LMFDB - Embedded newform 798.2.cc.b.641.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			641.10
Character	$\chi$	$=$	798.641
Dual form			798.2.cc.b.737.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.695693 + 1.58619i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.03648 - 0.182760i) q^{5} +(1.55252 - 0.767912i) q^{6} +(2.36188 - 1.19227i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.03202 - 2.20701i) q^{9} +(0.676517 + 0.806242i) q^{10} +(-1.62107 + 0.935926i) q^{11} +(-1.68290 - 0.409684i) q^{12} +(0.976245 - 0.172138i) q^{13} +(-2.57568 - 0.604855i) q^{14} +(1.01097 - 1.51692i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-5.61620 - 0.990287i) q^{17} +(0.137982 + 2.99683i) q^{18} +(1.89071 - 3.92750i) q^{19} -1.05247i q^{20} +(0.248030 + 4.57586i) q^{21} +(1.84341 + 0.325044i) q^{22} +(0.304481 - 0.836553i) q^{23} +(1.02584 + 1.39558i) q^{24} +(-3.65756 - 1.33124i) q^{25} +(-0.858496 - 0.495653i) q^{26} +(4.91441 - 1.68778i) q^{27} +(1.58430 + 2.11896i) q^{28} +(-0.502368 - 0.182847i) q^{29} +(-1.74950 + 0.512191i) q^{30} +4.43499i q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.356792 - 3.22245i) q^{33} +(3.66571 + 4.36863i) q^{34} +(-2.66595 + 0.804114i) q^{35} +(1.82062 - 2.38439i) q^{36} +(3.78576 - 2.18571i) q^{37} +(-3.97291 + 1.79331i) q^{38} +(-0.406122 + 1.66827i) q^{39} +(-0.676517 + 0.806242i) q^{40} +(2.05365 - 11.6468i) q^{41} +(2.75130 - 3.66474i) q^{42} +(-5.48400 - 4.60163i) q^{43} +(-1.20320 - 1.43392i) q^{44} +(1.70281 + 2.65890i) q^{45} +(-0.770972 + 0.445121i) q^{46} +(6.21253 - 1.09544i) q^{47} +(0.111227 - 1.72848i) q^{48} +(4.15697 - 5.63201i) q^{49} +(1.94615 + 3.37083i) q^{50} +(5.47794 - 8.21945i) q^{51} +(0.339046 + 0.931522i) q^{52} +(-0.440403 - 2.49765i) q^{53} +(-4.84954 - 1.86600i) q^{54} +(1.85126 - 0.673805i) q^{55} +(0.148403 - 2.64159i) q^{56} +(4.91442 + 5.73136i) q^{57} +(0.267305 + 0.462985i) q^{58} +(1.56059 - 8.85054i) q^{59} +(1.66943 + 0.732199i) q^{60} +(10.4078 + 3.78812i) q^{61} +(2.85076 - 3.39740i) q^{62} +(-7.43075 - 2.78997i) q^{63} +(-0.500000 - 0.866025i) q^{64} -1.04332 q^{65} +(-1.79803 + 2.69788i) q^{66} +(-3.47996 - 4.14726i) q^{67} -5.70284i q^{68} +(1.11511 + 1.06495i) q^{69} +(2.55911 + 1.09766i) q^{70} +(-5.23292 - 4.39094i) q^{71} +(-2.92734 + 0.656279i) q^{72} +(-0.262571 - 0.220323i) q^{73} +(-4.30500 - 0.759088i) q^{74} +(4.65615 - 4.87547i) q^{75} +(4.19615 + 1.17998i) q^{76} +(-2.71290 + 4.14330i) q^{77} +(1.38345 - 1.01692i) q^{78} +(-4.19853 - 11.5354i) q^{79} +(1.03648 - 0.182760i) q^{80} +(-0.741769 + 8.96938i) q^{81} +(-9.05961 + 7.60192i) q^{82} +(11.1341 - 6.42827i) q^{83} +(-4.46327 + 1.03885i) q^{84} +(5.64012 + 2.05283i) q^{85} +(1.24312 + 7.05010i) q^{86} +(0.639525 - 0.669648i) q^{87} +1.87185i q^{88} +(-5.36181 + 4.49910i) q^{89} +(0.404684 - 3.13138i) q^{90} +(2.10054 - 1.57052i) q^{91} +(0.876717 + 0.154589i) q^{92} +(-7.03475 - 3.08539i) q^{93} +(-5.46321 - 3.15419i) q^{94} +(-2.67748 + 3.72524i) q^{95} +(-1.19625 + 1.25259i) q^{96} +(1.99972 + 5.49418i) q^{97} +(-6.80461 + 1.64232i) q^{98} +(5.35965 + 1.67589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.695693	+	1.58619i	−0.401659	+	0.915790i
$3$	−0.695693	+	1.58619i	−0.401659	+	0.915790i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.03648	−	0.182760i	−0.463530	−	0.0817328i	−0.0629940	−	0.998014i	$-0.520065\pi$
$5$	−1.03648	−	0.182760i	−0.463530	−	0.0817328i	−0.400536	+	0.916281i	$0.631176\pi$
$6$	1.55252	−	0.767912i	0.633813	−	0.313499i
$7$	2.36188	−	1.19227i	0.892708	−	0.450637i
$7$	2.36188	−	1.19227i	0.892708	−	0.450637i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.03202	−	2.20701i	−0.677341	−	0.735669i
$10$	0.676517	+	0.806242i	0.213933	+	0.254956i
$11$	−1.62107	+	0.935926i	−0.488771	+	0.282192i	−0.724065	−	0.689732i	$-0.757728\pi$
$11$	−1.62107	+	0.935926i	−0.488771	+	0.282192i	0.235293	+	0.971924i	$0.424395\pi$
$12$	−1.68290	−	0.409684i	−0.485812	−	0.118266i
$13$	0.976245	−	0.172138i	0.270762	−	0.0477426i	−0.0366187	−	0.999329i	$-0.511659\pi$
$13$	0.976245	−	0.172138i	0.270762	−	0.0477426i	0.307380	+	0.951587i	$0.400548\pi$
$14$	−2.57568	−	0.604855i	−0.688381	−	0.161654i
$15$	1.01097	−	1.51692i	0.261031	−	0.391667i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−5.61620	−	0.990287i	−1.36213	−	0.240180i	−0.555637	−	0.831425i	$-0.687525\pi$
$17$	−5.61620	−	0.990287i	−1.36213	−	0.240180i	−0.806492	+	0.591245i	$0.798637\pi$
$18$	0.137982	+	2.99683i	0.0325227	+	0.706358i
$19$	1.89071	−	3.92750i	0.433758	−	0.901029i
$19$	1.89071	−	3.92750i	0.433758	−	0.901029i
$20$		−	1.05247i		−	0.235340i
$21$	0.248030	+	4.57586i	0.0541246	+	0.998534i
$22$	1.84341	+	0.325044i	0.393017	+	0.0692995i
$23$	0.304481	−	0.836553i	0.0634886	−	0.174433i	−0.903892	−	0.427761i	$-0.859303\pi$
$23$	0.304481	−	0.836553i	0.0634886	−	0.174433i	0.967381	+	0.253327i	$0.0815249\pi$
$24$	1.02584	+	1.39558i	0.209398	+	0.284873i
$25$	−3.65756	−	1.33124i	−0.731513	−	0.266249i
$26$	−0.858496	−	0.495653i	−0.168365	−	0.0972055i
$27$	4.91441	−	1.68778i	0.945778	−	0.324814i
$28$	1.58430	+	2.11896i	0.299404	+	0.400447i
$29$	−0.502368	−	0.182847i	−0.0932874	−	0.0339538i	0.294955	−	0.955511i	$-0.404695\pi$
$29$	−0.502368	−	0.182847i	−0.0932874	−	0.0339538i	−0.388242	+	0.921557i	$0.626918\pi$
$30$	−1.74950	+	0.512191i	−0.319414	+	0.0935128i
$31$			4.43499i			0.796547i	0.917267	+	0.398274i	$0.130391\pi$
$31$			4.43499i			0.796547i	−0.917267	+	0.398274i	$0.869609\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.356792	−	3.22245i	−0.0621095	−	0.560957i
$34$	3.66571	+	4.36863i	0.628665	+	0.749213i
$35$	−2.66595	+	0.804114i	−0.450628	+	0.135920i
$36$	1.82062	−	2.38439i	0.303437	−	0.397399i
$37$	3.78576	−	2.18571i	0.622374	−	0.359328i	−0.155419	−	0.987849i	$-0.549673\pi$
$37$	3.78576	−	2.18571i	0.622374	−	0.359328i	0.777793	+	0.628521i	$0.216339\pi$
$38$	−3.97291	+	1.79331i	−0.644491	+	0.290914i
$39$	−0.406122	+	1.66827i	−0.0650316	+	0.267137i
$40$	−0.676517	+	0.806242i	−0.106967	+	0.127478i
$41$	2.05365	−	11.6468i	0.320726	−	1.81893i	−0.217424	−	0.976077i	$-0.569766\pi$
$41$	2.05365	−	11.6468i	0.320726	−	1.81893i	0.538150	−	0.842849i	$-0.319123\pi$
$42$	2.75130	−	3.66474i	0.424535	−	0.565482i
$43$	−5.48400	−	4.60163i	−0.836303	−	0.701741i	0.120426	−	0.992722i	$-0.461574\pi$
$43$	−5.48400	−	4.60163i	−0.836303	−	0.701741i	−0.956729	+	0.290981i	$0.906018\pi$
$44$	−1.20320	−	1.43392i	−0.181390	−	0.216172i
$45$	1.70281	+	2.65890i	0.253839	+	0.396366i
$46$	−0.770972	+	0.445121i	−0.113674	+	0.0656295i
$47$	6.21253	−	1.09544i	0.906191	−	0.159786i	0.298918	−	0.954279i	$-0.403374\pi$
$47$	6.21253	−	1.09544i	0.906191	−	0.159786i	0.607273	+	0.794493i	$0.292263\pi$
$48$	0.111227	−	1.72848i	0.0160543	−	0.249484i
$49$	4.15697	−	5.63201i	0.593853	−	0.804573i
$50$	1.94615	+	3.37083i	0.275227	+	0.476707i
$51$	5.47794	−	8.21945i	0.767065	−	1.15095i
$52$	0.339046	+	0.931522i	0.0470173	+	0.129179i
$53$	−0.440403	−	2.49765i	−0.0604940	−	0.343079i	−1.00000		0.000545724i	$-0.999826\pi$
$53$	−0.440403	−	2.49765i	−0.0604940	−	0.343079i	0.939506	−	0.342533i	$-0.111285\pi$
$54$	−4.84954	−	1.86600i	−0.659939	−	0.253931i
$55$	1.85126	−	0.673805i	0.249624	−	0.0908559i
$56$	0.148403	−	2.64159i	0.0198312	−	0.352997i
$57$	4.91442	+	5.73136i	0.650931	+	0.759137i
$58$	0.267305	+	0.462985i	0.0350988	+	0.0607929i
$59$	1.56059	−	8.85054i	0.203171	−	1.15224i	−0.697120	−	0.716954i	$-0.745536\pi$
$59$	1.56059	−	8.85054i	0.203171	−	1.15224i	0.900292	−	0.435287i	$-0.143353\pi$
$60$	1.66943	+	0.732199i	0.215522	+	0.0945264i
$61$	10.4078	+	3.78812i	1.33258	+	0.485020i	0.907468	−	0.420121i	$-0.138012\pi$
$61$	10.4078	+	3.78812i	1.33258	+	0.485020i	0.425112	+	0.905141i	$0.360235\pi$
$62$	2.85076	−	3.39740i	0.362046	−	0.431470i
$63$	−7.43075	−	2.78997i	−0.936187	−	0.351503i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.04332			−0.129408
$66$	−1.79803	+	2.69788i	−0.221322	+	0.332086i
$67$	−3.47996	−	4.14726i	−0.425145	−	0.506668i	0.510370	−	0.859955i	$-0.329508\pi$
$67$	−3.47996	−	4.14726i	−0.425145	−	0.506668i	−0.935515	+	0.353287i	$0.885064\pi$
$68$		−	5.70284i		−	0.691571i
$69$	1.11511	+	1.06495i	0.134244	+	0.128205i
$70$	2.55911	+	1.09766i	0.305873	+	0.131195i
$71$	−5.23292	−	4.39094i	−0.621034	−	0.521109i	0.277095	−	0.960843i	$-0.410628\pi$
$71$	−5.23292	−	4.39094i	−0.621034	−	0.521109i	−0.898128	+	0.439733i	$0.855073\pi$
$72$	−2.92734	+	0.656279i	−0.344990	+	0.0773432i
$73$	−0.262571	−	0.220323i	−0.0307316	−	0.0257869i	0.627292	−	0.778784i	$-0.284163\pi$
$73$	−0.262571	−	0.220323i	−0.0307316	−	0.0257869i	−0.658024	+	0.752997i	$0.728608\pi$
$74$	−4.30500	−	0.759088i	−0.500446	−	0.0882422i
$75$	4.65615	−	4.87547i	0.537646	−	0.562971i
$76$	4.19615	+	1.17998i	0.481331	+	0.135353i
$77$	−2.71290	+	4.14330i	−0.309164	+	0.472173i
$78$	1.38345	−	1.01692i	0.156645	−	0.115143i
$79$	−4.19853	−	11.5354i	−0.472371	−	1.29783i	−0.915841	−	0.401541i	$-0.868475\pi$
$79$	−4.19853	−	11.5354i	−0.472371	−	1.29783i	0.443470	−	0.896289i	$-0.353747\pi$
$80$	1.03648	−	0.182760i	0.115882	−	0.0204332i
$81$	−0.741769	+	8.96938i	−0.0824188	+	0.996598i
$82$	−9.05961	+	7.60192i	−1.00047	+	0.839491i
$83$	11.1341	−	6.42827i	1.22213	−	0.705595i	0.256755	−	0.966477i	$-0.417347\pi$
$83$	11.1341	−	6.42827i	1.22213	−	0.705595i	0.965371	+	0.260882i	$0.0840134\pi$
$84$	−4.46327	+	1.03885i	−0.486983	+	0.113348i
$85$	5.64012	+	2.05283i	0.611757	+	0.222661i
$86$	1.24312	+	7.05010i	0.134049	+	0.760232i
$87$	0.639525	−	0.669648i	0.0685643	−	0.0717938i
$88$			1.87185i			0.199540i
$89$	−5.36181	+	4.49910i	−0.568351	+	0.476903i	−0.881098	−	0.472933i	$-0.843195\pi$
$89$	−5.36181	+	4.49910i	−0.568351	+	0.476903i	0.312747	+	0.949836i	$0.398751\pi$
$90$	0.404684	−	3.13138i	0.0426574	−	0.330076i
$91$	2.10054	−	1.57052i	0.220196	−	0.164635i
$92$	0.876717	+	0.154589i	0.0914040	+	0.0161170i
$93$	−7.03475	−	3.08539i	−0.729470	−	0.319940i
$94$	−5.46321	−	3.15419i	−0.563487	−	0.325329i
$95$	−2.67748	+	3.72524i	−0.274703	+	0.382202i
$96$	−1.19625	+	1.25259i	−0.122092	+	0.127842i
$97$	1.99972	+	5.49418i	0.203041	+	0.557849i	0.998863	−	0.0476813i	$-0.0151832\pi$
$97$	1.99972	+	5.49418i	0.203041	+	0.557849i	−0.795822	+	0.605531i	$0.792961\pi$
$98$	−6.80461	+	1.64232i	−0.687370	+	0.165899i
$99$	5.35965	+	1.67589i	0.538665	+	0.168434i
$100$	0.675891	−	3.83317i	0.0675891	−	0.383317i
$101$	−3.05899	+	8.40451i	−0.304381	+	0.836280i	0.689344	+	0.724434i	$0.257899\pi$
$101$	−3.05899	+	8.40451i	−0.304381	+	0.836280i	−0.993726	+	0.111846i	$0.964324\pi$
$102$	−9.47970	+	2.77531i	−0.938630	+	0.274797i
$103$		−	9.30203i		−	0.916556i	−0.888809	−	0.458278i	$-0.848466\pi$
$103$		−	9.30203i		−	0.916556i	0.888809	−	0.458278i	$-0.151534\pi$
$104$	0.339046	−	0.931522i	0.0332462	−	0.0913433i
$105$	0.579205	−	4.78814i	0.0565247	−	0.467274i
$106$	−1.26809	+	2.19640i	−0.123168	+	0.213333i
$107$	−3.38635	+	5.86532i	−0.327370	+	0.567022i	−0.981989	−	0.188937i	$-0.939496\pi$
$107$	−3.38635	+	5.86532i	−0.327370	+	0.567022i	0.654619	+	0.755959i	$0.272829\pi$
$108$	2.51552	+	4.54667i	0.242056	+	0.437503i
$109$	0.410883	+	1.12889i	0.0393554	+	0.108128i	0.957814	−	0.287390i	$-0.0927874\pi$
$109$	0.410883	+	1.12889i	0.0393554	+	0.108128i	−0.918458	+	0.395518i	$0.870565\pi$
$110$	−1.85126	−	0.673805i	−0.176511	−	0.0642448i
$111$	0.833232	+	7.52552i	0.0790868	+	0.714291i
$112$	−1.81166	+	1.92818i	−0.171186	+	0.182196i
$113$	−8.69260			−0.817731			−0.408866	−	0.912595i	$-0.634075\pi$
$113$	−8.69260			−0.817731			−0.408866	+	0.912595i	$0.634075\pi$
$114$	−0.0806162	−	7.54940i	−0.00755040	−	0.707066i
$115$	−0.468478	+	0.811428i	−0.0436858	+	0.0756660i
$116$	0.0928339	−	0.526487i	0.00861941	−	0.0488831i
$117$	−2.36366	−	1.80479i	−0.218521	−	0.166853i
$118$	−6.88449	+	5.77678i	−0.633769	+	0.531795i
$119$	−14.4455	+	4.35710i	−1.32422	+	0.399414i
$120$	−0.808208	−	1.63398i	−0.0737789	−	0.149162i
$121$	−3.74809	+	6.49188i	−0.340735	+	0.590170i
$122$	−5.53787	−	9.59187i	−0.501375	−	0.868407i
$123$	17.0454	+	11.3601i	1.53693	+	1.02430i
$124$	−4.36761	+	0.770128i	−0.392223	+	0.0691595i
$125$	8.10506	+	4.67946i	0.724938	+	0.418543i
$126$	3.89893	+	6.91364i	0.347344	+	0.615916i
$127$	−17.0116	+	2.99960i	−1.50954	+	0.266172i	−0.866311	−	0.499506i	$-0.833515\pi$
$127$	−17.0116	+	2.99960i	−1.50954	+	0.266172i	−0.643225	+	0.765677i	$0.722404\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	11.1143	−	5.49738i	0.978556	−	0.484017i
$130$	0.799232	+	0.670635i	0.0700973	+	0.0588186i
$131$	−10.8379	+	12.9161i	−0.946913	+	1.12849i	0.0446680	+	0.999002i	$0.485777\pi$
$131$	−10.8379	+	12.9161i	−0.946913	+	1.12849i	−0.991581	+	0.129486i	$0.958667\pi$
$132$	3.11154	−	0.910944i	0.270825	−	0.0792875i
$133$	−0.217017	−	11.5305i	−0.0188177	−	0.999823i
$134$			5.41386i			0.467686i
$135$	−5.40216	+	0.851202i	−0.464944	+	0.0732598i
$136$	−3.66571	+	4.36863i	−0.314332	+	0.374607i
$137$	19.0777	−	3.36392i	1.62992	−	0.287399i	0.717471	−	0.696588i	$-0.245299\pi$
$137$	19.0777	−	3.36392i	1.62992	−	0.287399i	0.912450	+	0.409189i	$0.134188\pi$
$138$	−0.169688	−	1.53258i	−0.0144448	−	0.130462i
$139$	−2.32747	−	13.1998i	−0.197414	−	1.11959i	−0.908939	−	0.416928i	$-0.863107\pi$
$139$	−2.32747	−	13.1998i	−0.197414	−	1.11959i	0.711526	−	0.702660i	$-0.248005\pi$
$140$	−1.25484	−	2.48582i	−0.106053	−	0.210090i
$141$	−2.58444	+	10.6164i	−0.217649	+	0.894060i
$142$	1.18621	+	6.72732i	0.0995443	+	0.564544i
$143$	−1.42145	+	1.19274i	−0.118868	+	0.0997421i
$144$	2.66432	+	1.37892i	0.222026	+	0.114910i
$145$	0.487280	+	0.281331i	0.0404664	+	0.0233633i
$146$	0.0595200	+	0.337555i	0.00492591	+	0.0279362i
$147$	6.04149	+	10.5119i	0.498293	+	0.867008i
$148$	2.80989	+	3.34870i	0.230972	+	0.275261i
$149$	3.72567	+	10.2362i	0.305218	+	0.838581i	0.993572	+	0.113205i	$0.0361117\pi$
$149$	3.72567	+	10.2362i	0.305218	+	0.838581i	−0.688353	+	0.725376i	$0.741666\pi$
$150$	−6.70071	+	0.741908i	−0.547111	+	0.0605765i
$151$	−0.738010	−	0.426090i	−0.0600584	−	0.0346747i	0.469670	−	0.882842i	$-0.344373\pi$
$151$	−0.738010	−	0.426090i	−0.0600584	−	0.0346747i	−0.529729	+	0.848167i	$0.677706\pi$
$152$	−2.45596	−	3.60115i	−0.199204	−	0.292092i
$153$	9.22667	+	14.4073i	0.745932	+	1.16476i
$154$	4.74147	−	1.43014i	0.382078	−	0.115244i
$155$	0.810539	−	4.59680i	0.0651041	−	0.369223i
$156$	−1.71345	−	0.110260i	−0.137186	−	0.00882788i
$157$	12.5518	−	4.56849i	1.00174	−	0.364605i	0.211487	−	0.977381i	$-0.432169\pi$
$157$	12.5518	−	4.56849i	1.00174	−	0.364605i	0.790257	+	0.612776i	$0.209947\pi$
$158$	−4.19853	+	11.5354i	−0.334017	+	0.917704i
$159$	4.26814	+	1.03903i	0.338486	+	0.0824007i
$160$	−0.911469	−	0.526237i	−0.0720580	−	0.0416027i
$161$	−0.278252	−	2.33886i	−0.0219293	−	0.184328i
$162$	6.33363	−	6.39414i	0.497617	−	0.502371i
$163$	−0.472645			−0.0370204			−0.0185102	−	0.999829i	$-0.505892\pi$
$163$	−0.472645			−0.0370204			−0.0185102	+	0.999829i	$0.505892\pi$
$164$	11.8265			0.923493
$165$	−0.219126	+	3.40523i	−0.0170589	+	0.265097i
$166$	−12.6612	−	2.23252i	−0.982702	−	0.173277i
$167$	14.4091	−	12.0906i	1.11501	−	0.935601i	0.116664	−	0.993171i	$-0.462780\pi$
$167$	14.4091	−	12.0906i	1.11501	−	0.935601i	0.998341	+	0.0575705i	$0.0183354\pi$
$168$	4.08682	+	2.07313i	0.315305	+	0.159945i
$169$	−11.2926	+	4.11016i	−0.868660	+	0.316166i
$170$	−3.00104	−	5.19796i	−0.230170	−	0.398665i
$171$	−12.5100	+	3.80795i	−0.956662	+	0.291202i
$172$	3.57943	−	6.19975i	0.272929	−	0.472727i
$173$	−13.9583	−	11.7124i	−1.06123	−	0.890475i	−0.0669980	−	0.997753i	$-0.521342\pi$
$173$	−13.9583	−	11.7124i	−1.06123	−	0.890475i	−0.994229	+	0.107278i	$0.965787\pi$
$174$	−0.920346	+	0.101901i	−0.0697712	+	0.00772512i
$175$	−10.2259	+	1.21657i	−0.773009	+	0.0919640i
$176$	1.20320	−	1.43392i	0.0906948	−	0.108086i
$177$	12.9530	+	8.63265i	0.973605	+	0.648870i
$178$	6.99935			0.524624
$179$	4.60775	+	7.98085i	0.344399	+	0.596517i	0.985244	−	0.171153i	$-0.0547493\pi$
$179$	4.60775	+	7.98085i	0.344399	+	0.596517i	−0.640845	+	0.767670i	$0.721416\pi$
$180$	−2.32282	+	2.13865i	−0.173133	+	0.159406i
$181$	4.87189	−	13.3854i	0.362125	−	0.994930i	−0.616152	−	0.787627i	$-0.711309\pi$
$181$	4.87189	−	13.3854i	0.362125	−	0.994930i	0.978277	−	0.207303i	$-0.0664686\pi$
$182$	−2.61862	−	0.147113i	−0.194105	−	0.0109047i
$183$	−13.2493	+	13.8734i	−0.979418	+	1.02555i
$184$	−0.572236	−	0.681965i	−0.0421858	−	0.0502751i
$185$	−4.32334	+	1.57357i	−0.317858	+	0.115691i
$186$	3.40568	+	6.88540i	0.249717	+	0.504862i
$187$	10.0311	−	3.65102i	0.733546	−	0.266989i
$188$	2.15759	+	5.92793i	0.157358	+	0.432339i
$189$	9.59495	−	9.84565i	0.697930	−	0.716166i
$190$	4.44561	−	1.13265i	0.322518	−	0.0821712i
$191$	5.58459	−	3.22427i	0.404087	−	0.233300i	−0.284159	−	0.958777i	$-0.591714\pi$
$191$	5.58459	−	3.22427i	0.404087	−	0.233300i	0.688246	+	0.725477i	$0.258381\pi$
$192$	1.72153	−	0.190609i	0.124241	−	0.0137560i
$193$	2.62266	−	3.12557i	0.188783	−	0.224983i	−0.663348	−	0.748311i	$-0.730865\pi$
$193$	2.62266	−	3.12557i	0.188783	−	0.224983i	0.852132	+	0.523328i	$0.175310\pi$
$194$	1.99972	−	5.49418i	0.143571	−	0.394459i
$195$	0.725832	−	1.65491i	0.0519779	−	0.118511i
$196$	6.26830	+	3.11583i	0.447736	+	0.222559i
$197$	−9.84238	+	5.68250i	−0.701241	+	0.404861i	−0.807809	−	0.589444i	$-0.799347\pi$
$197$	−9.84238	+	5.68250i	−0.701241	+	0.404861i	0.106569	+	0.994305i	$0.466014\pi$
$198$	−3.02848	−	4.72893i	−0.215225	−	0.336070i
$199$	−15.4591	+	12.9717i	−1.09587	+	0.919541i	−0.997140	−	0.0755739i	$-0.975921\pi$
$199$	−15.4591	+	12.9717i	−1.09587	+	0.919541i	−0.0987258	+	0.995115i	$0.531477\pi$
$200$	−2.98167	+	2.50192i	−0.210836	+	0.176913i
$201$	8.99934	−	2.63468i	0.634765	−	0.185836i
$202$	7.74564	−	4.47195i	0.544981	−	0.314645i
$203$	−1.40454	+	0.167096i	−0.0985792	+	0.0117279i
$204$	9.04581	+	3.96742i	0.633333	+	0.277775i
$205$	−4.25715	+	11.6964i	−0.297332	+	0.816913i
$206$	−5.97923	+	7.12577i	−0.416593	+	0.496476i
$207$	−2.46499	+	1.02790i	−0.171329	+	0.0714443i
$208$	−0.858496	+	0.495653i	−0.0595260	+	0.0343673i
$209$	0.610874	+	8.13631i	0.0422551	+	0.562800i
$210$	−3.52145	+	3.29562i	−0.243003	+	0.227419i
$211$	−1.22419	−	3.36344i	−0.0842769	−	0.231549i	0.890395	−	0.455189i	$-0.150428\pi$
$211$	−1.22419	−	3.36344i	−0.0842769	−	0.231549i	−0.974672	+	0.223640i	$0.928206\pi$
$212$	2.38323	−	0.867425i	0.163681	−	0.0595750i
$213$	10.6054	−	5.24568i	0.726670	−	0.359428i
$214$	6.36425	−	2.31640i	0.435051	−	0.158346i
$215$	4.84309	+	5.77177i	0.330296	+	0.393632i
$216$	0.995541	−	5.09989i	0.0677380	−	0.347004i
$217$	5.28771	+	10.4749i	0.358953	+	0.711084i
$218$	0.410883	−	1.12889i	0.0278285	−	0.0764582i
$219$	0.532144	−	0.263211i	0.0359590	−	0.0177862i
$220$	0.985037	+	1.70613i	0.0664112	+	0.115028i
$221$	−5.65325			−0.380279
$222$	4.19902	−	6.30048i	0.281820	−	0.422860i
$223$	−12.2269	+	14.5714i	−0.818773	+	0.975776i	−0.999971	−	0.00767088i	$-0.997558\pi$
$223$	−12.2269	+	14.5714i	−0.818773	+	0.975776i	0.181197	+	0.983447i	$0.442003\pi$
$224$	2.62722	−	0.312558i	0.175539	−	0.0208837i
$225$	4.49419	+	10.7774i	0.299612	+	0.718493i
$226$	6.65892	+	5.58750i	0.442945	+	0.371675i
$227$	7.22767	−	12.5187i	0.479718	−	0.830895i	−0.520012	−	0.854159i	$-0.674072\pi$
$227$	7.22767	−	12.5187i	0.479718	−	0.830895i	0.999729	+	0.0232638i	$0.00740577\pi$
$228$	−4.79091	+	5.83500i	−0.317286	+	0.386432i
$229$	3.58839	+	6.21527i	0.237127	+	0.410716i	0.959889	−	0.280381i	$-0.0904608\pi$
$229$	3.58839	+	6.21527i	0.237127	+	0.410716i	−0.722762	+	0.691098i	$0.757127\pi$
$230$	0.880451	−	0.320458i	0.0580552	−	0.0211304i
$231$	−4.68474	−	7.18565i	−0.308233	−	0.472781i
$232$	−0.409534	+	0.343640i	−0.0268872	+	0.0225611i
$233$	−10.3116	−	1.81821i	−0.675532	−	0.119115i	−0.174651	−	0.984630i	$-0.555880\pi$
$233$	−10.3116	−	1.81821i	−0.675532	−	0.119115i	−0.500882	+	0.865516i	$0.666991\pi$
$234$	0.650573	+	2.90188i	0.0425293	+	0.189702i
$235$	−6.63940			−0.433106
$236$	8.98707			0.585008
$237$	21.2182	+	1.36539i	1.37827	+	0.0886916i
$238$	13.8666	+	5.94765i	0.898837	+	0.385529i
$239$	−13.5839	−	7.84269i	−0.878672	−	0.507302i	−0.00845179	−	0.999964i	$-0.502690\pi$
$239$	−13.5839	−	7.84269i	−0.878672	−	0.507302i	−0.870220	+	0.492663i	$0.836024\pi$
$240$	−0.431182	+	1.77121i	−0.0278327	+	0.114331i
$241$	−8.11569	+	22.2977i	−0.522777	+	1.43632i	0.344639	+	0.938735i	$0.388001\pi$
$241$	−8.11569	+	22.2977i	−0.522777	+	1.43632i	−0.867416	+	0.497583i	$0.834221\pi$
$242$	7.04410	−	2.56384i	0.452812	−	0.164810i
$243$	−13.7111	−	7.41652i	−0.879570	−	0.475770i
$244$	−1.92328	+	10.9075i	−0.123125	+	0.698279i
$245$	−5.33795	+	5.07776i	−0.341029	+	0.324406i
$246$	−5.75541	−	19.6589i	−0.366951	−	1.25341i
$247$	1.16972	−	4.15966i	0.0744276	−	0.264673i
$248$	3.84081	+	2.21749i	0.243892	+	0.140811i
$249$	2.45058	+	22.1329i	0.155299	+	1.40262i
$250$	−3.20094	−	8.79450i	−0.202445	−	0.556213i
$251$	6.44090	+	7.67596i	0.406546	+	0.484503i	0.930004	−	0.367549i	$-0.119803\pi$
$251$	6.44090	+	7.67596i	0.406546	+	0.484503i	−0.523458	+	0.852051i	$0.675358\pi$
$252$	1.45725	−	7.80234i	0.0917979	−	0.491501i
$253$	0.289367	+	1.64108i	0.0181924	+	0.103174i
$254$	14.9598	+	8.63702i	0.938658	+	0.541935i
$255$	−7.17998	+	7.51818i	−0.449628	+	0.470807i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.13238	+	6.42204i	0.0706358	+	0.400596i	0.999541	+	0.0302792i	$0.00963965\pi$
$257$	1.13238	+	6.42204i	0.0706358	+	0.400596i	−0.928906	+	0.370316i	$0.879249\pi$
$258$	−12.0477	−	2.93287i	−0.750054	−	0.182593i
$259$	6.33555	−	9.67603i	0.393672	−	0.601239i
$260$	−0.181171	−	1.02747i	−0.0112358	−	0.0637211i
$261$	0.617278	+	1.48028i	0.0382086	+	0.0916270i
$262$	16.6047	−	2.92785i	1.02584	−	0.180883i
$263$	−8.03631	+	9.57730i	−0.495540	+	0.590562i	−0.954618	−	0.297834i	$-0.903736\pi$
$263$	−8.03631	+	9.57730i	−0.495540	+	0.590562i	0.459077	+	0.888396i	$0.348180\pi$
$264$	−2.96912	−	1.30223i	−0.182737	−	0.0801470i
$265$			2.66926i			0.163972i
$266$	−7.24543	+	8.97239i	−0.444246	+	0.550132i
$267$	−3.40626	−	11.6349i	−0.208460	−	0.712042i
$268$	3.47996	−	4.14726i	0.212573	−	0.253334i
$269$	19.7045	+	16.5341i	1.20141	+	1.00810i	0.999589	+	0.0286773i	$0.00912952\pi$
$269$	19.7045	+	16.5341i	1.20141	+	1.00810i	0.201818	+	0.979423i	$0.435315\pi$
$270$	4.68544	+	2.82039i	0.285147	+	0.171643i
$271$	−2.26193	+	12.8280i	−0.137402	+	0.779247i	0.835755	+	0.549103i	$0.185031\pi$
$271$	−2.26193	+	12.8280i	−0.137402	+	0.779247i	−0.973157	+	0.230143i	$0.926080\pi$
$272$	5.61620	−	0.990287i	0.340532	−	0.0600450i
$273$	1.02982	+	4.42446i	0.0623275	+	0.267781i
$274$	−16.7767	−	9.68602i	−1.01352	−	0.585154i
$275$	7.17512	−	1.26517i	0.432676	−	0.0762924i
$276$	−0.855134	+	1.28310i	−0.0514730	+	0.0772333i
$277$	0.0455918	+	0.0789674i	0.00273935	+	0.00474469i	0.867392	−	0.497626i	$-0.165795\pi$
$277$	0.0455918	+	0.0789674i	0.00273935	+	0.00474469i	−0.864652	+	0.502370i	$0.832461\pi$
$278$	−6.70169	+	11.6077i	−0.401941	+	0.696182i
$279$	9.78805	−	9.01199i	0.585995	−	0.539534i
$280$	−0.636594	+	2.71084i	−0.0380438	+	0.162004i
$281$	−11.4306	+	9.59138i	−0.681890	+	0.572174i	−0.916558	−	0.399902i	$-0.869044\pi$
$281$	−11.4306	+	9.59138i	−0.681890	+	0.572174i	0.234668	+	0.972076i	$0.424600\pi$
$282$	8.80387	−	6.47137i	0.524263	−	0.385364i
$283$	4.07800	−	23.1275i	0.242412	−	1.37479i	−0.584015	−	0.811743i	$-0.698519\pi$
$283$	4.07800	−	23.1275i	0.242412	−	1.37479i	0.826427	−	0.563044i	$-0.190370\pi$
$284$	3.41555	−	5.91590i	0.202675	−	0.351044i
$285$	−4.04625	−	6.83862i	−0.239679	−	0.405085i
$286$	1.85558			0.109723
$287$	−9.03570	−	29.9569i	−0.533360	−	1.76830i
$288$	−1.15464	−	2.76890i	−0.0680375	−	0.163159i
$289$	14.5863	+	5.30896i	0.858015	+	0.312292i
$290$	−0.192442	−	0.528729i	−0.0113006	−	0.0310481i
$291$	−10.1060	−	0.650322i	−0.592425	−	0.0381225i
$292$	0.171381	−	0.296841i	0.0100293	−	0.0173713i
$293$	13.2074	−	22.8760i	0.771587	−	1.33643i	−0.165106	−	0.986276i	$-0.552797\pi$
$293$	13.2074	−	22.8760i	0.771587	−	1.33643i	0.936693	−	0.350152i	$-0.113870\pi$
$294$	2.12888	−	11.9360i	0.124159	−	0.696121i
$295$	−3.23505	+	8.88823i	−0.188352	+	0.517493i
$296$		−	4.37141i		−	0.254083i
$297$	−6.38696	+	7.33553i	−0.370609	+	0.425651i
$298$	3.72567	−	10.2362i	0.215822	−	0.592966i
$299$	0.153245	−	0.869094i	0.00886237	−	0.0502610i
$300$	5.60993	+	3.73880i	0.323890	+	0.215860i
$301$	−18.4390	−	4.33007i	−1.06280	−	0.249581i
$302$	0.291463	+	0.800788i	0.0167718	+	0.0460802i
$303$	−11.2031	−	10.6991i	−0.643599	−	0.614648i
$304$	−0.433401	+	4.33730i	−0.0248572	+	0.248761i
$305$	−10.0952	−	5.82846i	−0.578049	−	0.333737i
$306$	2.19278	−	16.9674i	0.125353	−	0.969962i
$307$	−4.14587	−	0.731029i	−0.236618	−	0.0417221i	0.0540818	−	0.998537i	$-0.482777\pi$
$307$	−4.14587	−	0.731029i	−0.236618	−	0.0417221i	−0.290699	+	0.956814i	$0.593888\pi$
$308$	−4.55145	−	1.95221i	−0.259343	−	0.111237i
$309$	14.7548	+	6.47135i	0.839372	+	0.368143i
$310$	−3.57567	+	3.00035i	−0.203085	+	0.170408i
$311$			6.55434i			0.371662i	0.982582	+	0.185831i	$0.0594977\pi$
$311$			6.55434i			0.371662i	−0.982582	+	0.185831i	$0.940502\pi$
$312$	1.24170	+	1.18585i	0.0702976	+	0.0671354i
$313$	0.705102	+	3.99883i	0.0398547	+	0.226027i	0.998229	−	0.0594874i	$-0.0189466\pi$
$313$	0.705102	+	3.99883i	0.0398547	+	0.226027i	−0.958374	+	0.285515i	$0.907835\pi$
$314$	−12.5518	−	4.56849i	−0.708340	−	0.257815i
$315$	7.19196	+	4.24980i	0.405221	+	0.239449i
$316$	10.6310	−	6.13784i	0.598043	−	0.345280i
$317$	20.8174	−	17.4678i	1.16922	−	0.981091i	0.169229	−	0.985577i	$-0.445872\pi$
$317$	20.8174	−	17.4678i	1.16922	−	0.981091i	0.999990	+	0.00448552i	$0.00142779\pi$
$318$	−2.60171	−	3.53945i	−0.145897	−	0.198483i
$319$	0.985506	−	0.173771i	0.0551777	−	0.00972932i
$320$	0.359967	+	0.989002i	0.0201228	+	0.0552869i
$321$	−6.94768	−	9.45187i	−0.387782	−	0.527552i
$322$	−1.29024	+	1.97053i	−0.0719022	+	0.109813i
$323$	−14.5079	+	20.1853i	−0.807243	+	1.12314i
$324$	−8.96192	+	0.827017i	−0.497885	+	0.0459454i
$325$	−3.79984	−	0.670014i	−0.210777	−	0.0371657i
$326$	0.362067	+	0.303810i	0.0200530	+	0.0168265i
$327$	−2.07649	−	0.133622i	−0.114830	−	0.00738931i
$328$	−9.05961	−	7.60192i	−0.500233	−	0.419746i
$329$	13.3672	−	9.99432i	0.736958	−	0.551005i
$330$	2.35670	−	2.46770i	0.129732	−	0.135843i
$331$			5.66114i			0.311164i	0.987823	+	0.155582i	$0.0497253\pi$
$331$			5.66114i			0.311164i	−0.987823	+	0.155582i	$0.950275\pi$
$332$	8.26403	+	9.84868i	0.453547	+	0.540517i
$333$	−12.5166	−	3.91379i	−0.685906	−	0.214474i
$334$	−18.8097			−1.02922
$335$	2.84897	+	4.93457i	0.155656	+	0.269604i
$336$	−1.79811	−	4.21507i	−0.0980948	−	0.229951i
$337$	−3.91473	+	4.66539i	−0.213249	+	0.254140i	−0.862056	−	0.506812i	$-0.830824\pi$
$337$	−3.91473	+	4.66539i	−0.213249	+	0.254140i	0.648807	+	0.760953i	$0.275268\pi$
$338$	11.2926	+	4.11016i	0.614235	+	0.223563i
$339$	6.04738	−	13.7882i	0.328449	−	0.748870i
$340$	−1.04225	+	5.91090i	−0.0565240	+	0.320564i
$341$	−4.15082	−	7.18943i	−0.224779	−	0.389329i
$342$	12.0309	+	5.12419i	0.650557	+	0.277085i
$343$	3.10339	−	18.2584i	0.167567	−	0.985861i
$344$	−6.72713	+	2.44847i	−0.362702	+	0.132013i
$345$	−0.961165	−	1.30760i	−0.0517474	−	0.0703989i
$346$	3.16408	+	17.9444i	0.170102	+	0.964697i
$347$	−11.2853	−	31.0061i	−0.605826	−	1.66449i	−0.739247	−	0.673434i	$-0.764818\pi$
$347$	−11.2853	−	31.0061i	−0.605826	−	1.66449i	0.133421	−	0.991059i	$-0.457404\pi$
$348$	0.770527	+	0.513526i	0.0413046	+	0.0275279i
$349$	9.07276	+	15.7145i	0.485654	+	0.841177i	0.999864	−	0.0164873i	$-0.00524830\pi$
$349$	9.07276	+	15.7145i	0.485654	+	0.841177i	−0.514210	+	0.857664i	$0.671915\pi$
$350$	8.61552	+	5.64116i	0.460519	+	0.301533i
$351$	4.50713	−	2.49365i	0.240573	−	0.133101i
$352$	−1.84341	+	0.325044i	−0.0982543	+	0.0173249i
$353$	−7.00198	+	4.04260i	−0.372678	+	0.215166i	−0.674628	−	0.738158i	$-0.735696\pi$
$353$	−7.00198	+	4.04260i	−0.372678	+	0.215166i	0.301950	+	0.953324i	$0.402363\pi$
$354$	−4.37359	−	14.9390i	−0.232454	−	0.793999i
$355$	4.62135	+	5.50751i	0.245276	+	0.292309i
$356$	−5.36181	−	4.49910i	−0.284176	−	0.238452i
$357$	3.13843	−	25.9446i	0.166103	−	1.37313i
$358$	1.60025	−	9.07549i	0.0845761	−	0.479655i
$359$	−5.99221	+	7.14124i	−0.316257	+	0.376900i	−0.900631	−	0.434584i	$-0.856895\pi$
$359$	−5.99221	+	7.14124i	−0.316257	+	0.376900i	0.584375	+	0.811484i	$0.301340\pi$
$360$	3.15408	−	0.145223i	0.166235	−	0.00765390i
$361$	−11.8505	−	14.8515i	−0.623708	−	0.781657i
$362$	−12.3361	+	7.12223i	−0.648369	+	0.374336i
$363$	−7.68986	−	10.4615i	−0.403613	−	0.549089i
$364$	1.91142	+	1.79591i	0.100185	+	0.0941313i
$365$	0.231885	+	0.276349i	0.0121374	+	0.0144648i
$366$	19.0672	−	2.11114i	0.996659	−	0.110351i
$367$	−23.6398	−	8.60420i	−1.23399	−	0.449135i	−0.359027	−	0.933327i	$-0.616892\pi$
$367$	−23.6398	−	8.60420i	−1.23399	−	0.449135i	−0.874962	+	0.484192i	$0.839114\pi$
$368$			0.890242i			0.0464071i
$369$	−29.8777	+	19.1342i	−1.55537	+	0.996085i
$370$	4.32334	+	1.57357i	0.224760	+	0.0818058i
$371$	−4.01806	−	5.37407i	−0.208607	−	0.279008i
$372$	1.81694	−	7.46365i	0.0942042	−	0.386972i
$373$	−23.4094	−	13.5154i	−1.21209	−	0.699802i	−0.248878	−	0.968535i	$-0.580062\pi$
$373$	−23.4094	−	13.5154i	−1.21209	−	0.699802i	−0.963215	+	0.268733i	$0.913395\pi$
$374$	−10.0311	−	3.65102i	−0.518695	−	0.188790i
$375$	−13.0612	+	9.60073i	−0.674475	+	0.495779i
$376$	2.15759	−	5.92793i	0.111269	−	0.305710i
$377$	−0.521909	−	0.0920267i	−0.0268797	−	0.00473962i
$378$	−13.6788	+	1.37469i	−0.703563	+	0.0707064i
$379$		−	23.7656i		−	1.22076i	−0.792109	−	0.610379i	$-0.791017\pi$
$379$		−	23.7656i		−	1.22076i	0.792109	−	0.610379i	$-0.208983\pi$
$380$	−4.13359	−	1.98992i	−0.212049	−	0.102081i
$381$	7.07690	−	29.0705i	0.362560	−	1.48933i
$382$	−6.35057	−	1.11978i	−0.324923	−	0.0572927i
$383$	15.9906	−	5.82010i	0.817081	−	0.297393i	0.100536	−	0.994933i	$-0.467944\pi$
$383$	15.9906	−	5.82010i	0.817081	−	0.297393i	0.716546	+	0.697540i	$0.245722\pi$
$384$	−1.44129	−	0.960564i	−0.0735505	−	0.0490186i
$385$	3.56911	−	3.79866i	0.181899	−	0.193598i
$386$	−4.01815	+	0.708508i	−0.204518	+	0.0360621i
$387$	0.987795	+	21.4538i	0.0502124	+	1.09056i
$388$	−5.06346	+	2.92339i	−0.257058	+	0.148413i
$389$	5.91659	+	7.05112i	0.299983	+	0.357506i	0.894889	−	0.446290i	$-0.147255\pi$
$389$	5.91659	+	7.05112i	0.299983	+	0.357506i	−0.594905	+	0.803796i	$0.702810\pi$
$390$	−1.61978	+	0.801180i	−0.0820206	+	0.0405693i
$391$	−2.53845	+	4.39673i	−0.128375	+	0.222352i
$392$	−2.79898	−	6.41605i	−0.141370	−	0.324060i
$393$	−12.9476	−	26.1767i	−0.653121	−	1.32044i
$394$	11.1923	+	1.97351i	0.563862	+	0.0994241i
$395$	2.24350	+	12.7235i	0.112883	+	0.640191i
$396$	−0.719741	+	5.56924i	−0.0361683	+	0.279865i
$397$	−14.9341	−	12.5312i	−0.749522	−	0.628924i	0.185854	−	0.982577i	$-0.440495\pi$
$397$	−14.9341	−	12.5312i	−0.749522	−	0.628924i	−0.935376	+	0.353654i	$0.884939\pi$
$398$	20.1804			1.01155
$399$	18.4406	+	7.67747i	0.923186	+	0.384354i
$400$	3.89230			0.194615
$401$	12.4082	+	10.4117i	0.619637	+	0.519937i	0.897690	−	0.440629i	$-0.145244\pi$
$401$	12.4082	+	10.4117i	0.619637	+	0.519937i	−0.278052	+	0.960566i	$0.589689\pi$
$402$	−8.58743	−	3.76639i	−0.428302	−	0.187850i
$403$	0.763432	+	4.32964i	0.0380292	+	0.215675i
$404$	−8.80802	−	1.55309i	−0.438215	−	0.0772692i
$405$	2.40808	−	9.16106i	0.119658	−	0.455217i
$406$	1.18335	+	0.774816i	0.0587285	+	0.0384535i
$407$	−4.09132	+	7.08637i	−0.202799	+	0.351258i
$408$	−4.37928	−	8.85376i	−0.216807	−	0.438326i
$409$	−15.5240	−	18.5007i	−0.767610	−	0.914802i	0.230693	−	0.973026i	$-0.425901\pi$
$409$	−15.5240	−	18.5007i	−0.767610	−	0.914802i	−0.998304	+	0.0582244i	$0.981456\pi$
$410$	10.7795	−	6.22353i	0.532360	−	0.307358i
$411$	−7.93642	+	32.6012i	−0.391475	+	1.60810i
$412$	9.16071	−	1.61528i	0.451316	−	0.0795791i
$413$	−6.86632	−	22.7646i	−0.337870	−	1.12017i
$414$	2.54902	+	0.797046i	0.125277	+	0.0391727i
$415$	−12.7151	+	4.62793i	−0.624162	+	0.227176i
$416$	0.976245	+	0.172138i	0.0478644	+	0.00843978i
$417$	22.5566	+	5.49115i	1.10460	+	0.268903i
$418$	4.76196	−	6.62544i	0.232915	−	0.324061i
$419$		−	16.9464i		−	0.827887i	−0.910303	−	0.413944i	$-0.864151\pi$
$419$		−	16.9464i		−	0.827887i	0.910303	−	0.413944i	$-0.135849\pi$
$420$	4.81597	−	0.261045i	0.234995	−	0.0127377i
$421$	15.2275	+	2.68502i	0.742144	+	0.130860i	0.531922	−	0.846794i	$-0.321470\pi$
$421$	15.2275	+	2.68502i	0.742144	+	0.130860i	0.210222	+	0.977654i	$0.432581\pi$
$422$	−1.22419	+	3.36344i	−0.0595928	+	0.163730i
$423$	−15.0416	−	11.4852i	−0.731350	−	0.558428i
$424$	−2.38323	−	0.867425i	−0.115740	−	0.0421259i
$425$	19.2233	+	11.0986i	0.932467	+	0.538360i
$426$	−11.4961	−	2.79859i	−0.556986	−	0.135592i
$427$	29.0984	−	3.46181i	1.40817	−	0.167529i
$428$	−6.36425	−	2.31640i	−0.307628	−	0.111967i
$429$	−0.903024	−	3.08448i	−0.0435984	−	0.148920i
$430$		−	7.53451i		−	0.363346i
$431$	7.33883	+	2.67112i	0.353499	+	0.128663i	0.512665	−	0.858589i	$-0.328658\pi$
$431$	7.33883	+	2.67112i	0.353499	+	0.128663i	−0.159166	+	0.987252i	$0.550880\pi$
$432$	−4.04078	+	3.26682i	−0.194412	+	0.157175i
$433$	−8.93963	−	10.6538i	−0.429611	−	0.511991i	0.507199	−	0.861829i	$-0.330681\pi$
$433$	−8.93963	−	10.6538i	−0.429611	−	0.511991i	−0.936810	+	0.349838i	$0.886237\pi$
$434$	2.68252	−	11.4231i	0.128765	−	0.548328i
$435$	−0.785242	+	0.577200i	−0.0376495	+	0.0276746i
$436$	−1.04039	+	0.600671i	−0.0498257	+	0.0287669i
$437$	−2.70988	−	2.77752i	−0.129631	−	0.132867i
$438$	−0.576835	−	0.140424i	−0.0275623	−	0.00670973i
$439$	18.6894	−	22.2732i	0.891997	−	1.06304i	−0.105644	−	0.994404i	$-0.533691\pi$
$439$	18.6894	−	22.2732i	0.891997	−	1.06304i	0.997642	−	0.0686369i	$-0.0218650\pi$
$440$	0.342100	−	1.94014i	0.0163090	−	0.0924928i
$441$	−20.8770	+	2.26990i	−0.994141	+	0.108091i
$442$	4.33064	+	3.63384i	0.205988	+	0.172844i
$443$	23.0548	+	27.4756i	1.09537	+	1.30541i	0.948685	+	0.316222i	$0.102414\pi$
$443$	23.0548	+	27.4756i	1.09537	+	1.30541i	0.146680	+	0.989184i	$0.453141\pi$
$444$	−7.26650	+	2.12737i	−0.344853	+	0.100960i
$445$	6.37969	−	3.68332i	0.302426	−	0.174606i
$446$	18.7327	−	3.30308i	0.887018	−	0.156405i
$447$	−18.8285	−	1.21161i	−0.890557	−	0.0573073i
$448$	−2.21348	−	1.44931i	−0.104577	−	0.0684736i
$449$	11.6109	+	20.1106i	0.547951	+	0.949079i	0.998415	+	0.0562844i	$0.0179253\pi$
$449$	11.6109	+	20.1106i	0.547951	+	0.949079i	−0.450464	+	0.892795i	$0.648741\pi$
$450$	3.48483	−	11.1448i	0.164276	−	0.525369i
$451$	7.57144	+	20.8024i	0.356525	+	0.979545i
$452$	−1.50945	−	8.56054i	−0.0709988	−	0.402654i
$453$	1.18929	−	0.874199i	0.0558777	−	0.0410735i
$454$	−13.5836	+	4.94402i	−0.637509	+	0.232034i
$455$	−2.46421	+	1.24392i	−0.115524	+	0.0583161i
$456$	7.42071	−	1.39033i	0.347507	−	0.0651082i
$457$	15.7196	+	27.2272i	0.735334	+	1.27364i	0.954577	+	0.297965i	$0.0963080\pi$
$457$	15.7196	+	27.2272i	0.735334	+	1.27364i	−0.219243	+	0.975670i	$0.570359\pi$
$458$	1.24623	−	7.06774i	0.0582327	−	0.330254i
$459$	−29.2717	+	4.61224i	−1.36628	+	0.215281i
$460$	−0.880451	−	0.320458i	−0.0410512	−	0.0149414i
$461$	−7.20753	+	8.58960i	−0.335688	+	0.400058i	−0.907312	−	0.420458i	$-0.861869\pi$
$461$	−7.20753	+	8.58960i	−0.335688	+	0.400058i	0.571624	+	0.820516i	$0.306314\pi$
$462$	−1.03013	+	8.51582i	−0.0479261	+	0.396192i
$463$	6.03312	+	10.4497i	0.280383	+	0.485637i	0.971479	−	0.237126i	$-0.0762053\pi$
$463$	6.03312	+	10.4497i	0.280383	+	0.485637i	−0.691096	+	0.722763i	$0.742872\pi$
$464$	0.534609			0.0248186
$465$	6.72752	+	4.48363i	0.311981	+	0.207923i
$466$	6.73039	+	8.02097i	0.311779	+	0.371564i
$467$		−	19.4184i		−	0.898574i	−0.893387	−	0.449287i	$-0.851678\pi$
$467$		−	19.4184i		−	0.898574i	0.893387	−	0.449287i	$-0.148322\pi$
$468$	1.36693	−	2.64115i	0.0631862	−	0.122087i
$469$	−13.1639	−	5.64627i	−0.607854	−	0.260721i
$470$	5.08607	+	4.26772i	0.234603	+	0.196855i
$471$	−1.48570	+	23.0879i	−0.0684576	+	1.06383i
$472$	−6.88449	−	5.77678i	−0.316885	−	0.265898i
$473$	13.1967	+	2.32694i	0.606787	+	0.106993i
$474$	−15.3764	−	14.6848i	−0.706263	−	0.674493i
$475$	−12.1438	+	11.8481i	−0.557198	+	0.543627i
$476$	−6.79934	−	13.4694i	−0.311647	−	0.617370i
$477$	−4.61742	+	6.04725i	−0.211417	+	0.276885i
$478$	5.36472	+	14.7394i	0.245376	+	0.674166i
$479$	−24.5951	+	4.33677i	−1.12378	+	0.198152i	−0.704499	−	0.709705i	$-0.748828\pi$
$479$	−24.5951	+	4.33677i	−1.12378	+	0.198152i	−0.419279	+	0.907858i	$0.637717\pi$
$480$	1.46882	−	1.07967i	0.0670420	−	0.0492798i
$481$	3.31958	−	2.78546i	0.151360	−	0.127006i
$482$	20.5496	−	11.8643i	0.936010	−	0.540406i
$483$	3.90347	+	1.18577i	0.177614	+	0.0539544i
$484$	−7.04410	−	2.56384i	−0.320186	−	0.116538i
$485$	−1.06856	−	6.06010i	−0.0485208	−	0.275175i
$486$	5.73609	+	14.4947i	0.260194	+	0.657494i
$487$			17.5936i			0.797243i	0.917116	+	0.398621i	$0.130511\pi$
$487$			17.5936i			0.797243i	−0.917116	+	0.398621i	$0.869489\pi$
$488$	8.48450	−	7.11934i	0.384075	−	0.322278i
$489$	0.328815	−	0.749706i	0.0148696	−	0.0339029i
$490$	7.35303	−	0.458627i	0.332176	−	0.0207187i
$491$	−24.0923	−	4.24813i	−1.08727	−	0.191715i	−0.398843	−	0.917019i	$-0.630588\pi$
$491$	−24.0923	−	4.24813i	−1.08727	−	0.191715i	−0.688429	+	0.725304i	$0.741699\pi$
$492$	−8.22760	+	18.7591i	−0.370929	+	0.845725i
$493$	2.64033	+	1.52439i	0.118914	+	0.0686553i
$494$	−3.56984	+	2.43460i	−0.160615	+	0.109538i
$495$	−5.24891	−	2.71657i	−0.235921	−	0.122101i
$496$	−1.51686	−	4.16753i	−0.0681088	−	0.187127i
$497$	−17.5947	−	4.13182i	−0.789232	−	0.185338i
$498$	12.3495	−	18.5300i	0.553396	−	0.830350i
$499$	−6.13602	+	34.7991i	−0.274686	+	1.55782i	0.465271	+	0.885168i	$0.345957\pi$
$499$	−6.13602	+	34.7991i	−0.274686	+	1.55782i	−0.739957	+	0.672654i	$0.765154\pi$
$500$	−3.20094	+	8.79450i	−0.143150	+	0.393302i
$501$	9.15381	+	31.2669i	0.408962	+	1.39690i
$502$		−	10.0203i		−	0.447226i
$503$	7.45363	−	20.4787i	0.332341	−	0.913099i	−0.655161	−	0.755490i	$-0.727399\pi$
$503$	7.45363	−	20.4787i	0.332341	−	0.913099i	0.987502	−	0.157610i	$-0.0503788\pi$
$504$	−6.13156	+	5.04024i	−0.273121	+	0.224510i
$505$	4.70661	−	8.15208i	0.209441	−	0.362763i
$506$	0.833200	−	1.44314i	0.0370403	−	0.0641556i
$507$	1.33665	−	20.7716i	0.0593628	−	0.922501i
$508$	−5.90807	−	16.2323i	−0.262128	−	0.720191i
$509$	16.1222	+	5.86799i	0.714602	+	0.260094i	0.673633	−	0.739066i	$-0.264733\pi$
$509$	16.1222	+	5.86799i	0.714602	+	0.260094i	0.0409697	+	0.999160i	$0.486955\pi$
$510$	10.3328	−	1.14405i	0.457543	−	0.0506595i
$511$	−0.882847	−	0.207322i	−0.0390549	−	0.00917136i
$512$	−1.00000			−0.0441942
$513$	2.66295	−	22.4924i	0.117572	−	0.993064i
$514$	3.26055	−	5.64744i	0.143817	−	0.249098i
$515$	−1.70004	+	9.64141i	−0.0749127	+	0.424851i
$516$	7.34383	+	9.99080i	0.323294	+	0.439820i
$517$	−9.04571	+	7.59025i	−0.397830	+	0.333819i
$518$	−11.0729	+	3.33986i	−0.486517	+	0.146745i
$519$	28.2888	−	13.9923i	1.24174	−	0.614194i
$520$	−0.521661	+	0.903544i	−0.0228764	+	0.0396230i
$521$	14.5582	+	25.2155i	0.637804	+	1.10471i	0.985914	+	0.167255i	$0.0534904\pi$
$521$	14.5582	+	25.2155i	0.637804	+	1.10471i	−0.348109	+	0.937454i	$0.613176\pi$
$522$	0.478643	−	1.53074i	0.0209496	−	0.0669986i
$523$	28.9317	−	5.10143i	1.26509	−	0.223070i	0.499454	−	0.866340i	$-0.333534\pi$
$523$	28.9317	−	5.10143i	1.26509	−	0.223070i	0.765639	+	0.643270i	$0.222423\pi$
$524$	−14.6019	−	8.43040i	−0.637886	−	0.368284i
$525$	5.18440	−	17.0667i	0.226266	−	0.744851i
$526$	12.3123	−	2.17100i	0.536844	−	0.0946600i
$527$	4.39191	−	24.9078i	0.191315	−	1.08500i
$528$	1.43742	+	2.90608i	0.0625556	+	0.126471i
$529$	17.0119	+	14.2747i	0.739648	+	0.620639i
$530$	1.71577	−	2.04477i	0.0745283	−	0.0888193i
$531$	−22.7044	+	14.5403i	−0.985285	+	0.630993i
$532$	11.3177	−	2.21597i	0.490683	−	0.0960746i
$533$		−	11.7237i		−	0.507808i
$534$	−4.86940	+	11.1023i	−0.210720	+	0.480445i
$535$	4.58184	−	5.46043i	0.198090	−	0.236075i
$536$	−5.33161	+	0.940107i	−0.230291	+	0.0406064i
$537$	−15.8648	+	1.75656i	−0.684615	+	0.0758011i
$538$	−4.46666	−	25.3317i	−0.192571	−	1.09213i
$539$	−1.46760	+	13.0205i	−0.0632142	+	0.560833i
$540$	−1.77635	−	5.17228i	−0.0764418	−	0.222580i
$541$	−0.880485	−	4.99348i	−0.0378550	−	0.214686i	0.960013	−	0.279957i	$-0.0903201\pi$
$541$	−0.880485	−	4.99348i	−0.0378550	−	0.214686i	−0.997868	+	0.0652704i	$0.979209\pi$
$542$	9.97843	−	8.37289i	0.428610	−	0.359647i
$543$	17.8425	+	17.0399i	0.765696	+	0.731253i
$544$	−4.93880	−	2.85142i	−0.211749	−	0.122254i
$545$	−0.219557	−	1.24517i	−0.00940480	−	0.0533373i
$546$	2.05510	−	4.05129i	0.0879503	−	0.173379i
$547$	1.44754	+	1.72511i	0.0618922	+	0.0737603i	0.796102	−	0.605162i	$-0.206892\pi$
$547$	1.44754	+	1.72511i	0.0618922	+	0.0737603i	−0.734210	+	0.678922i	$0.762447\pi$
$548$	6.62563	+	18.2038i	0.283033	+	0.777626i
$549$	−12.7884	−	30.6676i	−0.545797	−	1.30886i
$550$	−6.30969	−	3.64290i	−0.269046	−	0.155334i
$551$	−1.66796	+	1.62734i	−0.0710576	+	0.0693270i
$552$	1.47983	−	0.433240i	0.0629857	−	0.0184399i
$553$	−23.6697	−	22.2394i	−1.00654	−	0.945715i
$554$	0.0158339	−	0.0897984i	0.000672717	−	0.00381517i
$555$	0.511734	−	7.95237i	0.0217219	−	0.337559i
$556$	12.5951	−	4.58423i	0.534149	−	0.194415i
$557$	3.93909	−	10.8226i	0.166905	−	0.458567i	−0.827839	−	0.560966i	$-0.810430\pi$
$557$	3.93909	−	10.8226i	0.166905	−	0.458567i	0.994743	+	0.102399i	$0.0326520\pi$
$558$	−13.2909	+	0.611949i	−0.562648	+	0.0259059i
$559$	−6.14585	−	3.54831i	−0.259942	−	0.150077i
$560$	2.23015	−	1.66743i	0.0942412	−	0.0704618i
$561$	−1.18734	+	18.4512i	−0.0501294	+	0.779012i
$562$	14.9215			0.629427
$563$	8.56704			0.361058			0.180529	−	0.983570i	$-0.442219\pi$
$563$	8.56704			0.361058			0.180529	+	0.983570i	$0.442219\pi$
$564$	−10.9039	−	0.701663i	−0.459136	−	0.0295453i
$565$	9.00974	+	1.58866i	0.379043	+	0.0668355i
$566$	−17.9900	+	15.0954i	−0.756176	+	0.634507i
$567$	8.94197	+	22.0690i	0.375528	+	0.926811i
$568$	−6.41913	+	2.33637i	−0.269341	+	0.0980320i
$569$	−14.2910	−	24.7527i	−0.599109	−	1.03769i	−0.992953	−	0.118510i	$-0.962188\pi$
$569$	−14.2910	−	24.7527i	−0.599109	−	1.03769i	0.393843	−	0.919178i	$-0.371145\pi$
$570$	−1.29617	+	7.83957i	−0.0542907	+	0.328364i
$571$	−2.53556	+	4.39171i	−0.106110	+	0.183788i	−0.914191	−	0.405283i	$-0.867173\pi$
$571$	−2.53556	+	4.39171i	−0.106110	+	0.183788i	0.808081	+	0.589071i	$0.200506\pi$
$572$	−1.42145	−	1.19274i	−0.0594340	−	0.0498710i
$573$	1.22915	+	11.1013i	0.0513485	+	0.463765i
$574$	−12.3342	+	28.7563i	−0.514819	+	1.20027i
$575$	−2.22731	+	2.65441i	−0.0928854	+	0.110697i
$576$	−0.895314	+	2.86329i	−0.0373047	+	0.119304i
$577$	34.6706			1.44336			0.721679	−	0.692228i	$-0.243371\pi$
$577$	34.6706			1.44336			0.721679	+	0.692228i	$0.243371\pi$
$578$	−7.76118	−	13.4428i	−0.322823	−	0.559145i
$579$	3.13319	+	6.33448i	0.130211	+	0.263252i
$580$	−0.192442	+	0.528729i	−0.00799071	+	0.0219543i
$581$	18.6332	−	28.4577i	0.773034	−	1.18062i
$582$	7.32364	+	6.99420i	0.303575	+	0.289919i
$583$	3.05154	+	3.63668i	0.126382	+	0.150616i
$584$	−0.322091	+	0.117232i	−0.0133282	+	0.00485108i
$585$	2.12006	+	2.30262i	0.0876535	+	0.0952017i
$586$	−24.8219	+	9.03442i	−1.02538	+	0.373208i
$587$	14.3723	+	39.4875i	0.593207	+	1.62982i	0.764515	+	0.644606i	$0.222979\pi$
$587$	14.3723	+	39.4875i	0.593207	+	1.62982i	−0.171307	+	0.985218i	$0.554799\pi$
$588$	−9.30313	+	7.77508i	−0.383654	+	0.320639i
$589$	17.4184	+	8.38526i	0.717713	+	0.345509i
$590$	8.19144	−	4.72933i	0.337236	−	0.194703i
$591$	−2.16627	−	19.5652i	−0.0891086	−	0.804805i
$592$	−2.80989	+	3.34870i	−0.115486	+	0.137631i
$593$	5.52428	−	15.1778i	0.226855	−	0.623279i	−0.773084	−	0.634303i	$-0.781287\pi$
$593$	5.52428	−	15.1778i	0.226855	−	0.623279i	0.999939	+	0.0110245i	$0.00350928\pi$
$594$	9.60789	−	1.51388i	0.394216	−	0.0621154i
$595$	15.7688	−	1.87600i	0.646459	−	0.0769085i
$596$	−9.43372	+	5.44656i	−0.386420	+	0.223100i
$597$	−9.82088	−	33.5455i	−0.401942	−	1.37292i
$598$	−0.676035	+	0.567261i	−0.0276451	+	0.0231970i
$599$	20.4597	−	17.1677i	0.835960	−	0.701454i	−0.120691	−	0.992690i	$-0.538511\pi$
$599$	20.4597	−	17.1677i	0.835960	−	0.701454i	0.956651	+	0.291236i	$0.0940666\pi$
$600$	−1.89420	−	6.47008i	−0.0773305	−	0.264140i
$601$	−24.0442	+	13.8819i	−0.980783	+	0.566256i	−0.902507	−	0.430676i	$-0.858275\pi$
$601$	−24.0442	+	13.8819i	−0.980783	+	0.566256i	−0.0782768	+	0.996932i	$0.524942\pi$
$602$	11.3417	+	15.1694i	0.462255	+	0.618257i
$603$	−2.08167	+	16.1076i	−0.0847721	+	0.655953i
$604$	0.291463	−	0.800788i	0.0118595	−	0.0325836i
$605$	5.07129	−	6.04373i	0.206177	−	0.245712i
$606$	1.70479	+	15.3972i	0.0692523	+	0.625468i
$607$	31.6139	−	18.2523i	1.28317	−	0.740838i	0.305742	−	0.952114i	$-0.401095\pi$
$607$	31.6139	−	18.2523i	1.28317	−	0.740838i	0.977426	+	0.211277i	$0.0677621\pi$
$608$	3.11997	−	3.04398i	0.126531	−	0.123450i
$609$	0.712080	−	2.34412i	0.0288549	−	0.0949884i
$610$	3.98690	+	10.9539i	0.161425	+	0.443511i
$611$	5.87639	−	2.13883i	0.237733	−	0.0865278i
$612$	−12.5862	+	11.5883i	−0.508767	+	0.468429i
$613$	7.76055	−	2.82461i	0.313446	−	0.114085i	−0.180507	−	0.983574i	$-0.557774\pi$
$613$	7.76055	−	2.82461i	0.313446	−	0.114085i	0.493953	+	0.869489i	$0.335552\pi$
$614$	2.70603	+	3.22492i	0.109206	+	0.130147i
$615$	−15.5911	−	14.8898i	−0.628694	−	0.600413i
$616$	2.23176	+	4.42109i	0.0899200	+	0.178131i
$617$	13.1198	−	36.0464i	0.528184	−	1.45117i	−0.333023	−	0.942919i	$-0.608069\pi$
$617$	13.1198	−	36.0464i	0.528184	−	1.45117i	0.861207	−	0.508254i	$-0.169709\pi$
$618$	−7.14314	−	14.4416i	−0.287339	−	0.580925i
$619$	−0.330397	−	0.572264i	−0.0132798	−	0.0230012i	0.859309	−	0.511457i	$-0.170894\pi$
$619$	−0.330397	−	0.572264i	−0.0132798	−	0.0230012i	−0.872589	+	0.488455i	$0.837561\pi$
$620$	4.66771			0.187460
$621$	0.0844215	−	4.62506i	0.00338772	−	0.185597i
$622$	4.21305	−	5.02091i	0.168928	−	0.201320i
$623$	−7.29983	+	17.0191i	−0.292461	+	0.681855i
$624$	−0.188952	−	1.70656i	−0.00756413	−	0.0683172i
$625$	7.36282	+	6.17814i	0.294513	+	0.247126i
$626$	2.03026	−	3.51651i	0.0811455	−	0.140548i
$627$	−13.3307	−	4.69141i	−0.532379	−	0.187357i
$628$	6.67868	+	11.5678i	0.266508	+	0.461606i
$629$	−23.4260	+	8.52638i	−0.934057	+	0.339969i
$630$	−2.77764	−	7.87844i	−0.110664	−	0.313885i
$631$	30.5970	−	25.6739i	1.21805	−	1.02206i	0.219122	−	0.975697i	$-0.429681\pi$
$631$	30.5970	−	25.6739i	1.21805	−	1.02206i	0.998925	−	0.0463650i	$-0.0147637\pi$
$632$	−12.0892	−	2.13165i	−0.480882	−	0.0847924i
$633$	6.18673	+	0.398116i	0.245900	+	0.0158237i
$634$	−27.1751			−1.07926
$635$	18.1805			0.721470
$636$	−0.282092	+	4.38373i	−0.0111857	+	0.173826i
$637$	3.08874	−	6.21380i	0.122380	−	0.246200i
$638$	−0.866639	−	0.500354i	−0.0343106	−	0.0198092i
$639$	0.942569	+	20.4716i	0.0372875	+	0.809844i
$640$	0.359967	−	0.989002i	0.0142290	−	0.0390937i
$641$	−25.3368	+	9.22184i	−1.00074	+	0.364241i	−0.789871	−	0.613273i	$-0.789853\pi$
$641$	−25.3368	+	9.22184i	−1.00074	+	0.364241i	−0.210872	+	0.977514i	$0.567630\pi$
$642$	−0.753308	+	11.7064i	−0.0297307	+	0.462016i
$643$	−3.68150	+	20.8788i	−0.145184	+	0.823380i	0.822035	+	0.569437i	$0.192839\pi$
$643$	−3.68150	+	20.8788i	−0.145184	+	0.823380i	−0.967219	+	0.253943i	$0.918272\pi$
$644$	2.25501	−	0.680164i	0.0888600	−	0.0268022i
$645$	−12.5245	+	3.66670i	−0.493150	+	0.144376i
$646$	24.0886	−	6.13728i	0.947752	−	0.241468i
$647$	10.7066	+	6.18146i	0.420920	+	0.243018i	0.695471	−	0.718554i	$-0.255196\pi$
$647$	10.7066	+	6.18146i	0.420920	+	0.243018i	−0.274551	+	0.961573i	$0.588529\pi$
$648$	7.39683	+	5.12708i	0.290575	+	0.201411i
$649$	5.75362	+	15.8079i	0.225849	+	0.620516i
$650$	2.48017	+	2.95575i	0.0972802	+	0.115934i
$651$	−20.2939	+	1.10001i	−0.795380	+	0.0431128i
$652$	−0.0820739	−	0.465464i	−0.00321426	−	0.0182290i
$653$	36.2384	+	20.9223i	1.41812	+	0.818751i	0.996134	−	0.0878512i	$-0.0280000\pi$
$653$	36.2384	+	20.9223i	1.41812	+	0.818751i	0.421985	+	0.906603i	$0.361333\pi$
$654$	1.50479	+	1.43710i	0.0588420	+	0.0561951i
$655$	13.5939	−	11.4066i	0.531157	−	0.445694i
$656$	2.05365	+	11.6468i	0.0801814	+	0.454732i
$657$	0.0472951	+	1.02720i	0.00184516	+	0.0400748i
$658$	−16.6641	−	0.936182i	−0.649635	−	0.0364962i
$659$	4.25222	+	24.1156i	0.165643	+	0.939409i	0.948399	+	0.317080i	$0.102702\pi$
$659$	4.25222	+	24.1156i	0.165643	+	0.939409i	−0.782756	+	0.622329i	$0.786187\pi$
$660$	−3.39154	+	0.375514i	−0.132016	+	0.0146169i
$661$	−20.5869	+	3.63002i	−0.800736	+	0.141191i	−0.559018	−	0.829155i	$-0.688822\pi$
$661$	−20.5869	+	3.63002i	−0.800736	+	0.141191i	−0.241718	+	0.970347i	$0.577711\pi$
$662$	3.63891	−	4.33668i	0.141430	−	0.168550i
$663$	3.93293	−	8.96716i	0.152742	−	0.348256i
$664$		−	12.8565i		−	0.498931i
$665$	−1.88239	+	11.9909i	−0.0729958	+	0.464986i
$666$	7.07255	+	11.0437i	0.274056	+	0.427933i
$667$	−0.305923	+	0.364584i	−0.0118454	+	0.0141168i
$668$	14.4091	+	12.0906i	0.557503	+	0.467800i
$669$	−14.6070	−	29.5315i	−0.564738	−	1.14175i
$670$	0.989438	−	5.61138i	0.0382253	−	0.216787i
$671$	−20.4172	+	3.60010i	−0.788196	+	0.138980i
$672$	−1.33196	+	4.38473i	−0.0513816	+	0.169145i
$673$	6.07430	+	3.50700i	0.234147	+	0.135185i	0.612484	−	0.790483i	$-0.290171\pi$
$673$	6.07430	+	3.50700i	0.234147	+	0.135185i	−0.378337	+	0.925668i	$0.623504\pi$
$674$	5.99771	−	1.05756i	0.231023	−	0.0407356i
$675$	−20.2216	−	0.369106i	−0.778330	−	0.0142069i
$676$	−6.00866	−	10.4073i	−0.231102	−	0.400281i
$677$	−20.4028	+	35.3386i	−0.784142	+	1.35817i	0.145368	+	0.989378i	$0.453563\pi$
$677$	−20.4028	+	35.3386i	−0.784142	+	1.35817i	−0.929510	+	0.368797i	$0.879770\pi$
$678$	−13.4954	+	6.67515i	−0.518288	+	0.256358i
$679$	11.2737	+	10.5924i	0.432643	+	0.406499i
$680$	4.59787	−	3.85807i	0.176320	−	0.147950i
$681$	14.8288	+	20.1737i	0.568243	+	0.773057i
$682$	−1.44156	+	8.17552i	−0.0552004	+	0.313057i
$683$	15.6213	−	27.0569i	0.597732	−	1.03530i	−0.395423	−	0.918499i	$-0.629402\pi$
$683$	15.6213	−	27.0569i	0.597732	−	1.03530i	0.993155	−	0.116803i	$-0.0372647\pi$
$684$	−5.92244	−	11.6587i	−0.226450	−	0.445781i
$685$	−20.3886			−0.779007
$686$	−14.1136	+	11.9919i	−0.538860	+	0.457854i
$687$	−12.3550	+	1.36796i	−0.471374	+	0.0521909i
$688$	6.72713	+	2.44847i	0.256469	+	0.0933472i
$689$	−0.859883	−	2.36251i	−0.0327589	−	0.0900044i
$690$	−0.104215	+	1.61951i	−0.00396740	+	0.0616535i
$691$	0.154125	−	0.266953i	0.00586320	−	0.0101554i	−0.863079	−	0.505069i	$-0.831467\pi$
$691$	0.154125	−	0.266953i	0.00586320	−	0.0101554i	0.868942	+	0.494914i	$0.164800\pi$
$692$	9.11061	−	15.7800i	0.346333	−	0.599867i
$693$	14.6570	−	2.43189i	0.556773	−	0.0923800i
$694$	−11.2853	+	31.0061i	−0.428384	+	1.17697i
$695$			14.1067i			0.535098i
$696$	−0.260170	−	0.888669i	−0.00986171	−	0.0336849i
$697$	−23.0674	+	63.3771i	−0.873739	+	2.40058i
$698$	3.15094	−	17.8698i	0.119265	−	0.676384i
$699$	10.0577	−	15.0912i	0.380417	−	0.570802i
$700$	−2.97380	−	9.85933i	−0.112399	−	0.372648i
$701$	15.5894	+	42.8316i	0.588805	+	1.61773i	0.772692	+	0.634781i	$0.218909\pi$
$701$	15.5894	+	42.8316i	0.588805	+	1.61773i	−0.183888	+	0.982947i	$0.558868\pi$
$702$	−5.05555	−	0.986885i	−0.190809	−	0.0372476i
$703$	−1.42660	−	19.0011i	−0.0538053	−	0.716639i
$704$	1.62107	+	0.935926i	0.0610964	+	0.0352740i
$705$	4.61898	−	10.5314i	0.173961	−	0.396634i
$706$	7.96236	+	1.40398i	0.299667	+	0.0528395i
$707$	2.79549	+	23.4976i	0.105135	+	0.883719i
$708$	−6.25224	+	14.2552i	−0.234974	+	0.535745i
$709$	28.2906	−	23.7386i	1.06247	−	0.891522i	0.0681246	−	0.997677i	$-0.478298\pi$
$709$	28.2906	−	23.7386i	1.06247	−	0.891522i	0.994350	+	0.106155i	$0.0338540\pi$
$710$		−	7.18955i		−	0.269819i
$711$	−16.9271	+	32.7063i	−0.634817	+	1.22658i
$712$	1.21542	+	6.89302i	0.0455500	+	0.258327i
$713$	3.71010	+	1.35037i	0.138944	+	0.0505717i
$714$	−19.0810	+	17.8573i	−0.714089	+	0.668294i
$715$	1.69130	−	0.976473i	0.0632511	−	0.0365180i
$716$	−7.05948	+	5.92361i	−0.263825	+	0.221376i
$717$	21.8903	−	16.0907i	0.817508	−	0.600917i
$718$	9.18060	−	1.61879i	0.342617	−	0.0604126i
$719$	12.5628	+	34.5159i	0.468513	+	1.28723i	0.918934	+	0.394412i	$0.129052\pi$
$719$	12.5628	+	34.5159i	0.468513	+	1.28723i	−0.450421	+	0.892816i	$0.648726\pi$
$720$	−2.50951	−	1.91616i	−0.0935240	−	0.0714109i
$721$	−11.0905	−	21.9703i	−0.413034	−	0.818216i
$722$	−0.468381	+	18.9942i	−0.0174313	+	0.706892i
$723$	−29.7224	−	28.3854i	−1.10539	−	1.05566i
$724$	14.0281	+	2.47353i	0.521349	+	0.0919278i
$725$	1.59403	+	1.33755i	0.0592008	+	0.0496754i
$726$	−0.833779	+	12.9570i	−0.0309444	+	0.480878i
$727$	−5.65877	−	4.74827i	−0.209872	−	0.176104i	0.531792	−	0.846875i	$-0.321519\pi$
$727$	−5.65877	−	4.74827i	−0.209872	−	0.176104i	−0.741664	+	0.670771i	$0.765963\pi$
$728$	−0.309841	−	2.60438i	−0.0114835	−	0.0965248i
$729$	21.3028	−	16.5889i	0.788992	−	0.614403i
$730$		−	0.360748i		−	0.0133519i
$731$	26.2423	+	31.2744i	0.970608	+	1.15673i
$732$	−15.9633	−	10.6389i	−0.590022	−	0.393227i
$733$	−27.1301			−1.00207			−0.501036	−	0.865426i	$-0.667048\pi$
$733$	−27.1301			−1.00207			−0.501036	+	0.865426i	$0.667048\pi$
$734$	12.5785	+	21.7866i	0.464281	+	0.804158i
$735$	−4.34075	−	11.9996i	−0.160111	−	0.442611i
$736$	0.572236	−	0.681965i	0.0210929	−	0.0251375i
$737$	9.52279	+	3.46601i	0.350777	+	0.127672i
$738$	35.1868	+	4.54737i	1.29524	+	0.167391i
$739$	5.62730	−	31.9140i	0.207004	−	1.17398i	−0.687252	−	0.726419i	$-0.741183\pi$
$739$	5.62730	−	31.9140i	0.207004	−	1.17398i	0.894255	−	0.447557i	$-0.147706\pi$
$740$	−2.30040	−	3.98441i	−0.0845644	−	0.146470i
$741$	5.78426	+	4.74925i	0.212490	+	0.174468i
$742$	−0.376377	+	6.69954i	−0.0138172	+	0.245948i
$743$	38.4964	−	14.0116i	1.41230	−	0.514034i	0.480494	−	0.876998i	$-0.340457\pi$
$743$	38.4964	−	14.0116i	1.41230	−	0.514034i	0.931803	+	0.362964i	$0.118235\pi$
$744$	−6.18940	+	4.54958i	−0.226914	+	0.166796i
$745$	−1.99083	−	11.2905i	−0.0729383	−	0.413654i
$746$	9.24510	+	25.4007i	0.338487	+	0.929985i
$747$	−36.8120	−	11.5106i	−1.34688	−	0.421152i
$748$	5.33743	+	9.24471i	0.195156	+	0.338020i
$749$	−1.00509	+	17.8906i	−0.0367251	+	0.653710i
$750$	16.1767	+	1.04097i	0.590688	+	0.0380107i
$751$	−21.4206	+	3.77702i	−0.781648	+	0.137826i	−0.550212	−	0.835025i	$-0.685453\pi$
$751$	−21.4206	+	3.77702i	−0.781648	+	0.137826i	−0.231435	+	0.972850i	$0.574342\pi$
$752$	−5.46321	+	3.15419i	−0.199223	+	0.115021i
$753$	−16.6565	+	4.87640i	−0.606995	+	0.177706i
$754$	0.340652	+	0.405974i	0.0124058	+	0.0147847i
$755$	0.687064	+	0.576515i	0.0250048	+	0.0209815i
$756$	11.3622	+	7.73951i	0.413240	+	0.281483i
$757$	−2.92526	+	16.5900i	−0.106320	+	0.602972i	0.884364	+	0.466797i	$0.154592\pi$
$757$	−2.92526	+	16.5900i	−0.106320	+	0.602972i	−0.990685	+	0.136175i	$0.956519\pi$
$758$	−15.2762	+	18.2055i	−0.554858	+	0.661254i
$759$	−2.80439	−	0.682698i	−0.101793	−	0.0247804i
$760$	1.88742	+	4.18139i	0.0684638	+	0.151675i
$761$	−14.7467	+	8.51399i	−0.534566	+	0.308632i	−0.742874	−	0.669431i	$-0.766538\pi$
$761$	−14.7467	+	8.51399i	−0.534566	+	0.308632i	0.208308	+	0.978063i	$0.433204\pi$
$762$	−24.1074	+	17.7204i	−0.873318	+	0.641941i
$763$	2.31640	+	2.17642i	0.0838594	+	0.0787918i
$764$	4.14504	+	4.93986i	0.149962	+	0.178718i
$765$	−6.93022	−	16.6192i	−0.250563	−	0.600868i
$766$	−15.9906	−	5.82010i	−0.577764	−	0.210289i
$767$		−	8.90893i		−	0.321683i
$768$	0.486654	+	1.66228i	0.0175606	+	0.0599823i
$769$	−0.999831	−	0.363909i	−0.0360548	−	0.0131229i	0.323930	−	0.946081i	$-0.394996\pi$
$769$	−0.999831	−	0.363909i	−0.0360548	−	0.0131229i	−0.359985	+	0.932958i	$0.617218\pi$
$770$	−5.17583	+	0.615763i	−0.186524	+	0.0221906i
$771$	−10.9744	−	2.67159i	−0.395233	−	0.0962151i
$772$	3.53350	+	2.04007i	0.127174	+	0.0734237i
$773$	−10.4877	−	3.81721i	−0.377216	−	0.137295i	0.146452	−	0.989218i	$-0.453215\pi$
$773$	−10.4877	−	3.81721i	−0.377216	−	0.137295i	−0.523668	+	0.851922i	$0.675437\pi$
$774$	13.0336	−	17.0695i	0.468482	−	0.613552i
$775$	5.90405	−	16.2213i	0.212080	−	0.582685i
$776$	5.75796	+	1.01528i	0.206699	+	0.0364465i
$777$	10.9405	+	16.7810i	0.392487	+	0.602014i
$778$		−	9.20459i		−	0.330000i
$779$	−41.8600	−	30.0864i	−1.49979	−	1.07796i
$780$	1.75581	+	0.427433i	0.0628681	+	0.0153046i
$781$	12.5925	+	2.22040i	0.450596	+	0.0794523i
$782$	4.77073	−	1.73640i	0.170601	−	0.0620937i
$783$	−2.77745	−	0.0506969i	−0.0992579	−	0.00181176i
$784$	−1.98002	+	6.71413i	−0.0707149	+	0.239790i
$785$	−13.8447	+	2.44119i	−0.494138	+	0.0871299i
$786$	−6.90761	+	28.3751i	−0.246386	+	1.01211i
$787$	23.5609	−	13.6029i	0.839857	−	0.484891i	−0.0173589	−	0.999849i	$-0.505526\pi$
$787$	23.5609	−	13.6029i	0.839857	−	0.484891i	0.857215	+	0.514958i	$0.172192\pi$
$788$	−7.30528	−	8.70610i	−0.260240	−	0.310142i
$789$	−9.60066	−	19.4100i	−0.341792	−	0.691015i
$790$	6.45991	−	11.1889i	0.229833	−	0.398083i
$791$	−20.5309	+	10.3639i	−0.729995	+	0.368499i
$792$	4.13119	−	3.80364i	0.146795	−	0.135157i
$793$	10.8126	+	1.90656i	0.383968	+	0.0677039i
$794$	3.38529	+	19.1989i	0.120139	+	0.681345i
$795$	−4.23397	−	1.85699i	−0.150163	−	0.0658606i
$796$	−15.4591	−	12.9717i	−0.547933	−	0.459770i
$797$	3.81264			0.135051			0.0675253	−	0.997718i	$-0.478490\pi$
$797$	3.81264			0.135051			0.0675253	+	0.997718i	$0.478490\pi$
$798$	−9.19135	−	17.7347i	−0.325370	−	0.627801i
$799$	−35.9756			−1.27273
$800$	−2.98167	−	2.50192i	−0.105418	−	0.0884563i
$801$	20.8249	+	2.69130i	0.735811	+	0.0950925i
$802$	−2.81272	−	15.9517i	−0.0993205	−	0.563274i
$803$	0.631853	+	0.111413i	0.0222976	+	0.00393167i
$804$	4.15737	+	8.40512i	0.146619	+	0.296426i
$805$	−0.139047	+	2.47505i	−0.00490077	+	0.0872340i
$806$	2.19821	−	3.80742i	0.0774288	−	0.134111i
$807$	−39.9346	+	19.7526i	−1.40576	+	0.695324i
$808$	5.74902	+	6.85142i	0.202250	+	0.241032i
$809$	15.2224	−	8.78867i	0.535192	−	0.308993i	−0.207936	−	0.978142i	$-0.566675\pi$
$809$	15.2224	−	8.78867i	0.535192	−	0.308993i	0.743128	+	0.669149i	$0.233341\pi$
$810$	−7.73331	+	5.46989i	−0.271721	+	0.192192i
$811$	18.4511	−	3.25343i	0.647907	−	0.114243i	0.159969	−	0.987122i	$-0.448861\pi$
$811$	18.4511	−	3.25343i	0.647907	−	0.114243i	0.487937	+	0.872879i	$0.337749\pi$
$812$	−0.408453	−	1.35418i	−0.0143339	−	0.0475225i
$813$	−18.7741	−	12.5122i	−0.658437	−	0.438823i
$814$	7.68916	−	2.79863i	0.269505	−	0.0980918i
$815$	0.489889	+	0.0863806i	0.0171601	+	0.00302578i
$816$	−2.33636	+	9.59732i	−0.0817890	+	0.335973i
$817$	−28.4415	+	12.8381i	−0.995043	+	0.449148i
$818$			24.1510i			0.844419i
$819$	−7.73450	−	1.44458i	−0.270265	−	0.0504776i
$820$	−12.2580	−	2.16141i	−0.428067	−	0.0754797i
$821$	−5.19761	+	14.2803i	−0.181398	+	0.498386i	−0.996748	−	0.0805817i	$-0.974322\pi$
$821$	−5.19761	+	14.2803i	−0.181398	+	0.498386i	0.815350	+	0.578968i	$0.196544\pi$
$822$	27.0353	−	19.8726i	0.942965	−	0.693136i
$823$	9.18551	+	3.34325i	0.320187	+	0.116538i	0.497113	−	0.867686i	$-0.334393\pi$
$823$	9.18551	+	3.34325i	0.320187	+	0.116538i	−0.176927	+	0.984224i	$0.556616\pi$
$824$	−8.05579	−	4.65101i	−0.280637	−	0.162026i
$825$	−2.98488	+	12.2613i	−0.103920	+	0.426884i
$826$	−9.37287	+	21.8523i	−0.326124	+	0.760337i
$827$	9.82428	+	3.57574i	0.341624	+	0.124341i	0.507134	−	0.861867i	$-0.330705\pi$
$827$	9.82428	+	3.57574i	0.341624	+	0.124341i	−0.165510	+	0.986208i	$0.552927\pi$
$828$	−1.44033	−	2.24905i	−0.0500549	−	0.0781599i
$829$			4.10926i			0.142720i	0.997451	+	0.0713602i	$0.0227340\pi$
$829$			4.10926i			0.142720i	−0.997451	+	0.0713602i	$0.977266\pi$
$830$	12.7151	+	4.62793i	0.441349	+	0.160638i
$831$	−0.156975	+	0.0173804i	−0.00544542	+	0.000602921i
$832$	−0.637199	−	0.759384i	−0.0220909	−	0.0263269i
$833$	−28.9237	+	27.5139i	−1.00215	+	0.953300i
$834$	−13.7497	−	18.7056i	−0.476113	−	0.647720i
$835$	−17.1444	+	9.89835i	−0.593308	+	0.342546i
$836$	−7.90663	+	2.01445i	−0.273456	+	0.0696712i
$837$	7.48529	+	21.7953i	0.258730	+	0.753357i
$838$	−10.8930	+	12.9817i	−0.376291	+	0.448446i
$839$	0.993776	−	5.63598i	0.0343090	−	0.194576i	−0.962836	−	0.270087i	$-0.912948\pi$
$839$	0.993776	−	5.63598i	0.0343090	−	0.194576i	0.997145	+	0.0755109i	$0.0240588\pi$
$840$	−3.85704	−	2.89567i	−0.133081	−	0.0999103i
$841$	−21.9963	−	18.4571i	−0.758495	−	0.636453i
$842$	−9.93906	−	11.8449i	−0.342523	−	0.408203i
$843$	−7.26163	−	24.8037i	−0.250104	−	0.854286i
$844$	3.09976	−	1.78965i	0.106698	−	0.0616023i
$845$	12.4558	−	2.19629i	0.428491	−	0.0755545i
$846$	4.14005	+	18.4667i	0.142338	+	0.634899i
$847$	−1.11245	+	19.8018i	−0.0382244	+	0.680397i
$848$	1.26809	+	2.19640i	0.0435464	+	0.0754246i
$849$	33.8477	+	22.5581i	1.16165	+	0.774194i
$850$	−7.59187	−	20.8585i	−0.260399	−	0.715441i
$851$	−0.675772	−	3.83249i	−0.0231652	−	0.131376i
$852$	7.00760	+	9.53337i	0.240076	+	0.326608i
$853$	2.42726	−	0.883452i	0.0831079	−	0.0302488i	−0.300132	−	0.953898i	$-0.597031\pi$
$853$	2.42726	−	0.883452i	0.0831079	−	0.0302488i	0.383240	+	0.923649i	$0.374808\pi$
$854$	−24.5159	−	16.0522i	−0.838917	−	0.549295i
$855$	13.6623	−	1.66056i	0.467242	−	0.0567900i
$856$	3.38635	+	5.86532i	0.115743	+	0.200473i
$857$	5.37376	−	30.4761i	0.183564	−	1.04104i	−0.744222	−	0.667932i	$-0.767180\pi$
$857$	5.37376	−	30.4761i	0.183564	−	1.04104i	0.927786	−	0.373112i	$-0.121709\pi$
$858$	−1.29091	+	2.94330i	−0.0440710	+	0.100483i
$859$	6.01925	+	2.19083i	0.205374	+	0.0747501i	0.442659	−	0.896690i	$-0.354035\pi$
$859$	6.01925	+	2.19083i	0.205374	+	0.0747501i	−0.237285	+	0.971440i	$0.576257\pi$
$860$	−4.84309	+	5.77177i	−0.165148	+	0.196816i
$861$	53.8035	+	6.50844i	1.83362	+	0.221807i
$862$	−3.90491	−	6.76351i	−0.133002	−	0.230366i
$863$	−47.7194			−1.62439			−0.812194	−	0.583388i	$-0.801727\pi$
$863$	−47.7194			−1.62439			−0.812194	+	0.583388i	$0.801727\pi$
$864$	5.19529	+	0.0948299i	0.176747	+	0.00322618i
$865$	12.3270	+	14.6907i	0.419129	+	0.499499i
$866$			13.9076i			0.472600i
$867$	−18.5686	+	19.4432i	−0.630623	+	0.660326i
$868$	−9.39758	+	7.02633i	−0.318975	+	0.238489i
$869$	17.6024	+	14.7701i	0.597119	+	0.501042i
$870$	0.972548	+	0.0625834i	0.0329725	+	0.00212177i
$871$	−4.11120	−	3.44971i	−0.139303	−	0.116889i
$872$	1.18309	+	0.208611i	0.0400645	+	0.00706445i
$873$	8.06222	−	15.5777i	0.272865	−	0.527225i
$874$	0.290528	+	3.86958i	0.00982726	+	0.130891i
$875$	24.7224	+	1.38889i	0.835769	+	0.0469531i
$876$	0.351618	+	0.478354i	0.0118801	+	0.0161621i
$877$	−14.5473	−	39.9684i	−0.491227	−	1.34964i	−0.899558	−	0.436802i	$-0.856111\pi$
$877$	−14.5473	−	39.9684i	−0.491227	−	1.34964i	0.408330	−	0.912834i	$-0.366111\pi$
$878$	−28.6338	+	5.04892i	−0.966346	+	0.170393i
$879$	27.0974	+	36.8642i	0.913972	+	1.24340i
$880$	−1.50916	+	1.26634i	−0.0508739	+	0.0426883i
$881$	−0.125123	+	0.0722396i	−0.00421549	+	0.00243381i	−0.502106	−	0.864806i	$-0.667441\pi$
$881$	−0.125123	+	0.0722396i	−0.00421549	+	0.00243381i	0.497891	+	0.867240i	$0.334108\pi$
$882$	17.4517	+	11.6806i	0.587631	+	0.393307i
$883$	19.7625	+	7.19298i	0.665062	+	0.242063i	0.652420	−	0.757857i	$-0.273754\pi$
$883$	19.7625	+	7.19298i	0.665062	+	0.242063i	0.0126418	+	0.999920i	$0.495976\pi$
$884$	−0.981677	−	5.56737i	−0.0330174	−	0.187251i
$885$	−11.8479	−	11.3149i	−0.398261	−	0.380346i
$886$		−	35.8669i		−	1.20497i
$887$	31.1086	−	26.1032i	1.04453	−	0.876461i	0.0520181	−	0.998646i	$-0.483435\pi$
$887$	31.1086	−	26.1032i	1.04453	−	0.876461i	0.992507	+	0.122185i	$0.0389902\pi$
$888$	6.93391	+	3.04116i	0.232687	+	0.102055i
$889$	−36.6031	+	27.3672i	−1.22763	+	0.917865i
$890$	−7.25472	−	1.27920i	−0.243179	−	0.0428790i
$891$	−7.19221	−	15.2342i	−0.240948	−	0.510366i
$892$	−16.4732	−	9.51083i	−0.551565	−	0.318446i
$893$	7.44376	−	26.4709i	0.249096	−	0.885813i
$894$	13.6446	+	13.0309i	0.456345	+	0.435817i
$895$	−3.31728	−	9.11414i	−0.110884	−	0.304652i
$896$	0.764022	+	2.53304i	0.0255242	+	0.0846228i
$897$	1.27194	+	0.847699i	0.0424689	+	0.0283038i
$898$	4.03241	−	22.8690i	0.134563	−	0.763147i
$899$	0.810924	−	2.22800i	0.0270458	−	0.0743078i
$900$	−9.83325	+	6.29738i	−0.327775	+	0.209913i
$901$			14.4634i			0.481847i
$902$	7.57144	−	20.8024i	0.252101	−	0.692643i
$903$	19.6962	−	26.2354i	0.655448	−	0.873058i
$904$	−4.34630	+	7.52801i	−0.144556	+	0.250378i
$905$	−7.49596	+	12.9834i	−0.249174	+	0.431582i
$906$	−1.47297	−	0.0947857i	−0.0489363	−	0.00314905i
$907$	3.55857	+	9.77708i	0.118160	+	0.324643i	0.984647	−	0.174557i	$-0.0558495\pi$
$907$	3.55857	+	9.77708i	0.118160	+	0.324643i	−0.866487	+	0.499200i	$0.833627\pi$
$908$	13.5836	+	4.94402i	0.450787	+	0.164073i
$909$	24.7648	−	10.3269i	0.821395	−	0.342523i
$910$	2.68727	+	0.631059i	0.0890822	+	0.0209194i
$911$	−30.7585			−1.01907			−0.509537	−	0.860449i	$-0.670183\pi$
$911$	−30.7585			−1.01907			−0.509537	+	0.860449i	$0.670183\pi$
$912$	−6.57828	−	3.70489i	−0.217829	−	0.122681i
$913$	−12.0328	+	20.8414i	−0.398227	+	0.689749i
$914$	5.45937	−	30.9617i	0.180580	−	1.02412i
$915$	16.2682	−	11.9581i	0.537811	−	0.395323i
$916$	−5.49773	+	4.61314i	−0.181650	+	0.152422i
$917$	−10.1983	+	43.4281i	−0.336779	+	1.43412i
$918$	25.3881	+	15.2823i	0.837932	+	0.504391i
$919$	22.1071	−	38.2906i	0.729246	−	1.26309i	−0.227956	−	0.973671i	$-0.573204\pi$
$919$	22.1071	−	38.2906i	0.729246	−	1.26309i	0.957202	−	0.289420i	$-0.0934624\pi$
$920$	0.468478	+	0.811428i	0.0154453	+	0.0267520i
$921$	4.04381	−	6.06759i	0.133248	−	0.199934i
$922$	11.0426	−	1.94711i	0.363668	−	0.0641245i
$923$	−5.86447	−	3.38585i	−0.193031	−	0.111447i
$924$	6.26299	−	5.86134i	0.206037	−	0.192824i
$925$	−16.7564	+	2.95460i	−0.550946	+	0.0971466i
$926$	2.09528	−	11.8829i	0.0688552	−	0.390497i
$927$	−20.5296	+	18.9019i	−0.674282	+	0.620821i
$928$	−0.409534	−	0.343640i	−0.0134436	−	0.0112805i
$929$	−16.1079	+	19.1966i	−0.528482	+	0.629820i	−0.962564	−	0.271053i	$-0.912628\pi$
$929$	−16.1079	+	19.1966i	−0.528482	+	0.629820i	0.434083	+	0.900873i	$0.357073\pi$
$930$	−2.27156	−	7.75903i	−0.0744874	−	0.254429i
$931$	−14.2601	−	26.9750i	−0.467355	−	0.884069i
$932$		−	10.4706i		−	0.342977i
$933$	−10.3964	−	4.55980i	−0.340364	−	0.149281i
$934$	−12.4819	+	14.8753i	−0.408419	+	0.486735i
$935$	−11.0643	+	1.95094i	−0.361842	+	0.0638026i
$936$	−2.74483	+	1.14460i	−0.0897175	+	0.0374123i
$937$	−0.329237	−	1.86720i	−0.0107557	−	0.0609987i	0.978958	−	0.204064i	$-0.0654151\pi$
$937$	−0.329237	−	1.86720i	−0.0107557	−	0.0609987i	−0.989713	+	0.143066i	$0.954304\pi$
$938$	6.45480	+	12.7869i	0.210757	+	0.417507i
$939$	−6.83345	−	1.66353i	−0.223001	−	0.0542873i
$940$	−1.15292	−	6.53853i	−0.0376041	−	0.213263i
$941$	27.6799	−	23.2262i	0.902338	−	0.757151i	−0.0683081	−	0.997664i	$-0.521760\pi$
$941$	27.6799	−	23.2262i	0.902338	−	0.757151i	0.970646	+	0.240513i	$0.0773157\pi$
$942$	15.9787	−	16.7313i	0.520615	−	0.545137i
$943$	−9.11788	−	5.26421i	−0.296919	−	0.171426i
$944$	1.56059	+	8.85054i	0.0507928	+	0.288060i
$945$	−11.7444	+	8.45129i	−0.382046	+	0.274920i
$946$	−8.61356	−	10.2652i	−0.280051	−	0.333752i
$947$	−16.8158	−	46.2010i	−0.546439	−	1.50133i	−0.838485	−	0.544925i	$-0.816558\pi$
$947$	−16.8158	−	46.2010i	−0.546439	−	1.50133i	0.292045	−	0.956404i	$-0.405664\pi$
$948$	2.33986	+	21.1330i	0.0759950	+	0.686367i
$949$	−0.294260	−	0.169891i	−0.00955208	−	0.00551490i
$950$	16.9185	−	1.27024i	0.548909	−	0.0412121i
$951$	13.2249	+	45.1726i	0.428846	+	1.46482i
$952$	−3.44939	+	14.6887i	−0.111795	+	0.476064i
$953$	0.0958865	−	0.543800i	0.00310607	−	0.0176154i	−0.983215	−	0.182449i	$-0.941598\pi$
$953$	0.0958865	−	0.543800i	0.00310607	−	0.0176154i	0.986321	+	0.164834i	$0.0527087\pi$
$954$	7.42425	−	1.66444i	0.240369	−	0.0538883i
$955$	−6.37761	+	2.32126i	−0.206375	+	0.0751142i
$956$	5.36472	−	14.7394i	0.173507	−	0.476708i
$957$	−0.409975	+	1.68409i	−0.0132526	+	0.0544390i
$958$	21.6285	+	12.4872i	0.698786	+	0.403444i
$959$	41.0487	−	30.6910i	1.32553	−	0.991065i
$960$	−1.81918	−	0.117064i	−0.0587136	−	0.00377822i
$961$	11.3309			0.365512
$962$	−4.33341			−0.139715
$963$	19.8259	−	4.44478i	0.638882	−	0.143231i
$964$	−23.3682	−	4.12044i	−0.752639	−	0.132710i
$965$	−3.28958	+	2.76028i	−0.105895	+	0.0888566i
$966$	−2.22803	−	3.41745i	−0.0716858	−	0.109955i
$967$	25.2632	−	9.19504i	0.812409	−	0.295693i	0.0977902	−	0.995207i	$-0.468823\pi$
$967$	25.2632	−	9.19504i	0.812409	−	0.295693i	0.714618	+	0.699515i	$0.246600\pi$
$968$	3.74809	+	6.49188i	0.120468	+	0.208657i
$969$	−21.9247	−	37.0551i	−0.704322	−	1.19038i
$970$	−3.07679	+	5.32916i	−0.0987898	+	0.171109i
$971$	26.3340	+	22.0968i	0.845098	+	0.709121i	0.958704	−	0.284405i	$-0.0917959\pi$
$971$	26.3340	+	22.0968i	0.845098	+	0.709121i	−0.113607	+	0.993526i	$0.536240\pi$
$972$	4.92294	−	14.7907i	0.157903	−	0.474412i
$973$	−21.2349	−	28.4013i	−0.680760	−	0.910503i
$974$	11.3090	−	13.4775i	0.362362	−	0.431847i
$975$	3.70629	−	5.56116i	0.118696	−	0.178100i
$976$	−11.0757			−0.354526
$977$	−24.7138	−	42.8056i	−0.790665	−	1.36947i	−0.925556	−	0.378612i	$-0.876402\pi$
$977$	−24.7138	−	42.8056i	−0.790665	−	1.36947i	0.134890	−	0.990861i	$-0.456932\pi$
$978$	−0.733789	+	0.362950i	−0.0234640	+	0.0116058i
$979$	4.48106	−	12.3116i	0.143215	−	0.393481i
$980$	−5.92755	−	4.37511i	−0.189349	−	0.139758i
$981$	1.65655	−	3.20075i	0.0528895	−	0.102192i
$982$	15.7252	+	18.7405i	0.501810	+	0.598034i
$983$	0.147924	−	0.0538399i	0.00471804	−	0.00171723i	−0.339660	−	0.940548i	$-0.610312\pi$
$983$	0.147924	−	0.0538399i	0.00471804	−	0.00171723i	0.344378	+	0.938831i	$0.388090\pi$
$984$	18.3608	−	9.08170i	0.585322	−	0.289514i
$985$	11.2400	−	4.09103i	0.358136	−	0.130351i
$986$	−1.04275	−	2.86492i	−0.0332078	−	0.0912378i
$987$	6.55346	+	28.1560i	0.208599	+	0.896215i
$988$	4.29959	+	0.429633i	0.136788	+	0.0136684i
$989$	−5.51928	+	3.18656i	−0.175503	+	0.101327i
$990$	2.27472	+	5.45494i	0.0722953	+	0.173369i
$991$	27.0458	−	32.2320i	0.859139	−	1.02388i	−0.140291	−	0.990110i	$-0.544804\pi$
$991$	27.0458	−	32.2320i	0.859139	−	1.02388i	0.999430	−	0.0337715i	$-0.0107518\pi$
$992$	−1.51686	+	4.16753i	−0.0481602	+	0.132319i
$993$	−8.97966	−	3.93841i	−0.284961	−	0.124982i
$994$	10.8225	+	14.4748i	0.343268	+	0.459114i
$995$	18.3938	−	10.6197i	0.583123	−	0.336666i
$996$	−21.3711	+	6.25669i	−0.677171	+	0.198251i
$997$	−30.7044	+	25.7641i	−0.972420	+	0.815957i	−0.982929	−	0.183988i	$-0.941099\pi$
$997$	−30.7044	+	25.7641i	−0.972420	+	0.815957i	0.0105090	+	0.999945i	$0.496655\pi$
$998$	27.0689	−	22.7135i	0.856851	−	0.718984i
$999$	14.9157	−	17.1310i	0.471913	−	0.542000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.641.10	yes	162
3.2	odd	2		798.2.cc.a.641.6	yes	162
7.2	even	3		798.2.bu.b.527.8	yes	162
19.15	odd	18		798.2.bu.a.53.13	✓	162
21.2	odd	6		798.2.bu.a.527.13	yes	162
57.53	even	18		798.2.bu.b.53.8	yes	162
133.72	odd	18		798.2.cc.a.737.6	yes	162
399.338	even	18	inner	798.2.cc.b.737.10	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.13	✓	162	19.15	odd	18
798.2.bu.a.527.13	yes	162	21.2	odd	6
798.2.bu.b.53.8	yes	162	57.53	even	18
798.2.bu.b.527.8	yes	162	7.2	even	3
798.2.cc.a.641.6	yes	162	3.2	odd	2
798.2.cc.a.737.6	yes	162	133.72	odd	18
798.2.cc.b.641.10	yes	162	1.1	even	1	trivial
798.2.cc.b.737.10	yes	162	399.338	even	18	inner

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.695693 + 1.58619i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.03648 - 0.182760i) q^{5} +(1.55252 - 0.767912i) q^{6} +(2.36188 - 1.19227i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.03202 - 2.20701i) q^{9} +(0.676517 + 0.806242i) q^{10} +(-1.62107 + 0.935926i) q^{11} +(-1.68290 - 0.409684i) q^{12} +(0.976245 - 0.172138i) q^{13} +(-2.57568 - 0.604855i) q^{14} +(1.01097 - 1.51692i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-5.61620 - 0.990287i) q^{17} +(0.137982 + 2.99683i) q^{18} +(1.89071 - 3.92750i) q^{19} -1.05247i q^{20} +(0.248030 + 4.57586i) q^{21} +(1.84341 + 0.325044i) q^{22} +(0.304481 - 0.836553i) q^{23} +(1.02584 + 1.39558i) q^{24} +(-3.65756 - 1.33124i) q^{25} +(-0.858496 - 0.495653i) q^{26} +(4.91441 - 1.68778i) q^{27} +(1.58430 + 2.11896i) q^{28} +(-0.502368 - 0.182847i) q^{29} +(-1.74950 + 0.512191i) q^{30} +4.43499i q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.356792 - 3.22245i) q^{33} +(3.66571 + 4.36863i) q^{34} +(-2.66595 + 0.804114i) q^{35} +(1.82062 - 2.38439i) q^{36} +(3.78576 - 2.18571i) q^{37} +(-3.97291 + 1.79331i) q^{38} +(-0.406122 + 1.66827i) q^{39} +(-0.676517 + 0.806242i) q^{40} +(2.05365 - 11.6468i) q^{41} +(2.75130 - 3.66474i) q^{42} +(-5.48400 - 4.60163i) q^{43} +(-1.20320 - 1.43392i) q^{44} +(1.70281 + 2.65890i) q^{45} +(-0.770972 + 0.445121i) q^{46} +(6.21253 - 1.09544i) q^{47} +(0.111227 - 1.72848i) q^{48} +(4.15697 - 5.63201i) q^{49} +(1.94615 + 3.37083i) q^{50} +(5.47794 - 8.21945i) q^{51} +(0.339046 + 0.931522i) q^{52} +(-0.440403 - 2.49765i) q^{53} +(-4.84954 - 1.86600i) q^{54} +(1.85126 - 0.673805i) q^{55} +(0.148403 - 2.64159i) q^{56} +(4.91442 + 5.73136i) q^{57} +(0.267305 + 0.462985i) q^{58} +(1.56059 - 8.85054i) q^{59} +(1.66943 + 0.732199i) q^{60} +(10.4078 + 3.78812i) q^{61} +(2.85076 - 3.39740i) q^{62} +(-7.43075 - 2.78997i) q^{63} +(-0.500000 - 0.866025i) q^{64} -1.04332 q^{65} +(-1.79803 + 2.69788i) q^{66} +(-3.47996 - 4.14726i) q^{67} -5.70284i q^{68} +(1.11511 + 1.06495i) q^{69} +(2.55911 + 1.09766i) q^{70} +(-5.23292 - 4.39094i) q^{71} +(-2.92734 + 0.656279i) q^{72} +(-0.262571 - 0.220323i) q^{73} +(-4.30500 - 0.759088i) q^{74} +(4.65615 - 4.87547i) q^{75} +(4.19615 + 1.17998i) q^{76} +(-2.71290 + 4.14330i) q^{77} +(1.38345 - 1.01692i) q^{78} +(-4.19853 - 11.5354i) q^{79} +(1.03648 - 0.182760i) q^{80} +(-0.741769 + 8.96938i) q^{81} +(-9.05961 + 7.60192i) q^{82} +(11.1341 - 6.42827i) q^{83} +(-4.46327 + 1.03885i) q^{84} +(5.64012 + 2.05283i) q^{85} +(1.24312 + 7.05010i) q^{86} +(0.639525 - 0.669648i) q^{87} +1.87185i q^{88} +(-5.36181 + 4.49910i) q^{89} +(0.404684 - 3.13138i) q^{90} +(2.10054 - 1.57052i) q^{91} +(0.876717 + 0.154589i) q^{92} +(-7.03475 - 3.08539i) q^{93} +(-5.46321 - 3.15419i) q^{94} +(-2.67748 + 3.72524i) q^{95} +(-1.19625 + 1.25259i) q^{96} +(1.99972 + 5.49418i) q^{97} +(-6.80461 + 1.64232i) q^{98} +(5.35965 + 1.67589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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