LMFDB - Embedded newform 185.2.v.a.104.8

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			104.8
Character	$\chi$	$=$	185.104
Dual form			185.2.v.a.169.8

$q$-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} +(-1.21688 + 1.87595i) q^{5} +0.122504i q^{6} +(3.51024 - 0.618951i) q^{7} +(0.338800 - 0.586820i) q^{8} +(1.90333 + 1.59708i) q^{9} +(0.0856423 - 0.371833i) 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} +(0.966738 + 1.28153i) 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} +(-0.539338 - 4.37390i) 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} +(-2.03839 - 4.56563i) 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} +(-0.229812 - 0.149073i) q^{30} -2.55670i q^{31} +(0.348703 + 1.97760i) q^{32} +(2.58231 + 3.07748i) q^{33} +(-1.01592 - 0.369763i) q^{34} +(-3.11043 + 7.33824i) q^{35} -4.89689 q^{36} +(-5.12643 - 3.27409i) q^{37} +0.199797i q^{38} +(0.448951 + 1.23348i) q^{39} +(0.688565 + 1.34966i) q^{40} +(-0.879400 + 0.737904i) q^{41} +(0.0758240 + 0.430019i) q^{42} -1.23182 q^{43} +(-1.91517 - 10.8615i) q^{44} +(-5.31218 + 1.62709i) 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} +(0.593324 + 0.613138i) 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} +(-5.68654 - 11.1463i) 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} +(-3.08308 - 0.710110i) 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} +(-0.500362 - 4.05781i) q^{65} +(-0.593689 - 0.342766i) q^{66} +(10.4395 - 1.84077i) q^{67} -12.4866 q^{68} +(-5.87350 + 1.03566i) q^{69} +(0.0704793 - 1.35823i) 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} +(-13.5456 + 4.14894i) 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} +(0.756853 - 0.570942i) 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} +(1.57669 + 2.09010i) 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 $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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	$-0.630327\pi$
$2$	−0.160351	+	0.0583632i	−0.113386	+	0.0412690i	0.284704	+	0.958615i	$0.408105\pi$
$3$	0.245536	−	0.674605i	0.141760	−	0.389483i	−0.848412	−	0.529337i	$-0.822441\pi$
$3$	0.245536	−	0.674605i	0.141760	−	0.389483i	0.990172	+	0.139853i	$0.0446631\pi$
$4$	−1.50978	+	1.26686i	−0.754891	+	0.633429i
$5$	−1.21688	+	1.87595i	−0.544206	+	0.838951i
$5$	−1.21688	+	1.87595i	−0.544206	+	0.838951i
$6$			0.122504i			0.0500121i
$7$	3.51024	−	0.618951i	1.32675	−	0.233941i	0.535032	−	0.844832i	$-0.320300\pi$
$7$	3.51024	−	0.618951i	1.32675	−	0.233941i	0.791715	+	0.610891i	$0.209188\pi$
$8$	0.338800	−	0.586820i	0.119784	−	0.207472i
$9$	1.90333	+	1.59708i	0.634443	+	0.532361i
$10$	0.0856423	−	0.371833i	0.0270825	−	0.117584i
$11$	−2.79800	+	4.84627i	−0.843628	+	1.46121i	0.0431797	+	0.999067i	$0.486251\pi$
$11$	−2.79800	+	4.84627i	−0.843628	+	1.46121i	−0.886808	+	0.462139i	$0.847082\pi$
$12$	0.483922	+	1.32957i	0.139696	+	0.383813i
$13$	−1.40068	+	1.17531i	−0.388478	+	0.325972i	−0.816020	−	0.578024i	$-0.803824\pi$
$13$	−1.40068	+	1.17531i	−0.388478	+	0.325972i	0.427542	+	0.903995i	$0.359380\pi$
$14$	−0.526749	+	0.304118i	−0.140779	+	0.0812791i
$15$	0.966738	+	1.28153i	0.249611	+	0.330889i
$16$	0.664401	−	3.76801i	0.166100	−	0.942002i
$17$	4.85332	+	4.07242i	1.17710	+	0.987706i	0.999994	+	0.00351439i	$0.00111867\pi$
$17$	4.85332	+	4.07242i	1.17710	+	0.987706i	0.177108	+	0.984191i	$0.443326\pi$
$18$	−0.398412	−	0.145010i	−0.0939067	−	0.0341792i
$19$	0.400455	−	1.10024i	0.0918708	−	0.252413i	−0.885244	−	0.465128i	$-0.846008\pi$
$19$	0.400455	−	1.10024i	0.0918708	−	0.252413i	0.977114	+	0.212715i	$0.0682306\pi$
$20$	−0.539338	−	4.37390i	−0.120600	−	0.978033i
$21$	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	−0.865911	−	0.500198i	$-0.833261\pi$
$23$	−4.15386	−	7.19469i	−0.866139	−	1.50020i	−0.000228074	−	1.00000i	$-0.500073\pi$
$24$	−0.312684	−	0.372642i	−0.0638263	−	0.0760652i
$25$	−2.03839	−	4.56563i	−0.407679	−	0.913125i
$26$	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	0.744789	−	0.667300i	$-0.232550\pi$
$29$	2.90414	+	1.67670i	0.539285	+	0.311356i	−0.205504	+	0.978656i	$0.565883\pi$
$30$	−0.229812	−	0.149073i	−0.0419577	−	0.0272169i
$31$		−	2.55670i		−	0.459196i	−0.973286	−	0.229598i	$-0.926259\pi$
$31$		−	2.55670i		−	0.459196i	0.973286	−	0.229598i	$-0.0737411\pi$
$32$	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
$35$	−3.11043	+	7.33824i	−0.525759	+	1.24039i
$36$	−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
$40$	0.688565	+	1.34966i	0.108872	+	0.213401i
$41$	−0.879400	+	0.737904i	−0.137339	+	0.115241i	−0.708869	−	0.705340i	$-0.750794\pi$
$41$	−0.879400	+	0.737904i	−0.137339	+	0.115241i	0.571530	+	0.820581i	$0.306350\pi$
$42$	0.0758240	+	0.430019i	0.0116999	+	0.0663534i
$43$	−1.23182			−0.187850			−0.0939251	−	0.995579i	$-0.529941\pi$
$43$	−1.23182			−0.187850			−0.0939251	+	0.995579i	$0.529941\pi$
$44$	−1.91517	−	10.8615i	−0.288723	−	1.63743i
$45$	−5.31218	+	1.62709i	−0.791893	+	0.242553i
$46$	1.08598	+	0.911247i	0.160119	+	0.134356i
$47$	4.82340	−	2.78479i	0.703565	−	0.406204i	−0.105109	−	0.994461i	$-0.533519\pi$
$47$	4.82340	−	2.78479i	0.703565	−	0.406204i	0.808674	+	0.588257i	$0.200186\pi$
$48$	−2.37878	−	1.37339i	−0.343348	−	0.198232i
$49$	5.36086	−	1.95119i	0.765837	−	0.278742i
$50$	0.593324	+	0.613138i	0.0839087	+	0.0867108i
$51$	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	$-0.228549\pi$
$53$	8.99680	+	1.58638i	1.23581	+	0.217906i	0.482688	+	0.875792i	$0.339660\pi$
$54$	−0.431882	+	0.514697i	−0.0587717	+	0.0700413i
$55$	−5.68654	−	11.1463i	−0.766773	−	1.50296i
$56$	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	−0.518113	−	0.855312i	$-0.673365\pi$
$59$	−9.96639	−	1.75734i	−1.29751	−	0.228787i	−0.779401	+	0.626526i	$0.784476\pi$
$60$	−3.08308	−	0.710110i	−0.398024	−	0.0916748i
$61$	2.36411	+	2.81744i	0.302693	+	0.360736i	0.895854	−	0.444348i	$-0.146565\pi$
$61$	2.36411	+	2.81744i	0.302693	+	0.360736i	−0.593161	+	0.805084i	$0.702120\pi$
$62$	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
$65$	−0.500362	−	4.05781i	−0.0620623	−	0.503310i
$66$	−0.593689	−	0.342766i	−0.0730780	−	0.0421916i
$67$	10.4395	−	1.84077i	1.27539	−	0.224886i	0.505370	−	0.862902i	$-0.331356\pi$
$67$	10.4395	−	1.84077i	1.27539	−	0.224886i	0.770023	+	0.638016i	$0.220245\pi$
$68$	−12.4866			−1.51423
$69$	−5.87350	+	1.03566i	−0.707086	+	0.124678i
$70$	0.0704793	−	1.35823i	0.00842389	−	0.162340i
$71$	6.13971	+	2.23467i	0.728650	+	0.265207i	0.679593	−	0.733589i	$-0.262156\pi$
$71$	6.13971	+	2.23467i	0.728650	+	0.265207i	0.0490566	+	0.998796i	$0.484379\pi$
$72$	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	0.694012	−	0.719964i	$-0.255842\pi$
$79$	14.1537	−	2.49567i	1.59241	−	0.280785i	0.898400	+	0.439179i	$0.144731\pi$
$80$	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	$-0.771446\pi$
$83$	0.232963	−	0.277634i	0.0255710	−	0.0304743i	0.778678	+	0.627423i	$0.215890\pi$
$84$	2.52162	+	4.36758i	0.275131	+	0.476542i
$85$	−13.5456	+	4.14894i	−1.46922	+	0.450016i
$86$	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	−0.460926	−	0.887439i	$-0.652483\pi$
$89$	−11.2979	−	1.99213i	−1.19758	−	0.211165i	−0.736650	+	0.676274i	$0.763594\pi$
$90$	0.756853	−	0.570942i	0.0797794	−	0.0601826i
$91$	−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
$95$	1.57669	+	2.09010i	0.161765	+	0.214440i
$96$	1.41971	+	0.250334i	0.144899	+	0.0255496i
$97$	−1.67715	−	2.90491i	−0.170289	−	0.294949i	0.768232	−	0.640171i	$-0.221137\pi$
$97$	−1.67715	−	2.90491i	−0.170289	−	0.294949i	−0.938521	+	0.345223i	$0.887803\pi$
$98$	−0.745743	+	0.625753i	−0.0753315	+	0.0632106i
$99$	−13.0654	+	4.75542i	−1.31312	+	0.477938i
$100$	8.86153	+	4.31075i	0.886153	+	0.431075i
$101$	2.77691	+	4.80974i	0.276313	+	0.478587i	0.970465	−	0.241240i	$-0.0775542\pi$
$101$	2.77691	+	4.80974i	0.276313	+	0.478587i	−0.694153	+	0.719828i	$0.744221\pi$
$102$	−0.498888	+	0.594551i	−0.0493972	+	0.0588693i
$103$	4.00145	−	6.93072i	0.394275	−	0.682904i	−0.598733	−	0.800948i	$-0.704329\pi$
$103$	4.00145	−	6.93072i	0.394275	−	0.682904i	0.993008	+	0.118044i	$0.0376624\pi$
$104$	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	$-0.179107\pi$
$107$	1.79573	+	2.14007i	0.173600	+	0.206889i	−0.672228	+	0.740344i	$0.734662\pi$
$108$	−2.65413	+	7.29217i	−0.255394	+	0.701689i
$109$	−4.17259	−	11.4641i	−0.399661	−	1.09806i	−0.962450	−	0.271459i	$-0.912494\pi$
$109$	−4.17259	−	11.4641i	−0.399661	−	1.09806i	0.562789	−	0.826601i	$-0.309728\pi$
$110$	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	$-0.639384\pi$
$113$	−1.77213	+	0.645004i	−0.166708	+	0.0606769i	0.257318	+	0.966327i	$0.417161\pi$
$114$	0.134784	+	0.0490574i	0.0126237	+	0.00459465i
$115$	18.5517	+	0.962655i	1.72995	+	0.0897681i
$116$	−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
$120$	1.07956	−	0.133118i	0.0985497	−	0.0121520i
$121$	−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
$125$	11.0454	+	1.73190i	0.987929	+	0.154906i
$126$	−1.48828	−	0.262424i	−0.132586	−	0.0233786i
$127$	−8.46771	−	1.49309i	−0.751388	−	0.132490i	−0.215178	−	0.976575i	$-0.569033\pi$
$127$	−8.46771	−	1.49309i	−0.751388	−	0.132490i	−0.536210	+	0.844085i	$0.680144\pi$
$128$	−4.03210	−	3.38333i	−0.356391	−	0.299047i
$129$	−0.302455	+	0.830989i	−0.0266297	+	0.0731645i
$130$	0.317061	+	0.621474i	0.0278081	+	0.0545068i
$131$	−2.93728	+	3.50052i	−0.256631	+	0.305841i	−0.878942	−	0.476929i	$-0.841750\pi$
$131$	−2.93728	+	3.50052i	−0.256631	+	0.305841i	0.622310	+	0.782771i	$0.286194\pi$
$132$	−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
$135$	−0.456246	+	8.79248i	−0.0392674	+	0.756736i
$136$	4.03408	−	1.46828i	0.345919	−	0.125904i
$137$	−5.91663	−	3.41597i	−0.505492	−	0.291846i	0.225487	−	0.974246i	$-0.427603\pi$
$137$	−5.91663	−	3.41597i	−0.505492	−	0.291846i	−0.730979	+	0.682400i	$0.760936\pi$
$138$	0.881380	−	0.508865i	0.0750280	−	0.0433175i
$139$	2.54684	+	2.13705i	0.216020	+	0.181263i	0.744376	−	0.667760i	$-0.232747\pi$
$139$	2.54684	+	2.13705i	0.216020	+	0.181263i	−0.528356	+	0.849023i	$0.677191\pi$
$140$	−4.60043	−	15.0196i	−0.388807	−	1.26939i
$141$	−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
$145$	−6.67941	+	3.40767i	−0.554695	+	0.282992i
$146$	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	$0.662878\pi$
$150$	0.559308	−	0.249712i	0.0456673	−	0.0203889i
$151$	20.4486	+	7.44269i	1.66408	+	0.605677i	0.990997	−	0.133885i	$-0.0427453\pi$
$151$	20.4486	+	7.44269i	1.66408	+	0.605677i	0.673088	+	0.739562i	$0.264968\pi$
$152$	−0.509969	−	0.607758i	−0.0413640	−	0.0492956i
$153$	2.73347	+	15.5023i	0.220988	+	1.25329i
$154$		−	3.40369i		−	0.274277i
$155$	4.79624	+	3.11120i	0.385243	+	0.249897i
$156$	−2.24047	−	1.29353i	−0.179381	−	0.103566i
$157$	−9.97130	+	11.8833i	−0.795796	+	0.948393i	−0.999531	−	0.0306333i	$-0.990248\pi$
$157$	−9.97130	+	11.8833i	−0.795796	+	0.948393i	0.203735	+	0.979026i	$0.434692\pi$
$158$	−2.12390	+	1.22624i	−0.168969	+	0.0975542i
$159$	3.27922	−	5.67977i	0.260059	−	0.450435i
$160$	−4.13421	−	1.75235i	−0.326838	−	0.138535i
$161$	−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	−0.864224	−	0.503107i	$-0.832190\pi$
$163$	1.53146	−	8.68536i	0.119954	−	0.680290i	0.984178	−	0.177184i	$-0.0566986\pi$
$164$	0.392883	−	2.22815i	0.0306790	−	0.173989i
$165$	−8.91557	+	1.09936i	−0.694076	+	0.0855853i
$166$	−0.0211523	+	0.0581155i	−0.00164174	+	0.00451064i
$167$	−9.66821	−	3.51894i	−0.748149	−	0.272304i	−0.0603221	−	0.998179i	$-0.519213\pi$
$167$	−9.66821	−	3.51894i	−0.748149	−	0.272304i	−0.687826	+	0.725875i	$0.741435\pi$
$168$	−1.32824	−	1.11453i	−0.102476	−	0.0859877i
$169$	−1.67688	+	9.51005i	−0.128991	+	0.731542i
$170$	1.92991	−	1.45585i	0.148017	−	0.111659i
$171$	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	−0.967736	−	0.251965i	$-0.918923\pi$
$173$	−5.10817	−	14.0346i	−0.388367	−	1.06703i	0.579369	−	0.815065i	$-0.303299\pi$
$174$	−0.205403	+	0.355769i	−0.0155716	+	0.0269708i
$175$	−9.98116	−	14.7648i	−0.754505	−	1.11611i
$176$	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	$-0.950422\pi$
$179$		−	4.15086i		−	0.310250i	0.987895	−	0.155125i	$-0.0495780\pi$
$180$	5.95894	−	9.18633i	0.444153	−	0.684709i
$181$	10.5148	−	8.82295i	0.781558	−	0.655805i	−0.162083	−	0.986777i	$-0.551821\pi$
$181$	10.5148	−	8.82295i	0.781558	−	0.655805i	0.943640	+	0.330972i	$0.107377\pi$
$182$	0.380372	−	1.04506i	0.0281950	−	0.0774652i
$183$	2.48113	−	0.903057i	0.183410	−	0.0667559i
$184$	−5.62932			−0.414999
$185$	12.3803	−	5.63276i	0.910218	−	0.414129i
$186$	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
$190$	−0.374810	−	0.243130i	−0.0271916	−	0.0176385i
$191$			1.78215i			0.128952i	0.997919	+	0.0644759i	$0.0205376\pi$
$191$			1.78215i			0.128952i	−0.997919	+	0.0644759i	$0.979462\pi$
$192$	5.16784	−	0.911229i	0.372957	−	0.0657623i
$193$	−7.43780	+	12.8826i	−0.535384	+	0.927313i	0.463760	+	0.885961i	$0.346500\pi$
$193$	−7.43780	+	12.8826i	−0.535384	+	0.927313i	−0.999145	+	0.0413522i	$0.986833\pi$
$194$	0.438473	+	0.367922i	0.0314805	+	0.0264153i
$195$	−2.86028	−	0.658793i	−0.204829	−	0.0471772i
$196$	−5.62184	+	9.73732i	−0.401560	+	0.695523i
$197$	4.50971	+	12.3903i	0.321304	+	0.882775i	0.990230	+	0.139446i	$0.0445320\pi$
$197$	4.50971	+	12.3903i	0.321304	+	0.882775i	−0.668926	+	0.743329i	$0.733246\pi$
$198$	1.81752	−	1.52508i	0.129165	−	0.108383i
$199$	−6.44509	+	3.72107i	−0.456880	+	0.263780i	−0.710731	−	0.703463i	$-0.751636\pi$
$199$	−6.44509	+	3.72107i	−0.456880	+	0.263780i	0.253851	+	0.967243i	$0.418303\pi$
$200$	−3.36981	−	0.350666i	−0.238281	−	0.0247959i
$201$	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
$205$	−0.314147	−	2.54765i	−0.0219410	−	0.177936i
$206$	−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
$210$	−0.898965	−	0.381041i	−0.0620344	−	0.0262943i
$211$	0.649216	−	1.12448i	0.0446939	−	0.0774121i	−0.842813	−	0.538206i	$-0.819102\pi$
$211$	0.649216	−	1.12448i	0.0446939	−	0.0774121i	0.887507	+	0.460794i	$0.152435\pi$
$212$	−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
$215$	1.49898	−	2.31083i	0.102229	−	0.157597i
$216$		−	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
$220$	22.7062	+	9.62437i	1.53085	+	0.648875i
$221$	−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
$225$	3.41195	−	11.9454i	0.227463	−	0.796359i
$226$	0.246520	−	0.206855i	0.0163983	−	0.0137598i
$227$	−5.17109	−	29.3267i	−0.343217	−	1.94648i	−0.322099	−	0.946706i	$-0.604389\pi$
$227$	−5.17109	−	29.3267i	−0.343217	−	1.94648i	−0.0211181	−	0.999777i	$-0.506723\pi$
$228$	1.65663			0.109713
$229$	−2.55052	−	14.4647i	−0.168543	−	0.955856i	−0.945336	−	0.326099i	$-0.894266\pi$
$229$	−2.55052	−	14.4647i	−0.168543	−	0.955856i	0.776792	−	0.629757i	$-0.216845\pi$
$230$	−3.03097	+	0.928370i	−0.199856	+	0.0612149i
$231$	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	$-0.485148\pi$
$233$	−12.1370	−	7.00728i	−0.795119	−	0.459062i	−0.841761	+	0.539850i	$0.818481\pi$
$234$	0.728479	−	0.265145i	0.0476221	−	0.0173330i
$235$	−0.645374	+	12.4372i	−0.0420996	+	0.811316i
$236$	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	−0.324260	−	0.945968i	$-0.605115\pi$
$239$	10.2597	−	12.2270i	0.663643	−	0.790899i	0.987904	+	0.155068i	$0.0495598\pi$
$240$	5.47111	−	2.79123i	0.353159	−	0.180173i
$241$	−7.57694	+	20.8175i	−0.488074	+	1.34097i	0.414349	+	0.910118i	$0.364009\pi$
$241$	−7.57694	+	20.8175i	−0.488074	+	1.34097i	−0.902422	+	0.430853i	$0.858213\pi$
$242$	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
$245$	−2.86319	+	12.4311i	−0.182922	+	0.794193i
$246$	−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
$250$	−1.87222	+	0.366931i	−0.118410	+	0.0232068i
$251$	−15.0176	−	8.67039i	−0.947900	−	0.547270i	−0.0554721	−	0.998460i	$-0.517666\pi$
$251$	−15.0176	−	8.67039i	−0.947900	−	0.547270i	−0.892428	+	0.451190i	$0.851000\pi$
$252$	−17.1893	+	3.03093i	−1.08282	+	0.190931i
$253$	46.4899			2.92280
$254$	1.44495	−	0.254784i	0.0906643	−	0.0159866i
$255$	−0.527032	+	10.1566i	−0.0330040	+	0.636032i
$256$	−12.8935	−	4.69287i	−0.805846	−	0.293304i
$257$	−11.1247	+	4.04907i	−0.693942	+	0.252574i	−0.664822	−	0.747002i	$-0.731493\pi$
$257$	−11.1247	+	4.04907i	−0.693942	+	0.252574i	−0.0291200	+	0.999576i	$0.509270\pi$
$258$		−	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	$-0.165453\pi$
$263$	3.69854	+	4.40775i	0.228062	+	0.271793i	−0.639863	+	0.768489i	$0.721009\pi$
$264$	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	0.862538	+	0.505993i	$0.168874\pi$
$269$	14.2604	+	24.6997i	0.869471	+	1.50597i	0.00693373	+	0.999976i	$0.497793\pi$
$270$	−0.439997	−	1.43651i	−0.0267774	−	0.0874235i
$271$	−12.0165	+	4.37366i	−0.729953	+	0.265681i	−0.680145	−	0.733078i	$-0.738083\pi$
$271$	−12.0165	+	4.37366i	−0.729953	+	0.265681i	−0.0498079	+	0.998759i	$0.515861\pi$
$272$	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
$275$	27.8297	+	2.89599i	1.67819	+	0.174635i
$276$	7.55568	−	9.00450i	0.454798	−	0.542007i
$277$	13.0605	+	4.75363i	0.784729	+	0.285618i	0.703143	−	0.711048i	$-0.251779\pi$
$277$	13.0605	+	4.75363i	0.784729	+	0.285618i	0.0815860	+	0.996666i	$0.474001\pi$
$278$	−0.533115	−	0.194038i	−0.0319741	−	0.0116376i
$279$	4.08325	−	4.86623i	0.244458	−	0.291334i
$280$	3.25241	+	4.31146i	0.194368	+	0.257659i
$281$	6.16133	+	1.08641i	0.367554	+	0.0648097i	0.354375	−	0.935103i	$-0.384694\pi$
$281$	6.16133	+	1.08641i	0.367554	+	0.0648097i	0.0131793	+	0.999913i	$0.495805\pi$
$282$	0.341148	+	0.590887i	0.0203151	+	0.0351868i
$283$	−8.74151	+	7.33500i	−0.519629	+	0.436021i	−0.864502	−	0.502629i	$-0.832366\pi$
$283$	−8.74151	+	7.33500i	−0.519629	+	0.436021i	0.344873	+	0.938649i	$0.387922\pi$
$284$	−12.1006	+	4.40427i	−0.718041	+	0.261346i
$285$	1.79713	−	0.550451i	0.106453	−	0.0326059i
$286$	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	−0.509505	−	0.860468i	$-0.670171\pi$
$293$	7.42711	−	20.4058i	0.433896	−	1.19212i	0.943401	−	0.331653i	$-0.107606\pi$
$294$	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
$300$	5.08388	−	4.91959i	0.293518	−	0.284033i
$301$	−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
$305$	−8.16222	+	1.00647i	−0.467367	+	0.0576302i
$306$	−1.34308	−	2.32628i	−0.0767787	−	0.132985i
$307$	6.09472	+	3.51879i	0.347844	+	0.200828i	0.663735	−	0.747968i	$-0.268970\pi$
$307$	6.09472	+	3.51879i	0.347844	+	0.200828i	−0.315891	+	0.948795i	$0.602303\pi$
$308$	−13.4454	−	36.9410i	−0.766125	−	2.10491i
$309$	−3.69300	−	4.40114i	−0.210087	−	0.250372i
$310$	−0.950663	−	0.218961i	−0.0539940	−	0.0124362i
$311$	−13.3911	−	2.36122i	−0.759342	−	0.133892i	−0.219446	−	0.975625i	$-0.570425\pi$
$311$	−13.3911	−	2.36122i	−0.759342	−	0.133892i	−0.539895	+	0.841732i	$0.681536\pi$
$312$	0.875937	+	0.154451i	0.0495902	+	0.00874409i
$313$	−0.0869709	−	0.0729772i	−0.00491588	−	0.00412492i	0.640326	−	0.768103i	$-0.278799\pi$
$313$	−0.0869709	−	0.0729772i	−0.00491588	−	0.00412492i	−0.645242	+	0.763978i	$0.723244\pi$
$314$	0.905363	−	2.48747i	0.0510926	−	0.140376i
$315$	−17.6400	+	8.99947i	−0.993899	+	0.507063i
$316$	−18.2073	+	21.6986i	−1.02424	+	1.22064i
$317$	2.72456	+	0.480414i	0.153027	+	0.0269828i	0.249637	−	0.968340i	$-0.419689\pi$
$317$	2.72456	+	0.480414i	0.153027	+	0.0269828i	−0.0966099	+	0.995322i	$0.530800\pi$
$318$	−0.194338	+	1.10214i	−0.0108979	+	0.0618052i
$319$	−16.2515	+	9.38283i	−0.909911	+	0.525337i
$320$	−16.3228	−	0.846999i	−0.912473	−	0.0473487i
$321$	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
$325$	8.22115	+	3.99923i	0.456027	+	0.221837i
$326$	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
$330$	1.36546	−	0.696625i	0.0751662	−	0.0383480i
$331$	−1.86733	−	5.13046i	−0.102638	−	0.281996i	0.877735	−	0.479146i	$-0.159054\pi$
$331$	−1.86733	−	5.13046i	−0.102638	−	0.281996i	−0.980373	+	0.197150i	$0.936831\pi$
$332$			0.714298i			0.0392022i
$333$	−4.52829	−	14.4190i	−0.248149	−	0.790157i
$334$	1.75569			0.0960670
$335$	−9.25049	+	21.8241i	−0.505409	+	1.19238i
$336$	−9.20016	−	3.34859i	−0.501910	−	0.182680i
$337$	6.52449	+	7.77558i	0.355411	+	0.423563i	0.913894	−	0.405954i	$-0.133061\pi$
$337$	6.52449	+	7.77558i	0.355411	+	0.423563i	−0.558482	+	0.829517i	$0.688616\pi$
$338$	−0.286147	−	1.62282i	−0.0155643	−	0.0882697i
$339$			1.35386i			0.0735317i
$340$	15.1948	−	23.4243i	0.824051	−	1.27036i
$341$	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
$345$	5.20451	−	12.2787i	0.280202	−	0.661062i
$346$	1.63821	+	1.95234i	0.0880705	+	0.104958i
$347$	11.3707	+	19.6945i	0.610409	+	1.05726i	0.991171	+	0.132586i	$0.0423281\pi$
$347$	11.3707	+	19.6945i	0.610409	+	1.05726i	−0.380763	+	0.924673i	$0.624339\pi$
$348$	−0.823912	+	4.67264i	−0.0441663	+	0.250480i
$349$	4.05073	−	22.9728i	0.216830	−	1.22971i	−0.660871	−	0.750499i	$-0.729813\pi$
$349$	4.05073	−	22.9728i	0.216830	−	1.22971i	0.877702	−	0.479207i	$-0.159076\pi$
$350$	2.46221	+	1.78502i	0.131611	+	0.0954135i
$351$	−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	$-0.458168\pi$
$353$	−15.4537	−	12.9672i	−0.822520	−	0.690176i	−0.953561	+	0.301201i	$0.902613\pi$
$354$	0.215282	−	1.22092i	0.0114421	−	0.0648914i
$355$	−11.6634	+	8.79847i	−0.619031	+	0.466975i
$356$	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	−0.827002	−	0.562200i	$-0.809955\pi$
$359$	1.39032	−	2.40811i	0.0733784	−	0.127095i	0.900380	+	0.435105i	$0.143289\pi$
$360$	−0.844959	+	3.66855i	−0.0445332	+	0.193350i
$361$	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
$365$	12.2864	+	7.96985i	0.643098	+	0.417161i
$366$	−0.345148	+	0.289613i	−0.0180411	+	0.0151383i
$367$	11.1898	−	30.7438i	0.584104	−	1.60481i	−0.196995	−	0.980404i	$-0.563118\pi$
$367$	11.1898	−	30.7438i	0.584104	−	1.60481i	0.781099	−	0.624407i	$-0.214659\pi$
$368$	−29.8695	+	10.8716i	−1.55705	+	0.566722i
$369$	−2.85228			−0.148484
$370$	−1.65645	+	1.62578i	−0.0861150	+	0.0845200i
$371$	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	$-0.977290\pi$
$373$	−3.62199	+	9.95135i	−0.187540	+	0.515261i	0.809916	+	0.586546i	$0.199512\pi$
$374$	4.63450	−	3.88881i	0.239644	−	0.201085i
$375$	3.88039	−	7.02603i	0.200382	−	0.362822i
$376$		−	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	0.757135	−	0.653258i	$-0.226598\pi$
$379$	4.77502	+	4.00671i	0.245276	+	0.205811i	−0.511859	+	0.859070i	$0.671043\pi$
$380$	−5.02833	−	1.15815i	−0.257948	−	0.0594118i
$381$	−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	$-0.664120\pi$
$383$	5.44267	−	4.56694i	0.278108	−	0.233360i	0.771163	+	0.636638i	$0.219675\pi$
$384$	−3.27244	+	1.88934i	−0.166996	+	0.0964152i
$385$	−26.8601	−	35.6064i	−1.36892	−	1.81467i
$386$	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	−0.847476	−	0.530834i	$-0.821879\pi$
$389$	2.81925	−	7.74584i	0.142942	−	0.392730i	0.990418	+	0.138104i	$0.0441010\pi$
$390$	0.497099	−	0.0612964i	0.0251716	−	0.00310386i
$391$	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
$395$	−12.5416	+	29.5885i	−0.631035	+	1.48876i
$396$	13.7015	−	23.7317i	0.688526	−	1.19256i
$397$	−7.05262	+	4.07183i	−0.353961	+	0.204360i	−0.666428	−	0.745569i	$-0.732178\pi$
$397$	−7.05262	+	4.07183i	−0.353961	+	0.204360i	0.312467	+	0.949928i	$0.398844\pi$
$398$	0.816305	−	0.972835i	0.0409177	−	0.0487638i
$399$	−2.59467	−	1.49803i	−0.129896	−	0.0749955i
$400$	−18.5576	+	4.64728i	−0.927881	+	0.232364i
$401$		−	0.784302i		−	0.0391662i	−0.999808	−	0.0195831i	$-0.993766\pi$
$401$		−	0.784302i		−	0.0391662i	0.999808	−	0.0195831i	$-0.00623389\pi$
$402$	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
$405$	−9.52630	−	4.03788i	−0.473366	−	0.200644i
$406$	−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	0.792614	+	0.609724i	$0.208720\pi$
$409$	11.6764	+	32.0806i	0.577359	+	1.58628i	−0.215254	+	0.976558i	$0.569058\pi$
$410$	0.199063	+	0.390185i	0.00983102	+	0.0192699i
$411$	−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
$415$	0.237340	+	0.774875i	0.0116506	+	0.0380371i
$416$	−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	−0.788396	−	0.615168i	$-0.789088\pi$
$419$	−20.4064	+	7.42733i	−0.996920	+	0.362849i	−0.208524	+	0.978017i	$0.566866\pi$
$420$	−11.2619	−	0.584385i	−0.549523	−	0.0285151i
$421$	−23.9644	+	13.8359i	−1.16795	+	0.674318i	−0.953197	−	0.302350i	$-0.902229\pi$
$421$	−23.9644	+	13.8359i	−1.16795	+	0.674318i	−0.214756	+	0.976668i	$0.568896\pi$
$422$	−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
$425$	8.70015	−	30.4596i	0.422019	−	1.47751i
$426$	−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
$430$	−0.105496	+	0.458030i	−0.00508745	+	0.0220882i
$431$	2.12509	+	2.53258i	0.102362	+	0.121990i	0.814793	−	0.579752i	$-0.196850\pi$
$431$	2.12509	+	2.53258i	0.102362	+	0.121990i	−0.712431	+	0.701742i	$0.752406\pi$
$432$	−5.15255	−	14.1565i	−0.247902	−	0.681106i
$433$	−13.9148	−	8.03371i	−0.668702	−	0.386076i	0.126882	−	0.991918i	$-0.459503\pi$
$433$	−13.9148	−	8.03371i	−0.668702	−	0.386076i	−0.795585	+	0.605842i	$0.792836\pi$
$434$	0.777538	+	1.34674i	0.0373230	+	0.0646454i
$435$	0.658795	+	5.34267i	0.0315868	+	0.256161i
$436$	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	−0.704820	−	0.709386i	$-0.748972\pi$
$439$	−23.5611	+	4.15446i	−1.12451	+	0.198282i	−0.419690	+	0.907667i	$0.637861\pi$
$440$	−8.46744	−	0.439380i	−0.403670	−	0.0209466i
$441$	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	−0.616082	−	0.787682i	$-0.711281\pi$
$449$	−19.6132	+	3.45834i	−0.925606	+	0.163209i	−0.309524	+	0.950892i	$0.600170\pi$
$450$	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
$455$	−4.26798	−	13.9342i	−0.200086	−	0.653246i
$456$	−0.535212	+	0.194801i	−0.0250636	+	0.00912240i
$457$	9.81757	−	8.23792i	0.459247	−	0.385354i	−0.383607	−	0.923496i	$-0.625318\pi$
$457$	9.81757	−	8.23792i	0.459247	−	0.385354i	0.842854	+	0.538143i	$0.180874\pi$
$458$	1.25319	+	2.17058i	0.0585576	+	0.101425i
$459$	24.5667	+	4.33177i	1.14667	+	0.202190i
$460$	−29.2285	+	22.0489i	−1.36279	+	1.02804i
$461$	−14.6976	+	17.5159i	−0.684535	+	0.815797i	−0.990683	−	0.136187i	$-0.956515\pi$
$461$	−14.6976	+	17.5159i	−0.684535	+	0.815797i	0.306148	+	0.951984i	$0.400960\pi$
$462$	−2.29615	−	0.835729i	−0.106826	−	0.0388816i
$463$	−10.7259	−	3.90392i	−0.498476	−	0.181430i	0.0805325	−	0.996752i	$-0.474338\pi$
$463$	−10.7259	−	3.90392i	−0.498476	−	0.181430i	−0.579008	+	0.815322i	$0.696560\pi$
$464$	8.24735	−	9.82880i	0.382873	−	0.456291i
$465$	3.27648	−	2.47166i	0.151943	−	0.114620i
$466$	2.35515	+	0.415276i	0.109100	+	0.0192373i
$467$	−7.15751	−	12.3972i	−0.331210	−	0.573673i	0.651539	−	0.758615i	$-0.274124\pi$
$467$	−7.15751	−	12.3972i	−0.331210	−	0.573673i	−0.982749	+	0.184942i	$0.940790\pi$
$468$	6.85896	−	5.75535i	0.317056	−	0.266041i
$469$	35.5060	−	12.9231i	1.63951	−	0.596734i
$470$	−0.622389	−	2.03199i	−0.0287087	−	0.0937289i
$471$	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	0.899075	−	0.437795i	$-0.144240\pi$
$479$	−1.55534	−	4.27327i	−0.0710654	−	0.195251i	−0.970140	+	0.242544i	$0.922018\pi$
$480$	−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
$485$	7.49036	+	0.388679i	0.340120	+	0.0176490i
$486$	−2.54328	+	0.448449i	−0.115366	+	0.0203421i
$487$	21.4485			0.971926			0.485963	−	0.873979i	$-0.338469\pi$
$487$	21.4485			0.971926			0.485963	+	0.873979i	$0.338469\pi$
$488$	2.45429	−	0.432757i	0.111100	−	0.0195900i
$489$	−5.48316	−	3.16570i	−0.247957	−	0.143158i
$490$	−0.266401	−	2.16045i	−0.0120348	−	0.0975990i
$491$	−0.812860	−	1.40792i	−0.0366839	−	0.0635383i	0.847101	−	0.531433i	$-0.178346\pi$
$491$	−0.812860	−	1.40792i	−0.0366839	−	0.0635383i	−0.883784	+	0.467894i	$0.845013\pi$
$492$	−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
$495$	6.97812	−	30.2969i	0.313643	−	1.36174i
$496$	−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	−0.934658	−	0.355548i	$-0.884294\pi$
$499$	0.220549	−	0.605952i	0.00987311	−	0.0271262i	0.944531	+	0.328421i	$0.106517\pi$
$500$	−18.8702	+	11.3781i	−0.843901	+	0.508846i
$501$	−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	$-0.987630\pi$
$503$	−1.05352	+	5.97480i	−0.0469741	+	0.266403i	0.952271	+	0.305254i	$0.0987414\pi$
$504$	5.19697	−	3.00047i	0.231491	−	0.133652i
$505$	−12.4020	−	0.643547i	−0.551883	−	0.0286375i
$506$	−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	0.0596059	−	0.998222i	$-0.481016\pi$
$509$	−20.6005	−	17.2859i	−0.913100	−	0.766182i	−0.972706	+	0.232040i	$0.925460\pi$
$510$	−0.508262	−	1.65939i	−0.0225062	−	0.0734790i
$511$	−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
$515$	8.13240	+	15.9404i	0.358357	+	0.702418i
$516$	−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
$520$	−2.55073	−	1.08117i	−0.111857	−	0.0474123i
$521$	12.4894	+	4.54577i	0.547171	+	0.199154i	0.600789	−	0.799408i	$-0.294853\pi$
$521$	12.4894	+	4.54577i	0.547171	+	0.199154i	−0.0536184	+	0.998562i	$0.517075\pi$
$522$	−0.913905	−	1.08915i	−0.0400005	−	0.0476708i
$523$	3.52997	+	20.0195i	0.154355	+	0.875391i	0.959373	+	0.282140i	$0.0910444\pi$
$523$	3.52997	+	20.0195i	0.154355	+	0.875391i	−0.805018	+	0.593250i	$0.797845\pi$
$524$		−	9.00614i		−	0.393435i
$525$	−12.4111	+	3.10805i	−0.541666	+	0.135646i
$526$	−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
$530$	1.36037	−	3.20944i	0.0590909	−	0.139409i
$531$	−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
$535$	−6.19987	+	0.764495i	−0.268044	+	0.0330520i
$536$	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
$540$	−10.4500	−	13.8527i	−0.449696	−	0.596127i
$541$	−1.25114	+	0.722345i	−0.0537906	+	0.0310560i	−0.526654	−	0.850080i	$-0.676554\pi$
$541$	−1.25114	+	0.722345i	−0.0537906	+	0.0310560i	0.472864	+	0.881136i	$0.343220\pi$
$542$	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
$545$	26.5836	+	6.12287i	1.13872	+	0.262275i
$546$	−0.611610	−	0.513201i	−0.0261745	−	0.0219630i
$547$	13.9639	−	24.1863i	0.597055	−	1.03413i	−0.396198	−	0.918165i	$-0.629671\pi$
$547$	13.9639	−	24.1863i	0.597055	−	1.03413i	0.993253	−	0.115965i	$-0.0369960\pi$
$548$	13.2604	−	2.33816i	0.566455	−	0.0998813i
$549$			9.13819i			0.390008i
$550$	−4.63155	+	1.15985i	−0.197490	+	0.0494563i
$551$	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
$555$	−0.760075	−	9.73486i	−0.0322634	−	0.413222i
$556$	−6.55252			−0.277889
$557$	17.6238	−	6.41452i	0.746742	−	0.271792i	0.0595080	−	0.998228i	$-0.481047\pi$
$557$	17.6238	−	6.41452i	0.746742	−	0.271792i	0.687234	+	0.726436i	$0.258825\pi$
$558$	−0.370747	+	1.01862i	−0.0156950	+	0.0431216i
$559$	1.72538	−	1.44776i	0.0729757	−	0.0612338i
$560$	25.5840	+	16.5957i	1.08112	+	0.701295i
$561$			25.4522i			1.07459i
$562$	−1.05138	+	0.185388i	−0.0443500	+	0.00782010i
$563$	−13.4083	+	23.2239i	−0.565094	+	0.978771i	0.431947	+	0.901899i	$0.357827\pi$
$563$	−13.4083	+	23.2239i	−0.565094	+	0.978771i	−0.997041	+	0.0768721i	$0.975507\pi$
$564$	6.03672	+	5.06541i	0.254192	+	0.213292i
$565$	0.946482	−	4.10933i	0.0398188	−	0.172881i
$566$	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	−0.270113	−	0.962829i	$-0.587061\pi$
$569$	10.2253	−	5.90356i	0.428665	−	0.247490i	0.698778	+	0.715339i	$0.253728\pi$
$570$	−0.256046	+	0.193152i	−0.0107246	+	0.00809023i
$571$	−1.37023	+	7.77099i	−0.0573425	+	0.325206i	−0.999962	−	0.00866199i	$-0.997243\pi$
$571$	−1.37023	+	7.77099i	−0.0573425	+	0.325206i	0.942620	+	0.333868i	$0.108354\pi$
$572$	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
$575$	−24.3811	+	33.6306i	−1.01676	+	1.40249i
$576$	−3.15373	+	17.8857i	−0.131405	+	0.745236i
$577$	−1.51113	+	8.57004i	−0.0629092	+	0.356776i	0.937062	+	0.349163i	$0.113534\pi$
$577$	−1.51113	+	8.57004i	−0.0629092	+	0.356776i	−0.999971	+	0.00761221i	$0.997577\pi$
$578$	−1.97427	−	3.41953i	−0.0821187	−	0.142234i
$579$	6.86445	+	8.18073i	0.285277	+	0.339980i
$580$	5.76742	−	13.6067i	0.239479	−	0.564988i
$581$	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
$585$	5.52831	−	8.52248i	0.228568	−	0.352361i
$586$			3.70557i			0.153076i
$587$	1.36555	+	7.74442i	0.0563623	+	0.319647i	0.999934	−	0.0115229i	$-0.00366793\pi$
$587$	1.36555	+	7.74442i	0.0563623	+	0.319647i	−0.943571	+	0.331169i	$0.892557\pi$
$588$	5.18848	+	6.18339i	0.213969	+	0.254999i
$589$	−2.81298	−	1.02384i	−0.115907	−	0.0421867i
$590$	−1.50698	+	3.55533i	−0.0620415	+	0.146370i
$591$	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
$595$	−44.9803	+	22.9478i	−1.84401	+	0.940769i
$596$	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	0.974029	+	0.226421i	$0.0727027\pi$
$599$	3.33298	+	18.9023i	0.136182	+	0.772326i	−0.837848	+	0.545904i	$0.816186\pi$
$600$	−1.06397	+	2.18719i	−0.0434364	+	0.0892916i
$601$	18.8863	+	15.8475i	0.770389	+	0.646433i	0.940808	−	0.338939i	$-0.110068\pi$
$601$	18.8863	+	15.8475i	0.770389	+	0.646433i	−0.170420	+	0.985372i	$0.554512\pi$
$602$	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
$605$	45.3650	+	2.35401i	1.84435	+	0.0957043i
$606$	−0.589213	+	0.340183i	−0.0239352	+	0.0138190i
$607$	4.53572	−	25.7234i	0.184099	−	1.04408i	−0.743008	−	0.669283i	$-0.766602\pi$
$607$	4.53572	−	25.7234i	0.184099	−	1.04408i	0.927107	−	0.374796i	$-0.122287\pi$
$608$	2.31547	+	0.408280i	0.0939049	+	0.0165580i
$609$	5.51573	−	6.57340i	0.223509	−	0.266367i
$610$	1.25008	−	0.637761i	0.0506144	−	0.0258222i
$611$	−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	$-0.698671\pi$
$613$	−34.9372	−	6.16036i	−1.41110	−	0.248815i	−0.826696	+	0.562649i	$0.809782\pi$
$614$	−1.18266	−	0.208536i	−0.0477285	−	0.00841582i
$615$	−1.79579	−	0.413616i	−0.0724134	−	0.0166786i
$616$	8.68769	+	10.3536i	0.350037	+	0.417158i
$617$	−0.750439	−	2.06181i	−0.0302115	−	0.0830055i	0.923670	−	0.383189i	$-0.125174\pi$
$617$	−0.750439	−	2.06181i	−0.0302115	−	0.0830055i	−0.953881	+	0.300184i	$0.902952\pi$
$618$	0.849042	+	0.490195i	0.0341535	+	0.0197185i
$619$	−19.0489	−	32.9936i	−0.765639	−	1.32613i	−0.939908	−	0.341427i	$-0.889090\pi$
$619$	−19.0489	−	32.9936i	−0.765639	−	1.32613i	0.174269	−	0.984698i	$-0.444244\pi$
$620$	−11.1827	+	1.37892i	−0.449109	+	0.0553788i
$621$	−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
$625$	−16.6899	+	18.6131i	−0.667596	+	0.744524i
$626$	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	0.910728	−	0.413006i	$-0.135521\pi$
$631$	−1.31640	−	3.61678i	−0.0524050	−	0.143982i	−0.963133	+	0.269024i	$0.913299\pi$
$632$	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
$640$	11.2536	−	3.44691i	0.444836	−	0.136251i
$641$	41.2918	−	15.0290i	1.63093	−	0.593609i	0.645508	−	0.763753i	$-0.276646\pi$
$641$	41.2918	−	15.0290i	1.63093	−	0.593609i	0.985419	+	0.170144i	$0.0544234\pi$
$642$	−0.262168	+	0.219985i	−0.0103469	+	0.00868211i
$643$	−15.3709	−	26.6233i	−0.606171	−	1.04992i	−0.991865	−	0.127292i	$-0.959371\pi$
$643$	−15.3709	−	26.6233i	−0.606171	−	1.04992i	0.385694	−	0.922627i	$-0.373962\pi$
$644$	57.4750	+	10.1344i	2.26483	+	0.399351i
$645$	−1.19084	−	1.57861i	−0.0468894	−	0.0621576i
$646$	−0.813657	+	0.969679i	−0.0320129	+	0.0381515i
$647$	−24.4503	−	8.89918i	−0.961241	−	0.349863i	−0.186721	−	0.982413i	$-0.559786\pi$
$647$	−24.4503	−	8.89918i	−0.961241	−	0.349863i	−0.774519	+	0.632550i	$0.782008\pi$
$648$	2.94631	+	1.07237i	0.115742	+	0.0421266i
$649$	36.4025	−	43.3828i	1.42892	−	1.70292i
$650$	−1.55168	−	0.161470i	−0.0608619	−	0.00633336i
$651$	−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	$-0.613363\pi$
$653$	13.1297	−	11.0171i	0.513806	−	0.431134i	0.862466	+	0.506115i	$0.168919\pi$
$654$	1.40440	−	0.511159i	0.0549163	−	0.0199879i
$655$	−2.99247	−	9.76992i	−0.116926	−	0.381742i
$656$	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	−0.998842	−	0.0481068i	$-0.984681\pi$
$659$	−1.96874	−	11.1653i	−0.0766911	−	0.434937i	0.922151	−	0.386830i	$-0.126430\pi$
$660$	12.0678	−	12.9546i	0.469740	−	0.504256i
$661$	20.2994	−	3.57933i	0.789556	−	0.139220i	0.235693	−	0.971828i	$-0.424264\pi$
$661$	20.2994	−	3.57933i	0.789556	−	0.139220i	0.553863	+	0.832608i	$0.313153\pi$
$662$	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
$670$	0.209607	−	4.03941i	0.00809783	−	0.156056i
$671$	−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	$-0.528172\pi$
$673$	4.39031	−	0.774129i	0.169234	−	0.0298405i	0.257623	+	0.966246i	$0.417061\pi$
$674$	−1.50002	−	0.866036i	−0.0577786	−	0.0333585i
$675$	−15.9391	−	11.5553i	−0.613495	−	0.444764i
$676$	−9.51616	−	16.4825i	−0.366006	−	0.633941i
$677$	−43.7861	−	25.2799i	−1.68284	−	0.971587i	−0.959760	−	0.280821i	$-0.909393\pi$
$677$	−43.7861	−	25.2799i	−1.68284	−	0.971587i	−0.723078	−	0.690766i	$-0.757273\pi$
$678$	−0.0790157	−	0.217094i	−0.00303458	−	0.00833744i
$679$	−7.68519	−	9.15885i	−0.294931	−	0.351485i
$680$	−2.15457	+	9.35447i	−0.0826239	+	0.358727i
$681$	−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	$-0.444924\pi$
$683$	−20.0722	−	16.8426i	−0.768043	−	0.644465i	−0.940207	+	0.340604i	$0.889369\pi$
$684$	−1.96099	+	5.38777i	−0.0749802	+	0.206006i
$685$	13.6080	−	6.94248i	0.519936	−	0.265259i
$686$	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
$690$	−0.117929	+	2.27266i	−0.00448949	+	0.0865185i
$691$	−19.0751	+	6.94277i	−0.725651	+	0.264115i	−0.678323	−	0.734764i	$-0.737293\pi$
$691$	−19.0751	+	6.94277i	−0.725651	+	0.264115i	−0.0473282	+	0.998879i	$0.515071\pi$
$692$	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
$695$	−7.10822	+	2.17721i	−0.269630	+	0.0825863i
$696$	−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
$700$	33.7743	+	9.64692i	1.27655	+	0.364619i
$701$	−0.514224	−	1.41282i	−0.0194220	−	0.0533614i	0.929603	−	0.368563i	$-0.120150\pi$
$701$	−0.514224	−	1.41282i	−0.0194220	−	0.0533614i	−0.949025	+	0.315202i	$0.897928\pi$
$702$		−	1.22852i		−	0.0463674i
$703$	−5.65520	+	4.32919i	−0.213290	+	0.163278i
$704$	−40.9045			−1.54165
$705$	8.23176	+	3.48916i	0.310026	+	0.131409i
$706$	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	$-0.875214\pi$
$709$		−	20.3464i		−	0.764124i	0.924137	−	0.382062i	$-0.124786\pi$
$710$	1.35674	−	2.09156i	0.0509177	−	0.0784950i
$711$	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
$715$	21.0653	+	8.92886i	0.787797	+	0.333920i
$716$	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	−0.522547	−	0.852611i	$-0.675018\pi$
$719$	6.97428	−	39.5531i	0.260097	−	1.47508i	0.782643	−	0.622470i	$-0.213871\pi$
$720$	2.60148	+	21.0974i	0.0969514	+	0.786253i
$721$	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
$725$	1.73543	−	16.6770i	0.0644522	−	0.619368i
$726$	2.15527	−	1.24434i	0.0799895	−	0.0461820i
$727$	−31.1285	+	26.1199i	−1.15449	+	0.968734i	−0.999815	−	0.0192316i	$-0.993878\pi$
$727$	−31.1285	+	26.1199i	−1.15449	+	0.968734i	−0.154677	+	0.987965i	$0.549434\pi$
$728$	1.51041	+	4.14982i	0.0559796	+	0.153803i
$729$	−1.50842	+	2.61266i	−0.0558675	+	0.0967653i
$730$	−2.43528	−	0.560906i	−0.0901338	−	0.0207601i
$731$	−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	$-0.228993\pi$
$733$	45.6035	−	8.04113i	1.68440	−	0.297006i	0.932205	+	0.361930i	$0.117882\pi$
$734$			5.58288i			0.206068i
$735$	7.68305	+	4.98380i	0.283394	+	0.183830i
$736$	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	$0.744663\pi$
$740$	−11.5557	+	24.1883i	−0.424795	+	0.889181i
$741$	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	$-0.868413\pi$
$743$	1.19858	−	3.29307i	0.0439716	−	0.120811i	0.959735	+	0.280907i	$0.0906353\pi$
$744$	−0.952732	+	0.799437i	−0.0349288	+	0.0293088i
$745$	14.5467	−	22.4252i	0.532948	−	0.821596i
$746$		−	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
$750$	−0.212165	+	1.35311i	−0.00774716	+	0.0494084i
$751$	11.9496	−	20.6973i	0.436047	−	0.755255i	−0.561334	−	0.827590i	$-0.689712\pi$
$751$	11.9496	−	20.6973i	0.436047	−	0.755255i	0.997380	+	0.0723345i	$0.0230449\pi$
$752$	−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
$755$	−38.8457	+	29.3038i	−1.41374	+	1.06647i
$756$	−4.80316	+	27.2400i	−0.174689	+	0.990711i
$757$	−2.15994	−	1.81240i	−0.0785042	−	0.0658729i	0.602691	−	0.797975i	$-0.294095\pi$
$757$	−2.15994	−	1.81240i	−0.0785042	−	0.0658729i	−0.681195	+	0.732102i	$0.738540\pi$
$758$	−0.999525	−	0.363797i	−0.0363044	−	0.0132137i
$759$	11.4150	−	31.3623i	0.414337	−	1.13838i
$760$	1.76070	−	0.217108i	0.0638672	−	0.00787535i
$761$	5.05316	−	28.6579i	0.183177	−	1.03885i	−0.745098	−	0.666955i	$-0.767597\pi$
$761$	5.05316	−	28.6579i	0.183177	−	1.03885i	0.928275	−	0.371894i	$-0.121291\pi$
$762$	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
$765$	−32.4079	−	13.7366i	−1.17171	−	0.496648i
$766$	−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	0.861240	−	0.508199i	$-0.169688\pi$
$769$	23.6197	+	13.6368i	0.851747	+	0.491756i	−0.00949305	+	0.999955i	$0.503022\pi$
$770$	6.38516	+	4.14189i	0.230105	+	0.149263i
$771$			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	$-0.182227\pi$
$773$	4.47919	+	5.33809i	0.161105	+	0.191998i	−0.679453	+	0.733719i	$0.737783\pi$
$774$	0.490771	+	0.178626i	0.0176404	+	0.00642058i
$775$	−11.6729	+	5.21155i	−0.419304	+	0.187205i
$776$	−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
$780$	5.15300	−	2.62893i	0.184507	−	0.0941308i
$781$	−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
$785$	−10.1587	−	33.1663i	−0.362578	−	1.18376i
$786$	−0.428828	−	0.359829i	−0.0152958	−	0.0128347i
$787$	−15.6550	+	9.03840i	−0.558040	+	0.322184i	−0.752358	−	0.658754i	$-0.771084\pi$
$787$	−15.6550	+	9.03840i	−0.558040	+	0.322184i	0.194319	+	0.980938i	$0.437750\pi$
$788$	−22.5055	−	12.9935i	−0.801724	−	0.462876i
$789$	3.88161	−	1.41279i	0.138189	−	0.0502967i
$790$	0.284180	−	5.47653i	0.0101107	−	0.194846i
$791$	−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
$795$	6.66456	+	13.0633i	0.236368	+	0.463306i
$796$	5.01661	−	13.7830i	0.177809	−	0.488526i
$797$	−5.51566	−	4.62819i	−0.195375	−	0.163939i	0.539852	−	0.841760i	$-0.318480\pi$
$797$	−5.51566	−	4.62819i	−0.195375	−	0.163939i	−0.735227	+	0.677821i	$0.762924\pi$
$798$	0.503489	+	0.0887788i	0.0178233	+	0.00314273i
$799$	34.7503	+	6.12742i	1.22938	+	0.216772i
$800$	8.31817	−	5.62317i	0.294092	−	0.198809i
$801$	−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
$805$	65.7167	−	8.10341i	2.31621	−	0.285608i
$806$	−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	0.213320	−	0.976982i	$-0.431572\pi$
$809$	21.2731	−	3.75102i	0.747923	−	0.131879i	0.534603	+	0.845103i	$0.320461\pi$
$810$	1.76322	+	0.0914943i	0.0619532	+	0.00321478i
$811$	−23.9554	−	8.71906i	−0.841189	−	0.306168i	−0.114746	−	0.993395i	$-0.536606\pi$
$811$	−23.9554	−	8.71906i	−0.841189	−	0.306168i	−0.726443	+	0.687227i	$0.758828\pi$
$812$	−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	0.963489	−	0.267750i	$-0.0862800\pi$
$821$	−0.959028	−	5.43892i	−0.0334703	−	0.189820i	−0.996959	+	0.0779301i	$0.975169\pi$
$822$	0.418470	−	0.724812i	0.0145958	−	0.0252807i
$823$	−12.5080	+	14.9064i	−0.436001	+	0.519605i	−0.938644	−	0.344889i	$-0.887917\pi$
$823$	−12.5080	+	14.9064i	−0.436001	+	0.519605i	0.502643	+	0.864494i	$0.332361\pi$
$824$	−2.71139	−	4.69626i	−0.0944557	−	0.163602i
$825$	8.78685	−	18.0630i	0.305919	−	0.628872i
$826$	5.78422	−	2.10528i	0.201259	−	0.0732522i
$827$	−15.9070	+	13.3476i	−0.553141	+	0.464140i	−0.876003	−	0.482306i	$-0.839799\pi$
$827$	−15.9070	+	13.3476i	−0.553141	+	0.464140i	0.322862	+	0.946446i	$0.395355\pi$
$828$	20.3410	+	35.2316i	0.706898	+	1.22438i
$829$	19.7559	+	3.48349i	0.686149	+	0.120987i	0.505845	−	0.862624i	$-0.331181\pi$
$829$	19.7559	+	3.48349i	0.686149	+	0.120987i	0.180304	+	0.983611i	$0.442292\pi$
$830$	−0.0832820	−	0.110400i	−0.00289076	−	0.00383205i
$831$	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
$835$	18.3664	−	13.8550i	0.635597	−	0.479471i
$836$	−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	−0.375593	−	0.926785i	$-0.622561\pi$
$839$	−1.95773	+	0.712555i	−0.0675883	+	0.0246001i	0.308005	+	0.951385i	$0.400339\pi$
$840$	3.70712	−	1.13547i	0.127908	−	0.0391774i
$841$	−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	$-0.721708\pi$
$853$	−18.6900	+	6.80260i	−0.639933	+	0.232917i	0.00161596	+	0.999999i	$0.499486\pi$
$854$	−2.10213	−	0.765111i	−0.0719332	−	0.0261816i
$855$	−0.337094	+	6.49626i	−0.0115284	+	0.222167i
$856$	1.86423	−	0.328714i	0.0637181	−	0.0112352i
$857$	−26.3623			−0.900519			−0.450259	−	0.892898i	$-0.648668\pi$
$857$	−26.3623			−0.900519			−0.450259	+	0.892898i	$0.648668\pi$
$858$	1.23442	−	0.217662i	0.0421424	−	0.00743085i
$859$	41.7109	+	24.0818i	1.42316	+	0.821660i	0.996567	−	0.0827856i	$-0.0263817\pi$
$859$	41.7109	+	24.0818i	1.42316	+	0.821660i	0.426589	+	0.904445i	$0.359715\pi$
$860$	0.664365	+	5.38784i	0.0226547	+	0.183724i
$861$	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	0.900862	+	0.434105i	$0.142935\pi$
$863$	14.3888	+	39.5328i	0.489799	+	1.34571i	−0.411064	+	0.911607i	$0.634843\pi$
$864$	5.08234	+	6.05690i	0.172905	+	0.206060i
$865$	32.5443	+	7.49576i	1.10654	+	0.254863i
$866$	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
$870$	−0.417454	−	0.818255i	−0.0141530	−	0.0277415i
$871$	−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
$875$	39.8439	−	0.757162i	1.34697	−	0.0255967i
$876$	8.70786	−	3.16940i	0.294211	−	0.107084i
$877$	−43.2041	−	24.9439i	−1.45890	−	0.842296i	−0.459942	−	0.887949i	$-0.652130\pi$
$877$	−43.2041	−	24.9439i	−1.45890	−	0.842296i	−0.998957	+	0.0456525i	$0.985463\pi$
$878$	3.53559	−	2.04127i	0.119320	−	0.0688897i
$879$	−11.9422	−	10.0207i	−0.402802	−	0.337991i
$880$	−45.7773	+	14.0214i	−1.54315	+	0.472660i
$881$	2.81023	+	15.9376i	0.0946791	+	0.536952i	0.994845	+	0.101405i	$0.0323338\pi$
$881$	2.81023	+	15.9376i	0.0946791	+	0.536952i	−0.900166	+	0.435547i	$0.856555\pi$
$882$	−2.41877			−0.0814444
$883$	5.49453	+	31.1610i	0.184906	+	1.04865i	0.926077	+	0.377335i	$0.123160\pi$
$883$	5.49453	+	31.1610i	0.184906	+	1.04865i	−0.741171	+	0.671316i	$0.765729\pi$
$884$	17.4897	−	14.6756i	0.588243	−	0.493595i
$885$	−7.38280	−	14.4711i	−0.248170	−	0.486441i
$886$	−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
$890$	−1.70832	+	4.03032i	−0.0572629	+	0.135097i
$891$	−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
$895$	7.78681	+	5.05111i	0.260284	+	0.168840i
$896$	−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
$900$	9.98180	+	22.3574i	0.332727	+	0.745246i
$901$	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
$905$	3.75618	+	30.4617i	0.124860	+	1.01258i
$906$	−0.911760	+	2.50504i	−0.0302912	+	0.0832244i
$907$	54.2679	+	19.7519i	1.80194	+	0.655851i	0.998141	+	0.0609459i	$0.0194117\pi$
$907$	54.2679	+	19.7519i	1.80194	+	0.655851i	0.803796	+	0.594905i	$0.202810\pi$
$908$	44.9600	+	37.7259i	1.49205	+	1.25198i
$909$	−2.39619	+	13.5895i	−0.0794766	+	0.450734i
$910$	1.49762	+	1.98528i	0.0496457	+	0.0658113i
$911$	−8.80962	+	5.08623i	−0.291876	+	0.168514i	−0.638787	−	0.769383i	$-0.720564\pi$
$911$	−8.80962	+	5.08623i	−0.291876	+	0.168514i	0.346912	+	0.937898i	$0.387230\pi$
$912$	−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
$915$	−1.32515	+	5.75340i	−0.0438081	+	0.190201i
$916$	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	$0.00115456\pi$
$919$			0.219914i			0.00725429i	−0.999993	+	0.00362715i	$0.998845\pi$
$920$	6.85022	−	10.5603i	0.225845	−	0.348164i
$921$	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
$925$	−4.49859	+	30.0793i	−0.147913	+	0.989000i
$926$	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	−0.409409	+	0.912351i	$0.634265\pi$
$929$	−42.0310	+	35.2682i	−1.37899	+	1.15711i	−0.969583	+	0.244761i	$0.921290\pi$
$930$	−0.381135	+	0.587559i	−0.0124979	+	0.0192668i
$931$		−	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
$935$	17.7936	−	77.2543i	0.581912	−	2.52648i
$936$	−1.53917	+	2.66593i	−0.0503095	+	0.0871386i
$937$	−15.0914	−	41.4633i	−0.493015	−	1.35455i	−0.897908	−	0.440183i	$-0.854914\pi$
$937$	−15.0914	−	41.4633i	−0.493015	−	1.35455i	0.404893	−	0.914364i	$-0.367309\pi$
$938$	−4.93920	+	4.14448i	−0.161271	+	0.135322i
$939$	−0.0705853	+	0.0407524i	−0.00230346	+	0.00132991i
$940$	−14.7818	−	19.5951i	−0.482130	−	0.639122i
$941$	−3.08919	+	17.5197i	−0.100705	+	0.571125i	0.892144	+	0.451750i	$0.149200\pi$
$941$	−3.08919	+	17.5197i	−0.100705	+	0.571125i	−0.992849	+	0.119375i	$0.961911\pi$
$942$	−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
$945$	3.84057	+	31.1461i	0.124934	+	1.01318i
$946$	−0.204259	+	1.15841i	−0.00664102	+	0.0376631i
$947$	−8.06428	+	45.7348i	−0.262054	+	1.48618i	0.515242	+	0.857045i	$0.327702\pi$
$947$	−8.06428	+	45.7348i	−0.262054	+	1.48618i	−0.777295	+	0.629136i	$0.783409\pi$
$948$	10.1674	+	17.6105i	0.330223	+	0.571963i
$949$	7.69756	+	9.17359i	0.249873	+	0.297787i
$950$	0.912200	−	0.407266i	0.0295957	−	0.0132134i
$951$	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	0.248513	−	0.968629i	$-0.420058\pi$
$953$	35.7875	−	42.6499i	1.15927	−	1.38157i	0.910759	−	0.412938i	$-0.135497\pi$
$954$	−3.35440	−	1.93666i	−0.108603	−	0.0627017i
$955$	−3.34323	−	2.16867i	−0.108184	−	0.0701764i
$956$			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
$960$	−4.57923	+	10.8035i	−0.147794	+	0.348681i
$961$	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
$965$	−15.1163	−	29.6296i	−0.486611	−	0.953811i
$966$	2.77890	−	2.33177i	0.0894095	−	0.0750235i
$967$	0.982962	+	5.57465i	0.0316099	+	0.179269i	0.996525	−	0.0832930i	$-0.0265437\pi$
$967$	0.982962	+	5.57465i	0.0316099	+	0.179269i	−0.964915	+	0.262562i	$0.915433\pi$
$968$	−13.7656			−0.442442
$969$	−0.924743	−	5.24448i	−0.0297070	−	0.168477i
$970$	−1.22377	+	0.374836i	−0.0392930	+	0.0120353i
$971$	−8.95214	−	7.51173i	−0.287288	−	0.241063i	0.487742	−	0.872988i	$-0.337821\pi$
$971$	−8.95214	−	7.51173i	−0.287288	−	0.241063i	−0.775030	+	0.631925i	$0.782265\pi$
$972$	−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
$975$	4.71649	−	4.56407i	0.151048	−	0.146167i
$976$	12.1868	−	7.03607i	0.390091	−	0.225219i
$977$	−4.65601	+	26.4056i	−0.148959	+	0.844788i	0.815144	+	0.579259i	$0.196658\pi$
$977$	−4.65601	+	26.4056i	−0.148959	+	0.844788i	−0.964103	+	0.265530i	$0.914453\pi$
$978$	1.06399	+	0.187611i	0.0340227	+	0.00599913i
$979$	41.2659	−	49.1788i	1.31886	−	1.57176i
$980$	−11.4256	−	22.3955i	−0.364978	−	0.715397i
$981$	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	$-0.264884\pi$
$983$	33.0168	+	5.82176i	1.05307	+	0.185685i	0.379792	+	0.925072i	$0.375996\pi$
$984$	0.549948	+	0.0969706i	0.0175317	+	0.00309131i
$985$	−28.7315	−	6.61757i	−0.915460	−	0.210853i
$986$	−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
$990$	0.649269	+	5.26541i	0.0206351	+	0.167346i
$991$	6.47557	+	3.73867i	0.205703	+	0.118763i	0.599313	−	0.800515i	$-0.295441\pi$
$991$	6.47557	+	3.73867i	0.205703	+	0.118763i	−0.393610	+	0.919278i	$0.628774\pi$
$992$	5.05611	−	0.891528i	0.160532	−	0.0283061i
$993$	−3.91953			−0.124383
$994$	−3.91369	+	0.690089i	−0.124135	+	0.0218883i
$995$	0.862357	−	16.6188i	0.0273386	−	0.526851i
$996$	0.481869	+	0.175386i	0.0152686	+	0.00555732i
$997$	29.0340	−	10.5675i	0.919516	−	0.334676i	0.161470	−	0.986878i	$-0.448376\pi$
$997$	29.0340	−	10.5675i	0.919516	−	0.334676i	0.758046	+	0.652201i	$0.226154\pi$
$998$			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.104.8	✓	96
5.2	odd	4		925.2.bb.e.326.8		96
5.3	odd	4		925.2.bb.e.326.9		96
5.4	even	2	inner	185.2.v.a.104.9	yes	96
37.21	even	18	inner	185.2.v.a.169.9	yes	96
185.58	odd	36		925.2.bb.e.576.9		96
185.132	odd	36		925.2.bb.e.576.8		96
185.169	even	18	inner	185.2.v.a.169.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.8	✓	96	1.1	even	1	trivial
185.2.v.a.104.9	yes	96	5.4	even	2	inner
185.2.v.a.169.8	yes	96	185.169	even	18	inner
185.2.v.a.169.9	yes	96	37.21	even	18	inner
925.2.bb.e.326.8		96	5.2	odd	4
925.2.bb.e.326.9		96	5.3	odd	4
925.2.bb.e.576.8		96	185.132	odd	36
925.2.bb.e.576.9		96	185.58	odd	36

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} +(-1.21688 + 1.87595i) q^{5} +0.122504i q^{6} +(3.51024 - 0.618951i) q^{7} +(0.338800 - 0.586820i) q^{8} +(1.90333 + 1.59708i) q^{9} +(0.0856423 - 0.371833i) 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} +(0.966738 + 1.28153i) 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} +(-0.539338 - 4.37390i) 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} +(-2.03839 - 4.56563i) 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} +(-0.229812 - 0.149073i) q^{30} -2.55670i q^{31} +(0.348703 + 1.97760i) q^{32} +(2.58231 + 3.07748i) q^{33} +(-1.01592 - 0.369763i) q^{34} +(-3.11043 + 7.33824i) q^{35} -4.89689 q^{36} +(-5.12643 - 3.27409i) q^{37} +0.199797i q^{38} +(0.448951 + 1.23348i) q^{39} +(0.688565 + 1.34966i) q^{40} +(-0.879400 + 0.737904i) q^{41} +(0.0758240 + 0.430019i) q^{42} -1.23182 q^{43} +(-1.91517 - 10.8615i) q^{44} +(-5.31218 + 1.62709i) 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} +(0.593324 + 0.613138i) 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} +(-5.68654 - 11.1463i) 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} +(-3.08308 - 0.710110i) 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} +(-0.500362 - 4.05781i) q^{65} +(-0.593689 - 0.342766i) q^{66} +(10.4395 - 1.84077i) q^{67} -12.4866 q^{68} +(-5.87350 + 1.03566i) q^{69} +(0.0704793 - 1.35823i) 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} +(-13.5456 + 4.14894i) 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} +(0.756853 - 0.570942i) 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} +(1.57669 + 2.09010i) 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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