LMFDB - Embedded newform 731.2.e.b.307.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.13
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.482661 q^{2} +(-0.0594428 + 0.102958i) q^{3} -1.76704 q^{4} +(0.220118 - 0.381256i) q^{5} +(0.0286908 - 0.0496939i) q^{6} +(-2.49924 - 4.32882i) q^{7} +1.81820 q^{8} +(1.49293 + 2.58584i) q^{9} +O(q^{10})$	\(q-0.482661 q^{2} +(-0.0594428 + 0.102958i) q^{3} -1.76704 q^{4} +(0.220118 - 0.381256i) q^{5} +(0.0286908 - 0.0496939i) q^{6} +(-2.49924 - 4.32882i) q^{7} +1.81820 q^{8} +(1.49293 + 2.58584i) q^{9} +(-0.106243 + 0.184018i) q^{10} -4.05955 q^{11} +(0.105038 - 0.181931i) q^{12} +(1.12306 + 1.94520i) q^{13} +(1.20629 + 2.08935i) q^{14} +(0.0261689 + 0.0453259i) q^{15} +2.65650 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.720581 - 1.24808i) q^{18} +(-1.18294 + 2.04891i) q^{19} +(-0.388957 + 0.673694i) q^{20} +0.594248 q^{21} +1.95939 q^{22} +(-0.880883 + 1.52573i) q^{23} +(-0.108079 + 0.187199i) q^{24} +(2.40310 + 4.16228i) q^{25} +(-0.542059 - 0.938874i) q^{26} -0.711634 q^{27} +(4.41626 + 7.64919i) q^{28} +(2.51559 + 4.35713i) q^{29} +(-0.0126307 - 0.0218771i) q^{30} +(3.35822 - 5.81660i) q^{31} -4.91860 q^{32} +(0.241311 - 0.417963i) q^{33} +(0.241331 + 0.417997i) q^{34} -2.20052 q^{35} +(-2.63807 - 4.56927i) q^{36} +(-5.96042 + 10.3238i) q^{37} +(0.570958 - 0.988928i) q^{38} -0.267032 q^{39} +(0.400220 - 0.693201i) q^{40} +5.69532 q^{41} -0.286821 q^{42} +(-1.14519 + 6.45667i) q^{43} +7.17337 q^{44} +1.31449 q^{45} +(0.425168 - 0.736413i) q^{46} +4.99904 q^{47} +(-0.157910 + 0.273508i) q^{48} +(-8.99244 + 15.5754i) q^{49} +(-1.15988 - 2.00897i) q^{50} +0.118886 q^{51} +(-1.98450 - 3.43725i) q^{52} +(-4.54265 + 7.86810i) q^{53} +0.343478 q^{54} +(-0.893581 + 1.54773i) q^{55} +(-4.54414 - 7.87067i) q^{56} +(-0.140634 - 0.243586i) q^{57} +(-1.21418 - 2.10302i) q^{58} -14.1065 q^{59} +(-0.0462414 - 0.0800925i) q^{60} +(-3.90311 - 6.76038i) q^{61} +(-1.62088 + 2.80745i) q^{62} +(7.46241 - 12.9253i) q^{63} -2.93898 q^{64} +0.988827 q^{65} +(-0.116471 + 0.201735i) q^{66} +(-3.14993 + 5.45584i) q^{67} +(0.883519 + 1.53030i) q^{68} +(-0.104724 - 0.181388i) q^{69} +1.06210 q^{70} +(-0.781438 - 1.35349i) q^{71} +(2.71446 + 4.70158i) q^{72} +(0.488942 + 0.846873i) q^{73} +(2.87687 - 4.98288i) q^{74} -0.571387 q^{75} +(2.09029 - 3.62049i) q^{76} +(10.1458 + 17.5730i) q^{77} +0.128886 q^{78} +(3.73510 + 6.46938i) q^{79} +(0.584744 - 1.01281i) q^{80} +(-4.43650 + 7.68424i) q^{81} -2.74891 q^{82} +(0.540709 - 0.936536i) q^{83} -1.05006 q^{84} -0.440237 q^{85} +(0.552740 - 3.11638i) q^{86} -0.598136 q^{87} -7.38109 q^{88} +(8.52396 - 14.7639i) q^{89} -0.634452 q^{90} +(5.61362 - 9.72307i) q^{91} +(1.55655 - 2.69603i) q^{92} +(0.399244 + 0.691510i) q^{93} -2.41284 q^{94} +(0.520772 + 0.902003i) q^{95} +(0.292375 - 0.506409i) q^{96} +13.6563 q^{97} +(4.34031 - 7.51763i) q^{98} +(-6.06063 - 10.4973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.482661			−0.341293			−0.170647	−	0.985332i	$-0.554586\pi$
$2$	−0.482661			−0.341293			−0.170647	+	0.985332i	$0.554586\pi$
$3$	−0.0594428	+	0.102958i	−0.0343193	+	0.0594428i	−0.882675	−	0.469984i	$-0.844260\pi$
$3$	−0.0594428	+	0.102958i	−0.0343193	+	0.0594428i	0.848356	+	0.529427i	$0.177593\pi$
$4$	−1.76704			−0.883519
$5$	0.220118	−	0.381256i	0.0984399	−	0.170503i	−0.812599	−	0.582823i	$-0.801948\pi$
$5$	0.220118	−	0.381256i	0.0984399	−	0.170503i	0.911039	+	0.412320i	$0.135281\pi$
$6$	0.0286908	−	0.0496939i	0.0117130	−	0.0202874i
$7$	−2.49924	−	4.32882i	−0.944626	−	1.63614i	−0.756499	−	0.653995i	$-0.773092\pi$
$7$	−2.49924	−	4.32882i	−0.944626	−	1.63614i	−0.188126	−	0.982145i	$-0.560241\pi$
$8$	1.81820			0.642832
$9$	1.49293	+	2.58584i	0.497644	+	0.861945i
$10$	−0.106243	+	0.184018i	−0.0335969	+	0.0581915i
$11$	−4.05955			−1.22400			−0.612000	−	0.790858i	$-0.709635\pi$
$11$	−4.05955			−1.22400			−0.612000	+	0.790858i	$0.709635\pi$
$12$	0.105038	−	0.181931i	0.0303218	−	0.0525189i
$13$	1.12306	+	1.94520i	0.311482	+	0.539502i	0.978683	−	0.205375i	$-0.0658414\pi$
$13$	1.12306	+	1.94520i	0.311482	+	0.539502i	−0.667202	+	0.744877i	$0.732508\pi$
$14$	1.20629	+	2.08935i	0.322394	+	0.558403i
$15$	0.0261689	+	0.0453259i	0.00675678	+	0.0117031i
$16$	2.65650			0.664125
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	−0.720581	−	1.24808i	−0.169843	−	0.294176i
$19$	−1.18294	+	2.04891i	−0.271384	+	0.470051i	−0.969217	−	0.246210i	$-0.920815\pi$
$19$	−1.18294	+	2.04891i	−0.271384	+	0.470051i	0.697832	+	0.716261i	$0.254148\pi$
$20$	−0.388957	+	0.673694i	−0.0869735	+	0.150643i
$21$	0.594248			0.129676
$22$	1.95939			0.417743
$23$	−0.880883	+	1.52573i	−0.183677	+	0.318138i	−0.943130	−	0.332425i	$-0.892133\pi$
$23$	−0.880883	+	1.52573i	−0.183677	+	0.318138i	0.759453	+	0.650562i	$0.225467\pi$
$24$	−0.108079	+	0.187199i	−0.0220616	+	0.0382118i
$25$	2.40310	+	4.16228i	0.480619	+	0.832457i
$26$	−0.542059	−	0.938874i	−0.106307	−	0.184128i
$27$	−0.711634			−0.136954
$28$	4.41626	+	7.64919i	0.834595	+	1.44556i
$29$	2.51559	+	4.35713i	0.467134	+	0.809099i	0.999295	−	0.0375436i	$-0.0119533\pi$
$29$	2.51559	+	4.35713i	0.467134	+	0.809099i	−0.532161	+	0.846643i	$0.678620\pi$
$30$	−0.0126307	−	0.0218771i	−0.00230604	−	0.00399418i
$31$	3.35822	−	5.81660i	0.603153	−	1.04469i	−0.389187	−	0.921159i	$-0.627244\pi$
$31$	3.35822	−	5.81660i	0.603153	−	1.04469i	0.992340	−	0.123533i	$-0.0394226\pi$
$32$	−4.91860			−0.869493
$33$	0.241311	−	0.417963i	0.0420068	−	0.0727580i
$34$	0.241331	+	0.417997i	0.0413879	+	0.0716859i
$35$	−2.20052			−0.371955
$36$	−2.63807	−	4.56927i	−0.439678	−	0.761545i
$37$	−5.96042	+	10.3238i	−0.979888	+	1.69722i	−0.317128	+	0.948383i	$0.602719\pi$
$37$	−5.96042	+	10.3238i	−0.979888	+	1.69722i	−0.662759	+	0.748832i	$0.730615\pi$
$38$	0.570958	−	0.988928i	0.0926216	−	0.160425i
$39$	−0.267032			−0.0427594
$40$	0.400220	−	0.693201i	0.0632803	−	0.109605i
$41$	5.69532			0.889459			0.444730	−	0.895665i	$-0.353300\pi$
$41$	5.69532			0.889459			0.444730	+	0.895665i	$0.353300\pi$
$42$	−0.286821			−0.0442574
$43$	−1.14519	+	6.45667i	−0.174640	+	0.984632i
$43$	−1.14519	+	6.45667i	−0.174640	+	0.984632i
$44$	7.17337			1.08143
$45$	1.31449			0.195952
$46$	0.425168	−	0.736413i	0.0626876	−	0.108578i
$47$	4.99904			0.729185			0.364592	−	0.931167i	$-0.381208\pi$
$47$	4.99904			0.729185			0.364592	+	0.931167i	$0.381208\pi$
$48$	−0.157910	+	0.273508i	−0.0227923	+	0.0394774i
$49$	−8.99244	+	15.5754i	−1.28463	+	2.22505i
$50$	−1.15988	−	2.00897i	−0.164032	−	0.284112i
$51$	0.118886			0.0166473
$52$	−1.98450	−	3.43725i	−0.275200	−	0.476660i
$53$	−4.54265	+	7.86810i	−0.623981	+	1.08077i	0.364756	+	0.931103i	$0.381153\pi$
$53$	−4.54265	+	7.86810i	−0.623981	+	1.08077i	−0.988737	+	0.149664i	$0.952181\pi$
$54$	0.343478			0.0467415
$55$	−0.893581	+	1.54773i	−0.120490	+	0.208695i
$56$	−4.54414	−	7.87067i	−0.607236	−	1.05176i
$57$	−0.140634	−	0.243586i	−0.0186275	−	0.0322637i
$58$	−1.21418	−	2.10302i	−0.159430	−	0.276140i
$59$	−14.1065			−1.83652			−0.918258	−	0.395984i	$-0.870404\pi$
$59$	−14.1065			−1.83652			−0.918258	+	0.395984i	$0.870404\pi$
$60$	−0.0462414	−	0.0800925i	−0.00596974	−	0.0103399i
$61$	−3.90311	−	6.76038i	−0.499742	−	0.865578i	0.500258	−	0.865876i	$-0.333238\pi$
$61$	−3.90311	−	6.76038i	−0.499742	−	0.865578i	−1.00000		0.000297990i	$0.999905\pi$
$62$	−1.62088	+	2.80745i	−0.205852	+	0.356546i
$63$	7.46241	−	12.9253i	0.940175	−	1.62843i
$64$	−2.93898			−0.367372
$65$	0.988827			0.122649
$66$	−0.116471	+	0.201735i	−0.0143367	+	0.0248318i
$67$	−3.14993	+	5.45584i	−0.384825	+	0.666537i	−0.991745	−	0.128226i	$-0.959072\pi$
$67$	−3.14993	+	5.45584i	−0.384825	+	0.666537i	0.606920	+	0.794763i	$0.292405\pi$
$68$	0.883519	+	1.53030i	0.107142	+	0.185576i
$69$	−0.104724	−	0.181388i	−0.0126073	−	0.0218365i
$70$	1.06210			0.126946
$71$	−0.781438	−	1.35349i	−0.0927396	−	0.160630i	0.815923	−	0.578160i	$-0.196229\pi$
$71$	−0.781438	−	1.35349i	−0.0927396	−	0.160630i	−0.908663	+	0.417530i	$0.862896\pi$
$72$	2.71446	+	4.70158i	0.319902	+	0.554086i
$73$	0.488942	+	0.846873i	0.0572264	+	0.0991190i	0.893219	−	0.449621i	$-0.148441\pi$
$73$	0.488942	+	0.846873i	0.0572264	+	0.0991190i	−0.835993	+	0.548740i	$0.815108\pi$
$74$	2.87687	−	4.98288i	0.334429	−	0.579248i
$75$	−0.571387			−0.0659781
$76$	2.09029	−	3.62049i	0.239773	−	0.415299i
$77$	10.1458	+	17.5730i	1.15622	+	2.00263i
$78$	0.128886			0.0145935
$79$	3.73510	+	6.46938i	0.420231	+	0.727862i	0.995962	−	0.0897774i	$-0.0286156\pi$
$79$	3.73510	+	6.46938i	0.420231	+	0.727862i	−0.575730	+	0.817640i	$0.695282\pi$
$80$	0.584744	−	1.01281i	0.0653764	−	0.113235i
$81$	−4.43650	+	7.68424i	−0.492944	+	0.853804i
$82$	−2.74891			−0.303566
$83$	0.540709	−	0.936536i	0.0593505	−	0.102798i	−0.834824	−	0.550518i	$-0.814430\pi$
$83$	0.540709	−	0.936536i	0.0593505	−	0.102798i	0.894174	+	0.447720i	$0.147764\pi$
$84$	−1.05006			−0.114571
$85$	−0.440237			−0.0477504
$86$	0.552740	−	3.11638i	0.0596034	−	0.336048i
$87$	−0.598136			−0.0641269
$88$	−7.38109			−0.786826
$89$	8.52396	−	14.7639i	0.903538	−	1.56497i	0.0806703	−	0.996741i	$-0.474294\pi$
$89$	8.52396	−	14.7639i	0.903538	−	1.56497i	0.822868	−	0.568233i	$-0.192373\pi$
$90$	−0.634452			−0.0668772
$91$	5.61362	−	9.72307i	0.588467	−	1.01925i
$92$	1.55655	−	2.69603i	0.162282	−	0.281081i
$93$	0.399244	+	0.691510i	0.0413996	+	0.0717063i
$94$	−2.41284			−0.248866
$95$	0.520772	+	0.902003i	0.0534301	+	0.0925436i
$96$	0.292375	−	0.506409i	0.0298404	−	0.0516851i
$97$	13.6563			1.38659			0.693296	−	0.720653i	$-0.256158\pi$
$97$	13.6563			1.38659			0.693296	+	0.720653i	$0.256158\pi$
$98$	4.34031	−	7.51763i	0.438437	−	0.759395i
$99$	−6.06063	−	10.4973i	−0.609116	−	1.05502i
$100$	−4.24636	−	7.35491i	−0.424636	−	0.735491i
$101$	4.45615	+	7.71828i	0.443404	+	0.767998i	0.997939	−	0.0641620i	$-0.0204374\pi$
$101$	4.45615	+	7.71828i	0.443404	+	0.767998i	−0.554536	+	0.832160i	$0.687104\pi$
$102$	−0.0573815			−0.00568162
$103$	3.74949	+	6.49431i	0.369448	+	0.639903i	0.989479	−	0.144674i	$-0.0462133\pi$
$103$	3.74949	+	6.49431i	0.369448	+	0.639903i	−0.620031	+	0.784577i	$0.712880\pi$
$104$	2.04196	+	3.53678i	0.200230	+	0.346809i
$105$	0.130805	−	0.226561i	0.0127653	−	0.0221101i
$106$	2.19256	−	3.79763i	0.212961	−	0.368859i
$107$	5.58849			0.540259			0.270130	−	0.962824i	$-0.412933\pi$
$107$	5.58849			0.540259			0.270130	+	0.962824i	$0.412933\pi$
$108$	1.25748			0.121001
$109$	7.10210	−	12.3012i	0.680258	−	1.17824i	−0.294644	−	0.955607i	$-0.595201\pi$
$109$	7.10210	−	12.3012i	0.680258	−	1.17824i	0.974902	−	0.222634i	$-0.0714655\pi$
$110$	0.431297	−	0.747028i	0.0411225	−	0.0712263i
$111$	−0.708609	−	1.22735i	−0.0672582	−	0.116495i
$112$	−6.63924	−	11.4995i	−0.627349	−	1.08660i
$113$	−17.5165			−1.64782			−0.823908	−	0.566724i	$-0.808211\pi$
$113$	−17.5165			−1.64782			−0.823908	+	0.566724i	$0.808211\pi$
$114$	0.0678787	+	0.117569i	0.00635742	+	0.0110114i
$115$	0.387797	+	0.671684i	0.0361622	+	0.0626348i
$116$	−4.44515	−	7.69922i	−0.412722	−	0.714855i
$117$	−3.35332	+	5.80811i	−0.310014	+	0.536960i
$118$	6.80868			0.626790
$119$	−2.49924	+	4.32882i	−0.229105	+	0.396822i
$120$	0.0475804	+	0.0824117i	0.00434348	+	0.00752312i
$121$	5.47992			0.498175
$122$	1.88388	+	3.26298i	0.170559	+	0.295416i
$123$	−0.338546	+	0.586379i	−0.0305256	+	0.0528720i
$124$	−5.93409	+	10.2782i	−0.532897	+	0.923005i
$125$	4.31704			0.386128
$126$	−3.60182	+	6.23853i	−0.320875	+	0.555772i
$127$	8.71315			0.773167			0.386584	−	0.922254i	$-0.373655\pi$
$127$	8.71315			0.773167			0.386584	+	0.922254i	$0.373655\pi$
$128$	11.2557			0.994875
$129$	−0.596692	−	0.501709i	−0.0525358	−	0.0441730i
$130$	−0.477269			−0.0418592
$131$	−13.7715			−1.20322			−0.601610	−	0.798790i	$-0.705474\pi$
$131$	−13.7715			−1.20322			−0.601610	+	0.798790i	$0.705474\pi$
$132$	−0.426406	+	0.738556i	−0.0371138	+	0.0642831i
$133$	11.8258			1.02543
$134$	1.52035	−	2.63332i	0.131338	−	0.227485i
$135$	−0.156644	+	0.271315i	−0.0134817	+	0.0233510i
$136$	−0.909102	−	1.57461i	−0.0779549	−	0.135022i
$137$	−16.4225			−1.40307			−0.701535	−	0.712635i	$-0.747502\pi$
$137$	−16.4225			−1.40307			−0.701535	+	0.712635i	$0.747502\pi$
$138$	0.0505464	+	0.0875489i	0.00430280	+	0.00745266i
$139$	0.262418	−	0.454521i	0.0222580	−	0.0385520i	−0.854682	−	0.519152i	$-0.826248\pi$
$139$	0.262418	−	0.454521i	0.0222580	−	0.0385520i	0.876940	+	0.480600i	$0.159581\pi$
$140$	3.88840			0.328630
$141$	−0.297157	+	0.514691i	−0.0250251	+	0.0433448i
$142$	0.377170	+	0.653278i	0.0316514	+	0.0548218i
$143$	−4.55913	−	7.89664i	−0.381253	−	0.660350i
$144$	3.96597	+	6.86927i	0.330498	+	0.572439i
$145$	2.21491			0.183938
$146$	−0.235994	−	0.408753i	−0.0195310	−	0.0338286i
$147$	−1.06907	−	1.85169i	−0.0881756	−	0.152725i
$148$	10.5323	−	18.2425i	0.865749	−	1.49952i
$149$	−2.67280	+	4.62943i	−0.218965	+	0.379258i	−0.954492	−	0.298238i	$-0.903601\pi$
$149$	−2.67280	+	4.62943i	−0.218965	+	0.379258i	0.735527	+	0.677495i	$0.236935\pi$
$150$	0.275787			0.0225179
$151$	−3.37353			−0.274534			−0.137267	−	0.990534i	$-0.543832\pi$
$151$	−3.37353			−0.274534			−0.137267	+	0.990534i	$0.543832\pi$
$152$	−2.15082	+	3.72533i	−0.174455	+	0.302164i
$153$	1.49293	−	2.58584i	0.120696	−	0.209052i
$154$	−4.89699	−	8.48183i	−0.394610	−	0.683485i
$155$	−1.47841	−	2.56068i	−0.118749	−	0.205679i
$156$	0.471856			0.0377787
$157$	−9.54386	−	16.5304i	−0.761683	−	1.31927i	−0.941983	−	0.335661i	$-0.891040\pi$
$157$	−9.54386	−	16.5304i	−0.761683	−	1.31927i	0.180300	−	0.983612i	$-0.442293\pi$
$158$	−1.80279	−	3.12252i	−0.143422	−	0.248414i
$159$	−0.540056	−	0.935405i	−0.0428292	−	0.0741824i
$160$	−1.08267	+	1.87525i	−0.0855928	+	0.148251i
$161$	8.80617			0.694023
$162$	2.14133	−	3.70889i	0.168239	−	0.291398i
$163$	8.93140	+	15.4696i	0.699561	+	1.21168i	0.968619	+	0.248552i	$0.0799546\pi$
$163$	8.93140	+	15.4696i	0.699561	+	1.21168i	−0.269057	+	0.963124i	$0.586712\pi$
$164$	−10.0638			−0.785854
$165$	−0.106234	−	0.184002i	−0.00827030	−	0.0143246i
$166$	−0.260980	+	0.452030i	−0.0202559	+	0.0350843i
$167$	−11.3815	+	19.7133i	−0.880724	+	1.52546i	−0.0301855	+	0.999544i	$0.509610\pi$
$167$	−11.3815	+	19.7133i	−0.880724	+	1.52546i	−0.850538	+	0.525914i	$0.823724\pi$
$168$	1.08047			0.0833597
$169$	3.97746	−	6.88916i	0.305958	−	0.529935i
$170$	0.212485			0.0162969
$171$	−7.06418			−0.540211
$172$	2.02360	−	11.4092i	0.154298	−	0.869941i
$173$	−8.84492			−0.672467			−0.336233	−	0.941779i	$-0.609153\pi$
$173$	−8.84492			−0.672467			−0.336233	+	0.941779i	$0.609153\pi$
$174$	0.288697			0.0218861
$175$	12.0118	−	20.8051i	0.908010	−	1.57272i
$176$	−10.7842			−0.812888
$177$	0.838532	−	1.45238i	0.0630280	−	0.109168i
$178$	−4.11419	+	7.12598i	−0.308371	+	0.534115i
$179$	−10.9645	−	18.9911i	−0.819526	−	1.41946i	−0.906032	−	0.423209i	$-0.860904\pi$
$179$	−10.9645	−	18.9911i	−0.819526	−	1.41946i	0.0865067	−	0.996251i	$-0.472430\pi$
$180$	−2.32275			−0.173127
$181$	−2.21805	−	3.84177i	−0.164866	−	0.285557i	0.771741	−	0.635936i	$-0.219386\pi$
$181$	−2.21805	−	3.84177i	−0.164866	−	0.285557i	−0.936608	+	0.350380i	$0.886053\pi$
$182$	−2.70948	+	4.69295i	−0.200840	+	0.347865i
$183$	0.928047			0.0686032
$184$	−1.60162	+	2.77410i	−0.118073	+	0.204509i
$185$	2.62400	+	4.54489i	0.192920	+	0.334147i
$186$	−0.192700	−	0.333765i	−0.0141294	−	0.0244729i
$187$	2.02977	+	3.51567i	0.148432	+	0.257091i
$188$	−8.83349			−0.644249
$189$	1.77855	+	3.08053i	0.129370	+	0.224076i
$190$	−0.251357	−	0.435362i	−0.0182353	−	0.0315845i
$191$	6.52253	−	11.2973i	0.471953	−	0.817447i	−0.527532	−	0.849535i	$-0.676882\pi$
$191$	6.52253	−	11.2973i	0.471953	−	0.817447i	0.999485	+	0.0320881i	$0.0102157\pi$
$192$	0.174701	−	0.302591i	0.0126080	−	0.0218377i
$193$	13.9328			1.00291			0.501453	−	0.865185i	$-0.332799\pi$
$193$	13.9328			1.00291			0.501453	+	0.865185i	$0.332799\pi$
$194$	−6.59139			−0.473234
$195$	−0.0587787	+	0.101808i	−0.00420923	+	0.00729060i
$196$	15.8900	−	27.5223i	1.13500	−	1.96588i
$197$	7.79120	+	13.4948i	0.555100	+	0.961462i	0.997896	+	0.0648392i	$0.0206535\pi$
$197$	7.79120	+	13.4948i	0.555100	+	0.961462i	−0.442795	+	0.896623i	$0.646013\pi$
$198$	2.92523	+	5.06665i	0.207887	+	0.360071i
$199$	12.3138			0.872905			0.436453	−	0.899727i	$-0.356235\pi$
$199$	12.3138			0.872905			0.436453	+	0.899727i	$0.356235\pi$
$200$	4.36932	+	7.56788i	0.308958	+	0.535130i
$201$	−0.374481	−	0.648621i	−0.0264139	−	0.0457502i
$202$	−2.15081	−	3.72532i	−0.151331	−	0.262112i
$203$	12.5742	−	21.7791i	0.882533	−	1.52859i
$204$	−0.210075			−0.0147082
$205$	1.25364	−	2.17137i	0.0875583	−	0.151655i
$206$	−1.80974	−	3.13455i	−0.126090	−	0.218395i
$207$	−5.26040			−0.365623
$208$	2.98342	+	5.16743i	0.206863	+	0.358297i
$209$	4.80219	−	8.31763i	0.332174	−	0.575343i
$210$	−0.0631345	+	0.109352i	−0.00435670	+	0.00754602i
$211$	−11.3511			−0.781439			−0.390719	−	0.920510i	$-0.627774\pi$
$211$	−11.3511			−0.781439			−0.390719	+	0.920510i	$0.627774\pi$
$212$	8.02704	−	13.9032i	0.551299	−	0.954878i
$213$	0.185803			0.0127310
$214$	−2.69735			−0.184387
$215$	2.20957	+	1.85784i	0.150691	+	0.126704i
$216$	−1.29390			−0.0880384
$217$	−33.5720			−2.27902
$218$	−3.42791	+	5.93731i	−0.232167	+	0.402126i
$219$	−0.116256			−0.00785588
$220$	1.57899	−	2.73489i	0.106456	−	0.184386i
$221$	1.12306	−	1.94520i	0.0755454	−	0.130848i
$222$	0.342018	+	0.592393i	0.0229548	+	0.0397588i
$223$	2.28897			0.153281			0.0766405	−	0.997059i	$-0.475581\pi$
$223$	2.28897			0.153281			0.0766405	+	0.997059i	$0.475581\pi$
$224$	12.2928	+	21.2917i	0.821346	+	1.42261i
$225$	−7.17532	+	12.4280i	−0.478355	+	0.828535i
$226$	8.45455			0.562388
$227$	−0.573579	+	0.993467i	−0.0380697	+	0.0659387i	−0.884432	−	0.466668i	$-0.845454\pi$
$227$	−0.573579	+	0.993467i	−0.0380697	+	0.0659387i	0.846363	+	0.532607i	$0.178788\pi$
$228$	0.248506	+	0.430425i	0.0164577	+	0.0285056i
$229$	−8.80178	−	15.2451i	−0.581638	−	1.00743i	−0.995285	−	0.0969892i	$-0.969079\pi$
$229$	−8.80178	−	15.2451i	−0.581638	−	1.00743i	0.413648	−	0.910437i	$-0.364255\pi$
$230$	−0.187175	−	0.324196i	−0.0123419	−	0.0213768i
$231$	−2.41238			−0.158723
$232$	4.57386	+	7.92216i	0.300289	+	0.520115i
$233$	5.70253	+	9.87706i	0.373585	+	0.647068i	0.990114	−	0.140264i	$-0.0447951\pi$
$233$	5.70253	+	9.87706i	0.373585	+	0.647068i	−0.616529	+	0.787332i	$0.711462\pi$
$234$	1.61852	−	2.80335i	0.105806	−	0.183261i
$235$	1.10038	−	1.90591i	0.0717809	−	0.124328i
$236$	24.9268			1.62260
$237$	−0.888099			−0.0576882
$238$	1.20629	−	2.08935i	0.0781921	−	0.135433i
$239$	−12.6931	+	21.9851i	−0.821047	+	1.42209i	0.0838566	+	0.996478i	$0.473276\pi$
$239$	−12.6931	+	21.9851i	−0.821047	+	1.42209i	−0.904903	+	0.425617i	$0.860057\pi$
$240$	0.0695177	+	0.120408i	0.00448735	+	0.00777231i
$241$	−7.49168	−	12.9760i	−0.482582	−	0.835856i	0.517218	−	0.855854i	$-0.326968\pi$
$241$	−7.49168	−	12.9760i	−0.482582	−	0.835856i	−0.999800	+	0.0199973i	$0.993634\pi$
$242$	−2.64495			−0.170024
$243$	−1.59489	−	2.76242i	−0.102312	−	0.177210i
$244$	6.89694	+	11.9459i	0.441531	+	0.764755i
$245$	3.95880	+	6.85685i	0.252919	+	0.438068i
$246$	0.163403	−	0.283022i	0.0104182	−	0.0180448i
$247$	−5.31405			−0.338125
$248$	6.10592	−	10.5758i	0.387726	−	0.671562i
$249$	0.0642826	+	0.111341i	0.00407374	+	0.00705593i
$250$	−2.08367			−0.131783
$251$	8.62276	+	14.9351i	0.544264	+	0.942693i	0.998653	+	0.0518894i	$0.0165243\pi$
$251$	8.62276	+	14.9351i	0.544264	+	0.942693i	−0.454389	+	0.890803i	$0.650142\pi$
$252$	−13.1864	+	22.8394i	−0.830663	+	1.43875i
$253$	3.57599	−	6.19379i	0.224820	−	0.389400i
$254$	−4.20550			−0.263877
$255$	0.0261689	−	0.0453259i	0.00163876	−	0.00283842i
$256$	0.445252			0.0278283
$257$	−15.2049			−0.948458			−0.474229	−	0.880401i	$-0.657273\pi$
$257$	−15.2049			−0.948458			−0.474229	+	0.880401i	$0.657273\pi$
$258$	0.288000	+	0.242156i	0.0179301	+	0.0150760i
$259$	59.5862			3.70251
$260$	−1.74729			−0.108363
$261$	−7.51122	+	13.0098i	−0.464933	+	0.805288i
$262$	6.64697			0.410651
$263$	−8.19054	+	14.1864i	−0.505050	+	0.874773i	0.494933	+	0.868931i	$0.335193\pi$
$263$	−8.19054	+	14.1864i	−0.505050	+	0.874773i	−0.999983	+	0.00584147i	$0.998141\pi$
$264$	0.438753	−	0.759942i	0.0270034	−	0.0467712i
$265$	1.99984	+	3.46383i	0.122849	+	0.212781i
$266$	−5.70785			−0.349971
$267$	1.01338	+	1.75522i	0.0620176	+	0.107418i
$268$	5.56605	−	9.64067i	0.340000	−	0.588898i
$269$	−11.1381			−0.679102			−0.339551	−	0.940588i	$-0.610275\pi$
$269$	−11.1381			−0.679102			−0.339551	+	0.940588i	$0.610275\pi$
$270$	0.0756058	−	0.130953i	0.00460122	−	0.00796955i
$271$	8.65985	+	14.9993i	0.526048	+	0.911143i	0.999540	+	0.0303440i	$0.00966029\pi$
$271$	8.65985	+	14.9993i	0.526048	+	0.911143i	−0.473491	+	0.880799i	$0.657006\pi$
$272$	−1.32825	−	2.30060i	−0.0805369	−	0.139494i
$273$	0.667379	+	1.15593i	0.0403916	+	0.0699603i
$274$	7.92652			0.478858
$275$	−9.75548	−	16.8970i	−0.588278	−	1.01893i
$276$	0.185052	+	0.320519i	0.0111388	+	0.0192930i
$277$	2.04487	−	3.54182i	0.122864	−	0.212808i	−0.798032	−	0.602615i	$-0.794125\pi$
$277$	2.04487	−	3.54182i	0.122864	−	0.212808i	0.920896	+	0.389808i	$0.127459\pi$
$278$	−0.126659	+	0.219380i	−0.00759650	+	0.0131575i
$279$	20.0544			1.20062
$280$	−4.00099			−0.239105
$281$	−1.38999	+	2.40753i	−0.0829197	+	0.143621i	−0.904503	−	0.426468i	$-0.859758\pi$
$281$	−1.38999	+	2.40753i	−0.0829197	+	0.143621i	0.821583	+	0.570089i	$0.193091\pi$
$282$	0.143426	−	0.248422i	0.00854091	−	0.0147933i
$283$	−14.0193	−	24.2822i	−0.833362	−	1.44342i	−0.895358	−	0.445348i	$-0.853080\pi$
$283$	−14.0193	−	24.2822i	−0.833362	−	1.44342i	0.0619960	−	0.998076i	$-0.480253\pi$
$284$	1.38083	+	2.39167i	0.0819372	+	0.141919i
$285$	−0.123825			−0.00733474
$286$	2.20052	+	3.81140i	0.130119	+	0.225373i
$287$	−14.2340	−	24.6540i	−0.840206	−	1.45528i
$288$	−7.34314	−	12.7187i	−0.432699	−	0.749456i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−1.06905			−0.0627769
$291$	−0.811771	+	1.40603i	−0.0475869	+	0.0824229i
$292$	−0.863980	−	1.49646i	−0.0505606	−	0.0875735i
$293$	−4.79455			−0.280100			−0.140050	−	0.990144i	$-0.544726\pi$
$293$	−4.79455			−0.280100			−0.140050	+	0.990144i	$0.544726\pi$
$294$	0.516000	+	0.893738i	0.0300937	+	0.0521239i
$295$	−3.10511	+	5.37820i	−0.180786	+	0.313131i
$296$	−10.8373	+	18.7707i	−0.629903	+	1.09102i
$297$	2.88891			0.167632
$298$	1.29006	−	2.23445i	0.0747311	−	0.129438i
$299$	−3.95715			−0.228848
$300$	1.00966			0.0582929
$301$	30.8118	−	11.1795i	1.77597	−	0.644373i
$302$	1.62827			0.0936966
$303$	−1.05955			−0.0608693
$304$	−3.14247	+	5.44292i	−0.180233	+	0.312173i
$305$	−3.43658			−0.196778
$306$	−0.720581	+	1.24808i	−0.0411929	+	0.0713482i
$307$	−15.4252	+	26.7172i	−0.880363	+	1.52483i	−0.0294250	+	0.999567i	$0.509368\pi$
$307$	−15.4252	+	26.7172i	−0.880363	+	1.52483i	−0.850938	+	0.525266i	$0.823966\pi$
$308$	−17.9280	−	31.0522i	−1.02154	−	1.76936i
$309$	−0.891522			−0.0507169
$310$	0.713571	+	1.23594i	0.0405281	+	0.0701968i
$311$	−4.34735	+	7.52983i	−0.246516	+	0.426978i	−0.962557	−	0.271081i	$-0.912619\pi$
$311$	−4.34735	+	7.52983i	−0.246516	+	0.426978i	0.716041	+	0.698058i	$0.245952\pi$
$312$	−0.485519			−0.0274871
$313$	−11.9179	+	20.6424i	−0.673638	+	1.16678i	0.303227	+	0.952918i	$0.401936\pi$
$313$	−11.9179	+	20.6424i	−0.673638	+	1.16678i	−0.976865	+	0.213857i	$0.931397\pi$
$314$	4.60645	+	7.97861i	0.259957	+	0.450259i
$315$	−3.28523	−	5.69018i	−0.185101	−	0.320605i
$316$	−6.60006	−	11.4316i	−0.371282	−	0.643080i
$317$	−24.1016			−1.35368			−0.676841	−	0.736130i	$-0.736651\pi$
$317$	−24.1016			−1.35368			−0.676841	+	0.736130i	$0.736651\pi$
$318$	0.260664	+	0.451484i	0.0146173	+	0.0253180i
$319$	−10.2122	−	17.6880i	−0.571772	−	0.990337i
$320$	−0.646923	+	1.12050i	−0.0361641	+	0.0626381i
$321$	−0.332195	+	0.575379i	−0.0185413	+	0.0321145i
$322$	−4.25040			−0.236865
$323$	2.36587			0.131641
$324$	7.83946	−	13.5783i	0.435526	−	0.754352i
$325$	−5.39766	+	9.34902i	−0.299408	+	0.518590i
$326$	−4.31084	−	7.46660i	−0.238756	−	0.413537i
$327$	0.844338	+	1.46244i	0.0466920	+	0.0808729i
$328$	10.3553			0.571773
$329$	−12.4938	−	21.6399i	−0.688807	−	1.19305i
$330$	0.0512750	+	0.0888109i	0.00282260	+	0.00488888i
$331$	7.41225	+	12.8384i	0.407414	+	0.705662i	0.994599	−	0.103791i	$-0.0330973\pi$
$331$	7.41225	+	12.8384i	0.407414	+	0.705662i	−0.587185	+	0.809453i	$0.699764\pi$
$332$	−0.955454	+	1.65489i	−0.0524373	+	0.0908241i
$333$	−35.5941			−1.95054
$334$	5.49339	−	9.51483i	0.300585	−	0.520628i
$335$	1.38671	+	2.40186i	0.0757643	+	0.131228i
$336$	1.57862			0.0861208
$337$	−9.64253	−	16.7014i	−0.525262	−	0.909781i	−0.999567	−	0.0294201i	$-0.990634\pi$
$337$	−9.64253	−	16.7014i	−0.525262	−	0.909781i	0.474305	−	0.880361i	$-0.342699\pi$
$338$	−1.91977	+	3.32513i	−0.104422	+	0.180863i
$339$	1.04123	−	1.80347i	0.0565519	−	0.0979508i
$340$	0.777915			0.0421883
$341$	−13.6328	+	23.6128i	−0.738259	+	1.27870i
$342$	3.40961			0.184370
$343$	54.9078			2.96474
$344$	−2.08219	+	11.7395i	−0.112264	+	0.632953i
$345$	−0.0922070			−0.00496426
$346$	4.26910			0.229508
$347$	−9.57139	+	16.5781i	−0.513819	+	0.889960i	0.486053	+	0.873930i	$0.338436\pi$
$347$	−9.57139	+	16.5781i	−0.513819	+	0.889960i	−0.999871	+	0.0160309i	$0.994897\pi$
$348$	1.05693			0.0566573
$349$	11.6206	−	20.1275i	0.622037	−	1.07740i	−0.367068	−	0.930194i	$-0.619639\pi$
$349$	11.6206	−	20.1275i	0.622037	−	1.07740i	0.989106	−	0.147206i	$-0.0470281\pi$
$350$	−5.79766	+	10.0418i	−0.309898	+	0.536759i
$351$	−0.799209	−	1.38427i	−0.0426586	−	0.0738869i
$352$	19.9673			1.06426
$353$	−12.6709	−	21.9466i	−0.674402	−	1.16810i	−0.976643	−	0.214867i	$-0.931068\pi$
$353$	−12.6709	−	21.9466i	−0.674402	−	1.16810i	0.302241	−	0.953231i	$-0.402265\pi$
$354$	−0.404727	+	0.701008i	−0.0215110	+	0.0372582i
$355$	−0.688035			−0.0365171
$356$	−15.0622	+	26.0884i	−0.798293	+	1.38268i
$357$	−0.297124	−	0.514634i	−0.0157255	−	0.0272373i
$358$	5.29214	+	9.16626i	0.279699	+	0.484452i
$359$	12.7736	+	22.1245i	0.674164	+	1.16769i	0.976713	+	0.214552i	$0.0688290\pi$
$359$	12.7736	+	22.1245i	0.674164	+	1.16769i	−0.302549	+	0.953134i	$0.597838\pi$
$360$	2.39001			0.125964
$361$	6.70132	+	11.6070i	0.352701	+	0.610896i
$362$	1.07057	+	1.85428i	0.0562678	+	0.0974586i
$363$	−0.325742	+	0.564202i	−0.0170970	+	0.0296129i
$364$	−9.91948	+	17.1810i	−0.519922	+	0.900531i
$365$	0.430501			0.0225334
$366$	−0.447933			−0.0234138
$367$	−7.29835	+	12.6411i	−0.380971	+	0.659861i	−0.991201	−	0.132363i	$-0.957743\pi$
$367$	−7.29835	+	12.6411i	−0.380971	+	0.659861i	0.610231	+	0.792224i	$0.291077\pi$
$368$	−2.34006	+	4.05311i	−0.121984	+	0.211283i
$369$	8.50273	+	14.7272i	0.442634	+	0.766665i
$370$	−1.26650	−	2.19365i	−0.0658423	−	0.114042i
$371$	45.4128			2.35771
$372$	−0.705479	−	1.22192i	−0.0365774	−	0.0633538i
$373$	12.1032	+	20.9633i	0.626678	+	1.08544i	0.988214	+	0.153080i	$0.0489192\pi$
$373$	12.1032	+	20.9633i	0.626678	+	1.08544i	−0.361536	+	0.932358i	$0.617747\pi$
$374$	−0.979694	−	1.69688i	−0.0506587	−	0.0877435i
$375$	−0.256617	+	0.444474i	−0.0132517	+	0.0229525i
$376$	9.08927			0.468744
$377$	−5.65034	+	9.78667i	−0.291007	+	0.504039i
$378$	−0.858436	−	1.48685i	−0.0441532	−	0.0764755i
$379$	−17.4127			−0.894430			−0.447215	−	0.894426i	$-0.647584\pi$
$379$	−17.4127			−0.894430			−0.447215	+	0.894426i	$0.647584\pi$
$380$	−0.920224	−	1.59387i	−0.0472065	−	0.0817640i
$381$	−0.517934	+	0.897089i	−0.0265346	+	0.0459593i
$382$	−3.14817	+	5.45279i	−0.161074	+	0.278989i
$383$	35.2774			1.80259			0.901297	−	0.433203i	$-0.142617\pi$
$383$	35.2774			1.80259			0.901297	+	0.433203i	$0.142617\pi$
$384$	−0.669072	+	1.15887i	−0.0341434	+	0.0591382i
$385$	8.93310			0.455273
$386$	−6.72484			−0.342285
$387$	−18.4056	+	6.67809i	−0.935608	+	0.339467i
$388$	−24.1313			−1.22508
$389$	5.00225			0.253624			0.126812	−	0.991927i	$-0.459526\pi$
$389$	5.00225			0.253624			0.126812	+	0.991927i	$0.459526\pi$
$390$	0.0283702	−	0.0491386i	0.00143658	−	0.00248823i
$391$	1.76177			0.0890963
$392$	−16.3501	+	28.3192i	−0.825805	+	1.43034i
$393$	0.818616	−	1.41788i	0.0412937	−	0.0715228i
$394$	−3.76051	−	6.51340i	−0.189452	−	0.328140i
$395$	3.28865			0.165470
$396$	10.7094	+	18.5492i	0.538166	+	0.932131i
$397$	−0.604710	+	1.04739i	−0.0303495	+	0.0525669i	−0.880801	−	0.473486i	$-0.842995\pi$
$397$	−0.604710	+	1.04739i	−0.0303495	+	0.0525669i	0.850452	+	0.526053i	$0.176329\pi$
$398$	−5.94342			−0.297917
$399$	−0.702958	+	1.21756i	−0.0351919	+	0.0609542i
$400$	6.38382	+	11.0571i	0.319191	+	0.552855i
$401$	5.77034	+	9.99452i	0.288157	+	0.499103i	0.973370	−	0.229240i	$-0.0736241\pi$
$401$	5.77034	+	9.99452i	0.288157	+	0.499103i	−0.685213	+	0.728343i	$0.740291\pi$
$402$	0.180748	+	0.313064i	0.00901488	+	0.0156142i
$403$	15.0860			0.751485
$404$	−7.87419	−	13.6385i	−0.391756	−	0.678541i
$405$	1.95311	+	3.38288i	0.0970507	+	0.168097i
$406$	−6.06906	+	10.5119i	−0.301203	+	0.521698i
$407$	24.1966	−	41.9098i	1.19938	−	2.07739i
$408$	0.216158			0.0107014
$409$	10.9945			0.543645			0.271822	−	0.962347i	$-0.412374\pi$
$409$	10.9945			0.543645			0.271822	+	0.962347i	$0.412374\pi$
$410$	−0.605086	+	1.04804i	−0.0298830	+	0.0517590i
$411$	0.976201	−	1.69083i	0.0481524	−	0.0834025i
$412$	−6.62549	−	11.4757i	−0.326415	−	0.565367i
$413$	35.2557	+	61.0646i	1.73482	+	3.00479i
$414$	2.53899			0.124785
$415$	−0.238040	−	0.412297i	−0.0116849	−	0.0202389i
$416$	−5.52390	−	9.56767i	−0.270831	−	0.469094i
$417$	0.0311977	+	0.0540360i	0.00152776	+	0.00264616i
$418$	−2.31783	+	4.01460i	−0.113369	+	0.196361i
$419$	−8.76851			−0.428370			−0.214185	−	0.976793i	$-0.568710\pi$
$419$	−8.76851			−0.428370			−0.214185	+	0.976793i	$0.568710\pi$
$420$	−0.231137	+	0.400342i	−0.0112783	+	0.0195347i
$421$	14.7663	+	25.5760i	0.719666	+	1.24650i	0.961132	+	0.276088i	$0.0890382\pi$
$421$	14.7663	+	25.5760i	0.719666	+	1.24650i	−0.241467	+	0.970409i	$0.577628\pi$
$422$	5.47872			0.266700
$423$	7.46323	+	12.9267i	0.362875	+	0.628518i
$424$	−8.25947	+	14.3058i	−0.401115	+	0.694752i
$425$	2.40310	−	4.16228i	0.116567	−	0.201900i
$426$	−0.0896802			−0.00434502
$427$	−19.5096	+	33.7917i	−0.944138	+	1.63529i
$428$	−9.87507			−0.477329
$429$	1.08403			0.0523374
$430$	−1.06647	−	0.896708i	−0.0514299	−	0.0432431i
$431$	−4.18030			−0.201358			−0.100679	−	0.994919i	$-0.532101\pi$
$431$	−4.18030			−0.201358			−0.100679	+	0.994919i	$0.532101\pi$
$432$	−1.89045			−0.0909545
$433$	17.4922	−	30.2973i	0.840621	−	1.45600i	−0.0487503	−	0.998811i	$-0.515524\pi$
$433$	17.4922	−	30.2973i	0.840621	−	1.45600i	0.889371	−	0.457186i	$-0.151143\pi$
$434$	16.2039			0.777813
$435$	−0.131661	+	0.228043i	−0.00631264	+	0.0109338i
$436$	−12.5497	+	21.7367i	−0.601021	+	1.04100i
$437$	−2.08406	−	3.60969i	−0.0996940	−	0.172675i
$438$	0.0561125			0.00268116
$439$	3.32887	+	5.76577i	0.158878	+	0.275185i	0.934464	−	0.356057i	$-0.115879\pi$
$439$	3.32887	+	5.76577i	0.158878	+	0.275185i	−0.775586	+	0.631242i	$0.782546\pi$
$440$	−1.62471	+	2.81408i	−0.0774551	+	0.134156i
$441$	−53.7005			−2.55716
$442$	−0.542059	+	0.938874i	−0.0257831	+	0.0446577i
$443$	−8.31794	−	14.4071i	−0.395197	−	0.684502i	0.597929	−	0.801549i	$-0.295990\pi$
$443$	−8.31794	−	14.4071i	−0.395197	−	0.684502i	−0.993126	+	0.117047i	$0.962657\pi$
$444$	1.25214	+	2.16877i	0.0594239	+	0.102925i
$445$	−3.75256	−	6.49962i	−0.177888	−	0.308112i
$446$	−1.10480			−0.0523138
$447$	−0.317758	−	0.550373i	−0.0150294	−	0.0260317i
$448$	7.34523	+	12.7223i	0.347029	+	0.601072i
$449$	−6.60879	+	11.4468i	−0.311888	+	0.540206i	−0.978771	−	0.204956i	$-0.934295\pi$
$449$	−6.60879	+	11.4468i	−0.311888	+	0.540206i	0.666883	+	0.745162i	$0.267628\pi$
$450$	3.46325	−	5.99853i	0.163259	−	0.282773i
$451$	−23.1204			−1.08870
$452$	30.9524			1.45588
$453$	0.200532	−	0.347332i	0.00942183	−	0.0163191i
$454$	0.276844	−	0.479508i	0.0129929	−	0.0225044i
$455$	−2.47132	−	4.28045i	−0.115857	−	0.200671i
$456$	−0.255702	−	0.442888i	−0.0119743	−	0.0207401i
$457$	6.34677			0.296889			0.148445	−	0.988921i	$-0.452573\pi$
$457$	6.34677			0.296889			0.148445	+	0.988921i	$0.452573\pi$
$458$	4.24828	+	7.35824i	0.198509	+	0.343828i
$459$	0.355817	+	0.616293i	0.0166081	+	0.0287661i
$460$	−0.685252	−	1.18689i	−0.0319500	−	0.0553391i
$461$	−3.45467	+	5.98367i	−0.160900	+	0.278687i	−0.935192	−	0.354142i	$-0.884773\pi$
$461$	−3.45467	+	5.98367i	−0.160900	+	0.278687i	0.774292	+	0.632829i	$0.218106\pi$
$462$	1.16436			0.0541711
$463$	−8.63794	+	14.9614i	−0.401439	+	0.695313i	−0.993900	−	0.110286i	$-0.964823\pi$
$463$	−8.63794	+	14.9614i	−0.401439	+	0.695313i	0.592461	+	0.805599i	$0.298157\pi$
$464$	6.68267	+	11.5747i	0.310235	+	0.537343i
$465$	0.351523			0.0163015
$466$	−2.75239	−	4.76728i	−0.127502	−	0.220840i
$467$	4.21583	−	7.30204i	0.195086	−	0.337898i	−0.751843	−	0.659342i	$-0.770835\pi$
$467$	4.21583	−	7.30204i	0.195086	−	0.337898i	0.946929	+	0.321444i	$0.104168\pi$
$468$	5.92544	−	10.2632i	0.273903	−	0.474415i
$469$	31.4898			1.45406
$470$	−0.531111	+	0.919911i	−0.0244983	+	0.0424323i
$471$	2.26926			0.104562
$472$	−25.6486			−1.18057
$473$	4.64896	−	26.2111i	0.213759	−	1.20519i
$474$	0.428651			0.0196886
$475$	−11.3708			−0.521730
$476$	4.41626	−	7.64919i	0.202419	−	0.350600i
$477$	−27.1275			−1.24208
$478$	6.12646	−	10.6113i	0.280218	−	0.485351i
$479$	17.8376	−	30.8956i	0.815020	−	1.41166i	−0.0942943	−	0.995544i	$-0.530059\pi$
$479$	17.8376	−	30.8956i	0.815020	−	1.41166i	0.909314	−	0.416111i	$-0.136607\pi$
$480$	−0.128714	−	0.222940i	−0.00587498	−	0.0101758i
$481$	−26.7757			−1.22087
$482$	3.61595	+	6.26301i	0.164702	+	0.285272i
$483$	−0.523463	+	0.906665i	−0.0238184	+	0.0412547i
$484$	−9.68323			−0.440147
$485$	3.00601	−	5.20656i	0.136496	−	0.236418i
$486$	0.769790	+	1.33332i	0.0349184	+	0.0604804i
$487$	2.42632	+	4.20250i	0.109947	+	0.190434i	0.915749	−	0.401752i	$-0.131599\pi$
$487$	2.42632	+	4.20250i	0.109947	+	0.190434i	−0.805802	+	0.592186i	$0.798265\pi$
$488$	−7.09665	−	12.2918i	−0.321250	−	0.556422i
$489$	−2.12363			−0.0960339
$490$	−1.91076	−	3.30954i	−0.0863194	−	0.149510i
$491$	−7.08777	−	12.2764i	−0.319867	−	0.554025i	0.660593	−	0.750744i	$-0.270305\pi$
$491$	−7.08777	−	12.2764i	−0.319867	−	0.554025i	−0.980460	+	0.196719i	$0.936971\pi$
$492$	0.598223	−	1.03615i	0.0269700	−	0.0467134i
$493$	2.51559	−	4.35713i	0.113297	−	0.196235i
$494$	2.56489			0.115400
$495$	−5.33622			−0.239845
$496$	8.92109	−	15.4518i	0.400569	−	0.693806i
$497$	−3.90601	+	6.76540i	−0.175208	+	0.303470i
$498$	−0.0310267	−	0.0537399i	−0.00139034	−	0.00240814i
$499$	−3.26118	−	5.64853i	−0.145991	−	0.252863i	0.783752	−	0.621075i	$-0.213304\pi$
$499$	−3.26118	−	5.64853i	−0.145991	−	0.252863i	−0.929742	+	0.368211i	$0.879970\pi$
$500$	−7.62838			−0.341152
$501$	−1.35309	−	2.34362i	−0.0604517	−	0.104705i
$502$	−4.16188	−	7.20858i	−0.185754	−	0.321735i
$503$	−8.58139	−	14.8634i	−0.382625	−	0.662727i	0.608811	−	0.793315i	$-0.291647\pi$
$503$	−8.58139	−	14.8634i	−0.382625	−	0.662727i	−0.991437	+	0.130588i	$0.958313\pi$
$504$	13.5682	−	23.5008i	0.604375	−	1.04681i
$505$	3.92352			0.174594
$506$	−1.72599	+	2.98950i	−0.0767296	+	0.132900i
$507$	0.472863	+	0.819022i	0.0210006	+	0.0363741i
$508$	−15.3965			−0.683108
$509$	−13.0035	−	22.5227i	−0.576369	−	0.998300i	−0.995891	−	0.0905550i	$-0.971136\pi$
$509$	−13.0035	−	22.5227i	−0.576369	−	0.998300i	0.419523	−	0.907745i	$-0.362197\pi$
$510$	−0.0126307	+	0.0218771i	−0.000559298	+	0.000968732i
$511$	2.44397	−	4.23309i	0.108115	−	0.187261i
$512$	−22.7264			−1.00437
$513$	0.841817	−	1.45807i	0.0371671	−	0.0643754i
$514$	7.33884			0.323702
$515$	3.30133			0.145474
$516$	1.05438	+	0.886539i	0.0464164	+	0.0390277i
$517$	−20.2938			−0.892522
$518$	−28.7600			−1.26364
$519$	0.525767	−	0.910655i	0.0230786	−	0.0399733i
$520$	1.79789			0.0788427
$521$	−8.56733	+	14.8390i	−0.375341	+	0.650111i	−0.990378	−	0.138388i	$-0.955808\pi$
$521$	−8.56733	+	14.8390i	−0.375341	+	0.650111i	0.615037	+	0.788499i	$0.289141\pi$
$522$	3.62538	−	6.27934i	0.158678	−	0.274839i
$523$	−3.76018	−	6.51282i	−0.164421	−	0.284786i	0.772028	−	0.635588i	$-0.219242\pi$
$523$	−3.76018	−	6.51282i	−0.164421	−	0.284786i	−0.936450	+	0.350802i	$0.885909\pi$
$524$	24.3347			1.06307
$525$	1.42804	+	2.47343i	0.0623246	+	0.107949i
$526$	3.95326	−	6.84724i	0.172370	−	0.298554i
$527$	−6.71643			−0.292572
$528$	0.641042	−	1.11032i	0.0278978	−	0.0483204i
$529$	9.94809	+	17.2306i	0.432526	+	0.749156i
$530$	−0.965246	−	1.67186i	−0.0419276	−	0.0726208i
$531$	−21.0601	−	36.4772i	−0.913931	−	1.58298i
$532$	−20.8966			−0.905983
$533$	6.39620	+	11.0785i	0.277050	+	0.479865i
$534$	−0.489118	−	0.847177i	−0.0211662	−	0.0366609i
$535$	1.23013	−	2.13064i	0.0531831	−	0.0921158i
$536$	−5.72722	+	9.91983i	−0.247378	+	0.428471i
$537$	2.60704			0.112502
$538$	5.37593			0.231773
$539$	36.5052	−	63.2289i	1.57239	−	2.72346i
$540$	0.276795	−	0.479423i	0.0119114	−	0.0206311i
$541$	0.316167	+	0.547618i	0.0135931	+	0.0235439i	0.872742	−	0.488182i	$-0.162340\pi$
$541$	0.316167	+	0.547618i	0.0135931	+	0.0235439i	−0.859149	+	0.511726i	$0.829006\pi$
$542$	−4.17978	−	7.23959i	−0.179537	−	0.310967i
$543$	0.527388			0.0226324
$544$	2.45930	+	4.25963i	0.105442	+	0.182630i
$545$	−3.12660	−	5.41544i	−0.133929	−	0.231972i
$546$	−0.322118	−	0.557925i	−0.0137854	−	0.0238770i
$547$	12.4316	−	21.5321i	0.531536	−	0.920647i	−0.467787	−	0.883841i	$-0.654948\pi$
$547$	12.4316	−	21.5321i	0.531536	−	0.920647i	0.999322	−	0.0368057i	$-0.0117183\pi$
$548$	29.0192			1.23964
$549$	11.6542	−	20.1856i	0.497387	−	0.861500i
$550$	4.70860	+	8.15553i	0.200775	+	0.347753i
$551$	−11.9031			−0.507091
$552$	−0.190410	−	0.329800i	−0.00810440	−	0.0140372i
$553$	18.6698	−	32.3371i	0.793923	−	1.37511i
$554$	−0.986981	+	1.70950i	−0.0419328	+	0.0726298i
$555$	−0.623911			−0.0264835
$556$	−0.463702	+	0.803156i	−0.0196654	+	0.0340614i
$557$	35.7064			1.51293			0.756465	−	0.654035i	$-0.226925\pi$
$557$	35.7064			1.51293			0.756465	+	0.654035i	$0.226925\pi$
$558$	−9.67947			−0.409765
$559$	−13.8456	+	5.02362i	−0.585608	+	0.212476i
$560$	−5.84567			−0.247025
$561$	−0.482622			−0.0203763
$562$	0.670893	−	1.16202i	0.0282999	−	0.0490169i
$563$	−24.1949			−1.01969			−0.509846	−	0.860266i	$-0.670298\pi$
$563$	−24.1949			−1.01969			−0.509846	+	0.860266i	$0.670298\pi$
$564$	0.525088	−	0.909479i	0.0221102	−	0.0382960i
$565$	−3.85571	+	6.67828i	−0.162211	+	0.280957i
$566$	6.76658	+	11.7201i	0.284421	+	0.492631i
$567$	44.3516			1.86259
$568$	−1.42081	−	2.46092i	−0.0596160	−	0.103258i
$569$	−0.148197	+	0.256685i	−0.00621276	+	0.0107608i	−0.869115	−	0.494610i	$-0.835311\pi$
$569$	−0.148197	+	0.256685i	−0.00621276	+	0.0107608i	0.862902	+	0.505371i	$0.168644\pi$
$570$	0.0597654			0.00250330
$571$	0.839131	−	1.45342i	0.0351165	−	0.0608236i	−0.847933	−	0.530103i	$-0.822153\pi$
$571$	0.839131	−	1.45342i	0.0351165	−	0.0608236i	0.883050	+	0.469280i	$0.155486\pi$
$572$	8.05615	+	13.9537i	0.336845	+	0.583432i
$573$	0.775435	+	1.34309i	0.0323942	+	0.0561085i
$574$	6.87020	+	11.8995i	0.286757	+	0.496677i
$575$	−8.46738			−0.353114
$576$	−4.38770	−	7.59972i	−0.182821	−	0.316655i
$577$	5.03585	+	8.72235i	0.209645	+	0.363116i	0.951603	−	0.307331i	$-0.0994357\pi$
$577$	5.03585	+	8.72235i	0.209645	+	0.363116i	−0.741958	+	0.670447i	$0.766102\pi$
$578$	0.241331	−	0.417997i	0.0100380	−	0.0173864i
$579$	−0.828206	+	1.43450i	−0.0344191	+	0.0596156i
$580$	−3.91383			−0.162513
$581$	−5.40546			−0.224256
$582$	0.391811	−	0.678636i	0.0162411	−	0.0281304i
$583$	18.4411	−	31.9409i	0.763753	−	1.32286i
$584$	0.888997	+	1.53979i	0.0367870	+	0.0637169i
$585$	1.47625	+	2.55694i	0.0610355	+	0.105717i
$586$	2.31414			0.0955964
$587$	−0.475685	−	0.823911i	−0.0196336	−	0.0340064i	0.856042	−	0.516907i	$-0.172917\pi$
$587$	−0.475685	−	0.823911i	−0.0196336	−	0.0340064i	−0.875675	+	0.482900i	$0.839583\pi$
$588$	1.88909	+	3.27200i	0.0779048	+	0.134935i
$589$	7.94511	+	13.7613i	0.327373	+	0.567026i
$590$	1.49872	−	2.59585i	0.0617011	−	0.106870i
$591$	−1.85252			−0.0762027
$592$	−15.8339	+	27.4250i	−0.650768	+	1.12716i
$593$	10.8818	+	18.8478i	0.446861	+	0.773986i	0.998180	−	0.0603086i	$-0.0192085\pi$
$593$	10.8818	+	18.8478i	0.446861	+	0.773986i	−0.551319	+	0.834295i	$0.685875\pi$
$594$	−1.39437			−0.0572115
$595$	1.10026	+	1.90570i	0.0451062	+	0.0781262i
$596$	4.72294	−	8.18038i	0.193459	−	0.335081i
$597$	−0.731969	+	1.26781i	−0.0299575	+	0.0518879i
$598$	1.90996			0.0781042
$599$	12.5810	−	21.7909i	0.514046	−	0.890353i	−0.485822	−	0.874058i	$-0.661480\pi$
$599$	12.5810	−	21.7909i	0.514046	−	0.890353i	0.999867	−	0.0162952i	$-0.00518717\pi$
$600$	−1.03890			−0.0424129
$601$	1.81758			0.0741406			0.0370703	−	0.999313i	$-0.488197\pi$
$601$	1.81758			0.0741406			0.0370703	+	0.999313i	$0.488197\pi$
$602$	−14.8717	+	5.39590i	−0.606125	+	0.219920i
$603$	−18.8105			−0.766024
$604$	5.96116			0.242556
$605$	1.20623	−	2.08925i	0.0490403	−	0.0849402i
$606$	0.511402			0.0207743
$607$	−9.43511	+	16.3421i	−0.382959	+	0.663305i	−0.991484	−	0.130230i	$-0.958428\pi$
$607$	−9.43511	+	16.3421i	−0.382959	+	0.663305i	0.608524	+	0.793535i	$0.291762\pi$
$608$	5.81839	−	10.0777i	0.235967	−	0.408707i
$609$	1.49489	+	2.58922i	0.0605759	+	0.104921i
$610$	1.65871			0.0671590
$611$	5.61424	+	9.72414i	0.227128	+	0.393397i
$612$	−2.63807	+	4.56927i	−0.106638	+	0.184702i
$613$	30.6062			1.23617			0.618087	−	0.786110i	$-0.287908\pi$
$613$	30.6062			1.23617			0.618087	+	0.786110i	$0.287908\pi$
$614$	7.44515	−	12.8954i	0.300462	−	0.520415i
$615$	0.149040	+	0.258145i	0.00600988	+	0.0104094i
$616$	18.4471	+	31.9514i	0.743256	+	1.28736i
$617$	−17.5081	−	30.3248i	−0.704848	−	1.22083i	−0.966747	−	0.255737i	$-0.917682\pi$
$617$	−17.5081	−	30.3248i	−0.704848	−	1.22083i	0.261899	−	0.965095i	$-0.415651\pi$
$618$	0.430303			0.0173093
$619$	−7.97766	−	13.8177i	−0.320649	−	0.555381i	0.659973	−	0.751289i	$-0.270568\pi$
$619$	−7.97766	−	13.8177i	−0.320649	−	0.555381i	−0.980622	+	0.195908i	$0.937234\pi$
$620$	2.61241	+	4.52482i	0.104917	+	0.181721i
$621$	0.626866	−	1.08576i	0.0251553	−	0.0435702i
$622$	2.09830	−	3.63436i	0.0841341	−	0.145725i
$623$	−85.2138			−3.41402
$624$	−0.709371			−0.0283976
$625$	−11.0652	+	19.1655i	−0.442609	+	0.766621i
$626$	5.75230	−	9.96328i	0.229908	−	0.398213i
$627$	0.570911	+	0.988847i	0.0228000	+	0.0394907i
$628$	16.8644	+	29.2099i	0.672961	+	1.16560i
$629$	11.9208			0.475315
$630$	1.58565	+	2.74643i	0.0631739	+	0.109420i
$631$	−17.6906	−	30.6410i	−0.704252	−	1.21980i	−0.966961	−	0.254925i	$-0.917949\pi$
$631$	−17.6906	−	30.6410i	−0.704252	−	1.21980i	0.262709	−	0.964875i	$-0.415384\pi$
$632$	6.79117	+	11.7627i	0.270138	+	0.467893i
$633$	0.674739	−	1.16868i	0.0268185	−	0.0464509i
$634$	11.6329			0.462002
$635$	1.91792	−	3.32194i	0.0761105	−	0.131827i
$636$	0.954300	+	1.65290i	0.0378404	+	0.0655416i
$637$	−40.3963			−1.60056
$638$	4.92902	+	8.53731i	0.195142	+	0.337995i
$639$	2.33327	−	4.04134i	0.0923027	−	0.159873i
$640$	2.47759	−	4.29131i	0.0979354	−	0.169629i
$641$	37.8446			1.49477			0.747387	−	0.664389i	$-0.231308\pi$
$641$	37.8446			1.49477			0.747387	+	0.664389i	$0.231308\pi$
$642$	0.160338	−	0.277713i	0.00632803	−	0.0109605i
$643$	9.15007			0.360844			0.180422	−	0.983589i	$-0.442254\pi$
$643$	9.15007			0.360844			0.180422	+	0.983589i	$0.442254\pi$
$644$	−15.5608			−0.613183
$645$	−0.322622	+	0.117057i	−0.0127032	+	0.00460912i
$646$	−1.14192			−0.0449281
$647$	8.32611			0.327333			0.163666	−	0.986516i	$-0.447668\pi$
$647$	8.32611			0.327333			0.163666	+	0.986516i	$0.447668\pi$
$648$	−8.06646	+	13.9715i	−0.316880	+	0.548853i
$649$	57.2662			2.24789
$650$	2.60524	−	4.51241i	0.102186	−	0.176991i
$651$	1.99561	−	3.45651i	0.0782143	−	0.135471i
$652$	−15.7821	−	27.3354i	−0.618076	−	1.07054i
$653$	−1.89496			−0.0741554			−0.0370777	−	0.999312i	$-0.511805\pi$
$653$	−1.89496			−0.0741554			−0.0370777	+	0.999312i	$0.511805\pi$
$654$	−0.407529	−	0.705862i	−0.0159357	−	0.0276014i
$655$	−3.03136	+	5.25046i	−0.118445	+	0.205153i
$656$	15.1296			0.590712
$657$	−1.45992	+	2.52865i	−0.0569568	+	0.0986520i
$658$	6.03029	+	10.4448i	0.235085	+	0.407179i
$659$	−7.24668	−	12.5516i	−0.282291	−	0.488942i	0.689658	−	0.724135i	$-0.257761\pi$
$659$	−7.24668	−	12.5516i	−0.282291	−	0.488942i	−0.971949	+	0.235194i	$0.924428\pi$
$660$	0.187719	+	0.325139i	0.00730696	+	0.0126560i
$661$	22.5377			0.876617			0.438308	−	0.898825i	$-0.355578\pi$
$661$	22.5377			0.876617			0.438308	+	0.898825i	$0.355578\pi$
$662$	−3.57761	−	6.19660i	−0.139048	−	0.240838i
$663$	0.133516	+	0.231257i	0.00518533	+	0.00898126i
$664$	0.983120	−	1.70281i	0.0381524	−	0.0660820i
$665$	2.60307	−	4.50865i	0.100943	−	0.174838i
$666$	17.1799			0.665707
$667$	−8.86377			−0.343207
$668$	20.1115	−	34.8341i	0.778136	−	1.34777i
$669$	−0.136063	+	0.235668i	−0.00526050	+	0.00911146i
$670$	−0.669314	−	1.15929i	−0.0258578	−	0.0447871i
$671$	15.8449	+	27.4441i	0.611684	+	1.05947i
$672$	−2.92287			−0.112752
$673$	−4.71946	−	8.17435i	−0.181922	−	0.315098i	0.760613	−	0.649206i	$-0.224899\pi$
$673$	−4.71946	−	8.17435i	−0.181922	−	0.315098i	−0.942535	+	0.334107i	$0.891565\pi$
$674$	4.65408	+	8.06110i	0.179268	+	0.310502i
$675$	−1.71012	−	2.96202i	−0.0658227	−	0.114008i
$676$	−7.02832	+	12.1734i	−0.270320	+	0.468208i
$677$	16.9972			0.653255			0.326627	−	0.945153i	$-0.394088\pi$
$677$	16.9972			0.653255			0.326627	+	0.945153i	$0.394088\pi$
$678$	−0.502562	+	0.870464i	−0.0193008	+	0.0334300i
$679$	−34.1305	−	59.1158i	−1.30981	−	2.26866i
$680$	−0.800440			−0.0306955
$681$	−0.0681903	−	0.118109i	−0.00261306	−	0.00452595i
$682$	6.58004	−	11.3970i	0.251963	−	0.436413i
$683$	−0.754711	+	1.30720i	−0.0288782	+	0.0500186i	−0.880103	−	0.474782i	$-0.842527\pi$
$683$	−0.754711	+	1.30720i	−0.0288782	+	0.0500186i	0.851225	+	0.524801i	$0.175860\pi$
$684$	12.4827			0.477287
$685$	−3.61490	+	6.26118i	−0.138118	+	0.239228i
$686$	−26.5019			−1.01185
$687$	2.09281			0.0798457
$688$	−3.04220	+	17.1521i	−0.115983	+	0.653919i
$689$	−20.4067			−0.777435
$690$	0.0445047			0.00169427
$691$	17.3434	−	30.0397i	0.659776	−	1.14276i	−0.320898	−	0.947114i	$-0.603985\pi$
$691$	17.3434	−	30.0397i	0.659776	−	1.14276i	0.980674	−	0.195651i	$-0.0626820\pi$
$692$	15.6293			0.594137
$693$	−30.2940	+	52.4707i	−1.15077	+	1.99320i
$694$	4.61974	−	8.00162i	0.175363	−	0.303737i
$695$	−0.115526	−	0.200097i	−0.00438215	−	0.00759011i
$696$	−1.08753			−0.0412228
$697$	−2.84766	−	4.93229i	−0.107863	−	0.186824i
$698$	−5.60882	+	9.71477i	−0.212297	+	0.367709i
$699$	−1.35590			−0.0512847
$700$	−21.2254	+	36.7635i	−0.802244	+	1.38953i
$701$	5.60210	+	9.70312i	0.211588	+	0.366482i	0.952212	−	0.305439i	$-0.0988031\pi$
$701$	5.60210	+	9.70312i	0.211588	+	0.366482i	−0.740623	+	0.671920i	$0.765470\pi$
$702$	0.385748	+	0.668134i	0.0145591	+	0.0252171i
$703$	−14.1016	−	24.4247i	−0.531852	−	0.921195i
$704$	11.9309			0.449664
$705$	0.130819	+	0.226586i	0.00492694	+	0.00853372i
$706$	6.11574	+	10.5928i	0.230169	+	0.398664i
$707$	22.2740	−	38.5798i	0.837701	−	1.45094i
$708$	−1.48172	+	2.56641i	−0.0556864	+	0.0964517i
$709$	−37.7551			−1.41792			−0.708960	−	0.705248i	$-0.750836\pi$
$709$	−37.7551			−1.41792			−0.708960	+	0.705248i	$0.750836\pi$
$710$	0.332088			0.0124630
$711$	−11.1525	+	19.3167i	−0.418252	+	0.724433i
$712$	15.4983	−	26.8438i	0.580823	−	1.00602i
$713$	5.91639	+	10.2475i	0.221571	+	0.383771i
$714$	0.143410	+	0.248394i	0.00536700	+	0.00929592i
$715$	−4.01419			−0.150122
$716$	19.3747	+	33.5580i	0.724066	+	1.25412i
$717$	−1.50902	−	2.61371i	−0.0563556	−	0.0976107i
$718$	−6.16531	−	10.6786i	−0.230087	−	0.398523i
$719$	−4.52332	+	7.83463i	−0.168692	+	0.292182i	−0.937960	−	0.346743i	$-0.887288\pi$
$719$	−4.52332	+	7.83463i	−0.168692	+	0.292182i	0.769269	+	0.638926i	$0.220621\pi$
$720$	3.49193			0.130137
$721$	18.7418	−	32.4617i	0.697981	−	1.20894i
$722$	−3.23447	−	5.60227i	−0.120375	−	0.208495i
$723$	1.78131			0.0662475
$724$	3.91938	+	6.78856i	0.145663	+	0.252295i
$725$	−12.0904	+	20.9412i	−0.449027	+	0.777737i
$726$	0.157223	−	0.272319i	0.00583510	−	0.0101067i
$727$	−13.7898			−0.511436			−0.255718	−	0.966751i	$-0.582312\pi$
$727$	−13.7898			−0.511436			−0.255718	+	0.966751i	$0.582312\pi$
$728$	10.2067	−	17.6785i	0.378286	−	0.655210i
$729$	−26.2398			−0.971843
$730$	−0.207786			−0.00769051
$731$	6.16423	−	2.23657i	0.227992	−	0.0827225i
$732$	−1.63989			−0.0606123
$733$	14.3900			0.531506			0.265753	−	0.964041i	$-0.414380\pi$
$733$	14.3900			0.531506			0.265753	+	0.964041i	$0.414380\pi$
$734$	3.52263	−	6.10138i	0.130023	−	0.225206i
$735$	−0.941289			−0.0347200
$736$	4.33271	−	7.50447i	0.159706	−	0.276618i
$737$	12.7873	−	22.1482i	0.471026	−	0.815841i
$738$	−4.10394	−	7.10823i	−0.151068	−	0.261658i
$739$	6.05618			0.222780			0.111390	−	0.993777i	$-0.464470\pi$
$739$	6.05618			0.222780			0.111390	+	0.993777i	$0.464470\pi$
$740$	−4.63670	−	8.03100i	−0.170449	−	0.295225i
$741$	0.315882	−	0.547124i	0.0116042	−	0.0200991i
$742$	−21.9190			−0.804672
$743$	−0.394441	+	0.683192i	−0.0144706	+	0.0250639i	−0.873170	−	0.487416i	$-0.837940\pi$
$743$	−0.394441	+	0.683192i	−0.0144706	+	0.0250639i	0.858699	+	0.512480i	$0.171273\pi$
$744$	0.725906	+	1.25731i	0.0266130	+	0.0460951i
$745$	1.17667	+	2.03804i	0.0431097	+	0.0746682i
$746$	−5.84173	−	10.1182i	−0.213881	−	0.370453i
$747$	3.22897			0.118142
$748$	−3.58669	−	6.21232i	−0.131142	−	0.227145i
$749$	−13.9670	−	24.1915i	−0.510343	−	0.883939i
$750$	0.123859	−	0.214531i	0.00452270	−	0.00783355i
$751$	−3.96685	+	6.87078i	−0.144752	+	0.250718i	−0.929281	−	0.369375i	$-0.879572\pi$
$751$	−3.96685	+	6.87078i	−0.144752	+	0.250718i	0.784528	+	0.620093i	$0.212905\pi$
$752$	13.2799			0.484270
$753$	−2.05025			−0.0747151
$754$	2.72720	−	4.72365i	0.0993188	−	0.172025i
$755$	−0.742576	+	1.28618i	−0.0270251	+	0.0468089i
$756$	−3.14276	−	5.44342i	−0.114301	−	0.197975i
$757$	−6.52926	−	11.3090i	−0.237310	−	0.411033i	0.722631	−	0.691234i	$-0.242932\pi$
$757$	−6.52926	−	11.3090i	−0.237310	−	0.411033i	−0.959942	+	0.280200i	$0.909599\pi$
$758$	8.40444			0.305263
$759$	0.425133	+	0.736353i	0.0154314	+	0.0267279i
$760$	0.946870	+	1.64003i	0.0343466	+	0.0594900i
$761$	−3.30699	−	5.72788i	−0.119878	−	0.207635i	0.799841	−	0.600212i	$-0.204917\pi$
$761$	−3.30699	−	5.72788i	−0.119878	−	0.207635i	−0.919719	+	0.392577i	$0.871584\pi$
$762$	0.249987	−	0.432990i	0.00905607	−	0.0156856i
$763$	−70.9995			−2.57036
$764$	−11.5255	+	19.9628i	−0.416980	+	0.722230i
$765$	−0.657244	−	1.13838i	−0.0237627	−	0.0411582i
$766$	−17.0271			−0.615213
$767$	−15.8425	−	27.4401i	−0.572041	−	0.990804i
$768$	−0.0264671	+	0.0458423i	−0.000955047	+	0.00165419i
$769$	18.2766	−	31.6560i	0.659072	−	1.14155i	−0.321785	−	0.946813i	$-0.604283\pi$
$769$	18.2766	−	31.6560i	0.659072	−	1.14155i	0.980856	−	0.194733i	$-0.0623840\pi$
$770$	−4.31167			−0.155382
$771$	0.903825	−	1.56547i	0.0325504	−	0.0563790i
$772$	−24.6198			−0.886087
$773$	−17.8071			−0.640478			−0.320239	−	0.947337i	$-0.603763\pi$
$773$	−17.8071			−0.640478			−0.320239	+	0.947337i	$0.603763\pi$
$774$	8.88366	−	3.22326i	0.319317	−	0.115858i
$775$	32.2805			1.15955
$776$	24.8300			0.891346
$777$	−3.54197	+	6.13488i	−0.127068	+	0.220087i
$778$	−2.41439			−0.0865601
$779$	−6.73720	+	11.6692i	−0.241385	+	0.418092i
$780$	0.103864	−	0.179898i	0.00371893	−	0.00644138i
$781$	3.17228	+	5.49456i	0.113513	+	0.196611i
$782$	−0.850336			−0.0304080
$783$	−1.79018	−	3.10068i	−0.0639758	−	0.110809i
$784$	−23.8884	+	41.3759i	−0.853158	+	1.47771i
$785$	−8.40311			−0.299920
$786$	−0.395114	+	0.684358i	−0.0140933	+	0.0244103i
$787$	7.86477	+	13.6222i	0.280349	+	0.485578i	0.971471	−	0.237160i	$-0.0762165\pi$
$787$	7.86477	+	13.6222i	0.280349	+	0.485578i	−0.691122	+	0.722738i	$0.742883\pi$
$788$	−13.7674	−	23.8458i	−0.490442	−	0.849470i
$789$	−0.973738	−	1.68656i	−0.0346660	−	0.0600432i
$790$	−1.58731			−0.0564738
$791$	43.7781	+	75.8258i	1.55657	+	2.69606i
$792$	−11.0195	−	19.0863i	−0.391560	−	0.678201i
$793$	8.76688	−	15.1847i	0.311321	−	0.539224i
$794$	0.291870	−	0.505534i	0.0103581	−	0.0179407i
$795$	−0.475505			−0.0168644
$796$	−21.7590			−0.771228
$797$	−17.0953	+	29.6099i	−0.605545	+	1.04883i	0.386420	+	0.922323i	$0.373712\pi$
$797$	−17.0953	+	29.6099i	−0.605545	+	1.04883i	−0.991965	+	0.126512i	$0.959622\pi$
$798$	0.339291	−	0.587669i	0.0120108	−	0.0208033i
$799$	−2.49952	−	4.32930i	−0.0884267	−	0.153159i
$800$	−11.8199	−	20.4726i	−0.417895	−	0.723816i
$801$	50.9028			1.79856
$802$	−2.78512	−	4.82397i	−0.0983461	−	0.170340i
$803$	−1.98488	−	3.43792i	−0.0700451	−	0.121322i
$804$	0.661723	+	1.14614i	0.0233372	+	0.0404212i
$805$	1.93840	−	3.35740i	0.0683196	−	0.118333i
$806$	−7.28141			−0.256477
$807$	0.662080	−	1.14676i	0.0233063	−	0.0403677i
$808$	8.10220	+	14.0334i	0.285034	+	0.493694i
$809$	16.0640			0.564780			0.282390	−	0.959300i	$-0.408873\pi$
$809$	16.0640			0.564780			0.282390	+	0.959300i	$0.408873\pi$
$810$	−0.942690	−	1.63279i	−0.0331228	−	0.0573703i
$811$	15.0159	−	26.0084i	0.527281	−	0.913277i	−0.472214	−	0.881484i	$-0.656545\pi$
$811$	15.0159	−	26.0084i	0.527281	−	0.913277i	0.999494	−	0.0317927i	$-0.0101216\pi$
$812$	−22.2190	+	38.4845i	−0.779735	+	1.35054i
$813$	−2.05906			−0.0722145
$814$	−11.6788	+	20.2282i	−0.409341	+	0.708999i
$815$	7.86386			0.275459
$816$	0.315820			0.0110559
$817$	−11.8744	−	9.98422i	−0.415433	−	0.349303i
$818$	−5.30664			−0.185542
$819$	33.5230			1.17139
$820$	−2.21524	+	3.83690i	−0.0773594	+	0.133990i
$821$	31.3097			1.09272			0.546358	−	0.837551i	$-0.316014\pi$
$821$	31.3097			1.09272			0.546358	+	0.837551i	$0.316014\pi$
$822$	−0.471175	+	0.816098i	−0.0164341	+	0.0284647i
$823$	27.2902	−	47.2681i	0.951278	−	1.64766i	0.208613	−	0.977998i	$-0.433105\pi$
$823$	27.2902	−	47.2681i	0.951278	−	1.64766i	0.742665	−	0.669664i	$-0.233562\pi$
$824$	6.81734	+	11.8080i	0.237493	+	0.411351i
$825$	2.31957			0.0807572
$826$	−17.0166	−	29.4736i	−0.592082	−	1.02552i
$827$	0.697963	−	1.20891i	0.0242705	−	0.0420378i	−0.853635	−	0.520872i	$-0.825607\pi$
$827$	0.697963	−	1.20891i	0.0242705	−	0.0420378i	0.877906	+	0.478834i	$0.158940\pi$
$828$	9.29532			0.323035
$829$	−23.2608	+	40.2889i	−0.807881	+	1.39929i	0.106447	+	0.994318i	$0.466052\pi$
$829$	−23.2608	+	40.2889i	−0.807881	+	1.39929i	−0.914329	+	0.404973i	$0.867281\pi$
$830$	0.114893	+	0.199000i	0.00398798	+	0.00690739i
$831$	0.243106	+	0.421072i	0.00843325	+	0.0146068i
$832$	−3.30066	−	5.71691i	−0.114430	−	0.198198i
$833$	17.9849			0.623139
$834$	−0.0150579	−	0.0260811i	−0.000521414	−	0.000903115i
$835$	5.01053	+	8.67850i	0.173397	+	0.300332i
$836$	−8.48565	+	14.6976i	−0.293482	+	0.508326i
$837$	−2.38982	+	4.13929i	−0.0826042	+	0.143075i
$838$	4.23222			0.146200
$839$	−32.0226			−1.10554			−0.552772	−	0.833332i	$-0.686430\pi$
$839$	−32.0226			−1.10554			−0.552772	+	0.833332i	$0.686430\pi$
$840$	0.237830	−	0.411934i	0.00820592	−	0.0142131i
$841$	1.84359	−	3.19319i	0.0635720	−	0.110110i
$842$	−7.12713	−	12.3445i	−0.245617	−	0.425421i
$843$	−0.165250	−	0.286221i	−0.00569150	−	0.00985796i
$844$	20.0577			0.690416
$845$	−1.75102	−	3.03286i	−0.0602370	−	0.104334i
$846$	−3.60221	−	6.23922i	−0.123847	−	0.214509i
$847$	−13.6957	−	23.7216i	−0.470589	−	0.815083i
$848$	−12.0675	+	20.9016i	−0.414401	+	0.717764i
$849$	3.33339			0.114402
$850$	−1.15988	+	2.00897i	−0.0397836	+	0.0689073i
$851$	−10.5009	−	18.1880i	−0.359965	−	0.623478i
$852$	−0.328322			−0.0112481
$853$	16.9113	+	29.2912i	0.579031	+	1.00291i	0.995591	+	0.0938027i	$0.0299023\pi$
$853$	16.9113	+	29.2912i	0.579031	+	1.00291i	−0.416560	+	0.909108i	$0.636764\pi$
$854$	9.41655	−	16.3100i	0.322228	−	0.558115i
$855$	−1.55496	+	2.69326i	−0.0531783	+	0.0921076i
$856$	10.1610			0.347296
$857$	−23.4289	+	40.5801i	−0.800317	+	1.38619i	0.119090	+	0.992883i	$0.462002\pi$
$857$	−23.4289	+	40.5801i	−0.800317	+	1.38619i	−0.919407	+	0.393306i	$0.871331\pi$
$858$	−0.523219			−0.0178624
$859$	35.8682			1.22381			0.611904	−	0.790932i	$-0.290404\pi$
$859$	35.8682			1.22381			0.611904	+	0.790932i	$0.290404\pi$
$860$	−3.90439	−	3.28288i	−0.133138	−	0.111945i
$861$	3.38443			0.115341
$862$	2.01767			0.0687220
$863$	−3.60919	+	6.25131i	−0.122858	+	0.212797i	−0.920894	−	0.389814i	$-0.872539\pi$
$863$	−3.60919	+	6.25131i	−0.122858	+	0.212797i	0.798035	+	0.602611i	$0.205873\pi$
$864$	3.50024			0.119081
$865$	−1.94693	+	3.37218i	−0.0661975	+	0.114657i
$866$	−8.44280	+	14.6234i	−0.286898	+	0.496922i
$867$	−0.0594428	−	0.102958i	−0.00201878	−	0.00349664i
$868$	59.3230			2.01355
$869$	−15.1628	−	26.2628i	−0.514363	−	0.890903i
$870$	0.0635475	−	0.110067i	0.00215446	−	0.00373164i
$871$	−14.1503			−0.479464
$872$	12.9131	−	22.3661i	0.437292	−	0.757411i
$873$	20.3880	+	35.3131i	0.690029	+	1.19517i
$874$	1.00589	+	1.74226i	0.0340249	+	0.0589328i
$875$	−10.7893	−	18.6877i	−0.364747	−	0.631759i
$876$	0.205430			0.00694082
$877$	−7.25460	−	12.5653i	−0.244970	−	0.424301i	0.717153	−	0.696916i	$-0.245445\pi$
$877$	−7.25460	−	12.5653i	−0.244970	−	0.424301i	−0.962123	+	0.272615i	$0.912112\pi$
$878$	−1.60672	−	2.78291i	−0.0542240	−	0.0939188i
$879$	0.285001	−	0.493637i	0.00961286	−	0.0166500i
$880$	−2.37380	+	4.11153i	−0.0800206	+	0.138600i
$881$	35.6857			1.20228			0.601141	−	0.799143i	$-0.294713\pi$
$881$	35.6857			1.20228			0.601141	+	0.799143i	$0.294713\pi$
$882$	25.9191			0.872743
$883$	−6.89525	+	11.9429i	−0.232044	+	0.401912i	−0.958409	−	0.285397i	$-0.907875\pi$
$883$	−6.89525	+	11.9429i	−0.232044	+	0.401912i	0.726366	+	0.687308i	$0.241208\pi$
$884$	−1.98450	+	3.43725i	−0.0667458	+	0.115607i
$885$	−0.369153	−	0.639391i	−0.0124089	−	0.0214929i
$886$	4.01475	+	6.95375i	0.134878	+	0.233616i
$887$	9.96820			0.334699			0.167350	−	0.985898i	$-0.446479\pi$
$887$	9.96820			0.334699			0.167350	+	0.985898i	$0.446479\pi$
$888$	−1.28840	−	2.23157i	−0.0432357	−	0.0748865i
$889$	−21.7763	−	37.7177i	−0.730354	−	1.26501i
$890$	1.81122	+	3.13712i	0.0607121	+	0.105156i
$891$	18.0102	−	31.1945i	0.603363	−	1.04506i
$892$	−4.04471			−0.135427
$893$	−5.91355	+	10.2426i	−0.197889	+	0.342754i
$894$	0.153369	+	0.265644i	0.00512944	+	0.00888445i
$895$	−9.65395			−0.322696
$896$	−28.1308	−	48.7240i	−0.939784	−	1.62775i
$897$	0.235224	−	0.407420i	0.00785390	−	0.0136034i
$898$	3.18981	−	5.52491i	0.106445	−	0.184369i
$899$	33.7916			1.12701
$900$	12.6791	−	21.9608i	0.422636	−	0.732026i
$901$	9.08530			0.302675
$902$	11.1593			0.371565
$903$	−0.680528	+	3.83686i	−0.0226466	+	0.127683i
$904$	−31.8486			−1.05927
$905$	−1.95293			−0.0649177
$906$	−0.0967892	+	0.167644i	−0.00321561	+	0.00556959i
$907$	57.4266			1.90682			0.953410	−	0.301677i	$-0.0975465\pi$
$907$	57.4266			1.90682			0.953410	+	0.301677i	$0.0975465\pi$
$908$	1.01354	−	1.75549i	0.0336353	−	0.0582581i
$909$	−13.3055	+	23.0458i	−0.441315	+	0.764380i
$910$	1.19281	+	2.06601i	0.0395413	+	0.0684875i
$911$	11.2416			0.372450			0.186225	−	0.982507i	$-0.440375\pi$
$911$	11.2416			0.372450			0.186225	+	0.982507i	$0.440375\pi$
$912$	−0.373594	−	0.647085i	−0.0123709	−	0.0214271i
$913$	−2.19503	+	3.80191i	−0.0726450	+	0.125825i
$914$	−3.06334			−0.101326
$915$	0.204280	−	0.353824i	0.00675329	−	0.0116970i
$916$	15.5531	+	26.9387i	0.513888	+	0.890080i
$917$	34.4183	+	59.6143i	1.13659	+	1.96864i
$918$	−0.171739	−	0.297461i	−0.00566823	−	0.00981767i
$919$	−39.7638			−1.31169			−0.655843	−	0.754898i	$-0.727687\pi$
$919$	−39.7638			−1.31169			−0.655843	+	0.754898i	$0.727687\pi$
$920$	0.705094	+	1.22126i	0.0232463	+	0.0402637i
$921$	−1.83384	−	3.17630i	−0.0604269	−	0.104663i
$922$	1.66744	−	2.88809i	0.0549141	−	0.0951141i
$923$	1.75521	−	3.04011i	0.0577734	−	0.100066i
$924$	4.26277			0.140235
$925$	−57.2939			−1.88381
$926$	4.16920	−	7.22127i	0.137008	−	0.237306i
$927$	−11.1955	+	19.3911i	−0.367708	+	0.636889i
$928$	−12.3732	−	21.4310i	−0.406170	−	0.703507i
$929$	10.0143	+	17.3454i	0.328560	+	0.569083i	0.982226	−	0.187700i	$-0.0601034\pi$
$929$	10.0143	+	17.3454i	0.328560	+	0.569083i	−0.653666	+	0.756783i	$0.726770\pi$
$930$	−0.169667			−0.00556359
$931$	−21.2750	−	36.8493i	−0.697259	−	1.20769i
$932$	−10.0766	−	17.4531i	−0.330069	−	0.571697i
$933$	−0.516838	−	0.895189i	−0.0169205	−	0.0293072i
$934$	−2.03482	+	3.52441i	−0.0665814	+	0.115322i
$935$	1.78716			0.0584464
$936$	−6.09701	+	10.5603i	−0.199287	+	0.345175i
$937$	−9.61020	−	16.6454i	−0.313952	−	0.543780i	0.665262	−	0.746610i	$-0.268320\pi$
$937$	−9.61020	−	16.6454i	−0.313952	−	0.543780i	−0.979214	+	0.202829i	$0.934986\pi$
$938$	−15.1989			−0.496262
$939$	−1.41686	−	2.45408i	−0.0462376	−	0.0800859i
$940$	−1.94441	+	3.36782i	−0.0634198	+	0.109846i
$941$	−0.0471236	+	0.0816205i	−0.00153619	+	0.00266075i	−0.866792	−	0.498669i	$-0.833822\pi$
$941$	−0.0471236	+	0.0816205i	−0.00153619	+	0.00266075i	0.865256	+	0.501330i	$0.167156\pi$
$942$	−1.09528			−0.0356862
$943$	−5.01691	+	8.68954i	−0.163373	+	0.282970i
$944$	−37.4740			−1.21967
$945$	1.56596			0.0509407
$946$	−2.24387	+	12.6511i	−0.0729546	+	0.411323i
$947$	−29.4271			−0.956251			−0.478125	−	0.878292i	$-0.658684\pi$
$947$	−29.4271			−0.956251			−0.478125	+	0.878292i	$0.658684\pi$
$948$	1.56930			0.0509686
$949$	−1.09823	+	1.90218i	−0.0356499	+	0.0617475i
$950$	5.48827			0.178063
$951$	1.43267	−	2.48145i	0.0464574	−	0.0804666i
$952$	−4.54414	+	7.87067i	−0.147276	+	0.255090i
$953$	−5.22325	−	9.04694i	−0.169198	−	0.293059i	0.768940	−	0.639321i	$-0.220784\pi$
$953$	−5.22325	−	9.04694i	−0.169198	−	0.293059i	−0.938138	+	0.346262i	$0.887451\pi$
$954$	13.0934			0.423914
$955$	−2.87145	−	4.97350i	−0.0929181	−	0.160939i
$956$	22.4291	−	38.8484i	0.725410	−	1.25645i
$957$	2.42816			0.0784913
$958$	−8.60951	+	14.9121i	−0.278161	+	0.481788i
$959$	41.0439	+	71.0901i	1.32538	+	2.29562i
$960$	−0.0769099	−	0.133212i	−0.00248226	−	0.00429939i
$961$	−7.05522	−	12.2200i	−0.227588	−	0.394194i
$962$	12.9236			0.416674
$963$	8.34323	+	14.4509i	0.268857	+	0.465674i
$964$	13.2381	+	22.9290i	0.426370	+	0.738495i
$965$	3.06687	−	5.31197i	0.0987260	−	0.170998i
$966$	0.252656	−	0.437612i	0.00812906	−	0.0140799i
$967$	50.0201			1.60854			0.804270	−	0.594265i	$-0.202557\pi$
$967$	50.0201			1.60854			0.804270	+	0.594265i	$0.202557\pi$
$968$	9.96362			0.320243
$969$	−0.140634	+	0.243586i	−0.00451782	+	0.00782509i
$970$	−1.45089	+	2.51301i	−0.0465851	+	0.0806878i
$971$	0.556931	+	0.964632i	0.0178728	+	0.0309565i	0.874823	−	0.484442i	$-0.160977\pi$
$971$	0.556931	+	0.964632i	0.0178728	+	0.0309565i	−0.856951	+	0.515398i	$0.827644\pi$
$972$	2.81822	+	4.88131i	0.0903946	+	0.156568i
$973$	−2.62339			−0.0841019
$974$	−1.17109	−	2.02839i	−0.0375241	−	0.0649937i
$975$	−0.641704	−	1.11146i	−0.0205510	−	0.0355953i
$976$	−10.3686	−	17.9589i	−0.331891	−	0.574852i
$977$	−7.88572	+	13.6585i	−0.252287	+	0.436973i	−0.964155	−	0.265340i	$-0.914516\pi$
$977$	−7.88572	+	13.6585i	−0.252287	+	0.436973i	0.711868	+	0.702313i	$0.247849\pi$
$978$	1.02499			0.0327757
$979$	−34.6034	+	59.9349i	−1.10593	+	1.91553i
$980$	−6.99535	−	12.1163i	−0.223458	−	0.387041i
$981$	42.4118			1.35411
$982$	3.42099	+	5.92533i	0.109168	+	0.189085i
$983$	−30.7273	+	53.2212i	−0.980048	+	1.69749i	−0.317892	+	0.948127i	$0.602975\pi$
$983$	−30.7273	+	53.2212i	−0.980048	+	1.69749i	−0.662156	+	0.749366i	$0.730358\pi$
$984$	−0.615545	+	1.06616i	−0.0196229	+	0.0339878i
$985$	6.85995			0.218576
$986$	−1.21418	+	2.10302i	−0.0386674	+	0.0669738i
$987$	2.97067			0.0945575
$988$	9.39013			0.298740
$989$	−8.84237	−	7.43482i	−0.281171	−	0.236414i
$990$	2.57559			0.0818576
$991$	1.55503			0.0493970			0.0246985	−	0.999695i	$-0.492137\pi$
$991$	1.55503			0.0493970			0.0246985	+	0.999695i	$0.492137\pi$
$992$	−16.5177	+	28.6095i	−0.524438	+	0.908353i
$993$	−1.76242			−0.0559287
$994$	1.88528	−	3.26540i	0.0597974	−	0.103572i
$995$	2.71050	−	4.69473i	0.0859287	−	0.148833i
$996$	−0.113590	−	0.196743i	−0.00359923	−	0.00623405i
$997$	26.5211			0.839931			0.419966	−	0.907540i	$-0.362042\pi$
$997$	26.5211			0.839931			0.419966	+	0.907540i	$0.362042\pi$
$998$	1.57405	+	2.72633i	0.0498256	+	0.0863005i
$999$	4.24164	−	7.34673i	0.134199	−	0.232440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.13	✓	58
43.36	even	3	inner	731.2.e.b.681.13	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.13	✓	58	1.1	even	1	trivial
731.2.e.b.681.13	yes	58	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.482661 q^{2} +(-0.0594428 + 0.102958i) q^{3} -1.76704 q^{4} +(0.220118 - 0.381256i) q^{5} +(0.0286908 - 0.0496939i) q^{6} +(-2.49924 - 4.32882i) q^{7} +1.81820 q^{8} +(1.49293 + 2.58584i) q^{9} +O(q^{10})\)	\(q-0.482661 q^{2} +(-0.0594428 + 0.102958i) q^{3} -1.76704 q^{4} +(0.220118 - 0.381256i) q^{5} +(0.0286908 - 0.0496939i) q^{6} +(-2.49924 - 4.32882i) q^{7} +1.81820 q^{8} +(1.49293 + 2.58584i) q^{9} +(-0.106243 + 0.184018i) q^{10} -4.05955 q^{11} +(0.105038 - 0.181931i) q^{12} +(1.12306 + 1.94520i) q^{13} +(1.20629 + 2.08935i) q^{14} +(0.0261689 + 0.0453259i) q^{15} +2.65650 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.720581 - 1.24808i) q^{18} +(-1.18294 + 2.04891i) q^{19} +(-0.388957 + 0.673694i) q^{20} +0.594248 q^{21} +1.95939 q^{22} +(-0.880883 + 1.52573i) q^{23} +(-0.108079 + 0.187199i) q^{24} +(2.40310 + 4.16228i) q^{25} +(-0.542059 - 0.938874i) q^{26} -0.711634 q^{27} +(4.41626 + 7.64919i) q^{28} +(2.51559 + 4.35713i) q^{29} +(-0.0126307 - 0.0218771i) q^{30} +(3.35822 - 5.81660i) q^{31} -4.91860 q^{32} +(0.241311 - 0.417963i) q^{33} +(0.241331 + 0.417997i) q^{34} -2.20052 q^{35} +(-2.63807 - 4.56927i) q^{36} +(-5.96042 + 10.3238i) q^{37} +(0.570958 - 0.988928i) q^{38} -0.267032 q^{39} +(0.400220 - 0.693201i) q^{40} +5.69532 q^{41} -0.286821 q^{42} +(-1.14519 + 6.45667i) q^{43} +7.17337 q^{44} +1.31449 q^{45} +(0.425168 - 0.736413i) q^{46} +4.99904 q^{47} +(-0.157910 + 0.273508i) q^{48} +(-8.99244 + 15.5754i) q^{49} +(-1.15988 - 2.00897i) q^{50} +0.118886 q^{51} +(-1.98450 - 3.43725i) q^{52} +(-4.54265 + 7.86810i) q^{53} +0.343478 q^{54} +(-0.893581 + 1.54773i) q^{55} +(-4.54414 - 7.87067i) q^{56} +(-0.140634 - 0.243586i) q^{57} +(-1.21418 - 2.10302i) q^{58} -14.1065 q^{59} +(-0.0462414 - 0.0800925i) q^{60} +(-3.90311 - 6.76038i) q^{61} +(-1.62088 + 2.80745i) q^{62} +(7.46241 - 12.9253i) q^{63} -2.93898 q^{64} +0.988827 q^{65} +(-0.116471 + 0.201735i) q^{66} +(-3.14993 + 5.45584i) q^{67} +(0.883519 + 1.53030i) q^{68} +(-0.104724 - 0.181388i) q^{69} +1.06210 q^{70} +(-0.781438 - 1.35349i) q^{71} +(2.71446 + 4.70158i) q^{72} +(0.488942 + 0.846873i) q^{73} +(2.87687 - 4.98288i) q^{74} -0.571387 q^{75} +(2.09029 - 3.62049i) q^{76} +(10.1458 + 17.5730i) q^{77} +0.128886 q^{78} +(3.73510 + 6.46938i) q^{79} +(0.584744 - 1.01281i) q^{80} +(-4.43650 + 7.68424i) q^{81} -2.74891 q^{82} +(0.540709 - 0.936536i) q^{83} -1.05006 q^{84} -0.440237 q^{85} +(0.552740 - 3.11638i) q^{86} -0.598136 q^{87} -7.38109 q^{88} +(8.52396 - 14.7639i) q^{89} -0.634452 q^{90} +(5.61362 - 9.72307i) q^{91} +(1.55655 - 2.69603i) q^{92} +(0.399244 + 0.691510i) q^{93} -2.41284 q^{94} +(0.520772 + 0.902003i) q^{95} +(0.292375 - 0.506409i) q^{96} +13.6563 q^{97} +(4.34031 - 7.51763i) q^{98} +(-6.06063 - 10.4973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

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