LMFDB - Embedded newform 261.2.e.a.88.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(88,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.88"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			88.11
Character	$\chi$	$=$	261.88
Dual form			261.2.e.a.175.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13175 - 1.96024i) q^{2} +(-1.24509 - 1.20406i) q^{3} +(-1.56171 - 2.70495i) q^{4} +(-0.731092 - 1.26629i) q^{5} +(-3.76937 + 1.07799i) q^{6} +(0.881947 - 1.52758i) q^{7} -2.54284 q^{8} +(0.100498 + 2.99832i) q^{9} -3.30965 q^{10} +(-0.717272 + 1.24235i) q^{11} +(-1.31245 + 5.24829i) q^{12} +(1.19084 + 2.06259i) q^{13} +(-1.99628 - 3.45766i) q^{14} +(-0.614407 + 2.45692i) q^{15} +(0.245562 - 0.425326i) q^{16} -0.663204 q^{17} +(5.99117 + 3.19634i) q^{18} -0.285880 q^{19} +(-2.28350 + 3.95514i) q^{20} +(-2.93739 + 0.840057i) q^{21} +(1.62354 + 2.81206i) q^{22} +(-3.84389 - 6.65780i) q^{23} +(3.16606 + 3.06172i) q^{24} +(1.43101 - 2.47858i) q^{25} +5.39091 q^{26} +(3.48501 - 3.85418i) q^{27} -5.50937 q^{28} +(0.500000 - 0.866025i) q^{29} +(4.12081 + 3.98500i) q^{30} +(3.61809 + 6.26671i) q^{31} +(-3.09867 - 5.36705i) q^{32} +(2.38893 - 0.683203i) q^{33} +(-0.750579 + 1.30004i) q^{34} -2.57914 q^{35} +(7.95336 - 4.95433i) q^{36} +6.07502 q^{37} +(-0.323544 + 0.560395i) q^{38} +(1.00078 - 4.00195i) q^{39} +(1.85905 + 3.21996i) q^{40} +(1.67673 + 2.90417i) q^{41} +(-1.67767 + 6.70874i) q^{42} +(1.17479 - 2.03480i) q^{43} +4.48067 q^{44} +(3.72326 - 2.31930i) q^{45} -17.4012 q^{46} +(4.40603 - 7.63146i) q^{47} +(-0.817864 + 0.233899i) q^{48} +(1.94434 + 3.36769i) q^{49} +(-3.23908 - 5.61026i) q^{50} +(0.825748 + 0.798535i) q^{51} +(3.71948 - 6.44232i) q^{52} +0.00781588 q^{53} +(-3.61098 - 11.1934i) q^{54} +2.09757 q^{55} +(-2.24265 + 3.88438i) q^{56} +(0.355947 + 0.344216i) q^{57} +(-1.13175 - 1.96024i) q^{58} +(1.57842 + 2.73391i) q^{59} +(7.60537 - 2.17504i) q^{60} +(-6.81256 + 11.7997i) q^{61} +16.3791 q^{62} +(4.66879 + 2.49084i) q^{63} -13.0454 q^{64} +(1.74122 - 3.01589i) q^{65} +(1.36442 - 5.45610i) q^{66} +(1.84074 + 3.18825i) q^{67} +(1.03573 + 1.79394i) q^{68} +(-3.23039 + 12.9178i) q^{69} +(-2.91893 + 5.05574i) q^{70} -6.67561 q^{71} +(-0.255550 - 7.62423i) q^{72} -7.35076 q^{73} +(6.87539 - 11.9085i) q^{74} +(-4.76609 + 1.36304i) q^{75} +(0.446461 + 0.773293i) q^{76} +(1.26519 + 2.19138i) q^{77} +(-6.71217 - 6.49096i) q^{78} +(8.22196 - 14.2409i) q^{79} -0.718114 q^{80} +(-8.97980 + 0.602649i) q^{81} +7.59052 q^{82} +(-4.61219 + 7.98855i) q^{83} +(6.85966 + 6.63359i) q^{84} +(0.484863 + 0.839807i) q^{85} +(-2.65914 - 4.60577i) q^{86} +(-1.66529 + 0.476251i) q^{87} +(1.82390 - 3.15910i) q^{88} +12.8442 q^{89} +(-0.332613 - 9.92336i) q^{90} +4.20102 q^{91} +(-12.0060 + 20.7951i) q^{92} +(3.04063 - 12.1590i) q^{93} +(-9.97302 - 17.2738i) q^{94} +(0.209005 + 0.362007i) q^{95} +(-2.60411 + 10.4134i) q^{96} +(-3.30966 + 5.73249i) q^{97} +8.80201 q^{98} +(-3.79705 - 2.02575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) $ 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.13175	−	1.96024i	0.800266	−	1.38610i	−0.119174	−	0.992873i	$-0.538025\pi$
$2$	1.13175	−	1.96024i	0.800266	−	1.38610i	0.919441	−	0.393229i	$-0.128642\pi$
$3$	−1.24509	−	1.20406i	−0.718853	−	0.695162i
$3$	−1.24509	−	1.20406i	−0.718853	−	0.695162i
$4$	−1.56171	−	2.70495i	−0.780853	−	1.35248i
$5$	−0.731092	−	1.26629i	−0.326954	−	0.566301i	0.654952	−	0.755671i	$-0.272689\pi$
$5$	−0.731092	−	1.26629i	−0.326954	−	0.566301i	−0.981906	+	0.189370i	$0.939356\pi$
$6$	−3.76937	+	1.07799i	−1.53884	+	0.440089i
$7$	0.881947	−	1.52758i	0.333345	−	0.577370i	−0.649821	−	0.760087i	$-0.725156\pi$
$7$	0.881947	−	1.52758i	0.333345	−	0.577370i	0.983165	+	0.182718i	$0.0584894\pi$
$8$	−2.54284			−0.899028
$9$	0.100498	+	2.99832i	0.0334993	+	0.999439i
$10$	−3.30965			−1.04660
$11$	−0.717272	+	1.24235i	−0.216266	+	0.374583i	−0.953663	−	0.300876i	$-0.902721\pi$
$11$	−0.717272	+	1.24235i	−0.216266	+	0.374583i	0.737398	+	0.675459i	$0.236054\pi$
$12$	−1.31245	+	5.24829i	−0.378872	+	1.51505i
$13$	1.19084	+	2.06259i	0.330279	+	0.572060i	0.982566	−	0.185912i	$-0.0595238\pi$
$13$	1.19084	+	2.06259i	0.330279	+	0.572060i	−0.652288	+	0.757972i	$0.726191\pi$
$14$	−1.99628	−	3.45766i	−0.533529	−	0.924099i
$15$	−0.614407	+	2.45692i	−0.158639	+	0.634373i
$16$	0.245562	−	0.425326i	0.0613906	−	0.106332i
$17$	−0.663204			−0.160851			−0.0804253	−	0.996761i	$-0.525628\pi$
$17$	−0.663204			−0.160851			−0.0804253	+	0.996761i	$0.525628\pi$
$18$	5.99117	+	3.19634i	1.41213	+	0.753384i
$19$	−0.285880			−0.0655854			−0.0327927	−	0.999462i	$-0.510440\pi$
$19$	−0.285880			−0.0655854			−0.0327927	+	0.999462i	$0.510440\pi$
$20$	−2.28350	+	3.95514i	−0.510606	+	0.884396i
$21$	−2.93739	+	0.840057i	−0.640991	+	0.183315i
$22$	1.62354	+	2.81206i	0.346140	+	0.599532i
$23$	−3.84389	−	6.65780i	−0.801505	−	1.38825i	−0.918625	−	0.395130i	$-0.870699\pi$
$23$	−3.84389	−	6.65780i	−0.801505	−	1.38825i	0.117120	−	0.993118i	$-0.462634\pi$
$24$	3.16606	+	3.06172i	0.646269	+	0.624970i
$25$	1.43101	−	2.47858i	0.286202	−	0.495716i
$26$	5.39091			1.05724
$27$	3.48501	−	3.85418i	0.670691	−	0.741737i
$28$	−5.50937			−1.04117
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$30$	4.12081	+	3.98500i	0.752353	+	0.727558i
$31$	3.61809	+	6.26671i	0.649828	+	1.12553i	0.983164	+	0.182727i	$0.0584923\pi$
$31$	3.61809	+	6.26671i	0.649828	+	1.12553i	−0.333336	+	0.942808i	$0.608174\pi$
$32$	−3.09867	−	5.36705i	−0.547772	−	0.948769i
$33$	2.38893	−	0.683203i	0.415859	−	0.118930i
$34$	−0.750579	+	1.30004i	−0.128723	+	0.222955i
$35$	−2.57914			−0.435954
$36$	7.95336	−	4.95433i	1.32556	−	0.825722i
$37$	6.07502			0.998728			0.499364	−	0.866392i	$-0.333567\pi$
$37$	6.07502			0.998728			0.499364	+	0.866392i	$0.333567\pi$
$38$	−0.323544	+	0.560395i	−0.0524858	+	0.0909081i
$39$	1.00078	−	4.00195i	0.160252	−	0.640824i
$40$	1.85905	+	3.21996i	0.293941	+	0.509121i
$41$	1.67673	+	2.90417i	0.261861	+	0.453556i	0.966736	−	0.255775i	$-0.0823306\pi$
$41$	1.67673	+	2.90417i	0.261861	+	0.453556i	−0.704876	+	0.709331i	$0.748997\pi$
$42$	−1.67767	+	6.70874i	−0.258870	+	1.03518i
$43$	1.17479	−	2.03480i	0.179154	−	0.310305i	−0.762437	−	0.647063i	$-0.775997\pi$
$43$	1.17479	−	2.03480i	0.179154	−	0.310305i	0.941591	+	0.336758i	$0.109330\pi$
$44$	4.48067			0.675486
$45$	3.72326	−	2.31930i	0.555031	−	0.345741i
$46$	−17.4012			−2.56567
$47$	4.40603	−	7.63146i	0.642685	−	1.11316i	−0.342146	−	0.939647i	$-0.611154\pi$
$47$	4.40603	−	7.63146i	0.642685	−	1.11316i	0.984831	−	0.173516i	$-0.0555130\pi$
$48$	−0.817864	+	0.233899i	−0.118048	+	0.0337604i
$49$	1.94434	+	3.36769i	0.277763	+	0.481099i
$50$	−3.23908	−	5.61026i	−0.458076	−	0.793410i
$51$	0.825748	+	0.798535i	0.115628	+	0.111817i
$52$	3.71948	−	6.44232i	0.515799	−	0.893389i
$53$	0.00781588			0.00107359			0.000536797	−	1.00000i	$-0.499829\pi$
$53$	0.00781588			0.00107359			0.000536797		1.00000i	$0.499829\pi$
$54$	−3.61098	−	11.1934i	−0.491392	−	1.52323i
$55$	2.09757			0.282836
$56$	−2.24265	+	3.88438i	−0.299686	+	0.519072i
$57$	0.355947	+	0.344216i	0.0471463	+	0.0455925i
$58$	−1.13175	−	1.96024i	−0.148606	−	0.257393i
$59$	1.57842	+	2.73391i	0.205493	+	0.355925i	0.950290	−	0.311367i	$-0.100787\pi$
$59$	1.57842	+	2.73391i	0.205493	+	0.355925i	−0.744796	+	0.667292i	$0.767453\pi$
$60$	7.60537	−	2.17504i	0.981849	−	0.280797i
$61$	−6.81256	+	11.7997i	−0.872259	+	1.51080i	−0.0126052	+	0.999921i	$0.504012\pi$
$61$	−6.81256	+	11.7997i	−0.872259	+	1.51080i	−0.859654	+	0.510877i	$0.829321\pi$
$62$	16.3791			2.08014
$63$	4.66879	+	2.49084i	0.588213	+	0.313816i
$64$	−13.0454			−1.63067
$65$	1.74122	−	3.01589i	0.215972	−	0.374075i
$66$	1.36442	−	5.45610i	0.167948	−	0.671599i
$67$	1.84074	+	3.18825i	0.224882	+	0.389507i	0.956284	−	0.292439i	$-0.0944670\pi$
$67$	1.84074	+	3.18825i	0.224882	+	0.389507i	−0.731402	+	0.681947i	$0.761134\pi$
$68$	1.03573	+	1.79394i	0.125601	+	0.217547i
$69$	−3.23039	+	12.9178i	−0.388893	+	1.55512i
$70$	−2.91893	+	5.05574i	−0.348879	+	0.604276i
$71$	−6.67561			−0.792249			−0.396125	−	0.918197i	$-0.629645\pi$
$71$	−6.67561			−0.792249			−0.396125	+	0.918197i	$0.629645\pi$
$72$	−0.255550	−	7.62423i	−0.0301168	−	0.898524i
$73$	−7.35076			−0.860341			−0.430171	−	0.902748i	$-0.641547\pi$
$73$	−7.35076			−0.860341			−0.430171	+	0.902748i	$0.641547\pi$
$74$	6.87539	−	11.9085i	0.799248	−	1.38434i
$75$	−4.76609	+	1.36304i	−0.550340	+	0.157390i
$76$	0.446461	+	0.773293i	0.0512126	+	0.0887028i
$77$	1.26519	+	2.19138i	0.144182	+	0.249730i
$78$	−6.71217	−	6.49096i	−0.760004	−	0.734956i
$79$	8.22196	−	14.2409i	0.925043	−	1.60222i	0.133552	−	0.991042i	$-0.457362\pi$
$79$	8.22196	−	14.2409i	0.925043	−	1.60222i	0.791492	−	0.611180i	$-0.209305\pi$
$80$	−0.718114			−0.0802876
$81$	−8.97980	+	0.602649i	−0.997756	+	0.0669611i
$82$	7.59052			0.838233
$83$	−4.61219	+	7.98855i	−0.506254	+	0.876857i	0.493720	+	0.869621i	$0.335637\pi$
$83$	−4.61219	+	7.98855i	−0.506254	+	0.876857i	−0.999974	+	0.00723635i	$0.997697\pi$
$84$	6.85966	+	6.63359i	0.748450	+	0.723784i
$85$	0.484863	+	0.839807i	0.0525908	+	0.0910899i
$86$	−2.65914	−	4.60577i	−0.286743	−	0.496653i
$87$	−1.66529	+	0.476251i	−0.178538	+	0.0510595i
$88$	1.82390	−	3.15910i	0.194429	−	0.336761i
$89$	12.8442			1.36148			0.680740	−	0.732525i	$-0.261658\pi$
$89$	12.8442			1.36148			0.680740	+	0.732525i	$0.261658\pi$
$90$	−0.332613	−	9.92336i	−0.0350605	−	1.04601i
$91$	4.20102			0.440387
$92$	−12.0060	+	20.7951i	−1.25172	+	2.16804i
$93$	3.04063	−	12.1590i	0.315298	−	1.26083i
$94$	−9.97302	−	17.2738i	−1.02864	−	1.78165i
$95$	0.209005	+	0.362007i	0.0214434	+	0.0371411i
$96$	−2.60411	+	10.4134i	−0.265781	+	1.06282i
$97$	−3.30966	+	5.73249i	−0.336045	+	0.582046i	−0.983685	−	0.179900i	$-0.942423\pi$
$97$	−3.30966	+	5.73249i	−0.336045	+	0.582046i	0.647640	+	0.761946i	$0.275756\pi$
$98$	8.80201			0.889137
$99$	−3.79705	−	2.02575i	−0.381617	−	0.203596i
$100$	−8.93926			−0.893926
$101$	−1.23661	+	2.14188i	−0.123048	+	0.213125i	−0.920968	−	0.389638i	$-0.872600\pi$
$101$	−1.23661	+	2.14188i	−0.123048	+	0.213125i	0.797921	+	0.602763i	$0.205933\pi$
$102$	2.49986	−	0.714929i	0.247523	−	0.0707885i
$103$	5.45940	+	9.45596i	0.537931	+	0.931724i	0.999015	+	0.0443673i	$0.0141272\pi$
$103$	5.45940	+	9.45596i	0.537931	+	0.931724i	−0.461084	+	0.887356i	$0.652539\pi$
$104$	−3.02811	−	5.24483i	−0.296930	−	0.514298i
$105$	3.21126	+	3.10542i	0.313387	+	0.303058i
$106$	0.00884560	−	0.0153210i	0.000859161	−	0.00148811i
$107$	5.90085			0.570456			0.285228	−	0.958460i	$-0.407931\pi$
$107$	5.90085			0.570456			0.285228	+	0.958460i	$0.407931\pi$
$108$	−15.8679	−	3.40770i	−1.52689	−	0.327906i
$109$	−5.82189			−0.557636			−0.278818	−	0.960344i	$-0.589943\pi$
$109$	−5.82189			−0.557636			−0.278818	+	0.960344i	$0.589943\pi$
$110$	2.37391	−	4.11174i	0.226344	−	0.392039i
$111$	−7.56395	−	7.31467i	−0.717938	−	0.694278i
$112$	−0.433146	−	0.750231i	−0.0409284	−	0.0708901i
$113$	9.73668	+	16.8644i	0.915950	+	1.58647i	0.805505	+	0.592589i	$0.201894\pi$
$113$	9.73668	+	16.8644i	0.915950	+	1.58647i	0.110444	+	0.993882i	$0.464773\pi$
$114$	1.07759	−	0.308177i	0.100925	−	0.0288634i
$115$	−5.62047	+	9.73493i	−0.524111	+	0.907787i
$116$	−3.12341			−0.290001
$117$	−6.06462	+	3.77779i	−0.560675	+	0.349257i
$118$	7.14551			0.657798
$119$	−0.584911	+	1.01309i	−0.0536187	+	0.0928702i
$120$	1.56234	−	6.24754i	0.142621	−	0.570320i
$121$	4.47104	+	7.74407i	0.406458	+	0.704007i
$122$	15.4202	+	26.7086i	1.39608	+	2.41808i
$123$	1.40911	−	5.63483i	0.127056	−	0.508076i
$124$	11.3008	−	19.5735i	1.01484	−	1.75775i
$125$	−11.4957			−1.02821
$126$	10.1665	−	6.33298i	0.905708	−	0.564186i
$127$	21.6824			1.92400			0.962001	−	0.273046i	$-0.0880311\pi$
$127$	21.6824			1.92400			0.962001	+	0.273046i	$0.0880311\pi$
$128$	−8.56675	+	14.8380i	−0.757201	+	1.31151i
$129$	−3.91274	+	1.11900i	−0.344498	+	0.0985220i
$130$	−3.94125	−	6.82645i	−0.345671	−	0.598719i
$131$	−2.80373	−	4.85619i	−0.244963	−	0.424288i	0.717158	−	0.696910i	$-0.245442\pi$
$131$	−2.80373	−	4.85619i	−0.244963	−	0.424288i	−0.962121	+	0.272622i	$0.912109\pi$
$132$	−5.57884	−	5.39498i	−0.485575	−	0.469572i
$133$	−0.252131	+	0.436704i	−0.0218625	+	0.0378670i
$134$	8.33301			0.719863
$135$	−7.42836	−	1.59527i	−0.639332	−	0.137299i
$136$	1.68642			0.144609
$137$	0.254845	−	0.441404i	0.0217728	−	0.0377117i	−0.854934	−	0.518737i	$-0.826402\pi$
$137$	0.254845	−	0.441404i	0.0217728	−	0.0377117i	0.876707	+	0.481026i	$0.159736\pi$
$138$	21.6661	+	20.9521i	1.84434	+	1.78356i
$139$	−3.42541	−	5.93299i	−0.290540	−	0.503230i	0.683398	−	0.730046i	$-0.260502\pi$
$139$	−3.42541	−	5.93299i	−0.290540	−	0.503230i	−0.973937	+	0.226817i	$0.927168\pi$
$140$	4.02785	+	6.97644i	0.340416	+	0.589617i
$141$	−14.6746	+	4.19675i	−1.23582	+	0.353430i
$142$	−7.55511	+	13.0858i	−0.634010	+	1.09814i
$143$	−3.41662			−0.285712
$144$	1.29994	+	0.693529i	0.108328	+	0.0577941i
$145$	−1.46218			−0.121428
$146$	−8.31920	+	14.4093i	−0.688502	+	1.19252i
$147$	1.63402	−	6.53418i	0.134771	−	0.538930i
$148$	−9.48740	−	16.4327i	−0.779859	−	1.35076i
$149$	4.45540	+	7.71697i	0.365000	+	0.632199i	0.988776	−	0.149404i	$-0.0477356\pi$
$149$	4.45540	+	7.71697i	0.365000	+	0.632199i	−0.623776	+	0.781603i	$0.714402\pi$
$150$	−2.72211	+	10.8853i	−0.222260	+	0.888782i
$151$	−4.64985	+	8.05377i	−0.378399	+	0.655407i	−0.990830	−	0.135118i	$-0.956859\pi$
$151$	−4.64985	+	8.05377i	−0.378399	+	0.655407i	0.612430	+	0.790525i	$0.290192\pi$
$152$	0.726947			0.0589632
$153$	−0.0666506	−	1.98849i	−0.00538838	−	0.160760i
$154$	5.72751			0.461536
$155$	5.29031	−	9.16308i	0.424928	−	0.735997i
$156$	−12.3880	+	3.54281i	−0.991834	+	0.283652i
$157$	2.75908	+	4.77887i	0.220199	+	0.381395i	0.954868	−	0.297030i	$-0.0959961\pi$
$157$	2.75908	+	4.77887i	0.220199	+	0.381395i	−0.734670	+	0.678425i	$0.762663\pi$
$158$	−18.6104	−	32.2341i	−1.48056	−	2.56441i
$159$	−0.00973147	−	0.00941075i	−0.000771756	−	0.000746321i
$160$	−4.53082	+	7.84761i	−0.358193	+	0.620408i
$161$	−13.5604			−1.06871
$162$	−8.98153	+	18.2847i	−0.705655	+	1.43658i
$163$	8.91481			0.698262			0.349131	−	0.937074i	$-0.386477\pi$
$163$	8.91481			0.698262			0.349131	+	0.937074i	$0.386477\pi$
$164$	5.23710	−	9.07093i	0.408949	−	0.708321i
$165$	−2.61166	−	2.52559i	−0.203317	−	0.196617i
$166$	10.4397	+	18.0820i	0.810276	+	1.40344i
$167$	−10.4926	−	18.1737i	−0.811941	−	1.40632i	−0.911504	−	0.411291i	$-0.865078\pi$
$167$	−10.4926	−	18.1737i	−0.811941	−	1.40632i	0.0995636	−	0.995031i	$-0.468255\pi$
$168$	7.46931	−	2.13613i	0.576269	−	0.164806i
$169$	3.66381	−	6.34591i	0.281832	−	0.488147i
$170$	2.19497			0.168346
$171$	−0.0287304	−	0.857159i	−0.00219707	−	0.0655486i
$172$	−7.33873			−0.559573
$173$	−5.32925	+	9.23053i	−0.405175	+	0.701784i	−0.994342	−	0.106227i	$-0.966123\pi$
$173$	−5.32925	+	9.23053i	−0.405175	+	0.701784i	0.589167	+	0.808012i	$0.299456\pi$
$174$	−0.951117	+	3.80337i	−0.0721040	+	0.288333i
$175$	−2.52415	−	4.37196i	−0.190808	−	0.330489i
$176$	0.352270	+	0.610149i	0.0265533	+	0.0459917i
$177$	1.32650	−	5.30448i	0.0997060	−	0.398709i
$178$	14.5364	−	25.1777i	1.08955	−	1.88715i
$179$	−23.8704			−1.78415			−0.892077	−	0.451883i	$-0.850752\pi$
$179$	−23.8704			−1.78415			−0.892077	+	0.451883i	$0.850752\pi$
$180$	−12.0882	−	6.44917i	−0.901004	−	0.480693i
$181$	2.52801			0.187905			0.0939527	−	0.995577i	$-0.470050\pi$
$181$	2.52801			0.187905			0.0939527	+	0.995577i	$0.470050\pi$
$182$	4.75450	−	8.23503i	0.352427	−	0.610421i
$183$	22.6898	−	6.48899i	1.67728	−	0.479680i
$184$	9.77437	+	16.9297i	0.720576	+	1.24807i
$185$	−4.44140	−	7.69273i	−0.326538	−	0.565581i
$186$	−20.3934	−	19.7213i	−1.49532	−	1.44604i
$187$	0.475697	−	0.823932i	0.0347864	−	0.0602519i
$188$	−27.5237			−2.00737
$189$	−2.81396	−	8.72280i	−0.204685	−	0.634491i
$190$	0.946162			0.0686418
$191$	11.5484	−	20.0024i	0.835611	−	1.44732i	−0.0579218	−	0.998321i	$-0.518447\pi$
$191$	11.5484	−	20.0024i	0.835611	−	1.44732i	0.893532	−	0.448999i	$-0.148219\pi$
$192$	16.2427	+	15.7074i	1.17221	+	1.13358i
$193$	−4.65930	−	8.07014i	−0.335384	−	0.580901i	0.648175	−	0.761492i	$-0.275533\pi$
$193$	−4.65930	−	8.07014i	−0.335384	−	0.580901i	−0.983558	+	0.180590i	$0.942199\pi$
$194$	7.49139	+	12.9755i	0.537850	+	0.931584i
$195$	−5.79928	+	1.65852i	−0.415295	+	0.118769i
$196$	6.07297	−	10.5187i	0.433784	−	0.751335i
$197$	−22.5831			−1.60898			−0.804488	−	0.593969i	$-0.797560\pi$
$197$	−22.5831			−1.60898			−0.804488	+	0.593969i	$0.797560\pi$
$198$	−8.26827	+	5.15050i	−0.587600	+	0.366030i
$199$	−23.9744			−1.69950			−0.849751	−	0.527185i	$-0.823248\pi$
$199$	−23.9744			−1.69950			−0.849751	+	0.527185i	$0.823248\pi$
$200$	−3.63882	+	6.30263i	−0.257304	+	0.445663i
$201$	1.54695	−	6.18602i	0.109113	−	0.436328i
$202$	2.79907	+	4.84812i	0.196942	+	0.341113i
$203$	−0.881947	−	1.52758i	−0.0619005	−	0.107215i
$204$	0.870423	−	3.48069i	0.0609418	−	0.243697i
$205$	2.45168	−	4.24644i	0.171233	−	0.296584i
$206$	24.7147			1.72195
$207$	19.5759	−	12.1943i	1.36062	−	0.847561i
$208$	1.16970			0.0811041
$209$	0.205054	−	0.355164i	0.0141839	−	0.0245672i
$210$	9.72172	−	2.78029i	0.670863	−	0.191858i
$211$	4.30373	+	7.45428i	0.296281	+	0.513173i	0.975282	−	0.220964i	$-0.0709202\pi$
$211$	4.30373	+	7.45428i	0.296281	+	0.513173i	−0.679001	+	0.734137i	$0.737587\pi$
$212$	−0.0122061	−	0.0211416i	−0.000838318	−	0.00145201i
$213$	8.31173	+	8.03781i	0.569511	+	0.550742i
$214$	6.67827	−	11.5671i	0.456517	−	0.790711i
$215$	−3.43553			−0.234301
$216$	−8.86181	+	9.80054i	−0.602970	+	0.666843i
$217$	12.7638			0.866466
$218$	−6.58891	+	11.4123i	−0.446257	+	0.772941i
$219$	9.15236	+	8.85073i	0.618459	+	0.598077i
$220$	−3.27578	−	5.67382i	−0.220853	−	0.382529i
$221$	−0.789768	−	1.36792i	−0.0531255	−	0.0920161i
$222$	−22.8990	+	6.54883i	−1.53688	+	0.439529i
$223$	11.3007	−	19.5733i	0.756748	−	1.31073i	−0.187753	−	0.982216i	$-0.560121\pi$
$223$	11.3007	−	19.5733i	0.756748	−	1.31073i	0.944501	−	0.328509i	$-0.106546\pi$
$224$	−10.9314			−0.730387
$225$	7.57539	+	4.04153i	0.505026	+	0.269435i
$226$	44.0778			2.93201
$227$	−8.93738	+	15.4800i	−0.593195	+	1.02744i	0.400604	+	0.916251i	$0.368800\pi$
$227$	−8.93738	+	15.4800i	−0.593195	+	1.02744i	−0.993799	+	0.111192i	$0.964533\pi$
$228$	0.375204	−	1.50038i	0.0248485	−	0.0993653i
$229$	0.464394	+	0.804354i	0.0306880	+	0.0531532i	0.880962	−	0.473188i	$-0.156897\pi$
$229$	0.464394	+	0.804354i	0.0306880	+	0.0531532i	−0.850274	+	0.526341i	$0.823563\pi$
$230$	12.7219	+	22.0350i	0.838857	+	1.45294i
$231$	1.06326	−	4.25182i	0.0699575	−	0.279749i
$232$	−1.27142	+	2.20216i	−0.0834727	+	0.144579i
$233$	−5.04912			−0.330779			−0.165389	−	0.986228i	$-0.552888\pi$
$233$	−5.04912			−0.330779			−0.165389	+	0.986228i	$0.552888\pi$
$234$	0.541776	+	16.1637i	0.0354170	+	1.05665i
$235$	−12.8848			−0.840514
$236$	4.93007	−	8.53913i	0.320920	−	0.555850i
$237$	−27.3839	+	7.83145i	−1.77877	+	0.508707i
$238$	1.32394	+	2.29314i	0.0858184	+	0.148642i
$239$	6.92322	+	11.9914i	0.447826	+	0.775657i	0.998244	−	0.0592317i	$-0.0188651\pi$
$239$	6.92322	+	11.9914i	0.447826	+	0.775657i	−0.550418	+	0.834889i	$0.685532\pi$
$240$	0.894117	+	0.864650i	0.0577150	+	0.0558129i
$241$	6.14639	−	10.6459i	0.395924	−	0.685760i	−0.597295	−	0.802022i	$-0.703758\pi$
$241$	6.14639	−	10.6459i	0.395924	−	0.685760i	0.993219	+	0.116262i	$0.0370912\pi$
$242$	20.2404			1.30110
$243$	11.9063	+	10.0618i	0.763788	+	0.645467i
$244$	42.5569			2.72442
$245$	2.84298	−	4.92419i	0.181631	−	0.314595i
$246$	−9.45088	−	9.13942i	−0.602566	−	0.582708i
$247$	−0.340437	−	0.589654i	−0.0216615	−	0.0375188i
$248$	−9.20021	−	15.9352i	−0.584214	−	1.01189i
$249$	15.3613	−	4.39313i	0.973480	−	0.278403i
$250$	−13.0102	+	22.5344i	−0.822840	+	1.42520i
$251$	−20.8490			−1.31598			−0.657989	−	0.753028i	$-0.728593\pi$
$251$	−20.8490			−1.31598			−0.657989	+	0.753028i	$0.728593\pi$
$252$	−0.553680	−	16.5188i	−0.0348786	−	1.04059i
$253$	11.0284			0.693352
$254$	24.5390	−	42.5028i	1.53971	−	2.66686i
$255$	0.407477	−	1.62944i	0.0255172	−	0.102039i
$256$	6.34541	+	10.9906i	0.396588	+	0.686911i
$257$	7.54729	+	13.0723i	0.470787	+	0.815428i	0.999442	−	0.0334096i	$-0.0106366\pi$
$257$	7.54729	+	13.0723i	0.470787	+	0.815428i	−0.528654	+	0.848837i	$0.677303\pi$
$258$	−2.23473	+	8.93635i	−0.139128	+	0.556353i
$259$	5.35785	−	9.28007i	0.332921	−	0.576635i
$260$	−10.8771			−0.674570
$261$	2.64687	+	1.41212i	0.163837	+	0.0874083i
$262$	−12.6924			−0.784141
$263$	8.86362	−	15.3522i	0.546554	−	0.946660i	−0.451953	−	0.892042i	$-0.649272\pi$
$263$	8.86362	−	15.3522i	0.546554	−	0.946660i	0.998507	−	0.0546182i	$-0.0173942\pi$
$264$	−6.07465	+	1.73727i	−0.373869	+	0.106922i
$265$	−0.00571412	−	0.00989715i	−0.000351016	−	0.000607977i
$266$	0.570698	+	0.988478i	0.0349917	+	0.0606074i
$267$	−15.9921	−	15.4651i	−0.978704	−	0.946449i
$268$	5.74939	−	9.95823i	0.351200	−	0.608296i
$269$	23.9256			1.45877			0.729386	−	0.684102i	$-0.239806\pi$
$269$	23.9256			1.45877			0.729386	+	0.684102i	$0.239806\pi$
$270$	−11.5342	+	12.7560i	−0.701946	+	0.776303i
$271$	−28.4934			−1.73085			−0.865424	−	0.501040i	$-0.832951\pi$
$271$	−28.4934			−1.73085			−0.865424	+	0.501040i	$0.832951\pi$
$272$	−0.162858	+	0.282078i	−0.00987471	+	0.0171035i
$273$	−5.23065	−	5.05827i	−0.316573	−	0.306140i
$274$	−0.576840	−	0.999115i	−0.0348482	−	0.0603588i
$275$	2.05285	+	3.55563i	0.123791	+	0.214413i
$276$	39.9870	−	11.4358i	2.40694	−	0.688353i
$277$	−2.53946	+	4.39848i	−0.152581	+	0.264279i	−0.932176	−	0.362006i	$-0.882092\pi$
$277$	−2.53946	+	4.39848i	−0.152581	+	0.264279i	0.779594	+	0.626285i	$0.215425\pi$
$278$	−15.5068			−0.930037
$279$	−18.4260	+	11.4780i	−1.10313	+	0.687168i
$280$	6.55832			0.391935
$281$	−1.74766	+	3.02704i	−0.104257	+	0.180578i	−0.913434	−	0.406986i	$-0.866580\pi$
$281$	−1.74766	+	3.02704i	−0.104257	+	0.180578i	0.809178	+	0.587564i	$0.199913\pi$
$282$	−8.38129	+	33.5155i	−0.499099	+	1.99582i
$283$	6.02754	+	10.4400i	0.358300	+	0.620594i	0.987677	−	0.156506i	$-0.0500231\pi$
$283$	6.02754	+	10.4400i	0.358300	+	0.620594i	−0.629377	+	0.777100i	$0.716690\pi$
$284$	10.4253	+	18.0572i	0.618630	+	1.07150i
$285$	0.175647	−	0.702384i	0.0104044	−	0.0416056i
$286$	−3.86675	+	6.69740i	−0.228646	+	0.396026i
$287$	5.91513			0.349159
$288$	15.7807	−	9.83016i	0.929886	−	0.579247i
$289$	−16.5602			−0.974127
$290$	−1.65482	+	2.86624i	−0.0971745	+	0.168311i
$291$	11.0231	−	3.15246i	0.646183	−	0.184800i
$292$	11.4797	+	19.8835i	0.671800	+	1.16359i
$293$	9.68514	+	16.7752i	0.565812	+	0.980015i	0.996974	+	0.0777406i	$0.0247706\pi$
$293$	9.68514	+	16.7752i	0.565812	+	0.980015i	−0.431161	+	0.902275i	$0.641896\pi$
$294$	−10.9593	−	10.5981i	−0.639159	−	0.618094i
$295$	2.30795	−	3.99748i	0.134374	−	0.232742i
$296$	−15.4478			−0.897885
$297$	2.28854	+	7.09410i	0.132795	+	0.411641i
$298$	20.1695			1.16839
$299$	9.15489	−	15.8567i	0.529441	−	0.917018i
$300$	11.1302	+	10.7634i	0.642602	+	0.621424i
$301$	−2.07221	−	3.58918i	−0.119440	−	0.206877i
$302$	10.5249	+	18.2297i	0.605640	+	1.04900i
$303$	4.11863	−	1.17788i	0.236609	−	0.0676673i
$304$	−0.0702014	+	0.121592i	−0.00402633	+	0.00697380i
$305$	19.9224			1.14076
$306$	−3.97337	−	2.11982i	−0.227142	−	0.121182i
$307$	−15.7614			−0.899548			−0.449774	−	0.893142i	$-0.648496\pi$
$307$	−15.7614			−0.899548			−0.449774	+	0.893142i	$0.648496\pi$
$308$	3.95171	−	6.84457i	0.225170	−	0.390005i
$309$	4.58806	−	18.3469i	0.261006	−	1.04372i
$310$	−11.9746	−	20.7406i	−0.680111	−	1.17799i
$311$	14.2571	+	24.6940i	0.808446	+	1.40027i	0.913940	+	0.405849i	$0.133024\pi$
$311$	14.2571	+	24.6940i	0.808446	+	1.40027i	−0.105495	+	0.994420i	$0.533643\pi$
$312$	−2.54481	+	10.1763i	−0.144071	+	0.576119i
$313$	8.23796	−	14.2686i	0.465637	−	0.806507i	−0.533593	−	0.845741i	$-0.679159\pi$
$313$	8.23796	−	14.2686i	0.465637	−	0.806507i	0.999230	+	0.0392346i	$0.0124920\pi$
$314$	12.4903			0.704870
$315$	−0.259198	−	7.73307i	−0.0146042	−	0.435709i
$316$	−51.3612			−2.88929
$317$	−6.11191	+	10.5861i	−0.343279	+	0.594577i	−0.985040	−	0.172328i	$-0.944871\pi$
$317$	−6.11191	+	10.5861i	−0.343279	+	0.594577i	0.641761	+	0.766905i	$0.278204\pi$
$318$	−0.0294609	+	0.00842546i	−0.00165209	+	0.000472476i
$319$	0.717272	+	1.24235i	0.0401595	+	0.0695583i
$320$	9.53737	+	16.5192i	0.533155	+	0.923452i
$321$	−7.34708	−	7.10495i	−0.410074	−	0.396560i
$322$	−15.3470	+	26.5817i	−0.855253	+	1.48134i
$323$	0.189597			0.0105495
$324$	15.6539	+	23.3488i	0.869664	+	1.29715i
$325$	6.81640			0.378106
$326$	10.0893	−	17.4752i	0.558796	−	0.967862i
$327$	7.24878	+	7.00988i	0.400858	+	0.387648i
$328$	−4.26364	−	7.38484i	−0.235420	−	0.407760i
$329$	−7.77176	−	13.4611i	−0.428471	−	0.742134i
$330$	−7.90650	+	2.26116i	−0.435239	+	0.124473i
$331$	−6.38665	+	11.0620i	−0.351042	+	0.608022i	−0.986432	−	0.164169i	$-0.947506\pi$
$331$	−6.38665	+	11.0620i	−0.351042	+	0.608022i	0.635390	+	0.772191i	$0.280839\pi$
$332$	28.8115			1.58124
$333$	0.610528	+	18.2148i	0.0334567	+	0.998167i
$334$	−47.4998			−2.59908
$335$	2.69150	−	4.66181i	0.147052	−	0.254702i
$336$	−0.364014	+	1.45564i	−0.0198586	+	0.0794115i
$337$	−17.0671	−	29.5611i	−0.929706	−	1.61030i	−0.783812	−	0.620998i	$-0.786728\pi$
$337$	−17.0671	−	29.5611i	−0.929706	−	1.61030i	−0.145894	−	0.989300i	$-0.546606\pi$
$338$	−8.29302	−	14.3639i	−0.451081	−	0.781295i
$339$	8.18267	−	32.7212i	0.444421	−	1.77717i
$340$	1.51443	−	2.62306i	0.0821313	−	0.142256i
$341$	−10.3806			−0.562141
$342$	−1.71276	−	0.913769i	−0.0926153	−	0.0494110i
$343$	19.2065			1.03705
$344$	−2.98731	+	5.17417i	−0.161065	+	0.278973i
$345$	18.7194	−	5.35351i	1.00782	−	0.288223i
$346$	12.0627	+	20.8933i	0.648496	+	1.12323i
$347$	−4.00518	−	6.93718i	−0.215010	−	0.372408i	0.738266	−	0.674510i	$-0.235645\pi$
$347$	−4.00518	−	6.93718i	−0.215010	−	0.372408i	−0.953276	+	0.302102i	$0.902312\pi$
$348$	3.88893	+	3.76076i	0.208468	+	0.201598i
$349$	15.7160	−	27.2209i	0.841258	−	1.45710i	−0.0475738	−	0.998868i	$-0.515149\pi$
$349$	15.7160	−	27.2209i	0.841258	−	1.45710i	0.888832	−	0.458234i	$-0.151518\pi$
$350$	−11.4268			−0.610788
$351$	12.0997	+	2.59845i	0.645833	+	0.138695i
$352$	8.89034			0.473857
$353$	−6.74396	+	11.6809i	−0.358945	+	0.621710i	−0.987785	−	0.155824i	$-0.950197\pi$
$353$	−6.74396	+	11.6809i	−0.358945	+	0.621710i	0.628840	+	0.777535i	$0.283530\pi$
$354$	−8.89681	−	8.60360i	−0.472860	−	0.457276i
$355$	4.88048	+	8.45324i	0.259029	+	0.448652i
$356$	−20.0588	−	34.7429i	−1.06311	−	1.84137i
$357$	1.94809	−	0.557129i	0.103104	−	0.0294864i
$358$	−27.0152	+	46.7917i	−1.42780	+	2.47302i
$359$	5.91834			0.312358			0.156179	−	0.987729i	$-0.450082\pi$
$359$	5.91834			0.312358			0.156179	+	0.987729i	$0.450082\pi$
$360$	−9.46764	+	5.89761i	−0.498988	+	0.310831i
$361$	−18.9183			−0.995699
$362$	2.86107	−	4.95551i	0.150374	−	0.260456i
$363$	3.75745	−	15.0255i	0.197215	−	0.788632i
$364$	−6.56076	−	11.3636i	−0.343877	−	0.595613i
$365$	5.37408	+	9.30818i	0.281292	+	0.487212i
$366$	12.9591	−	51.8214i	0.677382	−	2.70875i
$367$	−3.61791	+	6.26640i	−0.188853	+	0.327103i	−0.944868	−	0.327451i	$-0.893810\pi$
$367$	−3.61791	+	6.26640i	−0.188853	+	0.327103i	0.756015	+	0.654554i	$0.227144\pi$
$368$	−3.77565			−0.196820
$369$	−8.53913	+	5.31922i	−0.444529	+	0.276907i
$370$	−20.1062			−1.04527
$371$	0.00689319	−	0.0119394i	0.000357876	−	0.000619860i
$372$	−37.6381	+	10.7640i	−1.95144	+	0.558089i
$373$	−4.47576	−	7.75224i	−0.231746	−	0.401396i	0.726576	−	0.687086i	$-0.241111\pi$
$373$	−4.47576	−	7.75224i	−0.231746	−	0.401396i	−0.958322	+	0.285690i	$0.907777\pi$
$374$	−1.07674	−	1.86497i	−0.0556768	−	0.0964351i
$375$	14.3132	+	13.8415i	0.739130	+	0.714771i
$376$	−11.2038	+	19.4056i	−0.577792	+	1.00077i
$377$	2.38168			0.122663
$378$	−20.2835	−	4.35597i	−1.04327	−	0.224047i
$379$	−29.7903			−1.53023			−0.765113	−	0.643896i	$-0.777317\pi$
$379$	−29.7903			−1.53023			−0.765113	+	0.643896i	$0.777317\pi$
$380$	0.652807	−	1.13070i	0.0334883	−	0.0580035i
$381$	−26.9965	−	26.1068i	−1.38307	−	1.33749i
$382$	−26.1397	−	45.2752i	−1.33742	−	2.31648i
$383$	13.8020	+	23.9058i	0.705250	+	1.22153i	0.966601	+	0.256285i	$0.0824987\pi$
$383$	13.8020	+	23.9058i	0.705250	+	1.22153i	−0.261351	+	0.965244i	$0.584168\pi$
$384$	28.5322	−	8.15985i	1.45603	−	0.416406i
$385$	1.84994	−	3.20419i	0.0942817	−	0.163301i
$386$	−21.0926			−1.07358
$387$	6.21905	+	3.31791i	0.316132	+	0.168659i
$388$	20.6748			1.04961
$389$	−2.70738	+	4.68932i	−0.137270	+	0.237758i	−0.926462	−	0.376388i	$-0.877166\pi$
$389$	−2.70738	+	4.68932i	−0.137270	+	0.237758i	0.789193	+	0.614146i	$0.210499\pi$
$390$	−3.31221	+	13.2450i	−0.167720	+	0.670688i
$391$	2.54928	+	4.41548i	0.128923	+	0.223300i
$392$	−4.94414	−	8.56349i	−0.249717	−	0.432522i
$393$	−2.35624	+	9.42224i	−0.118857	+	0.475289i
$394$	−25.5583	+	44.2683i	−1.28761	+	2.23020i
$395$	−24.0440			−1.20979
$396$	0.450298	+	13.4345i	0.0226283	+	0.675107i
$397$	−18.3688			−0.921902			−0.460951	−	0.887426i	$-0.652492\pi$
$397$	−18.3688			−0.921902			−0.460951	+	0.887426i	$0.652492\pi$
$398$	−27.1330	+	46.9957i	−1.36005	+	2.35568i
$399$	0.839742	−	0.240156i	0.0420397	−	0.0120228i
$400$	−0.702804	−	1.21729i	−0.0351402	−	0.0608646i
$401$	−12.0907	−	20.9416i	−0.603779	−	1.04578i	−0.992243	−	0.124312i	$-0.960328\pi$
$401$	−12.0907	−	20.9416i	−0.603779	−	1.04578i	0.388464	−	0.921464i	$-0.373006\pi$
$402$	−10.3753	−	10.0334i	−0.517475	−	0.500421i
$403$	−8.61711	+	14.9253i	−0.429249	+	0.743481i
$404$	7.72490			0.384328
$405$	7.32819	+	10.9304i	0.364140	+	0.543137i
$406$	−3.99257			−0.198148
$407$	−4.35744	+	7.54731i	−0.215990	+	0.374106i
$408$	−2.09974	−	2.03054i	−0.103953	−	0.100527i
$409$	−7.28888	−	12.6247i	−0.360412	−	0.624252i	0.627617	−	0.778523i	$-0.284031\pi$
$409$	−7.28888	−	12.6247i	−0.360412	−	0.624252i	−0.988029	+	0.154271i	$0.950697\pi$
$410$	−5.54937	−	9.61179i	−0.274064	−	0.474692i
$411$	−0.848779	+	0.242740i	−0.0418672	+	0.0119735i
$412$	17.0520	−	29.5349i	0.840090	−	1.45508i
$413$	5.56835			0.274000
$414$	−1.74879	−	52.1744i	−0.0859483	−	2.56423i
$415$	13.4877			0.662087
$416$	7.38001	−	12.7826i	0.361835	−	0.626717i
$417$	−2.87871	+	11.5115i	−0.140971	+	0.563721i
$418$	−0.464138	−	0.803911i	−0.0227017	−	0.0393206i
$419$	−17.6943	−	30.6475i	−0.864425	−	1.49723i	−0.867617	−	0.497233i	$-0.834350\pi$
$419$	−17.6943	−	30.6475i	−0.864425	−	1.49723i	0.00319248	−	0.999995i	$-0.498984\pi$
$420$	3.38499	−	13.5361i	0.165171	−	0.660492i
$421$	−10.9101	+	18.8969i	−0.531728	+	0.920980i	0.467586	+	0.883947i	$0.345124\pi$
$421$	−10.9101	+	18.8969i	−0.531728	+	0.920980i	−0.999314	+	0.0370321i	$0.988210\pi$
$422$	19.4829			0.948415
$423$	23.3243	+	12.4437i	1.13407	+	0.605034i
$424$	−0.0198745			−0.000965191
$425$	−0.949051	+	1.64380i	−0.0460357	+	0.0797362i
$426$	25.1629	−	7.19626i	1.21914	−	0.348660i
$427$	12.0166	+	20.8134i	0.581526	+	1.00723i
$428$	−9.21538	−	15.9615i	−0.445442	−	0.771529i
$429$	4.25399	+	4.11380i	0.205385	+	0.198616i
$430$	−3.88815	+	6.73448i	−0.187503	+	0.324765i
$431$	10.7425			0.517447			0.258723	−	0.965951i	$-0.416698\pi$
$431$	10.7425			0.517447			0.258723	+	0.965951i	$0.416698\pi$
$432$	−0.783496	−	2.42871i	−0.0376960	−	0.116851i
$433$	−5.53089			−0.265797			−0.132899	−	0.991130i	$-0.542429\pi$
$433$	−5.53089			−0.265797			−0.132899	+	0.991130i	$0.542429\pi$
$434$	14.4455	−	25.0203i	0.693404	−	1.20101i
$435$	1.82055	+	1.76055i	0.0872887	+	0.0844119i
$436$	9.09208	+	15.7479i	0.435432	+	0.754190i
$437$	1.09889	+	1.90333i	0.0525671	+	0.0910488i
$438$	27.7077	−	7.92407i	1.32393	−	0.378627i
$439$	−5.31095	+	9.19883i	−0.253478	+	0.439036i	−0.964481	−	0.264153i	$-0.914908\pi$
$439$	−5.31095	+	9.19883i	−0.253478	+	0.439036i	0.711003	+	0.703189i	$0.248241\pi$
$440$	−5.33377			−0.254277
$441$	−9.90201	+	6.16819i	−0.471524	+	0.293723i
$442$	−3.57527			−0.170058
$443$	−15.0933	+	26.1424i	−0.717105	+	1.24206i	0.245036	+	0.969514i	$0.421200\pi$
$443$	−15.0933	+	26.1424i	−0.717105	+	1.24206i	−0.962142	+	0.272549i	$0.912133\pi$
$444$	−7.97318	+	31.8835i	−0.378390	+	1.51312i
$445$	−9.39027	−	16.2644i	−0.445141	−	0.771007i
$446$	−25.5790	−	44.3041i	−1.21120	−	2.09786i
$447$	3.74430	−	14.9729i	0.177099	−	0.708192i
$448$	−11.5053	+	19.9278i	−0.543576	+	0.941501i
$449$	21.6802			1.02315			0.511575	−	0.859238i	$-0.329062\pi$
$449$	21.6802			1.02315			0.511575	+	0.859238i	$0.329062\pi$
$450$	16.4958	−	10.2756i	0.777620	−	0.484397i
$451$	−4.81067			−0.226526
$452$	30.4116	−	52.6745i	1.43044	−	2.47760i
$453$	15.4867	−	4.42899i	0.727627	−	0.208092i
$454$	20.2297	+	35.0389i	0.949428	+	1.64446i
$455$	−3.07133	−	5.31970i	−0.143986	−	0.249392i
$456$	−0.905114	−	0.875284i	−0.0423858	−	0.0409889i
$457$	0.956722	−	1.65709i	0.0447536	−	0.0775155i	−0.842781	−	0.538257i	$-0.819083\pi$
$457$	0.956722	−	1.65709i	0.0447536	−	0.0775155i	0.887534	+	0.460741i	$0.152416\pi$
$458$	2.10231			0.0982344
$459$	−2.31127	+	2.55611i	−0.107881	+	0.119309i
$460$	35.1100			1.63701
$461$	−0.807267	+	1.39823i	−0.0375982	+	0.0651220i	−0.884212	−	0.467085i	$-0.845304\pi$
$461$	−0.807267	+	1.39823i	−0.0375982	+	0.0651220i	0.846614	+	0.532207i	$0.178637\pi$
$462$	−7.13126	−	6.89624i	−0.331776	−	0.320842i
$463$	8.50836	+	14.7369i	0.395417	+	0.684883i	0.993154	−	0.116809i	$-0.0372667\pi$
$463$	8.50836	+	14.7369i	0.395417	+	0.684883i	−0.597737	+	0.801692i	$0.703933\pi$
$464$	−0.245562	−	0.425326i	−0.0113999	−	0.0197453i
$465$	−17.6198	+	5.03903i	−0.817098	+	0.233680i
$466$	−5.71433	+	9.89751i	−0.264711	+	0.458493i
$467$	6.91091			0.319799			0.159899	−	0.987133i	$-0.448883\pi$
$467$	6.91091			0.319799			0.159899	+	0.987133i	$0.448883\pi$
$468$	19.6899	+	10.5047i	0.910167	+	0.485581i
$469$	6.49374			0.299853
$470$	−14.5824	+	25.2574i	−0.672635	+	1.16504i
$471$	2.31872	−	9.27221i	0.106841	−	0.427241i
$472$	−4.01367	−	6.95189i	−0.184744	−	0.319987i
$473$	1.68529	+	2.91901i	0.0774899	+	0.134216i
$474$	−15.6401	+	62.5423i	−0.718373	+	2.87266i
$475$	−0.409097	+	0.708578i	−0.0187707	+	0.0325118i
$476$	3.65383			0.167473
$477$	0.000785480		0.0234345i	3.59646e−5		0.00107299i
$478$	31.3414			1.43352
$479$	−6.90186	+	11.9544i	−0.315354	+	0.546209i	−0.979513	−	0.201382i	$-0.935457\pi$
$479$	−6.90186	+	11.9544i	−0.315354	+	0.546209i	0.664159	+	0.747592i	$0.268790\pi$
$480$	15.0902	−	4.31562i	0.688772	−	0.196980i
$481$	7.23437	+	12.5303i	0.329859	+	0.571332i
$482$	−13.9123	−	24.0968i	−0.633689	−	1.09758i
$483$	16.8839	+	16.3275i	0.768246	+	0.742927i
$484$	13.9649	−	24.1879i	0.634768	−	1.09945i
$485$	9.67865			0.439485
$486$	33.1986	−	11.9518i	1.50592	−	0.542143i
$487$	−0.945988			−0.0428668			−0.0214334	−	0.999770i	$-0.506823\pi$
$487$	−0.945988			−0.0428668			−0.0214334	+	0.999770i	$0.506823\pi$
$488$	17.3232	−	30.0047i	0.784186	−	1.35825i
$489$	−11.0997	−	10.7339i	−0.501948	−	0.485405i
$490$	−6.43507	−	11.1459i	−0.290707	−	0.503519i
$491$	6.32763	+	10.9598i	0.285562	+	0.494608i	0.972745	−	0.231876i	$-0.0744864\pi$
$491$	6.32763	+	10.9598i	0.285562	+	0.494608i	−0.687183	+	0.726484i	$0.741153\pi$
$492$	−17.4426	+	4.98836i	−0.786372	+	0.224893i
$493$	−0.331602	+	0.574351i	−0.0149346	+	0.0258675i
$494$	−1.54115			−0.0693398
$495$	0.210801	+	6.28916i	0.00947480	+	0.282677i
$496$	3.55386			0.159573
$497$	−5.88753	+	10.1975i	−0.264092	+	0.457421i
$498$	8.77346	−	35.0837i	0.393148	−	1.57214i
$499$	3.48698	+	6.03963i	0.156099	+	0.270371i	0.933459	−	0.358685i	$-0.116775\pi$
$499$	3.48698	+	6.03963i	0.156099	+	0.270371i	−0.777360	+	0.629056i	$0.783441\pi$
$500$	17.9529	+	31.0954i	0.802879	+	1.39063i
$501$	−8.81793	+	35.2615i	−0.393956	+	1.57537i
$502$	−23.5958	+	40.8691i	−1.05313	+	1.82408i
$503$	3.36486			0.150032			0.0750159	−	0.997182i	$-0.476099\pi$
$503$	3.36486			0.150032			0.0750159	+	0.997182i	$0.476099\pi$
$504$	−11.8720	−	6.33379i	−0.528820	−	0.282130i
$505$	3.61631			0.160924
$506$	12.4814	−	21.6184i	0.554866	−	0.961057i
$507$	−12.2026	+	3.48979i	−0.541937	+	0.154987i
$508$	−33.8615	−	58.6499i	−1.50236	−	2.60217i
$509$	11.1958	+	19.3916i	0.496243	+	0.859519i	0.999991	−	0.00433226i	$-0.00137900\pi$
$509$	11.1958	+	19.3916i	0.496243	+	0.859519i	−0.503747	+	0.863851i	$0.668046\pi$
$510$	−2.73293	−	2.64287i	−0.121016	−	0.117028i
$511$	−6.48298	+	11.2289i	−0.286790	+	0.496735i
$512$	−5.54136			−0.244896
$513$	−0.996296	+	1.10183i	−0.0439875	+	0.0486471i
$514$	34.1665			1.50702
$515$	7.98265	−	13.8263i	0.351757	−	0.609262i
$516$	9.13738	+	8.83625i	0.402251	+	0.388994i
$517$	6.32064	+	10.9477i	0.277981	+	0.481478i
$518$	−12.1275	−	21.0054i	−0.532850	−	0.922924i
$519$	17.7495	−	5.07613i	0.779115	−	0.222817i
$520$	−4.42765	+	7.66891i	−0.194165	+	0.336304i
$521$	13.9330			0.610418			0.305209	−	0.952285i	$-0.401274\pi$
$521$	13.9330			0.610418			0.305209	+	0.952285i	$0.401274\pi$
$522$	5.76369	−	3.59034i	0.252270	−	0.157145i
$523$	−21.2111			−0.927494			−0.463747	−	0.885968i	$-0.653495\pi$
$523$	−21.2111			−0.927494			−0.463747	+	0.885968i	$0.653495\pi$
$524$	−8.75719	+	15.1679i	−0.382559	+	0.662612i
$525$	−2.12129	+	8.48270i	−0.0925805	+	0.370215i
$526$	−20.0628	−	34.7497i	−0.874778	−	1.51516i
$527$	−2.39953	−	4.15611i	−0.104525	−	0.181043i
$528$	0.296046	−	1.18384i	0.0128838	−	0.0515202i
$529$	−18.0509	+	31.2651i	−0.784822	+	1.35935i
$530$	−0.0258678			−0.00112362
$531$	−8.03850	+	5.00737i	−0.348841	+	0.217301i
$532$	1.57502			0.0682857
$533$	−3.99342	+	6.91680i	−0.172974	+	0.299600i
$534$	−48.4145	+	13.8459i	−2.09510	+	0.599172i
$535$	−4.31406	−	7.47217i	−0.186513	−	0.323050i
$536$	−4.68070	−	8.10721i	−0.202175	−	0.350178i
$537$	29.7207	+	28.7412i	1.28254	+	1.24028i
$538$	27.0778	−	46.9001i	1.16741	−	2.02201i
$539$	−5.57848			−0.240282
$540$	7.28578	+	22.5847i	0.313530	+	0.971892i
$541$	45.2940			1.94734			0.973671	−	0.227959i	$-0.0732051\pi$
$541$	45.2940			1.94734			0.973671	+	0.227959i	$0.0732051\pi$
$542$	−32.2473	+	55.8540i	−1.38514	+	2.39913i
$543$	−3.14760	−	3.04386i	−0.135076	−	0.130625i
$544$	2.05505	+	3.55944i	0.0881094	+	0.152610i
$545$	4.25634	+	7.37219i	0.182321	+	0.315790i
$546$	−15.8352	+	4.52867i	−0.677685	+	0.193809i
$547$	17.7954	−	30.8225i	0.760874	−	1.31787i	−0.181526	−	0.983386i	$-0.558104\pi$
$547$	17.7954	−	30.8225i	0.760874	−	1.31787i	0.942400	−	0.334487i	$-0.108563\pi$
$548$	−1.59197			−0.0680055
$549$	−36.0639	−	19.2404i	−1.53917	−	0.821159i
$550$	9.29321			0.396264
$551$	−0.142940	+	0.247580i	−0.00608945	+	0.0105472i
$552$	8.21435	−	32.8479i	0.349626	−	1.39810i
$553$	−14.5027	−	25.1194i	−0.616716	−	1.06818i
$554$	5.74806	+	9.95593i	0.244212	+	0.422987i
$555$	−3.73254	+	14.9258i	−0.158437	+	0.633566i
$556$	−10.6990	+	18.5312i	−0.453738	+	0.785897i
$557$	9.23517			0.391307			0.195653	−	0.980673i	$-0.437317\pi$
$557$	9.23517			0.391307			0.195653	+	0.980673i	$0.437317\pi$
$558$	1.64606	+	49.1096i	0.0696833	+	2.07897i
$559$	5.59596			0.236684
$560$	−0.633339	+	1.09697i	−0.0267634	+	0.0463556i
$561$	−1.58435	+	0.453103i	−0.0668911	+	0.0191300i
$562$	3.95582	+	6.85169i	0.166866	+	0.289021i
$563$	2.58331	+	4.47443i	0.108874	+	0.188575i	0.915314	−	0.402741i	$-0.131942\pi$
$563$	2.58331	+	4.47443i	0.108874	+	0.188575i	−0.806441	+	0.591315i	$0.798609\pi$
$564$	34.2694	+	33.1400i	1.44300	+	1.39545i
$565$	14.2368	−	24.6589i	0.598947	−	1.03741i
$566$	27.2866			1.14694
$567$	−6.99911	+	14.2488i	−0.293935	+	0.598395i
$568$	16.9750			0.712254
$569$	10.5893	−	18.3411i	0.443925	−	0.768900i	−0.554052	−	0.832482i	$-0.686919\pi$
$569$	10.5893	−	18.3411i	0.443925	−	0.768900i	0.997977	+	0.0635821i	$0.0202525\pi$
$570$	−1.17806	−	1.13923i	−0.0493434	−	0.0477172i
$571$	11.8163	+	20.4665i	0.494498	+	0.856496i	0.999980	−	0.00634158i	$-0.00201860\pi$
$571$	11.8163	+	20.4665i	0.494498	+	0.856496i	−0.505482	+	0.862837i	$0.668685\pi$
$572$	5.33575	+	9.24179i	0.223099	+	0.386419i
$573$	−38.4627	+	10.9999i	−1.60680	+	0.459526i
$574$	6.69444	−	11.5951i	0.279420	−	0.483970i
$575$	−22.0026			−0.917570
$576$	−1.31103	−	39.1142i	−0.0546264	−	1.62976i
$577$	4.37201			0.182009			0.0910047	−	0.995850i	$-0.470992\pi$
$577$	4.37201			0.182009			0.0910047	+	0.995850i	$0.470992\pi$
$578$	−18.7419	+	32.4620i	−0.779561	+	1.35024i
$579$	−3.91566	+	15.6581i	−0.162729	+	0.650729i
$580$	2.28350	+	3.95514i	0.0948172	+	0.164228i
$581$	8.13542	+	14.0910i	0.337514	+	0.584591i
$582$	6.29574	−	25.1757i	0.260967	−	1.04357i
$583$	−0.00560611	+	0.00971006i	−0.000232181	+	0.000402150i
$584$	18.6918			0.773471
$585$	9.21757	+	4.91765i	0.381100	+	0.203320i
$586$	43.8446			1.81120
$587$	8.99614	−	15.5818i	0.371311	−	0.643129i	−0.618457	−	0.785819i	$-0.712242\pi$
$587$	8.99614	−	15.5818i	0.371311	−	0.643129i	0.989767	+	0.142690i	$0.0455752\pi$
$588$	−20.2265	+	5.78452i	−0.834126	+	0.238550i
$589$	−1.03434	−	1.79153i	−0.0426192	−	0.0738187i
$590$	−5.22402	−	9.04828i	−0.215070	−	0.372512i
$591$	28.1179	+	27.1913i	1.15662	+	1.11850i
$592$	1.49180	−	2.58387i	0.0613125	−	0.106196i
$593$	13.8703			0.569586			0.284793	−	0.958589i	$-0.408075\pi$
$593$	13.8703			0.569586			0.284793	+	0.958589i	$0.408075\pi$
$594$	16.4962	+	3.54263i	0.676848	+	0.145356i
$595$	1.71049			0.0701234
$596$	13.9160	−	24.1033i	0.570023	−	0.987309i
$597$	29.8503	+	28.8665i	1.22169	+	1.18143i
$598$	−20.7220	−	35.8916i	−0.847387	−	1.46772i
$599$	−2.06494	−	3.57659i	−0.0843713	−	0.146135i	0.820752	−	0.571285i	$-0.193555\pi$
$599$	−2.06494	−	3.57659i	−0.0843713	−	0.146135i	−0.905123	+	0.425149i	$0.860222\pi$
$600$	12.1194	−	3.46599i	0.494772	−	0.141498i
$601$	−5.72025	+	9.90777i	−0.233334	+	0.404146i	−0.958787	−	0.284125i	$-0.908297\pi$
$601$	−5.72025	+	9.90777i	−0.233334	+	0.404146i	0.725453	+	0.688271i	$0.241630\pi$
$602$	−9.38089			−0.382336
$603$	−9.37440	+	5.83953i	−0.381755	+	0.237804i
$604$	29.0468			1.18190
$605$	6.53748	−	11.3233i	0.265787	−	0.460356i
$606$	2.35232	−	9.40658i	0.0955567	−	0.382116i
$607$	−12.9831	−	22.4873i	−0.526966	−	0.912733i	−0.999506	−	0.0314233i	$-0.989996\pi$
$607$	−12.9831	−	22.4873i	−0.526966	−	0.912733i	0.472540	−	0.881309i	$-0.343337\pi$
$608$	0.885847	+	1.53433i	0.0359258	+	0.0622254i
$609$	−0.741185	+	2.96388i	−0.0300343	+	0.120103i
$610$	22.5472	−	39.0528i	0.912908	−	1.58120i
$611$	20.9875			0.849061
$612$	−5.27470	+	3.28573i	−0.213217	+	0.132818i
$613$	16.6330			0.671802			0.335901	−	0.941897i	$-0.390959\pi$
$613$	16.6330			0.671802			0.335901	+	0.941897i	$0.390959\pi$
$614$	−17.8379	+	30.8961i	−0.719878	+	1.24687i
$615$	−8.16551	+	2.33523i	−0.329265	+	0.0941657i
$616$	−3.21717	−	5.57231i	−0.129624	−	0.224515i
$617$	−7.70289	−	13.3418i	−0.310107	−	0.537121i	0.668279	−	0.743911i	$-0.267031\pi$
$617$	−7.70289	−	13.3418i	−0.310107	−	0.537121i	−0.978385	+	0.206791i	$0.933698\pi$
$618$	−30.7720	−	29.7578i	−1.23783	−	1.19704i
$619$	5.43317	−	9.41053i	0.218378	−	0.378241i	−0.735935	−	0.677053i	$-0.763257\pi$
$619$	5.43317	−	9.41053i	0.218378	−	0.378241i	0.954312	+	0.298812i	$0.0965902\pi$
$620$	−33.0476			−1.32722
$621$	−39.0564	−	8.38751i	−1.56728	−	0.336579i
$622$	64.5417			2.58789
$623$	11.3279	−	19.6205i	0.453842	−	0.786077i
$624$	−1.45638	−	1.40838i	−0.0583019	−	0.0563805i
$625$	1.24937	+	2.16398i	0.0499749	+	0.0865590i
$626$	−18.6466	−	32.2968i	−0.745267	−	1.29084i
$627$	−0.682947	+	0.195314i	−0.0272743	+	0.00780010i
$628$	8.61774	−	14.9264i	0.343885	−	0.595627i
$629$	−4.02898			−0.160646
$630$	−15.4520	−	8.24379i	−0.615624	−	0.328440i
$631$	−27.3487			−1.08874			−0.544368	−	0.838846i	$-0.683231\pi$
$631$	−27.3487			−1.08874			−0.544368	+	0.838846i	$0.683231\pi$
$632$	−20.9071	+	36.2122i	−0.831640	+	1.44044i
$633$	3.61684	−	14.4632i	0.143756	−	0.574860i
$634$	13.8343	+	23.9617i	0.549429	+	0.951639i
$635$	−15.8518	−	27.4562i	−0.629060	−	1.08956i
$636$	−0.0102580	+	0.0410200i	−0.000406755	+	0.00162655i
$637$	−4.63078	+	8.02075i	−0.183478	+	0.317794i
$638$	3.24708			0.128553
$639$	−0.670885	−	20.0156i	−0.0265398	−	0.791804i
$640$	25.0523			0.990280
$641$	−17.1686	+	29.7368i	−0.678118	+	1.17453i	0.297429	+	0.954744i	$0.403871\pi$
$641$	−17.1686	+	29.7368i	−0.678118	+	1.17453i	−0.975547	+	0.219791i	$0.929462\pi$
$642$	−22.2425	+	6.36107i	−0.877841	+	0.251051i
$643$	2.86466	+	4.96174i	0.112971	+	0.195672i	0.916967	−	0.398963i	$-0.130630\pi$
$643$	2.86466	+	4.96174i	0.112971	+	0.195672i	−0.803996	+	0.594635i	$0.797297\pi$
$644$	21.1774	+	36.6803i	0.834505	+	1.44541i
$645$	4.27754	+	4.13657i	0.168428	+	0.162877i
$646$	0.214576	−	0.371656i	0.00844237	−	0.0146226i
$647$	−15.7957			−0.620995			−0.310497	−	0.950574i	$-0.600496\pi$
$647$	−15.7957			−0.620995			−0.310497	+	0.950574i	$0.600496\pi$
$648$	22.8342	−	1.53244i	0.897011	−	0.0601999i
$649$	−4.52864			−0.177765
$650$	7.71445	−	13.3618i	0.302586	−	0.524093i
$651$	−15.8921	−	15.3684i	−0.622862	−	0.602335i
$652$	−13.9223	−	24.1141i	−0.545240	−	0.944383i
$653$	−18.4183	−	31.9014i	−0.720762	−	1.24840i	−0.960695	−	0.277607i	$-0.910459\pi$
$653$	−18.4183	−	31.9014i	−0.720762	−	1.24840i	0.239932	−	0.970790i	$-0.422875\pi$
$654$	21.9449	−	6.27596i	0.858113	−	0.245409i
$655$	−4.09956	+	7.10065i	−0.160183	+	0.277445i
$656$	1.64696			0.0643031
$657$	−0.738736	−	22.0399i	−0.0288209	−	0.859858i
$658$	−35.1827			−1.37156
$659$	−2.63438	+	4.56288i	−0.102621	+	0.177744i	−0.912764	−	0.408488i	$-0.866056\pi$
$659$	−2.63438	+	4.56288i	−0.102621	+	0.177744i	0.810143	+	0.586233i	$0.199389\pi$
$660$	−2.75295	+	11.0086i	−0.107159	+	0.428511i
$661$	−20.7503	−	35.9405i	−0.807091	−	1.39792i	−0.914870	−	0.403748i	$-0.867707\pi$
$661$	−20.7503	−	35.9405i	−0.807091	−	1.39792i	0.107779	−	0.994175i	$-0.465626\pi$
$662$	14.4561	+	25.0388i	0.561854	+	0.973160i
$663$	−0.663718	+	2.65411i	−0.0257767	+	0.103077i
$664$	11.7280	−	20.3136i	0.455136	−	0.788320i
$665$	0.737324			0.0285922
$666$	36.3965	+	19.4178i	1.41034	+	0.752425i
$667$	−7.68777			−0.297672
$668$	−32.7727	+	56.7639i	−1.26801	+	2.19626i
$669$	−37.6377	+	10.7639i	−1.45516	+	0.416157i
$670$	−6.09220	−	10.5520i	−0.235362	−	0.407659i
$671$	−9.77292	−	16.9272i	−0.377279	−	0.653467i
$672$	13.6106	+	13.1621i	0.525041	+	0.507737i
$673$	10.4142	−	18.0379i	0.401438	−	0.695312i	−0.592461	−	0.805599i	$-0.701844\pi$
$673$	10.4142	−	18.0379i	0.401438	−	0.695312i	0.993900	+	0.110287i	$0.0351770\pi$
$674$	−77.2628			−2.97605
$675$	−4.56581	−	14.1533i	−0.175738	−	0.544759i
$676$	−22.8872			−0.880276
$677$	9.31711	−	16.1377i	0.358085	−	0.620222i	−0.629556	−	0.776956i	$-0.716763\pi$
$677$	9.31711	−	16.1377i	0.358085	−	0.620222i	0.987641	+	0.156733i	$0.0500963\pi$
$678$	−54.8809	−	53.0722i	−2.10769	−	2.03823i
$679$	5.83788	+	10.1115i	0.224037	+	0.388044i
$680$	−1.23293	−	2.13549i	−0.0472806	−	0.0818924i
$681$	29.7666	−	8.51288i	1.14066	−	0.326214i
$682$	−11.7482	+	20.3485i	−0.449863	+	0.779186i
$683$	−10.7800			−0.412486			−0.206243	−	0.978501i	$-0.566124\pi$
$683$	−10.7800			−0.412486			−0.206243	+	0.978501i	$0.566124\pi$
$684$	−2.27371	+	1.41634i	−0.0869374	+	0.0541553i
$685$	−0.745259			−0.0284749
$686$	21.7369	−	37.6494i	0.829918	−	1.43746i
$687$	0.390275	−	1.56065i	0.0148899	−	0.0595425i
$688$	−0.576970	−	0.999342i	−0.0219968	−	0.0380996i
$689$	0.00930744	+	0.0161210i	0.000354585	+	0.000614160i
$690$	10.6914	−	42.7534i	0.407016	−	1.62759i
$691$	11.0235	−	19.0933i	0.419355	−	0.726344i	−0.576520	−	0.817083i	$-0.695590\pi$
$691$	11.0235	−	19.0933i	0.419355	−	0.726344i	0.995875	+	0.0907393i	$0.0289230\pi$
$692$	33.2909			1.26553
$693$	−6.44329	+	4.01367i	−0.244760	+	0.152467i
$694$	−18.1314			−0.688260
$695$	−5.00858	+	8.67512i	−0.189986	+	0.329066i
$696$	4.23455	−	1.21103i	0.160510	−	0.0459040i
$697$	−1.11201	−	1.92606i	−0.0421204	−	0.0729547i
$698$	−35.5731	−	61.6144i	−1.34646	−	2.33214i
$699$	6.28661	+	6.07942i	0.237781	+	0.229945i
$700$	−7.88396	+	13.6554i	−0.297986	+	0.516126i
$701$	45.4881			1.71806			0.859031	−	0.511924i	$-0.171067\pi$
$701$	45.4881			1.71806			0.859031	+	0.511924i	$0.171067\pi$
$702$	18.7874	−	20.7775i	0.709084	−	0.784198i
$703$	−1.73673			−0.0655020
$704$	9.35708	−	16.2069i	0.352658	−	0.610822i
$705$	16.0428	+	15.5141i	0.604206	+	0.584294i
$706$	15.2649	+	26.4396i	0.574503	+	0.995068i
$707$	2.18125	+	3.77804i	0.0820345	+	0.142088i
$708$	−16.4200	+	4.69590i	−0.617100	+	0.176483i
$709$	−1.81515	+	3.14393i	−0.0681694	+	0.118073i	−0.898096	−	0.439800i	$-0.855049\pi$
$709$	−1.81515	+	3.14393i	−0.0681694	+	0.118073i	0.829926	+	0.557873i	$0.188383\pi$
$710$	22.0939			0.829169
$711$	43.5249	+	23.2209i	1.63231	+	0.870851i
$712$	−32.6606			−1.22401
$713$	27.8150	−	48.1770i	1.04168	−	1.80424i
$714$	1.11264	−	4.44926i	0.0416394	−	0.166509i
$715$	2.49786	+	4.32642i	0.0934147	+	0.161799i
$716$	37.2785	+	64.5682i	1.39316	+	2.41303i
$717$	5.81825	−	23.2663i	0.217287	−	0.868895i
$718$	6.69807	−	11.6014i	0.249970	−	0.432960i
$719$	9.11334			0.339870			0.169935	−	0.985455i	$-0.445644\pi$
$719$	9.11334			0.339870			0.169935	+	0.985455i	$0.445644\pi$
$720$	−0.0721690	−	2.15313i	−0.00268958	−	0.0802425i
$721$	19.2596			0.717265
$722$	−21.4107	+	37.0844i	−0.796824	+	1.38014i
$723$	−20.4710	+	5.85445i	−0.761325	+	0.217729i
$724$	−3.94800	−	6.83814i	−0.146726	−	0.254138i
$725$	−1.43101	−	2.47858i	−0.0531464	−	0.0920522i
$726$	−25.2011	−	24.3705i	−0.935300	−	0.904476i
$727$	−9.06354	+	15.6985i	−0.336148	+	0.582226i	−0.983705	−	0.179792i	$-0.942458\pi$
$727$	−9.06354	+	15.6985i	−0.336148	+	0.582226i	0.647557	+	0.762017i	$0.275791\pi$
$728$	−10.6825			−0.395920
$729$	−2.70939	−	26.8637i	−0.100348	−	0.994952i
$730$	24.3284			0.900435
$731$	−0.779128	+	1.34949i	−0.0288171	+	0.0499127i
$732$	−52.9871	−	51.2409i	−1.95846	−	1.89392i
$733$	18.6683	+	32.3345i	0.689530	+	1.19430i	0.971990	+	0.235022i	$0.0755163\pi$
$733$	18.6683	+	32.3345i	0.689530	+	1.19430i	−0.282460	+	0.959279i	$0.591150\pi$
$734$	8.18912	+	14.1840i	0.302266	+	0.523540i
$735$	−9.46876	+	2.70795i	−0.349261	+	0.0998841i
$736$	−23.8218	+	41.2606i	−0.878084	+	1.52089i
$737$	−5.28124			−0.194537
$738$	0.762832	+	22.7588i	0.0280802	+	0.837763i
$739$	−32.8190			−1.20727			−0.603633	−	0.797262i	$-0.706281\pi$
$739$	−32.8190			−1.20727			−0.603633	+	0.797262i	$0.706281\pi$
$740$	−13.8723	+	24.0276i	−0.509957	+	0.883271i
$741$	−0.286102	+	1.14408i	−0.0105102	+	0.0420287i
$742$	−0.0156027	−	0.0270247i	−0.000572793	−	0.000992107i
$743$	3.71938	+	6.44215i	0.136451	+	0.236340i	0.926151	−	0.377154i	$-0.123097\pi$
$743$	3.71938	+	6.44215i	0.136451	+	0.236340i	−0.789700	+	0.613493i	$0.789764\pi$
$744$	−7.73182	+	30.9184i	−0.283462	+	1.13352i
$745$	6.51461	−	11.2836i	0.238677	−	0.413400i
$746$	−20.2617			−0.741835
$747$	−24.4157	−	13.0260i	−0.893324	−	0.476596i
$748$	−2.97160			−0.108652
$749$	5.20423	−	9.01400i	0.190159	−	0.329364i
$750$	43.3316	−	12.3923i	1.58225	−	0.452503i
$751$	25.2026	+	43.6521i	0.919655	+	1.59289i	0.799939	+	0.600081i	$0.204865\pi$
$751$	25.2026	+	43.6521i	0.919655	+	1.59289i	0.119716	+	0.992808i	$0.461802\pi$
$752$	−2.16391	−	3.74800i	−0.0789096	−	0.136675i
$753$	25.9589	+	25.1034i	0.945994	+	0.914817i
$754$	2.69546	−	4.66867i	0.0981627	−	0.170023i
$755$	13.5979			0.494877
$756$	−19.2002	+	21.2341i	−0.698305	+	0.772276i
$757$	19.6133			0.712857			0.356429	−	0.934323i	$-0.383994\pi$
$757$	19.6133			0.712857			0.356429	+	0.934323i	$0.383994\pi$
$758$	−33.7151	+	58.3963i	−1.22459	+	2.12105i
$759$	−13.7314	−	13.2789i	−0.498418	−	0.481992i
$760$	−0.531465	−	0.920524i	−0.0192782	−	0.0333909i
$761$	−0.251528	−	0.435659i	−0.00911788	−	0.0157926i	0.861430	−	0.507876i	$-0.169569\pi$
$761$	−0.251528	−	0.435659i	−0.00911788	−	0.0157926i	−0.870548	+	0.492083i	$0.836236\pi$
$762$	−81.7290	+	23.3735i	−2.96073	+	0.846732i
$763$	−5.13460	+	8.89339i	−0.185885	+	0.321962i
$764$	−72.1406			−2.60996
$765$	−2.46928	+	1.53817i	−0.0892770	+	0.0556127i
$766$	62.4816			2.25755
$767$	−3.75929	+	6.51129i	−0.135740	+	0.235109i
$768$	5.33266	−	21.3245i	0.192426	−	0.769481i
$769$	2.52537	+	4.37407i	0.0910671	+	0.157733i	0.907960	−	0.419056i	$-0.137639\pi$
$769$	2.52537	+	4.37407i	0.0910671	+	0.157733i	−0.816893	+	0.576789i	$0.804306\pi$
$770$	−4.18733	−	7.25268i	−0.150901	−	0.261368i
$771$	6.34272	−	25.3636i	0.228427	−	0.913446i
$772$	−14.5529	+	25.2064i	−0.523770	+	0.907197i
$773$	46.3875			1.66844			0.834221	−	0.551430i	$-0.185918\pi$
$773$	46.3875			1.66844			0.834221	+	0.551430i	$0.185918\pi$
$774$	13.5423	−	8.43582i	0.486768	−	0.303219i
$775$	20.7101			0.743928
$776$	8.41591	−	14.5768i	0.302114	−	0.523276i
$777$	−17.8447	+	5.10337i	−0.640176	+	0.183082i
$778$	6.12814	+	10.6143i	0.219705	+	0.380540i
$779$	−0.479343	−	0.830246i	−0.0171742	−	0.0297467i
$780$	13.5430	+	13.0967i	0.484917	+	0.468935i
$781$	4.78823	−	8.29345i	0.171336	−	0.296763i
$782$	11.5406			0.412690
$783$	−1.59531	−	4.94520i	−0.0570118	−	0.176727i
$784$	1.90983			0.0682081
$785$	4.03428	−	6.98758i	0.143990	−	0.249397i
$786$	15.8032	+	15.2824i	0.563682	+	0.545105i
$787$	7.97319	+	13.8100i	0.284213	+	0.492272i	0.972418	−	0.233245i	$-0.0749343\pi$
$787$	7.97319	+	13.8100i	0.284213	+	0.492272i	−0.688205	+	0.725517i	$0.741601\pi$
$788$	35.2681	+	61.0861i	1.25637	+	2.17610i
$789$	−29.5210	+	8.44263i	−1.05097	+	0.300565i
$790$	−27.2118	+	47.1322i	−0.968152	+	1.67689i
$791$	34.3489			1.22131
$792$	9.65526	+	5.15116i	0.343085	+	0.183038i
$793$	−32.4506			−1.15236
$794$	−20.7888	+	36.0073i	−0.737767	+	1.27785i
$795$	−0.00480213	+	0.0192030i	−0.000170314	+	0.000681059i
$796$	37.4410	+	64.8497i	1.32706	+	2.29854i
$797$	6.46710	+	11.2013i	0.229076	+	0.396772i	0.957535	−	0.288318i	$-0.0930961\pi$
$797$	6.46710	+	11.2013i	0.229076	+	0.396772i	−0.728458	+	0.685090i	$0.759763\pi$
$798$	0.479612	−	1.91790i	0.0169781	−	0.0678928i
$799$	−2.92209	+	5.06121i	−0.103376	+	0.179053i
$800$	−17.7369			−0.627093
$801$	1.29081	+	38.5109i	0.0456086	+	1.36072i
$802$	−54.7343			−1.93274
$803$	5.27249	−	9.13222i	0.186062	−	0.322269i
$804$	−19.1488	+	5.47631i	−0.675325	+	0.193134i
$805$	9.91390	+	17.1714i	0.349419	+	0.605212i
$806$	19.5048	+	33.7833i	0.687027	+	1.18997i
$807$	−29.7896	−	28.8078i	−1.04864	−	1.01408i
$808$	3.14450	−	5.44644i	0.110623	−	0.191605i
$809$	−50.5530			−1.77735			−0.888675	−	0.458537i	$-0.848374\pi$
$809$	−50.5530			−1.77735			−0.888675	+	0.458537i	$0.848374\pi$
$810$	29.7200	−	1.99456i	1.04425	−	0.0700816i
$811$	−31.4465			−1.10424			−0.552119	−	0.833766i	$-0.686180\pi$
$811$	−31.4465			−1.10424			−0.552119	+	0.833766i	$0.686180\pi$
$812$	−2.75468	+	4.77125i	−0.0966704	+	0.167438i
$813$	35.4768	+	34.3076i	1.24423	+	1.20322i
$814$	9.86305	+	17.0833i	0.345700	+	0.598770i
$815$	−6.51754	−	11.2887i	−0.228300	−	0.395427i
$816$	0.542410	−	0.155123i	0.0189882	−	0.00543038i
$817$	−0.335851	+	0.581710i	−0.0117499	+	0.0203515i
$818$	−32.9967			−1.15370
$819$	0.422194	+	12.5960i	0.0147527	+	0.440140i
$820$	−15.3152			−0.534831
$821$	−8.40864	+	14.5642i	−0.293464	+	0.508294i	−0.974626	−	0.223838i	$-0.928141\pi$
$821$	−8.40864	+	14.5642i	−0.293464	+	0.508294i	0.681163	+	0.732132i	$0.261475\pi$
$822$	−0.484774	+	1.93854i	−0.0169084	+	0.0676142i
$823$	−19.6739	−	34.0762i	−0.685790	−	1.18782i	−0.973188	−	0.230012i	$-0.926123\pi$
$823$	−19.6739	−	34.0762i	−0.685790	−	1.18782i	0.287398	−	0.957811i	$-0.407210\pi$
$824$	−13.8824	−	24.0450i	−0.483615	−	0.837646i
$825$	1.72520	−	6.89882i	0.0600639	−	0.240186i
$826$	6.30196	−	10.9153i	0.219273	−	0.379793i
$827$	20.2910			0.705586			0.352793	−	0.935701i	$-0.385232\pi$
$827$	20.2910			0.705586			0.352793	+	0.935701i	$0.385232\pi$
$828$	−63.5568	−	33.9080i	−2.20875	−	1.17839i
$829$	36.1253			1.25468			0.627342	−	0.778744i	$-0.284143\pi$
$829$	36.1253			1.25468			0.627342	+	0.778744i	$0.284143\pi$
$830$	15.2647	−	26.4393i	0.529846	−	0.917720i
$831$	8.45787	−	2.41884i	0.293400	−	0.0839088i
$832$	−15.5349	−	26.9073i	−0.538577	−	0.932842i
$833$	−1.28949	−	2.23347i	−0.0446783	−	0.0773851i
$834$	19.3074	+	18.6711i	0.668560	+	0.646527i
$835$	−15.3421	+	26.5733i	−0.530935	+	0.919606i
$836$	−1.28093			−0.0443020
$837$	36.7621	+	7.89481i	1.27068	+	0.272885i
$838$	−80.1021			−2.76708
$839$	−2.03478	+	3.52435i	−0.0702485	+	0.121674i	−0.899010	−	0.437928i	$-0.855713\pi$
$839$	−2.03478	+	3.52435i	−0.0702485	+	0.121674i	0.828762	+	0.559602i	$0.189046\pi$
$840$	−8.16570	−	7.89659i	−0.281743	−	0.272458i
$841$	−0.500000	−	0.866025i	−0.0172414	−	0.0298629i
$842$	24.6951	+	42.7731i	0.851048	+	1.47406i
$843$	5.82072	−	1.66465i	0.200476	−	0.0573337i
$844$	13.4423	−	23.2828i	0.462703	−	0.801426i
$845$	−10.7143			−0.368584
$846$	50.7900	−	31.6383i	1.74620	−	1.08775i
$847$	15.7729			0.541963
$848$	0.00191928	−	0.00332430i	6.59085e−5	−	0.000114157i
$849$	5.06553	−	20.2563i	0.173848	−	0.695193i
$850$	2.14817	+	3.72074i	0.0736817	+	0.127620i
$851$	−23.3517	−	40.4463i	−0.800486	−	1.38648i
$852$	8.76141	−	35.0355i	0.300161	−	1.20030i
$853$	6.73851	−	11.6714i	0.230722	−	0.399622i	−0.727299	−	0.686321i	$-0.759224\pi$
$853$	6.73851	−	11.6714i	0.230722	−	0.399622i	0.958021	+	0.286699i	$0.0925578\pi$
$854$	54.3992			1.86150
$855$	−1.06441	+	0.663043i	−0.0364019	+	0.0226756i
$856$	−15.0049			−0.512856
$857$	−3.64126	+	6.30684i	−0.124383	+	0.215438i	−0.921492	−	0.388398i	$-0.873028\pi$
$857$	−3.64126	+	6.30684i	−0.124383	+	0.215438i	0.797109	+	0.603836i	$0.206362\pi$
$858$	12.8785	−	3.68309i	0.439665	−	0.125739i
$859$	−8.72287	−	15.1085i	−0.297621	−	0.515494i	0.677970	−	0.735089i	$-0.262860\pi$
$859$	−8.72287	−	15.1085i	−0.297621	−	0.515494i	−0.975591	+	0.219595i	$0.929526\pi$
$860$	5.36529	+	9.29295i	0.182955	+	0.316887i
$861$	−7.36487	−	7.12215i	−0.250994	−	0.242722i
$862$	12.1578	−	21.0579i	0.414095	−	0.717234i
$863$	1.70196			0.0579352			0.0289676	−	0.999580i	$-0.490778\pi$
$863$	1.70196			0.0579352			0.0289676	+	0.999580i	$0.490778\pi$
$864$	−31.4844	−	6.76141i	−1.07112	−	0.230028i
$865$	15.5847			0.529895
$866$	−6.25957	+	10.8419i	−0.212709	+	0.368422i
$867$	20.6189	+	19.9394i	0.700254	+	0.677176i
$868$	−19.9334	−	34.5256i	−0.676583	−	1.17188i
$869$	11.7948	+	20.4291i	0.400110	+	0.693011i
$870$	5.51151	−	1.57622i	0.186858	−	0.0534390i
$871$	−4.38404	+	7.59339i	−0.148548	+	0.257292i
$872$	14.8041			0.501331
$873$	−17.5204	−	9.34729i	−0.592977	−	0.316358i
$874$	4.97467			0.168271
$875$	−10.1386	+	17.5606i	−0.342748	+	0.593656i
$876$	9.64752	−	38.5789i	0.325959	−	1.30346i
$877$	−26.2019	−	45.3830i	−0.884775	−	1.53248i	−0.845971	−	0.533229i	$-0.820978\pi$
$877$	−26.2019	−	45.3830i	−0.884775	−	1.53248i	−0.0388044	−	0.999247i	$-0.512355\pi$
$878$	12.0213	+	20.8215i	0.405699	+	0.702692i
$879$	8.13936	−	32.5480i	0.274534	−	1.09782i
$880$	0.515083	−	0.892150i	0.0173634	−	0.0300744i
$881$	42.1454			1.41992			0.709958	−	0.704244i	$-0.248714\pi$
$881$	42.1454			1.41992			0.709958	+	0.704244i	$0.248714\pi$
$882$	0.884584	+	26.3912i	0.0297855	+	0.888638i
$883$	−10.1296			−0.340889			−0.170444	−	0.985367i	$-0.554520\pi$
$883$	−10.1296			−0.340889			−0.170444	+	0.985367i	$0.554520\pi$
$884$	−2.46677	+	4.27257i	−0.0829665	+	0.143702i
$885$	−7.68679	+	2.19833i	−0.258389	+	0.0738959i
$886$	34.1637	+	59.1732i	1.14775	+	1.98796i
$887$	−3.14458	−	5.44656i	−0.105585	−	0.182878i	0.808392	−	0.588644i	$-0.200338\pi$
$887$	−3.14458	−	5.44656i	−0.105585	−	0.182878i	−0.913977	+	0.405766i	$0.867005\pi$
$888$	19.2339	+	18.6000i	0.645447	+	0.624175i
$889$	19.1227	−	33.1215i	0.641356	−	1.11086i
$890$	−42.5096			−1.42493
$891$	5.69225	−	11.5883i	0.190698	−	0.388224i
$892$	−70.5932			−2.36363
$893$	−1.25960	+	2.18168i	−0.0421508	+	0.0730073i
$894$	−25.1129	−	24.2853i	−0.839901	−	0.812220i
$895$	17.4514	+	30.2267i	0.583337	+	1.01037i
$896$	15.1108	+	26.1727i	0.504818	+	0.874370i
$897$	−30.4910	+	8.72006i	−1.01807	+	0.291154i
$898$	24.5365	−	42.4985i	0.818793	−	1.41819i
$899$	7.23618			0.241340
$900$	−0.898378	−	26.8027i	−0.0299459	−	0.893425i
$901$	−0.00518352			−0.000172688
$902$	−5.44447	+	9.43009i	−0.181281	+	0.313988i
$903$	−1.74148	+	6.96391i	−0.0579528	+	0.231744i
$904$	−24.7588	−	42.8835i	−0.823465	−	1.42628i
$905$	−1.84821	−	3.20119i	−0.0614364	−	0.106411i
$906$	8.84509	−	35.3702i	0.293859	−	1.17509i
$907$	13.0499	−	22.6031i	0.433316	−	0.750525i	−0.563841	−	0.825883i	$-0.690677\pi$
$907$	13.0499	−	22.6031i	0.433316	−	0.750525i	0.997156	+	0.0753588i	$0.0240102\pi$
$908$	55.8302			1.85279
$909$	−6.54630	−	3.49250i	−0.217127	−	0.115839i
$910$	−13.9039			−0.460910
$911$	2.33554	−	4.04527i	0.0773799	−	0.134026i	−0.824739	−	0.565514i	$-0.808678\pi$
$911$	2.33554	−	4.04527i	0.0773799	−	0.134026i	0.902119	+	0.431488i	$0.142011\pi$
$912$	0.233811	−	0.0668670i	0.00774226	−	0.00221419i
$913$	−6.61639	−	11.4599i	−0.218970	−	0.379268i
$914$	−2.16554	−	3.75082i	−0.0716296	−	0.124066i
$915$	−24.8052	−	23.9877i	−0.820035	−	0.793010i
$916$	1.45049	−	2.51233i	0.0479257	−	0.0830097i
$917$	−9.89095			−0.326628
$918$	2.39481	+	7.42353i	0.0790407	+	0.245013i
$919$	20.5273			0.677133			0.338566	−	0.940943i	$-0.390058\pi$
$919$	20.5273			0.677133			0.338566	+	0.940943i	$0.390058\pi$
$920$	14.2919	−	24.7543i	0.471191	−	0.816126i
$921$	19.6243	+	18.9776i	0.646643	+	0.625332i
$922$	1.82725	+	3.16488i	0.0601771	+	0.104230i
$923$	−7.94957	−	13.7691i	−0.261663	−	0.453214i
$924$	−13.1615	+	3.76402i	−0.432981	+	0.123827i
$925$	8.69342	−	15.0574i	0.285838	−	0.495086i
$926$	38.5173			1.26576
$927$	−27.8033	+	17.3193i	−0.913180	+	0.568841i
$928$	−6.19733			−0.203437
$929$	28.3875	−	49.1687i	0.931365	−	1.61317i	0.150373	−	0.988629i	$-0.451952\pi$
$929$	28.3875	−	49.1687i	0.931365	−	1.61317i	0.780991	−	0.624542i	$-0.214714\pi$
$930$	−10.0634	+	40.2420i	−0.329992	+	1.31959i
$931$	−0.555848	−	0.962757i	−0.0182172	−	0.0315531i
$932$	7.88524	+	13.6576i	0.258290	+	0.447371i
$933$	11.9816	−	47.9126i	0.392260	−	1.56859i
$934$	7.82141	−	13.5471i	0.255924	−	0.443274i
$935$	−1.39111			−0.0454943
$936$	15.4213	−	9.60631i	0.504062	−	0.313992i
$937$	13.0085			0.424968			0.212484	−	0.977165i	$-0.431845\pi$
$937$	13.0085			0.424968			0.212484	+	0.977165i	$0.431845\pi$
$938$	7.34927	−	12.7293i	0.239962	−	0.415627i
$939$	−27.4371	+	7.84668i	−0.895377	+	0.256067i
$940$	20.1223	+	34.8529i	0.656318	+	1.13678i
$941$	−13.4236	−	23.2503i	−0.437595	−	0.757937i	0.559908	−	0.828555i	$-0.310836\pi$
$941$	−13.4236	−	23.2503i	−0.437595	−	0.757937i	−0.997503	+	0.0706173i	$0.977503\pi$
$942$	−15.5516	−	15.0391i	−0.506698	−	0.489999i
$943$	12.8903	−	22.3266i	0.419765	−	0.727055i
$944$	1.55041			0.0504614
$945$	−8.98832	+	9.94045i	−0.292390	+	0.323363i
$946$	7.62931			0.248050
$947$	−10.2241	+	17.7087i	−0.332240	+	0.575456i	−0.982951	−	0.183870i	$-0.941138\pi$
$947$	−10.2241	+	17.7087i	−0.332240	+	0.575456i	0.650711	+	0.759325i	$0.274471\pi$
$948$	63.9493	+	61.8417i	2.07698	+	2.00853i
$949$	−8.75356	−	15.1616i	−0.284153	−	0.492167i
$950$	0.925990	+	1.60386i	0.0300431	+	0.0520362i
$951$	20.3562	−	5.82161i	0.660094	−	0.188779i
$952$	1.48733	−	2.57613i	0.0482047	−	0.0834930i
$953$	3.76009			0.121801			0.0609006	−	0.998144i	$-0.480603\pi$
$953$	3.76009			0.121801			0.0609006	+	0.998144i	$0.480603\pi$
$954$	0.0468263	+	0.0249822i	0.00151606	+	0.000808828i
$955$	−33.7717			−1.09283
$956$	21.6241	−	37.4540i	0.699372	−	1.21135i
$957$	0.602792	−	2.41047i	0.0194855	−	0.0779196i
$958$	15.6223	+	27.0587i	0.504735	+	0.874226i
$959$	−0.449519	−	0.778589i	−0.0145157	−	0.0251420i
$960$	8.01517	−	32.0514i	0.258688	−	1.03446i
$961$	−10.6811	+	18.5003i	−0.344552	+	0.596782i
$962$	32.7499			1.05590
$963$	0.593023	+	17.6926i	0.0191099	+	0.570136i
$964$	−38.3954			−1.23663
$965$	−6.81275	+	11.8000i	−0.219310	+	0.379856i
$966$	51.1142	−	14.6180i	1.64457	−	0.470327i
$967$	−22.4141	−	38.8224i	−0.720789	−	1.24844i	−0.960684	−	0.277644i	$-0.910446\pi$
$967$	−22.4141	−	38.8224i	−0.720789	−	1.24844i	0.239895	−	0.970799i	$-0.422887\pi$
$968$	−11.3691	−	19.6919i	−0.365418	−	0.632922i
$969$	−0.236065	−	0.228285i	−0.00758350	−	0.00733358i
$970$	10.9538	−	18.9725i	0.351705	−	0.609171i
$971$	−45.2241			−1.45131			−0.725655	−	0.688058i	$-0.758463\pi$
$971$	−45.2241			−1.45131			−0.725655	+	0.688058i	$0.758463\pi$
$972$	8.62267	−	47.9196i	0.276572	−	1.53702i
$973$	−12.0841			−0.387400
$974$	−1.07062	+	1.85437i	−0.0343049	+	0.0594178i
$975$	−8.48703	−	8.20733i	−0.271803	−	0.262845i
$976$	3.34582	+	5.79512i	0.107097	+	0.185497i
$977$	−3.08873	−	5.34983i	−0.0988172	−	0.171156i	0.812378	−	0.583131i	$-0.198173\pi$
$977$	−3.08873	−	5.34983i	−0.0988172	−	0.171156i	−0.911195	+	0.411975i	$0.864839\pi$
$978$	−33.6032	+	9.61010i	−1.07451	+	0.307297i
$979$	−9.21276	+	15.9570i	−0.294441	+	0.509987i
$980$	−17.7596			−0.567309
$981$	−0.585088	−	17.4559i	−0.0186804	−	0.557323i
$982$	28.6451			0.914103
$983$	3.48916	−	6.04340i	0.111287	−	0.192754i	−0.805003	−	0.593271i	$-0.797836\pi$
$983$	3.48916	−	6.04340i	0.111287	−	0.192754i	0.916289	+	0.400517i	$0.131169\pi$
$984$	−3.58315	+	14.3285i	−0.114227	+	0.456774i
$985$	16.5103	+	28.5966i	0.526061	+	0.911165i
$986$	0.750579	+	1.30004i	0.0239033	+	0.0414018i
$987$	−6.53136	+	26.1179i	−0.207896	+	0.831342i
$988$	−1.06332	+	1.84173i	−0.0338289	+	0.0585933i
$989$	−18.0631			−0.574373
$990$	12.5669	+	6.70453i	0.399401	+	0.213084i
$991$	−9.35659			−0.297222			−0.148611	−	0.988896i	$-0.547480\pi$
$991$	−9.35659			−0.297222			−0.148611	+	0.988896i	$0.547480\pi$
$992$	22.4225	−	38.8369i	0.711915	−	1.23307i
$993$	21.2712	−	6.08330i	0.675022	−	0.193048i
$994$	13.3264	+	23.0820i	0.422688	+	0.732117i
$995$	17.5275	+	30.3585i	0.555659	+	0.962430i
$996$	−35.8730	−	34.6907i	−1.13668	−	1.09922i
$997$	1.64965	−	2.85727i	0.0522448	−	0.0904907i	−0.838720	−	0.544562i	$-0.816696\pi$
$997$	1.64965	−	2.85727i	0.0522448	−	0.0904907i	0.890965	+	0.454072i	$0.150029\pi$
$998$	15.7855			0.499683
$999$	21.1715	−	23.4142i	0.669838	−	0.740793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.e.a.88.11	✓	22
3.2	odd	2		783.2.e.a.262.1		22
9.2	odd	6		2349.2.a.e.1.11		11
9.4	even	3	inner	261.2.e.a.175.11	yes	22
9.5	odd	6		783.2.e.a.523.1		22
9.7	even	3		2349.2.a.f.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.11	✓	22	1.1	even	1	trivial
261.2.e.a.175.11	yes	22	9.4	even	3	inner
783.2.e.a.262.1		22	3.2	odd	2
783.2.e.a.523.1		22	9.5	odd	6
2349.2.a.e.1.11		11	9.2	odd	6
2349.2.a.f.1.1		11	9.7	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13175 - 1.96024i) q^{2} +(-1.24509 - 1.20406i) q^{3} +(-1.56171 - 2.70495i) q^{4} +(-0.731092 - 1.26629i) q^{5} +(-3.76937 + 1.07799i) q^{6} +(0.881947 - 1.52758i) q^{7} -2.54284 q^{8} +(0.100498 + 2.99832i) q^{9} -3.30965 q^{10} +(-0.717272 + 1.24235i) q^{11} +(-1.31245 + 5.24829i) q^{12} +(1.19084 + 2.06259i) q^{13} +(-1.99628 - 3.45766i) q^{14} +(-0.614407 + 2.45692i) q^{15} +(0.245562 - 0.425326i) q^{16} -0.663204 q^{17} +(5.99117 + 3.19634i) q^{18} -0.285880 q^{19} +(-2.28350 + 3.95514i) q^{20} +(-2.93739 + 0.840057i) q^{21} +(1.62354 + 2.81206i) q^{22} +(-3.84389 - 6.65780i) q^{23} +(3.16606 + 3.06172i) q^{24} +(1.43101 - 2.47858i) q^{25} +5.39091 q^{26} +(3.48501 - 3.85418i) q^{27} -5.50937 q^{28} +(0.500000 - 0.866025i) q^{29} +(4.12081 + 3.98500i) q^{30} +(3.61809 + 6.26671i) q^{31} +(-3.09867 - 5.36705i) q^{32} +(2.38893 - 0.683203i) q^{33} +(-0.750579 + 1.30004i) q^{34} -2.57914 q^{35} +(7.95336 - 4.95433i) q^{36} +6.07502 q^{37} +(-0.323544 + 0.560395i) q^{38} +(1.00078 - 4.00195i) q^{39} +(1.85905 + 3.21996i) q^{40} +(1.67673 + 2.90417i) q^{41} +(-1.67767 + 6.70874i) q^{42} +(1.17479 - 2.03480i) q^{43} +4.48067 q^{44} +(3.72326 - 2.31930i) q^{45} -17.4012 q^{46} +(4.40603 - 7.63146i) q^{47} +(-0.817864 + 0.233899i) q^{48} +(1.94434 + 3.36769i) q^{49} +(-3.23908 - 5.61026i) q^{50} +(0.825748 + 0.798535i) q^{51} +(3.71948 - 6.44232i) q^{52} +0.00781588 q^{53} +(-3.61098 - 11.1934i) q^{54} +2.09757 q^{55} +(-2.24265 + 3.88438i) q^{56} +(0.355947 + 0.344216i) q^{57} +(-1.13175 - 1.96024i) q^{58} +(1.57842 + 2.73391i) q^{59} +(7.60537 - 2.17504i) q^{60} +(-6.81256 + 11.7997i) q^{61} +16.3791 q^{62} +(4.66879 + 2.49084i) q^{63} -13.0454 q^{64} +(1.74122 - 3.01589i) q^{65} +(1.36442 - 5.45610i) q^{66} +(1.84074 + 3.18825i) q^{67} +(1.03573 + 1.79394i) q^{68} +(-3.23039 + 12.9178i) q^{69} +(-2.91893 + 5.05574i) q^{70} -6.67561 q^{71} +(-0.255550 - 7.62423i) q^{72} -7.35076 q^{73} +(6.87539 - 11.9085i) q^{74} +(-4.76609 + 1.36304i) q^{75} +(0.446461 + 0.773293i) q^{76} +(1.26519 + 2.19138i) q^{77} +(-6.71217 - 6.49096i) q^{78} +(8.22196 - 14.2409i) q^{79} -0.718114 q^{80} +(-8.97980 + 0.602649i) q^{81} +7.59052 q^{82} +(-4.61219 + 7.98855i) q^{83} +(6.85966 + 6.63359i) q^{84} +(0.484863 + 0.839807i) q^{85} +(-2.65914 - 4.60577i) q^{86} +(-1.66529 + 0.476251i) q^{87} +(1.82390 - 3.15910i) q^{88} +12.8442 q^{89} +(-0.332613 - 9.92336i) q^{90} +4.20102 q^{91} +(-12.0060 + 20.7951i) q^{92} +(3.04063 - 12.1590i) q^{93} +(-9.97302 - 17.2738i) q^{94} +(0.209005 + 0.362007i) q^{95} +(-2.60411 + 10.4134i) q^{96} +(-3.30966 + 5.73249i) q^{97} +8.80201 q^{98} +(-3.79705 - 2.02575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) \) 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

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