LMFDB - Embedded newform 690.2.i.f.47.9

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			47.9
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) q^{3} -1.00000i q^{4} +(1.96911 + 1.05954i) q^{5} +(-1.68468 + 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.35555 + 2.67628i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) 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} +(-0.906765 + 1.47573i) q^{12} +(-0.734549 + 0.734549i) q^{13} -0.878491 q^{14} +(-1.94512 - 3.34911i) q^{15} -1.00000 q^{16} +(2.50190 - 2.50190i) q^{17} +(2.85094 + 0.933895i) 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} +(0.426330 - 5.17863i) q^{27} +(-0.621187 + 0.621187i) q^{28} +7.83802 q^{29} +(-3.74358 - 0.992773i) q^{30} -7.07325 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.74439 + 6.09386i) 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} +(1.29641 + 0.796585i) q^{42} +(-6.31426 + 6.31426i) q^{43} -4.12939 q^{44} +(-0.166392 + 6.70614i) q^{45} +1.00000 q^{46} +(0.0280085 - 0.0280085i) q^{47} +(1.47573 + 0.906765i) 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} +(-7.14645 + 11.6306i) q^{57} +(5.54232 - 5.54232i) q^{58} +10.9630 q^{59} +(-3.34911 + 1.94512i) q^{60} +11.0841 q^{61} +(-5.00154 + 5.00154i) q^{62} +(0.820418 - 2.50452i) 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} +(0.933895 - 2.85094i) q^{72} +(-8.48742 + 8.48742i) q^{73} -9.14409 q^{74} +(-0.281632 - 8.65567i) q^{75} -7.88126 q^{76} +(-2.56512 + 2.56512i) q^{77} +(0.941956 - 1.53300i) 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} +(-11.5668 - 7.10725i) q^{87} +(-2.91992 + 2.91992i) q^{88} +6.08809 q^{89} +(4.62430 + 4.85961i) q^{90} +0.912584 q^{91} +(0.707107 - 0.707107i) q^{92} +(10.4382 + 6.41378i) 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
$3$	−1.47573	−	0.906765i	−0.852013	−	0.523521i
$3$	−1.47573	−	0.906765i	−0.852013	−	0.523521i
$4$		−	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	$-0.786105\pi$
$11$		−	4.12939i		−	1.24506i	0.782597	−	0.622529i	$-0.213895\pi$
$12$	−0.906765	+	1.47573i	−0.261761	+	0.426006i
$13$	−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
$15$	−1.94512	−	3.34911i	−0.502227	−	0.864736i
$16$	−1.00000			−0.250000
$17$	2.50190	−	2.50190i	0.606801	−	0.606801i	−0.335308	−	0.942109i	$-0.608840\pi$
$17$	2.50190	−	2.50190i	0.606801	−	0.606801i	0.942109	+	0.335308i	$0.108840\pi$
$18$	2.85094	+	0.933895i	0.671972	+	0.220121i
$19$		−	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
$27$	0.426330	−	5.17863i	0.0820472	−	0.996628i
$28$	−0.621187	+	0.621187i	−0.117393	+	0.117393i
$29$	7.83802			1.45548			0.727742	−	0.685851i	$-0.240570\pi$
$29$	7.83802			1.45548			0.727742	+	0.685851i	$0.240570\pi$
$30$	−3.74358	−	0.992773i	−0.683481	−	0.181255i
$31$	−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
$33$	−3.74439	+	6.09386i	−0.651814	+	1.06080i
$34$		−	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	$0.0441954\pi$
$41$			1.77236i			0.276796i	−0.990377	+	0.138398i	$0.955805\pi$
$42$	1.29641	+	0.796585i	0.200041	+	0.122916i
$43$	−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
$45$	−0.166392	+	6.70614i	−0.0248043	+	0.999692i
$46$	1.00000			0.147442
$47$	0.0280085	−	0.0280085i	0.00408546	−	0.00408546i	−0.705061	−	0.709147i	$-0.749080\pi$
$47$	0.0280085	−	0.0280085i	0.00408546	−	0.00408546i	0.709147	+	0.705061i	$0.249080\pi$
$48$	1.47573	+	0.906765i	0.213003	+	0.130880i
$49$		−	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	$-0.852027\pi$
$53$	−9.77127	−	9.77127i	−1.34219	−	1.34219i	−0.448307	−	0.893880i	$-0.647973\pi$
$54$	−3.36039	−	3.96331i	−0.457291	−	0.539338i
$55$	4.37524	−	8.13121i	0.589958	−	1.09641i
$56$			0.878491i			0.117393i
$57$	−7.14645	+	11.6306i	−0.946571	+	1.54051i
$58$	5.54232	−	5.54232i	0.727742	−	0.727742i
$59$	10.9630			1.42726			0.713629	−	0.700524i	$-0.247050\pi$
$59$	10.9630			1.42726			0.713629	+	0.700524i	$0.247050\pi$
$60$	−3.34911	+	1.94512i	−0.432368	+	0.251113i
$61$	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
$63$	0.820418	−	2.50452i	0.103363	−	0.315540i
$64$			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	$0.0427417\pi$
$71$			2.25608i			0.267747i	−0.990998	+	0.133874i	$0.957258\pi$
$72$	0.933895	−	2.85094i	0.110061	−	0.335986i
$73$	−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
$75$	−0.281632	−	8.65567i	−0.0325201	−	0.999471i
$76$	−7.88126			−0.904042
$77$	−2.56512	+	2.56512i	−0.292323	+	0.292323i
$78$	0.941956	−	1.53300i	0.106655	−	0.173578i
$79$		−	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	0.818043	−	0.575156i	$-0.195059\pi$
$83$	2.21281	+	2.21281i	0.242887	+	0.242887i	−0.575156	+	0.818043i	$0.695059\pi$
$84$	1.47997	−	0.353433i	0.161478	−	0.0385627i
$85$	7.57738	−	2.27565i	0.821882	−	0.246829i
$86$			8.92971i			0.962915i
$87$	−11.5668	−	7.10725i	−1.24009	−	0.761977i
$88$	−2.91992	+	2.91992i	−0.311264	+	0.311264i
$89$	6.08809			0.645336			0.322668	−	0.946512i	$-0.395420\pi$
$89$	6.08809			0.645336			0.322668	+	0.946512i	$0.395420\pi$
$90$	4.62430	+	4.85961i	0.487444	+	0.512248i
$91$	0.912584			0.0956648
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	10.4382	+	6.41378i	1.08239	+	0.665078i
$94$		−	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	$0.0215911\pi$
$101$			1.36233i			0.135557i	−0.997700	+	0.0677786i	$0.978409\pi$
$102$	−3.20834	+	5.22147i	−0.317673	+	0.517002i
$103$	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
$105$	−0.872142	+	3.28870i	−0.0851123	+	0.320944i
$106$	−13.8187			−1.34219
$107$	2.39803	−	2.39803i	0.231826	−	0.231826i	−0.581628	−	0.813455i	$-0.697584\pi$
$107$	2.39803	−	2.39803i	0.231826	−	0.231826i	0.813455	+	0.581628i	$0.197584\pi$
$108$	−5.17863	−	0.426330i	−0.498314	−	0.0410236i
$109$		−	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	0.484597	−	0.874737i	$-0.338966\pi$
$113$	−4.14725	−	4.14725i	−0.390140	−	0.390140i	−0.874737	+	0.484597i	$0.838966\pi$
$114$	3.17077	+	13.2774i	0.296970	+	1.24354i
$115$	0.643162	+	2.14157i	0.0599752	+	0.199703i
$116$		−	7.83802i		−	0.727742i
$117$	−2.96158	−	0.970139i	−0.273798	−	0.0896893i
$118$	7.75200	−	7.75200i	0.713629	−	0.713629i
$119$	−3.10830			−0.284937
$120$	−0.992773	+	3.74358i	−0.0906274	+	0.341741i
$121$	−6.05185			−0.550168
$122$	7.83764	−	7.83764i	0.709587	−	0.709587i
$123$	1.60712	−	2.61553i	0.144909	−	0.235834i
$124$			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	$-0.962545\pi$
$131$		−	2.68737i		−	0.234797i	0.993085	−	0.117398i	$-0.0374554\pi$
$132$	6.09386	+	3.74439i	0.530402	+	0.325907i
$133$	−4.89573	+	4.89573i	−0.424514	+	0.424514i
$134$	15.3143			1.32295
$135$	6.32645	−	9.74557i	0.544494	−	0.838765i
$136$	−3.53823			−0.303401
$137$	−3.75896	+	3.75896i	−0.321150	+	0.321150i	−0.849208	−	0.528058i	$-0.822920\pi$
$137$	−3.75896	+	3.75896i	−0.321150	+	0.321150i	0.528058	+	0.849208i	$0.322920\pi$
$138$	−1.47573	−	0.906765i	−0.125622	−	0.0771890i
$139$			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
$147$	−5.64757	+	9.19122i	−0.465803	+	0.758079i
$148$	−6.46585	+	6.46585i	−0.531489	+	0.531489i
$149$	6.11984			0.501357			0.250678	−	0.968070i	$-0.419346\pi$
$149$	6.11984			0.501357			0.250678	+	0.968070i	$0.419346\pi$
$150$	−6.31963	−	5.92134i	−0.515996	−	0.483476i
$151$	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
$153$	10.0873	+	3.30433i	0.815507	+	0.267140i
$154$			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
$162$	1.36523	+	8.89585i	0.107263	+	0.698924i
$163$	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
$165$	−13.8298	+	8.03214i	−1.07665	+	0.625301i
$166$	3.12938			0.242887
$167$	7.75358	−	7.75358i	0.599990	−	0.599990i	−0.340320	−	0.940310i	$-0.610535\pi$
$167$	7.75358	−	7.75358i	0.599990	−	0.599990i	0.940310	+	0.340320i	$0.110535\pi$
$168$	0.796585	−	1.29641i	0.0614579	−	0.100021i
$169$			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	0.981964	−	0.189066i	$-0.0605459\pi$
$173$	10.4290	+	10.4290i	0.792899	+	0.792899i	−0.189066	+	0.981964i	$0.560546\pi$
$174$	−13.2045	+	3.15338i	−1.00103	+	0.239057i
$175$	0.880797	−	4.30324i	0.0665820	−	0.325294i
$176$			4.12939i			0.311264i
$177$	−16.1784	−	9.94085i	−1.21604	−	0.747200i
$178$	4.30493	−	4.30493i	0.322668	−	0.322668i
$179$	−0.719378			−0.0537688			−0.0268844	−	0.999639i	$-0.508559\pi$
$179$	−0.719378			−0.0537688			−0.0268844	+	0.999639i	$0.508559\pi$
$180$	6.70614	+	0.166392i	0.499846	+	0.0124022i
$181$	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
$183$	−16.3571	−	10.0507i	−1.20915	−	0.742967i
$184$		−	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	$-0.874423\pi$
$191$		−	10.6239i		−	0.768718i	0.923184	−	0.384359i	$-0.125577\pi$
$192$	0.906765	−	1.47573i	0.0654402	−	0.106502i
$193$	−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
$195$	3.88886	+	1.03130i	0.278487	+	0.0738530i
$196$	−6.22825			−0.444875
$197$	−10.4745	+	10.4745i	−0.746279	+	0.746279i	−0.973778	−	0.227499i	$-0.926945\pi$
$197$	−10.4745	+	10.4745i	−0.746279	+	0.746279i	0.227499	+	0.973778i	$0.426945\pi$
$198$	3.85642	−	11.7726i	0.274064	−	0.836644i
$199$		−	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
$207$	−0.933895	+	2.85094i	−0.0649102	+	0.198154i
$208$	0.734549	−	0.734549i	0.0509318	−	0.0509318i
$209$	−32.5448			−2.25117
$210$	1.70877	+	2.94216i	0.117916	+	0.203028i
$211$	−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
$213$	2.04574	−	3.32936i	0.140171	−	0.228124i
$214$		−	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
$222$	13.4942	+	8.29154i	0.905671	+	0.556492i
$223$	−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
$225$	−7.43305	+	13.0288i	−0.495537	+	0.868587i
$226$	−5.86509			−0.390140
$227$	−8.11980	+	8.11980i	−0.538930	+	0.538930i	−0.923215	−	0.384284i	$-0.874448\pi$
$227$	−8.11980	+	8.11980i	−0.538930	+	0.538930i	0.384284	+	0.923215i	$0.374448\pi$
$228$	11.6306	+	7.14645i	0.770255	+	0.473285i
$229$		−	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	0.118163	−	0.992994i	$-0.462299\pi$
$233$	−13.3537	−	13.3537i	−0.874831	−	0.874831i	−0.992994	+	0.118163i	$0.962299\pi$
$234$	−2.78014	+	1.40816i	−0.181744	+	0.0920543i
$235$	0.0848278	−	0.0254757i	0.00553356	−	0.00166185i
$236$		−	10.9630i		−	0.713629i
$237$	−1.79734	+	2.92510i	−0.116750	+	0.190006i
$238$	−2.19790	+	2.19790i	−0.142469	+	0.142469i
$239$	−5.29769			−0.342679			−0.171340	−	0.985212i	$-0.554810\pi$
$239$	−5.29769			−0.342679			−0.171340	+	0.985212i	$0.554810\pi$
$240$	1.94512	+	3.34911i	0.125557	+	0.216184i
$241$	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
$243$	14.4374	−	5.87893i	0.926159	−	0.377134i
$244$		−	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	$0.188167\pi$
$251$			17.6589i			1.11462i	−0.830304	+	0.557310i	$0.811833\pi$
$252$	−2.50452	−	0.820418i	−0.157770	−	0.0516815i
$253$	2.91992	−	2.91992i	0.183574	−	0.183574i
$254$	11.7963			0.740167
$255$	−13.2456	−	3.51266i	−0.829474	−	0.219971i
$256$	1.00000			0.0625000
$257$	3.83128	−	3.83128i	0.238989	−	0.238989i	−0.577442	−	0.816431i	$-0.695949\pi$
$257$	3.83128	−	3.83128i	0.238989	−	0.238989i	0.816431	+	0.577442i	$0.195949\pi$
$258$	8.09715	−	13.1778i	0.504106	−	0.820416i
$259$			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	0.330321	−	0.943869i	$-0.392843\pi$
$263$	−9.95007	−	9.95007i	−0.613548	−	0.613548i	−0.943869	+	0.330321i	$0.892843\pi$
$264$	6.95669	−	1.66133i	0.428155	−	0.102248i
$265$	−8.88764	−	29.5937i	−0.545963	−	1.81793i
$266$			6.92361i			0.424514i
$267$	−8.98437	−	5.52047i	−0.549835	−	0.337847i
$268$	10.8288	−	10.8288i	0.661477	−	0.661477i
$269$	10.4792			0.638928			0.319464	−	0.947598i	$-0.396497\pi$
$269$	10.4792			0.638928			0.319464	+	0.947598i	$0.396497\pi$
$270$	−2.41768	−	11.3646i	−0.147136	−	0.691629i
$271$	−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
$273$	−1.34673	−	0.827499i	−0.0815076	−	0.0500825i
$274$			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	$0.255037\pi$
$281$			24.0787i			1.43641i	−0.695830	+	0.718206i	$0.744963\pi$
$282$	−0.0359170	+	0.0584537i	−0.00213883	+	0.00348087i
$283$	−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
$285$	−26.3952	+	15.3300i	−1.56352	+	0.908068i
$286$	4.28964			0.253652
$287$	1.10097	−	1.10097i	0.0649880	−	0.0649880i
$288$	−2.85094	−	0.933895i	−0.167993	−	0.0550303i
$289$			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	$0.00863783\pi$
$293$	17.5754	+	17.5754i	1.02677	+	1.02677i	0.0271332	+	0.999632i	$0.491362\pi$
$294$	2.50574	+	10.4926i	0.146138	+	0.611941i
$295$	21.5873	+	11.6157i	1.25686	+	0.676292i
$296$			9.14409i			0.531489i
$297$	−21.3846	−	1.76048i	−1.24086	−	0.102153i
$298$	4.32738	−	4.32738i	0.250678	−	0.250678i
$299$	−1.03881			−0.0600759
$300$	−8.65567	+	0.281632i	−0.499736	+	0.0162600i
$301$	7.84466			0.452159
$302$	5.66375	−	5.66375i	0.325912	−	0.325912i
$303$	1.23532	−	2.01043i	0.0709670	−	0.115496i
$304$			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	$-0.986014\pi$
$311$		−	1.54924i		−	0.0878496i	0.999035	−	0.0439248i	$-0.0139862\pi$
$312$	−1.53300	−	0.941956i	−0.0867890	−	0.0533277i
$313$	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
$315$	4.26913	−	4.06240i	0.240538	−	0.228891i
$316$	−1.98214			−0.111504
$317$	17.7857	−	17.7857i	0.998943	−	0.998943i	−0.00105667	−	0.999999i	$-0.500336\pi$
$317$	17.7857	−	17.7857i	0.998943	−	0.998943i	0.999999	+	0.00105667i	$0.000336349\pi$
$318$	20.3926	+	12.5303i	1.14356	+	0.702663i
$319$		−	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
$327$	−0.482310	+	0.784943i	−0.0266718	+	0.0434075i
$328$	1.25325	−	1.25325i	0.0691991	−	0.0691991i
$329$	−0.0347970			−0.00191842
$330$	−4.09955	+	15.4587i	−0.225673	+	0.850974i
$331$	−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
$333$	8.53962	−	26.0692i	0.467968	−	1.42858i
$334$		−	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
$342$	7.36027	−	22.4690i	0.397998	−	1.21498i
$343$	−8.21722	+	8.21722i	−0.443688	+	0.443688i
$344$	8.92971			0.481457
$345$	0.992773	−	3.74358i	0.0534491	−	0.201548i
$346$	14.7488			0.792899
$347$	11.2296	−	11.2296i	0.602837	−	0.602837i	−0.338228	−	0.941064i	$-0.609827\pi$
$347$	11.2296	−	11.2296i	0.602837	−	0.602837i	0.941064	+	0.338228i	$0.109827\pi$
$348$	−7.10725	+	11.5668i	−0.380988	+	0.620045i
$349$		−	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	0.952706	−	0.303893i	$-0.0982865\pi$
$353$	12.1901	+	12.1901i	0.648813	+	0.648813i	−0.303893	+	0.952706i	$0.598287\pi$
$354$	−18.4691	+	4.41060i	−0.981621	+	0.234421i
$355$	−2.39040	+	4.44246i	−0.126869	+	0.235781i
$356$		−	6.08809i		−	0.322668i
$357$	4.58701	+	2.81850i	0.242770	+	0.149171i
$358$	−0.508677	+	0.508677i	−0.0268844	+	0.0268844i
$359$	−7.16299			−0.378048			−0.189024	−	0.981972i	$-0.560532\pi$
$359$	−7.16299			−0.378048			−0.189024	+	0.981972i	$0.560532\pi$
$360$	4.85961	−	4.62430i	0.256124	−	0.243722i
$361$	−43.1142			−2.26917
$362$	11.8197	−	11.8197i	0.621229	−	0.621229i
$363$	8.93089	+	5.48761i	0.468750	+	0.288025i
$364$		−	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
$372$	6.41378	−	10.4382i	0.332539	−	0.541196i
$373$	−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
$375$	8.61645	−	17.3423i	0.444952	−	0.895555i
$376$	−0.0396100			−0.00204273
$377$	−5.75741	+	5.75741i	−0.296522	+	0.296522i
$378$	−0.374527	+	4.54938i	−0.0192636	+	0.233995i
$379$			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	0.176836	−	0.984240i	$-0.443414\pi$
$383$	−15.8012	−	15.8012i	−0.807405	−	0.807405i	−0.984240	+	0.176836i	$0.943414\pi$
$384$	−0.402318	−	1.68468i	−0.0205307	−	0.0859709i
$385$	−7.76884	+	2.33315i	−0.395937	+	0.118909i
$386$			1.03641i			0.0527520i
$387$	−25.4580	−	8.33941i	−1.29410	−	0.423916i
$388$	11.8246	−	11.8246i	0.600303	−	0.600303i
$389$	−1.35053			−0.0684745			−0.0342372	−	0.999414i	$-0.510900\pi$
$389$	−1.35053			−0.0684745			−0.0342372	+	0.999414i	$0.510900\pi$
$390$	3.47908	−	2.02060i	0.176170	−	0.102317i
$391$	3.53823			0.178936
$392$	−4.40404	+	4.40404i	−0.222438	+	0.222438i
$393$	−2.43682	+	3.96583i	−0.122921	+	0.200050i
$394$			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	$0.105831\pi$
$401$			13.0718i			0.652775i	−0.945236	+	0.326387i	$0.894169\pi$
$402$	−22.5998	−	13.8865i	−1.12717	−	0.692595i
$403$	5.19565	−	5.19565i	0.258814	−	0.258814i
$404$	1.36233			0.0677786
$405$	−18.1731	+	8.64521i	−0.903027	+	0.429584i
$406$	−6.88563			−0.341728
$407$	−26.7000	+	26.7000i	−1.32347	+	1.32347i
$408$	5.22147	+	3.20834i	0.258501	+	0.158837i
$409$		−	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
$417$	18.8433	−	30.6669i	0.922762	−	1.50176i
$418$	−23.0126	+	23.0126i	−1.12558	+	1.12558i
$419$	28.4327			1.38903			0.694514	−	0.719480i	$-0.255620\pi$
$419$	28.4327			1.38903			0.694514	+	0.719480i	$0.255620\pi$
$420$	3.28870	+	0.872142i	0.160472	+	0.0425562i
$421$	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
$423$	0.112926	+	0.0369916i	0.00549063	+	0.00179859i
$424$			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	$-0.775202\pi$
$431$		−	26.9458i		−	1.29793i	0.760817	−	0.648967i	$-0.224798\pi$
$432$	−0.426330	+	5.17863i	−0.0205118	+	0.249157i
$433$	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
$435$	−15.2459	−	26.2504i	−0.730983	−	1.25861i
$436$	−0.531902			−0.0254735
$437$	5.57289	−	5.57289i	0.266588	−	0.266588i
$438$	10.8839	−	17.7132i	0.520054	−	0.846370i
$439$		−	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	0.503859	−	0.863786i	$-0.331913\pi$
$443$	−7.57559	−	7.57559i	−0.359927	−	0.359927i	−0.863786	+	0.503859i	$0.831913\pi$
$444$	15.4048	−	3.67883i	0.731082	−	0.174590i
$445$	11.9881	+	6.45056i	0.568290	+	0.305786i
$446$			11.1399i			0.527491i
$447$	−9.03122	−	5.54926i	−0.427162	−	0.262471i
$448$	0.621187	−	0.621187i	0.0293483	−	0.0293483i
$449$	−31.6647			−1.49435			−0.747174	−	0.664628i	$-0.768590\pi$
$449$	−31.6647			−1.49435			−0.747174	+	0.664628i	$0.768590\pi$
$450$	3.95679	+	14.4687i	0.186525	+	0.682062i
$451$	7.31877			0.344627
$452$	−4.14725	+	4.14725i	−0.195070	+	0.195070i
$453$	−11.8202	−	7.26297i	−0.555363	−	0.341244i
$454$			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	$-0.853235\pi$
$461$		−	19.1053i		−	0.889824i	0.895574	−	0.444912i	$-0.146765\pi$
$462$	3.28941	−	5.35340i	0.153037	−	0.249063i
$463$	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
$465$	13.7583	+	23.6891i	0.638025	+	1.09856i
$466$	−18.8850			−0.874831
$467$	13.5425	−	13.5425i	0.626673	−	0.626673i	−0.320557	−	0.947229i	$-0.603870\pi$
$467$	13.5425	−	13.5425i	0.626673	−	0.626673i	0.947229	+	0.320557i	$0.103870\pi$
$468$	−0.970139	+	2.96158i	−0.0448447	+	0.136899i
$469$		−	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
$477$	12.9052	−	39.3961i	0.590888	−	1.80382i
$478$	−3.74603	+	3.74603i	−0.171340	+	0.171340i
$479$	−10.1525			−0.463880			−0.231940	−	0.972730i	$-0.574507\pi$
$479$	−10.1525			−0.463880			−0.231940	+	0.972730i	$0.574507\pi$
$480$	3.74358	+	0.992773i	0.170870	+	0.0453137i
$481$	9.49896			0.433115
$482$	2.29328	−	2.29328i	0.104456	−	0.104456i
$483$	−0.796585	+	1.29641i	−0.0362459	+	0.0589889i
$484$			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	$0.359857\pi$
$491$			40.0908i			1.80927i	−0.426186	+	0.904636i	$0.640143\pi$
$492$	−2.61553	−	1.60712i	−0.117917	−	0.0724544i
$493$	19.6100	−	19.6100i	0.883189	−	0.883189i
$494$	8.18712			0.368356
$495$	27.6923	+	0.687099i	1.24467	+	0.0308828i
$496$	7.07325			0.317598
$497$	1.40145	−	1.40145i	0.0628635	−	0.0628635i
$498$	−4.61812	−	2.83761i	−0.206943	−	0.127157i
$499$		−	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	0.815935	−	0.578144i	$-0.196223\pi$
$503$	5.33310	+	5.33310i	0.237791	+	0.237791i	−0.578144	+	0.815935i	$0.696223\pi$
$504$	−2.35109	+	1.19084i	−0.104726	+	0.0530443i
$505$	−1.44344	+	2.68258i	−0.0642323	+	0.119373i
$506$		−	4.12939i		−	0.183574i
$507$	10.8094	−	17.5920i	0.480064	−	0.781287i
$508$	8.34126	−	8.34126i	0.370084	−	0.370084i
$509$	−0.551066			−0.0244256			−0.0122128	−	0.999925i	$-0.503888\pi$
$509$	−0.551066			−0.0244256			−0.0122128	+	0.999925i	$0.503888\pi$
$510$	−11.8499	+	6.88226i	−0.524723	+	0.304752i
$511$	10.5445			0.466463
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−40.8141	−	3.36002i	−1.80199	−	0.148348i
$514$		−	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	$0.0547387\pi$
$521$			7.81178i			0.342240i	−0.985250	+	0.171120i	$0.945261\pi$
$522$	22.3457	+	7.31989i	0.978045	+	0.320383i
$523$	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
$525$	−5.20184	+	5.55174i	−0.227027	+	0.242298i
$526$	−14.0715			−0.613548
$527$	−17.6966	+	17.6966i	−0.770876	+	0.770876i
$528$	3.74439	−	6.09386i	0.162954	−	0.265201i
$529$			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
$537$	1.06161	+	0.652307i	0.0458117	+	0.0281491i
$538$	7.40991	−	7.40991i	0.319464	−	0.319464i
$539$	−25.7189			−1.10779
$540$	−9.74557	−	6.32645i	−0.419382	−	0.272247i
$541$	−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
$543$	−24.6676	−	15.1571i	−1.05859	−	0.650453i
$544$			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
$552$	−0.906765	+	1.47573i	−0.0385945	+	0.0628112i
$553$	−1.23128	+	1.23128i	−0.0523593	+	0.0523593i
$554$	−11.5578			−0.491042
$555$	−9.07800	+	34.2316i	−0.385340	+	1.45305i
$556$	20.7808			0.881303
$557$	19.7470	−	19.7470i	0.836707	−	0.836707i	−0.151717	−	0.988424i	$-0.548480\pi$
$557$	19.7470	−	19.7470i	0.836707	−	0.836707i	0.988424	+	0.151717i	$0.0484803\pi$
$558$	−20.1654	−	6.60568i	−0.853669	−	0.279641i
$559$		−	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	0.944593	−	0.328244i	$-0.106457\pi$
$563$	14.6245	+	14.6245i	0.616349	+	0.616349i	−0.328244	+	0.944593i	$0.606457\pi$
$564$	0.0159358	+	0.0667301i	0.000671019	+	0.00280985i
$565$	−3.77221	−	12.5605i	−0.158698	−	0.528426i
$566$			27.2563i			1.14567i
$567$	7.81492	−	1.19934i	0.328196	−	0.0503676i
$568$	1.59529	−	1.59529i	0.0669369	−	0.0669369i
$569$	−45.5814			−1.91087			−0.955436	−	0.295197i	$-0.904615\pi$
$569$	−45.5814			−1.91087			−0.955436	+	0.295197i	$0.904615\pi$
$570$	−7.82430	+	29.5041i	−0.327724	+	1.23579i
$571$	−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
$573$	−9.63337	+	15.6780i	−0.402440	+	0.654957i
$574$		−	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
$582$	−24.6779	−	15.1634i	−1.02293	−	0.628543i
$583$	−40.3494	+	40.3494i	−1.67110	+	1.67110i
$584$	12.0030			0.496689
$585$	−4.80376	−	5.04821i	−0.198611	−	0.208718i
$586$	24.8553			1.02677
$587$	−1.72536	+	1.72536i	−0.0712134	+	0.0712134i	−0.741816	−	0.670603i	$-0.766035\pi$
$587$	−1.72536	+	1.72536i	−0.0712134	+	0.0712134i	0.670603	+	0.741816i	$0.266035\pi$
$588$	9.19122	+	5.64757i	0.379039	+	0.232902i
$589$			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	0.647744	−	0.761858i	$-0.275713\pi$
$593$	−2.77888	−	2.77888i	−0.114115	−	0.114115i	−0.761858	+	0.647744i	$0.775713\pi$
$594$	−16.3660	+	13.8763i	−0.671507	+	0.569353i
$595$	−6.12057	−	3.29336i	−0.250919	−	0.135015i
$596$		−	6.11984i		−	0.250678i
$597$	−2.74218	+	4.46280i	−0.112230	+	0.182650i
$598$	−0.734549	+	0.734549i	−0.0300379	+	0.0300379i
$599$	37.0107			1.51222			0.756108	−	0.654447i	$-0.227098\pi$
$599$	37.0107			1.51222			0.756108	+	0.654447i	$0.227098\pi$
$600$	−5.92134	+	6.31963i	−0.241738	+	0.257998i
$601$	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
$603$	−14.3020	+	43.6601i	−0.582421	+	1.77798i
$604$		−	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
$612$	3.30433	−	10.0873i	0.133570	−	0.407753i
$613$	−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
$615$	5.93583	−	3.44745i	0.239356	−	0.139014i
$616$	3.62763			0.146161
$617$	−3.87788	+	3.87788i	−0.156118	+	0.156118i	−0.780844	−	0.624726i	$-0.785211\pi$
$617$	−3.87788	+	3.87788i	−0.156118	+	0.156118i	0.624726	+	0.780844i	$0.285211\pi$
$618$	−4.32911	+	7.04547i	−0.174142	+	0.283410i
$619$		−	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
$627$	48.0273	+	29.5105i	1.91802	+	1.17854i
$628$	−9.56563	+	9.56563i	−0.381710	+	0.381710i
$629$	−32.3539			−1.29003
$630$	0.146174	−	5.89128i	0.00582372	−	0.234714i
$631$	−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
$633$	28.4966	+	17.5098i	1.13264	+	0.695952i
$634$		−	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	$0.0171691\pi$
$641$			2.72989i			0.107824i	−0.998546	+	0.0539121i	$0.982831\pi$
$642$	−3.07514	+	5.00468i	−0.121366	+	0.197519i
$643$	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
$645$	33.4291	+	8.86517i	1.31627	+	0.349066i
$646$	−27.8857			−1.09715
$647$	9.72994	−	9.72994i	0.382523	−	0.382523i	−0.489487	−	0.872011i	$-0.662816\pi$
$647$	9.72994	−	9.72994i	0.382523	−	0.382523i	0.872011	+	0.489487i	$0.162816\pi$
$648$	8.89585	−	1.36523i	0.349462	−	0.0536313i
$649$		−	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	0.989295	−	0.145928i	$-0.0466169\pi$
$653$	21.5513	+	21.5513i	0.843367	+	0.843367i	−0.145928	+	0.989295i	$0.546617\pi$
$654$	0.213994	+	0.896084i	0.00836782	+	0.0350396i
$655$	2.84737	−	5.29172i	0.111256	−	0.206765i
$656$		−	1.77236i		−	0.0691991i
$657$	−34.2199	−	11.2096i	−1.33504	−	0.437327i
$658$	−0.0246052	+	0.0246052i	−0.000959211	+	0.000959211i
$659$	44.3615			1.72808			0.864039	−	0.503425i	$-0.167927\pi$
$659$	44.3615			1.72808			0.864039	+	0.503425i	$0.167927\pi$
$660$	8.03214	+	13.8298i	0.312651	+	0.538323i
$661$	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
$663$	3.33285	−	5.42410i	0.129437	−	0.210655i
$664$		−	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
$672$	−1.29641	−	0.796585i	−0.0500103	−	0.0307289i
$673$	−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
$675$	22.7832	−	12.4869i	0.876927	−	0.480623i
$676$	11.9209			0.458495
$677$	−8.39686	+	8.39686i	−0.322718	+	0.322718i	−0.849809	−	0.527091i	$-0.823283\pi$
$677$	−8.39686	+	8.39686i	−0.322718	+	0.322718i	0.527091	+	0.849809i	$0.323283\pi$
$678$	8.65529	+	5.31826i	0.332404	+	0.204247i
$679$		−	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	0.944396	−	0.328811i	$-0.106648\pi$
$683$	16.0879	+	16.0879i	0.615584	+	0.615584i	−0.328811	+	0.944396i	$0.606648\pi$
$684$	−10.6835	−	21.0925i	−0.408492	−	0.806490i
$685$	−11.3845	+	3.41903i	−0.434981	+	0.130634i
$686$			11.6209i			0.443688i
$687$	−8.00744	+	13.0318i	−0.305503	+	0.497196i
$688$	6.31426	−	6.31426i	0.240729	−	0.240729i
$689$	14.3549			0.546880
$690$	−1.94512	−	3.34911i	−0.0740493	−	0.127498i
$691$	−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
$693$	−10.3421	−	3.38783i	−0.392865	−	0.128693i
$694$		−	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	$-0.830930\pi$
$701$		−	26.8220i		−	1.01305i	0.862225	−	0.506526i	$-0.169070\pi$
$702$	5.37961	+	0.442875i	0.203040	+	0.0167152i
$703$	−50.9590	+	50.9590i	−1.92196	+	1.92196i
$704$	4.12939			0.155632
$705$	−0.148283	−	0.0393238i	−0.00558467	−	0.00148102i
$706$	17.2394			0.648813
$707$	0.846263	−	0.846263i	0.0318270	−	0.0318270i
$708$	−9.94085	+	16.1784i	−0.373600	+	0.608021i
$709$		−	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
$717$	7.81796	+	4.80376i	0.291967	+	0.179400i
$718$	−5.06500	+	5.06500i	−0.189024	+	0.189024i
$719$	−34.9727			−1.30426			−0.652130	−	0.758107i	$-0.726125\pi$
$719$	−34.9727			−1.30426			−0.652130	+	0.758107i	$0.726125\pi$
$720$	0.166392	−	6.70614i	0.00620108	−	0.249923i
$721$	−4.19412			−0.156197
$722$	−30.4864	+	30.4864i	−1.13459	+	1.13459i
$723$	−4.78606	−	2.94081i	−0.177996	−	0.109370i
$724$		−	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
$732$	−10.0507	+	16.3571i	−0.371484	+	0.604577i
$733$	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
$735$	−20.8591	+	12.1147i	−0.769399	+	0.446856i
$736$	−1.00000			−0.0368605
$737$	44.7165	−	44.7165i	1.64715	−	1.64715i
$738$	−1.65520	+	5.05289i	−0.0609288	+	0.185999i
$739$			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	0.789212	−	0.614121i	$-0.210489\pi$
$743$	4.77261	+	4.77261i	0.175090	+	0.175090i	−0.614121	+	0.789212i	$0.710489\pi$
$744$	−2.84570	−	11.9162i	−0.104328	−	0.436867i
$745$	12.0506	+	6.48420i	0.441500	+	0.237563i
$746$			4.06268i			0.148745i
$747$	−2.92251	+	8.92166i	−0.106929	+	0.326427i
$748$	−10.3313	+	10.3313i	−0.377751	+	0.377751i
$749$	−2.97925			−0.108859
$750$	−6.17014	−	18.3556i	−0.225302	−	0.670253i
$751$	−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
$753$	16.0125	−	26.0598i	0.583528	−	0.949671i
$754$			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	$-0.938935\pi$
$761$		−	10.5196i		−	0.381334i	0.981655	−	0.190667i	$-0.0610650\pi$
$762$	−17.4082	−	10.6965i	−0.630632	−	0.387493i
$763$	−0.330410	+	0.330410i	−0.0119617	+	0.0119617i
$764$	−10.6239			−0.384359
$765$	16.3618	+	17.1944i	0.591563	+	0.621666i
$766$	−22.3463			−0.807405
$767$	−8.05284	+	8.05284i	−0.290771	+	0.290771i
$768$	−1.47573	−	0.906765i	−0.0532508	−	0.0327201i
$769$		−	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	0.823459	−	0.567375i	$-0.192041\pi$
$773$	7.11987	+	7.11987i	0.256084	+	0.256084i	−0.567375	+	0.823459i	$0.692041\pi$
$774$	−23.8984	+	12.1047i	−0.859010	+	0.435094i
$775$	−19.4851	−	29.5145i	−0.699926	−	1.06019i
$776$		−	16.7225i		−	0.600303i
$777$	7.28404	−	11.8545i	0.261314	−	0.425279i
$778$	−0.954967	+	0.954967i	−0.0342372	+	0.0342372i
$779$	13.9684			0.500471
$780$	1.03130	−	3.88886i	0.0369265	−	0.139244i
$781$	9.31623			0.333361
$782$	2.50190	−	2.50190i	0.0894679	−	0.0894679i
$783$	3.34158	−	40.5902i	0.119418	−	1.45058i
$784$			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
$792$	−11.7726	−	3.85642i	−0.418322	−	0.137032i
$793$	−8.14181	+	8.14181i	−0.289124	+	0.289124i
$794$	−7.08495			−0.251435
$795$	−13.7188	+	51.7313i	−0.486555	+	1.83472i
$796$	−3.02413			−0.107188
$797$	13.4137	−	13.4137i	0.475136	−	0.475136i	−0.428436	−	0.903572i	$-0.640935\pi$
$797$	13.4137	−	13.4137i	0.475136	−	0.475136i	0.903572	+	0.428436i	$0.140935\pi$
$798$	6.27809	−	10.2174i	0.222242	−	0.361691i
$799$		−	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
$807$	−15.4645	−	9.50218i	−0.544375	−	0.334492i
$808$	0.963314	−	0.963314i	0.0338893	−	0.0338893i
$809$	−38.5121			−1.35401			−0.677007	−	0.735977i	$-0.736723\pi$
$809$	−38.5121			−1.35401			−0.677007	+	0.735977i	$0.736723\pi$
$810$	−6.73721	+	18.9634i	−0.236721	+	0.666305i
$811$	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
$813$	22.7636	+	13.9871i	0.798354	+	0.490551i
$814$			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	$-0.993211\pi$
$821$		−	1.22214i		−	0.0426530i	0.999773	−	0.0213265i	$-0.00678895\pi$
$822$	4.82034	−	7.84493i	0.168129	−	0.273623i
$823$	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
$825$	−35.7426	+	1.16297i	−1.24440	+	0.0404894i
$826$	−9.63087			−0.335101
$827$	25.7734	−	25.7734i	0.896227	−	0.896227i	−0.0988727	−	0.995100i	$-0.531524\pi$
$827$	25.7734	−	25.7734i	0.896227	−	0.896227i	0.995100	+	0.0988727i	$0.0315237\pi$
$828$	2.85094	+	0.933895i	0.0990769	+	0.0324551i
$829$		−	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
$837$	−3.01554	+	36.6298i	−0.104232	+	1.26611i
$838$	20.1049	−	20.1049i	0.694514	−	0.694514i
$839$	0.301061			0.0103938			0.00519690	−	0.999986i	$-0.498346\pi$
$839$	0.301061			0.0103938			0.00519690	+	0.999986i	$0.498346\pi$
$840$	2.94216	−	1.70877i	0.101514	−	0.0589580i
$841$	32.4346			1.11843
$842$	16.9824	−	16.9824i	0.585252	−	0.585252i
$843$	21.8337	−	35.5336i	0.751993	−	1.22384i
$844$			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
$852$	−3.32936	−	2.04574i	−0.114062	−	0.0700857i
$853$	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
$855$	52.8528	+	1.31138i	1.80753	+	0.0448483i
$856$	−3.39132			−0.115913
$857$	−4.73782	+	4.73782i	−0.161841	+	0.161841i	−0.783382	−	0.621541i	$-0.786507\pi$
$857$	−4.73782	+	4.73782i	−0.161841	+	0.161841i	0.621541	+	0.783382i	$0.286507\pi$
$858$	−6.33035	−	3.88970i	−0.216115	−	0.132792i
$859$			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	0.489090	−	0.872234i	$-0.337329\pi$
$863$	−11.2556	−	11.2556i	−0.383144	−	0.383144i	−0.872234	+	0.489090i	$0.837329\pi$
$864$	3.36039	+	3.96331i	0.114323	+	0.134834i
$865$	9.48585	+	31.5856i	0.322529	+	1.07394i
$866$		−	14.3670i		−	0.488212i
$867$	4.06316	−	6.61266i	0.137992	−	0.224578i
$868$	4.39381	−	4.39381i	0.149136	−	0.149136i
$869$	−8.18503			−0.277658
$870$	−29.3423	−	7.78138i	−0.994796	−	0.263813i
$871$	−15.9086			−0.539043
$872$	−0.376112	+	0.376112i	−0.0127367	+	0.0127367i
$873$	−15.6171	+	47.6748i	−0.528558	+	1.61355i
$874$		−	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	$-0.691196\pi$
$881$		−	48.9725i		−	1.64992i	0.565188	−	0.824962i	$-0.308804\pi$
$882$	5.81654	−	17.7564i	0.195853	−	0.597888i
$883$	−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
$885$	−21.3243	−	36.7162i	−0.716807	−	1.23420i
$886$	−10.7135			−0.359927
$887$	35.8940	−	35.8940i	1.20520	−	1.20520i	0.232638	−	0.972563i	$-0.425264\pi$
$887$	35.8940	−	35.8940i	1.20520	−	1.20520i	0.972563	−	0.232638i	$-0.0747358\pi$
$888$	8.29154	−	13.4942i	0.278246	−	0.452836i
$889$		−	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
$897$	1.53300	+	0.941956i	0.0511854	+	0.0314510i
$898$	−22.3903	+	22.3903i	−0.747174	+	0.747174i
$899$	−55.4403			−1.84904
$900$	13.0288	+	7.43305i	0.434293	+	0.247768i
$901$	−48.8936			−1.62888
$902$	5.17515	−	5.17515i	0.172314	−	0.172314i
$903$	−11.5766	−	7.11327i	−0.385245	−	0.236715i
$904$			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	$0.225508\pi$
$911$			39.2776i			1.30132i	−0.759368	+	0.650662i	$0.774492\pi$
$912$	7.14645	−	11.6306i	0.236643	−	0.385128i
$913$	9.13753	−	9.13753i	0.302408	−	0.302408i
$914$	−38.4890			−1.27310
$915$	−21.5598	−	37.1218i	−0.712746	−	1.22721i
$916$	−8.83078			−0.291777
$917$	−1.66936	+	1.66936i	−0.0551271	+	0.0551271i
$918$	−18.3232	−	1.50845i	−0.604755	−	0.0497863i
$919$		−	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
$927$	13.6110	+	4.45863i	0.447045	+	0.146441i
$928$	−5.54232	+	5.54232i	−0.181936	+	0.181936i
$929$	−7.70924			−0.252932			−0.126466	−	0.991971i	$-0.540363\pi$
$929$	−7.70924			−0.252932			−0.126466	+	0.991971i	$0.540363\pi$
$930$	26.4793	+	7.02213i	0.868290	+	0.230265i
$931$	−49.0865			−1.60874
$932$	−13.3537	+	13.3537i	−0.437416	+	0.437416i
$933$	−1.40480	+	2.28626i	−0.0459911	+	0.0748489i
$934$		−	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	$-0.899421\pi$
$941$		−	19.0647i		−	0.621492i	0.950493	−	0.310746i	$-0.100579\pi$
$942$	19.9634	+	12.2666i	0.650444	+	0.399667i
$943$	−1.25325	+	1.25325i	−0.0408114	+	0.0408114i
$944$	−10.9630			−0.356815
$945$	−9.98372	+	2.12391i	−0.324770	+	0.0690909i
$946$	36.8742			1.19888
$947$	16.0189	−	16.0189i	0.520543	−	0.520543i	−0.397192	−	0.917735i	$-0.630015\pi$
$947$	16.0189	−	16.0189i	0.520543	−	0.520543i	0.917735	+	0.397192i	$0.130015\pi$
$948$	2.92510	+	1.79734i	0.0950029	+	0.0583748i
$949$		−	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	0.976990	−	0.213286i	$-0.0684166\pi$
$953$	23.5761	+	23.5761i	0.763704	+	0.763704i	−0.213286	+	0.976990i	$0.568417\pi$
$954$	−18.7319	−	36.9826i	−0.606468	−	1.19736i
$955$	11.2564	−	20.9196i	0.364249	−	0.676941i
$956$			5.29769i			0.171340i
$957$	−29.3486	+	47.7638i	−0.948705	+	1.54398i
$958$	−7.17891	+	7.17891i	−0.231940	+	0.231940i
$959$	4.67003			0.150803
$960$	3.34911	−	1.94512i	0.108092	−	0.0627783i
$961$	19.0309			0.613899
$962$	6.71678	−	6.71678i	0.216558	−	0.216558i
$963$	9.66845	+	3.16714i	0.311561	+	0.102060i
$964$		−	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	$-0.591274\pi$
$971$		−	59.7771i		−	1.91834i	0.282833	−	0.959169i	$-0.408726\pi$
$972$	−5.87893	−	14.4374i	−0.188567	−	0.463079i
$973$	12.9088	−	12.9088i	0.413836	−	0.413836i
$974$	9.21274			0.295195
$975$	6.56489	+	6.15114i	0.210245	+	0.196994i
$976$	−11.0841			−0.354793
$977$	−1.55002	+	1.55002i	−0.0495896	+	0.0495896i	−0.731467	−	0.681877i	$-0.761164\pi$
$977$	−1.55002	+	1.55002i	−0.0495896	+	0.0495896i	0.681877	+	0.731467i	$0.261164\pi$
$978$	−1.66805	+	2.71470i	−0.0533384	+	0.0868064i
$979$		−	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	0.618565	−	0.785733i	$-0.287714\pi$
$983$	−5.24119	−	5.24119i	−0.167168	−	0.167168i	−0.785733	+	0.618565i	$0.787714\pi$
$984$	−2.98586	+	0.713053i	−0.0951857	+	0.0227313i
$985$	−31.7236	+	9.52730i	−1.01080	+	0.303565i
$986$		−	27.7327i		−	0.883189i
$987$	0.0513510	+	0.0315527i	0.00163452	+	0.00100434i
$988$	5.78917	−	5.78917i	0.184178	−	0.184178i
$989$	−8.92971			−0.283948
$990$	20.0672	−	19.0955i	0.637779	−	0.606896i
$991$	−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
$993$	14.3004	+	8.78692i	0.453810	+	0.278845i
$994$		−	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.47.9	yes	32
3.2	odd	2	inner	690.2.i.f.47.6	✓	32
5.3	odd	4	inner	690.2.i.f.323.6	yes	32
15.8	even	4	inner	690.2.i.f.323.9	yes	32

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) q^{3} -1.00000i q^{4} +(1.96911 + 1.05954i) q^{5} +(-1.68468 + 0.402318i) q^{6} +(-0.621187 - 0.621187i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.35555 + 2.67628i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.47573 - 0.906765i) 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} +(-0.906765 + 1.47573i) q^{12} +(-0.734549 + 0.734549i) q^{13} -0.878491 q^{14} +(-1.94512 - 3.34911i) q^{15} -1.00000 q^{16} +(2.50190 - 2.50190i) q^{17} +(2.85094 + 0.933895i) 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} +(0.426330 - 5.17863i) q^{27} +(-0.621187 + 0.621187i) q^{28} +7.83802 q^{29} +(-3.74358 - 0.992773i) q^{30} -7.07325 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.74439 + 6.09386i) 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} +(1.29641 + 0.796585i) q^{42} +(-6.31426 + 6.31426i) q^{43} -4.12939 q^{44} +(-0.166392 + 6.70614i) q^{45} +1.00000 q^{46} +(0.0280085 - 0.0280085i) q^{47} +(1.47573 + 0.906765i) 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} +(-7.14645 + 11.6306i) q^{57} +(5.54232 - 5.54232i) q^{58} +10.9630 q^{59} +(-3.34911 + 1.94512i) q^{60} +11.0841 q^{61} +(-5.00154 + 5.00154i) q^{62} +(0.820418 - 2.50452i) 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} +(0.933895 - 2.85094i) q^{72} +(-8.48742 + 8.48742i) q^{73} -9.14409 q^{74} +(-0.281632 - 8.65567i) q^{75} -7.88126 q^{76} +(-2.56512 + 2.56512i) q^{77} +(0.941956 - 1.53300i) 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} +(-11.5668 - 7.10725i) q^{87} +(-2.91992 + 2.91992i) q^{88} +6.08809 q^{89} +(4.62430 + 4.85961i) q^{90} +0.912584 q^{91} +(0.707107 - 0.707107i) q^{92} +(10.4382 + 6.41378i) 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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