LMFDB - Embedded newform 483.2.i.h.415.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.6
Root			$-0.0131282 - 0.0227388i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0131282 - 0.0227388i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.999655 + 1.73145i) q^{4} +(-1.38914 + 2.40606i) q^{5} +0.0262565 q^{6} +(-2.58821 - 0.548771i) q^{7} +0.105008 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0131282 - 0.0227388i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.999655 + 1.73145i) q^{4} +(-1.38914 + 2.40606i) q^{5} +0.0262565 q^{6} +(-2.58821 - 0.548771i) q^{7} +0.105008 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0364740 + 0.0631748i) q^{10} +(-0.330078 - 0.571712i) q^{11} +(-0.999655 + 1.73145i) q^{12} +4.12488 q^{13} +(-0.0464571 + 0.0516484i) q^{14} -2.77828 q^{15} +(-1.99793 + 3.46052i) q^{16} +(-2.06190 - 3.57132i) q^{17} +(0.0131282 + 0.0227388i) q^{18} +(-2.38414 + 4.12946i) q^{19} -5.55465 q^{20} +(-0.818857 - 2.51584i) q^{21} -0.0173334 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.0525039 + 0.0909395i) q^{24} +(-1.35943 - 2.35460i) q^{25} +(0.0541524 - 0.0937947i) q^{26} -1.00000 q^{27} +(-1.63715 - 5.02995i) q^{28} -1.78025 q^{29} +(-0.0364740 + 0.0631748i) q^{30} +(1.81214 + 3.13872i) q^{31} +(0.157467 + 0.272740i) q^{32} +(0.330078 - 0.571712i) q^{33} -0.108277 q^{34} +(4.91577 - 5.46509i) q^{35} -1.99931 q^{36} +(4.03105 - 6.98199i) q^{37} +(0.0625993 + 0.108425i) q^{38} +(2.06244 + 3.57225i) q^{39} +(-0.145871 + 0.252656i) q^{40} -7.99969 q^{41} +(-0.0679574 - 0.0144088i) q^{42} +12.5842 q^{43} +(0.659929 - 1.14303i) q^{44} +(-1.38914 - 2.40606i) q^{45} +(0.0131282 + 0.0227388i) q^{46} +(-5.88109 + 10.1864i) q^{47} -3.99586 q^{48} +(6.39770 + 2.84067i) q^{49} -0.0713876 q^{50} +(2.06190 - 3.57132i) q^{51} +(4.12346 + 7.14203i) q^{52} +(0.0304128 + 0.0526766i) q^{53} +(-0.0131282 + 0.0227388i) q^{54} +1.83410 q^{55} +(-0.271783 - 0.0576253i) q^{56} -4.76829 q^{57} +(-0.0233715 + 0.0404806i) q^{58} +(4.49359 + 7.78312i) q^{59} +(-2.77732 - 4.81047i) q^{60} +(-1.35633 + 2.34924i) q^{61} +0.0951611 q^{62} +(1.76936 - 1.96707i) q^{63} -7.98346 q^{64} +(-5.73004 + 9.92471i) q^{65} +(-0.00866669 - 0.0150112i) q^{66} +(1.34291 + 2.32600i) q^{67} +(4.12239 - 7.14018i) q^{68} -1.00000 q^{69} +(-0.0597339 - 0.183526i) q^{70} +12.4462 q^{71} +(-0.0525039 + 0.0909395i) q^{72} +(7.14354 + 12.3730i) q^{73} +(-0.105841 - 0.183323i) q^{74} +(1.35943 - 2.35460i) q^{75} -9.53329 q^{76} +(0.540574 + 1.66085i) q^{77} +0.108305 q^{78} +(3.47399 - 6.01712i) q^{79} +(-5.55082 - 9.61430i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.105022 + 0.181903i) q^{82} +9.40856 q^{83} +(3.53749 - 3.93279i) q^{84} +11.4571 q^{85} +(0.165208 - 0.286150i) q^{86} +(-0.890123 - 1.54174i) q^{87} +(-0.0346608 - 0.0600343i) q^{88} +(2.96215 - 5.13060i) q^{89} -0.0729480 q^{90} +(-10.6761 - 2.26361i) q^{91} -1.99931 q^{92} +(-1.81214 + 3.13872i) q^{93} +(0.154417 + 0.267458i) q^{94} +(-6.62383 - 11.4728i) q^{95} +(-0.157467 + 0.272740i) q^{96} +2.53740 q^{97} +(0.148584 - 0.108183i) q^{98} +0.660156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.0131282	−	0.0227388i	0.00928307	−	0.0160788i	−0.861347	−	0.508018i	$-0.830378\pi$
$2$	0.0131282	−	0.0227388i	0.00928307	−	0.0160788i	0.870630	+	0.491939i	$0.163712\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.999655	+	1.73145i	0.499828	+	0.865727i
$5$	−1.38914	+	2.40606i	−0.621243	+	1.07602i	0.368012	+	0.929821i	$0.380039\pi$
$5$	−1.38914	+	2.40606i	−0.621243	+	1.07602i	−0.989255	+	0.146203i	$0.953295\pi$
$6$	0.0262565			0.0107192
$7$	−2.58821	−	0.548771i	−0.978253	−	0.207416i
$7$	−2.58821	−	0.548771i	−0.978253	−	0.207416i
$8$	0.105008			0.0371259
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0364740	+	0.0631748i	0.0115341	+	0.0199776i
$11$	−0.330078	−	0.571712i	−0.0995223	−	0.172378i	0.811965	−	0.583706i	$-0.198398\pi$
$11$	−0.330078	−	0.571712i	−0.0995223	−	0.172378i	−0.911487	+	0.411329i	$0.865065\pi$
$12$	−0.999655	+	1.73145i	−0.288576	+	0.499828i
$13$	4.12488			1.14404			0.572018	−	0.820241i	$-0.306161\pi$
$13$	4.12488			1.14404			0.572018	+	0.820241i	$0.306161\pi$
$14$	−0.0464571	+	0.0516484i	−0.0124162	+	0.0138036i
$15$	−2.77828			−0.717349
$16$	−1.99793	+	3.46052i	−0.499483	+	0.865130i
$17$	−2.06190	−	3.57132i	−0.500085	−	0.866173i	−1.00000		9.81912e-5i	$-0.999969\pi$
$17$	−2.06190	−	3.57132i	−0.500085	−	0.866173i	0.499915	−	0.866074i	$-0.333365\pi$
$18$	0.0131282	+	0.0227388i	0.00309436	+	0.00535958i
$19$	−2.38414	+	4.12946i	−0.546960	+	0.947363i	0.451520	+	0.892261i	$0.350882\pi$
$19$	−2.38414	+	4.12946i	−0.546960	+	0.947363i	−0.998481	+	0.0551022i	$0.982452\pi$
$20$	−5.55465			−1.24206
$21$	−0.818857	−	2.51584i	−0.178689	−	0.549002i
$22$	−0.0173334			−0.00369549
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	0.0525039	+	0.0909395i	0.0107173	+	0.0185629i
$25$	−1.35943	−	2.35460i	−0.271885	−	0.470919i
$26$	0.0541524	−	0.0937947i	0.0106202	−	0.0183947i
$27$	−1.00000			−0.192450
$28$	−1.63715	−	5.02995i	−0.309392	−	0.950572i
$29$	−1.78025			−0.330583			−0.165292	−	0.986245i	$-0.552857\pi$
$29$	−1.78025			−0.330583			−0.165292	+	0.986245i	$0.552857\pi$
$30$	−0.0364740	+	0.0631748i	−0.00665921	+	0.0115341i
$31$	1.81214	+	3.13872i	0.325471	+	0.563732i	0.981607	−	0.190910i	$-0.0611440\pi$
$31$	1.81214	+	3.13872i	0.325471	+	0.563732i	−0.656137	+	0.754642i	$0.727811\pi$
$32$	0.157467	+	0.272740i	0.0278364	+	0.0482141i
$33$	0.330078	−	0.571712i	0.0574592	−	0.0995223i
$34$	−0.108277			−0.0185693
$35$	4.91577	−	5.46509i	0.830917	−	0.923768i
$36$	−1.99931			−0.333218
$37$	4.03105	−	6.98199i	0.662701	−	1.14783i	−0.317202	−	0.948358i	$-0.602743\pi$
$37$	4.03105	−	6.98199i	0.662701	−	1.14783i	0.979903	−	0.199474i	$-0.0639233\pi$
$38$	0.0625993	+	0.108425i	0.0101549	+	0.0175889i
$39$	2.06244	+	3.57225i	0.330254	+	0.572018i
$40$	−0.145871	+	0.252656i	−0.0230642	+	0.0399484i
$41$	−7.99969			−1.24934			−0.624671	−	0.780888i	$-0.714767\pi$
$41$	−7.99969			−1.24934			−0.624671	+	0.780888i	$0.714767\pi$
$42$	−0.0679574	−	0.0144088i	−0.0104861	−	0.00222333i
$43$	12.5842			1.91907			0.959536	−	0.281585i	$-0.0908601\pi$
$43$	12.5842			1.91907			0.959536	+	0.281585i	$0.0908601\pi$
$44$	0.659929	−	1.14303i	0.0994880	−	0.172318i
$45$	−1.38914	−	2.40606i	−0.207081	−	0.358675i
$46$	0.0131282	+	0.0227388i	0.00193565	+	0.00335265i
$47$	−5.88109	+	10.1864i	−0.857846	+	1.48583i	0.0161343	+	0.999870i	$0.494864\pi$
$47$	−5.88109	+	10.1864i	−0.857846	+	1.48583i	−0.873980	+	0.485962i	$0.838469\pi$
$48$	−3.99586			−0.576753
$49$	6.39770	+	2.84067i	0.913957	+	0.405811i
$50$	−0.0713876			−0.0100957
$51$	2.06190	−	3.57132i	0.288724	−	0.500085i
$52$	4.12346	+	7.14203i	0.571820	+	0.990422i
$53$	0.0304128	+	0.0526766i	0.00417752	+	0.00723568i	0.868107	−	0.496378i	$-0.165337\pi$
$53$	0.0304128	+	0.0526766i	0.00417752	+	0.00723568i	−0.863929	+	0.503613i	$0.832004\pi$
$54$	−0.0131282	+	0.0227388i	−0.00178653	+	0.00309436i
$55$	1.83410			0.247310
$56$	−0.271783	−	0.0576253i	−0.0363185	−	0.00770050i
$57$	−4.76829			−0.631575
$58$	−0.0233715	+	0.0404806i	−0.00306883	+	0.00531537i
$59$	4.49359	+	7.78312i	0.585015	+	1.01328i	0.994874	+	0.101127i	$0.0322447\pi$
$59$	4.49359	+	7.78312i	0.585015	+	1.01328i	−0.409859	+	0.912149i	$0.634422\pi$
$60$	−2.77732	−	4.81047i	−0.358551	−	0.621029i
$61$	−1.35633	+	2.34924i	−0.173661	+	0.300789i	−0.939697	−	0.342008i	$-0.888893\pi$
$61$	−1.35633	+	2.34924i	−0.173661	+	0.300789i	0.766036	+	0.642797i	$0.222226\pi$
$62$	0.0951611			0.0120855
$63$	1.76936	−	1.96707i	0.222918	−	0.247828i
$64$	−7.98346			−0.997932
$65$	−5.73004	+	9.92471i	−0.710724	+	1.23101i
$66$	−0.00866669	−	0.0150112i	−0.00106680	−	0.00184774i
$67$	1.34291	+	2.32600i	0.164063	+	0.284166i	0.936322	−	0.351142i	$-0.114207\pi$
$67$	1.34291	+	2.32600i	0.164063	+	0.284166i	−0.772259	+	0.635308i	$0.780873\pi$
$68$	4.12239	−	7.14018i	0.499913	−	0.865874i
$69$	−1.00000			−0.120386
$70$	−0.0597339	−	0.183526i	−0.00713957	−	0.0219355i
$71$	12.4462			1.47709			0.738545	−	0.674205i	$-0.235513\pi$
$71$	12.4462			1.47709			0.738545	+	0.674205i	$0.235513\pi$
$72$	−0.0525039	+	0.0909395i	−0.00618765	+	0.0107173i
$73$	7.14354	+	12.3730i	0.836088	+	1.44815i	0.893142	+	0.449775i	$0.148496\pi$
$73$	7.14354	+	12.3730i	0.836088	+	1.44815i	−0.0570543	+	0.998371i	$0.518171\pi$
$74$	−0.105841	−	0.183323i	−0.0123038	−	0.0213108i
$75$	1.35943	−	2.35460i	0.156973	−	0.271885i
$76$	−9.53329			−1.09354
$77$	0.540574	+	1.66085i	0.0616041	+	0.189271i
$78$	0.108305			0.0122631
$79$	3.47399	−	6.01712i	0.390854	−	0.676979i	−0.601708	−	0.798716i	$-0.705513\pi$
$79$	3.47399	−	6.01712i	0.390854	−	0.676979i	0.992562	+	0.121737i	$0.0388464\pi$
$80$	−5.55082	−	9.61430i	−0.620600	−	1.07491i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.105022	+	0.181903i	−0.0115977	+	0.0200879i
$83$	9.40856			1.03272			0.516362	−	0.856371i	$-0.327286\pi$
$83$	9.40856			1.03272			0.516362	+	0.856371i	$0.327286\pi$
$84$	3.53749	−	3.93279i	0.385972	−	0.429103i
$85$	11.4571			1.24270
$86$	0.165208	−	0.286150i	0.0178149	−	0.0308563i
$87$	−0.890123	−	1.54174i	−0.0954312	−	0.165292i
$88$	−0.0346608	−	0.0600343i	−0.00369485	−	0.00639967i
$89$	2.96215	−	5.13060i	0.313987	−	0.543842i	−0.665234	−	0.746635i	$-0.731668\pi$
$89$	2.96215	−	5.13060i	0.313987	−	0.543842i	0.979222	+	0.202793i	$0.0650017\pi$
$90$	−0.0729480			−0.00768939
$91$	−10.6761	−	2.26361i	−1.11916	−	0.237291i
$92$	−1.99931			−0.208443
$93$	−1.81214	+	3.13872i	−0.187911	+	0.325471i
$94$	0.154417	+	0.267458i	0.0159269	+	0.0275862i
$95$	−6.62383	−	11.4728i	−0.679590	−	1.17708i
$96$	−0.157467	+	0.272740i	−0.0160714	+	0.0278364i
$97$	2.53740			0.257634			0.128817	−	0.991668i	$-0.458882\pi$
$97$	2.53740			0.257634			0.128817	+	0.991668i	$0.458882\pi$
$98$	0.148584	−	0.108183i	0.0150093	−	0.0109281i
$99$	0.660156			0.0663482
$100$	2.71792	−	4.70757i	0.271792	−	0.470757i
$101$	−3.35589	−	5.81257i	−0.333923	−	0.578372i	0.649354	−	0.760486i	$-0.275039\pi$
$101$	−3.35589	−	5.81257i	−0.333923	−	0.578372i	−0.983277	+	0.182114i	$0.941706\pi$
$102$	−0.0541384	−	0.0937704i	−0.00536050	−	0.00928465i
$103$	−5.37391	+	9.30788i	−0.529507	+	0.917132i	0.469901	+	0.882719i	$0.344290\pi$
$103$	−5.37391	+	9.30788i	−0.529507	+	0.917132i	−0.999408	+	0.0344133i	$0.989044\pi$
$104$	0.433145			0.0424733
$105$	7.19079	+	1.52464i	0.701749	+	0.148790i
$106$	0.00159707			0.000155121
$107$	0.242278	−	0.419638i	0.0234219	−	0.0405679i	−0.854077	−	0.520147i	$-0.825877\pi$
$107$	0.242278	−	0.419638i	0.0234219	−	0.0405679i	0.877499	+	0.479579i	$0.159211\pi$
$108$	−0.999655	−	1.73145i	−0.0961919	−	0.166609i
$109$	−6.23260	−	10.7952i	−0.596975	−	1.03399i	−0.993265	−	0.115866i	$-0.963036\pi$
$109$	−6.23260	−	10.7952i	−0.596975	−	1.03399i	0.396290	−	0.918126i	$-0.370298\pi$
$110$	0.0240785	−	0.0417052i	0.00229580	−	0.00397644i
$111$	8.06211			0.765221
$112$	7.07011	−	7.86016i	0.668062	−	0.742715i
$113$	9.28875			0.873812			0.436906	−	0.899507i	$-0.356074\pi$
$113$	9.28875			0.873812			0.436906	+	0.899507i	$0.356074\pi$
$114$	−0.0625993	+	0.108425i	−0.00586296	+	0.0101549i
$115$	−1.38914	−	2.40606i	−0.129538	−	0.224367i
$116$	−1.77963	−	3.08241i	−0.165235	−	0.286195i
$117$	−2.06244	+	3.57225i	−0.190673	+	0.330254i
$118$	0.235972			0.0217229
$119$	3.37681	+	10.3749i	0.309552	+	0.951062i
$120$	−0.291742			−0.0266322
$121$	5.28210	−	9.14886i	0.480191	−	0.831715i
$122$	0.0356126	+	0.0616828i	0.00322421	+	0.00558450i
$123$	−3.99984	−	6.92793i	−0.360654	−	0.624671i
$124$	−3.62304	+	6.27529i	−0.325358	+	0.563537i
$125$	−6.33767			−0.566858
$126$	−0.0215003	−	0.0660573i	−0.00191540	−	0.00588485i
$127$	2.40074			0.213031			0.106515	−	0.994311i	$-0.466031\pi$
$127$	2.40074			0.213031			0.106515	+	0.994311i	$0.466031\pi$
$128$	−0.419742	+	0.727014i	−0.0371003	+	0.0642596i
$129$	6.29210	+	10.8982i	0.553989	+	0.959536i
$130$	0.150451	+	0.260588i	0.0131954	+	0.0228551i
$131$	10.0752	−	17.4508i	0.880278	−	1.52469i	0.0292458	−	0.999572i	$-0.490689\pi$
$131$	10.0752	−	17.4508i	0.880278	−	1.52469i	0.851032	−	0.525114i	$-0.175977\pi$
$132$	1.31986			0.114879
$133$	8.43680	−	9.37957i	0.731564	−	0.813312i
$134$	0.0705204			0.00609204
$135$	1.38914	−	2.40606i	0.119558	−	0.207081i
$136$	−0.216516	−	0.375017i	−0.0185661	−	0.0321574i
$137$	−3.50329	−	6.06788i	−0.299306	−	0.518414i	0.676671	−	0.736285i	$-0.263422\pi$
$137$	−3.50329	−	6.06788i	−0.299306	−	0.518414i	−0.975977	+	0.217872i	$0.930089\pi$
$138$	−0.0131282	+	0.0227388i	−0.00111755	+	0.00193565i
$139$	−2.88510			−0.244711			−0.122356	−	0.992486i	$-0.539045\pi$
$139$	−2.88510			−0.244711			−0.122356	+	0.992486i	$0.539045\pi$
$140$	14.3766	+	3.04823i	1.21505	+	0.257623i
$141$	−11.7622			−0.990555
$142$	0.163396	−	0.283011i	0.0137119	−	0.0237497i
$143$	−1.36153	−	2.35824i	−0.113857	−	0.197206i
$144$	−1.99793	−	3.46052i	−0.166494	−	0.288377i
$145$	2.47301	−	4.28338i	0.205373	−	0.355716i
$146$	0.375128			0.0310458
$147$	0.738754	+	6.96091i	0.0609314	+	0.574126i
$148$	16.1187			1.32495
$149$	−9.53041	+	16.5072i	−0.780762	+	1.35232i	0.150737	+	0.988574i	$0.451835\pi$
$149$	−9.53041	+	16.5072i	−0.780762	+	1.35232i	−0.931498	+	0.363745i	$0.881498\pi$
$150$	−0.0356938	−	0.0618234i	−0.00291438	−	0.00504786i
$151$	2.53145	+	4.38460i	0.206006	+	0.356813i	0.950453	−	0.310869i	$-0.100620\pi$
$151$	2.53145	+	4.38460i	0.206006	+	0.356813i	−0.744447	+	0.667682i	$0.767287\pi$
$152$	−0.250354	+	0.433626i	−0.0203064	+	0.0351717i
$153$	4.12381			0.333390
$154$	0.0448625	+	0.00951206i	0.00361512	+	0.000766504i
$155$	−10.0693			−0.808785
$156$	−4.12346	+	7.14203i	−0.330141	+	0.571820i
$157$	1.37194	+	2.37627i	0.109493	+	0.189647i	0.915565	−	0.402170i	$-0.131744\pi$
$157$	1.37194	+	2.37627i	0.109493	+	0.189647i	−0.806072	+	0.591817i	$0.798411\pi$
$158$	−0.0912147	−	0.157988i	−0.00725665	−	0.0125689i
$159$	−0.0304128	+	0.0526766i	−0.00241189	+	0.00417752i
$160$	−0.874973			−0.0691727
$161$	1.76936	−	1.96707i	0.139445	−	0.155027i
$162$	−0.0262565			−0.00206290
$163$	−7.65440	+	13.2578i	−0.599539	+	1.03843i	0.393350	+	0.919389i	$0.371316\pi$
$163$	−7.65440	+	13.2578i	−0.599539	+	1.03843i	−0.992889	+	0.119043i	$0.962017\pi$
$164$	−7.99693	−	13.8511i	−0.624455	−	1.08159i
$165$	0.917050	+	1.58838i	0.0713923	+	0.123655i
$166$	0.123518	−	0.213939i	0.00958685	−	0.0166049i
$167$	13.0016			1.00610			0.503049	−	0.864258i	$-0.332212\pi$
$167$	13.0016			1.00610			0.503049	+	0.864258i	$0.332212\pi$
$168$	−0.0859864	−	0.264183i	−0.00663400	−	0.0203822i
$169$	4.01461			0.308816
$170$	0.150412	−	0.260521i	0.0115360	−	0.0199810i
$171$	−2.38414	−	4.12946i	−0.182320	−	0.315788i
$172$	12.5799	+	21.7890i	0.959206	+	1.66139i
$173$	5.21101	−	9.02574i	0.396186	−	0.686214i	−0.597066	−	0.802192i	$-0.703667\pi$
$173$	5.21101	−	9.02574i	0.396186	−	0.686214i	0.993252	+	0.115978i	$0.0370002\pi$
$174$	−0.0467430			−0.00354358
$175$	2.22635	+	6.84021i	0.168296	+	0.517071i
$176$	2.63789			0.198839
$177$	−4.49359	+	7.78312i	−0.337759	+	0.585015i
$178$	−0.0777757	−	0.134711i	−0.00582953	−	0.0100971i
$179$	−9.61157	−	16.6477i	−0.718402	−	1.24431i	−0.961633	−	0.274341i	$-0.911540\pi$
$179$	−9.61157	−	16.6477i	−0.718402	−	1.24431i	0.243230	−	0.969969i	$-0.421793\pi$
$180$	2.77732	−	4.81047i	0.207010	−	0.358551i
$181$	−11.1552			−0.829162			−0.414581	−	0.910012i	$-0.636072\pi$
$181$	−11.1552			−0.829162			−0.414581	+	0.910012i	$0.636072\pi$
$182$	−0.191630	+	0.213043i	−0.0142045	+	0.0157918i
$183$	−2.71267			−0.200526
$184$	−0.0525039	+	0.0909395i	−0.00387064	+	0.00670415i
$185$	11.1994	+	19.3979i	0.823397	+	1.42616i
$186$	0.0475805	+	0.0824119i	0.00348877	+	0.00604273i
$187$	−1.36118	+	2.35763i	−0.0995392	+	0.172407i
$188$	−23.5163			−1.71510
$189$	2.58821	+	0.548771i	0.188265	+	0.0399172i
$190$	−0.347837			−0.0252347
$191$	−9.61731	+	16.6577i	−0.695884	+	1.20531i	0.273998	+	0.961730i	$0.411654\pi$
$191$	−9.61731	+	16.6577i	−0.695884	+	1.20531i	−0.969882	+	0.243576i	$0.921679\pi$
$192$	−3.99173	−	6.91388i	−0.288078	−	0.498966i
$193$	−8.72634	−	15.1145i	−0.628136	−	1.08796i	−0.987925	−	0.154930i	$-0.950485\pi$
$193$	−8.72634	−	15.1145i	−0.628136	−	1.08796i	0.359790	−	0.933033i	$-0.382849\pi$
$194$	0.0333116	−	0.0576974i	0.00239163	−	0.00414243i
$195$	−11.4601			−0.820673
$196$	1.47700	+	13.9170i	0.105500	+	0.994073i
$197$	−1.16239			−0.0828168			−0.0414084	−	0.999142i	$-0.513184\pi$
$197$	−1.16239			−0.0828168			−0.0414084	+	0.999142i	$0.513184\pi$
$198$	0.00866669	−	0.0150112i	0.000615915	−	0.00106680i
$199$	−8.48842	−	14.7024i	−0.601728	−	1.04222i	−0.992559	−	0.121761i	$-0.961146\pi$
$199$	−8.48842	−	14.7024i	−0.601728	−	1.04222i	0.390831	−	0.920462i	$-0.372188\pi$
$200$	−0.142751	−	0.247251i	−0.0100940	−	0.0174833i
$201$	−1.34291	+	2.32600i	−0.0947219	+	0.164063i
$202$	−0.176228			−0.0123993
$203$	4.60766	+	0.976948i	0.323394	+	0.0685683i
$204$	8.24477			0.577249
$205$	11.1127	−	19.2478i	0.776145	−	1.34432i
$206$	0.141100	+	0.244392i	0.00983090	+	0.0170276i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−8.24122	+	14.2742i	−0.571426	+	0.989739i
$209$	3.14782			0.217739
$210$	0.129071	−	0.143494i	0.00890674	−	0.00990202i
$211$	11.6924			0.804938			0.402469	−	0.915434i	$-0.368152\pi$
$211$	11.6924			0.804938			0.402469	+	0.915434i	$0.368152\pi$
$212$	−0.0608047	+	0.105317i	−0.00417608	+	0.00723319i
$213$	6.22309	+	10.7787i	0.426399	+	0.738545i
$214$	−0.00636137	−	0.0110182i	−0.000434854	−	0.000753189i
$215$	−17.4812	+	30.2784i	−1.19221	+	2.06497i
$216$	−0.105008			−0.00714488
$217$	−2.96777	−	9.11814i	−0.201466	−	0.618980i
$218$	−0.327293			−0.0221671
$219$	−7.14354	+	12.3730i	−0.482715	+	0.836088i
$220$	1.83347	+	3.17566i	0.123612	+	0.214103i
$221$	−8.50510	−	14.7313i	−0.572115	−	0.990932i
$222$	0.105841	−	0.183323i	0.00710360	−	0.0123038i
$223$	−15.5087			−1.03854			−0.519270	−	0.854610i	$-0.673796\pi$
$223$	−15.5087			−1.03854			−0.519270	+	0.854610i	$0.673796\pi$
$224$	−0.257885	−	0.792323i	−0.0172307	−	0.0529393i
$225$	2.71885			0.181257
$226$	0.121945	−	0.211215i	0.00811166	−	0.0140498i
$227$	7.66648	+	13.2787i	0.508842	+	0.881340i	0.999948	+	0.0102402i	$0.00325962\pi$
$227$	7.66648	+	13.2787i	0.508842	+	0.881340i	−0.491105	+	0.871100i	$0.663407\pi$
$228$	−4.76665	−	8.25607i	−0.315679	−	0.546772i
$229$	3.20242	−	5.54675i	0.211622	−	0.366540i	−0.740600	−	0.671946i	$-0.765459\pi$
$229$	3.20242	−	5.54675i	0.211622	−	0.366540i	0.952222	+	0.305406i	$0.0987922\pi$
$230$	−0.0729480			−0.00481005
$231$	−1.16805	+	1.29858i	−0.0768522	+	0.0854400i
$232$	−0.186940			−0.0122732
$233$	13.0715	−	22.6405i	0.856344	−	1.48323i	−0.0190487	−	0.999819i	$-0.506064\pi$
$233$	13.0715	−	22.6405i	0.856344	−	1.48323i	0.875393	−	0.483413i	$-0.160603\pi$
$234$	0.0541524	+	0.0937947i	0.00354005	+	0.00613155i
$235$	−16.3393	−	28.3006i	−1.06586	−	1.84613i
$236$	−8.98407	+	15.5609i	−0.584813	+	1.01293i
$237$	6.94797			0.451319
$238$	0.280243	+	0.0594191i	0.0181655	+	0.00385157i
$239$	17.6773			1.14345			0.571724	−	0.820446i	$-0.306275\pi$
$239$	17.6773			1.14345			0.571724	+	0.820446i	$0.306275\pi$
$240$	5.55082	−	9.61430i	0.358304	−	0.620600i
$241$	−2.87985	−	4.98804i	−0.185507	−	0.321308i	0.758240	−	0.651975i	$-0.226059\pi$
$241$	−2.87985	−	4.98804i	−0.185507	−	0.321308i	−0.943747	+	0.330668i	$0.892726\pi$
$242$	−0.138689	−	0.240217i	−0.00891529	−	0.0154417i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.42347			−0.347202
$245$	−15.7222	+	11.4472i	−1.00445	+	0.731333i
$246$	−0.210044			−0.0133919
$247$	−9.83430	+	17.0335i	−0.625742	+	1.08382i
$248$	0.190289	+	0.329591i	0.0120834	+	0.0209290i
$249$	4.70428	+	8.14805i	0.298122	+	0.516362i
$250$	−0.0832025	+	0.144111i	−0.00526219	+	0.00911438i
$251$	−10.3866			−0.655597			−0.327798	−	0.944748i	$-0.606307\pi$
$251$	−10.3866			−0.655597			−0.327798	+	0.944748i	$0.606307\pi$
$252$	5.17464	+	1.09716i	0.325972	+	0.0691148i
$253$	0.660156			0.0415037
$254$	0.0315175	−	0.0545898i	0.00197758	−	0.00342527i
$255$	5.72855	+	9.92214i	0.358736	+	0.621348i
$256$	−7.97244	−	13.8087i	−0.498277	−	0.863042i
$257$	1.34924	−	2.33695i	0.0841633	−	0.145775i	−0.820871	−	0.571114i	$-0.806512\pi$
$257$	1.34924	−	2.33695i	0.0841633	−	0.145775i	0.905034	+	0.425338i	$0.139845\pi$
$258$	0.330417			0.0205709
$259$	−14.2647	+	15.8588i	−0.886368	+	0.985415i
$260$	−22.9122			−1.42096
$261$	0.890123	−	1.54174i	0.0550972	−	0.0954312i
$262$	−0.264540	−	0.458198i	−0.0163434	−	0.0283075i
$263$	10.5745	+	18.3156i	0.652053	+	1.12939i	0.982624	+	0.185607i	$0.0594253\pi$
$263$	10.5745	+	18.3156i	0.652053	+	1.12939i	−0.330571	+	0.943781i	$0.607241\pi$
$264$	0.0346608	−	0.0600343i	0.00213322	−	0.00369485i
$265$	−0.168991			−0.0103810
$266$	−0.102520	−	0.314980i	−0.00628589	−	0.0193127i
$267$	5.92430			0.362561
$268$	−2.68490	+	4.65039i	−0.164007	+	0.284068i
$269$	14.2705	+	24.7173i	0.870090	+	1.50704i	0.861903	+	0.507073i	$0.169273\pi$
$269$	14.2705	+	24.7173i	0.870090	+	1.50704i	0.00818685	+	0.999966i	$0.497394\pi$
$270$	−0.0364740	−	0.0631748i	−0.00221974	−	0.00384469i
$271$	−7.57362	+	13.1179i	−0.460065	+	0.796856i	−0.998964	−	0.0455148i	$-0.985507\pi$
$271$	−7.57362	+	13.1179i	−0.460065	+	0.796856i	0.538899	+	0.842371i	$0.318841\pi$
$272$	16.4782			0.999136
$273$	−3.37768	−	10.3775i	−0.204427	−	0.628078i
$274$	−0.183968			−0.0111139
$275$	−0.897434	+	1.55440i	−0.0541173	+	0.0937339i
$276$	−0.999655	−	1.73145i	−0.0601722	−	0.104221i
$277$	−2.11859	−	3.66950i	−0.127294	−	0.220479i	0.795334	−	0.606172i	$-0.207296\pi$
$277$	−2.11859	−	3.66950i	−0.127294	−	0.220479i	−0.922627	+	0.385693i	$0.873962\pi$
$278$	−0.0378764	+	0.0656038i	−0.00227167	+	0.00393465i
$279$	−3.62429			−0.216980
$280$	0.516195	−	0.573877i	0.0308485	−	0.0342957i
$281$	0.762123			0.0454645			0.0227322	−	0.999742i	$-0.492763\pi$
$281$	0.762123			0.0454645			0.0227322	+	0.999742i	$0.492763\pi$
$282$	−0.154417	+	0.267458i	−0.00919539	+	0.0159269i
$283$	−8.58570	−	14.8709i	−0.510367	−	0.883981i	−0.999928	−	0.0120120i	$-0.996176\pi$
$283$	−8.58570	−	14.8709i	−0.510367	−	0.883981i	0.489561	−	0.871969i	$-0.337157\pi$
$284$	12.4419	+	21.5500i	0.738290	+	1.27876i
$285$	6.62383	−	11.4728i	0.392362	−	0.679590i
$286$	−0.0714981			−0.00422777
$287$	20.7049	+	4.39000i	1.22217	+	0.259133i
$288$	−0.314933			−0.0185576
$289$	−0.00289139	+	0.00500804i	−0.000170082	+	0.000294590i
$290$	−0.0649327	−	0.112467i	−0.00381298	−	0.00660427i
$291$	1.26870	+	2.19745i	0.0743724	+	0.128817i
$292$	−14.2821	+	24.7374i	−0.835799	+	1.44765i
$293$	−1.15566			−0.0675144			−0.0337572	−	0.999430i	$-0.510747\pi$
$293$	−1.15566			−0.0675144			−0.0337572	+	0.999430i	$0.510747\pi$
$294$	0.167981	+	0.0745861i	0.00979686	+	0.00434995i
$295$	−24.9689			−1.45375
$296$	0.423292	−	0.733164i	0.0246034	−	0.0426143i
$297$	0.330078	+	0.571712i	0.0191531	+	0.0331741i
$298$	0.250235	+	0.433420i	0.0144957	+	0.0251074i
$299$	−2.06244	+	3.57225i	−0.119274	+	0.206588i
$300$	5.43583			0.313838
$301$	−32.5706	−	6.90585i	−1.87734	−	0.398046i
$302$	0.132934			0.00764949
$303$	3.35589	−	5.81257i	0.192791	−	0.333923i
$304$	−9.52672	−	16.5008i	−0.546395	−	0.946383i
$305$	−3.76828	−	6.52685i	−0.215771	−	0.373727i
$306$	0.0541384	−	0.0937704i	0.00309488	−	0.00536050i
$307$	31.0365			1.77135			0.885673	−	0.464310i	$-0.153698\pi$
$307$	31.0365			1.77135			0.885673	+	0.464310i	$0.153698\pi$
$308$	−2.33530	+	2.59626i	−0.133066	+	0.147935i
$309$	−10.7478			−0.611422
$310$	−0.132192	+	0.228964i	−0.00750801	+	0.0130043i
$311$	−8.80703	−	15.2542i	−0.499401	−	0.864987i	0.500599	−	0.865679i	$-0.333113\pi$
$311$	−8.80703	−	15.2542i	−0.499401	−	0.864987i	−1.00000		0.000691900i	$0.999780\pi$
$312$	0.216572	+	0.375114i	0.0122610	+	0.0212367i
$313$	−7.87031	+	13.6318i	−0.444856	+	0.770514i	−0.998042	−	0.0625441i	$-0.980079\pi$
$313$	−7.87031	+	13.6318i	−0.444856	+	0.770514i	0.553186	+	0.833058i	$0.313412\pi$
$314$	0.0720446			0.00406571
$315$	2.27502	+	6.98973i	0.128183	+	0.393826i
$316$	13.8912			0.781438
$317$	2.61070	−	4.52186i	0.146631	−	0.253973i	−0.783349	−	0.621582i	$-0.786490\pi$
$317$	2.61070	−	4.52186i	0.146631	−	0.253973i	0.929980	+	0.367609i	$0.119824\pi$
$318$	0.000798534		0.00138310i	4.47796e−5		7.75605e-5i
$319$	0.587620	+	1.01779i	0.0329004	+	0.0569852i
$320$	11.0902	−	19.2087i	0.619958	−	1.07380i
$321$	0.484556			0.0270453
$322$	−0.0215003	−	0.0660573i	−0.00119817	−	0.00368123i
$323$	19.6635			1.09411
$324$	0.999655	−	1.73145i	0.0555364	−	0.0961919i
$325$	−5.60747	−	9.71242i	−0.311046	−	0.538748i
$326$	0.200978	+	0.348104i	0.0111311	+	0.0192797i
$327$	6.23260	−	10.7952i	0.344664	−	0.596975i
$328$	−0.840030			−0.0463829
$329$	20.8115	−	23.1371i	1.14738	−	1.27559i
$330$	0.0481570			0.00265096
$331$	6.97246	−	12.0767i	0.383241	−	0.663793i	−0.608282	−	0.793721i	$-0.708141\pi$
$331$	6.97246	−	12.0767i	0.383241	−	0.663793i	0.991524	+	0.129927i	$0.0414744\pi$
$332$	9.40532	+	16.2905i	0.516184	+	0.894057i
$333$	4.03105	+	6.98199i	0.220900	+	0.382611i
$334$	0.170689	−	0.295642i	0.00933967	−	0.0161768i
$335$	−7.46199			−0.407692
$336$	10.3422	+	2.19282i	0.564211	+	0.119628i
$337$	9.28645			0.505865			0.252933	−	0.967484i	$-0.418605\pi$
$337$	9.28645			0.505865			0.252933	+	0.967484i	$0.418605\pi$
$338$	0.0527048	−	0.0912874i	0.00286676	−	0.00496538i
$339$	4.64438	+	8.04429i	0.252248	+	0.436906i
$340$	11.4532	+	19.8374i	0.621134	+	1.07584i
$341$	1.19630	−	2.07205i	0.0647832	−	0.112208i
$342$	−0.125199			−0.00676996
$343$	−14.9997	−	10.8631i	−0.809910	−	0.586555i
$344$	1.32144			0.0712473
$345$	1.38914	−	2.40606i	0.0747888	−	0.129538i
$346$	−0.136823	−	0.236984i	−0.00735565	−	0.0127404i
$347$	−3.83747	−	6.64670i	−0.206006	−	0.356813i	0.744447	−	0.667682i	$-0.232713\pi$
$347$	−3.83747	−	6.64670i	−0.206006	−	0.356813i	−0.950453	+	0.310869i	$0.899380\pi$
$348$	1.77963	−	3.08241i	0.0953983	−	0.165235i
$349$	5.71924			0.306144			0.153072	−	0.988215i	$-0.451083\pi$
$349$	5.71924			0.306144			0.153072	+	0.988215i	$0.451083\pi$
$350$	0.184766	+	0.0391754i	0.00987617	+	0.00209401i
$351$	−4.12488			−0.220170
$352$	0.103953	−	0.180051i	0.00554069	−	0.00959675i
$353$	−6.70980	−	11.6217i	−0.357127	−	0.618561i	0.630353	−	0.776309i	$-0.282910\pi$
$353$	−6.70980	−	11.6217i	−0.357127	−	0.618561i	−0.987480	+	0.157747i	$0.949577\pi$
$354$	0.117986	+	0.204357i	0.00627087	+	0.0108615i
$355$	−17.2895	+	29.9463i	−0.917631	+	1.58938i
$356$	11.8445			0.627758
$357$	−7.29649	+	8.11183i	−0.386171	+	0.429324i
$358$	−0.504732			−0.0266759
$359$	−8.93291	+	15.4723i	−0.471461	+	0.816594i	−0.999467	−	0.0326463i	$-0.989607\pi$
$359$	−8.93291	+	15.4723i	−0.471461	+	0.816594i	0.528006	+	0.849241i	$0.322940\pi$
$360$	−0.145871	−	0.252656i	−0.00768806	−	0.0133161i
$361$	−1.86829	−	3.23597i	−0.0983311	−	0.170314i
$362$	−0.146449	+	0.253656i	−0.00769717	+	0.0133319i
$363$	10.5642			0.554476
$364$	−6.75304	−	20.7479i	−0.353956	−	1.08749i
$365$	−39.6935			−2.07765
$366$	−0.0356126	+	0.0616828i	−0.00186150	+	0.00322421i
$367$	−13.0761	−	22.6484i	−0.682566	−	1.18224i	−0.974195	−	0.225707i	$-0.927531\pi$
$367$	−13.0761	−	22.6484i	−0.682566	−	1.18224i	0.291630	−	0.956531i	$-0.405803\pi$
$368$	−1.99793	−	3.46052i	−0.104149	−	0.180392i
$369$	3.99984	−	6.92793i	0.208224	−	0.360654i
$370$	0.588114			0.0305746
$371$	−0.0498075	−	0.153028i	−0.00258588	−	0.00794481i
$372$	−7.24608			−0.375692
$373$	−10.0650	+	17.4331i	−0.521147	+	0.902653i	0.478551	+	0.878060i	$0.341162\pi$
$373$	−10.0650	+	17.4331i	−0.521147	+	0.902653i	−0.999698	+	0.0245929i	$0.992171\pi$
$374$	0.0357398	+	0.0619031i	0.00184806	+	0.00320093i
$375$	−3.16883	−	5.48858i	−0.163638	−	0.283429i
$376$	−0.617561	+	1.06965i	−0.0318483	+	0.0551628i
$377$	−7.34330			−0.378199
$378$	0.0464571	−	0.0516484i	0.00238950	−	0.00265651i
$379$	8.04896			0.413447			0.206724	−	0.978399i	$-0.433720\pi$
$379$	8.04896			0.413447			0.206724	+	0.978399i	$0.433720\pi$
$380$	13.2431	−	22.9377i	0.679356	−	1.17668i
$381$	1.20037	+	2.07910i	0.0614967	+	0.106515i
$382$	0.252517	+	0.437372i	0.0129199	+	0.0223779i
$383$	−10.0347	+	17.3806i	−0.512749	+	0.888107i	0.487142	+	0.873323i	$0.338039\pi$
$383$	−10.0347	+	17.3806i	−0.512749	+	0.888107i	−0.999891	+	0.0147842i	$0.995294\pi$
$384$	−0.839484			−0.0428397
$385$	−4.74704	−	1.00650i	−0.241932	−	0.0512961i
$386$	−0.458246			−0.0233241
$387$	−6.29210	+	10.8982i	−0.319845	+	0.553989i
$388$	2.53652	+	4.39339i	0.128772	+	0.223040i
$389$	−6.22581	−	10.7834i	−0.315661	−	0.546741i	0.663917	−	0.747806i	$-0.268893\pi$
$389$	−6.22581	−	10.7834i	−0.315661	−	0.546741i	−0.979578	+	0.201066i	$0.935560\pi$
$390$	−0.150451	+	0.260588i	−0.00761837	+	0.0131954i
$391$	4.12381			0.208550
$392$	0.671809	+	0.298293i	0.0339315	+	0.0150661i
$393$	20.1505			1.01646
$394$	−0.0152601	+	0.0264313i	−0.000768795	+	0.00133159i
$395$	9.65171	+	16.7173i	0.485630	+	0.841137i
$396$	0.659929	+	1.14303i	0.0331627	+	0.0574394i
$397$	3.46764	−	6.00613i	0.174036	−	0.301439i	−0.765791	−	0.643089i	$-0.777652\pi$
$397$	3.46764	−	6.00613i	0.174036	−	0.301439i	0.939827	+	0.341650i	$0.110986\pi$
$398$	−0.445752			−0.0223435
$399$	12.3414	+	2.61670i	0.617840	+	0.130999i
$400$	10.8642			0.543208
$401$	7.20807	−	12.4847i	0.359954	−	0.623458i	−0.627999	−	0.778214i	$-0.716126\pi$
$401$	7.20807	−	12.4847i	0.359954	−	0.623458i	0.987953	+	0.154756i	$0.0494591\pi$
$402$	0.0352602	+	0.0610725i	0.00175862	+	0.00304602i
$403$	7.47487	+	12.9469i	0.372350	+	0.644929i
$404$	6.70946	−	11.6211i	0.333808	−	0.578173i
$405$	2.77828			0.138054
$406$	0.0827051	−	0.0919469i	0.00410458	−	0.00456325i
$407$	−5.32225			−0.263814
$408$	0.216516	−	0.375017i	0.0107191	−	0.0185661i
$409$	−12.0132	−	20.8075i	−0.594016	−	1.02887i	−0.993685	−	0.112207i	$-0.964208\pi$
$409$	−12.0132	−	20.8075i	−0.594016	−	1.02887i	0.399668	−	0.916660i	$-0.369125\pi$
$410$	−0.291780	−	0.505379i	−0.0144100	−	0.0249589i
$411$	3.50329	−	6.06788i	0.172805	−	0.299306i
$412$	−21.4882			−1.05865
$413$	−7.35921	−	22.6103i	−0.362123	−	1.11258i
$414$	−0.0262565			−0.00129044
$415$	−13.0698	+	22.6376i	−0.641572	+	1.11124i
$416$	0.649530	+	1.12502i	0.0318458	+	0.0551586i
$417$	−1.44255	−	2.49857i	−0.0706421	−	0.122356i
$418$	0.0413253	−	0.0715775i	0.00202129	−	0.00350097i
$419$	31.8946			1.55815			0.779076	−	0.626930i	$-0.215689\pi$
$419$	31.8946			1.55815			0.779076	+	0.626930i	$0.215689\pi$
$420$	4.54846	+	13.9746i	0.221942	+	0.681892i
$421$	−18.8400			−0.918205			−0.459102	−	0.888383i	$-0.651829\pi$
$421$	−18.8400			−0.918205			−0.459102	+	0.888383i	$0.651829\pi$
$422$	0.153501	−	0.265871i	0.00747230	−	0.0129424i
$423$	−5.88109	−	10.1864i	−0.285949	−	0.495277i
$424$	0.00319359	+	0.00553145i	0.000155094	+	0.000268631i
$425$	−5.60601	+	9.70990i	−0.271932	+	0.470999i
$426$	0.326793			0.0158332
$427$	4.79968	−	5.33602i	0.232273	−	0.258228i
$428$	0.968777			0.0468276
$429$	1.36153	−	2.35824i	0.0657354	−	0.113857i
$430$	0.458996	+	0.795004i	0.0221347	+	0.0383385i
$431$	18.1715	+	31.4740i	0.875292	+	1.51605i	0.856451	+	0.516228i	$0.172664\pi$
$431$	18.1715	+	31.4740i	0.875292	+	1.51605i	0.0188408	+	0.999822i	$0.494002\pi$
$432$	1.99793	−	3.46052i	0.0961255	−	0.166494i
$433$	21.5486			1.03556			0.517780	−	0.855514i	$-0.326759\pi$
$433$	21.5486			1.03556			0.517780	+	0.855514i	$0.326759\pi$
$434$	−0.246297	−	0.0522217i	−0.0118226	−	0.00250672i
$435$	4.94603			0.237144
$436$	12.4609	−	21.5829i	0.596769	−	1.03363i
$437$	−2.38414	−	4.12946i	−0.114049	−	0.197539i
$438$	0.187564	+	0.324871i	0.00896216	+	0.0155229i
$439$	5.36875	−	9.29896i	0.256237	−	0.443815i	−0.708994	−	0.705215i	$-0.750851\pi$
$439$	5.36875	−	9.29896i	0.256237	−	0.443815i	0.965231	+	0.261400i	$0.0841840\pi$
$440$	0.192595			0.00918160
$441$	−5.65895	+	4.12023i	−0.269474	+	0.196202i
$442$	−0.446628			−0.0212439
$443$	16.9765	−	29.4042i	0.806580	−	1.39704i	−0.108639	−	0.994081i	$-0.534649\pi$
$443$	16.9765	−	29.4042i	0.806580	−	1.39704i	0.915219	−	0.402957i	$-0.132017\pi$
$444$	8.05933	+	13.9592i	0.382479	+	0.662473i
$445$	8.22969	+	14.2542i	0.390125	+	0.675716i
$446$	−0.203602	+	0.352649i	−0.00964083	+	0.0166984i
$447$	−19.0608			−0.901546
$448$	20.6629	+	4.38109i	0.976230	+	0.206987i
$449$	6.94219			0.327622			0.163811	−	0.986492i	$-0.447621\pi$
$449$	6.94219			0.327622			0.163811	+	0.986492i	$0.447621\pi$
$450$	0.0356938	−	0.0618234i	0.00168262	−	0.00291438i
$451$	2.64052	+	4.57352i	0.124337	+	0.215359i
$452$	9.28555	+	16.0830i	0.436755	+	0.756483i
$453$	−2.53145	+	4.38460i	−0.118938	+	0.206006i
$454$	0.402590			0.0188945
$455$	20.2770	−	22.5428i	0.950598	−	1.05682i
$456$	−0.500708			−0.0234478
$457$	19.7755	−	34.2521i	0.925057	−	1.60225i	0.133587	−	0.991037i	$-0.457350\pi$
$457$	19.7755	−	34.2521i	0.925057	−	1.60225i	0.791470	−	0.611208i	$-0.209316\pi$
$458$	−0.0840843	−	0.145638i	−0.00392900	−	0.00680523i
$459$	2.06190	+	3.57132i	0.0962414	+	0.166695i
$460$	2.77732	−	4.81047i	0.129493	−	0.224289i
$461$	−4.90582			−0.228487			−0.114243	−	0.993453i	$-0.536444\pi$
$461$	−4.90582			−0.228487			−0.114243	+	0.993453i	$0.536444\pi$
$462$	0.0141936	+	0.0436081i	0.000660344	+	0.00202883i
$463$	−0.772106			−0.0358828			−0.0179414	−	0.999839i	$-0.505711\pi$
$463$	−0.772106			−0.0358828			−0.0179414	+	0.999839i	$0.505711\pi$
$464$	3.55681	−	6.16058i	0.165121	−	0.285998i
$465$	−5.03465	−	8.72026i	−0.233476	−	0.404393i
$466$	−0.343212	−	0.594461i	−0.0158990	−	0.0275379i
$467$	9.59886	−	16.6257i	0.444182	−	0.769347i	−0.553812	−	0.832641i	$-0.686828\pi$
$467$	9.59886	−	16.6257i	0.444182	−	0.769347i	0.997995	+	0.0632949i	$0.0201609\pi$
$468$	−8.24691			−0.381214
$469$	−2.19931	−	6.75713i	−0.101555	−	0.312015i
$470$	−0.858027			−0.0395778
$471$	−1.37194	+	2.37627i	−0.0632156	+	0.109493i
$472$	0.471862	+	0.817289i	0.0217192	+	0.0376188i
$473$	−4.15377	−	7.19454i	−0.190990	−	0.330805i
$474$	0.0912147	−	0.157988i	0.00418963	−	0.00725665i
$475$	12.9643			0.594842
$476$	−14.5879	+	16.2181i	−0.668637	+	0.743354i
$477$	−0.0608257			−0.00278502
$478$	0.232072	−	0.401960i	0.0106147	−	0.0183852i
$479$	9.10522	+	15.7707i	0.416028	+	0.720582i	0.995536	−	0.0943848i	$-0.0300884\pi$
$479$	9.10522	+	15.7707i	0.416028	+	0.720582i	−0.579508	+	0.814967i	$0.696755\pi$
$480$	−0.437487	−	0.757749i	−0.0199684	−	0.0345864i
$481$	16.6276	−	28.7998i	0.758153	−	1.31316i
$482$	−0.151229			−0.00688830
$483$	2.58821	+	0.548771i	0.117768	+	0.0249700i
$484$	21.1211			0.960050
$485$	−3.52480	+	6.10514i	−0.160053	+	0.277220i
$486$	−0.0131282	−	0.0227388i	−0.000595509	−	0.00103145i
$487$	14.4406	+	25.0119i	0.654367	+	1.13340i	0.982052	+	0.188611i	$0.0603984\pi$
$487$	14.4406	+	25.0119i	0.654367	+	1.13340i	−0.327684	+	0.944787i	$0.606268\pi$
$488$	−0.142426	+	0.246689i	−0.00644731	+	0.0111671i
$489$	−15.3088			−0.692288
$490$	0.0538906	+	0.507784i	0.00243453	+	0.0229393i
$491$	−23.6817			−1.06874			−0.534369	−	0.845251i	$-0.679451\pi$
$491$	−23.6817			−1.06874			−0.534369	+	0.845251i	$0.679451\pi$
$492$	7.99693	−	13.8511i	0.360530	−	0.624455i
$493$	3.67070	+	6.35783i	0.165320	+	0.286342i
$494$	0.258214	+	0.447240i	0.0116176	+	0.0201223i
$495$	−0.917050	+	1.58838i	−0.0412183	+	0.0713923i
$496$	−14.4822			−0.650268
$497$	−32.2134	−	6.83010i	−1.44497	−	0.306372i
$498$	0.247036			0.0110699
$499$	−12.6849	+	21.9710i	−0.567856	+	0.983556i	0.428922	+	0.903342i	$0.358894\pi$
$499$	−12.6849	+	21.9710i	−0.567856	+	0.983556i	−0.996778	+	0.0802139i	$0.974440\pi$
$500$	−6.33548	−	10.9734i	−0.283332	−	0.490745i
$501$	6.50082	+	11.2598i	0.290435	+	0.503049i
$502$	−0.136358	+	0.236179i	−0.00608595	+	0.0105412i
$503$	−29.2636			−1.30480			−0.652400	−	0.757874i	$-0.726238\pi$
$503$	−29.2636			−1.30480			−0.652400	+	0.757874i	$0.726238\pi$
$504$	0.185796	−	0.206558i	0.00827603	−	0.00920083i
$505$	18.6472			0.829790
$506$	0.00866669	−	0.0150112i	0.000385281	−	0.000667327i
$507$	2.00731	+	3.47676i	0.0891476	+	0.154408i
$508$	2.39991	+	4.15676i	0.106479	+	0.184427i
$509$	20.3431	−	35.2353i	0.901692	−	1.56178i	0.0763952	−	0.997078i	$-0.475659\pi$
$509$	20.3431	−	35.2353i	0.901692	−	1.56178i	0.825297	−	0.564699i	$-0.191008\pi$
$510$	0.300823			0.0133207
$511$	−11.6991	−	35.9440i	−0.517536	−	1.59007i
$512$	−2.09762			−0.0927028
$513$	2.38414	−	4.12946i	0.105263	−	0.182320i
$514$	−0.0354263	−	0.0613602i	−0.00156259	−	0.00270648i
$515$	−14.9302	−	25.8599i	−0.657904	−	1.13952i
$516$	−12.5799	+	21.7890i	−0.553798	+	0.959206i
$517$	7.76488			0.341499
$518$	0.173338	+	0.532561i	0.00761603	+	0.0233994i
$519$	10.4220			0.457476
$520$	−0.601699	+	1.04217i	−0.0263862	+	0.0457023i
$521$	16.8982	+	29.2686i	0.740326	+	1.28228i	0.952347	+	0.305017i	$0.0986621\pi$
$521$	16.8982	+	29.2686i	0.740326	+	1.28228i	−0.212021	+	0.977265i	$0.568005\pi$
$522$	−0.0233715	−	0.0404806i	−0.00102294	−	0.00177179i
$523$	−6.42837	+	11.1343i	−0.281093	+	0.486867i	−0.971654	−	0.236407i	$-0.924030\pi$
$523$	−6.42837	+	11.1343i	−0.281093	+	0.486867i	0.690561	+	0.723274i	$0.257364\pi$
$524$	40.2871			1.75995
$525$	−4.81062	+	5.34818i	−0.209953	+	0.233414i
$526$	0.555300			0.0242122
$527$	7.47293	−	12.9435i	0.325526	−	0.563827i
$528$	1.31895	+	2.28448i	0.0573998	+	0.0994194i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−0.00221855	+	0.00384265i	−9.63678e−5	+	0.000166914i
$531$	−8.98717			−0.390010
$532$	24.6742	+	5.23160i	1.06976	+	0.226818i
$533$	−32.9977			−1.42929
$534$	0.0777757	−	0.134711i	0.00336568	−	0.00582953i
$535$	0.673116	+	1.16587i	0.0291014	+	0.0504050i
$536$	0.141017	+	0.244248i	0.00609099	+	0.0105499i
$537$	9.61157	−	16.6477i	0.414770	−	0.718402i
$538$	0.749388			0.0323084
$539$	−0.487693	−	4.59529i	−0.0210064	−	0.197933i
$540$	5.55465			0.239034
$541$	5.75329	−	9.96499i	0.247353	−	0.428428i	−0.715437	−	0.698677i	$-0.753773\pi$
$541$	5.75329	−	9.96499i	0.247353	−	0.428428i	0.962791	+	0.270248i	$0.0871059\pi$
$542$	0.198857	+	0.344430i	0.00854163	+	0.0147945i
$543$	−5.57762	−	9.66071i	−0.239358	−	0.414581i
$544$	0.649362	−	1.12473i	0.0278412	−	0.0482223i
$545$	34.6319			1.48347
$546$	−0.280316	−	0.0594346i	−0.0119964	−	0.00254356i
$547$	8.26280			0.353292			0.176646	−	0.984274i	$-0.443475\pi$
$547$	8.26280			0.353292			0.176646	+	0.984274i	$0.443475\pi$
$548$	7.00417	−	12.1316i	0.299203	−	0.518235i
$549$	−1.35633	−	2.34924i	−0.0578869	−	0.100263i
$550$	0.0235635	+	0.0408131i	0.00100475	+	0.00174028i
$551$	4.24436	−	7.35145i	0.180816	−	0.313182i
$552$	−0.105008			−0.00446943
$553$	−12.2934	+	13.6672i	−0.522770	+	0.581187i
$554$	−0.111253			−0.00472670
$555$	−11.1994	+	19.3979i	−0.475388	+	0.823397i
$556$	−2.88411	−	4.99542i	−0.122314	−	0.211853i
$557$	11.3001	+	19.5724i	0.478802	+	0.829309i	0.999705	−	0.0243068i	$-0.00773785\pi$
$557$	11.3001	+	19.5724i	0.478802	+	0.829309i	−0.520903	+	0.853616i	$0.674405\pi$
$558$	−0.0475805	+	0.0824119i	−0.00201424	+	0.00348877i
$559$	51.9083			2.19549
$560$	9.09066	+	27.9300i	0.384150	+	1.18026i
$561$	−2.72236			−0.114938
$562$	0.0100053	−	0.0173298i	0.000422050	−	0.000731012i
$563$	5.07518	+	8.79046i	0.213893	+	0.370474i	0.952930	−	0.303192i	$-0.0980522\pi$
$563$	5.07518	+	8.79046i	0.213893	+	0.370474i	−0.739036	+	0.673665i	$0.764719\pi$
$564$	−11.7581	−	20.3657i	−0.495107	−	0.857550i
$565$	−12.9034	+	22.3493i	−0.542850	+	0.940243i
$566$	−0.450860			−0.0189511
$567$	0.818857	+	2.51584i	0.0343888	+	0.105656i
$568$	1.30695			0.0548382
$569$	−18.2877	+	31.6752i	−0.766659	+	1.32789i	0.172707	+	0.984973i	$0.444749\pi$
$569$	−18.2877	+	31.6752i	−0.766659	+	1.32789i	−0.939365	+	0.342918i	$0.888585\pi$
$570$	−0.173918	−	0.301236i	−0.00728464	−	0.0126174i
$571$	−4.07243	−	7.05365i	−0.170426	−	0.295186i	0.768143	−	0.640278i	$-0.221181\pi$
$571$	−4.07243	−	7.05365i	−0.170426	−	0.295186i	−0.938569	+	0.345092i	$0.887848\pi$
$572$	2.72212	−	4.71486i	0.113818	−	0.197138i
$573$	−19.2346			−0.803538
$574$	0.371642	−	0.413172i	0.0155121	−	0.0172454i
$575$	2.71885			0.113384
$576$	3.99173	−	6.91388i	0.166322	−	0.288078i
$577$	3.65944	+	6.33833i	0.152344	+	0.263868i	0.932089	−	0.362230i	$-0.117984\pi$
$577$	3.65944	+	6.33833i	0.152344	+	0.263868i	−0.779745	+	0.626098i	$0.784651\pi$
$578$	7.59178e−5	0	0.000131493i	3.15776e−6	0	5.46941e-6i
$579$	8.72634	−	15.1145i	0.362654	−	0.628136i
$580$	9.88864			0.410604
$581$	−24.3514	−	5.16315i	−1.01026	−	0.214203i
$582$	0.0666232			0.00276162
$583$	0.0200772	−	0.0347748i	0.000831513	−	0.00144022i
$584$	0.750127	+	1.29926i	0.0310405	+	0.0537637i
$585$	−5.73004	−	9.92471i	−0.236908	−	0.410336i
$586$	−0.0151718	+	0.0262783i	−0.000626741	+	0.00108555i
$587$	−46.8386			−1.93324			−0.966618	−	0.256223i	$-0.917522\pi$
$587$	−46.8386			−1.93324			−0.966618	+	0.256223i	$0.917522\pi$
$588$	−11.3140	+	8.23763i	−0.466581	+	0.339714i
$589$	−17.2816			−0.712078
$590$	−0.327798	+	0.567763i	−0.0134952	+	0.0233744i
$591$	−0.581195	−	1.00666i	−0.0239072	−	0.0414084i
$592$	16.1075	+	27.8991i	0.662016	+	1.14664i
$593$	8.03777	−	13.9218i	0.330072	−	0.571701i	−0.652454	−	0.757828i	$-0.726260\pi$
$593$	8.03777	−	13.9218i	0.330072	−	0.571701i	0.982526	+	0.186128i	$0.0595938\pi$
$594$	0.0173334			0.000711197
$595$	−29.6534	−	6.28733i	−1.21567	−	0.257755i
$596$	−38.1085			−1.56099
$597$	8.48842	−	14.7024i	0.347408	−	0.601728i
$598$	0.0541524	+	0.0937947i	0.00221446	+	0.00383555i
$599$	13.7899	+	23.8848i	0.563439	+	0.975905i	0.997193	+	0.0748736i	$0.0238553\pi$
$599$	13.7899	+	23.8848i	0.563439	+	0.975905i	−0.433754	+	0.901031i	$0.642811\pi$
$600$	0.142751	−	0.247251i	0.00582776	−	0.0100940i
$601$	−32.9659			−1.34471			−0.672353	−	0.740231i	$-0.734716\pi$
$601$	−32.9659			−1.34471			−0.672353	+	0.740231i	$0.734716\pi$
$602$	−0.584625	+	0.649954i	−0.0238276	+	0.0264902i
$603$	−2.68583			−0.109375
$604$	−5.06115	+	8.76617i	−0.205935	+	0.356690i
$605$	14.6752	+	25.4181i	0.596630	+	1.03339i
$606$	−0.0881139	−	0.152618i	−0.00357938	−	0.00619967i
$607$	18.4202	−	31.9047i	0.747653	−	1.29497i	−0.201292	−	0.979531i	$-0.564514\pi$
$607$	18.4202	−	31.9047i	0.747653	−	1.29497i	0.948945	−	0.315442i	$-0.102153\pi$
$608$	−1.50169			−0.0609017
$609$	1.45777	+	4.47882i	0.0590717	+	0.181491i
$610$	−0.197884			−0.00801208
$611$	−24.2588	+	42.0174i	−0.981405	+	1.69984i
$612$	4.12239	+	7.14018i	0.166638	+	0.288625i
$613$	−11.0658	−	19.1665i	−0.446943	−	0.774129i	0.551242	−	0.834345i	$-0.314154\pi$
$613$	−11.0658	−	19.1665i	−0.446943	−	0.774129i	−0.998185	+	0.0602168i	$0.980821\pi$
$614$	0.407455	−	0.705732i	0.0164435	−	0.0284810i
$615$	22.2254			0.896214
$616$	0.0567645	+	0.174402i	0.00228711	+	0.00702687i
$617$	25.5349			1.02800			0.513998	−	0.857792i	$-0.328164\pi$
$617$	25.5349			1.02800			0.513998	+	0.857792i	$0.328164\pi$
$618$	−0.141100	+	0.244392i	−0.00567587	+	0.00983090i
$619$	−15.1917	−	26.3129i	−0.610607	−	1.05760i	−0.991138	−	0.132835i	$-0.957592\pi$
$619$	−15.1917	−	26.3129i	−0.610607	−	1.05760i	0.380531	−	0.924768i	$-0.375741\pi$
$620$	−10.0658	−	17.4345i	−0.404253	−	0.700187i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−0.462483			−0.0185439
$623$	−10.4822	+	11.6535i	−0.419961	+	0.466889i
$624$	−16.4824			−0.659826
$625$	15.6011	−	27.0218i	0.624042	−	1.08087i
$626$	0.206647	+	0.357923i	0.00825927	+	0.0143055i
$627$	1.57391	+	2.72609i	0.0628558	+	0.108869i
$628$	−2.74293	+	4.75090i	−0.109455	+	0.189581i
$629$	−33.2466			−1.32563
$630$	0.188805	+	0.0400317i	0.00752217	+	0.00159490i
$631$	−23.5164			−0.936175			−0.468087	−	0.883682i	$-0.655057\pi$
$631$	−23.5164			−0.936175			−0.468087	+	0.883682i	$0.655057\pi$
$632$	0.364796	−	0.631845i	0.0145108	−	0.0251334i
$633$	5.84620	+	10.1259i	0.232366	+	0.402469i
$634$	−0.0685477	−	0.118728i	−0.00272238	−	0.00471530i
$635$	−3.33496	+	5.77632i	−0.132344	+	0.229226i
$636$	−0.121609			−0.00482213
$637$	26.3897	+	11.7174i	1.04560	+	0.464262i
$638$	0.0308577			0.00122167
$639$	−6.22309	+	10.7787i	−0.246182	+	0.426399i
$640$	−1.16616	−	2.01985i	−0.0460966	−	0.0798416i
$641$	−10.8055	−	18.7157i	−0.426793	−	0.739227i	0.569793	−	0.821788i	$-0.307023\pi$
$641$	−10.8055	−	18.7157i	−0.426793	−	0.739227i	−0.996586	+	0.0825610i	$0.973690\pi$
$642$	0.00636137	−	0.0110182i	0.000251063	−	0.000434854i
$643$	−12.5132			−0.493472			−0.246736	−	0.969083i	$-0.579358\pi$
$643$	−12.5132			−0.493472			−0.246736	+	0.969083i	$0.579358\pi$
$644$	5.17464	+	1.09716i	0.203910	+	0.0432343i
$645$	−34.9625			−1.37665
$646$	0.258147	−	0.447124i	0.0101567	−	0.0175919i
$647$	−9.42170	−	16.3189i	−0.370405	−	0.641561i	0.619223	−	0.785216i	$-0.287448\pi$
$647$	−9.42170	−	16.3189i	−0.370405	−	0.641561i	−0.989628	+	0.143655i	$0.954115\pi$
$648$	−0.0525039	−	0.0909395i	−0.00206255	−	0.00357244i
$649$	2.96647	−	5.13807i	0.116444	−	0.201687i
$650$	−0.294465			−0.0115499
$651$	6.41266	−	7.12924i	0.251332	−	0.279417i
$652$	−30.6071			−1.19866
$653$	−16.3318	+	28.2874i	−0.639111	+	1.10697i	0.346517	+	0.938044i	$0.387364\pi$
$653$	−16.3318	+	28.2874i	−0.639111	+	1.10697i	−0.985628	+	0.168929i	$0.945969\pi$
$654$	−0.163646	−	0.283444i	−0.00639908	−	0.0110835i
$655$	27.9919	+	48.4833i	1.09373	+	1.89440i
$656$	15.9828	−	27.6831i	0.624025	−	1.08084i
$657$	−14.2871			−0.557392
$658$	−0.252891	−	0.776978i	−0.00985871	−	0.0302897i
$659$	−31.3480			−1.22114			−0.610571	−	0.791961i	$-0.709060\pi$
$659$	−31.3480			−1.22114			−0.610571	+	0.791961i	$0.709060\pi$
$660$	−1.83347	+	3.17566i	−0.0713676	+	0.123612i
$661$	−18.9962	−	32.9024i	−0.738866	−	1.27975i	−0.953006	−	0.302951i	$-0.902028\pi$
$661$	−18.9962	−	32.9024i	−0.738866	−	1.27975i	0.214140	−	0.976803i	$-0.431305\pi$
$662$	−0.183072	−	0.317091i	−0.00711531	−	0.0123241i
$663$	8.50510	−	14.7313i	0.330311	−	0.572115i
$664$	0.987973			0.0383408
$665$	10.8479	+	33.3290i	0.420665	+	1.29244i
$666$	0.211683			0.00820253
$667$	0.890123	−	1.54174i	0.0344657	−	0.0596963i
$668$	12.9972	+	22.5117i	0.502875	+	0.871006i
$669$	−7.75435	−	13.4309i	−0.299800	−	0.519270i
$670$	−0.0979629	+	0.169677i	−0.00378464	+	0.00655518i
$671$	1.79079			0.0691325
$672$	0.557229	−	0.619496i	0.0214956	−	0.0238976i
$673$	10.3170			0.397691			0.198845	−	0.980031i	$-0.436281\pi$
$673$	10.3170			0.397691			0.198845	+	0.980031i	$0.436281\pi$
$674$	0.121915	−	0.211163i	0.00469598	−	0.00813368i
$675$	1.35943	+	2.35460i	0.0523244	+	0.0906284i
$676$	4.01323	+	6.95111i	0.154355	+	0.267351i
$677$	13.6599	−	23.6597i	0.524993	−	0.909315i	−0.474583	−	0.880211i	$-0.657401\pi$
$677$	13.6599	−	23.6597i	0.524993	−	0.909315i	0.999576	−	0.0291045i	$-0.00926556\pi$
$678$	0.243890			0.00936654
$679$	−6.56733	−	1.39245i	−0.252031	−	0.0534374i
$680$	1.20309			0.0461362
$681$	−7.66648	+	13.2787i	−0.293780	+	0.508842i
$682$	−0.0314106	−	0.0544047i	−0.00120277	−	0.00208326i
$683$	10.6541	+	18.4535i	0.407669	+	0.706103i	0.994628	−	0.103514i	$-0.0330085\pi$
$683$	10.6541	+	18.4535i	0.407669	+	0.706103i	−0.586959	+	0.809616i	$0.699675\pi$
$684$	4.76665	−	8.25607i	0.182257	−	0.315679i
$685$	19.4663			0.743768
$686$	−0.443935	+	0.198462i	−0.0169495	+	0.00757731i
$687$	6.40484			0.244360
$688$	−25.1424	+	43.5479i	−0.958544	+	1.66025i
$689$	0.125449	+	0.217284i	0.00477923	+	0.00827788i
$690$	−0.0364740	−	0.0631748i	−0.00138854	−	0.00240502i
$691$	10.3351	−	17.9009i	0.393166	−	0.680984i	−0.599699	−	0.800226i	$-0.704713\pi$
$691$	10.3351	−	17.9009i	0.393166	−	0.680984i	0.992865	+	0.119242i	$0.0380464\pi$
$692$	20.8369			0.792099
$693$	−1.70863	−	0.362275i	−0.0649053	−	0.0137617i
$694$	−0.201517			−0.00764949
$695$	4.00782	−	6.94174i	0.152025	−	0.263315i
$696$	−0.0934699	−	0.161895i	−0.00354297	−	0.00613660i
$697$	16.4946	+	28.5695i	0.624777	+	1.08215i
$698$	0.0750836	−	0.130049i	0.00284195	−	0.00492241i
$699$	26.1430			0.988821
$700$	−9.61793	+	10.6927i	−0.363523	+	0.404145i
$701$	−1.93401			−0.0730465			−0.0365232	−	0.999333i	$-0.511628\pi$
$701$	−1.93401			−0.0730465			−0.0365232	+	0.999333i	$0.511628\pi$
$702$	−0.0541524	+	0.0937947i	−0.00204385	+	0.00354005i
$703$	19.2212	+	33.2921i	0.724942	+	1.25564i
$704$	2.63516	+	4.56424i	0.0993165	+	0.172021i
$705$	16.3393	−	28.3006i	0.615375	−	1.06586i
$706$	−0.352352			−0.0132609
$707$	5.49599	+	16.8858i	0.206698	+	0.635055i
$708$	−17.9681			−0.675284
$709$	−12.6664	+	21.9389i	−0.475698	+	0.823933i	−0.999612	−	0.0278379i	$-0.991138\pi$
$709$	−12.6664	+	21.9389i	−0.475698	+	0.823933i	0.523915	+	0.851771i	$0.324471\pi$
$710$	0.453961	+	0.786284i	0.0170369	+	0.0295087i
$711$	3.47399	+	6.01712i	0.130285	+	0.225660i
$712$	0.311049	−	0.538753i	0.0116571	−	0.0201906i
$713$	−3.62429			−0.135731
$714$	0.0886631	+	0.272407i	0.00331813	+	0.0101946i
$715$	7.56544			0.282931
$716$	19.2165	−	33.2840i	0.718155	−	1.24388i
$717$	8.83864	+	15.3090i	0.330085	+	0.571724i
$718$	0.234547	+	0.406247i	0.00875321	+	0.0151610i
$719$	5.86374	−	10.1563i	0.218681	−	0.378766i	−0.735724	−	0.677281i	$-0.763158\pi$
$719$	5.86374	−	10.1563i	0.218681	−	0.378766i	0.954405	+	0.298515i	$0.0964914\pi$
$720$	11.1016			0.413734
$721$	19.0167	−	21.1417i	0.708219	−	0.787359i
$722$	−0.0981095			−0.00365126
$723$	2.87985	−	4.98804i	0.107103	−	0.185507i
$724$	−11.1514	−	19.3148i	−0.414438	−	0.717828i
$725$	2.42011	+	4.19176i	0.0898808	+	0.155678i
$726$	0.138689	−	0.240217i	0.00514724	−	0.00891529i
$727$	13.4547			0.499007			0.249503	−	0.968374i	$-0.419733\pi$
$727$	13.4547			0.499007			0.249503	+	0.968374i	$0.419733\pi$
$728$	−1.12107	−	0.237697i	−0.0415496	−	0.00880965i
$729$	1.00000			0.0370370
$730$	−0.521106	+	0.902583i	−0.0192870	+	0.0334061i
$731$	−25.9474	−	44.9422i	−0.959700	−	1.66225i
$732$	−2.71173	−	4.69686i	−0.100229	−	0.173601i
$733$	−10.3971	+	18.0083i	−0.384025	+	0.665151i	−0.991633	−	0.129086i	$-0.958796\pi$
$733$	−10.3971	+	18.0083i	−0.384025	+	0.665151i	0.607608	+	0.794237i	$0.292129\pi$
$734$	−0.686664			−0.0253452
$735$	−17.7746	−	7.89220i	−0.655627	−	0.291108i
$736$	−0.314933			−0.0116086
$737$	0.886533	−	1.53552i	0.0326559	−	0.0565616i
$738$	−0.105022	−	0.181903i	−0.00386591	−	0.00669595i
$739$	11.6762	+	20.2238i	0.429517	+	0.743945i	0.996830	−	0.0795569i	$-0.0253505\pi$
$739$	11.6762	+	20.2238i	0.429517	+	0.743945i	−0.567313	+	0.823502i	$0.692017\pi$
$740$	−22.3911	+	38.7825i	−0.823113	+	1.42567i
$741$	−19.6686			−0.722544
$742$	−0.00413356		0.000876425i	−0.000151748		3.21746e-5i
$743$	6.11578			0.224366			0.112183	−	0.993688i	$-0.464216\pi$
$743$	6.11578			0.224366			0.112183	+	0.993688i	$0.464216\pi$
$744$	−0.190289	+	0.329591i	−0.00697635	+	0.0120834i
$745$	−26.4782	−	45.8616i	−0.970085	−	1.68024i
$746$	0.264272	+	0.457733i	0.00967569	+	0.0167588i
$747$	−4.70428	+	8.14805i	−0.172121	+	0.298122i
$748$	−5.44284			−0.199010
$749$	−0.857352	+	0.953157i	−0.0313270	+	0.0348276i
$750$	−0.166405			−0.00607625
$751$	−12.2516	+	21.2204i	−0.447068	+	0.774344i	−0.998194	−	0.0600780i	$-0.980865\pi$
$751$	−12.2516	+	21.2204i	−0.447068	+	0.774344i	0.551126	+	0.834422i	$0.314198\pi$
$752$	−23.5000	−	40.7033i	−0.856959	−	1.48430i
$753$	−5.19330	−	8.99506i	−0.189254	−	0.327798i
$754$	−0.0964046	+	0.166978i	−0.00351085	+	0.00608097i
$755$	−14.0662			−0.511920
$756$	1.63715	+	5.02995i	0.0595426	+	0.182938i
$757$	23.0058			0.836160			0.418080	−	0.908410i	$-0.362703\pi$
$757$	23.0058			0.836160			0.418080	+	0.908410i	$0.362703\pi$
$758$	0.105669	−	0.183024i	0.00383806	−	0.00664771i
$759$	0.330078	+	0.571712i	0.0119811	+	0.0207518i
$760$	−0.695554	−	1.20473i	−0.0252304	−	0.0437003i
$761$	5.32349	−	9.22056i	0.192976	−	0.334245i	−0.753259	−	0.657724i	$-0.771519\pi$
$761$	5.32349	−	9.22056i	0.192976	−	0.334245i	0.946235	+	0.323479i	$0.104853\pi$
$762$	0.0630349			0.00228351
$763$	10.2072	+	31.3605i	0.369526	+	1.13533i
$764$	−38.4560			−1.39129
$765$	−5.72855	+	9.92214i	−0.207116	+	0.358736i
$766$	0.263476	+	0.456354i	0.00951977	+	0.0164887i
$767$	18.5355	+	32.1044i	0.669278	+	1.15922i
$768$	7.97244	−	13.8087i	0.287681	−	0.498277i
$769$	17.0235			0.613883			0.306942	−	0.951728i	$-0.400694\pi$
$769$	17.0235			0.613883			0.306942	+	0.951728i	$0.400694\pi$
$770$	−0.0852070	+	0.0947284i	−0.00307065	+	0.00341378i
$771$	2.69848			0.0971834
$772$	17.4467	−	30.2185i	0.627919	−	1.08759i
$773$	3.92164	+	6.79247i	0.141051	+	0.244308i	0.927893	−	0.372847i	$-0.121618\pi$
$773$	3.92164	+	6.79247i	0.141051	+	0.244308i	−0.786841	+	0.617155i	$0.788285\pi$
$774$	0.165208	+	0.286150i	0.00593830	+	0.0102854i
$775$	4.92695	−	8.53373i	0.176981	−	0.306541i
$776$	0.266447			0.00956488
$777$	−20.8665	−	4.42425i	−0.748580	−	0.158719i
$778$	−0.326936			−0.0117212
$779$	19.0724	−	33.0344i	0.683340	−	1.18358i
$780$	−11.4561	−	19.8426i	−0.410195	−	0.710479i
$781$	−4.10821	−	7.11563i	−0.147003	−	0.254617i
$782$	0.0541384	−	0.0937704i	0.00193598	−	0.00335322i
$783$	1.78025			0.0636208
$784$	−22.6124	+	16.4639i	−0.807585	+	0.587996i
$785$	−7.62327			−0.272086
$786$	0.264540	−	0.458198i	0.00943585	−	0.0163434i
$787$	20.4790	+	35.4706i	0.729997	+	1.26439i	0.956884	+	0.290471i	$0.0938119\pi$
$787$	20.4790	+	35.4706i	0.729997	+	1.26439i	−0.226887	+	0.973921i	$0.572855\pi$
$788$	−1.16199	−	2.01262i	−0.0413941	−	0.0716968i
$789$	−10.5745	+	18.3156i	−0.376463	+	0.652053i
$790$	0.506840			0.0180326
$791$	−24.0413	−	5.09740i	−0.854809	−	0.181243i
$792$	0.0693216			0.00246324
$793$	−5.59471	+	9.69033i	−0.198674	+	0.344114i
$794$	−0.0910481	−	0.157700i	−0.00323118	−	0.00559656i
$795$	−0.0844954	−	0.146350i	−0.00299674	−	0.00519051i
$796$	16.9710	−	29.3946i	0.601521	−	1.04186i
$797$	−11.8092			−0.418303			−0.209151	−	0.977883i	$-0.567070\pi$
$797$	−11.8092			−0.418303			−0.209151	+	0.977883i	$0.567070\pi$
$798$	0.221521	−	0.246275i	0.00784175	−	0.00871803i
$799$	48.5050			1.71598
$800$	0.428128	−	0.741540i	0.0151366	−	0.0262174i
$801$	2.96215	+	5.13060i	0.104662	+	0.181281i
$802$	−0.189259	−	0.327806i	−0.00668295	−	0.0115752i
$803$	4.71585	−	8.16809i	0.166419	−	0.288246i
$804$	−5.36981			−0.189378
$805$	2.27502	+	6.98973i	0.0801838	+	0.246355i
$806$	0.392528			0.0138262
$807$	−14.2705	+	24.7173i	−0.502347	+	0.870090i
$808$	−0.352395	−	0.610366i	−0.0123972	−	0.0214726i
$809$	−6.52389	−	11.2997i	−0.229368	−	0.397277i	0.728253	−	0.685308i	$-0.240333\pi$
$809$	−6.52389	−	11.2997i	−0.229368	−	0.397277i	−0.957621	+	0.288032i	$0.906999\pi$
$810$	0.0364740	−	0.0631748i	0.00128156	−	0.00221974i
$811$	−51.3449			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$811$	−51.3449			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$812$	2.91453	+	8.95456i	0.102280	+	0.314243i
$813$	−15.1472			−0.531237
$814$	−0.0698718	+	0.121021i	−0.00244900	+	0.00424180i
$815$	−21.2661	−	36.8339i	−0.744919	−	1.29024i
$816$	8.23909	+	14.2705i	0.288426	+	0.499568i
$817$	−30.0026	+	51.9659i	−1.04966	+	1.81806i
$818$	−0.630851			−0.0220572
$819$	7.29838	−	8.11394i	0.255026	−	0.283524i
$820$	44.4355			1.55175
$821$	−28.1511	+	48.7591i	−0.982479	+	1.70170i	−0.329835	+	0.944039i	$0.606993\pi$
$821$	−28.1511	+	48.7591i	−0.982479	+	1.70170i	−0.652644	+	0.757665i	$0.726340\pi$
$822$	−0.0919841	−	0.159321i	−0.00320831	−	0.00555696i
$823$	6.77827	+	11.7403i	0.236276	+	0.409241i	0.959643	−	0.281222i	$-0.0907398\pi$
$823$	6.77827	+	11.7403i	0.236276	+	0.409241i	−0.723367	+	0.690464i	$0.757407\pi$
$824$	−0.564302	+	0.977400i	−0.0196584	+	0.0340494i
$825$	−1.79487			−0.0624893
$826$	−0.610745	−	0.129494i	−0.0212505	−	0.00450569i
$827$	3.80574			0.132339			0.0661693	−	0.997808i	$-0.478922\pi$
$827$	3.80574			0.132339			0.0661693	+	0.997808i	$0.478922\pi$
$828$	0.999655	−	1.73145i	0.0347404	−	0.0601722i
$829$	19.4462	+	33.6818i	0.675395	+	1.16982i	0.976353	+	0.216181i	$0.0693600\pi$
$829$	19.4462	+	33.6818i	0.675395	+	1.16982i	−0.300959	+	0.953637i	$0.597307\pi$
$830$	0.343168	+	0.594384i	0.0119115	+	0.0206314i
$831$	2.11859	−	3.66950i	0.0734929	−	0.127294i
$832$	−32.9308			−1.14167
$833$	−3.04648	−	28.7054i	−0.105554	−	0.994585i
$834$	−0.0757527			−0.00262310
$835$	−18.0611	+	31.2828i	−0.625031	+	1.08259i
$836$	3.14673	+	5.45030i	0.108832	+	0.188502i
$837$	−1.81214	−	3.13872i	−0.0626368	−	0.108490i
$838$	0.418720	−	0.725244i	0.0144644	−	0.0250531i
$839$	5.77279			0.199299			0.0996495	−	0.995023i	$-0.468228\pi$
$839$	5.77279			0.199299			0.0996495	+	0.995023i	$0.468228\pi$
$840$	0.755089	+	0.160099i	0.0260531	+	0.00552395i
$841$	−25.8307			−0.890715
$842$	−0.247336	+	0.428398i	−0.00852376	+	0.0147636i
$843$	0.381062	+	0.660018i	0.0131245	+	0.0227322i
$844$	11.6884	+	20.2449i	0.402330	+	0.696857i
$845$	−5.57686	+	9.65941i	−0.191850	+	0.332294i
$846$	−0.308834			−0.0106179
$847$	−18.6918	+	20.7805i	−0.642259	+	0.714028i
$848$	−0.243051			−0.00834641
$849$	8.58570	−	14.8709i	0.294660	−	0.510367i
$850$	0.147194	+	0.254948i	0.00504872	+	0.00874464i
$851$	4.03105	+	6.98199i	0.138183	+	0.239339i
$852$	−12.4419	+	21.5500i	−0.426252	+	0.738290i
$853$	6.63846			0.227296			0.113648	−	0.993521i	$-0.463746\pi$
$853$	6.63846			0.227296			0.113648	+	0.993521i	$0.463746\pi$
$854$	−0.0583232	−	0.179191i	−0.00199578	−	0.00613181i
$855$	13.2477			0.453060
$856$	0.0254411	−	0.0440653i	0.000869558	−	0.00150612i
$857$	12.8921	+	22.3297i	0.440385	+	0.762770i	0.997718	−	0.0675197i	$-0.0215085\pi$
$857$	12.8921	+	22.3297i	0.440385	+	0.762770i	−0.557333	+	0.830289i	$0.688175\pi$
$858$	−0.0357490	−	0.0619192i	−0.00122045	−	0.00211389i
$859$	−10.5535	+	18.2792i	−0.360081	+	0.623679i	−0.987974	−	0.154621i	$-0.950584\pi$
$859$	−10.5535	+	18.2792i	−0.360081	+	0.623679i	0.627893	+	0.778300i	$0.283918\pi$
$860$	−69.9008			−2.38360
$861$	6.55060	+	20.1260i	0.223244	+	0.685891i
$862$	0.954242			0.0325016
$863$	−6.22738	+	10.7861i	−0.211982	+	0.367164i	−0.952335	−	0.305055i	$-0.901325\pi$
$863$	−6.22738	+	10.7861i	−0.211982	+	0.367164i	0.740353	+	0.672219i	$0.234659\pi$
$864$	−0.157467	−	0.272740i	−0.00535712	−	0.00927881i
$865$	14.4777	+	25.0761i	0.492255	+	0.852612i
$866$	0.282895	−	0.489989i	0.00961318	−	0.0166505i
$867$	−0.00578278			−0.000196394
$868$	12.8209	−	14.2536i	0.435169	−	0.483797i
$869$	−4.58675			−0.155595
$870$	0.0649327	−	0.112467i	0.00220142	−	0.00381298i
$871$	5.53936	+	9.59445i	0.187694	+	0.325095i
$872$	−0.654472	−	1.13358i	−0.0221632	−	0.0383878i
$873$	−1.26870	+	2.19745i	−0.0429390	+	0.0743724i
$874$	−0.125199			−0.00423490
$875$	16.4032	+	3.47793i	0.554531	+	0.117576i
$876$	−28.5643			−0.965098
$877$	22.9536	−	39.7568i	0.775088	−	1.34249i	−0.159657	−	0.987172i	$-0.551039\pi$
$877$	22.9536	−	39.7568i	0.775088	−	1.34249i	0.934745	−	0.355319i	$-0.115628\pi$
$878$	−0.140965	−	0.244158i	−0.00475733	−	0.00823993i
$879$	−0.577830	−	1.00083i	−0.0194897	−	0.0337572i
$880$	−3.66441	+	6.34694i	−0.123527	+	0.213955i
$881$	17.7656			0.598539			0.299269	−	0.954169i	$-0.403257\pi$
$881$	17.7656			0.598539			0.299269	+	0.954169i	$0.403257\pi$
$882$	0.0193971	+	0.182769i	0.000653134	+	0.00615415i
$883$	8.07698			0.271812			0.135906	−	0.990722i	$-0.456605\pi$
$883$	8.07698			0.271812			0.135906	+	0.990722i	$0.456605\pi$
$884$	17.0043	−	29.4524i	0.571918	−	0.990590i
$885$	−12.4845	−	21.6237i	−0.419660	−	0.726873i
$886$	−0.445745	−	0.772052i	−0.0149751	−	0.0259376i
$887$	25.8359	−	44.7491i	0.867484	−	1.50253i	0.00292545	−	0.999996i	$-0.499069\pi$
$887$	25.8359	−	44.7491i	0.867484	−	1.50253i	0.864559	−	0.502531i	$-0.167598\pi$
$888$	0.846585			0.0284095
$889$	−6.21362	−	1.31745i	−0.208398	−	0.0441860i
$890$	0.432166			0.0144862
$891$	−0.330078	+	0.571712i	−0.0110580	+	0.0191531i
$892$	−15.5034	−	26.8526i	−0.519091	−	0.899091i
$893$	−28.0427	−	48.5715i	−0.938415	−	1.62538i
$894$	−0.250235	+	0.433420i	−0.00836912	+	0.0144957i
$895$	53.4073			1.78521
$896$	1.48535	−	1.65133i	0.0496219	−	0.0551669i
$897$	−4.12488			−0.137726
$898$	0.0911388	−	0.157857i	0.00304134	−	0.00526776i
$899$	−3.22606	−	5.58770i	−0.107595	−	0.186360i
$900$	2.71792	+	4.70757i	0.0905972	+	0.156919i
$901$	0.125417	−	0.217228i	0.00417823	−	0.00723691i
$902$	0.138662			0.00461693
$903$	−10.3047	−	31.6599i	−0.342918	−	1.05358i
$904$	0.975392			0.0324411
$905$	15.4962	−	26.8402i	0.515111	−	0.892198i
$906$	0.0664669	+	0.115124i	0.00220822	+	0.00382474i
$907$	−19.3898	−	33.5841i	−0.643826	−	1.11514i	−0.984571	−	0.174984i	$-0.944013\pi$
$907$	−19.3898	−	33.5841i	−0.643826	−	1.11514i	0.340745	−	0.940156i	$-0.389321\pi$
$908$	−15.3277	+	26.5483i	−0.508667	+	0.881037i
$909$	6.71178			0.222616
$910$	−0.246395	−	0.757021i	−0.00816792	−	0.0250950i
$911$	9.13030			0.302500			0.151250	−	0.988496i	$-0.451670\pi$
$911$	9.13030			0.302500			0.151250	+	0.988496i	$0.451670\pi$
$912$	9.52672	−	16.5008i	0.315461	−	0.546395i
$913$	−3.10556	−	5.37899i	−0.102779	−	0.178018i
$914$	−0.519234	−	0.899340i	−0.0171747	−	0.0297475i
$915$	3.76828	−	6.52685i	0.124576	−	0.215771i
$916$	12.8053			0.423098
$917$	−35.6534	+	39.6375i	−1.17738	+	1.30894i
$918$	0.108277			0.00357366
$919$	−1.87461	+	3.24692i	−0.0618377	+	0.107106i	−0.895287	−	0.445490i	$-0.853029\pi$
$919$	−1.87461	+	3.24692i	−0.0618377	+	0.107106i	0.833449	+	0.552596i	$0.186363\pi$
$920$	−0.145871	−	0.252656i	−0.00480922	−	0.00832981i
$921$	15.5182	+	26.8784i	0.511343	+	0.885673i
$922$	−0.0644048	+	0.111552i	−0.00212106	+	0.00367378i
$923$	51.3389			1.68984
$924$	−3.41607	−	0.724300i	−0.112381	−	0.0238277i
$925$	−21.9197			−0.720715
$926$	−0.0101364	+	0.0175568i	−0.000333103	+	0.000576951i
$927$	−5.37391	−	9.30788i	−0.176502	−	0.305711i
$928$	−0.280329	−	0.485544i	−0.00920226	−	0.0159388i
$929$	−22.2160	+	38.4792i	−0.728883	+	1.26246i	0.228472	+	0.973550i	$0.426627\pi$
$929$	−22.2160	+	38.4792i	−0.728883	+	1.26246i	−0.957355	+	0.288913i	$0.906706\pi$
$930$	−0.264384			−0.00866950
$931$	−26.9835	+	19.6465i	−0.884348	+	0.643887i
$932$	52.2681			1.71210
$933$	8.80703	−	15.2542i	0.288329	−	0.499401i
$934$	−0.252033	−	0.436533i	−0.00824676	−	0.0142838i
$935$	−3.78174	−	6.55016i	−0.123676	−	0.214213i
$936$	−0.216572	+	0.375114i	−0.00707889	+	0.0122610i
$937$	59.8482			1.95516			0.977579	−	0.210571i	$-0.0675324\pi$
$937$	59.8482			1.95516			0.977579	+	0.210571i	$0.0675324\pi$
$938$	−0.182522	−	0.0386996i	−0.00595955	−	0.00126359i
$939$	−15.7406			−0.513676
$940$	32.6674	−	56.5816i	1.06549	−	1.84549i
$941$	−10.8539	−	18.7995i	−0.353827	−	0.612846i	0.633089	−	0.774079i	$-0.281787\pi$
$941$	−10.8539	−	18.7995i	−0.353827	−	0.612846i	−0.986916	+	0.161232i	$0.948453\pi$
$942$	0.0360223	+	0.0623925i	0.00117367	+	0.00203286i
$943$	3.99984	−	6.92793i	0.130253	−	0.225605i
$944$	−35.9115			−1.16882
$945$	−4.91577	+	5.46509i	−0.159910	+	0.177779i
$946$	−0.218127			−0.00709191
$947$	−8.28242	+	14.3456i	−0.269143	+	0.466169i	−0.968641	−	0.248466i	$-0.920074\pi$
$947$	−8.28242	+	14.3456i	−0.269143	+	0.466169i	0.699498	+	0.714635i	$0.253407\pi$
$948$	6.94558	+	12.0301i	0.225582	+	0.390719i
$949$	29.4662	+	51.0370i	0.956513	+	1.65673i
$950$	0.170198	−	0.294792i	0.00552196	−	0.00956432i
$951$	5.22139			0.169315
$952$	0.354591	+	1.08944i	0.0114924	+	0.0353090i
$953$	51.8971			1.68111			0.840555	−	0.541726i	$-0.182229\pi$
$953$	51.8971			1.68111			0.840555	+	0.541726i	$0.182229\pi$
$954$	−0.000798534		0.00138310i	−2.58535e−5		4.47796e-5i
$955$	−26.7196	−	46.2797i	−0.864626	−	1.49758i
$956$	17.6712	+	30.6074i	0.571527	+	0.989913i
$957$	−0.587620	+	1.01779i	−0.0189951	+	0.0329004i
$958$	0.478142			0.0154481
$959$	5.73739	+	17.6275i	0.185270	+	0.569221i
$960$	22.1803			0.715866
$961$	8.93227	−	15.4711i	0.288138	−	0.499069i
$962$	−0.436582	−	0.756183i	−0.0140760	−	0.0243803i
$963$	0.242278	+	0.419638i	0.00780730	+	0.0135226i
$964$	5.75770	−	9.97264i	0.185443	−	0.321197i
$965$	48.4885			1.56090
$966$	0.0464571	−	0.0516484i	0.00149473	−	0.00166176i
$967$	−1.28492			−0.0413202			−0.0206601	−	0.999787i	$-0.506577\pi$
$967$	−1.28492			−0.0413202			−0.0206601	+	0.999787i	$0.506577\pi$
$968$	0.554662	−	0.960702i	0.0178275	−	0.0308781i
$969$	9.83175	+	17.0291i	0.315841	+	0.547053i
$970$	0.0925490	+	0.160300i	0.00297157	+	0.00514691i
$971$	25.2486	−	43.7318i	0.810266	−	1.40342i	−0.102413	−	0.994742i	$-0.532656\pi$
$971$	25.2486	−	43.7318i	0.810266	−	1.40342i	0.912678	−	0.408679i	$-0.134010\pi$
$972$	1.99931			0.0641279
$973$	7.46727	+	1.58326i	0.239390	+	0.0507571i
$974$	0.758321			0.0242982
$975$	5.60747	−	9.71242i	0.179583	−	0.311046i
$976$	−5.41973	−	9.38725i	−0.173481	−	0.300478i
$977$	2.88750	+	5.00130i	0.0923794	+	0.160006i	0.908512	−	0.417859i	$-0.137219\pi$
$977$	2.88750	+	5.00130i	0.0923794	+	0.160006i	−0.816132	+	0.577865i	$0.803886\pi$
$978$	−0.200978	+	0.348104i	−0.00642656	+	0.0111311i
$979$	−3.91096			−0.124995
$980$	−35.5370	−	15.7789i	−1.13519	−	0.504040i
$981$	12.4652			0.397983
$982$	−0.310899	+	0.538492i	−0.00992117	+	0.0171840i
$983$	−22.1534	−	38.3708i	−0.706584	−	1.22384i	−0.966117	−	0.258106i	$-0.916902\pi$
$983$	−22.1534	−	38.3708i	−0.706584	−	1.22384i	0.259532	−	0.965734i	$-0.416432\pi$
$984$	−0.420015	−	0.727488i	−0.0133896	−	0.0231915i
$985$	1.61472	−	2.79678i	0.0514494	−	0.0891129i
$986$	0.192759			0.00613870
$987$	30.4430	+	6.45475i	0.969013	+	0.205457i
$988$	−39.3237			−1.25105
$989$	−6.29210	+	10.8982i	−0.200077	+	0.346544i
$990$	0.0240785	+	0.0417052i	0.000765266	+	0.00132548i
$991$	−4.72896	−	8.19080i	−0.150220	−	0.260189i	0.781088	−	0.624421i	$-0.214665\pi$
$991$	−4.72896	−	8.19080i	−0.150220	−	0.260189i	−0.931308	+	0.364232i	$0.881332\pi$
$992$	−0.570704	+	0.988488i	−0.0181199	+	0.0313845i
$993$	13.9449			0.442529
$994$	−0.578213	+	0.642825i	−0.0183398	+	0.0203892i
$995$	47.1665			1.49528
$996$	−9.40532	+	16.2905i	−0.298019	+	0.516184i
$997$	16.7234	+	28.9657i	0.529635	+	0.917354i	0.999402	+	0.0345640i	$0.0110043\pi$
$997$	16.7234	+	28.9657i	0.529635	+	0.917354i	−0.469768	+	0.882790i	$0.655662\pi$
$998$	0.333062	+	0.576881i	0.0105429	+	0.0182608i
$999$	−4.03105	+	6.98199i	−0.127537	+	0.220900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.6	yes	20
7.2	even	3		3381.2.a.bi.1.5		10
7.4	even	3	inner	483.2.i.h.277.6	✓	20
7.5	odd	6		3381.2.a.bj.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.6	✓	20	7.4	even	3	inner
483.2.i.h.415.6	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.5		10	7.2	even	3
3381.2.a.bj.1.5		10	7.5	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0131282 - 0.0227388i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.999655 + 1.73145i) q^{4} +(-1.38914 + 2.40606i) q^{5} +0.0262565 q^{6} +(-2.58821 - 0.548771i) q^{7} +0.105008 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0131282 - 0.0227388i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.999655 + 1.73145i) q^{4} +(-1.38914 + 2.40606i) q^{5} +0.0262565 q^{6} +(-2.58821 - 0.548771i) q^{7} +0.105008 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0364740 + 0.0631748i) q^{10} +(-0.330078 - 0.571712i) q^{11} +(-0.999655 + 1.73145i) q^{12} +4.12488 q^{13} +(-0.0464571 + 0.0516484i) q^{14} -2.77828 q^{15} +(-1.99793 + 3.46052i) q^{16} +(-2.06190 - 3.57132i) q^{17} +(0.0131282 + 0.0227388i) q^{18} +(-2.38414 + 4.12946i) q^{19} -5.55465 q^{20} +(-0.818857 - 2.51584i) q^{21} -0.0173334 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.0525039 + 0.0909395i) q^{24} +(-1.35943 - 2.35460i) q^{25} +(0.0541524 - 0.0937947i) q^{26} -1.00000 q^{27} +(-1.63715 - 5.02995i) q^{28} -1.78025 q^{29} +(-0.0364740 + 0.0631748i) q^{30} +(1.81214 + 3.13872i) q^{31} +(0.157467 + 0.272740i) q^{32} +(0.330078 - 0.571712i) q^{33} -0.108277 q^{34} +(4.91577 - 5.46509i) q^{35} -1.99931 q^{36} +(4.03105 - 6.98199i) q^{37} +(0.0625993 + 0.108425i) q^{38} +(2.06244 + 3.57225i) q^{39} +(-0.145871 + 0.252656i) q^{40} -7.99969 q^{41} +(-0.0679574 - 0.0144088i) q^{42} +12.5842 q^{43} +(0.659929 - 1.14303i) q^{44} +(-1.38914 - 2.40606i) q^{45} +(0.0131282 + 0.0227388i) q^{46} +(-5.88109 + 10.1864i) q^{47} -3.99586 q^{48} +(6.39770 + 2.84067i) q^{49} -0.0713876 q^{50} +(2.06190 - 3.57132i) q^{51} +(4.12346 + 7.14203i) q^{52} +(0.0304128 + 0.0526766i) q^{53} +(-0.0131282 + 0.0227388i) q^{54} +1.83410 q^{55} +(-0.271783 - 0.0576253i) q^{56} -4.76829 q^{57} +(-0.0233715 + 0.0404806i) q^{58} +(4.49359 + 7.78312i) q^{59} +(-2.77732 - 4.81047i) q^{60} +(-1.35633 + 2.34924i) q^{61} +0.0951611 q^{62} +(1.76936 - 1.96707i) q^{63} -7.98346 q^{64} +(-5.73004 + 9.92471i) q^{65} +(-0.00866669 - 0.0150112i) q^{66} +(1.34291 + 2.32600i) q^{67} +(4.12239 - 7.14018i) q^{68} -1.00000 q^{69} +(-0.0597339 - 0.183526i) q^{70} +12.4462 q^{71} +(-0.0525039 + 0.0909395i) q^{72} +(7.14354 + 12.3730i) q^{73} +(-0.105841 - 0.183323i) q^{74} +(1.35943 - 2.35460i) q^{75} -9.53329 q^{76} +(0.540574 + 1.66085i) q^{77} +0.108305 q^{78} +(3.47399 - 6.01712i) q^{79} +(-5.55082 - 9.61430i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.105022 + 0.181903i) q^{82} +9.40856 q^{83} +(3.53749 - 3.93279i) q^{84} +11.4571 q^{85} +(0.165208 - 0.286150i) q^{86} +(-0.890123 - 1.54174i) q^{87} +(-0.0346608 - 0.0600343i) q^{88} +(2.96215 - 5.13060i) q^{89} -0.0729480 q^{90} +(-10.6761 - 2.26361i) q^{91} -1.99931 q^{92} +(-1.81214 + 3.13872i) q^{93} +(0.154417 + 0.267458i) q^{94} +(-6.62383 - 11.4728i) q^{95} +(-0.157467 + 0.272740i) q^{96} +2.53740 q^{97} +(0.148584 - 0.108183i) q^{98} +0.660156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Introduction

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