LMFDB - Embedded newform 418.2.m.b.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	418.151
Dual form			418.2.m.b.227.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.809704 - 0.263089i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.31139 + 1.67932i) q^{5} +(0.500425 - 0.688776i) q^{6} +(1.24718 + 0.405232i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.84065 + 1.33731i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.809704 - 0.263089i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.31139 + 1.67932i) q^{5} +(0.500425 - 0.688776i) q^{6} +(1.24718 + 0.405232i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.84065 + 1.33731i) q^{9} +2.85703 q^{10} +(2.44512 - 2.24084i) q^{11} -0.851374i q^{12} +(-2.28629 + 1.66109i) q^{13} +(1.24718 - 0.405232i) q^{14} +(2.31335 + 0.751653i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.39494 + 3.29635i) q^{17} +(-0.703064 + 2.16381i) q^{18} +(2.33446 - 3.68108i) q^{19} +(2.31139 - 1.67932i) q^{20} +1.11646 q^{21} +(0.661011 - 3.25009i) q^{22} -2.64239 q^{23} +(-0.500425 - 0.688776i) q^{24} +(0.977304 + 3.00783i) q^{25} +(-0.873285 + 2.68769i) q^{26} +(-2.63982 + 3.63340i) q^{27} +(0.770798 - 1.06091i) q^{28} +(1.30214 - 4.00758i) q^{29} +(2.31335 - 0.751653i) q^{30} +(-4.00841 - 5.51710i) q^{31} -1.00000 q^{32} +(1.39029 - 2.45770i) q^{33} +4.07452i q^{34} +(2.20219 + 3.03106i) q^{35} +(0.703064 + 2.16381i) q^{36} +(1.80436 + 0.586271i) q^{37} +(-0.275068 - 4.35021i) q^{38} +(-1.41421 + 1.94649i) q^{39} +(0.882871 - 2.71720i) q^{40} +(-3.72107 - 11.4523i) q^{41} +(0.903232 - 0.656237i) q^{42} +0.0556763i q^{43} +(-1.37558 - 3.01791i) q^{44} -6.50021 q^{45} +(-2.13774 + 1.55316i) q^{46} +(2.47296 + 7.61099i) q^{47} +(-0.809704 - 0.263089i) q^{48} +(-4.27188 - 3.10370i) q^{49} +(2.55862 + 1.85894i) q^{50} +(-1.07196 + 3.29915i) q^{51} +(0.873285 + 2.68769i) q^{52} +(1.64175 + 2.25967i) q^{53} +4.49113i q^{54} +(9.41472 - 1.07331i) q^{55} -1.31136i q^{56} +(0.921769 - 3.59475i) q^{57} +(-1.30214 - 4.00758i) q^{58} +(4.90694 + 1.59436i) q^{59} +(1.42973 - 1.96785i) q^{60} +(-0.510447 + 0.702571i) q^{61} +(-6.48574 - 2.10734i) q^{62} +(-2.83753 + 0.921969i) q^{63} +(-0.809017 + 0.587785i) q^{64} -8.07399 q^{65} +(-0.319838 - 2.80551i) q^{66} +12.0034i q^{67} +(2.39494 + 3.29635i) q^{68} +(-2.13955 + 0.695183i) q^{69} +(3.56322 + 1.15776i) q^{70} +(-7.58053 + 10.4337i) q^{71} +(1.84065 + 1.33731i) q^{72} +(-8.29723 - 2.69593i) q^{73} +(1.80436 - 0.586271i) q^{74} +(1.58266 + 2.17834i) q^{75} +(-2.77952 - 3.35771i) q^{76} +(3.95756 - 1.80388i) q^{77} +2.40599i q^{78} +(-5.96646 + 4.33489i) q^{79} +(-0.882871 - 2.71720i) q^{80} +(0.927624 - 2.85493i) q^{81} +(-9.74189 - 7.07789i) q^{82} +(5.21194 - 7.17362i) q^{83} +(0.345004 - 1.06181i) q^{84} +(-11.0713 + 3.59727i) q^{85} +(0.0327257 + 0.0450431i) q^{86} -3.58754i q^{87} +(-2.88675 - 1.63299i) q^{88} +4.88162i q^{89} +(-5.25878 + 3.82073i) q^{90} +(-3.52453 + 1.14519i) q^{91} +(-0.816543 + 2.51306i) q^{92} +(-4.69711 - 3.41265i) q^{93} +(6.47430 + 4.70385i) q^{94} +(11.5775 - 4.58809i) q^{95} +(-0.809704 + 0.263089i) q^{96} +(7.58030 + 10.4334i) q^{97} -5.28034 q^{98} +(-1.50391 + 7.39448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.809704	−	0.263089i	0.467483	−	0.151894i	−0.0657973	−	0.997833i	$-0.520959\pi$
$3$	0.809704	−	0.263089i	0.467483	−	0.151894i	0.533280	+	0.845939i	$0.320959\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.31139	+	1.67932i	1.03368	+	0.751015i	0.969043	−	0.246894i	$-0.0794098\pi$
$5$	2.31139	+	1.67932i	1.03368	+	0.751015i	0.0646408	+	0.997909i	$0.479410\pi$
$6$	0.500425	−	0.688776i	0.204298	−	0.281192i
$7$	1.24718	+	0.405232i	0.471388	+	0.153163i	0.535072	−	0.844807i	$-0.320285\pi$
$7$	1.24718	+	0.405232i	0.471388	+	0.153163i	−0.0636830	+	0.997970i	$0.520285\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.84065	+	1.33731i	−0.613548	+	0.445769i
$10$	2.85703			0.903472
$11$	2.44512	−	2.24084i	0.737232	−	0.675640i
$11$	2.44512	−	2.24084i	0.737232	−	0.675640i
$12$		−	0.851374i		−	0.245770i
$13$	−2.28629	+	1.66109i	−0.634103	+	0.460703i	−0.857819	−	0.513952i	$-0.828181\pi$
$13$	−2.28629	+	1.66109i	−0.634103	+	0.460703i	0.223716	+	0.974654i	$0.428181\pi$
$14$	1.24718	−	0.405232i	0.333322	−	0.108303i
$15$	2.31335	+	0.751653i	0.597304	+	0.194076i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.39494	+	3.29635i	−0.580858	+	0.799483i	−0.993789	−	0.111279i	$-0.964505\pi$
$17$	−2.39494	+	3.29635i	−0.580858	+	0.799483i	0.412931	+	0.910762i	$0.364505\pi$
$18$	−0.703064	+	2.16381i	−0.165714	+	0.510015i
$19$	2.33446	−	3.68108i	0.535561	−	0.844497i
$19$	2.33446	−	3.68108i	0.535561	−	0.844497i
$20$	2.31139	−	1.67932i	0.516842	−	0.375507i
$21$	1.11646			0.243631
$22$	0.661011	−	3.25009i	0.140928	−	0.692921i
$23$	−2.64239			−0.550976			−0.275488	−	0.961304i	$-0.588839\pi$
$23$	−2.64239			−0.550976			−0.275488	+	0.961304i	$0.588839\pi$
$24$	−0.500425	−	0.688776i	−0.102149	−	0.140596i
$25$	0.977304	+	3.00783i	0.195461	+	0.601567i
$26$	−0.873285	+	2.68769i	−0.171265	+	0.527100i
$27$	−2.63982	+	3.63340i	−0.508034	+	0.699249i
$28$	0.770798	−	1.06091i	0.145667	−	0.200493i
$29$	1.30214	−	4.00758i	0.241802	−	0.744189i	−0.754344	−	0.656479i	$-0.772045\pi$
$29$	1.30214	−	4.00758i	0.241802	−	0.744189i	0.996146	−	0.0877102i	$-0.0279550\pi$
$30$	2.31335	−	0.751653i	0.422358	−	0.137232i
$31$	−4.00841	−	5.51710i	−0.719931	−	0.990900i	−0.999526	−	0.0307820i	$-0.990200\pi$
$31$	−4.00841	−	5.51710i	−0.719931	−	0.990900i	0.279595	−	0.960118i	$-0.409800\pi$
$32$	−1.00000			−0.176777
$33$	1.39029	−	2.45770i	0.242018	−	0.427832i
$34$			4.07452i			0.698774i
$35$	2.20219	+	3.03106i	0.372238	+	0.512342i
$36$	0.703064	+	2.16381i	0.117177	+	0.360635i
$37$	1.80436	+	0.586271i	0.296635	+	0.0963824i	0.453553	−	0.891229i	$-0.350156\pi$
$37$	1.80436	+	0.586271i	0.296635	+	0.0963824i	−0.156919	+	0.987611i	$0.550156\pi$
$38$	−0.275068	−	4.35021i	−0.0446218	−	0.705697i
$39$	−1.41421	+	1.94649i	−0.226454	+	0.311687i
$40$	0.882871	−	2.71720i	0.139594	−	0.429627i
$41$	−3.72107	−	11.4523i	−0.581133	−	1.78854i	−0.614273	−	0.789094i	$-0.710550\pi$
$41$	−3.72107	−	11.4523i	−0.581133	−	1.78854i	0.0331393	−	0.999451i	$-0.489450\pi$
$42$	0.903232	−	0.656237i	0.139372	−	0.101260i
$43$			0.0556763i			0.00849055i	0.999991	+	0.00424528i	$0.00135132\pi$
$43$			0.0556763i			0.00849055i	−0.999991	+	0.00424528i	$0.998649\pi$
$44$	−1.37558	−	3.01791i	−0.207377	−	0.454967i
$45$	−6.50021			−0.968994
$46$	−2.13774	+	1.55316i	−0.315192	+	0.229001i
$47$	2.47296	+	7.61099i	0.360719	+	1.11018i	0.952619	+	0.304166i	$0.0983779\pi$
$47$	2.47296	+	7.61099i	0.360719	+	1.11018i	−0.591900	+	0.806011i	$0.701622\pi$
$48$	−0.809704	−	0.263089i	−0.116871	−	0.0379736i
$49$	−4.27188	−	3.10370i	−0.610269	−	0.443386i
$50$	2.55862	+	1.85894i	0.361843	+	0.262894i
$51$	−1.07196	+	3.29915i	−0.150104	+	0.461974i
$52$	0.873285	+	2.68769i	0.121103	+	0.372716i
$53$	1.64175	+	2.25967i	0.225511	+	0.310389i	0.906747	−	0.421674i	$-0.138557\pi$
$53$	1.64175	+	2.25967i	0.225511	+	0.310389i	−0.681236	+	0.732064i	$0.738557\pi$
$54$			4.49113i			0.611166i
$55$	9.41472	−	1.07331i	1.26948	−	0.144725i
$56$		−	1.31136i		−	0.175238i
$57$	0.921769	−	3.59475i	0.122091	−	0.476137i
$58$	−1.30214	−	4.00758i	−0.170980	−	0.526221i
$59$	4.90694	+	1.59436i	0.638829	+	0.207568i	0.610482	−	0.792030i	$-0.290976\pi$
$59$	4.90694	+	1.59436i	0.638829	+	0.207568i	0.0283471	+	0.999598i	$0.490976\pi$
$60$	1.42973	−	1.96785i	0.184577	−	0.254049i
$61$	−0.510447	+	0.702571i	−0.0653561	+	0.0899550i	−0.840444	−	0.541899i	$-0.817706\pi$
$61$	−0.510447	+	0.702571i	−0.0653561	+	0.0899550i	0.775088	+	0.631854i	$0.217706\pi$
$62$	−6.48574	−	2.10734i	−0.823690	−	0.267633i
$63$	−2.83753	+	0.921969i	−0.357495	+	0.116157i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−8.07399			−1.00146
$66$	−0.319838	−	2.80551i	−0.0393694	−	0.345335i
$67$			12.0034i			1.46645i	0.679985	+	0.733226i	$0.261986\pi$
$67$			12.0034i			1.46645i	−0.679985	+	0.733226i	$0.738014\pi$
$68$	2.39494	+	3.29635i	0.290429	+	0.399742i
$69$	−2.13955	+	0.695183i	−0.257572	+	0.0836902i
$70$	3.56322	+	1.15776i	0.425886	+	0.138379i
$71$	−7.58053	+	10.4337i	−0.899644	+	1.23825i	0.0709381	+	0.997481i	$0.477401\pi$
$71$	−7.58053	+	10.4337i	−0.899644	+	1.23825i	−0.970582	+	0.240772i	$0.922599\pi$
$72$	1.84065	+	1.33731i	0.216922	+	0.157603i
$73$	−8.29723	−	2.69593i	−0.971117	−	0.315535i	−0.219850	−	0.975534i	$-0.570557\pi$
$73$	−8.29723	−	2.69593i	−0.971117	−	0.315535i	−0.751267	+	0.659999i	$0.770557\pi$
$74$	1.80436	−	0.586271i	0.209752	−	0.0681527i
$75$	1.58266	+	2.17834i	0.182749	+	0.251533i
$76$	−2.77952	−	3.35771i	−0.318833	−	0.385156i
$77$	3.95756	−	1.80388i	0.451006	−	0.205572i
$78$			2.40599i			0.272425i
$79$	−5.96646	+	4.33489i	−0.671279	+	0.487713i	−0.870453	−	0.492251i	$-0.836174\pi$
$79$	−5.96646	+	4.33489i	−0.671279	+	0.487713i	0.199174	+	0.979964i	$0.436174\pi$
$80$	−0.882871	−	2.71720i	−0.0987080	−	0.303792i
$81$	0.927624	−	2.85493i	0.103069	−	0.317215i
$82$	−9.74189	−	7.07789i	−1.07581	−	0.781623i
$83$	5.21194	−	7.17362i	0.572085	−	0.787408i	−0.420715	−	0.907193i	$-0.638221\pi$
$83$	5.21194	−	7.17362i	0.572085	−	0.787408i	0.992800	+	0.119785i	$0.0382207\pi$
$84$	0.345004	−	1.06181i	0.0376430	−	0.115853i
$85$	−11.0713	+	3.59727i	−1.20085	+	0.390179i
$86$	0.0327257	+	0.0450431i	0.00352890	+	0.00485712i
$87$		−	3.58754i		−	0.384624i
$88$	−2.88675	−	1.63299i	−0.307729	−	0.174077i
$89$			4.88162i			0.517450i	0.965951	+	0.258725i	$0.0833024\pi$
$89$			4.88162i			0.517450i	−0.965951	+	0.258725i	$0.916698\pi$
$90$	−5.25878	+	3.82073i	−0.554324	+	0.402740i
$91$	−3.52453	+	1.14519i	−0.369471	+	0.120049i
$92$	−0.816543	+	2.51306i	−0.0851305	+	0.262005i
$93$	−4.69711	−	3.41265i	−0.487068	−	0.353875i
$94$	6.47430	+	4.70385i	0.667773	+	0.485165i
$95$	11.5775	−	4.58809i	1.18783	−	0.470728i
$96$	−0.809704	+	0.263089i	−0.0826401	+	0.0268514i
$97$	7.58030	+	10.4334i	0.769663	+	1.05935i	0.996348	+	0.0853817i	$0.0272110\pi$
$97$	7.58030	+	10.4334i	0.769663	+	1.05935i	−0.226686	+	0.973968i	$0.572789\pi$
$98$	−5.28034			−0.533395
$99$	−1.50391	+	7.39448i	−0.151148	+	0.743173i
$100$	3.16262			0.316262
$101$	7.17220	+	9.87169i	0.713661	+	0.982269i	0.999711	+	0.0240548i	$0.00765761\pi$
$101$	7.17220	+	9.87169i	0.713661	+	0.982269i	−0.286050	+	0.958215i	$0.592342\pi$
$102$	1.07196	+	3.29915i	0.106140	+	0.326665i
$103$	−0.466399	−	0.151542i	−0.0459556	−	0.0149319i	0.285949	−	0.958245i	$-0.407691\pi$
$103$	−0.466399	−	0.151542i	−0.0459556	−	0.0149319i	−0.331905	+	0.943313i	$0.607691\pi$
$104$	2.28629	+	1.66109i	0.224189	+	0.162883i
$105$	2.58056	+	1.87489i	0.251837	+	0.182970i
$106$	2.65640	+	0.863116i	0.258012	+	0.0838333i
$107$	−2.60566	−	8.01938i	−0.251898	−	0.775263i	−0.994425	−	0.105447i	$-0.966373\pi$
$107$	−2.60566	−	8.01938i	−0.251898	−	0.775263i	0.742527	−	0.669816i	$-0.233627\pi$
$108$	2.63982	+	3.63340i	0.254017	+	0.349624i
$109$	1.39626			0.133737			0.0668687	−	0.997762i	$-0.478699\pi$
$109$	1.39626			0.133737			0.0668687	+	0.997762i	$0.478699\pi$
$110$	6.98579	−	6.40216i	0.666069	−	0.610422i
$111$	1.61524			0.153312
$112$	−0.770798	−	1.06091i	−0.0728335	−	0.100247i
$113$	−4.50020	+	1.46220i	−0.423343	+	0.137552i	−0.512938	−	0.858426i	$-0.671443\pi$
$113$	−4.50020	+	1.46220i	−0.423343	+	0.137552i	0.0895947	+	0.995978i	$0.471443\pi$
$114$	−1.36722	−	3.45002i	−0.128051	−	0.323124i
$115$	−6.10758	−	4.43742i	−0.569535	−	0.413791i
$116$	−3.40905	−	2.47682i	−0.316523	−	0.229967i
$117$	1.98687	−	6.11494i	0.183686	−	0.565327i
$118$	4.90694	−	1.59436i	0.451721	−	0.146773i
$119$	−4.32270	+	3.14063i	−0.396261	+	0.287901i
$120$		−	2.43240i		−	0.222047i
$121$	0.957247	−	10.9583i	0.0870224	−	0.996206i
$122$			0.868425i			0.0786235i
$123$	−6.02593	−	8.29398i	−0.543340	−	0.747843i
$124$	−6.48574	+	2.10734i	−0.582436	+	0.189245i
$125$	1.62217	−	4.99252i	0.145091	−	0.446544i
$126$	−1.75369	+	2.41375i	−0.156231	+	0.215034i
$127$	5.53950	+	4.02468i	0.491551	+	0.357133i	0.805780	−	0.592214i	$-0.201746\pi$
$127$	5.53950	+	4.02468i	0.491551	+	0.357133i	−0.314230	+	0.949347i	$0.601746\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	0.0146478	+	0.0450813i	0.00128967	+	0.00396919i
$130$	−6.53200	+	4.74577i	−0.572894	+	0.416232i
$131$		−	16.1245i		−	1.40880i	−0.709801	−	0.704402i	$-0.751215\pi$
$131$		−	16.1245i		−	1.40880i	0.709801	−	0.704402i	$-0.248785\pi$
$132$	−1.90779	−	2.08171i	−0.166052	−	0.181190i
$133$	4.40317	−	3.64495i	0.381803	−	0.316058i
$134$	7.05544	+	9.71098i	0.609497	+	0.838901i
$135$	−12.2033	+	3.96509i	−1.05029	+	0.341261i
$136$	3.87510	+	1.25909i	0.332287	+	0.107966i
$137$	−8.02627	−	5.83142i	−0.685730	−	0.498212i	0.189524	−	0.981876i	$-0.439306\pi$
$137$	−8.02627	−	5.83142i	−0.685730	−	0.498212i	−0.875254	+	0.483664i	$0.839306\pi$
$138$	−1.32232	+	1.82001i	−0.112563	+	0.154930i
$139$	9.96726	+	3.23856i	0.845412	+	0.274691i	0.699523	−	0.714610i	$-0.253396\pi$
$139$	9.96726	+	3.23856i	0.845412	+	0.274691i	0.145889	+	0.989301i	$0.453396\pi$
$140$	3.56322	−	1.15776i	0.301147	−	0.0978487i
$141$	4.00474	+	5.51205i	0.337260	+	0.464198i
$142$			12.8968i			1.08227i
$143$	−1.86802	+	9.18478i	−0.156212	+	0.768069i
$144$	2.27516			0.189597
$145$	9.73977	−	7.07636i	0.808844	−	0.587659i
$146$	−8.29723	+	2.69593i	−0.686683	+	0.223117i
$147$	−4.27551	−	1.38920i	−0.352638	−	0.114579i
$148$	1.11515	−	1.53488i	0.0916651	−	0.126166i
$149$	−6.52406	+	8.97960i	−0.534472	+	0.735637i	−0.987804	−	0.155705i	$-0.950235\pi$
$149$	−6.52406	+	8.97960i	−0.534472	+	0.735637i	0.453332	+	0.891342i	$0.350235\pi$
$150$	2.56079	+	0.832051i	0.209088	+	0.0679367i
$151$	5.65778	+	17.4129i	0.460424	+	1.41704i	0.864648	+	0.502379i	$0.167542\pi$
$151$	5.65778	+	17.4129i	0.460424	+	1.41704i	−0.404224	+	0.914660i	$0.632458\pi$
$152$	−4.22230	−	1.08268i	−0.342474	−	0.0878173i
$153$		−	9.27019i		−	0.749450i
$154$	2.14144	−	3.78557i	0.172562	−	0.305050i
$155$		−	19.4835i		−	1.56496i
$156$	1.41421	+	1.94649i	0.113227	+	0.155844i
$157$	0.147749	+	0.454725i	0.0117917	+	0.0362910i	0.956779	−	0.290815i	$-0.0939265\pi$
$157$	0.147749	+	0.454725i	0.0117917	+	0.0362910i	−0.944988	+	0.327106i	$0.893927\pi$
$158$	−2.27898	+	7.01399i	−0.181306	+	0.558003i
$159$	1.92382	+	1.39774i	0.152569	+	0.110848i
$160$	−2.31139	−	1.67932i	−0.182731	−	0.132762i
$161$	−3.29553	−	1.07078i	−0.259724	−	0.0843894i
$162$	−0.927624	−	2.85493i	−0.0728810	−	0.224305i
$163$	−6.68449	+	4.85656i	−0.523570	+	0.380396i	−0.817947	−	0.575294i	$-0.804888\pi$
$163$	−6.68449	+	4.85656i	−0.523570	+	0.380396i	0.294377	+	0.955689i	$0.404888\pi$
$164$	−12.0416			−0.940294
$165$	7.34076	−	3.34597i	0.571477	−	0.260483i
$166$		−	8.86709i		−	0.688219i
$167$	19.5784	−	14.2245i	1.51502	−	1.10073i	0.551134	−	0.834417i	$-0.314195\pi$
$167$	19.5784	−	14.2245i	1.51502	−	1.10073i	0.963887	−	0.266311i	$-0.0858047\pi$
$168$	−0.345004	−	1.06181i	−0.0266176	−	0.0819207i
$169$	−1.54931	+	4.76829i	−0.119178	+	0.366791i
$170$	−6.84242	+	9.41778i	−0.524790	+	0.722311i
$171$	0.625823	+	9.89744i	0.0478579	+	0.756876i
$172$	0.0529513	+	0.0172049i	0.00403750	+	0.00131186i
$173$	−6.98406	−	21.4947i	−0.530989	−	1.63421i	−0.752161	−	0.658980i	$-0.770988\pi$
$173$	−6.98406	−	21.4947i	−0.530989	−	1.63421i	0.221172	−	0.975235i	$-0.429012\pi$
$174$	−2.10870	−	2.90238i	−0.159860	−	0.220029i
$175$			4.14734i			0.313509i
$176$	−3.29528	+	0.375673i	−0.248391	+	0.0283174i
$177$	4.39263			0.330170
$178$	2.86934	+	3.94931i	0.215066	+	0.296013i
$179$	12.1354	−	3.94304i	0.907045	−	0.294717i	0.181903	−	0.983316i	$-0.441774\pi$
$179$	12.1354	−	3.94304i	0.907045	−	0.294717i	0.725142	+	0.688600i	$0.241774\pi$
$180$	−2.00868	+	6.18207i	−0.149718	+	0.460784i
$181$	−11.1224	+	15.3087i	−0.826725	+	1.13789i	0.161799	+	0.986824i	$0.448270\pi$
$181$	−11.1224	+	15.3087i	−0.826725	+	1.13789i	−0.988524	+	0.151066i	$0.951730\pi$
$182$	−2.17828	+	2.99815i	−0.161465	+	0.222237i
$183$	−0.228473	+	0.703168i	−0.0168892	+	0.0519796i
$184$	0.816543	+	2.51306i	0.0601963	+	0.185265i
$185$	3.18603	+	4.38519i	0.234242	+	0.322406i
$186$	−5.80595			−0.425713
$187$	1.53069	+	13.4267i	0.111935	+	0.981855i
$188$	8.00267			0.583655
$189$	−4.76470	+	3.46176i	−0.346581	+	0.251806i
$190$	6.66961	−	10.5169i	0.483864	−	0.762979i
$191$	4.67131	−	14.3768i	0.338004	−	1.04027i	−0.627220	−	0.778842i	$-0.715807\pi$
$191$	4.67131	−	14.3768i	0.338004	−	1.04027i	0.965223	−	0.261426i	$-0.0841928\pi$
$192$	−0.500425	+	0.688776i	−0.0361151	+	0.0497081i
$193$	15.6507	+	11.3709i	1.12656	+	0.818494i	0.985190	−	0.171463i	$-0.0548495\pi$
$193$	15.6507	+	11.3709i	1.12656	+	0.818494i	0.141369	+	0.989957i	$0.454850\pi$
$194$	12.2652	+	3.98520i	0.880589	+	0.286121i
$195$	−6.53755	+	2.12418i	−0.468164	+	0.152116i
$196$	−4.27188	+	3.10370i	−0.305134	+	0.221693i
$197$		−	17.4847i		−	1.24573i	−0.782328	−	0.622867i	$-0.785968\pi$
$197$		−	17.4847i		−	1.24573i	0.782328	−	0.622867i	$-0.214032\pi$
$198$	3.12968	+	6.86623i	0.222416	+	0.487962i
$199$	2.05975			0.146012			0.0730059	−	0.997332i	$-0.476741\pi$
$199$	2.05975			0.146012			0.0730059	+	0.997332i	$0.476741\pi$
$200$	2.55862	−	1.85894i	0.180921	−	0.131447i
$201$	3.15797	+	9.71923i	0.222746	+	0.685542i
$202$	11.6049	+	3.77065i	0.816515	+	0.265302i
$203$	3.24800	−	4.47049i	0.227965	−	0.313767i
$204$	2.80643	+	2.03899i	0.196489	+	0.142758i
$205$	10.6312	−	32.7195i	0.742516	−	2.28523i
$206$	−0.466399	+	0.151542i	−0.0324956	+	0.0105584i
$207$	4.86370	−	3.53369i	0.338051	−	0.245608i
$208$	2.82601			0.195948
$209$	−2.54068	−	14.2318i	−0.175743	−	0.984436i
$210$	3.18975			0.220114
$211$	0.154906	−	0.112546i	0.0106642	−	0.00774796i	−0.582440	−	0.812873i	$-0.697902\pi$
$211$	0.154906	−	0.112546i	0.0106642	−	0.00774796i	0.593105	+	0.805125i	$0.297902\pi$
$212$	2.65640	−	0.863116i	0.182442	−	0.0592791i
$213$	−3.39300	+	10.4426i	−0.232484	+	0.715513i
$214$	−6.82169	−	4.95625i	−0.466321	−	0.338802i
$215$	−0.0934983	+	0.128689i	−0.00637653	+	0.00877655i
$216$	4.27132	+	1.38784i	0.290627	+	0.0944303i
$217$	−2.76348	−	8.50513i	−0.187598	−	0.577366i
$218$	1.12960	−	0.820701i	0.0765060	−	0.0555849i
$219$	−7.42757			−0.501909
$220$	1.88853	−	9.28560i	0.127325	−	0.626035i
$221$		−	11.5146i		−	0.774557i
$222$	1.30675	−	0.949413i	0.0877036	−	0.0637204i
$223$	7.49321	−	2.43469i	0.501782	−	0.163039i	−0.0471795	−	0.998886i	$-0.515023\pi$
$223$	7.49321	−	2.43469i	0.501782	−	0.163039i	0.548962	+	0.835848i	$0.315023\pi$
$224$	−1.24718	−	0.405232i	−0.0833305	−	0.0270757i
$225$	−5.82127	−	4.22940i	−0.388085	−	0.281960i
$226$	−2.78128	+	3.82810i	−0.185008	+	0.254641i
$227$	−3.50701	+	10.7935i	−0.232769	+	0.716388i	0.764641	+	0.644456i	$0.222916\pi$
$227$	−3.50701	+	10.7935i	−0.232769	+	0.716388i	−0.997410	+	0.0719315i	$0.977084\pi$
$228$	−3.13397	−	1.98749i	−0.207552	−	0.131625i
$229$	20.7962	−	15.1093i	1.37425	−	0.998452i	0.376860	−	0.926270i	$-0.377004\pi$
$229$	20.7962	−	15.1093i	1.37425	−	0.998452i	0.997391	−	0.0721818i	$-0.0229962\pi$
$230$	−7.54938			−0.497792
$231$	2.72987	−	2.50180i	0.179612	−	0.164607i
$232$	−4.21382			−0.276651
$233$	10.3176	+	14.2009i	0.675926	+	0.930333i	0.999876	−	0.0157416i	$-0.00501091\pi$
$233$	10.3176	+	14.2009i	0.675926	+	0.930333i	−0.323950	+	0.946074i	$0.605011\pi$
$234$	−1.98687	−	6.11494i	−0.129885	−	0.399746i
$235$	−7.06533	+	21.7448i	−0.460891	+	1.41848i
$236$	3.03266	−	4.17409i	0.197409	−	0.271710i
$237$	−3.69061	+	5.07969i	−0.239731	+	0.329961i
$238$	−1.65113	+	5.08164i	−0.107027	+	0.329394i
$239$	16.0751	−	5.22312i	1.03981	−	0.337855i	0.261150	−	0.965298i	$-0.415898\pi$
$239$	16.0751	−	5.22312i	1.03981	−	0.337855i	0.778663	+	0.627443i	$0.215898\pi$
$240$	−1.42973	−	1.96785i	−0.0922886	−	0.127024i
$241$	−26.1327			−1.68336			−0.841679	−	0.539978i	$-0.818432\pi$
$241$	−26.1327			−1.68336			−0.841679	+	0.539978i	$0.818432\pi$
$242$	−5.66668	−	9.42808i	−0.364268	−	0.606060i
$243$		−	16.0291i		−	1.02827i
$244$	0.510447	+	0.702571i	0.0326781	+	0.0449775i
$245$	−4.66186	−	14.3477i	−0.297835	−	0.916642i
$246$	−9.75016	−	3.16802i	−0.621648	−	0.201986i
$247$	0.777343	+	12.2937i	0.0494612	+	0.782232i
$248$	−4.00841	+	5.51710i	−0.254534	+	0.350336i
$249$	2.33283	−	7.17972i	0.147837	−	0.454996i
$250$	−1.62217	−	4.99252i	−0.102595	−	0.315754i
$251$	5.62440	−	4.08636i	0.355009	−	0.257929i	−0.395958	−	0.918268i	$-0.629588\pi$
$251$	5.62440	−	4.08636i	0.355009	−	0.257929i	0.750967	+	0.660339i	$0.229588\pi$
$252$			2.98356i			0.187946i
$253$	−6.46096	+	5.92118i	−0.406197	+	0.372261i
$254$	6.84719			0.429631
$255$	−8.01805	+	5.82545i	−0.502110	+	0.364804i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	14.2137	+	4.61831i	0.886627	+	0.288082i	0.716706	−	0.697375i	$-0.245649\pi$
$257$	14.2137	+	4.61831i	0.886627	+	0.288082i	0.169921	+	0.985458i	$0.445649\pi$
$258$	0.0383485	+	0.0278618i	0.00238747	+	0.00173460i
$259$	2.01278	+	1.46237i	0.125068	+	0.0908671i
$260$	−2.49500	+	7.67883i	−0.154733	+	0.476221i
$261$	2.96259	+	9.11790i	0.183379	+	0.564384i
$262$	−9.47775	−	13.0450i	−0.585537	−	0.805923i
$263$		−	20.4253i		−	1.25948i	−0.776807	−	0.629739i	$-0.783162\pi$
$263$		−	20.4253i		−	1.25948i	0.776807	−	0.629739i	$-0.216838\pi$
$264$	−2.76704	−	0.562767i	−0.170299	−	0.0346359i
$265$			7.97998i			0.490206i
$266$	1.41979	−	5.53695i	0.0870528	−	0.339492i
$267$	1.28430	+	3.95267i	0.0785978	+	0.241899i
$268$	11.4159	+	3.70926i	0.697340	+	0.226579i
$269$	12.2009	−	16.7930i	0.743900	−	1.02389i	−0.254485	−	0.967077i	$-0.581906\pi$
$269$	12.2009	−	16.7930i	0.743900	−	1.02389i	0.998385	−	0.0568134i	$-0.0180940\pi$
$270$	−7.54205	+	10.3807i	−0.458995	+	0.631752i
$271$	2.97385	+	0.966261i	0.180648	+	0.0586962i	0.397944	−	0.917410i	$-0.369724\pi$
$271$	2.97385	+	0.966261i	0.180648	+	0.0586962i	−0.217296	+	0.976106i	$0.569724\pi$
$272$	3.87510	−	1.25909i	0.234962	−	0.0763438i
$273$	−2.55254	+	1.85453i	−0.154487	+	0.112241i
$274$	−9.92101			−0.599350
$275$	9.12971	+	5.16454i	0.550542	+	0.311433i
$276$			2.24966i			0.135414i
$277$	8.12951	+	11.1893i	0.488455	+	0.672300i	0.980102	−	0.198494i	$-0.0636051\pi$
$277$	8.12951	+	11.1893i	0.488455	+	0.672300i	−0.491647	+	0.870794i	$0.663605\pi$
$278$	9.96726	−	3.23856i	0.597797	−	0.194236i
$279$	14.7561	+	4.79455i	0.883425	+	0.287042i
$280$	2.20219	−	3.03106i	0.131606	−	0.181140i
$281$	−16.9088	−	12.2849i	−1.00869	−	0.732858i	−0.0447584	−	0.998998i	$-0.514252\pi$
$281$	−16.9088	−	12.2849i	−1.00869	−	0.732858i	−0.963935	+	0.266140i	$0.914252\pi$
$282$	6.47980	+	2.10541i	0.385866	+	0.125376i
$283$	6.29118	−	2.04413i	0.373972	−	0.121511i	−0.116000	−	0.993249i	$-0.537007\pi$
$283$	6.29118	−	2.04413i	0.373972	−	0.121511i	0.489972	+	0.871738i	$0.337007\pi$
$284$	7.58053	+	10.4337i	0.449822	+	0.619127i
$285$	8.16731	−	6.76092i	0.483789	−	0.400482i
$286$	3.88741	+	8.52864i	0.229868	+	0.504309i
$287$		−	15.7909i		−	0.932108i
$288$	1.84065	−	1.33731i	0.108461	−	0.0788016i
$289$	0.123087	+	0.378822i	0.00724040	+	0.0222837i
$290$	3.72026	−	11.4498i	0.218461	−	0.672354i
$291$	8.88271	+	6.45367i	0.520714	+	0.378321i
$292$	−5.12797	+	7.05804i	−0.300092	+	0.413041i
$293$	−1.73599	+	5.34282i	−0.101418	+	0.312131i	−0.988873	−	0.148763i	$-0.952471\pi$
$293$	−1.73599	+	5.34282i	−0.101418	+	0.312131i	0.887455	+	0.460894i	$0.152471\pi$
$294$	−4.27551	+	1.38920i	−0.249353	+	0.0810197i
$295$	8.66439	+	11.9255i	0.504461	+	0.694330i
$296$		−	1.89721i		−	0.110273i
$297$	1.68720	+	14.7995i	0.0979012	+	0.858757i
$298$			11.0994i			0.642970i
$299$	6.04127	−	4.38924i	0.349375	−	0.253836i
$300$	2.56079	−	0.832051i	0.147847	−	0.0480385i
$301$	−0.0225618	+	0.0694382i	−0.00130044	+	0.00400235i
$302$	14.8123	+	10.7617i	0.852350	+	0.619269i
$303$	8.40449	+	6.10622i	0.482825	+	0.350793i
$304$	−4.05230	+	1.60589i	−0.232415	+	0.0921043i
$305$	−2.35968	+	0.766707i	−0.135115	+	0.0439015i
$306$	−5.44888	−	7.49974i	−0.311492	−	0.428732i
$307$	−0.947323			−0.0540666			−0.0270333	−	0.999635i	$-0.508606\pi$
$307$	−0.947323			−0.0540666			−0.0270333	+	0.999635i	$0.508606\pi$
$308$	−0.492642	−	4.32130i	−0.0280709	−	0.246229i
$309$	−0.417514			−0.0237516
$310$	−11.4521	−	15.7625i	−0.650438	−	0.895251i
$311$	1.50689	+	4.63772i	0.0854477	+	0.262981i	0.984647	−	0.174559i	$-0.0558499\pi$
$311$	1.50689	+	4.63772i	0.0854477	+	0.262981i	−0.899199	+	0.437540i	$0.855850\pi$
$312$	2.28823	+	0.743492i	0.129546	+	0.0420919i
$313$	−15.3418	−	11.1465i	−0.867172	−	0.630038i	0.0626544	−	0.998035i	$-0.480043\pi$
$313$	−15.3418	−	11.1465i	−0.867172	−	0.630038i	−0.929827	+	0.367998i	$0.880043\pi$
$314$	0.386812	+	0.281035i	0.0218291	+	0.0158597i
$315$	−8.10691	−	2.63409i	−0.456773	−	0.148414i
$316$	2.27898	+	7.01399i	0.128203	+	0.394568i
$317$	11.2464	+	15.4794i	0.631661	+	0.869407i	0.998137	−	0.0610207i	$-0.0194356\pi$
$317$	11.2464	+	15.4794i	0.631661	+	0.869407i	−0.366475	+	0.930428i	$0.619436\pi$
$318$	2.37797			0.133350
$319$	−5.79646	−	12.7169i	−0.324540	−	0.712011i
$320$	−2.85703			−0.159713
$321$	−4.21962	−	5.80781i	−0.235516	−	0.324160i
$322$	−3.29553	+	1.07078i	−0.183652	+	0.0596723i
$323$	6.54324	+	16.5111i	0.364076	+	0.918705i
$324$	−2.42855	−	1.76445i	−0.134920	−	0.0980248i
$325$	−7.23067	−	5.25339i	−0.401086	−	0.291406i
$326$	−2.55325	+	7.85809i	−0.141411	+	0.435219i
$327$	1.13056	−	0.367341i	0.0625200	−	0.0203140i
$328$	−9.74189	+	7.07789i	−0.537906	+	0.390811i
$329$			10.4944i			0.578574i
$330$	3.97209	−	7.02174i	0.218656	−	0.386534i
$331$			18.7224i			1.02908i	0.857467	+	0.514539i	$0.172037\pi$
$331$			18.7224i			1.02908i	−0.857467	+	0.514539i	$0.827963\pi$
$332$	−5.21194	−	7.17362i	−0.286043	−	0.393704i
$333$	−4.10521	+	1.33386i	−0.224964	+	0.0730952i
$334$	7.47828	−	23.0158i	0.409193	−	1.25937i
$335$	−20.1576	+	27.7446i	−1.10133	+	1.51585i
$336$	−0.903232	−	0.656237i	−0.0492754	−	0.0358006i
$337$	−0.328149	+	1.00994i	−0.0178754	+	0.0550148i	−0.959596	−	0.281380i	$-0.909208\pi$
$337$	−0.328149	+	1.00994i	−0.0178754	+	0.0550148i	0.941721	+	0.336395i	$0.109208\pi$
$338$	1.54931	+	4.76829i	0.0842713	+	0.259361i
$339$	−3.25914	+	2.36790i	−0.177012	+	0.128607i
$340$			11.6410i			0.631323i
$341$	−22.1640	−	4.50777i	−1.20025	−	0.244109i
$342$	6.32387	+	7.63935i	0.341956	+	0.413089i
$343$	−9.46565	−	13.0284i	−0.511097	−	0.703465i
$344$	0.0529513	−	0.0172049i	0.00285494	−	0.000927627i
$345$	−6.11277	−	1.98616i	−0.329101	−	0.106931i
$346$	−18.2845	−	13.2845i	−0.982982	−	0.714178i
$347$	−10.5570	+	14.5304i	−0.566727	+	0.780033i	−0.992162	−	0.124956i	$-0.960121\pi$
$347$	−10.5570	+	14.5304i	−0.566727	+	0.780033i	0.425435	+	0.904989i	$0.360121\pi$
$348$	−3.41195	−	1.10861i	−0.182900	−	0.0594277i
$349$	−16.4368	+	5.34064i	−0.879841	+	0.285878i	−0.713891	−	0.700257i	$-0.753069\pi$
$349$	−16.4368	+	5.34064i	−0.879841	+	0.285878i	−0.165950	+	0.986134i	$0.553069\pi$
$350$	2.43774	+	3.35526i	0.130303	+	0.179346i
$351$		−	12.6920i		−	0.677448i
$352$	−2.44512	+	2.24084i	−0.130325	+	0.119437i
$353$	−8.88774			−0.473047			−0.236523	−	0.971626i	$-0.576008\pi$
$353$	−8.88774			−0.473047			−0.236523	+	0.971626i	$0.576008\pi$
$354$	3.55371	−	2.58192i	0.188878	−	0.137228i
$355$	−35.0431	+	11.3862i	−1.85989	+	0.604316i
$356$	4.64269	+	1.50850i	0.246062	+	0.0799505i
$357$	−2.67385	+	3.68023i	−0.141515	+	0.194779i
$358$	7.50011	−	10.3230i	0.396393	−	0.545589i
$359$	4.73893	+	1.53977i	0.250111	+	0.0812660i	0.431389	−	0.902166i	$-0.358024\pi$
$359$	4.73893	+	1.53977i	0.250111	+	0.0812660i	−0.181278	+	0.983432i	$0.558024\pi$
$360$	2.00868	+	6.18207i	0.105866	+	0.325824i
$361$	−8.10063	−	17.1866i	−0.426349	−	0.904559i
$362$			18.9226i			0.994552i
$363$	−2.10791	−	9.12480i	−0.110637	−	0.478928i
$364$			3.70591i			0.194243i
$365$	−14.6508	−	20.1650i	−0.766856	−	1.05549i
$366$	0.228473	+	0.703168i	0.0119425	+	0.0367552i
$367$	3.12508	−	9.61800i	0.163128	−	0.502056i	−0.835766	−	0.549086i	$-0.814976\pi$
$367$	3.12508	−	9.61800i	0.163128	−	0.502056i	0.998893	+	0.0470306i	$0.0149758\pi$
$368$	2.13774	+	1.55316i	0.111437	+	0.0809639i
$369$	22.1644	+	16.1034i	1.15383	+	0.838308i
$370$	5.15510	+	1.67499i	0.268001	+	0.0870788i
$371$	1.13186	+	3.48349i	0.0587630	+	0.180854i
$372$	−4.69711	+	3.41265i	−0.243534	+	0.176938i
$373$	12.1494			0.629074			0.314537	−	0.949245i	$-0.398151\pi$
$373$	12.1494			0.629074			0.314537	+	0.949245i	$0.398151\pi$
$374$	9.13035	+	9.96269i	0.472119	+	0.515158i
$375$		−	4.46924i		−	0.230790i
$376$	6.47430	−	4.70385i	0.333886	−	0.242583i
$377$	3.67987	+	11.3255i	0.189523	+	0.583291i
$378$	−1.81995	+	5.60124i	−0.0936083	+	0.288097i
$379$	−12.5431	+	17.2642i	−0.644298	+	0.886800i	−0.998836	−	0.0482416i	$-0.984638\pi$
$379$	−12.5431	+	17.2642i	−0.644298	+	0.886800i	0.354538	+	0.935042i	$0.384638\pi$
$380$	−0.785876	−	12.4287i	−0.0403146	−	0.637578i
$381$	5.54420	+	1.80142i	0.284038	+	0.0922896i
$382$	−4.67131	−	14.3768i	−0.239005	−	0.735581i
$383$	14.5554	+	20.0338i	0.743748	+	1.02368i	0.998394	+	0.0566471i	$0.0180410\pi$
$383$	14.5554	+	20.0338i	0.743748	+	1.02368i	−0.254646	+	0.967034i	$0.581959\pi$
$384$			0.851374i			0.0434465i
$385$	12.1768	+	2.47654i	0.620585	+	0.126216i
$386$	19.3453			0.984649
$387$	−0.0744563	−	0.102480i	−0.00378483	−	0.00520937i
$388$	12.2652	−	3.98520i	0.622670	−	0.202318i
$389$	−10.7768	+	33.1676i	−0.546405	+	1.68166i	0.171220	+	0.985233i	$0.445229\pi$
$389$	−10.7768	+	33.1676i	−0.546405	+	1.68166i	−0.717625	+	0.696430i	$0.754771\pi$
$390$	−4.04043	+	5.56117i	−0.204595	+	0.281601i
$391$	6.32836	−	8.71025i	0.320039	−	0.440496i
$392$	−1.63171	+	5.02190i	−0.0824140	+	0.253644i
$393$	−4.24218	−	13.0561i	−0.213990	−	0.658592i
$394$	−10.2773	−	14.1454i	−0.517760	−	0.712636i
$395$	−21.0705			−1.06017
$396$	6.56783	+	3.71532i	0.330046	+	0.186702i
$397$	−24.5144			−1.23034			−0.615172	−	0.788393i	$-0.710913\pi$
$397$	−24.5144			−1.23034			−0.615172	+	0.788393i	$0.710913\pi$
$398$	1.66637	−	1.21069i	0.0835277	−	0.0606864i
$399$	2.60632	−	4.10976i	0.130479	−	0.205745i
$400$	0.977304	−	3.00783i	0.0488652	−	0.150392i
$401$	12.2579	−	16.8716i	0.612131	−	0.842526i	−0.384619	−	0.923075i	$-0.625667\pi$
$401$	12.2579	−	16.8716i	0.612131	−	0.842526i	0.996751	+	0.0805489i	$0.0256673\pi$
$402$	8.26767	+	6.00682i	0.412354	+	0.299593i
$403$	18.3288	+	5.95537i	0.913020	+	0.296658i
$404$	11.6049	−	3.77065i	0.577363	−	0.187597i
$405$	6.93845	−	5.04108i	0.344774	−	0.250493i
$406$		−	5.52583i		−	0.274242i
$407$	5.72562	−	2.60978i	0.283808	−	0.129362i
$408$	3.46894			0.171738
$409$	−14.6656	+	10.6552i	−0.725167	+	0.526864i	−0.888031	−	0.459784i	$-0.847927\pi$
$409$	−14.6656	+	10.6552i	−0.725167	+	0.526864i	0.162864	+	0.986649i	$0.447927\pi$
$410$	−10.6312	−	32.7195i	−0.525038	−	1.61590i
$411$	−8.03309	−	2.61011i	−0.396243	−	0.128747i
$412$	−0.288250	+	0.396743i	−0.0142011	+	0.0195461i
$413$	5.47374	+	3.97690i	0.269345	+	0.195691i
$414$	1.85777	−	5.71762i	0.0913043	−	0.281006i
$415$	24.0936	−	7.82849i	1.18271	−	0.384286i
$416$	2.28629	−	1.66109i	0.112095	−	0.0814415i
$417$	8.92256			0.436940
$418$	−10.4207	−	10.0204i	−0.509694	−	0.490115i
$419$	−39.8106			−1.94488			−0.972439	−	0.233159i	$-0.925094\pi$
$419$	−39.8106			−1.94488			−0.972439	+	0.233159i	$0.925094\pi$
$420$	2.58056	−	1.87489i	0.125919	−	0.0914852i
$421$	−8.61467	+	2.79908i	−0.419853	+	0.136419i	−0.511322	−	0.859389i	$-0.670844\pi$
$421$	−8.61467	+	2.79908i	−0.419853	+	0.136419i	0.0914685	+	0.995808i	$0.470844\pi$
$422$	0.0591688	−	0.182103i	0.00288029	−	0.00886462i
$423$	−14.7301	−	10.7020i	−0.716201	−	0.520351i
$424$	1.64175	−	2.25967i	0.0797302	−	0.109739i
$425$	−12.2555	−	3.98204i	−0.594477	−	0.193157i
$426$	3.39300	+	10.4426i	0.164391	+	0.505944i
$427$	−0.921322	+	0.669380i	−0.0445859	+	0.0323936i
$428$	−8.43208			−0.407580
$429$	0.903866	+	7.92841i	0.0436390	+	0.382787i
$430$			0.159069i			0.00767098i
$431$	−10.7080	+	7.77984i	−0.515788	+	0.374742i	−0.815015	−	0.579440i	$-0.803271\pi$
$431$	−10.7080	+	7.77984i	−0.515788	+	0.374742i	0.299227	+	0.954182i	$0.403271\pi$
$432$	4.27132	−	1.38784i	0.205504	−	0.0667723i
$433$	−29.2229	−	9.49510i	−1.40436	−	0.456305i	−0.493764	−	0.869596i	$-0.664380\pi$
$433$	−29.2229	−	9.49510i	−1.40436	−	0.456305i	−0.910599	+	0.413290i	$0.864380\pi$
$434$	−7.23490	−	5.25646i	−0.347286	−	0.252318i
$435$	6.02462	−	8.29218i	0.288859	−	0.397580i
$436$	0.431468	−	1.32792i	0.0206636	−	0.0635959i
$437$	−6.16854	+	9.72683i	−0.295081	+	0.465297i
$438$	−6.00903	+	4.36582i	−0.287123	+	0.208607i
$439$	35.3158			1.68553			0.842766	−	0.538279i	$-0.180925\pi$
$439$	35.3158			1.68553			0.842766	+	0.538279i	$0.180925\pi$
$440$	−3.93008	−	8.62226i	−0.187359	−	0.411050i
$441$	12.0136			0.572077
$442$	−6.76812	−	9.31552i	−0.321927	−	0.443094i
$443$	−1.26094	−	3.88079i	−0.0599093	−	0.184382i	0.916623	−	0.399753i	$-0.130904\pi$
$443$	−1.26094	−	3.88079i	−0.0599093	−	0.184382i	−0.976532	+	0.215371i	$0.930904\pi$
$444$	0.499136	−	1.53618i	0.0236879	−	0.0729040i
$445$	−8.19780	+	11.2833i	−0.388613	+	0.534880i
$446$	4.63106	−	6.37410i	0.219287	−	0.301822i
$447$	−2.92013	+	8.98723i	−0.138117	+	0.425081i
$448$	−1.24718	+	0.405232i	−0.0589236	+	0.0191454i
$449$	−8.50432	−	11.7052i	−0.401344	−	0.552402i	0.559737	−	0.828670i	$-0.310902\pi$
$449$	−8.50432	−	11.7052i	−0.401344	−	0.552402i	−0.961081	+	0.276268i	$0.910902\pi$
$450$	−7.19548			−0.339198
$451$	−34.7612	−	19.6639i	−1.63684	−	0.925936i
$452$			4.73179i			0.222565i
$453$	9.16227	+	12.6108i	0.430481	+	0.592506i
$454$	3.50701	+	10.7935i	0.164592	+	0.506563i
$455$	−10.0697	−	3.27184i	−0.472075	−	0.153386i
$456$	−3.70366	+	0.234185i	−0.173440	+	0.0109667i
$457$	−2.81988	+	3.88124i	−0.131909	+	0.181557i	−0.869862	−	0.493295i	$-0.835792\pi$
$457$	−2.81988	+	3.88124i	−0.131909	+	0.181557i	0.737953	+	0.674852i	$0.235792\pi$
$458$	7.94344	−	24.4474i	0.371173	−	1.14235i
$459$	−5.65476	−	17.4036i	−0.263942	−	0.812329i
$460$	−6.10758	+	4.43742i	−0.284767	+	0.206896i
$461$		−	19.5465i		−	0.910373i	−0.890396	−	0.455187i	$-0.849573\pi$
$461$		−	19.5465i		−	0.910373i	0.890396	−	0.455187i	$-0.150427\pi$
$462$	0.737990	−	3.62858i	0.0343344	−	0.168817i
$463$	0.551841			0.0256462			0.0128231	−	0.999918i	$-0.495918\pi$
$463$	0.551841			0.0256462			0.0128231	+	0.999918i	$0.495918\pi$
$464$	−3.40905	+	2.47682i	−0.158261	+	0.114984i
$465$	−5.12590	−	15.7759i	−0.237708	−	0.731590i
$466$	16.6942	+	5.42427i	0.773343	+	0.251274i
$467$	20.4240	+	14.8389i	0.945111	+	0.686663i	0.949645	−	0.313327i	$-0.101443\pi$
$467$	20.4240	+	14.8389i	0.945111	+	0.686663i	−0.00453477	+	0.999990i	$0.501443\pi$
$468$	−5.20168	−	3.77924i	−0.240448	−	0.174696i
$469$	−4.86418	+	14.9704i	−0.224607	+	0.691269i
$470$	7.06533	+	21.7448i	0.325899	+	1.00301i
$471$	0.239266	+	0.329321i	0.0110248	+	0.0151743i
$472$		−	5.15946i		−	0.237484i
$473$	0.124762	+	0.136135i	0.00573655	+	0.00625951i
$474$			6.27884i			0.288397i
$475$	13.3535	+	3.42412i	0.612702	+	0.157110i
$476$	1.65113	+	5.08164i	0.0756792	+	0.232917i
$477$	−6.04374	−	1.96373i	−0.276724	−	0.0899130i
$478$	9.93496	−	13.6743i	0.454415	−	0.625448i
$479$	−4.61891	+	6.35739i	−0.211043	+	0.290476i	−0.901395	−	0.432998i	$-0.857456\pi$
$479$	−4.61891	+	6.35739i	−0.211043	+	0.290476i	0.690352	+	0.723474i	$0.257456\pi$
$480$	−2.31335	−	0.751653i	−0.105590	−	0.0343081i
$481$	−5.09913	+	1.65681i	−0.232500	+	0.0755439i
$482$	−21.1418	+	15.3604i	−0.962984	+	0.699649i
$483$	−2.95011			−0.134235
$484$	−10.1261	−	4.29669i	−0.460279	−	0.195304i
$485$			36.8453i			1.67306i
$486$	−9.42167	−	12.9678i	−0.427376	−	0.588232i
$487$	39.4233	−	12.8094i	1.78644	−	0.580450i	0.787102	−	0.616822i	$-0.211580\pi$
$487$	39.4233	−	12.8094i	1.78644	−	0.580450i	0.999338	+	0.0363727i	$0.0115804\pi$
$488$	0.825921	+	0.268358i	0.0373877	+	0.0121480i
$489$	−4.13475	+	5.69100i	−0.186980	+	0.257356i
$490$	−12.2049	−	8.86738i	−0.551361	−	0.400587i
$491$	−30.5997	−	9.94245i	−1.38095	−	0.448696i	−0.477965	−	0.878379i	$-0.658626\pi$
$491$	−30.5997	−	9.94245i	−1.38095	−	0.448696i	−0.902980	+	0.429682i	$0.858626\pi$
$492$	−9.75016	+	3.16802i	−0.439571	+	0.142825i
$493$	10.0919	+	13.8902i	0.454514	+	0.625585i
$494$	7.85496	+	9.48893i	0.353411	+	0.426927i
$495$	−15.8938	+	14.5659i	−0.714374	+	0.654691i
$496$			6.81951i			0.306205i
$497$	−13.6823	+	9.94080i	−0.613737	+	0.445906i
$498$	−2.33283	−	7.17972i	−0.104537	−	0.321731i
$499$	−13.0905	+	40.2886i	−0.586013	+	1.80356i	0.00914839	+	0.999958i	$0.497088\pi$
$499$	−13.0905	+	40.2886i	−0.586013	+	1.80356i	−0.595162	+	0.803606i	$0.702912\pi$
$500$	−4.24689	−	3.08554i	−0.189927	−	0.137990i
$501$	12.1104	−	16.6685i	0.541052	−	0.744695i
$502$	2.14833	−	6.61188i	0.0958846	−	0.295103i
$503$	15.4403	−	5.01687i	0.688450	−	0.223691i	0.0561591	−	0.998422i	$-0.482115\pi$
$503$	15.4403	−	5.01687i	0.688450	−	0.223691i	0.632291	+	0.774731i	$0.282115\pi$
$504$	1.75369	+	2.41375i	0.0781156	+	0.107517i
$505$			34.8617i			1.55133i
$506$	−1.74665	+	8.58799i	−0.0776480	+	0.381783i
$507$			4.26851i			0.189571i
$508$	5.53950	−	4.02468i	0.245775	−	0.178566i
$509$	27.8639	−	9.05354i	1.23505	−	0.401291i	0.382507	−	0.923953i	$-0.375061\pi$
$509$	27.8639	−	9.05354i	1.23505	−	0.401291i	0.852540	+	0.522662i	$0.175061\pi$
$510$	−3.06262	+	9.42578i	−0.135615	+	0.417381i
$511$	−9.25563	−	6.72461i	−0.409445	−	0.297479i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	7.21229	+	18.1994i	0.318430	+	0.803523i
$514$	14.2137	−	4.61831i	0.626940	−	0.203705i
$515$	−0.823540	−	1.13351i	−0.0362895	−	0.0499482i
$516$	0.0474013			0.00208673
$517$	23.1017	+	13.0683i	1.01601	+	0.574743i
$518$	2.48793			0.109313
$519$	−11.3101	−	15.5670i	−0.496456	−	0.683314i
$520$	2.49500	+	7.67883i	0.109413	+	0.336739i
$521$	−9.24731	−	3.00463i	−0.405132	−	0.131635i	0.0993603	−	0.995052i	$-0.468320\pi$
$521$	−9.24731	−	3.00463i	−0.405132	−	0.131635i	−0.504492	+	0.863416i	$0.668320\pi$
$522$	7.75615	+	5.63517i	0.339477	+	0.246645i
$523$	−24.5184	−	17.8137i	−1.07211	−	0.778937i	−0.0958235	−	0.995398i	$-0.530548\pi$
$523$	−24.5184	−	17.8137i	−1.07211	−	0.778937i	−0.976291	+	0.216461i	$0.930548\pi$
$524$	−15.3353	−	4.98275i	−0.669926	−	0.217672i
$525$	1.09112	+	3.35812i	0.0476203	+	0.146560i
$526$	−12.0057	−	16.5244i	−0.523473	−	0.720499i
$527$	27.7862			1.21039
$528$	−2.56937	+	1.17114i	−0.111817	+	0.0509671i
$529$	−16.0178			−0.696425
$530$	4.69052	+	6.45594i	0.203743	+	0.280428i
$531$	−11.1641	+	3.62743i	−0.484480	+	0.157417i
$532$	−2.10590	−	5.31402i	−0.0913025	−	0.230392i
$533$	27.5307	+	20.0022i	1.19249	+	0.866391i
$534$	3.36234	+	2.44288i	0.145503	+	0.105714i
$535$	7.44444	−	22.9116i	0.321851	−	0.990556i
$536$	11.4159	−	3.70926i	0.493094	−	0.160216i
$537$	8.78875	−	6.38540i	0.379262	−	0.275550i
$538$		−	20.7573i		−	0.894913i
$539$	−17.4002	+	1.98368i	−0.749479	+	0.0854432i
$540$			12.8313i			0.552172i
$541$	9.95058	+	13.6958i	0.427809	+	0.588829i	0.967449	−	0.253068i	$-0.0814395\pi$
$541$	9.95058	+	13.6958i	0.427809	+	0.588829i	−0.539640	+	0.841896i	$0.681439\pi$
$542$	2.97385	−	0.966261i	0.127738	−	0.0415045i
$543$	−4.97834	+	15.3217i	−0.213641	+	0.657519i
$544$	2.39494	−	3.29635i	0.102682	−	0.141330i
$545$	3.22730	+	2.34477i	0.138242	+	0.100439i
$546$	−0.974985	+	3.00069i	−0.0417255	+	0.128418i
$547$	−0.579160	−	1.78247i	−0.0247631	−	0.0762130i	0.937911	−	0.346875i	$-0.112757\pi$
$547$	−0.579160	−	1.78247i	−0.0247631	−	0.0762130i	−0.962674	+	0.270662i	$0.912757\pi$
$548$	−8.02627	+	5.83142i	−0.342865	+	0.249106i
$549$		−	1.97581i		−	0.0843255i
$550$	10.4217	−	1.18811i	0.444384	−	0.0506613i
$551$	−11.7124	−	14.1488i	−0.498966	−	0.602759i
$552$	1.32232	+	1.82001i	0.0562815	+	0.0774649i
$553$	−9.19786	+	2.98857i	−0.391133	+	0.127087i
$554$	13.1538	+	4.27393i	0.558852	+	0.181582i
$555$	3.73344	+	2.71250i	0.158476	+	0.115139i
$556$	6.16011	−	8.47866i	0.261247	−	0.359575i
$557$	−3.30539	−	1.07399i	−0.140054	−	0.0455062i	0.238151	−	0.971228i	$-0.423459\pi$
$557$	−3.30539	−	1.07399i	−0.140054	−	0.0455062i	−0.378205	+	0.925722i	$0.623459\pi$
$558$	14.7561	−	4.79455i	0.624676	−	0.202970i
$559$	−0.0924831	−	0.127292i	−0.00391162	−	0.00538388i
$560$		−	3.74659i		−	0.158322i
$561$	4.77181	+	10.4689i	0.201466	+	0.441999i
$562$	−20.9004			−0.881630
$563$	20.9459	−	15.2181i	0.882763	−	0.641365i	−0.0512182	−	0.998687i	$-0.516310\pi$
$563$	20.9459	−	15.2181i	0.882763	−	0.641365i	0.933981	+	0.357323i	$0.116310\pi$
$564$	6.47980	−	2.10541i	0.272849	−	0.0886539i
$565$	−12.8572	−	4.17756i	−0.540907	−	0.175751i
$566$	3.88816	−	5.35160i	0.163432	−	0.224944i
$567$	2.31382	−	3.18470i	0.0971714	−	0.133745i
$568$	12.2656	+	3.98532i	0.514651	+	0.167220i
$569$	8.18503	+	25.1909i	0.343134	+	1.05606i	0.962575	+	0.271015i	$0.0873594\pi$
$569$	8.18503	+	25.1909i	0.343134	+	1.05606i	−0.619441	+	0.785043i	$0.712641\pi$
$570$	2.63352	−	10.2703i	0.110306	−	0.430176i
$571$			7.18205i			0.300559i	0.988644	+	0.150280i	$0.0480174\pi$
$571$			7.18205i			0.300559i	−0.988644	+	0.150280i	$0.951983\pi$
$572$	8.15799	+	4.61485i	0.341103	+	0.192956i
$573$		−	12.8699i		−	0.537649i
$574$	−9.28166	−	12.7751i	−0.387409	−	0.533223i
$575$	−2.58242	−	7.94787i	−0.107694	−	0.331449i
$576$	0.703064	−	2.16381i	0.0292943	−	0.0901587i
$577$	25.5541	+	18.5661i	1.06383	+	0.772918i	0.974793	−	0.223110i	$-0.0716209\pi$
$577$	25.5541	+	18.5661i	1.06383	+	0.772918i	0.0890374	+	0.996028i	$0.471621\pi$
$578$	0.322246	+	0.234125i	0.0134037	+	0.00973832i
$579$	15.6640	+	5.08953i	0.650972	+	0.211514i
$580$	−3.72026	−	11.4498i	−0.154475	−	0.475426i
$581$	9.40720	−	6.83473i	0.390276	−	0.283552i
$582$	10.9796			0.455120
$583$	9.07783	+	1.84627i	0.375965	+	0.0764648i
$584$			8.72422i			0.361011i
$585$	14.8614	−	10.7974i	0.614442	−	0.446418i
$586$	1.73599	+	5.34282i	0.0717130	+	0.220710i
$587$	6.11993	−	18.8352i	0.252597	−	0.777412i	−0.741697	−	0.670735i	$-0.765979\pi$
$587$	6.11993	−	18.8352i	0.252597	−	0.777412i	0.994294	−	0.106677i	$-0.0340212\pi$
$588$	−2.64241	+	3.63697i	−0.108971	+	0.149986i
$589$	−29.6663	+	1.87583i	−1.22238	+	0.0772920i
$590$	14.0193	+	4.55514i	0.577165	+	0.187532i
$591$	−4.60003	−	14.1574i	−0.189220	−	0.582359i
$592$	−1.11515	−	1.53488i	−0.0458326	−	0.0630831i
$593$			22.0577i			0.905802i	0.891561	+	0.452901i	$0.149611\pi$
$593$			22.0577i			0.905802i	−0.891561	+	0.452901i	$0.850389\pi$
$594$	10.0639	+	10.9814i	0.412928	+	0.450571i
$595$	−15.2656			−0.625827
$596$	6.52406	+	8.97960i	0.267236	+	0.367819i
$597$	1.66779	−	0.541897i	0.0682580	−	0.0221784i
$598$	2.30756	−	7.10193i	0.0943631	−	0.290420i
$599$	−0.390047	+	0.536853i	−0.0159369	+	0.0219352i	−0.816911	−	0.576764i	$-0.804315\pi$
$599$	−0.390047	+	0.536853i	−0.0159369	+	0.0219352i	0.800974	+	0.598699i	$0.204315\pi$
$600$	1.58266	−	2.17834i	0.0646116	−	0.0889303i
$601$	5.41201	−	16.6564i	0.220760	−	0.679431i	−0.777934	−	0.628346i	$-0.783732\pi$
$601$	5.41201	−	16.6564i	0.220760	−	0.679431i	0.998694	−	0.0510845i	$-0.0162678\pi$
$602$	0.0225618	+	0.0694382i	0.000919552	+	0.00283009i
$603$	−16.0523	−	22.0941i	−0.653699	−	0.899740i
$604$	18.3090			0.744982
$605$	20.6150	−	23.7213i	0.838119	−	0.964407i
$606$	10.3885			0.422005
$607$	−2.65415	+	1.92836i	−0.107729	+	0.0782696i	−0.640345	−	0.768087i	$-0.721209\pi$
$607$	−2.65415	+	1.92836i	−0.107729	+	0.0782696i	0.532617	+	0.846357i	$0.321209\pi$
$608$	−2.33446	+	3.68108i	−0.0946747	+	0.149287i
$609$	1.45379	−	4.47429i	0.0589104	−	0.181307i
$610$	−1.45836	+	2.00727i	−0.0590474	+	0.0812718i
$611$	−18.2964	−	13.2931i	−0.740194	−	0.537783i
$612$	−8.81647	−	2.86465i	−0.356385	−	0.115796i
$613$	26.6715	−	8.66610i	1.07725	−	0.350020i	0.283944	−	0.958841i	$-0.408357\pi$
$613$	26.6715	−	8.66610i	1.07725	−	0.350020i	0.793308	+	0.608820i	$0.208357\pi$
$614$	−0.766401	+	0.556823i	−0.0309294	+	0.0224715i
$615$		−	29.2901i		−	1.18109i
$616$	−2.93855	−	3.20643i	−0.118398	−	0.129191i
$617$	25.0977			1.01040			0.505198	−	0.863004i	$-0.331420\pi$
$617$	25.0977			1.01040			0.505198	+	0.863004i	$0.331420\pi$
$618$	−0.337776	+	0.245409i	−0.0135874	+	0.00987179i
$619$	8.56122	+	26.3487i	0.344105	+	1.05904i	0.962061	+	0.272833i	$0.0879606\pi$
$619$	8.56122	+	26.3487i	0.344105	+	1.05904i	−0.617957	+	0.786212i	$0.712039\pi$
$620$	−18.5300	−	6.02075i	−0.744181	−	0.241799i
$621$	6.97544	−	9.60087i	0.279915	−	0.385269i
$622$	3.94508	+	2.86627i	0.158183	+	0.114927i
$623$	−1.97819	+	6.08824i	−0.0792544	+	0.243920i
$624$	2.28823	−	0.743492i	0.0916026	−	0.0297635i
$625$	24.9266	−	18.1102i	0.997063	−	0.724408i
$626$	−18.9636			−0.757936
$627$	−5.80144	−	10.8551i	−0.231687	−	0.433513i
$628$	0.478126			0.0190793
$629$	−6.25389	+	4.54371i	−0.249359	+	0.181170i
$630$	−8.10691	+	2.63409i	−0.322987	+	0.104945i
$631$	3.15654	−	9.71484i	0.125660	−	0.386742i	−0.868361	−	0.495933i	$-0.834826\pi$
$631$	3.15654	−	9.71484i	0.125660	−	0.386742i	0.994021	+	0.109191i	$0.0348262\pi$
$632$	5.96646	+	4.33489i	0.237333	+	0.172433i
$633$	0.0958184	−	0.131883i	0.00380844	−	0.00524187i
$634$	18.1971	+	5.91259i	0.722698	+	0.234819i
$635$	6.04519	+	18.6052i	0.239896	+	0.738324i
$636$	1.92382	−	1.39774i	0.0762845	−	0.0554239i
$637$	14.9223			0.591242
$638$	−12.1643	−	6.88113i	−0.481588	−	0.272427i
$639$		−	29.3423i		−	1.16076i
$640$	−2.31139	+	1.67932i	−0.0913656	+	0.0663810i
$641$	34.1185	−	11.0858i	1.34760	−	0.437861i	0.455715	−	0.890126i	$-0.349384\pi$
$641$	34.1185	−	11.0858i	1.34760	−	0.437861i	0.891884	+	0.452265i	$0.149384\pi$
$642$	−6.82749	−	2.21839i	−0.269460	−	0.0875527i
$643$	−13.0783	−	9.50191i	−0.515756	−	0.374719i	0.299247	−	0.954176i	$-0.403265\pi$
$643$	−13.0783	−	9.50191i	−0.515756	−	0.374719i	−0.815003	+	0.579457i	$0.803265\pi$
$644$	−2.03675	+	2.80334i	−0.0802591	+	0.110467i
$645$	−0.0418493	+	0.128799i	−0.00164781	+	0.00507145i
$646$	14.9986	+	9.51178i	0.590112	+	0.374236i
$647$	−7.98052	+	5.79819i	−0.313747	+	0.227950i	−0.733502	−	0.679687i	$-0.762116\pi$
$647$	−7.98052	+	5.79819i	−0.313747	+	0.227950i	0.419756	+	0.907637i	$0.362116\pi$
$648$	−3.00186			−0.117924
$649$	15.5708	−	7.09728i	0.611207	−	0.278592i
$650$	−8.93760			−0.350562
$651$	−4.47521	−	6.15960i	−0.175397	−	0.241414i
$652$	2.55325	+	7.85809i	0.0999929	+	0.307746i
$653$	11.4356	−	35.1951i	0.447509	−	1.37729i	−0.432200	−	0.901778i	$-0.642263\pi$
$653$	11.4356	−	35.1951i	0.447509	−	1.37729i	0.879709	−	0.475512i	$-0.157737\pi$
$654$	0.698723	−	0.961710i	0.0273222	−	0.0376058i
$655$	27.0782	−	37.2700i	1.05803	−	1.45626i
$656$	−3.72107	+	11.4523i	−0.145283	+	0.447136i
$657$	18.8775	−	6.13369i	0.736483	−	0.239298i
$658$	6.16844	+	8.49013i	0.240471	+	0.330980i
$659$	26.2496			1.02254			0.511269	−	0.859421i	$-0.329176\pi$
$659$	26.2496			1.02254			0.511269	+	0.859421i	$0.329176\pi$
$660$	−0.913787	−	8.01544i	−0.0355691	−	0.312001i
$661$		−	2.85354i		−	0.110990i	−0.998459	−	0.0554950i	$-0.982326\pi$
$661$		−	2.85354i		−	0.110990i	0.998459	−	0.0554950i	$-0.0176737\pi$
$662$	11.0048	+	15.1468i	0.427712	+	0.588695i
$663$	−3.02937	−	9.32344i	−0.117651	−	0.362092i
$664$	−8.43310	−	2.74008i	−0.327268	−	0.106336i
$665$	16.2985	−	1.03057i	0.632028	−	0.0399636i
$666$	−2.53716	+	3.49210i	−0.0983129	+	0.135316i
$667$	−3.44077	+	10.5896i	−0.133227	+	0.410031i
$668$	−7.47828	−	23.0158i	−0.289343	−	0.890507i
$669$	5.42674	−	3.94276i	0.209810	−	0.152436i
$670$			34.2942i			1.32490i
$671$	0.326244	+	2.86170i	0.0125945	+	0.110475i
$672$	−1.11646			−0.0430682
$673$	−22.7162	+	16.5043i	−0.875643	+	0.636192i	−0.932095	−	0.362213i	$-0.882021\pi$
$673$	−22.7162	+	16.5043i	−0.875643	+	0.636192i	0.0564520	+	0.998405i	$0.482021\pi$
$674$	0.328149	+	1.00994i	0.0126398	+	0.0389013i
$675$	−13.5086	−	4.38921i	−0.519946	−	0.168941i
$676$	4.05615	+	2.94696i	0.156006	+	0.113345i
$677$	10.0100	+	7.27266i	0.384714	+	0.279511i	0.763286	−	0.646061i	$-0.223585\pi$
$677$	10.0100	+	7.27266i	0.384714	+	0.279511i	−0.378572	+	0.925572i	$0.623585\pi$
$678$	−1.24488	+	3.83135i	−0.0478094	+	0.147142i
$679$	5.22603	+	16.0841i	0.200556	+	0.617249i
$680$	6.84242	+	9.41778i	0.262395	+	0.361155i
$681$			9.66218i			0.370255i
$682$	−20.5806	+	9.38081i	−0.788074	+	0.359210i
$683$		−	44.6770i		−	1.70952i	−0.519025	−	0.854759i	$-0.673705\pi$
$683$		−	44.6770i		−	1.70952i	0.519025	−	0.854759i	$-0.326295\pi$
$684$	9.60641	+	2.46328i	0.367310	+	0.0941860i
$685$	−8.75897	−	26.9573i	−0.334663	−	1.02999i
$686$	−15.3158	−	4.97639i	−0.584758	−	0.189999i
$687$	12.8637	−	17.7053i	0.490780	−	0.675501i
$688$	0.0327257	−	0.0450431i	0.00124766	−	0.00171725i
$689$	−7.50701	−	2.43918i	−0.285994	−	0.0929252i
$690$	−6.11277	+	1.98616i	−0.232709	+	0.0756118i
$691$	−19.4984	+	14.1664i	−0.741754	+	0.538916i	−0.893260	−	0.449541i	$-0.851588\pi$
$691$	−19.4984	+	14.1664i	−0.741754	+	0.538916i	0.151506	+	0.988456i	$0.451588\pi$
$692$	−22.6009			−0.859158
$693$	−4.87212	+	8.61279i	−0.185077	+	0.327173i
$694$			17.9606i			0.681773i
$695$	17.5996	+	24.2238i	0.667591	+	0.918861i
$696$	−3.41195	+	1.10861i	−0.129330	+	0.0420217i
$697$	46.6625	+	15.1616i	1.76747	+	0.574285i
$698$	−10.1585	+	13.9820i	−0.384505	+	0.529225i
$699$	12.0903	+	8.78410i	0.457296	+	0.332245i
$700$	3.94435	+	1.28160i	0.149082	+	0.0484398i
$701$	−20.7067	+	6.72803i	−0.782083	+	0.254114i	−0.672729	−	0.739889i	$-0.734878\pi$
$701$	−20.7067	+	6.72803i	−0.782083	+	0.254114i	−0.109353	+	0.994003i	$0.534878\pi$
$702$	−7.46016	−	10.2680i	−0.281566	−	0.387542i
$703$	6.37030	−	5.27335i	0.240260	−	0.198888i
$704$	−0.661011	+	3.25009i	−0.0249128	+	0.122492i
$705$			19.4657i			0.733121i
$706$	−7.19034	+	5.22408i	−0.270612	+	0.196611i
$707$	4.94467	+	15.2181i	0.185964	+	0.572337i
$708$	1.35740	−	4.17764i	0.0510141	−	0.157005i
$709$	32.5897	+	23.6778i	1.22393	+	0.889239i	0.996420	−	0.0845365i	$-0.0269410\pi$
$709$	32.5897	+	23.6778i	1.22393	+	0.889239i	0.227512	+	0.973775i	$0.426941\pi$
$710$	−21.6578	+	29.8094i	−0.812803	+	1.11873i
$711$	5.18506	−	15.9580i	0.194455	−	0.598471i
$712$	4.64269	−	1.50850i	0.173992	−	0.0565335i
$713$	10.5918	+	14.5783i	0.396665	+	0.545962i
$714$			4.54902i			0.170243i
$715$	−19.7419	+	18.0926i	−0.738305	+	0.676623i
$716$		−	12.7600i		−	0.476862i
$717$	11.6419	−	8.45836i	0.434776	−	0.315883i
$718$	4.73893	−	1.53977i	0.176855	−	0.0574637i
$719$	15.4819	−	47.6483i	0.577376	−	1.77698i	−0.0505671	−	0.998721i	$-0.516103\pi$
$719$	15.4819	−	47.6483i	0.577376	−	1.77698i	0.627943	−	0.778259i	$-0.283897\pi$
$720$	5.25878	+	3.82073i	0.195983	+	0.142390i
$721$	−0.520272	−	0.378000i	−0.0193759	−	0.0140774i
$722$	−16.6556	−	9.14283i	−0.619857	−	0.340261i
$723$	−21.1598	+	6.87523i	−0.786941	+	0.255693i
$724$	11.1224	+	15.3087i	0.413362	+	0.568945i
$725$	13.3267			0.494942
$726$	−7.06876	−	6.14312i	−0.262346	−	0.227993i
$727$	−13.3890			−0.496572			−0.248286	−	0.968687i	$-0.579867\pi$
$727$	−13.3890			−0.496572			−0.248286	+	0.968687i	$0.579867\pi$
$728$	2.17828	+	2.99815i	0.0807325	+	0.111119i
$729$	−1.43421	−	4.41403i	−0.0531188	−	0.163483i
$730$	−23.7054	−	7.70236i	−0.877377	−	0.285077i
$731$	−0.183529	−	0.133341i	−0.00678805	−	0.00493181i
$732$	0.598150	+	0.434582i	0.0221083	+	0.0160626i
$733$	−24.9635	−	8.11115i	−0.922050	−	0.299592i	−0.190742	−	0.981640i	$-0.561089\pi$
$733$	−24.9635	−	8.11115i	−0.922050	−	0.299592i	−0.731307	+	0.682048i	$0.761089\pi$
$734$	−3.12508	−	9.61800i	−0.115349	−	0.355007i
$735$	−7.54945	−	10.3909i	−0.278466	−	0.383275i
$736$	2.64239			0.0973997
$737$	26.8978	+	29.3499i	0.990793	+	1.08112i
$738$	27.3967			1.00849
$739$	−1.57997	−	2.17464i	−0.0581202	−	0.0799956i	0.778968	−	0.627064i	$-0.215744\pi$
$739$	−1.57997	−	2.17464i	−0.0581202	−	0.0799956i	−0.837088	+	0.547069i	$0.815744\pi$
$740$	5.15510	−	1.67499i	0.189505	−	0.0615740i
$741$	3.86376	+	9.74978i	0.141939	+	0.358167i
$742$	2.96324	+	2.15292i	0.108784	+	0.0790361i
$743$	4.52294	+	3.28611i	0.165931	+	0.120556i	0.667652	−	0.744474i	$-0.267300\pi$
$743$	4.52294	+	3.28611i	0.165931	+	0.120556i	−0.501721	+	0.865029i	$0.667300\pi$
$744$	−1.79414	+	5.52179i	−0.0657763	+	0.202438i
$745$	−30.1592	+	9.79933i	−1.10495	+	0.359020i
$746$	9.82910	−	7.14126i	0.359869	−	0.261460i
$747$			20.1741i			0.738131i
$748$	13.2425	+	2.69330i	0.484195	+	0.0984768i
$749$		−	11.0575i		−	0.404032i
$750$	−2.62695	−	3.61569i	−0.0959227	−	0.132026i
$751$	8.65543	−	2.81232i	0.315841	−	0.102623i	−0.146807	−	0.989165i	$-0.546899\pi$
$751$	8.65543	−	2.81232i	0.315841	−	0.102623i	0.462648	+	0.886542i	$0.346899\pi$
$752$	2.47296	−	7.61099i	0.0901796	−	0.277544i
$753$	3.47902	−	4.78846i	0.126783	−	0.174501i
$754$	9.63401	+	6.99952i	0.350850	+	0.254908i
$755$	−16.1645	+	49.7491i	−0.588285	+	1.81056i
$756$	1.81995	+	5.60124i	0.0661910	+	0.203715i
$757$	0.252503	−	0.183454i	0.00917738	−	0.00666776i	−0.583187	−	0.812338i	$-0.698195\pi$
$757$	0.252503	−	0.183454i	0.00917738	−	0.00666776i	0.592364	+	0.805670i	$0.298195\pi$
$758$			21.3397i			0.775092i
$759$	−3.67367	+	6.49421i	−0.133346	+	0.235725i
$760$	−7.94119	−	9.59309i	−0.288057	−	0.347978i
$761$	−23.3616	−	32.1544i	−0.846856	−	1.16560i	−0.984547	−	0.175122i	$-0.943968\pi$
$761$	−23.3616	−	32.1544i	−0.846856	−	1.16560i	0.137691	−	0.990475i	$-0.456032\pi$
$762$	5.54420	−	1.80142i	0.200845	−	0.0652586i
$763$	1.74138	+	0.565810i	0.0630423	+	0.0204837i
$764$	−12.2296	−	8.88535i	−0.442453	−	0.321461i
$765$	15.5676	−	21.4270i	0.562848	−	0.774694i
$766$	23.5512	+	7.65225i	0.850939	+	0.276487i
$767$	−13.8671	+	4.50568i	−0.500711	+	0.162691i
$768$	0.500425	+	0.688776i	0.0180575	+	0.0248541i
$769$		−	30.1976i		−	1.08895i	−0.838776	−	0.544476i	$-0.816729\pi$
$769$		−	30.1976i		−	1.08895i	0.838776	−	0.544476i	$-0.183271\pi$
$770$	11.3069	−	5.15375i	0.407471	−	0.185728i
$771$	12.7239			0.458241
$772$	15.6507	−	11.3709i	0.563280	−	0.409247i
$773$	−39.1170	+	12.7099i	−1.40694	+	0.457143i	−0.911429	−	0.411458i	$-0.865020\pi$
$773$	−39.1170	+	12.7099i	−1.40694	+	0.457143i	−0.495513	+	0.868601i	$0.665020\pi$
$774$	−0.120473	−	0.0391440i	−0.00433031	−	0.00140700i
$775$	12.6771	−	17.4485i	0.455374	−	0.626769i
$776$	7.58030	−	10.4334i	0.272117	−	0.374537i
$777$	2.01449	+	0.654546i	0.0722693	+	0.0234817i
$778$	10.7768	+	33.1676i	0.386367	+	1.18912i
$779$	−50.8434	−	13.0373i	−1.82165	−	0.467109i
$780$			6.87399i			0.246128i
$781$	4.84497	+	42.4985i	0.173367	+	1.52071i
$782$		−	10.7665i		−	0.385008i
$783$	11.1237	+	15.3105i	0.397530	+	0.547153i
$784$	1.63171	+	5.02190i	0.0582755	+	0.179354i
$785$	−0.422123	+	1.29916i	−0.0150662	+	0.0463691i
$786$	−11.1062	−	8.06910i	−0.396144	−	0.287815i
$787$	−13.1599	−	9.56123i	−0.469100	−	0.340821i	0.327991	−	0.944681i	$-0.393629\pi$
$787$	−13.1599	−	9.56123i	−0.469100	−	0.340821i	−0.797090	+	0.603860i	$0.793629\pi$
$788$	−16.6289	−	5.40307i	−0.592382	−	0.192476i
$789$	−5.37367	−	16.5385i	−0.191308	−	0.588784i
$790$	−17.0464	+	12.3849i	−0.606482	+	0.440635i
$791$	−6.20507			−0.220627
$792$	7.49730	−	0.854717i	0.266405	−	0.0303711i
$793$		−	2.45418i		−	0.0871504i
$794$	−19.8326	+	14.4092i	−0.703832	+	0.511364i
$795$	2.09944	+	6.46143i	0.0744596	+	0.229163i
$796$	0.636498	−	1.95894i	0.0225601	−	0.0694327i
$797$	−33.0514	+	45.4914i	−1.17074	+	1.61139i	−0.512116	+	0.858916i	$0.671138\pi$
$797$	−33.0514	+	45.4914i	−1.17074	+	1.61139i	−0.658625	+	0.752471i	$0.728862\pi$
$798$	−0.307101	−	4.85682i	−0.0108713	−	0.171930i
$799$	−31.0111	−	10.0761i	−1.09709	−	0.356468i
$800$	−0.977304	−	3.00783i	−0.0345529	−	0.106343i
$801$	−6.52822	−	8.98532i	−0.230663	−	0.317481i
$802$		−	20.8544i		−	0.736395i
$803$	−26.3289	+	12.0009i	−0.929126	+	0.423502i
$804$	10.2194			0.360411
$805$	−5.81905	−	8.00923i	−0.205094	−	0.282288i
$806$	18.3288	−	5.95537i	0.645603	−	0.209769i
$807$	5.46103	−	16.8073i	0.192237	−	0.591646i
$808$	7.17220	−	9.87169i	0.252317	−	0.347285i
$809$	−27.3226	+	37.6064i	−0.960613	+	1.32217i	−0.0139648	+	0.999902i	$0.504445\pi$
$809$	−27.3226	+	37.6064i	−0.960613	+	1.32217i	−0.946648	+	0.322268i	$0.895555\pi$
$810$	2.65025	−	8.15663i	0.0931203	−	0.286595i
$811$	−10.4240	−	32.0817i	−0.366035	−	1.12654i	−0.949330	−	0.314280i	$-0.898237\pi$
$811$	−10.4240	−	32.0817i	−0.366035	−	1.12654i	0.583295	−	0.812260i	$-0.301763\pi$
$812$	−3.24800	−	4.47049i	−0.113983	−	0.156884i
$813$	2.66215			0.0933656
$814$	3.09813	−	5.47679i	0.108590	−	0.191961i
$815$	−23.6062			−0.826888
$816$	2.80643	−	2.03899i	0.0982446	−	0.0713789i
$817$	0.204949	+	0.129974i	0.00717024	+	0.00454721i
$818$	−5.60176	+	17.2404i	−0.195861	+	0.602798i
$819$	4.95594	−	6.82127i	0.173175	−	0.238355i
$820$	−27.8329	−	20.2218i	−0.971966	−	0.706174i
$821$	3.94283	+	1.28110i	0.137606	+	0.0447109i	0.377010	−	0.926209i	$-0.376952\pi$
$821$	3.94283	+	1.28110i	0.137606	+	0.0447109i	−0.239404	+	0.970920i	$0.576952\pi$
$822$	−8.03309	+	2.61011i	−0.280186	+	0.0910380i
$823$	4.46436	−	3.24355i	0.155618	−	0.113063i	−0.507252	−	0.861798i	$-0.669339\pi$
$823$	4.46436	−	3.24355i	0.155618	−	0.113063i	0.662869	+	0.748735i	$0.269339\pi$
$824$			0.490401i			0.0170839i
$825$	8.75110	+	1.77982i	0.304674	+	0.0619654i
$826$	6.76591			0.235416
$827$	−8.75797	+	6.36304i	−0.304545	+	0.221265i	−0.729552	−	0.683925i	$-0.760271\pi$
$827$	−8.75797	+	6.36304i	−0.304545	+	0.221265i	0.425008	+	0.905190i	$0.360271\pi$
$828$	−1.85777	−	5.71762i	−0.0645619	−	0.198701i
$829$	−31.9630	−	10.3854i	−1.11012	−	0.360701i	−0.304133	−	0.952630i	$-0.598367\pi$
$829$	−31.9630	−	10.3854i	−1.11012	−	0.360701i	−0.805990	+	0.591929i	$0.798367\pi$
$830$	14.8907	−	20.4953i	0.516863	−	0.711401i
$831$	9.52628	+	6.92125i	0.330463	+	0.240095i
$832$	0.873285	−	2.68769i	0.0302757	−	0.0931790i
$833$	20.4618	−	6.64844i	0.708960	−	0.230355i
$834$	7.21851	−	5.24455i	0.249956	−	0.181604i
$835$	69.1408			2.39271
$836$	−14.3204	−	1.98154i	−0.495281	−	0.0685332i
$837$	30.6273			1.05864
$838$	−32.2075	+	23.4001i	−1.11259	+	0.808343i
$839$	−52.8717	+	17.1791i	−1.82533	+	0.593087i	−0.825756	+	0.564027i	$0.809251\pi$
$839$	−52.8717	+	17.1791i	−1.82533	+	0.593087i	−0.999578	+	0.0290602i	$0.990749\pi$
$840$	0.985687	−	3.03363i	0.0340094	−	0.104670i
$841$	9.09636	+	6.60889i	0.313667	+	0.227893i
$842$	−5.32416	+	7.32807i	−0.183483	+	0.252542i
$843$	−16.9231	−	5.49866i	−0.582864	−	0.189384i
$844$	−0.0591688	−	0.182103i	−0.00203667	−	0.00626823i
$845$	−11.5885	+	8.41956i	−0.398658	+	0.289642i
$846$	−18.2074			−0.625983
$847$	5.63450	−	13.2790i	0.193604	−	0.456272i
$848$		−	2.79310i		−	0.0959156i
$849$	4.55621	−	3.31028i	0.156369	−	0.113608i
$850$	−12.2555	+	3.98204i	−0.420359	+	0.136583i
$851$	−4.76781	−	1.54916i	−0.163439	−	0.0531044i
$852$	8.88298	+	6.45386i	0.304326	+	0.221106i
$853$	−25.4196	+	34.9871i	−0.870350	+	1.19793i	0.108651	+	0.994080i	$0.465347\pi$
$853$	−25.4196	+	34.9871i	−0.870350	+	1.19793i	−0.979001	+	0.203854i	$0.934653\pi$
$854$	−0.351914	+	1.08308i	−0.0120422	+	0.0370622i
$855$	−15.1745	+	23.9278i	−0.518955	+	0.818312i
$856$	−6.82169	+	4.95625i	−0.233161	+	0.169401i
$857$	−33.4070			−1.14116			−0.570581	−	0.821241i	$-0.693282\pi$
$857$	−33.4070			−1.14116			−0.570581	+	0.821241i	$0.693282\pi$
$858$	5.39144	+	5.88294i	0.184061	+	0.200840i
$859$	36.6856			1.25169			0.625847	−	0.779945i	$-0.284753\pi$
$859$	36.6856			1.25169			0.625847	+	0.779945i	$0.284753\pi$
$860$	0.0934983	+	0.128689i	0.00318827	+	0.00438827i
$861$	−4.15441	−	12.7860i	−0.141582	−	0.435745i
$862$	−4.09010	+	12.5880i	−0.139309	+	0.428750i
$863$	25.2324	−	34.7294i	0.858920	−	1.18220i	−0.122905	−	0.992418i	$-0.539221\pi$
$863$	25.2324	−	34.7294i	0.858920	−	1.18220i	0.981826	−	0.189784i	$-0.0607788\pi$
$864$	2.63982	−	3.63340i	0.0898086	−	0.123611i
$865$	19.9537	−	61.4111i	0.678446	−	2.08804i
$866$	−29.2229	+	9.49510i	−0.993035	+	0.322657i
$867$	0.199328	+	0.274351i	0.00676953	+	0.00931746i
$868$	−8.94282			−0.303539
$869$	−4.87492	+	23.9692i	−0.165370	+	0.813100i
$870$		−	10.2497i		−	0.347497i
$871$	−19.9387	−	27.4433i	−0.675598	−	0.929881i
$872$	−0.431468	−	1.32792i	−0.0146114	−	0.0449691i
$873$	−27.9053	−	9.06698i	−0.944451	−	0.306871i
$874$	0.726835	+	11.4949i	0.0245856	+	0.388822i
$875$	4.04626	−	5.56919i	0.136788	−	0.188273i
$876$	−2.29525	+	7.06404i	−0.0775492	+	0.238672i
$877$	−3.00287	−	9.24189i	−0.101400	−	0.312077i	0.887469	−	0.460868i	$-0.152462\pi$
$877$	−3.00287	−	9.24189i	−0.101400	−	0.312077i	−0.988869	+	0.148791i	$0.952462\pi$
$878$	28.5711	−	20.7581i	0.964228	−	0.700553i
$879$			4.78283i			0.161321i
$880$	−8.24754	−	4.66551i	−0.278025	−	0.157274i
$881$	27.7754			0.935776			0.467888	−	0.883788i	$-0.345015\pi$
$881$	27.7754			0.935776			0.467888	+	0.883788i	$0.345015\pi$
$882$	9.71923	−	7.06143i	0.327263	−	0.237771i
$883$	3.72039	+	11.4502i	0.125201	+	0.385330i	0.993938	−	0.109945i	$-0.0350675\pi$
$883$	3.72039	+	11.4502i	0.125201	+	0.385330i	−0.868737	+	0.495275i	$0.835067\pi$
$884$	−10.9511	−	3.55821i	−0.368324	−	0.119676i
$885$	10.1531	+	7.37664i	0.341292	+	0.247963i
$886$	−3.30120	−	2.39846i	−0.110906	−	0.0805778i
$887$	−15.6564	+	48.1855i	−0.525691	+	1.61791i	0.237256	+	0.971447i	$0.423752\pi$
$887$	−15.6564	+	48.1855i	−0.525691	+	1.61791i	−0.762946	+	0.646462i	$0.776248\pi$
$888$	−0.499136	−	1.53618i	−0.0167499	−	0.0515509i
$889$	5.27780	+	7.26427i	0.177012	+	0.243636i
$890$			13.9469i			0.467502i
$891$	−4.12930	−	9.05932i	−0.138337	−	0.303499i
$892$		−	7.87882i		−	0.263802i
$893$	33.7897	+	8.66437i	1.13073	+	0.289942i
$894$	2.92013	+	8.98723i	0.0976636	+	0.300578i
$895$	34.6713	+	11.2654i	1.15893	+	0.376561i
$896$	−0.770798	+	1.06091i	−0.0257505	+	0.0354426i
$897$	3.73688	−	5.14337i	0.124771	−	0.171732i
$898$	−13.7603	−	4.47099i	−0.459187	−	0.149199i
$899$	−27.3297	+	8.87997i	−0.911498	+	0.296164i
$900$	−5.82127	+	4.22940i	−0.194042	+	0.140980i
$901$	−11.3805			−0.379141
$902$	−39.6806	+	4.52372i	−1.32122	+	0.150623i
$903$			0.0621602i			0.00206856i
$904$	2.78128	+	3.82810i	0.0925038	+	0.127321i
$905$	−51.4165	+	16.7062i	−1.70914	+	0.555334i
$906$	14.8249	+	4.81689i	0.492523	+	0.160030i
$907$	6.03089	−	8.30081i	0.200252	−	0.275624i	−0.697067	−	0.717006i	$-0.745512\pi$
$907$	6.03089	−	8.30081i	0.200252	−	0.275624i	0.897319	+	0.441383i	$0.145512\pi$
$908$	9.18148	+	6.67073i	0.304698	+	0.221376i
$909$	−26.4030	−	8.57884i	−0.875731	−	0.284542i
$910$	−10.0697	+	3.27184i	−0.333807	+	0.108461i
$911$	−2.54204	−	3.49881i	−0.0842214	−	0.115921i	0.764827	−	0.644235i	$-0.222824\pi$
$911$	−2.54204	−	3.49881i	−0.0842214	−	0.115921i	−0.849049	+	0.528314i	$0.822824\pi$
$912$	−2.85867	+	2.36641i	−0.0946600	+	0.0783598i
$913$	−3.33113	−	29.2195i	−0.110244	−	0.967025i
$914$			4.79747i			0.158686i
$915$	−1.70893	+	1.24161i	−0.0564956	+	0.0410464i
$916$	−7.94344	−	24.4474i	−0.262459	−	0.807765i
$917$	6.53417	−	20.1101i	0.215777	−	0.664094i
$918$	−14.8044	−	10.7560i	−0.488617	−	0.355001i
$919$	29.5099	−	40.6169i	0.973441	−	1.33983i	0.0331515	−	0.999450i	$-0.489446\pi$
$919$	29.5099	−	40.6169i	0.973441	−	1.33983i	0.940289	−	0.340376i	$-0.110554\pi$
$920$	−2.33289	+	7.17989i	−0.0769130	+	0.236714i
$921$	−0.767052	+	0.249230i	−0.0252752	+	0.00821242i
$922$	−11.4892	−	15.8135i	−0.378376	−	0.520790i
$923$		−	36.4464i		−	1.19965i
$924$	−1.53578	−	3.36936i	−0.0505234	−	0.110844i
$925$			6.00017i			0.197284i
$926$	0.446449	−	0.324364i	0.0146712	−	0.0106593i
$927$	1.06113	−	0.344783i	0.0348522	−	0.0113242i
$928$	−1.30214	+	4.00758i	−0.0427449	+	0.131555i
$929$	−32.5696	−	23.6632i	−1.06857	−	0.776364i	−0.0929181	−	0.995674i	$-0.529619\pi$
$929$	−32.5696	−	23.6632i	−1.06857	−	0.776364i	−0.975655	+	0.219310i	$0.929619\pi$
$930$	−13.4198	−	9.75005i	−0.440052	−	0.319717i
$931$	−21.3975	+	8.47966i	−0.701274	+	0.277910i
$932$	16.6942	−	5.42427i	0.546836	−	0.177678i
$933$	2.44026	+	3.35874i	0.0798907	+	0.109960i
$934$	25.2455			0.826057
$935$	−19.0097	+	33.6047i	−0.621683	+	1.09899i
$936$	−6.42963			−0.210159
$937$	3.21412	+	4.42385i	0.105001	+	0.144521i	0.858284	−	0.513175i	$-0.171531\pi$
$937$	3.21412	+	4.42385i	0.105001	+	0.144521i	−0.753283	+	0.657696i	$0.771531\pi$
$938$	4.86418	+	14.9704i	0.158821	+	0.488801i
$939$	−15.3549	−	4.98910i	−0.501088	−	0.162813i
$940$	18.4973	+	13.4391i	0.603314	+	0.438334i
$941$	4.93373	+	3.58456i	0.160835	+	0.116853i	0.665292	−	0.746584i	$-0.268307\pi$
$941$	4.93373	+	3.58456i	0.160835	+	0.116853i	−0.504457	+	0.863437i	$0.668307\pi$
$942$	0.387141	+	0.125790i	0.0126137	+	0.00409845i
$943$	9.83251	+	30.2614i	0.320191	+	0.985445i
$944$	−3.03266	−	4.17409i	−0.0987046	−	0.135855i
$945$	−16.8265			−0.547365
$946$	0.180953	+	0.0368027i	0.00588328	+	0.00119656i
$947$	1.66404			0.0540739			0.0270370	−	0.999634i	$-0.491393\pi$
$947$	1.66404			0.0540739			0.0270370	+	0.999634i	$0.491393\pi$
$948$	3.69061	+	5.07969i	0.119865	+	0.164981i
$949$	23.4480	−	7.61873i	0.761155	−	0.247314i
$950$	12.8159	−	5.07884i	0.415802	−	0.164779i
$951$	13.1787	+	9.57490i	0.427349	+	0.310487i
$952$	4.32270	+	3.14063i	0.140100	+	0.101788i
$953$	−13.6336	+	41.9599i	−0.441636	+	1.35921i	0.444496	+	0.895781i	$0.353383\pi$
$953$	−13.6336	+	41.9599i	−0.441636	+	1.35921i	−0.886131	+	0.463434i	$0.846617\pi$
$954$	−6.04374	+	1.96373i	−0.195673	+	0.0635781i
$955$	34.9404	−	25.3857i	1.13065	−	0.821463i
$956$		−	16.9024i		−	0.546662i
$957$	−8.03910	−	8.77196i	−0.259867	−	0.283557i
$958$			7.85816i			0.253886i
$959$	−7.64709	−	10.5253i	−0.246937	−	0.339880i
$960$	−2.31335	+	0.751653i	−0.0746631	+	0.0242595i
$961$	−4.79152	+	14.7468i	−0.154565	+	0.475703i
$962$	−3.15144	+	4.33758i	−0.101606	+	0.139849i
$963$	15.5205	+	11.2763i	0.500140	+	0.363373i
$964$	−8.07546	+	24.8537i	−0.260093	+	0.800484i
$965$	17.0794	+	52.5650i	0.549805	+	1.69213i
$966$	−2.38669	+	1.73403i	−0.0767905	+	0.0557916i
$967$		−	3.01082i		−	0.0968213i	−0.998828	−	0.0484107i	$-0.984584\pi$
$967$		−	3.01082i		−	0.0968213i	0.998828	−	0.0484107i	$-0.0154156\pi$
$968$	−10.7177	+	2.47590i	−0.344481	+	0.0795783i
$969$	9.64199	+	11.6477i	0.309745	+	0.374178i
$970$	21.6571	+	29.8085i	0.695369	+	0.957093i
$971$	2.66328	−	0.865352i	0.0854687	−	0.0277705i	−0.265971	−	0.963981i	$-0.585692\pi$
$971$	2.66328	−	0.865352i	0.0854687	−	0.0277705i	0.351439	+	0.936211i	$0.385692\pi$
$972$	−15.2446	−	4.95327i	−0.488970	−	0.158876i
$973$	11.1186	+	8.07811i	0.356445	+	0.258972i
$974$	24.3649	−	33.5355i	0.780703	−	1.07455i
$975$	−7.23682	−	2.35138i	−0.231764	−	0.0753046i
$976$	0.825921	−	0.268358i	0.0264371	−	0.00858993i
$977$	−9.98813	−	13.7475i	−0.319549	−	0.439821i	0.618781	−	0.785564i	$-0.287627\pi$
$977$	−9.98813	−	13.7475i	−0.319549	−	0.439821i	−0.938329	+	0.345743i	$0.887627\pi$
$978$			7.03446i			0.224937i
$979$	10.9389	+	11.9361i	0.349610	+	0.381481i
$980$	−15.0861			−0.481907
$981$	−2.57002	+	1.86723i	−0.0820544	+	0.0596160i
$982$	−30.5997	+	9.94245i	−0.976476	+	0.317276i
$983$	12.0690	+	3.92144i	0.384940	+	0.125075i	0.495093	−	0.868840i	$-0.335134\pi$
$983$	12.0690	+	3.92144i	0.384940	+	0.125075i	−0.110153	+	0.993915i	$0.535134\pi$
$984$	−6.02593	+	8.29398i	−0.192100	+	0.264403i
$985$	29.3624	−	40.4139i	0.935565	−	1.28769i
$986$	16.3290	+	5.30560i	0.520020	+	0.168965i
$987$	2.76095	+	8.49734i	0.0878822	+	0.270473i
$988$	11.9323	+	3.05968i	0.379615	+	0.0973413i
$989$		−	0.147118i		−	0.00467809i
$990$	−4.29671	+	21.1262i	−0.136558	+	0.671436i
$991$			14.3940i			0.457240i	0.973516	+	0.228620i	$0.0734214\pi$
$991$			14.3940i			0.457240i	−0.973516	+	0.228620i	$0.926579\pi$
$992$	4.00841	+	5.51710i	0.127267	+	0.175168i
$993$	4.92566	+	15.1596i	0.156311	+	0.481076i
$994$	−5.22619	+	16.0846i	−0.165765	+	0.510171i
$995$	4.76088	+	3.45898i	0.150930	+	0.109657i
$996$	−6.10743	−	4.43731i	−0.193521	−	0.140602i
$997$	−43.1674	−	14.0259i	−1.36713	−	0.444206i	−0.468710	−	0.883352i	$-0.655281\pi$
$997$	−43.1674	−	14.0259i	−1.36713	−	0.444206i	−0.898416	+	0.439146i	$0.855281\pi$
$998$	13.0905	+	40.2886i	0.414374	+	1.27531i
$999$	−6.89334	+	5.00831i	−0.218096	+	0.158456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.151.6	yes	40
11.7	odd	10		418.2.m.a.227.5	yes	40
19.18	odd	2		418.2.m.a.151.5	✓	40
209.18	even	10	inner	418.2.m.b.227.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.151.5	✓	40	19.18	odd	2
418.2.m.a.227.5	yes	40	11.7	odd	10
418.2.m.b.151.6	yes	40	1.1	even	1	trivial
418.2.m.b.227.6	yes	40	209.18	even	10	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.809704 - 0.263089i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.31139 + 1.67932i) q^{5} +(0.500425 - 0.688776i) q^{6} +(1.24718 + 0.405232i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.84065 + 1.33731i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.809704 - 0.263089i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.31139 + 1.67932i) q^{5} +(0.500425 - 0.688776i) q^{6} +(1.24718 + 0.405232i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.84065 + 1.33731i) q^{9} +2.85703 q^{10} +(2.44512 - 2.24084i) q^{11} -0.851374i q^{12} +(-2.28629 + 1.66109i) q^{13} +(1.24718 - 0.405232i) q^{14} +(2.31335 + 0.751653i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.39494 + 3.29635i) q^{17} +(-0.703064 + 2.16381i) q^{18} +(2.33446 - 3.68108i) q^{19} +(2.31139 - 1.67932i) q^{20} +1.11646 q^{21} +(0.661011 - 3.25009i) q^{22} -2.64239 q^{23} +(-0.500425 - 0.688776i) q^{24} +(0.977304 + 3.00783i) q^{25} +(-0.873285 + 2.68769i) q^{26} +(-2.63982 + 3.63340i) q^{27} +(0.770798 - 1.06091i) q^{28} +(1.30214 - 4.00758i) q^{29} +(2.31335 - 0.751653i) q^{30} +(-4.00841 - 5.51710i) q^{31} -1.00000 q^{32} +(1.39029 - 2.45770i) q^{33} +4.07452i q^{34} +(2.20219 + 3.03106i) q^{35} +(0.703064 + 2.16381i) q^{36} +(1.80436 + 0.586271i) q^{37} +(-0.275068 - 4.35021i) q^{38} +(-1.41421 + 1.94649i) q^{39} +(0.882871 - 2.71720i) q^{40} +(-3.72107 - 11.4523i) q^{41} +(0.903232 - 0.656237i) q^{42} +0.0556763i q^{43} +(-1.37558 - 3.01791i) q^{44} -6.50021 q^{45} +(-2.13774 + 1.55316i) q^{46} +(2.47296 + 7.61099i) q^{47} +(-0.809704 - 0.263089i) q^{48} +(-4.27188 - 3.10370i) q^{49} +(2.55862 + 1.85894i) q^{50} +(-1.07196 + 3.29915i) q^{51} +(0.873285 + 2.68769i) q^{52} +(1.64175 + 2.25967i) q^{53} +4.49113i q^{54} +(9.41472 - 1.07331i) q^{55} -1.31136i q^{56} +(0.921769 - 3.59475i) q^{57} +(-1.30214 - 4.00758i) q^{58} +(4.90694 + 1.59436i) q^{59} +(1.42973 - 1.96785i) q^{60} +(-0.510447 + 0.702571i) q^{61} +(-6.48574 - 2.10734i) q^{62} +(-2.83753 + 0.921969i) q^{63} +(-0.809017 + 0.587785i) q^{64} -8.07399 q^{65} +(-0.319838 - 2.80551i) q^{66} +12.0034i q^{67} +(2.39494 + 3.29635i) q^{68} +(-2.13955 + 0.695183i) q^{69} +(3.56322 + 1.15776i) q^{70} +(-7.58053 + 10.4337i) q^{71} +(1.84065 + 1.33731i) q^{72} +(-8.29723 - 2.69593i) q^{73} +(1.80436 - 0.586271i) q^{74} +(1.58266 + 2.17834i) q^{75} +(-2.77952 - 3.35771i) q^{76} +(3.95756 - 1.80388i) q^{77} +2.40599i q^{78} +(-5.96646 + 4.33489i) q^{79} +(-0.882871 - 2.71720i) q^{80} +(0.927624 - 2.85493i) q^{81} +(-9.74189 - 7.07789i) q^{82} +(5.21194 - 7.17362i) q^{83} +(0.345004 - 1.06181i) q^{84} +(-11.0713 + 3.59727i) q^{85} +(0.0327257 + 0.0450431i) q^{86} -3.58754i q^{87} +(-2.88675 - 1.63299i) q^{88} +4.88162i q^{89} +(-5.25878 + 3.82073i) q^{90} +(-3.52453 + 1.14519i) q^{91} +(-0.816543 + 2.51306i) q^{92} +(-4.69711 - 3.41265i) q^{93} +(6.47430 + 4.70385i) q^{94} +(11.5775 - 4.58809i) q^{95} +(-0.809704 + 0.263089i) q^{96} +(7.58030 + 10.4334i) q^{97} -5.28034 q^{98} +(-1.50391 + 7.39448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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