LMFDB - Embedded newform 195.2.bf.a.62.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (of order $12$, degree $4$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			62.5
Character	$\chi$	$=$	195.62
Dual form			195.2.bf.a.173.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.496187 + 1.85180i) q^{2} +(-0.676428 + 1.59450i) q^{3} +(-1.45090 - 0.837676i) q^{4} +(1.97286 + 1.05254i) q^{5} +(-2.61706 - 2.04378i) q^{6} +(0.527913 + 1.97020i) q^{7} +(-0.440097 + 0.440097i) q^{8} +(-2.08489 - 2.15713i) q^{9} +(-2.92799 + 3.13107i) q^{10} +(-0.0324046 - 0.0561264i) q^{11} +(2.31710 - 1.74683i) q^{12} +(3.39239 - 1.22133i) q^{13} -3.91035 q^{14} +(-3.01277 + 2.43376i) q^{15} +(-2.27195 - 3.93513i) q^{16} +(-1.31006 - 4.88919i) q^{17} +(5.02907 - 2.79045i) q^{18} +(1.37598 - 2.38327i) q^{19} +(-1.98073 - 3.17974i) q^{20} +(-3.49859 - 0.490937i) q^{21} +(0.120014 - 0.0321575i) q^{22} +(-1.36681 + 5.10100i) q^{23} +(-0.404043 - 0.999430i) q^{24} +(2.78433 + 4.15301i) q^{25} +(0.578399 + 6.88803i) q^{26} +(4.84984 - 1.86522i) q^{27} +(0.884440 - 3.30077i) q^{28} +(-1.40236 - 2.42895i) q^{29} +(-3.01194 - 6.78664i) q^{30} +0.312918i q^{31} +(7.21201 - 1.93245i) q^{32} +(0.111413 - 0.0137038i) q^{33} +9.70382 q^{34} +(-1.03221 + 4.44257i) q^{35} +(1.21798 + 4.87624i) q^{36} +(-1.21737 - 0.326192i) q^{37} +(3.73059 + 3.73059i) q^{38} +(-0.347286 + 6.23533i) q^{39} +(-1.33147 + 0.405030i) q^{40} +(5.66614 + 9.81404i) q^{41} +(2.64507 - 6.23507i) q^{42} +(2.53152 + 9.44778i) q^{43} +0.108578i q^{44} +(-1.84273 - 6.45014i) q^{45} +(-8.76782 - 5.06210i) q^{46} +(-0.638524 - 0.638524i) q^{47} +(7.81140 - 0.960802i) q^{48} +(2.45919 - 1.41981i) q^{49} +(-9.07208 + 3.09534i) q^{50} +(8.68200 + 1.21830i) q^{51} +(-5.94510 - 1.06970i) q^{52} +(-5.43756 - 5.43756i) q^{53} +(1.04758 + 9.90641i) q^{54} +(-0.00485451 - 0.144837i) q^{55} +(-1.09941 - 0.634745i) q^{56} +(2.86938 + 3.80612i) q^{57} +(5.19376 - 1.39166i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(6.40992 - 1.00742i) q^{60} +(-1.38357 + 2.39642i) q^{61} +(-0.579461 - 0.155266i) q^{62} +(3.14934 - 5.24643i) q^{63} +5.22623i q^{64} +(7.97821 + 1.16110i) q^{65} +(-0.0299051 + 0.213114i) q^{66} +(10.5842 + 2.83602i) q^{67} +(-2.19480 + 8.19111i) q^{68} +(-7.20902 - 5.62984i) q^{69} +(-7.71456 - 4.11579i) q^{70} +(6.90717 - 11.9636i) q^{71} +(1.86690 + 0.0317942i) q^{72} +(-7.38949 - 7.38949i) q^{73} +(1.20808 - 2.09246i) q^{74} +(-8.50539 + 1.63042i) q^{75} +(-3.99282 + 2.30525i) q^{76} +(0.0934734 - 0.0934734i) q^{77} +(-11.3742 - 3.73700i) q^{78} +5.34069i q^{79} +(-0.340359 - 10.1548i) q^{80} +(-0.306459 + 8.99478i) q^{81} +(-20.9851 + 5.62293i) q^{82} +(2.60495 - 2.60495i) q^{83} +(4.66484 + 3.64298i) q^{84} +(2.56151 - 11.0246i) q^{85} -18.7515 q^{86} +(4.82157 - 0.593053i) q^{87} +(0.0389622 + 0.0104399i) q^{88} +(12.5211 - 7.22908i) q^{89} +(12.8587 - 0.211877i) q^{90} +(4.19716 + 6.03893i) q^{91} +(6.25608 - 6.25608i) q^{92} +(-0.498950 - 0.211667i) q^{93} +(1.49924 - 0.865588i) q^{94} +(5.22310 - 3.25358i) q^{95} +(-1.79710 + 12.8068i) q^{96} +(-1.90959 - 7.12670i) q^{97} +(1.40899 + 5.25841i) q^{98} +(-0.0535122 + 0.186919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.496187	+	1.85180i	−0.350857	+	1.30942i	0.534761	+	0.845004i	$0.320402\pi$
$2$	−0.496187	+	1.85180i	−0.350857	+	1.30942i	−0.885618	+	0.464414i	$0.846265\pi$
$3$	−0.676428	+	1.59450i	−0.390536	+	0.920588i
$3$	−0.676428	+	1.59450i	−0.390536	+	0.920588i
$4$	−1.45090	−	0.837676i	−0.725448	−	0.418838i
$5$	1.97286	+	1.05254i	0.882289	+	0.470709i
$5$	1.97286	+	1.05254i	0.882289	+	0.470709i
$6$	−2.61706	−	2.04378i	−1.06841	−	0.834369i
$7$	0.527913	+	1.97020i	0.199532	+	0.744665i	0.991047	+	0.133515i	$0.0426263\pi$
$7$	0.527913	+	1.97020i	0.199532	+	0.744665i	−0.791514	+	0.611150i	$0.790707\pi$
$8$	−0.440097	+	0.440097i	−0.155598	+	0.155598i
$9$	−2.08489	−	2.15713i	−0.694964	−	0.719045i
$10$	−2.92799	+	3.13107i	−0.925912	+	0.990132i
$11$	−0.0324046	−	0.0561264i	−0.00977036	−	0.0169228i	0.861099	−	0.508438i	$-0.169777\pi$
$11$	−0.0324046	−	0.0561264i	−0.00977036	−	0.0169228i	−0.870869	+	0.491515i	$0.836443\pi$
$12$	2.31710	−	1.74683i	0.668890	−	0.504268i
$13$	3.39239	−	1.22133i	0.940881	−	0.338737i
$13$	3.39239	−	1.22133i	0.940881	−	0.338737i
$14$	−3.91035			−1.04508
$15$	−3.01277	+	2.43376i	−0.777894	+	0.628395i
$16$	−2.27195	−	3.93513i	−0.567988	−	0.983783i
$17$	−1.31006	−	4.88919i	−0.317735	−	1.18580i	−0.921416	−	0.388577i	$-0.872967\pi$
$17$	−1.31006	−	4.88919i	−0.317735	−	1.18580i	0.603681	−	0.797226i	$-0.293700\pi$
$18$	5.02907	−	2.79045i	1.18536	−	0.657715i
$19$	1.37598	−	2.38327i	0.315672	−	0.546760i	−0.663908	−	0.747814i	$-0.731103\pi$
$19$	1.37598	−	2.38327i	0.315672	−	0.546760i	0.979580	+	0.201054i	$0.0644368\pi$
$20$	−1.98073	−	3.17974i	−0.442904	−	0.711011i
$21$	−3.49859	−	0.490937i	−0.763454	−	0.107131i
$22$	0.120014	−	0.0321575i	0.0255870	−	0.00685601i
$23$	−1.36681	+	5.10100i	−0.284999	+	1.06363i	0.663840	+	0.747874i	$0.268925\pi$
$23$	−1.36681	+	5.10100i	−0.284999	+	1.06363i	−0.948840	+	0.315758i	$0.897741\pi$
$24$	−0.404043	−	0.999430i	−0.0824749	−	0.204008i
$25$	2.78433	+	4.15301i	0.556866	+	0.830602i
$26$	0.578399	+	6.88803i	0.113433	+	1.35085i
$27$	4.84984	−	1.86522i	0.933352	−	0.358962i
$28$	0.884440	−	3.30077i	0.167143	−	0.623788i
$29$	−1.40236	−	2.42895i	−0.260411	−	0.451045i	0.705940	−	0.708271i	$-0.250525\pi$
$29$	−1.40236	−	2.42895i	−0.260411	−	0.451045i	−0.966351	+	0.257226i	$0.917191\pi$
$30$	−3.01194	−	6.78664i	−0.549902	−	1.23907i
$31$			0.312918i			0.0562018i	0.999605	+	0.0281009i	$0.00894597\pi$
$31$			0.312918i			0.0562018i	−0.999605	+	0.0281009i	$0.991054\pi$
$32$	7.21201	−	1.93245i	1.27492	−	0.341613i
$33$	0.111413	−	0.0137038i	0.0193946	−	0.00238553i
$34$	9.70382			1.66419
$35$	−1.03221	+	4.44257i	−0.174475	+	0.750931i
$36$	1.21798	+	4.87624i	0.202997	+	0.812707i
$37$	−1.21737	−	0.326192i	−0.200134	−	0.0536257i	0.157359	−	0.987541i	$-0.449702\pi$
$37$	−1.21737	−	0.326192i	−0.200134	−	0.0536257i	−0.357493	+	0.933916i	$0.616369\pi$
$38$	3.73059	+	3.73059i	0.605181	+	0.605181i
$39$	−0.347286	+	6.23533i	−0.0556103	+	0.998453i
$40$	−1.33147	+	0.405030i	−0.210523	+	0.0640409i
$41$	5.66614	+	9.81404i	0.884903	+	1.53270i	0.845825	+	0.533460i	$0.179109\pi$
$41$	5.66614	+	9.81404i	0.884903	+	1.53270i	0.0390773	+	0.999236i	$0.487558\pi$
$42$	2.64507	−	6.23507i	0.408143	−	0.962092i
$43$	2.53152	+	9.44778i	0.386054	+	1.44077i	0.836499	+	0.547968i	$0.184599\pi$
$43$	2.53152	+	9.44778i	0.386054	+	1.44077i	−0.450445	+	0.892804i	$0.648735\pi$
$44$			0.108578i			0.0163688i
$45$	−1.84273	−	6.45014i	−0.274698	−	0.961531i
$46$	−8.76782	−	5.06210i	−1.29274	−	0.746366i
$47$	−0.638524	−	0.638524i	−0.0931382	−	0.0931382i	0.659003	−	0.752141i	$-0.270979\pi$
$47$	−0.638524	−	0.638524i	−0.0931382	−	0.0931382i	−0.752141	+	0.659003i	$0.770979\pi$
$48$	7.81140	−	0.960802i	1.12748	−	0.138680i
$49$	2.45919	−	1.41981i	0.351313	−	0.202830i
$50$	−9.07208	+	3.09534i	−1.28299	+	0.437747i
$51$	8.68200	+	1.21830i	1.21572	+	0.170596i
$52$	−5.94510	−	1.06970i	−0.824436	−	0.148340i
$53$	−5.43756	−	5.43756i	−0.746906	−	0.746906i	0.226991	−	0.973897i	$-0.427111\pi$
$53$	−5.43756	−	5.43756i	−0.746906	−	0.746906i	−0.973897	+	0.226991i	$0.927111\pi$
$54$	1.04758	+	9.90641i	0.142558	+	1.34809i
$55$	−0.00485451	−	0.144837i	−0.000654582	−	0.0195298i
$56$	−1.09941	−	0.634745i	−0.146915	−	0.0848214i
$57$	2.86938	+	3.80612i	0.380059	+	0.504133i
$58$	5.19376	−	1.39166i	0.681974	−	0.182734i
$59$	−5.86942	−	3.38871i	−0.764133	−	0.441172i	0.0666447	−	0.997777i	$-0.478771\pi$
$59$	−5.86942	−	3.38871i	−0.764133	−	0.441172i	−0.830778	+	0.556604i	$0.812104\pi$
$60$	6.40992	−	1.00742i	0.827518	−	0.130057i
$61$	−1.38357	+	2.39642i	−0.177149	+	0.306830i	−0.940903	−	0.338677i	$-0.890021\pi$
$61$	−1.38357	+	2.39642i	−0.177149	+	0.306830i	0.763754	+	0.645507i	$0.223354\pi$
$62$	−0.579461	−	0.155266i	−0.0735916	−	0.0197188i
$63$	3.14934	−	5.24643i	0.396780	−	0.660988i
$64$			5.22623i			0.653279i
$65$	7.97821	+	1.16110i	0.989575	+	0.144017i
$66$	−0.0299051	+	0.213114i	−0.00368107	+	0.0262326i
$67$	10.5842	+	2.83602i	1.29306	+	0.346475i	0.838823	−	0.544405i	$-0.183244\pi$
$67$	10.5842	+	2.83602i	1.29306	+	0.346475i	0.454239	+	0.890880i	$0.349911\pi$
$68$	−2.19480	+	8.19111i	−0.266159	+	0.993318i
$69$	−7.20902	−	5.62984i	−0.867864	−	0.677753i
$70$	−7.71456	−	4.11579i	−0.922067	−	0.491931i
$71$	6.90717	−	11.9636i	0.819730	−	1.41981i	−0.0861512	−	0.996282i	$-0.527457\pi$
$71$	6.90717	−	11.9636i	0.819730	−	1.41981i	0.905881	−	0.423532i	$-0.139210\pi$
$72$	1.86690	+	0.0317942i	0.220017	+	0.00374698i
$73$	−7.38949	−	7.38949i	−0.864874	−	0.864874i	0.127025	−	0.991900i	$-0.459457\pi$
$73$	−7.38949	−	7.38949i	−0.864874	−	0.864874i	−0.991900	+	0.127025i	$0.959457\pi$
$74$	1.20808	−	2.09246i	0.140437	−	0.243244i
$75$	−8.50539	+	1.63042i	−0.982118	+	0.188264i
$76$	−3.99282	+	2.30525i	−0.458007	+	0.264431i
$77$	0.0934734	−	0.0934734i	0.0106523	−	0.0106523i
$78$	−11.3742	−	3.73700i	−1.28788	−	0.423132i
$79$			5.34069i			0.600875i	0.953802	+	0.300437i	$0.0971326\pi$
$79$			5.34069i			0.600875i	−0.953802	+	0.300437i	$0.902867\pi$
$80$	−0.340359	−	10.1548i	−0.0380533	−	1.13534i
$81$	−0.306459	+	8.99478i	−0.0340510	+	0.999420i
$82$	−20.9851	+	5.62293i	−2.31741	+	0.620949i
$83$	2.60495	−	2.60495i	0.285931	−	0.285931i	−0.549538	−	0.835469i	$-0.685196\pi$
$83$	2.60495	−	2.60495i	0.285931	−	0.285931i	0.835469	+	0.549538i	$0.185196\pi$
$84$	4.66484	+	3.64298i	0.508976	+	0.397482i
$85$	2.56151	−	11.0246i	0.277834	−	1.19578i
$86$	−18.7515			−2.02202
$87$	4.82157	−	0.593053i	0.516926	−	0.0635820i
$88$	0.0389622	+	0.0104399i	0.00415339	+	0.00111290i
$89$	12.5211	−	7.22908i	1.32724	−	0.766281i	0.342366	−	0.939567i	$-0.388772\pi$
$89$	12.5211	−	7.22908i	1.32724	−	0.766281i	0.984872	+	0.173285i	$0.0554383\pi$
$90$	12.8587	−	0.211877i	1.35542	−	0.0223338i
$91$	4.19716	+	6.03893i	0.439982	+	0.633052i
$92$	6.25608	−	6.25608i	0.652242	−	0.652242i
$93$	−0.498950	−	0.211667i	−0.0517387	−	0.0219488i
$94$	1.49924	−	0.865588i	0.154635	−	0.0892786i
$95$	5.22310	−	3.25358i	0.535878	−	0.333810i
$96$	−1.79710	+	12.8068i	−0.183416	+	1.30708i
$97$	−1.90959	−	7.12670i	−0.193890	−	0.723607i	−0.992551	−	0.121827i	$-0.961125\pi$
$97$	−1.90959	−	7.12670i	−0.193890	−	0.723607i	0.798661	−	0.601781i	$-0.205542\pi$
$98$	1.40899	+	5.25841i	0.142329	+	0.531179i
$99$	−0.0535122	+	0.186919i	−0.00537818	+	0.0187860i
$100$	−0.560900	−	8.35796i	−0.0560900	−	0.835796i
$101$	10.1123	−	5.83835i	1.00621	−	0.580938i	0.0961330	−	0.995368i	$-0.469353\pi$
$101$	10.1123	−	5.83835i	1.00621	−	0.580938i	0.910081	+	0.414431i	$0.136019\pi$
$102$	−6.56393	+	15.4728i	−0.649926	+	1.53203i
$103$	−12.9298	+	12.9298i	−1.27401	+	1.27401i	−0.330042	+	0.943966i	$0.607063\pi$
$103$	−12.9298	+	12.9298i	−1.27401	+	1.27401i	−0.943966	+	0.330042i	$0.892937\pi$
$104$	−0.955477	+	2.03049i	−0.0936922	+	0.199106i
$105$	−6.38548	−	4.65094i	−0.623159	−	0.453885i
$106$	12.7673	−	7.37120i	1.24007	−	0.715955i
$107$	−14.4728	−	3.87796i	−1.39913	−	0.374897i	−0.521101	−	0.853495i	$-0.674478\pi$
$107$	−14.4728	−	3.87796i	−1.39913	−	0.374897i	−0.878034	+	0.478598i	$0.841145\pi$
$108$	−8.59907	−	1.35635i	−0.827446	−	0.130514i
$109$	−16.1230			−1.54430			−0.772152	−	0.635437i	$-0.780820\pi$
$109$	−16.1230			−1.54430			−0.772152	+	0.635437i	$0.780820\pi$
$110$	0.270616	+	0.0628765i	0.0258023	+	0.00599504i
$111$	1.34358	−	1.72045i	0.127527	−	0.163298i
$112$	6.55360	−	6.55360i	0.619257	−	0.619257i
$113$	−10.3184	+	2.76481i	−0.970675	+	0.260092i	−0.709113	−	0.705095i	$-0.750904\pi$
$113$	−10.3184	+	2.76481i	−0.970675	+	0.260092i	−0.261562	+	0.965187i	$0.584238\pi$
$114$	−8.47191	+	3.42497i	−0.793467	+	0.320777i
$115$	−8.06551	+	8.62493i	−0.752113	+	0.804279i
$116$			4.69888i			0.436280i
$117$	−9.70736	−	4.77150i	−0.897445	−	0.441126i
$118$	9.18753	−	9.18753i	0.845781	−	0.845781i
$119$	8.94108	−	5.16214i	0.819628	−	0.473212i
$120$	0.254819	−	2.39700i	0.0232617	−	0.218815i
$121$	5.49790	−	9.52264i	0.499809	−	0.865695i
$122$	−3.75117	−	3.75117i	−0.339615	−	0.339615i
$123$	−19.4813	+	2.39620i	−1.75657	+	0.216058i
$124$	0.262124	−	0.454012i	0.0235394	−	0.0407715i
$125$	1.12189	+	11.1239i	0.100345	+	0.994953i
$126$	8.15265	+	8.43515i	0.726296	+	0.751463i
$127$	−0.151301	+	0.564662i	−0.0134258	+	0.0501056i	−0.972314	−	0.233679i	$-0.924923\pi$
$127$	−0.151301	+	0.564662i	−0.0134258	+	0.0501056i	0.958888	+	0.283785i	$0.0915901\pi$
$128$	4.74611	+	1.27172i	0.419500	+	0.112405i
$129$	−16.7769	−	2.35421i	−1.47713	−	0.207277i
$130$	−6.10881	+	14.1979i	−0.535778	+	1.24524i
$131$			5.77110i			0.504223i	0.967698	+	0.252112i	$0.0811250\pi$
$131$			5.77110i			0.504223i	−0.967698	+	0.252112i	$0.918875\pi$
$132$	−0.173129	−	0.0734453i	−0.0150689	−	0.00639260i
$133$	5.42192	+	1.45280i	0.470140	+	0.125974i
$134$	−10.5035	+	18.1925i	−0.907361	+	1.57159i
$135$	11.5313	+	1.42482i	0.992453	+	0.122629i
$136$	2.72827	+	1.57517i	0.233947	+	0.135069i
$137$	7.02411	−	1.88211i	0.600111	−	0.160799i	0.0540406	−	0.998539i	$-0.482790\pi$
$137$	7.02411	−	1.88211i	0.600111	−	0.160799i	0.546070	+	0.837740i	$0.316123\pi$
$138$	14.0023	−	10.5562i	1.19196	−	0.898602i
$139$	−1.85213	−	1.06933i	−0.157096	−	0.0906994i	0.419391	−	0.907806i	$-0.362244\pi$
$139$	−1.85213	−	1.06933i	−0.157096	−	0.0906994i	−0.576487	+	0.817106i	$0.695577\pi$
$140$	5.21906	−	5.58105i	0.441091	−	0.471685i
$141$	1.45004	−	0.586214i	0.122116	−	0.0493681i
$142$	18.7268	+	18.7268i	1.57152	+	1.57152i
$143$	−0.178478	−	0.150826i	−0.0149251	−	0.0126127i
$144$	−3.75184	+	13.1052i	−0.312654	+	1.09210i
$145$	−0.210086	−	6.26801i	−0.0174467	−	0.520530i
$146$	17.3504	−	10.0173i	1.43593	−	0.829034i
$147$	0.600435	+	4.88159i	0.0495231	+	0.402627i
$148$	1.49303	+	1.49303i	0.122726	+	0.122726i
$149$	2.52248	+	1.45635i	0.206649	+	0.119309i	0.599753	−	0.800185i	$-0.295265\pi$
$149$	2.52248	+	1.45635i	0.206649	+	0.119309i	−0.393104	+	0.919494i	$0.628599\pi$
$150$	1.20107	−	16.5593i	0.0980669	−	1.35206i
$151$		−	12.1330i		−	0.987367i	−0.869642	−	0.493683i	$-0.835650\pi$
$151$		−	12.1330i		−	0.987367i	0.869642	−	0.493683i	$-0.164350\pi$
$152$	0.443305	+	1.65444i	0.0359568	+	0.134192i
$153$	−7.81532	+	13.0194i	−0.631831	+	1.05256i
$154$	0.126713	+	0.219474i	0.0102109	+	0.0176857i
$155$	−0.329358	+	0.617343i	−0.0264547	+	0.0495862i
$156$	5.72706	−	8.75591i	0.458532	−	0.701034i
$157$	0.818660	+	0.818660i	0.0653362	+	0.0653362i	0.739020	−	0.673684i	$-0.235289\pi$
$157$	0.818660	+	0.818660i	0.0653362	+	0.0653362i	−0.673684	+	0.739020i	$0.735289\pi$
$158$	−9.88987	−	2.64998i	−0.786796	−	0.210821i
$159$	12.3483	−	4.99210i	0.979286	−	0.395899i
$160$	16.2622	+	3.77846i	1.28564	+	0.298713i
$161$	−10.7715			−0.848916
$162$	−16.5044	−	5.03060i	−1.29671	−	0.395241i
$163$	17.5892	−	4.71302i	1.37769	−	0.369152i	0.507411	−	0.861704i	$-0.330603\pi$
$163$	17.5892	−	4.71302i	1.37769	−	0.369152i	0.870283	+	0.492552i	$0.163936\pi$
$164$		−	18.9856i		−	1.48252i
$165$	0.234226	+	0.0902309i	0.0182345	+	0.00702447i
$166$	3.53130	+	6.11638i	0.274082	+	0.474723i
$167$	1.59456	−	5.95097i	0.123391	−	0.460500i	−0.876387	−	0.481608i	$-0.840053\pi$
$167$	1.59456	−	5.95097i	0.123391	−	0.460500i	0.999777	+	0.0211085i	$0.00671954\pi$
$168$	1.75578	−	1.32366i	0.135461	−	0.102122i
$169$	10.0167	−	8.28650i	0.770514	−	0.637423i
$170$	19.1443	+	10.2136i	1.46830	+	0.783350i
$171$	−8.00981	+	2.00068i	−0.612525	+	0.152996i
$172$	4.24119	−	15.8283i	0.323388	−	1.20690i
$173$	3.24998	−	0.870829i	0.247091	−	0.0662079i	−0.133148	−	0.991096i	$-0.542508\pi$
$173$	3.24998	−	0.870829i	0.247091	−	0.0662079i	0.380239	+	0.924888i	$0.375842\pi$
$174$	−1.29419	+	9.22283i	−0.0981121	+	0.699181i
$175$	−6.71237	+	7.67811i	−0.507408	+	0.580411i
$176$	−0.147243	+	0.255033i	−0.0110989	+	0.0192238i
$177$	9.37355	−	7.06660i	0.704559	−	0.531158i
$178$	7.17396	+	26.7736i	0.537711	+	2.00676i
$179$	−1.62397	−	2.81281i	−0.121382	−	0.210239i	0.798931	−	0.601422i	$-0.205399\pi$
$179$	−1.62397	−	2.81281i	−0.121382	−	0.210239i	−0.920313	+	0.391183i	$0.872066\pi$
$180$	−2.72952	+	10.9021i	−0.203446	+	0.812595i
$181$	−6.71234			−0.498925			−0.249462	−	0.968385i	$-0.580254\pi$
$181$	−6.71234			−0.498925			−0.249462	+	0.968385i	$0.580254\pi$
$182$	−13.2655	+	4.77584i	−0.983301	+	0.354009i
$183$	−2.88522	−	3.82712i	−0.213281	−	0.282909i
$184$	−1.64341	−	2.84646i	−0.121154	−	0.209844i
$185$	−2.05836	−	1.92486i	−0.151334	−	0.141518i
$186$	0.639536	−	0.818927i	0.0468931	−	0.0600466i
$187$	−0.231961	+	0.231961i	−0.0169627	+	0.0169627i
$188$	0.391556	+	1.46131i	0.0285572	+	0.106577i
$189$	6.23515	+	8.57047i	0.453541	+	0.623410i
$190$	3.43333	+	11.2865i	0.249080	+	0.818808i
$191$	−1.36065	−	0.785571i	−0.0984531	−	0.0568419i	0.449965	−	0.893046i	$-0.351436\pi$
$191$	−1.36065	−	0.785571i	−0.0984531	−	0.0568419i	−0.548418	+	0.836204i	$0.684770\pi$
$192$	−8.33325	−	3.53517i	−0.601401	−	0.255129i
$193$	0.793102	−	2.95990i	0.0570888	−	0.213058i	−0.931489	−	0.363769i	$-0.881490\pi$
$193$	0.793102	−	2.95990i	0.0570888	−	0.213058i	0.988578	+	0.150711i	$0.0481563\pi$
$194$	14.1447			1.01553
$195$	−7.24807	+	11.9359i	−0.519045	+	0.854747i
$196$	−4.75737			−0.339812
$197$	−1.92918	+	7.19978i	−0.137448	+	0.512963i	0.862528	+	0.506010i	$0.168880\pi$
$197$	−1.92918	+	7.19978i	−0.137448	+	0.512963i	−0.999976	+	0.00695355i	$0.997787\pi$
$198$	−0.319583	−	0.191840i	−0.0227118	−	0.0136335i
$199$	−4.35231	−	2.51281i	−0.308527	−	0.178128i	0.337740	−	0.941239i	$-0.390338\pi$
$199$	−4.35231	−	2.51281i	−0.308527	−	0.178128i	−0.646267	+	0.763111i	$0.723671\pi$
$200$	−3.05310	−	0.602352i	−0.215887	−	0.0425927i
$201$	−11.6815	+	14.9581i	−0.823948	+	1.05507i
$202$	5.79383	+	21.6229i	0.407653	+	1.52138i
$203$	4.04520	−	4.04520i	0.283917	−	0.283917i
$204$	−11.5761	−	9.04032i	−0.810492	−	0.632949i
$205$	0.848840	+	25.3255i	0.0592856	+	1.76881i
$206$	−17.5277	−	30.3589i	−1.22121	−	2.11520i
$207$	13.8532	−	7.68664i	0.962863	−	0.534258i
$208$	−12.5135	−	10.5747i	−0.867653	−	0.733225i
$209$	−0.178353			−0.0123369
$210$	11.7810	−	9.51687i	0.812965	−	0.656727i
$211$	−7.34656	−	12.7246i	−0.505758	−	0.875999i	−0.999978	−	0.00666177i	$-0.997879\pi$
$211$	−7.34656	−	12.7246i	−0.505758	−	0.875999i	0.494220	−	0.869337i	$-0.335454\pi$
$212$	3.33443	+	12.4442i	0.229009	+	0.854674i
$213$	14.4038	+	19.1060i	0.986930	+	1.30912i
$214$	14.3624	−	24.8764i	0.981793	−	1.70052i
$215$	−4.94980	+	21.3036i	−0.337574	+	1.45290i
$216$	−1.31352	+	2.95528i	−0.0893737	+	0.201081i
$217$	−0.616511	+	0.165194i	−0.0418515	+	0.0112141i
$218$	8.00003	−	29.8565i	0.541831	−	2.02214i
$219$	16.7810	−	6.78412i	1.13396	−	0.458428i
$220$	−0.114283	+	0.214209i	−0.00770493	+	0.0144420i
$221$	−10.4156	−	14.9861i	−0.700627	−	1.00807i
$222$	2.51926	+	3.34170i	0.169082	+	0.224280i
$223$	1.08114	−	4.03489i	0.0723988	−	0.270196i	−0.920232	−	0.391373i	$-0.872000\pi$
$223$	1.08114	−	4.03489i	0.0723988	−	0.270196i	0.992631	+	0.121177i	$0.0386669\pi$
$224$	7.61463	+	13.1889i	0.508774	+	0.881222i
$225$	3.15358	−	14.6648i	0.210239	−	0.977650i
$226$		−	20.4795i		−	1.36227i
$227$	−22.6915	+	6.08018i	−1.50609	+	0.403556i	−0.915135	−	0.403148i	$-0.867916\pi$
$227$	−22.6915	+	6.08018i	−1.50609	+	0.403556i	−0.590956	+	0.806704i	$0.701249\pi$
$228$	−0.974886	−	7.92590i	−0.0645634	−	0.524906i
$229$	11.4151			0.754332			0.377166	−	0.926146i	$-0.376899\pi$
$229$	11.4151			0.754332			0.377166	+	0.926146i	$0.376899\pi$
$230$	−11.9696	−	19.2153i	−0.789252	−	1.26702i
$231$	0.0858158	+	0.212272i	0.00564626	+	0.0139665i
$232$	1.68615	+	0.451802i	0.110701	+	0.0296622i
$233$	−8.68792	−	8.68792i	−0.569164	−	0.569164i	0.362730	−	0.931894i	$-0.381845\pi$
$233$	−8.68792	−	8.68792i	−0.569164	−	0.569164i	−0.931894	+	0.362730i	$0.881845\pi$
$234$	13.6525	−	15.6085i	0.892493	−	1.02036i
$235$	−0.587646	−	1.93179i	−0.0383338	−	0.126016i
$236$	5.67728	+	9.83333i	0.369559	+	0.640096i
$237$	−8.51576	−	3.61259i	−0.553158	−	0.234663i
$238$	5.12277	+	19.1185i	0.332060	+	1.23927i
$239$			8.54627i			0.552812i	0.961041	+	0.276406i	$0.0891435\pi$
$239$			8.54627i			0.552812i	−0.961041	+	0.276406i	$0.910856\pi$
$240$	16.4221	+	6.32626i	1.06004	+	0.408359i
$241$	−17.8914	−	10.3296i	−1.15249	−	0.665388i	−0.202995	−	0.979180i	$-0.565067\pi$
$241$	−17.8914	−	10.3296i	−1.15249	−	0.665388i	−0.949492	+	0.313792i	$0.898401\pi$
$242$	14.9060	+	14.9060i	0.958194	+	0.958194i
$243$	−14.1349	−	6.57297i	−0.906756	−	0.421656i
$244$	4.01485	−	2.31797i	0.257024	−	0.148393i
$245$	6.34603	−	0.212701i	0.405433	−	0.0135890i
$246$	5.22909	−	37.2643i	0.333395	−	2.37589i
$247$	1.75710	−	9.76553i	0.111802	−	0.621366i
$248$	−0.137714	−	0.137714i	−0.00874487	−	0.00874487i
$249$	2.39155	+	5.91567i	0.151558	+	0.374890i
$250$	−21.1559	−	3.44203i	−1.33802	−	0.217693i
$251$	17.9829	+	10.3824i	1.13507	+	0.655333i	0.945205	−	0.326477i	$-0.105862\pi$
$251$	17.9829	+	10.3824i	1.13507	+	0.655333i	0.189865	+	0.981810i	$0.439195\pi$
$252$	−8.96417	+	4.97390i	−0.564690	+	0.313326i
$253$	0.330592	−	0.0885818i	0.0207841	−	0.00556909i
$254$	−0.970565	−	0.560356i	−0.0608987	−	0.0351599i
$255$	15.8460	+	11.5416i	0.992317	+	0.722766i
$256$	−9.93615	+	17.2099i	−0.621009	+	1.07562i
$257$	22.4808	+	6.02371i	1.40231	+	0.375749i	0.879175	−	0.476499i	$-0.158095\pi$
$257$	22.4808	+	6.02371i	1.40231	+	0.375749i	0.523138	+	0.852248i	$0.324761\pi$
$258$	12.6840	−	29.8993i	0.789672	−	1.86145i
$259$		−	2.57066i		−	0.159733i
$260$	−10.6029	−	8.36779i	−0.657566	−	0.518948i
$261$	−2.31582	+	8.08917i	−0.143345	+	0.500707i
$262$	−10.6869	−	2.86355i	−0.660239	−	0.176911i
$263$	5.86610	−	21.8926i	0.361719	−	1.34996i	−0.510095	−	0.860118i	$-0.670390\pi$
$263$	5.86610	−	21.8926i	0.361719	−	1.34996i	0.871814	−	0.489837i	$-0.162944\pi$
$264$	−0.0430016	+	0.0550637i	−0.00264657	+	0.00338893i
$265$	−5.00429	−	16.4508i	−0.307411	−	1.01056i
$266$	−5.38057	+	9.31942i	−0.329904	+	0.571410i
$267$	3.05716	+	24.8550i	0.187095	+	1.52110i
$268$	−12.9809	−	12.9809i	−0.792933	−	0.792933i
$269$	−4.58057	+	7.93378i	−0.279282	+	0.483731i	−0.971207	−	0.238239i	$-0.923430\pi$
$269$	−4.58057	+	7.93378i	−0.279282	+	0.483731i	0.691924	+	0.721970i	$0.256763\pi$
$270$	−8.36014	+	20.6466i	−0.508782	+	1.25651i
$271$	−7.38686	+	4.26480i	−0.448720	+	0.259068i	−0.707289	−	0.706924i	$-0.750082\pi$
$271$	−7.38686	+	4.26480i	−0.448720	+	0.259068i	0.258570	+	0.965993i	$0.416749\pi$
$272$	−16.2632	+	16.2632i	−0.986104	+	0.986104i
$273$	−12.4682	+	2.60749i	−0.754609	+	0.157813i
$274$			13.9411i			0.842213i
$275$	0.142869	−	0.290851i	0.00861530	−	0.0175390i
$276$	5.74356	+	14.2071i	0.345722	+	0.855169i
$277$	−21.2717	+	5.69974i	−1.27809	+	0.342464i	−0.833126	−	0.553083i	$-0.813451\pi$
$277$	−21.2717	+	5.69974i	−1.27809	+	0.342464i	−0.444967	+	0.895547i	$0.646785\pi$
$278$	2.89919	−	2.89919i	0.173882	−	0.173882i
$279$	0.675007	−	0.652401i	0.0404116	−	0.0390582i
$280$	−1.50089	−	2.40943i	−0.0896952	−	0.143991i
$281$	−1.14521			−0.0683174			−0.0341587	−	0.999416i	$-0.510875\pi$
$281$	−1.14521			−0.0683174			−0.0341587	+	0.999416i	$0.510875\pi$
$282$	0.366055	+	2.97606i	0.0217983	+	0.177222i
$283$	−9.42831	−	2.52631i	−0.560455	−	0.150174i	−0.0325397	−	0.999470i	$-0.510360\pi$
$283$	−9.42831	−	2.52631i	−0.560455	−	0.150174i	−0.527915	+	0.849297i	$0.677026\pi$
$284$	−20.0432	+	11.5719i	−1.18934	+	0.686668i
$285$	1.65480	+	10.5291i	0.0980220	+	0.623688i
$286$	0.367858	−	0.255668i	0.0217519	−	0.0151179i
$287$	−16.3444	+	16.3444i	−0.964779	+	0.964779i
$288$	−19.2048	−	11.5283i	−1.13165	−	0.679313i
$289$	−7.46552	+	4.31022i	−0.439148	+	0.253542i
$290$	11.7113	+	2.72107i	0.687712	+	0.159787i
$291$	12.6553	+	1.77584i	0.741865	+	0.104102i
$292$	4.53139	+	16.9114i	0.265180	+	0.989664i
$293$	5.80825	+	21.6767i	0.339321	+	1.26636i	0.899108	+	0.437728i	$0.144217\pi$
$293$	5.80825	+	21.6767i	0.339321	+	1.26636i	−0.559786	+	0.828637i	$0.689117\pi$
$294$	−9.33763	−	1.31030i	−0.544582	−	0.0764181i
$295$	−8.01278	−	12.8632i	−0.466522	−	0.748926i
$296$	0.679316	−	0.392203i	0.0394844	−	0.0227963i
$297$	−0.261846	−	0.211762i	−0.0151938	−	0.0122877i
$298$	−3.94849	+	3.94849i	−0.228730	+	0.228730i
$299$	1.59327	+	18.9739i	0.0921413	+	1.09729i
$300$	13.7062	+	4.75920i	0.791328	+	0.274772i
$301$	−17.2776	+	9.97521i	−0.995863	+	0.574962i
$302$	22.4678	+	6.02022i	1.29288	+	0.346425i
$303$	2.46903	+	20.0734i	0.141842	+	1.15319i
$304$	−12.5047			−0.717191
$305$	−5.25192	+	3.27153i	−0.300724	+	0.187327i
$306$	−20.2314	−	20.9324i	−1.15655	−	1.19663i
$307$	−8.67444	+	8.67444i	−0.495076	+	0.495076i	−0.909901	−	0.414825i	$-0.863843\pi$
$307$	−8.67444	+	8.67444i	−0.495076	+	0.495076i	0.414825	+	0.909901i	$0.363843\pi$
$308$	−0.213921	+	0.0573199i	−0.0121893	+	0.00326610i
$309$	−11.8705	−	29.3626i	−0.675291	−	1.67038i
$310$	−0.979771	−	0.916222i	−0.0556472	−	0.0520379i
$311$			3.86942i			0.219415i	0.993964	+	0.109707i	$0.0349913\pi$
$311$			3.86942i			0.219415i	−0.993964	+	0.109707i	$0.965009\pi$
$312$	−2.59131	−	2.89699i	−0.146704	−	0.164010i
$313$	22.5004	−	22.5004i	1.27180	−	1.27180i	0.326658	−	0.945143i	$-0.394078\pi$
$313$	22.5004	−	22.5004i	1.27180	−	1.27180i	0.945143	−	0.326658i	$-0.105922\pi$
$314$	−1.92220	+	1.10978i	−0.108476	+	0.0626287i
$315$	11.7353	−	7.03565i	0.661207	−	0.396414i
$316$	4.47377	−	7.74879i	0.251669	−	0.435903i
$317$	1.27451	+	1.27451i	0.0715836	+	0.0715836i	0.741992	−	0.670409i	$-0.233881\pi$
$317$	1.27451	+	1.27451i	0.0715836	+	0.0715836i	−0.670409	+	0.741992i	$0.733881\pi$
$318$	3.11726	+	25.3436i	0.174807	+	1.42120i
$319$	−0.0908856	+	0.157419i	−0.00508862	+	0.00881375i
$320$	−5.50080	+	10.3106i	−0.307504	+	0.576381i
$321$	15.9732	−	20.4537i	0.891538	−	1.14162i
$322$	5.34470	−	19.9467i	0.297849	−	1.11159i
$323$	−13.4549	−	3.60522i	−0.748650	−	0.200600i
$324$	7.97935	−	12.7938i	0.443297	−	0.710766i
$325$	14.5178	+	10.6881i	0.805301	+	0.592867i
$326$			34.9102i			1.93350i
$327$	10.9061	−	25.7082i	0.603106	−	1.42167i
$328$	−6.81278	−	1.82548i	−0.376173	−	0.100795i
$329$	0.920933	−	1.59510i	0.0507727	−	0.0879409i
$330$	−0.283309	+	0.388968i	−0.0155957	+	0.0214120i
$331$	2.71099	+	1.56519i	0.149009	+	0.0860307i	0.572651	−	0.819799i	$-0.305915\pi$
$331$	2.71099	+	1.56519i	0.149009	+	0.0860307i	−0.423642	+	0.905830i	$0.639248\pi$
$332$	−5.96162	+	1.59741i	−0.327186	+	0.0876693i
$333$	1.83444	+	3.30610i	0.100526	+	0.181173i
$334$	10.2288	+	5.90559i	0.559694	+	0.323139i
$335$	17.8960	+	16.7353i	0.977765	+	0.914347i
$336$	6.01671	+	14.8828i	0.328239	+	0.811923i
$337$	−20.2542	−	20.2542i	−1.10332	−	1.10332i	−0.994008	−	0.109311i	$-0.965136\pi$
$337$	−20.2542	−	20.2542i	−1.10332	−	1.10332i	−0.109311	−	0.994008i	$-0.534864\pi$
$338$	10.3748	+	22.6605i	0.564312	+	1.23257i
$339$	2.57116	−	18.3230i	0.139646	−	0.995167i
$340$	−12.9515	+	13.8498i	−0.702393	+	0.751110i
$341$	0.0175630	−	0.0101400i	0.000951090	−	0.000549112i
$342$	0.269511	−	15.8252i	0.0145735	−	0.855731i
$343$	14.1915	+	14.1915i	0.766272	+	0.766272i
$344$	−5.27205	−	3.04382i	−0.284250	−	0.164112i
$345$	−8.29675	−	18.6946i	−0.446682	−	1.00649i
$346$			6.45039i			0.346775i
$347$	−8.30799	−	31.0059i	−0.445996	−	1.66448i	−0.713292	−	0.700867i	$-0.752797\pi$
$347$	−8.30799	−	31.0059i	−0.445996	−	1.66448i	0.267296	−	0.963615i	$-0.413870\pi$
$348$	−7.49238	−	3.17845i	−0.401634	−	0.170383i
$349$	9.95791	+	17.2476i	0.533035	+	0.923243i	0.999256	+	0.0385748i	$0.0122818\pi$
$349$	9.95791	+	17.2476i	0.533035	+	0.923243i	−0.466221	+	0.884668i	$0.654385\pi$
$350$	−10.8877	−	16.2397i	−0.581972	−	0.868050i
$351$	14.1745	−	12.2508i	0.756579	−	0.653902i
$352$	−0.342164	−	0.342164i	−0.0182374	−	0.0182374i
$353$	−5.14341	−	1.37817i	−0.273756	−	0.0733527i	0.119329	−	0.992855i	$-0.461926\pi$
$353$	−5.14341	−	1.37817i	−0.273756	−	0.0733527i	−0.393085	+	0.919502i	$0.628592\pi$
$354$	8.43486	+	20.8643i	0.448308	+	1.10892i
$355$	26.2190	−	16.3324i	1.39156	−	0.866831i
$356$	−24.2225			−1.28379
$357$	2.18306	+	17.7484i	0.115540	+	0.939346i
$358$	6.01454	−	1.61159i	0.317878	−	0.0851752i
$359$		−	18.4430i		−	0.973387i	−0.873573	−	0.486693i	$-0.838203\pi$
$359$		−	18.4430i		−	0.973387i	0.873573	−	0.486693i	$-0.161797\pi$
$360$	3.64967	+	2.02771i	0.192354	+	0.106870i
$361$	5.71335	+	9.89581i	0.300703	+	0.520832i
$362$	3.33058	−	12.4299i	0.175051	−	0.653301i
$363$	11.4650	+	15.2078i	0.601755	+	0.798203i
$364$	−1.03098	−	12.2777i	−0.0540380	−	0.643528i
$365$	−6.80070	−	22.3561i	−0.355965	−	1.17017i
$366$	8.51866	−	3.44386i	0.445277	−	0.180014i
$367$	−7.94586	+	29.6544i	−0.414770	+	1.54794i	0.370524	+	0.928823i	$0.379178\pi$
$367$	−7.94586	+	29.6544i	−0.414770	+	1.54794i	−0.785295	+	0.619122i	$0.787489\pi$
$368$	23.1784	−	6.21064i	1.20826	−	0.323752i
$369$	9.35693	−	32.6838i	0.487102	−	1.70145i
$370$	4.58577	−	2.85658i	0.238403	−	0.148506i
$371$	7.84251	−	13.5836i	0.407163	−	0.705227i
$372$	0.546617	+	0.725065i	0.0283408	+	0.0375928i
$373$	−6.36353	−	23.7490i	−0.329491	−	1.22968i	−0.909719	−	0.415224i	$-0.863703\pi$
$373$	−6.36353	−	23.7490i	−0.329491	−	1.22968i	0.580228	−	0.814454i	$-0.302963\pi$
$374$	−0.314449	−	0.544641i	−0.0162597	−	0.0281627i
$375$	−18.4960	−	5.73567i	−0.955130	−	0.296188i
$376$	0.562024			0.0289842
$377$	−7.72391	−	6.52722i	−0.397802	−	0.336169i
$378$	−18.9646	+	7.29367i	−0.975432	+	0.375146i
$379$	11.2914	+	19.5573i	0.580002	+	1.00459i	0.995478	+	0.0949885i	$0.0302814\pi$
$379$	11.2914	+	19.5573i	0.580002	+	1.00459i	−0.415477	+	0.909604i	$0.636385\pi$
$380$	−10.3036	+	0.345348i	−0.528564	+	0.0177160i
$381$	−0.798012	−	0.623202i	−0.0408834	−	0.0319276i
$382$	2.12985	−	2.12985i	0.108973	−	0.108973i
$383$	0.474622	+	1.77131i	0.0242521	+	0.0905099i	0.976991	−	0.213280i	$-0.0684146\pi$
$383$	0.474622	+	1.77131i	0.0242521	+	0.0905099i	−0.952739	+	0.303790i	$0.901748\pi$
$384$	−5.23815	+	6.70746i	−0.267308	+	0.342289i
$385$	0.282794	−	0.0860255i	0.0144125	−	0.00438426i
$386$	5.08760	+	2.93733i	0.258952	+	0.149506i
$387$	15.1022	−	25.1584i	0.767687	−	1.27887i
$388$	−3.19924	+	11.9397i	−0.162417	+	0.606148i
$389$	15.3065			0.776072			0.388036	−	0.921644i	$-0.373154\pi$
$389$	15.3065			0.776072			0.388036	+	0.921644i	$0.373154\pi$
$390$	−18.5064	−	19.3444i	−0.937110	−	0.979541i
$391$	26.7304			1.35181
$392$	−0.457426	+	1.70714i	−0.0231035	+	0.0862234i
$393$	−9.20205	−	3.90373i	−0.464182	−	0.196917i
$394$	−12.3753	−	7.14488i	−0.623459	−	0.359954i
$395$	−5.62127	+	10.5364i	−0.282837	+	0.530145i
$396$	0.234218	−	0.226374i	0.0117699	−	0.0113757i
$397$	−2.07456	−	7.74235i	−0.104119	−	0.388578i	0.894125	−	0.447818i	$-0.147799\pi$
$397$	−2.07456	−	7.74235i	−0.104119	−	0.388578i	−0.998244	+	0.0592405i	$0.981132\pi$
$398$	6.81277	−	6.81277i	0.341493	−	0.341493i
$399$	−5.98403	+	7.66256i	−0.299576	+	0.383608i
$400$	10.0168	−	20.3921i	0.500840	−	1.01961i
$401$	−2.14596	−	3.71692i	−0.107164	−	0.185614i	0.807456	−	0.589928i	$-0.200844\pi$
$401$	−2.14596	−	3.71692i	−0.107164	−	0.185614i	−0.914620	+	0.404314i	$0.867510\pi$
$402$	−21.9032	−	29.0537i	−1.09243	−	1.44907i
$403$	0.382178	+	1.06154i	0.0190376	+	0.0528792i
$404$	−19.5626			−0.973275
$405$	−10.0719	+	17.4229i	−0.500479	+	0.865749i
$406$	5.48370	+	9.49805i	0.272152	+	0.471380i
$407$	0.0211403	+	0.0788966i	0.00104789	+	0.00391076i
$408$	−4.35709	+	3.28475i	−0.215708	+	0.162619i
$409$	−18.8150	+	32.5886i	−0.930343	+	1.61140i	−0.147607	+	0.989046i	$0.547157\pi$
$409$	−18.8150	+	32.5886i	−0.930343	+	1.61140i	−0.782735	+	0.622355i	$0.786176\pi$
$410$	−47.3189	−	10.9943i	−2.33691	−	0.542971i
$411$	−1.75028	+	12.4731i	−0.0863349	+	0.615252i
$412$	29.5907	−	7.92881i	1.45783	−	0.390624i
$413$	3.57789	−	13.3529i	0.176056	−	0.657051i
$414$	7.36031	+	29.4673i	0.361740	+	1.44824i
$415$	7.88101	−	2.39739i	0.386863	−	0.117683i
$416$	22.1058	−	15.3639i	1.08383	−	0.753278i
$417$	2.95789	−	2.22991i	0.144848	−	0.109199i
$418$	0.0884963	−	0.330273i	0.00432850	−	0.0161542i
$419$	−6.05083	−	10.4803i	−0.295602	−	0.511998i	0.679522	−	0.733655i	$-0.262187\pi$
$419$	−6.05083	−	10.4803i	−0.295602	−	0.511998i	−0.975125	+	0.221656i	$0.928854\pi$
$420$	5.36869	+	12.0970i	0.261965	+	0.590273i
$421$			22.2934i			1.08651i	0.839567	+	0.543256i	$0.182809\pi$
$421$			22.2934i			1.08651i	−0.839567	+	0.543256i	$0.817191\pi$
$422$	27.2087	−	7.29054i	1.32450	−	0.354898i
$423$	−0.0461292	+	2.70863i	−0.00224288	+	0.131698i
$424$	4.78611			0.232434
$425$	16.6572	−	19.0538i	0.807995	−	0.924245i
$426$	−42.5274	+	17.1927i	−2.06046	+	0.832988i
$427$	−5.45183	−	1.46081i	−0.263833	−	0.0706937i
$428$	17.7500	+	17.7500i	0.857979	+	0.857979i
$429$	0.361221	−	0.182562i	0.0174399	−	0.00881416i
$430$	−36.9940	−	19.7366i	−1.78401	−	0.951784i
$431$	0.197713	+	0.342449i	0.00952349	+	0.0164952i	0.870748	−	0.491730i	$-0.163635\pi$
$431$	0.197713	+	0.342449i	0.00952349	+	0.0164952i	−0.861224	+	0.508225i	$0.830302\pi$
$432$	−18.3585	−	14.8471i	−0.883274	−	0.714330i
$433$	2.90501	+	10.8417i	0.139606	+	0.521017i	0.999936	+	0.0112798i	$0.00359055\pi$
$433$	2.90501	+	10.8417i	0.139606	+	0.521017i	−0.860330	+	0.509737i	$0.829743\pi$
$434$		−	1.22362i		−	0.0587357i
$435$	10.1365	+	3.90487i	0.486007	+	0.187224i
$436$	23.3928	+	13.5059i	1.12031	+	0.646813i
$437$	10.2764	+	10.2764i	0.491585	+	0.491585i
$438$	4.23627	+	34.4413i	0.202417	+	1.64567i
$439$	18.5828	−	10.7288i	0.886911	−	0.512058i	0.0139799	−	0.999902i	$-0.495550\pi$
$439$	18.5828	−	10.7288i	0.886911	−	0.512058i	0.872931	+	0.487844i	$0.162217\pi$
$440$	0.0658786	+	0.0616057i	0.00314064	+	0.00293693i
$441$	−8.18987	−	2.34464i	−0.389994	−	0.111650i
$442$	32.9192	−	11.8516i	1.56581	−	0.563724i
$443$	−15.8402	−	15.8402i	−0.752590	−	0.752590i	0.222372	−	0.974962i	$-0.428620\pi$
$443$	−15.8402	−	15.8402i	−0.752590	−	0.752590i	−0.974962	+	0.222372i	$0.928620\pi$
$444$	−3.39057	+	1.37072i	−0.160909	+	0.0650513i
$445$	32.3113	−	1.08298i	1.53170	−	0.0513383i
$446$	6.93533	+	4.00412i	0.328398	+	0.189600i
$447$	−4.02843	+	3.03698i	−0.190538	+	0.143644i
$448$	−10.2967	+	2.75900i	−0.486474	+	0.130350i
$449$	17.4060	+	10.0493i	0.821438	+	0.474257i	0.850912	−	0.525308i	$-0.176050\pi$
$449$	17.4060	+	10.0493i	0.821438	+	0.474257i	−0.0294742	+	0.999566i	$0.509383\pi$
$450$	25.5914	+	13.1162i	1.20639	+	0.618306i
$451$	0.367218	−	0.636041i	0.0172916	−	0.0299500i
$452$	17.2870	+	4.63203i	0.813111	+	0.217872i
$453$	19.3461	+	8.20708i	0.908958	+	0.385602i
$454$		−	45.0370i		−	2.11369i
$455$	1.92420	+	16.3316i	0.0902078	+	0.765638i
$456$	−2.93787	−	0.412255i	−0.137578	−	0.0193056i
$457$	22.6812	+	6.07741i	1.06098	+	0.284289i	0.746783	−	0.665068i	$-0.231598\pi$
$457$	22.6812	+	6.07741i	1.06098	+	0.284289i	0.314199	+	0.949357i	$0.398264\pi$
$458$	−5.66403	+	21.1385i	−0.264663	+	0.987735i
$459$	−15.4730	−	21.2683i	−0.722217	−	0.992717i
$460$	18.9271	−	5.75760i	0.882481	−	0.268449i
$461$	2.45668	−	4.25509i	0.114419	−	0.198179i	−0.803128	−	0.595806i	$-0.796833\pi$
$461$	2.45668	−	4.25509i	0.114419	−	0.198179i	0.917547	+	0.397627i	$0.130166\pi$
$462$	−0.435665	+	0.0535868i	−0.0202690	+	0.00249308i
$463$	−8.17642	−	8.17642i	−0.379991	−	0.379991i	0.491108	−	0.871099i	$-0.336592\pi$
$463$	−8.17642	−	8.17642i	−0.379991	−	0.379991i	−0.871099	+	0.491108i	$0.836592\pi$
$464$	−6.37217	+	11.0369i	−0.295820	+	0.512376i
$465$	−0.761570	−	0.942751i	−0.0353170	−	0.0437190i
$466$	20.3991	−	11.7774i	0.944969	−	0.545578i
$467$	−18.4859	+	18.4859i	−0.855427	+	0.855427i	−0.990795	−	0.135368i	$-0.956778\pi$
$467$	−18.4859	+	18.4859i	−0.855427	+	0.855427i	0.135368	+	0.990795i	$0.456778\pi$
$468$	10.0874	+	15.0546i	0.466290	+	0.695898i
$469$			22.3501i			1.03203i
$470$	3.86886	−	0.129673i	0.178457	−	0.00598137i
$471$	−1.85912	+	0.751593i	−0.0856638	+	0.0346316i
$472$	4.07447	−	1.09175i	0.187543	−	0.0502519i
$473$	0.448237	−	0.448237i	0.0206100	−	0.0206100i
$474$	10.9152	−	13.9769i	0.501351	−	0.641981i
$475$	13.7289	−	0.921345i	0.629927	−	0.0422742i
$476$	−17.2968			−0.792797
$477$	−0.392829	+	23.0663i	−0.0179864	+	1.05613i
$478$	−15.8260	−	4.24055i	−0.723862	−	0.193958i
$479$	−16.1211	+	9.30755i	−0.736594	+	0.425273i	−0.820830	−	0.571173i	$-0.806488\pi$
$479$	−16.1211	+	9.30755i	−0.736594	+	0.425273i	0.0842357	+	0.996446i	$0.473155\pi$
$480$	−17.0250	+	23.3744i	−0.777082	+	1.06689i
$481$	−4.52818	+	0.380238i	−0.206467	+	0.0173374i
$482$	28.0058	−	28.0058i	1.27563	−	1.27563i
$483$	7.28617	−	17.1753i	0.331532	−	0.781502i
$484$	−15.9538	+	9.21091i	−0.725171	+	0.418678i
$485$	3.73376	−	16.0699i	0.169541	−	0.729696i
$486$	19.1854	−	22.9136i	0.870266	−	1.03938i
$487$	−8.68654	−	32.4186i	−0.393625	−	1.46903i	−0.824110	−	0.566430i	$-0.808324\pi$
$487$	−8.68654	−	32.4186i	−0.393625	−	1.46903i	0.430485	−	0.902598i	$-0.358343\pi$
$488$	−0.445751	−	1.66356i	−0.0201782	−	0.0753060i
$489$	−4.38291	+	31.2341i	−0.198202	+	1.41245i
$490$	−2.75494	+	11.8571i	−0.124456	+	0.535649i
$491$	−26.7145	+	15.4236i	−1.20561	+	0.696059i	−0.961797	−	0.273764i	$-0.911731\pi$
$491$	−26.7145	+	15.4236i	−1.20561	+	0.696059i	−0.243812	+	0.969822i	$0.578398\pi$
$492$	30.2726	+	12.8424i	1.36479	+	0.578978i
$493$	−10.0385	+	10.0385i	−0.452109	+	0.452109i
$494$	17.2119	+	8.09933i	0.774401	+	0.364406i
$495$	−0.302311	+	0.312440i	−0.0135879	+	0.0140431i
$496$	1.23138	−	0.710935i	0.0552904	−	0.0319219i
$497$	27.2170	+	7.29277i	1.22085	+	0.327125i
$498$	−12.1413	+	1.49338i	−0.544063	+	0.0669198i
$499$	−10.3869			−0.464982			−0.232491	−	0.972598i	$-0.574688\pi$
$499$	−10.3869			−0.464982			−0.232491	+	0.972598i	$0.574688\pi$
$500$	7.69048	−	17.0794i	0.343929	−	0.763815i
$501$	8.41024	+	6.56793i	0.375742	+	0.293433i
$502$	−28.1490	+	28.1490i	−1.25635	+	1.25635i
$503$	6.62041	−	1.77393i	0.295189	−	0.0790957i	−0.108185	−	0.994131i	$-0.534504\pi$
$503$	6.62041	−	1.77393i	0.295189	−	0.0790957i	0.403374	+	0.915035i	$0.367837\pi$
$504$	0.922921	+	3.69495i	0.0411102	+	0.164586i
$505$	26.0953	−	0.874639i	1.16122	−	0.0389209i
$506$			0.656142i			0.0291691i
$507$	6.43729	+	21.5769i	0.285890	+	0.958262i
$508$	0.692525	−	0.692525i	0.0307258	−	0.0307258i
$509$	−16.1412	+	9.31914i	−0.715447	+	0.413064i	−0.813075	−	0.582159i	$-0.802208\pi$
$509$	−16.1412	+	9.31914i	−0.715447	+	0.413064i	0.0976275	+	0.995223i	$0.468875\pi$
$510$	−29.2354	+	23.6168i	−1.29456	+	1.04577i
$511$	10.6578	−	18.4598i	0.471471	−	0.816612i
$512$	−19.9903	−	19.9903i	−0.883454	−	0.883454i
$513$	2.22796	−	14.1250i	0.0983668	−	0.623634i
$514$	−22.3094	+	38.6409i	−0.984024	+	1.70438i
$515$	−39.1177	+	11.8995i	−1.72373	+	0.524356i
$516$	22.3695	+	17.4693i	0.984763	+	0.769044i
$517$	−0.0151469	+	0.0565292i	−0.000666162	+	0.00248615i
$518$	4.76033	+	1.27553i	0.209157	+	0.0560434i
$519$	−0.809834	+	5.77116i	−0.0355478	+	0.253326i
$520$	−4.02218	+	3.00019i	−0.176384	+	0.131567i
$521$			15.0847i			0.660871i	0.943829	+	0.330435i	$0.107196\pi$
$521$			15.0847i			0.660871i	−0.943829	+	0.330435i	$0.892804\pi$
$522$	−13.8304	−	8.30217i	−0.605341	−	0.363376i
$523$	−1.55097	−	0.415581i	−0.0678191	−	0.0181721i	0.224750	−	0.974416i	$-0.427843\pi$
$523$	−1.55097	−	0.415581i	−0.0678191	−	0.0181721i	−0.292569	+	0.956244i	$0.594510\pi$
$524$	4.83431	−	8.37327i	0.211188	−	0.365788i
$525$	−7.70235	−	15.8966i	−0.336158	−	0.693784i
$526$	37.6299	+	21.7257i	1.64074	+	0.947283i
$527$	1.52992	−	0.409940i	0.0666443	−	0.0178573i
$528$	−0.307052	−	0.407292i	−0.0133627	−	0.0177251i
$529$	−4.23345	−	2.44419i	−0.184063	−	0.106269i
$530$	32.9465	−	1.10427i	1.43111	−	0.0479666i
$531$	4.92719	+	19.7262i	0.213822	+	0.856045i
$532$	−6.64967	−	6.64967i	−0.288300	−	0.288300i
$533$	31.2080	+	26.3729i	1.35177	+	1.14234i
$534$	−47.5433	−	6.67148i	−2.05740	−	0.288703i
$535$	−24.4710	−	22.8838i	−1.05797	−	0.989352i
$536$	−5.90618	+	3.40994i	−0.255108	+	0.147287i
$537$	5.58353	−	0.686775i	0.240947	−	0.0296365i
$538$	−12.4189	−	12.4189i	−0.535418	−	0.535418i
$539$	−0.159378	−	0.0920170i	−0.00686490	−	0.00396345i
$540$	−15.5371	−	11.7267i	−0.668611	−	0.504638i
$541$			27.8477i			1.19727i	0.801023	+	0.598634i	$0.204290\pi$
$541$			27.8477i			1.19727i	−0.801023	+	0.598634i	$0.795710\pi$
$542$	−4.23228	−	15.7951i	−0.181792	−	0.678458i
$543$	4.54041	−	10.7029i	0.194848	−	0.459304i
$544$	−18.8963	−	32.7293i	−0.810171	−	1.40326i
$545$	−31.8084	−	16.9701i	−1.36252	−	0.726918i
$546$	1.35801	−	24.3823i	0.0581175	−	1.04347i
$547$	−4.94438	−	4.94438i	−0.211406	−	0.211406i	0.593458	−	0.804865i	$-0.297762\pi$
$547$	−4.94438	−	4.94438i	−0.211406	−	0.211406i	−0.804865	+	0.593458i	$0.797762\pi$
$548$	−11.7679	−	3.15319i	−0.502698	−	0.134697i
$549$	8.05400	−	2.01172i	0.343737	−	0.0858581i
$550$	0.467708	+	0.408880i	0.0199431	+	0.0174347i
$551$	−7.71847			−0.328818
$552$	5.65034	−	0.694992i	0.240495	−	0.0295808i
$553$	−10.5222	+	2.81942i	−0.447450	+	0.119894i
$554$		−	42.2190i		−	1.79371i
$555$	4.46152	−	1.98004i	0.189381	−	0.0840481i
$556$	1.79150	+	3.10298i	0.0759767	+	0.131595i
$557$	0.531756	−	1.98454i	0.0225312	−	0.0840877i	−0.953745	−	0.300618i	$-0.902807\pi$
$557$	0.531756	−	1.98454i	0.0225312	−	0.0840877i	0.976276	+	0.216530i	$0.0694739\pi$
$558$	0.873183	+	1.57369i	0.0369648	+	0.0666195i
$559$	20.1268	+	28.9588i	0.851274	+	1.22482i
$560$	19.8272	−	6.03141i	0.837853	−	0.254874i
$561$	−0.212958	−	0.526768i	−0.00899110	−	0.0222402i
$562$	0.568237	−	2.12069i	0.0239697	−	0.0894560i
$563$	−17.7814	+	4.76452i	−0.749399	+	0.200801i	−0.613251	−	0.789888i	$-0.710139\pi$
$563$	−17.7814	+	4.76452i	−0.749399	+	0.200801i	−0.136147	+	0.990689i	$0.543472\pi$
$564$	−2.59492	−	0.364131i	−0.109266	−	0.0153327i
$565$	−23.2668	−	5.40594i	−0.978843	−	0.227430i
$566$	9.35642	−	16.2058i	0.393280	−	0.681180i
$567$	−17.8833	+	4.14468i	−0.751027	+	0.174060i
$568$	2.22531	+	8.30495i	0.0933717	+	0.348468i
$569$	2.39632	+	4.15054i	0.100459	+	0.174000i	0.911874	−	0.410471i	$-0.134636\pi$
$569$	2.39632	+	4.15054i	0.100459	+	0.174000i	−0.811415	+	0.584471i	$0.801302\pi$
$570$	−20.3188	−	2.16003i	−0.851060	−	0.0904738i
$571$	−11.0204			−0.461190			−0.230595	−	0.973050i	$-0.574067\pi$
$571$	−11.0204			−0.461190			−0.230595	+	0.973050i	$0.574067\pi$
$572$	0.132610	+	0.368340i	0.00554472	+	0.0154011i
$573$	2.17298	−	1.63818i	0.0907774	−	0.0684359i
$574$	−22.1566	−	38.3763i	−0.924798	−	1.60180i
$575$	−24.9902	+	8.52650i	−1.04216	+	0.355580i
$576$	11.2737	−	10.8961i	0.469737	−	0.454005i
$577$	20.8346	−	20.8346i	0.867358	−	0.867358i	−0.124822	−	0.992179i	$-0.539836\pi$
$577$	20.8346	−	20.8346i	0.867358	−	0.867358i	0.992179	+	0.124822i	$0.0398358\pi$
$578$	−4.27735	−	15.9633i	−0.177914	−	0.663986i
$579$	4.18310	+	3.26676i	0.173844	+	0.135762i
$580$	−4.94574	+	9.27022i	−0.205361	+	0.384925i
$581$	6.50746	+	3.75708i	0.269975	+	0.155870i
$582$	−9.56788	+	22.5538i	−0.396601	+	0.934886i
$583$	−0.128989	+	0.481393i	−0.00534217	+	0.0199373i
$584$	6.50418			0.269145
$585$	−14.1290	−	19.6308i	−0.584164	−	0.811636i
$586$	−43.0228			−1.77725
$587$	7.06095	−	26.3518i	0.291437	−	1.08766i	−0.652569	−	0.757729i	$-0.726309\pi$
$587$	7.06095	−	26.3518i	0.291437	−	1.08766i	0.944006	−	0.329928i	$-0.107024\pi$
$588$	3.21802	−	7.58565i	0.132709	−	0.312827i
$589$	0.745769	+	0.430570i	0.0307289	+	0.0177413i
$590$	27.7959	−	8.45547i	1.14434	−	0.348106i
$591$	−10.1751	−	7.94622i	−0.418549	−	0.326864i
$592$	1.48219	+	5.53159i	0.0609175	+	0.227347i
$593$	−10.8114	+	10.8114i	−0.443972	+	0.443972i	−0.893344	−	0.449373i	$-0.851648\pi$
$593$	−10.8114	+	10.8114i	−0.443972	+	0.443972i	0.449373	+	0.893344i	$0.351648\pi$
$594$	0.522065	−	0.379811i	0.0214206	−	0.0155838i
$595$	23.0728	−	0.773336i	0.945893	−	0.0317037i
$596$	−2.43990	−	4.22603i	−0.0999422	−	0.173105i
$597$	6.95071	−	5.24005i	0.284474	−	0.214461i
$598$	−35.9264	−	6.46421i	−1.46914	−	0.264341i
$599$	19.7870			0.808476			0.404238	−	0.914654i	$-0.367537\pi$
$599$	19.7870			0.808476			0.404238	+	0.914654i	$0.367537\pi$
$600$	3.02566	−	4.46074i	0.123522	−	0.182109i
$601$	5.88386	+	10.1912i	0.240008	+	0.415706i	0.960716	−	0.277533i	$-0.0895167\pi$
$601$	5.88386	+	10.1912i	0.240008	+	0.415706i	−0.720708	+	0.693238i	$0.756183\pi$
$602$	−9.89915	−	36.9441i	−0.403459	−	1.50573i
$603$	−15.9492	−	28.7443i	−0.649500	−	1.17056i
$604$	−10.1635	+	17.6037i	−0.413547	+	0.716284i
$605$	20.8695	−	13.0001i	0.848466	−	0.528528i
$606$	−38.3969	−	5.38802i	−1.55977	−	0.218873i
$607$	−37.4060	+	10.0229i	−1.51826	+	0.406817i	−0.919170	−	0.393861i	$-0.871139\pi$
$607$	−37.4060	+	10.0229i	−1.51826	+	0.406817i	−0.599094	+	0.800679i	$0.704472\pi$
$608$	5.31804	−	19.8472i	0.215675	−	0.804910i
$609$	3.71380	+	9.18637i	0.150491	+	0.372250i
$610$	−3.45228	−	11.3488i	−0.139779	−	0.459498i
$611$	−2.94597	−	1.38627i	−0.119181	−	0.0560826i
$612$	22.2453	−	12.3431i	0.899211	−	0.498940i
$613$	−1.57858	+	5.89134i	−0.0637583	+	0.237949i	−0.990450	−	0.137874i	$-0.955973\pi$
$613$	−1.57858	+	5.89134i	−0.0637583	+	0.237949i	0.926692	+	0.375823i	$0.122640\pi$
$614$	−11.7591	−	20.3674i	−0.474560	−	0.821963i
$615$	−40.9559	−	15.7774i	−1.65150	−	0.636207i
$616$			0.0822747i			0.00331494i
$617$	40.3273	−	10.8057i	1.62352	−	0.435020i	0.671484	−	0.741019i	$-0.265657\pi$
$617$	40.3273	−	10.8057i	1.62352	−	0.435020i	0.952032	+	0.306000i	$0.0989907\pi$
$618$	60.2636	−	7.41243i	2.42416	−	0.298172i
$619$	−38.9070			−1.56380			−0.781902	−	0.623402i	$-0.785750\pi$
$619$	−38.9070			−1.56380			−0.781902	+	0.623402i	$0.785750\pi$
$620$	0.994998	−	0.619806i	0.0399601	−	0.0248920i
$621$	2.88570	+	27.2884i	0.115799	+	1.09505i
$622$	−7.16537	−	1.91996i	−0.287305	−	0.0769832i
$623$	20.8528	+	20.8528i	0.835450	+	0.835450i
$624$	25.3259	−	12.7998i	1.01385	−	0.512400i
$625$	−9.49500	+	23.1267i	−0.379800	+	0.925069i
$626$	30.5018	+	52.8307i	1.21910	+	2.11154i
$627$	0.120643	−	0.284384i	0.00481801	−	0.0113572i
$628$	−0.502020	−	1.87356i	−0.0200328	−	0.0747633i
$629$			6.37927i			0.254358i
$630$	7.20571	+	25.2223i	0.287082	+	1.00488i
$631$	6.37109	+	3.67835i	0.253629	+	0.146433i	0.621425	−	0.783474i	$-0.286554\pi$
$631$	6.37109	+	3.67835i	0.253629	+	0.146433i	−0.367796	+	0.929907i	$0.619887\pi$
$632$	−2.35042	−	2.35042i	−0.0934947	−	0.0934947i
$633$	25.2589	−	3.10684i	1.00395	−	0.123486i
$634$	−2.99253	+	1.72774i	−0.118849	+	0.0686172i
$635$	−0.892822	+	0.954747i	−0.0354306	+	0.0378880i
$636$	−22.0979	−	3.10088i	−0.876239	−	0.122958i
$637$	6.60847	−	7.82006i	0.261837	−	0.309842i
$638$	−0.246411	−	0.246411i	−0.00975550	−	0.00975550i
$639$	−40.2077	+	10.0430i	−1.59059	+	0.397297i
$640$	8.02486	+	7.50437i	0.317210	+	0.296636i
$641$	−27.5842	−	15.9257i	−1.08951	−	0.629029i	−0.156064	−	0.987747i	$-0.549881\pi$
$641$	−27.5842	−	15.9257i	−1.08951	−	0.629029i	−0.933446	+	0.358718i	$0.883214\pi$
$642$	29.9504	+	39.7280i	1.18205	+	1.56794i
$643$	11.7226	−	3.14107i	0.462295	−	0.123872i	−0.0201514	−	0.999797i	$-0.506415\pi$
$643$	11.7226	−	3.14107i	0.462295	−	0.123872i	0.482447	+	0.875925i	$0.339748\pi$
$644$	15.6284	+	9.02306i	0.615845	+	0.355558i
$645$	−30.6206	−	22.3029i	−1.20568	−	0.878174i
$646$	13.3523	−	23.1268i	0.525338	−	0.909913i
$647$	−31.0824	−	8.32851i	−1.22198	−	0.327427i	−0.410526	−	0.911849i	$-0.634655\pi$
$647$	−31.0824	−	8.32851i	−1.22198	−	0.327427i	−0.811450	+	0.584422i	$0.801321\pi$
$648$	−3.82370	−	4.09345i	−0.150209	−	0.160806i
$649$			0.439239i			0.0172417i
$650$	−26.9956	+	21.5807i	−1.05886	+	0.846463i
$651$	0.153623	−	1.09477i	0.00602097	−	0.0429075i
$652$	−29.4681	−	7.89596i	−1.15406	−	0.309230i
$653$	−8.57665	+	32.0085i	−0.335630	+	1.25259i	0.567554	+	0.823336i	$0.307890\pi$
$653$	−8.57665	+	32.0085i	−0.335630	+	1.25259i	−0.903184	+	0.429253i	$0.858777\pi$
$654$	42.1949	+	32.9519i	1.64995	+	1.28852i
$655$	−6.07430	+	11.3856i	−0.237342	+	0.444871i
$656$	25.7464	−	44.5940i	1.00523	−	1.74110i
$657$	−0.533843	+	31.3464i	−0.0208272	+	1.22294i
$658$	2.49685	+	2.49685i	0.0973374	+	0.0973374i
$659$	−17.7029	+	30.6623i	−0.689606	+	1.19443i	0.282359	+	0.959309i	$0.408883\pi$
$659$	−17.7029	+	30.6623i	−0.689606	+	1.19443i	−0.971965	+	0.235124i	$0.924450\pi$
$660$	−0.264254	−	0.327121i	−0.0102861	−	0.0127332i
$661$	9.03793	−	5.21805i	0.351535	−	0.202959i	−0.313826	−	0.949480i	$-0.601611\pi$
$661$	9.03793	−	5.21805i	0.351535	−	0.202959i	0.665361	+	0.746522i	$0.268278\pi$
$662$	−4.24357	+	4.24357i	−0.164931	+	0.164931i
$663$	30.9407	−	6.47068i	1.20164	−	0.251300i
$664$			2.29286i			0.0889803i
$665$	9.16754	+	8.57293i	0.355502	+	0.332444i
$666$	−7.03245	+	1.75656i	−0.272502	+	0.0680652i
$667$	14.3068	−	3.83351i	0.553963	−	0.148434i
$668$	−7.29852	+	7.29852i	−0.282388	+	0.282388i
$669$	5.70233	+	4.45320i	0.220465	+	0.172171i
$670$	−39.8701	+	24.8360i	−1.54032	+	0.959497i
$671$	0.179337			0.00692322
$672$	−26.1806	+	3.22021i	−1.00994	+	0.124222i
$673$	−30.6699	−	8.21798i	−1.18224	−	0.316780i	−0.386425	−	0.922321i	$-0.626290\pi$
$673$	−30.6699	−	8.21798i	−1.18224	−	0.316780i	−0.795814	+	0.605541i	$0.792957\pi$
$674$	47.5566	−	27.4568i	1.83181	−	1.05760i
$675$	21.2498	+	14.9480i	0.817907	+	0.575350i
$676$	−21.4746	+	3.63212i	−0.825945	+	0.139697i
$677$	−10.8855	+	10.8855i	−0.418365	+	0.418365i	−0.884640	−	0.466275i	$-0.845596\pi$
$677$	−10.8855	+	10.8855i	−0.418365	+	0.418365i	0.466275	+	0.884640i	$0.345596\pi$
$678$	32.6546	+	13.8529i	1.25409	+	0.532017i
$679$	13.0329	−	7.52456i	0.500158	−	0.288766i
$680$	3.72456	+	5.97918i	0.142831	+	0.229291i
$681$	5.65431	−	40.2946i	0.216674	−	1.54409i
$682$	0.0100627	+	0.0375544i	0.000385320	+	0.00143803i
$683$	−5.64971	−	21.0850i	−0.216180	−	0.806796i	−0.985748	−	0.168230i	$-0.946195\pi$
$683$	−5.64971	−	21.0850i	−0.216180	−	0.806796i	0.769567	−	0.638566i	$-0.220472\pi$
$684$	13.2973	+	3.80684i	0.508436	+	0.145558i
$685$	15.8386	+	3.68002i	0.605160	+	0.140606i
$686$	−33.3215	+	19.2382i	−1.27222	+	0.734517i
$687$	−7.72150	+	18.2014i	−0.294593	+	0.694428i
$688$	31.4268	−	31.4268i	1.19813	−	1.19813i
$689$	−25.0874	−	11.8053i	−0.955755	−	0.449745i
$690$	38.7354	−	6.08785i	1.47463	−	0.231761i
$691$	−34.2377	+	19.7672i	−1.30246	+	0.751978i	−0.980826	−	0.194884i	$-0.937567\pi$
$691$	−34.2377	+	19.7672i	−1.30246	+	0.751978i	−0.321639	+	0.946863i	$0.604234\pi$
$692$	−5.44485	−	1.45894i	−0.206982	−	0.0554607i
$693$	−0.396517	−	0.00675285i	−0.0150624	−	0.000256520i
$694$	61.5388			2.33598
$695$	−2.52849	−	4.05908i	−0.0959110	−	0.153970i
$696$	−1.86096	+	2.38296i	−0.0705394	+	0.0903258i
$697$	40.5598	−	40.5598i	1.53631	−	1.53631i
$698$	−36.8800	+	9.88198i	−1.39593	+	0.374038i
$699$	19.7297	−	7.97618i	0.746245	−	0.301687i
$700$	16.1707	−	5.51736i	0.611196	−	0.208537i
$701$			22.5069i			0.850074i	0.905176	+	0.425037i	$0.139739\pi$
$701$			22.5069i			0.850074i	−0.905176	+	0.425037i	$0.860261\pi$
$702$	15.6529	+	32.3270i	0.590779	+	1.22010i
$703$	−2.45248	+	2.45248i	−0.0924970	+	0.0924970i
$704$	0.293330	−	0.169354i	0.0110553	−	0.00638277i
$705$	3.47774	+	0.369709i	0.130979	+	0.0139240i
$706$	5.10419	−	8.84072i	0.192099	−	0.332725i
$707$	16.8411	+	16.8411i	0.633376	+	0.633376i
$708$	−19.5196	+	2.40091i	−0.733590	+	0.0902316i
$709$	20.0553	−	34.7369i	0.753194	−	1.30457i	−0.193073	−	0.981184i	$-0.561846\pi$
$709$	20.0553	−	34.7369i	0.753194	−	1.30457i	0.946267	−	0.323386i	$-0.104821\pi$
$710$	17.2347	+	56.6561i	0.646806	+	2.12626i
$711$	11.5206	−	11.1348i	0.432056	−	0.417586i
$712$	−2.32902	+	8.69201i	−0.0872836	+	0.325747i
$713$	−1.59620	−	0.427700i	−0.0597780	−	0.0160175i
$714$	−33.9496	−	4.76396i	−1.27053	−	0.178287i
$715$	−0.193362	−	0.485414i	−0.00723134	−	0.0181534i
$716$			5.44145i			0.203357i
$717$	−13.6271	−	5.78094i	−0.508912	−	0.215893i
$718$	34.1528	+	9.15120i	1.27457	+	0.341520i
$719$	−5.00371	+	8.66669i	−0.186607	+	0.323213i	−0.944117	−	0.329611i	$-0.893082\pi$
$719$	−5.00371	+	8.66669i	−0.186607	+	0.323213i	0.757510	+	0.652824i	$0.226416\pi$
$720$	−21.1956	+	21.9058i	−0.789913	+	0.816380i
$721$	−32.3000	−	18.6484i	−1.20292	−	0.694503i
$722$	−21.1599	+	5.66978i	−0.787490	+	0.211007i
$723$	28.5728	−	21.5407i	1.06264	−	0.801107i
$724$	9.73892	+	5.62277i	0.361944	+	0.208968i
$725$	6.18284	−	12.5870i	0.229625	−	0.467470i
$726$	−33.8505	+	13.6849i	−1.25631	+	0.507893i
$727$	−6.32057	−	6.32057i	−0.234417	−	0.234417i	0.580116	−	0.814534i	$-0.303007\pi$
$727$	−6.32057	−	6.32057i	−0.234417	−	0.234417i	−0.814534	+	0.580116i	$0.803007\pi$
$728$	−4.50487	−	0.810558i	−0.166962	−	0.0300413i
$729$	20.0419	−	18.0921i	0.742292	−	0.670076i
$730$	44.7734	−	1.50068i	1.65714	−	0.0555426i
$731$	42.8756	−	24.7542i	1.58581	−	0.915568i
$732$	0.980265	+	7.96963i	0.0362316	+	0.294566i
$733$	23.4455	+	23.4455i	0.865981	+	0.865981i	0.992025	−	0.126044i	$-0.0402280\pi$
$733$	23.4455	+	23.4455i	0.865981	+	0.865981i	−0.126044	+	0.992025i	$0.540228\pi$
$734$	−50.9712	−	29.4282i	−1.88138	−	1.08622i
$735$	−3.95348	+	10.2627i	−0.145826	+	0.378544i
$736$			39.4298i			1.45340i
$737$	−0.183800	−	0.685952i	−0.00677037	−	0.0252674i
$738$	55.8810	+	33.5444i	2.05701	+	1.23479i
$739$	−3.41081	−	5.90770i	−0.125469	−	0.217318i	0.796447	−	0.604708i	$-0.206710\pi$
$739$	−3.41081	−	5.90770i	−0.125469	−	0.217318i	−0.921916	+	0.387390i	$0.873377\pi$
$740$	1.37407	+	4.51700i	0.0505116	+	0.166048i
$741$	14.3826	+	9.40738i	0.528359	+	0.345589i
$742$	21.2628	+	21.2628i	0.780580	+	0.780580i
$743$	18.6549	+	4.99856i	0.684381	+	0.183379i	0.584224	−	0.811592i	$-0.301399\pi$
$743$	18.6549	+	4.99856i	0.684381	+	0.183379i	0.100157	+	0.994972i	$0.468065\pi$
$744$	0.312740	−	0.126432i	0.0114656	−	0.00463524i
$745$	3.44362	+	5.52817i	0.126164	+	0.202537i
$746$	47.1359			1.72577
$747$	−11.0503	−	0.188191i	−0.404308	−	0.00688555i
$748$	0.530860	−	0.142243i	0.0194102	−	0.00520094i
$749$		−	30.5614i		−	1.11669i
$750$	19.7988	−	31.4049i	0.722949	−	1.14674i
$751$	−19.9689	−	34.5872i	−0.728677	−	1.26211i	−0.957442	−	0.288624i	$-0.906802\pi$
$751$	−19.9689	−	34.5872i	−0.728677	−	1.26211i	0.228765	−	0.973482i	$-0.426531\pi$
$752$	−1.06198	+	3.96337i	−0.0387265	+	0.144529i
$753$	−28.7190	+	21.6508i	−1.04658	+	0.789001i
$754$	15.9196	−	11.0644i	0.579757	−	0.402941i
$755$	12.7704	−	23.9366i	0.464762	−	0.871142i
$756$	−1.86729	−	17.6579i	−0.0679126	−	0.642212i
$757$	−10.8250	+	40.3994i	−0.393440	+	1.46834i	0.430980	+	0.902362i	$0.358168\pi$
$757$	−10.8250	+	40.3994i	−0.393440	+	1.46834i	−0.824420	+	0.565978i	$0.808499\pi$
$758$	−41.8188	+	11.2053i	−1.51893	+	0.406996i
$759$	−0.0823774	+	0.587050i	−0.00299011	+	0.0213086i
$760$	−0.866778	+	3.73056i	−0.0314413	+	0.135322i
$761$	0.0958031	−	0.165936i	0.00347286	−	0.00601517i	−0.864284	−	0.503005i	$-0.832228\pi$
$761$	0.0958031	−	0.165936i	0.00347286	−	0.00601517i	0.867757	+	0.496989i	$0.165561\pi$
$762$	1.55001	−	1.16853i	0.0561508	−	0.0423314i
$763$	−8.51155	−	31.7655i	−0.308139	−	1.14999i
$764$	1.31611	+	2.27956i	0.0476151	+	0.0824717i
$765$	−29.1219	+	17.4595i	−1.05291	+	0.631249i
$766$	−3.51561			−0.127024
$767$	−24.0501	−	4.32732i	−0.868400	−	0.156250i
$768$	−20.7202	−	27.4845i	−0.747676	−	0.991761i
$769$	4.49084	+	7.77836i	0.161944	+	0.280495i	0.935566	−	0.353153i	$-0.114890\pi$
$769$	4.49084	+	7.77836i	0.161944	+	0.280495i	−0.773622	+	0.633647i	$0.781557\pi$
$770$	0.0189828	+	0.566362i	0.000684094	+	0.0204103i
$771$	−24.8115	+	31.7711i	−0.893563	+	1.14421i
$772$	−3.63014	+	3.63014i	−0.130652	+	0.130652i
$773$	4.59533	+	17.1500i	0.165282	+	0.616842i	0.998004	+	0.0631504i	$0.0201148\pi$
$773$	4.59533	+	17.1500i	0.165282	+	0.616842i	−0.832722	+	0.553692i	$0.813219\pi$
$774$	39.0948	+	40.4494i	1.40523	+	1.45393i
$775$	−1.29955	+	0.871268i	−0.0466813	+	0.0312969i
$776$	3.97685	+	2.29603i	0.142761	+	0.0824228i
$777$	4.09892	+	1.73886i	0.147048	+	0.0623814i
$778$	−7.59490	+	28.3446i	−0.272290	+	1.01620i
$779$	31.1860			1.11736
$780$	20.5146	−	11.2462i	0.734541	−	0.402679i
$781$	−0.895297			−0.0320362
$782$	−13.2633	+	49.4992i	−0.474293	+	1.77009i
$783$	−11.3317	−	9.16432i	−0.404963	−	0.327506i
$784$	−11.1743	−	6.45149i	−0.399082	−	0.230410i
$785$	0.753429	+	2.47677i	0.0268910	+	0.0883997i
$786$	11.7949	−	15.1033i	0.420709	−	0.538718i
$787$	−8.41390	−	31.4011i	−0.299923	−	1.11933i	−0.937228	−	0.348717i	$-0.886618\pi$
$787$	−8.41390	−	31.4011i	−0.299923	−	1.11933i	0.637305	−	0.770612i	$-0.280049\pi$
$788$	8.83012	−	8.83012i	0.314560	−	0.314560i
$789$	30.9398	+	24.1623i	1.10149	+	0.860200i
$790$	−16.7221	−	15.6375i	−0.594945	−	0.556357i
$791$	−10.8945	−	18.8698i	−0.387362	−	0.670931i
$792$	−0.0587118	−	0.105813i	−0.00208623	−	0.00375990i
$793$	−1.76680	+	9.81941i	−0.0627409	+	0.348698i
$794$	15.3666			0.545341
$795$	29.6159	+	3.14838i	1.05037	+	0.111662i
$796$	4.20984	+	7.29165i	0.149214	+	0.258446i
$797$	5.63774	+	21.0403i	0.199699	+	0.745287i	0.991000	+	0.133860i	$0.0427374\pi$
$797$	5.63774	+	21.0403i	0.199699	+	0.745287i	−0.791301	+	0.611427i	$0.790596\pi$
$798$	−11.2203	−	14.8833i	−0.397194	−	0.526862i
$799$	−2.28536	+	3.95837i	−0.0808503	+	0.140037i
$800$	28.1061	+	24.5710i	0.993701	+	0.868715i
$801$	−41.6993	−	11.9379i	−1.47337	−	0.421806i
$802$	7.94777	−	2.12960i	0.280645	−	0.0751987i
$803$	−0.175292	+	0.654199i	−0.00618593	+	0.0230862i
$804$	29.4787	−	11.9174i	1.03963	−	0.420296i
$805$	−21.2507	−	11.3374i	−0.748989	−	0.399592i
$806$	−2.15539	+	0.180992i	−0.0759205	+	0.00637516i
$807$	−9.55203	−	12.6704i	−0.336247	−	0.446018i
$808$	−1.88096	+	7.01984i	−0.0661720	+	0.246957i
$809$	−9.05040	−	15.6758i	−0.318195	−	0.551130i	0.661916	−	0.749578i	$-0.269743\pi$
$809$	−9.05040	−	15.6758i	−0.318195	−	0.551130i	−0.980112	+	0.198448i	$0.936410\pi$
$810$	−27.2660	−	27.2962i	−0.958030	−	0.959090i
$811$			23.9232i			0.840056i	0.907511	+	0.420028i	$0.137980\pi$
$811$			23.9232i			0.840056i	−0.907511	+	0.420028i	$0.862020\pi$
$812$	−9.25772	+	2.48060i	−0.324882	+	0.0870520i
$813$	−1.80358	−	14.6632i	−0.0632542	−	0.514261i
$814$	−0.156590			−0.00548848
$815$	39.6616	+	9.21520i	1.38929	+	0.322794i
$816$	−14.9309	−	36.9327i	−0.522686	−	1.29290i
$817$	25.9999	+	6.96666i	0.909623	+	0.243733i
$818$	−51.0116	−	51.0116i	−1.78358	−	1.78358i
$819$	4.27617	−	21.6444i	0.149421	−	0.756315i
$820$	19.9830	−	37.4558i	0.697837	−	1.30801i
$821$	−9.77979	−	16.9391i	−0.341317	−	0.591179i	0.643360	−	0.765563i	$-0.277540\pi$
$821$	−9.77979	−	16.9391i	−0.341317	−	0.591179i	−0.984678	+	0.174385i	$0.944206\pi$
$822$	−22.2292	−	9.43015i	−0.775331	−	0.328914i
$823$	−1.15104	−	4.29575i	−0.0401228	−	0.149740i	0.942958	−	0.332911i	$-0.108031\pi$
$823$	−1.15104	−	4.29575i	−0.0401228	−	0.149740i	−0.983081	+	0.183170i	$0.941364\pi$
$824$		−	11.3807i		−	0.396466i
$825$	0.367124	+	0.424545i	0.0127816	+	0.0147807i
$826$	22.9515	+	13.2510i	0.798584	+	0.461063i
$827$	0.374621	+	0.374621i	0.0130268	+	0.0130268i	0.713590	−	0.700563i	$-0.247068\pi$
$827$	0.374621	+	0.374621i	0.0130268	+	0.0130268i	−0.700563	+	0.713590i	$0.747068\pi$
$828$	−26.5385	−	0.451962i	−0.922275	−	0.0157067i
$829$	−29.3227	+	16.9295i	−1.01842	+	0.587985i	−0.913646	−	0.406511i	$-0.866745\pi$
$829$	−29.3227	+	16.9295i	−1.01842	+	0.587985i	−0.104774	+	0.994496i	$0.533412\pi$
$830$	0.529021	+	15.7836i	0.0183626	+	0.547856i
$831$	5.30052	−	37.7733i	0.183873	−	1.31034i
$832$	6.38298	+	17.7294i	0.221290	+	0.614658i
$833$	−10.1634	−	10.1634i	−0.352141	−	0.352141i
$834$	2.66168	+	6.58386i	0.0921664	+	0.227980i
$835$	9.40945	−	10.0621i	0.325627	−	0.348213i
$836$	0.258771	+	0.149402i	0.00894979	+	0.00516717i
$837$	0.583663	+	1.51760i	0.0201743	+	0.0524561i
$838$	22.4098	−	6.00469i	0.774134	−	0.207429i
$839$	−26.5275	−	15.3157i	−0.915831	−	0.528755i	−0.0335282	−	0.999438i	$-0.510674\pi$
$839$	−26.5275	−	15.3157i	−0.915831	−	0.528755i	−0.882303	+	0.470683i	$0.844008\pi$
$840$	4.85710	−	0.763366i	0.167586	−	0.0263386i
$841$	10.5668	−	18.3022i	0.364372	−	0.631111i
$842$	−41.2828	−	11.0617i	−1.42270	−	0.381211i
$843$	0.774650	−	1.82604i	0.0266804	−	0.0628921i
$844$			24.6161i			0.847323i
$845$	28.4833	−	5.80514i	0.979856	−	0.199703i
$846$	−4.99295	−	1.42941i	−0.171661	−	0.0491442i
$847$	21.6639	+	5.80483i	0.744381	+	0.199456i
$848$	−9.04366	+	33.7514i	−0.310560	+	1.15903i
$849$	10.4058	−	13.3246i	0.357126	−	0.457300i
$850$	27.0186	+	40.3001i	0.926732	+	1.38228i
$851$	3.32782	−	5.76395i	0.114076	−	0.197586i
$852$	−4.89374	−	39.7865i	−0.167657	−	1.36306i
$853$	5.73121	+	5.73121i	0.196233	+	0.196233i	0.798383	−	0.602150i	$-0.205689\pi$
$853$	5.73121	+	5.73121i	0.196233	+	0.196233i	−0.602150	+	0.798383i	$0.705689\pi$
$854$	5.41026	−	9.37085i	0.185135	−	0.320664i
$855$	−17.9080	−	4.48356i	−0.612441	−	0.153335i
$856$	8.07610	−	4.66274i	0.276035	−	0.159369i
$857$	−13.1772	+	13.1772i	−0.450125	+	0.450125i	−0.895396	−	0.445271i	$-0.853107\pi$
$857$	−13.1772	+	13.1772i	−0.450125	+	0.450125i	0.445271	+	0.895396i	$0.353107\pi$
$858$	0.158834	+	0.759492i	0.00542250	+	0.0259286i
$859$		−	11.2173i		−	0.382729i	−0.981519	−	0.191365i	$-0.938709\pi$
$859$		−	11.2173i		−	0.382729i	0.981519	−	0.191365i	$-0.0612913\pi$
$860$	25.0272	−	26.7631i	0.853420	−	0.912612i
$861$	−15.0054	−	37.1170i	−0.511383	−	1.26494i
$862$	−0.732248	+	0.196205i	−0.0249405	+	0.00668278i
$863$	9.74312	−	9.74312i	0.331659	−	0.331659i	−0.521557	−	0.853216i	$-0.674649\pi$
$863$	9.74312	−	9.74312i	0.331659	−	0.331659i	0.853216	+	0.521557i	$0.174649\pi$
$864$	31.3726	−	22.8241i	1.06732	−	0.776491i
$865$	7.32832	+	1.70270i	0.249170	+	0.0578936i
$866$	−21.5180			−0.731210
$867$	−1.82278	−	14.8194i	−0.0619049	−	0.503292i
$868$	1.03287	+	0.276757i	0.0350580	+	0.00939376i
$869$	0.299754	−	0.173063i	0.0101685	−	0.00587076i
$870$	−12.2606	+	16.8331i	−0.415674	+	0.570697i
$871$	39.3694	−	3.30591i	1.33398	−	0.112017i
$872$	7.09569	−	7.09569i	0.240290	−	0.240290i
$873$	−11.3920	+	18.9777i	−0.385560	+	0.642296i
$874$	−24.1287	+	13.9307i	−0.816166	+	0.471214i
$875$	−21.3241	+	8.08280i	−0.720884	+	0.273249i
$876$	−30.0304	−	4.21400i	−1.01463	−	0.142378i
$877$	13.5555	+	50.5897i	0.457736	+	1.70829i	0.679919	+	0.733287i	$0.262015\pi$
$877$	13.5555	+	50.5897i	0.457736	+	1.70829i	−0.222183	+	0.975005i	$0.571318\pi$
$878$	10.6470	+	39.7351i	0.359319	+	1.34100i
$879$	−38.4924	−	5.40142i	−1.29832	−	0.182186i
$880$	−0.558922	+	0.348165i	−0.0188413	+	0.0117366i
$881$	6.05038	−	3.49319i	0.203842	−	0.117688i	−0.394604	−	0.918851i	$-0.629118\pi$
$881$	6.05038	−	3.49319i	0.203842	−	0.117688i	0.598446	+	0.801163i	$0.295785\pi$
$882$	8.40551	−	14.0026i	0.283028	−	0.471491i
$883$	40.5116	−	40.5116i	1.36332	−	1.36332i	0.493681	−	0.869643i	$-0.335651\pi$
$883$	40.5116	−	40.5116i	1.36332	−	1.36332i	0.869643	−	0.493681i	$-0.164349\pi$
$884$	2.55845	+	30.4681i	0.0860501	+	1.02475i
$885$	25.9305	−	4.07538i	0.871645	−	0.136992i
$886$	37.1925	−	21.4731i	1.24951	−	0.721403i
$887$	3.23586	+	0.867046i	0.108650	+	0.0291126i	0.312734	−	0.949841i	$-0.398755\pi$
$887$	3.23586	+	0.867046i	0.108650	+	0.0291126i	−0.204085	+	0.978953i	$0.565422\pi$
$888$	0.165862	+	1.34847i	0.00556596	+	0.0452517i
$889$	−1.19237			−0.0399908
$890$	−14.0270	+	60.3713i	−0.470186	+	2.02365i
$891$	0.514776	−	0.274272i	0.0172456	−	0.00918846i
$892$	−4.94855	+	4.94855i	−0.165690	+	0.165690i
$893$	−2.40037	+	0.643178i	−0.0803254	+	0.0215231i
$894$	−3.62502	−	8.96675i	−0.121239	−	0.299893i
$895$	−0.243286	−	7.25856i	−0.00813217	−	0.242627i
$896$			10.0221i			0.334816i
$897$	−31.3318	−	10.2940i	−1.04614	−	0.343707i
$898$	−27.2459	+	27.2459i	−0.909208	+	0.909208i
$899$	0.760064	−	0.438823i	0.0253495	−	0.0146356i
$900$	−16.8598	+	18.6354i	−0.561994	+	0.621179i
$901$	−19.4618	+	33.7088i	−0.648366	+	1.12300i
$902$	0.995609	+	0.995609i	0.0331501	+	0.0331501i
$903$	−4.21849	−	34.2967i	−0.140383	−	1.14132i
$904$	3.32432	−	5.75789i	0.110565	−	0.191505i
$905$	−13.2425	−	7.06499i	−0.440195	−	0.234848i
$906$	−24.7971	+	31.7527i	−0.823829	+	1.05491i
$907$	0.640173	−	2.38916i	0.0212566	−	0.0793307i	−0.954483	−	0.298266i	$-0.903592\pi$
$907$	0.640173	−	2.38916i	0.0212566	−	0.0793307i	0.975739	+	0.218935i	$0.0702584\pi$
$908$	38.0163	+	10.1864i	1.26162	+	0.338049i
$909$	−33.6772	−	9.64131i	−1.11700	−	0.319782i
$910$	−31.1976	−	4.54032i	−1.03419	−	0.150510i
$911$			38.3512i			1.27063i	0.772253	+	0.635316i	$0.219130\pi$
$911$			38.3512i			1.27063i	−0.772253	+	0.635316i	$0.780870\pi$
$912$	8.45849	−	19.9387i	0.280089	−	0.660237i
$913$	−0.230619	−	0.0617942i	−0.00763238	−	0.00204509i
$914$	−22.5082	+	38.9854i	−0.744506	+	1.28952i
$915$	−1.66393	−	10.5872i	−0.0550079	−	0.350001i
$916$	−16.5621	−	9.56216i	−0.547229	−	0.315943i
$917$	−11.3702	+	3.04664i	−0.375478	+	0.100609i
$918$	47.0620	−	18.0998i	1.55328	−	0.597382i
$919$	−8.63426	−	4.98500i	−0.284818	−	0.164440i	0.350785	−	0.936456i	$-0.385915\pi$
$919$	−8.63426	−	4.98500i	−0.284818	−	0.164440i	−0.635603	+	0.772016i	$0.719248\pi$
$920$	−0.246197	−	7.34541i	−0.00811689	−	0.242171i
$921$	−7.96380	−	19.6991i	−0.262416	−	0.649106i
$922$	6.66059	+	6.66059i	0.219355	+	0.219355i
$923$	8.82033	−	49.0211i	0.290325	−	1.61355i
$924$	0.0533051	−	0.379870i	0.00175361	−	0.0124968i
$925$	−2.03487	−	5.96397i	−0.0669062	−	0.196094i
$926$	19.1981	−	11.0840i	0.630889	−	0.364244i
$927$	54.8484	+	0.934092i	1.80146	+	0.0306796i
$928$	−14.8076	−	14.8076i	−0.486085	−	0.486085i
$929$	34.8259	+	20.1067i	1.14260	+	0.659681i	0.947073	−	0.321017i	$-0.104025\pi$
$929$	34.8259	+	20.1067i	1.14260	+	0.659681i	0.195527	+	0.980698i	$0.437358\pi$
$930$	2.12366	−	0.942491i	0.0696377	−	0.0309055i
$931$		−	7.81455i		−	0.256111i
$932$	5.32761	+	19.8829i	0.174512	+	0.651287i
$933$	−6.16980	−	2.61738i	−0.201990	−	0.0856892i
$934$	−25.0597	−	43.4047i	−0.819979	−	1.42024i
$935$	−0.701774	+	0.213478i	−0.0229505	+	0.00698149i
$936$	6.37210	−	2.17225i	0.208279	−	0.0710023i
$937$	−27.2652	−	27.2652i	−0.890716	−	0.890716i	0.103874	−	0.994590i	$-0.466876\pi$
$937$	−27.2652	−	27.2652i	−0.890716	−	0.890716i	−0.994590	+	0.103874i	$0.966876\pi$
$938$	−41.3878	−	11.0898i	−1.35136	−	0.362096i
$939$	20.6571	+	51.0970i	0.674120	+	1.66749i
$940$	−0.765596	+	3.29508i	−0.0249710	+	0.107474i
$941$	−18.4961			−0.602957			−0.301479	−	0.953473i	$-0.597480\pi$
$941$	−18.4961			−0.602957			−0.301479	+	0.953473i	$0.597480\pi$
$942$	−0.469324	−	3.81565i	−0.0152914	−	0.124320i
$943$	−57.8060	+	15.4891i	−1.88242	+	0.504393i
$944$			30.7959i			1.00232i
$945$	3.28033	+	23.4710i	0.106709	+	0.763513i
$946$	0.607634	+	1.05245i	0.0197559	+	0.0342182i
$947$	−7.58936	+	28.3239i	−0.246621	+	0.920403i	0.725941	+	0.687757i	$0.241405\pi$
$947$	−7.58936	+	28.3239i	−0.246621	+	0.920403i	−0.972562	+	0.232645i	$0.925262\pi$
$948$	9.32930	+	12.3749i	0.303002	+	0.401919i
$949$	−34.0931	−	16.0430i	−1.10671	−	0.520779i
$950$	−5.10598	+	25.8804i	−0.165660	+	0.839670i
$951$	−2.89433	+	1.17010i	−0.0938550	+	0.0379431i
$952$	−1.66310	+	6.20678i	−0.0539015	+	0.201163i
$953$	6.32491	−	1.69476i	0.204884	−	0.0548985i	−0.154917	−	0.987927i	$-0.549511\pi$
$953$	6.32491	−	1.69476i	0.204884	−	0.0548985i	0.359801	+	0.933029i	$0.382844\pi$
$954$	−42.5191	−	12.1726i	−1.37661	−	0.394103i
$955$	−1.85752	−	2.98195i	−0.0601080	−	0.0964937i
$956$	7.15900	−	12.3998i	0.231539	−	0.401037i
$957$	−0.189527	−	0.251400i	−0.00612654	−	0.00812660i
$958$	−9.23657	−	34.4714i	−0.298420	−	1.11372i
$959$	7.41624	+	12.8453i	0.239483	+	0.414797i
$960$	−12.7194	−	15.7454i	−0.410518	−	0.508182i
$961$	30.9021			0.996841
$962$	1.54270	−	8.57393i	0.0497387	−	0.276435i
$963$	21.8088	+	39.3048i	0.702780	+	1.26658i
$964$	17.3057	+	29.9744i	0.557380	+	0.965410i
$965$	4.68008	−	5.00469i	0.150657	−	0.161107i
$966$	28.1898	+	22.0147i	0.906992	+	0.708310i
$967$	−28.2870	+	28.2870i	−0.909648	+	0.909648i	−0.996244	−	0.0865951i	$-0.972401\pi$
$967$	−28.2870	+	28.2870i	−0.909648	+	0.909648i	0.0865951	+	0.996244i	$0.472401\pi$
$968$	1.77128	+	6.61049i	0.0569310	+	0.212469i
$969$	14.8498	−	19.0152i	0.477044	−	0.610856i
$970$	27.9055	+	14.8878i	0.895992	+	0.478020i
$971$	−18.4125	−	10.6304i	−0.590884	−	0.341147i	0.174563	−	0.984646i	$-0.444149\pi$
$971$	−18.4125	−	10.6304i	−0.590884	−	0.341147i	−0.765447	+	0.643499i	$0.777482\pi$
$972$	15.0023	+	21.3772i	0.481199	+	0.685673i
$973$	1.12903	−	4.21359i	0.0361949	−	0.135081i
$974$	64.3428			2.06168
$975$	−26.8624	+	15.9189i	−0.860284	+	0.509814i
$976$	12.5736			0.402473
$977$	7.09314	−	26.4720i	0.226930	−	0.846913i	−0.754692	−	0.656079i	$-0.772214\pi$
$977$	7.09314	−	26.4720i	0.226930	−	0.846913i	0.981622	−	0.190835i	$-0.0611194\pi$
$978$	−55.6645	−	23.6142i	−1.77995	−	0.755099i
$979$	−0.811485	−	0.468511i	−0.0259352	−	0.0149737i
$980$	−9.38561	−	5.00731i	−0.299812	−	0.159953i
$981$	33.6147	+	34.7795i	1.07324	+	1.11042i
$982$	−15.3060	−	57.1228i	−0.488435	−	1.82286i
$983$	8.33022	−	8.33022i	0.265693	−	0.265693i	−0.561669	−	0.827362i	$-0.689841\pi$
$983$	8.33022	−	8.33022i	0.265693	−	0.265693i	0.827362	+	0.561669i	$0.189841\pi$
$984$	7.51909	−	9.62821i	0.239700	−	0.306936i
$985$	−11.3840	+	12.1736i	−0.362725	+	0.387884i
$986$	−13.6082	−	23.5701i	−0.433374	−	0.750625i
$987$	1.92045	+	2.54740i	0.0611287	+	0.0810848i
$988$	−10.7297	+	12.6969i	−0.341358	+	0.403942i
$989$	−51.6532			−1.64248
$990$	−0.428573	−	0.714847i	−0.0136209	−	0.0227193i
$991$	−11.6131	−	20.1145i	−0.368903	−	0.638959i	0.620491	−	0.784213i	$-0.286933\pi$
$991$	−11.6131	−	20.1145i	−0.368903	−	0.638959i	−0.989394	+	0.145255i	$0.953600\pi$
$992$	0.604700	+	2.25677i	0.0191992	+	0.0716525i
$993$	−4.32949	+	3.26395i	−0.137392	+	0.103578i
$994$	−27.0094	+	46.7817i	−0.856688	+	1.48383i
$995$	−5.94167	−	9.53839i	−0.188364	−	0.302387i
$996$	1.48553	−	10.5864i	0.0470707	−	0.335442i
$997$	16.0824	−	4.30927i	0.509335	−	0.136476i	0.00500582	−	0.999987i	$-0.498407\pi$
$997$	16.0824	−	4.30927i	0.509335	−	0.136476i	0.504329	+	0.863512i	$0.331740\pi$
$998$	5.15386	−	19.2345i	0.163143	−	0.608856i
$999$	−6.51246	+	0.688680i	−0.206045	+	0.0217889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.62.5	yes	96
3.2	odd	2	inner	195.2.bf.a.62.20	yes	96
5.2	odd	4		975.2.bn.d.218.5		96
5.3	odd	4	inner	195.2.bf.a.23.20	yes	96
5.4	even	2		975.2.bn.d.257.20		96
13.4	even	6	inner	195.2.bf.a.17.5	✓	96
15.2	even	4		975.2.bn.d.218.20		96
15.8	even	4	inner	195.2.bf.a.23.5	yes	96
15.14	odd	2		975.2.bn.d.257.5		96
39.17	odd	6	inner	195.2.bf.a.17.20	yes	96
65.4	even	6		975.2.bn.d.407.20		96
65.17	odd	12		975.2.bn.d.368.5		96
65.43	odd	12	inner	195.2.bf.a.173.20	yes	96
195.17	even	12		975.2.bn.d.368.20		96
195.134	odd	6		975.2.bn.d.407.5		96
195.173	even	12	inner	195.2.bf.a.173.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.5	✓	96	13.4	even	6	inner
195.2.bf.a.17.20	yes	96	39.17	odd	6	inner
195.2.bf.a.23.5	yes	96	15.8	even	4	inner
195.2.bf.a.23.20	yes	96	5.3	odd	4	inner
195.2.bf.a.62.5	yes	96	1.1	even	1	trivial
195.2.bf.a.62.20	yes	96	3.2	odd	2	inner
195.2.bf.a.173.5	yes	96	195.173	even	12	inner
195.2.bf.a.173.20	yes	96	65.43	odd	12	inner
975.2.bn.d.218.5		96	5.2	odd	4
975.2.bn.d.218.20		96	15.2	even	4
975.2.bn.d.257.5		96	15.14	odd	2
975.2.bn.d.257.20		96	5.4	even	2
975.2.bn.d.368.5		96	65.17	odd	12
975.2.bn.d.368.20		96	195.17	even	12
975.2.bn.d.407.5		96	195.134	odd	6
975.2.bn.d.407.20		96	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.496187 + 1.85180i) q^{2} +(-0.676428 + 1.59450i) q^{3} +(-1.45090 - 0.837676i) q^{4} +(1.97286 + 1.05254i) q^{5} +(-2.61706 - 2.04378i) q^{6} +(0.527913 + 1.97020i) q^{7} +(-0.440097 + 0.440097i) q^{8} +(-2.08489 - 2.15713i) q^{9} +(-2.92799 + 3.13107i) q^{10} +(-0.0324046 - 0.0561264i) q^{11} +(2.31710 - 1.74683i) q^{12} +(3.39239 - 1.22133i) q^{13} -3.91035 q^{14} +(-3.01277 + 2.43376i) q^{15} +(-2.27195 - 3.93513i) q^{16} +(-1.31006 - 4.88919i) q^{17} +(5.02907 - 2.79045i) q^{18} +(1.37598 - 2.38327i) q^{19} +(-1.98073 - 3.17974i) q^{20} +(-3.49859 - 0.490937i) q^{21} +(0.120014 - 0.0321575i) q^{22} +(-1.36681 + 5.10100i) q^{23} +(-0.404043 - 0.999430i) q^{24} +(2.78433 + 4.15301i) q^{25} +(0.578399 + 6.88803i) q^{26} +(4.84984 - 1.86522i) q^{27} +(0.884440 - 3.30077i) q^{28} +(-1.40236 - 2.42895i) q^{29} +(-3.01194 - 6.78664i) q^{30} +0.312918i q^{31} +(7.21201 - 1.93245i) q^{32} +(0.111413 - 0.0137038i) q^{33} +9.70382 q^{34} +(-1.03221 + 4.44257i) q^{35} +(1.21798 + 4.87624i) q^{36} +(-1.21737 - 0.326192i) q^{37} +(3.73059 + 3.73059i) q^{38} +(-0.347286 + 6.23533i) q^{39} +(-1.33147 + 0.405030i) q^{40} +(5.66614 + 9.81404i) q^{41} +(2.64507 - 6.23507i) q^{42} +(2.53152 + 9.44778i) q^{43} +0.108578i q^{44} +(-1.84273 - 6.45014i) q^{45} +(-8.76782 - 5.06210i) q^{46} +(-0.638524 - 0.638524i) q^{47} +(7.81140 - 0.960802i) q^{48} +(2.45919 - 1.41981i) q^{49} +(-9.07208 + 3.09534i) q^{50} +(8.68200 + 1.21830i) q^{51} +(-5.94510 - 1.06970i) q^{52} +(-5.43756 - 5.43756i) q^{53} +(1.04758 + 9.90641i) q^{54} +(-0.00485451 - 0.144837i) q^{55} +(-1.09941 - 0.634745i) q^{56} +(2.86938 + 3.80612i) q^{57} +(5.19376 - 1.39166i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(6.40992 - 1.00742i) q^{60} +(-1.38357 + 2.39642i) q^{61} +(-0.579461 - 0.155266i) q^{62} +(3.14934 - 5.24643i) q^{63} +5.22623i q^{64} +(7.97821 + 1.16110i) q^{65} +(-0.0299051 + 0.213114i) q^{66} +(10.5842 + 2.83602i) q^{67} +(-2.19480 + 8.19111i) q^{68} +(-7.20902 - 5.62984i) q^{69} +(-7.71456 - 4.11579i) q^{70} +(6.90717 - 11.9636i) q^{71} +(1.86690 + 0.0317942i) q^{72} +(-7.38949 - 7.38949i) q^{73} +(1.20808 - 2.09246i) q^{74} +(-8.50539 + 1.63042i) q^{75} +(-3.99282 + 2.30525i) q^{76} +(0.0934734 - 0.0934734i) q^{77} +(-11.3742 - 3.73700i) q^{78} +5.34069i q^{79} +(-0.340359 - 10.1548i) q^{80} +(-0.306459 + 8.99478i) q^{81} +(-20.9851 + 5.62293i) q^{82} +(2.60495 - 2.60495i) q^{83} +(4.66484 + 3.64298i) q^{84} +(2.56151 - 11.0246i) q^{85} -18.7515 q^{86} +(4.82157 - 0.593053i) q^{87} +(0.0389622 + 0.0104399i) q^{88} +(12.5211 - 7.22908i) q^{89} +(12.8587 - 0.211877i) q^{90} +(4.19716 + 6.03893i) q^{91} +(6.25608 - 6.25608i) q^{92} +(-0.498950 - 0.211667i) q^{93} +(1.49924 - 0.865588i) q^{94} +(5.22310 - 3.25358i) q^{95} +(-1.79710 + 12.8068i) q^{96} +(-1.90959 - 7.12670i) q^{97} +(1.40899 + 5.25841i) q^{98} +(-0.0535122 + 0.186919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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