LMFDB - Embedded newform 336.2.s.c.155.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.2
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38145 - 0.302633i) q^{2} +(1.42461 + 0.985133i) q^{3} +(1.81683 + 0.836146i) q^{4} +(-0.766553 + 0.766553i) q^{5} +(-1.66990 - 1.79205i) q^{6} -1.00000 q^{7} +(-2.25682 - 1.70493i) q^{8} +(1.05903 + 2.80686i) q^{9} +O(q^{10})$	\(q+(-1.38145 - 0.302633i) q^{2} +(1.42461 + 0.985133i) q^{3} +(1.81683 + 0.836146i) q^{4} +(-0.766553 + 0.766553i) q^{5} +(-1.66990 - 1.79205i) q^{6} -1.00000 q^{7} +(-2.25682 - 1.70493i) q^{8} +(1.05903 + 2.80686i) q^{9} +(1.29094 - 0.826974i) q^{10} +(3.09355 + 3.09355i) q^{11} +(1.76455 + 2.98100i) q^{12} +(0.262549 - 0.262549i) q^{13} +(1.38145 + 0.302633i) q^{14} +(-1.84720 + 0.336883i) q^{15} +(2.60172 + 3.03826i) q^{16} +2.68766i q^{17} +(-0.613548 - 4.19804i) q^{18} +(-2.44019 - 2.44019i) q^{19} +(-2.03365 + 0.751744i) q^{20} +(-1.42461 - 0.985133i) q^{21} +(-3.33739 - 5.20981i) q^{22} +3.24607i q^{23} +(-1.53550 - 4.65212i) q^{24} +3.82479i q^{25} +(-0.442155 + 0.283243i) q^{26} +(-1.25643 + 5.04196i) q^{27} +(-1.81683 - 0.836146i) q^{28} +(-3.28972 - 3.28972i) q^{29} +(2.65377 + 0.0936344i) q^{30} -3.76875i q^{31} +(-2.67468 - 4.98459i) q^{32} +(1.35954 + 7.45466i) q^{33} +(0.813374 - 3.71288i) q^{34} +(0.766553 - 0.766553i) q^{35} +(-0.422876 + 5.98508i) q^{36} +(4.88595 + 4.88595i) q^{37} +(2.63253 + 4.10949i) q^{38} +(0.632675 - 0.115384i) q^{39} +(3.03689 - 0.423052i) q^{40} +11.2823 q^{41} +(1.66990 + 1.79205i) q^{42} +(-0.938292 + 0.938292i) q^{43} +(3.03379 + 8.20711i) q^{44} +(-2.96341 - 1.33981i) q^{45} +(0.982368 - 4.48430i) q^{46} +0.764222 q^{47} +(0.713342 + 6.89138i) q^{48} +1.00000 q^{49} +(1.15751 - 5.28377i) q^{50} +(-2.64770 + 3.82887i) q^{51} +(0.696535 - 0.257477i) q^{52} +(-4.14619 + 4.14619i) q^{53} +(3.26156 - 6.58500i) q^{54} -4.74274 q^{55} +(2.25682 + 1.70493i) q^{56} +(-1.07241 - 5.88023i) q^{57} +(3.54902 + 5.54018i) q^{58} +(-2.63246 - 2.63246i) q^{59} +(-3.63772 - 0.932468i) q^{60} +(10.7072 - 10.7072i) q^{61} +(-1.14055 + 5.20635i) q^{62} +(-1.05903 - 2.80686i) q^{63} +(2.18644 + 7.69542i) q^{64} +0.402516i q^{65} +(0.377877 - 10.7097i) q^{66} +(-8.41087 - 8.41087i) q^{67} +(-2.24728 + 4.88301i) q^{68} +(-3.19781 + 4.62439i) q^{69} +(-1.29094 + 0.826974i) q^{70} -13.7602i q^{71} +(2.39546 - 8.14013i) q^{72} -6.79488i q^{73} +(-5.27106 - 8.22835i) q^{74} +(-3.76793 + 5.44884i) q^{75} +(-2.39305 - 6.47375i) q^{76} +(-3.09355 - 3.09355i) q^{77} +(-0.908931 - 0.0320703i) q^{78} +3.83558i q^{79} +(-4.32335 - 0.334634i) q^{80} +(-6.75693 + 5.94508i) q^{81} +(-15.5859 - 3.41439i) q^{82} +(-0.107522 + 0.107522i) q^{83} +(-1.76455 - 2.98100i) q^{84} +(-2.06023 - 2.06023i) q^{85} +(1.58016 - 1.01225i) q^{86} +(-1.44576 - 7.92738i) q^{87} +(-1.70730 - 12.2559i) q^{88} +9.00266 q^{89} +(3.68834 + 2.74771i) q^{90} +(-0.262549 + 0.262549i) q^{91} +(-2.71419 + 5.89755i) q^{92} +(3.71272 - 5.36900i) q^{93} +(-1.05574 - 0.231278i) q^{94} +3.74107 q^{95} +(1.10011 - 9.73600i) q^{96} +18.1447 q^{97} +(-1.38145 - 0.302633i) q^{98} +(-5.40701 + 11.9593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.38145	−	0.302633i	−0.976835	−	0.213994i
$2$	−1.38145	−	0.302633i	−0.976835	−	0.213994i
$3$	1.42461	+	0.985133i	0.822499	+	0.568767i
$3$	1.42461	+	0.985133i	0.822499	+	0.568767i
$4$	1.81683	+	0.836146i	0.908413	+	0.418073i
$5$	−0.766553	+	0.766553i	−0.342813	+	0.342813i	−0.857424	−	0.514611i	$-0.827936\pi$
$5$	−0.766553	+	0.766553i	−0.342813	+	0.342813i	0.514611	+	0.857424i	$0.327936\pi$
$6$	−1.66990	−	1.79205i	−0.681733	−	0.731601i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.25682	−	1.70493i	−0.797905	−	0.602783i
$9$	1.05903	+	2.80686i	0.353009	+	0.935620i
$10$	1.29094	−	0.826974i	0.408232	−	0.261512i
$11$	3.09355	+	3.09355i	0.932741	+	0.932741i	0.997876	−	0.0651356i	$-0.0207480\pi$
$11$	3.09355	+	3.09355i	0.932741	+	0.932741i	−0.0651356	+	0.997876i	$0.520748\pi$
$12$	1.76455	+	2.98100i	0.509383	+	0.860540i
$13$	0.262549	−	0.262549i	0.0728180	−	0.0728180i	−0.669760	−	0.742578i	$-0.733603\pi$
$13$	0.262549	−	0.262549i	0.0728180	−	0.0728180i	0.742578	+	0.669760i	$0.233603\pi$
$14$	1.38145	+	0.302633i	0.369209	+	0.0808820i
$15$	−1.84720	+	0.336883i	−0.476944	+	0.0869827i
$16$	2.60172	+	3.03826i	0.650430	+	0.759566i
$17$			2.68766i			0.651853i	0.945395	+	0.325927i	$0.105676\pi$
$17$			2.68766i			0.651853i	−0.945395	+	0.325927i	$0.894324\pi$
$18$	−0.613548	−	4.19804i	−0.144615	−	0.989488i
$19$	−2.44019	−	2.44019i	−0.559818	−	0.559818i	0.369438	−	0.929255i	$-0.379550\pi$
$19$	−2.44019	−	2.44019i	−0.559818	−	0.559818i	−0.929255	+	0.369438i	$0.879550\pi$
$20$	−2.03365	+	0.751744i	−0.454737	+	0.168095i
$21$	−1.42461	−	0.985133i	−0.310875	−	0.214974i
$22$	−3.33739	−	5.20981i	−0.711533	−	1.11073i
$23$			3.24607i			0.676853i	0.940993	+	0.338427i	$0.109895\pi$
$23$			3.24607i			0.676853i	−0.940993	+	0.338427i	$0.890105\pi$
$24$	−1.53550	−	4.65212i	−0.313433	−	0.949610i
$25$			3.82479i			0.764958i
$26$	−0.442155	+	0.283243i	−0.0867137	+	0.0555486i
$27$	−1.25643	+	5.04196i	−0.241800	+	0.970326i
$28$	−1.81683	−	0.836146i	−0.343348	−	0.158017i
$29$	−3.28972	−	3.28972i	−0.610886	−	0.610886i	0.332291	−	0.943177i	$-0.392178\pi$
$29$	−3.28972	−	3.28972i	−0.610886	−	0.610886i	−0.943177	+	0.332291i	$0.892178\pi$
$30$	2.65377	+	0.0936344i	0.484509	+	0.0170952i
$31$		−	3.76875i		−	0.676888i	−0.940987	−	0.338444i	$-0.890099\pi$
$31$		−	3.76875i		−	0.676888i	0.940987	−	0.338444i	$-0.109901\pi$
$32$	−2.67468	−	4.98459i	−0.472821	−	0.881159i
$33$	1.35954	+	7.45466i	0.236666	+	1.29769i
$34$	0.813374	−	3.71288i	0.139492	−	0.636753i
$35$	0.766553	−	0.766553i	0.129571	−	0.129571i
$36$	−0.422876	+	5.98508i	−0.0704794	+	0.997513i
$37$	4.88595	+	4.88595i	0.803245	+	0.803245i	0.983601	−	0.180357i	$-0.0577252\pi$
$37$	4.88595	+	4.88595i	0.803245	+	0.803245i	−0.180357	+	0.983601i	$0.557725\pi$
$38$	2.63253	+	4.10949i	0.427052	+	0.666647i
$39$	0.632675	−	0.115384i	0.101309	−	0.0184763i
$40$	3.03689	−	0.423052i	0.480174	−	0.0668905i
$41$	11.2823			1.76200			0.880998	−	0.473120i	$-0.156872\pi$
$41$	11.2823			1.76200			0.880998	+	0.473120i	$0.156872\pi$
$42$	1.66990	+	1.79205i	0.257671	+	0.276519i
$43$	−0.938292	+	0.938292i	−0.143088	+	0.143088i	−0.775022	−	0.631934i	$-0.782261\pi$
$43$	−0.938292	+	0.938292i	−0.143088	+	0.143088i	0.631934	+	0.775022i	$0.282261\pi$
$44$	3.03379	+	8.20711i	0.457361	+	1.23727i
$45$	−2.96341	−	1.33981i	−0.441759	−	0.199727i
$46$	0.982368	−	4.48430i	0.144842	−	0.661174i
$47$	0.764222			0.111473			0.0557366	−	0.998446i	$-0.482249\pi$
$47$	0.764222			0.111473			0.0557366	+	0.998446i	$0.482249\pi$
$48$	0.713342	+	6.89138i	0.102962	+	0.994685i
$49$	1.00000			0.142857
$50$	1.15751	−	5.28377i	0.163696	−	0.747238i
$51$	−2.64770	+	3.82887i	−0.370752	+	0.536149i
$52$	0.696535	−	0.257477i	0.0965921	−	0.0357056i
$53$	−4.14619	+	4.14619i	−0.569523	+	0.569523i	−0.931995	−	0.362471i	$-0.881933\pi$
$53$	−4.14619	+	4.14619i	−0.569523	+	0.569523i	0.362471	+	0.931995i	$0.381933\pi$
$54$	3.26156	−	6.58500i	0.443842	−	0.896105i
$55$	−4.74274			−0.639512
$56$	2.25682	+	1.70493i	0.301580	+	0.227831i
$57$	−1.07241	−	5.88023i	−0.142044	−	0.778855i
$58$	3.54902	+	5.54018i	0.466009	+	0.727461i
$59$	−2.63246	−	2.63246i	−0.342717	−	0.342717i	0.514671	−	0.857388i	$-0.327914\pi$
$59$	−2.63246	−	2.63246i	−0.342717	−	0.342717i	−0.857388	+	0.514671i	$0.827914\pi$
$60$	−3.63772	−	0.932468i	−0.469628	−	0.120381i
$61$	10.7072	−	10.7072i	1.37092	−	1.37092i	0.511830	−	0.859087i	$-0.328968\pi$
$61$	10.7072	−	10.7072i	1.37092	−	1.37092i	0.859087	−	0.511830i	$-0.171032\pi$
$62$	−1.14055	+	5.20635i	−0.144850	+	0.661208i
$63$	−1.05903	−	2.80686i	−0.133425	−	0.353631i
$64$	2.18644	+	7.69542i	0.273305	+	0.961927i
$65$			0.402516i			0.0499259i
$66$	0.377877	−	10.7097i	0.0465134	−	1.31827i
$67$	−8.41087	−	8.41087i	−1.02755	−	1.02755i	−0.999610	−	0.0279421i	$-0.991105\pi$
$67$	−8.41087	−	8.41087i	−1.02755	−	1.02755i	−0.0279421	−	0.999610i	$-0.508895\pi$
$68$	−2.24728	+	4.88301i	−0.272522	+	0.592152i
$69$	−3.19781	+	4.62439i	−0.384971	+	0.556711i
$70$	−1.29094	+	0.826974i	−0.154297	+	0.0988423i
$71$		−	13.7602i		−	1.63303i	−0.577322	−	0.816516i	$-0.695902\pi$
$71$		−	13.7602i		−	1.63303i	0.577322	−	0.816516i	$-0.304098\pi$
$72$	2.39546	−	8.14013i	0.282308	−	0.959324i
$73$		−	6.79488i		−	0.795281i	−0.917541	−	0.397641i	$-0.869829\pi$
$73$		−	6.79488i		−	0.795281i	0.917541	−	0.397641i	$-0.130171\pi$
$74$	−5.27106	−	8.22835i	−0.612748	−	0.956527i
$75$	−3.76793	+	5.44884i	−0.435083	+	0.629177i
$76$	−2.39305	−	6.47375i	−0.274501	−	0.742591i
$77$	−3.09355	−	3.09355i	−0.352543	−	0.352543i
$78$	−0.908931	−	0.0320703i	−0.102916	−	0.00363125i
$79$			3.83558i			0.431536i	0.976445	+	0.215768i	$0.0692255\pi$
$79$			3.83558i			0.431536i	−0.976445	+	0.215768i	$0.930775\pi$
$80$	−4.32335	−	0.334634i	−0.483365	−	0.0374133i
$81$	−6.75693	+	5.94508i	−0.750770	+	0.660564i
$82$	−15.5859	−	3.41439i	−1.72118	−	0.377056i
$83$	−0.107522	+	0.107522i	−0.0118021	+	0.0118021i	−0.712983	−	0.701181i	$-0.752656\pi$
$83$	−0.107522	+	0.107522i	−0.0118021	+	0.0118021i	0.701181	+	0.712983i	$0.252656\pi$
$84$	−1.76455	−	2.98100i	−0.192529	−	0.325253i
$85$	−2.06023	−	2.06023i	−0.223464	−	0.223464i
$86$	1.58016	−	1.01225i	0.170393	−	0.109154i
$87$	−1.44576	−	7.92738i	−0.155001	−	0.849905i
$88$	−1.70730	−	12.2559i	−0.181998	−	1.30648i
$89$	9.00266			0.954280			0.477140	−	0.878827i	$-0.341674\pi$
$89$	9.00266			0.954280			0.477140	+	0.878827i	$0.341674\pi$
$90$	3.68834	+	2.74771i	0.388785	+	0.289634i
$91$	−0.262549	+	0.262549i	−0.0275226	+	0.0275226i
$92$	−2.71419	+	5.89755i	−0.282974	+	0.614862i
$93$	3.71272	−	5.36900i	0.384991	−	0.556739i
$94$	−1.05574	−	0.231278i	−0.108891	−	0.0238545i
$95$	3.74107			0.383826
$96$	1.10011	−	9.73600i	0.112279	−	0.993677i
$97$	18.1447			1.84232			0.921160	−	0.389185i	$-0.127243\pi$
$97$	18.1447			1.84232			0.921160	+	0.389185i	$0.127243\pi$
$98$	−1.38145	−	0.302633i	−0.139548	−	0.0305705i
$99$	−5.40701	+	11.9593i	−0.543425	+	1.20196i
$100$	−3.19808	+	6.94899i	−0.319808	+	0.694899i
$101$	7.24602	−	7.24602i	0.721006	−	0.721006i	−0.247804	−	0.968810i	$-0.579709\pi$
$101$	7.24602	−	7.24602i	0.721006	−	0.721006i	0.968810	+	0.247804i	$0.0797091\pi$
$102$	4.81642	−	4.48812i	0.476896	−	0.444390i
$103$	−17.2202			−1.69676			−0.848378	−	0.529390i	$-0.822421\pi$
$103$	−17.2202			−1.69676			−0.848378	+	0.529390i	$0.822421\pi$
$104$	−1.04015	+	0.144898i	−0.101995	+	0.0142084i
$105$	1.84720	−	0.336883i	0.180268	−	0.0328764i
$106$	6.98255	−	4.47300i	0.678205	−	0.434456i
$107$	−7.02957	−	7.02957i	−0.679574	−	0.679574i	0.280330	−	0.959904i	$-0.409556\pi$
$107$	−7.02957	−	7.02957i	−0.679574	−	0.679574i	−0.959904	+	0.280330i	$0.909556\pi$
$108$	−6.49853	+	8.10981i	−0.625322	+	0.780367i
$109$	−1.85810	+	1.85810i	−0.177973	+	0.177973i	−0.790472	−	0.612498i	$-0.790165\pi$
$109$	−1.85810	+	1.85810i	−0.177973	+	0.177973i	0.612498	+	0.790472i	$0.290165\pi$
$110$	6.55188	+	1.43531i	0.624697	+	0.136851i
$111$	2.14726	+	11.7739i	0.203809	+	1.11753i
$112$	−2.60172	−	3.03826i	−0.245839	−	0.287089i
$113$		−	15.6715i		−	1.47425i	−0.675755	−	0.737126i	$-0.736182\pi$
$113$		−	15.6715i		−	1.47425i	0.675755	−	0.737126i	$-0.263818\pi$
$114$	−0.298069	+	8.44781i	−0.0279167	+	0.791209i
$115$	−2.48829	−	2.48829i	−0.232034	−	0.232034i
$116$	−3.22617	−	8.72754i	−0.299542	−	0.810332i
$117$	1.01498	+	0.458892i	0.0938353	+	0.0424246i
$118$	2.83995	+	4.43329i	0.261439	+	0.408117i
$119$		−	2.68766i		−	0.246377i
$120$	4.74314	+	2.38905i	0.432988	+	0.218090i
$121$			8.14012i			0.740011i
$122$	−18.0319	+	11.5512i	−1.63253	+	1.04579i
$123$	16.0728	+	11.1145i	1.44924	+	1.00216i
$124$	3.15123	−	6.84717i	0.282988	−	0.614894i
$125$	−6.76467	−	6.76467i	−0.605051	−	0.605051i
$126$	0.613548	+	4.19804i	0.0546592	+	0.373991i
$127$		−	0.874680i		−	0.0776153i	−0.999247	−	0.0388076i	$-0.987644\pi$
$127$		−	0.874680i		−	0.0776153i	0.999247	−	0.0388076i	$-0.0123560\pi$
$128$	−0.691584	−	11.2926i	−0.0611280	−	0.998130i
$129$	−2.26104	+	0.412358i	−0.199074	+	0.0363061i
$130$	0.121814	−	0.556056i	0.0106838	−	0.0487694i
$131$	2.96129	−	2.96129i	0.258729	−	0.258729i	−0.565808	−	0.824537i	$-0.691436\pi$
$131$	2.96129	−	2.96129i	0.258729	−	0.258729i	0.824537	+	0.565808i	$0.191436\pi$
$132$	−3.76313	+	14.6806i	−0.327538	+	1.27778i
$133$	2.44019	+	2.44019i	0.211591	+	0.211591i
$134$	9.07382	+	14.1646i	0.783859	+	1.22364i
$135$	−2.90181	−	4.82805i	−0.249748	−	0.415533i
$136$	4.58227	−	6.06556i	0.392926	−	0.520117i
$137$	13.5561			1.15817			0.579086	−	0.815266i	$-0.303410\pi$
$137$	13.5561			1.15817			0.579086	+	0.815266i	$0.303410\pi$
$138$	5.81712	−	5.42061i	0.495186	−	0.461433i
$139$	0.262462	−	0.262462i	0.0222618	−	0.0222618i	−0.695888	−	0.718150i	$-0.744989\pi$
$139$	0.262462	−	0.262462i	0.0222618	−	0.0222618i	0.718150	+	0.695888i	$0.244989\pi$
$140$	2.03365	−	0.751744i	0.171874	−	0.0635340i
$141$	1.08872	+	0.752860i	0.0916866	+	0.0634022i
$142$	−4.16428	+	19.0090i	−0.349459	+	1.59520i
$143$	1.62442			0.135841
$144$	−5.77269	+	10.5203i	−0.481058	+	0.876689i
$145$	5.04350			0.418839
$146$	−2.05635	+	9.38682i	−0.170185	+	0.776858i
$147$	1.42461	+	0.985133i	0.117500	+	0.0812524i
$148$	4.79155	+	12.9623i	0.393863	+	1.06549i
$149$	−14.9894	+	14.9894i	−1.22798	+	1.22798i	−0.263254	+	0.964726i	$0.584796\pi$
$149$	−14.9894	+	14.9894i	−1.22798	+	1.22798i	−0.964726	+	0.263254i	$0.915204\pi$
$150$	6.85421	−	6.38702i	0.559644	−	0.521498i
$151$	13.2687			1.07979			0.539895	−	0.841733i	$-0.318464\pi$
$151$	13.2687			1.07979			0.539895	+	0.841733i	$0.318464\pi$
$152$	1.34671	+	9.66740i	0.109233	+	0.784130i
$153$	−7.54389	+	2.84630i	−0.609887	+	0.230110i
$154$	3.33739	+	5.20981i	0.268934	+	0.419818i
$155$	2.88895	+	2.88895i	0.232046	+	0.232046i
$156$	1.24594	+	0.319376i	0.0997550	+	0.0255705i
$157$	−7.89825	+	7.89825i	−0.630349	+	0.630349i	−0.948156	−	0.317807i	$-0.897054\pi$
$157$	−7.89825	+	7.89825i	−0.630349	+	0.630349i	0.317807	+	0.948156i	$0.397054\pi$
$158$	1.16077	−	5.29867i	0.0923459	−	0.421539i
$159$	−9.99126	+	1.82216i	−0.792358	+	0.144506i
$160$	5.87123	+	1.77067i	0.464162	+	0.139984i
$161$		−	3.24607i		−	0.255826i
$162$	11.1336	−	6.16798i	0.874735	−	0.484602i
$163$	2.20835	+	2.20835i	0.172971	+	0.172971i	0.788283	−	0.615312i	$-0.210970\pi$
$163$	2.20835	+	2.20835i	0.172971	+	0.172971i	−0.615312	+	0.788283i	$0.710970\pi$
$164$	20.4980	+	9.43363i	1.60062	+	0.736643i
$165$	−6.75656	−	4.67223i	−0.525998	−	0.363733i
$166$	0.181076	−	0.115997i	0.0140542	−	0.00900310i
$167$		−	18.4786i		−	1.42992i	−0.699166	−	0.714959i	$-0.746445\pi$
$167$		−	18.4786i		−	1.42992i	0.699166	−	0.714959i	$-0.253555\pi$
$168$	1.53550	+	4.65212i	0.118467	+	0.358919i
$169$			12.8621i			0.989395i
$170$	2.22262	+	3.46961i	0.170467	+	0.266107i
$171$	4.26504	−	9.43349i	0.326156	−	0.721397i
$172$	−2.48926	+	0.920165i	−0.189805	+	0.0701619i
$173$	−0.866535	−	0.866535i	−0.0658814	−	0.0658814i	0.673398	−	0.739280i	$-0.264834\pi$
$173$	−0.866535	−	0.866535i	−0.0658814	−	0.0658814i	−0.739280	+	0.673398i	$0.764834\pi$
$174$	−0.401839	+	11.3888i	−0.0304633	+	0.863386i
$175$		−	3.82479i		−	0.289127i
$176$	−1.35047	+	17.4476i	−0.101796	+	1.31516i
$177$	−1.15690	−	6.34355i	−0.0869583	−	0.476810i
$178$	−12.4367	−	2.72450i	−0.932174	−	0.204210i
$179$	−12.2237	+	12.2237i	−0.913642	+	0.913642i	−0.996557	−	0.0829148i	$-0.973577\pi$
$179$	−12.2237	+	12.2237i	−0.913642	+	0.913642i	0.0829148	+	0.996557i	$0.473577\pi$
$180$	−4.26373	−	4.91204i	−0.317799	−	0.366122i
$181$	3.58486	+	3.58486i	0.266461	+	0.266461i	0.827672	−	0.561212i	$-0.189665\pi$
$181$	3.58486	+	3.58486i	0.266461	+	0.266461i	−0.561212	+	0.827672i	$0.689665\pi$
$182$	0.442155	−	0.283243i	0.0327747	−	0.0209954i
$183$	25.8016	−	4.70557i	1.90731	−	0.347846i
$184$	5.53432	−	7.32579i	0.407995	−	0.540065i
$185$	−7.49068			−0.550725
$186$	−6.75378	+	6.29343i	−0.495212	+	0.461457i
$187$	−8.31441	+	8.31441i	−0.608010	+	0.608010i
$188$	1.38846	+	0.639001i	0.101264	+	0.0466039i
$189$	1.25643	−	5.04196i	0.0913919	−	0.366749i
$190$	−5.16811	−	1.13217i	−0.374934	−	0.0821362i
$191$	22.9268			1.65892			0.829461	−	0.558564i	$-0.188648\pi$
$191$	22.9268			1.65892			0.829461	+	0.558564i	$0.188648\pi$
$192$	−4.46618	+	13.1169i	−0.322319	+	0.946631i
$193$	−3.43127			−0.246989			−0.123494	−	0.992345i	$-0.539410\pi$
$193$	−3.43127			−0.246989			−0.123494	+	0.992345i	$0.539410\pi$
$194$	−25.0661	−	5.49119i	−1.79964	−	0.394245i
$195$	−0.396531	+	0.573428i	−0.0283962	+	0.0410640i
$196$	1.81683	+	0.836146i	0.129773	+	0.0597247i
$197$	−8.61873	+	8.61873i	−0.614059	+	0.614059i	−0.944001	−	0.329942i	$-0.892971\pi$
$197$	−8.61873	+	8.61873i	−0.614059	+	0.614059i	0.329942	+	0.944001i	$0.392971\pi$
$198$	11.0888	−	14.8849i	0.788048	−	1.05782i
$199$	13.4959			0.956701			0.478351	−	0.878169i	$-0.341235\pi$
$199$	13.4959			0.956701			0.478351	+	0.878169i	$0.341235\pi$
$200$	6.52099	−	8.63185i	0.461104	−	0.610364i
$201$	−3.69639	−	20.2680i	−0.260723	−	1.42960i
$202$	−12.2029	+	7.81715i	−0.858594	+	0.550013i
$203$	3.28972	+	3.28972i	0.230893	+	0.230893i
$204$	−8.01191	+	4.74252i	−0.560946	+	0.332043i
$205$	−8.64847	+	8.64847i	−0.604035	+	0.604035i
$206$	23.7889	+	5.21140i	1.65745	+	0.363095i
$207$	−9.11127	+	3.43768i	−0.633277	+	0.238935i
$208$	1.48077	+	0.114614i	0.102673	+	0.00794707i
$209$		−	15.0977i		−	1.04433i
$210$	−2.65377	−	0.0936344i	−0.183127	−	0.00646139i
$211$	8.78164	+	8.78164i	0.604553	+	0.604553i	0.941517	−	0.336964i	$-0.109400\pi$
$211$	8.78164	+	8.78164i	0.604553	+	0.604553i	−0.336964	+	0.941517i	$0.609400\pi$
$212$	−10.9997	+	4.06609i	−0.755465	+	0.279260i
$213$	13.5556	−	19.6029i	0.928815	−	1.34317i
$214$	7.58365	+	11.8384i	0.518407	+	0.809257i
$215$		−	1.43850i		−	0.0981050i
$216$	11.4317	−	9.23666i	0.777830	−	0.628475i
$217$			3.76875i			0.255839i
$218$	3.12920	−	2.00455i	0.211936	−	0.135766i
$219$	6.69386	−	9.68006i	0.452329	−	0.654118i
$220$	−8.61675	−	3.96563i	−0.580941	−	0.267362i
$221$	0.705642	+	0.705642i	0.0474666	+	0.0474666i
$222$	0.596818	−	16.9149i	0.0400558	−	1.13525i
$223$		−	10.6418i		−	0.712629i	−0.934366	−	0.356314i	$-0.884033\pi$
$223$		−	10.6418i		−	0.712629i	0.934366	−	0.356314i	$-0.115967\pi$
$224$	2.67468	+	4.98459i	0.178709	+	0.333047i
$225$	−10.7357	+	4.05056i	−0.715710	+	0.270037i
$226$	−4.74271	+	21.6495i	−0.315480	+	1.44010i
$227$	−1.76217	+	1.76217i	−0.116960	+	0.116960i	−0.763164	−	0.646205i	$-0.776355\pi$
$227$	−1.76217	+	1.76217i	−0.116960	+	0.116960i	0.646205	+	0.763164i	$0.276355\pi$
$228$	2.96835	−	11.5800i	0.196584	−	0.766907i
$229$	2.67283	+	2.67283i	0.176626	+	0.176626i	0.789883	−	0.613257i	$-0.210141\pi$
$229$	2.67283	+	2.67283i	0.176626	+	0.176626i	−0.613257	+	0.789883i	$0.710141\pi$
$230$	2.68442	+	4.19049i	0.177005	+	0.276313i
$231$	−1.35954	−	7.45466i	−0.0894515	−	0.490481i
$232$	1.81556	+	13.0330i	0.119197	+	0.855661i
$233$	−0.740966			−0.0485423			−0.0242712	−	0.999705i	$-0.507727\pi$
$233$	−0.740966			−0.0485423			−0.0242712	+	0.999705i	$0.507727\pi$
$234$	−1.26328	−	0.941105i	−0.0825831	−	0.0615220i
$235$	−0.585817	+	0.585817i	−0.0382145	+	0.0382145i
$236$	−2.58160	−	6.98384i	−0.168048	−	0.454609i
$237$	−3.77855	+	5.46420i	−0.245443	+	0.354938i
$238$	−0.813374	+	3.71288i	−0.0527232	+	0.240670i
$239$	4.05725			0.262441			0.131221	−	0.991353i	$-0.458110\pi$
$239$	4.05725			0.262441			0.131221	+	0.991353i	$0.458110\pi$
$240$	−5.82943	−	4.73580i	−0.376288	−	0.305694i
$241$	−22.5065			−1.44977			−0.724885	−	0.688870i	$-0.758107\pi$
$241$	−22.5065			−1.44977			−0.724885	+	0.688870i	$0.758107\pi$
$242$	2.46347	−	11.2452i	0.158358	−	0.722869i
$243$	−15.4827	+	1.81295i	−0.993214	+	0.116301i
$244$	28.4059	−	10.5004i	1.81850	−	0.672216i
$245$	−0.766553	+	0.766553i	−0.0489733	+	0.0489733i
$246$	−18.8403	−	20.2184i	−1.20121	−	1.28908i
$247$	−1.28134			−0.0815296
$248$	−6.42545	+	8.50538i	−0.408016	+	0.540092i
$249$	−0.259100	+	0.0472534i	−0.0164198	+	0.00299456i
$250$	7.29787	+	11.3923i	0.461558	+	0.720512i
$251$	−19.1167	−	19.1167i	−1.20664	−	1.20664i	−0.972110	−	0.234526i	$-0.924646\pi$
$251$	−19.1167	−	19.1167i	−1.20664	−	1.20664i	−0.234526	−	0.972110i	$-0.575354\pi$
$252$	0.422876	−	5.98508i	0.0266387	−	0.377025i
$253$	−10.0419	+	10.0419i	−0.631328	+	0.631328i
$254$	−0.264707	+	1.20833i	−0.0166092	+	0.0758173i
$255$	−0.905426	−	4.96464i	−0.0567000	−	0.310898i
$256$	−2.46210	+	15.8094i	−0.153881	+	0.988089i
$257$			7.40089i			0.461655i	0.972995	+	0.230827i	$0.0741433\pi$
$257$			7.40089i			0.461655i	−0.972995	+	0.230827i	$0.925857\pi$
$258$	3.24832	+	0.114612i	0.202231	+	0.00713545i
$259$	−4.88595	−	4.88595i	−0.303598	−	0.303598i
$260$	−0.336562	+	0.731301i	−0.0208727	+	0.0453534i
$261$	5.74989	−	12.7177i	0.355909	−	0.787205i
$262$	−4.98706	+	3.19470i	−0.308102	+	0.197369i
$263$			16.5931i			1.02317i	0.859232	+	0.511586i	$0.170942\pi$
$263$			16.5931i			1.02317i	−0.859232	+	0.511586i	$0.829058\pi$
$264$	9.64142	−	19.1417i	0.593388	−	1.17809i
$265$		−	6.35656i		−	0.390480i
$266$	−2.63253	−	4.10949i	−0.161411	−	0.251969i
$267$	12.8253	+	8.86881i	0.784894	+	0.542762i
$268$	−8.24838	−	22.3138i	−0.503850	−	1.36303i
$269$	−13.9816	−	13.9816i	−0.852471	−	0.852471i	0.137966	−	0.990437i	$-0.455944\pi$
$269$	−13.9816	−	13.9816i	−0.852471	−	0.852471i	−0.990437	+	0.137966i	$0.955944\pi$
$270$	2.54759	+	7.54791i	0.155041	+	0.459351i
$271$			7.27474i			0.441909i	0.975284	+	0.220955i	$0.0709173\pi$
$271$			7.27474i			0.441909i	−0.975284	+	0.220955i	$0.929083\pi$
$272$	−8.16582	+	6.99254i	−0.495126	+	0.423985i
$273$	−0.632675	+	0.115384i	−0.0382913	+	0.00698337i
$274$	−18.7271	−	4.10251i	−1.13134	−	0.247841i
$275$	−11.8322	+	11.8322i	−0.713508	+	0.713508i
$276$	−9.67654	+	5.72787i	−0.582459	+	0.344778i
$277$	−3.36999	−	3.36999i	−0.202483	−	0.202483i	0.598580	−	0.801063i	$-0.295732\pi$
$277$	−3.36999	−	3.36999i	−0.202483	−	0.202483i	−0.801063	+	0.598580i	$0.795732\pi$
$278$	−0.442009	+	0.283150i	−0.0265099	+	0.0169822i
$279$	10.5784	−	3.99121i	0.633310	−	0.238947i
$280$	−3.03689	+	0.423052i	−0.181489	+	0.0252822i
$281$	23.9375			1.42799			0.713997	−	0.700149i	$-0.246883\pi$
$281$	23.9375			1.42799			0.713997	+	0.700149i	$0.246883\pi$
$282$	−1.27617	−	1.36952i	−0.0759950	−	0.0815539i
$283$	17.1984	−	17.1984i	1.02234	−	1.02234i	0.0225944	−	0.999745i	$-0.492807\pi$
$283$	17.1984	−	17.1984i	1.02234	−	1.02234i	0.999745	−	0.0225944i	$-0.00719264\pi$
$284$	11.5055	−	24.9999i	0.682727	−	1.48347i
$285$	5.32956	+	3.68545i	0.315696	+	0.218307i
$286$	−2.24406	−	0.491602i	−0.132694	−	0.0290690i
$287$	−11.2823			−0.665972
$288$	11.1585	−	12.7863i	0.657520	−	0.753437i
$289$	9.77648			0.575087
$290$	−6.96735	−	1.52633i	−0.409137	−	0.0896290i
$291$	25.8492	+	17.8750i	1.51531	+	1.04785i
$292$	5.68151	−	12.3451i	0.332485	−	0.722444i
$293$	−11.3212	+	11.3212i	−0.661394	+	0.661394i	−0.955708	−	0.294315i	$-0.904909\pi$
$293$	−11.3212	+	11.3212i	−0.661394	+	0.661394i	0.294315	+	0.955708i	$0.404909\pi$
$294$	−1.66990	−	1.79205i	−0.0973905	−	0.104514i
$295$	4.03584			0.234976
$296$	−2.69650	−	19.3569i	−0.156731	−	1.12510i
$297$	−19.4844	+	11.7107i	−1.13060	+	0.679526i
$298$	25.2435	−	16.1709i	1.46231	−	0.936755i
$299$	0.852253	+	0.852253i	0.0492871	+	0.0492871i
$300$	−11.4017	+	6.74906i	−0.658277	+	0.389657i
$301$	0.938292	−	0.938292i	0.0540822	−	0.0540822i
$302$	−18.3301	−	4.01554i	−1.05478	−	0.231068i
$303$	17.4610	−	3.18446i	1.00311	−	0.182942i
$304$	1.06525	−	13.7626i	0.0610963	−	0.789341i
$305$			16.4153i			0.939936i
$306$	11.2829	−	1.64901i	0.645001	−	0.0942676i
$307$	−19.0113	−	19.0113i	−1.08503	−	1.08503i	−0.996032	−	0.0890009i	$-0.971633\pi$
$307$	−19.0113	−	19.0113i	−1.08503	−	1.08503i	−0.0890009	−	0.996032i	$-0.528367\pi$
$308$	−3.03379	−	8.20711i	−0.172866	−	0.467643i
$309$	−24.5321	−	16.9642i	−1.39558	−	0.965059i
$310$	−3.11666	−	4.86524i	−0.177014	−	0.276327i
$311$			28.7635i			1.63103i	0.578737	+	0.815514i	$0.303546\pi$
$311$			28.7635i			1.63103i	−0.578737	+	0.815514i	$0.696454\pi$
$312$	−1.62455	−	0.818265i	−0.0919723	−	0.0463251i
$313$			20.0305i			1.13219i	0.824339	+	0.566096i	$0.191547\pi$
$313$			20.0305i			1.13219i	−0.824339	+	0.566096i	$0.808453\pi$
$314$	13.3013	−	8.52079i	0.750637	−	0.480856i
$315$	2.96341	+	1.33981i	0.166969	+	0.0754896i
$316$	−3.20710	+	6.96858i	−0.180413	+	0.392013i
$317$	22.5290	+	22.5290i	1.26535	+	1.26535i	0.948462	+	0.316891i	$0.102639\pi$
$317$	22.5290	+	22.5290i	1.26535	+	1.26535i	0.316891	+	0.948462i	$0.397361\pi$
$318$	14.3539	+	0.506457i	0.804927	+	0.0284007i
$319$		−	20.3539i		−	1.13960i
$320$	−7.57497	−	4.22292i	−0.423454	−	0.236069i
$321$	−3.08933	−	16.9395i	−0.172430	−	0.945468i
$322$	−0.982368	+	4.48430i	−0.0547452	+	0.249900i
$323$	6.55840	−	6.55840i	0.364919	−	0.364919i
$324$	−17.2471	+	5.15140i	−0.958173	+	0.286189i
$325$	1.00420	+	1.00420i	0.0557027	+	0.0557027i
$326$	−2.38241	−	3.71905i	−0.131950	−	0.205979i
$327$	−4.47754	+	0.816591i	−0.247608	+	0.0451576i
$328$	−25.4620	−	19.2355i	−1.40591	−	1.06210i
$329$	−0.764222			−0.0421329
$330$	7.91990	+	8.49923i	0.435976	+	0.467867i
$331$	−10.9663	+	10.9663i	−0.602763	+	0.602763i	−0.941045	−	0.338282i	$-0.890154\pi$
$331$	−10.9663	+	10.9663i	−0.602763	+	0.602763i	0.338282	+	0.941045i	$0.390154\pi$
$332$	−0.285253	+	0.105445i	−0.0156553	+	0.00578703i
$333$	−8.53982	+	18.8885i	−0.467979	+	1.03508i
$334$	−5.59224	+	25.5274i	−0.305993	+	1.39679i
$335$	12.8948			0.704516
$336$	−0.713342	−	6.89138i	−0.0389160	−	0.375956i
$337$	−31.9429			−1.74004			−0.870020	−	0.493016i	$-0.835894\pi$
$337$	−31.9429			−1.74004			−0.870020	+	0.493016i	$0.835894\pi$
$338$	3.89250	−	17.7684i	0.211724	−	0.966476i
$339$	15.4385	−	22.3258i	0.838505	−	1.21257i
$340$	−2.02043	−	5.46575i	−0.109573	−	0.296422i
$341$	11.6588	−	11.6588i	0.631361	−	0.631361i
$342$	−8.74684	+	11.7412i	−0.472975	+	0.634891i
$343$	−1.00000			−0.0539949
$344$	3.71727	−	0.517833i	0.200422	−	0.0279197i
$345$	−1.09355	−	5.99613i	−0.0588745	−	0.322821i
$346$	0.934836	+	1.45932i	0.0502571	+	0.0784535i
$347$	17.8392	+	17.8392i	0.957656	+	0.957656i	0.999139	−	0.0414832i	$-0.0132083\pi$
$347$	17.8392	+	17.8392i	0.957656	+	0.957656i	−0.0414832	+	0.999139i	$0.513208\pi$
$348$	4.00176	−	15.6115i	0.214517	−	0.836867i
$349$	18.9731	−	18.9731i	1.01561	−	1.01561i	0.0157305	−	0.999876i	$-0.494993\pi$
$349$	18.9731	−	18.9731i	1.01561	−	1.01561i	0.999876	−	0.0157305i	$-0.00500739\pi$
$350$	−1.15751	+	5.28377i	−0.0618714	+	0.282429i
$351$	0.993887	+	1.65364i	0.0530498	+	0.0882646i
$352$	7.14582	−	23.6943i	0.380874	−	1.26291i
$353$			23.1220i			1.23066i	0.788271	+	0.615329i	$0.210977\pi$
$353$			23.1220i			1.23066i	−0.788271	+	0.615329i	$0.789023\pi$
$354$	−0.321554	+	9.11343i	−0.0170904	+	0.484373i
$355$	10.5479	+	10.5479i	0.559825	+	0.559825i
$356$	16.3563	+	7.52753i	0.866880	+	0.398958i
$357$	2.64770	−	3.82887i	0.140131	−	0.202645i
$358$	20.5858	−	13.1872i	1.08799	−	0.696964i
$359$			30.5132i			1.61043i	0.592986	+	0.805213i	$0.297949\pi$
$359$			30.5132i			1.61043i	−0.592986	+	0.805213i	$0.702051\pi$
$360$	4.40359	+	8.07610i	0.232090	+	0.425648i
$361$		−	7.09096i		−	0.373208i
$362$	−3.86743	−	6.03722i	−0.203267	−	0.317309i
$363$	−8.01910	+	11.5965i	−0.420894	+	0.608658i
$364$	−0.696535	+	0.257477i	−0.0365084	+	0.0134955i
$365$	5.20864	+	5.20864i	0.272633	+	0.272633i
$366$	−37.0678	−	1.30788i	−1.93756	−	0.0683642i
$367$			24.0298i			1.25434i	0.778881	+	0.627172i	$0.215788\pi$
$367$			24.0298i			1.25434i	−0.778881	+	0.627172i	$0.784212\pi$
$368$	−9.86243	+	8.44537i	−0.514115	+	0.440246i
$369$	11.9482	+	31.6678i	0.622000	+	1.64856i
$370$	10.3480	+	2.26692i	0.537968	+	0.117852i
$371$	4.14619	−	4.14619i	0.215260	−	0.215260i
$372$	11.2346	−	6.65017i	0.582489	−	0.344795i
$373$	−1.44743	−	1.44743i	−0.0749453	−	0.0749453i	0.668641	−	0.743586i	$-0.266877\pi$
$373$	−1.44743	−	1.44743i	−0.0749453	−	0.0749453i	−0.743586	+	0.668641i	$0.766877\pi$
$374$	14.0022	−	8.96976i	0.724036	−	0.463815i
$375$	−2.97292	−	16.3011i	−0.153521	−	0.841786i
$376$	−1.72471	−	1.30294i	−0.0889450	−	0.0671941i
$377$	−1.72743			−0.0889670
$378$	−3.26156	+	6.58500i	−0.167757	+	0.338696i
$379$	17.3532	−	17.3532i	0.891372	−	0.891372i	−0.103280	−	0.994652i	$-0.532934\pi$
$379$	17.3532	−	17.3532i	0.891372	−	0.891372i	0.994652	+	0.103280i	$0.0329339\pi$
$380$	6.79688	+	3.12808i	0.348672	+	0.160467i
$381$	0.861676	−	1.24608i	0.0441450	−	0.0638385i
$382$	−31.6723	−	6.93839i	−1.62049	−	0.354999i
$383$	3.29068			0.168146			0.0840729	−	0.996460i	$-0.473207\pi$
$383$	3.29068			0.168146			0.0840729	+	0.996460i	$0.473207\pi$
$384$	10.1394	−	16.7688i	0.517425	−	0.855728i
$385$	4.74274			0.241713
$386$	4.74015	+	1.03842i	0.241267	+	0.0528540i
$387$	−3.62733	−	1.63998i	−0.184388	−	0.0833648i
$388$	32.9658	+	15.1716i	1.67359	+	0.770224i
$389$	−15.9506	+	15.9506i	−0.808728	+	0.808728i	−0.984441	−	0.175713i	$-0.943777\pi$
$389$	−15.9506	+	15.9506i	−0.808728	+	0.808728i	0.175713	+	0.984441i	$0.443777\pi$
$390$	0.721327	−	0.672160i	0.0365258	−	0.0340362i
$391$	−8.72434			−0.441209
$392$	−2.25682	−	1.70493i	−0.113986	−	0.0861119i
$393$	7.13594	−	1.30142i	0.359960	−	0.0656478i
$394$	14.5147	−	9.29806i	0.731239	−	0.468430i
$395$	−2.94017	−	2.94017i	−0.147936	−	0.147936i
$396$	−19.8233	+	17.2070i	−0.996160	+	0.864682i
$397$	0.355551	−	0.355551i	0.0178446	−	0.0178446i	−0.698128	−	0.715973i	$-0.745983\pi$
$397$	0.355551	−	0.355551i	0.0178446	−	0.0178446i	0.715973	+	0.698128i	$0.245983\pi$
$398$	−18.6440	−	4.08431i	−0.934539	−	0.204728i
$399$	1.07241	+	5.88023i	0.0536875	+	0.294380i
$400$	−11.6207	+	9.95104i	−0.581036	+	0.497552i
$401$		−	21.6901i		−	1.08315i	−0.840652	−	0.541576i	$-0.817828\pi$
$401$		−	21.6901i		−	1.08315i	0.840652	−	0.541576i	$-0.182172\pi$
$402$	−1.02739	+	29.1180i	−0.0512414	+	1.45227i
$403$	−0.989482	−	0.989482i	−0.0492896	−	0.0492896i
$404$	19.2235	−	7.10603i	0.956404	−	0.353538i
$405$	0.622325	−	9.73676i	0.0309236	−	0.483824i
$406$	−3.54902	−	5.54018i	−0.176135	−	0.274954i
$407$			30.2299i			1.49844i
$408$	12.5033	−	4.12691i	0.619007	−	0.204312i
$409$		−	13.8029i		−	0.682508i	−0.939971	−	0.341254i	$-0.889148\pi$
$409$		−	13.8029i		−	0.682508i	0.939971	−	0.341254i	$-0.110852\pi$
$410$	14.5648	−	9.33015i	0.719303	−	0.460783i
$411$	19.3121	+	13.3545i	0.952595	+	0.658730i
$412$	−31.2861	−	14.3986i	−1.54136	−	0.709368i
$413$	2.63246	+	2.63246i	0.129535	+	0.129535i
$414$	13.6272	−	1.99162i	0.669738	−	0.0978829i
$415$		−	0.164843i		−	0.00809180i
$416$	−2.01093	−	0.606464i	−0.0985940	−	0.0297344i
$417$	0.632466	−	0.115346i	0.0309720	−	0.00564852i
$418$	−4.56906	+	20.8568i	−0.223480	+	1.02014i
$419$	−8.43616	+	8.43616i	−0.412133	+	0.412133i	−0.882481	−	0.470348i	$-0.844128\pi$
$419$	−8.43616	+	8.43616i	−0.412133	+	0.412133i	0.470348	+	0.882481i	$0.344128\pi$
$420$	3.63772	+	0.932468i	0.177503	+	0.0454998i
$421$	−5.33124	−	5.33124i	−0.259829	−	0.259829i	0.565155	−	0.824984i	$-0.308816\pi$
$421$	−5.33124	−	5.33124i	−0.259829	−	0.259829i	−0.824984	+	0.565155i	$0.808816\pi$
$422$	−9.47382	−	14.7890i	−0.461178	−	0.719919i
$423$	0.809331	+	2.14506i	0.0393510	+	0.104297i
$424$	16.4262	−	2.28824i	0.797725	−	0.111127i
$425$	−10.2797			−0.498641
$426$	−24.6589	+	22.9781i	−1.19473	+	1.11329i
$427$	−10.7072	+	10.7072i	−0.518158	+	0.518158i
$428$	−6.89377	−	18.6493i	−0.333223	−	0.901446i
$429$	2.31416	+	1.60027i	0.111729	+	0.0772616i
$430$	−0.435338	+	1.98722i	−0.0209938	+	0.0958324i
$431$	−25.7527			−1.24046			−0.620232	−	0.784419i	$-0.712961\pi$
$431$	−25.7527			−1.24046			−0.620232	+	0.784419i	$0.712961\pi$
$432$	−18.5877	+	9.30041i	−0.894301	+	0.447466i
$433$	6.76490			0.325101			0.162550	−	0.986700i	$-0.448028\pi$
$433$	6.76490			0.325101			0.162550	+	0.986700i	$0.448028\pi$
$434$	1.14055	−	5.20635i	0.0547480	−	0.249913i
$435$	7.18501	+	4.96851i	0.344495	+	0.238222i
$436$	−4.92948	+	1.82220i	−0.236079	+	0.0872676i
$437$	7.92103	−	7.92103i	0.378914	−	0.378914i
$438$	−12.1768	+	11.3468i	−0.581828	+	0.542170i
$439$	−2.54261			−0.121352			−0.0606762	−	0.998158i	$-0.519326\pi$
$439$	−2.54261			−0.121352			−0.0606762	+	0.998158i	$0.519326\pi$
$440$	10.7035	+	8.08604i	0.510270	+	0.385487i
$441$	1.05903	+	2.80686i	0.0504298	+	0.133660i
$442$	−0.761262	−	1.18836i	−0.0362095	−	0.0565246i
$443$	−24.5321	−	24.5321i	−1.16555	−	1.16555i	−0.983240	−	0.182313i	$-0.941641\pi$
$443$	−24.5321	−	24.5321i	−1.16555	−	1.16555i	−0.182313	−	0.983240i	$-0.558359\pi$
$444$	−5.94347	+	23.1865i	−0.282065	+	1.10038i
$445$	−6.90102	+	6.90102i	−0.327140	+	0.327140i
$446$	−3.22056	+	14.7012i	−0.152498	+	0.696121i
$447$	−36.1206	+	6.58750i	−1.70845	+	0.311578i
$448$	−2.18644	−	7.69542i	−0.103300	−	0.363574i
$449$		−	27.7538i		−	1.30978i	−0.755724	−	0.654891i	$-0.772715\pi$
$449$		−	27.7538i		−	1.30978i	0.755724	−	0.654891i	$-0.227285\pi$
$450$	16.0566	−	2.34669i	0.756917	−	0.110624i
$451$	34.9023	+	34.9023i	1.64349	+	1.64349i
$452$	13.1037	−	28.4724i	0.616345	−	1.33923i
$453$	18.9027	+	13.0714i	0.888126	+	0.614148i
$454$	2.96765	−	1.90107i	0.139279	−	0.0892216i
$455$		−	0.402516i		−	0.0188702i
$456$	−7.60514	+	15.0990i	−0.356143	+	0.707074i
$457$		−	25.1096i		−	1.17458i	−0.809378	−	0.587288i	$-0.800196\pi$
$457$		−	25.1096i		−	1.17458i	0.809378	−	0.587288i	$-0.199804\pi$
$458$	−2.88351	−	4.50128i	−0.134737	−	0.210331i
$459$	−13.5511	−	3.37686i	−0.632510	−	0.157618i
$460$	−2.44022	−	6.60136i	−0.113776	−	0.307790i
$461$	−1.51791	−	1.51791i	−0.0706959	−	0.0706959i	0.670875	−	0.741571i	$-0.265919\pi$
$461$	−1.51791	−	1.51791i	−0.0706959	−	0.0706959i	−0.741571	+	0.670875i	$0.765919\pi$
$462$	−0.377877	+	10.7097i	−0.0175804	+	0.498261i
$463$		−	10.9075i		−	0.506915i	−0.967347	−	0.253457i	$-0.918432\pi$
$463$		−	10.9075i		−	0.506915i	0.967347	−	0.253457i	$-0.0815678\pi$
$464$	1.43611	−	18.5540i	0.0666697	−	0.861347i
$465$	1.26963	+	6.96162i	0.0588775	+	0.322838i
$466$	1.02361	+	0.224241i	0.0474178	+	0.0103877i
$467$	26.0440	−	26.0440i	1.20517	−	1.20517i	0.232601	−	0.972572i	$-0.425276\pi$
$467$	26.0440	−	26.0440i	1.20517	−	1.20517i	0.972572	−	0.232601i	$-0.0747237\pi$
$468$	1.46035	+	1.68240i	0.0675047	+	0.0777691i
$469$	8.41087	+	8.41087i	0.388378	+	0.388378i
$470$	0.986566	−	0.631991i	0.0455069	−	0.0291516i
$471$	−19.0327	+	3.47110i	−0.876983	+	0.159940i
$472$	1.45282	+	10.4291i	0.0668717	+	0.480039i
$473$	−5.80531			−0.266928
$474$	6.87354	−	6.40502i	0.315712	−	0.294192i
$475$	9.33321	−	9.33321i	0.428237	−	0.428237i
$476$	2.24728	−	4.88301i	0.103004	−	0.223813i
$477$	−16.0287	−	7.24686i	−0.733904	−	0.331811i
$478$	−5.60490	−	1.22786i	−0.256362	−	0.0561608i
$479$	−17.6724			−0.807473			−0.403737	−	0.914875i	$-0.632289\pi$
$479$	−17.6724			−0.807473			−0.403737	+	0.914875i	$0.632289\pi$
$480$	6.61987	+	8.30646i	0.302155	+	0.379136i
$481$	2.56560			0.116981
$482$	31.0917	+	6.81120i	1.41619	+	0.310242i
$483$	3.19781	−	4.62439i	0.145506	−	0.210417i
$484$	−6.80633	+	14.7892i	−0.309379	+	0.672236i
$485$	−13.9089	+	13.9089i	−0.631571	+	0.631571i
$486$	21.9373	+	2.18106i	0.995094	+	0.0989349i
$487$	−7.46608			−0.338321			−0.169160	−	0.985589i	$-0.554106\pi$
$487$	−7.46608			−0.338321			−0.169160	+	0.985589i	$0.554106\pi$
$488$	−42.4192	+	5.90919i	−1.92023	+	0.267496i
$489$	0.970518	+	5.32155i	0.0438883	+	0.240649i
$490$	1.29094	−	0.826974i	0.0583188	−	0.0373589i
$491$	−21.8771	−	21.8771i	−0.987300	−	0.987300i	0.0126204	−	0.999920i	$-0.495983\pi$
$491$	−21.8771	−	21.8771i	−0.987300	−	0.987300i	−0.999920	+	0.0126204i	$0.995983\pi$
$492$	19.9082	+	33.6325i	0.897531	+	1.51627i
$493$	8.84165	−	8.84165i	0.398208	−	0.398208i
$494$	1.77011	+	0.387775i	0.0796410	+	0.0174468i
$495$	−5.02269	−	13.3122i	−0.225753	−	0.598340i
$496$	11.4505	−	9.80524i	0.514141	−	0.440268i
$497$			13.7602i			0.617228i
$498$	0.372235	+	0.0131338i	0.0166803	+	0.000588539i
$499$	−18.1129	−	18.1129i	−0.810843	−	0.810843i	0.173917	−	0.984760i	$-0.444357\pi$
$499$	−18.1129	−	18.1129i	−0.810843	−	0.810843i	−0.984760	+	0.173917i	$0.944357\pi$
$500$	−6.63399	−	17.9465i	−0.296681	−	0.802592i
$501$	18.2039	−	26.3248i	0.813290	−	1.17611i
$502$	20.6235	+	32.1942i	0.920472	+	1.43690i
$503$			8.65417i			0.385871i	0.981211	+	0.192935i	$0.0618007\pi$
$503$			8.65417i			0.385871i	−0.981211	+	0.192935i	$0.938199\pi$
$504$	−2.39546	+	8.14013i	−0.106702	+	0.362590i
$505$			11.1089i			0.494340i
$506$	16.9114	−	10.8334i	0.751804	−	0.481604i
$507$	−12.6709	+	18.3235i	−0.562735	+	0.813776i
$508$	0.731360	−	1.58914i	0.0324488	−	0.0705068i
$509$	0.578725	+	0.578725i	0.0256515	+	0.0256515i	0.719816	−	0.694165i	$-0.244226\pi$
$509$	0.578725	+	0.578725i	0.0256515	+	0.0256515i	−0.694165	+	0.719816i	$0.744226\pi$
$510$	−0.251657	+	7.13242i	−0.0111436	+	0.315829i
$511$			6.79488i			0.300588i
$512$	8.18573	−	21.0949i	0.361762	−	0.932271i
$513$	15.3693	−	9.23741i	0.678570	−	0.407842i
$514$	2.23975	−	10.2240i	0.0987912	−	0.450961i
$515$	13.2002	−	13.2002i	0.581670	−	0.581670i
$516$	−4.45271	−	1.14138i	−0.196020	−	0.0502464i
$517$	2.36416	+	2.36416i	0.103976	+	0.103976i
$518$	5.27106	+	8.22835i	0.231597	+	0.361533i
$519$	−0.380822	−	2.08813i	−0.0167162	−	0.0916586i
$520$	0.686260	−	0.908404i	0.0300945	−	0.0398361i
$521$	−13.3576			−0.585206			−0.292603	−	0.956234i	$-0.594522\pi$
$521$	−13.3576			−0.585206			−0.292603	+	0.956234i	$0.594522\pi$
$522$	−11.7920	+	15.8288i	−0.516121	+	0.692808i
$523$	−7.10147	+	7.10147i	−0.310526	+	0.310526i	−0.845113	−	0.534588i	$-0.820467\pi$
$523$	−7.10147	+	7.10147i	−0.310526	+	0.310526i	0.534588	+	0.845113i	$0.320467\pi$
$524$	7.85621	−	2.90408i	0.343200	−	0.126865i
$525$	3.76793	−	5.44884i	0.164446	−	0.237807i
$526$	5.02160	−	22.9225i	0.218952	−	0.999470i
$527$	10.1291			0.441231
$528$	−19.1121	+	23.5256i	−0.831747	+	1.02382i
$529$	12.4630			0.541870
$530$	−1.92370	+	8.78129i	−0.0835603	+	0.381435i
$531$	4.60110	−	10.1768i	0.199671	−	0.441635i
$532$	2.39305	+	6.47375i	0.103752	+	0.280673i
$533$	2.96215	−	2.96215i	0.128305	−	0.128305i
$534$	−15.0335	−	16.1332i	−0.650564	−	0.698152i
$535$	10.7771			0.465934
$536$	4.64187	+	33.3217i	0.200498	+	1.43928i
$537$	−29.4560	+	5.37203i	−1.27112	+	0.231820i
$538$	15.0836	+	23.5462i	0.650300	+	1.01515i
$539$	3.09355	+	3.09355i	0.133249	+	0.133249i
$540$	−1.23513	−	11.1981i	−0.0531517	−	0.481888i
$541$	14.0412	−	14.0412i	0.603678	−	0.603678i	−0.337609	−	0.941287i	$-0.609618\pi$
$541$	14.0412	−	14.0412i	0.603678	−	0.603678i	0.941287	+	0.337609i	$0.109618\pi$
$542$	2.20158	−	10.0497i	0.0945658	−	0.431672i
$543$	1.57547	+	8.63860i	0.0676097	+	0.370718i
$544$	13.3969	−	7.18862i	0.574386	−	0.308210i
$545$		−	2.84866i		−	0.122023i
$546$	0.908931	+	0.0320703i	0.0388986	+	0.00137248i
$547$	7.03679	+	7.03679i	0.300871	+	0.300871i	0.841355	−	0.540483i	$-0.181759\pi$
$547$	7.03679	+	7.03679i	0.300871	+	0.300871i	−0.540483	+	0.841355i	$0.681759\pi$
$548$	24.6290	+	11.3348i	1.05210	+	0.484200i
$549$	41.3928	+	18.7144i	1.76660	+	0.798711i
$550$	19.9264	−	12.7648i	0.849666	−	0.544293i
$551$			16.0551i			0.683970i
$552$	15.1011	−	4.98436i	0.642747	−	0.212148i
$553$		−	3.83558i		−	0.163105i
$554$	3.63562	+	5.67536i	0.154463	+	0.241123i
$555$	−10.6713	−	7.37931i	−0.452971	−	0.313234i
$556$	0.696305	−	0.257392i	0.0295299	−	0.0109158i
$557$	−15.3000	−	15.3000i	−0.648280	−	0.648280i	0.304297	−	0.952577i	$-0.401578\pi$
$557$	−15.3000	−	15.3000i	−0.648280	−	0.648280i	−0.952577	+	0.304297i	$0.901578\pi$
$558$	−15.8214	+	2.31231i	−0.669772	+	0.0978879i
$559$			0.492695i			0.0208388i
$560$	4.32335	+	0.334634i	0.182695	+	0.0141409i
$561$	−20.0356	+	3.65399i	−0.845904	+	0.154272i
$562$	−33.0686	−	7.24428i	−1.39491	−	0.305582i
$563$	18.1230	−	18.1230i	0.763793	−	0.763793i	−0.213213	−	0.977006i	$-0.568393\pi$
$563$	18.1230	−	18.1230i	0.763793	−	0.763793i	0.977006	+	0.213213i	$0.0683928\pi$
$564$	1.34851	+	2.27814i	0.0567826	+	0.0959271i
$565$	12.0131	+	12.0131i	0.505393	+	0.505393i
$566$	−28.9636	+	18.5540i	−1.21743	+	0.779883i
$567$	6.75693	−	5.94508i	0.283764	−	0.249670i
$568$	−23.4601	+	31.0542i	−0.984364	+	1.30301i
$569$	−4.23430			−0.177511			−0.0887555	−	0.996053i	$-0.528289\pi$
$569$	−4.23430			−0.177511			−0.0887555	+	0.996053i	$0.528289\pi$
$570$	−6.24721	−	6.70418i	−0.261667	−	0.280807i
$571$	−0.713850	+	0.713850i	−0.0298737	+	0.0298737i	−0.721886	−	0.692012i	$-0.756724\pi$
$571$	−0.713850	+	0.713850i	−0.0298737	+	0.0298737i	0.692012	+	0.721886i	$0.256724\pi$
$572$	2.95129	+	1.35825i	0.123399	+	0.0567913i
$573$	32.6617	+	22.5859i	1.36446	+	0.943540i
$574$	15.5859	+	3.41439i	0.650545	+	0.142514i
$575$	−12.4156			−0.517764
$576$	−19.2845	+	14.2867i	−0.803519	+	0.595279i
$577$	−11.2780			−0.469508			−0.234754	−	0.972055i	$-0.575428\pi$
$577$	−11.2780			−0.469508			−0.234754	+	0.972055i	$0.575428\pi$
$578$	−13.5058	−	2.95868i	−0.561765	−	0.123065i
$579$	−4.88823	−	3.38026i	−0.203148	−	0.140479i
$580$	9.16316	+	4.21710i	0.380479	+	0.175105i
$581$	0.107522	−	0.107522i	0.00446076	−	0.00446076i
$582$	−30.2999	−	32.5163i	−1.25597	−	1.34784i
$583$	−25.6529			−1.06244
$584$	−11.5848	+	15.3348i	−0.479382	+	0.634559i
$585$	−1.12980	+	0.426275i	−0.0467117	+	0.0176243i
$586$	19.0659	−	12.2136i	0.787606	−	0.504538i
$587$	1.93378	+	1.93378i	0.0798157	+	0.0798157i	0.745888	−	0.666072i	$-0.232026\pi$
$587$	1.93378	+	1.93378i	0.0798157	+	0.0798157i	−0.666072	+	0.745888i	$0.732026\pi$
$588$	1.76455	+	2.98100i	0.0727690	+	0.122934i
$589$	−9.19646	+	9.19646i	−0.378934	+	0.378934i
$590$	−5.57532	−	1.22138i	−0.229532	−	0.0502833i
$591$	−20.7689	+	3.78773i	−0.854319	+	0.155807i
$592$	−2.13293	+	27.5567i	−0.0876630	+	1.13257i
$593$		−	5.46475i		−	0.224410i	−0.993685	−	0.112205i	$-0.964209\pi$
$593$		−	5.46475i		−	0.224410i	0.993685	−	0.112205i	$-0.0357914\pi$
$594$	30.4608	−	10.2812i	1.24982	−	0.421844i
$595$	2.06023	+	2.06023i	0.0844614	+	0.0844614i
$596$	−39.7665	+	14.6998i	−1.62890	+	0.602129i
$597$	19.2264	+	13.2953i	0.786886	+	0.544140i
$598$	−0.919428	−	1.43527i	−0.0375982	−	0.0586925i
$599$		−	2.30973i		−	0.0943728i	−0.998886	−	0.0471864i	$-0.984975\pi$
$599$		−	2.30973i		−	0.0943728i	0.998886	−	0.0471864i	$-0.0150255\pi$
$600$	17.7934	−	5.87298i	0.726412	−	0.239763i
$601$		−	9.20218i		−	0.375365i	−0.982230	−	0.187682i	$-0.939902\pi$
$601$		−	9.20218i		−	0.375365i	0.982230	−	0.187682i	$-0.0600975\pi$
$602$	−1.58016	+	1.01225i	−0.0644027	+	0.0412562i
$603$	14.7008	−	32.5155i	0.598663	−	1.32413i
$604$	24.1069	+	11.0945i	0.980895	+	0.451431i
$605$	−6.23984	−	6.23984i	−0.253685	−	0.253685i
$606$	−25.0853	−	0.885100i	−1.01902	−	0.0359547i
$607$		−	17.5119i		−	0.710784i	−0.934717	−	0.355392i	$-0.884347\pi$
$607$		−	17.5119i		−	0.710784i	0.934717	−	0.355392i	$-0.115653\pi$
$608$	−5.63661	+	18.6900i	−0.228595	+	0.757982i
$609$	1.44576	+	7.92738i	0.0585850	+	0.321234i
$610$	4.96780	−	22.6769i	0.201140	−	0.918163i
$611$	0.200646	−	0.200646i	0.00811725	−	0.00811725i
$612$	−16.0859	−	1.13655i	−0.650232	−	0.0459422i
$613$	12.0484	+	12.0484i	0.486629	+	0.486629i	0.907241	−	0.420611i	$-0.138184\pi$
$613$	12.0484	+	12.0484i	0.486629	+	0.486629i	−0.420611	+	0.907241i	$0.638184\pi$
$614$	20.5098	+	32.0167i	0.827708	+	1.29209i
$615$	−20.8406	+	3.80080i	−0.840374	+	0.153263i
$616$	1.70730	+	12.2559i	0.0687890	+	0.493803i
$617$	−17.2962			−0.696320			−0.348160	−	0.937435i	$-0.613193\pi$
$617$	−17.2962			−0.696320			−0.348160	+	0.937435i	$0.613193\pi$
$618$	28.7560	+	30.8594i	1.15674	+	1.24135i
$619$	−8.03863	+	8.03863i	−0.323100	+	0.323100i	−0.849955	−	0.526855i	$-0.823371\pi$
$619$	−8.03863	+	8.03863i	−0.323100	+	0.323100i	0.526855	+	0.849955i	$0.323371\pi$
$620$	2.83314	+	7.66430i	0.113782	+	0.307806i
$621$	−16.3666	−	4.07847i	−0.656768	−	0.163663i
$622$	8.70477	−	39.7354i	0.349030	−	1.59325i
$623$	−9.00266			−0.360684
$624$	1.99661	+	1.62204i	0.0799285	+	0.0649335i
$625$	−8.75299			−0.350120
$626$	6.06189	−	27.6712i	0.242282	−	1.10597i
$627$	14.8732	−	21.5083i	0.593980	−	0.858960i
$628$	−20.9538	+	7.74566i	−0.836149	+	0.309086i
$629$	−13.1318	+	13.1318i	−0.523598	+	0.523598i
$630$	−3.68834	−	2.74771i	−0.146947	−	0.109471i
$631$	32.3346			1.28722			0.643610	−	0.765353i	$-0.277436\pi$
$631$	32.3346			1.28722			0.643610	+	0.765353i	$0.277436\pi$
$632$	6.53938	−	8.65619i	0.260123	−	0.344325i
$633$	3.85933	+	21.1615i	0.153395	+	0.841094i
$634$	−24.3047	−	37.9407i	−0.965264	−	1.50682i
$635$	0.670489	+	0.670489i	0.0266075	+	0.0266075i
$636$	−19.6760	−	5.04361i	−0.780203	−	0.199992i
$637$	0.262549	−	0.262549i	0.0104026	−	0.0104026i
$638$	−6.15974	+	28.1179i	−0.243866	+	1.11320i
$639$	38.6229	−	14.5724i	1.52790	−	0.576475i
$640$	9.18648	+	8.12621i	0.363127	+	0.321217i
$641$			26.9406i			1.06409i	0.846717	+	0.532044i	$0.178576\pi$
$641$			26.9406i			1.06409i	−0.846717	+	0.532044i	$0.821424\pi$
$642$	−0.858661	+	24.3360i	−0.0338887	+	0.960465i
$643$	−2.08209	−	2.08209i	−0.0821098	−	0.0821098i	0.664859	−	0.746969i	$-0.268492\pi$
$643$	−2.08209	−	2.08209i	−0.0821098	−	0.0821098i	−0.746969	+	0.664859i	$0.768492\pi$
$644$	2.71419	−	5.89755i	0.106954	−	0.232396i
$645$	1.41712	−	2.04930i	0.0557989	−	0.0806912i
$646$	−11.0449	+	7.07534i	−0.434556	+	0.278375i
$647$			0.704788i			0.0277081i	0.999904	+	0.0138540i	$0.00441002\pi$
$647$			0.704788i			0.0277081i	−0.999904	+	0.0138540i	$0.995590\pi$
$648$	25.3851	−	1.89688i	0.997220	−	0.0745166i
$649$		−	16.2873i		−	0.639332i
$650$	−1.08335	−	1.69115i	−0.0424923	−	0.0663324i
$651$	−3.71272	+	5.36900i	−0.145513	+	0.210428i
$652$	2.16569	+	5.85869i	0.0848148	+	0.229444i
$653$	28.0029	+	28.0029i	1.09584	+	1.09584i	0.994892	+	0.100947i	$0.0321872\pi$
$653$	28.0029	+	28.0029i	1.09584	+	1.09584i	0.100947	+	0.994892i	$0.467813\pi$
$654$	6.43264	+	0.226966i	0.251536	+	0.00887509i
$655$			4.53997i			0.177391i
$656$	29.3533	+	34.2786i	1.14606	+	1.33835i
$657$	19.0723	−	7.19596i	0.744081	−	0.280741i
$658$	1.05574	+	0.231278i	0.0411569	+	0.00901617i
$659$	7.83856	−	7.83856i	0.305347	−	0.305347i	−0.537755	−	0.843101i	$-0.680727\pi$
$659$	7.83856	−	7.83856i	0.305347	−	0.305347i	0.843101	+	0.537755i	$0.180727\pi$
$660$	−8.36883	−	14.1381i	−0.325756	−	0.550325i
$661$	−26.4193	−	26.4193i	−1.02759	−	1.02759i	−0.999608	−	0.0279814i	$-0.991092\pi$
$661$	−26.4193	−	26.4193i	−1.02759	−	1.02759i	−0.0279814	−	0.999608i	$-0.508908\pi$
$662$	18.4682	−	11.8307i	0.717788	−	0.459813i
$663$	0.310114	+	1.70042i	0.0120438	+	0.0660387i
$664$	0.425974	−	0.0593401i	0.0165310	−	0.00230284i
$665$	−3.74107			−0.145072
$666$	17.5136	−	23.5092i	0.678640	−	0.910962i
$667$	10.6787	−	10.6787i	0.413480	−	0.413480i
$668$	15.4508	−	33.5725i	0.597810	−	1.29896i
$669$	10.4836	−	15.1604i	0.405319	−	0.586136i
$670$	−17.8135	−	3.90238i	−0.688196	−	0.150762i
$671$	66.2466			2.55742
$672$	−1.10011	+	9.73600i	−0.0424376	+	0.375574i
$673$	32.2415			1.24282			0.621410	−	0.783486i	$-0.286560\pi$
$673$	32.2415			1.24282			0.621410	+	0.783486i	$0.286560\pi$
$674$	44.1276	+	9.66696i	1.69973	+	0.372357i
$675$	−19.2845	−	4.80558i	−0.742259	−	0.184967i
$676$	−10.7546	+	23.3683i	−0.413639	+	0.898780i
$677$	32.8347	−	32.8347i	1.26194	−	1.26194i	0.311789	−	0.950151i	$-0.399072\pi$
$677$	32.8347	−	32.8347i	1.26194	−	1.26194i	0.950151	−	0.311789i	$-0.100928\pi$
$678$	−28.0841	+	26.1698i	−1.07856	+	1.00505i
$679$	−18.1447			−0.696331
$680$	1.13702	+	8.16212i	0.0436028	+	0.313003i
$681$	−4.24638	+	0.774435i	−0.162722	+	0.0296764i
$682$	−19.6345	+	12.5778i	−0.751842	+	0.481628i
$683$	−15.6297	−	15.6297i	−0.598056	−	0.598056i	0.341739	−	0.939795i	$-0.388984\pi$
$683$	−15.6297	−	15.6297i	−0.598056	−	0.598056i	−0.939795	+	0.341739i	$0.888984\pi$
$684$	15.6366	−	13.5728i	0.597881	−	0.518970i
$685$	−10.3914	+	10.3914i	−0.397036	+	0.397036i
$686$	1.38145	+	0.302633i	0.0527441	+	0.0115546i
$687$	1.17465	+	6.44084i	0.0448156	+	0.245733i
$688$	−5.29195	−	0.409606i	−0.201754	−	0.0156161i
$689$			2.17716i			0.0829431i
$690$	−0.303944	+	8.61432i	−0.0115710	+	0.327942i
$691$	−16.0088	−	16.0088i	−0.609003	−	0.609003i	0.333682	−	0.942686i	$-0.391709\pi$
$691$	−16.0088	−	16.0088i	−0.609003	−	0.609003i	−0.942686	+	0.333682i	$0.891709\pi$
$692$	−0.849794	−	2.29889i	−0.0323043	−	0.0873908i
$693$	5.40701	−	11.9593i	0.205395	−	0.454297i
$694$	−19.2452	−	30.0427i	−0.730540	−	1.14040i
$695$			0.402383i			0.0152632i
$696$	−10.2528	+	20.3556i	−0.388632	+	0.771576i
$697$			30.3229i			1.14856i
$698$	−31.9523	+	20.4686i	−1.20941	+	0.774747i
$699$	−1.05559	−	0.729950i	−0.0399260	−	0.0276093i
$700$	3.19808	−	6.94899i	0.120876	−	0.262647i
$701$	6.13145	+	6.13145i	0.231582	+	0.231582i	0.813353	−	0.581771i	$-0.197640\pi$
$701$	6.13145	+	6.13145i	0.231582	+	0.231582i	−0.581771	+	0.813353i	$0.697640\pi$
$702$	−0.872565	−	2.58520i	−0.0329328	−	0.0975723i
$703$		−	23.8453i		−	0.899341i
$704$	−17.0423	+	30.5700i	−0.642306	+	1.15215i
$705$	−1.41167	+	0.257453i	−0.0531665	+	0.00969624i
$706$	6.99746	−	31.9419i	0.263353	−	1.20215i
$707$	−7.24602	+	7.24602i	−0.272515	+	0.272515i
$708$	3.20223	−	12.4925i	0.120347	−	0.469496i
$709$	−28.7473	−	28.7473i	−1.07963	−	1.07963i	−0.996542	−	0.0830852i	$-0.973523\pi$
$709$	−28.7473	−	28.7473i	−1.07963	−	1.07963i	−0.0830852	−	0.996542i	$-0.526477\pi$
$710$	−11.3793	−	17.7636i	−0.427058	−	0.666656i
$711$	−10.7659	+	4.06198i	−0.403754	+	0.152336i
$712$	−20.3173	−	15.3489i	−0.761425	−	0.575223i
$713$	12.2336			0.458153
$714$	−4.81642	+	4.48812i	−0.180250	+	0.167964i
$715$	−1.24520	+	1.24520i	−0.0465679	+	0.0465679i
$716$	−32.4291	+	11.9875i	−1.21193	+	0.447996i
$717$	5.77999	+	3.99693i	0.215858	+	0.149268i
$718$	9.23430	−	42.1526i	0.344621	−	1.57312i
$719$	−37.8458			−1.41141			−0.705706	−	0.708505i	$-0.749370\pi$
$719$	−37.8458			−1.41141			−0.705706	+	0.708505i	$0.749370\pi$
$720$	−3.63927	−	12.4894i	−0.135628	−	0.465453i
$721$	17.2202			0.641314
$722$	−2.14596	+	9.79583i	−0.0798642	+	0.364563i
$723$	−32.0630	−	22.1719i	−1.19243	−	0.824581i
$724$	3.51561	+	9.51055i	0.130657	+	0.353457i
$725$	12.5825	−	12.5825i	0.467302	−	0.467302i
$726$	14.5875	−	13.5932i	0.541393	−	0.504490i
$727$	−26.7204			−0.991005			−0.495503	−	0.868606i	$-0.665016\pi$
$727$	−26.7204			−0.991005			−0.495503	+	0.868606i	$0.665016\pi$
$728$	1.04015	−	0.144898i	0.0385506	−	0.00537027i
$729$	−23.8428	−	12.6697i	−0.883065	−	0.469250i
$730$	−5.61919	−	8.77180i	−0.207976	−	0.324659i
$731$	−2.52181	−	2.52181i	−0.0932725	−	0.0932725i
$732$	50.8116	+	13.0247i	1.87805	+	0.481407i
$733$	−19.2237	+	19.2237i	−0.710045	+	0.710045i	−0.966544	−	0.256500i	$-0.917431\pi$
$733$	−19.2237	+	19.2237i	−0.710045	+	0.710045i	0.256500	+	0.966544i	$0.417431\pi$
$734$	7.27220	−	33.1960i	0.268422	−	1.22529i
$735$	−1.84720	+	0.336883i	−0.0681349	+	0.0124261i
$736$	16.1803	−	8.68220i	0.596415	−	0.320030i
$737$		−	52.0389i		−	1.91688i
$738$	−6.92222	−	47.3635i	−0.254811	−	1.74347i
$739$	2.40651	+	2.40651i	0.0885250	+	0.0885250i	0.749983	−	0.661458i	$-0.230062\pi$
$739$	2.40651	+	2.40651i	0.0885250	+	0.0885250i	−0.661458	+	0.749983i	$0.730062\pi$
$740$	−13.6093	−	6.26330i	−0.500286	−	0.230243i
$741$	−1.82541	−	1.26229i	−0.0670580	−	0.0463713i
$742$	−6.98255	+	4.47300i	−0.256337	+	0.164209i
$743$			2.79821i			0.102656i	0.998682	+	0.0513282i	$0.0163455\pi$
$743$			2.79821i			0.102656i	−0.998682	+	0.0513282i	$0.983655\pi$
$744$	−17.5327	+	5.78693i	−0.642779	+	0.212159i
$745$		−	22.9804i		−	0.841936i
$746$	1.56152	+	2.43760i	0.0571714	+	0.0892470i
$747$	−0.415667	−	0.187930i	−0.0152085	−	0.00687601i
$748$	−22.0579	+	8.15379i	−0.806517	+	0.298132i
$749$	7.02957	+	7.02957i	0.256855	+	0.256855i
$750$	−0.826304	+	23.4189i	−0.0301724	+	0.855139i
$751$			51.0005i			1.86104i	0.366246	+	0.930518i	$0.380643\pi$
$751$			51.0005i			1.86104i	−0.366246	+	0.930518i	$0.619357\pi$
$752$	1.98829	+	2.32191i	0.0725055	+	0.0846712i
$753$	−8.40135	−	46.0663i	−0.306162	−	1.67875i
$754$	2.38636	+	0.522776i	0.0869061	+	0.0190384i
$755$	−10.1711	+	10.1711i	−0.370166	+	0.370166i
$756$	6.49853	−	8.10981i	0.236349	−	0.294951i
$757$	−6.19243	−	6.19243i	−0.225068	−	0.225068i	0.585561	−	0.810629i	$-0.300874\pi$
$757$	−6.19243	−	6.19243i	−0.225068	−	0.225068i	−0.810629	+	0.585561i	$0.800874\pi$
$758$	−29.2242	+	18.7209i	−1.06147	+	0.679975i
$759$	−24.1984	+	4.41318i	−0.878346	+	0.160188i
$760$	−8.44291	−	6.37825i	−0.306256	−	0.231364i
$761$	−11.4162			−0.413837			−0.206919	−	0.978358i	$-0.566344\pi$
$761$	−11.4162			−0.413837			−0.206919	+	0.978358i	$0.566344\pi$
$762$	−1.56747	+	1.46063i	−0.0567834	+	0.0529129i
$763$	1.85810	−	1.85810i	0.0672677	−	0.0672677i
$764$	41.6540	+	19.1701i	1.50699	+	0.693551i
$765$	3.60095	−	7.96463i	0.130193	−	0.287962i
$766$	−4.54592	−	0.995867i	−0.164251	−	0.0359821i
$767$	−1.38230			−0.0499119
$768$	−19.0819	+	20.0968i	−0.688560	+	0.725180i
$769$	−3.36949			−0.121507			−0.0607535	−	0.998153i	$-0.519350\pi$
$769$	−3.36949			−0.121507			−0.0607535	+	0.998153i	$0.519350\pi$
$770$	−6.55188	−	1.43531i	−0.236113	−	0.0517250i
$771$	−7.29086	+	10.5434i	−0.262574	+	0.379711i
$772$	−6.23403	−	2.86905i	−0.224368	−	0.103259i
$773$	11.1451	−	11.1451i	0.400860	−	0.400860i	−0.477676	−	0.878536i	$-0.658521\pi$
$773$	11.1451	−	11.1451i	0.400860	−	0.400860i	0.878536	+	0.477676i	$0.158521\pi$
$774$	4.51468	+	3.36330i	0.162277	+	0.120891i
$775$	14.4147			0.517791
$776$	−40.9493	−	30.9355i	−1.47000	−	1.11052i
$777$	−2.14726	−	11.7739i	−0.0770326	−	0.422385i
$778$	26.8622	−	17.2079i	0.963057	−	0.616932i
$779$	−27.5309	−	27.5309i	−0.986397	−	0.986397i
$780$	−1.19990	+	0.710261i	−0.0429632	+	0.0254314i
$781$	42.5678	−	42.5678i	1.52320	−	1.52320i
$782$	12.0523	+	2.64027i	0.430988	+	0.0944159i
$783$	20.7200	−	12.4533i	0.740471	−	0.445046i
$784$	2.60172	+	3.03826i	0.0929186	+	0.108509i
$785$		−	12.1089i		−	0.432184i
$786$	−10.2518	−	0.361721i	−0.365670	−	0.0129022i
$787$	7.85840	+	7.85840i	0.280122	+	0.280122i	0.833158	−	0.553036i	$-0.186531\pi$
$787$	7.85840	+	7.85840i	0.280122	+	0.280122i	−0.553036	+	0.833158i	$0.686531\pi$
$788$	−22.8653	+	8.45222i	−0.814541	+	0.301098i
$789$	−16.3464	+	23.6386i	−0.581946	+	0.841557i
$790$	3.17192	+	4.95150i	0.112852	+	0.176167i
$791$			15.6715i			0.557215i
$792$	32.5924	−	17.7714i	1.15812	−	0.631480i
$793$		−	5.62233i		−	0.199655i
$794$	−0.598778	+	0.383575i	−0.0212498	+	0.0136126i
$795$	6.26205	−	9.05561i	0.222092	−	0.321170i
$796$	24.5198	+	11.2846i	0.869080	+	0.399971i
$797$	24.9703	+	24.9703i	0.884494	+	0.884494i	0.993987	−	0.109494i	$-0.0349230\pi$
$797$	24.9703	+	24.9703i	0.884494	+	0.884494i	−0.109494	+	0.993987i	$0.534923\pi$
$798$	0.298069	−	8.44781i	0.0105515	−	0.299049i
$799$			2.05397i			0.0726642i
$800$	19.0650	−	10.2301i	0.674050	−	0.361688i
$801$	9.53405	+	25.2692i	0.336869	+	0.892843i
$802$	−6.56414	+	29.9639i	−0.231788	+	1.05806i
$803$	21.0203	−	21.0203i	0.741791	−	0.741791i
$804$	10.2313	−	39.9142i	0.360832	−	1.40767i
$805$	2.48829	+	2.48829i	0.0877006	+	0.0877006i
$806$	1.06747	+	1.66637i	0.0376001	+	0.0586955i
$807$	−6.14458	−	33.6920i	−0.216299	−	1.18601i
$808$	−28.7069	+	3.99900i	−1.00990	+	0.140684i
$809$	−16.3328			−0.574232			−0.287116	−	0.957896i	$-0.592697\pi$
$809$	−16.3328			−0.574232			−0.287116	+	0.957896i	$0.592697\pi$
$810$	−3.80638	+	13.2625i	−0.133742	+	0.465998i
$811$	−21.0730	+	21.0730i	−0.739973	+	0.739973i	−0.972573	−	0.232599i	$-0.925277\pi$
$811$	−21.0730	+	21.0730i	−0.739973	+	0.739973i	0.232599	+	0.972573i	$0.425277\pi$
$812$	3.22617	+	8.72754i	0.113216	+	0.306277i
$813$	−7.16659	+	10.3637i	−0.251343	+	0.363470i
$814$	9.14854	−	41.7611i	0.320656	−	1.46373i
$815$	−3.38563			−0.118594
$816$	−18.5217	+	1.91722i	−0.648389	+	0.0671162i
$817$	4.57922			0.160207
$818$	−4.17720	+	19.0680i	−0.146052	+	0.666698i
$819$	−1.01498	−	0.458892i	−0.0354664	−	0.0160350i
$820$	−22.9442	+	8.48139i	−0.801245	+	0.296183i
$821$	−32.3716	+	32.3716i	−1.12978	+	1.12978i	−0.139565	+	0.990213i	$0.544570\pi$
$821$	−32.3716	+	32.3716i	−1.12978	+	1.12978i	−0.990213	+	0.139565i	$0.955430\pi$
$822$	−22.6372	−	24.2931i	−0.789564	−	0.847319i
$823$	15.8594			0.552824			0.276412	−	0.961039i	$-0.410854\pi$
$823$	15.8594			0.552824			0.276412	+	0.961039i	$0.410854\pi$
$824$	38.8628	+	29.3592i	1.35385	+	1.02278i
$825$	−28.5125	+	5.19998i	−0.992679	+	0.181040i
$826$	−2.83995	−	4.43329i	−0.0988145	−	0.154254i
$827$	11.4655	+	11.4655i	0.398693	+	0.398693i	0.877772	−	0.479079i	$-0.159029\pi$
$827$	11.4655	+	11.4655i	0.398693	+	0.398693i	−0.479079	+	0.877772i	$0.659029\pi$
$828$	−19.4280	−	1.37269i	−0.675170	−	0.0477042i
$829$	−14.1050	+	14.1050i	−0.489888	+	0.489888i	−0.908271	−	0.418383i	$-0.862597\pi$
$829$	−14.1050	+	14.1050i	−0.489888	+	0.489888i	0.418383	+	0.908271i	$0.362597\pi$
$830$	−0.0498867	+	0.227722i	−0.00173159	+	0.00790435i
$831$	−1.48103	−	8.12081i	−0.0513765	−	0.281708i
$832$	2.59447	+	1.44638i	0.0899472	+	0.0501441i
$833$			2.68766i			0.0931219i
$834$	−0.908630	−	0.0320597i	−0.0314633	−	0.00111014i
$835$	14.1649	+	14.1649i	0.490195	+	0.490195i
$836$	12.6239	−	27.4299i	0.436606	−	0.948683i
$837$	19.0019	+	4.73517i	0.656802	+	0.163672i
$838$	14.2072	−	9.10110i	0.490780	−	0.314392i
$839$			9.65631i			0.333373i	0.986010	+	0.166686i	$0.0533067\pi$
$839$			9.65631i			0.333373i	−0.986010	+	0.166686i	$0.946693\pi$
$840$	−4.74314	−	2.38905i	−0.163654	−	0.0824302i
$841$		−	7.35545i		−	0.253636i
$842$	5.75146	+	8.97827i	0.198208	+	0.309412i
$843$	34.1017	+	23.5817i	1.17452	+	0.812195i
$844$	8.61199	+	23.2975i	0.296437	+	0.801932i
$845$	−9.85951	−	9.85951i	−0.339178	−	0.339178i
$846$	−0.468887	−	3.20823i	−0.0161207	−	0.110301i
$847$		−	8.14012i		−	0.279698i
$848$	−23.3845	−	1.81000i	−0.803026	−	0.0621556i
$849$	41.4437	−	7.55830i	1.42235	−	0.259400i
$850$	14.2010	+	3.11099i	0.487090	+	0.106706i
$851$	−15.8601	+	15.8601i	−0.543679	+	0.543679i
$852$	41.0191	−	24.2806i	1.40529	−	0.831839i
$853$	21.2847	+	21.2847i	0.728773	+	0.728773i	0.970375	−	0.241602i	$-0.0776729\pi$
$853$	21.2847	+	21.2847i	0.728773	+	0.728773i	−0.241602	+	0.970375i	$0.577673\pi$
$854$	18.0319	−	11.5512i	0.617037	−	0.395272i
$855$	3.96189	+	10.5007i	0.135494	+	0.359115i
$856$	3.87954	+	27.8494i	0.132600	+	0.951872i
$857$	4.52066			0.154423			0.0772115	−	0.997015i	$-0.475398\pi$
$857$	4.52066			0.154423			0.0772115	+	0.997015i	$0.475398\pi$
$858$	−2.71261	−	2.91103i	−0.0926071	−	0.0993811i
$859$	13.1351	−	13.1351i	0.448164	−	0.448164i	−0.446579	−	0.894744i	$-0.647358\pi$
$859$	13.1351	−	13.1351i	0.448164	−	0.448164i	0.894744	+	0.446579i	$0.147358\pi$
$860$	1.20280	−	2.61351i	0.0410150	−	0.0891199i
$861$	−16.0728	−	11.1145i	−0.547761	−	0.378783i
$862$	35.5761	+	7.79361i	1.21173	+	0.265451i
$863$	9.02247			0.307128			0.153564	−	0.988139i	$-0.450925\pi$
$863$	9.02247			0.307128			0.153564	+	0.988139i	$0.450925\pi$
$864$	28.4926	−	7.22284i	0.969339	−	0.245726i
$865$	1.32849			0.0451700
$866$	−9.34540	−	2.04728i	−0.317570	−	0.0695694i
$867$	13.9277	+	9.63114i	0.473009	+	0.327091i
$868$	−3.15123	+	6.84717i	−0.106960	+	0.232408i
$869$	−11.8655	+	11.8655i	−0.402511	+	0.402511i
$870$	−8.42213	−	9.03819i	−0.285537	−	0.306423i
$871$	−4.41653			−0.149648
$872$	7.36131	−	1.02546i	0.249285	−	0.0347266i
$873$	19.2158	+	50.9297i	0.650355	+	1.72371i
$874$	−13.3397	+	8.54537i	−0.451222	+	0.289052i
$875$	6.76467	+	6.76467i	0.228688	+	0.228688i
$876$	20.2555	−	11.9899i	0.684371	−	0.405103i
$877$	2.14142	−	2.14142i	0.0723106	−	0.0723106i	−0.670027	−	0.742337i	$-0.733717\pi$
$877$	2.14142	−	2.14142i	0.0723106	−	0.0723106i	0.742337	+	0.670027i	$0.233717\pi$
$878$	3.51250	+	0.769478i	0.118541	+	0.0259686i
$879$	−27.2813	+	4.97542i	−0.920174	+	0.167817i
$880$	−12.3393	−	14.4097i	−0.415958	−	0.485751i
$881$			12.6375i			0.425768i	0.977077	+	0.212884i	$0.0682856\pi$
$881$			12.6375i			0.425768i	−0.977077	+	0.212884i	$0.931714\pi$
$882$	−0.613548	−	4.19804i	−0.0206592	−	0.141355i
$883$	−23.7761	−	23.7761i	−0.800128	−	0.800128i	0.182987	−	0.983115i	$-0.441423\pi$
$883$	−23.7761	−	23.7761i	−0.800128	−	0.800128i	−0.983115	+	0.182987i	$0.941423\pi$
$884$	0.692010	+	1.87205i	0.0232748	+	0.0629639i
$885$	5.74950	+	3.97584i	0.193267	+	0.133646i
$886$	26.4657	+	41.3141i	0.889133	+	1.38798i
$887$		−	47.8477i		−	1.60657i	−0.595596	−	0.803284i	$-0.703084\pi$
$887$		−	47.8477i		−	1.60657i	0.595596	−	0.803284i	$-0.296916\pi$
$888$	15.2276	−	30.2324i	0.511006	−	1.01453i
$889$			0.874680i			0.0293358i
$890$	11.6219	−	7.44496i	0.389567	−	0.249556i
$891$	−39.2943	−	2.51149i	−1.31641	−	0.0841382i
$892$	8.89811	−	19.3343i	0.297931	−	0.647361i
$893$	−1.86484	−	1.86484i	−0.0624047	−	0.0624047i
$894$	51.8926	+	1.83096i	1.73555	+	0.0612363i
$895$		−	18.7402i		−	0.626417i
$896$	0.691584	+	11.2926i	0.0231042	+	0.377258i
$897$	0.374546	+	2.05371i	0.0125057	+	0.0685714i
$898$	−8.39919	+	38.3405i	−0.280285	+	1.27944i
$899$	−12.3981	+	12.3981i	−0.413501	+	0.413501i
$900$	−22.8917	−	1.61741i	−0.763056	−	0.0539138i
$901$	−11.1436	−	11.1436i	−0.371246	−	0.371246i
$902$	−37.6533	−	58.7785i	−1.25372	−	1.95711i
$903$	2.26104	−	0.412358i	0.0752428	−	0.0137224i
$904$	−26.7188	+	35.3677i	−0.888654	+	1.17631i
$905$	−5.49598			−0.182693
$906$	−22.1573	−	23.7781i	−0.736129	−	0.789975i
$907$	−25.2932	+	25.2932i	−0.839848	+	0.839848i	−0.988839	−	0.148991i	$-0.952398\pi$
$907$	−25.2932	+	25.2932i	−0.839848	+	0.839848i	0.148991	+	0.988839i	$0.452398\pi$
$908$	−4.67500	+	1.72813i	−0.155145	+	0.0573500i
$909$	28.0123	+	12.6648i	0.929109	+	0.420066i
$910$	−0.121814	+	0.556056i	−0.00403811	+	0.0184331i
$911$	37.1786			1.23178			0.615892	−	0.787831i	$-0.288796\pi$
$911$	37.1786			1.23178			0.615892	+	0.787831i	$0.288796\pi$
$912$	15.0756	−	18.5570i	0.499202	−	0.614482i
$913$	−0.665249			−0.0220165
$914$	−7.59897	+	34.6877i	−0.251352	+	1.14737i
$915$	−16.1712	+	23.3854i	−0.534605	+	0.773097i
$916$	2.62120	+	7.09095i	0.0866068	+	0.234292i
$917$	−2.96129	+	2.96129i	−0.0977903	+	0.0977903i
$918$	17.6982	+	8.76597i	0.584129	+	0.289320i
$919$	40.7166			1.34312			0.671558	−	0.740952i	$-0.265625\pi$
$919$	40.7166			1.34312			0.671558	+	0.740952i	$0.265625\pi$
$920$	1.37326	+	9.85796i	0.0452750	+	0.325007i
$921$	−8.35503	−	45.8124i	−0.275308	−	1.50957i
$922$	1.63755	+	2.55628i	0.0539298	+	0.0841867i
$923$	−3.61272	−	3.61272i	−0.118914	−	0.118914i
$924$	3.76313	−	14.6806i	0.123798	−	0.482957i
$925$	−18.6877	+	18.6877i	−0.614449	+	0.614449i
$926$	−3.30097	+	15.0682i	−0.108477	+	0.495172i
$927$	−18.2366	−	48.3347i	−0.598970	−	1.58752i
$928$	−7.59896	+	25.1969i	−0.249448	+	0.827127i
$929$		−	20.4674i		−	0.671513i	−0.941949	−	0.335756i	$-0.891008\pi$
$929$		−	20.4674i		−	0.671513i	0.941949	−	0.335756i	$-0.108992\pi$
$930$	0.352885	−	10.0014i	0.0115715	−	0.327958i
$931$	−2.44019	−	2.44019i	−0.0799740	−	0.0799740i
$932$	−1.34621	−	0.619556i	−0.0440965	−	0.0202942i
$933$	−28.3359	+	40.9768i	−0.927674	+	1.34152i
$934$	−43.8604	+	28.0968i	−1.43516	+	0.919356i
$935$		−	12.7469i		−	0.416868i
$936$	−1.50826	−	2.76611i	−0.0492989	−	0.0904131i
$937$			15.4186i			0.503704i	0.967766	+	0.251852i	$0.0810396\pi$
$937$			15.4186i			0.503704i	−0.967766	+	0.251852i	$0.918960\pi$
$938$	−9.07382	−	14.1646i	−0.296271	−	0.462492i
$939$	−19.7327	+	28.5357i	−0.643954	+	0.931227i
$940$	−1.55416	+	0.574499i	−0.0506910	+	0.0187381i
$941$	21.0694	+	21.0694i	0.686844	+	0.686844i	0.961533	−	0.274689i	$-0.0885749\pi$
$941$	21.0694	+	21.0694i	0.686844	+	0.686844i	−0.274689	+	0.961533i	$0.588575\pi$
$942$	27.3433	+	0.964770i	0.890893	+	0.0314339i
$943$			36.6231i			1.19261i
$944$	1.14918	−	14.8470i	0.0374028	−	0.483229i
$945$	2.90181	+	4.82805i	0.0943960	+	0.157057i
$946$	8.01976	+	1.75688i	0.260745	+	0.0571210i
$947$	2.08628	−	2.08628i	0.0677949	−	0.0677949i	−0.672396	−	0.740191i	$-0.734735\pi$
$947$	2.08628	−	2.08628i	0.0677949	−	0.0677949i	0.740191	+	0.672396i	$0.234735\pi$
$948$	−11.4338	+	6.76808i	−0.371354	+	0.219817i
$949$	−1.78399	−	1.78399i	−0.0579108	−	0.0579108i
$950$	−15.7179	+	10.0689i	−0.509957	+	0.326677i
$951$	9.90096	+	54.2890i	0.321061	+	1.76044i
$952$	−4.58227	+	6.06556i	−0.148512	+	0.196586i
$953$	−9.74445			−0.315654			−0.157827	−	0.987467i	$-0.550449\pi$
$953$	−9.74445			−0.315654			−0.157827	+	0.987467i	$0.550449\pi$
$954$	19.9498	+	14.8620i	0.645898	+	0.481175i
$955$	−17.5746	+	17.5746i	−0.568700	+	0.568700i
$956$	7.37131	+	3.39245i	0.238405	+	0.109720i
$957$	20.0512	−	28.9963i	0.648165	−	0.937317i
$958$	24.4136	+	5.34825i	0.788768	+	0.172794i
$959$	−13.5561			−0.437748
$960$	−6.63124	−	13.4784i	−0.214022	−	0.435013i
$961$	16.7965			0.541823
$962$	−3.54426	−	0.776434i	−0.114271	−	0.0250332i
$963$	12.2865	−	27.1755i	0.395928	−	0.875719i
$964$	−40.8904	−	18.8187i	−1.31699	−	0.606110i
$965$	2.63026	−	2.63026i	0.0846709	−	0.0846709i
$966$	−5.81712	+	5.42061i	−0.187163	+	0.174405i
$967$	−18.2255			−0.586091			−0.293046	−	0.956098i	$-0.594669\pi$
$967$	−18.2255			−0.586091			−0.293046	+	0.956098i	$0.594669\pi$
$968$	13.8783	−	18.3708i	0.446066	−	0.590459i
$969$	15.8041	−	2.88226i	0.507699	−	0.0925917i
$970$	23.4238	−	15.0052i	0.752093	−	0.481789i
$971$	2.70601	+	2.70601i	0.0868399	+	0.0868399i	0.749192	−	0.662352i	$-0.230442\pi$
$971$	2.70601	+	2.70601i	0.0868399	+	0.0868399i	−0.662352	+	0.749192i	$0.730442\pi$
$972$	−29.6452	−	9.65196i	−0.950871	−	0.309587i
$973$	−0.262462	+	0.262462i	−0.00841415	+	0.00841415i
$974$	10.3140	+	2.25948i	0.330483	+	0.0723984i
$975$	0.441321	+	2.41985i	0.0141336	+	0.0774973i
$976$	60.3885	+	4.67417i	1.93299	+	0.149616i
$977$			4.09093i			0.130880i	0.997856	+	0.0654402i	$0.0208452\pi$
$977$			4.09093i			0.130880i	−0.997856	+	0.0654402i	$0.979155\pi$
$978$	0.269749	−	7.64518i	0.00862564	−	0.244466i
$979$	27.8502	+	27.8502i	0.890096	+	0.890096i
$980$	−2.03365	+	0.751744i	−0.0649624	+	0.0240136i
$981$	−7.18319	−	3.24765i	−0.229342	−	0.103689i
$982$	23.6015	+	36.8429i	0.753153	+	1.17571i
$983$		−	37.9997i		−	1.21200i	−0.795464	−	0.606001i	$-0.792773\pi$
$983$		−	37.9997i		−	1.21200i	0.795464	−	0.606001i	$-0.207227\pi$
$984$	−17.3240	−	52.4865i	−0.552268	−	1.67321i
$985$		−	13.2134i		−	0.421015i
$986$	−14.8901	+	9.53856i	−0.474198	+	0.303770i
$987$	−1.08872	−	0.752860i	−0.0346543	−	0.0239638i
$988$	−2.32797	−	1.07139i	−0.0740626	−	0.0340853i
$989$	−3.04576	−	3.04576i	−0.0968497	−	0.0968497i
$990$	2.90990	+	19.9102i	0.0924828	+	0.632789i
$991$			37.3664i			1.18698i	0.804841	+	0.593491i	$0.202251\pi$
$991$			37.3664i			1.18698i	−0.804841	+	0.593491i	$0.797749\pi$
$992$	−18.7857	+	10.0802i	−0.596445	+	0.320046i
$993$	−26.4260	+	4.81944i	−0.838604	+	0.152940i
$994$	4.16428	−	19.0090i	0.132083	−	0.602930i
$995$	−10.3454	+	10.3454i	−0.327970	+	0.327970i
$996$	−0.510251	−	0.130794i	−0.0161679	−	0.00414437i
$997$	−22.5704	−	22.5704i	−0.714813	−	0.714813i	0.252725	−	0.967538i	$-0.418673\pi$
$997$	−22.5704	−	22.5704i	−0.714813	−	0.714813i	−0.967538	+	0.252725i	$0.918673\pi$
$998$	19.5405	+	30.5036i	0.618545	+	0.965575i
$999$	−30.7736	+	18.4959i	−0.973634	+	0.585185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.2	✓	40
3.2	odd	2	inner	336.2.s.c.155.19	yes	40
4.3	odd	2		1344.2.s.c.911.4		40
12.11	even	2		1344.2.s.c.911.7		40
16.3	odd	4	inner	336.2.s.c.323.19	yes	40
16.13	even	4		1344.2.s.c.239.7		40
48.29	odd	4		1344.2.s.c.239.4		40
48.35	even	4	inner	336.2.s.c.323.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.2	✓	40	1.1	even	1	trivial
336.2.s.c.155.19	yes	40	3.2	odd	2	inner
336.2.s.c.323.2	yes	40	48.35	even	4	inner
336.2.s.c.323.19	yes	40	16.3	odd	4	inner
1344.2.s.c.239.4		40	48.29	odd	4
1344.2.s.c.239.7		40	16.13	even	4
1344.2.s.c.911.4		40	4.3	odd	2
1344.2.s.c.911.7		40	12.11	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38145 - 0.302633i) q^{2} +(1.42461 + 0.985133i) q^{3} +(1.81683 + 0.836146i) q^{4} +(-0.766553 + 0.766553i) q^{5} +(-1.66990 - 1.79205i) q^{6} -1.00000 q^{7} +(-2.25682 - 1.70493i) q^{8} +(1.05903 + 2.80686i) q^{9} +O(q^{10})\)	\(q+(-1.38145 - 0.302633i) q^{2} +(1.42461 + 0.985133i) q^{3} +(1.81683 + 0.836146i) q^{4} +(-0.766553 + 0.766553i) q^{5} +(-1.66990 - 1.79205i) q^{6} -1.00000 q^{7} +(-2.25682 - 1.70493i) q^{8} +(1.05903 + 2.80686i) q^{9} +(1.29094 - 0.826974i) q^{10} +(3.09355 + 3.09355i) q^{11} +(1.76455 + 2.98100i) q^{12} +(0.262549 - 0.262549i) q^{13} +(1.38145 + 0.302633i) q^{14} +(-1.84720 + 0.336883i) q^{15} +(2.60172 + 3.03826i) q^{16} +2.68766i q^{17} +(-0.613548 - 4.19804i) q^{18} +(-2.44019 - 2.44019i) q^{19} +(-2.03365 + 0.751744i) q^{20} +(-1.42461 - 0.985133i) q^{21} +(-3.33739 - 5.20981i) q^{22} +3.24607i q^{23} +(-1.53550 - 4.65212i) q^{24} +3.82479i q^{25} +(-0.442155 + 0.283243i) q^{26} +(-1.25643 + 5.04196i) q^{27} +(-1.81683 - 0.836146i) q^{28} +(-3.28972 - 3.28972i) q^{29} +(2.65377 + 0.0936344i) q^{30} -3.76875i q^{31} +(-2.67468 - 4.98459i) q^{32} +(1.35954 + 7.45466i) q^{33} +(0.813374 - 3.71288i) q^{34} +(0.766553 - 0.766553i) q^{35} +(-0.422876 + 5.98508i) q^{36} +(4.88595 + 4.88595i) q^{37} +(2.63253 + 4.10949i) q^{38} +(0.632675 - 0.115384i) q^{39} +(3.03689 - 0.423052i) q^{40} +11.2823 q^{41} +(1.66990 + 1.79205i) q^{42} +(-0.938292 + 0.938292i) q^{43} +(3.03379 + 8.20711i) q^{44} +(-2.96341 - 1.33981i) q^{45} +(0.982368 - 4.48430i) q^{46} +0.764222 q^{47} +(0.713342 + 6.89138i) q^{48} +1.00000 q^{49} +(1.15751 - 5.28377i) q^{50} +(-2.64770 + 3.82887i) q^{51} +(0.696535 - 0.257477i) q^{52} +(-4.14619 + 4.14619i) q^{53} +(3.26156 - 6.58500i) q^{54} -4.74274 q^{55} +(2.25682 + 1.70493i) q^{56} +(-1.07241 - 5.88023i) q^{57} +(3.54902 + 5.54018i) q^{58} +(-2.63246 - 2.63246i) q^{59} +(-3.63772 - 0.932468i) q^{60} +(10.7072 - 10.7072i) q^{61} +(-1.14055 + 5.20635i) q^{62} +(-1.05903 - 2.80686i) q^{63} +(2.18644 + 7.69542i) q^{64} +0.402516i q^{65} +(0.377877 - 10.7097i) q^{66} +(-8.41087 - 8.41087i) q^{67} +(-2.24728 + 4.88301i) q^{68} +(-3.19781 + 4.62439i) q^{69} +(-1.29094 + 0.826974i) q^{70} -13.7602i q^{71} +(2.39546 - 8.14013i) q^{72} -6.79488i q^{73} +(-5.27106 - 8.22835i) q^{74} +(-3.76793 + 5.44884i) q^{75} +(-2.39305 - 6.47375i) q^{76} +(-3.09355 - 3.09355i) q^{77} +(-0.908931 - 0.0320703i) q^{78} +3.83558i q^{79} +(-4.32335 - 0.334634i) q^{80} +(-6.75693 + 5.94508i) q^{81} +(-15.5859 - 3.41439i) q^{82} +(-0.107522 + 0.107522i) q^{83} +(-1.76455 - 2.98100i) q^{84} +(-2.06023 - 2.06023i) q^{85} +(1.58016 - 1.01225i) q^{86} +(-1.44576 - 7.92738i) q^{87} +(-1.70730 - 12.2559i) q^{88} +9.00266 q^{89} +(3.68834 + 2.74771i) q^{90} +(-0.262549 + 0.262549i) q^{91} +(-2.71419 + 5.89755i) q^{92} +(3.71272 - 5.36900i) q^{93} +(-1.05574 - 0.231278i) q^{94} +3.74107 q^{95} +(1.10011 - 9.73600i) q^{96} +18.1447 q^{97} +(-1.38145 - 0.302633i) q^{98} +(-5.40701 + 11.9593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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