LMFDB - Embedded newform 185.2.v.a.169.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(4,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.v (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	185.169
Dual form			185.2.v.a.104.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.160351 + 0.0583632i) q^{2} +(-0.245536 - 0.674605i) q^{3} +(-1.50978 - 1.26686i) q^{4} +(-1.78511 + 1.34662i) q^{5} -0.122504i q^{6} +(-3.51024 - 0.618951i) q^{7} +(-0.338800 - 0.586820i) q^{8} +(1.90333 - 1.59708i) q^{9} +(-0.364838 + 0.111748i) q^{10} +(-2.79800 - 4.84627i) q^{11} +(-0.483922 + 1.32957i) q^{12} +(1.40068 + 1.17531i) q^{13} +(-0.526749 - 0.304118i) q^{14} +(1.34675 + 0.873599i) q^{15} +(0.664401 + 3.76801i) q^{16} +(-4.85332 + 4.07242i) q^{17} +(0.398412 - 0.145010i) q^{18} +(0.400455 + 1.10024i) q^{19} +(4.40110 + 0.228375i) q^{20} +(0.444344 + 2.52000i) q^{21} +(-0.165819 - 0.940407i) q^{22} +(4.15386 - 7.19469i) q^{23} +(-0.312684 + 0.372642i) q^{24} +(1.37323 - 4.80773i) q^{25} +(0.156006 + 0.270210i) q^{26} +(-3.40989 - 1.96870i) q^{27} +(4.51558 + 5.38146i) q^{28} +(2.90414 - 1.67670i) q^{29} +(0.164967 + 0.218683i) q^{30} +2.55670i q^{31} +(-0.348703 + 1.97760i) q^{32} +(-2.58231 + 3.07748i) q^{33} +(-1.01592 + 0.369763i) q^{34} +(7.09966 - 3.62207i) q^{35} -4.89689 q^{36} +(5.12643 - 3.27409i) q^{37} +0.199797i q^{38} +(0.448951 - 1.23348i) q^{39} +(1.39502 + 0.591301i) q^{40} +(-0.879400 - 0.737904i) q^{41} +(-0.0758240 + 0.430019i) q^{42} +1.23182 q^{43} +(-1.91517 + 10.8615i) q^{44} +(-1.24699 + 5.41403i) q^{45} +(1.08598 - 0.911247i) q^{46} +(-4.82340 - 2.78479i) q^{47} +(2.37878 - 1.37339i) q^{48} +(5.36086 + 1.95119i) q^{49} +(0.500793 - 0.690780i) q^{50} +(3.93894 + 2.27415i) q^{51} +(-0.625770 - 3.54892i) q^{52} +(-8.99680 + 1.58638i) q^{53} +(-0.431882 - 0.514697i) q^{54} +(11.5208 + 4.88329i) q^{55} +(0.826060 + 2.26958i) q^{56} +(0.643902 - 0.540298i) q^{57} +(0.563540 - 0.0993673i) q^{58} +(-9.96639 + 1.75734i) q^{59} +(-0.926566 - 3.02508i) q^{60} +(2.36411 - 2.81744i) q^{61} +(-0.149217 + 0.409970i) q^{62} +(-7.66966 + 4.42808i) q^{63} +(3.65480 - 6.33030i) q^{64} +(-4.08305 - 0.211872i) q^{65} +(-0.593689 + 0.342766i) q^{66} +(-10.4395 - 1.84077i) q^{67} +12.4866 q^{68} +(-5.87350 - 1.03566i) q^{69} +(1.34984 - 0.166446i) q^{70} +(6.13971 - 2.23467i) q^{71} +(-1.58205 - 0.575819i) q^{72} -6.54940i q^{73} +(1.01312 - 0.225811i) q^{74} +(-3.58049 + 0.254085i) q^{75} +(0.789250 - 2.16845i) q^{76} +(6.82205 + 18.7434i) q^{77} +(0.143980 - 0.171589i) q^{78} +(14.1537 + 2.49567i) q^{79} +(-6.26010 - 5.83161i) q^{80} +(0.803505 - 4.55690i) q^{81} +(-0.0979466 - 0.169649i) q^{82} +(-0.232963 - 0.277634i) q^{83} +(2.52162 - 4.36758i) q^{84} +(3.17970 - 13.8053i) q^{85} +(0.197524 + 0.0718927i) q^{86} +(-1.84418 - 1.54745i) q^{87} +(-1.89593 + 3.28384i) q^{88} +(-11.2979 + 1.99213i) q^{89} +(-0.515936 + 0.795369i) q^{90} +(-4.18926 - 4.99256i) q^{91} +(-15.3861 + 5.60007i) q^{92} +(1.72476 - 0.627761i) q^{93} +(-0.610910 - 0.728054i) q^{94} +(-2.19646 - 1.42479i) q^{95} +(1.41971 - 0.250334i) q^{96} +(1.67715 - 2.90491i) q^{97} +(0.745743 + 0.625753i) q^{98} +(-13.0654 - 4.75542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.160351	+	0.0583632i	0.113386	+	0.0412690i	0.398090	−	0.917346i	$-0.369673\pi$
$2$	0.160351	+	0.0583632i	0.113386	+	0.0412690i	−0.284704	+	0.958615i	$0.591895\pi$
$3$	−0.245536	−	0.674605i	−0.141760	−	0.389483i	0.848412	−	0.529337i	$-0.177559\pi$
$3$	−0.245536	−	0.674605i	−0.141760	−	0.389483i	−0.990172	+	0.139853i	$0.955337\pi$
$4$	−1.50978	−	1.26686i	−0.754891	−	0.633429i
$5$	−1.78511	+	1.34662i	−0.798325	+	0.602227i
$5$	−1.78511	+	1.34662i	−0.798325	+	0.602227i
$6$		−	0.122504i		−	0.0500121i
$7$	−3.51024	−	0.618951i	−1.32675	−	0.233941i	−0.535032	−	0.844832i	$-0.679700\pi$
$7$	−3.51024	−	0.618951i	−1.32675	−	0.233941i	−0.791715	+	0.610891i	$0.790812\pi$
$8$	−0.338800	−	0.586820i	−0.119784	−	0.207472i
$9$	1.90333	−	1.59708i	0.634443	−	0.532361i
$10$	−0.364838	+	0.111748i	−0.115372	+	0.0353378i
$11$	−2.79800	−	4.84627i	−0.843628	−	1.46121i	−0.886808	−	0.462139i	$-0.847082\pi$
$11$	−2.79800	−	4.84627i	−0.843628	−	1.46121i	0.0431797	−	0.999067i	$-0.486251\pi$
$12$	−0.483922	+	1.32957i	−0.139696	+	0.383813i
$13$	1.40068	+	1.17531i	0.388478	+	0.325972i	0.816020	−	0.578024i	$-0.196176\pi$
$13$	1.40068	+	1.17531i	0.388478	+	0.325972i	−0.427542	+	0.903995i	$0.640620\pi$
$14$	−0.526749	−	0.304118i	−0.140779	−	0.0812791i
$15$	1.34675	+	0.873599i	0.347728	+	0.225562i
$16$	0.664401	+	3.76801i	0.166100	+	0.942002i
$17$	−4.85332	+	4.07242i	−1.17710	+	0.987706i	−0.177108	+	0.984191i	$0.556674\pi$
$17$	−4.85332	+	4.07242i	−1.17710	+	0.987706i	−0.999994	+	0.00351439i	$0.998881\pi$
$18$	0.398412	−	0.145010i	0.0939067	−	0.0341792i
$19$	0.400455	+	1.10024i	0.0918708	+	0.252413i	0.977114	−	0.212715i	$-0.0682306\pi$
$19$	0.400455	+	1.10024i	0.0918708	+	0.252413i	−0.885244	+	0.465128i	$0.846008\pi$
$20$	4.40110	+	0.228375i	0.984117	+	0.0510663i
$21$	0.444344	+	2.52000i	0.0969639	+	0.549909i
$22$	−0.165819	−	0.940407i	−0.0353528	−	0.200495i
$23$	4.15386	−	7.19469i	0.866139	−	1.50020i	0.000228074	−	1.00000i	$-0.499927\pi$
$23$	4.15386	−	7.19469i	0.866139	−	1.50020i	0.865911	−	0.500198i	$-0.166739\pi$
$24$	−0.312684	+	0.372642i	−0.0638263	+	0.0760652i
$25$	1.37323	−	4.80773i	0.274645	−	0.961546i
$26$	0.156006	+	0.270210i	0.0305953	+	0.0529926i
$27$	−3.40989	−	1.96870i	−0.656234	−	0.378877i
$28$	4.51558	+	5.38146i	0.853365	+	1.01700i
$29$	2.90414	−	1.67670i	0.539285	−	0.311356i	−0.205504	−	0.978656i	$-0.565883\pi$
$29$	2.90414	−	1.67670i	0.539285	−	0.311356i	0.744789	+	0.667300i	$0.232550\pi$
$30$	0.164967	+	0.218683i	0.0301186	+	0.0399259i
$31$			2.55670i			0.459196i	0.973286	+	0.229598i	$0.0737411\pi$
$31$			2.55670i			0.459196i	−0.973286	+	0.229598i	$0.926259\pi$
$32$	−0.348703	+	1.97760i	−0.0616426	+	0.349593i
$33$	−2.58231	+	3.07748i	−0.449523	+	0.535720i
$34$	−1.01592	+	0.369763i	−0.174228	+	0.0634138i
$35$	7.09966	−	3.62207i	1.20006	−	0.612242i
$36$	−4.89689			−0.816149
$37$	5.12643	−	3.27409i	0.842780	−	0.538257i
$37$	5.12643	−	3.27409i	0.842780	−	0.538257i
$38$			0.199797i			0.0324114i
$39$	0.448951	−	1.23348i	0.0718898	−	0.197515i
$40$	1.39502	+	0.591301i	0.220572	+	0.0934929i
$41$	−0.879400	−	0.737904i	−0.137339	−	0.115241i	0.571530	−	0.820581i	$-0.306350\pi$
$41$	−0.879400	−	0.737904i	−0.137339	−	0.115241i	−0.708869	+	0.705340i	$0.750794\pi$
$42$	−0.0758240	+	0.430019i	−0.0116999	+	0.0663534i
$43$	1.23182			0.187850			0.0939251	−	0.995579i	$-0.470059\pi$
$43$	1.23182			0.187850			0.0939251	+	0.995579i	$0.470059\pi$
$44$	−1.91517	+	10.8615i	−0.288723	+	1.63743i
$45$	−1.24699	+	5.41403i	−0.185890	+	0.807076i
$46$	1.08598	−	0.911247i	0.160119	−	0.134356i
$47$	−4.82340	−	2.78479i	−0.703565	−	0.406204i	0.105109	−	0.994461i	$-0.466481\pi$
$47$	−4.82340	−	2.78479i	−0.703565	−	0.406204i	−0.808674	+	0.588257i	$0.799814\pi$
$48$	2.37878	−	1.37339i	0.343348	−	0.198232i
$49$	5.36086	+	1.95119i	0.765837	+	0.278742i
$50$	0.500793	−	0.690780i	0.0708228	−	0.0976911i
$51$	3.93894	+	2.27415i	0.551561	+	0.318444i
$52$	−0.625770	−	3.54892i	−0.0867787	−	0.492146i
$53$	−8.99680	+	1.58638i	−1.23581	+	0.217906i	−0.753117	−	0.657887i	$-0.771451\pi$
$53$	−8.99680	+	1.58638i	−1.23581	+	0.217906i	−0.482688	+	0.875792i	$0.660340\pi$
$54$	−0.431882	−	0.514697i	−0.0587717	−	0.0700413i
$55$	11.5208	+	4.88329i	1.55347	+	0.658462i
$56$	0.826060	+	2.26958i	0.110387	+	0.303285i
$57$	0.643902	−	0.540298i	0.0852870	−	0.0715643i
$58$	0.563540	−	0.0993673i	0.0739965	−	0.0130476i
$59$	−9.96639	+	1.75734i	−1.29751	+	0.228787i	−0.779401	−	0.626526i	$-0.784476\pi$
$59$	−9.96639	+	1.75734i	−1.29751	+	0.228787i	−0.518113	+	0.855312i	$0.673365\pi$
$60$	−0.926566	−	3.02508i	−0.119619	−	0.390536i
$61$	2.36411	−	2.81744i	0.302693	−	0.360736i	−0.593161	−	0.805084i	$-0.702120\pi$
$61$	2.36411	−	2.81744i	0.302693	−	0.360736i	0.895854	+	0.444348i	$0.146565\pi$
$62$	−0.149217	+	0.409970i	−0.0189506	+	0.0520662i
$63$	−7.66966	+	4.42808i	−0.966287	+	0.557886i
$64$	3.65480	−	6.33030i	0.456850	−	0.791288i
$65$	−4.08305	−	0.211872i	−0.506440	−	0.0262795i
$66$	−0.593689	+	0.342766i	−0.0730780	+	0.0421916i
$67$	−10.4395	−	1.84077i	−1.27539	−	0.224886i	−0.505370	−	0.862902i	$-0.668644\pi$
$67$	−10.4395	−	1.84077i	−1.27539	−	0.224886i	−0.770023	+	0.638016i	$0.779755\pi$
$68$	12.4866			1.51423
$69$	−5.87350	−	1.03566i	−0.707086	−	0.124678i
$70$	1.34984	−	0.166446i	0.161336	−	0.0198941i
$71$	6.13971	−	2.23467i	0.728650	−	0.265207i	0.0490566	−	0.998796i	$-0.484379\pi$
$71$	6.13971	−	2.23467i	0.728650	−	0.265207i	0.679593	+	0.733589i	$0.262156\pi$
$72$	−1.58205	−	0.575819i	−0.186446	−	0.0678609i
$73$		−	6.54940i		−	0.766549i	−0.923634	−	0.383275i	$-0.874796\pi$
$73$		−	6.54940i		−	0.766549i	0.923634	−	0.383275i	$-0.125204\pi$
$74$	1.01312	−	0.225811i	0.117773	−	0.0262499i
$75$	−3.58049	+	0.254085i	−0.413440	+	0.0293392i
$76$	0.789250	−	2.16845i	0.0905332	−	0.248738i
$77$	6.82205	+	18.7434i	0.777444	+	2.13601i
$78$	0.143980	−	0.171589i	0.0163025	−	0.0194286i
$79$	14.1537	+	2.49567i	1.59241	+	0.280785i	0.898400	−	0.439179i	$-0.144731\pi$
$79$	14.1537	+	2.49567i	1.59241	+	0.280785i	0.694012	+	0.719964i	$0.255842\pi$
$80$	−6.26010	−	5.83161i	−0.699901	−	0.651993i
$81$	0.803505	−	4.55690i	0.0892783	−	0.506322i
$82$	−0.0979466	−	0.169649i	−0.0108164	−	0.0187345i
$83$	−0.232963	−	0.277634i	−0.0255710	−	0.0304743i	0.753107	−	0.657898i	$-0.228554\pi$
$83$	−0.232963	−	0.277634i	−0.0255710	−	0.0304743i	−0.778678	+	0.627423i	$0.784110\pi$
$84$	2.52162	−	4.36758i	0.275131	−	0.476542i
$85$	3.17970	−	13.8053i	0.344887	−	1.49739i
$86$	0.197524	+	0.0718927i	0.0212995	+	0.00775239i
$87$	−1.84418	−	1.54745i	−0.197717	−	0.165904i
$88$	−1.89593	+	3.28384i	−0.202106	+	0.350058i
$89$	−11.2979	+	1.99213i	−1.19758	+	0.211165i	−0.736650	−	0.676274i	$-0.763594\pi$
$89$	−11.2979	+	1.99213i	−1.19758	+	0.211165i	−0.460926	+	0.887439i	$0.652483\pi$
$90$	−0.515936	+	0.795369i	−0.0543844	+	0.0838393i
$91$	−4.18926	−	4.99256i	−0.439154	−	0.523363i
$92$	−15.3861	+	5.60007i	−1.60411	+	0.583848i
$93$	1.72476	−	0.627761i	0.178849	−	0.0650958i
$94$	−0.610910	−	0.728054i	−0.0630106	−	0.0750931i
$95$	−2.19646	−	1.42479i	−0.225353	−	0.146180i
$96$	1.41971	−	0.250334i	0.144899	−	0.0255496i
$97$	1.67715	−	2.90491i	0.170289	−	0.294949i	−0.768232	−	0.640171i	$-0.778863\pi$
$97$	1.67715	−	2.90491i	0.170289	−	0.294949i	0.938521	+	0.345223i	$0.112197\pi$
$98$	0.745743	+	0.625753i	0.0753315	+	0.0632106i
$99$	−13.0654	−	4.75542i	−1.31312	−	0.477938i
$100$	−8.16398	+	5.51894i	−0.816398	+	0.551894i
$101$	2.77691	−	4.80974i	0.276313	−	0.478587i	−0.694153	−	0.719828i	$-0.744221\pi$
$101$	2.77691	−	4.80974i	0.276313	−	0.478587i	0.970465	+	0.241240i	$0.0775542\pi$
$102$	0.498888	+	0.594551i	0.0493972	+	0.0588693i
$103$	−4.00145	−	6.93072i	−0.394275	−	0.682904i	0.598733	−	0.800948i	$-0.295671\pi$
$103$	−4.00145	−	6.93072i	−0.394275	−	0.682904i	−0.993008	+	0.118044i	$0.962338\pi$
$104$	0.215143	−	1.22014i	0.0210966	−	0.119644i
$105$	−4.18669	−	3.90011i	−0.408579	−	0.380612i
$106$	−1.53524	−	0.270703i	−0.149115	−	0.0262930i
$107$	−1.79573	+	2.14007i	−0.173600	+	0.206889i	−0.845828	−	0.533456i	$-0.820893\pi$
$107$	−1.79573	+	2.14007i	−0.173600	+	0.206889i	0.672228	+	0.740344i	$0.265338\pi$
$108$	2.65413	+	7.29217i	0.255394	+	0.701689i
$109$	−4.17259	+	11.4641i	−0.399661	+	1.09806i	0.562789	+	0.826601i	$0.309728\pi$
$109$	−4.17259	+	11.4641i	−0.399661	+	1.09806i	−0.962450	+	0.271459i	$0.912494\pi$
$110$	1.56238	+	1.45543i	0.148967	+	0.138770i
$111$	−3.46744	−	2.65441i	−0.329115	−	0.251945i
$112$		−	13.6379i		−	1.28866i
$113$	1.77213	+	0.645004i	0.166708	+	0.0606769i	0.424026	−	0.905650i	$-0.360616\pi$
$113$	1.77213	+	0.645004i	0.166708	+	0.0606769i	−0.257318	+	0.966327i	$0.582839\pi$
$114$	0.134784	−	0.0490574i	0.0126237	−	0.00459465i
$115$	2.27343	+	18.4370i	0.211999	+	1.71926i
$116$	−6.50876	−	1.14767i	−0.604323	−	0.106558i
$117$	4.54301			0.420002
$118$	−1.70069	−	0.299877i	−0.156561	−	0.0276059i
$119$	19.5569	−	11.2912i	1.79278	−	1.03506i
$120$	0.0563672	−	1.08627i	0.00514560	−	0.0991626i
$121$	−10.1576	+	17.5934i	−0.923416	+	1.59940i
$122$	0.543523	−	0.313803i	0.0492082	−	0.0284104i
$123$	−0.281869	+	0.774429i	−0.0254153	+	0.0698280i
$124$	3.23897	−	3.86005i	0.290868	−	0.346643i
$125$	4.02282	+	10.4315i	0.359812	+	0.933025i
$126$	−1.48828	+	0.262424i	−0.132586	+	0.0233786i
$127$	8.46771	−	1.49309i	0.751388	−	0.132490i	0.215178	−	0.976575i	$-0.430967\pi$
$127$	8.46771	−	1.49309i	0.751388	−	0.132490i	0.536210	+	0.844085i	$0.319856\pi$
$128$	4.03210	−	3.38333i	0.356391	−	0.299047i
$129$	−0.302455	−	0.830989i	−0.0266297	−	0.0731645i
$130$	−0.642358	−	0.272274i	−0.0563385	−	0.0238800i
$131$	−2.93728	−	3.50052i	−0.256631	−	0.305841i	0.622310	−	0.782771i	$-0.286194\pi$
$131$	−2.93728	−	3.50052i	−0.256631	−	0.305841i	−0.878942	+	0.476929i	$0.841750\pi$
$132$	7.79745	−	1.37490i	0.678681	−	0.119670i
$133$	−0.724700	−	4.10998i	−0.0628395	−	0.356380i
$134$	−1.56656	−	0.904455i	−0.135330	−	0.0781331i
$135$	8.73813	−	1.07748i	0.752058	−	0.0927350i
$136$	4.03408	+	1.46828i	0.345919	+	0.125904i
$137$	5.91663	−	3.41597i	0.505492	−	0.291846i	−0.225487	−	0.974246i	$-0.572397\pi$
$137$	5.91663	−	3.41597i	0.505492	−	0.291846i	0.730979	+	0.682400i	$0.239064\pi$
$138$	−0.881380	−	0.508865i	−0.0750280	−	0.0433175i
$139$	2.54684	−	2.13705i	0.216020	−	0.181263i	−0.528356	−	0.849023i	$-0.677191\pi$
$139$	2.54684	−	2.13705i	0.216020	−	0.181263i	0.744376	+	0.667760i	$0.232747\pi$
$140$	−15.3076	−	3.52572i	−1.29373	−	0.297978i
$141$	−0.694315	+	3.93766i	−0.0584719	+	0.331611i
$142$	1.11493			0.0935632
$143$	1.77677	−	10.0766i	0.148581	−	0.842645i
$144$	7.28240	+	6.11066i	0.606866	+	0.509221i
$145$	−2.92632	+	6.90387i	−0.243017	+	0.573335i
$146$	0.382244	−	1.05021i	0.0316347	−	0.0869157i
$147$		−	4.09555i		−	0.337795i
$148$	−11.8876	−	1.55130i	−0.977155	−	0.127516i
$149$	−11.9540			−0.979313			−0.489656	−	0.871916i	$-0.662878\pi$
$149$	−11.9540			−0.979313			−0.489656	+	0.871916i	$0.662878\pi$
$150$	−0.588967	−	0.168226i	−0.0480889	−	0.0137356i
$151$	20.4486	−	7.44269i	1.66408	−	0.605677i	0.673088	−	0.739562i	$-0.264968\pi$
$151$	20.4486	−	7.44269i	1.66408	−	0.605677i	0.990997	+	0.133885i	$0.0427453\pi$
$152$	0.509969	−	0.607758i	0.0413640	−	0.0492956i
$153$	−2.73347	+	15.5023i	−0.220988	+	1.25329i
$154$			3.40369i			0.274277i
$155$	−3.44290	−	4.56398i	−0.276540	−	0.366588i
$156$	−2.24047	+	1.29353i	−0.179381	+	0.103566i
$157$	9.97130	+	11.8833i	0.795796	+	0.948393i	0.999531	−	0.0306333i	$-0.00975241\pi$
$157$	9.97130	+	11.8833i	0.795796	+	0.948393i	−0.203735	+	0.979026i	$0.565308\pi$
$158$	2.12390	+	1.22624i	0.168969	+	0.0975542i
$159$	3.27922	+	5.67977i	0.260059	+	0.450435i
$160$	−2.04060	−	3.99979i	−0.161323	−	0.316211i
$161$	−19.0342	+	22.6841i	−1.50011	+	1.78776i
$162$	0.394798	−	0.683811i	0.0310183	−	0.0537252i
$163$	−1.53146	−	8.68536i	−0.119954	−	0.680290i	−0.984178	−	0.177184i	$-0.943301\pi$
$163$	−1.53146	−	8.68536i	−0.119954	−	0.680290i	0.864224	−	0.503107i	$-0.167810\pi$
$164$	0.392883	+	2.22815i	0.0306790	+	0.173989i
$165$	0.465511	−	8.97102i	0.0362400	−	0.698393i
$166$	−0.0211523	−	0.0581155i	−0.00164174	−	0.00451064i
$167$	9.66821	−	3.51894i	0.748149	−	0.272304i	0.0603221	−	0.998179i	$-0.480787\pi$
$167$	9.66821	−	3.51894i	0.748149	−	0.272304i	0.687826	+	0.725875i	$0.258565\pi$
$168$	1.32824	−	1.11453i	0.102476	−	0.0859877i
$169$	−1.67688	−	9.51005i	−0.128991	−	0.731542i
$170$	1.31559	−	2.02812i	0.100901	−	0.155550i
$171$	2.51938	+	1.45456i	0.192662	+	0.111233i
$172$	−1.85977	−	1.56054i	−0.141807	−	0.118990i
$173$	5.10817	−	14.0346i	0.388367	−	1.06703i	−0.579369	−	0.815065i	$-0.696701\pi$
$173$	5.10817	−	14.0346i	0.388367	−	1.06703i	0.967736	−	0.251965i	$-0.0810768\pi$
$174$	−0.205403	−	0.355769i	−0.0155716	−	0.0269708i
$175$	−7.79611	+	16.0263i	−0.589330	+	1.21148i
$176$	16.4018	−	13.7627i	1.23633	−	1.03741i
$177$	3.63262	+	6.29188i	0.273044	+	0.472927i
$178$	−1.92790	−	0.339941i	−0.144502	−	0.0254797i
$179$			4.15086i			0.310250i	0.987895	+	0.155125i	$0.0495780\pi$
$179$			4.15086i			0.310250i	−0.987895	+	0.155125i	$0.950422\pi$
$180$	8.74148	−	6.59425i	0.651552	−	0.491507i
$181$	10.5148	+	8.82295i	0.781558	+	0.655805i	0.943640	−	0.330972i	$-0.107377\pi$
$181$	10.5148	+	8.82295i	0.781558	+	0.655805i	−0.162083	+	0.986777i	$0.551821\pi$
$182$	−0.380372	−	1.04506i	−0.0281950	−	0.0774652i
$183$	−2.48113	−	0.903057i	−0.183410	−	0.0667559i
$184$	−5.62932			−0.414999
$185$	−4.74228	+	12.7480i	−0.348660	+	0.937249i
$186$	0.313206			0.0229654
$187$	33.3156	+	12.1259i	2.43628	+	0.886733i
$188$	3.75435	+	10.3150i	0.273814	+	0.752298i
$189$	10.7510	+	9.02118i	0.782022	+	0.656194i
$190$	−0.269051	−	0.356660i	−0.0195190	−	0.0258748i
$191$		−	1.78215i		−	0.128952i	−0.997919	−	0.0644759i	$-0.979462\pi$
$191$		−	1.78215i		−	0.128952i	0.997919	−	0.0644759i	$-0.0205376\pi$
$192$	−5.16784	−	0.911229i	−0.372957	−	0.0657623i
$193$	7.43780	+	12.8826i	0.535384	+	0.927313i	0.999145	+	0.0413522i	$0.0131666\pi$
$193$	7.43780	+	12.8826i	0.535384	+	0.927313i	−0.463760	+	0.885961i	$0.653500\pi$
$194$	0.438473	−	0.367922i	0.0314805	−	0.0264153i
$195$	0.859607	+	2.80647i	0.0615578	+	0.200975i
$196$	−5.62184	−	9.73732i	−0.401560	−	0.695523i
$197$	−4.50971	+	12.3903i	−0.321304	+	0.882775i	0.668926	+	0.743329i	$0.266754\pi$
$197$	−4.50971	+	12.3903i	−0.321304	+	0.882775i	−0.990230	+	0.139446i	$0.955468\pi$
$198$	−1.81752	−	1.52508i	−0.129165	−	0.108383i
$199$	−6.44509	−	3.72107i	−0.456880	−	0.263780i	0.253851	−	0.967243i	$-0.418303\pi$
$199$	−6.44509	−	3.72107i	−0.456880	−	0.263780i	−0.710731	+	0.703463i	$0.751636\pi$
$200$	−3.28652	+	0.823024i	−0.232392	+	0.0581966i
$201$	1.32149	+	7.49454i	0.0932108	+	0.528624i
$202$	0.725993	−	0.609180i	0.0510807	−	0.0428618i
$203$	−11.2320	+	4.08812i	−0.788333	+	0.286930i
$204$	−3.06592	−	8.42354i	−0.214657	−	0.589766i
$205$	2.56350	+	0.133021i	0.179043	+	0.00929061i
$206$	−0.237140	−	1.34489i	−0.0165223	−	0.0937028i
$207$	−3.58436	−	20.3279i	−0.249130	−	1.41289i
$208$	−3.49796	+	6.05864i	−0.242540	+	0.420091i
$209$	4.21160	−	5.01919i	0.291323	−	0.347185i
$210$	−0.443719	−	0.869737i	−0.0306195	−	0.0600176i
$211$	0.649216	+	1.12448i	0.0446939	+	0.0774121i	0.887507	−	0.460794i	$-0.152435\pi$
$211$	0.649216	+	1.12448i	0.0446939	+	0.0774121i	−0.842813	+	0.538206i	$0.819102\pi$
$212$	15.5929	+	9.00258i	1.07093	+	0.618300i
$213$	−3.01504	−	3.59319i	−0.206587	−	0.246201i
$214$	−0.412850	+	0.238359i	−0.0282218	+	0.0162939i
$215$	−2.19893	+	1.65879i	−0.149966	+	0.113128i
$216$			2.66799i			0.181534i
$217$	1.58247	−	8.97462i	0.107425	−	0.609237i
$218$	−1.33816	+	1.59476i	−0.0906317	+	0.108011i
$219$	−4.41826	+	1.60811i	−0.298558	+	0.108666i
$220$	−11.2075	−	21.9679i	−0.755610	−	1.48108i
$221$	−11.5843			−0.779242
$222$	−0.401090	−	0.628009i	−0.0269194	−	0.0421492i
$223$			13.6327i			0.912914i	0.889746	+	0.456457i	$0.150882\pi$
$223$			13.6327i			0.912914i	−0.889746	+	0.456457i	$0.849118\pi$
$224$	2.44807	−	6.72601i	0.163568	−	0.449400i
$225$	−5.06464	−	11.3438i	−0.337642	−	0.756257i
$226$	0.246520	+	0.206855i	0.0163983	+	0.0137598i
$227$	5.17109	−	29.3267i	0.343217	−	1.94648i	0.0211181	−	0.999777i	$-0.493277\pi$
$227$	5.17109	−	29.3267i	0.343217	−	1.94648i	0.322099	−	0.946706i	$-0.395611\pi$
$228$	−1.65663			−0.109713
$229$	−2.55052	+	14.4647i	−0.168543	+	0.955856i	0.776792	+	0.629757i	$0.216845\pi$
$229$	−2.55052	+	14.4647i	−0.168543	+	0.955856i	−0.945336	+	0.326099i	$0.894266\pi$
$230$	−0.711492	+	3.08908i	−0.0469144	+	0.203688i
$231$	10.9693	−	9.20437i	0.721730	−	0.605603i
$232$	−1.96785	−	1.13614i	−0.129195	−	0.0745910i
$233$	12.1370	−	7.00728i	0.795119	−	0.459062i	−0.0466428	−	0.998912i	$-0.514852\pi$
$233$	12.1370	−	7.00728i	0.795119	−	0.459062i	0.841761	+	0.539850i	$0.181519\pi$
$234$	0.728479	+	0.265145i	0.0476221	+	0.0173330i
$235$	12.3604	−	1.52413i	0.806300	−	0.0994235i
$236$	17.2734	+	9.97279i	1.12440	+	0.649174i
$237$	−1.79164	−	10.1609i	−0.116380	−	0.660022i
$238$	3.79497	−	0.669156i	0.245992	−	0.0433750i
$239$	10.2597	+	12.2270i	0.663643	+	0.790899i	0.987904	−	0.155068i	$-0.0495598\pi$
$239$	10.2597	+	12.2270i	0.663643	+	0.790899i	−0.324260	+	0.945968i	$0.605115\pi$
$240$	−2.39695	+	5.65497i	−0.154722	+	0.365027i
$241$	−7.57694	−	20.8175i	−0.488074	−	1.34097i	−0.902422	−	0.430853i	$-0.858213\pi$
$241$	−7.57694	−	20.8175i	−0.488074	−	1.34097i	0.414349	−	0.910118i	$-0.364009\pi$
$242$	−2.65559	+	2.22830i	−0.170708	+	0.143241i
$243$	−14.9042	+	2.62801i	−0.956102	+	0.168587i
$244$	−7.13858	+	1.25872i	−0.457001	+	0.0805816i
$245$	−12.1972	+	3.73595i	−0.779252	+	0.238681i
$246$	−0.0903963	+	0.107730i	−0.00576346	+	0.00686862i
$247$	−0.732214	+	2.01174i	−0.0465897	+	0.128004i
$248$	1.50032	−	0.866210i	0.0952703	−	0.0550044i
$249$	−0.130093	+	0.225327i	−0.00824428	+	0.0142795i
$250$	0.0362485	+	1.90750i	0.00229256	+	0.120641i
$251$	−15.0176	+	8.67039i	−0.947900	+	0.547270i	−0.892428	−	0.451190i	$-0.851000\pi$
$251$	−15.0176	+	8.67039i	−0.947900	+	0.547270i	−0.0554721	+	0.998460i	$0.517666\pi$
$252$	17.1893	+	3.03093i	1.08282	+	0.190931i
$253$	−46.4899			−2.92280
$254$	1.44495	+	0.254784i	0.0906643	+	0.0159866i
$255$	−10.0938	+	1.24465i	−0.632101	+	0.0779432i
$256$	−12.8935	+	4.69287i	−0.805846	+	0.293304i
$257$	11.1247	+	4.04907i	0.693942	+	0.252574i	0.664822	−	0.747002i	$-0.268507\pi$
$257$	11.1247	+	4.04907i	0.693942	+	0.252574i	0.0291200	+	0.999576i	$0.490730\pi$
$258$		−	0.150903i		−	0.00939479i
$259$	−20.0215	+	8.31985i	−1.24408	+	0.516970i
$260$	5.89611	+	5.49253i	0.365661	+	0.340632i
$261$	2.84969	−	7.82947i	0.176392	−	0.484632i
$262$	−0.266696	−	0.732742i	−0.0164765	−	0.0452689i
$263$	−3.69854	+	4.40775i	−0.228062	+	0.271793i	−0.867925	−	0.496696i	$-0.834547\pi$
$263$	−3.69854	+	4.40775i	−0.228062	+	0.271793i	0.639863	+	0.768489i	$0.278991\pi$
$264$	2.68081	+	0.472699i	0.164993	+	0.0290926i
$265$	13.9240	−	14.9471i	0.855345	−	0.918195i
$266$	0.123665	−	0.701337i	0.00758236	−	0.0430017i
$267$	4.11794	+	7.13249i	0.252014	+	0.436501i
$268$	13.4294	+	16.0046i	0.820334	+	0.977636i
$269$	14.2604	−	24.6997i	0.869471	−	1.50597i	0.00693373	−	0.999976i	$-0.497793\pi$
$269$	14.2604	−	24.6997i	0.869471	−	1.50597i	0.862538	−	0.505993i	$-0.168874\pi$
$270$	1.46406	+	0.337209i	0.0890997	+	0.0205219i
$271$	−12.0165	−	4.37366i	−0.729953	−	0.265681i	−0.0498079	−	0.998759i	$-0.515861\pi$
$271$	−12.0165	−	4.37366i	−0.729953	−	0.265681i	−0.680145	+	0.733078i	$0.738083\pi$
$272$	−18.5694	−	15.5816i	−1.12594	−	0.944774i
$273$	−2.33939	+	4.05195i	−0.141587	+	0.245235i
$274$	1.14811	−	0.202442i	0.0693597	−	0.0122300i
$275$	−27.1418	+	6.79697i	−1.63671	+	0.409873i
$276$	7.55568	+	9.00450i	0.454798	+	0.542007i
$277$	−13.0605	+	4.75363i	−0.784729	+	0.285618i	−0.703143	−	0.711048i	$-0.748221\pi$
$277$	−13.0605	+	4.75363i	−0.784729	+	0.285618i	−0.0815860	+	0.996666i	$0.525999\pi$
$278$	0.533115	−	0.194038i	0.0319741	−	0.0116376i
$279$	4.08325	+	4.86623i	0.244458	+	0.291334i
$280$	−4.53087	−	2.93906i	−0.270771	−	0.175642i
$281$	6.16133	−	1.08641i	0.367554	−	0.0648097i	0.0131793	−	0.999913i	$-0.495805\pi$
$281$	6.16133	−	1.08641i	0.367554	−	0.0648097i	0.354375	+	0.935103i	$0.384694\pi$
$282$	−0.341148	+	0.590887i	−0.0203151	+	0.0351868i
$283$	8.74151	+	7.33500i	0.519629	+	0.436021i	0.864502	−	0.502629i	$-0.167634\pi$
$283$	8.74151	+	7.33500i	0.519629	+	0.436021i	−0.344873	+	0.938649i	$0.612078\pi$
$284$	−12.1006	−	4.40427i	−0.718041	−	0.261346i
$285$	−0.421859	+	1.83158i	−0.0249888	+	0.108494i
$286$	0.873008	−	1.51209i	0.0516221	−	0.0894120i
$287$	2.63018	+	3.13453i	0.155255	+	0.185025i
$288$	2.49469	+	4.32092i	0.147001	+	0.254613i
$289$	4.01809	−	22.7877i	0.236358	−	1.34045i
$290$	−0.872171	+	0.936256i	−0.0512156	+	0.0549789i
$291$	−2.37146	−	0.418153i	−0.139018	−	0.0245126i
$292$	−8.29716	+	9.88817i	−0.485555	+	0.578661i
$293$	−7.42711	−	20.4058i	−0.433896	−	1.19212i	−0.943401	−	0.331653i	$-0.892394\pi$
$293$	−7.42711	−	20.4058i	−0.433896	−	1.19212i	0.509505	−	0.860468i	$-0.329829\pi$
$294$	0.239029	−	0.656727i	0.0139405	−	0.0383011i
$295$	15.4246	−	16.5580i	0.898056	−	0.964043i
$296$	−3.65814	−	1.89903i	−0.212625	−	0.110379i
$297$			22.0337i			1.27853i
$298$	−1.91685	−	0.697675i	−0.111040	−	0.0404152i
$299$	14.2742	−	5.19538i	0.825498	−	0.300457i
$300$	5.72766	+	4.15236i	0.330686	+	0.239737i
$301$	−4.32397	−	0.762433i	−0.249230	−	0.0439459i
$302$	3.71334			0.213679
$303$	−3.92651	−	0.692349i	−0.225572	−	0.0397744i
$304$	−3.87966	+	2.23992i	−0.222514	+	0.128468i
$305$	−0.426176	+	8.21299i	−0.0244028	+	0.470274i
$306$	−1.34308	+	2.32628i	−0.0767787	+	0.132985i
$307$	−6.09472	+	3.51879i	−0.347844	+	0.200828i	−0.663735	−	0.747968i	$-0.731030\pi$
$307$	−6.09472	+	3.51879i	−0.347844	+	0.200828i	0.315891	+	0.948795i	$0.397697\pi$
$308$	13.4454	−	36.9410i	0.766125	−	2.10491i
$309$	−3.69300	+	4.40114i	−0.210087	+	0.250372i
$310$	−0.285705	−	0.932779i	−0.0162270	−	0.0529783i
$311$	−13.3911	+	2.36122i	−0.759342	+	0.133892i	−0.539895	−	0.841732i	$-0.681536\pi$
$311$	−13.3911	+	2.36122i	−0.759342	+	0.133892i	−0.219446	+	0.975625i	$0.570425\pi$
$312$	−0.875937	+	0.154451i	−0.0495902	+	0.00874409i
$313$	0.0869709	−	0.0729772i	0.00491588	−	0.00412492i	−0.640326	−	0.768103i	$-0.721201\pi$
$313$	0.0869709	−	0.0729772i	0.00491588	−	0.00412492i	0.645242	+	0.763978i	$0.276756\pi$
$314$	0.905363	+	2.48747i	0.0510926	+	0.140376i
$315$	7.72824	−	18.2327i	0.435437	−	1.02730i
$316$	−18.2073	−	21.6986i	−1.02424	−	1.22064i
$317$	−2.72456	+	0.480414i	−0.153027	+	0.0269828i	−0.249637	−	0.968340i	$-0.580311\pi$
$317$	−2.72456	+	0.480414i	−0.153027	+	0.0269828i	0.0966099	+	0.995322i	$0.469200\pi$
$318$	0.194338	+	1.10214i	0.0108979	+	0.0618052i
$319$	−16.2515	−	9.38283i	−0.909911	−	0.525337i
$320$	2.00029	+	16.2219i	0.111820	+	0.906832i
$321$	1.88462	+	0.685946i	0.105189	+	0.0382858i
$322$	−4.37608	+	2.52653i	−0.243869	+	0.140798i
$323$	−6.42418	−	3.70900i	−0.357451	−	0.206374i
$324$	−6.98606	+	5.86200i	−0.388115	+	0.325667i
$325$	7.57401	−	5.12011i	0.420130	−	0.284013i
$326$	0.261333	−	1.48209i	0.0144739	−	0.0820855i
$327$	8.75825			0.484332
$328$	−0.135075	+	0.766051i	−0.00745830	+	0.0422981i
$329$	15.2077	+	12.7607i	0.838425	+	0.703522i
$330$	0.598223	−	1.41135i	0.0329311	−	0.0776922i
$331$	−1.86733	+	5.13046i	−0.102638	+	0.281996i	−0.980373	−	0.197150i	$-0.936831\pi$
$331$	−1.86733	+	5.13046i	−0.102638	+	0.281996i	0.877735	+	0.479146i	$0.159054\pi$
$332$			0.714298i			0.0392022i
$333$	4.52829	−	14.4190i	0.248149	−	0.790157i
$334$	1.75569			0.0960670
$335$	21.1145	−	10.7721i	1.15361	−	0.588544i
$336$	−9.20016	+	3.34859i	−0.501910	+	0.182680i
$337$	−6.52449	+	7.77558i	−0.355411	+	0.423563i	−0.913894	−	0.405954i	$-0.866939\pi$
$337$	−6.52449	+	7.77558i	−0.355411	+	0.423563i	0.558482	+	0.829517i	$0.311384\pi$
$338$	0.286147	−	1.62282i	0.0155643	−	0.0882697i
$339$		−	1.35386i		−	0.0735317i
$340$	−22.2900	+	16.8147i	−1.20884	+	0.911907i
$341$	12.3904	−	7.15363i	0.670980	−	0.387391i
$342$	0.319093	+	0.380280i	0.0172546	+	0.0205632i
$343$	3.99777	+	2.30812i	0.215860	+	0.124627i
$344$	−0.417340	−	0.722854i	−0.0225015	−	0.0389737i
$345$	11.8795	−	6.06061i	0.639569	−	0.326292i
$346$	1.63821	−	1.95234i	0.0880705	−	0.104958i
$347$	−11.3707	+	19.6945i	−0.610409	+	1.05726i	0.380763	+	0.924673i	$0.375661\pi$
$347$	−11.3707	+	19.6945i	−0.610409	+	1.05726i	−0.991171	+	0.132586i	$0.957672\pi$
$348$	0.823912	+	4.67264i	0.0441663	+	0.250480i
$349$	4.05073	+	22.9728i	0.216830	+	1.22971i	0.877702	+	0.479207i	$0.159076\pi$
$349$	4.05073	+	22.9728i	0.216830	+	1.22971i	−0.660871	+	0.750499i	$0.729813\pi$
$350$	−2.18546	+	2.11484i	−0.116818	+	0.113043i
$351$	−2.46233	−	6.76519i	−0.131429	−	0.361099i
$352$	10.5596	−	3.84339i	0.562831	−	0.204854i
$353$	15.4537	−	12.9672i	0.822520	−	0.690176i	−0.131041	−	0.991377i	$-0.541832\pi$
$353$	15.4537	−	12.9672i	0.822520	−	0.690176i	0.953561	+	0.301201i	$0.0973874\pi$
$354$	0.215282	+	1.22092i	0.0114421	+	0.0648914i
$355$	−7.95080	+	12.2570i	−0.421985	+	0.650534i
$356$	19.5811	+	11.3052i	1.03780	+	0.599173i
$357$	−12.4190	−	10.4208i	−0.657285	−	0.551528i
$358$	−0.242257	+	0.665596i	−0.0128037	+	0.0351778i
$359$	1.39032	+	2.40811i	0.0733784	+	0.127095i	0.900380	−	0.435105i	$-0.143289\pi$
$359$	1.39032	+	2.40811i	0.0733784	+	0.127095i	−0.827002	+	0.562200i	$0.809955\pi$
$360$	3.59954	−	1.10252i	0.189712	−	0.0581079i
$361$	13.5047	−	11.3318i	0.710772	−	0.596409i
$362$	1.17113	+	2.02845i	0.0615530	+	0.106613i
$363$	14.3627	+	2.53253i	0.753845	+	0.132923i
$364$			12.8449i			0.673255i
$365$	8.81956	+	11.6914i	0.461637	+	0.611956i
$366$	−0.345148	−	0.289613i	−0.0180411	−	0.0151383i
$367$	−11.1898	−	30.7438i	−0.584104	−	1.60481i	−0.781099	−	0.624407i	$-0.785341\pi$
$367$	−11.1898	−	30.7438i	−0.584104	−	1.60481i	0.196995	−	0.980404i	$-0.436882\pi$
$368$	29.8695	+	10.8716i	1.55705	+	0.566722i
$369$	−2.85228			−0.148484
$370$	−1.50444	+	1.76738i	−0.0782123	+	0.0918818i
$371$	32.5628			1.69058
$372$	−3.39930	−	1.23724i	−0.176245	−	0.0641480i
$373$	3.62199	+	9.95135i	0.187540	+	0.515261i	0.997456	−	0.0712842i	$-0.0227097\pi$
$373$	3.62199	+	9.95135i	0.187540	+	0.515261i	−0.809916	+	0.586546i	$0.800488\pi$
$374$	4.63450	+	3.88881i	0.239644	+	0.201085i
$375$	6.04942	−	5.27514i	0.312390	−	0.272407i
$376$			3.77395i			0.194627i
$377$	6.03840	+	1.06473i	0.310993	+	0.0548365i
$378$	1.19744	+	2.07402i	0.0615896	+	0.106676i
$379$	4.77502	−	4.00671i	0.245276	−	0.205811i	−0.511859	−	0.859070i	$-0.671043\pi$
$379$	4.77502	−	4.00671i	0.245276	−	0.205811i	0.757135	+	0.653258i	$0.226598\pi$
$380$	1.51118	+	4.93373i	0.0775217	+	0.253095i
$381$	−3.08637	−	5.34575i	−0.158120	−	0.273871i
$382$	0.104012	−	0.285770i	0.00532171	−	0.0146213i
$383$	−5.44267	−	4.56694i	−0.278108	−	0.233360i	0.493055	−	0.869998i	$-0.335880\pi$
$383$	−5.44267	−	4.56694i	−0.278108	−	0.233360i	−0.771163	+	0.636638i	$0.780325\pi$
$384$	−3.27244	−	1.88934i	−0.166996	−	0.0964152i
$385$	−37.4184	−	24.2723i	−1.90702	−	1.23703i
$386$	0.440790	+	2.49984i	0.0224356	+	0.127239i
$387$	2.34455	−	1.96731i	0.119180	−	0.100004i
$388$	−6.21223	+	2.26107i	−0.315378	+	0.114788i
$389$	2.81925	+	7.74584i	0.142942	+	0.392730i	0.990418	−	0.138104i	$-0.0441010\pi$
$389$	2.81925	+	7.74584i	0.142942	+	0.392730i	−0.847476	+	0.530834i	$0.821879\pi$
$390$	−0.0259552	+	0.500191i	−0.00131429	+	0.0253282i
$391$	9.13980	+	51.8344i	0.462219	+	2.62138i
$392$	−0.671263	−	3.80692i	−0.0339039	−	0.192279i
$393$	−1.64026	+	2.84101i	−0.0827400	+	0.143310i
$394$	−1.44628	+	1.72361i	−0.0728624	+	0.0868340i
$395$	−28.6265	+	14.6046i	−1.44036	+	0.734835i
$396$	13.7015	+	23.7317i	0.688526	+	1.19256i
$397$	7.05262	+	4.07183i	0.353961	+	0.204360i	0.666428	−	0.745569i	$-0.267822\pi$
$397$	7.05262	+	4.07183i	0.353961	+	0.204360i	−0.312467	+	0.949928i	$0.601156\pi$
$398$	−0.816305	−	0.972835i	−0.0409177	−	0.0487638i
$399$	−2.59467	+	1.49803i	−0.129896	+	0.0749955i
$400$	19.0279	+	1.98007i	0.951396	+	0.0990035i
$401$			0.784302i			0.0391662i	0.999808	+	0.0195831i	$0.00623389\pi$
$401$			0.784302i			0.0391662i	−0.999808	+	0.0195831i	$0.993766\pi$
$402$	−0.225502	+	1.27889i	−0.0112470	+	0.0637851i
$403$	−3.00490	+	3.58110i	−0.149685	+	0.178387i
$404$	−10.2858	+	3.74372i	−0.511737	+	0.186257i
$405$	4.70207	+	9.21658i	0.233648	+	0.457976i
$406$	−2.03967			−0.101227
$407$	−30.2109	−	15.6832i	−1.49750	−	0.777387i
$408$		−	3.08193i		−	0.152578i
$409$	11.6764	−	32.0806i	0.577359	−	1.58628i	−0.215254	−	0.976558i	$-0.569058\pi$
$409$	11.6764	−	32.0806i	0.577359	−	1.58628i	0.792614	−	0.609724i	$-0.208720\pi$
$410$	0.403298	+	0.170944i	0.0199174	+	0.00844233i
$411$	−3.75717	−	3.15264i	−0.185328	−	0.155508i
$412$	−2.73891	+	15.5332i	−0.134937	+	0.765264i
$413$	36.0722			1.77499
$414$	0.611644	−	3.46881i	0.0300607	−	0.170483i
$415$	0.789732	+	0.181895i	0.0387664	+	0.00892887i
$416$	−2.81270	+	2.36014i	−0.137904	+	0.115715i
$417$	−2.06701	−	1.19339i	−0.101222	−	0.0584405i
$418$	0.968272	−	0.559032i	0.0473597	−	0.0273432i
$419$	−20.4064	−	7.42733i	−0.996920	−	0.362849i	−0.208524	−	0.978017i	$-0.566866\pi$
$419$	−20.4064	−	7.42733i	−0.996920	−	0.362849i	−0.788396	+	0.615168i	$0.789088\pi$
$420$	1.38010	+	11.1923i	0.0673419	+	0.546127i
$421$	−23.9644	−	13.8359i	−1.16795	−	0.674318i	−0.214756	−	0.976668i	$-0.568896\pi$
$421$	−23.9644	−	13.8359i	−1.16795	−	0.674318i	−0.953197	+	0.302350i	$0.902229\pi$
$422$	0.0384748	+	0.218202i	0.00187293	+	0.0106219i
$423$	−13.6281	+	2.40300i	−0.662619	+	0.116838i
$424$	3.97904	+	4.74203i	0.193239	+	0.230293i
$425$	12.9144	+	28.9258i	0.626438	+	1.40311i
$426$	−0.273757	−	0.752140i	−0.0132636	−	0.0364413i
$427$	−10.0424	+	8.42662i	−0.485988	+	0.407793i
$428$	5.42233	−	0.956104i	0.262098	−	0.0462150i
$429$	−7.23396	+	1.27554i	−0.349259	+	0.0615838i
$430$	−0.449413	+	0.137653i	−0.0216726	+	0.00663821i
$431$	2.12509	−	2.53258i	0.102362	−	0.121990i	−0.712431	−	0.701742i	$-0.752406\pi$
$431$	2.12509	−	2.53258i	0.102362	−	0.121990i	0.814793	+	0.579752i	$0.196850\pi$
$432$	5.15255	−	14.1565i	0.247902	−	0.681106i
$433$	13.9148	−	8.03371i	0.668702	−	0.386076i	−0.126882	−	0.991918i	$-0.540497\pi$
$433$	13.9148	−	8.03371i	0.668702	−	0.386076i	0.795585	+	0.605842i	$0.207164\pi$
$434$	0.777538	−	1.34674i	0.0373230	−	0.0646454i
$435$	5.37590	+	0.278958i	0.257755	+	0.0133750i
$436$	20.8231	−	12.0222i	0.997244	−	0.575759i
$437$	9.57934	+	1.68910i	0.458242	+	0.0808004i
$438$	−0.802329			−0.0383368
$439$	−23.5611	−	4.15446i	−1.12451	−	0.198282i	−0.419690	−	0.907667i	$-0.637861\pi$
$439$	−23.5611	−	4.15446i	−1.12451	−	0.198282i	−0.704820	+	0.709386i	$0.748972\pi$
$440$	−1.03765	−	8.41510i	−0.0494681	−	0.401174i
$441$	13.3197	−	4.84797i	0.634271	−	0.230856i
$442$	−1.85755	−	0.676094i	−0.0883548	−	0.0321585i
$443$			1.64369i			0.0780942i	0.999237	+	0.0390471i	$0.0124322\pi$
$443$			1.64369i			0.0780942i	−0.999237	+	0.0390471i	$0.987568\pi$
$444$	1.87233	+	8.40034i	0.0888566	+	0.398662i
$445$	17.4854	−	18.7702i	0.828886	−	0.889791i
$446$	−0.795648	+	2.18602i	−0.0376750	+	0.103511i
$447$	2.93515	+	8.06425i	0.138828	+	0.381426i
$448$	−16.7474	+	19.9588i	−0.791239	+	0.942962i
$449$	−19.6132	−	3.45834i	−0.925606	−	0.163209i	−0.309524	−	0.950892i	$-0.600170\pi$
$449$	−19.6132	−	3.45834i	−0.925606	−	0.163209i	−0.616082	+	0.787682i	$0.711281\pi$
$450$	−0.150059	−	2.11459i	−0.00707385	−	0.0996828i
$451$	−1.11553	+	6.32646i	−0.0525281	+	0.297902i
$452$	−1.85841	−	3.21886i	−0.0874122	−	0.151402i
$453$	−10.0417	−	11.9673i	−0.471802	−	0.562272i
$454$	2.54079	−	4.40078i	0.119245	−	0.206539i
$455$	14.2014	+	3.27093i	0.665771	+	0.153344i
$456$	−0.535212	−	0.194801i	−0.0250636	−	0.00912240i
$457$	−9.81757	−	8.23792i	−0.459247	−	0.385354i	0.383607	−	0.923496i	$-0.374682\pi$
$457$	−9.81757	−	8.23792i	−0.459247	−	0.385354i	−0.842854	+	0.538143i	$0.819126\pi$
$458$	−1.25319	+	2.17058i	−0.0585576	+	0.101425i
$459$	24.5667	−	4.33177i	1.14667	−	0.202190i
$460$	19.9247	−	30.7160i	0.928992	−	1.43214i
$461$	−14.6976	−	17.5159i	−0.684535	−	0.815797i	0.306148	−	0.951984i	$-0.400960\pi$
$461$	−14.6976	−	17.5159i	−0.684535	−	0.815797i	−0.990683	+	0.136187i	$0.956515\pi$
$462$	2.29615	−	0.835729i	0.106826	−	0.0388816i
$463$	10.7259	−	3.90392i	0.498476	−	0.181430i	−0.0805325	−	0.996752i	$-0.525662\pi$
$463$	10.7259	−	3.90392i	0.498476	−	0.181430i	0.579008	+	0.815322i	$0.303440\pi$
$464$	8.24735	+	9.82880i	0.382873	+	0.456291i
$465$	−2.23353	+	3.44322i	−0.103577	+	0.159675i
$466$	2.35515	−	0.415276i	0.109100	−	0.0192373i
$467$	7.15751	−	12.3972i	0.331210	−	0.573673i	−0.651539	−	0.758615i	$-0.725876\pi$
$467$	7.15751	−	12.3972i	0.331210	−	0.573673i	0.982749	+	0.184942i	$0.0592097\pi$
$468$	−6.85896	−	5.75535i	−0.317056	−	0.266041i
$469$	35.5060	+	12.9231i	1.63951	+	0.596734i
$470$	2.07095	+	0.476992i	0.0955260	+	0.0220020i
$471$	5.56824	−	9.64447i	0.256571	−	0.444394i
$472$	4.40786	+	5.25308i	0.202888	+	0.241793i
$473$	−3.44662	−	5.96972i	−0.158476	−	0.274488i
$474$	0.305730	−	1.73388i	0.0140427	−	0.0796398i
$475$	5.83958	−	0.414398i	0.267938	−	0.0190139i
$476$	−43.8311	−	7.72860i	−2.00899	−	0.354240i
$477$	−14.5903	+	17.3880i	−0.668044	+	0.796143i
$478$	0.931548	+	2.55941i	0.0426080	+	0.117064i
$479$	−1.55534	+	4.27327i	−0.0710654	+	0.195251i	−0.970140	−	0.242544i	$-0.922018\pi$
$479$	−1.55534	+	4.27327i	−0.0710654	+	0.195251i	0.899075	+	0.437795i	$0.144240\pi$
$480$	−2.19724	+	2.35869i	−0.100290	+	0.107659i
$481$	11.0285	+	1.43919i	0.502858	+	0.0656214i
$482$		−	3.78033i		−	0.172189i
$483$	19.9764	+	7.27081i	0.908957	+	0.330833i
$484$	37.6241	−	13.6941i	1.71019	−	0.622457i
$485$	0.917913	+	7.44406i	0.0416803	+	0.338017i
$486$	−2.54328	−	0.448449i	−0.115366	−	0.0203421i
$487$	−21.4485			−0.971926			−0.485963	−	0.873979i	$-0.661531\pi$
$487$	−21.4485			−0.971926			−0.485963	+	0.873979i	$0.661531\pi$
$488$	−2.45429	−	0.432757i	−0.111100	−	0.0195900i
$489$	−5.48316	+	3.16570i	−0.247957	+	0.143158i
$490$	−2.17388	−	0.112804i	−0.0982061	−	0.00509596i
$491$	−0.812860	+	1.40792i	−0.0366839	+	0.0635383i	−0.883784	−	0.467894i	$-0.845013\pi$
$491$	−0.812860	+	1.40792i	−0.0366839	+	0.0635383i	0.847101	+	0.531433i	$0.178346\pi$
$492$	1.40665	−	0.812132i	0.0634168	−	0.0366137i
$493$	−7.26646	+	19.9644i	−0.327265	+	0.899152i
$494$	−0.234823	+	0.279851i	−0.0105652	+	0.0125911i
$495$	29.7269	−	9.10520i	1.33613	−	0.409249i
$496$	−9.63365	+	1.69867i	−0.432564	+	0.0762726i
$497$	−22.9350	+	4.04407i	−1.02878	+	0.181401i
$498$	−0.0340113	+	0.0285389i	−0.00152408	+	0.00127886i
$499$	0.220549	+	0.605952i	0.00987311	+	0.0271262i	0.944531	−	0.328421i	$-0.106517\pi$
$499$	0.220549	+	0.605952i	0.00987311	+	0.0271262i	−0.934658	+	0.355548i	$0.884294\pi$
$500$	7.14168	−	20.8457i	0.319386	−	0.932248i
$501$	−4.74779	−	5.65820i	−0.212116	−	0.252790i
$502$	−2.91412	+	0.513838i	−0.130063	+	0.0229337i
$503$	1.05352	+	5.97480i	0.0469741	+	0.266403i	0.999245	−	0.0388508i	$-0.0123697\pi$
$503$	1.05352	+	5.97480i	0.0469741	+	0.266403i	−0.952271	+	0.305254i	$0.901259\pi$
$504$	5.19697	+	3.00047i	0.231491	+	0.133652i
$505$	1.51982	+	12.3254i	0.0676310	+	0.548471i
$506$	−7.45473	−	2.71330i	−0.331403	−	0.120621i
$507$	−6.00379	+	3.46629i	−0.266638	+	0.153943i
$508$	−14.6759	−	8.47315i	−0.651139	−	0.375935i
$509$	−20.6005	+	17.2859i	−0.913100	+	0.766182i	−0.972706	−	0.232040i	$-0.925460\pi$
$509$	−20.6005	+	17.2859i	−0.913100	+	0.766182i	0.0596059	+	0.998222i	$0.481016\pi$
$510$	−1.69120	−	0.389526i	−0.0748878	−	0.0172485i
$511$	−4.05376	+	22.9900i	−0.179328	+	1.01702i
$512$	−12.8685			−0.568711
$513$	0.800540	−	4.54009i	0.0353447	−	0.200450i
$514$	1.54755	+	1.29855i	0.0682596	+	0.0572766i
$515$	16.4761	+	6.98365i	0.726023	+	0.307736i
$516$	−0.596104	+	1.63778i	−0.0262420	+	0.0720993i
$517$			31.1674i			1.37074i
$518$	−3.69605	+	0.165580i	−0.162395	+	0.00727519i
$519$	−10.7220			−0.470646
$520$	1.25901	+	2.46780i	0.0552112	+	0.108220i
$521$	12.4894	−	4.54577i	0.547171	−	0.199154i	−0.0536184	−	0.998562i	$-0.517075\pi$
$521$	12.4894	−	4.54577i	0.547171	−	0.199154i	0.600789	+	0.799408i	$0.294853\pi$
$522$	0.913905	−	1.08915i	0.0400005	−	0.0476708i
$523$	−3.52997	+	20.0195i	−0.154355	+	0.875391i	0.805018	+	0.593250i	$0.202155\pi$
$523$	−3.52997	+	20.0195i	−0.154355	+	0.875391i	−0.959373	+	0.282140i	$0.908956\pi$
$524$			9.00614i			0.393435i
$525$	12.7257	+	1.32425i	0.555394	+	0.0577949i
$526$	−0.850316	+	0.490930i	−0.0370755	+	0.0214056i
$527$	−10.4119	−	12.4084i	−0.453551	−	0.540521i
$528$	−13.3116	−	7.68548i	−0.579315	−	0.334468i
$529$	−23.0091	−	39.8529i	−1.00039	−	1.73273i
$530$	3.10510	−	1.58414i	0.134877	−	0.0688108i
$531$	−16.1627	+	19.2620i	−0.701401	+	0.835898i
$532$	−4.11262	+	7.12327i	−0.178305	+	0.308833i
$533$	−0.364491	−	2.06713i	−0.0157878	−	0.0895373i
$534$	0.244044	+	1.38404i	0.0105608	+	0.0598933i
$535$	0.323715	−	6.23843i	0.0139954	−	0.269711i
$536$	2.45672	+	6.74978i	0.106114	+	0.291546i
$537$	2.80019	−	1.01919i	0.120837	−	0.0439811i
$538$	3.72823	−	3.12835i	0.160735	−	0.134873i
$539$	−5.54365	−	31.4396i	−0.238782	−	1.35420i
$540$	−14.5577	−	9.44320i	−0.626463	−	0.406371i
$541$	−1.25114	−	0.722345i	−0.0537906	−	0.0310560i	0.472864	−	0.881136i	$-0.343220\pi$
$541$	−1.25114	−	0.722345i	−0.0537906	−	0.0310560i	−0.526654	+	0.850080i	$0.676554\pi$
$542$	−1.67161	−	1.40265i	−0.0718017	−	0.0602488i
$543$	3.37025	−	9.25968i	0.144631	−	0.397371i
$544$	−6.36122	−	11.0180i	−0.272735	−	0.472391i
$545$	−7.98925	−	26.0835i	−0.342222	−	1.11730i
$546$	−0.611610	+	0.513201i	−0.0261745	+	0.0219630i
$547$	−13.9639	−	24.1863i	−0.597055	−	1.03413i	−0.993253	−	0.115965i	$-0.963004\pi$
$547$	−13.9639	−	24.1863i	−0.597055	−	1.03413i	0.396198	−	0.918165i	$-0.370329\pi$
$548$	−13.2604	−	2.33816i	−0.566455	−	0.0998813i
$549$		−	9.13819i		−	0.390008i
$550$	−4.74893	−	0.494179i	−0.202495	−	0.0210719i
$551$	3.00776	+	2.52381i	0.128135	+	0.107518i
$552$	1.38220	+	3.79756i	0.0588304	+	0.161635i
$553$	−48.1381	−	17.5208i	−2.04704	−	0.745061i
$554$	−2.37171			−0.100764
$555$	9.76425	+	0.0690801i	0.414469	+	0.00293229i
$556$	−6.55252			−0.277889
$557$	−17.6238	−	6.41452i	−0.746742	−	0.271792i	−0.0595080	−	0.998228i	$-0.518953\pi$
$557$	−17.6238	−	6.41452i	−0.746742	−	0.271792i	−0.687234	+	0.726436i	$0.741175\pi$
$558$	0.370747	+	1.01862i	0.0156950	+	0.0431216i
$559$	1.72538	+	1.44776i	0.0729757	+	0.0612338i
$560$	18.3650	+	24.3450i	0.776063	+	1.02877i
$561$		−	25.4522i		−	1.07459i
$562$	1.05138	+	0.185388i	0.0443500	+	0.00782010i
$563$	13.4083	+	23.2239i	0.565094	+	0.978771i	0.997041	+	0.0768721i	$0.0244933\pi$
$563$	13.4083	+	23.2239i	0.565094	+	0.978771i	−0.431947	+	0.901899i	$0.642173\pi$
$564$	6.03672	−	5.06541i	0.254192	−	0.213292i
$565$	−4.03203	+	1.23499i	−0.169629	+	0.0519564i
$566$	0.973621	+	1.68636i	0.0409243	+	0.0708830i
$567$	−5.64099	+	15.4985i	−0.236899	+	0.650876i
$568$	−3.39149	−	2.84580i	−0.142304	−	0.119407i
$569$	10.2253	+	5.90356i	0.428665	+	0.247490i	0.698778	−	0.715339i	$-0.253728\pi$
$569$	10.2253	+	5.90356i	0.428665	+	0.247490i	−0.270113	+	0.962829i	$0.587061\pi$
$570$	−0.174543	+	0.269076i	−0.00731079	+	0.0112704i
$571$	−1.37023	−	7.77099i	−0.0573425	−	0.325206i	0.942620	−	0.333868i	$-0.108354\pi$
$571$	−1.37023	−	7.77099i	−0.0573425	−	0.325206i	−0.999962	+	0.00866199i	$0.997243\pi$
$572$	−15.4481	+	12.9625i	−0.645918	+	0.541990i
$573$	−1.20225	+	0.437582i	−0.0502246	+	0.0182803i
$574$	0.238812	+	0.656132i	0.00996784	+	0.0273864i
$575$	−28.8859	−	29.8506i	−1.20463	−	1.24485i
$576$	−3.15373	−	17.8857i	−0.131405	−	0.745236i
$577$	1.51113	+	8.57004i	0.0629092	+	0.356776i	0.999971	+	0.00761221i	$0.00242306\pi$
$577$	1.51113	+	8.57004i	0.0629092	+	0.356776i	−0.937062	+	0.349163i	$0.886466\pi$
$578$	1.97427	−	3.41953i	0.0821187	−	0.142234i
$579$	6.86445	−	8.18073i	0.285277	−	0.339980i
$580$	13.1643	−	6.71611i	0.546619	−	0.278871i
$581$	0.645914	+	1.11876i	0.0267970	+	0.0464138i
$582$	−0.355863	−	0.205458i	−0.0147510	−	0.00851649i
$583$	32.8610	+	39.1623i	1.36096	+	1.62193i
$584$	−3.84332	+	2.21894i	−0.159038	+	0.0918204i
$585$	−8.10977	+	6.11771i	−0.335298	+	0.252936i
$586$		−	3.70557i		−	0.153076i
$587$	−1.36555	+	7.74442i	−0.0563623	+	0.319647i	−0.999934	−	0.0115229i	$-0.996332\pi$
$587$	−1.36555	+	7.74442i	−0.0563623	+	0.319647i	0.943571	+	0.331169i	$0.107443\pi$
$588$	−5.18848	+	6.18339i	−0.213969	+	0.254999i
$589$	−2.81298	+	1.02384i	−0.115907	+	0.0421867i
$590$	3.43974	−	1.75487i	0.141612	−	0.0722468i
$591$	9.46588			0.389374
$592$	15.7428	+	17.1411i	0.647026	+	0.704496i
$593$		−	5.03777i		−	0.206877i	−0.994636	−	0.103438i	$-0.967016\pi$
$593$		−	5.03777i		−	0.206877i	0.994636	−	0.103438i	$-0.0329844\pi$
$594$	−1.28596	+	3.53314i	−0.0527634	+	0.144966i
$595$	−19.7063	+	46.4918i	−0.807880	+	1.90598i
$596$	18.0480	+	15.1441i	0.739275	+	0.620325i
$597$	−0.927752	+	5.26154i	−0.0379704	+	0.215341i
$598$	2.59211			0.105999
$599$	3.33298	−	18.9023i	0.136182	−	0.772326i	−0.837848	−	0.545904i	$-0.816186\pi$
$599$	3.33298	−	18.9023i	0.136182	−	0.772326i	0.974029	−	0.226421i	$-0.0727027\pi$
$600$	1.36217	+	2.01502i	0.0556106	+	0.0822628i
$601$	18.8863	−	15.8475i	0.770389	−	0.646433i	−0.170420	−	0.985372i	$-0.554512\pi$
$601$	18.8863	−	15.8475i	0.770389	−	0.646433i	0.940808	+	0.338939i	$0.110068\pi$
$602$	−0.648858	−	0.374618i	−0.0264455	−	0.0152683i
$603$	−22.8098	+	13.1692i	−0.928885	+	0.536292i
$604$	−40.3018	−	14.6687i	−1.63986	−	0.596859i
$605$	−5.55930	−	45.0846i	−0.226018	−	1.83295i
$606$	−0.589213	−	0.340183i	−0.0239352	−	0.0138190i
$607$	−4.53572	−	25.7234i	−0.184099	−	1.04408i	−0.927107	−	0.374796i	$-0.877713\pi$
$607$	−4.53572	−	25.7234i	−0.184099	−	1.04408i	0.743008	−	0.669283i	$-0.233398\pi$
$608$	−2.31547	+	0.408280i	−0.0939049	+	0.0165580i
$609$	5.51573	+	6.57340i	0.223509	+	0.266367i
$610$	−0.547674	+	1.29209i	−0.0221747	+	0.0523152i
$611$	−3.48304	−	9.56957i	−0.140909	−	0.387143i
$612$	23.7662	−	19.9422i	0.960690	−	0.806115i
$613$	34.9372	−	6.16036i	1.41110	−	0.248815i	0.584403	−	0.811464i	$-0.301329\pi$
$613$	34.9372	−	6.16036i	1.41110	−	0.248815i	0.826696	+	0.562649i	$0.190218\pi$
$614$	−1.18266	+	0.208536i	−0.0477285	+	0.00841582i
$615$	−0.539695	−	1.76201i	−0.0217626	−	0.0710512i
$616$	8.68769	−	10.3536i	0.350037	−	0.417158i
$617$	0.750439	−	2.06181i	0.0302115	−	0.0830055i	−0.923670	−	0.383189i	$-0.874826\pi$
$617$	0.750439	−	2.06181i	0.0302115	−	0.0830055i	0.953881	+	0.300184i	$0.0970480\pi$
$618$	−0.849042	+	0.490195i	−0.0341535	+	0.0197185i
$619$	−19.0489	+	32.9936i	−0.765639	+	1.32613i	0.174269	+	0.984698i	$0.444244\pi$
$619$	−19.0489	+	32.9936i	−0.765639	+	1.32613i	−0.939908	+	0.341427i	$0.889090\pi$
$620$	−0.583887	+	11.2523i	−0.0234494	+	0.451902i
$621$	−28.3284	+	16.3554i	−1.13678	+	0.656321i
$622$	−2.28510	−	0.402924i	−0.0916240	−	0.0161558i
$623$	40.8914			1.63828
$624$	4.94606	+	0.872124i	0.198001	+	0.0349129i
$625$	−21.2285	−	13.2042i	−0.849140	−	0.528168i
$626$	0.0182051	−	0.00662611i	0.000727622	−	0.000264833i
$627$	−4.42007	−	1.60877i	−0.176521	−	0.0642482i
$628$		−	30.5735i		−	1.22001i
$629$	−11.5467	+	36.7672i	−0.460399	+	1.46600i
$630$	2.30335	−	2.47260i	0.0917678	−	0.0985108i
$631$	−1.31640	+	3.61678i	−0.0524050	+	0.143982i	−0.963133	−	0.269024i	$-0.913299\pi$
$631$	−1.31640	+	3.61678i	−0.0524050	+	0.143982i	0.910728	+	0.413006i	$0.135521\pi$
$632$	−3.33076	−	9.15118i	−0.132490	−	0.364014i
$633$	0.599171	−	0.714064i	0.0238149	−	0.0283815i
$634$	−0.464926	−	0.0819791i	−0.0184646	−	0.00325580i
$635$	−13.1052	+	14.0681i	−0.520063	+	0.558276i
$636$	2.24456	−	12.7295i	0.0890025	−	0.504758i
$637$	5.21558	+	9.03364i	0.206649	+	0.357926i
$638$	−2.05835	−	2.45304i	−0.0814907	−	0.0971168i
$639$	8.11694	−	14.0589i	0.321101	−	0.556163i
$640$	−2.64167	+	11.4693i	−0.104421	+	0.453365i
$641$	41.2918	+	15.0290i	1.63093	+	0.593609i	0.985419	−	0.170144i	$-0.0544234\pi$
$641$	41.2918	+	15.0290i	1.63093	+	0.593609i	0.645508	+	0.763753i	$0.276646\pi$
$642$	0.262168	+	0.219985i	0.0103469	+	0.00868211i
$643$	15.3709	−	26.6233i	0.606171	−	1.04992i	−0.385694	−	0.922627i	$-0.626038\pi$
$643$	15.3709	−	26.6233i	0.606171	−	1.04992i	0.991865	−	0.127292i	$-0.0406287\pi$
$644$	57.4750	−	10.1344i	2.26483	−	0.399351i
$645$	1.65894	+	1.07611i	0.0653208	+	0.0423719i
$646$	−0.813657	−	0.969679i	−0.0320129	−	0.0381515i
$647$	24.4503	−	8.89918i	0.961241	−	0.349863i	0.186721	−	0.982413i	$-0.440214\pi$
$647$	24.4503	−	8.89918i	0.961241	−	0.349863i	0.774519	+	0.632550i	$0.217992\pi$
$648$	−2.94631	+	1.07237i	−0.115742	+	0.0421266i
$649$	36.4025	+	43.3828i	1.42892	+	1.70292i
$650$	1.51333	−	0.378974i	0.0593576	−	0.0148646i
$651$	−6.44288	+	1.13605i	−0.252516	+	0.0445254i
$652$	−8.69094	+	15.0532i	−0.340364	+	0.589527i
$653$	−13.1297	−	11.0171i	−0.513806	−	0.431134i	0.348660	−	0.937249i	$-0.386637\pi$
$653$	−13.1297	−	11.0171i	−0.513806	−	0.431134i	−0.862466	+	0.506115i	$0.831081\pi$
$654$	1.40440	+	0.511159i	0.0549163	+	0.0199879i
$655$	9.95723	+	2.29340i	0.389061	+	0.0896105i
$656$	2.19615	−	3.80385i	0.0857454	−	0.148515i
$657$	−10.4599	−	12.4657i	−0.408081	−	0.486332i
$658$	1.69381	+	2.93377i	0.0660317	+	0.114370i
$659$	−1.96874	+	11.1653i	−0.0766911	+	0.434937i	0.922151	+	0.386830i	$0.126430\pi$
$659$	−1.96874	+	11.1653i	−0.0766911	+	0.434937i	−0.998842	+	0.0481068i	$0.984681\pi$
$660$	−12.0678	+	12.9546i	−0.469740	+	0.504256i
$661$	20.2994	+	3.57933i	0.789556	+	0.139220i	0.553863	−	0.832608i	$-0.313153\pi$
$661$	20.2994	+	3.57933i	0.789556	+	0.139220i	0.235693	+	0.971828i	$0.424264\pi$
$662$	−0.598860	+	0.713693i	−0.0232753	+	0.0277385i
$663$	2.84436	+	7.81480i	0.110466	+	0.303502i
$664$	−0.0839933	+	0.230770i	−0.00325957	+	0.00895560i
$665$	6.82825	+	6.36086i	0.264788	+	0.246664i
$666$	1.56766	−	2.04782i	0.0607455	−	0.0793516i
$667$		−	27.8592i		−	1.07871i
$668$	−19.0549	−	6.93541i	−0.737256	−	0.268339i
$669$	9.19669	−	3.34732i	0.355565	−	0.129415i
$670$	4.01444	−	0.495014i	0.155091	−	0.0191241i
$671$	−20.2688	−	3.57394i	−0.782470	−	0.137970i
$672$	−5.13849			−0.198221
$673$	−4.39031	−	0.774129i	−0.169234	−	0.0298405i	0.0883891	−	0.996086i	$-0.471828\pi$
$673$	−4.39031	−	0.774129i	−0.169234	−	0.0298405i	−0.257623	+	0.966246i	$0.582939\pi$
$674$	−1.50002	+	0.866036i	−0.0577786	+	0.0333585i
$675$	−14.1475	+	13.6904i	−0.544539	+	0.526942i
$676$	−9.51616	+	16.4825i	−0.366006	+	0.633941i
$677$	43.7861	−	25.2799i	1.68284	−	0.971587i	0.723078	−	0.690766i	$-0.242727\pi$
$677$	43.7861	−	25.2799i	1.68284	−	0.971587i	0.959760	−	0.280821i	$-0.0906067\pi$
$678$	0.0790157	−	0.217094i	0.00303458	−	0.00833744i
$679$	−7.68519	+	9.15885i	−0.294931	+	0.351485i
$680$	−9.17849	+	2.81132i	−0.351979	+	0.107809i
$681$	−21.0536	+	3.71232i	−0.806777	+	0.142257i
$682$	2.40433	−	0.423949i	0.0920667	−	0.0162338i
$683$	20.0722	−	16.8426i	0.768043	−	0.644465i	−0.172164	−	0.985068i	$-0.555076\pi$
$683$	20.0722	−	16.8426i	0.768043	−	0.644465i	0.940207	+	0.340604i	$0.110631\pi$
$684$	−1.96099	−	5.38777i	−0.0749802	−	0.206006i
$685$	−5.96182	+	14.0653i	−0.227789	+	0.537409i
$686$	0.506340	+	0.603432i	0.0193321	+	0.0230392i
$687$	10.3842	−	1.83102i	0.396183	−	0.0698577i
$688$	0.818420	+	4.64149i	0.0312020	+	0.176955i
$689$	−14.4661	−	8.35200i	−0.551114	−	0.318186i
$690$	2.25861	−	0.278505i	0.0859837	−	0.0106025i
$691$	−19.0751	−	6.94277i	−0.725651	−	0.264115i	−0.0473282	−	0.998879i	$-0.515071\pi$
$691$	−19.0751	−	6.94277i	−0.725651	−	0.264115i	−0.678323	+	0.734764i	$0.737293\pi$
$692$	−25.4921	+	14.7179i	−0.969063	+	0.559489i
$693$	42.9194	+	24.7795i	1.63037	+	0.941296i
$694$	−2.97274	+	2.49442i	−0.112844	+	0.0946870i
$695$	−1.66859	+	7.24450i	−0.0632932	+	0.274800i
$696$	−0.283266	+	1.60648i	−0.0107372	+	0.0608935i
$697$	7.27306			0.275487
$698$	−0.691226	+	3.92014i	−0.0261633	+	0.148379i
$699$	−7.70721	−	6.46711i	−0.291513	−	0.244609i
$700$	32.0735	−	14.3197i	1.21226	−	0.541234i
$701$	−0.514224	+	1.41282i	−0.0194220	+	0.0533614i	−0.949025	−	0.315202i	$-0.897928\pi$
$701$	−0.514224	+	1.41282i	−0.0194220	+	0.0533614i	0.929603	+	0.368563i	$0.120150\pi$
$702$		−	1.22852i		−	0.0463674i
$703$	5.65520	+	4.32919i	0.213290	+	0.163278i
$704$	−40.9045			−1.54165
$705$	−4.06310	−	7.96412i	−0.153025	−	0.299946i
$706$	3.23484	−	1.17739i	0.121745	−	0.0443115i
$707$	−12.7246	+	15.1646i	−0.478558	+	0.570323i
$708$	2.48646	−	14.1014i	0.0934467	−	0.529963i
$709$			20.3464i			0.764124i	0.924137	+	0.382062i	$0.124786\pi$
$709$			20.3464i			0.764124i	−0.924137	+	0.382062i	$0.875214\pi$
$710$	−1.99028	+	1.50139i	−0.0746938	+	0.0563463i
$711$	30.9249	−	17.8545i	1.15977	−	0.669595i
$712$	4.99676	+	5.95490i	0.187261	+	0.223169i
$713$	18.3946	+	10.6202i	0.688885	+	0.397728i
$714$	−1.38322	−	2.39581i	−0.0517657	−	0.0896608i
$715$	10.3976	+	20.3804i	0.388848	+	0.762184i
$716$	5.25855	−	6.26689i	0.196521	−	0.234205i
$717$	5.72928	−	9.92340i	0.213964	−	0.370596i
$718$	0.0823953	+	0.467287i	0.00307497	+	0.0174390i
$719$	6.97428	+	39.5531i	0.260097	+	1.47508i	0.782643	+	0.622470i	$0.213871\pi$
$719$	6.97428	+	39.5531i	0.260097	+	1.47508i	−0.522547	+	0.852611i	$0.675018\pi$
$720$	−21.2286	−	1.10156i	−0.791143	−	0.0410528i
$721$	9.75630	+	26.8052i	0.363344	+	0.998278i
$722$	2.82685	−	1.02889i	0.105205	−	0.0382913i
$723$	−12.1832	+	10.2229i	−0.453096	+	0.380193i
$724$	−4.69761	−	26.6415i	−0.174585	−	0.990123i
$725$	−4.07310	−	16.2648i	−0.151271	−	0.604059i
$726$	2.15527	+	1.24434i	0.0799895	+	0.0461820i
$727$	31.1285	+	26.1199i	1.15449	+	0.968734i	0.999815	−	0.0192316i	$-0.00612199\pi$
$727$	31.1285	+	26.1199i	1.15449	+	0.968734i	0.154677	+	0.987965i	$0.450566\pi$
$728$	−1.51041	+	4.14982i	−0.0559796	+	0.153803i
$729$	−1.50842	−	2.61266i	−0.0558675	−	0.0967653i
$730$	0.731882	+	2.38947i	0.0270882	+	0.0884382i
$731$	−5.97839	+	5.01647i	−0.221119	+	0.185541i
$732$	2.60192	+	4.50666i	0.0961698	+	0.166571i
$733$	−45.6035	−	8.04113i	−1.68440	−	0.297006i	−0.752199	−	0.658936i	$-0.771007\pi$
$733$	−45.6035	−	8.04113i	−1.68440	−	0.297006i	−0.932205	+	0.361930i	$0.882118\pi$
$734$		−	5.58288i		−	0.206068i
$735$	5.51515	+	7.31100i	0.203429	+	0.269670i
$736$	12.7797	+	10.7235i	0.471067	+	0.395272i
$737$	20.2889	+	55.7434i	0.747352	+	2.05333i
$738$	−0.457367	−	0.166468i	−0.0168359	−	0.00612778i
$739$	−37.7948			−1.39030			−0.695152	−	0.718863i	$-0.744663\pi$
$739$	−37.7948			−1.39030			−0.695152	+	0.718863i	$0.744663\pi$
$740$	23.3097	−	13.2389i	0.856881	−	0.486670i
$741$	1.53692			0.0564600
$742$	5.22150	+	1.90047i	0.191687	+	0.0697684i
$743$	−1.19858	−	3.29307i	−0.0439716	−	0.120811i	0.915763	−	0.401718i	$-0.131587\pi$
$743$	−1.19858	−	3.29307i	−0.0439716	−	0.120811i	−0.959735	+	0.280907i	$0.909365\pi$
$744$	−0.952732	−	0.799437i	−0.0349288	−	0.0293088i
$745$	21.3393	−	16.0975i	0.781810	−	0.589768i
$746$			1.80710i			0.0661628i
$747$	−0.886810	−	0.156368i	−0.0324467	−	0.00572122i
$748$	−34.9375	−	60.5136i	−1.27744	−	2.21260i
$749$	7.62806	−	6.40070i	0.278723	−	0.233877i
$750$	1.27791	−	0.492813i	0.0466625	−	0.0179950i
$751$	11.9496	+	20.6973i	0.436047	+	0.755255i	0.997380	−	0.0723345i	$-0.0230449\pi$
$751$	11.9496	+	20.6973i	0.436047	+	0.755255i	−0.561334	+	0.827590i	$0.689712\pi$
$752$	7.28844	−	20.0248i	0.265782	−	0.730230i
$753$	9.53644	+	8.00203i	0.347527	+	0.291610i
$754$	0.906125	+	0.523151i	0.0329991	+	0.0190521i
$755$	−26.4805	+	40.8225i	−0.963725	+	1.48568i
$756$	−4.80316	−	27.2400i	−0.174689	−	0.990711i
$757$	2.15994	−	1.81240i	0.0785042	−	0.0658729i	−0.602691	−	0.797975i	$-0.705905\pi$
$757$	2.15994	−	1.81240i	0.0785042	−	0.0658729i	0.681195	+	0.732102i	$0.261460\pi$
$758$	0.999525	−	0.363797i	0.0363044	−	0.0132137i
$759$	11.4150	+	31.3623i	0.414337	+	1.13838i
$760$	−0.0919317	+	1.77165i	−0.00333471	+	0.0642644i
$761$	5.05316	+	28.6579i	0.183177	+	1.03885i	0.928275	+	0.371894i	$0.121291\pi$
$761$	5.05316	+	28.6579i	0.183177	+	1.03885i	−0.745098	+	0.666955i	$0.767597\pi$
$762$	−0.182909	−	1.03733i	−0.00662610	−	0.0375785i
$763$	21.7425	−	37.6591i	0.787131	−	1.36335i
$764$	−2.25773	+	2.69066i	−0.0816819	+	0.0973446i
$765$	−15.9962	−	31.3542i	−0.578342	−	1.13361i
$766$	−0.606199	−	1.04997i	−0.0219029	−	0.0379369i
$767$	−16.0251	−	9.25210i	−0.578633	−	0.334074i
$768$	6.33166	+	7.54578i	0.228474	+	0.272285i
$769$	23.6197	−	13.6368i	0.851747	−	0.491756i	−0.00949305	−	0.999955i	$-0.503022\pi$
$769$	23.6197	−	13.6368i	0.851747	−	0.491756i	0.861240	+	0.508199i	$0.169688\pi$
$770$	−4.58348	−	6.07596i	−0.165177	−	0.218962i
$771$		−	8.49900i		−	0.306084i
$772$	5.09102	−	28.8726i	0.183230	−	1.03915i
$773$	−4.47919	+	5.33809i	−0.161105	+	0.191998i	−0.840558	−	0.541721i	$-0.817773\pi$
$773$	−4.47919	+	5.33809i	−0.161105	+	0.191998i	0.679453	+	0.733719i	$0.262217\pi$
$774$	0.490771	−	0.178626i	0.0176404	−	0.00642058i
$775$	12.2919	+	3.51092i	0.441538	+	0.126116i
$776$	−2.27287			−0.0815914
$777$	10.5286	+	11.4638i	0.377712	+	0.411261i
$778$			1.40660i			0.0504289i
$779$	0.459713	−	1.26305i	0.0164709	−	0.0452535i
$780$	2.25758	−	5.32616i	0.0808343	−	0.190707i
$781$	−28.0087	−	23.5021i	−1.00223	−	0.840972i
$782$	−1.55964	+	8.84514i	−0.0557725	+	0.316302i
$783$	−13.2037			−0.471863
$784$	−3.79035	+	21.4961i	−0.135369	+	0.767719i
$785$	−33.8022	−	7.78548i	−1.20645	−	0.277876i
$786$	−0.428828	+	0.359829i	−0.0152958	+	0.0128347i
$787$	15.6550	+	9.03840i	0.558040	+	0.322184i	0.752358	−	0.658754i	$-0.228916\pi$
$787$	15.6550	+	9.03840i	0.558040	+	0.322184i	−0.194319	+	0.980938i	$0.562250\pi$
$788$	22.5055	−	12.9935i	0.801724	−	0.462876i
$789$	3.88161	+	1.41279i	0.138189	+	0.0502967i
$790$	−5.44268	+	0.671127i	−0.193642	+	0.0238776i
$791$	−5.82140	−	3.36099i	−0.206985	−	0.119503i
$792$	1.63599	+	9.27818i	0.0581325	+	0.329686i
$793$	6.62271	−	1.16776i	0.235179	−	0.0414684i
$794$	0.893253	+	1.06454i	0.0317004	+	0.0377790i
$795$	−13.5023	−	5.72315i	−0.478876	−	0.202979i
$796$	5.01661	+	13.7830i	0.177809	+	0.488526i
$797$	5.51566	−	4.62819i	0.195375	−	0.163939i	−0.539852	−	0.841760i	$-0.681520\pi$
$797$	5.51566	−	4.62819i	0.195375	−	0.163939i	0.735227	+	0.677821i	$0.237076\pi$
$798$	−0.503489	+	0.0887788i	−0.0178233	+	0.00314273i
$799$	34.7503	−	6.12742i	1.22938	−	0.216772i
$800$	9.02889	+	4.39216i	0.319219	+	0.155286i
$801$	−18.3221	+	21.8354i	−0.647378	+	0.771515i
$802$	−0.0457743	+	0.125764i	−0.00161635	+	0.00444088i
$803$	−31.7402	+	18.3252i	−1.12009	+	0.646682i
$804$	7.49936	−	12.9893i	0.264482	−	0.458096i
$805$	3.43128	−	66.1254i	0.120937	−	2.33062i
$806$	−0.690845	+	0.398860i	−0.0243340	+	0.0140492i
$807$	−20.1640	−	3.55546i	−0.709806	−	0.125158i
$808$	−3.76327			−0.132391
$809$	21.2731	+	3.75102i	0.747923	+	0.131879i	0.534603	−	0.845103i	$-0.320461\pi$
$809$	21.2731	+	3.75102i	0.747923	+	0.131879i	0.213320	+	0.976982i	$0.431572\pi$
$810$	0.216075	+	1.75232i	0.00759212	+	0.0615702i
$811$	−23.9554	+	8.71906i	−0.841189	+	0.306168i	−0.726443	−	0.687227i	$-0.758828\pi$
$811$	−23.9554	+	8.71906i	−0.841189	+	0.306168i	−0.114746	+	0.993395i	$0.536606\pi$
$812$	22.1370	+	8.05720i	0.776856	+	0.282752i
$813$			9.18031i			0.321967i
$814$	−3.92904	−	4.27803i	−0.137713	−	0.149945i
$815$	14.4297	+	13.4420i	0.505451	+	0.470853i
$816$	−5.95196	+	16.3529i	−0.208360	+	0.572465i
$817$	0.493287	+	1.35530i	0.0172579	+	0.0474158i
$818$	3.74465	−	4.46270i	0.130928	−	0.156035i
$819$	−15.9471	−	2.81190i	−0.557236	−	0.0982557i
$820$	−3.70181	−	3.44842i	−0.129273	−	0.120424i
$821$	−0.959028	+	5.43892i	−0.0334703	+	0.189820i	−0.996959	−	0.0779301i	$-0.975169\pi$
$821$	−0.959028	+	5.43892i	−0.0334703	+	0.189820i	0.963489	+	0.267750i	$0.0862800\pi$
$822$	−0.418470	−	0.724812i	−0.0145958	−	0.0252807i
$823$	12.5080	+	14.9064i	0.436001	+	0.519605i	0.938644	−	0.344889i	$-0.112083\pi$
$823$	12.5080	+	14.9064i	0.436001	+	0.519605i	−0.502643	+	0.864494i	$0.667639\pi$
$824$	−2.71139	+	4.69626i	−0.0944557	+	0.163602i
$825$	11.2496	+	16.6411i	0.391660	+	0.579369i
$826$	5.78422	+	2.10528i	0.201259	+	0.0732522i
$827$	15.9070	+	13.3476i	0.553141	+	0.464140i	0.876003	−	0.482306i	$-0.160201\pi$
$827$	15.9070	+	13.3476i	0.553141	+	0.464140i	−0.322862	+	0.946446i	$0.604645\pi$
$828$	−20.3410	+	35.2316i	−0.706898	+	1.22438i
$829$	19.7559	−	3.48349i	0.686149	−	0.120987i	0.180304	−	0.983611i	$-0.442292\pi$
$829$	19.7559	−	3.48349i	0.686149	−	0.120987i	0.505845	+	0.862624i	$0.331181\pi$
$830$	0.116019	+	0.0752583i	0.00402707	+	0.00261225i
$831$	6.41365	+	7.64349i	0.222487	+	0.265150i
$832$	12.5592	−	4.57119i	0.435413	−	0.158478i
$833$	−33.9640	+	12.3619i	−1.17678	+	0.428314i
$834$	−0.261798	−	0.311999i	−0.00906532	−	0.0108036i
$835$	−12.5201	+	19.3011i	−0.433277	+	0.667942i
$836$	−12.7172	+	2.24239i	−0.439834	+	0.0775545i
$837$	5.03337	−	8.71806i	0.173979	−	0.301340i
$838$	−2.83872	−	2.38197i	−0.0980619	−	0.0822837i
$839$	−1.95773	−	0.712555i	−0.0675883	−	0.0246001i	0.308005	−	0.951385i	$-0.400339\pi$
$839$	−1.95773	−	0.712555i	−0.0675883	−	0.0246001i	−0.375593	+	0.926785i	$0.622561\pi$
$840$	−0.870212	+	3.77819i	−0.0300251	+	0.130360i
$841$	−8.87733	+	15.3760i	−0.306115	+	0.530206i
$842$	−3.03522	−	3.61724i	−0.104601	−	0.124658i
$843$	−2.24573	−	3.88971i	−0.0773469	−	0.133969i
$844$	0.444376	−	2.52018i	0.0152960	−	0.0867481i
$845$	15.7998	+	14.7184i	0.543531	+	0.506327i
$846$	−2.32553	−	0.410053i	−0.0799532	−	0.0140979i
$847$	46.5450	−	55.4702i	1.59931	−	1.90598i
$848$	−11.9550	−	32.8460i	−0.410535	−	1.12794i
$849$	2.80187	−	7.69808i	0.0961599	−	0.264197i
$850$	0.382637	+	5.39201i	0.0131243	+	0.184944i
$851$	−2.26161	−	50.4832i	−0.0775271	−	1.73054i
$852$			9.24456i			0.316713i
$853$	18.6900	+	6.80260i	0.639933	+	0.232917i	0.641549	−	0.767082i	$-0.278292\pi$
$853$	18.6900	+	6.80260i	0.639933	+	0.232917i	−0.00161596	+	0.999999i	$0.500514\pi$
$854$	−2.10213	+	0.765111i	−0.0719332	+	0.0261816i
$855$	−6.45611	+	0.796091i	−0.220794	+	0.0272257i
$856$	1.86423	+	0.328714i	0.0637181	+	0.0112352i
$857$	26.3623			0.900519			0.450259	−	0.892898i	$-0.351332\pi$
$857$	26.3623			0.900519			0.450259	+	0.892898i	$0.351332\pi$
$858$	−1.23442	−	0.217662i	−0.0421424	−	0.00743085i
$859$	41.7109	−	24.0818i	1.42316	−	0.821660i	0.426589	−	0.904445i	$-0.359715\pi$
$859$	41.7109	−	24.0818i	1.42316	−	0.821660i	0.996567	+	0.0827856i	$0.0263817\pi$
$860$	5.42135	+	0.281317i	0.184867	+	0.00959282i
$861$	1.46876	−	2.54397i	0.0500553	−	0.0866983i
$862$	0.488570	−	0.282076i	0.0166408	−	0.00960756i
$863$	−14.3888	+	39.5328i	−0.489799	+	1.34571i	0.411064	+	0.911607i	$0.365157\pi$
$863$	−14.3888	+	39.5328i	−0.489799	+	1.34571i	−0.900862	+	0.434105i	$0.857065\pi$
$864$	5.08234	−	6.05690i	0.172905	−	0.206060i
$865$	9.78062	+	31.9320i	0.332551	+	1.08572i
$866$	2.70013	−	0.476106i	0.0917542	−	0.0161787i
$867$	−16.3593	+	2.88458i	−0.555590	+	0.0979656i
$868$	−13.7588	+	11.5450i	−0.467003	+	0.391862i
$869$	−27.5072	−	75.5754i	−0.933118	−	2.56372i
$870$	0.845752	+	0.358486i	0.0286737	+	0.0121538i
$871$	−12.4590	−	14.8480i	−0.422156	−	0.503105i
$872$	8.14102	−	1.43548i	0.275690	−	0.0486116i
$873$	−1.44721	−	8.20754i	−0.0489807	−	0.277783i
$874$	1.43748	+	0.829930i	0.0486235	+	0.0280728i
$875$	−7.66449	−	39.1071i	−0.259107	−	1.32206i
$876$	8.70786	+	3.16940i	0.294211	+	0.107084i
$877$	43.2041	−	24.9439i	1.45890	−	0.842296i	0.459942	−	0.887949i	$-0.347870\pi$
$877$	43.2041	−	24.9439i	1.45890	−	0.842296i	0.998957	+	0.0456525i	$0.0145367\pi$
$878$	−3.53559	−	2.04127i	−0.119320	−	0.0688897i
$879$	−11.9422	+	10.0207i	−0.402802	+	0.337991i
$880$	−10.7458	+	46.6550i	−0.362241	+	1.57274i
$881$	2.81023	−	15.9376i	0.0946791	−	0.536952i	−0.900166	−	0.435547i	$-0.856555\pi$
$881$	2.81023	−	15.9376i	0.0946791	−	0.536952i	0.994845	−	0.101405i	$-0.0323338\pi$
$882$	2.41877			0.0814444
$883$	−5.49453	+	31.1610i	−0.184906	+	1.04865i	0.741171	+	0.671316i	$0.234271\pi$
$883$	−5.49453	+	31.1610i	−0.184906	+	1.04865i	−0.926077	+	0.377335i	$0.876840\pi$
$884$	17.4897	+	14.6756i	0.588243	+	0.493595i
$885$	−14.9574	−	6.33994i	−0.502788	−	0.213115i
$886$	−0.0959311	+	0.263568i	−0.00322287	+	0.00885475i
$887$		−	29.3969i		−	0.987051i	−0.869731	−	0.493526i	$-0.835708\pi$
$887$		−	29.3969i		−	0.987051i	0.869731	−	0.493526i	$-0.164292\pi$
$888$	−0.382888	+	2.93408i	−0.0128489	+	0.0984612i
$889$	−30.6479			−1.02790
$890$	3.89929	−	1.98932i	0.130704	−	0.0666822i
$891$	−24.3322	+	8.85619i	−0.815159	+	0.296694i
$892$	17.2707	−	20.5824i	0.578266	−	0.689150i
$893$	1.13239	−	6.42209i	0.0378939	−	0.214907i
$894$			1.46442i			0.0489775i
$895$	−5.58963	−	7.40973i	−0.186841	−	0.247680i
$896$	−16.2478	+	9.38065i	−0.542800	+	0.313386i
$897$	−7.00966	−	8.35379i	−0.234046	−	0.278925i
$898$	−2.94317	−	1.69924i	−0.0982149	−	0.0567044i
$899$	4.28682	+	7.42499i	0.142973	+	0.247637i
$900$	−6.72454	+	23.5429i	−0.224151	+	0.784764i
$901$	37.2039	−	44.3379i	1.23944	−	1.47711i
$902$	−0.548109	+	0.949352i	−0.0182500	+	0.0316100i
$903$	0.547351	+	3.10418i	0.0182147	+	0.103301i
$904$	−0.221899	−	1.25845i	−0.00738025	−	0.0418555i
$905$	−30.6512	−	1.59051i	−1.01888	−	0.0528702i
$906$	−0.911760	−	2.50504i	−0.0302912	−	0.0832244i
$907$	−54.2679	+	19.7519i	−1.80194	+	0.655851i	−0.803796	+	0.594905i	$0.797190\pi$
$907$	−54.2679	+	19.7519i	−1.80194	+	0.655851i	−0.998141	+	0.0609459i	$0.980588\pi$
$908$	−44.9600	+	37.7259i	−1.49205	+	1.25198i
$909$	−2.39619	−	13.5895i	−0.0794766	−	0.450734i
$910$	2.08631	+	1.35333i	0.0691605	+	0.0448626i
$911$	−8.80962	−	5.08623i	−0.291876	−	0.168514i	0.346912	−	0.937898i	$-0.387230\pi$
$911$	−8.80962	−	5.08623i	−0.291876	−	0.168514i	−0.638787	+	0.769383i	$0.720564\pi$
$912$	2.46366	+	2.06725i	0.0815799	+	0.0684536i
$913$	−0.693662	+	1.90582i	−0.0229569	+	0.0630735i
$914$	−1.09347	−	1.89395i	−0.0361688	−	0.0626462i
$915$	5.64516	−	1.72908i	0.186623	−	0.0571618i
$916$	22.1755	−	18.6074i	0.732699	−	0.614807i
$917$	8.14392	+	14.1057i	0.268936	+	0.465811i
$918$	4.19212	+	0.739183i	0.138360	+	0.0243967i
$919$		−	0.219914i		−	0.00725429i	−0.999993	−	0.00362715i	$-0.998845\pi$
$919$		−	0.219914i		−	0.00725429i	0.999993	−	0.00362715i	$-0.00115456\pi$
$920$	10.0489	−	7.58055i	0.331304	−	0.249923i
$921$	3.87027	+	3.24754i	0.127530	+	0.107010i
$922$	−1.33450	−	3.66650i	−0.0439493	−	0.120750i
$923$	11.2262	+	4.08600i	0.369514	+	0.134492i
$924$	−28.2220			−0.928434
$925$	−8.70119	−	29.1426i	−0.286093	−	0.958202i
$926$	1.94776			0.0640074
$927$	−18.6850	−	6.80079i	−0.613697	−	0.223367i
$928$	2.30316	+	6.32788i	0.0756049	+	0.207723i
$929$	−42.0310	−	35.2682i	−1.37899	−	1.15711i	−0.969583	−	0.244761i	$-0.921290\pi$
$929$	−42.0310	−	35.2682i	−1.37899	−	1.15711i	−0.409409	−	0.912351i	$-0.634265\pi$
$930$	−0.559106	+	0.421769i	−0.0183338	+	0.0138304i
$931$			6.67960i			0.218915i
$932$	−27.2014	−	4.79634i	−0.891011	−	0.157109i
$933$	4.88090	+	8.45396i	0.159793	+	0.276770i
$934$	1.87126	−	1.57017i	0.0612294	−	0.0513775i
$935$	−75.8009	+	23.2174i	−2.47896	+	0.759291i
$936$	−1.53917	−	2.66593i	−0.0503095	−	0.0871386i
$937$	15.0914	−	41.4633i	0.493015	−	1.35455i	−0.404893	−	0.914364i	$-0.632691\pi$
$937$	15.0914	−	41.4633i	0.493015	−	1.35455i	0.897908	−	0.440183i	$-0.145086\pi$
$938$	4.93920	+	4.14448i	0.161271	+	0.135322i
$939$	−0.0705853	−	0.0407524i	−0.00230346	−	0.00132991i
$940$	−20.5923	−	13.3577i	−0.671647	−	0.435680i
$941$	−3.08919	−	17.5197i	−0.100705	−	0.571125i	−0.992849	−	0.119375i	$-0.961911\pi$
$941$	−3.08919	−	17.5197i	−0.100705	−	0.571125i	0.892144	−	0.451750i	$-0.149200\pi$
$942$	1.45576	−	1.22153i	0.0474311	−	0.0397994i
$943$	−8.96190	+	3.26186i	−0.291839	+	0.106221i
$944$	−13.2434	−	36.3858i	−0.431035	−	1.18426i
$945$	−31.3399	−	1.62624i	−1.01949	−	0.0529016i
$946$	−0.204259	−	1.15841i	−0.00664102	−	0.0376631i
$947$	8.06428	+	45.7348i	0.262054	+	1.48618i	0.777295	+	0.629136i	$0.216591\pi$
$947$	8.06428	+	45.7348i	0.262054	+	1.48618i	−0.515242	+	0.857045i	$0.672298\pi$
$948$	−10.1674	+	17.6105i	−0.330223	+	0.571963i
$949$	7.69756	−	9.17359i	0.249873	−	0.297787i
$950$	0.960571	+	0.274367i	0.0311650	+	0.00890164i
$951$	0.993069	+	1.72005i	0.0322025	+	0.0557763i
$952$	−13.2518	−	7.65093i	−0.429493	−	0.247968i
$953$	−35.7875	−	42.6499i	−1.15927	−	1.38157i	−0.910759	−	0.412938i	$-0.864503\pi$
$953$	−35.7875	−	42.6499i	−1.15927	−	1.38157i	−0.248513	−	0.968629i	$-0.579942\pi$
$954$	−3.35440	+	1.93666i	−0.108603	+	0.0627017i
$955$	2.39988	+	3.18133i	0.0776583	+	0.102946i
$956$		−	31.4577i		−	1.01741i
$957$	−2.33936	+	13.2672i	−0.0756209	+	0.428867i
$958$	−0.498803	+	0.594450i	−0.0161156	+	0.0192058i
$959$	−22.8831	+	8.32877i	−0.738934	+	0.268950i
$960$	10.4522	−	5.33247i	0.337344	−	0.172105i
$961$	24.4633			0.789139
$962$	1.68445	+	0.874437i	0.0543087	+	0.0281930i
$963$			6.94120i			0.223677i
$964$	−14.9332	+	41.0288i	−0.480968	+	1.32145i
$965$	−30.6253	−	12.9810i	−0.985864	−	0.417874i
$966$	2.77890	+	2.33177i	0.0894095	+	0.0750235i
$967$	−0.982962	+	5.57465i	−0.0316099	+	0.179269i	−0.996525	−	0.0832930i	$-0.973456\pi$
$967$	−0.982962	+	5.57465i	−0.0316099	+	0.179269i	0.964915	+	0.262562i	$0.0845674\pi$
$968$	13.7656			0.442442
$969$	−0.924743	+	5.24448i	−0.0297070	+	0.168477i
$970$	−0.287270	+	1.24724i	−0.00922368	+	0.0400464i
$971$	−8.95214	+	7.51173i	−0.287288	+	0.241063i	−0.775030	−	0.631925i	$-0.782265\pi$
$971$	−8.95214	+	7.51173i	−0.287288	+	0.241063i	0.487742	+	0.872988i	$0.337821\pi$
$972$	25.8314	+	14.9137i	0.828541	+	0.478358i
$973$	−10.2628	+	5.92521i	−0.329009	+	0.189953i
$974$	−3.43930	−	1.25180i	−0.110202	−	0.0401104i
$975$	−5.31374	−	3.85229i	−0.170176	−	0.123372i
$976$	12.1868	+	7.03607i	0.390091	+	0.225219i
$977$	4.65601	+	26.4056i	0.148959	+	0.844788i	0.964103	+	0.265530i	$0.0855468\pi$
$977$	4.65601	+	26.4056i	0.148959	+	0.844788i	−0.815144	+	0.579259i	$0.803342\pi$
$978$	−1.06399	+	0.187611i	−0.0340227	+	0.00599913i
$979$	41.2659	+	49.1788i	1.31886	+	1.57176i
$980$	23.1481	+	9.81169i	0.739438	+	0.313423i
$981$	10.3673	+	28.4839i	0.331002	+	0.909421i
$982$	−0.212514	+	0.178320i	−0.00678159	+	0.00569043i
$983$	−33.0168	+	5.82176i	−1.05307	+	0.185685i	−0.673281	−	0.739387i	$-0.735116\pi$
$983$	−33.0168	+	5.82176i	−1.05307	+	0.185685i	−0.379792	+	0.925072i	$0.624004\pi$
$984$	0.549948	−	0.0969706i	0.0175317	−	0.00309131i
$985$	−8.63475	−	28.1910i	−0.275126	−	0.898239i
$986$	−2.33037	+	2.77723i	−0.0742142	+	0.0884451i
$987$	4.87443	−	13.3924i	0.155155	−	0.426284i
$988$	3.65408	−	2.10968i	0.116252	−	0.0671179i
$989$	5.11679	−	8.86254i	0.162704	−	0.281812i
$990$	5.29816	+	0.274924i	0.168387	+	0.00873767i
$991$	6.47557	−	3.73867i	0.205703	−	0.118763i	−0.393610	−	0.919278i	$-0.628774\pi$
$991$	6.47557	−	3.73867i	0.205703	−	0.118763i	0.599313	+	0.800515i	$0.295441\pi$
$992$	−5.05611	−	0.891528i	−0.160532	−	0.0283061i
$993$	3.91953			0.124383
$994$	−3.91369	−	0.690089i	−0.124135	−	0.0218883i
$995$	16.5161	−	2.03657i	0.523594	−	0.0645635i
$996$	0.481869	−	0.175386i	0.0152686	−	0.00555732i
$997$	−29.0340	−	10.5675i	−0.919516	−	0.334676i	−0.161470	−	0.986878i	$-0.551624\pi$
$997$	−29.0340	−	10.5675i	−0.919516	−	0.334676i	−0.758046	+	0.652201i	$0.773846\pi$
$998$			0.110037i			0.00348317i
$999$	−23.9263	+	1.07188i	−0.756995	+	0.0339128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.v.a.169.9	yes	96
5.2	odd	4		925.2.bb.e.576.8		96
5.3	odd	4		925.2.bb.e.576.9		96
5.4	even	2	inner	185.2.v.a.169.8	yes	96
37.30	even	18	inner	185.2.v.a.104.8	✓	96
185.67	odd	36		925.2.bb.e.326.8		96
185.104	even	18	inner	185.2.v.a.104.9	yes	96
185.178	odd	36		925.2.bb.e.326.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.8	✓	96	37.30	even	18	inner
185.2.v.a.104.9	yes	96	185.104	even	18	inner
185.2.v.a.169.8	yes	96	5.4	even	2	inner
185.2.v.a.169.9	yes	96	1.1	even	1	trivial
925.2.bb.e.326.8		96	185.67	odd	36
925.2.bb.e.326.9		96	185.178	odd	36
925.2.bb.e.576.8		96	5.2	odd	4
925.2.bb.e.576.9		96	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160351 + 0.0583632i) q^{2} +(-0.245536 - 0.674605i) q^{3} +(-1.50978 - 1.26686i) q^{4} +(-1.78511 + 1.34662i) q^{5} -0.122504i q^{6} +(-3.51024 - 0.618951i) q^{7} +(-0.338800 - 0.586820i) q^{8} +(1.90333 - 1.59708i) q^{9} +(-0.364838 + 0.111748i) q^{10} +(-2.79800 - 4.84627i) q^{11} +(-0.483922 + 1.32957i) q^{12} +(1.40068 + 1.17531i) q^{13} +(-0.526749 - 0.304118i) q^{14} +(1.34675 + 0.873599i) q^{15} +(0.664401 + 3.76801i) q^{16} +(-4.85332 + 4.07242i) q^{17} +(0.398412 - 0.145010i) q^{18} +(0.400455 + 1.10024i) q^{19} +(4.40110 + 0.228375i) q^{20} +(0.444344 + 2.52000i) q^{21} +(-0.165819 - 0.940407i) q^{22} +(4.15386 - 7.19469i) q^{23} +(-0.312684 + 0.372642i) q^{24} +(1.37323 - 4.80773i) q^{25} +(0.156006 + 0.270210i) q^{26} +(-3.40989 - 1.96870i) q^{27} +(4.51558 + 5.38146i) q^{28} +(2.90414 - 1.67670i) q^{29} +(0.164967 + 0.218683i) q^{30} +2.55670i q^{31} +(-0.348703 + 1.97760i) q^{32} +(-2.58231 + 3.07748i) q^{33} +(-1.01592 + 0.369763i) q^{34} +(7.09966 - 3.62207i) q^{35} -4.89689 q^{36} +(5.12643 - 3.27409i) q^{37} +0.199797i q^{38} +(0.448951 - 1.23348i) q^{39} +(1.39502 + 0.591301i) q^{40} +(-0.879400 - 0.737904i) q^{41} +(-0.0758240 + 0.430019i) q^{42} +1.23182 q^{43} +(-1.91517 + 10.8615i) q^{44} +(-1.24699 + 5.41403i) q^{45} +(1.08598 - 0.911247i) q^{46} +(-4.82340 - 2.78479i) q^{47} +(2.37878 - 1.37339i) q^{48} +(5.36086 + 1.95119i) q^{49} +(0.500793 - 0.690780i) q^{50} +(3.93894 + 2.27415i) q^{51} +(-0.625770 - 3.54892i) q^{52} +(-8.99680 + 1.58638i) q^{53} +(-0.431882 - 0.514697i) q^{54} +(11.5208 + 4.88329i) q^{55} +(0.826060 + 2.26958i) q^{56} +(0.643902 - 0.540298i) q^{57} +(0.563540 - 0.0993673i) q^{58} +(-9.96639 + 1.75734i) q^{59} +(-0.926566 - 3.02508i) q^{60} +(2.36411 - 2.81744i) q^{61} +(-0.149217 + 0.409970i) q^{62} +(-7.66966 + 4.42808i) q^{63} +(3.65480 - 6.33030i) q^{64} +(-4.08305 - 0.211872i) q^{65} +(-0.593689 + 0.342766i) q^{66} +(-10.4395 - 1.84077i) q^{67} +12.4866 q^{68} +(-5.87350 - 1.03566i) q^{69} +(1.34984 - 0.166446i) q^{70} +(6.13971 - 2.23467i) q^{71} +(-1.58205 - 0.575819i) q^{72} -6.54940i q^{73} +(1.01312 - 0.225811i) q^{74} +(-3.58049 + 0.254085i) q^{75} +(0.789250 - 2.16845i) q^{76} +(6.82205 + 18.7434i) q^{77} +(0.143980 - 0.171589i) q^{78} +(14.1537 + 2.49567i) q^{79} +(-6.26010 - 5.83161i) q^{80} +(0.803505 - 4.55690i) q^{81} +(-0.0979466 - 0.169649i) q^{82} +(-0.232963 - 0.277634i) q^{83} +(2.52162 - 4.36758i) q^{84} +(3.17970 - 13.8053i) q^{85} +(0.197524 + 0.0718927i) q^{86} +(-1.84418 - 1.54745i) q^{87} +(-1.89593 + 3.28384i) q^{88} +(-11.2979 + 1.99213i) q^{89} +(-0.515936 + 0.795369i) q^{90} +(-4.18926 - 4.99256i) q^{91} +(-15.3861 + 5.60007i) q^{92} +(1.72476 - 0.627761i) q^{93} +(-0.610910 - 0.728054i) q^{94} +(-2.19646 - 1.42479i) q^{95} +(1.41971 - 0.250334i) q^{96} +(1.67715 - 2.90491i) q^{97} +(0.745743 + 0.625753i) q^{98} +(-13.0654 - 4.75542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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