LMFDB - Embedded newform 152.2.p.a.125.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(45,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("152.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.p (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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.18
Character	$\chi$	$=$	152.125
Dual form			152.2.p.a.45.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41356 - 0.0430601i) q^{2} +(-0.0638311 - 0.0368529i) q^{3} +(1.99629 - 0.121736i) q^{4} +(1.95840 + 1.13068i) q^{5} +(-0.0918158 - 0.0493451i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 - 2.59337i) q^{9} +O(q^{10})$	\(q+(1.41356 - 0.0430601i) q^{2} +(-0.0638311 - 0.0368529i) q^{3} +(1.99629 - 0.121736i) q^{4} +(1.95840 + 1.13068i) q^{5} +(-0.0918158 - 0.0493451i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 - 2.59337i) q^{9} +(2.81699 + 1.51395i) q^{10} +1.98019i q^{11} +(-0.131912 - 0.0657986i) q^{12} +(-0.432449 + 0.249675i) q^{13} +(-6.64740 + 0.202494i) q^{14} +(-0.0833377 - 0.144345i) q^{15} +(3.97036 - 0.486040i) q^{16} +(0.371220 - 0.642972i) q^{17} +(-2.22817 - 3.60141i) q^{18} +(-1.13983 - 4.20723i) q^{19} +(4.04717 + 2.01876i) q^{20} +(0.300172 + 0.173304i) q^{21} +(0.0852672 + 2.79912i) q^{22} +(1.59672 + 2.76560i) q^{23} +(-0.189298 - 0.0873300i) q^{24} +(0.0568756 + 0.0985114i) q^{25} +(-0.600541 + 0.371551i) q^{26} +0.441834i q^{27} +(-9.38776 + 0.572475i) q^{28} +(-5.22471 + 3.01649i) q^{29} +(-0.124018 - 0.200452i) q^{30} -5.44101 q^{31} +(5.59141 - 0.858010i) q^{32} +(0.0729758 - 0.126398i) q^{33} +(0.497055 - 0.924863i) q^{34} +(-9.20955 - 5.31714i) q^{35} +(-3.30472 - 4.99485i) q^{36} +10.3168i q^{37} +(-1.79237 - 5.89808i) q^{38} +0.0368049 q^{39} +(5.80784 + 2.67936i) q^{40} +(2.77027 - 4.79824i) q^{41} +(0.431773 + 0.232050i) q^{42} +(6.56065 + 3.78779i) q^{43} +(0.241060 + 3.95304i) q^{44} -6.77180i q^{45} +(2.37615 + 3.84058i) q^{46} +(-0.782377 - 1.35512i) q^{47} +(-0.271344 - 0.115295i) q^{48} +15.1145 q^{49} +(0.0846389 + 0.136803i) q^{50} +(-0.0473908 + 0.0273611i) q^{51} +(-0.832900 + 0.551068i) q^{52} +(10.0885 - 5.82458i) q^{53} +(0.0190254 + 0.624559i) q^{54} +(-2.23896 + 3.87800i) q^{55} +(-13.2455 + 1.21346i) q^{56} +(-0.0822924 + 0.310558i) q^{57} +(-7.25554 + 4.48896i) q^{58} +(-4.10945 - 2.37259i) q^{59} +(-0.183938 - 0.278010i) q^{60} +(1.51215 - 0.873042i) q^{61} +(-7.69118 + 0.234290i) q^{62} +(7.04113 + 12.1956i) q^{63} +(7.86683 - 1.45361i) q^{64} -1.12921 q^{65} +(0.0977129 - 0.181813i) q^{66} +(9.42749 - 5.44296i) q^{67} +(0.662791 - 1.32875i) q^{68} -0.235375i q^{69} +(-13.2472 - 7.11952i) q^{70} +(5.42083 - 9.38916i) q^{71} +(-4.88649 - 6.91821i) q^{72} +(-6.23576 + 10.8007i) q^{73} +(0.444244 + 14.5835i) q^{74} -0.00838412i q^{75} +(-2.78759 - 8.26010i) q^{76} -9.31205i q^{77} +(0.0520259 - 0.00158482i) q^{78} +(0.834855 - 1.44601i) q^{79} +(8.32509 + 3.53735i) q^{80} +(-4.47557 + 7.75191i) q^{81} +(3.70932 - 6.90188i) q^{82} +15.5733i q^{83} +(0.620329 + 0.309425i) q^{84} +(1.45399 - 0.839462i) q^{85} +(9.43696 + 5.07176i) q^{86} +0.444666 q^{87} +(0.510971 + 5.57747i) q^{88} +(-2.90236 - 5.02703i) q^{89} +(-0.291594 - 9.57233i) q^{90} +(2.03364 - 1.17412i) q^{91} +(3.52419 + 5.32657i) q^{92} +(0.347306 + 0.200517i) q^{93} +(-1.16429 - 1.88185i) q^{94} +(2.52480 - 9.52820i) q^{95} +(-0.388526 - 0.151292i) q^{96} +(-0.605380 + 1.04855i) q^{97} +(21.3652 - 0.650829i) q^{98} +(5.13537 - 2.96491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.41356	−	0.0430601i	0.999536	−	0.0304481i
$2$	1.41356	−	0.0430601i	0.999536	−	0.0304481i
$3$	−0.0638311	−	0.0368529i	−0.0368529	−	0.0212770i	0.481460	−	0.876468i	$-0.340107\pi$
$3$	−0.0638311	−	0.0368529i	−0.0368529	−	0.0212770i	−0.518313	+	0.855191i	$0.673440\pi$
$4$	1.99629	−	0.121736i	0.998146	−	0.0608679i
$5$	1.95840	+	1.13068i	0.875821	+	0.505656i	0.869278	−	0.494323i	$-0.164584\pi$
$5$	1.95840	+	1.13068i	0.875821	+	0.505656i	0.00654285	+	0.999979i	$0.497917\pi$
$6$	−0.0918158	−	0.0493451i	−0.0374837	−	0.0201451i
$7$	−4.70260			−1.77742			−0.888708	−	0.458474i	$-0.848396\pi$
$7$	−4.70260			−1.77742			−0.888708	+	0.458474i	$0.848396\pi$
$8$	2.81663	−	0.258041i	0.995830	−	0.0912313i
$9$	−1.49728	−	2.59337i	−0.499095	−	0.864457i
$10$	2.81699	+	1.51395i	0.890811	+	0.478754i
$11$			1.98019i			0.597050i	0.954402	+	0.298525i	$0.0964947\pi$
$11$			1.98019i			0.597050i	−0.954402	+	0.298525i	$0.903505\pi$
$12$	−0.131912	−	0.0657986i	−0.0380797	−	0.0189944i
$13$	−0.432449	+	0.249675i	−0.119940	+	0.0692473i	−0.558770	−	0.829323i	$-0.688726\pi$
$13$	−0.432449	+	0.249675i	−0.119940	+	0.0692473i	0.438830	+	0.898570i	$0.355393\pi$
$14$	−6.64740	+	0.202494i	−1.77659	+	0.0541189i
$15$	−0.0833377	−	0.144345i	−0.0215177	−	0.0372698i
$16$	3.97036	−	0.486040i	0.992590	−	0.121510i
$17$	0.371220	−	0.642972i	0.0900341	−	0.155944i	−0.817491	−	0.575941i	$-0.804636\pi$
$17$	0.371220	−	0.642972i	0.0900341	−	0.155944i	0.907525	+	0.419998i	$0.137969\pi$
$18$	−2.22817	−	3.60141i	−0.525184	−	0.848860i
$19$	−1.13983	−	4.20723i	−0.261494	−	0.965205i
$19$	−1.13983	−	4.20723i	−0.261494	−	0.965205i
$20$	4.04717	+	2.01876i	0.904975	+	0.451409i
$21$	0.300172	+	0.173304i	0.0655029	+	0.0378181i
$22$	0.0852672	+	2.79912i	0.0181790	+	0.596774i
$23$	1.59672	+	2.76560i	0.332939	+	0.576668i	0.983087	−	0.183140i	$-0.0586262\pi$
$23$	1.59672	+	2.76560i	0.332939	+	0.576668i	−0.650147	+	0.759808i	$0.725293\pi$
$24$	−0.189298	−	0.0873300i	−0.0386403	−	0.0178262i
$25$	0.0568756	+	0.0985114i	0.0113751	+	0.0197023i
$26$	−0.600541	+	0.371551i	−0.117776	+	0.0728671i
$27$			0.441834i			0.0850311i
$28$	−9.38776	+	0.572475i	−1.77412	+	0.108188i
$29$	−5.22471	+	3.01649i	−0.970205	+	0.560148i	−0.899299	−	0.437335i	$-0.855922\pi$
$29$	−5.22471	+	3.01649i	−0.970205	+	0.560148i	−0.0709062	+	0.997483i	$0.522589\pi$
$30$	−0.124018	−	0.200452i	−0.0226425	−	0.0365973i
$31$	−5.44101			−0.977234			−0.488617	−	0.872498i	$-0.662498\pi$
$31$	−5.44101			−0.977234			−0.488617	+	0.872498i	$0.662498\pi$
$32$	5.59141	−	0.858010i	0.988430	−	0.151676i
$33$	0.0729758	−	0.126398i	0.0127035	−	0.0220030i
$34$	0.497055	−	0.924863i	0.0852442	−	0.158613i
$35$	−9.20955	−	5.31714i	−1.55670	−	0.898760i
$36$	−3.30472	−	4.99485i	−0.550787	−	0.832475i
$37$			10.3168i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$37$			10.3168i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$38$	−1.79237	−	5.89808i	−0.290761	−	0.956796i
$39$	0.0368049			0.00589351
$40$	5.80784	+	2.67936i	0.918300	+	0.423645i
$41$	2.77027	−	4.79824i	0.432643	−	0.749359i	−0.564457	−	0.825462i	$-0.690914\pi$
$41$	2.77027	−	4.79824i	0.432643	−	0.749359i	0.997100	+	0.0761031i	$0.0242478\pi$
$42$	0.431773	+	0.232050i	0.0666241	+	0.0358062i
$43$	6.56065	+	3.78779i	1.00049	+	0.577633i	0.908393	−	0.418117i	$-0.137310\pi$
$43$	6.56065	+	3.78779i	1.00049	+	0.577633i	0.0920962	+	0.995750i	$0.470643\pi$
$44$	0.241060	+	3.95304i	0.0363412	+	0.595943i
$45$		−	6.77180i		−	1.00948i
$46$	2.37615	+	3.84058i	0.350344	+	0.566263i
$47$	−0.782377	−	1.35512i	−0.114121	−	0.197664i	0.803307	−	0.595565i	$-0.203072\pi$
$47$	−0.782377	−	1.35512i	−0.114121	−	0.197664i	−0.917428	+	0.397901i	$0.869739\pi$
$48$	−0.271344	−	0.115295i	−0.0391652	−	0.0166414i
$49$	15.1145			2.15921
$50$	0.0846389	+	0.136803i	0.0119697	+	0.0193468i
$51$	−0.0473908	+	0.0273611i	−0.00663604	+	0.00383132i
$52$	−0.832900	+	0.551068i	−0.115503	+	0.0764194i
$53$	10.0885	−	5.82458i	1.38576	−	0.800068i	0.392925	−	0.919571i	$-0.371463\pi$
$53$	10.0885	−	5.82458i	1.38576	−	0.800068i	0.992834	+	0.119503i	$0.0381300\pi$
$54$	0.0190254	+	0.624559i	0.00258903	+	0.0849916i
$55$	−2.23896	+	3.87800i	−0.301902	+	0.522909i
$56$	−13.2455	+	1.21346i	−1.77000	+	0.162156i
$57$	−0.0822924	+	0.310558i	−0.0108999	+	0.0411344i
$58$	−7.25554	+	4.48896i	−0.952700	+	0.589429i
$59$	−4.10945	−	2.37259i	−0.535005	−	0.308885i	0.208047	−	0.978119i	$-0.433289\pi$
$59$	−4.10945	−	2.37259i	−0.535005	−	0.308885i	−0.743052	+	0.669233i	$0.766623\pi$
$60$	−0.183938	−	0.278010i	−0.0237463	−	0.0358909i
$61$	1.51215	−	0.873042i	0.193611	−	0.111782i	−0.400061	−	0.916489i	$-0.631011\pi$
$61$	1.51215	−	0.873042i	0.193611	−	0.111782i	0.593672	+	0.804707i	$0.297678\pi$
$62$	−7.69118	+	0.234290i	−0.976781	+	0.0297549i
$63$	7.04113	+	12.1956i	0.887099	+	1.53650i
$64$	7.86683	−	1.45361i	0.983354	−	0.181702i
$65$	−1.12921			−0.140061
$66$	0.0977129	−	0.181813i	0.0120276	−	0.0223796i
$67$	9.42749	−	5.44296i	1.15175	−	0.664964i	0.202438	−	0.979295i	$-0.435114\pi$
$67$	9.42749	−	5.44296i	1.15175	−	0.664964i	0.949313	+	0.314332i	$0.101780\pi$
$68$	0.662791	−	1.32875i	0.0803752	−	0.161135i
$69$		−	0.235375i		−	0.0283359i
$70$	−13.2472	−	7.11952i	−1.58334	−	0.850945i
$71$	5.42083	−	9.38916i	0.643335	−	1.11429i	−0.341349	−	0.939937i	$-0.610884\pi$
$71$	5.42083	−	9.38916i	0.643335	−	1.11429i	0.984683	−	0.174352i	$-0.0557829\pi$
$72$	−4.88649	−	6.91821i	−0.575879	−	0.815319i
$73$	−6.23576	+	10.8007i	−0.729841	+	1.26412i	0.227109	+	0.973869i	$0.427073\pi$
$73$	−6.23576	+	10.8007i	−0.729841	+	1.26412i	−0.956950	+	0.290252i	$0.906261\pi$
$74$	0.444244	+	14.5835i	0.0516423	+	1.69529i
$75$		−	0.00838412i		−	0.000968115i
$76$	−2.78759	−	8.26010i	−0.319759	−	0.947499i
$77$		−	9.31205i		−	1.06121i
$78$	0.0520259	−	0.00158482i	0.00589078	−	0.000179446i
$79$	0.834855	−	1.44601i	0.0939285	−	0.162689i	−0.815232	−	0.579134i	$-0.803391\pi$
$79$	0.834855	−	1.44601i	0.0939285	−	0.162689i	0.909161	+	0.416445i	$0.136724\pi$
$80$	8.32509	+	3.53735i	0.930774	+	0.395488i
$81$	−4.47557	+	7.75191i	−0.497285	+	0.861324i
$82$	3.70932	−	6.90188i	0.409626	−	0.762185i
$83$			15.5733i			1.70939i	0.519130	+	0.854695i	$0.326256\pi$
$83$			15.5733i			1.70939i	−0.519130	+	0.854695i	$0.673744\pi$
$84$	0.620329	+	0.309425i	0.0676834	+	0.0337610i
$85$	1.45399	−	0.839462i	0.157708	−	0.0910525i
$86$	9.43696	+	5.07176i	1.01761	+	0.546902i
$87$	0.444666			0.0476732
$88$	0.510971	+	5.57747i	0.0544697	+	0.594561i
$89$	−2.90236	−	5.02703i	−0.307649	−	0.532864i	0.670198	−	0.742182i	$-0.266209\pi$
$89$	−2.90236	−	5.02703i	−0.307649	−	0.532864i	−0.977848	+	0.209318i	$0.932876\pi$
$90$	−0.291594	−	9.57233i	−0.0307367	−	1.00901i
$91$	2.03364	−	1.17412i	0.213183	−	0.123081i
$92$	3.52419	+	5.32657i	0.367423	+	0.555334i
$93$	0.347306	+	0.200517i	0.0360139	+	0.0207926i
$94$	−1.16429	−	1.88185i	−0.120087	−	0.194098i
$95$	2.52480	−	9.52820i	0.259040	−	0.977573i
$96$	−0.388526	−	0.151292i	−0.0396537	−	0.0154412i
$97$	−0.605380	+	1.04855i	−0.0614670	+	0.106464i	−0.895121	−	0.445823i	$-0.852911\pi$
$97$	−0.605380	+	1.04855i	−0.0614670	+	0.106464i	0.833654	+	0.552287i	$0.186245\pi$
$98$	21.3652	−	0.650829i	2.15821	−	0.0657437i
$99$	5.13537	−	2.96491i	0.516124	−	0.297985i
$100$	0.125533	+	0.189734i	0.0125533	+	0.0189734i
$101$	−12.9353	+	7.46822i	−1.28711	+	0.743115i	−0.978138	−	0.207955i	$-0.933319\pi$
$101$	−12.9353	+	7.46822i	−1.28711	+	0.743115i	−0.308975	+	0.951070i	$0.599986\pi$
$102$	−0.0658114	+	0.0407171i	−0.00651630	+	0.00403159i
$103$	11.6211			1.14506			0.572530	−	0.819884i	$-0.305962\pi$
$103$	11.6211			1.14506			0.572530	+	0.819884i	$0.305962\pi$
$104$	−1.15362	+	0.814831i	−0.113122	+	0.0799008i
$105$	0.391904	+	0.678798i	0.0382459	+	0.0662439i
$106$	14.0098	−	8.66780i	1.36076	−	0.841891i
$107$		−	7.66606i		−	0.741106i	−0.928811	−	0.370553i	$-0.879168\pi$
$107$		−	7.66606i		−	0.741106i	0.928811	−	0.370553i	$-0.120832\pi$
$108$	0.0537870	+	0.882030i	0.00517566	+	0.0848734i
$109$	−2.28507	−	1.31929i	−0.218870	−	0.126365i	0.386557	−	0.922266i	$-0.373664\pi$
$109$	−2.28507	−	1.31929i	−0.218870	−	0.126365i	−0.605427	+	0.795901i	$0.706998\pi$
$110$	−2.99792	+	5.57819i	−0.285840	+	0.531859i
$111$	0.380206	−	0.658536i	0.0360875	−	0.0625055i
$112$	−18.6710	+	2.28565i	−1.76425	+	0.215974i
$113$	−8.94264			−0.841253			−0.420627	−	0.907234i	$-0.638190\pi$
$113$	−8.94264			−0.841253			−0.420627	+	0.907234i	$0.638190\pi$
$114$	−0.102952	+	0.442535i	−0.00964238	+	0.0414472i
$115$			7.22153i			0.673411i
$116$	−10.0628	+	6.65783i	−0.934311	+	0.618164i
$117$	1.29500	+	0.747668i	0.119723	+	0.0691219i
$118$	−5.91111	−	3.17684i	−0.544162	−	0.292452i
$119$	−1.74570	+	3.02364i	−0.160028	+	0.277177i
$120$	−0.271979	−	0.385063i	−0.0248281	−	0.0351512i
$121$	7.07884			0.643531
$122$	2.09992	−	1.29921i	0.190118	−	0.117625i
$123$	−0.353658	+	0.204185i	−0.0318883	+	0.0184107i
$124$	−10.8618	+	0.662365i	−0.975422	+	0.0594822i
$125$		−	11.0496i		−	0.988304i
$126$	10.4782	+	16.9360i	0.933471	+	1.50878i
$127$	−2.38102	−	4.12405i	−0.211281	−	0.365950i	0.740834	−	0.671688i	$-0.234430\pi$
$127$	−2.38102	−	4.12405i	−0.211281	−	0.365950i	−0.952116	+	0.305738i	$0.901097\pi$
$128$	11.0576	−	2.39351i	0.977365	−	0.211559i
$129$	−0.279182	−	0.483558i	−0.0245806	−	0.0425749i
$130$	−1.59620	+	0.0486238i	−0.139996	+	0.00426459i
$131$	4.31780	+	2.49288i	0.377248	+	0.217804i	0.676620	−	0.736332i	$-0.263444\pi$
$131$	4.31780	+	2.49288i	0.377248	+	0.217804i	−0.299372	+	0.954136i	$0.596777\pi$
$132$	0.130294	−	0.261211i	0.0113406	−	0.0227355i
$133$	5.36014	+	19.7849i	0.464783	+	1.71557i
$134$	13.0919	−	8.09989i	1.13097	−	0.699724i
$135$	−0.499573	+	0.865287i	−0.0429964	+	0.0744720i
$136$	0.879677	−	1.90681i	0.0754317	−	0.163507i
$137$	−4.00007	−	6.92833i	−0.341749	−	0.591927i	0.643008	−	0.765859i	$-0.277686\pi$
$137$	−4.00007	−	6.92833i	−0.341749	−	0.591927i	−0.984758	+	0.173932i	$0.944353\pi$
$138$	−0.0101353	−	0.332717i	−0.000862772	−	0.0283227i
$139$	−6.90837	+	3.98855i	−0.585960	+	0.338304i	−0.763498	−	0.645810i	$-0.776520\pi$
$139$	−6.90837	+	3.98855i	−0.585960	+	0.338304i	0.177538	+	0.984114i	$0.443187\pi$
$140$	−19.0322	−	9.49343i	−1.60852	−	0.802341i
$141$			0.115331i			0.00971266i
$142$	7.25837	−	13.5055i	0.609108	−	1.13336i
$143$	−0.494404	−	0.856333i	−0.0413441	−	0.0716101i
$144$	−7.20524	−	9.56888i	−0.600437	−	0.797407i
$145$	−13.6427			−1.13297
$146$	−8.34954	+	15.5359i	−0.691012	+	1.28576i
$147$	−0.964772	−	0.557012i	−0.0795731	−	0.0459415i
$148$	1.25593	+	20.5954i	0.103237	+	1.69293i
$149$	−4.57651	−	2.64225i	−0.374922	−	0.216462i	0.300684	−	0.953724i	$-0.402785\pi$
$149$	−4.57651	−	2.64225i	−0.374922	−	0.216462i	−0.675607	+	0.737262i	$0.736118\pi$
$150$	−0.000361021	−	0.0118514i	−2.94772e−5	−	0.000967666i
$151$	−3.63598			−0.295892			−0.147946	−	0.988995i	$-0.547266\pi$
$151$	−3.63598			−0.295892			−0.147946	+	0.988995i	$0.547266\pi$
$152$	−4.29611	−	11.5561i	−0.348460	−	0.937324i
$153$	−2.22329			−0.179742
$154$	−0.400978	−	13.1631i	−0.0323117	−	1.06071i
$155$	−10.6556	−	6.15204i	−0.855882	−	0.494144i
$156$	0.0734734	−	0.00448048i	0.00588258	−	0.000358725i
$157$	−16.5481	−	9.55404i	−1.32068	−	0.762496i	−0.336844	−	0.941561i	$-0.609359\pi$
$157$	−16.5481	−	9.55404i	−1.32068	−	0.762496i	−0.983837	+	0.179065i	$0.942693\pi$
$158$	1.11785	−	2.07997i	0.0889314	−	0.165473i
$159$	−0.858611			−0.0680923
$160$	11.9203	+	4.64177i	0.942384	+	0.366964i
$161$	−7.50874	−	13.0055i	−0.591772	−	1.02498i
$162$	−5.99268	+	11.1505i	−0.470829	+	0.876066i
$163$			9.73237i			0.762298i	0.924514	+	0.381149i	$0.124472\pi$
$163$			9.73237i			0.762298i	−0.924514	+	0.381149i	$0.875528\pi$
$164$	4.94614	−	9.91593i	0.386229	−	0.774304i
$165$	0.285831	−	0.165025i	0.0222519	−	0.0128472i
$166$	0.670587	+	22.0137i	0.0520476	+	1.70860i
$167$	−9.40182	−	16.2844i	−0.727535	−	1.26013i	−0.957922	−	0.287029i	$-0.907333\pi$
$167$	−9.40182	−	16.2844i	−0.727535	−	1.26013i	0.230387	−	0.973099i	$-0.426001\pi$
$168$	0.890194	+	0.410678i	0.0686800	+	0.0316845i
$169$	−6.37533	+	11.0424i	−0.490410	+	0.849414i
$170$	2.01915	−	1.24924i	0.154862	−	0.0958122i
$171$	−9.20427	+	9.25541i	−0.703868	+	0.707779i
$172$	13.5581	+	6.76287i	1.03379	+	0.515664i
$173$	−10.1721	−	5.87286i	−0.773370	−	0.446505i	0.0607055	−	0.998156i	$-0.480665\pi$
$173$	−10.1721	−	5.87286i	−0.773370	−	0.446505i	−0.834075	+	0.551650i	$0.813998\pi$
$174$	0.628560	−	0.0191473i	0.0476510	−	0.00145155i
$175$	−0.267463	−	0.463260i	−0.0202183	−	0.0350192i
$176$	0.962453	+	7.86208i	0.0725476	+	0.592626i
$177$	0.174874	+	0.302890i	0.0131443	+	0.0227666i
$178$	−4.31912	−	6.98103i	−0.323731	−	0.523250i
$179$			11.1964i			0.836860i	0.908249	+	0.418430i	$0.137420\pi$
$179$			11.1964i			0.836860i	−0.908249	+	0.418430i	$0.862580\pi$
$180$	−0.824370	−	13.5185i	−0.0614449	−	1.00761i
$181$	10.2345	−	5.90892i	0.760728	−	0.439206i	−0.0688293	−	0.997628i	$-0.521926\pi$
$181$	10.2345	−	5.90892i	0.760728	−	0.439206i	0.829557	+	0.558422i	$0.188593\pi$
$182$	2.82410	−	1.74726i	0.209337	−	0.129515i
$183$	−0.128697			−0.00951352
$184$	5.21102	+	7.37767i	0.384161	+	0.543889i
$185$	−11.6651	+	20.2045i	−0.857632	+	1.48546i
$186$	0.499571	+	0.268487i	0.0366303	+	0.0196864i
$187$	1.27321	+	0.735087i	0.0931062	+	0.0537549i
$188$	−1.72682	−	2.60997i	−0.125941	−	0.190351i
$189$		−	2.07777i		−	0.151136i
$190$	3.15867	−	13.5774i	0.229154	−	0.985007i
$191$	12.6474			0.915135			0.457568	−	0.889175i	$-0.348721\pi$
$191$	12.6474			0.915135			0.457568	+	0.889175i	$0.348721\pi$
$192$	−0.555718	−	0.197130i	−0.0401055	−	0.0142266i
$193$	−3.67277	+	6.36143i	−0.264372	+	0.457906i	−0.967399	−	0.253258i	$-0.918498\pi$
$193$	−3.67277	+	6.36143i	−0.264372	+	0.457906i	0.703027	+	0.711163i	$0.251831\pi$
$194$	−0.810589	+	1.50825i	−0.0581969	+	0.108286i
$195$	0.0720786	+	0.0416146i	0.00516166	+	0.00298009i
$196$	30.1729	−	1.83997i	2.15520	−	0.131426i
$197$			12.1000i			0.862092i	0.902330	+	0.431046i	$0.141855\pi$
$197$			12.1000i			0.862092i	−0.902330	+	0.431046i	$0.858145\pi$
$198$	7.13148	−	4.41220i	0.506812	−	0.313561i
$199$	−3.73560	−	6.47025i	−0.264810	−	0.458664i	0.702704	−	0.711482i	$-0.251976\pi$
$199$	−3.73560	−	6.47025i	−0.264810	−	0.458664i	−0.967514	+	0.252819i	$0.918642\pi$
$200$	0.185618	+	0.262794i	0.0131251	+	0.0185824i
$201$	−0.802356			−0.0565938
$202$	−17.9633	+	11.1138i	−1.26389	+	0.781961i
$203$	24.5697	−	14.1853i	1.72446	−	0.995616i
$204$	−0.0912750	+	0.0603898i	−0.00639053	+	0.00422813i
$205$	10.8505	−	6.26457i	0.757835	−	0.437536i
$206$	16.4271	−	0.500405i	1.14453	−	0.0348649i
$207$	4.78149	−	8.28178i	0.332337	−	0.575624i
$208$	−1.59563	+	1.20149i	−0.110637	+	0.0833081i
$209$	8.33113	−	2.25707i	0.576276	−	0.156125i
$210$	0.583208	+	0.942644i	0.0402452	+	0.0650486i
$211$	5.04276	+	2.91144i	0.347158	+	0.200432i	0.663433	−	0.748236i	$-0.269099\pi$
$211$	5.04276	+	2.91144i	0.347158	+	0.200432i	−0.316275	+	0.948668i	$0.602432\pi$
$212$	19.4305	−	12.8557i	1.33449	−	0.882933i
$213$	−0.692036	+	0.399547i	−0.0474175	+	0.0273765i
$214$	−0.330101	−	10.8364i	−0.0225653	−	0.740763i
$215$	8.56556	+	14.8360i	0.584166	+	1.01181i
$216$	0.114011	+	1.24448i	0.00775749	+	0.0846765i
$217$	25.5869			1.73695
$218$	−3.28689	−	1.76649i	−0.222616	−	0.119642i
$219$	0.796071	−	0.459612i	0.0537935	−	0.0310577i
$220$	−3.99753	+	8.01418i	−0.269514	+	0.540316i
$221$			0.370737i			0.0249385i
$222$	0.509086	−	0.947250i	0.0341676	−	0.0635753i
$223$	−3.54133	+	6.13377i	−0.237145	+	0.410748i	−0.959894	−	0.280363i	$-0.909545\pi$
$223$	−3.54133	+	6.13377i	−0.237145	+	0.410748i	0.722749	+	0.691111i	$0.242878\pi$
$224$	−26.2942	+	4.03488i	−1.75685	+	0.269592i
$225$	0.170318	−	0.294999i	0.0113545	−	0.0196666i
$226$	−12.6409	+	0.385071i	−0.840863	+	0.0256145i
$227$			10.8506i			0.720179i	0.932918	+	0.360090i	$0.117254\pi$
$227$			10.8506i			0.720179i	−0.932918	+	0.360090i	$0.882746\pi$
$228$	−0.126474	+	0.629982i	−0.00837592	+	0.0417216i
$229$		−	5.71559i		−	0.377697i	−0.982006	−	0.188848i	$-0.939525\pi$
$229$		−	5.71559i		−	0.377697i	0.982006	−	0.188848i	$-0.0604755\pi$
$230$	0.310959	+	10.2080i	0.0205041	+	0.673099i
$231$	−0.343176	+	0.594399i	−0.0225793	+	0.0391086i
$232$	−13.9377	+	9.84453i	−0.915056	+	0.646325i
$233$	11.6711	−	20.2149i	0.764598	−	1.32432i	−0.175860	−	0.984415i	$-0.556271\pi$
$233$	11.6711	−	20.2149i	0.764598	−	1.32432i	0.940459	−	0.339908i	$-0.110396\pi$
$234$	1.86275	+	1.00111i	0.121772	+	0.0654445i
$235$		−	3.53847i		−	0.230825i
$236$	−8.49249	−	4.23612i	−0.552814	−	0.275748i
$237$	−0.106579	+	0.0615336i	−0.00692307	+	0.00399704i
$238$	−2.33745	+	4.34926i	−0.151514	+	0.281921i
$239$	−10.4517			−0.676063			−0.338032	−	0.941135i	$-0.609761\pi$
$239$	−10.4517			−0.676063			−0.338032	+	0.941135i	$0.609761\pi$
$240$	−0.401038	−	0.532597i	−0.0258869	−	0.0343790i
$241$	−10.3416	−	17.9122i	−0.666160	−	1.15382i	−0.978969	−	0.204007i	$-0.934603\pi$
$241$	−10.3416	−	17.9122i	−0.666160	−	1.15382i	0.312809	−	0.949816i	$-0.398730\pi$
$242$	10.0063	−	0.304815i	0.643232	−	0.0195943i
$243$	1.71928	−	0.992627i	0.110292	−	0.0636770i
$244$	2.91242	−	1.92693i	0.186449	−	0.123359i
$245$	29.6001	+	17.0896i	1.89108	+	1.09182i
$246$	−0.491124	+	0.303855i	−0.0313129	+	0.0193731i
$247$	1.54336	+	1.53483i	0.0982014	+	0.0976588i
$248$	−15.3253	+	1.40400i	−0.973159	+	0.0891543i
$249$	0.573921	−	0.994060i	0.0363708	−	0.0629960i
$250$	−0.475795	−	15.6192i	−0.0300919	−	0.987845i
$251$	−0.147363	+	0.0850803i	−0.00930149	+	0.00537022i	−0.504644	−	0.863328i	$-0.668376\pi$
$251$	−0.147363	+	0.0850803i	−0.00930149	+	0.00537022i	0.495342	+	0.868698i	$0.335043\pi$
$252$	15.5408	+	23.4888i	0.978977	+	1.47966i
$253$	−5.47643	+	3.16182i	−0.344300	+	0.198782i
$254$	−3.54329	−	5.72706i	−0.222326	−	0.359347i
$255$	−0.123747			−0.00774931
$256$	15.5275	−	3.85951i	0.970471	−	0.241219i
$257$	7.27034	+	12.5926i	0.453511	+	0.785504i	0.998601	−	0.0528730i	$-0.0168379\pi$
$257$	7.27034	+	12.5926i	0.453511	+	0.785504i	−0.545090	+	0.838378i	$0.683505\pi$
$258$	−0.415462	−	0.671515i	−0.0258655	−	0.0418067i
$259$		−	48.5160i		−	3.01464i
$260$	−2.25423	+	0.137465i	−0.139801	+	0.00852522i
$261$	15.6458	+	9.03308i	0.968448	+	0.559134i
$262$	6.21080	+	3.33791i	0.383704	+	0.206217i
$263$	−7.54036	+	13.0603i	−0.464959	+	0.805332i	−0.999200	−	0.0400000i	$-0.987264\pi$
$263$	−7.54036	+	13.0603i	−0.464959	+	0.805332i	0.534241	+	0.845332i	$0.320598\pi$
$264$	0.172930	−	0.374847i	0.0106431	−	0.0230702i
$265$	26.3430			1.61824
$266$	8.42881	+	27.7363i	0.516804	+	1.70062i
$267$			0.427841i			0.0261835i
$268$	18.1574	−	12.0134i	1.10914	−	0.733835i
$269$	−6.34397	−	3.66269i	−0.386799	−	0.223318i	0.293973	−	0.955814i	$-0.405022\pi$
$269$	−6.34397	−	3.66269i	−0.386799	−	0.223318i	−0.680772	+	0.732495i	$0.738356\pi$
$270$	−0.668917	+	1.24464i	−0.0407090	+	0.0757466i
$271$	−4.12352	+	7.14215i	−0.250486	+	0.433855i	−0.963660	−	0.267133i	$-0.913924\pi$
$271$	−4.12352	+	7.14215i	−0.250486	+	0.433855i	0.713174	+	0.700987i	$0.247257\pi$
$272$	1.16137	−	2.73326i	0.0704182	−	0.165728i
$273$	−0.173079			−0.0104752
$274$	−5.95267	−	9.62135i	−0.359614	−	0.581247i
$275$	−0.195072	+	0.112625i	−0.0117633	+	0.00679152i
$276$	−0.0286536	−	0.469878i	−0.00172474	−	0.0282833i
$277$			17.2973i			1.03929i	0.854382	+	0.519646i	$0.173936\pi$
$277$			17.2973i			1.03929i	−0.854382	+	0.519646i	$0.826064\pi$
$278$	−9.59363	+	5.93552i	−0.575388	+	0.355989i
$279$	8.14673	+	14.1106i	0.487732	+	0.844777i
$280$	−27.3120	−	12.6000i	−1.63220	−	0.752993i
$281$	−12.5105	−	21.6688i	−0.746312	−	1.29265i	−0.949579	−	0.313527i	$-0.898489\pi$
$281$	−12.5105	−	21.6688i	−0.746312	−	1.29265i	0.203267	−	0.979123i	$-0.434844\pi$
$282$	0.00496618	+	0.163028i	0.000295732	+	0.00970816i
$283$	−16.0653	−	9.27531i	−0.954984	−	0.551360i	−0.0603582	−	0.998177i	$-0.519224\pi$
$283$	−16.0653	−	9.27531i	−0.954984	−	0.551360i	−0.894626	+	0.446817i	$0.852558\pi$
$284$	9.67857	−	19.4034i	0.574317	−	1.15138i
$285$	−0.512303	+	0.515149i	−0.0303462	+	0.0305148i
$286$	−0.735742	−	1.18919i	−0.0435053	−	0.0703181i
$287$	−13.0275	+	22.5642i	−0.768986	+	1.33192i
$288$	−10.5971	−	13.2159i	−0.624438	−	0.778755i
$289$	8.22439	+	14.2451i	0.483788	+	0.837945i
$290$	−19.2848	+	0.587457i	−1.13244	+	0.0344967i
$291$	0.0772841	−	0.0446200i	0.00453048	−	0.00261567i
$292$	−11.1336	+	22.3204i	−0.651543	+	1.30620i
$293$		−	1.02282i		−	0.0597535i	−0.999554	−	0.0298768i	$-0.990489\pi$
$293$		−	1.02282i		−	0.0597535i	0.999554	−	0.0298768i	$-0.00951149\pi$
$294$	−1.38775	−	0.745825i	−0.0809350	−	0.0434974i
$295$	−5.36529	−	9.29295i	−0.312379	−	0.541057i
$296$	2.66217	+	29.0588i	0.154735	+	1.68901i
$297$	−0.874917			−0.0507678
$298$	−6.58294	−	3.53791i	−0.381339	−	0.204946i
$299$	−1.38100	−	0.797322i	−0.0798654	−	0.0461103i
$300$	−0.00102065	−	0.0167372i	−5.89271e−5	−	0.000966320i
$301$	−30.8521	−	17.8125i	−1.77829	−	1.02669i
$302$	−5.13966	+	0.156565i	−0.295754	+	0.00900933i
$303$	1.10090			0.0632451
$304$	−6.57040	−	16.1502i	−0.376838	−	0.926279i
$305$	3.94853			0.226092
$306$	−3.14274	+	0.0957349i	−0.179659	+	0.00547280i
$307$	−22.7524	−	13.1361i	−1.29855	−	0.749717i	−0.318395	−	0.947958i	$-0.603144\pi$
$307$	−22.7524	−	13.1361i	−1.29855	−	0.749717i	−0.980153	+	0.198241i	$0.936477\pi$
$308$	−1.13361	−	18.5896i	−0.0645934	−	1.05924i
$309$	−0.741787	−	0.428271i	−0.0421988	−	0.0243635i
$310$	−15.3273	−	8.23743i	−0.870531	−	0.467855i
$311$	24.2028			1.37241			0.686207	−	0.727407i	$-0.259275\pi$
$311$	24.2028			1.37241			0.686207	+	0.727407i	$0.259275\pi$
$312$	0.103666	−	0.00949718i	0.00586893	−	0.000537672i
$313$	14.3528	+	24.8598i	0.811270	+	1.40516i	0.911976	+	0.410244i	$0.134557\pi$
$313$	14.3528	+	24.8598i	0.811270	+	1.40516i	−0.100706	+	0.994916i	$0.532110\pi$
$314$	−23.8031	−	12.7926i	−1.34329	−	0.721930i
$315$			31.8451i			1.79427i
$316$	1.49058	−	2.98829i	0.0838518	−	0.168104i
$317$	−8.87555	+	5.12430i	−0.498501	+	0.287809i	−0.728094	−	0.685477i	$-0.759594\pi$
$317$	−8.87555	+	5.12430i	−0.498501	+	0.287809i	0.229594	+	0.973287i	$0.426260\pi$
$318$	−1.21370	+	0.0369718i	−0.0680607	+	0.00207328i
$319$	−5.97323	−	10.3459i	−0.334437	−	0.579261i
$320$	17.0499	+	6.04812i	0.953120	+	0.338100i
$321$	−0.282517	+	0.489333i	−0.0157685	+	0.0273119i
$322$	−11.1741	−	18.0607i	−0.622706	−	1.00649i
$323$	−3.12826	−	0.828933i	−0.174061	−	0.0461231i
$324$	−7.99085	+	16.0199i	−0.443936	+	0.889995i
$325$	−0.0491916	−	0.0284008i	−0.00272866	−	0.00157539i
$326$	0.419076	+	13.7573i	0.0232105	+	0.761945i
$327$	0.0972391	+	0.168423i	0.00537733	+	0.00931381i
$328$	6.56467	−	14.2297i	0.362474	−	0.785705i
$329$	3.67921	+	6.37257i	0.202841	+	0.351331i
$330$	0.396933	−	0.245580i	0.0218504	−	0.0135187i
$331$		−	16.6930i		−	0.917528i	−0.888558	−	0.458764i	$-0.848292\pi$
$331$		−	16.6930i		−	0.917528i	0.888558	−	0.458764i	$-0.151708\pi$
$332$	1.89583	+	31.0888i	0.104047	+	1.70622i
$333$	26.7554	−	15.4473i	1.46619	−	0.846504i
$334$	−13.9912	−	22.6142i	−0.765566	−	1.23739i
$335$	24.6170			1.34497
$336$	1.27602	+	0.542186i	0.0696129	+	0.0295787i
$337$	14.1278	−	24.4701i	0.769591	−	1.33297i	−0.168194	−	0.985754i	$-0.553794\pi$
$337$	14.1278	−	24.4701i	0.769591	−	1.33297i	0.937785	−	0.347216i	$-0.112873\pi$
$338$	−8.53641	+	15.8836i	−0.464319	+	0.863953i
$339$	0.570819	+	0.329562i	0.0310026	+	0.0178994i
$340$	2.80040	−	1.85281i	0.151873	−	0.100483i
$341$		−	10.7742i		−	0.583458i
$342$	−12.6122	+	13.4794i	−0.681991	+	0.728882i
$343$	−38.1591			−2.06040
$344$	19.4563	+	8.97590i	1.04902	+	0.483948i
$345$	0.266134	−	0.460958i	0.0143282	−	0.0248171i
$346$	−14.6317	−	7.86362i	−0.786607	−	0.422751i
$347$	22.6793	+	13.0939i	1.21749	+	0.702918i	0.964380	−	0.264519i	$-0.0852132\pi$
$347$	22.6793	+	13.0939i	1.21749	+	0.702918i	0.253110	+	0.967438i	$0.418547\pi$
$348$	0.887682	−	0.0541317i	0.0475848	−	0.00290176i
$349$		−	7.01947i		−	0.375743i	−0.982194	−	0.187872i	$-0.939841\pi$
$349$		−	7.01947i		−	0.375743i	0.982194	−	0.187872i	$-0.0601589\pi$
$350$	−0.398023	−	0.643328i	−0.0212752	−	0.0343873i
$351$	−0.110315	−	0.191071i	−0.00588817	−	0.0101986i
$352$	1.69902	+	11.0721i	0.0905583	+	0.590143i
$353$	13.7525			0.731969			0.365985	−	0.930621i	$-0.380732\pi$
$353$	13.7525			0.731969			0.365985	+	0.930621i	$0.380732\pi$
$354$	0.260237	+	0.420623i	0.0138314	+	0.0223559i
$355$	21.2323	−	12.2585i	1.12689	−	0.650612i
$356$	−6.40593	−	9.68210i	−0.339513	−	0.513150i
$357$	0.222860	−	0.128668i	0.0117950	−	0.00680984i
$358$	0.482119	+	15.8268i	0.0254808	+	0.836472i
$359$	1.49285	−	2.58569i	0.0787895	−	0.136467i	−0.823938	−	0.566679i	$-0.808228\pi$
$359$	1.49285	−	2.58569i	0.0787895	−	0.136467i	0.902728	+	0.430212i	$0.141561\pi$
$360$	−1.74740	−	19.0737i	−0.0920961	−	1.00527i
$361$	−16.4016	+	9.59102i	−0.863242	+	0.504790i
$362$	14.2127	−	8.79329i	0.747002	−	0.462165i
$363$	−0.451850	−	0.260876i	−0.0237160	−	0.0136924i
$364$	3.91680	−	2.59145i	0.205296	−	0.135829i
$365$	−24.4242	+	14.1013i	−1.27842	+	0.738096i
$366$	−0.181920	+	0.00554168i	−0.00950911	+	0.000289668i
$367$	−9.97261	−	17.2731i	−0.520566	−	0.901647i	−0.999714	−	0.0239129i	$-0.992388\pi$
$367$	−9.97261	−	17.2731i	−0.520566	−	0.901647i	0.479148	−	0.877734i	$-0.340946\pi$
$368$	7.68376	+	10.2044i	0.400543	+	0.531940i
$369$	−16.5915			−0.863719
$370$	−15.6192	+	29.0625i	−0.812005	+	1.51089i
$371$	−47.4421	+	27.3907i	−2.46307	+	1.42205i
$372$	0.717733	+	0.358011i	0.0372127	+	0.0185620i
$373$			16.8878i			0.874416i	0.899360	+	0.437208i	$0.144033\pi$
$373$			16.8878i			0.874416i	−0.899360	+	0.437208i	$0.855967\pi$
$374$	1.83141	+	0.984264i	0.0946998	+	0.0508951i
$375$	−0.407209	+	0.705306i	−0.0210282	+	0.0364219i
$376$	−2.55334	−	3.61498i	−0.131679	−	0.186428i
$377$	1.50628	−	2.60896i	0.0775775	−	0.134368i
$378$	−0.0894689	−	2.93705i	−0.00460179	−	0.151066i
$379$			26.5474i			1.36365i	0.731517	+	0.681824i	$0.238813\pi$
$379$			26.5474i			1.36365i	−0.731517	+	0.681824i	$0.761187\pi$
$380$	3.88032	−	19.3284i	0.199056	−	0.991527i
$381$			0.350990i			0.0179818i
$382$	17.8779	−	0.544599i	0.914711	−	0.0278641i
$383$	2.38085	−	4.12375i	0.121656	−	0.210714i	−0.798765	−	0.601643i	$-0.794513\pi$
$383$	2.38085	−	4.12375i	0.121656	−	0.210714i	0.920421	+	0.390929i	$0.127846\pi$
$384$	−0.794028	−	0.254725i	−0.0405201	−	0.0129989i
$385$	10.5290	−	18.2367i	0.536605	−	0.929428i
$386$	−4.91775	+	9.15040i	−0.250307	+	0.465743i
$387$		−	22.6856i		−	1.15317i
$388$	−1.08087	+	2.16691i	−0.0548728	+	0.110008i
$389$	17.0129	−	9.82241i	0.862589	−	0.498016i	−0.00228917	−	0.999997i	$-0.500729\pi$
$389$	17.0129	−	9.82241i	0.862589	−	0.498016i	0.864879	+	0.501981i	$0.167395\pi$
$390$	0.103679	+	0.0557210i	0.00525000	+	0.00282154i
$391$	2.37094			0.119904
$392$	42.5719	−	3.90015i	2.15020	−	0.196987i
$393$	−0.183740	−	0.318247i	−0.00926845	−	0.0160534i
$394$	0.521029	+	17.1041i	0.0262490	+	0.861693i
$395$	3.26995	−	1.88791i	0.164529	−	0.0949909i
$396$	9.89077	−	6.54398i	0.497030	−	0.328848i
$397$	22.1285	+	12.7759i	1.11060	+	0.641203i	0.938984	−	0.343962i	$-0.111769\pi$
$397$	22.1285	+	12.7759i	1.11060	+	0.641203i	0.171612	+	0.985165i	$0.445102\pi$
$398$	−5.55909	−	8.98521i	−0.278652	−	0.450388i
$399$	0.386988	−	1.46043i	0.0193736	−	0.0731130i
$400$	0.273697	+	0.363482i	0.0136849	+	0.0181741i
$401$	4.14055	−	7.17165i	0.206769	−	0.358135i	−0.743926	−	0.668262i	$-0.767038\pi$
$401$	4.14055	−	7.17165i	0.206769	−	0.358135i	0.950695	+	0.310127i	$0.100372\pi$
$402$	−1.13418	+	0.0345495i	−0.0565676	+	0.00172317i
$403$	2.35296	−	1.35848i	0.117209	−	0.0676708i
$404$	−24.9135	+	16.4834i	−1.23949	+	0.820081i
$405$	−17.5299	+	10.1209i	−0.871066	+	0.502910i
$406$	34.1199	−	21.1098i	1.69334	−	1.04766i
$407$	−20.4293			−1.01265
$408$	−0.126422	+	0.0892948i	−0.00625883	+	0.00442075i
$409$	−8.00331	−	13.8621i	−0.395738	−	0.685439i	0.597457	−	0.801901i	$-0.296178\pi$
$409$	−8.00331	−	13.8621i	−0.395738	−	0.685439i	−0.993195	+	0.116462i	$0.962845\pi$
$410$	15.0681	−	9.32255i	0.744162	−	0.460408i
$411$			0.589657i			0.0290856i
$412$	23.1991	−	1.41470i	1.14294	−	0.0696974i
$413$	19.3251	+	11.1574i	0.950927	+	0.549018i
$414$	6.40230	−	11.9127i	0.314656	−	0.585476i
$415$	−17.6084	+	30.4987i	−0.864363	+	1.49712i
$416$	−2.20378	+	1.76708i	−0.108049	+	0.0866381i
$417$	0.587958			0.0287924
$418$	11.6793	−	3.54924i	0.571255	−	0.173599i
$419$		−	24.4736i		−	1.19562i	−0.801640	−	0.597808i	$-0.796039\pi$
$419$		−	24.4736i		−	1.19562i	0.801640	−	0.597808i	$-0.203961\pi$
$420$	0.864988	+	1.30737i	0.0422071	+	0.0637931i
$421$	10.0033	+	5.77541i	0.487532	+	0.281476i	0.723550	−	0.690272i	$-0.242509\pi$
$421$	10.0033	+	5.77541i	0.487532	+	0.281476i	−0.236018	+	0.971749i	$0.575843\pi$
$422$	7.25360	+	3.89835i	0.353100	+	0.189769i
$423$	−2.34288	+	4.05799i	−0.113915	+	0.197306i
$424$	26.9125	−	19.0089i	1.30699	−	0.923156i
$425$	0.0844535			0.00409659
$426$	−0.961028	+	0.594582i	−0.0465620	+	0.0288076i
$427$	−7.11106	+	4.10557i	−0.344128	+	0.198682i
$428$	−0.933234	−	15.3037i	−0.0451096	−	0.739732i
$429$			0.0728809i			0.00351872i
$430$	12.7468	+	20.6027i	0.614703	+	0.993550i
$431$	6.07769	+	10.5269i	0.292752	+	0.507061i	0.974459	−	0.224564i	$-0.0720956\pi$
$431$	6.07769	+	10.5269i	0.292752	+	0.507061i	−0.681707	+	0.731625i	$0.738762\pi$
$432$	0.214749	+	1.75424i	0.0103321	+	0.0844010i
$433$	19.2219	+	33.2932i	0.923744	+	1.59997i	0.793570	+	0.608480i	$0.208220\pi$
$433$	19.2219	+	33.2932i	0.923744	+	1.59997i	0.130174	+	0.991491i	$0.458446\pi$
$434$	36.1685	−	1.10177i	1.73615	−	0.0528868i
$435$	0.870831	+	0.502775i	0.0417532	+	0.0241062i
$436$	−4.72227	−	2.35551i	−0.226156	−	0.112808i
$437$	9.81555	−	9.87008i	0.469541	−	0.472150i
$438$	1.10550	−	0.683967i	0.0528229	−	0.0326812i
$439$	9.70327	−	16.8066i	0.463112	−	0.802133i	−0.536002	−	0.844217i	$-0.680066\pi$
$439$	9.70327	−	16.8066i	0.463112	−	0.802133i	0.999114	+	0.0420834i	$0.0133995\pi$
$440$	−5.30565	+	11.5006i	−0.252937	+	0.548272i
$441$	−22.6306	−	39.1974i	−1.07765	−	1.86654i
$442$	0.0159640	+	0.524058i	0.000759328	+	0.0249269i
$443$	16.3666	−	9.44924i	0.777599	−	0.448947i	−0.0579798	−	0.998318i	$-0.518466\pi$
$443$	16.3666	−	9.44924i	0.777599	−	0.448947i	0.835579	+	0.549371i	$0.185133\pi$
$444$	0.678834	−	1.36091i	0.0322161	−	0.0645861i
$445$		−	13.1266i		−	0.622259i
$446$	−4.74176	+	8.82293i	−0.224529	+	0.417778i
$447$	0.194749	+	0.337315i	0.00921132	+	0.0159545i
$448$	−36.9946	+	6.83576i	−1.74783	+	0.322959i
$449$	−25.1997			−1.18925			−0.594624	−	0.804004i	$-0.702699\pi$
$449$	−25.1997			−1.18925			−0.594624	+	0.804004i	$0.702699\pi$
$450$	0.228051	−	0.424332i	0.0107504	−	0.0200032i
$451$	9.50144	+	5.48566i	0.447405	+	0.258310i
$452$	−17.8521	+	1.08864i	−0.839693	+	0.0512053i
$453$	0.232088	+	0.133996i	0.0109045	+	0.00629570i
$454$	0.467227	+	15.3379i	0.0219281	+	0.719845i
$455$	5.31022			0.248947
$456$	−0.151651	+	0.895963i	−0.00710169	+	0.0419573i
$457$	6.45543			0.301972			0.150986	−	0.988536i	$-0.451755\pi$
$457$	6.45543			0.301972			0.150986	+	0.988536i	$0.451755\pi$
$458$	−0.246114	−	8.07932i	−0.0115001	−	0.377522i
$459$	0.284087	+	0.164018i	0.0132601	+	0.00765570i
$460$	0.879118	+	14.4163i	0.0409891	+	0.672162i
$461$	2.49112	+	1.43825i	0.116023	+	0.0669858i	0.556888	−	0.830587i	$-0.311995\pi$
$461$	2.49112	+	1.43825i	0.116023	+	0.0669858i	−0.440866	+	0.897573i	$0.645328\pi$
$462$	−0.459505	+	0.854994i	−0.0213781	+	0.0397779i
$463$	−29.6723			−1.37899			−0.689494	−	0.724292i	$-0.742167\pi$
$463$	−29.6723			−1.37899			−0.689494	+	0.724292i	$0.742167\pi$
$464$	−19.2779	+	14.5160i	−0.894952	+	0.673887i
$465$	0.453441	+	0.785383i	0.0210278	+	0.0364213i
$466$	15.6273	−	29.0775i	0.723921	−	1.34699i
$467$			12.3400i			0.571026i	0.958375	+	0.285513i	$0.0921639\pi$
$467$			12.3400i			0.571026i	−0.958375	+	0.285513i	$0.907836\pi$
$468$	2.67621	+	1.33492i	0.123708	+	0.0617065i
$469$	−44.3337	+	25.5961i	−2.04714	+	1.18192i
$470$	−0.152367	−	5.00184i	−0.00702816	−	0.230718i
$471$	0.704188	+	1.21969i	0.0324473	+	0.0562003i
$472$	−12.1870	−	5.62231i	−0.560954	−	0.258788i
$473$	−7.50055	+	12.9913i	−0.344876	+	0.597342i
$474$	−0.148006	+	0.0915707i	−0.00679816	+	0.00420598i
$475$	0.349632	−	0.351575i	0.0160422	−	0.0161314i
$476$	−3.11684	+	6.24858i	−0.142860	+	0.286403i
$477$	−30.2106	−	17.4421i	−1.38325	−	0.798619i
$478$	−14.7741	+	0.450050i	−0.675750	+	0.0205848i
$479$	−3.99982	−	6.92789i	−0.182756	−	0.316543i	0.760062	−	0.649851i	$-0.225169\pi$
$479$	−3.99982	−	6.92789i	−0.182756	−	0.316543i	−0.942818	+	0.333307i	$0.891835\pi$
$480$	−0.589824	−	0.735588i	−0.0269217	−	0.0335748i
$481$	−2.57586	−	4.46151i	−0.117449	−	0.203428i
$482$	−15.3897	−	24.8746i	−0.700983	−	1.13301i
$483$			1.10688i			0.0503646i
$484$	14.1314	−	0.861748i	0.642338	−	0.0391704i
$485$	−2.37115	+	1.36898i	−0.107668	+	0.0621623i
$486$	2.38756	−	1.47717i	0.108302	−	0.0670057i
$487$	11.3433			0.514013			0.257007	−	0.966410i	$-0.417264\pi$
$487$	11.3433			0.514013			0.257007	+	0.966410i	$0.417264\pi$
$488$	4.03390	−	2.84924i	0.182606	−	0.128979i
$489$	0.358666	−	0.621228i	0.0162194	−	0.0280929i
$490$	42.5773	+	22.8826i	1.92345	+	1.03373i
$491$	−20.0056	−	11.5502i	−0.902840	−	0.521255i	−0.0247197	−	0.999694i	$-0.507869\pi$
$491$	−20.0056	−	11.5502i	−0.902840	−	0.521255i	−0.878121	+	0.478439i	$0.841203\pi$
$492$	−0.681148	+	0.450665i	−0.0307085	+	0.0203175i
$493$			4.47913i			0.201730i
$494$	2.24771	+	2.10311i	0.101129	+	0.0946235i
$495$	13.4095			0.602710
$496$	−21.6028	+	2.64455i	−0.969993	+	0.118744i
$497$	−25.4920	+	44.1535i	−1.14347	+	1.98055i
$498$	0.768466	−	1.42987i	0.0344358	−	0.0640742i
$499$	17.4946	+	10.1005i	0.783166	+	0.452161i	0.837551	−	0.546359i	$-0.183986\pi$
$499$	17.4946	+	10.1005i	0.783166	+	0.452161i	−0.0543850	+	0.998520i	$0.517320\pi$
$500$	−1.34513	−	22.0582i	−0.0601559	−	0.986471i
$501$			1.38594i			0.0619191i
$502$	−0.204643	+	0.126611i	−0.00913367	+	0.00565094i
$503$	−2.59755	−	4.49909i	−0.115819	−	0.200604i	0.802288	−	0.596937i	$-0.203616\pi$
$503$	−2.59755	−	4.49909i	−0.115819	−	0.200604i	−0.918107	+	0.396333i	$0.870283\pi$
$504$	22.9792	+	32.5336i	1.02358	+	1.44916i
$505$	−33.7767			−1.50304
$506$	−7.60510	+	4.70522i	−0.338088	+	0.209173i
$507$	0.813888	−	0.469898i	0.0361460	−	0.0208689i
$508$	−5.25526	−	7.94295i	−0.233164	−	0.352411i
$509$	26.5099	−	15.3055i	1.17503	−	0.678404i	0.220171	−	0.975461i	$-0.429338\pi$
$509$	26.5099	−	15.3055i	1.17503	−	0.678404i	0.954860	+	0.297057i	$0.0960051\pi$
$510$	−0.174923	+	0.00532853i	−0.00774571	+	0.000235951i
$511$	29.3243	−	50.7912i	1.29723	−	2.24687i
$512$	21.7829	−	6.12426i	0.962676	−	0.270656i
$513$	1.85890	−	0.503614i	0.0820724	−	0.0222351i
$514$	10.8193	+	17.4873i	0.477218	+	0.771332i
$515$	22.7587	+	13.1397i	1.00287	+	0.579006i
$516$	−0.616195	−	0.931336i	−0.0271265	−	0.0409998i
$517$	2.68339	−	1.54926i	0.118015	−	0.0681363i
$518$	−2.08910	−	68.5802i	−0.0917899	−	3.01324i
$519$	0.432864	+	0.749742i	0.0190006	+	0.0329100i
$520$	−3.18057	+	0.291382i	−0.139477	+	0.0127780i
$521$	−24.6215			−1.07869			−0.539343	−	0.842086i	$-0.681327\pi$
$521$	−24.6215			−1.07869			−0.539343	+	0.842086i	$0.681327\pi$
$522$	22.5051	+	12.0951i	0.985023	+	0.529387i
$523$	28.6708	−	16.5531i	1.25369	−	0.723816i	0.281847	−	0.959459i	$-0.409053\pi$
$523$	28.6708	−	16.5531i	1.25369	−	0.723816i	0.971840	+	0.235643i	$0.0757196\pi$
$524$	8.92305	+	4.45089i	0.389805	+	0.194438i
$525$			0.0394272i			0.00172074i
$526$	−10.0964	+	18.7862i	−0.440222	+	0.819116i
$527$	−2.01981	+	3.49842i	−0.0879844	+	0.152393i
$528$	0.228306	−	0.537314i	0.00993574	−	0.0233836i
$529$	6.40096	−	11.0868i	0.278303	−	0.482034i
$530$	37.2373	−	1.13433i	1.61749	−	0.0492721i
$531$			14.2098i			0.616652i
$532$	13.1089	+	38.8440i	0.568345	+	1.68410i
$533$			2.76666i			0.119837i
$534$	0.0184229	+	0.604779i	0.000797236	+	0.0261713i
$535$	8.66787	−	15.0132i	0.374745	−	0.649077i
$536$	25.1493	−	17.7635i	1.08628	−	0.767266i
$537$	0.412621	−	0.714680i	0.0178059	−	0.0308407i
$538$	−9.12529	−	4.90426i	−0.393419	−	0.211438i
$539$			29.9295i			1.28916i
$540$	−0.891958	+	1.78818i	−0.0383838	+	0.0769510i
$541$	15.7964	−	9.12004i	0.679139	−	0.392101i	−0.120391	−	0.992727i	$-0.538415\pi$
$541$	15.7964	−	9.12004i	0.679139	−	0.392101i	0.799531	+	0.600625i	$0.205082\pi$
$542$	−5.52130	+	10.2734i	−0.237160	+	0.441280i
$543$	−0.871043			−0.0373800
$544$	1.52397	−	3.91363i	0.0653395	−	0.167795i
$545$	−2.98338	−	5.16737i	−0.127794	−	0.221346i
$546$	−0.244657	+	0.00745279i	−0.0104704	+	0.000318950i
$547$	−18.9714	+	10.9532i	−0.811160	+	0.468323i	−0.847358	−	0.531021i	$-0.821808\pi$
$547$	−18.9714	+	10.9532i	−0.811160	+	0.468323i	0.0361988	+	0.999345i	$0.488475\pi$
$548$	−8.82874	−	13.3440i	−0.377145	−	0.570028i
$549$	−4.52825	−	2.61438i	−0.193261	−	0.111579i
$550$	−0.270895	+	0.167601i	−0.0115510	+	0.00714654i
$551$	18.6463	+	18.5433i	0.794360	+	0.789971i
$552$	−0.0607365	−	0.662966i	−0.00258512	−	0.0282177i
$553$	−3.92599	+	6.80001i	−0.166950	+	0.289166i
$554$	0.744821	+	24.4507i	0.0316444	+	1.03881i
$555$	1.48919	−	0.859782i	0.0632125	−	0.0364957i
$556$	−13.3056	+	8.80330i	−0.564282	+	0.373343i
$557$	−24.5414	+	14.1690i	−1.03985	+	0.600359i	−0.919791	−	0.392408i	$-0.871642\pi$
$557$	−24.5414	+	14.1690i	−1.03985	+	0.600359i	−0.120061	+	0.992767i	$0.538309\pi$
$558$	12.1235	+	19.5953i	0.513228	+	0.829535i
$559$	−3.78286			−0.159998
$560$	−39.1496	−	16.6347i	−1.65437	−	0.702946i
$561$	−0.0541802	−	0.0938428i	−0.00228749	−	0.00396205i
$562$	−18.6173	−	30.0914i	−0.785325	−	1.26933i
$563$			5.98383i			0.252188i	0.992018	+	0.126094i	$0.0402442\pi$
$563$			5.98383i			0.252188i	−0.992018	+	0.126094i	$0.959756\pi$
$564$	0.0140400	+	0.230235i	0.000591189	+	0.00969465i
$565$	−17.5132	−	10.1113i	−0.736787	−	0.425384i
$566$	−23.1086	−	12.4194i	−0.971329	−	0.522027i
$567$	21.0468	−	36.4541i	0.883883	−	1.53093i
$568$	12.8457	−	27.8446i	0.538994	−	1.16833i
$569$	26.0900			1.09375			0.546875	−	0.837214i	$-0.315817\pi$
$569$	26.0900			1.09375			0.546875	+	0.837214i	$0.315817\pi$
$570$	−0.701988	+	0.750253i	−0.0294030	+	0.0314246i
$571$			17.5053i			0.732573i	0.930502	+	0.366287i	$0.119371\pi$
$571$			17.5053i			0.732573i	−0.930502	+	0.366287i	$0.880629\pi$
$572$	−1.09122	−	1.64930i	−0.0456262	−	0.0689608i
$573$	−0.807299	−	0.466094i	−0.0337254	−	0.0194714i
$574$	−17.4434	+	32.4568i	−0.728075	+	1.35472i
$575$	−0.181629	+	0.314591i	−0.00757445	+	0.0131193i
$576$	−15.5486	−	18.2251i	−0.647860	−	0.759381i
$577$	−4.31463			−0.179621			−0.0898103	−	0.995959i	$-0.528626\pi$
$577$	−4.31463			−0.179621			−0.0898103	+	0.995959i	$0.528626\pi$
$578$	12.2390	+	19.7821i	0.509077	+	0.822826i
$579$	0.468874	−	0.270705i	0.0194858	−	0.0112501i
$580$	−27.2349	+	1.66081i	−1.13087	+	0.0689614i
$581$		−	73.2350i		−	3.03830i
$582$	0.107324	−	0.0664008i	0.00444873	−	0.00275240i
$583$	11.5338	+	19.9771i	0.477681	+	0.827368i
$584$	−14.7768	+	32.0306i	−0.611470	+	1.32543i
$585$	1.69075	+	2.92846i	0.0699037	+	0.121077i
$586$	−0.0440425	−	1.44581i	−0.00181938	−	0.0597258i
$587$	−22.3055	−	12.8781i	−0.920645	−	0.531535i	−0.0368044	−	0.999322i	$-0.511718\pi$
$587$	−22.3055	−	12.8781i	−0.920645	−	0.531535i	−0.883841	+	0.467788i	$0.845051\pi$
$588$	−1.99378	−	0.994510i	−0.0822219	−	0.0410129i
$589$	6.20180	+	22.8916i	0.255541	+	0.943231i
$590$	−7.98430	−	12.9051i	−0.328708	−	0.531294i
$591$	0.445922	−	0.772359i	0.0183428	−	0.0317706i
$592$	5.01440	+	40.9616i	0.206091	+	1.68351i
$593$	18.0229	+	31.2166i	0.740112	+	1.28191i	0.952444	+	0.304714i	$0.0985610\pi$
$593$	18.0229	+	31.2166i	0.740112	+	1.28191i	−0.212331	+	0.977198i	$0.568106\pi$
$594$	−1.23675	+	0.0376740i	−0.0507443	+	0.00154578i
$595$	−6.83754	+	3.94766i	−0.280312	+	0.161838i
$596$	−9.45771	−	4.71758i	−0.387403	−	0.193239i
$597$			0.550671i			0.0225374i
$598$	−1.98646	−	1.06759i	−0.0812324	−	0.0436572i
$599$	−6.14336	−	10.6406i	−0.251011	−	0.434763i	0.712794	−	0.701374i	$-0.247430\pi$
$599$	−6.14336	−	10.6406i	−0.251011	−	0.434763i	−0.963804	+	0.266610i	$0.914096\pi$
$600$	−0.00216345	−	0.0236150i	−8.83224e−5	−	0.000964078i
$601$	−9.74846			−0.397648			−0.198824	−	0.980035i	$-0.563712\pi$
$601$	−9.74846			−0.397648			−0.198824	+	0.980035i	$0.563712\pi$
$602$	−44.3782	−	23.8505i	−1.80872	−	0.972072i
$603$	−28.2312	−	16.2993i	−1.14967	−	0.663760i
$604$	−7.25847	+	0.442628i	−0.295343	+	0.0180103i
$605$	13.8632	+	8.00390i	0.563618	+	0.325405i
$606$	1.55619	−	0.0474049i	0.0632158	−	0.00192569i
$607$	28.3299			1.14988			0.574938	−	0.818197i	$-0.305026\pi$
$607$	28.3299			1.14988			0.574938	+	0.818197i	$0.305026\pi$
$608$	−9.98307	−	22.5464i	−0.404867	−	0.914376i
$609$	−2.09108			−0.0847350
$610$	5.58147	−	0.170024i	0.225987	−	0.00688406i
$611$	0.676677	+	0.390680i	0.0273754	+	0.0158052i
$612$	−4.43833	+	0.270654i	−0.179409	+	0.0109405i
$613$	−17.4855	−	10.0952i	−0.706232	−	0.407743i	0.103433	−	0.994636i	$-0.467017\pi$
$613$	−17.4855	−	10.0952i	−0.706232	−	0.407743i	−0.809664	+	0.586893i	$0.800351\pi$
$614$	−32.7275	−	17.5889i	−1.32077	−	0.709832i
$615$	−0.923470			−0.0372379
$616$	−2.40289	−	26.2286i	−0.0968153	−	1.05678i
$617$	6.87561	+	11.9089i	0.276801	+	0.479434i	0.970588	−	0.240746i	$-0.0773922\pi$
$617$	6.87561	+	11.9089i	0.276801	+	0.479434i	−0.693787	+	0.720181i	$0.744059\pi$
$618$	−1.06700	−	0.573445i	−0.0429211	−	0.0230673i
$619$			4.39271i			0.176558i	0.996096	+	0.0882791i	$0.0281367\pi$
$619$			4.39271i			0.176558i	−0.996096	+	0.0882791i	$0.971863\pi$
$620$	−22.0207	−	10.9841i	−0.884373	−	0.441132i
$621$	−1.22194	+	0.705487i	−0.0490347	+	0.0283102i
$622$	34.2120	−	1.04217i	1.37178	−	0.0417873i
$623$	13.6486	+	23.6401i	0.546821	+	0.947122i
$624$	0.146129	−	0.0178887i	0.00584984	−	0.000716120i
$625$	12.7779	−	22.1320i	0.511116	−	0.885279i
$626$	21.3590	+	34.5228i	0.853678	+	1.37981i
$627$	−0.614965	−	0.162955i	−0.0245593	−	0.00650779i
$628$	−34.1979	−	17.0582i	−1.36464	−	0.680695i
$629$	6.63345	+	3.82982i	0.264493	+	0.152705i
$630$	1.37125	+	45.0148i	0.0546319	+	1.79343i
$631$	13.8673	+	24.0188i	0.552047	+	0.956173i	0.998127	+	0.0611800i	$0.0194864\pi$
$631$	13.8673	+	24.0188i	0.552047	+	0.956173i	−0.446080	+	0.894993i	$0.647180\pi$
$632$	1.97835	−	4.28831i	0.0786945	−	0.170580i
$633$	−0.214590	−	0.371681i	−0.00852919	−	0.0147730i
$634$	−12.3255	+	7.62568i	−0.489506	+	0.302854i
$635$		−	10.7687i		−	0.427343i
$636$	−1.71404	+	0.104524i	−0.0679660	+	0.00414463i
$637$	−6.53623	+	3.77370i	−0.258975	+	0.149519i
$638$	−8.88900	−	14.3674i	−0.351919	−	0.568810i
$639$	−32.4661			−1.28434
$640$	24.3615	+	7.81520i	0.962973	+	0.308923i
$641$	2.60078	−	4.50468i	0.102725	−	0.177924i	−0.810082	−	0.586317i	$-0.800577\pi$
$641$	2.60078	−	4.50468i	0.102725	−	0.177924i	0.912806	+	0.408393i	$0.133911\pi$
$642$	−0.378283	+	0.703866i	−0.0149296	+	0.0277794i
$643$	9.12347	+	5.26744i	0.359794	+	0.207727i	0.668991	−	0.743271i	$-0.266727\pi$
$643$	9.12347	+	5.26744i	0.359794	+	0.207727i	−0.309196	+	0.950998i	$0.600060\pi$
$644$	−16.5729	−	25.0487i	−0.653063	−	0.987059i
$645$		−	1.26266i		−	0.0497173i
$646$	−4.45767	−	1.03704i	−0.175385	−	0.0408019i
$647$	−29.5690			−1.16248			−0.581239	−	0.813733i	$-0.697432\pi$
$647$	−29.5690			−1.16248			−0.581239	+	0.813733i	$0.697432\pi$
$648$	−10.6057	+	22.9892i	−0.416632	+	0.903100i
$649$	4.69819	−	8.13750i	0.184420	−	0.319425i
$650$	−0.0707581	−	0.0380280i	−0.00277536	−	0.00149158i
$651$	−1.63324	−	0.942951i	−0.0640117	−	0.0369572i
$652$	1.18478	+	19.4286i	0.0463995	+	0.760885i
$653$		−	5.92429i		−	0.231835i	−0.993259	−	0.115918i	$-0.963019\pi$
$653$		−	5.92429i		−	0.231835i	0.993259	−	0.115918i	$-0.0369809\pi$
$654$	0.144705	+	0.233889i	0.00565843	+	0.00914577i
$655$	5.63730	+	9.76410i	0.220268	+	0.381515i
$656$	8.66681	−	20.3972i	0.338382	−	0.796377i
$657$	37.3468			1.45704
$658$	5.47518	+	8.84958i	0.213445	+	0.344992i
$659$	13.1894	−	7.61488i	0.513785	−	0.296634i	−0.220603	−	0.975364i	$-0.570803\pi$
$659$	13.1894	−	7.61488i	0.513785	−	0.296634i	0.734388	+	0.678730i	$0.237469\pi$
$660$	0.550513	−	0.364233i	0.0214287	−	0.0141778i
$661$	7.12782	−	4.11525i	0.277240	−	0.160065i	−0.354933	−	0.934892i	$-0.615496\pi$
$661$	7.12782	−	4.11525i	0.277240	−	0.160065i	0.632173	+	0.774827i	$0.282163\pi$
$662$	−0.718799	−	23.5965i	−0.0279369	−	0.917102i
$663$	0.0136627	−	0.0236645i	0.000530617	−	0.000919055i
$664$	4.01855	+	43.8642i	0.155950	+	1.70226i
$665$	−11.8731	+	44.8073i	−0.460421	+	1.73755i
$666$	37.1552	−	22.9877i	1.43973	−	0.890754i
$667$	−16.6848	−	9.63299i	−0.646039	−	0.372991i
$668$	−20.7512	−	31.3639i	−0.802887	−	1.21351i
$669$	0.452094	−	0.261017i	0.0174790	−	0.0100915i
$670$	34.7976	−	1.06001i	1.34435	−	0.0409517i
$671$	1.72879	+	2.99435i	0.0667393	+	0.115596i
$672$	1.82708	+	0.711465i	0.0704812	+	0.0274454i
$673$	−5.85922			−0.225856			−0.112928	−	0.993603i	$-0.536023\pi$
$673$	−5.85922			−0.225856			−0.112928	+	0.993603i	$0.536023\pi$
$674$	18.9168	−	35.1982i	0.728648	−	1.35578i
$675$	−0.0435257	+	0.0251296i	−0.00167531	+	0.000967239i
$676$	−11.3828	+	22.8199i	−0.437798	+	0.877690i
$677$		−	2.54790i		−	0.0979236i	−0.998801	−	0.0489618i	$-0.984409\pi$
$677$		−	2.54790i		−	0.0979236i	0.998801	−	0.0489618i	$-0.0155913\pi$
$678$	0.821076	+	0.441276i	0.0315332	+	0.0169471i
$679$	2.84686	−	4.93091i	0.109252	−	0.189231i
$680$	3.87874	−	2.73965i	0.148743	−	0.105061i
$681$	0.399876	−	0.692605i	0.0153233	−	0.0265407i
$682$	−0.463939	−	15.2300i	−0.0177652	−	0.583187i
$683$		−	24.9303i		−	0.953930i	−0.878922	−	0.476965i	$-0.841737\pi$
$683$		−	24.9303i		−	0.953930i	0.878922	−	0.476965i	$-0.158263\pi$
$684$	−17.2477	+	19.5970i	−0.659482	+	0.749310i
$685$		−	18.0912i		−	0.691230i
$686$	−53.9400	+	1.64313i	−2.05944	+	0.0627350i
$687$	−0.210636	+	0.364832i	−0.00803627	+	0.0139192i
$688$	27.8892	+	11.8502i	1.06326	+	0.451783i
$689$	−2.90850	+	5.03767i	−0.110805	+	0.191920i
$690$	0.356347	−	0.663051i	0.0135659	−	0.0252419i
$691$			51.3756i			1.95442i	0.212277	+	0.977209i	$0.431912\pi$
$691$			51.3756i			1.95442i	−0.212277	+	0.977209i	$0.568088\pi$
$692$	−21.0214	−	10.4856i	−0.799114	−	0.398604i
$693$	−24.1496	+	13.9428i	−0.917368	+	0.529643i
$694$	32.6224	+	17.5324i	1.23833	+	0.665522i
$695$	−18.0391			−0.684262
$696$	1.25246	−	0.114742i	0.0474743	−	0.00434928i
$697$	−2.05676	−	3.56241i	−0.0779052	−	0.134936i
$698$	−0.302259	−	9.92242i	−0.0114407	−	0.375569i
$699$	−1.48996	+	0.860227i	−0.0563553	+	0.0325368i
$700$	−0.590330	−	0.892242i	−0.0223124	−	0.0337236i
$701$	10.9994	+	6.35049i	0.415441	+	0.239855i	0.693125	−	0.720818i	$-0.256234\pi$
$701$	10.9994	+	6.35049i	0.415441	+	0.239855i	−0.277684	+	0.960672i	$0.589567\pi$
$702$	−0.164164	−	0.265340i	−0.00619597	−	0.0100146i
$703$	43.4054	−	11.7594i	1.63706	−	0.443514i
$704$	2.87843	+	15.5778i	0.108485	+	0.587112i
$705$	−0.130403	+	0.225865i	−0.00491126	+	0.00850656i
$706$	19.4399	−	0.592181i	0.731630	−	0.0222870i
$707$	60.8297	−	35.1200i	2.28774	−	1.32082i
$708$	0.385972	+	0.583369i	0.0145057	+	0.0219244i
$709$	10.6515	−	6.14967i	0.400027	−	0.230956i	−0.286469	−	0.958090i	$-0.592481\pi$
$709$	10.6515	−	6.14967i	0.400027	−	0.230956i	0.686496	+	0.727134i	$0.259148\pi$
$710$	29.4852	−	18.2423i	1.10656	−	0.684622i
$711$	−5.00006			−0.187517
$712$	−9.47206	−	13.4104i	−0.354980	−	0.502575i
$713$	−8.68778	−	15.0477i	−0.325360	−	0.563540i
$714$	0.309485	−	0.191476i	0.0115822	−	0.00716582i
$715$		−	2.23605i		−	0.0836235i
$716$	1.36301	+	22.3513i	0.0509379	+	0.835309i
$717$	0.667142	+	0.385175i	0.0249149	+	0.0143846i
$718$	1.99889	−	3.71930i	0.0745978	−	0.138803i
$719$	17.5424	−	30.3843i	0.654222	−	1.13314i	−0.327867	−	0.944724i	$-0.606330\pi$
$719$	17.5424	−	30.3843i	0.654222	−	1.13314i	0.982088	−	0.188421i	$-0.0603369\pi$
$720$	−3.29137	−	26.8865i	−0.122662	−	1.00200i
$721$	−54.6494			−2.03525
$722$	−22.7716	+	14.2637i	−0.847472	+	0.530840i
$723$			1.52447i			0.0566957i
$724$	19.7118	−	13.0418i	0.732584	−	0.484696i
$725$	−0.594317	−	0.343129i	−0.0220724	−	0.0127435i
$726$	−0.649950	−	0.349306i	−0.0241219	−	0.0129640i
$727$	−12.3695	+	21.4246i	−0.458759	+	0.794593i	−0.998896	−	0.0469839i	$-0.985039\pi$
$727$	−12.3695	+	21.4246i	−0.458759	+	0.794593i	0.540137	+	0.841577i	$0.318372\pi$
$728$	5.42503	−	3.83183i	0.201065	−	0.142017i
$729$	26.7071			0.989151
$730$	−33.9178	+	20.9847i	−1.25535	+	0.776679i
$731$	4.87089	−	2.81221i	0.180156	−	0.104013i
$732$	−0.256916	+	0.0156670i	−0.00949588	+	0.000579068i
$733$		−	20.0808i		−	0.741701i	−0.928693	−	0.370851i	$-0.879066\pi$
$733$		−	20.0808i		−	0.741701i	0.928693	−	0.370851i	$-0.120934\pi$
$734$	−14.8406	−	23.9871i	−0.547778	−	0.885379i
$735$	−1.25960	−	2.18170i	−0.0464612	−	0.0804731i
$736$	11.3008	+	14.0936i	0.416554	+	0.519497i
$737$	10.7781	+	18.6682i	0.397017	+	0.687653i
$738$	−23.4530	+	0.714431i	−0.863318	+	0.0262986i
$739$	1.16064	+	0.670093i	0.0426947	+	0.0246498i	0.521195	−	0.853437i	$-0.325486\pi$
$739$	1.16064	+	0.670093i	0.0426947	+	0.0246498i	−0.478501	+	0.878087i	$0.658820\pi$
$740$	−20.8273	+	41.7541i	−0.765625	+	1.53491i
$741$	−0.0419512	−	0.154847i	−0.00154112	−	0.00568844i
$742$	−65.8827	+	40.7612i	−2.41863	+	1.49639i
$743$	5.99092	−	10.3766i	0.219786	−	0.380680i	−0.734957	−	0.678114i	$-0.762798\pi$
$743$	5.99092	−	10.3766i	0.219786	−	0.380680i	0.954742	+	0.297434i	$0.0961309\pi$
$744$	1.02997	+	0.475163i	0.0377607	+	0.0174203i
$745$	−5.97508	−	10.3491i	−0.218910	−	0.379163i
$746$	0.727188	+	23.8718i	0.0266243	+	0.874010i
$747$	40.3873	−	23.3176i	1.47770	−	0.853148i
$748$	2.63118	+	1.31245i	0.0962055	+	0.0479880i
$749$			36.0504i			1.31725i
$750$	−0.545243	+	1.01453i	−0.0199094	+	0.0370452i
$751$	9.58183	+	16.5962i	0.349646	+	0.605605i	0.986187	−	0.165639i	$-0.0529686\pi$
$751$	9.58183	+	16.5962i	0.349646	+	0.605605i	−0.636541	+	0.771243i	$0.719635\pi$
$752$	−3.76496	−	5.00004i	−0.137294	−	0.182333i
$753$	0.0125418			0.000457049
$754$	2.01687	−	3.75277i	0.0734503	−	0.136668i
$755$	−7.12068	−	4.11113i	−0.259148	−	0.149619i
$756$	−0.252939	−	4.14784i	−0.00919930	−	0.150855i
$757$	35.7919	+	20.6645i	1.30088	+	0.751062i	0.980555	−	0.196246i	$-0.0628750\pi$
$757$	35.7919	+	20.6645i	1.30088	+	0.751062i	0.320324	+	0.947308i	$0.396208\pi$
$758$	1.14313	+	37.5263i	0.0415204	+	1.36302i
$759$	0.466088			0.0169179
$760$	4.65278	−	27.4889i	0.168774	−	0.997129i
$761$	30.3361			1.09968			0.549841	−	0.835269i	$-0.314688\pi$
$761$	30.3361			1.09968			0.549841	+	0.835269i	$0.314688\pi$
$762$	0.0151137	+	0.496145i	0.000547510	+	0.0179734i
$763$	10.7458	+	6.20408i	0.389023	+	0.224603i
$764$	25.2479	−	1.53964i	0.913438	−	0.0557023i
$765$	−4.35408	−	2.51383i	−0.157422	−	0.0908876i
$766$	3.18789	−	5.93167i	0.115183	−	0.214320i
$767$	2.36951			0.0855579
$768$	−1.13337	−	0.325878i	−0.0408971	−	0.0117591i
$769$	7.68635	+	13.3131i	0.277177	+	0.480084i	0.970682	−	0.240367i	$-0.0772679\pi$
$769$	7.68635	+	13.3131i	0.277177	+	0.480084i	−0.693505	+	0.720452i	$0.743935\pi$
$770$	14.0980	−	26.2320i	0.508057	−	0.945335i
$771$		−	1.07173i		−	0.0385975i
$772$	−6.55751	+	13.1464i	−0.236010	+	0.473149i
$773$	14.3035	−	8.25814i	0.514462	−	0.297025i	−0.220204	−	0.975454i	$-0.570672\pi$
$773$	14.3035	−	8.25814i	0.514462	−	0.297025i	0.734666	+	0.678429i	$0.237339\pi$
$774$	−0.976843	−	32.0674i	−0.0351119	−	1.15264i
$775$	−0.309461	−	0.536001i	−0.0111162	−	0.0192537i
$776$	−1.43456	+	3.10959i	−0.0514978	+	0.111628i
$777$	−1.78796	+	3.09683i	−0.0641426	+	0.111098i
$778$	23.6258	−	14.6171i	0.847026	−	0.524049i
$779$	−23.3449	−	6.18599i	−0.836419	−	0.221636i
$780$	0.148956	+	0.0743004i	0.00533348	+	0.00266038i
$781$	18.5923	+	10.7343i	0.665286	+	0.384103i
$782$	3.35146	−	0.102093i	0.119848	−	0.00365083i
$783$	−1.33279	−	2.30846i	−0.0476300	−	0.0824976i
$784$	60.0098	−	7.34623i	2.14321	−	0.262365i
$785$	−21.6051	−	37.4212i	−0.771120	−	1.33562i
$786$	−0.273431	−	0.441948i	−0.00975295	−	0.0157638i
$787$			45.6546i			1.62741i	0.581277	+	0.813705i	$0.302553\pi$
$787$			45.6546i			1.62741i	−0.581277	+	0.813705i	$0.697447\pi$
$788$	1.47301	+	24.1552i	0.0524737	+	0.860494i
$789$	0.962620	−	0.555769i	0.0342702	−	0.0197859i
$790$	4.54097	−	2.80947i	0.161561	−	0.0999565i
$791$	42.0537			1.49526
$792$	13.6994	−	9.67620i	0.486787	−	0.343829i
$793$	−0.435953	+	0.755093i	−0.0154811	+	0.0268141i
$794$	31.8300	+	17.1066i	1.12960	+	0.607090i
$795$	−1.68150	−	0.970815i	−0.0596367	−	0.0344312i
$796$	−8.24501	−	12.4617i	−0.292236	−	0.441695i
$797$			21.7112i			0.769052i	0.923114	+	0.384526i	$0.125635\pi$
$797$			21.7112i			0.769052i	−0.923114	+	0.384526i	$0.874365\pi$
$798$	0.484144	−	2.08107i	0.0171385	−	0.0736690i
$799$	−1.16174			−0.0410993
$800$	0.402538	+	0.502018i	0.0142319	+	0.0177490i
$801$	−8.69131	+	15.0538i	−0.307092	+	0.531900i
$802$	5.54410	−	10.3158i	0.195769	−	0.364265i
$803$	−21.3874	−	12.3480i	−0.754744	−	0.435752i
$804$	−1.60174	+	0.0976754i	−0.0564889	+	0.00344475i
$805$		−	33.9600i		−	1.19693i
$806$	3.26755	−	2.02161i	0.115094	−	0.0712082i
$807$	0.269962	+	0.467588i	0.00950310	+	0.0164599i
$808$	−34.5070	+	24.3731i	−1.21395	+	0.857441i
$809$	4.74208			0.166723			0.0833613	−	0.996519i	$-0.473434\pi$
$809$	4.74208			0.166723			0.0833613	+	0.996519i	$0.473434\pi$
$810$	−24.3437	+	15.0613i	−0.855350	+	0.529199i
$811$	17.1243	−	9.88671i	0.601315	−	0.347169i	−0.168244	−	0.985745i	$-0.553810\pi$
$811$	17.1243	−	9.88671i	0.601315	−	0.347169i	0.769559	+	0.638576i	$0.220476\pi$
$812$	47.3215	−	31.3091i	1.66066	−	1.09873i
$813$	0.526418	−	0.303928i	0.0184623	−	0.0106592i
$814$	−28.8781	+	0.879689i	−1.01218	+	0.0308331i
$815$	−11.0042	+	19.0598i	−0.385460	+	0.667637i
$816$	−0.174860	+	0.131667i	−0.00612132	+	0.00460927i
$817$	8.45812	−	31.9196i	0.295912	−	1.11672i
$818$	−11.9100	−	19.2503i	−0.416425	−	0.673072i
$819$	−6.08986	−	3.51598i	−0.212797	−	0.122858i
$820$	20.8982	−	13.8268i	0.729798	−	0.482853i
$821$	−4.45174	+	2.57021i	−0.155367	+	0.0897011i	−0.575668	−	0.817684i	$-0.695258\pi$
$821$	−4.45174	+	2.57021i	−0.155367	+	0.0897011i	0.420301	+	0.907385i	$0.361925\pi$
$822$	0.0253907	+	0.833515i	0.000885601	+	0.0290722i
$823$	−11.4962	−	19.9120i	−0.400731	−	0.694087i	0.593083	−	0.805141i	$-0.297911\pi$
$823$	−11.4962	−	19.9120i	−0.400731	−	0.694087i	−0.993814	+	0.111054i	$0.964577\pi$
$824$	32.7323	−	2.99872i	1.14029	−	0.104465i
$825$	0.0166022			0.000578014
$826$	27.7976	+	14.9394i	0.967202	+	0.519809i
$827$	12.7107	−	7.33853i	0.441994	−	0.255186i	−0.262449	−	0.964946i	$-0.584530\pi$
$827$	12.7107	−	7.33853i	0.441994	−	0.255186i	0.704443	+	0.709760i	$0.251197\pi$
$828$	8.53706	−	17.1149i	0.296683	−	0.594785i
$829$			41.7030i			1.44840i	0.689588	+	0.724202i	$0.257792\pi$
$829$			41.7030i			1.44840i	−0.689588	+	0.724202i	$0.742208\pi$
$830$	−23.5772	+	43.8698i	−0.818378	+	1.52274i
$831$	0.637454	−	1.10410i	0.0221130	−	0.0383009i
$832$	−3.03907	+	2.59276i	−0.105361	+	0.0898878i
$833$	5.61079	−	9.71817i	0.194402	−	0.336715i
$834$	0.831113	−	0.0253175i	0.0287791	−	0.000876674i
$835$		−	42.5218i		−	1.47153i
$836$	16.3566	−	5.51997i	0.565705	−	0.190912i
$837$		−	2.40402i		−	0.0830952i
$838$	−1.05384	−	34.5949i	−0.0364042	−	1.19506i
$839$	−21.9878	+	38.0839i	−0.759102	+	1.31480i	0.184208	+	0.982887i	$0.441028\pi$
$839$	−21.9878	+	38.0839i	−0.759102	+	1.31480i	−0.943309	+	0.331915i	$0.892305\pi$
$840$	1.27901	+	1.81080i	0.0441299	+	0.0624784i
$841$	3.69842	−	6.40585i	0.127532	−	0.220891i
$842$	14.3889	+	7.73314i	0.495876	+	0.266502i
$843$			1.84419i			0.0635172i
$844$	10.4212	+	5.19820i	0.358714	+	0.178929i
$845$	−24.9708	+	14.4169i	−0.859022	+	0.495957i
$846$	−3.13706	+	5.83709i	−0.107854	+	0.200683i
$847$	−33.2890			−1.14382
$848$	37.2239	−	28.0291i	1.27827	−	0.962523i
$849$	0.683644	+	1.18411i	0.0234626	+	0.0406384i
$850$	0.119380	−	0.00363657i	0.00409469	−	0.000124733i
$851$	−28.5323	+	16.4731i	−0.978075	+	0.564692i
$852$	−1.33287	+	0.881858i	−0.0456632	+	0.0302119i
$853$	−35.8544	−	20.7005i	−1.22763	−	0.708773i	−0.261097	−	0.965313i	$-0.584084\pi$
$853$	−35.8544	−	20.7005i	−1.22763	−	0.708773i	−0.966534	+	0.256540i	$0.917417\pi$
$854$	−9.87510	+	6.10966i	−0.337919	+	0.209068i
$855$	−28.4905	+	7.71867i	−0.974355	+	0.263973i
$856$	−1.97816	−	21.5925i	−0.0676121	−	0.738016i
$857$	11.4143	−	19.7701i	0.389903	−	0.675333i	−0.602533	−	0.798094i	$-0.705842\pi$
$857$	11.4143	−	19.7701i	0.389903	−	0.675333i	0.992436	+	0.122762i	$0.0391750\pi$
$858$	0.00313825	+	0.103021i	0.000107138	+	0.00351709i
$859$	−41.9571	+	24.2239i	−1.43156	+	0.826509i	−0.997240	−	0.0742508i	$-0.976343\pi$
$859$	−41.9571	+	24.2239i	−1.43156	+	0.826509i	−0.434317	+	0.900760i	$0.643010\pi$
$860$	18.9054	+	28.5742i	0.644670	+	0.974373i
$861$	1.66311	−	0.960199i	0.0566787	−	0.0327235i
$862$	9.04445	+	14.6186i	0.308055	+	0.497912i
$863$	−54.0511			−1.83992			−0.919960	−	0.392013i	$-0.871779\pi$
$863$	−54.0511			−1.83992			−0.919960	+	0.392013i	$0.871779\pi$
$864$	0.379098	+	2.47048i	0.0128972	+	0.0840473i
$865$	−13.2807	−	23.0028i	−0.451556	−	0.782118i
$866$	28.6048	+	46.2342i	0.972031	+	1.57110i
$867$		−	1.21237i		−	0.0411743i
$868$	51.0789	−	3.11484i	1.73373	−	0.105725i
$869$	2.86338	+	1.65317i	0.0971335	+	0.0560800i
$870$	1.25262	+	0.673203i	0.0424678	+	0.0228237i
$871$	−2.71794	+	4.70761i	−0.0920939	+	0.159511i
$872$	−6.77663	−	3.12630i	−0.229486	−	0.105870i
$873$	3.62570			0.122711
$874$	13.4498	−	14.3746i	0.454948	−	0.486228i
$875$			51.9617i			1.75663i
$876$	1.53324	−	1.01443i	0.0518034	−	0.0342744i
$877$	21.3846	+	12.3464i	0.722106	+	0.416908i	0.815527	−	0.578718i	$-0.196447\pi$
$877$	21.3846	+	12.3464i	0.722106	+	0.416908i	−0.0934212	+	0.995627i	$0.529780\pi$
$878$	12.9924	−	24.1749i	0.438474	−	0.815862i
$879$	−0.0376937	+	0.0652875i	−0.00127138	+	0.00220209i
$880$	−7.00463	+	16.4853i	−0.236126	+	0.555719i
$881$	22.1718			0.746988			0.373494	−	0.927633i	$-0.378160\pi$
$881$	22.1718			0.746988			0.373494	+	0.927633i	$0.378160\pi$
$882$	−33.6775	−	54.4333i	−1.13398	−	1.83287i
$883$	−37.4154	+	21.6018i	−1.25913	+	0.726959i	−0.972905	−	0.231204i	$-0.925734\pi$
$883$	−37.4154	+	21.6018i	−1.25913	+	0.726959i	−0.286224	+	0.958163i	$0.592400\pi$
$884$	0.0451319	+	0.740099i	0.00151795	+	0.0248922i
$885$			0.790906i			0.0265860i
$886$	22.7282	−	14.0618i	0.763569	−	0.472415i
$887$	−15.8289	−	27.4165i	−0.531483	−	0.920556i	−0.999325	−	0.0367436i	$-0.988302\pi$
$887$	−15.8289	−	27.4165i	−0.531483	−	0.920556i	0.467841	−	0.883812i	$-0.345032\pi$
$888$	0.900971	−	1.95296i	0.0302346	−	0.0655371i
$889$	11.1970	+	19.3938i	0.375535	+	0.650446i
$890$	−0.565230	−	18.5552i	−0.0189466	−	0.621970i
$891$	−15.3503	−	8.86249i	−0.514254	−	0.296904i
$892$	−6.32284	+	12.6759i	−0.211704	+	0.424421i
$893$	−4.80952	+	4.83624i	−0.160944	+	0.161839i
$894$	0.289814	+	0.468429i	0.00969283	+	0.0156666i
$895$	−12.6596	+	21.9270i	−0.423163	+	0.732940i
$896$	−51.9996	+	11.2557i	−1.73718	+	0.376028i
$897$	0.0587673	+	0.101788i	0.00196218	+	0.00339860i
$898$	−35.6212	+	1.08510i	−1.18870	+	0.0362103i
$899$	28.4277	−	16.4127i	0.948117	−	0.547396i
$900$	0.304092	−	0.609638i	0.0101364	−	0.0203213i
$901$		−	8.64881i		−	0.288134i
$902$	13.6670	+	7.34516i	0.455063	+	0.244567i
$903$	1.31288	+	2.27398i	0.0436900	+	0.0756733i
$904$	−25.1881	+	2.30757i	−0.837745	+	0.0767486i
$905$	26.7244			0.888348
$906$	0.333840	+	0.179418i	0.0110911	+	0.00596076i
$907$	−24.1186	−	13.9249i	−0.800847	−	0.462369i	0.0429205	−	0.999078i	$-0.486334\pi$
$907$	−24.1186	−	13.9249i	−0.800847	−	0.462369i	−0.843767	+	0.536709i	$0.819667\pi$
$908$	1.32091	+	21.6610i	0.0438358	+	0.718844i
$909$	38.7357	+	22.3641i	1.28478	+	0.741770i
$910$	7.50630	−	0.228658i	0.248831	−	0.00757995i
$911$	−45.6102			−1.51113			−0.755567	−	0.655071i	$-0.772639\pi$
$911$	−45.6102			−1.51113			−0.755567	+	0.655071i	$0.772639\pi$
$912$	−0.175787	+	1.27303i	−0.00582088	+	0.0421541i
$913$	−30.8381			−1.02059
$914$	9.12512	−	0.277971i	0.301832	−	0.00919447i
$915$	−0.252039	−	0.145515i	−0.00833215	−	0.00481057i
$916$	−0.695792	−	11.4100i	−0.0229896	−	0.376997i
$917$	−20.3049	−	11.7230i	−0.670526	−	0.387128i
$918$	0.408636	+	0.219616i	0.0134870	+	0.00724840i
$919$	−41.3141			−1.36283			−0.681413	−	0.731899i	$-0.738634\pi$
$919$	−41.3141			−1.36283			−0.681413	+	0.731899i	$0.738634\pi$
$920$	1.86345	+	20.3404i	0.0614361	+	0.670603i
$921$	0.968208	+	1.67698i	0.0319035	+	0.0552585i
$922$	3.58327	+	1.92578i	0.118009	+	0.0634221i
$923$			5.41378i			0.178197i
$924$	−0.612720	+	1.22837i	−0.0201570	+	0.0404104i
$925$	−1.01633	+	0.586777i	−0.0334166	+	0.0192931i
$926$	−41.9435	+	1.27769i	−1.37835	+	0.0419875i
$927$	−17.4001	−	30.1378i	−0.571494	−	0.989856i
$928$	−26.6253	+	21.3493i	−0.874019	+	0.700824i
$929$	3.58663	−	6.21223i	0.117674	−	0.203817i	−0.801172	−	0.598435i	$-0.795790\pi$
$929$	3.58663	−	6.21223i	0.117674	−	0.203817i	0.918845	+	0.394618i	$0.129123\pi$
$930$	0.674784	+	1.09066i	0.0221270	+	0.0357641i
$931$	−17.2278	−	63.5900i	−0.564620	−	2.08408i
$932$	20.8380	−	41.7757i	0.682572	−	1.36841i
$933$	−1.54489	−	0.891942i	−0.0505774	−	0.0292009i
$934$	0.531360	+	17.4433i	0.0173866	+	0.570761i
$935$	1.66230	+	2.87918i	0.0543629	+	0.0941593i
$936$	3.84046	+	1.77174i	0.125529	+	0.0579112i
$937$	−10.0009	−	17.3221i	−0.326716	−	0.565889i	0.655142	−	0.755506i	$-0.272609\pi$
$937$	−10.0009	−	17.3221i	−0.326716	−	0.565889i	−0.981858	+	0.189616i	$0.939276\pi$
$938$	−61.5661	+	38.0906i	−2.01020	+	1.24370i
$939$		−	2.11577i		−	0.0690457i
$940$	−0.430759	−	7.06383i	−0.0140498	−	0.230397i
$941$	−31.3632	+	18.1076i	−1.02241	+	0.590289i	−0.914801	−	0.403904i	$-0.867653\pi$
$941$	−31.3632	+	18.1076i	−1.02241	+	0.590289i	−0.107610	+	0.994193i	$0.534320\pi$
$942$	1.04793	+	1.69378i	0.0341434	+	0.0551863i
$943$	17.6934			0.576175
$944$	−17.4692	−	7.42269i	−0.568573	−	0.241588i
$945$	2.34929	−	4.06910i	0.0764226	−	0.132368i
$946$	−10.0431	+	18.6870i	−0.326528	+	0.607566i
$947$	−29.1318	−	16.8192i	−0.946656	−	0.546552i	−0.0546155	−	0.998507i	$-0.517393\pi$
$947$	−29.1318	−	16.8192i	−0.946656	−	0.546552i	−0.892041	+	0.451955i	$0.850727\pi$
$948$	−0.205273	+	0.135814i	−0.00666695	+	0.00441102i
$949$		−	6.22765i		−	0.202158i
$950$	0.479086	−	0.512026i	0.0155436	−	0.0166123i
$951$	0.755381			0.0244949
$952$	−4.13677	+	8.96695i	−0.134074	+	0.290620i
$953$	19.7258	−	34.1662i	0.638983	−	1.10675i	−0.346674	−	0.937986i	$-0.612689\pi$
$953$	19.7258	−	34.1662i	0.638983	−	1.10675i	0.985656	−	0.168765i	$-0.0539777\pi$
$954$	−43.4555	−	23.3546i	−1.40692	−	0.756132i
$955$	24.7687	+	14.3002i	0.801495	+	0.462743i
$956$	−20.8646	+	1.27234i	−0.674810	+	0.0411505i
$957$			0.880523i			0.0284633i
$958$	−5.95229	−	9.62074i	−0.192310	−	0.310832i
$959$	18.8107	+	32.5812i	0.607431	+	1.05210i
$960$	−0.865425	−	1.01440i	−0.0279315	−	0.0327395i
$961$	−1.39543			−0.0450140
$962$	−3.83323	−	6.19569i	−0.123588	−	0.199757i
$963$	−19.8810	+	11.4783i	−0.640655	+	0.369882i
$964$	−22.8254	−	34.4989i	−0.735156	−	1.11114i
$965$	−14.3855	+	8.30546i	−0.463085	+	0.267362i
$966$	0.0476621	+	1.56463i	0.00153350	+	0.0503413i
$967$	−6.05042	+	10.4796i	−0.194568	+	0.337002i	−0.946759	−	0.321943i	$-0.895664\pi$
$967$	−6.05042	+	10.4796i	−0.194568	+	0.337002i	0.752191	+	0.658946i	$0.228997\pi$
$968$	19.9385	−	1.82663i	0.640847	−	0.0587101i
$969$	0.169132	+	0.168197i	0.00543329	+	0.00540327i
$970$	−3.29280	+	2.03724i	−0.105726	+	0.0654117i
$971$	24.1496	+	13.9428i	0.774997	+	0.447445i	0.834654	−	0.550774i	$-0.185667\pi$
$971$	24.1496	+	13.9428i	0.774997	+	0.447445i	−0.0596571	+	0.998219i	$0.519001\pi$
$972$	3.31135	−	2.19087i	0.106211	−	0.0702722i
$973$	32.4873	−	18.7565i	1.04149	−	0.601307i
$974$	16.0344	−	0.488442i	0.513775	−	0.0156507i
$975$	0.00209330	+	0.00362571i	6.70394e−5	+	0.000116116i
$976$	5.57946	−	4.20126i	0.178594	−	0.134479i
$977$	6.91747			0.221310			0.110655	−	0.993859i	$-0.464705\pi$
$977$	6.91747			0.221310			0.110655	+	0.993859i	$0.464705\pi$
$978$	0.480245	−	0.893586i	0.0153565	−	0.0285737i
$979$	9.95449	−	5.74723i	0.318147	−	0.183682i
$980$	61.1708	+	30.5125i	1.95403	+	0.974685i
$981$			7.90138i			0.252272i
$982$	−28.7764	−	15.4655i	−0.918293	−	0.493524i
$983$	20.4691	−	35.4536i	0.652864	−	1.13079i	−0.329560	−	0.944135i	$-0.606901\pi$
$983$	20.4691	−	35.4536i	0.652864	−	1.13079i	0.982425	−	0.186660i	$-0.0597661\pi$
$984$	−0.943437	+	0.666371i	−0.0300757	+	0.0212431i
$985$	−13.6813	+	23.6967i	−0.435922	+	0.755039i
$986$	0.192871	+	6.33150i	0.00614228	+	0.201636i
$987$		−	0.542358i		−	0.0172634i
$988$	3.26783	+	2.87608i	0.103964	+	0.0915004i
$989$			24.1922i			0.769267i
$990$	18.9550	−	0.577412i	0.602431	−	0.0183514i
$991$	−0.898204	+	1.55573i	−0.0285324	+	0.0494195i	−0.879939	−	0.475087i	$-0.842417\pi$
$991$	−0.898204	+	1.55573i	−0.0285324	+	0.0494195i	0.851407	+	0.524506i	$0.175750\pi$
$992$	−30.4229	+	4.66844i	−0.965927	+	0.148223i
$993$	−0.615184	+	1.06553i	−0.0195223	+	0.0338136i
$994$	−34.1332	+	63.5112i	−1.08264	+	2.01445i
$995$		−	16.8951i		−	0.535610i
$996$	1.02470	−	2.05430i	0.0324689	−	0.0650930i
$997$	−1.49295	+	0.861952i	−0.0472821	+	0.0272983i	−0.523455	−	0.852054i	$-0.675357\pi$
$997$	−1.49295	+	0.861952i	−0.0472821	+	0.0272983i	0.476173	+	0.879352i	$0.342024\pi$
$998$	25.1646	+	13.5243i	0.796571	+	0.428106i
$999$	−4.55834			−0.144219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.p.a.125.18	yes	36
4.3	odd	2		608.2.t.a.49.10		36
8.3	odd	2		608.2.t.a.49.9		36
8.5	even	2	inner	152.2.p.a.125.7	yes	36
19.7	even	3	inner	152.2.p.a.45.7	✓	36
76.7	odd	6		608.2.t.a.273.9		36
152.45	even	6	inner	152.2.p.a.45.18	yes	36
152.83	odd	6		608.2.t.a.273.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.p.a.45.7	✓	36	19.7	even	3	inner
152.2.p.a.45.18	yes	36	152.45	even	6	inner
152.2.p.a.125.7	yes	36	8.5	even	2	inner
152.2.p.a.125.18	yes	36	1.1	even	1	trivial
608.2.t.a.49.9		36	8.3	odd	2
608.2.t.a.49.10		36	4.3	odd	2
608.2.t.a.273.9		36	76.7	odd	6
608.2.t.a.273.10		36	152.83	odd	6

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41356 - 0.0430601i) q^{2} +(-0.0638311 - 0.0368529i) q^{3} +(1.99629 - 0.121736i) q^{4} +(1.95840 + 1.13068i) q^{5} +(-0.0918158 - 0.0493451i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 - 2.59337i) q^{9} +O(q^{10})\)	\(q+(1.41356 - 0.0430601i) q^{2} +(-0.0638311 - 0.0368529i) q^{3} +(1.99629 - 0.121736i) q^{4} +(1.95840 + 1.13068i) q^{5} +(-0.0918158 - 0.0493451i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 - 2.59337i) q^{9} +(2.81699 + 1.51395i) q^{10} +1.98019i q^{11} +(-0.131912 - 0.0657986i) q^{12} +(-0.432449 + 0.249675i) q^{13} +(-6.64740 + 0.202494i) q^{14} +(-0.0833377 - 0.144345i) q^{15} +(3.97036 - 0.486040i) q^{16} +(0.371220 - 0.642972i) q^{17} +(-2.22817 - 3.60141i) q^{18} +(-1.13983 - 4.20723i) q^{19} +(4.04717 + 2.01876i) q^{20} +(0.300172 + 0.173304i) q^{21} +(0.0852672 + 2.79912i) q^{22} +(1.59672 + 2.76560i) q^{23} +(-0.189298 - 0.0873300i) q^{24} +(0.0568756 + 0.0985114i) q^{25} +(-0.600541 + 0.371551i) q^{26} +0.441834i q^{27} +(-9.38776 + 0.572475i) q^{28} +(-5.22471 + 3.01649i) q^{29} +(-0.124018 - 0.200452i) q^{30} -5.44101 q^{31} +(5.59141 - 0.858010i) q^{32} +(0.0729758 - 0.126398i) q^{33} +(0.497055 - 0.924863i) q^{34} +(-9.20955 - 5.31714i) q^{35} +(-3.30472 - 4.99485i) q^{36} +10.3168i q^{37} +(-1.79237 - 5.89808i) q^{38} +0.0368049 q^{39} +(5.80784 + 2.67936i) q^{40} +(2.77027 - 4.79824i) q^{41} +(0.431773 + 0.232050i) q^{42} +(6.56065 + 3.78779i) q^{43} +(0.241060 + 3.95304i) q^{44} -6.77180i q^{45} +(2.37615 + 3.84058i) q^{46} +(-0.782377 - 1.35512i) q^{47} +(-0.271344 - 0.115295i) q^{48} +15.1145 q^{49} +(0.0846389 + 0.136803i) q^{50} +(-0.0473908 + 0.0273611i) q^{51} +(-0.832900 + 0.551068i) q^{52} +(10.0885 - 5.82458i) q^{53} +(0.0190254 + 0.624559i) q^{54} +(-2.23896 + 3.87800i) q^{55} +(-13.2455 + 1.21346i) q^{56} +(-0.0822924 + 0.310558i) q^{57} +(-7.25554 + 4.48896i) q^{58} +(-4.10945 - 2.37259i) q^{59} +(-0.183938 - 0.278010i) q^{60} +(1.51215 - 0.873042i) q^{61} +(-7.69118 + 0.234290i) q^{62} +(7.04113 + 12.1956i) q^{63} +(7.86683 - 1.45361i) q^{64} -1.12921 q^{65} +(0.0977129 - 0.181813i) q^{66} +(9.42749 - 5.44296i) q^{67} +(0.662791 - 1.32875i) q^{68} -0.235375i q^{69} +(-13.2472 - 7.11952i) q^{70} +(5.42083 - 9.38916i) q^{71} +(-4.88649 - 6.91821i) q^{72} +(-6.23576 + 10.8007i) q^{73} +(0.444244 + 14.5835i) q^{74} -0.00838412i q^{75} +(-2.78759 - 8.26010i) q^{76} -9.31205i q^{77} +(0.0520259 - 0.00158482i) q^{78} +(0.834855 - 1.44601i) q^{79} +(8.32509 + 3.53735i) q^{80} +(-4.47557 + 7.75191i) q^{81} +(3.70932 - 6.90188i) q^{82} +15.5733i q^{83} +(0.620329 + 0.309425i) q^{84} +(1.45399 - 0.839462i) q^{85} +(9.43696 + 5.07176i) q^{86} +0.444666 q^{87} +(0.510971 + 5.57747i) q^{88} +(-2.90236 - 5.02703i) q^{89} +(-0.291594 - 9.57233i) q^{90} +(2.03364 - 1.17412i) q^{91} +(3.52419 + 5.32657i) q^{92} +(0.347306 + 0.200517i) q^{93} +(-1.16429 - 1.88185i) q^{94} +(2.52480 - 9.52820i) q^{95} +(-0.388526 - 0.151292i) q^{96} +(-0.605380 + 1.04855i) q^{97} +(21.3652 - 0.650829i) q^{98} +(5.13537 - 2.96491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

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