LMFDB - Embedded newform 336.2.s.c.155.19

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			155.19
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38145 + 0.302633i) q^{2} +(0.985133 + 1.42461i) q^{3} +(1.81683 + 0.836146i) q^{4} +(0.766553 - 0.766553i) q^{5} +(0.929782 + 2.26617i) q^{6} -1.00000 q^{7} +(2.25682 + 1.70493i) q^{8} +(-1.05903 + 2.80686i) q^{9} +O(q^{10})$	\(q+(1.38145 + 0.302633i) q^{2} +(0.985133 + 1.42461i) q^{3} +(1.81683 + 0.836146i) q^{4} +(0.766553 - 0.766553i) q^{5} +(0.929782 + 2.26617i) 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} +(0.598634 + 3.41198i) 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} +(-2.31244 + 3.55705i) q^{18} +(-2.44019 - 2.44019i) q^{19} +(2.03365 - 0.751744i) q^{20} +(-0.985133 - 1.42461i) q^{21} +(-3.33739 - 5.20981i) q^{22} -3.24607i q^{23} +(-0.205592 + 4.89466i) q^{24} +3.82479i q^{25} +(0.442155 - 0.283243i) q^{26} +(-5.04196 + 1.25643i) q^{27} +(-1.81683 - 0.836146i) q^{28} +(3.28972 + 3.28972i) q^{29} +(2.44986 + 1.02441i) 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} +(-4.27101 + 4.21408i) 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} +(-0.929782 - 2.26617i) q^{42} +(-0.938292 + 0.938292i) q^{43} +(-3.03379 - 8.20711i) q^{44} +(1.33981 + 2.96341i) q^{45} +(0.982368 - 4.48430i) q^{46} -0.764222 q^{47} +(-1.76530 + 6.69953i) q^{48} +1.00000 q^{49} +(-1.15751 + 5.28377i) q^{50} +(3.82887 - 2.64770i) q^{51} +(0.696535 - 0.257477i) q^{52} +(4.14619 - 4.14619i) q^{53} +(-7.34547 + 0.209838i) 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} +(3.07435 + 2.15658i) 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} +(4.13417 - 9.88683i) q^{66} +(-8.41087 - 8.41087i) q^{67} +(2.24728 - 4.88301i) q^{68} +(4.62439 - 3.19781i) q^{69} +(-1.29094 + 0.826974i) q^{70} +13.7602i q^{71} +(-7.17552 + 4.52900i) q^{72} -6.79488i q^{73} +(5.27106 + 8.22835i) q^{74} +(-5.44884 + 3.76793i) q^{75} +(-2.39305 - 6.47375i) q^{76} +(3.09355 + 3.09355i) q^{77} +(0.839093 + 0.350866i) 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} +(-0.598634 - 3.41198i) 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} +(0.954058 + 4.49928i) q^{90} +(-0.262549 + 0.262549i) q^{91} +(2.71419 - 5.89755i) q^{92} +(5.36900 - 3.71272i) q^{93} +(-1.05574 - 0.231278i) q^{94} -3.74107 q^{95} +(-4.46618 + 8.72085i) q^{96} +18.1447 q^{97} +(1.38145 + 0.302633i) q^{98} +(11.9593 - 5.40701i) 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
$3$	0.985133	+	1.42461i	0.568767	+	0.822499i
$3$	0.985133	+	1.42461i	0.568767	+	0.822499i
$4$	1.81683	+	0.836146i	0.908413	+	0.418073i
$5$	0.766553	−	0.766553i	0.342813	−	0.342813i	−0.514611	−	0.857424i	$-0.672064\pi$
$5$	0.766553	−	0.766553i	0.342813	−	0.342813i	0.857424	+	0.514611i	$0.172064\pi$
$6$	0.929782	+	2.26617i	0.379582	+	0.925158i
$7$	−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	0.0651356	−	0.997876i	$-0.479252\pi$
$11$	−3.09355	−	3.09355i	−0.932741	−	0.932741i	−0.997876	+	0.0651356i	$0.979252\pi$
$12$	0.598634	+	3.41198i	0.172811	+	0.984955i
$13$	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	$-0.894324\pi$
$17$		−	2.68766i		−	0.651853i	0.945395	−	0.325927i	$-0.105676\pi$
$18$	−2.31244	+	3.55705i	−0.545048	+	0.838405i
$19$	−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
$21$	−0.985133	−	1.42461i	−0.214974	−	0.310875i
$22$	−3.33739	−	5.20981i	−0.711533	−	1.11073i
$23$		−	3.24607i		−	0.676853i	−0.940993	−	0.338427i	$-0.890105\pi$
$23$		−	3.24607i		−	0.676853i	0.940993	−	0.338427i	$-0.109895\pi$
$24$	−0.205592	+	4.89466i	−0.0419664	+	0.999119i
$25$			3.82479i			0.764958i
$26$	0.442155	−	0.283243i	0.0867137	−	0.0555486i
$27$	−5.04196	+	1.25643i	−0.970326	+	0.241800i
$28$	−1.81683	−	0.836146i	−0.343348	−	0.158017i
$29$	3.28972	+	3.28972i	0.610886	+	0.610886i	0.943177	−	0.332291i	$-0.107822\pi$
$29$	3.28972	+	3.28972i	0.610886	+	0.610886i	−0.332291	+	0.943177i	$0.607822\pi$
$30$	2.44986	+	1.02441i	0.447282	+	0.187031i
$31$		−	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
$36$	−4.27101	+	4.21408i	−0.711835	+	0.702346i
$37$	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	$-0.843128\pi$
$41$	−11.2823			−1.76200			−0.880998	+	0.473120i	$0.843128\pi$
$42$	−0.929782	−	2.26617i	−0.143468	−	0.349677i
$43$	−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
$45$	1.33981	+	2.96341i	0.199727	+	0.441759i
$46$	0.982368	−	4.48430i	0.144842	−	0.661174i
$47$	−0.764222			−0.111473			−0.0557366	−	0.998446i	$-0.517751\pi$
$47$	−0.764222			−0.111473			−0.0557366	+	0.998446i	$0.517751\pi$
$48$	−1.76530	+	6.69953i	−0.254799	+	0.966994i
$49$	1.00000			0.142857
$50$	−1.15751	+	5.28377i	−0.163696	+	0.747238i
$51$	3.82887	−	2.64770i	0.536149	−	0.370752i
$52$	0.696535	−	0.257477i	0.0965921	−	0.0357056i
$53$	4.14619	−	4.14619i	0.569523	−	0.569523i	−0.362471	−	0.931995i	$-0.618067\pi$
$53$	4.14619	−	4.14619i	0.569523	−	0.569523i	0.931995	+	0.362471i	$0.118067\pi$
$54$	−7.34547	+	0.209838i	−0.999592	+	0.0285553i
$55$	−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	0.857388	−	0.514671i	$-0.172086\pi$
$59$	2.63246	+	2.63246i	0.342717	+	0.342717i	−0.514671	+	0.857388i	$0.672086\pi$
$60$	3.07435	+	2.15658i	0.396897	+	0.278414i
$61$	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
$66$	4.13417	−	9.88683i	0.508881	−	1.21698i
$67$	−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
$69$	4.62439	−	3.19781i	0.556711	−	0.384971i
$70$	−1.29094	+	0.826974i	−0.154297	+	0.0988423i
$71$			13.7602i			1.63303i	0.577322	+	0.816516i	$0.304098\pi$
$71$			13.7602i			1.63303i	−0.577322	+	0.816516i	$0.695902\pi$
$72$	−7.17552	+	4.52900i	−0.845643	+	0.533748i
$73$		−	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
$75$	−5.44884	+	3.76793i	−0.629177	+	0.435083i
$76$	−2.39305	−	6.47375i	−0.274501	−	0.742591i
$77$	3.09355	+	3.09355i	0.352543	+	0.352543i
$78$	0.839093	+	0.350866i	0.0950085	+	0.0397278i
$79$			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	−0.701181	−	0.712983i	$-0.747344\pi$
$83$	0.107522	−	0.107522i	0.0118021	−	0.0118021i	0.712983	+	0.701181i	$0.247344\pi$
$84$	−0.598634	−	3.41198i	−0.0653164	−	0.372278i
$85$	−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	$-0.658326\pi$
$89$	−9.00266			−0.954280			−0.477140	+	0.878827i	$0.658326\pi$
$90$	0.954058	+	4.49928i	0.100567	+	0.474266i
$91$	−0.262549	+	0.262549i	−0.0275226	+	0.0275226i
$92$	2.71419	−	5.89755i	0.282974	−	0.614862i
$93$	5.36900	−	3.71272i	0.556739	−	0.384991i
$94$	−1.05574	−	0.231278i	−0.108891	−	0.0238545i
$95$	−3.74107			−0.383826
$96$	−4.46618	+	8.72085i	−0.455827	+	0.890068i
$97$	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
$99$	11.9593	−	5.40701i	1.20196	−	0.543425i
$100$	−3.19808	+	6.94899i	−0.319808	+	0.694899i
$101$	−7.24602	+	7.24602i	−0.721006	+	0.721006i	−0.968810	−	0.247804i	$-0.920291\pi$
$101$	−7.24602	+	7.24602i	−0.721006	+	0.721006i	0.247804	+	0.968810i	$0.420291\pi$
$102$	6.09068	−	2.49894i	0.603067	−	0.247432i
$103$	−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	0.959904	−	0.280330i	$-0.0904437\pi$
$107$	7.02957	+	7.02957i	0.679574	+	0.679574i	−0.280330	+	0.959904i	$0.590444\pi$
$108$	−10.2109	−	1.93310i	−0.982547	−	0.186013i
$109$	−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	$0.263818\pi$
$113$			15.6715i			1.47425i	−0.675755	+	0.737126i	$0.736182\pi$
$114$	3.26103	−	7.79871i	0.305423	−	0.730417i
$115$	−2.48829	−	2.48829i	−0.232034	−	0.232034i
$116$	3.22617	+	8.72754i	0.299542	+	0.810332i
$117$	0.458892	+	1.01498i	0.0424246	+	0.0938353i
$118$	2.83995	+	4.43329i	0.261439	+	0.408117i
$119$			2.68766i			0.246377i
$120$	3.59442	+	3.90962i	0.328124	+	0.356898i
$121$			8.14012i			0.740011i
$122$	18.0319	−	11.5512i	1.63253	−	1.04579i
$123$	−11.1145	−	16.0728i	−1.00216	−	1.44924i
$124$	3.15123	−	6.84717i	0.282988	−	0.614894i
$125$	6.76467	+	6.76467i	0.605051	+	0.605051i
$126$	2.31244	−	3.55705i	0.206009	−	0.316887i
$127$		−	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	−0.824537	−	0.565808i	$-0.808564\pi$
$131$	−2.96129	+	2.96129i	−0.258729	+	0.258729i	0.565808	+	0.824537i	$0.308564\pi$
$132$	8.70324	−	12.4071i	0.757520	−	1.07990i
$133$	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	$-0.696590\pi$
$137$	−13.5561			−1.15817			−0.579086	+	0.815266i	$0.696590\pi$
$138$	7.35614	−	3.01814i	0.626196	−	0.256921i
$139$	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
$141$	−0.752860	−	1.08872i	−0.0634022	−	0.0916866i
$142$	−4.16428	+	19.0090i	−0.349459	+	1.59520i
$143$	−1.62442			−0.135841
$144$	−11.2833	+	4.08506i	−0.940273	+	0.340422i
$145$	5.04350			0.418839
$146$	2.05635	−	9.38682i	0.170185	−	0.776858i
$147$	0.985133	+	1.42461i	0.0812524	+	0.117500i
$148$	4.79155	+	12.9623i	0.393863	+	1.06549i
$149$	14.9894	−	14.9894i	1.22798	−	1.22798i	0.263254	−	0.964726i	$-0.415204\pi$
$149$	14.9894	−	14.9894i	1.22798	−	1.22798i	0.964726	−	0.263254i	$-0.0847959\pi$
$150$	−8.66761	+	3.55622i	−0.707708	+	0.290364i
$151$	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
$156$	1.05298	+	0.738642i	0.0843062	+	0.0591387i
$157$	−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
$162$	−7.53520	−	10.2577i	−0.592021	−	0.805922i
$163$	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
$165$	−4.67223	−	6.75656i	−0.363733	−	0.525998i
$166$	0.181076	−	0.115997i	0.0140542	−	0.00900310i
$167$			18.4786i			1.42992i	0.699166	+	0.714959i	$0.253555\pi$
$167$			18.4786i			1.42992i	−0.699166	+	0.714959i	$0.746445\pi$
$168$	0.205592	−	4.89466i	0.0158618	−	0.377631i
$169$			12.8621i			0.989395i
$170$	−2.22262	−	3.46961i	−0.170467	−	0.266107i
$171$	9.43349	−	4.26504i	0.721397	−	0.326156i
$172$	−2.48926	+	0.920165i	−0.189805	+	0.0701619i
$173$	0.866535	+	0.866535i	0.0658814	+	0.0658814i	0.739280	−	0.673398i	$-0.235166\pi$
$173$	0.866535	+	0.866535i	0.0658814	+	0.0658814i	−0.673398	+	0.739280i	$0.735166\pi$
$174$	−4.39633	+	10.5138i	−0.333285	+	0.797048i
$175$		−	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	−0.0829148	−	0.996557i	$-0.526423\pi$
$179$	12.2237	−	12.2237i	0.913642	−	0.913642i	0.996557	+	0.0829148i	$0.0264230\pi$
$180$	−0.0436429	+	6.50427i	−0.00325295	+	0.484800i
$181$	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
$186$	8.54061	−	3.50412i	0.626228	−	0.256934i
$187$	−8.31441	+	8.31441i	−0.608010	+	0.608010i
$188$	−1.38846	−	0.639001i	−0.101264	−	0.0466039i
$189$	5.04196	−	1.25643i	0.366749	−	0.0913919i
$190$	−5.16811	−	1.13217i	−0.374934	−	0.0821362i
$191$	−22.9268			−1.65892			−0.829461	−	0.558564i	$-0.811352\pi$
$191$	−22.9268			−1.65892			−0.829461	+	0.558564i	$0.811352\pi$
$192$	−8.80903	+	10.6958i	−0.635737	+	0.771906i
$193$	−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
$195$	0.573428	−	0.396531i	0.0410640	−	0.0283962i
$196$	1.81683	+	0.836146i	0.129773	+	0.0597247i
$197$	8.61873	−	8.61873i	0.614059	−	0.614059i	−0.329942	−	0.944001i	$-0.607029\pi$
$197$	8.61873	−	8.61873i	0.614059	−	0.614059i	0.944001	+	0.329942i	$0.107029\pi$
$198$	18.1576	−	3.85026i	1.29040	−	0.273626i
$199$	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
$204$	9.17025	−	1.60893i	0.642046	−	0.112647i
$205$	−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
$210$	−2.44986	−	1.02441i	−0.169057	−	0.0706910i
$211$	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
$213$	−19.6029	+	13.5556i	−1.34317	+	0.928815i
$214$	7.58365	+	11.8384i	0.518407	+	0.809257i
$215$			1.43850i			0.0981050i
$216$	−13.5209	−	5.76065i	−0.919981	−	0.391962i
$217$			3.76875i			0.255839i
$218$	−3.12920	+	2.00455i	−0.211936	+	0.135766i
$219$	9.68006	−	6.69386i	0.654118	−	0.452329i
$220$	−8.61675	−	3.96563i	−0.580941	−	0.267362i
$221$	−0.705642	−	0.705642i	−0.0474666	−	0.0474666i
$222$	−6.52950	+	15.6152i	−0.438231	+	1.04803i
$223$		−	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	−0.646205	−	0.763164i	$-0.723645\pi$
$227$	1.76217	−	1.76217i	0.116960	−	0.116960i	0.763164	+	0.646205i	$0.223645\pi$
$228$	6.86511	−	9.78667i	0.454653	−	0.648138i
$229$	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	$-0.492273\pi$
$233$	0.740966			0.0485423			0.0242712	+	0.999705i	$0.492273\pi$
$234$	0.326770	+	1.54103i	0.0213616	+	0.100740i
$235$	−0.585817	+	0.585817i	−0.0382145	+	0.0382145i
$236$	2.58160	+	6.98384i	0.168048	+	0.454609i
$237$	−5.46420	+	3.77855i	−0.354938	+	0.245443i
$238$	−0.813374	+	3.71288i	−0.0527232	+	0.240670i
$239$	−4.05725			−0.262441			−0.131221	−	0.991353i	$-0.541890\pi$
$239$	−4.05725			−0.262441			−0.131221	+	0.991353i	$0.541890\pi$
$240$	3.78235	+	6.48875i	0.244150	+	0.418847i
$241$	−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
$243$	1.81295	−	15.4827i	0.116301	−	0.993214i
$244$	28.4059	−	10.5004i	1.81850	−	0.672216i
$245$	0.766553	−	0.766553i	0.0489733	−	0.0489733i
$246$	−10.4901	−	25.5675i	−0.668822	−	1.63013i
$247$	−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	$0.0753538\pi$
$251$	19.1167	+	19.1167i	1.20664	+	1.20664i	0.234526	+	0.972110i	$0.424646\pi$
$252$	4.27101	−	4.21408i	0.269048	−	0.265462i
$253$	−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	$-0.925857\pi$
$257$		−	7.40089i		−	0.461655i	0.972995	−	0.230827i	$-0.0741433\pi$
$258$	−2.99873	−	1.25392i	−0.186693	−	0.0780655i
$259$	−4.88595	−	4.88595i	−0.303598	−	0.303598i
$260$	0.336562	−	0.731301i	0.0208727	−	0.0453534i
$261$	−12.7177	+	5.74989i	−0.787205	+	0.355909i
$262$	−4.98706	+	3.19470i	−0.308102	+	0.197369i
$263$		−	16.5931i		−	1.02317i	−0.859232	−	0.511586i	$-0.829058\pi$
$263$		−	16.5931i		−	1.02317i	0.859232	−	0.511586i	$-0.170942\pi$
$264$	15.7779	−	14.5059i	0.971063	−	0.892775i
$265$		−	6.35656i		−	0.390480i
$266$	2.63253	+	4.10949i	0.161411	+	0.251969i
$267$	−8.86881	−	12.8253i	−0.542762	−	0.784894i
$268$	−8.24838	−	22.3138i	−0.503850	−	1.36303i
$269$	13.9816	+	13.9816i	0.852471	+	0.852471i	0.990437	−	0.137966i	$-0.0440565\pi$
$269$	13.9816	+	13.9816i	0.852471	+	0.852471i	−0.137966	+	0.990437i	$0.544056\pi$
$270$	−5.46984	+	5.79155i	−0.332884	+	0.352462i
$271$			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
$276$	11.0756	−	1.94321i	0.666670	−	0.116968i
$277$	−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	$-0.753117\pi$
$281$	−23.9375			−1.42799			−0.713997	+	0.700149i	$0.753117\pi$
$282$	−0.710559	−	1.73185i	−0.0423132	−	0.103130i
$283$	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
$285$	−3.68545	−	5.32956i	−0.218307	−	0.315696i
$286$	−2.24406	−	0.491602i	−0.132694	−	0.0290690i
$287$	11.2823			0.665972
$288$	−16.8236	+	2.22864i	−0.991340	+	0.131324i
$289$	9.77648			0.575087
$290$	6.96735	+	1.52633i	0.409137	+	0.0896290i
$291$	17.8750	+	25.8492i	1.04785	+	1.51531i
$292$	5.68151	−	12.3451i	0.332485	−	0.722444i
$293$	11.3212	−	11.3212i	0.661394	−	0.661394i	−0.294315	−	0.955708i	$-0.595091\pi$
$293$	11.3212	−	11.3212i	0.661394	−	0.661394i	0.955708	+	0.294315i	$0.0950915\pi$
$294$	0.929782	+	2.26617i	0.0542260	+	0.132165i
$295$	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
$300$	−13.0501	+	2.28965i	−0.753450	+	0.132193i
$301$	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
$306$	9.56014	+	6.21506i	0.546517	+	0.355291i
$307$	−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
$309$	−16.9642	−	24.5321i	−0.965059	−	1.39558i
$310$	−3.11666	−	4.86524i	−0.177014	−	0.276327i
$311$		−	28.7635i		−	1.63103i	−0.578737	−	0.815514i	$-0.696454\pi$
$311$		−	28.7635i		−	1.63103i	0.578737	−	0.815514i	$-0.303546\pi$
$312$	1.23111	+	1.33907i	0.0696979	+	0.0758097i
$313$			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
$315$	−1.33981	−	2.96341i	−0.0754896	−	0.166969i
$316$	−3.20710	+	6.96858i	−0.180413	+	0.392013i
$317$	−22.5290	−	22.5290i	−1.26535	−	1.26535i	−0.948462	−	0.316891i	$-0.897361\pi$
$317$	−22.5290	−	22.5290i	−1.26535	−	1.26535i	−0.316891	−	0.948462i	$-0.602639\pi$
$318$	13.2510	+	5.54091i	0.743080	+	0.310719i
$319$		−	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
$324$	−7.30521	−	16.4510i	−0.405845	−	0.913942i
$325$	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
$330$	−4.40972	−	10.7478i	−0.242747	−	0.591649i
$331$	−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
$333$	−18.8885	+	8.53982i	−1.03508	+	0.467979i
$334$	−5.59224	+	25.5274i	−0.305993	+	1.39679i
$335$	−12.8948			−0.704516
$336$	1.76530	−	6.69953i	0.0963051	−	0.365489i
$337$	−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
$339$	−22.3258	+	15.4385i	−1.21257	+	0.838505i
$340$	−2.02043	−	5.46575i	−0.109573	−	0.296422i
$341$	−11.6588	+	11.6588i	−0.631361	+	0.631361i
$342$	14.3227	−	3.03708i	0.774481	−	0.164226i
$343$	−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	0.0414832	−	0.999139i	$-0.486792\pi$
$347$	−17.8392	−	17.8392i	−0.957656	−	0.957656i	−0.999139	+	0.0414832i	$0.986792\pi$
$348$	−9.25514	+	13.1938i	−0.496128	+	0.707263i
$349$	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	$-0.789023\pi$
$353$		−	23.1220i		−	1.23066i	0.788271	−	0.615329i	$-0.210977\pi$
$354$	−3.51797	+	8.41320i	−0.186978	+	0.447156i
$355$	10.5479	+	10.5479i	0.559825	+	0.559825i
$356$	−16.3563	−	7.52753i	−0.866880	−	0.398958i
$357$	−3.82887	+	2.64770i	−0.202645	+	0.140131i
$358$	20.5858	−	13.1872i	1.08799	−	0.696964i
$359$		−	30.5132i		−	1.61043i	−0.592986	−	0.805213i	$-0.702051\pi$
$359$		−	30.5132i		−	1.61043i	0.592986	−	0.805213i	$-0.297949\pi$
$360$	−2.02870	+	8.97214i	−0.106922	+	0.472874i
$361$		−	7.09096i		−	0.373208i
$362$	3.86743	+	6.03722i	0.203267	+	0.317309i
$363$	−11.5965	+	8.01910i	−0.608658	+	0.420894i
$364$	−0.696535	+	0.257477i	−0.0365084	+	0.0134955i
$365$	−5.20864	−	5.20864i	−0.272633	−	0.272633i
$366$	34.2197	+	14.3089i	1.78869	+	0.747940i
$367$			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
$372$	12.8589	−	2.25610i	0.666704	−	0.116974i
$373$	−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
$378$	7.34547	−	0.209838i	0.377810	−	0.0107929i
$379$	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
$381$	1.24608	−	0.861676i	0.0638385	−	0.0441450i
$382$	−31.6723	−	6.93839i	−1.62049	−	0.354999i
$383$	−3.29068			−0.168146			−0.0840729	−	0.996460i	$-0.526793\pi$
$383$	−3.29068			−0.168146			−0.0840729	+	0.996460i	$0.526793\pi$
$384$	−15.4062	+	12.1099i	−0.786193	+	0.617981i
$385$	4.74274			0.241713
$386$	−4.74015	−	1.03842i	−0.241267	−	0.0528540i
$387$	−1.63998	−	3.62733i	−0.0833648	−	0.184388i
$388$	32.9658	+	15.1716i	1.67359	+	0.770224i
$389$	15.9506	−	15.9506i	0.808728	−	0.808728i	−0.175713	−	0.984441i	$-0.556223\pi$
$389$	15.9506	−	15.9506i	0.808728	−	0.808728i	0.984441	+	0.175713i	$0.0562231\pi$
$390$	0.912167	−	0.374252i	0.0461894	−	0.0189510i
$391$	−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
$396$	26.2491	+	0.176128i	1.31907	+	0.00885077i
$397$	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	$0.182172\pi$
$401$			21.6901i			1.08315i	−0.840652	+	0.541576i	$0.817828\pi$
$402$	11.2402	−	26.8807i	0.560608	−	1.34069i
$403$	−0.989482	−	0.989482i	−0.0492896	−	0.0492896i
$404$	−19.2235	+	7.10603i	−0.956404	+	0.353538i
$405$	−9.73676	+	0.622325i	−0.483824	+	0.0309236i
$406$	−3.54902	−	5.54018i	−0.176135	−	0.274954i
$407$		−	30.2299i		−	1.49844i
$408$	13.1552	+	0.552563i	0.651279	+	0.0273559i
$409$		−	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
$411$	−13.3545	−	19.3121i	−0.658730	−	0.952595i
$412$	−31.2861	−	14.3986i	−1.54136	−	0.709368i
$413$	−2.63246	−	2.63246i	−0.129535	−	0.129535i
$414$	11.5464	+	7.50636i	0.567477	+	0.368917i
$415$		−	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	−0.470348	−	0.882481i	$-0.655872\pi$
$419$	8.43616	−	8.43616i	0.412133	−	0.412133i	0.882481	+	0.470348i	$0.155872\pi$
$420$	−3.07435	−	2.15658i	−0.150013	−	0.105230i
$421$	−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
$426$	−31.1828	+	12.7940i	−1.51081	+	0.619869i
$427$	−10.7072	+	10.7072i	−0.518158	+	0.518158i
$428$	6.89377	+	18.6493i	0.333223	+	0.901446i
$429$	−1.60027	−	2.31416i	−0.0772616	−	0.111729i
$430$	−0.435338	+	1.98722i	−0.0209938	+	0.0958324i
$431$	25.7527			1.24046			0.620232	−	0.784419i	$-0.287039\pi$
$431$	25.7527			1.24046			0.620232	+	0.784419i	$0.287039\pi$
$432$	−16.9351	−	12.0499i	−0.814792	−	0.579753i
$433$	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
$435$	4.96851	+	7.18501i	0.238222	+	0.344495i
$436$	−4.92948	+	1.82220i	−0.236079	+	0.0872676i
$437$	−7.92103	+	7.92103i	−0.378914	+	0.378914i
$438$	15.3983	−	6.31776i	0.735761	−	0.301874i
$439$	−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	$0.0583586\pi$
$443$	24.5321	+	24.5321i	1.16555	+	1.16555i	0.182313	+	0.983240i	$0.441641\pi$
$444$	−13.7459	+	19.5957i	−0.652350	+	0.929969i
$445$	−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	$0.227285\pi$
$449$			27.7538i			1.30978i	−0.755724	+	0.654891i	$0.772715\pi$
$450$	−13.6050	−	8.84461i	−0.641345	−	0.416939i
$451$	34.9023	+	34.9023i	1.64349	+	1.64349i
$452$	−13.1037	+	28.4724i	−0.616345	+	1.33923i
$453$	13.0714	+	18.9027i	0.614148	+	0.888126i
$454$	2.96765	−	1.90107i	0.139279	−	0.0892216i
$455$			0.402516i			0.0188702i
$456$	12.4456	−	11.4422i	0.582818	−	0.535831i
$457$		−	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
$459$	3.37686	+	13.5511i	0.157618	+	0.632510i
$460$	−2.44022	−	6.60136i	−0.113776	−	0.307790i
$461$	1.51791	+	1.51791i	0.0706959	+	0.0706959i	0.741571	−	0.670875i	$-0.234081\pi$
$461$	1.51791	+	1.51791i	0.0706959	+	0.0706959i	−0.670875	+	0.741571i	$0.734081\pi$
$462$	−4.13417	+	9.88683i	−0.192339	+	0.459977i
$463$		−	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	$0.574724\pi$
$467$	−26.0440	+	26.0440i	−1.20517	+	1.20517i	−0.972572	+	0.232601i	$0.925276\pi$
$468$	−0.0149479	+	2.22775i	−0.000690969	+	0.102978i
$469$	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
$474$	−8.69205	+	3.56625i	−0.399239	+	0.163803i
$475$	9.33321	−	9.33321i	0.428237	−	0.428237i
$476$	−2.24728	+	4.88301i	−0.103004	+	0.223813i
$477$	7.24686	+	16.0287i	0.331811	+	0.733904i
$478$	−5.60490	−	1.22786i	−0.256362	−	0.0561608i
$479$	17.6724			0.807473			0.403737	−	0.914875i	$-0.367711\pi$
$479$	17.6724			0.807473			0.403737	+	0.914875i	$0.367711\pi$
$480$	3.26143	+	10.1086i	0.148863	+	0.461391i
$481$	2.56560			0.116981
$482$	−31.0917	−	6.81120i	−1.41619	−	0.310242i
$483$	−4.62439	+	3.19781i	−0.210417	+	0.145506i
$484$	−6.80633	+	14.7892i	−0.309379	+	0.672236i
$485$	13.9089	−	13.9089i	0.631571	−	0.631571i
$486$	7.19007	−	20.8399i	0.326148	−	0.945319i
$487$	−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	0.999920	−	0.0126204i	$-0.00401730\pi$
$491$	21.8771	+	21.8771i	0.987300	+	0.987300i	−0.0126204	+	0.999920i	$0.504017\pi$
$492$	−6.75396	−	38.4950i	−0.304492	−	1.73549i
$493$	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
$498$	0.343634	+	0.143691i	0.0153986	+	0.00643893i
$499$	−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
$501$	−26.3248	+	18.2039i	−1.17611	+	0.813290i
$502$	20.6235	+	32.1942i	0.920472	+	1.43690i
$503$		−	8.65417i		−	0.385871i	−0.981211	−	0.192935i	$-0.938199\pi$
$503$		−	8.65417i		−	0.385871i	0.981211	−	0.192935i	$-0.0618007\pi$
$504$	7.17552	−	4.52900i	0.319623	−	0.201738i
$505$			11.1089i			0.494340i
$506$	−16.9114	+	10.8334i	−0.751804	+	0.481604i
$507$	−18.3235	+	12.6709i	−0.813776	+	0.562735i
$508$	0.731360	−	1.58914i	0.0324488	−	0.0705068i
$509$	−0.578725	−	0.578725i	−0.0256515	−	0.0256515i	0.694165	−	0.719816i	$-0.255774\pi$
$509$	−0.578725	−	0.578725i	−0.0256515	−	0.0256515i	−0.719816	+	0.694165i	$0.755774\pi$
$510$	2.75326	−	6.58440i	0.121917	−	0.291562i
$511$			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
$516$	−3.76313	−	2.63974i	−0.165663	−	0.116208i
$517$	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	$-0.405478\pi$
$521$	13.3576			0.585206			0.292603	+	0.956234i	$0.405478\pi$
$522$	−19.3090	+	4.09441i	−0.845132	+	0.179208i
$523$	−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
$525$	5.44884	−	3.76793i	0.237807	−	0.164446i
$526$	5.02160	−	22.9225i	0.218952	−	0.999470i
$527$	−10.1291			−0.441231
$528$	26.1864	−	15.2643i	1.13962	−	0.664293i
$529$	12.4630			0.541870
$530$	1.92370	−	8.78129i	0.0835603	−	0.381435i
$531$	−10.1768	+	4.60110i	−0.441635	+	0.199671i
$532$	2.39305	+	6.47375i	0.103752	+	0.280673i
$533$	−2.96215	+	2.96215i	−0.128305	+	0.128305i
$534$	−8.37050	−	20.4015i	−0.362227	−	0.882860i
$535$	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
$540$	−9.30905	+	6.34540i	−0.400598	+	0.273063i
$541$	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
$546$	−0.839093	−	0.350866i	−0.0359098	−	0.0150157i
$547$	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
$549$	18.7144	+	41.3928i	0.798711	+	1.76660i
$550$	19.9264	−	12.7648i	0.849666	−	0.544293i
$551$		−	16.0551i		−	0.683970i
$552$	15.8884	+	0.667368i	0.676257	+	0.0284051i
$553$		−	3.83558i		−	0.163105i
$554$	−3.63562	−	5.67536i	−0.154463	−	0.241123i
$555$	7.37931	+	10.6713i	0.313234	+	0.452971i
$556$	0.696305	−	0.257392i	0.0295299	−	0.0109158i
$557$	15.3000	+	15.3000i	0.648280	+	0.648280i	0.952577	−	0.304297i	$-0.0984216\pi$
$557$	15.3000	+	15.3000i	0.648280	+	0.648280i	−0.304297	+	0.952577i	$0.598422\pi$
$558$	13.4056	+	8.71502i	0.567506	+	0.368936i
$559$			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	−0.977006	−	0.213213i	$-0.931607\pi$
$563$	−18.1230	+	18.1230i	−0.763793	+	0.763793i	0.213213	+	0.977006i	$0.431607\pi$
$564$	−0.457489	−	2.60751i	−0.0192638	−	0.109796i
$565$	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	$-0.471711\pi$
$569$	4.23430			0.177511			0.0887555	+	0.996053i	$0.471711\pi$
$570$	−3.47838	−	8.47788i	−0.145693	−	0.355099i
$571$	−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
$573$	−22.5859	−	32.6617i	−0.943540	−	1.36446i
$574$	15.5859	+	3.41439i	0.650545	+	0.142514i
$575$	12.4156			0.517764
$576$	−23.9155	−	2.01261i	−0.996478	−	0.0838588i
$577$	−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
$579$	−3.38026	−	4.88823i	−0.140479	−	0.203148i
$580$	9.16316	+	4.21710i	0.380479	+	0.175105i
$581$	−0.107522	+	0.107522i	−0.00446076	+	0.00446076i
$582$	16.8706	+	41.1190i	0.699311	+	1.70444i
$583$	−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	0.666072	−	0.745888i	$-0.267974\pi$
$587$	−1.93378	−	1.93378i	−0.0798157	−	0.0798157i	−0.745888	+	0.666072i	$0.767974\pi$
$588$	0.598634	+	3.41198i	0.0246873	+	0.140708i
$589$	−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	$0.0357914\pi$
$593$			5.46475i			0.224410i	−0.993685	+	0.112205i	$0.964209\pi$
$594$	23.3727	+	22.0745i	0.958995	+	0.905726i
$595$	2.06023	+	2.06023i	0.0844614	+	0.0844614i
$596$	39.7665	−	14.6998i	1.62890	−	0.602129i
$597$	13.2953	+	19.2264i	0.544140	+	0.786886i
$598$	−0.919428	−	1.43527i	−0.0375982	−	0.0586925i
$599$			2.30973i			0.0943728i	0.998886	+	0.0471864i	$0.0150255\pi$
$599$			2.30973i			0.0943728i	−0.998886	+	0.0471864i	$0.984975\pi$
$600$	−18.7211	−	0.786349i	−0.764284	−	0.0321025i
$601$		−	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
$603$	32.5155	−	14.7008i	1.32413	−	0.598663i
$604$	24.1069	+	11.0945i	0.980895	+	0.451431i
$605$	6.23984	+	6.23984i	0.253685	+	0.253685i
$606$	−23.1579	−	9.68346i	−0.940725	−	0.393364i
$607$		−	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
$612$	11.3260	+	11.4790i	0.457827	+	0.464012i
$613$	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	$-0.386807\pi$
$617$	17.2962			0.696320			0.348160	+	0.937435i	$0.386807\pi$
$618$	−16.0110	−	39.0238i	−0.644058	−	1.56977i
$619$	−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
$621$	4.07847	+	16.3666i	0.163663	+	0.656768i
$622$	8.70477	−	39.7354i	0.349030	−	1.59325i
$623$	9.00266			0.360684
$624$	1.29548	+	2.22243i	0.0518606	+	0.0889685i
$625$	−8.75299			−0.350120
$626$	−6.06189	+	27.6712i	−0.242282	+	1.10597i
$627$	−21.5083	+	14.8732i	−0.858960	+	0.593980i
$628$	−20.9538	+	7.74566i	−0.836149	+	0.309086i
$629$	13.1318	−	13.1318i	0.523598	−	0.523598i
$630$	−0.954058	−	4.49928i	−0.0380106	−	0.179256i
$631$	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
$636$	16.6288	+	11.6647i	0.659375	+	0.462535i
$637$	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	$-0.821424\pi$
$641$		−	26.9406i		−	1.06409i	0.846717	−	0.532044i	$-0.178576\pi$
$642$	−9.39421	+	22.4661i	−0.370760	+	0.886668i
$643$	−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
$645$	−2.04930	+	1.41712i	−0.0806912	+	0.0557989i
$646$	−11.0449	+	7.07534i	−0.434556	+	0.278375i
$647$		−	0.704788i		−	0.0277081i	−0.999904	−	0.0138540i	$-0.995590\pi$
$647$		−	0.704788i		−	0.0277081i	0.999904	−	0.0138540i	$-0.00441002\pi$
$648$	−5.11321	−	24.9370i	−0.200866	−	0.979619i
$649$		−	16.2873i		−	0.639332i
$650$	1.08335	+	1.69115i	0.0424923	+	0.0663324i
$651$	−5.36900	+	3.71272i	−0.210428	+	0.145513i
$652$	2.16569	+	5.85869i	0.0848148	+	0.229444i
$653$	−28.0029	−	28.0029i	−1.09584	−	1.09584i	−0.994892	−	0.100947i	$-0.967813\pi$
$653$	−28.0029	−	28.0029i	−1.09584	−	1.09584i	−0.100947	−	0.994892i	$-0.532187\pi$
$654$	−5.93838	−	2.48313i	−0.232209	−	0.0970981i
$655$			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	−0.843101	−	0.537755i	$-0.819273\pi$
$659$	−7.83856	+	7.83856i	−0.305347	+	0.305347i	0.537755	+	0.843101i	$0.319273\pi$
$660$	−2.83917	−	16.1822i	−0.110515	−	0.629890i
$661$	−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
$666$	−28.6780	+	6.08108i	−1.11125	+	0.235637i
$667$	10.6787	−	10.6787i	0.413480	−	0.413480i
$668$	−15.4508	+	33.5725i	−0.597810	+	1.29896i
$669$	15.1604	−	10.4836i	0.586136	−	0.405319i
$670$	−17.8135	−	3.90238i	−0.688196	−	0.150762i
$671$	−66.2466			−2.55742
$672$	4.46618	−	8.72085i	0.172287	−	0.336414i
$673$	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
$675$	−4.80558	−	19.2845i	−0.184967	−	0.742259i
$676$	−10.7546	+	23.3683i	−0.413639	+	0.898780i
$677$	−32.8347	+	32.8347i	−1.26194	+	1.26194i	−0.311789	+	0.950151i	$0.600928\pi$
$677$	−32.8347	+	32.8347i	−1.26194	+	1.26194i	−0.950151	+	0.311789i	$0.899072\pi$
$678$	−35.5142	+	14.5711i	−1.36392	+	0.559599i
$679$	−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	0.939795	−	0.341739i	$-0.111016\pi$
$683$	15.6297	+	15.6297i	0.598056	+	0.598056i	−0.341739	+	0.939795i	$0.611016\pi$
$684$	20.7052	+	0.138930i	0.791684	+	0.00531210i
$685$	−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
$690$	3.32531	−	7.95244i	0.126592	−	0.302744i
$691$	−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
$693$	−11.9593	+	5.40701i	−0.454297	+	0.205395i
$694$	−19.2452	−	30.0427i	−0.730540	−	1.14040i
$695$		−	0.402383i		−	0.0152632i
$696$	−16.7784	+	15.4257i	−0.635985	+	0.584711i
$697$			30.3229i			1.14856i
$698$	31.9523	−	20.4686i	1.20941	−	0.774747i
$699$	0.729950	+	1.05559i	0.0276093	+	0.0399260i
$700$	3.19808	−	6.94899i	0.120876	−	0.262647i
$701$	−6.13145	−	6.13145i	−0.231582	−	0.231582i	0.581771	−	0.813353i	$-0.302360\pi$
$701$	−6.13145	−	6.13145i	−0.231582	−	0.231582i	−0.813353	+	0.581771i	$0.802360\pi$
$702$	−1.87345	+	1.98364i	−0.0707089	+	0.0748676i
$703$		−	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
$708$	−7.40603	+	10.5578i	−0.278335	+	0.396786i
$709$	−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
$714$	−6.09068	+	2.49894i	−0.227938	+	0.0935204i
$715$	−1.24520	+	1.24520i	−0.0465679	+	0.0465679i
$716$	32.4291	−	11.9875i	1.21193	−	0.447996i
$717$	−3.99693	−	5.77999i	−0.149268	−	0.215858i
$718$	9.23430	−	42.1526i	0.344621	−	1.57312i
$719$	37.8458			1.41141			0.705706	−	0.708505i	$-0.250630\pi$
$719$	37.8458			1.41141			0.705706	+	0.708505i	$0.250630\pi$
$720$	−5.51781	+	11.7806i	−0.205637	+	0.439039i
$721$	17.2202			0.641314
$722$	2.14596	−	9.79583i	0.0798642	−	0.364563i
$723$	−22.1719	−	32.0630i	−0.824581	−	1.19243i
$724$	3.51561	+	9.51055i	0.130657	+	0.353457i
$725$	−12.5825	+	12.5825i	−0.467302	+	0.467302i
$726$	−18.4469	+	7.56853i	−0.684627	+	0.280895i
$727$	−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
$732$	42.9425	+	30.1231i	1.58720	+	1.11338i
$733$	−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
$738$	26.0896	−	40.1316i	0.960373	−	1.47727i
$739$	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
$741$	−1.26229	−	1.82541i	−0.0463713	−	0.0670580i
$742$	−6.98255	+	4.47300i	−0.256337	+	0.164209i
$743$		−	2.79821i		−	0.102656i	−0.998682	−	0.0513282i	$-0.983655\pi$
$743$		−	2.79821i		−	0.102656i	0.998682	−	0.0513282i	$-0.0163455\pi$
$744$	18.4468	+	0.774827i	0.676291	+	0.0284065i
$745$		−	22.9804i		−	0.841936i
$746$	−1.56152	−	2.43760i	−0.0571714	−	0.0892470i
$747$	0.187930	+	0.415667i	0.00687601	+	0.0152085i
$748$	−22.0579	+	8.15379i	−0.806517	+	0.298132i
$749$	−7.02957	−	7.02957i	−0.256855	−	0.256855i
$750$	−9.04020	+	21.6195i	−0.330101	+	0.789434i
$751$			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
$756$	10.2109	+	1.93310i	0.371368	+	0.0703061i
$757$	−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	$-0.433656\pi$
$761$	11.4162			0.413837			0.206919	+	0.978358i	$0.433656\pi$
$762$	1.98217	−	0.813261i	0.0718064	−	0.0294613i
$763$	1.85810	−	1.85810i	0.0672677	−	0.0672677i
$764$	−41.6540	−	19.1701i	−1.50699	−	0.693551i
$765$	7.96463	−	3.60095i	0.287962	−	0.130193i
$766$	−4.54592	−	0.995867i	−0.164251	−	0.0359821i
$767$	1.38230			0.0499119
$768$	−24.9478	+	12.0669i	−0.900225	+	0.435425i
$769$	−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
$771$	10.5434	−	7.29086i	0.379711	−	0.262574i
$772$	−6.23403	−	2.86905i	−0.224368	−	0.103259i
$773$	−11.1451	+	11.1451i	−0.400860	+	0.400860i	−0.878536	−	0.477676i	$-0.841479\pi$
$773$	−11.1451	+	11.1451i	−0.400860	+	0.400860i	0.477676	+	0.878536i	$0.341479\pi$
$774$	−1.16780	−	5.50730i	−0.0419759	−	0.197956i
$775$	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
$780$	1.37338	−	0.240960i	0.0491748	−	0.00862774i
$781$	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
$786$	−9.46411	−	3.95742i	−0.337574	−	0.141156i
$787$	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
$789$	23.6386	−	16.3464i	0.841557	−	0.581946i
$790$	3.17192	+	4.95150i	0.112852	+	0.176167i
$791$		−	15.6715i		−	0.557215i
$792$	36.2086	+	8.18714i	1.28661	+	0.290917i
$793$		−	5.62233i		−	0.199655i
$794$	0.598778	−	0.383575i	0.0212498	−	0.0136126i
$795$	9.05561	−	6.26205i	0.321170	−	0.222092i
$796$	24.5198	+	11.2846i	0.869080	+	0.399971i
$797$	−24.9703	−	24.9703i	−0.884494	−	0.884494i	0.109494	−	0.993987i	$-0.465077\pi$
$797$	−24.9703	−	24.9703i	−0.884494	−	0.884494i	−0.993987	+	0.109494i	$0.965077\pi$
$798$	−3.26103	+	7.79871i	−0.115439	+	0.276071i
$799$			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
$804$	23.6627	−	33.7328i	0.834520	−	1.18966i
$805$	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	$-0.407303\pi$
$809$	16.3328			0.574232			0.287116	+	0.957896i	$0.407303\pi$
$810$	−13.6392	−	2.08695i	−0.479233	−	0.0733280i
$811$	−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
$813$	−10.3637	+	7.16659i	−0.363470	+	0.251343i
$814$	9.14854	−	41.7611i	0.320656	−	1.46373i
$815$	3.38563			0.118594
$816$	18.0061	+	4.74453i	0.630338	+	0.166092i
$817$	4.57922			0.160207
$818$	4.17720	−	19.0680i	0.146052	−	0.666698i
$819$	−0.458892	−	1.01498i	−0.0160350	−	0.0354664i
$820$	−22.9442	+	8.48139i	−0.801245	+	0.296183i
$821$	32.3716	−	32.3716i	1.12978	−	1.12978i	0.139565	−	0.990213i	$-0.455430\pi$
$821$	32.3716	−	32.3716i	1.12978	−	1.12978i	0.990213	−	0.139565i	$-0.0445704\pi$
$822$	−12.6042	−	30.7203i	−0.439621	−	1.07149i
$823$	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	0.479079	−	0.877772i	$-0.340971\pi$
$827$	−11.4655	−	11.4655i	−0.398693	−	0.398693i	−0.877772	+	0.479079i	$0.840971\pi$
$828$	13.6792	+	13.8640i	0.475385	+	0.481808i
$829$	−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
$834$	0.838815	+	0.350750i	0.0290458	+	0.0121455i
$835$	14.1649	+	14.1649i	0.490195	+	0.490195i
$836$	−12.6239	+	27.4299i	−0.436606	+	0.948683i
$837$	4.73517	+	19.0019i	0.163672	+	0.656802i
$838$	14.2072	−	9.10110i	0.490780	−	0.314392i
$839$		−	9.65631i		−	0.333373i	−0.986010	−	0.166686i	$-0.946693\pi$
$839$		−	9.65631i		−	0.333373i	0.986010	−	0.166686i	$-0.0533067\pi$
$840$	−3.59442	−	3.90962i	−0.124019	−	0.134895i
$841$		−	7.35545i		−	0.253636i
$842$	−5.75146	−	8.97827i	−0.198208	−	0.309412i
$843$	−23.5817	−	34.1017i	−0.812195	−	1.17452i
$844$	8.61199	+	23.2975i	0.296437	+	0.801932i
$845$	9.85951	+	9.85951i	0.339178	+	0.339178i
$846$	1.76722	−	2.71837i	0.0607582	−	0.0934596i
$847$		−	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
$852$	−46.9495	+	8.23731i	−1.60846	+	0.282206i
$853$	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	$-0.524602\pi$
$857$	−4.52066			−0.154423			−0.0772115	+	0.997015i	$0.524602\pi$
$858$	−1.51035	−	3.68120i	−0.0515626	−	0.125674i
$859$	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
$861$	11.1145	+	16.0728i	0.378783	+	0.547761i
$862$	35.5761	+	7.79361i	1.21173	+	0.265451i
$863$	−9.02247			−0.307128			−0.153564	−	0.988139i	$-0.549075\pi$
$863$	−9.02247			−0.307128			−0.153564	+	0.988139i	$0.549075\pi$
$864$	−19.7484	−	21.7716i	−0.671854	−	0.740683i
$865$	1.32849			0.0451700
$866$	9.34540	+	2.04728i	0.317570	+	0.0695694i
$867$	9.63114	+	13.9277i	0.327091	+	0.473009i
$868$	−3.15123	+	6.84717i	−0.106960	+	0.232408i
$869$	11.8655	−	11.8655i	0.402511	−	0.402511i
$870$	4.68935	+	11.4294i	0.158984	+	0.387493i
$871$	−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
$876$	23.1840	−	4.06765i	0.783316	−	0.137433i
$877$	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	$-0.931714\pi$
$881$		−	12.6375i		−	0.425768i	0.977077	−	0.212884i	$-0.0682856\pi$
$882$	−2.31244	+	3.55705i	−0.0778640	+	0.119772i
$883$	−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
$885$	3.97584	+	5.74950i	0.133646	+	0.193267i
$886$	26.4657	+	41.3141i	0.889133	+	1.38798i
$887$			47.8477i			1.60657i	0.595596	+	0.803284i	$0.296916\pi$
$887$			47.8477i			1.60657i	−0.595596	+	0.803284i	$0.703084\pi$
$888$	−24.9196	+	22.9105i	−0.836246	+	0.768828i
$889$			0.874680i			0.0293358i
$890$	−11.6219	+	7.44496i	−0.389567	+	0.249556i
$891$	2.51149	+	39.2943i	0.0841382	+	1.31641i
$892$	8.89811	−	19.3343i	0.297931	−	0.647361i
$893$	1.86484	+	1.86484i	0.0624047	+	0.0624047i
$894$	47.9054	+	20.0316i	1.60220	+	0.669957i
$895$		−	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
$900$	−16.1180	−	16.3357i	−0.537266	−	0.544524i
$901$	−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
$906$	12.3370	+	30.0690i	0.409868	+	0.998976i
$907$	−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
$909$	−12.6648	−	28.0123i	−0.420066	−	0.929109i
$910$	−0.121814	+	0.556056i	−0.00403811	+	0.0184331i
$911$	−37.1786			−1.23178			−0.615892	−	0.787831i	$-0.711204\pi$
$911$	−37.1786			−1.23178			−0.615892	+	0.787831i	$0.711204\pi$
$912$	20.6558	−	12.0405i	0.683982	−	0.398699i
$913$	−0.665249			−0.0220165
$914$	7.59897	−	34.6877i	0.251352	−	1.14737i
$915$	23.3854	−	16.1712i	0.773097	−	0.534605i
$916$	2.62120	+	7.09095i	0.0866068	+	0.234292i
$917$	2.96129	−	2.96129i	0.0977903	−	0.0977903i
$918$	0.563972	+	19.7421i	0.0186139	+	0.651587i
$919$	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
$924$	−8.70324	+	12.4071i	−0.286316	+	0.408162i
$925$	−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	$0.108992\pi$
$929$			20.4674i			0.671513i	−0.941949	+	0.335756i	$0.891008\pi$
$930$	3.86074	−	9.23293i	0.126599	−	0.302760i
$931$	−2.44019	−	2.44019i	−0.0799740	−	0.0799740i
$932$	1.34621	+	0.619556i	0.0440965	+	0.0202942i
$933$	40.9768	−	28.3359i	1.34152	−	0.927674i
$934$	−43.8604	+	28.0968i	−1.43516	+	0.919356i
$935$			12.7469i			0.416868i
$936$	−0.694840	+	3.07301i	−0.0227116	+	0.100445i
$937$			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
$939$	−28.5357	+	19.7327i	−0.931227	+	0.643954i
$940$	−1.55416	+	0.574499i	−0.0506910	+	0.0187381i
$941$	−21.0694	−	21.0694i	−0.686844	−	0.686844i	0.274689	−	0.961533i	$-0.411425\pi$
$941$	−21.0694	−	21.0694i	−0.686844	−	0.686844i	−0.961533	+	0.274689i	$0.911425\pi$
$942$	−25.2424	−	10.5551i	−0.822441	−	0.343903i
$943$			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	−0.740191	−	0.672396i	$-0.765265\pi$
$947$	−2.08628	+	2.08628i	−0.0677949	+	0.0677949i	0.672396	+	0.740191i	$0.265265\pi$
$948$	−13.0869	+	2.29611i	−0.425044	+	0.0745741i
$949$	−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	$-0.449551\pi$
$953$	9.74445			0.315654			0.157827	+	0.987467i	$0.449551\pi$
$954$	5.16038	+	24.3361i	0.167074	+	0.787909i
$955$	−17.5746	+	17.5746i	−0.568700	+	0.568700i
$956$	−7.37131	−	3.39245i	−0.238405	−	0.109720i
$957$	28.9963	−	20.0512i	0.937317	−	0.648165i
$958$	24.4136	+	5.34825i	0.788768	+	0.172794i
$959$	13.5561			0.437748
$960$	1.44634	+	14.9515i	0.0466803	+	0.482558i
$961$	16.7965			0.541823
$962$	3.54426	+	0.776434i	0.114271	+	0.0250332i
$963$	−27.1755	+	12.2865i	−0.875719	+	0.395928i
$964$	−40.8904	−	18.8187i	−1.31699	−	0.606110i
$965$	−2.63026	+	2.63026i	−0.0846709	+	0.0846709i
$966$	−7.35614	+	3.01814i	−0.236680	+	0.0971070i
$967$	−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	0.662352	−	0.749192i	$-0.269558\pi$
$971$	−2.70601	−	2.70601i	−0.0868399	−	0.0868399i	−0.749192	+	0.662352i	$0.769558\pi$
$972$	16.2396	−	26.6135i	0.520885	−	0.853627i
$973$	−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	$-0.979155\pi$
$977$		−	4.09093i		−	0.130880i	0.997856	−	0.0654402i	$-0.0208452\pi$
$978$	−2.95120	+	7.05776i	−0.0943690	+	0.225682i
$979$	27.8502	+	27.8502i	0.890096	+	0.890096i
$980$	2.03365	−	0.751744i	0.0649624	−	0.0240136i
$981$	−3.24765	−	7.18319i	−0.103689	−	0.229342i
$982$	23.6015	+	36.8429i	0.753153	+	1.17571i
$983$			37.9997i			1.21200i	0.795464	+	0.606001i	$0.207227\pi$
$983$			37.9997i			1.21200i	−0.795464	+	0.606001i	$0.792773\pi$
$984$	2.31955	−	55.2230i	0.0739446	−	1.76044i
$985$		−	13.2134i		−	0.421015i
$986$	14.8901	−	9.53856i	0.474198	−	0.303770i
$987$	0.752860	+	1.08872i	0.0239638	+	0.0346543i
$988$	−2.32797	−	1.07139i	−0.0740626	−	0.0340853i
$989$	3.04576	+	3.04576i	0.0968497	+	0.0968497i
$990$	10.9673	−	16.8702i	0.348565	−	0.536170i
$991$			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
$996$	0.431229	+	0.302497i	0.0136640	+	0.00958497i
$997$	−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.155.19	yes	40
3.2	odd	2	inner	336.2.s.c.155.2	✓	40
4.3	odd	2		1344.2.s.c.911.7		40
12.11	even	2		1344.2.s.c.911.4		40
16.3	odd	4	inner	336.2.s.c.323.2	yes	40
16.13	even	4		1344.2.s.c.239.4		40
48.29	odd	4		1344.2.s.c.239.7		40
48.35	even	4	inner	336.2.s.c.323.19	yes	40

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

\(f(q)\)	\(=\)	\(q+(1.38145 + 0.302633i) q^{2} +(0.985133 + 1.42461i) q^{3} +(1.81683 + 0.836146i) q^{4} +(0.766553 - 0.766553i) q^{5} +(0.929782 + 2.26617i) q^{6} -1.00000 q^{7} +(2.25682 + 1.70493i) q^{8} +(-1.05903 + 2.80686i) q^{9} +O(q^{10})\)	\(q+(1.38145 + 0.302633i) q^{2} +(0.985133 + 1.42461i) q^{3} +(1.81683 + 0.836146i) q^{4} +(0.766553 - 0.766553i) q^{5} +(0.929782 + 2.26617i) 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} +(0.598634 + 3.41198i) 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} +(-2.31244 + 3.55705i) q^{18} +(-2.44019 - 2.44019i) q^{19} +(2.03365 - 0.751744i) q^{20} +(-0.985133 - 1.42461i) q^{21} +(-3.33739 - 5.20981i) q^{22} -3.24607i q^{23} +(-0.205592 + 4.89466i) q^{24} +3.82479i q^{25} +(0.442155 - 0.283243i) q^{26} +(-5.04196 + 1.25643i) q^{27} +(-1.81683 - 0.836146i) q^{28} +(3.28972 + 3.28972i) q^{29} +(2.44986 + 1.02441i) 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} +(-4.27101 + 4.21408i) 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} +(-0.929782 - 2.26617i) q^{42} +(-0.938292 + 0.938292i) q^{43} +(-3.03379 - 8.20711i) q^{44} +(1.33981 + 2.96341i) q^{45} +(0.982368 - 4.48430i) q^{46} -0.764222 q^{47} +(-1.76530 + 6.69953i) q^{48} +1.00000 q^{49} +(-1.15751 + 5.28377i) q^{50} +(3.82887 - 2.64770i) q^{51} +(0.696535 - 0.257477i) q^{52} +(4.14619 - 4.14619i) q^{53} +(-7.34547 + 0.209838i) 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} +(3.07435 + 2.15658i) 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} +(4.13417 - 9.88683i) q^{66} +(-8.41087 - 8.41087i) q^{67} +(2.24728 - 4.88301i) q^{68} +(4.62439 - 3.19781i) q^{69} +(-1.29094 + 0.826974i) q^{70} +13.7602i q^{71} +(-7.17552 + 4.52900i) q^{72} -6.79488i q^{73} +(5.27106 + 8.22835i) q^{74} +(-5.44884 + 3.76793i) q^{75} +(-2.39305 - 6.47375i) q^{76} +(3.09355 + 3.09355i) q^{77} +(0.839093 + 0.350866i) 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} +(-0.598634 - 3.41198i) 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} +(0.954058 + 4.49928i) q^{90} +(-0.262549 + 0.262549i) q^{91} +(2.71419 - 5.89755i) q^{92} +(5.36900 - 3.71272i) q^{93} +(-1.05574 - 0.231278i) q^{94} -3.74107 q^{95} +(-4.46618 + 8.72085i) q^{96} +18.1447 q^{97} +(1.38145 + 0.302633i) q^{98} +(11.9593 - 5.40701i) 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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