LMFDB - Embedded newform 117.2.r.b.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(43,117)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	117.43
Dual form			117.2.r.b.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67544 - 0.967314i) q^{2} +(-1.73126 + 0.0524448i) q^{3} +(0.871392 - 1.50930i) q^{4} +(2.26677 - 1.30872i) q^{5} +(-2.84988 + 1.76254i) q^{6} -2.32894i q^{7} +0.497616i q^{8} +(2.99450 - 0.181591i) q^{9} +(2.53189 - 4.38536i) q^{10} +(-4.66542 + 2.69358i) q^{11} +(-1.42945 + 2.65868i) q^{12} +(-1.31974 + 3.35534i) q^{13} +(-2.25282 - 3.90199i) q^{14} +(-3.85573 + 2.38461i) q^{15} +(2.22414 + 3.85232i) q^{16} +(0.835786 + 1.44762i) q^{17} +(4.84144 - 3.20086i) q^{18} +(1.90355 - 1.09901i) q^{19} -4.56164i q^{20} +(0.122141 + 4.03200i) q^{21} +(-5.21107 + 9.02585i) q^{22} -4.20875 q^{23} +(-0.0260974 - 0.861500i) q^{24} +(0.925505 - 1.60302i) q^{25} +(1.03453 + 6.89826i) q^{26} +(-5.17472 + 0.471426i) q^{27} +(-3.51506 - 2.02942i) q^{28} +(-2.86254 - 4.95807i) q^{29} +(-4.15336 + 7.72497i) q^{30} +(7.55059 - 4.35934i) q^{31} +(6.59090 + 3.80526i) q^{32} +(7.93577 - 4.90795i) q^{33} +(2.80061 + 1.61693i) q^{34} +(-3.04794 - 5.27918i) q^{35} +(2.33531 - 4.67782i) q^{36} +(-1.22479 - 0.707130i) q^{37} +(2.12618 - 3.68265i) q^{38} +(2.10884 - 5.87816i) q^{39} +(0.651240 + 1.12798i) q^{40} -1.52349i q^{41} +(4.10485 + 6.63721i) q^{42} +1.87767 q^{43} +9.38866i q^{44} +(6.55020 - 4.33059i) q^{45} +(-7.05150 + 4.07119i) q^{46} +(-4.47809 - 2.58543i) q^{47} +(-4.05258 - 6.55270i) q^{48} +1.57603 q^{49} -3.58101i q^{50} +(-1.52288 - 2.46238i) q^{51} +(3.91419 + 4.91569i) q^{52} -9.81151 q^{53} +(-8.21390 + 5.79543i) q^{54} +(-7.05029 + 12.2115i) q^{55} +1.15892 q^{56} +(-3.23789 + 2.00250i) q^{57} +(-9.59202 - 5.53796i) q^{58} +(6.59276 + 3.80633i) q^{59} +(0.239234 + 7.89737i) q^{60} -0.934170 q^{61} +(8.43369 - 14.6076i) q^{62} +(-0.422915 - 6.97401i) q^{63} +5.82698 q^{64} +(1.39966 + 9.33296i) q^{65} +(8.54835 - 15.8993i) q^{66} -2.06839i q^{67} +2.91319 q^{68} +(7.28643 - 0.220727i) q^{69} +(-10.2133 - 5.89662i) q^{70} +(-10.9702 + 6.33363i) q^{71} +(0.0903625 + 1.49011i) q^{72} -12.6627i q^{73} -2.73607 q^{74} +(-1.51822 + 2.82378i) q^{75} -3.83068i q^{76} +(6.27319 + 10.8655i) q^{77} +(-2.15281 - 11.8884i) q^{78} +(3.46731 - 6.00556i) q^{79} +(10.0832 + 5.82155i) q^{80} +(8.93405 - 1.08755i) q^{81} +(-1.47369 - 2.55251i) q^{82} +(7.95495 + 4.59279i) q^{83} +(6.19191 + 3.32910i) q^{84} +(3.78907 + 2.18762i) q^{85} +(3.14592 - 1.81630i) q^{86} +(5.21582 + 8.43357i) q^{87} +(-1.34037 - 2.32158i) q^{88} +(8.62292 + 4.97845i) q^{89} +(6.78540 - 13.5917i) q^{90} +(7.81439 + 3.07359i) q^{91} +(-3.66748 + 6.35226i) q^{92} +(-12.8434 + 7.94312i) q^{93} -10.0037 q^{94} +(2.87660 - 4.98242i) q^{95} +(-11.6101 - 6.24222i) q^{96} -2.35207i q^{97} +(2.64054 - 1.52452i) q^{98} +(-13.4815 + 8.91312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.67544	−	0.967314i	1.18471	−	0.683994i	0.227613	−	0.973752i	$-0.426908\pi$
$2$	1.67544	−	0.967314i	1.18471	−	0.683994i	0.957100	+	0.289758i	$0.0935747\pi$
$3$	−1.73126	+	0.0524448i	−0.999541	+	0.0302790i
$3$	−1.73126	+	0.0524448i	−0.999541	+	0.0302790i
$4$	0.871392	−	1.50930i	0.435696	−	0.754648i
$5$	2.26677	−	1.30872i	1.01373	−	0.585278i	0.101449	−	0.994841i	$-0.467652\pi$
$5$	2.26677	−	1.30872i	1.01373	−	0.585278i	0.912282	+	0.409563i	$0.134319\pi$
$6$	−2.84988	+	1.76254i	−1.16346	+	0.719553i
$7$		−	2.32894i		−	0.880257i	−0.897935	−	0.440129i	$-0.854933\pi$
$7$		−	2.32894i		−	0.880257i	0.897935	−	0.440129i	$-0.145067\pi$
$8$			0.497616i			0.175934i
$9$	2.99450	−	0.181591i	0.998166	−	0.0605303i
$10$	2.53189	−	4.38536i	0.800654	−	1.38677i
$11$	−4.66542	+	2.69358i	−1.40668	+	0.812145i	−0.995066	−	0.0992152i	$-0.968367\pi$
$11$	−4.66542	+	2.69358i	−1.40668	+	0.812145i	−0.411610	+	0.911360i	$0.635033\pi$
$12$	−1.42945	+	2.65868i	−0.412646	+	0.767494i
$13$	−1.31974	+	3.35534i	−0.366030	+	0.930603i
$13$	−1.31974	+	3.35534i	−0.366030	+	0.930603i
$14$	−2.25282	−	3.90199i	−0.602091	−	1.04285i
$15$	−3.85573	+	2.38461i	−0.995545	+	0.615705i
$16$	2.22414	+	3.85232i	0.556034	+	0.963079i
$17$	0.835786	+	1.44762i	0.202708	+	0.351100i	0.949400	−	0.314069i	$-0.101692\pi$
$17$	0.835786	+	1.44762i	0.202708	+	0.351100i	−0.746692	+	0.665170i	$0.768359\pi$
$18$	4.84144	−	3.20086i	1.14114	−	0.754451i
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	−0.265495	−	0.964112i	$-0.585535\pi$
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	0.702198	+	0.711982i	$0.252202\pi$
$20$		−	4.56164i		−	1.02001i
$21$	0.122141	+	4.03200i	0.0266533	+	0.879854i
$22$	−5.21107	+	9.02585i	−1.11100	+	1.92432i
$23$	−4.20875			−0.877586			−0.438793	−	0.898588i	$-0.644594\pi$
$23$	−4.20875			−0.877586			−0.438793	+	0.898588i	$0.644594\pi$
$24$	−0.0260974	−	0.861500i	−0.00532710	−	0.175853i
$25$	0.925505	−	1.60302i	0.185101	−	0.320604i
$26$	1.03453	+	6.89826i	0.202887	+	1.35286i
$27$	−5.17472	+	0.471426i	−0.995876	+	0.0907261i
$28$	−3.51506	−	2.02942i	−0.664284	−	0.383525i
$29$	−2.86254	−	4.95807i	−0.531561	−	0.920690i	−0.999321	−	0.0368352i	$-0.988272\pi$
$29$	−2.86254	−	4.95807i	−0.531561	−	0.920690i	0.467760	−	0.883855i	$-0.345061\pi$
$30$	−4.15336	+	7.72497i	−0.758296	+	1.41038i
$31$	7.55059	−	4.35934i	1.35613	−	0.782960i	0.367027	−	0.930210i	$-0.380376\pi$
$31$	7.55059	−	4.35934i	1.35613	−	0.782960i	0.989099	+	0.147251i	$0.0470424\pi$
$32$	6.59090	+	3.80526i	1.16512	+	0.672681i
$33$	7.93577	−	4.90795i	1.38144	−	0.854365i
$34$	2.80061	+	1.61693i	0.480301	+	0.277302i
$35$	−3.04794	−	5.27918i	−0.515195	−	0.892344i
$36$	2.33531	−	4.67782i	0.389218	−	0.779637i
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	0.395933	−	0.918279i	$-0.370421\pi$
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	−0.597287	+	0.802028i	$0.703755\pi$
$38$	2.12618	−	3.68265i	0.344912	−	0.597405i
$39$	2.10884	−	5.87816i	0.337684	−	0.941260i
$40$	0.651240	+	1.12798i	0.102970	+	0.178350i
$41$		−	1.52349i		−	0.237929i	−0.992899	−	0.118964i	$-0.962043\pi$
$41$		−	1.52349i		−	0.237929i	0.992899	−	0.118964i	$-0.0379574\pi$
$42$	4.10485	+	6.63721i	0.633391	+	1.02414i
$43$	1.87767			0.286342			0.143171	−	0.989698i	$-0.454270\pi$
$43$	1.87767			0.286342			0.143171	+	0.989698i	$0.454270\pi$
$44$			9.38866i			1.41539i
$45$	6.55020	−	4.33059i	0.976446	−	0.645566i
$46$	−7.05150	+	4.07119i	−1.03969	+	0.600264i
$47$	−4.47809	−	2.58543i	−0.653196	−	0.377123i	0.136483	−	0.990642i	$-0.456420\pi$
$47$	−4.47809	−	2.58543i	−0.653196	−	0.377123i	−0.789680	+	0.613519i	$0.789753\pi$
$48$	−4.05258	−	6.55270i	−0.584940	−	0.945801i
$49$	1.57603			0.225147
$50$		−	3.58101i		−	0.506432i
$51$	−1.52288	−	2.46238i	−0.213246	−	0.344802i
$52$	3.91419	+	4.91569i	0.542800	+	0.681684i
$53$	−9.81151			−1.34771			−0.673857	−	0.738862i	$-0.735364\pi$
$53$	−9.81151			−1.34771			−0.673857	+	0.738862i	$0.735364\pi$
$54$	−8.21390	+	5.79543i	−1.11777	+	0.788658i
$55$	−7.05029	+	12.2115i	−0.950661	+	1.64659i
$56$	1.15892			0.154867
$57$	−3.23789	+	2.00250i	−0.428869	+	0.265238i
$58$	−9.59202	−	5.53796i	−1.25949	−	0.727169i
$59$	6.59276	+	3.80633i	0.858304	+	0.495542i	0.863444	−	0.504445i	$-0.168303\pi$
$59$	6.59276	+	3.80633i	0.858304	+	0.495542i	−0.00513984	+	0.999987i	$0.501636\pi$
$60$	0.239234	+	7.89737i	0.0308850	+	1.01955i
$61$	−0.934170			−0.119608			−0.0598041	−	0.998210i	$-0.519048\pi$
$61$	−0.934170			−0.119608			−0.0598041	+	0.998210i	$0.519048\pi$
$62$	8.43369	−	14.6076i	1.07108	−	1.85516i
$63$	−0.422915	−	6.97401i	−0.0532822	−	0.878643i
$64$	5.82698			0.728372
$65$	1.39966	+	9.33296i	0.173606	+	1.15761i
$66$	8.54835	−	15.8993i	1.05223	−	1.95707i
$67$		−	2.06839i		−	0.252694i	−0.991986	−	0.126347i	$-0.959675\pi$
$67$		−	2.06839i		−	0.252694i	0.991986	−	0.126347i	$-0.0403253\pi$
$68$	2.91319			0.353276
$69$	7.28643	−	0.220727i	0.877184	−	0.0265725i
$70$	−10.2133	−	5.89662i	−1.22072	−	0.704781i
$71$	−10.9702	+	6.33363i	−1.30192	+	0.751664i	−0.980733	−	0.195352i	$-0.937415\pi$
$71$	−10.9702	+	6.33363i	−1.30192	+	0.751664i	−0.321187	+	0.947016i	$0.604082\pi$
$72$	0.0903625	+	1.49011i	0.0106493	+	0.175611i
$73$		−	12.6627i		−	1.48206i	−0.671473	−	0.741029i	$-0.734338\pi$
$73$		−	12.6627i		−	1.48206i	0.671473	−	0.741029i	$-0.265662\pi$
$74$	−2.73607			−0.318061
$75$	−1.51822	+	2.82378i	−0.175308	+	0.326062i
$76$		−	3.83068i		−	0.439410i
$77$	6.27319	+	10.8655i	0.714896	+	1.23824i
$78$	−2.15281	−	11.8884i	−0.243757	−	1.34610i
$79$	3.46731	−	6.00556i	0.390103	−	0.675678i	−0.602360	−	0.798225i	$-0.705773\pi$
$79$	3.46731	−	6.00556i	0.390103	−	0.675678i	0.992463	+	0.122547i	$0.0391061\pi$
$80$	10.0832	+	5.82155i	1.12734	+	0.650869i
$81$	8.93405	−	1.08755i	0.992672	−	0.120839i
$82$	−1.47369	−	2.55251i	−0.162742	−	0.281877i
$83$	7.95495	+	4.59279i	0.873169	+	0.504124i	0.868400	−	0.495864i	$-0.165149\pi$
$83$	7.95495	+	4.59279i	0.873169	+	0.504124i	0.00476882	+	0.999989i	$0.498482\pi$
$84$	6.19191	+	3.32910i	0.675593	+	0.363235i
$85$	3.78907	+	2.18762i	0.410983	+	0.237281i
$86$	3.14592	−	1.81630i	0.339233	−	0.195856i
$87$	5.21582	+	8.43357i	0.559195	+	0.904173i
$88$	−1.34037	−	2.32158i	−0.142884	−	0.247482i
$89$	8.62292	+	4.97845i	0.914028	+	0.527714i	0.881725	−	0.471764i	$-0.156383\pi$
$89$	8.62292	+	4.97845i	0.914028	+	0.527714i	0.0323029	+	0.999478i	$0.489716\pi$
$90$	6.78540	−	13.5917i	0.715244	−	1.43269i
$91$	7.81439	+	3.07359i	0.819170	+	0.322200i
$92$	−3.66748	+	6.35226i	−0.382361	+	0.662268i
$93$	−12.8434	+	7.94312i	−1.33180	+	0.823663i
$94$	−10.0037			−1.03180
$95$	2.87660	−	4.98242i	0.295133	−	0.511186i
$96$	−11.6101	−	6.24222i	−1.18495	−	0.637094i
$97$		−	2.35207i		−	0.238816i	−0.992845	−	0.119408i	$-0.961900\pi$
$97$		−	2.35207i		−	0.238816i	0.992845	−	0.119408i	$-0.0380997\pi$
$98$	2.64054	−	1.52452i	0.266735	−	0.153999i
$99$	−13.4815	+	8.91312i	−1.35494	+	0.895802i
$100$	−1.61296	−	2.79372i	−0.161296	−	0.279372i
$101$	−6.12862	−	10.6151i	−0.609820	−	1.05624i	−0.991270	−	0.131850i	$-0.957908\pi$
$101$	−6.12862	−	10.6151i	−0.609820	−	1.05624i	0.381449	−	0.924390i	$-0.375425\pi$
$102$	−4.93338	−	2.65245i	−0.488477	−	0.262632i
$103$	−5.10150	−	8.83607i	−0.502666	−	0.870643i	−0.999995	−	0.00308139i	$-0.999019\pi$
$103$	−5.10150	−	8.83607i	−0.502666	−	0.870643i	0.497329	−	0.867562i	$-0.334314\pi$
$104$	−1.66967	−	0.656723i	−0.163724	−	0.0643970i
$105$	5.55363	+	8.97977i	0.541978	+	0.876336i
$106$	−16.4386	+	9.49081i	−1.59665	+	0.921829i
$107$	2.96835	−	5.14133i	0.286961	−	0.497032i	−0.686122	−	0.727487i	$-0.740688\pi$
$107$	2.96835	−	5.14133i	0.286961	−	0.497032i	0.973083	+	0.230455i	$0.0740215\pi$
$108$	−3.79769	+	8.22099i	−0.365433	+	0.791065i
$109$			12.1858i			1.16719i	0.812046	+	0.583594i	$0.198354\pi$
$109$			12.1858i			1.16719i	−0.812046	+	0.583594i	$0.801646\pi$
$110$			27.2794i			2.60099i
$111$	2.15750	+	1.15999i	0.204781	+	0.110101i
$112$	8.97182	−	5.17988i	0.847757	−	0.489453i
$113$	0.437255	−	0.757348i	0.0411335	−	0.0712453i	−0.844726	−	0.535199i	$-0.820236\pi$
$113$	0.437255	−	0.757348i	0.0411335	−	0.0712453i	0.885859	+	0.463954i	$0.153570\pi$
$114$	−3.48783	+	6.48712i	−0.326665	+	0.607575i
$115$	−9.54029	+	5.50809i	−0.889636	+	0.513632i
$116$	−9.97759			−0.926396
$117$	−3.34266	+	10.2872i	−0.309029	+	0.951053i
$118$	14.7277			1.35579
$119$	3.37143	−	1.94650i	0.309059	−	0.178435i
$120$	−1.18662	−	1.91867i	−0.108323	−	0.175150i
$121$	9.01074	−	15.6071i	0.819158	−	1.41882i
$122$	−1.56514	+	0.903635i	−0.141701	+	0.0818113i
$123$	0.0798990	+	2.63755i	0.00720425	+	0.237820i
$124$		−	15.1948i		−	1.36453i
$125$			8.24230i			0.737214i
$126$	−7.45463	−	11.2754i	−0.664111	−	1.00450i
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	0.195808	+	0.980642i	$0.437267\pi$
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	−0.947165	+	0.320746i	$0.896066\pi$
$128$	−3.41907	+	1.97400i	−0.302206	+	0.174479i
$129$	−3.25073	+	0.0984740i	−0.286211	+	0.00867016i
$130$	11.3729	+	14.2829i	0.997472	+	1.25269i
$131$	6.88997	+	11.9338i	0.601980	+	1.04266i	0.992521	+	0.122074i	$0.0389546\pi$
$131$	6.88997	+	11.9338i	0.601980	+	1.04266i	−0.390541	+	0.920585i	$0.627712\pi$
$132$	−0.492387	−	16.2542i	−0.0428568	−	1.41474i
$133$	−2.55954	−	4.43325i	−0.221940	−	0.384411i
$134$	−2.00078	−	3.46546i	−0.172841	−	0.299370i
$135$	−11.1130	+	7.84089i	−0.956451	+	0.674836i
$136$	−0.720360	+	0.415900i	−0.0617704	+	0.0356631i
$137$		−	6.79867i		−	0.580850i	−0.956898	−	0.290425i	$-0.906203\pi$
$137$		−	6.79867i		−	0.580850i	0.956898	−	0.290425i	$-0.0937967\pi$
$138$	11.9944	−	7.41808i	1.02104	−	0.631469i
$139$	−4.68625	+	8.11682i	−0.397482	+	0.688460i	−0.993415	−	0.114575i	$-0.963449\pi$
$139$	−4.68625	+	8.11682i	−0.397482	+	0.688460i	0.595932	+	0.803035i	$0.296783\pi$
$140$	−10.6238			−0.897875
$141$	7.88831	+	4.24118i	0.664316	+	0.357172i
$142$	−12.2532	+	21.2232i	−1.02827	+	1.78101i
$143$	−2.88074	−	19.2089i	−0.240899	−	1.60633i
$144$	7.35972	+	11.1319i	0.613310	+	0.927656i
$145$	−12.9775	−	7.49254i	−1.07772	−	0.622222i
$146$	−12.2488	−	21.2156i	−1.01372	−	1.75581i
$147$	−2.72851	+	0.0826546i	−0.225044	+	0.00681724i
$148$	−2.13454	+	1.23238i	−0.175458	+	0.101301i
$149$	−13.0873	−	7.55597i	−1.07216	−	0.619009i	−0.143386	−	0.989667i	$-0.545799\pi$
$149$	−13.0873	−	7.55597i	−1.07216	−	0.619009i	−0.928769	+	0.370658i	$0.879132\pi$
$150$	0.187806	+	6.19965i	0.0153343	+	0.506200i
$151$	16.8896	+	9.75122i	1.37446	+	0.793543i	0.991486	−	0.130217i	$-0.0415673\pi$
$151$	16.8896	+	9.75122i	1.37446	+	0.793543i	0.382972	+	0.923760i	$0.374901\pi$
$152$	0.546886	+	0.947234i	0.0443583	+	0.0768308i
$153$	2.76564	+	4.18314i	0.223588	+	0.338187i
$154$	21.0207	+	12.1363i	1.69389	+	0.977970i
$155$	11.4103	−	19.7632i	0.916498	−	1.58742i
$156$	−7.03426	−	8.30505i	−0.563192	−	0.664936i
$157$	−1.95414	−	3.38466i	−0.155957	−	0.270125i	0.777450	−	0.628945i	$-0.216513\pi$
$157$	−1.95414	−	3.38466i	−0.155957	−	0.270125i	−0.933407	+	0.358819i	$0.883179\pi$
$158$		−	13.4159i		−	1.06731i
$159$	16.9862	−	0.514563i	1.34710	−	0.0408075i
$160$	19.9201			1.57482
$161$			9.80194i			0.772501i
$162$	13.9164	−	10.4641i	1.09338	−	0.822141i
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	−0.723541	−	0.690281i	$-0.757487\pi$
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	0.236030	+	0.971746i	$0.424154\pi$
$164$	−2.29939	−	1.32756i	−0.179552	−	0.103665i
$165$	11.5654	−	21.5109i	0.900368	−	1.67462i
$166$	17.7707			1.37927
$167$		−	5.99332i		−	0.463777i	−0.972742	−	0.231889i	$-0.925509\pi$
$167$		−	5.99332i		−	0.463777i	0.972742	−	0.231889i	$-0.0744905\pi$
$168$	−2.00638	+	0.0607793i	−0.154796	+	0.00468922i
$169$	−9.51658	−	8.85634i	−0.732045	−	0.681257i
$170$	8.46447			0.649195
$171$	5.50059	−	3.63666i	0.420641	−	0.278102i
$172$	1.63619	−	2.83396i	0.124758	−	0.216087i
$173$	−2.18231			−0.165918			−0.0829591	−	0.996553i	$-0.526437\pi$
$173$	−2.18231			−0.165918			−0.0829591	+	0.996553i	$0.526437\pi$
$174$	16.8967	+	9.08457i	1.28093	+	0.688699i
$175$	−3.73334	−	2.15545i	−0.282214	−	0.162936i
$176$	−20.7530	−	11.9818i	−1.56432	−	0.903160i
$177$	−11.6134	−	6.24398i	−0.872915	−	0.469326i
$178$	19.2629			1.44381
$179$	−1.46465	+	2.53684i	−0.109473	+	0.189612i	−0.915557	−	0.402189i	$-0.868250\pi$
$179$	−1.46465	+	2.53684i	−0.109473	+	0.189612i	0.806084	+	0.591801i	$0.201583\pi$
$180$	−0.828352	−	13.6598i	−0.0617417	−	1.01814i
$181$	23.2244			1.72625			0.863127	−	0.504986i	$-0.168502\pi$
$181$	23.2244			1.72625			0.863127	+	0.504986i	$0.168502\pi$
$182$	16.0656	−	2.40935i	1.19086	−	0.178593i
$183$	1.61729	−	0.0489924i	0.119553	−	0.00362162i
$184$		−	2.09434i		−	0.154397i
$185$	−3.70175			−0.272158
$186$	−13.8348	+	25.7318i	−1.01442	+	1.88675i
$187$	−7.79858	−	4.50251i	−0.570289	−	0.329256i
$188$	−7.80434	+	4.50584i	−0.569190	+	0.328622i
$189$	1.09792	+	12.0516i	0.0798623	+	0.876627i
$190$		−	11.1303i		−	0.807478i
$191$	9.62083			0.696139			0.348070	−	0.937469i	$-0.386837\pi$
$191$	9.62083			0.696139			0.348070	+	0.937469i	$0.386837\pi$
$192$	−10.0880	+	0.305595i	−0.728038	+	0.0220544i
$193$			20.0953i			1.44649i	0.690592	+	0.723245i	$0.257350\pi$
$193$			20.0953i			1.44649i	−0.690592	+	0.723245i	$0.742650\pi$
$194$	−2.27519	−	3.94074i	−0.163349	−	0.282929i
$195$	−2.91263	−	16.0843i	−0.208578	−	1.15182i
$196$	1.37334	−	2.37870i	0.0980958	−	0.169907i
$197$	10.3727	+	5.98869i	0.739025	+	0.426676i	0.821715	−	0.569899i	$-0.193018\pi$
$197$	10.3727	+	5.98869i	0.739025	+	0.426676i	−0.0826895	+	0.996575i	$0.526351\pi$
$198$	−13.9655	+	27.9742i	−0.992488	+	1.98804i
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	−0.988054	−	0.154108i	$-0.950750\pi$
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	0.360566	−	0.932734i	$-0.382584\pi$
$200$	0.797688	+	0.460546i	0.0564051	+	0.0325655i
$201$	0.108476	+	3.58092i	0.00765134	+	0.252578i
$202$	−20.5362	−	11.8566i	−1.44492	−	0.834227i
$203$	−11.5471	+	6.66670i	−0.810444	+	0.467910i
$204$	−5.04348	+	0.152782i	−0.353114	+	0.0106969i
$205$	−1.99382	−	3.45340i	−0.139254	−	0.241196i
$206$	−17.0945	−	9.86951i	−1.19103	−	0.687642i
$207$	−12.6031	+	0.764272i	−0.875977	+	0.0531205i
$208$	−15.8611	+	2.37867i	−1.09977	+	0.164931i
$209$	−5.92055	+	10.2547i	−0.409533	+	0.709333i
$210$	17.9910	+	9.67294i	1.24150	+	0.667496i
$211$	22.1908			1.52768			0.763840	−	0.645405i	$-0.223311\pi$
$211$	22.1908			1.52768			0.763840	+	0.645405i	$0.223311\pi$
$212$	−8.54967	+	14.8085i	−0.587194	+	1.01705i
$213$	18.6600	−	11.5405i	1.27856	−	0.790740i
$214$		−	11.4853i		−	0.785120i
$215$	4.25625	−	2.45735i	0.290274	−	0.167590i
$216$	−0.234589	−	2.57502i	−0.0159618	−	0.175208i
$217$	−10.1526	−	17.5849i	−0.689206	−	1.19374i
$218$	11.7875	+	20.4165i	0.798349	+	1.38278i
$219$	0.664094	+	21.9224i	0.0448753	+	1.48138i
$220$	12.2871	+	21.2820i	0.828399	+	1.43483i
$221$	−5.96029	+	0.893859i	−0.400932	+	0.0601275i
$222$	4.73684	−	0.143493i	0.317916	−	0.00963059i
$223$	3.75121	−	2.16576i	0.251199	−	0.145030i	−0.369114	−	0.929384i	$-0.620339\pi$
$223$	3.75121	−	2.16576i	0.251199	−	0.145030i	0.620313	+	0.784354i	$0.287005\pi$
$224$	8.86223	−	15.3498i	0.592132	−	1.02560i
$225$	2.48033	−	4.96831i	0.165355	−	0.331221i
$226$		−	1.69185i		−	0.112540i
$227$			2.95993i			0.196458i	0.995164	+	0.0982289i	$0.0313177\pi$
$227$			2.95993i			0.196458i	−0.995164	+	0.0982289i	$0.968682\pi$
$228$	0.200900	+	6.63190i	0.0133049	+	0.439208i
$229$	−9.82313	+	5.67139i	−0.649131	+	0.374776i	−0.788123	−	0.615518i	$-0.788947\pi$
$229$	−9.82313	+	5.67139i	−0.649131	+	0.374776i	0.138992	+	0.990293i	$0.455614\pi$
$230$	−10.6561	+	18.4569i	−0.702642	+	1.21701i
$231$	−11.4303	−	18.4819i	−0.752061	−	1.21602i
$232$	2.46721	−	1.42445i	0.161980	−	0.0935195i
$233$	2.31530			0.151680			0.0758401	−	0.997120i	$-0.475836\pi$
$233$	2.31530			0.151680			0.0758401	+	0.997120i	$0.475836\pi$
$234$	4.35055	+	20.4690i	0.284404	+	1.33810i
$235$	−13.5344			−0.882887
$236$	11.4898	−	6.63362i	0.747920	−	0.431812i
$237$	−5.68784	+	10.5790i	−0.369465	+	0.687180i
$238$	3.76575	−	6.52246i	0.244097	−	0.422789i
$239$	17.6746	−	10.2044i	1.14327	−	0.660069i	0.196034	−	0.980597i	$-0.437194\pi$
$239$	17.6746	−	10.2044i	1.14327	−	0.660069i	0.947239	+	0.320528i	$0.103860\pi$
$240$	−17.7619	−	9.54978i	−1.14653	−	0.616436i
$241$			8.74021i			0.563007i	0.959560	+	0.281503i	$0.0908330\pi$
$241$			8.74021i			0.563007i	−0.959560	+	0.281503i	$0.909167\pi$
$242$		−	34.8649i		−	2.24120i
$243$	−15.4101	+	2.35137i	−0.988558	+	0.150840i
$244$	−0.814028	+	1.40994i	−0.0521128	+	0.0902621i
$245$	3.57250	−	2.06258i	0.228239	−	0.131774i
$246$	2.68520	+	4.34176i	0.171202	+	0.276820i
$247$	1.17538	+	7.83745i	0.0747873	+	0.498685i
$248$	2.16927	+	3.75729i	0.137749	+	0.238588i
$249$	−14.0129	−	7.53410i	−0.888033	−	0.477454i
$250$	7.97290	+	13.8095i	0.504250	+	0.873387i
$251$	−9.27060	−	16.0571i	−0.585155	−	1.01352i	−0.994856	−	0.101298i	$-0.967700\pi$
$251$	−9.27060	−	16.0571i	−0.585155	−	1.01352i	0.409701	−	0.912220i	$-0.365633\pi$
$252$	−10.8944	−	5.43880i	−0.686281	−	0.342612i
$253$	19.6356	−	11.3366i	1.23448	−	0.712727i
$254$			32.7624i			2.05570i
$255$	−6.67459	−	3.58862i	−0.417979	−	0.224728i
$256$	−9.64593	+	16.7072i	−0.602871	+	1.04420i
$257$	14.3767			0.896794			0.448397	−	0.893834i	$-0.351995\pi$
$257$	14.3767			0.896794			0.448397	+	0.893834i	$0.351995\pi$
$258$	−5.35113	+	3.30946i	−0.333147	+	0.206038i
$259$	−1.64687	+	2.85245i	−0.102331	+	0.177243i
$260$	15.3058	+	6.02017i	0.949228	+	0.373355i
$261$	−9.47222	−	14.3271i	−0.586316	−	0.886827i
$262$	23.0874	+	13.3295i	1.42635	+	0.823501i
$263$	−2.80356	−	4.85591i	−0.172875	−	0.299428i	0.766549	−	0.642186i	$-0.221972\pi$
$263$	−2.80356	−	4.85591i	−0.172875	−	0.299428i	−0.939424	+	0.342758i	$0.888639\pi$
$264$	2.44228	+	3.94896i	0.150312	+	0.243042i
$265$	−22.2405	+	12.8405i	−1.36622	+	0.788788i
$266$	−8.57668	−	4.95175i	−0.525870	−	0.303611i
$267$	−15.1896	−	8.16674i	−0.929587	−	0.499796i
$268$	−3.12181	−	1.80238i	−0.190695	−	0.110098i
$269$	−1.16337	−	2.01502i	−0.0709319	−	0.122858i	0.828378	−	0.560169i	$-0.189264\pi$
$269$	−1.16337	−	2.01502i	−0.0709319	−	0.122858i	−0.899310	+	0.437312i	$0.855931\pi$
$270$	−11.0345	+	23.8866i	−0.671535	+	1.45369i
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	0.547766	−	0.836631i	$-0.315478\pi$
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	−0.450661	+	0.892695i	$0.648812\pi$
$272$	−3.71780	+	6.43942i	−0.225425	+	0.390447i
$273$	−13.6899	−	4.91136i	−0.828551	−	0.297249i
$274$	−6.57645	−	11.3907i	−0.397298	−	0.688140i
$275$			9.97168i			0.601315i
$276$	6.01620	−	11.1897i	0.362133	−	0.673542i
$277$	−0.535705			−0.0321874			−0.0160937	−	0.999870i	$-0.505123\pi$
$277$	−0.535705			−0.0321874			−0.0160937	+	0.999870i	$0.505123\pi$
$278$			18.1323i			1.08750i
$279$	21.8186	−	14.4251i	1.30625	−	0.863611i
$280$	2.62700	−	1.51670i	0.156993	−	0.0906402i
$281$	18.0707	+	10.4331i	1.07801	+	0.622387i	0.930358	−	0.366653i	$-0.119496\pi$
$281$	18.0707	+	10.4331i	1.07801	+	0.622387i	0.147648	+	0.989040i	$0.452830\pi$
$282$	17.3189	−	0.524641i	1.03133	−	0.0312419i
$283$	−8.73057			−0.518979			−0.259489	−	0.965746i	$-0.583554\pi$
$283$	−8.73057			−0.518979			−0.259489	+	0.965746i	$0.583554\pi$
$284$			22.0763i			1.30999i
$285$	−4.71884	+	8.77671i	−0.279520	+	0.519888i
$286$	−23.4075	−	29.3967i	−1.38411	−	1.73826i
$287$	−3.54811			−0.209439
$288$	20.4274	+	10.1980i	1.20370	+	0.600923i
$289$	7.10292	−	12.3026i	0.417819	−	0.723684i
$290$	−28.9906			−1.70238
$291$	0.123354	+	4.07203i	0.00723112	+	0.238707i
$292$	−19.1118	−	11.0342i	−1.11843	−	0.645727i
$293$	2.63922	+	1.52376i	0.154185	+	0.0890188i	0.575107	−	0.818078i	$-0.304960\pi$
$293$	2.63922	+	1.52376i	0.154185	+	0.0890188i	−0.420922	+	0.907097i	$0.638294\pi$
$294$	−4.49150	+	2.77781i	−0.261949	+	0.162005i
$295$	19.9257			1.16012
$296$	0.351879	−	0.609473i	0.0204526	−	0.0354249i
$297$	22.8724	−	16.1379i	1.32719	−	0.936418i
$298$	−29.2360			−1.69359
$299$	5.55446	−	14.1218i	0.321222	−	0.816684i
$300$	2.93896	+	4.75206i	0.169681	+	0.274360i
$301$		−	4.37298i		−	0.252055i
$302$	37.7300			2.17112
$303$	11.1669	+	18.0560i	0.641523	+	1.03729i
$304$	8.46748	+	4.88870i	0.485644	+	0.280386i
$305$	−2.11755	+	1.22257i	−0.121251	+	0.0700040i
$306$	8.68005	+	4.33334i	0.496206	+	0.247721i
$307$			22.0214i			1.25683i	0.777880	+	0.628413i	$0.216295\pi$
$307$			22.0214i			1.25683i	−0.777880	+	0.628413i	$0.783705\pi$
$308$	21.8656			1.24591
$309$	9.29542	+	15.0299i	0.528798	+	0.855024i
$310$		−	44.1494i		−	2.50752i
$311$	3.39883	+	5.88694i	0.192730	+	0.333818i	0.946154	−	0.323717i	$-0.104933\pi$
$311$	3.39883	+	5.88694i	0.192730	+	0.333818i	−0.753424	+	0.657535i	$0.771599\pi$
$312$	2.92507	+	1.04939i	0.165599	+	0.0594100i
$313$	3.05617	−	5.29344i	0.172745	−	0.299203i	−0.766634	−	0.642085i	$-0.778070\pi$
$313$	3.05617	−	5.29344i	0.172745	−	0.299203i	0.939379	+	0.342882i	$0.111403\pi$
$314$	−6.54806	−	3.78052i	−0.369528	−	0.213347i
$315$	−10.0857	−	15.2550i	−0.568264	−	0.859523i
$316$	−6.04278	−	10.4664i	−0.339933	−	0.588781i
$317$	−15.0342	−	8.67999i	−0.844404	−	0.487517i	0.0143546	−	0.999897i	$-0.495431\pi$
$317$	−15.0342	−	8.67999i	−0.844404	−	0.487517i	−0.858759	+	0.512380i	$0.828764\pi$
$318$	27.9616	−	17.2931i	1.56801	−	0.969751i
$319$	26.7099	+	15.4210i	1.49547	+	0.863409i
$320$	13.2084	−	7.62589i	0.738374	−	0.426300i
$321$	−4.86934	+	9.05664i	−0.271780	+	0.505493i
$322$	9.48156	+	16.4225i	0.528386	+	0.915192i
$323$	3.18191	+	1.83708i	0.177046	+	0.102218i
$324$	6.14363	−	14.4318i	0.341313	−	0.801767i
$325$	4.15725	+	5.22095i	0.230603	+	0.289606i
$326$	−6.95209	+	12.0414i	−0.385041	+	0.666910i
$327$	−0.639082	−	21.0967i	−0.0353413	−	1.16665i
$328$	0.758111			0.0418597
$329$	−6.02130	+	10.4292i	−0.331965	+	0.574981i
$330$	−1.43066	−	47.2276i	−0.0787554	−	2.59979i
$331$			19.0684i			1.04810i	0.851689	+	0.524048i	$0.175579\pi$
$331$			19.0684i			1.04810i	−0.851689	+	0.524048i	$0.824421\pi$
$332$	13.8638	−	8.00425i	0.760873	−	0.439290i
$333$	−3.79603	−	1.89509i	−0.208021	−	0.103850i
$334$	−5.79743	−	10.0414i	−0.317221	−	0.549443i
$335$	−2.70695	−	4.68857i	−0.147896	−	0.256164i
$336$	−15.2609	+	9.43823i	−0.832548	+	0.514898i
$337$	−12.0678	−	20.9020i	−0.657372	−	1.13860i	−0.981293	−	0.192518i	$-0.938335\pi$
$337$	−12.0678	−	20.9020i	−0.657372	−	1.13860i	0.323921	−	0.946084i	$-0.394999\pi$
$338$	−24.5113	−	5.63271i	−1.33324	−	0.306379i
$339$	−0.717281	+	1.33409i	−0.0389574	+	0.0724581i
$340$	6.60354	−	3.81255i	0.358127	−	0.206765i
$341$	−23.4844	+	40.6762i	−1.27175	+	2.20274i
$342$	5.69811	−	11.4138i	0.308118	−	0.617187i
$343$		−	19.9731i		−	1.07844i
$344$			0.934358i			0.0503772i
$345$	16.2278	−	10.0363i	0.873676	−	0.540334i
$346$	−3.65633	+	2.11098i	−0.196565	+	0.113487i
$347$	−0.514596	+	0.891307i	−0.0276250	+	0.0478479i	−0.879507	−	0.475885i	$-0.842128\pi$
$347$	−0.514596	+	0.891307i	−0.0276250	+	0.0478479i	0.851882	+	0.523733i	$0.175461\pi$
$348$	17.2738	−	0.523273i	0.925971	−	0.0280504i
$349$	−24.5441	+	14.1705i	−1.31381	+	0.758531i	−0.982725	−	0.185069i	$-0.940749\pi$
$349$	−24.5441	+	14.1705i	−1.31381	+	0.758531i	−0.331088	+	0.943600i	$0.607416\pi$
$350$	−8.33997			−0.445790
$351$	5.24749	−	17.9851i	0.280090	−	0.959974i
$352$	−40.9991			−2.18526
$353$	−6.68067	+	3.85709i	−0.355576	+	0.205292i	−0.667138	−	0.744934i	$-0.732481\pi$
$353$	−6.68067	+	3.85709i	−0.355576	+	0.205292i	0.311562	+	0.950226i	$0.399148\pi$
$354$	−25.4974	+	0.772390i	−1.35517	+	0.0410521i
$355$	−16.5779	+	28.7138i	−0.879865	+	1.52397i
$356$	15.0279	−	8.67636i	0.796477	−	0.459846i
$357$	−5.73473	+	3.54670i	−0.303514	+	0.187711i
$358$			5.66709i			0.299515i
$359$			6.01669i			0.317549i	0.987315	+	0.158774i	$0.0507543\pi$
$359$			6.01669i			0.317549i	−0.987315	+	0.158774i	$0.949246\pi$
$360$	2.15497	+	3.25948i	0.113577	+	0.171790i
$361$	−7.08434	+	12.2704i	−0.372860	+	0.645813i
$362$	38.9110	−	22.4653i	2.04512	−	1.18075i
$363$	−14.7814	+	27.4924i	−0.775822	+	1.44298i
$364$	11.4484	−	9.11591i	0.600057	−	0.477804i
$365$	−16.5720	−	28.7035i	−0.867416	−	1.50241i
$366$	2.66227	−	1.64651i	0.139159	−	0.0860644i
$367$	−12.1955	−	21.1232i	−0.636600	−	1.10262i	−0.986174	−	0.165715i	$-0.947007\pi$
$367$	−12.1955	−	21.1232i	−0.636600	−	1.10262i	0.349573	−	0.936909i	$-0.386327\pi$
$368$	−9.36084	−	16.2134i	−0.487967	−	0.845184i
$369$	−0.276651	−	4.56208i	−0.0144019	−	0.237492i
$370$	−6.20204	+	3.58075i	−0.322429	+	0.186154i
$371$			22.8504i			1.18634i
$372$	0.796887	+	26.3060i	0.0413167	+	1.36390i
$373$	−2.68816	+	4.65604i	−0.139188	+	0.241080i	−0.927189	−	0.374593i	$-0.877783\pi$
$373$	−2.68816	+	4.65604i	−0.139188	+	0.241080i	0.788002	+	0.615673i	$0.211116\pi$
$374$	−17.4214			−0.900838
$375$	−0.432266	−	14.2695i	−0.0223221	−	0.736876i
$376$	1.28655	−	2.22837i	0.0663487	−	0.114919i
$377$	20.4138	−	3.06144i	1.05136	−	0.157672i
$378$	13.4972	+	19.1297i	0.694222	+	0.983926i
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.912296	−	0.409532i	$-0.134308\pi$
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.101482	+	0.994837i	$0.467641\pi$
$380$	−5.01330	−	8.68329i	−0.257177	−	0.445443i
$381$	13.8900	−	25.8345i	0.711608	−	1.32354i
$382$	16.1191	−	9.30637i	0.824725	−	0.476155i
$383$	21.5539	+	12.4441i	1.10135	+	0.635866i	0.936576	−	0.350465i	$-0.113976\pi$
$383$	21.5539	+	12.4441i	1.10135	+	0.635866i	0.164776	+	0.986331i	$0.447310\pi$
$384$	5.81576	−	3.59682i	0.296784	−	0.183549i
$385$	28.4398	+	16.4197i	1.44943	+	0.836826i
$386$	19.4384	+	33.6684i	0.989390	+	1.71367i
$387$	5.62268	−	0.340968i	0.285817	−	0.0173324i
$388$	−3.54996	−	2.04957i	−0.180222	−	0.104051i
$389$	−7.53659	+	13.0537i	−0.382120	+	0.661851i	−0.991365	−	0.131131i	$-0.958139\pi$
$389$	−7.53659	+	13.0537i	−0.382120	+	0.661851i	0.609245	+	0.792982i	$0.291473\pi$
$390$	−20.4385	−	24.1309i	−1.03495	−	1.22191i
$391$	−3.51762	−	6.09269i	−0.177894	−	0.308121i
$392$			0.784257i			0.0396110i
$393$	−12.5542	−	20.2991i	−0.633274	−	1.02395i
$394$	23.1718			1.16738
$395$		−	18.1510i		−	0.913275i
$396$	1.70490	+	28.1143i	0.0856742	+	1.41280i
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	−0.557461	−	0.830203i	$-0.688224\pi$
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	0.440246	+	0.897877i	$0.354891\pi$
$398$	−29.6613	−	17.1250i	−1.48679	−	0.858397i
$399$	4.66371	+	7.54085i	0.233478	+	0.377515i
$400$	8.23379			0.411690
$401$			1.21678i			0.0607632i	0.999538	+	0.0303816i	$0.00967226\pi$
$401$			1.21678i			0.0607632i	−0.999538	+	0.0303816i	$0.990328\pi$
$402$	3.64561	+	5.89467i	0.181827	+	0.293999i
$403$	4.66224	+	31.0880i	0.232242	+	1.54860i
$404$	−21.3617			−1.06279
$405$	18.8282	−	14.1574i	0.935579	−	0.703487i
$406$	−12.8976	+	22.3393i	−0.640096	+	1.10868i
$407$	7.61885			0.377652
$408$	1.22532	−	0.757809i	0.0606622	−	0.0375171i
$409$	−29.7979	−	17.2038i	−1.47341	−	0.850675i	−0.473860	−	0.880600i	$-0.657140\pi$
$409$	−29.7979	−	17.2038i	−1.47341	−	0.850675i	−0.999552	+	0.0299257i	$0.990473\pi$
$410$	−6.68104	−	3.85730i	−0.329953	−	0.190499i
$411$	0.356555	+	11.7703i	0.0175876	+	0.580584i
$412$	−17.7816			−0.876039
$413$	8.86472	−	15.3542i	0.436205	−	0.755528i
$414$	−20.3764	+	13.4717i	−1.00145	+	0.662096i
$415$	24.0427			1.18021
$416$	−21.4662	+	17.0928i	−1.05247	+	0.838041i
$417$	7.68741	−	14.2981i	0.376454	−	0.700179i
$418$			22.9081i			1.12047i
$419$	−21.7922			−1.06462			−0.532310	−	0.846549i	$-0.678676\pi$
$419$	−21.7922			−1.06462			−0.532310	+	0.846549i	$0.678676\pi$
$420$	18.3925	−	0.557163i	0.897463	−	0.0271868i
$421$	−22.4288	−	12.9493i	−1.09311	−	0.631109i	−0.158710	−	0.987325i	$-0.550733\pi$
$421$	−22.4288	−	12.9493i	−1.09311	−	0.631109i	−0.934404	+	0.356216i	$0.884067\pi$
$422$	37.1794	−	21.4655i	1.80986	−	1.04492i
$423$	−13.8791	−	6.92887i	−0.674826	−	0.336893i
$424$		−	4.88236i		−	0.237108i
$425$	3.09409			0.150086
$426$	20.1004	−	37.3854i	0.973869	−	1.81133i
$427$			2.17563i			0.105286i
$428$	−5.17320	−	8.96024i	−0.250056	−	0.433110i
$429$	5.99470	+	33.1044i	0.289427	+	1.59830i
$430$	4.75405	−	8.23426i	0.229261	−	0.397091i
$431$	24.4387	+	14.1097i	1.17717	+	0.679639i	0.955358	−	0.295450i	$-0.0954697\pi$
$431$	24.4387	+	14.1097i	1.17717	+	0.679639i	0.221812	+	0.975090i	$0.428803\pi$
$432$	−13.3254	−	18.8861i	−0.641117	−	0.908660i
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	0.984099	+	0.177622i	$0.0568403\pi$
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	−0.338225	+	0.941065i	$0.609826\pi$
$434$	−34.0202	−	19.6416i	−1.63302	−	0.942826i
$435$	22.8603	+	12.2909i	1.09607	+	0.589304i
$436$	18.3920	+	10.6186i	0.880815	+	0.508539i
$437$	−8.01155	+	4.62547i	−0.383245	+	0.221266i
$438$	22.3185	+	36.0872i	1.06642	+	1.72431i
$439$	−0.847943	−	1.46868i	−0.0404701	−	0.0700963i	0.845081	−	0.534639i	$-0.179552\pi$
$439$	−0.847943	−	1.46868i	−0.0404701	−	0.0700963i	−0.885551	+	0.464542i	$0.846219\pi$
$440$	−6.07662	−	3.50834i	−0.289691	−	0.167253i
$441$	4.71942	−	0.286193i	0.224734	−	0.0136282i
$442$	−9.12144	+	7.26307i	−0.433863	+	0.345469i
$443$	1.72899	−	2.99471i	0.0821470	−	0.142283i	−0.822025	−	0.569452i	$-0.807156\pi$
$443$	1.72899	−	2.99471i	0.0821470	−	0.142283i	0.904172	+	0.427169i	$0.140489\pi$
$444$	3.63080	−	2.24550i	0.172310	−	0.106567i
$445$	26.0616			1.23544
$446$	4.18994	−	7.25719i	0.198399	−	0.343638i
$447$	23.0538	+	12.3950i	1.09041	+	0.586261i
$448$		−	13.5707i		−	0.641155i
$449$	−24.3114	+	14.0362i	−1.14732	+	0.662408i	−0.948234	−	0.317574i	$-0.897132\pi$
$449$	−24.3114	+	14.0362i	−1.14732	+	0.662408i	−0.199090	+	0.979981i	$0.563799\pi$
$450$	−0.650280	−	10.7233i	−0.0306545	−	0.505503i
$451$	4.10363	+	7.10770i	0.193233	+	0.334689i
$452$	−0.762041	−	1.31989i	−0.0358434	−	0.0620826i
$453$	−29.7517	−	15.9961i	−1.39785	−	0.751562i
$454$	2.86319	+	4.95918i	0.134376	+	0.232746i
$455$	21.7359	−	3.25972i	1.01900	−	0.152818i
$456$	−0.996477	−	1.61122i	−0.0466643	−	0.0754525i
$457$	−8.53408	+	4.92715i	−0.399207	+	0.230482i	−0.686142	−	0.727468i	$-0.740697\pi$
$457$	−8.53408	+	4.92715i	−0.399207	+	0.230482i	0.286935	+	0.957950i	$0.407364\pi$
$458$	−10.9720	+	19.0041i	−0.512689	+	0.888004i
$459$	−5.00741	−	7.09704i	−0.233726	−	0.331261i
$460$			19.1988i			0.895150i
$461$		−	4.13747i		−	0.192701i	−0.995347	−	0.0963506i	$-0.969283\pi$
$461$		−	4.13747i		−	0.192701i	0.995347	−	0.0963506i	$-0.0307170\pi$
$462$	−37.0287	−	19.9086i	−1.72273	−	0.926232i
$463$	1.95999	−	1.13160i	0.0910883	−	0.0525898i	−0.453764	−	0.891122i	$-0.649919\pi$
$463$	1.95999	−	1.13160i	0.0910883	−	0.0525898i	0.544852	+	0.838532i	$0.316586\pi$
$464$	12.7334	−	22.0548i	0.591132	−	1.02387i
$465$	−18.7177	+	34.8137i	−0.868013	+	1.61444i
$466$	3.87913	−	2.23962i	0.179697	−	0.103748i
$467$	−11.5713			−0.535454			−0.267727	−	0.963495i	$-0.586273\pi$
$467$	−11.5713			−0.535454			−0.267727	+	0.963495i	$0.586273\pi$
$468$	12.6137	+	14.0093i	0.583067	+	0.647578i
$469$	−4.81716			−0.222436
$470$	−22.6760	+	13.0920i	−1.04597	+	0.603890i
$471$	3.56062	+	5.75723i	0.164065	+	0.265279i
$472$	−1.89409	+	3.28066i	−0.0871826	+	0.151005i
$473$	−8.76011	+	5.05765i	−0.402790	+	0.232551i
$474$	0.703595	+	23.2264i	0.0323172	+	1.06682i
$475$		−	4.06856i		−	0.186679i
$476$		−	6.78465i		−	0.310974i
$477$	−29.3806	+	1.78168i	−1.34524	+	0.0815776i
$478$	19.7417	−	34.1937i	0.902967	−	1.56398i
$479$	25.0597	−	14.4682i	1.14500	−	0.661069i	0.197340	−	0.980335i	$-0.436770\pi$
$479$	25.0597	−	14.4682i	1.14500	−	0.661069i	0.947665	+	0.319266i	$0.103436\pi$
$480$	−34.4868	+	1.04471i	−1.57410	+	0.0476841i
$481$	3.98906	−	3.17634i	0.181885	−	0.144829i
$482$	8.45453	+	14.6437i	0.385093	+	0.667001i
$483$	−0.514061	−	16.9697i	−0.0233906	−	0.772147i
$484$	−15.7038	−	27.1998i	−0.713808	−	1.23635i
$485$	−3.07820	−	5.33160i	−0.139774	−	0.242095i
$486$	−23.5441	+	18.8460i	−1.06798	+	0.854871i
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	−0.415061	−	0.909794i	$-0.636240\pi$
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	0.580374	+	0.814350i	$0.302906\pi$
$488$		−	0.464857i		−	0.0210431i
$489$	10.5871	−	6.54770i	0.478765	−	0.296097i
$490$	3.99033	−	6.91146i	0.180265	−	0.312228i
$491$	13.8719			0.626032			0.313016	−	0.949748i	$-0.398661\pi$
$491$	13.8719			0.626032			0.313016	+	0.949748i	$0.398661\pi$
$492$	4.05046	+	2.17775i	0.182609	+	0.0981804i
$493$	4.78495	−	8.28777i	0.215503	−	0.373262i
$494$	9.55054	+	11.9942i	0.429699	+	0.539644i
$495$	−18.8946	+	37.8475i	−0.849249	+	1.70112i
$496$	33.5871	+	19.3915i	1.50810	+	0.870704i
$497$	14.7507	+	25.5489i	0.661658	+	1.14602i
$498$	−30.7656	+	0.931980i	−1.37864	+	0.0417630i
$499$	9.03377	−	5.21565i	0.404407	−	0.233484i	−0.283977	−	0.958831i	$-0.591654\pi$
$499$	9.03377	−	5.21565i	0.404407	−	0.233484i	0.688384	+	0.725347i	$0.258321\pi$
$500$	12.4401	+	7.18228i	0.556337	+	0.321201i
$501$	0.314319	+	10.3760i	0.0140427	+	0.463565i
$502$	−31.0646	−	17.9352i	−1.38648	−	0.800485i
$503$	−13.8296	−	23.9535i	−0.616630	−	1.06803i	−0.990096	−	0.140390i	$-0.955164\pi$
$503$	−13.8296	−	23.9535i	−0.616630	−	1.06803i	0.373466	−	0.927644i	$-0.378169\pi$
$504$	3.47038	−	0.210449i	0.154583	−	0.00937414i
$505$	−27.7844	−	16.0413i	−1.23639	−	0.713829i
$506$	21.9321	−	37.9876i	0.975002	−	1.68875i
$507$	16.9401	+	14.8335i	0.752337	+	0.658779i
$508$	14.7568	+	25.5595i	0.654727	+	1.13402i
$509$		−	26.1536i		−	1.15924i	−0.814888	−	0.579618i	$-0.803202\pi$
$509$		−	26.1536i		−	1.15924i	0.814888	−	0.579618i	$-0.196798\pi$
$510$	−14.6542	+	0.443918i	−0.648898	+	0.0196570i
$511$	−29.4907			−1.30459
$512$			29.4266i			1.30048i
$513$	−9.33222	+	6.58447i	−0.412027	+	0.290711i
$514$	24.0873	−	13.9068i	1.06244	−	0.613402i
$515$	−23.1279	−	13.3529i	−1.01914	−	0.588399i
$516$	−2.68403	+	4.99212i	−0.118158	+	0.219766i
$517$	27.8562			1.22511
$518$			6.37214i			0.279976i
$519$	3.77814	−	0.114451i	0.165842	−	0.00502384i
$520$	−4.64423	+	0.696491i	−0.203663	+	0.0305431i
$521$	9.78810			0.428825			0.214412	−	0.976743i	$-0.431216\pi$
$521$	9.78810			0.428825			0.214412	+	0.976743i	$0.431216\pi$
$522$	−29.7289	−	14.8416i	−1.30120	−	0.649598i
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	−0.206425	−	0.978462i	$-0.566183\pi$
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	0.950586	−	0.310462i	$-0.100484\pi$
$524$	24.0155			1.04912
$525$	6.57642	+	3.53584i	0.287018	+	0.154317i
$526$	−9.39437	−	5.42384i	−0.409614	−	0.236491i
$527$	12.6214	+	7.28694i	0.549795	+	0.317424i
$528$	36.5572	+	19.6551i	1.59095	+	0.855380i
$529$	−5.28639			−0.229843
$530$	−24.8417	+	43.0270i	−1.07905	+	1.86897i
$531$	20.4332	+	10.2009i	0.886726	+	0.442680i
$532$	−8.92144			−0.386793
$533$	5.11181	+	2.01061i	0.221417	+	0.0870890i
$534$	−33.3490	+	1.01024i	−1.44315	+	0.0437173i
$535$		−	15.5390i		−	0.671809i
$536$	1.02926			0.0444574
$537$	2.40263	−	4.46874i	0.103681	−	0.192840i
$538$	−3.89831	−	2.25069i	−0.168068	−	0.0970340i
$539$	−7.35284	+	4.24516i	−0.316709	+	0.182852i
$540$	2.15048	+	23.6052i	0.0925418	+	1.01581i
$541$		−	21.1460i		−	0.909138i	−0.890711	−	0.454569i	$-0.849793\pi$
$541$		−	21.1460i		−	0.909138i	0.890711	−	0.454569i	$-0.150207\pi$
$542$	3.57104			0.153389
$543$	−40.2074	+	1.21800i	−1.72546	+	0.0522693i
$544$			12.7215i			0.545431i
$545$	15.9478	+	27.6224i	0.683129	+	1.18321i
$546$	−27.6874	+	5.01376i	−1.18491	+	0.214569i
$547$	0.443127	−	0.767519i	0.0189468	−	0.0328168i	−0.856397	−	0.516319i	$-0.827302\pi$
$547$	0.443127	−	0.767519i	0.0189468	−	0.0328168i	0.875343	+	0.483502i	$0.160635\pi$
$548$	−10.2612	−	5.92431i	−0.438337	−	0.253074i
$549$	−2.79737	+	0.169637i	−0.119389	+	0.00723992i
$550$	9.64575	+	16.7069i	0.411296	+	0.712386i
$551$	−10.8980	−	6.29194i	−0.464269	−	0.268046i
$552$	0.109837	+	3.62584i	0.00467499	+	0.154326i
$553$	−13.9866	−	8.07517i	−0.594771	−	0.343391i
$554$	−0.897540	+	0.518195i	−0.0381328	+	0.0220160i
$555$	6.40867	−	0.194138i	0.272033	−	0.00824068i
$556$	8.16712	+	14.1459i	0.346363	+	0.599918i
$557$	8.55128	+	4.93708i	0.362329	+	0.209191i	0.670102	−	0.742269i	$-0.266250\pi$
$557$	8.55128	+	4.93708i	0.362329	+	0.209191i	−0.307773	+	0.951460i	$0.599584\pi$
$558$	22.6021	−	45.2739i	0.956822	−	1.91660i
$559$	−2.47803	+	6.30021i	−0.104810	+	0.266471i
$560$	13.5580	−	23.4832i	0.572932	−	0.992347i
$561$	13.7375	+	7.38601i	0.579997	+	0.311838i
$562$	40.3684			1.70284
$563$	−2.64739	+	4.58542i	−0.111574	+	0.193252i	−0.916405	−	0.400252i	$-0.868923\pi$
$563$	−2.64739	+	4.58542i	−0.111574	+	0.193252i	0.804831	+	0.593504i	$0.202256\pi$
$564$	13.2750	−	8.21006i	0.558979	−	0.345706i
$565$		−	2.28898i		−	0.0962981i
$566$	−14.6275	+	8.44521i	−0.614841	+	0.354978i
$567$	−2.53284	−	20.8069i	−0.106369	−	0.873807i
$568$	−3.15172	−	5.45893i	−0.132243	−	0.229052i
$569$	1.91740	+	3.32104i	0.0803818	+	0.139225i	0.903414	−	0.428769i	$-0.141053\pi$
$569$	1.91740	+	3.32104i	0.0803818	+	0.139225i	−0.823032	+	0.567995i	$0.807719\pi$
$570$	0.583727	+	19.2694i	0.0244496	+	0.807107i
$571$	−20.0761	−	34.7728i	−0.840159	−	1.45520i	−0.889760	−	0.456429i	$-0.849128\pi$
$571$	−20.0761	−	34.7728i	−0.840159	−	1.45520i	0.0496009	−	0.998769i	$-0.484205\pi$
$572$	−31.5021	−	12.3906i	−1.31717	−	0.518076i
$573$	−16.6561	+	0.504563i	−0.695820	+	0.0210784i
$574$	−5.94464	+	3.43214i	−0.248124	+	0.143255i
$575$	−3.89522	+	6.74672i	−0.162442	+	0.281358i
$576$	17.4489	−	1.05813i	0.727036	−	0.0440886i
$577$			31.4632i			1.30983i	0.755702	+	0.654915i	$0.227296\pi$
$577$			31.4632i			1.30983i	−0.755702	+	0.654915i	$0.772704\pi$
$578$		−	27.4830i		−	1.14314i
$579$	−1.05389	−	34.7901i	−0.0437983	−	1.44583i
$580$	−22.6169	+	13.0579i	−0.939117	+	0.542199i
$581$	10.6963	−	18.5266i	0.443759	−	0.768613i
$582$	4.14560	+	6.70311i	0.171841	+	0.277853i
$583$	45.7748	−	26.4281i	1.89580	−	1.09454i
$584$	6.30116			0.260744
$585$	5.88605	+	27.6934i	0.243358	+	1.14498i
$586$	5.89580			0.243553
$587$	−30.0227	+	17.3336i	−1.23917	+	0.715436i	−0.968925	−	0.247356i	$-0.920438\pi$
$587$	−30.0227	+	17.3336i	−1.23917	+	0.715436i	−0.270246	+	0.962791i	$0.587105\pi$
$588$	−2.25285	+	4.19016i	−0.0929062	+	0.172799i
$589$	9.58193	−	16.5964i	0.394816	−	0.683842i
$590$	33.3843	−	19.2744i	1.37441	−	0.793515i
$591$	−18.2719	−	9.82396i	−0.751606	−	0.404104i
$592$		−	6.29101i		−	0.258559i
$593$			8.17407i			0.335669i	0.985815	+	0.167835i	$0.0536774\pi$
$593$			8.17407i			0.335669i	−0.985815	+	0.167835i	$0.946323\pi$
$594$	22.7108	−	49.1629i	0.931837	−	2.01718i
$595$	5.09484	−	8.82453i	0.208868	−	0.361770i
$596$	−22.8084	+	13.1684i	−0.934268	+	0.539400i
$597$	16.1288	+	26.0790i	0.660109	+	1.06734i
$598$	−4.35406	−	29.0331i	−0.178051	−	1.18725i
$599$	−20.5243	−	35.5492i	−0.838601	−	1.45250i	−0.891064	−	0.453877i	$-0.850041\pi$
$599$	−20.5243	−	35.5492i	−0.838601	−	1.45250i	0.0524634	−	0.998623i	$-0.483293\pi$
$600$	−1.40516	−	0.755488i	−0.0573653	−	0.0308427i
$601$	8.04257	+	13.9301i	0.328063	+	0.568222i	0.982128	−	0.188217i	$-0.0602707\pi$
$601$	8.04257	+	13.9301i	0.328063	+	0.568222i	−0.654064	+	0.756439i	$0.726937\pi$
$602$	−4.23005	−	7.32666i	−0.172404	−	0.298612i
$603$	−0.375601	−	6.19379i	−0.0152957	−	0.252231i
$604$	29.4350	−	16.9943i	1.19769	−	0.691488i
$605$		−	47.1702i		−	1.91774i
$606$	36.1753	+	19.4498i	1.46952	+	0.790094i
$607$	−6.15106	+	10.6539i	−0.249664	+	0.432430i	−0.963433	−	0.267951i	$-0.913653\pi$
$607$	−6.15106	+	10.6539i	−0.249664	+	0.432430i	0.713769	+	0.700382i	$0.246987\pi$
$608$	16.7281			0.678414
$609$	19.6413	−	12.1473i	0.795905	−	0.492235i
$610$	−2.36521	+	4.09667i	−0.0957647	+	0.165869i
$611$	14.5849	−	11.6134i	0.590041	−	0.469828i
$612$	8.72354	−	0.529009i	0.352628	−	0.0213839i
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	0.709101	−	0.705107i	$-0.249101\pi$
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	−0.256091	+	0.966653i	$0.582435\pi$
$614$	21.3016	+	36.8954i	0.859662	+	1.48898i
$615$	3.63293	+	5.87415i	0.146494	+	0.236869i
$616$	−5.40684	+	3.12164i	−0.217848	+	0.125774i
$617$	−34.1905	−	19.7399i	−1.37646	−	0.794699i	−0.384727	−	0.923030i	$-0.625705\pi$
$617$	−34.1905	−	19.7399i	−1.37646	−	0.794699i	−0.991731	+	0.128331i	$0.959038\pi$
$618$	30.1126	+	16.1901i	1.21131	+	0.651263i
$619$	−0.671784	−	0.387855i	−0.0270013	−	0.0155892i	0.486439	−	0.873715i	$-0.338296\pi$
$619$	−0.671784	−	0.387855i	−0.0270013	−	0.0155892i	−0.513440	+	0.858126i	$0.671629\pi$
$620$	−19.8857	−	34.4431i	−0.798630	−	1.38327i
$621$	21.7791	−	1.98412i	0.873967	−	0.0796199i
$622$	11.3890	+	6.57547i	0.456659	+	0.263652i
$623$	11.5945	−	20.0823i	0.464524	−	0.804580i
$624$	27.3349	−	4.94993i	1.09427	−	0.198156i
$625$	15.4144	+	26.6985i	0.616576	+	1.06794i
$626$		−	11.8251i		−	0.472626i
$627$	9.71219	−	18.0640i	0.387868	−	0.721408i
$628$	−6.81128			−0.271799
$629$		−	2.36404i		−	0.0942604i
$630$	−31.6543	−	15.8028i	−1.26114	−	0.629599i
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	−0.603801	−	0.797135i	$-0.706348\pi$
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	0.388438	+	0.921475i	$0.373015\pi$
$632$	2.98846	+	1.72539i	0.118875	+	0.0686323i
$633$	−38.4181	+	1.16380i	−1.52698	+	0.0462567i
$634$	−33.5851			−1.33384
$635$			44.3257i			1.75901i
$636$	14.0251	−	26.0857i	0.556130	−	1.03436i
$637$	−2.07995	+	5.28811i	−0.0824105	+	0.209523i
$638$	59.6677			2.36227
$639$	−31.7000	+	20.9581i	−1.25403	+	0.829091i
$640$	−5.16684	+	8.94922i	−0.204237	+	0.353749i
$641$	−26.3440			−1.04052			−0.520262	−	0.854007i	$-0.674166\pi$
$641$	−26.3440			−1.04052			−0.520262	+	0.854007i	$0.674166\pi$
$642$	0.602345	+	19.8840i	0.0237727	+	0.784760i
$643$	19.4866	+	11.2506i	0.768477	+	0.443681i	0.832331	−	0.554279i	$-0.187006\pi$
$643$	19.4866	+	11.2506i	0.768477	+	0.443681i	−0.0638539	+	0.997959i	$0.520339\pi$
$644$	14.7940	+	8.54134i	0.582967	+	0.336576i
$645$	−7.23978	+	4.47752i	−0.285066	+	0.176302i
$646$	7.10813			0.279665
$647$	−2.07443	+	3.59302i	−0.0815542	+	0.141256i	−0.903918	−	0.427706i	$-0.859322\pi$
$647$	−2.07443	+	3.59302i	−0.0815542	+	0.141256i	0.822363	+	0.568962i	$0.192655\pi$
$648$	0.541181	+	4.44572i	0.0212596	+	0.174644i
$649$	−41.0106			−1.60981
$650$	12.0155	+	4.72600i	0.471287	+	0.185369i
$651$	18.4991	+	29.9115i	0.725035	+	1.17232i
$652$			12.5254i			0.490533i
$653$	−4.45111			−0.174185			−0.0870927	−	0.996200i	$-0.527758\pi$
$653$	−4.45111			−0.174185			−0.0870927	+	0.996200i	$0.527758\pi$
$654$	−21.4779	−	34.7280i	−0.839852	−	1.35797i
$655$	31.2360	+	18.0341i	1.22049	+	0.704651i
$656$	5.86895	−	3.38844i	0.229144	−	0.132296i
$657$	−2.29943	−	37.9185i	−0.0897094	−	1.47934i
$658$			23.2980i			0.908249i
$659$	13.4141			0.522539			0.261269	−	0.965266i	$-0.415859\pi$
$659$	13.4141			0.522539			0.261269	+	0.965266i	$0.415859\pi$
$660$	−22.3883	−	36.2001i	−0.871464	−	1.40909i
$661$		−	5.54124i		−	0.215529i	−0.994176	−	0.107765i	$-0.965631\pi$
$661$		−	5.54124i		−	0.215529i	0.994176	−	0.107765i	$-0.0343693\pi$
$662$	18.4451	+	31.9479i	0.716891	+	1.24169i
$663$	10.2719	−	1.86009i	0.398928	−	0.0722397i
$664$	−2.28544	+	3.95851i	−0.0886924	+	0.153620i
$665$	−11.6038	−	6.69944i	−0.449975	−	0.259793i
$666$	−8.19315	+	0.496845i	−0.317478	+	0.0192524i
$667$	12.0477	+	20.8673i	0.466490	+	0.807985i
$668$	−9.04570	−	5.22254i	−0.349989	−	0.202066i
$669$	−6.38072	+	3.94622i	−0.246693	+	0.152570i
$670$	−9.07064	−	5.23694i	−0.350429	−	0.202321i
$671$	4.35829	−	2.51626i	0.168250	−	0.0971392i
$672$	−14.5378	+	27.0393i	−0.560807	+	1.04306i
$673$	−6.90677	−	11.9629i	−0.266236	−	0.461135i	0.701650	−	0.712521i	$-0.252447\pi$
$673$	−6.90677	−	11.9629i	−0.266236	−	0.461135i	−0.967887	+	0.251386i	$0.919114\pi$
$674$	−40.4375	−	23.3466i	−1.55759	−	0.899278i
$675$	−4.03352	+	8.73150i	−0.155250	+	0.336075i
$676$	−21.6595	+	6.64599i	−0.833058	+	0.255615i
$677$	4.70621	−	8.15139i	0.180874	−	0.313284i	−0.761304	−	0.648395i	$-0.775441\pi$
$677$	4.70621	−	8.15139i	0.180874	−	0.313284i	0.942179	+	0.335111i	$0.108774\pi$
$678$	0.0887288	+	2.92903i	0.00340761	+	0.112489i
$679$	−5.47783			−0.210220
$680$	−1.08860	+	1.88550i	−0.0417457	+	0.0723057i
$681$	−0.155233	−	5.12440i	−0.00594855	−	0.196368i
$682$			90.8673i			3.47949i
$683$	−16.9642	+	9.79429i	−0.649117	+	0.374768i	−0.788118	−	0.615524i	$-0.788944\pi$
$683$	−16.9642	+	9.79429i	−0.649117	+	0.374768i	0.139001	+	0.990292i	$0.455611\pi$
$684$	−0.695617	−	11.4710i	−0.0265976	−	0.438604i
$685$	−8.89757	−	15.4110i	−0.339959	−	0.588826i
$686$	−19.3202	−	33.4636i	−0.737650	−	1.27765i
$687$	16.7089	−	10.3338i	0.637485	−	0.394259i
$688$	4.17619	+	7.23337i	0.159216	+	0.275770i
$689$	12.9486	−	32.9209i	0.493303	−	1.25419i
$690$	17.4805	−	32.5125i	0.665470	−	1.23773i
$691$	−1.21540	+	0.701710i	−0.0462359	+	0.0266943i	−0.522940	−	0.852370i	$-0.675165\pi$
$691$	−1.21540	+	0.701710i	−0.0462359	+	0.0266943i	0.476704	+	0.879064i	$0.341831\pi$
$692$	−1.90165	+	3.29375i	−0.0722899	+	0.125210i
$693$	20.7581	+	31.3975i	0.788536	+	1.19269i
$694$			1.99110i			0.0755813i
$695$			24.5320i			0.930551i
$696$	−4.19667	+	2.59547i	−0.159075	+	0.0983812i
$697$	2.20544	−	1.27331i	0.0835369	−	0.0482300i
$698$	−27.4147	+	47.4836i	−1.03766	+	1.79728i
$699$	−4.00837	+	0.121425i	−0.151611	+	0.00459273i
$700$	−6.50641	+	3.75648i	−0.245919	+	0.141982i
$701$	19.4308			0.733892			0.366946	−	0.930242i	$-0.380403\pi$
$701$	19.4308			0.733892			0.366946	+	0.930242i	$0.380403\pi$
$702$	−8.60541	−	35.2089i	−0.324790	−	1.32887i
$703$	−3.10858			−0.117242
$704$	−27.1853	+	15.6954i	−1.02458	+	0.591544i
$705$	23.4315	−	0.709810i	0.882483	−	0.0267330i
$706$	−7.46203	+	12.9246i	−0.280837	+	0.486424i
$707$	−24.7219	+	14.2732i	−0.929763	+	0.536799i
$708$	−19.5438	+	12.0871i	−0.734502	+	0.454260i
$709$			3.65841i			0.137394i	0.997638	+	0.0686972i	$0.0218842\pi$
$709$			3.65841i			0.137394i	−0.997638	+	0.0686972i	$0.978116\pi$
$710$			64.1442i			2.40729i
$711$	9.29230	−	18.6133i	0.348489	−	0.698052i
$712$	−2.47735	+	4.29090i	−0.0928427	+	0.160808i
$713$	−31.7786	+	18.3474i	−1.19012	+	0.687114i
$714$	−6.17740	+	11.4896i	−0.231184	+	0.429986i
$715$	−31.6690	−	39.7721i	−1.18435	−	1.48739i
$716$	2.55256	+	4.42117i	0.0953937	+	0.165227i
$717$	−30.0640	+	18.5934i	−1.12276	+	0.694383i
$718$	5.82003	+	10.0806i	0.217202	+	0.376204i
$719$	3.56798	+	6.17992i	0.133063	+	0.230472i	0.924856	−	0.380318i	$-0.124185\pi$
$719$	3.56798	+	6.17992i	0.133063	+	0.230472i	−0.791793	+	0.610790i	$0.790852\pi$
$720$	31.2513	+	15.6016i	1.16467	+	0.581437i
$721$	−20.5787	+	11.8811i	−0.766390	+	0.442476i
$722$			27.4111i			1.02014i
$723$	−0.458379	−	15.1316i	−0.0170473	−	0.562748i
$724$	20.2375	−	35.0525i	0.752123	−	1.30271i
$725$	−10.5972			−0.393570
$726$	1.82848	+	60.3600i	0.0678613	+	2.24017i
$727$	−18.8741	+	32.6908i	−0.700000	+	1.21244i	0.268466	+	0.963289i	$0.413483\pi$
$727$	−18.8741	+	32.6908i	−0.700000	+	1.21244i	−0.968466	+	0.249146i	$0.919850\pi$
$728$	−1.52947	+	3.88856i	−0.0566859	+	0.144120i
$729$	26.5555	−	4.87900i	0.983538	−	0.180704i
$730$	−55.5305	−	32.0606i	−2.05528	−	1.18662i
$731$	1.56933	+	2.71816i	0.0580438	+	0.100535i
$732$	1.33535	−	2.48366i	0.0493559	−	0.0917986i
$733$	−25.7477	+	14.8654i	−0.951012	+	0.549067i	−0.893395	−	0.449272i	$-0.851684\pi$
$733$	−25.7477	+	14.8654i	−0.951012	+	0.549067i	−0.0576170	+	0.998339i	$0.518350\pi$
$734$	−40.8656	−	23.5938i	−1.50838	−	0.870862i
$735$	−6.07675	+	3.75822i	−0.224144	+	0.138624i
$736$	−27.7395	−	16.0154i	−1.02249	−	0.590335i
$737$	5.57138	+	9.64991i	0.205224	+	0.355459i
$738$	−4.87648	−	7.37587i	−0.179506	−	0.271510i
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.245023	−	0.969517i	$-0.578795\pi$
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.962138	+	0.272563i	$0.912129\pi$
$740$	−3.22567	+	5.58703i	−0.118578	+	0.205383i
$741$	−2.44591	−	13.5070i	−0.0898527	−	0.496192i
$742$	22.1035	+	38.2845i	0.811447	+	1.40547i
$743$			4.83226i			0.177279i	0.996064	+	0.0886393i	$0.0282518\pi$
$743$			4.83226i			0.177279i	−0.996064	+	0.0886393i	$0.971748\pi$
$744$	−3.95262	−	6.39107i	−0.144910	−	0.234308i
$745$	−39.5546			−1.44917
$746$			10.4012i			0.380815i
$747$	24.6551	+	12.3086i	0.902083	+	0.450347i
$748$	−13.5912	+	7.84691i	−0.496945	+	0.286911i
$749$	−11.9739	−	6.91312i	−0.437516	−	0.252600i
$750$	−14.5274	−	23.4896i	−0.530464	−	0.857718i
$751$	−34.2062			−1.24820			−0.624100	−	0.781344i	$-0.714534\pi$
$751$	−34.2062			−1.24820			−0.624100	+	0.781344i	$0.714534\pi$
$752$		−	23.0013i		−	0.838773i
$753$	16.8919	+	27.3128i	0.615575	+	0.995335i
$754$	31.2407	−	24.8758i	1.13772	−	0.905924i
$755$	51.0466			1.85777
$756$	19.1462	+	8.84460i	0.696340	+	0.321675i
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	−0.628579	−	0.777746i	$-0.716363\pi$
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	0.987837	+	0.155492i	$0.0496964\pi$
$758$	44.0889			1.60138
$759$	−33.3997	+	20.6564i	−1.21233	+	0.749779i
$760$	2.47933	+	1.43144i	0.0899348	+	0.0519239i
$761$	15.3847	+	8.88238i	0.557696	+	0.321986i	0.752220	−	0.658912i	$-0.228983\pi$
$761$	15.3847	+	8.88238i	0.557696	+	0.321986i	−0.194524	+	0.980898i	$0.562316\pi$
$762$	−1.71822	−	56.7201i	−0.0622445	−	2.05475i
$763$	28.3800			1.02742
$764$	8.38352	−	14.5207i	0.303305	−	0.525340i
$765$	11.7436	+	5.86277i	0.424592	+	0.211969i
$766$	48.1496			1.73971
$767$	−21.4722	+	17.0976i	−0.775318	+	0.617357i
$768$	15.8234	−	29.4304i	0.570977	−	1.06198i
$769$		−	16.2302i		−	0.585277i	−0.956223	−	0.292638i	$-0.905467\pi$
$769$		−	16.2302i		−	0.585277i	0.956223	−	0.292638i	$-0.0945332\pi$
$770$	63.5321			2.28954
$771$	−24.8898	+	0.753984i	−0.896383	+	0.0271541i
$772$	30.3297	+	17.5109i	1.09159	+	0.630230i
$773$	14.3635	−	8.29274i	0.516617	−	0.298269i	−0.218932	−	0.975740i	$-0.570257\pi$
$773$	14.3635	−	8.29274i	0.516617	−	0.298269i	0.735550	+	0.677471i	$0.236924\pi$
$774$	9.09062	−	6.01017i	0.326756	−	0.216031i
$775$		−	16.1383i		−	0.579706i
$776$	1.17043			0.0420158
$777$	2.70155	−	5.02470i	0.0969176	−	0.180260i
$778$			29.1610i			1.04547i
$779$	−1.67433	−	2.90003i	−0.0599891	−	0.103904i
$780$	−26.8141	−	9.61975i	−0.960098	−	0.344442i
$781$	34.1203	−	59.0981i	1.22092	−	2.11470i
$782$	−11.7871	−	6.80528i	−0.421506	−	0.243356i
$783$	17.1502	+	24.3072i	0.612899	+	0.868667i
$784$	3.50530	+	6.07137i	0.125189	+	0.216834i
$785$	−8.85916	−	5.11484i	−0.316197	−	0.182556i
$786$	−40.6693	−	21.8660i	−1.45063	−	0.779935i
$787$	8.87487	+	5.12391i	0.316355	+	0.182648i	0.649767	−	0.760134i	$-0.274867\pi$
$787$	8.87487	+	5.12391i	0.316355	+	0.182648i	−0.333412	+	0.942781i	$0.608200\pi$
$788$	18.0774	−	10.4370i	0.643981	−	0.371803i
$789$	5.10835	+	8.25979i	0.181862	+	0.294056i
$790$	−17.5577	−	30.4108i	−0.624675	−	1.08197i
$791$	−1.76382	−	1.01834i	−0.0627142	−	0.0362080i
$792$	−4.43531	−	6.70858i	−0.157602	−	0.238379i
$793$	1.23286	−	3.13445i	0.0437801	−	0.111308i
$794$	−2.60865	+	4.51831i	−0.0925774	+	0.160349i
$795$	37.8305	−	23.3967i	1.34171	−	0.829794i
$796$	−30.8536			−1.09358
$797$	10.1783	−	17.6293i	0.360534	−	0.624463i	−0.627515	−	0.778604i	$-0.715928\pi$
$797$	10.1783	−	17.6293i	0.360534	−	0.624463i	0.988049	+	0.154142i	$0.0492613\pi$
$798$	15.1081	+	8.12295i	0.534822	+	0.287549i
$799$		−	8.64345i		−	0.305783i
$800$	12.1998	−	7.04357i	0.431329	−	0.249028i
$801$	26.7254	+	13.3421i	0.944294	+	0.471420i
$802$	1.17701	+	2.03864i	0.0415617	+	0.0719870i
$803$	34.1080	+	59.0768i	1.20365	+	2.08478i
$804$	5.49919	+	2.95666i	0.193941	+	0.104273i
$805$	12.8280	+	22.2188i	0.452128	+	0.783109i
$806$	37.8831	+	47.5761i	1.33438	+	1.67580i
$807$	2.11977	+	3.42750i	0.0746194	+	0.120654i
$808$	5.28223	−	3.04970i	0.185828	−	0.107288i
$809$	18.8460	−	32.6423i	0.662591	−	1.14764i	−0.317342	−	0.948311i	$-0.602790\pi$
$809$	18.8460	−	32.6423i	0.662591	−	1.14764i	0.979932	−	0.199330i	$-0.0638765\pi$
$810$	17.8507	−	41.9326i	0.627211	−	1.47336i
$811$		−	28.8949i		−	1.01464i	−0.861758	−	0.507319i	$-0.830637\pi$
$811$		−	28.8949i		−	1.01464i	0.861758	−	0.507319i	$-0.169363\pi$
$812$			23.2372i			0.815467i
$813$	−2.81591	−	1.51399i	−0.0987584	−	0.0530978i
$814$	12.7649	−	7.36982i	0.447409	−	0.258312i
$815$	−9.40579	+	16.2913i	−0.329470	+	0.570659i
$816$	6.09876	−	11.3433i	0.213499	−	0.397094i
$817$	3.57423	−	2.06358i	0.125046	−	0.0721956i
$818$	−66.5660			−2.32743
$819$	23.9583	+	7.78485i	0.837171	+	0.272025i
$820$	−6.94960			−0.242691
$821$	4.48979	−	2.59218i	0.156695	−	0.0904677i	−0.419602	−	0.907708i	$-0.637830\pi$
$821$	4.48979	−	2.59218i	0.156695	−	0.0904677i	0.576297	+	0.817240i	$0.304497\pi$
$822$	11.9829	+	19.3754i	0.417952	+	0.675795i
$823$	−8.84424	+	15.3187i	−0.308291	+	0.533976i	−0.977989	−	0.208658i	$-0.933090\pi$
$823$	−8.84424	+	15.3187i	−0.308291	+	0.533976i	0.669698	+	0.742634i	$0.266424\pi$
$824$	4.39696	−	2.53859i	0.153176	−	0.0884359i
$825$	−0.522963	−	17.2635i	−0.0182072	−	0.601039i
$826$		−	34.2999i		−	1.19345i
$827$		−	15.0588i		−	0.523644i	−0.965116	−	0.261822i	$-0.915677\pi$
$827$		−	15.0588i		−	0.523644i	0.965116	−	0.261822i	$-0.0843234\pi$
$828$	−9.82874	+	19.6878i	−0.341572	+	0.684198i
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	−0.772335	−	0.635215i	$-0.780911\pi$
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	0.936280	+	0.351255i	$0.114245\pi$
$830$	40.2821	−	23.2569i	1.39821	−	0.807258i
$831$	0.927443	−	0.0280950i	0.0321726	−	0.000974603i
$832$	−7.69009	+	19.5515i	−0.266606	+	0.677825i
$833$	1.31722	+	2.28150i	0.0456391	+	0.0790492i
$834$	−0.950945	−	31.3916i	−0.0329285	−	1.08700i
$835$	−7.84359	−	13.5855i	−0.271439	−	0.470146i
$836$	10.3183	+	17.8717i	0.356864	+	0.618107i
$837$	−37.0171	+	26.1179i	−1.27950	+	0.902767i
$838$	−36.5115	+	21.0799i	−1.26127	+	0.728194i
$839$		−	29.9798i		−	1.03502i	−0.855678	−	0.517508i	$-0.826860\pi$
$839$		−	29.9798i		−	1.03502i	0.855678	−	0.517508i	$-0.173140\pi$
$840$	−4.46847	+	2.76357i	−0.154177	+	0.0953523i
$841$	−1.88830	+	3.27064i	−0.0651140	+	0.112781i
$842$	−50.1041			−1.72670
$843$	−31.8321	−	17.1147i	−1.09636	−	0.589461i
$844$	19.3369	−	33.4926i	0.665605	−	1.15286i
$845$	−33.1624	−	7.62075i	−1.14082	−	0.262162i
$846$	−29.9560	+	1.81658i	−1.02991	+	0.0624552i
$847$	−36.3479	−	20.9855i	−1.24893	−	0.721070i
$848$	−21.8221	−	37.7970i	−0.749375	−	1.29796i
$849$	15.1149	−	0.457873i	0.518741	−	0.0157142i
$850$	5.18396	−	2.99296i	0.177808	−	0.102658i
$851$	5.15482	+	2.97614i	0.176705	+	0.102021i
$852$	−1.15779	−	38.2198i	−0.0396652	−	1.30939i
$853$	45.8672	+	26.4814i	1.57046	+	0.906706i	0.996112	+	0.0880960i	$0.0280782\pi$
$853$	45.8672	+	26.4814i	1.57046	+	0.906706i	0.574349	+	0.818610i	$0.305255\pi$
$854$	2.10451	+	3.64513i	0.0720150	+	0.124734i
$855$	7.70922	−	15.4422i	0.263650	−	0.528113i
$856$	2.55841	+	1.47710i	0.0874446	+	0.0504862i
$857$	−15.1376	+	26.2190i	−0.517089	+	0.895624i	0.482714	+	0.875778i	$0.339651\pi$
$857$	−15.1376	+	26.2190i	−0.517089	+	0.895624i	−0.999803	+	0.0198464i	$0.993682\pi$
$858$	42.0661	+	49.6656i	1.43611	+	1.69555i
$859$	−24.2634	−	42.0254i	−0.827856	−	1.43389i	−0.899717	−	0.436475i	$-0.856227\pi$
$859$	−24.2634	−	42.0254i	−0.827856	−	1.43389i	0.0718602	−	0.997415i	$-0.477106\pi$
$860$		−	8.56525i		−	0.292073i
$861$	6.14269	−	0.186080i	0.209342	−	0.00634160i
$862$	54.5939			1.85948
$863$			21.2534i			0.723473i	0.932280	+	0.361737i	$0.117816\pi$
$863$			21.2534i			0.723473i	−0.932280	+	0.361737i	$0.882184\pi$
$864$	−35.9000	−	16.5840i	−1.22134	−	0.564200i
$865$	−4.94680	+	2.85604i	−0.168196	+	0.0971082i
$866$	45.0350	+	26.0010i	1.53035	+	0.883548i
$867$	−11.6518	+	21.6715i	−0.395715	+	0.736003i
$868$	−35.3877			−1.20114
$869$			37.3579i			1.26728i
$870$	50.1901	−	1.52041i	1.70160	−	0.0515466i
$871$	6.94015	+	2.72974i	0.235158	+	0.0924936i
$872$	−6.06384			−0.205348
$873$	−0.427114	−	7.04326i	−0.0144556	−	0.238378i
$874$	−8.94857	+	15.4994i	−0.302690	+	0.524274i
$875$	19.1958			0.648938
$876$	33.6661	+	18.1007i	1.13747	+	0.611566i
$877$	37.5511	+	21.6801i	1.26801	+	0.732085i	0.974611	−	0.223905i	$-0.0718806\pi$
$877$	37.5511	+	21.6801i	1.26801	+	0.732085i	0.293398	+	0.955990i	$0.405214\pi$
$878$	−2.84135	−	1.64045i	−0.0958909	−	0.0553626i
$879$	−4.64908	−	2.49960i	−0.156810	−	0.0843094i
$880$	−62.7232			−2.11440
$881$	25.4246	−	44.0368i	0.856578	−	1.48364i	−0.0185957	−	0.999827i	$-0.505920\pi$
$881$	25.4246	−	44.0368i	0.856578	−	1.48364i	0.875174	−	0.483809i	$-0.160747\pi$
$882$	7.63025	−	5.04466i	0.256924	−	0.169863i
$883$	29.1681			0.981586			0.490793	−	0.871276i	$-0.336707\pi$
$883$	29.1681			0.981586			0.490793	+	0.871276i	$0.336707\pi$
$884$	−3.84465	+	9.77474i	−0.129310	+	0.328760i
$885$	−34.4965	+	1.04500i	−1.15959	+	0.0351273i
$886$		−	6.68992i		−	0.224752i
$887$	−44.1138			−1.48120			−0.740598	−	0.671948i	$-0.765458\pi$
$887$	−44.1138			−1.48120			−0.740598	+	0.671948i	$0.765458\pi$
$888$	−0.577229	+	1.07361i	−0.0193706	+	0.0360279i
$889$	34.1560	+	19.7200i	1.14556	+	0.661387i
$890$	43.6646	−	25.2097i	1.46364	−	0.845033i
$891$	−38.7517	+	29.1384i	−1.29823	+	0.976174i
$892$		−	7.54891i		−	0.252756i
$893$	−11.3657			−0.380337
$894$	50.6150	−	1.53328i	1.69282	−	0.0512804i
$895$			7.66725i			0.256288i
$896$	4.59734	+	7.96282i	0.153586	+	0.266019i
$897$	−8.87557	+	24.7397i	−0.296347	+	0.826036i
$898$	−27.1548	+	47.0334i	−0.906166	+	1.56953i
$899$	−43.2278	−	24.9576i	−1.44173	−	0.832382i
$900$	−5.33731	−	8.07290i	−0.177910	−	0.269097i
$901$	−8.20032	−	14.2034i	−0.273192	−	0.473183i
$902$	13.7508	+	7.93901i	0.457850	+	0.264340i
$903$	0.229340	+	7.57075i	0.00763197	+	0.251939i
$904$	0.376868	+	0.217585i	0.0125344	+	0.00723677i
$905$	52.6444	−	30.3942i	1.74996	−	1.01034i
$906$	−65.3203	+	1.97874i	−2.17012	+	0.0657393i
$907$	−10.6027	−	18.3644i	−0.352057	−	0.609780i	0.634553	−	0.772879i	$-0.281184\pi$
$907$	−10.6027	−	18.3644i	−0.352057	−	0.609780i	−0.986610	+	0.163099i	$0.947851\pi$
$908$	4.46742	+	2.57926i	0.148256	+	0.0855959i
$909$	−20.2797	−	30.6739i	−0.672637	−	1.01739i
$910$	33.2640	−	26.4869i	1.10269	−	0.878032i
$911$	−18.2141	+	31.5478i	−0.603460	+	1.04522i	0.388833	+	0.921308i	$0.372878\pi$
$911$	−18.2141	+	31.5478i	−0.603460	+	1.04522i	−0.992293	+	0.123915i	$0.960455\pi$
$912$	−14.9158	−	8.01953i	−0.493911	−	0.265553i
$913$	−49.4842			−1.63769
$914$	−9.53220	+	16.5103i	−0.315297	+	0.546111i
$915$	3.60191	−	2.22763i	0.119075	−	0.0736433i
$916$			19.7680i			0.653154i
$917$	27.7931	−	16.0463i	0.917809	−	0.529897i
$918$	−15.2547	−	7.04691i	−0.503479	−	0.232583i
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	0.920318	−	0.391170i	$-0.127930\pi$
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	−0.798922	+	0.601434i	$0.794596\pi$
$920$	−2.74091	−	4.74740i	−0.0903652	−	0.156517i
$921$	−1.15491	−	38.1247i	−0.0380555	−	1.25625i
$922$	−4.00223	−	6.93207i	−0.131806	−	0.228296i
$923$	−6.77371	−	45.1674i	−0.222959	−	1.48670i
$924$	−37.8550	+	1.14674i	−1.24534	+	0.0377250i
$925$	−2.26709	+	1.30890i	−0.0745415	+	0.0430365i
$926$	2.18922	−	3.79184i	0.0719423	−	0.124608i
$927$	−16.8810	−	25.5332i	−0.554445	−	0.838620i
$928$		−	43.5709i		−	1.43028i
$929$		−	2.37037i		−	0.0777693i	−0.999244	−	0.0388847i	$-0.987620\pi$
$929$		−	2.37037i		−	0.0777693i	0.999244	−	0.0388847i	$-0.0123805\pi$
$930$	2.31541	+	76.4340i	0.0759252	+	2.50637i
$931$	3.00004	−	1.73208i	0.0983225	−	0.0567665i
$932$	2.01753	−	3.49447i	0.0660864	−	0.114465i
$933$	−6.19298	−	10.0136i	−0.202749	−	0.327829i
$934$	−19.3869	+	11.1930i	−0.634359	+	0.366247i
$935$	−23.5701			−0.770826
$936$	−5.11908	−	1.66336i	−0.167322	−	0.0543686i
$937$	36.8188			1.20282			0.601409	−	0.798941i	$-0.294606\pi$
$937$	36.8188			1.20282			0.601409	+	0.798941i	$0.294606\pi$
$938$	−8.07085	+	4.65971i	−0.263523	+	0.152145i
$939$	−5.01340	+	9.32458i	−0.163606	+	0.304296i
$940$	−11.7938	+	20.4274i	−0.384671	+	0.666269i
$941$	42.7909	−	24.7053i	1.39494	−	0.805371i	0.401086	−	0.916040i	$-0.368633\pi$
$941$	42.7909	−	24.7053i	1.39494	−	0.805371i	0.993857	+	0.110669i	$0.0352995\pi$
$942$	11.5346	+	6.20165i	0.375819	+	0.202061i
$943$			6.41198i			0.208803i
$944$			33.8632i			1.10215i
$945$	18.2610	+	25.8814i	0.594029	+	0.841923i
$946$	−9.78467	+	16.9476i	−0.318127	+	0.551012i
$947$	23.5464	−	13.5945i	0.765155	−	0.441763i	−0.0659882	−	0.997820i	$-0.521020\pi$
$947$	23.5464	−	13.5945i	0.765155	−	0.441763i	0.831144	+	0.556058i	$0.187687\pi$
$948$	11.0105	+	17.8031i	0.357605	+	0.578218i
$949$	42.4877	+	16.7115i	1.37921	+	0.542477i
$950$	−3.93558	−	6.81662i	−0.127687	−	0.221160i
$951$	26.4833	+	14.2388i	0.858779	+	0.461726i
$952$	0.968607	+	1.67768i	0.0313927	+	0.0543738i
$953$	27.1090	+	46.9542i	0.878147	+	1.52100i	0.853372	+	0.521303i	$0.174554\pi$
$953$	27.1090	+	46.9542i	0.878147	+	1.52100i	0.0247753	+	0.999693i	$0.492113\pi$
$954$	−47.5018	+	31.4053i	−1.53793	+	1.01678i
$955$	21.8082	−	12.5910i	0.705698	−	0.407435i
$956$		−	35.5682i		−	1.15036i
$957$	−47.0505	−	25.2969i	−1.52093	−	0.817732i
$958$	27.9906	−	48.4811i	0.904334	−	1.56635i
$959$	−15.8337			−0.511297
$960$	−22.4672	+	13.8951i	−0.725127	+	0.448462i
$961$	22.5076	−	38.9843i	0.726052	−	1.25756i
$962$	3.61090	−	9.18043i	0.116420	−	0.295989i
$963$	7.95510	−	15.9347i	0.256350	−	0.513490i
$964$	13.1916	+	7.61615i	0.424872	+	0.245300i
$965$	26.2991	+	45.5514i	0.846599	+	1.46635i
$966$	−17.2763	−	27.9344i	−0.555855	−	0.898774i
$967$	19.6716	−	11.3574i	0.632595	−	0.365229i	−0.149161	−	0.988813i	$-0.547657\pi$
$967$	19.6716	−	11.3574i	0.632595	−	0.365229i	0.781756	+	0.623584i	$0.214324\pi$
$968$	7.76632	+	4.48389i	0.249619	+	0.144118i
$969$	−5.60505	−	3.01358i	−0.180060	−	0.0968101i
$970$	−10.3147	−	5.95517i	−0.331184	−	0.191209i
$971$	−23.0225	−	39.8762i	−0.738828	−	1.27969i	−0.953023	−	0.302897i	$-0.902046\pi$
$971$	−23.0225	−	39.8762i	−0.738828	−	1.27969i	0.214195	−	0.976791i	$-0.431287\pi$
$972$	−9.87933	+	25.3074i	−0.316880	+	0.811734i
$973$	18.9036	+	10.9140i	0.606022	+	0.349887i
$974$	4.07483	−	7.05781i	0.130566	−	0.226147i
$975$	−7.47108	−	8.82078i	−0.239266	−	0.282491i
$976$	−2.07772	−	3.59872i	−0.0665062	−	0.115192i
$977$			31.9372i			1.02176i	0.859652	+	0.510881i	$0.170681\pi$
$977$			31.9372i			1.02176i	−0.859652	+	0.510881i	$0.829319\pi$
$978$	11.4043	−	21.2113i	0.364671	−	0.678263i
$979$	−53.6394			−1.71432
$980$		−	7.18928i		−	0.229653i
$981$	2.21283	+	36.4903i	0.0706502	+	1.16505i
$982$	23.2416	−	13.4185i	0.741668	−	0.428202i
$983$	2.20776	+	1.27465i	0.0704167	+	0.0406551i	0.534795	−	0.844982i	$-0.320389\pi$
$983$	2.20776	+	1.27465i	0.0704167	+	0.0406551i	−0.464378	+	0.885637i	$0.653722\pi$
$984$	−1.31249	+	0.0397590i	−0.0418405	+	0.00126747i
$985$	31.3501			0.998897
$986$		−	18.5142i		−	0.589612i
$987$	9.87747	−	18.3714i	0.314403	−	0.584769i
$988$	12.8532	+	5.05550i	0.408916	+	0.160837i
$989$	−7.90265			−0.251290
$990$	4.95369	+	81.6881i	0.157439	+	2.59622i
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	0.175949	+	0.984399i	$0.443701\pi$
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	−0.940489	+	0.339824i	$0.889633\pi$
$992$	66.3536			2.10673
$993$	−1.00004	−	33.0123i	−0.0317353	−	1.04761i
$994$	49.4276	+	28.5370i	1.56775	+	0.905140i
$995$	−40.1301	−	23.1691i	−1.27221	−	0.734510i
$996$	−23.5819	+	14.5845i	−0.747222	+	0.462127i
$997$	23.8264			0.754590			0.377295	−	0.926093i	$-0.376854\pi$
$997$	23.8264			0.754590			0.377295	+	0.926093i	$0.376854\pi$
$998$	10.0903	−	17.4770i	0.319404	−	0.553224i
$999$	6.67129	+	3.08181i	0.211070	+	0.0975041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.r.b.43.9	yes	22
3.2	odd	2		351.2.r.b.316.3		22
9.4	even	3		117.2.l.b.4.9	✓	22
9.5	odd	6		351.2.l.b.199.3		22
13.10	even	6		117.2.l.b.88.3	yes	22
39.23	odd	6		351.2.l.b.127.9		22
117.23	odd	6		351.2.r.b.10.3		22
117.49	even	6	inner	117.2.r.b.49.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.9	✓	22	9.4	even	3
117.2.l.b.88.3	yes	22	13.10	even	6
117.2.r.b.43.9	yes	22	1.1	even	1	trivial
117.2.r.b.49.9	yes	22	117.49	even	6	inner
351.2.l.b.127.9		22	39.23	odd	6
351.2.l.b.199.3		22	9.5	odd	6
351.2.r.b.10.3		22	117.23	odd	6
351.2.r.b.316.3		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67544 - 0.967314i) q^{2} +(-1.73126 + 0.0524448i) q^{3} +(0.871392 - 1.50930i) q^{4} +(2.26677 - 1.30872i) q^{5} +(-2.84988 + 1.76254i) q^{6} -2.32894i q^{7} +0.497616i q^{8} +(2.99450 - 0.181591i) q^{9} +(2.53189 - 4.38536i) q^{10} +(-4.66542 + 2.69358i) q^{11} +(-1.42945 + 2.65868i) q^{12} +(-1.31974 + 3.35534i) q^{13} +(-2.25282 - 3.90199i) q^{14} +(-3.85573 + 2.38461i) q^{15} +(2.22414 + 3.85232i) q^{16} +(0.835786 + 1.44762i) q^{17} +(4.84144 - 3.20086i) q^{18} +(1.90355 - 1.09901i) q^{19} -4.56164i q^{20} +(0.122141 + 4.03200i) q^{21} +(-5.21107 + 9.02585i) q^{22} -4.20875 q^{23} +(-0.0260974 - 0.861500i) q^{24} +(0.925505 - 1.60302i) q^{25} +(1.03453 + 6.89826i) q^{26} +(-5.17472 + 0.471426i) q^{27} +(-3.51506 - 2.02942i) q^{28} +(-2.86254 - 4.95807i) q^{29} +(-4.15336 + 7.72497i) q^{30} +(7.55059 - 4.35934i) q^{31} +(6.59090 + 3.80526i) q^{32} +(7.93577 - 4.90795i) q^{33} +(2.80061 + 1.61693i) q^{34} +(-3.04794 - 5.27918i) q^{35} +(2.33531 - 4.67782i) q^{36} +(-1.22479 - 0.707130i) q^{37} +(2.12618 - 3.68265i) q^{38} +(2.10884 - 5.87816i) q^{39} +(0.651240 + 1.12798i) q^{40} -1.52349i q^{41} +(4.10485 + 6.63721i) q^{42} +1.87767 q^{43} +9.38866i q^{44} +(6.55020 - 4.33059i) q^{45} +(-7.05150 + 4.07119i) q^{46} +(-4.47809 - 2.58543i) q^{47} +(-4.05258 - 6.55270i) q^{48} +1.57603 q^{49} -3.58101i q^{50} +(-1.52288 - 2.46238i) q^{51} +(3.91419 + 4.91569i) q^{52} -9.81151 q^{53} +(-8.21390 + 5.79543i) q^{54} +(-7.05029 + 12.2115i) q^{55} +1.15892 q^{56} +(-3.23789 + 2.00250i) q^{57} +(-9.59202 - 5.53796i) q^{58} +(6.59276 + 3.80633i) q^{59} +(0.239234 + 7.89737i) q^{60} -0.934170 q^{61} +(8.43369 - 14.6076i) q^{62} +(-0.422915 - 6.97401i) q^{63} +5.82698 q^{64} +(1.39966 + 9.33296i) q^{65} +(8.54835 - 15.8993i) q^{66} -2.06839i q^{67} +2.91319 q^{68} +(7.28643 - 0.220727i) q^{69} +(-10.2133 - 5.89662i) q^{70} +(-10.9702 + 6.33363i) q^{71} +(0.0903625 + 1.49011i) q^{72} -12.6627i q^{73} -2.73607 q^{74} +(-1.51822 + 2.82378i) q^{75} -3.83068i q^{76} +(6.27319 + 10.8655i) q^{77} +(-2.15281 - 11.8884i) q^{78} +(3.46731 - 6.00556i) q^{79} +(10.0832 + 5.82155i) q^{80} +(8.93405 - 1.08755i) q^{81} +(-1.47369 - 2.55251i) q^{82} +(7.95495 + 4.59279i) q^{83} +(6.19191 + 3.32910i) q^{84} +(3.78907 + 2.18762i) q^{85} +(3.14592 - 1.81630i) q^{86} +(5.21582 + 8.43357i) q^{87} +(-1.34037 - 2.32158i) q^{88} +(8.62292 + 4.97845i) q^{89} +(6.78540 - 13.5917i) q^{90} +(7.81439 + 3.07359i) q^{91} +(-3.66748 + 6.35226i) q^{92} +(-12.8434 + 7.94312i) q^{93} -10.0037 q^{94} +(2.87660 - 4.98242i) q^{95} +(-11.6101 - 6.24222i) q^{96} -2.35207i q^{97} +(2.64054 - 1.52452i) q^{98} +(-13.4815 + 8.91312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

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