.52209	+	53.4770i	0.121524	+	1.84513i
$841$	−13.2894	−	23.0179i	−0.458255	−	0.793721i
$842$	23.6356	−	4.42221i	0.814535	−	0.152400i
$843$	−38.1069	−	21.4736i	−1.31247	−	0.739588i
$844$	23.6981	−	9.18951i	0.815722	−	0.316316i
$845$	−23.4702	+	40.6516i	−0.807400	+	1.39846i
$846$	−12.7352	−	4.18853i	−0.437845	−	0.144005i
$847$	9.76543	−	17.8942i	0.335544	−	0.614851i
$848$	−19.1337	+	4.20334i	−0.657054	+	0.144343i
$849$	17.0135	−	30.1921i	0.583901	−	1.03619i
$850$	−14.8752	+	42.2347i	−0.510217	+	1.44864i
$851$	−19.9897	+	34.6232i	−0.685239	+	1.18687i
$852$	−2.37934	+	16.4980i	−0.0815147	+	0.565212i
$853$	−20.4122	+	35.3549i	−0.698899	+	1.21053i	0.269950	+	0.962874i	$0.412993\pi$
$853$	−20.4122	+	35.3549i	−0.698899	+	1.21053i	−0.968849	+	0.247654i	$0.920340\pi$
$854$	−24.5017	+	22.0419i	−0.838430	+	0.754257i
$855$	24.9179	+	13.7006i	0.852173	+	0.468549i
$856$	−12.4610	+	0.389978i	−0.425908	+	0.0133292i
$857$		−	43.8043i		−	1.49633i	−0.663514	−	0.748164i	$-0.730936\pi$
$857$		−	43.8043i		−	1.49633i	0.663514	−	0.748164i	$-0.269064\pi$
$858$	−4.38289	+	12.8716i	−0.149629	+	0.439430i
$859$		−	43.0076i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$859$		−	43.0076i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$860$	−25.1594	−	20.2322i	−0.857927	−	0.689914i
$861$	0.906956	−	0.0312853i	0.0309090	−	0.00106620i
$862$	−8.56959	+	24.3313i	−0.291881	+	0.828727i
$863$	−2.45117	−	1.41519i	−0.0834389	−	0.0481735i	0.457700	−	0.889107i	$-0.348673\pi$
$863$	−2.45117	−	1.41519i	−0.0834389	−	0.0481735i	−0.541139	+	0.840933i	$0.682007\pi$
$864$	12.3213	+	26.6868i	0.419178	+	0.907904i
$865$	22.4773	+	38.9319i	0.764252	+	1.32372i
$866$	0.0344492	+	0.0401961i	0.00117063	+	0.00136592i
$867$	−15.3138	−	8.62943i	−0.520083	−	0.293071i
$868$	31.2993	−	13.0109i	1.06237	−	0.441618i
$869$	32.4475	−	18.7336i	1.10071	−	0.635493i
$870$	−3.05993	−	15.4596i	−0.103741	−	0.524130i
$871$	−2.73644			−0.0927207
$872$	−28.7433	−	15.4169i	−0.973372	−	0.522081i
$873$	16.0568	+	8.82849i	0.543441	+	0.298799i
$874$	−5.41073	−	28.9189i	−0.183021	−	0.978197i
$875$	−37.1886	+	68.1442i	−1.25720	+	2.30370i
$876$	37.4753	−	14.9841i	1.26617	−	0.506264i
$877$		−	35.6911i		−	1.20520i	−0.798043	−	0.602601i	$-0.794131\pi$
$877$		−	35.6911i		−	1.20520i	0.798043	−	0.602601i	$-0.205869\pi$
$878$	7.70924	+	2.71523i	0.260174	+	0.0916345i
$879$	1.46704	−	0.867550i	0.0494821	−	0.0292618i
$880$	−68.1783	−	21.6405i	−2.29829	−	0.729500i
$881$		−	45.7341i		−	1.54082i	−0.637548	−	0.770411i	$-0.720051\pi$
$881$		−	45.7341i		−	1.54082i	0.637548	−	0.770411i	$-0.279949\pi$
$882$	28.6251	+	7.91221i	0.963858	+	0.266418i
$883$	48.9258			1.64648			0.823242	−	0.567690i	$-0.192163\pi$
$883$	48.9258			1.64648			0.823242	+	0.567690i	$0.192163\pi$
$884$	4.21078	−	5.23622i	0.141624	−	0.176113i
$885$	18.1802	−	32.2626i	0.611122	−	1.08449i
$886$	14.4239	+	5.08015i	0.484579	+	0.170671i
$887$	−21.3038			−0.715313			−0.357656	−	0.933853i	$-0.616424\pi$
$887$	−21.3038			−0.715313			−0.357656	+	0.933853i	$0.616424\pi$
$888$	−21.5636	+	0.900359i	−0.723627	+	0.0302141i
$889$	3.92765	+	2.14345i	0.131729	+	0.0718889i
$890$	−49.6585	+	9.29111i	−1.66456	+	0.311439i
$891$	−38.8903	+	1.62558i	−1.30288	+	0.0544589i
$892$	26.5098	+	21.3182i	0.887614	+	0.713787i
$893$			7.24383i			0.242405i
$894$	10.8367	−	9.48541i	0.362432	−	0.317240i
$895$	−0.225950	−	0.391357i	−0.00755267	−	0.0130816i
$896$	28.9876	+	7.46442i	0.968409	+	0.249369i
$897$	−10.2692	−	17.3654i	−0.342879	−	0.579814i
$898$	35.2110	−	30.1769i	1.17501	−	1.00701i
$899$	−8.63205	+	4.98372i	−0.287895	+	0.166216i
$900$	−9.60925	+	71.9393i	−0.320308	+	2.39798i
$901$	−6.40966	+	11.1019i	−0.213537	+	0.369857i
$902$	−0.402375	+	1.14245i	−0.0133976	+	0.0380393i
$903$	−15.1764	+	9.47427i	−0.505038	+	0.315284i
$904$	−11.9104	+	22.2058i	−0.396132	+	0.738553i
$905$	−28.7487			−0.955638
$906$	19.1357	−	16.7496i	0.635742	−	0.556469i
$907$	−49.8060			−1.65378			−0.826890	−	0.562364i	$-0.809892\pi$
$907$	−49.8060			−1.65378			−0.826890	+	0.562364i	$0.809892\pi$
$908$	21.6731	+	3.35710i	0.719247	+	0.111409i
$909$	−5.32215	+	0.111182i	−0.176525	+	0.00368767i
$910$	14.7626	−	13.2805i	0.489375	−	0.440245i
$911$	−51.2355	−	29.5808i	−1.69751	−	0.980057i	−0.948112	−	0.317936i	$-0.897010\pi$
$911$	−51.2355	−	29.5808i	−1.69751	−	0.980057i	−0.749397	−	0.662121i	$-0.769656\pi$
$912$	11.6178	−	10.8294i	0.384705	−	0.358598i
$913$	21.1885	+	12.2332i	0.701237	+	0.404859i
$914$	26.0312	+	9.16829i	0.861034	+	0.303260i
$915$	−54.2974	+	32.1093i	−1.79502	+	1.06150i
$916$	−1.83887	+	11.8716i	−0.0607581	+	0.392248i
$917$	−40.9841	−	22.3664i	−1.35341	−	0.738603i
$918$	18.3337	+	5.81839i	0.605103	+	0.192035i
$919$	−2.66770	−	1.54020i	−0.0879994	−	0.0508065i	0.455355	−	0.890310i	$-0.349512\pi$
$919$	−2.66770	−	1.54020i	−0.0879994	−	0.0508065i	−0.543354	+	0.839504i	$0.682846\pi$
$920$	90.2068	−	55.9143i	2.97403	−	1.84344i
$921$	−11.6793	+	0.121980i	−0.384848	+	0.00401937i
$922$	2.99077	+	15.9849i	0.0984959	+	0.526435i
$923$	5.34862	−	3.08803i	0.176052	−	0.101644i
$924$	−23.7607	+	31.7277i	−0.781669	+	1.04376i
$925$	−46.1508	−	26.6452i	−1.51743	−	0.876088i
$926$	−2.78994	+	7.92138i	−0.0916833	+	0.260313i
$927$	38.9926	−	0.814571i	1.28069	−	0.0267540i
$928$	−8.73634	−	1.07461i	−0.286785	−	0.0352759i
$929$	−18.6172	+	10.7486i	−0.610810	+	0.352651i	−0.773282	−	0.634062i	$-0.781386\pi$
$929$	−18.6172	+	10.7486i	−0.610810	+	0.352651i	0.162472	+	0.986713i	$0.448053\pi$
$930$	63.6430	−	12.5969i	2.08694	−	0.413069i
$931$	−0.771162	−	16.0284i	−0.0252738	−	0.525311i
$932$	−45.0138	−	36.1985i	−1.47448	−	1.18572i
$933$	−46.1648	−	26.0142i	−1.51137	−	0.851668i
$934$	−52.2617	+	9.77816i	−1.71006	+	0.319951i
$935$	−40.5371	+	23.4041i	−1.32570	+	0.765396i
$936$	4.94621	−	9.70301i	0.161672	−	0.317153i
$937$			17.6261i			0.575820i	0.957657	+	0.287910i	$0.0929604\pi$
$937$			17.6261i			0.575820i	−0.957657	+	0.287910i	$0.907040\pi$
$938$	−7.58566	−	2.46843i	−0.247681	−	0.0805970i
$939$	11.1013	+	18.7725i	0.362277	+	0.612617i
$940$	−24.3633	+	9.44747i	−0.794643	+	0.308142i
$941$	13.7771	−	23.8627i	0.449121	−	0.777900i	−0.549208	−	0.835686i	$-0.685071\pi$
$941$	13.7771	−	23.8627i	0.449121	−	0.777900i	0.998329	+	0.0577853i	$0.0184039\pi$
$942$	−23.4994	+	4.65125i	−0.765650	+	0.151546i
$943$	−0.898562	−	1.55635i	−0.0292612	−	0.0506819i
$944$	−13.9444	−	15.2764i	−0.453852	−	0.497205i
$945$	50.7256	+	25.6540i	1.65010	+	0.834526i
$946$	−4.39155	−	23.4717i	−0.142782	−	0.763130i
$947$	7.13268	+	12.3542i	0.231781	+	0.401456i	0.958332	−	0.285656i	$-0.0922115\pi$
$947$	7.13268	+	12.3542i	0.231781	+	0.401456i	−0.726551	+	0.687112i	$0.758878\pi$
$948$	−27.8649	+	11.1415i	−0.905011	+	0.361858i
$949$	−12.9506	−	7.47705i	−0.420395	−	0.242715i
$950$	38.5473	−	7.21220i	1.25064	−	0.233995i
$951$	27.7363	+	46.9026i	0.899412	+	1.52092i
$952$	16.3960	−	10.7169i	0.531398	−	0.347337i
$953$	−22.2354			−0.720274			−0.360137	−	0.932899i	$-0.617270\pi$
$953$	−22.2354			−0.720274			−0.360137	+	0.932899i	$0.617270\pi$
$954$	−6.49176	+	19.7381i	−0.210178	+	0.639046i
$955$	71.6961	−	41.3938i	2.32003	−	1.33947i
$956$	1.22868	+	3.16853i	0.0397383	+	0.102478i
$957$	5.72233	−	10.1548i	0.184977	−	0.328259i
$958$	28.8492	−	24.7246i	0.932074	−	0.798814i
$959$	4.03525	−	7.39419i	0.130305	−	0.238771i
$960$	51.5749	+	24.9506i	1.66457	+	0.805278i
$961$	−5.01659	−	8.68899i	−0.161826	−	0.280290i
$962$	5.20376	+	6.07187i	0.167776	+	0.195765i
$963$	−6.37105	+	11.5873i	−0.205304	+	0.373397i
$964$	−41.5102	−	6.42980i	−1.33695	−	0.207090i
$965$	−8.80995	+	15.2593i	−0.283602	+	0.491214i
$966$	−12.8026	−	57.4019i	−0.411917	−	1.84688i
$967$	−1.33682	+	0.771816i	−0.0429894	+	0.0248199i	−0.521341	−	0.853349i	$-0.674568\pi$
$967$	−1.33682	+	0.771816i	−0.0429894	+	0.0248199i	0.478351	+	0.878169i	$0.341235\pi$
$968$	−11.4815	−	18.5231i	−0.369029	−	0.595356i
$969$	−0.108541	−	10.3926i	−0.00348683	−	0.333858i
$970$	35.1068	−	6.56848i	1.12721	−	0.210901i
$971$	9.12179	+	5.26647i	0.292732	+	0.169009i	0.639173	−	0.769063i	$-0.279277\pi$
$971$	9.12179	+	5.26647i	0.292732	+	0.169009i	−0.346441	+	0.938072i	$0.612610\pi$
$972$	31.0166	+	3.15770i	0.994858	+	0.101283i
$973$	1.04169	+	43.3276i	0.0333950	+	1.38902i
$974$	1.53597	−	4.36102i	0.0492156	−	0.139736i
$975$	23.1471	−	13.6883i	0.741300	−	0.438375i
$976$	7.55973	+	34.4121i	0.241981	+	1.10150i
$977$	8.77022	−	15.1905i	0.280584	−	0.485986i	−0.690945	−	0.722908i	$-0.742805\pi$
$977$	8.77022	−	15.1905i	0.280584	−	0.485986i	0.971529	+	0.236922i	$0.0761385\pi$
$978$	31.0736	−	6.15043i	0.993625	−	0.196669i
$979$	−32.3599	−	18.6830i	−1.03423	−	0.597112i
$980$	52.9030	−	23.4981i	1.68992	−	0.750620i
$981$	−29.5927	+	17.9197i	−0.944821	+	0.572131i
$982$	17.3823	+	6.12214i	0.554693	+	0.195365i
$983$	40.7523			1.29980			0.649898	−	0.760022i	$-0.274812\pi$
$983$	40.7523			1.29980			0.649898	+	0.760022i	$0.274812\pi$
$984$	0.449604	−	0.859682i	0.0143329	−	0.0274057i
$985$		−	38.2110i		−	1.21750i
$986$	−4.37356	+	3.74827i	−0.139283	+	0.119369i
$987$	0.499205	+	14.4719i	0.0158899	+	0.460644i
$988$	−5.81537	−	0.900784i	−0.185012	−	0.0286577i
$989$	30.6829	+	17.7148i	0.975659	+	0.563297i
$990$	−56.5639	+	50.5638i	−1.79772	+	1.60702i
$991$	−31.7444	+	18.3276i	−1.00839	+	0.582196i	−0.910721	−	0.413023i	$-0.864473\pi$
$991$	−31.7444	+	18.3276i	−1.00839	+	0.582196i	−0.0976723	+	0.995219i	$0.531140\pi$
$992$	4.42388	−	35.9651i	0.140458	−	1.14189i
$993$	26.9082	−	15.9124i	0.853906	−	0.504966i
$994$	17.6125	−	3.73553i	0.558633	−	0.118484i
$995$	47.0109	+	81.4252i	1.49034	+	2.58135i
$996$	−15.3988	−	12.1205i	−0.487929	−	0.384053i
$997$	18.4513			0.584359			0.292179	−	0.956364i	$-0.405620\pi$
$997$	18.4513			0.584359			0.292179	+	0.956364i	$0.405620\pi$
$998$	24.7423	−	21.2048i	0.783203	−	0.671227i
$999$	−10.8191	+	20.1735i	−0.342302	+	0.638261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.70	yes	180
7.3	odd	6		504.2.bf.b.115.52	yes	180
8.3	odd	2	inner	504.2.cz.b.187.10	yes	180
9.4	even	3		504.2.bf.b.355.52	yes	180
56.3	even	6		504.2.bf.b.115.51	✓	180
63.31	odd	6	inner	504.2.cz.b.283.10	yes	180
72.67	odd	6		504.2.bf.b.355.51	yes	180
504.283	even	6	inner	504.2.cz.b.283.70	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.51	✓	180	56.3	even	6
504.2.bf.b.115.52	yes	180	7.3	odd	6
504.2.bf.b.355.51	yes	180	72.67	odd	6
504.2.bf.b.355.52	yes	180	9.4	even	3
504.2.cz.b.187.10	yes	180	8.3	odd	2	inner
504.2.cz.b.187.70	yes	180	1.1	even	1	trivial
504.2.cz.b.283.10	yes	180	63.31	odd	6	inner
504.2.cz.b.283.70	yes	180	504.283	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07381 - 0.920287i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(0.306143 - 1.97643i) q^{4} -4.13478 q^{5} +(1.61332 + 1.84315i) q^{6} +(1.26742 - 2.32242i) q^{7} +(-1.49014 - 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +O(q^{10})\)	\(q+(1.07381 - 0.920287i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(0.306143 - 1.97643i) q^{4} -4.13478 q^{5} +(1.61332 + 1.84315i) q^{6} +(1.26742 - 2.32242i) q^{7} +(-1.49014 - 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +(-4.43997 + 3.80518i) q^{10} -4.32492 q^{11} +(3.42863 + 0.494476i) q^{12} +(-0.641757 - 1.11156i) q^{13} +(-0.776322 - 3.66024i) q^{14} +(-0.0747925 - 7.16125i) q^{15} +(-3.81255 - 1.21014i) q^{16} +(-2.26685 + 1.30876i) q^{17} +(-3.16307 + 2.82754i) q^{18} +(1.98530 + 1.14621i) q^{19} +(-1.26583 + 8.17210i) q^{20} +(4.04526 + 2.15311i) q^{21} +(-4.64415 + 3.98017i) q^{22} -9.07493i q^{23} +(4.13676 - 2.62435i) q^{24} +12.0964 q^{25} +(-1.71208 - 0.603001i) q^{26} +(-0.162774 - 5.19360i) q^{27} +(-4.20209 - 3.21596i) q^{28} +(1.34755 + 0.778011i) q^{29} +(-6.67072 - 7.62100i) q^{30} +(-3.20286 + 5.54751i) q^{31} +(-5.20764 + 2.20918i) q^{32} +(-0.0782320 - 7.49058i) q^{33} +(-1.22973 + 3.49152i) q^{34} +(-5.24051 + 9.60269i) q^{35} +(-0.794391 + 5.94718i) q^{36} +(-3.81526 - 2.20274i) q^{37} +(3.18668 - 0.596228i) q^{38} +(1.91356 - 1.13160i) q^{39} +(6.16141 + 9.94022i) q^{40} +(0.171501 - 0.0990159i) q^{41} +(6.32533 - 1.41076i) q^{42} +(-1.95206 + 3.38106i) q^{43} +(-1.32405 + 8.54791i) q^{44} +(12.4016 - 0.259075i) q^{45} +(-8.35154 - 9.74477i) q^{46} +(1.57995 + 2.73655i) q^{47} +(2.02695 - 6.62506i) q^{48} +(-3.78728 - 5.88698i) q^{49} +(12.9892 - 11.1321i) q^{50} +(-2.30773 - 3.90241i) q^{51} +(-2.39338 + 0.928093i) q^{52} +(4.24135 - 2.44875i) q^{53} +(-4.95439 - 5.42715i) q^{54} +17.8826 q^{55} +(-7.47187 + 0.413790i) q^{56} +(-1.94928 + 3.45918i) q^{57} +(2.16301 - 0.404700i) q^{58} +(4.47816 + 2.58546i) q^{59} +(-14.1766 - 2.04455i) q^{60} +(-4.40409 - 7.62810i) q^{61} +(1.66604 + 8.90453i) q^{62} +(-3.65592 + 7.04516i) q^{63} +(-3.55895 + 7.16477i) q^{64} +(2.65352 + 4.59603i) q^{65} +(-6.97749 - 7.97147i) q^{66} +(1.06600 - 1.84636i) q^{67} +(1.89270 + 4.88093i) q^{68} +(15.7174 - 0.164153i) q^{69} +(3.20992 + 15.1343i) q^{70} +4.81184i q^{71} +(4.62009 + 7.11722i) q^{72} +(10.0900 - 5.82545i) q^{73} +(-6.12403 + 1.14581i) q^{74} +(0.218807 + 20.9504i) q^{75} +(2.87320 - 3.57290i) q^{76} +(-5.48150 + 10.0443i) q^{77} +(1.01340 - 2.97615i) q^{78} +(-7.50245 + 4.33154i) q^{79} +(15.7640 + 5.00366i) q^{80} +(8.99215 - 0.375863i) q^{81} +(0.0930362 - 0.264154i) q^{82} +(-4.89916 - 2.82853i) q^{83} +(5.49390 - 7.33601i) q^{84} +(9.37290 - 5.41145i) q^{85} +(1.01541 + 5.42707i) q^{86} +(-1.32311 + 2.34798i) q^{87} +(6.44475 + 10.3973i) q^{88} +(7.48220 + 4.31985i) q^{89} +(13.0786 - 11.6912i) q^{90} +(-3.39488 + 0.0816202i) q^{91} +(-17.9360 - 2.77823i) q^{92} +(-9.66598 - 5.44686i) q^{93} +(4.21498 + 1.48453i) q^{94} +(-8.20876 - 4.73933i) q^{95} +(-3.92040 - 8.97945i) q^{96} +(-5.28964 - 3.05398i) q^{97} +(-9.48454 - 2.83612i) q^{98} +(12.9719 - 0.270989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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