LMFDB - Embedded newform 690.2.i.f.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.906765 + 1.47573i) q^{3} -1.00000i q^{4} +(-1.96911 - 1.05954i) q^{5} +(-1.68468 - 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35555 + 2.67628i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.906765 + 1.47573i) q^{3} -1.00000i q^{4} +(-1.96911 - 1.05954i) q^{5} +(-1.68468 - 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35555 + 2.67628i) q^{9} +(2.14157 - 0.643162i) q^{10} +4.12939i q^{11} +(1.47573 - 0.906765i) q^{12} +(-0.734549 + 0.734549i) q^{13} +0.878491 q^{14} +(-0.221927 - 3.86662i) q^{15} -1.00000 q^{16} +(-2.50190 + 2.50190i) q^{17} +(-0.933895 - 2.85094i) q^{18} -7.88126i q^{19} +(-1.05954 + 1.96911i) q^{20} +(0.353433 - 1.47997i) q^{21} +(-2.91992 - 2.91992i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.402318 + 1.68468i) q^{24} +(2.75476 + 4.17269i) q^{25} -1.03881i q^{26} +(-5.17863 + 0.426330i) q^{27} +(-0.621187 + 0.621187i) q^{28} -7.83802 q^{29} +(2.89104 + 2.57719i) q^{30} -7.07325 q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.09386 + 3.74439i) q^{33} -3.53823i q^{34} +(0.565012 + 1.88135i) q^{35} +(2.67628 + 1.35555i) q^{36} +(-6.46585 - 6.46585i) q^{37} +(5.57289 + 5.57289i) q^{38} +(-1.75006 - 0.417931i) q^{39} +(-0.643162 - 2.14157i) q^{40} -1.77236i q^{41} +(0.796585 + 1.29641i) q^{42} +(-6.31426 + 6.31426i) q^{43} +4.12939 q^{44} +(5.50485 - 3.83362i) q^{45} +1.00000 q^{46} +(-0.0280085 + 0.0280085i) q^{47} +(-0.906765 - 1.47573i) q^{48} -6.22825i q^{49} +(-4.89844 - 1.00262i) q^{50} +(-5.96077 - 1.42349i) q^{51} +(0.734549 + 0.734549i) q^{52} +(9.77127 + 9.77127i) q^{53} +(3.36039 - 3.96331i) q^{54} +(4.37524 - 8.13121i) q^{55} -0.878491i q^{56} +(11.6306 - 7.14645i) q^{57} +(5.54232 - 5.54232i) q^{58} -10.9630 q^{59} +(-3.86662 + 0.221927i) q^{60} +11.0841 q^{61} +(5.00154 - 5.00154i) q^{62} +(2.50452 - 0.820418i) q^{63} +1.00000i q^{64} +(2.22469 - 0.668122i) q^{65} +(1.66133 - 6.95669i) q^{66} +(10.8288 + 10.8288i) q^{67} +(2.50190 + 2.50190i) q^{68} +(0.402318 - 1.68468i) q^{69} +(-1.72984 - 0.930794i) q^{70} -2.25608i q^{71} +(-2.85094 + 0.933895i) q^{72} +(-8.48742 + 8.48742i) q^{73} +9.14409 q^{74} +(-3.65983 + 7.84893i) q^{75} -7.88126 q^{76} +(2.56512 - 2.56512i) q^{77} +(1.53300 - 0.941956i) q^{78} -1.98214i q^{79} +(1.96911 + 1.05954i) q^{80} +(-5.32495 - 7.25568i) q^{81} +(1.25325 + 1.25325i) q^{82} +(-2.21281 - 2.21281i) q^{83} +(-1.47997 - 0.353433i) q^{84} +(7.57738 - 2.27565i) q^{85} -8.92971i q^{86} +(-7.10725 - 11.5668i) q^{87} +(-2.91992 + 2.91992i) q^{88} -6.08809 q^{89} +(-1.18174 + 6.60329i) q^{90} +0.912584 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-6.41378 - 10.4382i) q^{93} -0.0396100i q^{94} +(-8.35049 + 15.5190i) q^{95} +(1.68468 + 0.402318i) q^{96} +(11.8246 + 11.8246i) q^{97} +(4.40404 + 4.40404i) q^{98} +(-11.0514 - 5.59760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.906765	+	1.47573i	0.523521	+	0.852013i
$3$	0.906765	+	1.47573i	0.523521	+	0.852013i
$4$		−	1.00000i		−	0.500000i
$5$	−1.96911	−	1.05954i	−0.880611	−	0.473840i
$5$	−1.96911	−	1.05954i	−0.880611	−	0.473840i
$6$	−1.68468	−	0.402318i	−0.687767	−	0.164246i
$7$	−0.621187	−	0.621187i	−0.234787	−	0.234787i	0.579901	−	0.814687i	$-0.303091\pi$
$7$	−0.621187	−	0.621187i	−0.234787	−	0.234787i	−0.814687	+	0.579901i	$0.803091\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.35555	+	2.67628i	−0.451851	+	0.892093i
$10$	2.14157	−	0.643162i	0.677225	−	0.203386i
$11$			4.12939i			1.24506i	0.782597	+	0.622529i	$0.213895\pi$
$11$			4.12939i			1.24506i	−0.782597	+	0.622529i	$0.786105\pi$
$12$	1.47573	−	0.906765i	0.426006	−	0.261761i
$13$	−0.734549	+	0.734549i	−0.203727	+	0.203727i	−0.801595	−	0.597868i	$-0.796015\pi$
$13$	−0.734549	+	0.734549i	−0.203727	+	0.203727i	0.597868	+	0.801595i	$0.296015\pi$
$14$	0.878491			0.234787
$15$	−0.221927	−	3.86662i	−0.0573013	−	0.998357i
$16$	−1.00000			−0.250000
$17$	−2.50190	+	2.50190i	−0.606801	+	0.606801i	−0.942109	−	0.335308i	$-0.891160\pi$
$17$	−2.50190	+	2.50190i	−0.606801	+	0.606801i	0.335308	+	0.942109i	$0.391160\pi$
$18$	−0.933895	−	2.85094i	−0.220121	−	0.671972i
$19$		−	7.88126i		−	1.80808i	−0.427443	−	0.904042i	$-0.640586\pi$
$19$		−	7.88126i		−	1.80808i	0.427443	−	0.904042i	$-0.359414\pi$
$20$	−1.05954	+	1.96911i	−0.236920	+	0.440306i
$21$	0.353433	−	1.47997i	0.0771253	−	0.322957i
$22$	−2.91992	−	2.91992i	−0.622529	−	0.622529i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−0.402318	+	1.68468i	−0.0821228	+	0.343883i
$25$	2.75476	+	4.17269i	0.550952	+	0.834537i
$26$		−	1.03881i		−	0.203727i
$27$	−5.17863	+	0.426330i	−0.996628	+	0.0820472i
$28$	−0.621187	+	0.621187i	−0.117393	+	0.117393i
$29$	−7.83802			−1.45548			−0.727742	−	0.685851i	$-0.759430\pi$
$29$	−7.83802			−1.45548			−0.727742	+	0.685851i	$0.759430\pi$
$30$	2.89104	+	2.57719i	0.527829	+	0.470528i
$31$	−7.07325			−1.27039			−0.635197	−	0.772350i	$-0.719081\pi$
$31$	−7.07325			−1.27039			−0.635197	+	0.772350i	$0.719081\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.09386	+	3.74439i	−1.06080	+	0.651814i
$34$		−	3.53823i		−	0.606801i
$35$	0.565012	+	1.88135i	0.0955044	+	0.318007i
$36$	2.67628	+	1.35555i	0.446047	+	0.225925i
$37$	−6.46585	−	6.46585i	−1.06298	−	1.06298i	−0.997879	−	0.0651000i	$-0.979263\pi$
$37$	−6.46585	−	6.46585i	−1.06298	−	1.06298i	−0.0651000	−	0.997879i	$-0.520737\pi$
$38$	5.57289	+	5.57289i	0.904042	+	0.904042i
$39$	−1.75006	−	0.417931i	−0.280234	−	0.0669226i
$40$	−0.643162	−	2.14157i	−0.101693	−	0.338613i
$41$		−	1.77236i		−	0.276796i	−0.990377	−	0.138398i	$-0.955805\pi$
$41$		−	1.77236i		−	0.276796i	0.990377	−	0.138398i	$-0.0441954\pi$
$42$	0.796585	+	1.29641i	0.122916	+	0.200041i
$43$	−6.31426	+	6.31426i	−0.962915	+	0.962915i	−0.999337	−	0.0364216i	$-0.988404\pi$
$43$	−6.31426	+	6.31426i	−0.962915	+	0.962915i	0.0364216	+	0.999337i	$0.488404\pi$
$44$	4.12939			0.622529
$45$	5.50485	−	3.83362i	0.820614	−	0.571482i
$46$	1.00000			0.147442
$47$	−0.0280085	+	0.0280085i	−0.00408546	+	0.00408546i	−0.709147	−	0.705061i	$-0.750920\pi$
$47$	−0.0280085	+	0.0280085i	−0.00408546	+	0.00408546i	0.705061	+	0.709147i	$0.250920\pi$
$48$	−0.906765	−	1.47573i	−0.130880	−	0.213003i
$49$		−	6.22825i		−	0.889751i
$50$	−4.89844	−	1.00262i	−0.692744	−	0.141793i
$51$	−5.96077	−	1.42349i	−0.834675	−	0.199329i
$52$	0.734549	+	0.734549i	0.101864	+	0.101864i
$53$	9.77127	+	9.77127i	1.34219	+	1.34219i	0.893880	+	0.448307i	$0.147973\pi$
$53$	9.77127	+	9.77127i	1.34219	+	1.34219i	0.448307	+	0.893880i	$0.352027\pi$
$54$	3.36039	−	3.96331i	0.457291	−	0.539338i
$55$	4.37524	−	8.13121i	0.589958	−	1.09641i
$56$		−	0.878491i		−	0.117393i
$57$	11.6306	−	7.14645i	1.54051	−	0.946571i
$58$	5.54232	−	5.54232i	0.727742	−	0.727742i
$59$	−10.9630			−1.42726			−0.713629	−	0.700524i	$-0.752950\pi$
$59$	−10.9630			−1.42726			−0.713629	+	0.700524i	$0.752950\pi$
$60$	−3.86662	+	0.221927i	−0.499178	+	0.0286506i
$61$	11.0841			1.41917			0.709587	−	0.704618i	$-0.248882\pi$
$61$	11.0841			1.41917			0.709587	+	0.704618i	$0.248882\pi$
$62$	5.00154	−	5.00154i	0.635197	−	0.635197i
$63$	2.50452	−	0.820418i	0.315540	−	0.103363i
$64$			1.00000i			0.125000i
$65$	2.22469	−	0.668122i	0.275938	−	0.0828704i
$66$	1.66133	−	6.95669i	0.204495	−	0.856309i
$67$	10.8288	+	10.8288i	1.32295	+	1.32295i	0.911373	+	0.411581i	$0.135023\pi$
$67$	10.8288	+	10.8288i	1.32295	+	1.32295i	0.411581	+	0.911373i	$0.364977\pi$
$68$	2.50190	+	2.50190i	0.303401	+	0.303401i
$69$	0.402318	−	1.68468i	0.0484334	−	0.202811i
$70$	−1.72984	−	0.930794i	−0.206756	−	0.111251i
$71$		−	2.25608i		−	0.267747i	−0.990998	−	0.133874i	$-0.957258\pi$
$71$		−	2.25608i		−	0.267747i	0.990998	−	0.133874i	$-0.0427417\pi$
$72$	−2.85094	+	0.933895i	−0.335986	+	0.110061i
$73$	−8.48742	+	8.48742i	−0.993378	+	0.993378i	−0.999978	−	0.00660049i	$-0.997899\pi$
$73$	−8.48742	+	8.48742i	−0.993378	+	0.993378i	0.00660049	+	0.999978i	$0.497899\pi$
$74$	9.14409			1.06298
$75$	−3.65983	+	7.84893i	−0.422601	+	0.906316i
$76$	−7.88126			−0.904042
$77$	2.56512	−	2.56512i	0.292323	−	0.292323i
$78$	1.53300	−	0.941956i	0.173578	−	0.106655i
$79$		−	1.98214i		−	0.223008i	−0.993764	−	0.111504i	$-0.964433\pi$
$79$		−	1.98214i		−	0.223008i	0.993764	−	0.111504i	$-0.0355668\pi$
$80$	1.96911	+	1.05954i	0.220153	+	0.118460i
$81$	−5.32495	−	7.25568i	−0.591661	−	0.806187i
$82$	1.25325	+	1.25325i	0.138398	+	0.138398i
$83$	−2.21281	−	2.21281i	−0.242887	−	0.242887i	0.575156	−	0.818043i	$-0.304941\pi$
$83$	−2.21281	−	2.21281i	−0.242887	−	0.242887i	−0.818043	+	0.575156i	$0.804941\pi$
$84$	−1.47997	−	0.353433i	−0.161478	−	0.0385627i
$85$	7.57738	−	2.27565i	0.821882	−	0.246829i
$86$		−	8.92971i		−	0.962915i
$87$	−7.10725	−	11.5668i	−0.761977	−	1.24009i
$88$	−2.91992	+	2.91992i	−0.311264	+	0.311264i
$89$	−6.08809			−0.645336			−0.322668	−	0.946512i	$-0.604580\pi$
$89$	−6.08809			−0.645336			−0.322668	+	0.946512i	$0.604580\pi$
$90$	−1.18174	+	6.60329i	−0.124566	+	0.696048i
$91$	0.912584			0.0956648
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	−6.41378	−	10.4382i	−0.665078	−	1.08239i
$94$		−	0.0396100i		−	0.00408546i
$95$	−8.35049	+	15.5190i	−0.856742	+	1.59222i
$96$	1.68468	+	0.402318i	0.171942	+	0.0410614i
$97$	11.8246	+	11.8246i	1.20061	+	1.20061i	0.973982	+	0.226625i	$0.0727691\pi$
$97$	11.8246	+	11.8246i	1.20061	+	1.20061i	0.226625	+	0.973982i	$0.427231\pi$
$98$	4.40404	+	4.40404i	0.444875	+	0.444875i
$99$	−11.0514	−	5.59760i	−1.11071	−	0.562580i
$100$	4.17269	−	2.75476i	0.417269	−	0.275476i
$101$		−	1.36233i		−	0.135557i	−0.997700	−	0.0677786i	$-0.978409\pi$
$101$		−	1.36233i		−	0.135557i	0.997700	−	0.0677786i	$-0.0215911\pi$
$102$	5.22147	−	3.20834i	0.517002	−	0.317673i
$103$	3.37589	−	3.37589i	0.332636	−	0.332636i	−0.520950	−	0.853587i	$-0.674422\pi$
$103$	3.37589	−	3.37589i	0.332636	−	0.332636i	0.853587	+	0.520950i	$0.174422\pi$
$104$	−1.03881			−0.101864
$105$	−2.26403	+	2.53975i	−0.220947	+	0.247854i
$106$	−13.8187			−1.34219
$107$	−2.39803	+	2.39803i	−0.231826	+	0.231826i	−0.813455	−	0.581628i	$-0.802416\pi$
$107$	−2.39803	+	2.39803i	−0.231826	+	0.231826i	0.581628	+	0.813455i	$0.302416\pi$
$108$	0.426330	+	5.17863i	0.0410236	+	0.498314i
$109$		−	0.531902i		−	0.0509470i	−0.999675	−	0.0254735i	$-0.991891\pi$
$109$		−	0.531902i		−	0.0509470i	0.999675	−	0.0254735i	$-0.00810934\pi$
$110$	2.65587	+	8.84339i	0.253227	+	0.843185i
$111$	3.67883	−	15.4048i	0.349179	−	1.46216i
$112$	0.621187	+	0.621187i	0.0586966	+	0.0586966i
$113$	4.14725	+	4.14725i	0.390140	+	0.390140i	0.874737	−	0.484597i	$-0.161034\pi$
$113$	4.14725	+	4.14725i	0.390140	+	0.390140i	−0.484597	+	0.874737i	$0.661034\pi$
$114$	−3.17077	+	13.2774i	−0.296970	+	1.24354i
$115$	0.643162	+	2.14157i	0.0599752	+	0.199703i
$116$			7.83802i			0.727742i
$117$	−0.970139	−	2.96158i	−0.0896893	−	0.273798i
$118$	7.75200	−	7.75200i	0.713629	−	0.713629i
$119$	3.10830			0.284937
$120$	2.57719	−	2.89104i	0.235264	−	0.263915i
$121$	−6.05185			−0.550168
$122$	−7.83764	+	7.83764i	−0.709587	+	0.709587i
$123$	2.61553	−	1.60712i	0.235834	−	0.144909i
$124$			7.07325i			0.635197i
$125$	−1.00330	−	11.1352i	−0.0897376	−	0.995965i
$126$	−1.19084	+	2.35109i	−0.106089	+	0.209452i
$127$	8.34126	+	8.34126i	0.740167	+	0.740167i	0.972610	−	0.232443i	$-0.0746718\pi$
$127$	8.34126	+	8.34126i	0.740167	+	0.740167i	−0.232443	+	0.972610i	$0.574672\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−15.0437	−	3.59258i	−1.32452	−	0.316309i
$130$	−1.10066	+	2.04552i	−0.0965340	+	0.179404i
$131$			2.68737i			0.234797i	0.993085	+	0.117398i	$0.0374554\pi$
$131$			2.68737i			0.234797i	−0.993085	+	0.117398i	$0.962545\pi$
$132$	3.74439	+	6.09386i	0.325907	+	0.530402i
$133$	−4.89573	+	4.89573i	−0.424514	+	0.424514i
$134$	−15.3143			−1.32295
$135$	10.6490	+	4.64747i	0.916519	+	0.399990i
$136$	−3.53823			−0.303401
$137$	3.75896	−	3.75896i	0.321150	−	0.321150i	−0.528058	−	0.849208i	$-0.677080\pi$
$137$	3.75896	−	3.75896i	0.321150	−	0.321150i	0.849208	+	0.528058i	$0.177080\pi$
$138$	0.906765	+	1.47573i	0.0771890	+	0.125622i
$139$			20.7808i			1.76261i	0.472551	+	0.881303i	$0.343333\pi$
$139$			20.7808i			1.76261i	−0.472551	+	0.881303i	$0.656667\pi$
$140$	1.88135	−	0.565012i	0.159003	−	0.0477522i
$141$	−0.0667301	−	0.0159358i	−0.00561969	−	0.00134204i
$142$	1.59529	+	1.59529i	0.133874	+	0.133874i
$143$	−3.03324	−	3.03324i	−0.253652	−	0.253652i
$144$	1.35555	−	2.67628i	0.112963	−	0.223023i
$145$	15.4339	+	8.30468i	1.28172	+	0.689666i
$146$		−	12.0030i		−	0.993378i
$147$	9.19122	−	5.64757i	0.758079	−	0.465803i
$148$	−6.46585	+	6.46585i	−0.531489	+	0.531489i
$149$	−6.11984			−0.501357			−0.250678	−	0.968070i	$-0.580654\pi$
$149$	−6.11984			−0.501357			−0.250678	+	0.968070i	$0.580654\pi$
$150$	−2.96214	−	8.13792i	−0.241857	−	0.664458i
$151$	8.00975			0.651825			0.325912	−	0.945400i	$-0.394329\pi$
$151$	8.00975			0.651825			0.325912	+	0.945400i	$0.394329\pi$
$152$	5.57289	−	5.57289i	0.452021	−	0.452021i
$153$	−3.30433	−	10.0873i	−0.267140	−	0.815507i
$154$			3.62763i			0.292323i
$155$	13.9280	+	7.49438i	1.11872	+	0.601963i
$156$	−0.417931	+	1.75006i	−0.0334613	+	0.140117i
$157$	−9.56563	−	9.56563i	−0.763420	−	0.763420i	0.213519	−	0.976939i	$-0.431508\pi$
$157$	−9.56563	−	9.56563i	−0.763420	−	0.763420i	−0.976939	+	0.213519i	$0.931508\pi$
$158$	1.40159	+	1.40159i	0.111504	+	0.111504i
$159$	−5.55950	+	23.2800i	−0.440897	+	1.84622i
$160$	−2.14157	+	0.643162i	−0.169306	+	0.0508464i
$161$			0.878491i			0.0692348i
$162$	8.89585	+	1.36523i	0.698924	+	0.107263i
$163$	1.30077	−	1.30077i	0.101884	−	0.101884i	−0.654327	−	0.756211i	$-0.727048\pi$
$163$	1.30077	−	1.30077i	0.101884	−	0.101884i	0.756211	+	0.654327i	$0.227048\pi$
$164$	−1.77236			−0.138398
$165$	15.9668	−	0.916422i	1.24301	−	0.0713434i
$166$	3.12938			0.242887
$167$	−7.75358	+	7.75358i	−0.599990	+	0.599990i	−0.940310	−	0.340320i	$-0.889465\pi$
$167$	−7.75358	+	7.75358i	−0.599990	+	0.599990i	0.340320	+	0.940310i	$0.389465\pi$
$168$	1.29641	−	0.796585i	0.100021	−	0.0614579i
$169$			11.9209i			0.916991i
$170$	−3.74889	+	6.96715i	−0.287526	+	0.534356i
$171$	21.0925	+	10.6835i	1.61298	+	0.816985i
$172$	6.31426	+	6.31426i	0.481457	+	0.481457i
$173$	−10.4290	−	10.4290i	−0.792899	−	0.792899i	0.189066	−	0.981964i	$-0.439454\pi$
$173$	−10.4290	−	10.4290i	−0.792899	−	0.792899i	−0.981964	+	0.189066i	$0.939454\pi$
$174$	13.2045	+	3.15338i	1.00103	+	0.239057i
$175$	0.880797	−	4.30324i	0.0665820	−	0.325294i
$176$		−	4.12939i		−	0.311264i
$177$	−9.94085	−	16.1784i	−0.747200	−	1.21604i
$178$	4.30493	−	4.30493i	0.322668	−	0.322668i
$179$	0.719378			0.0537688			0.0268844	−	0.999639i	$-0.491441\pi$
$179$	0.719378			0.0537688			0.0268844	+	0.999639i	$0.491441\pi$
$180$	−3.83362	−	5.50485i	−0.285741	−	0.410307i
$181$	16.7156			1.24246			0.621229	−	0.783629i	$-0.286634\pi$
$181$	16.7156			1.24246			0.621229	+	0.783629i	$0.286634\pi$
$182$	−0.645294	+	0.645294i	−0.0478324	+	0.0478324i
$183$	10.0507	+	16.3571i	0.742967	+	1.20915i
$184$		−	1.00000i		−	0.0737210i
$185$	5.88113	+	19.5828i	0.432389	+	1.43975i
$186$	11.9162	+	2.84570i	0.873735	+	0.208657i
$187$	−10.3313	−	10.3313i	−0.755502	−	0.755502i
$188$	0.0280085	+	0.0280085i	0.00204273	+	0.00204273i
$189$	3.48173	+	2.95207i	0.253258	+	0.214731i
$190$	−5.06893	−	16.8783i	−0.367739	−	1.22448i
$191$			10.6239i			0.768718i	0.923184	+	0.384359i	$0.125577\pi$
$191$			10.6239i			0.768718i	−0.923184	+	0.384359i	$0.874423\pi$
$192$	−1.47573	+	0.906765i	−0.106502	+	0.0654402i
$193$	−0.732855	+	0.732855i	−0.0527520	+	0.0527520i	−0.732991	−	0.680239i	$-0.761876\pi$
$193$	−0.732855	+	0.732855i	−0.0527520	+	0.0527520i	0.680239	+	0.732991i	$0.261876\pi$
$194$	−16.7225			−1.20061
$195$	3.00324	+	2.67720i	0.215066	+	0.191719i
$196$	−6.22825			−0.444875
$197$	10.4745	−	10.4745i	0.746279	−	0.746279i	−0.227499	−	0.973778i	$-0.573055\pi$
$197$	10.4745	−	10.4745i	0.746279	−	0.746279i	0.973778	+	0.227499i	$0.0730548\pi$
$198$	11.7726	−	3.85642i	0.836644	−	0.274064i
$199$		−	3.02413i		−	0.214375i	−0.994239	−	0.107188i	$-0.965815\pi$
$199$		−	3.02413i		−	0.214375i	0.994239	−	0.107188i	$-0.0341845\pi$
$200$	−1.00262	+	4.89844i	−0.0708963	+	0.346372i
$201$	−6.16122	+	25.7997i	−0.434579	+	1.81977i
$202$	0.963314	+	0.963314i	0.0677786	+	0.0677786i
$203$	4.86887	+	4.86887i	0.341728	+	0.341728i
$204$	−1.42349	+	5.96077i	−0.0996644	+	0.417338i
$205$	−1.87788	+	3.48997i	−0.131157	+	0.243750i
$206$			4.77423i			0.332636i
$207$	2.85094	−	0.933895i	0.198154	−	0.0649102i
$208$	0.734549	−	0.734549i	0.0509318	−	0.0509318i
$209$	32.5448			2.25117
$210$	−0.194961	−	3.39679i	−0.0134536	−	0.234401i
$211$	−19.3102			−1.32937			−0.664684	−	0.747125i	$-0.731434\pi$
$211$	−19.3102			−1.32937			−0.664684	+	0.747125i	$0.731434\pi$
$212$	9.77127	−	9.77127i	0.671093	−	0.671093i
$213$	3.32936	−	2.04574i	0.228124	−	0.140171i
$214$		−	3.39132i		−	0.231826i
$215$	19.1236	−	5.74325i	1.30422	−	0.391686i
$216$	−3.96331	−	3.36039i	−0.269669	−	0.228645i
$217$	4.39381	+	4.39381i	0.298271	+	0.298271i
$218$	0.376112	+	0.376112i	0.0254735	+	0.0254735i
$219$	−20.2212	−	4.82904i	−1.36642	−	0.326316i
$220$	−8.13121	−	4.37524i	−0.548206	−	0.294979i
$221$		−	3.67554i		−	0.247244i
$222$	8.29154	+	13.4942i	0.556492	+	0.905671i
$223$	−7.87712	+	7.87712i	−0.527491	+	0.527491i	−0.919824	−	0.392332i	$-0.871668\pi$
$223$	−7.87712	+	7.87712i	−0.527491	+	0.527491i	0.392332	+	0.919824i	$0.371668\pi$
$224$	−0.878491			−0.0586966
$225$	−14.9015	+	1.71621i	−0.993433	+	0.114414i
$226$	−5.86509			−0.390140
$227$	8.11980	−	8.11980i	0.538930	−	0.538930i	−0.384284	−	0.923215i	$-0.625552\pi$
$227$	8.11980	−	8.11980i	0.538930	−	0.538930i	0.923215	+	0.384284i	$0.125552\pi$
$228$	−7.14645	−	11.6306i	−0.473285	−	0.770255i
$229$		−	8.83078i		−	0.583554i	−0.956486	−	0.291777i	$-0.905753\pi$
$229$		−	8.83078i		−	0.583554i	0.956486	−	0.291777i	$-0.0942465\pi$
$230$	−1.96911	−	1.05954i	−0.129839	−	0.0698639i
$231$	6.11139	+	1.45946i	0.402100	+	0.0960255i
$232$	−5.54232	−	5.54232i	−0.363871	−	0.363871i
$233$	13.3537	+	13.3537i	0.874831	+	0.874831i	0.992994	−	0.118163i	$-0.0377005\pi$
$233$	13.3537	+	13.3537i	0.874831	+	0.874831i	−0.118163	+	0.992994i	$0.537701\pi$
$234$	2.78014	+	1.40816i	0.181744	+	0.0920543i
$235$	0.0848278	−	0.0254757i	0.00553356	−	0.00166185i
$236$			10.9630i			0.713629i
$237$	2.92510	−	1.79734i	0.190006	−	0.116750i
$238$	−2.19790	+	2.19790i	−0.142469	+	0.142469i
$239$	5.29769			0.342679			0.171340	−	0.985212i	$-0.445190\pi$
$239$	5.29769			0.342679			0.171340	+	0.985212i	$0.445190\pi$
$240$	0.221927	+	3.86662i	0.0143253	+	0.249589i
$241$	3.24318			0.208912			0.104456	−	0.994530i	$-0.466690\pi$
$241$	3.24318			0.208912			0.104456	+	0.994530i	$0.466690\pi$
$242$	4.27930	−	4.27930i	0.275084	−	0.275084i
$243$	5.87893	−	14.4374i	0.377134	−	0.926159i
$244$		−	11.0841i		−	0.709587i
$245$	−6.59907	+	12.2641i	−0.421599	+	0.783524i
$246$	−0.713053	+	2.98586i	−0.0454626	+	0.190371i
$247$	5.78917	+	5.78917i	0.368356	+	0.368356i
$248$	−5.00154	−	5.00154i	−0.317598	−	0.317598i
$249$	1.25901	−	5.27200i	0.0797863	−	0.334099i
$250$	8.58324	+	7.16436i	0.542852	+	0.453114i
$251$		−	17.6589i		−	1.11462i	−0.830304	−	0.557310i	$-0.811833\pi$
$251$		−	17.6589i		−	1.11462i	0.830304	−	0.557310i	$-0.188167\pi$
$252$	−0.820418	−	2.50452i	−0.0516815	−	0.157770i
$253$	2.91992	−	2.91992i	0.183574	−	0.183574i
$254$	−11.7963			−0.740167
$255$	10.2292	+	9.11868i	0.640575	+	0.571034i
$256$	1.00000			0.0625000
$257$	−3.83128	+	3.83128i	−0.238989	+	0.238989i	−0.816431	−	0.577442i	$-0.804051\pi$
$257$	−3.83128	+	3.83128i	−0.238989	+	0.238989i	0.577442	+	0.816431i	$0.304051\pi$
$258$	13.1778	−	8.09715i	0.820416	−	0.504106i
$259$			8.03300i			0.499146i
$260$	−0.668122	−	2.22469i	−0.0414352	−	0.137969i
$261$	10.6249	−	20.9767i	0.657662	−	1.29843i
$262$	−1.90026	−	1.90026i	−0.117398	−	0.117398i
$263$	9.95007	+	9.95007i	0.613548	+	0.613548i	0.943869	−	0.330321i	$-0.107157\pi$
$263$	9.95007	+	9.95007i	0.613548	+	0.613548i	−0.330321	+	0.943869i	$0.607157\pi$
$264$	−6.95669	−	1.66133i	−0.428155	−	0.102248i
$265$	−8.88764	−	29.5937i	−0.545963	−	1.81793i
$266$		−	6.92361i		−	0.424514i
$267$	−5.52047	−	8.98437i	−0.337847	−	0.549835i
$268$	10.8288	−	10.8288i	0.661477	−	0.661477i
$269$	−10.4792			−0.638928			−0.319464	−	0.947598i	$-0.603503\pi$
$269$	−10.4792			−0.638928			−0.319464	+	0.947598i	$0.603503\pi$
$270$	−10.8162	+	4.24372i	−0.658255	+	0.258264i
$271$	−15.4253			−0.937021			−0.468511	−	0.883458i	$-0.655209\pi$
$271$	−15.4253			−0.937021			−0.468511	+	0.883458i	$0.655209\pi$
$272$	2.50190	−	2.50190i	0.151700	−	0.151700i
$273$	0.827499	+	1.34673i	0.0500825	+	0.0815076i
$274$			5.31597i			0.321150i
$275$	−17.2306	+	11.3755i	−1.03905	+	0.685967i
$276$	−1.68468	−	0.402318i	−0.101406	−	0.0242167i
$277$	−8.17257	−	8.17257i	−0.491042	−	0.491042i	0.417592	−	0.908634i	$-0.362874\pi$
$277$	−8.17257	−	8.17257i	−0.491042	−	0.491042i	−0.908634	+	0.417592i	$0.862874\pi$
$278$	−14.6943	−	14.6943i	−0.881303	−	0.881303i
$279$	9.58817	−	18.9300i	0.574028	−	1.13331i
$280$	−0.930794	+	1.72984i	−0.0556256	+	0.103378i
$281$		−	24.0787i		−	1.43641i	−0.695830	−	0.718206i	$-0.744963\pi$
$281$		−	24.0787i		−	1.43641i	0.695830	−	0.718206i	$-0.255037\pi$
$282$	0.0584537	−	0.0359170i	0.00348087	−	0.00213883i
$283$	−19.2731	+	19.2731i	−1.14567	+	1.14567i	−0.158271	+	0.987396i	$0.550592\pi$
$283$	−19.2731	+	19.2731i	−1.14567	+	1.14567i	−0.987396	+	0.158271i	$0.949408\pi$
$284$	−2.25608			−0.133874
$285$	−30.4738	+	1.74906i	−1.80511	+	0.103606i
$286$	4.28964			0.253652
$287$	−1.10097	+	1.10097i	−0.0649880	+	0.0649880i
$288$	0.933895	+	2.85094i	0.0550303	+	0.167993i
$289$			4.48094i			0.263585i
$290$	−16.7857	+	5.04112i	−0.985691	+	0.296025i
$291$	−6.72777	+	28.1721i	−0.394389	+	1.65148i
$292$	8.48742	+	8.48742i	0.496689	+	0.496689i
$293$	−17.5754	−	17.5754i	−1.02677	−	1.02677i	−0.999632	−	0.0271332i	$-0.991362\pi$
$293$	−17.5754	−	17.5754i	−1.02677	−	1.02677i	−0.0271332	−	0.999632i	$-0.508638\pi$
$294$	−2.50574	+	10.4926i	−0.146138	+	0.611941i
$295$	21.5873	+	11.6157i	1.25686	+	0.676292i
$296$		−	9.14409i		−	0.531489i
$297$	−1.76048	−	21.3846i	−0.102153	−	1.24086i
$298$	4.32738	−	4.32738i	0.250678	−	0.250678i
$299$	1.03881			0.0600759
$300$	7.84893	+	3.65983i	0.453158	+	0.211301i
$301$	7.84466			0.452159
$302$	−5.66375	+	5.66375i	−0.325912	+	0.325912i
$303$	2.01043	−	1.23532i	0.115496	−	0.0709670i
$304$			7.88126i			0.452021i
$305$	−21.8258	−	11.7440i	−1.24974	−	0.672461i
$306$	9.46929	+	4.79625i	0.541323	+	0.274184i
$307$	6.34290	+	6.34290i	0.362008	+	0.362008i	0.864552	−	0.502544i	$-0.167602\pi$
$307$	6.34290	+	6.34290i	0.362008	+	0.362008i	−0.502544	+	0.864552i	$0.667602\pi$
$308$	−2.56512	−	2.56512i	−0.146161	−	0.146161i
$309$	8.04304	+	1.92076i	0.457553	+	0.109268i
$310$	−15.1479	+	4.54925i	−0.860343	+	0.258380i
$311$			1.54924i			0.0878496i	0.999035	+	0.0439248i	$0.0139862\pi$
$311$			1.54924i			0.0878496i	−0.999035	+	0.0439248i	$0.986014\pi$
$312$	−0.941956	−	1.53300i	−0.0533277	−	0.0867890i
$313$	0.449127	−	0.449127i	0.0253861	−	0.0253861i	−0.694300	−	0.719686i	$-0.744286\pi$
$313$	0.449127	−	0.449127i	0.0253861	−	0.0253861i	0.719686	+	0.694300i	$0.244286\pi$
$314$	13.5278			0.763420
$315$	−5.80093	−	1.03814i	−0.326846	−	0.0584928i
$316$	−1.98214			−0.111504
$317$	−17.7857	+	17.7857i	−0.998943	+	0.998943i	−0.999999	−	0.00105667i	$-0.999664\pi$
$317$	−17.7857	+	17.7857i	−0.998943	+	0.998943i	0.00105667	+	0.999999i	$0.499664\pi$
$318$	−12.5303	−	20.3926i	−0.702663	−	1.14356i
$319$		−	32.3662i		−	1.81216i
$320$	1.05954	−	1.96911i	0.0592300	−	0.110076i
$321$	−5.71329	−	1.36439i	−0.318885	−	0.0761529i
$322$	−0.621187	−	0.621187i	−0.0346174	−	0.0346174i
$323$	19.7182	+	19.7182i	1.09715	+	1.09715i
$324$	−7.25568	+	5.32495i	−0.403093	+	0.295831i
$325$	−5.08854	−	1.04154i	−0.282262	−	0.0577740i
$326$			1.83956i			0.101884i
$327$	0.784943	−	0.482310i	0.0434075	−	0.0266718i
$328$	1.25325	−	1.25325i	0.0691991	−	0.0691991i
$329$	0.0347970			0.00191842
$330$	−10.6422	+	11.9382i	−0.585834	+	0.657178i
$331$	−9.69040			−0.532633			−0.266316	−	0.963886i	$-0.585807\pi$
$331$	−9.69040			−0.532633			−0.266316	+	0.963886i	$0.585807\pi$
$332$	−2.21281	+	2.21281i	−0.121443	+	0.121443i
$333$	26.0692	−	8.53962i	1.42858	−	0.467968i
$334$		−	10.9652i		−	0.599990i
$335$	−9.84958	−	32.7967i	−0.538140	−	1.79188i
$336$	−0.353433	+	1.47997i	−0.0192813	+	0.0807392i
$337$	4.98944	+	4.98944i	0.271792	+	0.271792i	0.829821	−	0.558029i	$-0.188442\pi$
$337$	4.98944	+	4.98944i	0.271792	+	0.271792i	−0.558029	+	0.829821i	$0.688442\pi$
$338$	−8.42933	−	8.42933i	−0.458495	−	0.458495i
$339$	−2.35963	+	9.88080i	−0.128158	+	0.536651i
$340$	−2.27565	−	7.57738i	−0.123415	−	0.410941i
$341$		−	29.2082i		−	1.58171i
$342$	−22.4690	+	7.36027i	−1.21498	+	0.397998i
$343$	−8.21722	+	8.21722i	−0.443688	+	0.443688i
$344$	−8.92971			−0.481457
$345$	−2.57719	+	2.89104i	−0.138751	+	0.155648i
$346$	14.7488			0.792899
$347$	−11.2296	+	11.2296i	−0.602837	+	0.602837i	−0.941064	−	0.338228i	$-0.890173\pi$
$347$	−11.2296	+	11.2296i	−0.602837	+	0.602837i	0.338228	+	0.941064i	$0.390173\pi$
$348$	−11.5668	+	7.10725i	−0.620045	+	0.380988i
$349$		−	23.8817i		−	1.27836i	−0.769059	−	0.639178i	$-0.779275\pi$
$349$		−	23.8817i		−	1.27836i	0.769059	−	0.639178i	$-0.220725\pi$
$350$	2.42003	+	3.66566i	0.129356	+	0.195938i
$351$	3.49080	−	4.11712i	0.186325	−	0.219756i
$352$	2.91992	+	2.91992i	0.155632	+	0.155632i
$353$	−12.1901	−	12.1901i	−0.648813	−	0.648813i	0.303893	−	0.952706i	$-0.401713\pi$
$353$	−12.1901	−	12.1901i	−0.648813	−	0.648813i	−0.952706	+	0.303893i	$0.901713\pi$
$354$	18.4691	+	4.41060i	0.981621	+	0.234421i
$355$	−2.39040	+	4.44246i	−0.126869	+	0.235781i
$356$			6.08809i			0.322668i
$357$	2.81850	+	4.58701i	0.149171	+	0.242770i
$358$	−0.508677	+	0.508677i	−0.0268844	+	0.0268844i
$359$	7.16299			0.378048			0.189024	−	0.981972i	$-0.439468\pi$
$359$	7.16299			0.378048			0.189024	+	0.981972i	$0.439468\pi$
$360$	6.60329	+	1.18174i	0.348024	+	0.0622829i
$361$	−43.1142			−2.26917
$362$	−11.8197	+	11.8197i	−0.621229	+	0.621229i
$363$	−5.48761	−	8.93089i	−0.288025	−	0.468750i
$364$		−	0.912584i		−	0.0478324i
$365$	25.7054	−	7.71989i	1.34548	−	0.404078i
$366$	−18.6731	−	4.45933i	−0.976060	−	0.233093i
$367$	13.3521	+	13.3521i	0.696971	+	0.696971i	0.963756	−	0.266785i	$-0.0859613\pi$
$367$	13.3521	+	13.3521i	0.696971	+	0.696971i	−0.266785	+	0.963756i	$0.585961\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	4.74334	+	2.40253i	0.246928	+	0.125071i
$370$	−18.0057	−	9.68851i	−0.936071	−	0.503682i
$371$		−	12.1396i		−	0.630255i
$372$	−10.4382	+	6.41378i	−0.541196	+	0.332539i
$373$	−2.87275	+	2.87275i	−0.148745	+	0.148745i	−0.777557	−	0.628812i	$-0.783541\pi$
$373$	−2.87275	+	2.87275i	−0.148745	+	0.148745i	0.628812	+	0.777557i	$0.283541\pi$
$374$	14.6107			0.755502
$375$	15.5228	−	11.5776i	0.801596	−	0.597867i
$376$	−0.0396100			−0.00204273
$377$	5.75741	−	5.75741i	0.296522	−	0.296522i
$378$	−4.54938	+	0.374527i	−0.233995	+	0.0192636i
$379$			24.7455i			1.27109i	0.772063	+	0.635546i	$0.219225\pi$
$379$			24.7455i			1.27109i	−0.772063	+	0.635546i	$0.780775\pi$
$380$	15.5190	+	8.35049i	0.796110	+	0.428371i
$381$	−4.74587	+	19.8730i	−0.243139	+	1.01813i
$382$	−7.51222	−	7.51222i	−0.384359	−	0.384359i
$383$	15.8012	+	15.8012i	0.807405	+	0.807405i	0.984240	−	0.176836i	$-0.0565861\pi$
$383$	15.8012	+	15.8012i	0.807405	+	0.807405i	−0.176836	+	0.984240i	$0.556586\pi$
$384$	0.402318	−	1.68468i	0.0205307	−	0.0859709i
$385$	−7.76884	+	2.33315i	−0.395937	+	0.118909i
$386$		−	1.03641i		−	0.0527520i
$387$	−8.33941	−	25.4580i	−0.423916	−	1.29410i
$388$	11.8246	−	11.8246i	0.600303	−	0.600303i
$389$	1.35053			0.0684745			0.0342372	−	0.999414i	$-0.489100\pi$
$389$	1.35053			0.0684745			0.0342372	+	0.999414i	$0.489100\pi$
$390$	−4.01668	+	0.230540i	−0.203392	+	0.0116738i
$391$	3.53823			0.178936
$392$	4.40404	−	4.40404i	0.222438	−	0.222438i
$393$	−3.96583	+	2.43682i	−0.200050	+	0.122921i
$394$			14.8132i			0.746279i
$395$	−2.10015	+	3.90305i	−0.105670	+	0.196384i
$396$	−5.59760	+	11.0514i	−0.281290	+	0.555354i
$397$	−5.00981	−	5.00981i	−0.251435	−	0.251435i	0.570124	−	0.821559i	$-0.306895\pi$
$397$	−5.00981	−	5.00981i	−0.251435	−	0.251435i	−0.821559	+	0.570124i	$0.806895\pi$
$398$	2.13839	+	2.13839i	0.107188	+	0.107188i
$399$	−11.6641	−	2.78549i	−0.583933	−	0.139449i
$400$	−2.75476	−	4.17269i	−0.137738	−	0.208634i
$401$		−	13.0718i		−	0.652775i	−0.945236	−	0.326387i	$-0.894169\pi$
$401$		−	13.0718i		−	0.652775i	0.945236	−	0.326387i	$-0.105831\pi$
$402$	−13.8865	−	22.5998i	−0.692595	−	1.12717i
$403$	5.19565	−	5.19565i	0.258814	−	0.258814i
$404$	−1.36233			−0.0677786
$405$	2.79773	+	19.9292i	0.139020	+	0.990290i
$406$	−6.88563			−0.341728
$407$	26.7000	−	26.7000i	1.32347	−	1.32347i
$408$	−3.20834	−	5.22147i	−0.158837	−	0.258501i
$409$		−	15.7658i		−	0.779567i	−0.920907	−	0.389784i	$-0.872550\pi$
$409$		−	15.7658i		−	0.779567i	0.920907	−	0.389784i	$-0.127450\pi$
$410$	−1.13992	−	3.79564i	−0.0562964	−	0.187454i
$411$	8.95570	+	2.13871i	0.441752	+	0.105495i
$412$	−3.37589	−	3.37589i	−0.166318	−	0.166318i
$413$	6.81006	+	6.81006i	0.335101	+	0.335101i
$414$	−1.35555	+	2.67628i	−0.0666218	+	0.131532i
$415$	2.01270	+	6.70180i	0.0987995	+	0.328978i
$416$			1.03881i			0.0509318i
$417$	−30.6669	+	18.8433i	−1.50176	+	0.922762i
$418$	−23.0126	+	23.0126i	−1.12558	+	1.12558i
$419$	−28.4327			−1.38903			−0.694514	−	0.719480i	$-0.744380\pi$
$419$	−28.4327			−1.38903			−0.694514	+	0.719480i	$0.744380\pi$
$420$	2.53975	+	2.26403i	0.123927	+	0.110474i
$421$	24.0167			1.17050			0.585252	−	0.810851i	$-0.300995\pi$
$421$	24.0167			1.17050			0.585252	+	0.810851i	$0.300995\pi$
$422$	13.6544	−	13.6544i	0.664684	−	0.664684i
$423$	−0.0369916	−	0.112926i	−0.00179859	−	0.00549063i
$424$			13.8187i			0.671093i
$425$	−17.3318	−	3.54752i	−0.840716	−	0.172080i
$426$	−0.907662	+	3.80077i	−0.0439764	+	0.184148i
$427$	−6.88529	−	6.88529i	−0.333203	−	0.333203i
$428$	2.39803	+	2.39803i	0.115913	+	0.115913i
$429$	1.72580	−	7.22667i	0.0833225	−	0.348907i
$430$	−9.46136	+	17.5835i	−0.456267	+	0.847954i
$431$			26.9458i			1.29793i	0.760817	+	0.648967i	$0.224798\pi$
$431$			26.9458i			1.29793i	−0.760817	+	0.648967i	$0.775202\pi$
$432$	5.17863	−	0.426330i	0.249157	−	0.0205118i
$433$	10.1590	−	10.1590i	0.488212	−	0.488212i	−0.419530	−	0.907742i	$-0.637805\pi$
$433$	10.1590	−	10.1590i	0.488212	−	0.488212i	0.907742	+	0.419530i	$0.137805\pi$
$434$	−6.21379			−0.298271
$435$	1.73947	+	30.3067i	0.0834011	+	1.45309i
$436$	−0.531902			−0.0254735
$437$	−5.57289	+	5.57289i	−0.266588	+	0.266588i
$438$	17.7132	−	10.8839i	0.846370	−	0.520054i
$439$		−	2.41233i		−	0.115134i	−0.998342	−	0.0575670i	$-0.981666\pi$
$439$		−	2.41233i		−	0.115134i	0.998342	−	0.0575670i	$-0.0183343\pi$
$440$	8.84339	−	2.65587i	0.421592	−	0.126613i
$441$	16.6686	+	8.44273i	0.793741	+	0.402035i
$442$	2.59900	+	2.59900i	0.123622	+	0.123622i
$443$	7.57559	+	7.57559i	0.359927	+	0.359927i	0.863786	−	0.503859i	$-0.168087\pi$
$443$	7.57559	+	7.57559i	0.359927	+	0.359927i	−0.503859	+	0.863786i	$0.668087\pi$
$444$	−15.4048	−	3.67883i	−0.731082	−	0.174590i
$445$	11.9881	+	6.45056i	0.568290	+	0.305786i
$446$		−	11.1399i		−	0.527491i
$447$	−5.54926	−	9.03122i	−0.262471	−	0.427162i
$448$	0.621187	−	0.621187i	0.0293483	−	0.0293483i
$449$	31.6647			1.49435			0.747174	−	0.664628i	$-0.231410\pi$
$449$	31.6647			1.49435			0.747174	+	0.664628i	$0.231410\pi$
$450$	9.32340	−	11.7505i	0.439509	−	0.553924i
$451$	7.31877			0.344627
$452$	4.14725	−	4.14725i	0.195070	−	0.195070i
$453$	7.26297	+	11.8202i	0.341244	+	0.555363i
$454$			11.4831i			0.538930i
$455$	−1.79697	−	0.966917i	−0.0842435	−	0.0453298i
$456$	13.2774	+	3.17077i	0.621770	+	0.148485i
$457$	−27.2159	−	27.2159i	−1.27310	−	1.27310i	−0.944451	−	0.328653i	$-0.893405\pi$
$457$	−27.2159	−	27.2159i	−1.27310	−	1.27310i	−0.328653	−	0.944451i	$-0.606595\pi$
$458$	6.24430	+	6.24430i	0.291777	+	0.291777i
$459$	11.8898	−	14.0231i	0.554969	−	0.654542i
$460$	2.14157	−	0.643162i	0.0998514	−	0.0299876i
$461$			19.1053i			0.889824i	0.895574	+	0.444912i	$0.146765\pi$
$461$			19.1053i			0.889824i	−0.895574	+	0.444912i	$0.853235\pi$
$462$	−5.35340	+	3.28941i	−0.249063	+	0.153037i
$463$	17.9935	−	17.9935i	0.836230	−	0.836230i	−0.152131	−	0.988360i	$-0.548613\pi$
$463$	17.9935	−	17.9935i	0.836230	−	0.836230i	0.988360	+	0.152131i	$0.0486135\pi$
$464$	7.83802			0.363871
$465$	1.56974	+	27.3496i	0.0727952	+	1.26831i
$466$	−18.8850			−0.874831
$467$	−13.5425	+	13.5425i	−0.626673	+	0.626673i	−0.947229	−	0.320557i	$-0.896130\pi$
$467$	−13.5425	+	13.5425i	−0.626673	+	0.626673i	0.320557	+	0.947229i	$0.396130\pi$
$468$	−2.96158	+	0.970139i	−0.136899	+	0.0448447i
$469$		−	13.4535i		−	0.621224i
$470$	−0.0419683	+	0.0779963i	−0.00193585	+	0.00359770i
$471$	5.44250	−	22.7901i	0.250777	−	1.05011i
$472$	−7.75200	−	7.75200i	−0.356815	−	0.356815i
$473$	−26.0740	−	26.0740i	−1.19888	−	1.19888i
$474$	−0.797451	+	3.33927i	−0.0366281	+	0.153378i
$475$	32.8860	−	21.7110i	1.50891	−	0.996168i
$476$		−	3.10830i		−	0.142469i
$477$	−39.3961	+	12.9052i	−1.80382	+	0.590888i
$478$	−3.74603	+	3.74603i	−0.171340	+	0.171340i
$479$	10.1525			0.463880			0.231940	−	0.972730i	$-0.425493\pi$
$479$	10.1525			0.463880			0.231940	+	0.972730i	$0.425493\pi$
$480$	−2.89104	−	2.57719i	−0.131957	−	0.117632i
$481$	9.49896			0.433115
$482$	−2.29328	+	2.29328i	−0.104456	+	0.104456i
$483$	−1.29641	+	0.796585i	−0.0589889	+	0.0362459i
$484$			6.05185i			0.275084i
$485$	−10.7553	−	35.8125i	−0.488373	−	1.62616i
$486$	6.05174	+	14.3658i	0.274513	+	0.651646i
$487$	6.51439	+	6.51439i	0.295195	+	0.295195i	0.839128	−	0.543933i	$-0.183066\pi$
$487$	6.51439	+	6.51439i	0.295195	+	0.295195i	−0.543933	+	0.839128i	$0.683066\pi$
$488$	7.83764	+	7.83764i	0.354793	+	0.354793i
$489$	3.09907	+	0.740089i	0.140145	+	0.0334680i
$490$	−4.00578	−	13.3383i	−0.180963	−	0.602562i
$491$		−	40.0908i		−	1.80927i	−0.426186	−	0.904636i	$-0.640143\pi$
$491$		−	40.0908i		−	1.80927i	0.426186	−	0.904636i	$-0.359857\pi$
$492$	−1.60712	−	2.61553i	−0.0724544	−	0.117917i
$493$	19.6100	−	19.6100i	0.883189	−	0.883189i
$494$	−8.18712			−0.368356
$495$	15.8305	+	22.7317i	0.711529	+	1.02171i
$496$	7.07325			0.317598
$497$	−1.40145	+	1.40145i	−0.0628635	+	0.0628635i
$498$	2.83761	+	4.61812i	0.127157	+	0.206943i
$499$		−	3.33567i		−	0.149325i	−0.997209	−	0.0746625i	$-0.976212\pi$
$499$		−	3.33567i		−	0.149325i	0.997209	−	0.0746625i	$-0.0237880\pi$
$500$	−11.1352	+	1.00330i	−0.497983	+	0.0448688i
$501$	−18.4729	−	4.41151i	−0.825307	−	0.197092i
$502$	12.4867	+	12.4867i	0.557310	+	0.557310i
$503$	−5.33310	−	5.33310i	−0.237791	−	0.237791i	0.578144	−	0.815935i	$-0.303777\pi$
$503$	−5.33310	−	5.33310i	−0.237791	−	0.237791i	−0.815935	+	0.578144i	$0.803777\pi$
$504$	2.35109	+	1.19084i	0.104726	+	0.0530443i
$505$	−1.44344	+	2.68258i	−0.0642323	+	0.119373i
$506$			4.12939i			0.183574i
$507$	−17.5920	+	10.8094i	−0.781287	+	0.480064i
$508$	8.34126	−	8.34126i	0.370084	−	0.370084i
$509$	0.551066			0.0244256			0.0122128	−	0.999925i	$-0.496112\pi$
$509$	0.551066			0.0244256			0.0122128	+	0.999925i	$0.496112\pi$
$510$	−13.6810	+	0.785228i	−0.605804	+	0.0347705i
$511$	10.5445			0.466463
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.36002	+	40.8141i	0.148348	+	1.80199i
$514$		−	5.41825i		−	0.238989i
$515$	−10.2244	+	3.07060i	−0.450540	+	0.135307i
$516$	−3.59258	+	15.0437i	−0.158155	+	0.662261i
$517$	−0.115658	−	0.115658i	−0.00508664	−	0.00508664i
$518$	−5.68019	−	5.68019i	−0.249573	−	0.249573i
$519$	5.93370	−	24.8469i	0.260460	−	1.09066i
$520$	2.04552	+	1.10066i	0.0897022	+	0.0482670i
$521$		−	7.81178i		−	0.342240i	−0.985250	−	0.171120i	$-0.945261\pi$
$521$		−	7.81178i		−	0.342240i	0.985250	−	0.171120i	$-0.0547387\pi$
$522$	7.31989	+	22.3457i	0.320383	+	0.978045i
$523$	3.95100	−	3.95100i	0.172765	−	0.172765i	−0.615428	−	0.788193i	$-0.711017\pi$
$523$	3.95100	−	3.95100i	0.172765	−	0.172765i	0.788193	+	0.615428i	$0.211017\pi$
$524$	2.68737			0.117398
$525$	7.14909	−	2.60221i	0.312012	−	0.113570i
$526$	−14.0715			−0.613548
$527$	17.6966	−	17.6966i	0.770876	−	0.770876i
$528$	6.09386	−	3.74439i	0.265201	−	0.162954i
$529$			1.00000i			0.0434783i
$530$	27.2104	+	14.6414i	1.18194	+	0.635981i
$531$	14.8609	−	29.3400i	0.644908	−	1.27325i
$532$	4.89573	+	4.89573i	0.212257	+	0.212257i
$533$	1.30189	+	1.30189i	0.0563909	+	0.0563909i
$534$	10.2565	+	2.44935i	0.443841	+	0.105994i
$535$	7.26278	−	2.18117i	0.313997	−	0.0943003i
$536$			15.3143i			0.661477i
$537$	0.652307	+	1.06161i	0.0281491	+	0.0458117i
$538$	7.40991	−	7.40991i	0.319464	−	0.319464i
$539$	25.7189			1.10779
$540$	4.64747	−	10.6490i	0.199995	−	0.458260i
$541$	−12.6873			−0.545469			−0.272735	−	0.962089i	$-0.587928\pi$
$541$	−12.6873			−0.545469			−0.272735	+	0.962089i	$0.587928\pi$
$542$	10.9073	−	10.9073i	0.468511	−	0.468511i
$543$	15.1571	+	24.6676i	0.650453	+	1.05859i
$544$			3.53823i			0.151700i
$545$	−0.563570	+	1.04737i	−0.0241407	+	0.0448645i
$546$	−1.53741	−	0.367149i	−0.0657951	−	0.0157125i
$547$	4.43286	+	4.43286i	0.189535	+	0.189535i	0.795495	−	0.605960i	$-0.207211\pi$
$547$	4.43286	+	4.43286i	0.189535	+	0.189535i	−0.605960	+	0.795495i	$0.707211\pi$
$548$	−3.75896	−	3.75896i	−0.160575	−	0.160575i
$549$	−15.0251	+	29.6641i	−0.641255	+	1.26603i
$550$	4.14023	−	20.2276i	0.176540	−	0.862507i
$551$			61.7735i			2.63164i
$552$	1.47573	−	0.906765i	0.0628112	−	0.0385945i
$553$	−1.23128	+	1.23128i	−0.0523593	+	0.0523593i
$554$	11.5578			0.491042
$555$	−23.5660	+	26.4359i	−1.00032	+	1.12214i
$556$	20.7808			0.881303
$557$	−19.7470	+	19.7470i	−0.836707	+	0.836707i	−0.988424	−	0.151717i	$-0.951520\pi$
$557$	−19.7470	+	19.7470i	−0.836707	+	0.836707i	0.151717	+	0.988424i	$0.451520\pi$
$558$	6.60568	+	20.1654i	0.279641	+	0.853669i
$559$		−	9.27626i		−	0.392344i
$560$	−0.565012	−	1.88135i	−0.0238761	−	0.0795017i
$561$	5.87816	−	24.6144i	0.248176	−	1.03922i
$562$	17.0262	+	17.0262i	0.718206	+	0.718206i
$563$	−14.6245	−	14.6245i	−0.616349	−	0.616349i	0.328244	−	0.944593i	$-0.393543\pi$
$563$	−14.6245	−	14.6245i	−0.616349	−	0.616349i	−0.944593	+	0.328244i	$0.893543\pi$
$564$	−0.0159358	+	0.0667301i	−0.000671019	+	0.00280985i
$565$	−3.77221	−	12.5605i	−0.158698	−	0.528426i
$566$		−	27.2563i		−	1.14567i
$567$	−1.19934	+	7.81492i	−0.0503676	+	0.328196i
$568$	1.59529	−	1.59529i	0.0669369	−	0.0669369i
$569$	45.5814			1.91087			0.955436	−	0.295197i	$-0.0953854\pi$
$569$	45.5814			1.91087			0.955436	+	0.295197i	$0.0953854\pi$
$570$	20.3115	−	22.7850i	0.850754	−	0.954360i
$571$	−13.8634			−0.580166			−0.290083	−	0.957001i	$-0.593683\pi$
$571$	−13.8634			−0.580166			−0.290083	+	0.957001i	$0.593683\pi$
$572$	−3.03324	+	3.03324i	−0.126826	+	0.126826i
$573$	−15.6780	+	9.63337i	−0.654957	+	0.402440i
$574$		−	1.55700i		−	0.0649880i
$575$	1.00262	−	4.89844i	0.0418123	−	0.204279i
$576$	−2.67628	−	1.35555i	−0.111512	−	0.0564814i
$577$	26.2357	+	26.2357i	1.09221	+	1.09221i	0.995293	+	0.0969147i	$0.0308974\pi$
$577$	26.2357	+	26.2357i	1.09221	+	1.09221i	0.0969147	+	0.995293i	$0.469103\pi$
$578$	−3.16851	−	3.16851i	−0.131792	−	0.131792i
$579$	−1.74602	−	0.416968i	−0.0725622	−	0.0173286i
$580$	8.30468	−	15.4339i	0.344833	−	0.640858i
$581$			2.74913i			0.114053i
$582$	−15.1634	−	24.6779i	−0.628543	−	1.02293i
$583$	−40.3494	+	40.3494i	−1.67110	+	1.67110i
$584$	−12.0030			−0.496689
$585$	−1.22760	+	6.85956i	−0.0507549	+	0.283608i
$586$	24.8553			1.02677
$587$	1.72536	−	1.72536i	0.0712134	−	0.0712134i	−0.670603	−	0.741816i	$-0.733965\pi$
$587$	1.72536	−	1.72536i	0.0712134	−	0.0712134i	0.741816	+	0.670603i	$0.233965\pi$
$588$	−5.64757	−	9.19122i	−0.232902	−	0.379039i
$589$			55.7461i			2.29698i
$590$	−23.4780	+	7.05097i	−0.966576	+	0.290284i
$591$	24.9555	+	5.95963i	1.02653	+	0.245146i
$592$	6.46585	+	6.46585i	0.265745	+	0.265745i
$593$	2.77888	+	2.77888i	0.114115	+	0.114115i	0.761858	−	0.647744i	$-0.224287\pi$
$593$	2.77888	+	2.77888i	0.114115	+	0.114115i	−0.647744	+	0.761858i	$0.724287\pi$
$594$	16.3660	+	13.8763i	0.671507	+	0.569353i
$595$	−6.12057	−	3.29336i	−0.250919	−	0.135015i
$596$			6.11984i			0.250678i
$597$	4.46280	−	2.74218i	0.182650	−	0.112230i
$598$	−0.734549	+	0.734549i	−0.0300379	+	0.0300379i
$599$	−37.0107			−1.51222			−0.756108	−	0.654447i	$-0.772902\pi$
$599$	−37.0107			−1.51222			−0.756108	+	0.654447i	$0.772902\pi$
$600$	−8.13792	+	2.96214i	−0.332229	+	0.120929i
$601$	34.9685			1.42639			0.713196	−	0.700964i	$-0.247247\pi$
$601$	34.9685			1.42639			0.713196	+	0.700964i	$0.247247\pi$
$602$	−5.54701	+	5.54701i	−0.226079	+	0.226079i
$603$	−43.6601	+	14.3020i	−1.77798	+	0.582421i
$604$		−	8.00975i		−	0.325912i
$605$	11.9167	+	6.41216i	0.484484	+	0.260692i
$606$	−0.548091	+	2.29509i	−0.0222647	+	0.0932317i
$607$	−3.77458	−	3.77458i	−0.153205	−	0.153205i	0.626343	−	0.779548i	$-0.284551\pi$
$607$	−3.77458	−	3.77458i	−0.153205	−	0.153205i	−0.779548	+	0.626343i	$0.784551\pi$
$608$	−5.57289	−	5.57289i	−0.226011	−	0.226011i
$609$	−2.77021	+	11.6001i	−0.112255	+	0.470058i
$610$	23.7374	−	7.12887i	0.961100	−	0.288640i
$611$		−	0.0411472i		−	0.00166464i
$612$	−10.0873	+	3.30433i	−0.407753	+	0.133570i
$613$	−12.5789	+	12.5789i	−0.508056	+	0.508056i	−0.913929	−	0.405873i	$-0.866967\pi$
$613$	−12.5789	+	12.5789i	−0.508056	+	0.508056i	0.405873	+	0.913929i	$0.366967\pi$
$614$	−8.97021			−0.362008
$615$	−6.85305	+	0.393335i	−0.276342	+	0.0158608i
$616$	3.62763			0.146161
$617$	3.87788	−	3.87788i	0.156118	−	0.156118i	−0.624726	−	0.780844i	$-0.714789\pi$
$617$	3.87788	−	3.87788i	0.156118	−	0.156118i	0.780844	+	0.624726i	$0.214789\pi$
$618$	−7.04547	+	4.32911i	−0.283410	+	0.174142i
$619$		−	8.64542i		−	0.347489i	−0.984791	−	0.173744i	$-0.944413\pi$
$619$		−	8.64542i		−	0.347489i	0.984791	−	0.173744i	$-0.0555867\pi$
$620$	7.49438	−	13.9280i	0.300981	−	0.559361i
$621$	3.96331	+	3.36039i	0.159042	+	0.134848i
$622$	−1.09548	−	1.09548i	−0.0439248	−	0.0439248i
$623$	3.78184	+	3.78184i	0.151516	+	0.151516i
$624$	1.75006	+	0.417931i	0.0700584	+	0.0167306i
$625$	−9.82260	+	22.9895i	−0.392904	+	0.919579i
$626$			0.635161i			0.0253861i
$627$	29.5105	+	48.0273i	1.17854	+	1.91802i
$628$	−9.56563	+	9.56563i	−0.381710	+	0.381710i
$629$	32.3539			1.29003
$630$	4.83596	−	3.36780i	0.192669	−	0.134176i
$631$	−41.6995			−1.66003			−0.830015	−	0.557742i	$-0.811668\pi$
$631$	−41.6995			−1.66003			−0.830015	+	0.557742i	$0.811668\pi$
$632$	1.40159	−	1.40159i	0.0557521	−	0.0557521i
$633$	−17.5098	−	28.4966i	−0.695952	−	1.13264i
$634$		−	25.1527i		−	0.998943i
$635$	−7.58695	−	25.2627i	−0.301079	−	1.00252i
$636$	23.2800	+	5.55950i	0.923112	+	0.220448i
$637$	4.57496	+	4.57496i	0.181266	+	0.181266i
$638$	22.8864	+	22.8864i	0.906081	+	0.906081i
$639$	6.03790	+	3.05824i	0.238856	+	0.120982i
$640$	0.643162	+	2.14157i	0.0254232	+	0.0846532i
$641$		−	2.72989i		−	0.107824i	−0.998546	−	0.0539121i	$-0.982831\pi$
$641$		−	2.72989i		−	0.107824i	0.998546	−	0.0539121i	$-0.0171691\pi$
$642$	5.00468	−	3.07514i	0.197519	−	0.121366i
$643$	17.4028	−	17.4028i	0.686298	−	0.686298i	−0.275114	−	0.961412i	$-0.588715\pi$
$643$	17.4028	−	17.4028i	0.686298	−	0.686298i	0.961412	+	0.275114i	$0.0887155\pi$
$644$	0.878491			0.0346174
$645$	25.8161	+	23.0135i	1.01651	+	0.906157i
$646$	−27.8857			−1.09715
$647$	−9.72994	+	9.72994i	−0.382523	+	0.382523i	−0.872011	−	0.489487i	$-0.837184\pi$
$647$	−9.72994	+	9.72994i	−0.382523	+	0.382523i	0.489487	+	0.872011i	$0.337184\pi$
$648$	1.36523	−	8.89585i	0.0536313	−	0.349462i
$649$		−	45.2704i		−	1.77702i
$650$	4.33462	−	2.86167i	0.170018	−	0.112244i
$651$	−2.49992	+	10.4682i	−0.0979795	+	0.410282i
$652$	−1.30077	−	1.30077i	−0.0509420	−	0.0509420i
$653$	−21.5513	−	21.5513i	−0.843367	−	0.843367i	0.145928	−	0.989295i	$-0.453383\pi$
$653$	−21.5513	−	21.5513i	−0.843367	−	0.843367i	−0.989295	+	0.145928i	$0.953383\pi$
$654$	−0.213994	+	0.896084i	−0.00836782	+	0.0350396i
$655$	2.84737	−	5.29172i	0.111256	−	0.206765i
$656$			1.77236i			0.0691991i
$657$	−11.2096	−	34.2199i	−0.437327	−	1.33504i
$658$	−0.0246052	+	0.0246052i	−0.000959211	+	0.000959211i
$659$	−44.3615			−1.72808			−0.864039	−	0.503425i	$-0.832073\pi$
$659$	−44.3615			−1.72808			−0.864039	+	0.503425i	$0.832073\pi$
$660$	−0.916422	−	15.9668i	−0.0356717	−	0.621506i
$661$	43.3242			1.68512			0.842559	−	0.538605i	$-0.181048\pi$
$661$	43.3242			1.68512			0.842559	+	0.538605i	$0.181048\pi$
$662$	6.85215	−	6.85215i	0.266316	−	0.266316i
$663$	5.42410	−	3.33285i	0.210655	−	0.129437i
$664$		−	3.12938i		−	0.121443i
$665$	14.8274	−	4.45300i	0.574983	−	0.172680i
$666$	−12.3953	+	24.4721i	−0.480308	+	0.948276i
$667$	5.54232	+	5.54232i	0.214599	+	0.214599i
$668$	7.75358	+	7.75358i	0.299995	+	0.299995i
$669$	−18.7672	−	4.48180i	−0.725582	−	0.173276i
$670$	30.1555	+	16.2261i	1.16501	+	0.626868i
$671$			45.7705i			1.76695i
$672$	−0.796585	−	1.29641i	−0.0307289	−	0.0500103i
$673$	−30.3342	+	30.3342i	−1.16930	+	1.16930i	−0.186921	+	0.982375i	$0.559851\pi$
$673$	−30.3342	+	30.3342i	−1.16930	+	1.16930i	−0.982375	+	0.186921i	$0.940149\pi$
$674$	−7.05614			−0.271792
$675$	−16.0448	−	20.4344i	−0.617566	−	0.786519i
$676$	11.9209			0.458495
$677$	8.39686	−	8.39686i	0.322718	−	0.322718i	−0.527091	−	0.849809i	$-0.676717\pi$
$677$	8.39686	−	8.39686i	0.322718	−	0.322718i	0.849809	+	0.527091i	$0.176717\pi$
$678$	−5.31826	−	8.65529i	−0.204247	−	0.332404i
$679$		−	14.6906i		−	0.563773i
$680$	6.96715	+	3.74889i	0.267178	+	0.143763i
$681$	19.3454	+	4.61987i	0.741317	+	0.177034i
$682$	20.6533	+	20.6533i	0.790856	+	0.790856i
$683$	−16.0879	−	16.0879i	−0.615584	−	0.615584i	0.328811	−	0.944396i	$-0.393352\pi$
$683$	−16.0879	−	16.0879i	−0.615584	−	0.615584i	−0.944396	+	0.328811i	$0.893352\pi$
$684$	10.6835	−	21.0925i	0.408492	−	0.806490i
$685$	−11.3845	+	3.41903i	−0.434981	+	0.130634i
$686$		−	11.6209i		−	0.443688i
$687$	13.0318	−	8.00744i	0.497196	−	0.305503i
$688$	6.31426	−	6.31426i	0.240729	−	0.240729i
$689$	−14.3549			−0.546880
$690$	−0.221927	−	3.86662i	−0.00844861	−	0.147200i
$691$	−13.0690			−0.497169			−0.248585	−	0.968610i	$-0.579965\pi$
$691$	−13.0690			−0.497169			−0.248585	+	0.968610i	$0.579965\pi$
$692$	−10.4290	+	10.4290i	−0.396449	+	0.396449i
$693$	3.38783	+	10.3421i	0.128693	+	0.392865i
$694$		−	15.8811i		−	0.602837i
$695$	22.0181	−	40.9197i	0.835193	−	1.55217i
$696$	3.15338	−	13.2045i	0.119528	−	0.500517i
$697$	4.43428	+	4.43428i	0.167960	+	0.167960i
$698$	16.8869	+	16.8869i	0.639178	+	0.639178i
$699$	−7.59778	+	31.8152i	−0.287374	+	1.20336i
$700$	−4.30324	−	0.880797i	−0.162647	−	0.0332910i
$701$			26.8220i			1.01305i	0.862225	+	0.506526i	$0.169070\pi$
$701$			26.8220i			1.01305i	−0.862225	+	0.506526i	$0.830930\pi$
$702$	0.442875	+	5.37961i	0.0167152	+	0.203040i
$703$	−50.9590	+	50.9590i	−1.92196	+	1.92196i
$704$	−4.12939			−0.155632
$705$	0.114514	+	0.102082i	0.00431285	+	0.00384465i
$706$	17.2394			0.648813
$707$	−0.846263	+	0.846263i	−0.0318270	+	0.0318270i
$708$	−16.1784	+	9.94085i	−0.608021	+	0.373600i
$709$		−	4.26519i		−	0.160183i	−0.996788	−	0.0800914i	$-0.974479\pi$
$709$		−	4.26519i		−	0.160183i	0.996788	−	0.0800914i	$-0.0255212\pi$
$710$	−1.45103	−	4.83156i	−0.0544560	−	0.181325i
$711$	5.30476	+	2.68690i	0.198944	+	0.100766i
$712$	−4.30493	−	4.30493i	−0.161334	−	0.161334i
$713$	5.00154	+	5.00154i	0.187309	+	0.187309i
$714$	−5.23649	−	1.25053i	−0.195971	−	0.0467997i
$715$	2.75894	+	9.18659i	0.103178	+	0.343559i
$716$		−	0.719378i		−	0.0268844i
$717$	4.80376	+	7.81796i	0.179400	+	0.291967i
$718$	−5.06500	+	5.06500i	−0.189024	+	0.189024i
$719$	34.9727			1.30426			0.652130	−	0.758107i	$-0.273875\pi$
$719$	34.9727			1.30426			0.652130	+	0.758107i	$0.273875\pi$
$720$	−5.50485	+	3.83362i	−0.205154	+	0.142871i
$721$	−4.19412			−0.156197
$722$	30.4864	−	30.4864i	1.13459	−	1.13459i
$723$	2.94081	+	4.78606i	0.109370	+	0.177996i
$724$		−	16.7156i		−	0.621229i
$725$	−21.5919	−	32.7056i	−0.801902	−	1.21466i
$726$	10.1954	+	2.43477i	0.378388	+	0.0903627i
$727$	13.4827	+	13.4827i	0.500044	+	0.500044i	0.911452	−	0.411407i	$-0.134963\pi$
$727$	13.4827	+	13.4827i	0.500044	+	0.500044i	−0.411407	+	0.911452i	$0.634963\pi$
$728$	0.645294	+	0.645294i	0.0239162	+	0.0239162i
$729$	26.6365	−	4.41561i	0.986537	−	0.163541i
$730$	−12.7177	+	23.6352i	−0.470702	+	0.874779i
$731$		−	31.5953i		−	1.16860i
$732$	16.3571	−	10.0507i	0.604577	−	0.371484i
$733$	32.6105	−	32.6105i	1.20450	−	1.20450i	0.231710	−	0.972785i	$-0.425568\pi$
$733$	32.6105	−	32.6105i	1.20450	−	1.20450i	0.972785	−	0.231710i	$-0.0744321\pi$
$734$	−18.8827			−0.696971
$735$	−24.0823	+	1.38222i	−0.888289	+	0.0509838i
$736$	−1.00000			−0.0368605
$737$	−44.7165	+	44.7165i	−1.64715	+	1.64715i
$738$	−5.05289	+	1.65520i	−0.185999	+	0.0609288i
$739$			7.71809i			0.283915i	0.989873	+	0.141957i	$0.0453396\pi$
$739$			7.71809i			0.283915i	−0.989873	+	0.141957i	$0.954660\pi$
$740$	19.5828	−	5.88113i	0.719876	−	0.216195i
$741$	−3.29383	+	13.7927i	−0.121002	+	0.506686i
$742$	8.58397	+	8.58397i	0.315127	+	0.315127i
$743$	−4.77261	−	4.77261i	−0.175090	−	0.175090i	0.614121	−	0.789212i	$-0.289511\pi$
$743$	−4.77261	−	4.77261i	−0.175090	−	0.175090i	−0.789212	+	0.614121i	$0.789511\pi$
$744$	2.84570	−	11.9162i	0.104328	−	0.436867i
$745$	12.0506	+	6.48420i	0.441500	+	0.237563i
$746$		−	4.06268i		−	0.148745i
$747$	8.92166	−	2.92251i	0.326427	−	0.106929i
$748$	−10.3313	+	10.3313i	−0.377751	+	0.377751i
$749$	2.97925			0.108859
$750$	−2.78967	+	19.1629i	−0.101864	+	0.699731i
$751$	−52.9204			−1.93109			−0.965547	−	0.260229i	$-0.916202\pi$
$751$	−52.9204			−1.93109			−0.965547	+	0.260229i	$0.916202\pi$
$752$	0.0280085	−	0.0280085i	0.00102137	−	0.00102137i
$753$	26.0598	−	16.0125i	0.949671	−	0.583528i
$754$			8.14220i			0.296522i
$755$	−15.7721	−	8.48664i	−0.574004	−	0.308860i
$756$	2.95207	−	3.48173i	0.107366	−	0.126629i
$757$	−4.25493	−	4.25493i	−0.154648	−	0.154648i	0.625542	−	0.780190i	$-0.284878\pi$
$757$	−4.25493	−	4.25493i	−0.154648	−	0.154648i	−0.780190	+	0.625542i	$0.784878\pi$
$758$	−17.4977	−	17.4977i	−0.635546	−	0.635546i
$759$	6.95669	+	1.66133i	0.252512	+	0.0603024i
$760$	−16.8783	+	5.06893i	−0.612240	+	0.183869i
$761$			10.5196i			0.381334i	0.981655	+	0.190667i	$0.0610650\pi$
$761$			10.5196i			0.381334i	−0.981655	+	0.190667i	$0.938935\pi$
$762$	−10.6965	−	17.4082i	−0.387493	−	0.630632i
$763$	−0.330410	+	0.330410i	−0.0119617	+	0.0119617i
$764$	10.6239			0.384359
$765$	−4.18125	+	23.3640i	−0.151173	+	0.844726i
$766$	−22.3463			−0.807405
$767$	8.05284	−	8.05284i	0.290771	−	0.290771i
$768$	0.906765	+	1.47573i	0.0327201	+	0.0532508i
$769$		−	20.7974i		−	0.749972i	−0.927030	−	0.374986i	$-0.877647\pi$
$769$		−	20.7974i		−	0.749972i	0.927030	−	0.374986i	$-0.122353\pi$
$770$	3.84361	−	7.14319i	0.138514	−	0.257423i
$771$	−9.12801	−	2.17986i	−0.328737	−	0.0785058i
$772$	0.732855	+	0.732855i	0.0263760	+	0.0263760i
$773$	−7.11987	−	7.11987i	−0.256084	−	0.256084i	0.567375	−	0.823459i	$-0.307959\pi$
$773$	−7.11987	−	7.11987i	−0.256084	−	0.256084i	−0.823459	+	0.567375i	$0.807959\pi$
$774$	23.8984	+	12.1047i	0.859010	+	0.435094i
$775$	−19.4851	−	29.5145i	−0.699926	−	1.06019i
$776$			16.7225i			0.600303i
$777$	−11.8545	+	7.28404i	−0.425279	+	0.261314i
$778$	−0.954967	+	0.954967i	−0.0342372	+	0.0342372i
$779$	−13.9684			−0.500471
$780$	2.67720	−	3.00324i	0.0958593	−	0.107533i
$781$	9.31623			0.333361
$782$	−2.50190	+	2.50190i	−0.0894679	+	0.0894679i
$783$	40.5902	−	3.34158i	1.45058	−	0.119418i
$784$			6.22825i			0.222438i
$785$	8.70060	+	28.9709i	0.310538	+	1.03402i
$786$	1.08118	−	4.52736i	0.0385644	−	0.161485i
$787$	−13.3738	−	13.3738i	−0.476724	−	0.476724i	0.427358	−	0.904082i	$-0.359444\pi$
$787$	−13.3738	−	13.3738i	−0.476724	−	0.476724i	−0.904082	+	0.427358i	$0.859444\pi$
$788$	−10.4745	−	10.4745i	−0.373140	−	0.373140i
$789$	−5.66123	+	23.7060i	−0.201545	+	0.843956i
$790$	−1.27484	−	4.24490i	−0.0453567	−	0.151027i
$791$		−	5.15243i		−	0.183199i
$792$	−3.85642	−	11.7726i	−0.137032	−	0.418322i
$793$	−8.14181	+	8.14181i	−0.289124	+	0.289124i
$794$	7.08495			0.251435
$795$	35.6133	−	39.9503i	1.26307	−	1.41689i
$796$	−3.02413			−0.107188
$797$	−13.4137	+	13.4137i	−0.475136	+	0.475136i	−0.903572	−	0.428436i	$-0.859065\pi$
$797$	−13.4137	+	13.4137i	−0.475136	+	0.475136i	0.428436	+	0.903572i	$0.359065\pi$
$798$	10.2174	−	6.27809i	0.361691	−	0.222242i
$799$		−	0.140149i		−	0.00495813i
$800$	4.89844	+	1.00262i	0.173186	+	0.0354481i
$801$	8.25273	−	16.2934i	0.291596	−	0.575700i
$802$	9.24316	+	9.24316i	0.326387	+	0.326387i
$803$	−35.0479	−	35.0479i	−1.23681	−	1.23681i
$804$	25.7997	+	6.16122i	0.909884	+	0.217290i
$805$	0.930794	−	1.72984i	0.0328062	−	0.0609689i
$806$			7.34775i			0.258814i
$807$	−9.50218	−	15.4645i	−0.334492	−	0.544375i
$808$	0.963314	−	0.963314i	0.0338893	−	0.0338893i
$809$	38.5121			1.35401			0.677007	−	0.735977i	$-0.263277\pi$
$809$	38.5121			1.35401			0.677007	+	0.735977i	$0.263277\pi$
$810$	−16.0704	−	12.1138i	−0.564655	−	0.425635i
$811$	19.8732			0.697842			0.348921	−	0.937152i	$-0.386548\pi$
$811$	19.8732			0.697842			0.348921	+	0.937152i	$0.386548\pi$
$812$	4.86887	−	4.86887i	0.170864	−	0.170864i
$813$	−13.9871	−	22.7636i	−0.490551	−	0.798354i
$814$			37.7595i			1.32347i
$815$	−3.93956	+	1.18314i	−0.137997	+	0.0414435i
$816$	5.96077	+	1.42349i	0.208669	+	0.0498322i
$817$	49.7643	+	49.7643i	1.74103	+	1.74103i
$818$	11.1481	+	11.1481i	0.389784	+	0.389784i
$819$	−1.23706	+	2.44233i	−0.0432262	+	0.0853419i
$820$	3.48997	+	1.87788i	0.121875	+	0.0655785i
$821$			1.22214i			0.0426530i	0.999773	+	0.0213265i	$0.00678895\pi$
$821$			1.22214i			0.0426530i	−0.999773	+	0.0213265i	$0.993211\pi$
$822$	−7.84493	+	4.82034i	−0.273623	+	0.168129i
$823$	8.41266	−	8.41266i	0.293247	−	0.293247i	−0.545115	−	0.838362i	$-0.683514\pi$
$823$	8.41266	−	8.41266i	0.293247	−	0.293247i	0.838362	+	0.545115i	$0.183514\pi$
$824$	4.77423			0.166318
$825$	−32.4113	−	15.1129i	−1.12842	−	0.526163i
$826$	−9.63087			−0.335101
$827$	−25.7734	+	25.7734i	−0.896227	+	0.896227i	−0.995100	−	0.0988727i	$-0.968476\pi$
$827$	−25.7734	+	25.7734i	−0.896227	+	0.896227i	0.0988727	+	0.995100i	$0.468476\pi$
$828$	−0.933895	−	2.85094i	−0.0324551	−	0.0990769i
$829$		−	9.26672i		−	0.321846i	−0.986967	−	0.160923i	$-0.948553\pi$
$829$		−	9.26672i		−	0.321846i	0.986967	−	0.160923i	$-0.0514471\pi$
$830$	−6.16208	−	3.31570i	−0.213889	−	0.115089i
$831$	4.64989	−	19.4711i	0.161303	−	0.675445i
$832$	−0.734549	−	0.734549i	−0.0254659	−	0.0254659i
$833$	15.5825	+	15.5825i	0.539902	+	0.539902i
$834$	8.36050	−	35.0090i	0.289501	−	1.21226i
$835$	23.4828	−	7.05241i	0.812657	−	0.244059i
$836$		−	32.5448i		−	1.12558i
$837$	36.6298	−	3.01554i	1.26611	−	0.104232i
$838$	20.1049	−	20.1049i	0.694514	−	0.694514i
$839$	−0.301061			−0.0103938			−0.00519690	−	0.999986i	$-0.501654\pi$
$839$	−0.301061			−0.0103938			−0.00519690	+	0.999986i	$0.501654\pi$
$840$	−3.39679	+	0.194961i	−0.117200	+	0.00672678i
$841$	32.4346			1.11843
$842$	−16.9824	+	16.9824i	−0.585252	+	0.585252i
$843$	35.5336	−	21.8337i	1.22384	−	0.751993i
$844$			19.3102i			0.664684i
$845$	12.6306	−	23.4735i	0.434507	−	0.807512i
$846$	0.106008	+	0.0536935i	0.00364461	+	0.00184602i
$847$	3.75933	+	3.75933i	0.129172	+	0.129172i
$848$	−9.77127	−	9.77127i	−0.335547	−	0.335547i
$849$	−45.9180	−	10.9657i	−1.57590	−	0.376341i
$850$	14.7639	−	9.74697i	0.506398	−	0.334318i
$851$			9.14409i			0.313455i
$852$	−2.04574	−	3.32936i	−0.0700857	−	0.114062i
$853$	7.46140	−	7.46140i	0.255474	−	0.255474i	−0.567737	−	0.823210i	$-0.692181\pi$
$853$	7.46140	−	7.46140i	0.255474	−	0.255474i	0.823210	+	0.567737i	$0.192181\pi$
$854$	9.73727			0.333203
$855$	−30.2138	−	43.3851i	−1.03329	−	1.48374i
$856$	−3.39132			−0.115913
$857$	4.73782	−	4.73782i	0.161841	−	0.161841i	−0.621541	−	0.783382i	$-0.713493\pi$
$857$	4.73782	−	4.73782i	0.161841	−	0.161841i	0.783382	+	0.621541i	$0.213493\pi$
$858$	3.88970	+	6.33035i	0.132792	+	0.216115i
$859$			8.54021i			0.291388i	0.989330	+	0.145694i	$0.0465416\pi$
$859$			8.54021i			0.291388i	−0.989330	+	0.145694i	$0.953458\pi$
$860$	−5.74325	−	19.1236i	−0.195843	−	0.652110i
$861$	−2.62305	−	0.626410i	−0.0893933	−	0.0213480i
$862$	−19.0536	−	19.0536i	−0.648967	−	0.648967i
$863$	11.2556	+	11.2556i	0.383144	+	0.383144i	0.872234	−	0.489090i	$-0.162671\pi$
$863$	11.2556	+	11.2556i	0.383144	+	0.383144i	−0.489090	+	0.872234i	$0.662671\pi$
$864$	−3.36039	+	3.96331i	−0.114323	+	0.134834i
$865$	9.48585	+	31.5856i	0.322529	+	1.07394i
$866$			14.3670i			0.488212i
$867$	−6.61266	+	4.06316i	−0.224578	+	0.137992i
$868$	4.39381	−	4.39381i	0.149136	−	0.149136i
$869$	8.18503			0.277658
$870$	−22.6600	−	20.2000i	−0.768247	−	0.684846i
$871$	−15.9086			−0.539043
$872$	0.376112	−	0.376112i	0.0127367	−	0.0127367i
$873$	−47.6748	+	15.6171i	−1.61355	+	0.528558i
$874$		−	7.88126i		−	0.266588i
$875$	−6.29382	+	7.54029i	−0.212770	+	0.254908i
$876$	−4.82904	+	20.2212i	−0.163158	+	0.683212i
$877$	−12.3346	−	12.3346i	−0.416510	−	0.416510i	0.467489	−	0.883999i	$-0.345159\pi$
$877$	−12.3346	−	12.3346i	−0.416510	−	0.416510i	−0.883999	+	0.467489i	$0.845159\pi$
$878$	1.70577	+	1.70577i	0.0575670	+	0.0575670i
$879$	9.99976	−	41.8733i	0.337283	−	1.41235i
$880$	−4.37524	+	8.13121i	−0.147489	+	0.274103i
$881$			48.9725i			1.64992i	0.565188	+	0.824962i	$0.308804\pi$
$881$			48.9725i			1.64992i	−0.565188	+	0.824962i	$0.691196\pi$
$882$	−17.7564	+	5.81654i	−0.597888	+	0.195853i
$883$	−20.3767	+	20.3767i	−0.685732	+	0.685732i	−0.961286	−	0.275554i	$-0.911139\pi$
$883$	−20.3767	+	20.3767i	−0.685732	+	0.685732i	0.275554	+	0.961286i	$0.411139\pi$
$884$	−3.67554			−0.123622
$885$	2.43298	+	42.3897i	0.0817837	+	1.42491i
$886$	−10.7135			−0.359927
$887$	−35.8940	+	35.8940i	−1.20520	+	1.20520i	−0.232638	+	0.972563i	$0.574736\pi$
$887$	−35.8940	+	35.8940i	−1.20520	+	1.20520i	−0.972563	+	0.232638i	$0.925264\pi$
$888$	13.4942	−	8.29154i	0.452836	−	0.278246i
$889$		−	10.3630i		−	0.347563i
$890$	−13.0381	+	3.91563i	−0.437038	+	0.131252i
$891$	29.9615	−	21.9888i	1.00375	−	0.736653i
$892$	7.87712	+	7.87712i	0.263746	+	0.263746i
$893$	0.220742	+	0.220742i	0.00738686	+	0.00738686i
$894$	10.3100	+	2.46212i	0.344817	+	0.0823457i
$895$	−1.41653	−	0.762208i	−0.0473494	−	0.0254778i
$896$			0.878491i			0.0293483i
$897$	0.941956	+	1.53300i	0.0314510	+	0.0511854i
$898$	−22.3903	+	22.3903i	−0.747174	+	0.747174i
$899$	55.4403			1.84904
$900$	1.71621	+	14.9015i	0.0572071	+	0.496717i
$901$	−48.8936			−1.62888
$902$	−5.17515	+	5.17515i	−0.172314	+	0.172314i
$903$	7.11327	+	11.5766i	0.236715	+	0.385245i
$904$			5.86509i			0.195070i
$905$	−32.9147	−	17.7108i	−1.09412	−	0.588726i
$906$	−13.4939	−	3.22247i	−0.448303	−	0.107059i
$907$	9.80890	+	9.80890i	0.325699	+	0.325699i	0.850948	−	0.525249i	$-0.176028\pi$
$907$	9.80890	+	9.80890i	0.325699	+	0.325699i	−0.525249	+	0.850948i	$0.676028\pi$
$908$	−8.11980	−	8.11980i	−0.269465	−	0.269465i
$909$	3.64598	+	1.84671i	0.120930	+	0.0612516i
$910$	1.95437	−	0.586939i	0.0647866	−	0.0194568i
$911$		−	39.2776i		−	1.30132i	−0.759368	−	0.650662i	$-0.774492\pi$
$911$		−	39.2776i		−	1.30132i	0.759368	−	0.650662i	$-0.225508\pi$
$912$	−11.6306	+	7.14645i	−0.385128	+	0.236643i
$913$	9.13753	−	9.13753i	0.302408	−	0.302408i
$914$	38.4890			1.27310
$915$	−2.45986	−	42.8580i	−0.0813204	−	1.41684i
$916$	−8.83078			−0.291777
$917$	1.66936	−	1.66936i	0.0551271	−	0.0551271i
$918$	1.50845	+	18.3232i	0.0497863	+	0.604755i
$919$		−	7.64006i		−	0.252022i	−0.992029	−	0.126011i	$-0.959782\pi$
$919$		−	7.64006i		−	0.252022i	0.992029	−	0.126011i	$-0.0402175\pi$
$920$	−1.05954	+	1.96911i	−0.0349319	+	0.0649195i
$921$	−3.60888	+	15.1119i	−0.118917	+	0.497954i
$922$	−13.5095	−	13.5095i	−0.444912	−	0.444912i
$923$	1.65720	+	1.65720i	0.0545474	+	0.0545474i
$924$	1.45946	−	6.11139i	0.0480127	−	0.201050i
$925$	9.16809	−	44.7918i	0.301445	−	1.47275i
$926$			25.4467i			0.836230i
$927$	4.45863	+	13.6110i	0.146441	+	0.447045i
$928$	−5.54232	+	5.54232i	−0.181936	+	0.181936i
$929$	7.70924			0.252932			0.126466	−	0.991971i	$-0.459637\pi$
$929$	7.70924			0.252932			0.126466	+	0.991971i	$0.459637\pi$
$930$	−20.4490	−	18.2291i	−0.670551	−	0.597755i
$931$	−49.0865			−1.60874
$932$	13.3537	−	13.3537i	0.437416	−	0.437416i
$933$	−2.28626	+	1.40480i	−0.0748489	+	0.0459911i
$934$		−	19.1520i		−	0.626673i
$935$	9.39706	+	31.2899i	0.307317	+	1.02329i
$936$	1.40816	−	2.78014i	0.0460271	−	0.0908718i
$937$	−10.1233	−	10.1233i	−0.330713	−	0.330713i	0.522144	−	0.852857i	$-0.325132\pi$
$937$	−10.1233	−	10.1233i	−0.330713	−	0.330713i	−0.852857	+	0.522144i	$0.825132\pi$
$938$	9.51304	+	9.51304i	0.310612	+	0.310612i
$939$	1.07004	+	0.255537i	0.0349195	+	0.00833912i
$940$	−0.0254757	−	0.0848278i	−0.000830925	−	0.00276678i
$941$			19.0647i			0.621492i	0.950493	+	0.310746i	$0.100579\pi$
$941$			19.0647i			0.621492i	−0.950493	+	0.310746i	$0.899421\pi$
$942$	12.2666	+	19.9634i	0.399667	+	0.650444i
$943$	−1.25325	+	1.25325i	−0.0408114	+	0.0408114i
$944$	10.9630			0.356815
$945$	−3.72807	−	9.50196i	−0.121274	−	0.309099i
$946$	36.8742			1.19888
$947$	−16.0189	+	16.0189i	−0.520543	+	0.520543i	−0.917735	−	0.397192i	$-0.869985\pi$
$947$	−16.0189	+	16.0189i	−0.520543	+	0.520543i	0.397192	+	0.917735i	$0.369985\pi$
$948$	−1.79734	−	2.92510i	−0.0583748	−	0.0950029i
$949$		−	12.4689i		−	0.404756i
$950$	−7.90195	+	38.6059i	−0.256373	+	1.25254i
$951$	−42.3743	−	10.1194i	−1.37408	−	0.328144i
$952$	2.19790	+	2.19790i	0.0712344	+	0.0712344i
$953$	−23.5761	−	23.5761i	−0.763704	−	0.763704i	0.213286	−	0.976990i	$-0.431583\pi$
$953$	−23.5761	−	23.5761i	−0.763704	−	0.763704i	−0.976990	+	0.213286i	$0.931583\pi$
$954$	18.7319	−	36.9826i	0.606468	−	1.19736i
$955$	11.2564	−	20.9196i	0.364249	−	0.676941i
$956$		−	5.29769i		−	0.171340i
$957$	47.7638	−	29.3486i	1.54398	−	0.948705i
$958$	−7.17891	+	7.17891i	−0.231940	+	0.231940i
$959$	−4.67003			−0.150803
$960$	3.86662	−	0.221927i	0.124795	−	0.00716266i
$961$	19.0309			0.613899
$962$	−6.71678	+	6.71678i	−0.216558	+	0.216558i
$963$	−3.16714	−	9.66845i	−0.102060	−	0.311561i
$964$		−	3.24318i		−	0.104456i
$965$	2.21956	−	0.666581i	0.0714500	−	0.0214580i
$966$	0.353433	−	1.47997i	0.0113715	−	0.0476174i
$967$	−27.9358	−	27.9358i	−0.898354	−	0.898354i	0.0969368	−	0.995291i	$-0.469096\pi$
$967$	−27.9358	−	27.9358i	−0.898354	−	0.898354i	−0.995291	+	0.0969368i	$0.969096\pi$
$968$	−4.27930	−	4.27930i	−0.137542	−	0.137542i
$969$	−11.2189	+	46.9784i	−0.360404	+	1.50916i
$970$	32.9284	+	17.7181i	1.05727	+	0.568895i
$971$			59.7771i			1.91834i	0.282833	+	0.959169i	$0.408726\pi$
$971$			59.7771i			1.91834i	−0.282833	+	0.959169i	$0.591274\pi$
$972$	−14.4374	−	5.87893i	−0.463079	−	0.188567i
$973$	12.9088	−	12.9088i	0.413836	−	0.413836i
$974$	−9.21274			−0.295195
$975$	−3.07709	−	8.45374i	−0.0985458	−	0.270736i
$976$	−11.0841			−0.354793
$977$	1.55002	−	1.55002i	0.0495896	−	0.0495896i	−0.681877	−	0.731467i	$-0.738836\pi$
$977$	1.55002	−	1.55002i	0.0495896	−	0.0495896i	0.731467	+	0.681877i	$0.238836\pi$
$978$	−2.71470	+	1.66805i	−0.0868064	+	0.0533384i
$979$		−	25.1401i		−	0.803481i
$980$	12.2641	+	6.59907i	0.391762	+	0.210800i
$981$	1.42352	+	0.721021i	0.0454495	+	0.0230204i
$982$	28.3485	+	28.3485i	0.904636	+	0.904636i
$983$	5.24119	+	5.24119i	0.167168	+	0.167168i	0.785733	−	0.618565i	$-0.212286\pi$
$983$	5.24119	+	5.24119i	0.167168	+	0.167168i	−0.618565	+	0.785733i	$0.712286\pi$
$984$	2.98586	+	0.713053i	0.0951857	+	0.0227313i
$985$	−31.7236	+	9.52730i	−1.01080	+	0.303565i
$986$			27.7327i			0.883189i
$987$	0.0315527	+	0.0513510i	0.00100434	+	0.00163452i
$988$	5.78917	−	5.78917i	0.184178	−	0.184178i
$989$	8.92971			0.283948
$990$	−27.2676	−	4.87985i	−0.866620	−	0.155092i
$991$	−9.17923			−0.291588			−0.145794	−	0.989315i	$-0.546574\pi$
$991$	−9.17923			−0.291588			−0.145794	+	0.989315i	$0.546574\pi$
$992$	−5.00154	+	5.00154i	−0.158799	+	0.158799i
$993$	−8.78692	−	14.3004i	−0.278845	−	0.453810i
$994$		−	1.98195i		−	0.0628635i
$995$	−3.20418	+	5.95484i	−0.101579	+	0.188781i
$996$	−5.27200	−	1.25901i	−0.167050	−	0.0398931i
$997$	−23.7592	−	23.7592i	−0.752462	−	0.752462i	0.222476	−	0.974938i	$-0.428586\pi$
$997$	−23.7592	−	23.7592i	−0.752462	−	0.752462i	−0.974938	+	0.222476i	$0.928586\pi$
$998$	2.35867	+	2.35867i	0.0746625	+	0.0746625i
$999$	36.2408	+	30.7277i	1.14661	+	0.972180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.6	✓	32
3.2	odd	2	inner	690.2.i.f.47.9	yes	32
5.3	odd	4	inner	690.2.i.f.323.9	yes	32
15.8	even	4	inner	690.2.i.f.323.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.6	✓	32	1.1	even	1	trivial
690.2.i.f.47.9	yes	32	3.2	odd	2	inner
690.2.i.f.323.6	yes	32	15.8	even	4	inner
690.2.i.f.323.9	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.906765 + 1.47573i) q^{3} -1.00000i q^{4} +(-1.96911 - 1.05954i) q^{5} +(-1.68468 - 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35555 + 2.67628i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.906765 + 1.47573i) q^{3} -1.00000i q^{4} +(-1.96911 - 1.05954i) q^{5} +(-1.68468 - 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.35555 + 2.67628i) q^{9} +(2.14157 - 0.643162i) q^{10} +4.12939i q^{11} +(1.47573 - 0.906765i) q^{12} +(-0.734549 + 0.734549i) q^{13} +0.878491 q^{14} +(-0.221927 - 3.86662i) q^{15} -1.00000 q^{16} +(-2.50190 + 2.50190i) q^{17} +(-0.933895 - 2.85094i) q^{18} -7.88126i q^{19} +(-1.05954 + 1.96911i) q^{20} +(0.353433 - 1.47997i) q^{21} +(-2.91992 - 2.91992i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.402318 + 1.68468i) q^{24} +(2.75476 + 4.17269i) q^{25} -1.03881i q^{26} +(-5.17863 + 0.426330i) q^{27} +(-0.621187 + 0.621187i) q^{28} -7.83802 q^{29} +(2.89104 + 2.57719i) q^{30} -7.07325 q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.09386 + 3.74439i) q^{33} -3.53823i q^{34} +(0.565012 + 1.88135i) q^{35} +(2.67628 + 1.35555i) q^{36} +(-6.46585 - 6.46585i) q^{37} +(5.57289 + 5.57289i) q^{38} +(-1.75006 - 0.417931i) q^{39} +(-0.643162 - 2.14157i) q^{40} -1.77236i q^{41} +(0.796585 + 1.29641i) q^{42} +(-6.31426 + 6.31426i) q^{43} +4.12939 q^{44} +(5.50485 - 3.83362i) q^{45} +1.00000 q^{46} +(-0.0280085 + 0.0280085i) q^{47} +(-0.906765 - 1.47573i) q^{48} -6.22825i q^{49} +(-4.89844 - 1.00262i) q^{50} +(-5.96077 - 1.42349i) q^{51} +(0.734549 + 0.734549i) q^{52} +(9.77127 + 9.77127i) q^{53} +(3.36039 - 3.96331i) q^{54} +(4.37524 - 8.13121i) q^{55} -0.878491i q^{56} +(11.6306 - 7.14645i) q^{57} +(5.54232 - 5.54232i) q^{58} -10.9630 q^{59} +(-3.86662 + 0.221927i) q^{60} +11.0841 q^{61} +(5.00154 - 5.00154i) q^{62} +(2.50452 - 0.820418i) q^{63} +1.00000i q^{64} +(2.22469 - 0.668122i) q^{65} +(1.66133 - 6.95669i) q^{66} +(10.8288 + 10.8288i) q^{67} +(2.50190 + 2.50190i) q^{68} +(0.402318 - 1.68468i) q^{69} +(-1.72984 - 0.930794i) q^{70} -2.25608i q^{71} +(-2.85094 + 0.933895i) q^{72} +(-8.48742 + 8.48742i) q^{73} +9.14409 q^{74} +(-3.65983 + 7.84893i) q^{75} -7.88126 q^{76} +(2.56512 - 2.56512i) q^{77} +(1.53300 - 0.941956i) q^{78} -1.98214i q^{79} +(1.96911 + 1.05954i) q^{80} +(-5.32495 - 7.25568i) q^{81} +(1.25325 + 1.25325i) q^{82} +(-2.21281 - 2.21281i) q^{83} +(-1.47997 - 0.353433i) q^{84} +(7.57738 - 2.27565i) q^{85} -8.92971i q^{86} +(-7.10725 - 11.5668i) q^{87} +(-2.91992 + 2.91992i) q^{88} -6.08809 q^{89} +(-1.18174 + 6.60329i) q^{90} +0.912584 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-6.41378 - 10.4382i) q^{93} -0.0396100i q^{94} +(-8.35049 + 15.5190i) q^{95} +(1.68468 + 0.402318i) q^{96} +(11.8246 + 11.8246i) q^{97} +(4.40404 + 4.40404i) q^{98} +(-11.0514 - 5.59760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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