LMFDB - Embedded newform 588.2.x.a.55.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(55,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 0, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [168,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			55.20
Character	$\chi$	$=$	588.55
Dual form			588.2.x.a.139.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.745941 - 1.20149i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-0.887143 - 1.79248i) q^{4} +(0.0475607 - 0.0987608i) q^{5} +(-1.19338 + 0.758851i) q^{6} +(-1.69059 + 2.03517i) q^{7} +(-2.81540 - 0.271193i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.0831823 - 0.130813i) q^{10} +(-0.607046 - 0.484103i) q^{11} +(0.0215610 + 1.99988i) q^{12} +(-3.65889 - 2.91786i) q^{13} +(1.18415 + 3.54933i) q^{14} +(-0.0857014 + 0.0683446i) q^{15} +(-2.42596 + 3.18037i) q^{16} +(-1.57832 - 0.360242i) q^{17} +(1.40445 - 0.165915i) q^{18} -6.49070 q^{19} +(-0.219220 + 0.00236343i) q^{20} +(2.40619 - 1.10011i) q^{21} +(-1.03446 + 0.368245i) q^{22} +(-3.61344 + 0.824745i) q^{23} +(2.41892 + 1.46589i) q^{24} +(3.10996 + 3.89976i) q^{25} +(-6.23509 + 2.21955i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(5.14779 + 1.22485i) q^{28} +(-1.30614 + 5.72258i) q^{29} +(0.0181869 + 0.153950i) q^{30} +4.12388 q^{31} +(2.01155 + 5.28712i) q^{32} +(0.336885 + 0.699549i) q^{33} +(-1.61016 + 1.62762i) q^{34} +(0.120590 + 0.263758i) q^{35} +(0.848291 - 1.81119i) q^{36} +(1.29408 - 5.66975i) q^{37} +(-4.84168 + 7.79849i) q^{38} +(2.03053 + 4.21644i) q^{39} +(-0.160685 + 0.265153i) q^{40} +(2.18982 - 4.54720i) q^{41} +(0.473112 - 3.71163i) q^{42} +(-1.15768 - 2.40394i) q^{43} +(-0.329208 + 1.51758i) q^{44} +(0.106868 - 0.0243919i) q^{45} +(-1.70450 + 4.95672i) q^{46} +(6.73395 - 8.44410i) q^{47} +(3.56562 - 1.81283i) q^{48} +(-1.28384 - 6.88126i) q^{49} +(7.00536 - 0.827579i) q^{50} +(1.26572 + 1.00938i) q^{51} +(-1.98425 + 9.14704i) q^{52} +(2.17573 + 9.53250i) q^{53} +(-1.33735 - 0.459883i) q^{54} +(-0.0766819 + 0.0369280i) q^{55} +(5.31159 - 5.27134i) q^{56} +(5.84792 + 2.81621i) q^{57} +(5.90130 + 5.83802i) q^{58} +(-6.47582 + 3.11859i) q^{59} +(0.198535 + 0.0929864i) q^{60} +(-15.1080 - 3.44831i) q^{61} +(3.07617 - 4.95479i) q^{62} +(-2.64522 - 0.0528441i) q^{63} +(7.85291 + 1.52703i) q^{64} +(-0.462190 + 0.222579i) q^{65} +(1.09180 + 0.117060i) q^{66} -14.3784i q^{67} +(0.754472 + 3.14869i) q^{68} +(3.61344 + 0.824745i) q^{69} +(0.406854 + 0.0518607i) q^{70} +(-10.7246 + 2.44781i) q^{71} +(-1.54334 - 2.37025i) q^{72} +(3.95395 - 3.15317i) q^{73} +(-5.84682 - 5.78413i) q^{74} +(-1.10993 - 4.86293i) q^{75} +(5.75817 + 11.6344i) q^{76} +(2.01150 - 0.417025i) q^{77} +(6.58065 + 0.705560i) q^{78} +0.854048i q^{79} +(0.198715 + 0.390850i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-3.82993 - 6.02298i) q^{82} +(-7.21987 - 9.05343i) q^{83} +(-4.10656 - 3.33709i) q^{84} +(-0.110644 + 0.138743i) q^{85} +(-3.75187 - 0.402266i) q^{86} +(3.65973 - 4.58915i) q^{87} +(1.57779 + 1.52757i) q^{88} +(-11.4673 + 9.14485i) q^{89} +(0.0504106 - 0.146595i) q^{90} +(12.1240 - 2.51356i) q^{91} +(4.68398 + 5.74535i) q^{92} +(-3.71548 - 1.78928i) q^{93} +(-5.12235 - 14.3896i) q^{94} +(-0.308702 + 0.641026i) q^{95} +(0.481652 - 5.63631i) q^{96} -3.64969i q^{97} +(-9.22542 - 3.59049i) q^{98} -0.776441i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31}+ \cdots - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{14}\right)$

Coefficient data

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

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

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

$2$	0.745941	−	1.20149i	0.527460	−	0.849580i
$2$	0.745941	−	1.20149i	0.527460	−	0.849580i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	−0.887143	−	1.79248i	−0.443571	−	0.896239i
$5$	0.0475607	−	0.0987608i	0.0212698	−	0.0441672i	−0.890063	−	0.455837i	$-0.849340\pi$
$5$	0.0475607	−	0.0987608i	0.0212698	−	0.0441672i	0.911333	+	0.411670i	$0.135054\pi$
$6$	−1.19338	+	0.758851i	−0.487194	+	0.309799i
$7$	−1.69059	+	2.03517i	−0.638981	+	0.769222i
$7$	−1.69059	+	2.03517i	−0.638981	+	0.769222i
$8$	−2.81540	−	0.271193i	−0.995393	−	0.0958812i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−0.0831823	−	0.130813i	−0.0263046	−	0.0413668i
$11$	−0.607046	−	0.484103i	−0.183031	−	0.145963i	0.527688	−	0.849438i	$-0.323059\pi$
$11$	−0.607046	−	0.484103i	−0.183031	−	0.145963i	−0.710719	+	0.703476i	$0.751630\pi$
$12$	0.0215610	+	1.99988i	0.00622411	+	0.577317i
$13$	−3.65889	−	2.91786i	−1.01479	−	0.809270i	−0.0330441	−	0.999454i	$-0.510520\pi$
$13$	−3.65889	−	2.91786i	−1.01479	−	0.809270i	−0.981748	+	0.190184i	$0.939092\pi$
$14$	1.18415	+	3.54933i	0.316479	+	0.948600i
$15$	−0.0857014	+	0.0683446i	−0.0221280	+	0.0176465i
$16$	−2.42596	+	3.18037i	−0.606489	+	0.795092i
$17$	−1.57832	−	0.360242i	−0.382799	−	0.0873715i	0.0267908	−	0.999641i	$-0.491471\pi$
$17$	−1.57832	−	0.360242i	−0.382799	−	0.0873715i	−0.409590	+	0.912270i	$0.634328\pi$
$18$	1.40445	−	0.165915i	0.331031	−	0.0391064i
$19$	−6.49070			−1.48907			−0.744534	−	0.667585i	$-0.767328\pi$
$19$	−6.49070			−1.48907			−0.744534	+	0.667585i	$0.767328\pi$
$20$	−0.219220	+	0.00236343i	−0.0490190	+	0.000528479i
$21$	2.40619	−	1.10011i	0.525074	−	0.240063i
$22$	−1.03446	+	0.368245i	−0.220548	+	0.0785102i
$23$	−3.61344	+	0.824745i	−0.753455	+	0.171971i	−0.581964	−	0.813214i	$-0.697716\pi$
$23$	−3.61344	+	0.824745i	−0.753455	+	0.171971i	−0.171491	+	0.985186i	$0.554858\pi$
$24$	2.41892	+	1.46589i	0.493760	+	0.299224i
$25$	3.10996	+	3.89976i	0.621991	+	0.779953i
$26$	−6.23509	+	2.21955i	−1.22280	+	0.435289i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	5.14779	+	1.22485i	0.972841	+	0.231475i
$29$	−1.30614	+	5.72258i	−0.242544	+	1.06266i	0.696147	+	0.717899i	$0.254896\pi$
$29$	−1.30614	+	5.72258i	−0.242544	+	1.06266i	−0.938692	+	0.344758i	$0.887961\pi$
$30$	0.0181869	+	0.153950i	0.00332046	+	0.0281073i
$31$	4.12388			0.740670			0.370335	−	0.928898i	$-0.379243\pi$
$31$	4.12388			0.740670			0.370335	+	0.928898i	$0.379243\pi$
$32$	2.01155	+	5.28712i	0.355595	+	0.934640i
$33$	0.336885	+	0.699549i	0.0586442	+	0.121776i
$34$	−1.61016	+	1.62762i	−0.276141	+	0.279134i
$35$	0.120590	+	0.263758i	0.0203834	+	0.0445832i
$36$	0.848291	−	1.81119i	0.141382	−	0.301865i
$37$	1.29408	−	5.66975i	0.212746	−	0.932101i	−0.749945	−	0.661500i	$-0.769920\pi$
$37$	1.29408	−	5.66975i	0.212746	−	0.932101i	0.962691	−	0.270602i	$-0.0872226\pi$
$38$	−4.84168	+	7.79849i	−0.785424	+	1.26508i
$39$	2.03053	+	4.21644i	0.325145	+	0.675170i
$40$	−0.160685	+	0.265153i	−0.0254066	+	0.0419243i
$41$	2.18982	−	4.54720i	0.341992	−	0.710153i	−0.657053	−	0.753844i	$-0.728197\pi$
$41$	2.18982	−	4.54720i	0.341992	−	0.710153i	0.999045	+	0.0436909i	$0.0139117\pi$
$42$	0.473112	−	3.71163i	0.0730028	−	0.572716i
$43$	−1.15768	−	2.40394i	−0.176544	−	0.366598i	0.793854	−	0.608109i	$-0.208071\pi$
$43$	−1.15768	−	2.40394i	−0.176544	−	0.366598i	−0.970398	+	0.241511i	$0.922357\pi$
$44$	−0.329208	+	1.51758i	−0.0496299	+	0.228785i
$45$	0.106868	−	0.0243919i	0.0159309	−	0.00363613i
$46$	−1.70450	+	4.95672i	−0.251314	+	0.730828i
$47$	6.73395	−	8.44410i	0.982247	−	1.23170i	0.00947034	−	0.999955i	$-0.496985\pi$
$47$	6.73395	−	8.44410i	0.982247	−	1.23170i	0.972777	−	0.231744i	$-0.0744431\pi$
$48$	3.56562	−	1.81283i	0.514653	−	0.261659i
$49$	−1.28384	−	6.88126i	−0.183406	−	0.983037i
$50$	7.00536	−	0.827579i	0.990708	−	0.117037i
$51$	1.26572	+	1.00938i	0.177236	+	0.141341i
$52$	−1.98425	+	9.14704i	−0.275166	+	1.26847i
$53$	2.17573	+	9.53250i	0.298860	+	1.30939i	0.871828	+	0.489812i	$0.162935\pi$
$53$	2.17573	+	9.53250i	0.298860	+	1.30939i	−0.572968	+	0.819577i	$0.694208\pi$
$54$	−1.33735	−	0.459883i	−0.181990	−	0.0625822i
$55$	−0.0766819	+	0.0369280i	−0.0103398	+	0.00497938i
$56$	5.31159	−	5.27134i	0.709791	−	0.704412i
$57$	5.84792	+	2.81621i	0.774575	+	0.373016i
$58$	5.90130	+	5.83802i	0.774879	+	0.766570i
$59$	−6.47582	+	3.11859i	−0.843080	+	0.406006i	−0.805004	−	0.593269i	$-0.797837\pi$
$59$	−6.47582	+	3.11859i	−0.843080	+	0.406006i	−0.0380759	+	0.999275i	$0.512123\pi$
$60$	0.198535	+	0.0929864i	0.0256308	+	0.0120045i
$61$	−15.1080	−	3.44831i	−1.93439	−	0.441511i	−0.995168	−	0.0981882i	$-0.968695\pi$
$61$	−15.1080	−	3.44831i	−1.93439	−	0.441511i	−0.939218	−	0.343323i	$-0.888448\pi$
$62$	3.07617	−	4.95479i	0.390674	−	0.629258i
$63$	−2.64522	−	0.0528441i	−0.333267	−	0.00665773i
$64$	7.85291	+	1.52703i	0.981614	+	0.190879i
$65$	−0.462190	+	0.222579i	−0.0573276	+	0.0276075i
$66$	1.09180	+	0.117060i	0.134391	+	0.0144090i
$67$		−	14.3784i		−	1.75660i	−0.478110	−	0.878300i	$-0.658678\pi$
$67$		−	14.3784i		−	1.75660i	0.478110	−	0.878300i	$-0.341322\pi$
$68$	0.754472	+	3.14869i	0.0914932	+	0.381835i
$69$	3.61344	+	0.824745i	0.435008	+	0.0992877i
$70$	0.406854	+	0.0518607i	0.0486284	+	0.00619854i
$71$	−10.7246	+	2.44781i	−1.27277	+	0.290502i	−0.804962	−	0.593327i	$-0.797814\pi$
$71$	−10.7246	+	2.44781i	−1.27277	+	0.290502i	−0.467811	+	0.883829i	$0.654957\pi$
$72$	−1.54334	−	2.37025i	−0.181885	−	0.279337i
$73$	3.95395	−	3.15317i	0.462774	−	0.369050i	−0.364171	−	0.931332i	$-0.618648\pi$
$73$	3.95395	−	3.15317i	0.462774	−	0.369050i	0.826946	+	0.562282i	$0.190076\pi$
$74$	−5.84682	−	5.78413i	−0.679679	−	0.672391i
$75$	−1.10993	−	4.86293i	−0.128164	−	0.561522i
$76$	5.75817	+	11.6344i	0.660508	+	1.33456i
$77$	2.01150	−	0.417025i	0.229231	−	0.0475244i
$78$	6.58065	+	0.705560i	0.745112	+	0.0798890i
$79$			0.854048i			0.0960879i	0.998845	+	0.0480440i	$0.0152988\pi$
$79$			0.854048i			0.0960879i	−0.998845	+	0.0480440i	$0.984701\pi$
$80$	0.198715	+	0.390850i	0.0222171	+	0.0436983i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−3.82993	−	6.02298i	−0.422945	−	0.665127i
$83$	−7.21987	−	9.05343i	−0.792484	−	0.993743i	−0.999880	−	0.0154862i	$-0.995070\pi$
$83$	−7.21987	−	9.05343i	−0.792484	−	0.993743i	0.207396	−	0.978257i	$-0.433501\pi$
$84$	−4.10656	−	3.33709i	−0.448062	−	0.364107i
$85$	−0.110644	+	0.138743i	−0.0120010	+	0.0150488i
$86$	−3.75187	−	0.402266i	−0.404574	−	0.0433774i
$87$	3.65973	−	4.58915i	0.392364	−	0.492009i
$88$	1.57779	+	1.52757i	0.168193	+	0.162839i
$89$	−11.4673	+	9.14485i	−1.21553	+	0.969353i	−0.999975	−	0.00713912i	$-0.997728\pi$
$89$	−11.4673	+	9.14485i	−1.21553	+	0.969353i	−0.215555	+	0.976492i	$0.569156\pi$
$90$	0.0504106	−	0.146595i	0.00531375	−	0.0154525i
$91$	12.1240	−	2.51356i	1.27094	−	0.263493i
$92$	4.68398	+	5.74535i	0.488339	+	0.598995i
$93$	−3.71548	−	1.78928i	−0.385278	−	0.185540i
$94$	−5.12235	−	14.3896i	−0.528330	−	1.48417i
$95$	−0.308702	+	0.641026i	−0.0316721	+	0.0657679i
$96$	0.481652	−	5.63631i	0.0491584	−	0.575254i
$97$		−	3.64969i		−	0.370569i	−0.982685	−	0.185285i	$-0.940679\pi$
$97$		−	3.64969i		−	0.370569i	0.982685	−	0.185285i	$-0.0593207\pi$
$98$	−9.22542	−	3.59049i	−0.931908	−	0.362695i
$99$		−	0.776441i		−	0.0780352i
$100$	4.23126	−	9.03418i	0.423126	−	0.903418i
$101$	−4.79759	+	9.96229i	−0.477378	+	0.991285i	0.513696	+	0.857972i	$0.328276\pi$
$101$	−4.79759	+	9.96229i	−0.477378	+	0.991285i	−0.991074	+	0.133313i	$0.957438\pi$
$102$	2.15690	−	0.767807i	0.213565	−	0.0760243i
$103$	−5.40810	−	2.60440i	−0.532876	−	0.256620i	0.148040	−	0.988981i	$-0.452704\pi$
$103$	−5.40810	−	2.60440i	−0.532876	−	0.256620i	−0.680916	+	0.732362i	$0.738418\pi$
$104$	9.50991	+	9.20721i	0.932523	+	0.902841i
$105$	0.00579256	−	0.289959i	0.000565296	−	0.0282971i
$106$	13.0761	+	4.49657i	1.27007	+	0.436746i
$107$	9.41315	−	7.50674i	0.910004	−	0.725704i	−0.0520266	−	0.998646i	$-0.516568\pi$
$107$	9.41315	−	7.50674i	0.910004	−	0.725704i	0.962031	+	0.272942i	$0.0879966\pi$
$108$	−1.55013	+	1.26376i	−0.149161	+	0.121606i
$109$	8.11846	−	10.1802i	0.777608	−	0.975089i	−0.222392	−	0.974957i	$-0.571387\pi$
$109$	8.11846	−	10.1802i	0.777608	−	0.975089i	1.00000		0.000132066i	$-4.20378e-5\pi$
$110$	−0.0128316	+	0.119678i	−0.00122345	+	0.0114109i
$111$	−3.62594	+	4.54679i	−0.344159	+	0.431562i
$112$	−2.37131	−	10.3139i	−0.224068	−	0.974574i
$113$	5.58992	+	7.00954i	0.525855	+	0.659402i	0.971841	−	0.235638i	$-0.0757181\pi$
$113$	5.58992	+	7.00954i	0.525855	+	0.659402i	−0.445985	+	0.895040i	$0.647147\pi$
$114$	7.74584	−	4.92547i	0.725464	−	0.461312i
$115$	−0.0904054	+	0.396092i	−0.00843035	+	0.0369358i
$116$	11.4163	−	2.73552i	1.05998	−	0.253986i
$117$		−	4.67989i		−	0.432656i
$118$	−1.08364	+	10.1069i	−0.0997568	+	0.930416i
$119$	3.40144	−	2.60314i	0.311810	−	0.238629i
$120$	0.259818	−	0.169175i	0.0237180	−	0.0154435i
$121$	−2.31358	−	10.1365i	−0.210326	−	0.921497i
$122$	−15.4128	+	15.5799i	−1.39541	+	1.41054i
$123$	−3.94591	+	3.14676i	−0.355791	+	0.283734i
$124$	−3.65847	−	7.39196i	−0.328540	−	0.663818i
$125$	1.06739	−	0.243626i	0.0954707	−	0.0217906i
$126$	−2.03667	+	3.13878i	−0.181441	+	0.279625i
$127$	7.38907	+	1.68651i	0.655674	+	0.149653i	0.537400	−	0.843328i	$-0.319407\pi$
$127$	7.38907	+	1.68651i	0.655674	+	0.149653i	0.118274	+	0.992981i	$0.462264\pi$
$128$	7.69252	−	8.29609i	0.679929	−	0.733278i
$129$			2.66818i			0.234920i
$130$	−0.0773408	+	0.721346i	−0.00678324	+	0.0632662i
$131$	1.29999	−	0.626040i	0.113580	−	0.0546974i	−0.376231	−	0.926526i	$-0.622780\pi$
$131$	1.29999	−	0.626040i	0.113580	−	0.0546974i	0.489811	+	0.871829i	$0.337066\pi$
$132$	0.955061	−	1.22446i	0.0831274	−	0.106575i
$133$	10.9731	−	13.2097i	0.951486	−	1.14542i
$134$	−17.2754	−	10.7254i	−1.49237	−	0.926536i
$135$	−0.106868	−	0.0243919i	−0.00919772	−	0.00209932i
$136$	4.34591	+	1.44225i	0.372659	+	0.123672i
$137$	4.37674	−	2.10773i	0.373930	−	0.180075i	−0.237474	−	0.971394i	$-0.576319\pi$
$137$	4.37674	−	2.10773i	0.373930	−	0.180075i	0.611404	+	0.791319i	$0.290605\pi$
$138$	3.68634	−	3.72630i	0.313802	−	0.317203i
$139$	4.45120	+	2.14358i	0.377546	+	0.181816i	0.613026	−	0.790063i	$-0.289952\pi$
$139$	4.45120	+	2.14358i	0.377546	+	0.181816i	−0.235480	+	0.971879i	$0.575666\pi$
$140$	0.365799	−	0.450145i	0.0309157	−	0.0380442i
$141$	−9.73084	+	4.68612i	−0.819484	+	0.394643i
$142$	−5.05888	+	14.7114i	−0.424532	+	1.23455i
$143$	0.808565	+	3.54256i	0.0676156	+	0.296243i
$144$	−3.99907	+	0.0862388i	−0.333256	+	0.00718657i
$145$	0.503045	+	0.401165i	0.0417756	+	0.0333150i
$146$	−0.839077	−	7.10269i	−0.0694425	−	0.587823i
$147$	−1.82896	+	6.75684i	−0.150850	+	0.557295i
$148$	−11.3109	+	2.71026i	−0.929754	+	0.222782i
$149$	−2.53180	+	3.17477i	−0.207413	+	0.260088i	−0.874647	−	0.484761i	$-0.838907\pi$
$149$	−2.53180	+	3.17477i	−0.207413	+	0.260088i	0.667234	+	0.744848i	$0.267478\pi$
$150$	−6.67069	−	2.29389i	−0.544659	−	0.187295i
$151$	1.29365	−	0.295268i	0.105276	−	0.0240285i	−0.169558	−	0.985520i	$-0.554234\pi$
$151$	1.29365	−	0.295268i	0.105276	−	0.0240285i	0.274834	+	0.961492i	$0.411377\pi$
$152$	18.2739	+	1.76023i	1.48221	+	0.142774i
$153$	−0.702420	−	1.45859i	−0.0567873	−	0.117920i
$154$	0.999407	−	2.72786i	0.0805345	−	0.219817i
$155$	0.196134	−	0.407277i	0.0157539	−	0.0327133i
$156$	5.75650	−	7.38026i	0.460889	−	0.590894i
$157$	4.12220	+	8.55983i	0.328987	+	0.683149i	0.998203	−	0.0599188i	$-0.0190842\pi$
$157$	4.12220	+	8.55983i	0.328987	+	0.683149i	−0.669216	+	0.743068i	$0.733370\pi$
$158$	1.02613	+	0.637070i	0.0816344	+	0.0506826i
$159$	2.17573	−	9.53250i	0.172547	−	0.755976i
$160$	0.617831	+	0.0527968i	0.0488438	+	0.00417395i
$161$	4.43034	−	8.74828i	0.349160	−	0.689461i
$162$	1.00538	+	0.994595i	0.0789898	+	0.0781428i
$163$	−0.993052	−	2.06209i	−0.0777819	−	0.161516i	0.858451	−	0.512895i	$-0.171427\pi$
$163$	−0.993052	−	2.06209i	−0.0777819	−	0.161516i	−0.936233	+	0.351379i	$0.885713\pi$
$164$	−10.0934	+	0.108818i	−0.788165	+	0.00849729i
$165$	0.0851105			0.00662584
$166$	−16.2632	+	1.92125i	−1.26227	+	0.149118i
$167$	−1.58304	+	6.93576i	−0.122499	+	0.536705i	0.876018	+	0.482278i	$0.160190\pi$
$167$	−1.58304	+	6.93576i	−0.122499	+	0.536705i	−0.998518	+	0.0544273i	$0.982667\pi$
$168$	−7.07273	+	2.44470i	−0.545673	+	0.188613i
$169$	1.98074	+	8.67821i	0.152365	+	0.667555i
$170$	0.0841641	+	0.236431i	0.00645509	+	0.0181335i
$171$	−4.04688	−	5.07463i	−0.309473	−	0.388067i
$172$	−3.28199	+	4.20775i	−0.250249	+	0.320838i
$173$	−20.8094	+	4.74962i	−1.58211	+	0.361107i	−0.921118	−	0.389283i	$-0.872723\pi$
$173$	−20.8094	+	4.74962i	−1.58211	+	0.361107i	−0.660995	+	0.750390i	$0.729866\pi$
$174$	−2.78387	−	7.82036i	−0.211044	−	0.592860i
$175$	−13.1943	−	0.263585i	−0.997398	−	0.0199252i
$176$	3.01229	−	0.756217i	0.227060	−	0.0570020i
$177$	7.18762			0.540255
$178$	2.43350	+	20.5993i	0.182399	+	1.54398i
$179$	11.9681	+	2.73164i	0.894538	+	0.204172i	0.644991	−	0.764190i	$-0.276861\pi$
$179$	11.9681	+	2.73164i	0.894538	+	0.204172i	0.249547	+	0.968363i	$0.419718\pi$
$180$	−0.138529	−	0.169919i	−0.0103253	−	0.0126650i
$181$	10.4869	−	8.36302i	0.779484	−	0.621618i	−0.150755	−	0.988571i	$-0.548170\pi$
$181$	10.4869	−	8.36302i	0.779484	−	0.621618i	0.930239	+	0.366953i	$0.119599\pi$
$182$	6.02379	−	16.4418i	0.446513	−	1.21875i
$183$	12.1157	+	9.66195i	0.895618	+	0.714232i
$184$	10.3969	−	1.34204i	0.766473	−	0.0989368i
$185$	−0.498401	−	0.397462i	−0.0366432	−	0.0292220i
$186$	−4.92133	+	3.12941i	−0.360850	+	0.229459i
$187$	0.783720	+	0.982754i	0.0573113	+	0.0718661i
$188$	−21.1098	−	4.57933i	−1.53959	−	0.333982i
$189$	2.36034	+	1.19533i	0.171689	+	0.0869475i
$190$	0.539911	+	0.849069i	0.0391693	+	0.0615980i
$191$	−9.23609	+	19.1789i	−0.668300	+	1.38774i	0.240559	+	0.970635i	$0.422669\pi$
$191$	−9.23609	+	19.1789i	−0.668300	+	1.38774i	−0.908859	+	0.417105i	$0.863045\pi$
$192$	−6.41267	−	4.78306i	−0.462795	−	0.345187i
$193$	3.21301	+	1.54731i	0.231278	+	0.111378i	0.545934	−	0.837828i	$-0.316175\pi$
$193$	3.21301	+	1.54731i	0.231278	+	0.111378i	−0.314656	+	0.949206i	$0.601889\pi$
$194$	−4.38505	−	2.72245i	−0.314828	−	0.195461i
$195$	0.512992			0.0367361
$196$	−11.1956	+	8.40592i	−0.799682	+	0.600423i
$197$	−0.624215			−0.0444735			−0.0222367	−	0.999753i	$-0.507079\pi$
$197$	−0.624215			−0.0444735			−0.0222367	+	0.999753i	$0.507079\pi$
$198$	−0.932884	−	0.579179i	−0.0662972	−	0.0411605i
$199$	7.34694	+	3.53810i	0.520811	+	0.250809i	0.675771	−	0.737112i	$-0.263811\pi$
$199$	7.34694	+	3.53810i	0.520811	+	0.250809i	−0.154961	+	0.987921i	$0.549525\pi$
$200$	−7.69817	−	11.8228i	−0.544343	−	0.835997i
$201$	−6.23855	+	12.9545i	−0.440033	+	0.913739i
$202$	8.39085	+	13.1955i	0.590378	+	0.928434i
$203$	−9.43829	−	12.3327i	−0.662438	−	0.865588i
$204$	0.686412	−	3.16423i	0.0480584	−	0.221540i
$205$	−0.344936	−	0.432536i	−0.0240914	−	0.0302096i
$206$	−7.16329	+	4.55503i	−0.499090	+	0.317364i
$207$	−2.89776	−	2.31088i	−0.201408	−	0.160618i
$208$	18.1562	−	4.55800i	1.25890	−	0.316040i
$209$	3.94015	+	3.14217i	0.272546	+	0.217348i
$210$	−0.344061	−	0.223252i	−0.0237425	−	0.0154059i
$211$	−16.9535	+	13.5199i	−1.16712	+	0.930751i	−0.998490	−	0.0549280i	$-0.982507\pi$
$211$	−16.9535	+	13.5199i	−1.16712	+	0.930751i	−0.168634	+	0.985679i	$0.553936\pi$
$212$	15.1566	−	12.3566i	1.04096	−	0.848657i
$213$	10.7246	+	2.44781i	0.734835	+	0.167721i
$214$	−1.99759	−	16.9094i	−0.136552	−	1.15590i
$215$	−0.292475			−0.0199466
$216$	0.362091	+	2.80515i	0.0246372	+	0.190867i
$217$	−6.97177	+	8.39280i	−0.473274	+	0.569740i
$218$	−6.17552	−	17.3481i	−0.418259	−	1.17496i
$219$	−4.93049	+	1.12535i	−0.333172	+	0.0760442i
$220$	0.134220	+	0.104690i	0.00904914	+	0.00705821i
$221$	4.72377	+	5.92342i	0.317755	+	0.398452i
$222$	2.75817	+	7.74816i	0.185116	+	0.520022i
$223$	−0.445651	−	1.95252i	−0.0298430	−	0.130751i	0.957812	−	0.287395i	$-0.0927894\pi$
$223$	−0.445651	−	1.95252i	−0.0298430	−	0.130751i	−0.987655	+	0.156645i	$0.949932\pi$
$224$	−14.1609	−	4.84448i	−0.946165	−	0.323685i
$225$	−1.10993	+	4.86293i	−0.0739954	+	0.324195i
$226$	12.5916	−	1.48751i	0.837582	−	0.0989479i
$227$	8.14688			0.540727			0.270364	−	0.962758i	$-0.412856\pi$
$227$	8.14688			0.540727			0.270364	+	0.962758i	$0.412856\pi$
$228$	−0.139946	−	12.9806i	−0.00926813	−	0.859664i
$229$	−8.02421	−	16.6624i	−0.530254	−	1.10108i	−0.978323	−	0.207085i	$-0.933602\pi$
$229$	−8.02421	−	16.6624i	−0.530254	−	1.10108i	0.448068	−	0.893999i	$-0.352112\pi$
$230$	0.408462	+	0.404082i	0.0269332	+	0.0266444i
$231$	−1.99323	−	0.497028i	−0.131145	−	0.0327021i
$232$	5.22923	−	15.7571i	0.343316	−	1.03451i
$233$	3.59725	−	15.7606i	0.235663	−	1.03251i	−0.709191	−	0.705017i	$-0.750939\pi$
$233$	3.59725	−	15.7606i	0.235663	−	1.03251i	0.944854	−	0.327492i	$-0.106203\pi$
$234$	−5.62283	−	3.49093i	−0.367576	−	0.228209i
$235$	−0.513675	−	1.06666i	−0.0335085	−	0.0695810i
$236$	11.3350	+	8.84114i	0.737845	+	0.575509i
$237$	0.370558	−	0.769471i	0.0240703	−	0.0499825i
$238$	−0.590359	−	6.02858i	−0.0382673	−	0.390775i
$239$	−1.28518	−	2.66870i	−0.0831313	−	0.172624i	0.855259	−	0.518200i	$-0.173398\pi$
$239$	−1.28518	−	2.66870i	−0.0831313	−	0.172624i	−0.938391	+	0.345576i	$0.887683\pi$
$240$	−0.00945317	−	0.438363i	−0.000610199	−	0.0282962i
$241$	−7.58264	+	1.73069i	−0.488441	+	0.111483i	−0.459647	−	0.888102i	$-0.652024\pi$
$241$	−7.58264	+	1.73069i	−0.488441	+	0.111483i	−0.0287944	+	0.999585i	$0.509167\pi$
$242$	−13.9046	−	4.78147i	−0.893823	−	0.307364i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	7.22196	+	30.1400i	0.462339	+	1.92951i
$245$	−0.740659	−	0.200484i	−0.0473190	−	0.0128084i
$246$	0.837372	+	7.08826i	0.0533889	+	0.451931i
$247$	23.7487	+	18.9390i	1.51110	+	1.20506i
$248$	−11.6103	−	1.11837i	−0.737258	−	0.0710163i
$249$	2.57674	+	11.2894i	0.163294	+	0.715439i
$250$	0.503500	−	1.46419i	0.0318442	−	0.0926036i
$251$	20.4080	−	9.82798i	1.28814	−	0.620337i	0.340673	−	0.940182i	$-0.389345\pi$
$251$	20.4080	−	9.82798i	1.28814	−	0.620337i	0.947470	+	0.319845i	$0.103631\pi$
$252$	2.25197	+	4.78839i	0.141861	+	0.301640i
$253$	2.59279	+	1.24862i	0.163007	+	0.0785001i
$254$	7.53813	−	7.61984i	0.472984	−	0.478111i
$255$	0.159885	−	0.0769965i	0.0100124	−	0.00482171i
$256$	−4.22948	−	15.4309i	−0.264343	−	0.964429i
$257$	9.69339	+	2.21245i	0.604657	+	0.138009i	0.513880	−	0.857862i	$-0.328208\pi$
$257$	9.69339	+	2.21245i	0.604657	+	0.138009i	0.0907773	+	0.995871i	$0.471065\pi$
$258$	3.20578	+	1.99030i	0.199583	+	0.123911i
$259$	9.35116	+	12.2189i	0.581053	+	0.759244i
$260$	0.808996	+	0.631006i	0.0501718	+	0.0391333i
$261$	−5.28846	+	2.54679i	−0.327347	+	0.157642i
$262$	0.217534	−	2.02890i	0.0134393	−	0.125346i
$263$			22.1915i			1.36838i	0.729302	+	0.684192i	$0.239845\pi$
$263$			22.1915i			1.36838i	−0.729302	+	0.684192i	$0.760155\pi$
$264$	−0.758752	−	2.06087i	−0.0466980	−	0.126838i
$265$	1.04492	+	0.238495i	0.0641887	+	0.0146506i
$266$	−7.68599	−	23.0377i	−0.471258	−	1.41253i
$267$	14.2995	−	3.26376i	0.875113	−	0.199739i
$268$	−25.7729	+	12.7557i	−1.57433	+	0.779177i
$269$	13.0458	−	10.4037i	0.795415	−	0.634322i	−0.139087	−	0.990280i	$-0.544417\pi$
$269$	13.0458	−	10.4037i	0.795415	−	0.634322i	0.934502	+	0.355958i	$0.115845\pi$
$270$	−0.109024	+	0.110205i	−0.00663497	+	0.00670689i
$271$	3.58886	+	15.7238i	0.218008	+	0.955155i	0.958948	+	0.283583i	$0.0915232\pi$
$271$	3.58886	+	15.7238i	0.218008	+	0.955155i	−0.740940	+	0.671571i	$0.765620\pi$
$272$	4.97464	−	4.14572i	0.301632	−	0.251371i
$273$	−12.0140	−	2.99577i	−0.727117	−	0.181312i
$274$	0.732384	−	6.83083i	0.0442450	−	0.412666i
$275$		−	3.87287i		−	0.233543i
$276$	−1.72730	−	7.20869i	−0.103971	−	0.433912i
$277$	−2.11058	+	9.24707i	−0.126813	+	0.555603i	0.871105	+	0.491097i	$0.163404\pi$
$277$	−2.11058	+	9.24707i	−0.126813	+	0.555603i	−0.997917	+	0.0645052i	$0.979453\pi$
$278$	5.89582	−	3.74907i	0.353608	−	0.224854i
$279$	2.57120	+	3.22418i	0.153933	+	0.193026i
$280$	−0.267979	−	0.775285i	−0.0160148	−	0.0463321i
$281$	−13.3405	+	16.7285i	−0.795830	+	0.997939i	0.203990	+	0.978973i	$0.434609\pi$
$281$	−13.3405	+	16.7285i	−0.795830	+	0.997939i	−0.999820	+	0.0189665i	$0.993962\pi$
$282$	−1.62832	+	15.1870i	−0.0969648	+	0.904376i
$283$	−1.47403	+	1.84838i	−0.0876221	+	0.109875i	−0.823710	−	0.567011i	$-0.808100\pi$
$283$	−1.47403	+	1.84838i	−0.0876221	+	0.109875i	0.736088	+	0.676886i	$0.236671\pi$
$284$	13.9019	+	17.0520i	0.824925	+	1.01185i
$285$	0.556262	−	0.443604i	0.0329501	−	0.0262768i
$286$	4.85948	+	1.67106i	0.287347	+	0.0988117i
$287$	5.55226	+	12.1441i	0.327740	+	0.716842i
$288$	−2.87946	+	4.86916i	−0.169674	+	0.286918i
$289$	−12.9551	−	6.23887i	−0.762067	−	0.366992i
$290$	0.857237	−	0.305157i	0.0503387	−	0.0179194i
$291$	−1.58354	+	3.28825i	−0.0928287	+	0.192761i
$292$	−9.15970	−	4.29005i	−0.536031	−	0.251056i
$293$			0.0132877i			0.000776276i	1.00000		0.000388138i	$0.000123548\pi$
$293$			0.0132877i			0.000776276i	−1.00000		0.000388138i	$0.999876\pi$
$294$	6.75396	+	7.23768i	0.393899	+	0.422110i
$295$			0.787880i			0.0458721i
$296$	−5.18095	+	15.6116i	−0.301137	+	0.907409i
$297$	−0.336885	+	0.699549i	−0.0195481	+	0.0405919i
$298$	1.92588	+	5.41012i	0.111563	+	0.313400i
$299$	15.6277	+	7.52589i	0.903772	+	0.435234i
$300$	−7.73202	+	6.30364i	−0.446408	+	0.363941i
$301$	6.84959	+	1.70800i	0.394804	+	0.0984474i
$302$	0.610228	−	1.77456i	0.0351147	−	0.102114i
$303$	8.64495	−	6.89412i	0.496640	−	0.396057i
$304$	15.7461	−	20.6428i	0.903103	−	1.18395i
$305$	−1.05911	+	1.32808i	−0.0606442	+	0.0760455i
$306$	−2.27644	−	0.244074i	−0.130135	−	0.0139528i
$307$	−12.4673	+	15.6335i	−0.711545	+	0.892250i	−0.997826	−	0.0658960i	$-0.979009\pi$
$307$	−12.4673	+	15.6335i	−0.711545	+	0.892250i	0.286281	+	0.958146i	$0.407581\pi$
$308$	−2.53199	−	3.23560i	−0.144274	−	0.184365i
$309$	3.74252	+	4.69297i	0.212905	+	0.266974i
$310$	−0.343034	−	0.539458i	−0.0194830	−	0.0306391i
$311$	−2.29775	+	10.0671i	−0.130293	+	0.570853i	0.867064	+	0.498197i	$0.166005\pi$
$311$	−2.29775	+	10.0671i	−0.130293	+	0.570853i	−0.997357	+	0.0726556i	$0.976853\pi$
$312$	−4.57327	−	12.4216i	−0.258911	−	0.703235i
$313$		−	2.12949i		−	0.120366i	−0.998187	−	0.0601829i	$-0.980832\pi$
$313$		−	2.12949i		−	0.120366i	0.998187	−	0.0601829i	$-0.0191684\pi$
$314$	13.3595	+	1.43237i	0.753917	+	0.0808331i
$315$	−0.131028	+	0.258731i	−0.00738256	+	0.0145778i
$316$	1.53086	−	0.757663i	0.0861178	−	0.0426219i
$317$	−4.26922	−	18.7047i	−0.239783	−	1.05056i	−0.941211	−	0.337819i	$-0.890311\pi$
$317$	−4.26922	−	18.7047i	−0.239783	−	1.05056i	0.701427	−	0.712741i	$-0.252546\pi$
$318$	−9.83021	−	9.72480i	−0.551251	−	0.545340i
$319$	3.56321	−	2.84156i	0.199501	−	0.159097i
$320$	0.524300	−	0.702933i	0.0293093	−	0.0392951i
$321$	−11.7380	+	2.67912i	−0.655152	+	0.149534i
$322$	−7.20618	−	11.8487i	−0.401584	−	0.660302i
$323$	10.2444	+	2.33822i	0.570014	+	0.130102i
$324$	1.94494	−	0.466036i	0.108052	−	0.0258909i
$325$		−	23.3432i		−	1.29485i
$326$	−3.21834	−	0.345062i	−0.178247	−	0.0191112i
$327$	−11.7315	+	5.64960i	−0.648755	+	0.312424i
$328$	−7.39837	+	12.2083i	−0.408506	+	0.674091i
$329$	5.80089	+	27.9802i	0.319813	+	1.54260i
$330$	0.0634874	−	0.102259i	0.00349487	−	0.00562918i
$331$	9.82766	+	2.24310i	0.540177	+	0.123292i	0.483900	−	0.875123i	$-0.339220\pi$
$331$	9.82766	+	2.24310i	0.540177	+	0.123292i	0.0562770	+	0.998415i	$0.482077\pi$
$332$	−9.82302	+	20.9731i	−0.539108	+	1.15105i
$333$	5.23964	−	2.52328i	0.287130	−	0.138275i
$334$	7.15237	+	7.07567i	0.391360	+	0.387164i
$335$	−1.42002	−	0.683846i	−0.0775840	−	0.0373625i
$336$	−2.33856	+	10.3214i	−0.127579	+	0.563078i
$337$	−11.9187	+	5.73975i	−0.649253	+	0.312664i	−0.729368	−	0.684122i	$-0.760186\pi$
$337$	−11.9187	+	5.73975i	−0.649253	+	0.312664i	0.0801145	+	0.996786i	$0.474471\pi$
$338$	11.9043	+	4.09360i	0.647507	+	0.222662i
$339$	−1.99502	−	8.74075i	−0.108355	−	0.474732i
$340$	0.346851	+	0.0752418i	0.0188106	+	0.00408056i
$341$	−2.50338	−	1.99638i	−0.135566	−	0.108110i
$342$	−9.11584	+	1.07690i	−0.492928	+	0.0582321i
$343$	16.1750	+	9.02051i	0.873367	+	0.487062i
$344$	2.60739	+	7.08201i	0.140581	+	0.381836i
$345$	0.253310	−	0.317641i	0.0136378	−	0.0171012i
$346$	−9.81602	+	28.5452i	−0.527713	+	1.53460i
$347$	−10.8720	+	2.48147i	−0.583642	+	0.133212i	−0.504140	−	0.863622i	$-0.668190\pi$
$347$	−10.8720	+	2.48147i	−0.583642	+	0.133212i	−0.0795025	+	0.996835i	$0.525333\pi$
$348$	−11.4727	−	2.48875i	−0.614999	−	0.133411i
$349$	−2.40729	−	4.99879i	−0.128859	−	0.267579i	0.826550	−	0.562863i	$-0.190300\pi$
$349$	−2.40729	−	4.99879i	−0.128859	−	0.267579i	−0.955410	+	0.295284i	$0.904586\pi$
$350$	−10.1589	+	15.6562i	−0.543016	+	0.836859i
$351$	−2.03053	+	4.21644i	−0.108382	+	0.225057i
$352$	1.33841	−	4.18332i	0.0713374	−	0.222972i
$353$	−9.39260	−	19.5039i	−0.499917	−	1.03809i	−0.986394	−	0.164396i	$-0.947433\pi$
$353$	−9.39260	−	19.5039i	−0.499917	−	1.03809i	0.486477	−	0.873693i	$-0.338282\pi$
$354$	5.36154	−	8.63584i	0.284963	−	0.458989i
$355$	−0.268320	+	1.17559i	−0.0142409	+	0.0623936i
$356$	26.5651	+	12.4421i	1.40795	+	0.659428i
$357$	−4.19405	+	0.869515i	−0.221973	+	0.0460196i
$358$	12.2095	−	12.3419i	0.645294	−	0.652288i
$359$	−3.57176	−	7.41684i	−0.188510	−	0.391446i	0.785198	−	0.619245i	$-0.212561\pi$
$359$	−3.57176	−	7.41684i	−0.188510	−	0.391446i	−0.973708	+	0.227799i	$0.926847\pi$
$360$	−0.307490	+	0.0396910i	−0.0162062	+	0.00209190i
$361$	23.1291			1.21732
$362$	−2.22545	−	18.8382i	−0.116967	−	0.990113i
$363$	−2.31358	+	10.1365i	−0.121432	+	0.532026i
$364$	−15.2612	−	19.5021i	−0.799906	−	1.02219i
$365$	−0.123357	−	0.540461i	−0.00645679	−	0.0282890i
$366$	20.6463	−	7.34961i	1.07920	−	0.384170i
$367$	−6.21310	−	7.79099i	−0.324321	−	0.406686i	0.592765	−	0.805376i	$-0.298036\pi$
$367$	−6.21310	−	7.79099i	−0.324321	−	0.406686i	−0.917086	+	0.398690i	$0.869465\pi$
$368$	6.14306	−	13.4929i	0.320229	−	0.703365i
$369$	4.92047	−	1.12307i	0.256150	−	0.0584645i
$370$	−0.849323	+	0.302340i	−0.0441542	+	0.0157179i
$371$	−23.0785	−	11.6875i	−1.19818	−	0.606786i
$372$	0.0889148	+	8.24728i	0.00461002	+	0.427601i
$373$	−35.2119			−1.82320			−0.911601	−	0.411076i	$-0.865153\pi$
$373$	−35.2119			−1.82320			−0.911601	+	0.411076i	$0.865153\pi$
$374$	1.76538	−	0.208553i	0.0912854	−	0.0107840i
$375$	−1.06739	−	0.243626i	−0.0551200	−	0.0125808i
$376$	−21.2487	+	21.9473i	−1.09582	+	1.13185i
$377$	21.4767	−	17.1271i	1.10611	−	0.882092i
$378$	3.19685	−	1.94427i	0.164428	−	0.100002i
$379$	−30.0899	−	23.9959i	−1.54562	−	1.23259i	−0.867263	−	0.497851i	$-0.834123\pi$
$379$	−30.0899	−	23.9959i	−1.54562	−	1.23259i	−0.678353	−	0.734736i	$-0.737306\pi$
$380$	1.42289	−	0.0153403i	0.0729926	−	0.000786941i
$381$	−5.92557	−	4.72549i	−0.303576	−	0.242094i
$382$	16.1537	+	25.4034i	0.826493	+	1.29975i
$383$	16.1928	+	20.3051i	0.827413	+	1.03754i	0.998631	+	0.0523102i	$0.0166584\pi$
$383$	16.1928	+	20.3051i	0.827413	+	1.03754i	−0.171218	+	0.985233i	$0.554770\pi$
$384$	−10.5303	+	4.13686i	−0.537370	+	0.211108i
$385$	0.0544823	−	0.218491i	0.00277668	−	0.0111353i
$386$	4.25579	−	2.70620i	0.216614	−	0.137742i
$387$	1.15768	−	2.40394i	0.0588481	−	0.122199i
$388$	−6.54198	+	3.23779i	−0.332119	+	0.164374i
$389$	12.6410	+	6.08756i	0.640922	+	0.308652i	0.725971	−	0.687725i	$-0.241391\pi$
$389$	12.6410	+	6.08756i	0.640922	+	0.308652i	−0.0850495	+	0.996377i	$0.527105\pi$
$390$	0.382662	−	0.616353i	0.0193768	−	0.0312102i
$391$	6.00029			0.303448
$392$	1.74838	+	19.7216i	0.0883066	+	0.996093i
$393$	−1.44287			−0.0727834
$394$	−0.465628	+	0.749986i	−0.0234580	+	0.0377838i
$395$	0.0843464	+	0.0406191i	0.00424393	+	0.00204377i
$396$	−1.39175	+	0.688814i	−0.0699382	+	0.0346142i
$397$	−7.90724	+	16.4195i	−0.396853	+	0.824074i	0.602804	+	0.797889i	$0.294050\pi$
$397$	−7.90724	+	16.4195i	−0.396853	+	0.824074i	−0.999657	+	0.0261844i	$0.991664\pi$
$398$	9.73136	−	6.18804i	0.487789	−	0.310178i
$399$	−15.6179	+	7.14047i	−0.781871	+	0.357471i
$400$	−19.9473	+	0.430158i	−0.997365	+	0.0215079i
$401$	−7.32304	−	9.18280i	−0.365695	−	0.458567i	0.564608	−	0.825359i	$-0.309027\pi$
$401$	−7.32304	−	9.18280i	−0.365695	−	0.458567i	−0.930303	+	0.366792i	$0.880456\pi$
$402$	10.9110	+	17.1588i	0.544194	+	0.855804i
$403$	−15.0888	−	12.0329i	−0.751627	−	0.599402i
$404$	22.1133	−	0.238406i	1.10018	−	0.0118612i
$405$	0.0857014	+	0.0683446i	0.00425854	+	0.00339607i
$406$	−21.8580	+	2.14049i	−1.08480	+	0.106231i
$407$	−3.53031	+	2.81533i	−0.174991	+	0.139551i
$408$	−3.28976	−	3.18504i	−0.162867	−	0.157683i
$409$	−14.3095	−	3.26605i	−0.707559	−	0.161496i	−0.146426	−	0.989222i	$-0.546777\pi$
$409$	−14.3095	−	3.26605i	−0.707559	−	0.161496i	−0.561133	+	0.827726i	$0.689634\pi$
$410$	−0.776988	+	0.0917895i	−0.0383727	+	0.00453316i
$411$	−4.85781			−0.239618
$412$	0.129421	+	12.0044i	0.00637609	+	0.591413i
$413$	4.60106	−	18.4517i	0.226403	−	0.907947i
$414$	−4.93806	+	1.75783i	−0.242692	+	0.0863928i
$415$	−1.23751	+	0.282453i	−0.0607468	+	0.0138651i
$416$	8.06707	−	25.2144i	0.395521	−	1.23624i
$417$	−3.08032	−	3.86260i	−0.150844	−	0.189153i
$418$	6.71439	−	2.39017i	0.328412	−	0.116907i
$419$	0.691920	+	3.03150i	0.0338025	+	0.148098i	0.989013	−	0.147829i	$-0.0472285\pi$
$419$	0.691920	+	3.03150i	0.0338025	+	0.148098i	−0.955210	+	0.295927i	$0.904371\pi$
$420$	−0.524884	+	0.246852i	−0.0256117	+	0.0120452i
$421$	−6.37929	+	27.9495i	−0.310908	+	1.36217i	0.542117	+	0.840303i	$0.317623\pi$
$421$	−6.37929	+	27.9495i	−0.310908	+	1.36217i	−0.853024	+	0.521872i	$0.825234\pi$
$422$	3.59774	+	30.4544i	0.175135	+	1.48250i
$423$	10.8004			0.525134
$424$	−3.54040	−	27.4278i	−0.171937	−	1.33201i
$425$	−3.50366	−	7.27542i	−0.169952	−	0.352910i
$426$	10.9409	−	11.0595i	0.530089	−	0.535835i
$427$	32.5593	−	24.9178i	1.57566	−	1.20586i
$428$	−21.8065	−	10.2133i	−1.05406	−	0.493680i
$429$	0.808565	−	3.54256i	0.0390379	−	0.171036i
$430$	−0.218169	+	0.351405i	−0.0105211	+	0.0169463i
$431$	15.1639	+	31.4882i	0.730421	+	1.51673i	0.851651	+	0.524109i	$0.175602\pi$
$431$	15.1639	+	31.4882i	0.730421	+	1.51673i	−0.121230	+	0.992624i	$0.538684\pi$
$432$	3.64046	+	1.65743i	0.175151	+	0.0797433i
$433$	2.32120	−	4.82003i	0.111550	−	0.231636i	−0.837719	−	0.546102i	$-0.816111\pi$
$433$	2.32120	−	4.82003i	0.111550	−	0.231636i	0.949269	+	0.314466i	$0.101825\pi$
$434$	4.88331	+	14.6370i	0.234406	+	0.702599i
$435$	−0.279169	−	0.579701i	−0.0133851	−	0.0277945i
$436$	−25.4501	−	5.52085i	−1.21884	−	0.264401i
$437$	23.4538	−	5.35317i	1.12195	−	0.256077i
$438$	−2.32576	+	6.76337i	−0.111129	+	0.323166i
$439$	−10.3729	+	13.0072i	−0.495072	+	0.620801i	−0.965110	−	0.261846i	$-0.915669\pi$
$439$	−10.3729	+	13.0072i	−0.495072	+	0.620801i	0.470038	+	0.882646i	$0.344240\pi$
$440$	0.225904	−	0.0831715i	0.0107696	−	0.00396505i
$441$	4.57952	−	5.29415i	0.218072	−	0.252102i
$442$	10.6406	−	1.25702i	0.506120	−	0.0597905i
$443$	−22.2038	−	17.7070i	−1.05494	−	0.841283i	−0.0672502	−	0.997736i	$-0.521423\pi$
$443$	−22.2038	−	17.7070i	−1.05494	−	0.841283i	−0.987685	+	0.156453i	$0.949994\pi$
$444$	11.3667	+	2.46577i	0.539442	+	0.117020i
$445$	0.357761	+	1.56745i	0.0169595	+	0.0743044i
$446$	−2.67836	−	0.921025i	−0.126824	−	0.0436118i
$447$	3.65855	−	1.76187i	0.173044	−	0.0833334i
$448$	−16.3838	+	13.4004i	−0.774061	+	0.633111i
$449$	15.1237	+	7.28321i	0.713734	+	0.343716i	0.755264	−	0.655421i	$-0.227509\pi$
$449$	15.1237	+	7.28321i	0.713734	+	0.343716i	−0.0415298	+	0.999137i	$0.513223\pi$
$450$	5.01480	+	4.96103i	0.236400	+	0.233865i
$451$	−3.53063	+	1.70026i	−0.166251	+	0.0800622i
$452$	7.60539	−	16.2383i	0.357727	−	0.763784i
$453$	−1.29365	−	0.295268i	−0.0607811	−	0.0138729i
$454$	6.07709	−	9.78837i	0.285212	−	0.459391i
$455$	0.328385	−	1.31692i	0.0153949	−	0.0617383i
$456$	−15.7005	−	9.51465i	−0.735241	−	0.445564i
$457$	−0.533566	+	0.256952i	−0.0249592	+	0.0120197i	−0.446322	−	0.894873i	$-0.647266\pi$
$457$	−0.533566	+	0.256952i	−0.0249592	+	0.0120197i	0.421363	+	0.906892i	$0.361552\pi$
$458$	−26.0053	−	2.78822i	−1.21515	−	0.130285i
$459$			1.61891i			0.0755643i
$460$	0.790189	−	0.189340i	0.0368427	−	0.00882804i
$461$	−10.9438	−	2.49785i	−0.509703	−	0.116336i	−0.0400680	−	0.999197i	$-0.512757\pi$
$461$	−10.9438	−	2.49785i	−0.509703	−	0.116336i	−0.469635	+	0.882861i	$0.655615\pi$
$462$	−2.08401	+	2.02409i	−0.0969569	+	0.0941693i
$463$	−34.1004	+	7.78320i	−1.58478	+	0.361716i	−0.922028	−	0.387123i	$-0.873469\pi$
$463$	−34.1004	+	7.78320i	−1.58478	+	0.361716i	−0.662752	+	0.748839i	$0.730612\pi$
$464$	−15.0313	−	18.0367i	−0.697809	−	0.837335i
$465$	−0.353422	+	0.281845i	−0.0163895	+	0.0130702i
$466$	−16.2528	−	16.0785i	−0.752895	−	0.744822i
$467$	−5.84314	−	25.6005i	−0.270388	−	1.18465i	−0.909556	−	0.415581i	$-0.863578\pi$
$467$	−5.84314	−	25.6005i	−0.270388	−	1.18465i	0.639168	−	0.769067i	$-0.279279\pi$
$468$	−8.38860	+	4.15173i	−0.387763	+	0.191914i
$469$	29.2625	+	24.3079i	1.35122	+	1.12243i
$470$	−1.66475	−	0.178490i	−0.0767890	−	0.00823312i
$471$		−	9.50070i		−	0.437769i
$472$	19.0777	−	7.02387i	0.878125	−	0.323300i
$473$	−0.460992	+	2.01974i	−0.0211965	+	0.0928677i
$474$	−0.648095	−	1.01920i	−0.0297680	−	0.0468134i
$475$	−20.1858	−	25.3122i	−0.926188	−	1.16140i
$476$	−7.68363	−	3.78766i	−0.352179	−	0.173607i
$477$	−6.09626	+	7.64447i	−0.279129	+	0.350016i
$478$	−4.16508	−	0.446569i	−0.190506	−	0.0204256i
$479$	−15.5133	+	19.4531i	−0.708822	+	0.888835i	−0.997648	−	0.0685468i	$-0.978164\pi$
$479$	−15.5133	+	19.4531i	−0.708822	+	0.888835i	0.288826	+	0.957382i	$0.406735\pi$
$480$	−0.533739	−	0.315635i	−0.0243617	−	0.0144067i
$481$	−21.2785	+	16.9690i	−0.970215	+	0.773720i
$482$	−3.57681	+	10.4014i	−0.162919	+	0.473773i
$483$	−7.78733	+	5.95968i	−0.354336	+	0.271175i
$484$	−16.1169	+	13.1395i	−0.732587	+	0.597251i
$485$	−0.360446	−	0.173581i	−0.0163670	−	0.00788193i
$486$	−0.474274	−	1.33232i	−0.0215135	−	0.0604351i
$487$	14.6999	−	30.5246i	0.666116	−	1.38320i	−0.244378	−	0.969680i	$-0.578584\pi$
$487$	14.6999	−	30.5246i	0.666116	−	1.38320i	0.910494	−	0.413523i	$-0.135702\pi$
$488$	41.5999	+	13.8055i	1.88314	+	0.624948i
$489$			2.28875i			0.103501i
$490$	−0.793367	+	0.740343i	−0.0358407	+	0.0334453i
$491$			0.619409i			0.0279535i	0.999902	+	0.0139768i	$0.00444909\pi$
$491$			0.619409i			0.0279535i	−0.999902	+	0.0139768i	$0.995551\pi$
$492$	9.14109	+	4.28134i	0.412112	+	0.193017i
$493$	4.12303	−	8.56155i	0.185692	−	0.385593i
$494$	40.4701	−	14.4064i	1.82084	−	0.648175i
$495$	−0.0766819	−	0.0369280i	−0.00344659	−	0.00165979i
$496$	−10.0043	+	13.1154i	−0.449208	+	0.588901i
$497$	13.1491	−	25.9646i	0.589817	−	1.16467i
$498$	15.4862	+	5.32534i	0.693954	+	0.238634i
$499$	27.7477	−	22.1281i	1.24216	−	0.990589i	0.242367	−	0.970185i	$-0.422076\pi$
$499$	27.7477	−	22.1281i	1.24216	−	0.990589i	0.999792	−	0.0204041i	$-0.00649528\pi$
$500$	−1.38363	−	1.69715i	−0.0618776	−	0.0758989i
$501$	4.43558	−	5.56205i	0.198167	−	0.248494i
$502$	3.41499	−	31.8511i	0.152418	−	1.42158i
$503$	9.47430	−	11.8804i	0.422438	−	0.529721i	−0.524382	−	0.851483i	$-0.675704\pi$
$503$	9.47430	−	11.8804i	0.422438	−	0.529721i	0.946821	+	0.321762i	$0.104275\pi$
$504$	7.43302	+	0.866143i	0.331093	+	0.0385811i
$505$	0.755707	+	0.947627i	0.0336285	+	0.0421688i
$506$	3.43427	−	2.18380i	0.152672	−	0.0970819i
$507$	1.98074	−	8.67821i	0.0879680	−	0.385413i
$508$	−3.53213	−	14.7409i	−0.156713	−	0.654022i
$509$			37.9800i			1.68344i	0.539918	+	0.841718i	$0.318455\pi$
$509$			37.9800i			1.68344i	−0.539918	+	0.841718i	$0.681545\pi$
$510$	0.0267545	−	0.249535i	0.00118471	−	0.0110496i
$511$	−0.267248	+	13.3777i	−0.0118223	+	0.591792i
$512$	−21.6949	−	6.42885i	−0.958789	−	0.284118i
$513$	1.44432	+	6.32796i	0.0637681	+	0.279386i
$514$	9.88894	−	9.99612i	0.436182	−	0.440910i
$515$	−0.514426	+	0.410241i	−0.0226683	+	0.0180774i
$516$	4.78265	−	2.36705i	0.210544	−	0.104204i
$517$	−8.17563	+	1.86603i	−0.359564	+	0.0820681i
$518$	21.6562	−	2.12073i	0.951520	−	0.0931794i
$519$	20.8094	+	4.74962i	0.913433	+	0.208485i
$520$	1.36161	−	0.501305i	0.0597105	−	0.0219837i
$521$		−	0.862494i		−	0.0377866i	−0.999822	−	0.0188933i	$-0.993986\pi$
$521$		−	0.862494i		−	0.0377866i	0.999822	−	0.0188933i	$-0.00601428\pi$
$522$	−0.884948	+	8.25377i	−0.0387331	+	0.361258i
$523$	−10.6367	+	5.12238i	−0.465111	+	0.223986i	−0.651737	−	0.758445i	$-0.725959\pi$
$523$	−10.6367	+	5.12238i	−0.465111	+	0.223986i	0.186625	+	0.982431i	$0.440245\pi$
$524$	−2.27543	−	1.77481i	−0.0994028	−	0.0775328i
$525$	11.7733	+	5.96229i	0.513830	+	0.260216i
$526$	26.6628	+	16.5535i	1.16255	+	0.721768i
$527$	−6.50881	−	1.48559i	−0.283528	−	0.0647135i
$528$	−3.04209	−	0.625656i	−0.132390	−	0.0272282i
$529$	−8.34550	+	4.01898i	−0.362848	+	0.174738i
$530$	1.06600	−	1.07755i	0.0463039	−	0.0468058i
$531$	−6.47582	−	3.11859i	−0.281027	−	0.135335i
$532$	−33.4127	−	7.95012i	−1.44863	−	0.344682i
$533$	−21.2804	+	10.2481i	−0.921756	+	0.443895i
$534$	6.74520	−	19.6152i	0.291893	−	0.848833i
$535$	−0.293675	−	1.28668i	−0.0126967	−	0.0556278i
$536$	−3.89932	+	40.4809i	−0.168425	+	1.74851i
$537$	−9.59767	−	7.65389i	−0.414170	−	0.330290i
$538$	−2.76848	−	23.4348i	−0.119358	−	1.01035i
$539$	−2.55189	+	4.79875i	−0.109918	+	0.206697i
$540$	0.0510851	+	0.213197i	0.00219835	+	0.00917455i
$541$	10.4682	−	13.1267i	0.450062	−	0.564360i	−0.504102	−	0.863644i	$-0.668176\pi$
$541$	10.4682	−	13.1267i	0.450062	−	0.564360i	0.954164	+	0.299284i	$0.0967477\pi$
$542$	21.5691	+	7.41709i	0.926471	+	0.318591i
$543$	−13.0769	+	2.98473i	−0.561185	+	0.128087i
$544$	−1.27023	−	9.06943i	−0.0544608	−	0.388849i
$545$	−0.619288	−	1.28596i	−0.0265274	−	0.0550847i
$546$	−12.5611	+	12.1999i	−0.537565	+	0.522109i
$547$	18.8623	−	39.1679i	0.806493	−	1.67470i	0.0706948	−	0.997498i	$-0.477478\pi$
$547$	18.8623	−	39.1679i	0.806493	−	1.67470i	0.735798	−	0.677201i	$-0.236807\pi$
$548$	−7.66084	−	5.97535i	−0.327255	−	0.255254i
$549$	−6.72371	−	13.9619i	−0.286961	−	0.595880i
$550$	−4.65321	−	2.88894i	−0.198413	−	0.123185i
$551$	8.47777	−	37.1435i	0.361165	−	1.58237i
$552$	−9.94961	−	3.30193i	−0.423484	−	0.140539i
$553$	−1.73813	−	1.44384i	−0.0739130	−	0.0613984i
$554$	9.53586	+	9.43361i	0.405140	+	0.400796i
$555$	0.276592	+	0.574349i	0.0117407	+	0.0243798i
$556$	−0.106521	−	9.88034i	−0.00451749	−	0.419020i
$557$	21.0813			0.893243			0.446622	−	0.894723i	$-0.352627\pi$
$557$	21.0813			0.893243			0.446622	+	0.894723i	$0.352627\pi$
$558$	5.79177	−	0.684211i	0.245185	−	0.0289650i
$559$	−2.77857	+	12.1737i	−0.117521	+	0.514893i
$560$	−1.13139	−	0.256344i	−0.0478100	−	0.0108325i
$561$	−0.279706	−	1.22547i	−0.0118092	−	0.0517396i
$562$	10.1478	+	28.5070i	0.428060	+	1.20249i
$563$	−15.5962	−	19.5570i	−0.657302	−	0.824231i	0.335744	−	0.941953i	$-0.391012\pi$
$563$	−15.5962	−	19.5570i	−0.657302	−	0.824231i	−0.993047	+	0.117722i	$0.962441\pi$
$564$	17.0324	+	13.2850i	0.717194	+	0.559401i
$565$	0.958128	−	0.218686i	0.0403087	−	0.00920020i
$566$	1.12126	+	3.14981i	0.0471301	+	0.132396i
$567$	−1.60795	−	2.10107i	−0.0675278	−	0.0882365i
$568$	30.8577	−	3.98314i	1.29476	−	0.167129i
$569$	−16.3811			−0.686731			−0.343365	−	0.939202i	$-0.611567\pi$
$569$	−16.3811			−0.686731			−0.343365	+	0.939202i	$0.611567\pi$
$570$	−0.118046	−	0.999244i	−0.00494439	−	0.0418537i
$571$	0.420582	+	0.0959951i	0.0176008	+	0.00401727i	0.231312	−	0.972880i	$-0.425698\pi$
$571$	0.420582	+	0.0959951i	0.0176008	+	0.00401727i	−0.213711	+	0.976897i	$0.568555\pi$
$572$	5.63264	−	4.59209i	0.235513	−	0.192005i
$573$	16.6429	−	13.2722i	0.695265	−	0.554456i
$574$	18.7326	+	2.38780i	0.781884	+	0.0996649i
$575$	−14.4540	−	11.5267i	−0.602772	−	0.480695i
$576$	3.70233	+	7.09174i	0.154264	+	0.295489i
$577$	26.7418	+	21.3259i	1.11328	+	0.887809i	0.994461	−	0.105108i	$-0.0335187\pi$
$577$	26.7418	+	21.3259i	1.11328	+	0.887809i	0.118816	+	0.992916i	$0.462090\pi$
$578$	−17.1597	+	10.9116i	−0.713749	+	0.453863i
$579$	−2.22347	−	2.78815i	−0.0924044	−	0.115872i
$580$	0.272807	−	1.25759i	0.0113277	−	0.0522185i
$581$	30.6311	+	0.611922i	1.27079	+	0.0253868i
$582$	2.76957	+	4.35545i	0.114802	+	0.180539i
$583$	3.29394	−	6.83994i	0.136421	−	0.283281i
$584$	−11.9870	+	7.80513i	−0.496027	+	0.322979i
$585$	−0.462190	−	0.222579i	−0.0191092	−	0.00920250i
$586$	0.0159650	+	0.00991186i	0.000659509	+	0.000409455i
$587$	46.3442			1.91283			0.956415	−	0.292012i	$-0.0943247\pi$
$587$	46.3442			1.91283			0.956415	+	0.292012i	$0.0943247\pi$
$588$	13.7340	−	2.71591i	0.566382	−	0.112002i
$589$	−26.7668			−1.10291
$590$	0.946627	+	0.587712i	0.0389720	+	0.0241957i
$591$	0.562398	+	0.270837i	0.0231340	+	0.0111407i
$592$	14.8925	+	17.8702i	0.612078	+	0.734462i
$593$	19.4710	−	40.4319i	0.799577	−	1.66034i	0.0496977	−	0.998764i	$-0.484174\pi$
$593$	19.4710	−	40.4319i	0.799577	−	1.66034i	0.749879	−	0.661575i	$-0.230112\pi$
$594$	0.589203	+	0.926586i	0.0241753	+	0.0380183i
$595$	−0.0953129	−	0.459736i	−0.00390745	−	0.0188473i
$596$	7.93678	+	1.72171i	0.325103	+	0.0705241i
$597$	−5.08424	−	6.37543i	−0.208084	−	0.260929i
$598$	20.6996	−	13.1626i	0.846470	−	0.538258i
$599$	−11.4603	−	9.13927i	−0.468254	−	0.373420i	0.360750	−	0.932663i	$-0.382521\pi$
$599$	−11.4603	−	9.13927i	−0.468254	−	0.373420i	−0.829004	+	0.559242i	$0.811092\pi$
$600$	1.80610	+	13.9921i	0.0737339	+	0.571224i
$601$	−7.27033	−	5.79790i	−0.296563	−	0.236501i	0.463892	−	0.885892i	$-0.346453\pi$
$601$	−7.27033	−	5.79790i	−0.296563	−	0.236501i	−0.760455	+	0.649391i	$0.775024\pi$
$602$	7.16153	−	6.95563i	0.291882	−	0.283490i
$603$	11.2415	−	8.96478i	0.457788	−	0.365074i
$604$	−1.67692	−	2.05690i	−0.0682327	−	0.0836940i
$605$	−1.11112	−	0.253606i	−0.0451735	−	0.0103105i
$606$	−1.83457	−	15.5294i	−0.0745242	−	0.630839i
$607$	−13.4308			−0.545140			−0.272570	−	0.962136i	$-0.587874\pi$
$607$	−13.4308			−0.545140			−0.272570	+	0.962136i	$0.587874\pi$
$608$	−13.0564	−	34.3171i	−0.529506	−	1.39174i
$609$	3.15263	+	15.2065i	0.127751	+	0.616200i
$610$	0.805636	+	2.26317i	0.0326193	+	0.0916331i
$611$	−49.2775	+	11.2473i	−1.99355	+	0.455016i
$612$	−1.99134	+	2.55305i	−0.0804953	+	0.103201i
$613$	21.6619	+	27.1632i	0.874917	+	1.09711i	0.994547	+	0.104293i	$0.0332580\pi$
$613$	21.6619	+	27.1632i	0.874917	+	1.09711i	−0.119629	+	0.992819i	$0.538171\pi$
$614$	9.48356	+	26.6409i	0.382725	+	1.07514i
$615$	0.123106	+	0.539363i	0.00496412	+	0.0217492i
$616$	−5.77625	+	0.628588i	−0.232732	+	0.0253265i
$617$	3.21604	−	14.0904i	0.129473	−	0.567259i	−0.868022	−	0.496525i	$-0.834609\pi$
$617$	3.21604	−	14.0904i	0.129473	−	0.567259i	0.997495	−	0.0707332i	$-0.0225339\pi$
$618$	8.43025	−	0.995909i	0.339114	−	0.0400613i
$619$	13.8820			0.557963			0.278981	−	0.960297i	$-0.410003\pi$
$619$	13.8820			0.557963			0.278981	+	0.960297i	$0.410003\pi$
$620$	−0.904035	+	0.00974649i	−0.0363069	+	0.000391429i
$621$	1.60813	+	3.33933i	0.0645322	+	0.134003i
$622$	10.3815	+	10.2702i	0.416261	+	0.411797i
$623$	0.775075	−	38.7980i	0.0310527	−	1.55441i
$624$	−18.3358	−	3.77106i	−0.734019	−	0.150963i
$625$	−5.52295	+	24.1976i	−0.220918	+	0.967905i
$626$	−2.55855	−	1.58847i	−0.102260	−	0.0634882i
$627$	−2.18662	−	4.54056i	−0.0873251	−	0.181333i
$628$	11.6863	−	14.9827i	0.466336	−	0.597877i
$629$	−4.08496	+	8.48251i	−0.162878	+	0.338220i
$630$	0.213123	+	0.350426i	0.00849103	+	0.0139613i
$631$	0.587423	+	1.21980i	0.0233849	+	0.0485593i	0.912334	−	0.409447i	$-0.134278\pi$
$631$	0.587423	+	1.21980i	0.0233849	+	0.0485593i	−0.888949	+	0.458006i	$0.848564\pi$
$632$	0.231612	−	2.40448i	0.00921302	−	0.0956452i
$633$	21.1406	−	4.82521i	0.840264	−	0.191785i
$634$	−25.6580	−	8.82319i	−1.01901	−	0.350413i
$635$	0.517990	−	0.649539i	0.0205558	−	0.0257762i
$636$	−19.0170	+	4.55674i	−0.754072	+	0.180686i
$637$	−15.3811	+	28.9238i	−0.609423	+	1.14600i
$638$	−0.756157	−	6.40079i	−0.0299366	−	0.253410i
$639$	−8.60044	−	6.85862i	−0.340228	−	0.271323i
$640$	−0.453467	−	1.15429i	−0.0179249	−	0.0456272i
$641$	−3.10376	−	13.5985i	−0.122591	−	0.537108i	−0.998506	−	0.0546417i	$-0.982598\pi$
$641$	−3.10376	−	13.5985i	−0.122591	−	0.537108i	0.875915	−	0.482466i	$-0.160259\pi$
$642$	−5.53694	+	16.1015i	−0.218525	+	0.635477i
$643$	−5.51514	+	2.65595i	−0.217496	+	0.104740i	−0.539460	−	0.842012i	$-0.681371\pi$
$643$	−5.51514	+	2.65595i	−0.217496	+	0.104740i	0.321964	+	0.946752i	$0.395657\pi$
$644$	−19.6114	−	0.180309i	−0.772799	−	0.00710518i
$645$	0.263511	+	0.126900i	0.0103757	+	0.00499669i
$646$	10.4511	−	10.5644i	0.411192	−	0.415649i
$647$	38.9962	−	18.7796i	1.53310	−	0.738301i	0.538551	−	0.842593i	$-0.318972\pi$
$647$	38.9962	−	18.7796i	1.53310	−	0.738301i	0.994547	+	0.104292i	$0.0332578\pi$
$648$	0.890878	−	2.68446i	0.0349970	−	0.105456i
$649$	5.44084	+	1.24184i	0.213572	+	0.0487463i
$650$	−28.0466	−	17.4127i	−1.10008	−	0.682981i
$651$	9.92284	−	4.53671i	0.388907	−	0.177808i
$652$	−2.81528	+	3.60940i	−0.110255	+	0.141355i
$653$	−38.3827	+	18.4841i	−1.50203	+	0.723340i	−0.990703	−	0.136045i	$-0.956561\pi$
$653$	−38.3827	+	18.4841i	−1.50203	+	0.723340i	−0.511329	+	0.859385i	$0.670847\pi$
$654$	−1.96310	+	18.3095i	−0.0767634	+	0.715960i
$655$		−	0.158162i		−	0.00617992i
$656$	9.14937	+	17.9957i	0.357223	+	0.702615i
$657$	4.93049	+	1.12535i	0.192357	+	0.0439042i
$658$	37.9450	+	13.9019i	1.47925	+	0.541953i
$659$	30.1174	−	6.87410i	1.17321	−	0.267777i	0.408869	−	0.912593i	$-0.365923\pi$
$659$	30.1174	−	6.87410i	1.17321	−	0.267777i	0.764338	+	0.644816i	$0.223066\pi$
$660$	−0.0755051	−	0.152559i	−0.00293903	−	0.00593834i
$661$	37.7148	−	30.0766i	1.46694	−	1.16984i	0.517585	−	0.855632i	$-0.326831\pi$
$661$	37.7148	−	30.0766i	1.46694	−	1.16984i	0.949353	−	0.314212i	$-0.101740\pi$
$662$	10.0259	−	10.1346i	0.389668	−	0.393892i
$663$	−1.68589	−	7.38638i	−0.0654746	−	0.286863i
$664$	17.8716	+	27.4470i	0.693551	+	1.06515i
$665$	−0.782711	−	1.71197i	−0.0303522	−	0.0663874i
$666$	0.876778	−	8.17757i	0.0339745	−	0.316875i
$667$		−	21.7555i		−	0.842375i
$668$	13.8366	−	3.31544i	0.535353	−	0.128278i
$669$	−0.445651	+	1.95252i	−0.0172299	+	0.0754889i
$670$	−1.88088	+	1.19603i	−0.0726649	+	0.0462066i
$671$	7.50193	+	9.40713i	0.289609	+	0.363158i
$672$	10.6566	+	10.5089i	0.411087	+	0.405390i
$673$	23.5570	−	29.5395i	0.908055	−	1.13867i	−0.0818090	−	0.996648i	$-0.526070\pi$
$673$	23.5570	−	29.5395i	0.908055	−	1.13867i	0.989864	−	0.142017i	$-0.0453588\pi$
$674$	−1.99443	+	18.6017i	−0.0768224	+	0.716510i
$675$	3.10996	−	3.89976i	0.119702	−	0.150102i
$676$	13.7983	−	11.2493i	0.530704	−	0.432664i
$677$	−12.1628	+	9.69953i	−0.467455	+	0.372783i	−0.828705	−	0.559686i	$-0.810922\pi$
$677$	−12.1628	+	9.69953i	−0.467455	+	0.372783i	0.361249	+	0.932469i	$0.382350\pi$
$678$	−11.9901	−	4.12310i	−0.460476	−	0.158347i
$679$	7.42773	+	6.17010i	0.285050	+	0.236787i
$680$	0.349132	−	0.360611i	0.0133886	−	0.0138288i
$681$	−7.34008	−	3.53480i	−0.281273	−	0.135454i
$682$	−4.26600	+	1.51860i	−0.163354	+	0.0581502i
$683$	−12.9468	+	26.8844i	−0.495397	+	1.02870i	0.492023	+	0.870582i	$0.336258\pi$
$683$	−12.9468	+	26.8844i	−0.495397	+	1.02870i	−0.987420	+	0.158120i	$0.949457\pi$
$684$	−5.50600	+	11.7559i	−0.210527	+	0.449497i
$685$		−	0.532495i		−	0.0203456i
$686$	22.9036	−	12.7053i	0.874465	−	0.485089i
$687$			18.4939i			0.705587i
$688$	10.4539	+	2.15002i	0.398551	+	0.0819686i
$689$	19.8538	−	41.2268i	0.756369	−	1.57062i
$690$	−0.192687	−	0.541291i	−0.00733547	−	0.0206066i
$691$	−3.18735	−	1.53495i	−0.121253	−	0.0583922i	0.372274	−	0.928123i	$-0.378578\pi$
$691$	−3.18735	−	1.53495i	−0.121253	−	0.0583922i	−0.493527	+	0.869731i	$0.664292\pi$
$692$	26.9745	+	33.0869i	1.02542	+	1.25777i
$693$	1.58019	+	1.31264i	0.0600265	+	0.0498630i
$694$	−5.12845	+	14.9137i	−0.194673	+	0.566115i
$695$	0.423404	−	0.337653i	0.0160606	−	0.0128079i
$696$	−11.5481	+	11.9278i	−0.437731	+	0.452122i
$697$	−5.09433	+	6.38808i	−0.192961	+	0.241966i
$698$	−7.80168	−	0.836476i	−0.295298	−	0.0316611i
$699$	−10.0793	+	12.6390i	−0.381233	+	0.478051i
$700$	11.2328	+	23.8844i	0.424559	+	0.902745i
$701$	−1.98681	−	2.49139i	−0.0750409	−	0.0940984i	0.742894	−	0.669409i	$-0.233453\pi$
$701$	−1.98681	−	2.49139i	−0.0750409	−	0.0940984i	−0.817935	+	0.575311i	$0.804881\pi$
$702$	3.55134	+	5.58487i	0.134037	+	0.210787i
$703$	−8.39950	+	36.8006i	−0.316793	+	1.38796i
$704$	−4.02784	−	4.72859i	−0.151805	−	0.178216i
$705$			1.18390i			0.0445882i
$706$	−30.4400	−	3.26370i	−1.14563	−	0.122831i
$707$	−12.1642	−	26.6060i	−0.457483	−	1.00062i
$708$	−6.37645	−	12.8837i	−0.239642	−	0.484197i
$709$	−3.66813	−	16.0711i	−0.137759	−	0.603564i	−0.995925	−	0.0901900i	$-0.971253\pi$
$709$	−3.66813	−	16.0711i	−0.137759	−	0.603564i	0.858165	−	0.513374i	$-0.171605\pi$
$710$	1.21230	+	1.19930i	0.0454968	+	0.0450090i
$711$	−0.667722	+	0.532490i	−0.0250415	+	0.0199699i
$712$	34.7650	−	22.6365i	1.30287	−	0.848340i
$713$	−14.9014	+	3.40115i	−0.558062	+	0.127374i
$714$	−2.08381	+	5.68771i	−0.0779845	+	0.212857i
$715$	0.388321	+	0.0886318i	0.0145224	+	0.00331464i
$716$	−5.72101	−	23.8759i	−0.213804	−	0.892285i
$717$			2.96204i			0.110619i
$718$	−11.5756	−	1.24110i	−0.431996	−	0.0463175i
$719$	−15.3666	+	7.40016i	−0.573077	+	0.275979i	−0.697895	−	0.716200i	$-0.745880\pi$
$719$	−15.3666	+	7.40016i	−0.573077	+	0.275979i	0.124818	+	0.992180i	$0.460165\pi$
$720$	−0.181681	+	0.399053i	−0.00677087	+	0.0148718i
$721$	14.4433	−	6.60345i	0.537895	−	0.245925i
$722$	17.2530	−	27.7894i	0.642090	−	1.03421i
$723$	7.58264	+	1.73069i	0.282002	+	0.0643650i
$724$	−24.2939	−	11.3783i	−0.902875	−	0.422872i
$725$	−26.3788	+	12.7033i	−0.979682	+	0.471790i
$726$	10.4530	+	10.3409i	0.387948	+	0.383788i
$727$	−17.2483	−	8.30633i	−0.639703	−	0.308065i	0.0857704	−	0.996315i	$-0.472665\pi$
$727$	−17.2483	−	8.30633i	−0.639703	−	0.308065i	−0.725473	+	0.688250i	$0.758379\pi$
$728$	−34.8156	+	3.78873i	−1.29035	+	0.140420i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−0.741374	−	0.254941i	−0.0274395	−	0.00943579i
$731$	0.961189	+	4.21124i	0.0355509	+	0.155758i
$732$	6.57048	−	30.2887i	0.242852	−	1.11950i
$733$	21.4561	+	17.1107i	0.792498	+	0.631996i	0.933729	−	0.357980i	$-0.116535\pi$
$733$	21.4561	+	17.1107i	0.792498	+	0.631996i	−0.141231	+	0.989977i	$0.545106\pi$
$734$	−13.9954	+	1.65335i	−0.516579	+	0.0610261i
$735$	0.580324	+	0.501990i	0.0214056	+	0.0185162i
$736$	−11.6292	−	17.4457i	−0.428656	−	0.643057i
$737$	−6.96062	+	8.72834i	−0.256398	+	0.321513i
$738$	2.32103	−	6.74962i	0.0854385	−	0.248457i
$739$	−26.8992	+	6.13957i	−0.989504	+	0.225848i	−0.686491	−	0.727139i	$-0.740850\pi$
$739$	−26.8992	+	6.13957i	−0.989504	+	0.225848i	−0.303013	+	0.952986i	$0.597993\pi$
$740$	−0.270288	+	1.24598i	−0.00993600	+	0.0458031i
$741$	−13.1795	−	27.3676i	−0.484163	−	1.00537i
$742$	−31.2576	+	19.0104i	−1.14750	+	0.697892i
$743$	19.2736	−	40.0221i	0.707082	−	1.46827i	−0.168753	−	0.985658i	$-0.553974\pi$
$743$	19.2736	−	40.0221i	0.707082	−	1.46827i	0.875834	−	0.482612i	$-0.160312\pi$
$744$	9.97532	+	6.04515i	0.365713	+	0.221626i
$745$	0.193129	+	0.401037i	0.00707570	+	0.0146928i
$746$	−26.2660	+	42.3066i	−0.961666	+	1.54896i
$747$	2.57674	−	11.2894i	0.0942781	−	0.413059i
$748$	1.06629	−	2.27664i	0.0389875	−	0.0832424i
$749$	−0.636236	+	31.8482i	−0.0232476	+	1.16371i
$750$	−1.08893	+	1.10073i	−0.0397620	+	0.0401930i
$751$	−13.8027	−	28.6616i	−0.503668	−	1.04588i	−0.985510	−	0.169620i	$-0.945746\pi$
$751$	−13.8027	−	28.6616i	−0.503668	−	1.04588i	0.481841	−	0.876259i	$-0.339968\pi$
$752$	10.5191	+	41.9014i	0.383592	+	1.52799i
$753$	−22.6512			−0.825455
$754$	−4.55764	−	38.5799i	−0.165979	−	1.40500i
$755$	0.0323661	−	0.141805i	0.00117792	−	0.00516082i
$756$	0.0486484	−	5.29128i	0.00176933	−	0.192442i
$757$	1.97938	+	8.67222i	0.0719417	+	0.315197i	0.998076	−	0.0619958i	$-0.0197465\pi$
$757$	1.97938	+	8.67222i	0.0719417	+	0.315197i	−0.926135	+	0.377193i	$0.876889\pi$
$758$	−51.2761	+	18.2531i	−1.86243	+	0.662983i
$759$	−1.79427	−	2.24994i	−0.0651277	−	0.0816676i
$760$	1.04296	−	1.72102i	0.0378321	−	0.0624281i
$761$	10.6314	−	2.42654i	0.385387	−	0.0879621i	−0.0254377	−	0.999676i	$-0.508098\pi$
$761$	10.6314	−	2.42654i	0.385387	−	0.0879621i	0.410825	+	0.911714i	$0.365241\pi$
$762$	−10.0977	+	3.59456i	−0.365803	+	0.130217i
$763$	6.99356	+	33.7330i	0.253184	+	1.22122i
$764$	42.5716	−	0.458968i	1.54018	−	0.0166049i
$765$	−0.177459			−0.00641604
$766$	36.4752	−	4.30900i	1.31790	−	0.155691i
$767$	32.7939	+	7.48500i	1.18412	+	0.270268i
$768$	−2.88457	+	15.7378i	−0.104088	+	0.567890i
$769$	−23.2610	+	18.5501i	−0.838814	+	0.668932i	−0.945593	−	0.325351i	$-0.894518\pi$
$769$	−23.2610	+	18.5501i	−0.838814	+	0.668932i	0.106779	+	0.994283i	$0.465946\pi$
$770$	−0.221873	−	0.228441i	−0.00799576	−	0.00823245i
$771$	−7.77350	−	6.19916i	−0.279956	−	0.223257i
$772$	−0.0768902	−	7.13194i	−0.00276734	−	0.256684i
$773$	−2.21789	−	1.76871i	−0.0797719	−	0.0636160i	0.582792	−	0.812621i	$-0.301960\pi$
$773$	−2.21789	−	1.76871i	−0.0797719	−	0.0636160i	−0.662564	+	0.749005i	$0.730532\pi$
$774$	−2.02475	−	3.18414i	−0.0727780	−	0.114451i
$775$	12.8251	+	16.0821i	0.460691	+	0.577688i
$776$	−0.989769	+	10.2753i	−0.0355306	+	0.368862i
$777$	−3.12353	−	15.0661i	−0.112056	−	0.540495i
$778$	16.7435	−	10.6470i	0.600285	−	0.381713i
$779$	−14.2134	+	29.5145i	−0.509249	+	1.05747i
$780$	−0.455097	−	0.919527i	−0.0162951	−	0.0329243i
$781$	7.69530	+	3.70586i	0.275359	+	0.132606i
$782$	4.47586	−	7.20927i	0.160057	−	0.257803i
$783$	5.86975			0.209768
$784$	24.9995	+	12.6105i	0.892839	+	0.450376i
$785$	1.04143			0.0371702
$786$	−1.07630	+	1.73360i	−0.0383903	+	0.0618353i
$787$	−41.1088	−	19.7970i	−1.46537	−	0.705685i	−0.480183	−	0.877168i	$-0.659430\pi$
$787$	−41.1088	−	19.7970i	−1.46537	−	0.705685i	−0.985187	+	0.171483i	$0.945144\pi$
$788$	0.553768	+	1.11889i	0.0197272	+	0.0398589i
$789$	9.62851	−	19.9938i	0.342784	−	0.711799i
$790$	0.111721	−	0.0710417i	0.00397485	−	0.00252755i
$791$	−23.7158	−	0.473775i	−0.843238	−	0.0168455i
$792$	−0.210565	+	2.18599i	−0.00748211	+	0.0776757i
$793$	45.2169	+	56.7002i	1.60570	+	2.01348i
$794$	13.8295	+	21.7485i	0.490792	+	0.771824i
$795$	−0.837958	−	0.668249i	−0.0297193	−	0.0237003i
$796$	−0.175819	−	16.3080i	−0.00623172	−	0.578023i
$797$	−20.8605	−	16.6357i	−0.738917	−	0.589267i	0.180024	−	0.983662i	$-0.442383\pi$
$797$	−20.8605	−	16.6357i	−0.738917	−	0.589267i	−0.918941	+	0.394396i	$0.870954\pi$
$798$	−3.07083	+	24.0910i	−0.108706	+	0.852813i
$799$	−13.6703	+	10.9017i	−0.483619	+	0.385673i
$800$	−14.3627	+	24.2873i	−0.507798	+	0.858686i
$801$	−14.2995	−	3.26376i	−0.505247	−	0.115319i
$802$	−16.4956	+	1.94871i	−0.582479	+	0.0688112i
$803$	−3.92668			−0.138570
$804$	28.7551	−	0.310012i	1.01411	−	0.0109333i
$805$	−0.653277	−	0.853618i	−0.0230250	−	0.0300861i
$806$	−25.7128	+	9.15315i	−0.905693	+	0.322406i
$807$	−16.2678	+	3.71302i	−0.572654	+	0.130705i
$808$	16.2088	−	26.7467i	0.570224	−	0.940946i
$809$	−25.9943	−	32.5958i	−0.913910	−	1.14601i	−0.988864	−	0.148819i	$-0.952453\pi$
$809$	−25.9943	−	32.5958i	−0.913910	−	1.14601i	0.0749549	−	0.997187i	$-0.476119\pi$
$810$	0.146043	−	0.0519881i	0.00513144	−	0.00182667i
$811$	−7.34892	−	32.1977i	−0.258056	−	1.13062i	−0.923327	−	0.384014i	$-0.874541\pi$
$811$	−7.34892	−	32.1977i	−0.258056	−	1.13062i	0.665272	−	0.746601i	$-0.268316\pi$
$812$	−13.7330	+	27.8588i	−0.481935	+	0.977653i
$813$	3.58886	−	15.7238i	0.125867	−	0.551459i
$814$	0.749177	+	6.34169i	0.0262586	+	0.222276i
$815$	−0.250884			−0.00878809
$816$	−6.28076	+	1.57675i	−0.219870	+	0.0551971i
$817$	7.51414	+	15.6033i	0.262886	+	0.545889i
$818$	−14.5982	+	14.7564i	−0.510413	+	0.515945i
$819$	9.52438	+	7.91175i	0.332809	+	0.276459i
$820$	−0.469304	+	1.00201i	−0.0163888	+	0.0349917i
$821$	4.75036	−	20.8127i	0.165789	−	0.726367i	−0.821861	−	0.569688i	$-0.807064\pi$
$821$	4.75036	−	20.8127i	0.165789	−	0.726367i	0.987650	−	0.156679i	$-0.0500789\pi$
$822$	−3.62364	+	5.83660i	−0.126389	+	0.203575i
$823$	−18.9541	−	39.3587i	−0.660700	−	1.37196i	−0.914455	−	0.404688i	$-0.867380\pi$
$823$	−18.9541	−	39.3587i	−0.660700	−	1.37196i	0.253755	−	0.967269i	$-0.418334\pi$
$824$	14.5197	+	8.79907i	0.505816	+	0.306530i
$825$	−1.68038	+	3.48934i	−0.0585032	+	0.121483i
$826$	−18.7373	−	19.2920i	−0.651954	−	0.671253i
$827$	−10.9852	−	22.8109i	−0.381991	−	0.793213i	−0.999975	−	0.00702223i	$-0.997765\pi$
$827$	−10.9852	−	22.8109i	−0.381991	−	0.793213i	0.617984	−	0.786190i	$-0.287950\pi$
$828$	−1.57149	+	7.24425i	−0.0546129	+	0.251755i
$829$	−14.3729	+	3.28052i	−0.499192	+	0.113937i	−0.464701	−	0.885468i	$-0.653838\pi$
$829$	−14.3729	+	3.28052i	−0.499192	+	0.113937i	−0.0344909	+	0.999405i	$0.510981\pi$
$830$	−0.583744	+	1.69754i	−0.0202620	+	0.0589225i
$831$	5.91372	−	7.41557i	0.205145	−	0.257243i
$832$	−24.2772	−	28.5010i	−0.841662	−	0.988093i
$833$	−0.452597	+	11.3233i	−0.0156816	+	0.392331i
$834$	−6.93861	+	0.819693i	−0.240264	+	0.0283837i
$835$	0.609690	+	0.486212i	0.0210992	+	0.0168261i
$836$	2.13679	−	9.85018i	0.0739023	−	0.340676i
$837$	−0.917649	−	4.02048i	−0.0317186	−	0.138968i
$838$	4.15844	+	1.42999i	0.143651	+	0.0493981i
$839$	−30.0133	+	14.4537i	−1.03618	+	0.498996i	−0.873061	−	0.487611i	$-0.837868\pi$
$839$	−30.0133	+	14.4537i	−1.03618	+	0.498996i	−0.163115	+	0.986607i	$0.552154\pi$
$840$	−0.0949433	+	0.814779i	−0.00327585	+	0.0281126i
$841$	−4.91383	−	2.36638i	−0.169442	−	0.0815992i
$842$	28.8224	+	28.5133i	0.993285	+	0.982634i
$843$	19.2776	−	9.28362i	0.663957	−	0.319745i
$844$	39.2743	+	18.3946i	1.35188	+	0.633168i
$845$	0.951272	+	0.217122i	0.0327248	+	0.00746921i
$846$	8.05648	−	12.9766i	0.276987	−	0.446143i
$847$	24.5407	+	12.4280i	0.843230	+	0.427032i
$848$	−35.5951	−	16.2058i	−1.22234	−	0.556509i
$849$	2.13004	−	1.02577i	0.0731027	−	0.0352044i
$850$	−11.3548	−	1.21744i	−0.389468	−	0.0417578i
$851$			21.5546i			0.738883i
$852$	−5.12657	−	21.3951i	−0.175634	−	0.732985i
$853$	1.15126	+	0.262768i	0.0394184	+	0.00899699i	0.242185	−	0.970230i	$-0.422136\pi$
$853$	1.15126	+	0.262768i	0.0394184	+	0.00899699i	−0.202766	+	0.979227i	$0.564993\pi$
$854$	−5.65104	−	57.7068i	−0.193375	−	1.97469i
$855$	−0.693647	+	0.158320i	−0.0237222	+	0.00541444i
$856$	−28.5375	+	18.5817i	−0.975393	+	0.635108i
$857$	−40.5251	+	32.3177i	−1.38431	+	1.10395i	−0.402219	+	0.915543i	$0.631761\pi$
$857$	−40.5251	+	32.3177i	−1.38431	+	1.10395i	−0.982091	+	0.188407i	$0.939668\pi$
$858$	−3.65319	−	3.61402i	−0.124718	−	0.123381i
$859$	12.7531	+	55.8749i	0.435130	+	1.90643i	0.422182	+	0.906511i	$0.361264\pi$
$859$	12.7531	+	55.8749i	0.435130	+	1.90643i	0.0129471	+	0.999916i	$0.495879\pi$
$860$	0.259467	+	0.524256i	0.00884776	+	0.0178770i
$861$	0.266705	−	13.3505i	0.00908927	−	0.454983i
$862$	49.1441	+	5.26910i	1.67385	+	0.179466i
$863$			46.3661i			1.57832i	0.614187	+	0.789160i	$0.289484\pi$
$863$			46.3661i			1.57832i	−0.614187	+	0.789160i	$0.710516\pi$
$864$	4.70695	−	3.13761i	0.160134	−	0.106744i
$865$	−0.520635	+	2.28105i	−0.0177021	+	0.0775581i
$866$	−4.05972	−	6.38435i	−0.137955	−	0.216949i
$867$	8.96524	+	11.2421i	0.304475	+	0.381800i
$868$	21.2289	+	5.05113i	0.720554	+	0.171446i
$869$	0.413447	−	0.518446i	0.0140252	−	0.0175871i
$870$	−0.904747	−	0.0970046i	−0.0306738	−	0.00328876i
$871$	−41.9542	+	52.6089i	−1.42156	+	1.78258i
$872$	−25.6175	+	26.4597i	−0.867518	+	0.896039i
$873$	2.85344	−	2.27554i	0.0965743	−	0.0770154i
$874$	11.0634	−	32.1726i	0.374224	−	1.08825i
$875$	−1.30870	+	2.58420i	−0.0442422	+	0.0873619i
$876$	6.39122	+	7.83945i	0.215939	+	0.264870i
$877$	28.7604	+	13.8503i	0.971169	+	0.467690i	0.851059	−	0.525070i	$-0.175961\pi$
$877$	28.7604	+	13.8503i	0.971169	+	0.467690i	0.120110	+	0.992761i	$0.461675\pi$
$878$	7.89042	+	22.1655i	0.266289	+	0.748051i
$879$	0.00576532	−	0.0119718i	0.000194460	−	0.000403799i
$880$	0.0685820	−	0.333462i	0.00231190	−	0.0112410i
$881$		−	15.1123i		−	0.509147i	−0.967053	−	0.254573i	$-0.918065\pi$
$881$		−	15.1123i		−	0.509147i	0.967053	−	0.254573i	$-0.0819351\pi$
$882$	−2.94479	−	9.45136i	−0.0991563	−	0.318244i
$883$			57.9874i			1.95143i	0.219039	+	0.975716i	$0.429708\pi$
$883$			57.9874i			1.95143i	−0.219039	+	0.975716i	$0.570292\pi$
$884$	6.42694	−	13.7222i	0.216161	−	0.461526i
$885$	0.341848	−	0.709855i	0.0114911	−	0.0238615i
$886$	−37.8374	+	13.4693i	−1.27117	+	0.452509i
$887$	26.9311	+	12.9693i	0.904259	+	0.435468i	0.827425	−	0.561576i	$-0.189805\pi$
$887$	26.9311	+	12.9693i	0.904259	+	0.435468i	0.0768335	+	0.997044i	$0.475519\pi$
$888$	11.4415	−	11.8177i	0.383952	−	0.396575i
$889$	−15.9242	+	12.1868i	−0.534080	+	0.408733i
$890$	2.15014	+	0.739383i	0.0720730	+	0.0247842i
$891$	0.607046	−	0.484103i	0.0203368	−	0.0162181i
$892$	−3.10450	+	2.53099i	−0.103946	+	0.0847437i
$893$	−43.7080	+	54.8081i	−1.46263	+	1.83408i
$894$	0.612207	−	5.70995i	0.0204752	−	0.190969i
$895$	0.838990	−	1.05206i	0.0280443	−	0.0351665i
$896$	3.87912	+	29.6808i	0.129592	+	0.991567i
$897$	−10.8147	−	13.5612i	−0.361092	−	0.452795i
$898$	20.0321	−	12.7381i	0.668480	−	0.425077i
$899$	−5.38637	+	23.5992i	−0.179645	+	0.787078i
$900$	9.70135	−	2.32458i	0.323378	−	0.0774861i
$901$		−	15.8291i		−	0.527345i
$902$	−0.590801	+	5.51030i	−0.0196715	+	0.183473i
$903$	−5.43020	−	4.51078i	−0.180706	−	0.150109i
$904$	−13.8369	−	21.2506i	−0.460208	−	0.706783i
$905$	−0.327174	−	1.43344i	−0.0108756	−	0.0476493i
$906$	−1.31975	+	1.33405i	−0.0438457	+	0.0443210i
$907$	31.7003	−	25.2801i	1.05259	−	0.839413i	0.0652250	−	0.997871i	$-0.479223\pi$
$907$	31.7003	−	25.2801i	1.05259	−	0.839413i	0.987366	+	0.158457i	$0.0506521\pi$
$908$	−7.22744	−	14.6031i	−0.239851	−	0.484621i
$909$	−10.7801	+	2.46048i	−0.357553	+	0.0816091i
$910$	−1.33731	−	1.37690i	−0.0443314	−	0.0456437i
$911$	−34.2254	−	7.81173i	−1.13394	−	0.258814i	−0.385946	−	0.922521i	$-0.626125\pi$
$911$	−34.2254	−	7.81173i	−1.13394	−	0.258814i	−0.747993	+	0.663707i	$0.768982\pi$
$912$	−23.1434	+	11.7665i	−0.766353	+	0.389629i
$913$			8.99101i			0.297559i
$914$	−0.0892847	+	0.832744i	−0.00295328	+	0.0275447i
$915$	1.53045	−	0.737027i	0.0505952	−	0.0243654i
$916$	−22.7484	+	29.1652i	−0.751629	+	0.963644i
$917$	−0.923637	+	3.70407i	−0.0305012	+	0.122319i
$918$	1.94510	+	1.20761i	0.0641979	+	0.0398572i
$919$	39.1159	+	8.92794i	1.29031	+	0.294506i	0.811986	−	0.583676i	$-0.198386\pi$
$919$	39.1159	+	8.92794i	1.29031	+	0.294506i	0.478327	+	0.878182i	$0.341243\pi$
$920$	0.361944	−	1.09064i	0.0119330	−	0.0359573i
$921$	18.0157	−	8.67593i	0.593639	−	0.285881i
$922$	−11.1646	+	11.2856i	−0.367685	+	0.371671i
$923$	46.3824	+	22.3366i	1.52669	+	0.735217i
$924$	0.877372	+	4.01376i	0.0288634	+	0.132043i
$925$	26.1352	−	12.5861i	0.859321	−	0.413827i
$926$	−16.0855	+	46.7770i	−0.528602	+	1.53719i
$927$	−1.33569	−	5.85204i	−0.0438698	−	0.192206i
$928$	−32.8834	+	4.60553i	−1.07945	+	0.151184i
$929$	19.0980	+	15.2302i	0.626587	+	0.499686i	0.884536	−	0.466472i	$-0.154475\pi$
$929$	19.0980	+	15.2302i	0.626587	+	0.499686i	−0.257949	+	0.966158i	$0.583047\pi$
$930$	0.0750006	+	0.634871i	0.00245937	+	0.0208183i
$931$	8.33304	+	44.6642i	0.273104	+	1.46381i
$932$	−31.4417	+	7.53389i	−1.02991	+	0.246781i
$933$	6.43815	−	8.07319i	0.210776	−	0.264304i
$934$	−35.1173	−	12.0760i	−1.14907	−	0.395138i
$935$	0.134332	−	0.0306603i	0.00439312	−	0.00100270i
$936$	−1.26915	+	13.1757i	−0.0414836	+	0.430663i
$937$	−11.5408	−	23.9646i	−0.377020	−	0.782891i	−1.00000		0.000652479i	$-0.999792\pi$
$937$	−11.5408	−	23.9646i	−0.377020	−	0.782891i	0.622980	−	0.782238i	$-0.285922\pi$
$938$	51.0337	−	17.0262i	1.66631	−	0.555926i
$939$	−0.923951	+	1.91860i	−0.0301520	+	0.0626113i
$940$	−1.45626	+	1.86703i	−0.0474978	+	0.0608957i
$941$	7.08218	+	14.7063i	0.230873	+	0.479412i	0.983933	−	0.178540i	$-0.0571374\pi$
$941$	7.08218	+	14.7063i	0.230873	+	0.479412i	−0.753060	+	0.657952i	$0.771423\pi$
$942$	−11.4150	−	7.08697i	−0.371920	−	0.230906i
$943$	−4.16250	+	18.2371i	−0.135550	+	0.593882i
$944$	5.79179	−	28.1611i	0.188507	−	0.916565i
$945$	0.230311	−	0.176258i	0.00749201	−	0.00573367i
$946$	2.08282	+	2.06048i	0.0677183	+	0.0669921i
$947$	−15.8143	−	32.8388i	−0.513896	−	1.06712i	−0.982937	−	0.183940i	$-0.941115\pi$
$947$	−15.8143	−	32.8388i	−0.513896	−	1.06712i	0.469041	−	0.883176i	$-0.344600\pi$
$948$	−1.70800	+	0.0184141i	−0.0554732	+	0.000598062i
$949$	−23.6676			−0.768281
$950$	−45.4697	+	5.37156i	−1.47523	+	0.174277i
$951$	−4.26922	+	18.7047i	−0.138439	+	0.606541i
$952$	−10.2824	+	6.40642i	−0.333253	+	0.207633i
$953$	−10.4977	−	45.9934i	−0.340054	−	1.48987i	−0.798958	−	0.601387i	$-0.794615\pi$
$953$	−10.4977	−	45.9934i	−0.340054	−	1.48987i	0.458904	−	0.888486i	$-0.348242\pi$
$954$	4.63728	+	13.0269i	0.150137	+	0.421762i
$955$	1.45485	+	1.82433i	0.0470779	+	0.0590338i
$956$	−3.64345	+	4.67117i	−0.117838	+	0.151077i
$957$	−4.44325	+	1.01414i	−0.143630	+	0.0327825i
$958$	11.8006	+	33.1499i	0.381261	+	1.07103i
$959$	−3.10966	+	12.4707i	−0.100416	+	0.402700i
$960$	−0.777369	+	0.405835i	−0.0250895	+	0.0130983i
$961$	−13.9936			−0.451408
$962$	4.51556	+	38.2237i	0.145587	+	1.23238i
$963$	11.7380	+	2.67912i	0.378252	+	0.0863336i
$964$	9.82911	+	12.0564i	0.316574	+	0.388309i
$965$	0.305626	−	0.243729i	0.00983845	−	0.00784591i
$966$	1.35158	+	13.8020i	0.0434864	+	0.444071i
$967$	33.5351	+	26.7433i	1.07842	+	0.860008i	0.990690	−	0.136137i	$-0.0434688\pi$
$967$	33.5351	+	26.7433i	1.07842	+	0.860008i	0.0877253	+	0.996145i	$0.472040\pi$
$968$	3.76471	+	29.1656i	0.121002	+	0.937417i
$969$	−8.21538	−	6.55155i	−0.263916	−	0.210466i
$970$	−0.477427	+	0.303589i	−0.0153293	+	0.00974766i
$971$	−14.3203	−	17.9571i	−0.459561	−	0.576271i	0.497020	−	0.867739i	$-0.334428\pi$
$971$	−14.3203	−	17.9571i	−0.459561	−	0.576271i	−0.956581	+	0.291468i	$0.905856\pi$
$972$	−1.95454	−	0.423996i	−0.0626919	−	0.0135997i
$973$	−11.8877	+	5.43504i	−0.381102	+	0.174239i
$974$	−25.7097	−	40.4313i	−0.823792	−	1.29550i
$975$	−10.1282	+	21.0315i	−0.324363	+	0.673548i
$976$	47.6183	−	39.6837i	1.52422	−	1.27024i
$977$	−17.0141	−	8.19358i	−0.544331	−	0.262136i	0.141448	−	0.989946i	$-0.454824\pi$
$977$	−17.0141	−	8.19358i	−0.544331	−	0.262136i	−0.685779	+	0.727810i	$0.740538\pi$
$978$	2.74991	+	1.70727i	0.0879323	+	0.0545926i
$979$	11.3882			0.363969
$980$	0.297707	+	1.50547i	0.00950991	+	0.0480906i
$981$	13.0210			0.415729
$982$	0.744212	+	0.462043i	0.0237488	+	0.0147444i
$983$	14.4708	+	6.96879i	0.461548	+	0.222270i	0.650183	−	0.759777i	$-0.274692\pi$
$983$	14.4708	+	6.96879i	0.461548	+	0.222270i	−0.188635	+	0.982047i	$0.560406\pi$
$984$	11.9627	−	7.78927i	0.381356	−	0.248313i
$985$	−0.0296881	+	0.0616479i	−0.000945941	+	0.00196427i
$986$	−7.21106	−	11.3402i	−0.229647	−	0.361145i
$987$	6.91374	−	27.7262i	0.220067	−	0.882535i
$988$	12.8792	−	59.3706i	0.409742	−	1.88883i
$989$	6.16585	+	7.73173i	0.196063	+	0.245855i
$990$	−0.101569	+	0.0645861i	−0.00322807	+	0.00205268i
$991$	−26.8126	−	21.3823i	−0.851729	−	0.679231i	0.0970130	−	0.995283i	$-0.469071\pi$
$991$	−26.8126	−	21.3823i	−0.851729	−	0.679231i	−0.948742	+	0.316052i	$0.897643\pi$
$992$	8.29539	+	21.8034i	0.263379	+	0.692260i
$993$	−7.88117	−	6.28502i	−0.250101	−	0.199449i
$994$	−21.3877	−	35.1665i	−0.678375	−	1.11541i
$995$	0.698851	−	0.557315i	0.0221551	−	0.0176681i
$996$	17.9501	−	14.6341i	0.568772	−	0.463699i
$997$	−1.52221	−	0.347434i	−0.0482088	−	0.0110033i	0.198349	−	0.980132i	$-0.436442\pi$
$997$	−1.52221	−	0.347434i	−0.0482088	−	0.0110033i	−0.246557	+	0.969128i	$0.579299\pi$
$998$	−5.88842	−	49.8448i	−0.186395	−	1.57781i
$999$	−5.81556			−0.183996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.a.55.20	✓	168
4.3	odd	2		588.2.x.b.55.21	yes	168
49.41	odd	14		588.2.x.b.139.21	yes	168
196.139	even	14	inner	588.2.x.a.139.20	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.55.20	✓	168	1.1	even	1	trivial
588.2.x.a.139.20	yes	168	196.139	even	14	inner
588.2.x.b.55.21	yes	168	4.3	odd	2
588.2.x.b.139.21	yes	168	49.41	odd	14

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.745941 - 1.20149i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-0.887143 - 1.79248i) q^{4} +(0.0475607 - 0.0987608i) q^{5} +(-1.19338 + 0.758851i) q^{6} +(-1.69059 + 2.03517i) q^{7} +(-2.81540 - 0.271193i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.0831823 - 0.130813i) q^{10} +(-0.607046 - 0.484103i) q^{11} +(0.0215610 + 1.99988i) q^{12} +(-3.65889 - 2.91786i) q^{13} +(1.18415 + 3.54933i) q^{14} +(-0.0857014 + 0.0683446i) q^{15} +(-2.42596 + 3.18037i) q^{16} +(-1.57832 - 0.360242i) q^{17} +(1.40445 - 0.165915i) q^{18} -6.49070 q^{19} +(-0.219220 + 0.00236343i) q^{20} +(2.40619 - 1.10011i) q^{21} +(-1.03446 + 0.368245i) q^{22} +(-3.61344 + 0.824745i) q^{23} +(2.41892 + 1.46589i) q^{24} +(3.10996 + 3.89976i) q^{25} +(-6.23509 + 2.21955i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(5.14779 + 1.22485i) q^{28} +(-1.30614 + 5.72258i) q^{29} +(0.0181869 + 0.153950i) q^{30} +4.12388 q^{31} +(2.01155 + 5.28712i) q^{32} +(0.336885 + 0.699549i) q^{33} +(-1.61016 + 1.62762i) q^{34} +(0.120590 + 0.263758i) q^{35} +(0.848291 - 1.81119i) q^{36} +(1.29408 - 5.66975i) q^{37} +(-4.84168 + 7.79849i) q^{38} +(2.03053 + 4.21644i) q^{39} +(-0.160685 + 0.265153i) q^{40} +(2.18982 - 4.54720i) q^{41} +(0.473112 - 3.71163i) q^{42} +(-1.15768 - 2.40394i) q^{43} +(-0.329208 + 1.51758i) q^{44} +(0.106868 - 0.0243919i) q^{45} +(-1.70450 + 4.95672i) q^{46} +(6.73395 - 8.44410i) q^{47} +(3.56562 - 1.81283i) q^{48} +(-1.28384 - 6.88126i) q^{49} +(7.00536 - 0.827579i) q^{50} +(1.26572 + 1.00938i) q^{51} +(-1.98425 + 9.14704i) q^{52} +(2.17573 + 9.53250i) q^{53} +(-1.33735 - 0.459883i) q^{54} +(-0.0766819 + 0.0369280i) q^{55} +(5.31159 - 5.27134i) q^{56} +(5.84792 + 2.81621i) q^{57} +(5.90130 + 5.83802i) q^{58} +(-6.47582 + 3.11859i) q^{59} +(0.198535 + 0.0929864i) q^{60} +(-15.1080 - 3.44831i) q^{61} +(3.07617 - 4.95479i) q^{62} +(-2.64522 - 0.0528441i) q^{63} +(7.85291 + 1.52703i) q^{64} +(-0.462190 + 0.222579i) q^{65} +(1.09180 + 0.117060i) q^{66} -14.3784i q^{67} +(0.754472 + 3.14869i) q^{68} +(3.61344 + 0.824745i) q^{69} +(0.406854 + 0.0518607i) q^{70} +(-10.7246 + 2.44781i) q^{71} +(-1.54334 - 2.37025i) q^{72} +(3.95395 - 3.15317i) q^{73} +(-5.84682 - 5.78413i) q^{74} +(-1.10993 - 4.86293i) q^{75} +(5.75817 + 11.6344i) q^{76} +(2.01150 - 0.417025i) q^{77} +(6.58065 + 0.705560i) q^{78} +0.854048i q^{79} +(0.198715 + 0.390850i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-3.82993 - 6.02298i) q^{82} +(-7.21987 - 9.05343i) q^{83} +(-4.10656 - 3.33709i) q^{84} +(-0.110644 + 0.138743i) q^{85} +(-3.75187 - 0.402266i) q^{86} +(3.65973 - 4.58915i) q^{87} +(1.57779 + 1.52757i) q^{88} +(-11.4673 + 9.14485i) q^{89} +(0.0504106 - 0.146595i) q^{90} +(12.1240 - 2.51356i) q^{91} +(4.68398 + 5.74535i) q^{92} +(-3.71548 - 1.78928i) q^{93} +(-5.12235 - 14.3896i) q^{94} +(-0.308702 + 0.641026i) q^{95} +(0.481652 - 5.63631i) q^{96} -3.64969i q^{97} +(-9.22542 - 3.59049i) q^{98} -0.776441i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31}+ \cdots - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more