LMFDB - Embedded newform 276.2.c.b.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04620 - 0.951558i) q^{2} +(1.08652 + 1.34888i) q^{3} +(0.189073 + 1.99104i) q^{4} -0.289949i q^{5} +(0.146820 - 2.44509i) q^{6} +1.62347i q^{7} +(1.69678 - 2.26295i) q^{8} +(-0.638952 + 2.93117i) q^{9} +O(q^{10})$	\(q+(-1.04620 - 0.951558i) q^{2} +(1.08652 + 1.34888i) q^{3} +(0.189073 + 1.99104i) q^{4} -0.289949i q^{5} +(0.146820 - 2.44509i) q^{6} +1.62347i q^{7} +(1.69678 - 2.26295i) q^{8} +(-0.638952 + 2.93117i) q^{9} +(-0.275904 + 0.303345i) q^{10} +0.671787 q^{11} +(-2.48025 + 2.41834i) q^{12} +0.807180 q^{13} +(1.54483 - 1.69848i) q^{14} +(0.391106 - 0.315035i) q^{15} +(-3.92850 + 0.752906i) q^{16} +3.08837i q^{17} +(3.45765 - 2.45859i) q^{18} +5.84877i q^{19} +(0.577301 - 0.0548216i) q^{20} +(-2.18987 + 1.76393i) q^{21} +(-0.702824 - 0.639245i) q^{22} -1.00000 q^{23} +(4.89603 - 0.169975i) q^{24} +4.91593 q^{25} +(-0.844473 - 0.768079i) q^{26} +(-4.64803 + 2.32290i) q^{27} +(-3.23240 + 0.306955i) q^{28} -3.12320i q^{29} +(-0.708950 - 0.0425704i) q^{30} -2.12983i q^{31} +(4.82644 + 2.95051i) q^{32} +(0.729909 + 0.906160i) q^{33} +(2.93876 - 3.23105i) q^{34} +0.470724 q^{35} +(-5.95689 - 0.717976i) q^{36} +7.38600 q^{37} +(5.56545 - 6.11899i) q^{38} +(0.877017 + 1.08879i) q^{39} +(-0.656139 - 0.491981i) q^{40} -4.70122i q^{41} +(3.96953 + 0.238358i) q^{42} -7.68893i q^{43} +(0.127017 + 1.33756i) q^{44} +(0.849889 + 0.185264i) q^{45} +(1.04620 + 0.951558i) q^{46} -1.47052 q^{47} +(-5.28397 - 4.48103i) q^{48} +4.36434 q^{49} +(-5.14305 - 4.67779i) q^{50} +(-4.16584 + 3.35557i) q^{51} +(0.152616 + 1.60713i) q^{52} -3.50905i q^{53} +(7.07314 + 1.99265i) q^{54} -0.194784i q^{55} +(3.67383 + 2.75468i) q^{56} +(-7.88929 + 6.35480i) q^{57} +(-2.97190 + 3.26749i) q^{58} -12.7702 q^{59} +(0.701197 + 0.719145i) q^{60} -2.00798 q^{61} +(-2.02666 + 2.22823i) q^{62} +(-4.75867 - 1.03732i) q^{63} +(-2.24184 - 7.67946i) q^{64} -0.234041i q^{65} +(0.0986319 - 1.64258i) q^{66} -2.36664i q^{67} +(-6.14907 + 0.583928i) q^{68} +(-1.08652 - 1.34888i) q^{69} +(-0.492472 - 0.447922i) q^{70} -4.11689 q^{71} +(5.54891 + 6.41947i) q^{72} -9.56775 q^{73} +(-7.72724 - 7.02821i) q^{74} +(5.34125 + 6.63100i) q^{75} +(-11.6452 + 1.10585i) q^{76} +1.09063i q^{77} +(0.118510 - 1.97362i) q^{78} -12.6712i q^{79} +(0.218304 + 1.13907i) q^{80} +(-8.18348 - 3.74575i) q^{81} +(-4.47349 + 4.91843i) q^{82} +15.6752 q^{83} +(-3.92611 - 4.02661i) q^{84} +0.895469 q^{85} +(-7.31647 + 8.04417i) q^{86} +(4.21282 - 3.39341i) q^{87} +(1.13988 - 1.52022i) q^{88} +5.78814i q^{89} +(-0.712866 - 1.00254i) q^{90} +1.31043i q^{91} +(-0.189073 - 1.99104i) q^{92} +(2.87289 - 2.31411i) q^{93} +(1.53846 + 1.39929i) q^{94} +1.69585 q^{95} +(1.26414 + 9.71607i) q^{96} -6.57624 q^{97} +(-4.56598 - 4.15292i) q^{98} +(-0.429240 + 1.96912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.04620	−	0.951558i	−0.739776	−	0.672853i
$2$	−1.04620	−	0.951558i	−0.739776	−	0.672853i
$3$	1.08652	+	1.34888i	0.627302	+	0.778776i
$3$	1.08652	+	1.34888i	0.627302	+	0.778776i
$4$	0.189073	+	1.99104i	0.0945367	+	0.995521i
$5$		−	0.289949i		−	0.129669i	−0.997896	−	0.0648346i	$-0.979348\pi$
$5$		−	0.289949i		−	0.129669i	0.997896	−	0.0648346i	$-0.0206520\pi$
$6$	0.146820	−	2.44509i	0.0599391	−	0.998202i
$7$			1.62347i			0.613615i	0.951772	+	0.306807i	$0.0992607\pi$
$7$			1.62347i			0.613615i	−0.951772	+	0.306807i	$0.900739\pi$
$8$	1.69678	−	2.26295i	0.599904	−	0.800072i
$9$	−0.638952	+	2.93117i	−0.212984	+	0.977056i
$10$	−0.275904	+	0.303345i	−0.0872484	+	0.0959261i
$11$	0.671787			0.202551			0.101276	−	0.994858i	$-0.467708\pi$
$11$	0.671787			0.202551			0.101276	+	0.994858i	$0.467708\pi$
$12$	−2.48025	+	2.41834i	−0.715985	+	0.698116i
$13$	0.807180			0.223871			0.111936	−	0.993715i	$-0.464295\pi$
$13$	0.807180			0.223871			0.111936	+	0.993715i	$0.464295\pi$
$14$	1.54483	−	1.69848i	0.412873	−	0.453937i
$15$	0.391106	−	0.315035i	0.100983	−	0.0813418i
$16$	−3.92850	+	0.752906i	−0.982126	+	0.188227i
$17$			3.08837i			0.749039i	0.927219	+	0.374520i	$0.122192\pi$
$17$			3.08837i			0.749039i	−0.927219	+	0.374520i	$0.877808\pi$
$18$	3.45765	−	2.45859i	0.814976	−	0.579495i
$19$			5.84877i			1.34180i	0.741548	+	0.670900i	$0.234092\pi$
$19$			5.84877i			1.34180i	−0.741548	+	0.670900i	$0.765908\pi$
$20$	0.577301	−	0.0548216i	0.129088	−	0.0122585i
$21$	−2.18987	+	1.76393i	−0.477868	+	0.384922i
$22$	−0.702824	−	0.639245i	−0.149843	−	0.136287i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	4.89603	−	0.169975i	0.999398	−	0.0346961i
$25$	4.91593			0.983186
$26$	−0.844473	−	0.768079i	−0.165615	−	0.150633i
$27$	−4.64803	+	2.32290i	−0.894513	+	0.447042i
$28$	−3.23240	+	0.306955i	−0.610867	+	0.0580091i
$29$		−	3.12320i		−	0.579963i	−0.957032	−	0.289981i	$-0.906351\pi$
$29$		−	3.12320i		−	0.579963i	0.957032	−	0.289981i	$-0.0936492\pi$
$30$	−0.708950	−	0.0425704i	−0.129436	−	0.00777225i
$31$		−	2.12983i		−	0.382529i	−0.981538	−	0.191265i	$-0.938741\pi$
$31$		−	2.12983i		−	0.382529i	0.981538	−	0.191265i	$-0.0612589\pi$
$32$	4.82644	+	2.95051i	0.853202	+	0.521581i
$33$	0.729909	+	0.906160i	0.127061	+	0.157742i
$34$	2.93876	−	3.23105i	0.503994	−	0.554121i
$35$	0.470724			0.0795669
$36$	−5.95689	−	0.717976i	−0.992815	−	0.119663i
$37$	7.38600			1.21425			0.607125	−	0.794606i	$-0.292323\pi$
$37$	7.38600			1.21425			0.607125	+	0.794606i	$0.292323\pi$
$38$	5.56545	−	6.11899i	0.902835	−	0.992632i
$39$	0.877017	+	1.08879i	0.140435	+	0.174346i
$40$	−0.656139	−	0.491981i	−0.103745	−	0.0777891i
$41$		−	4.70122i		−	0.734208i	−0.930180	−	0.367104i	$-0.880349\pi$
$41$		−	4.70122i		−	0.734208i	0.930180	−	0.367104i	$-0.119651\pi$
$42$	3.96953	+	0.238358i	0.612512	+	0.0367795i
$43$		−	7.68893i		−	1.17255i	−0.810112	−	0.586276i	$-0.800594\pi$
$43$		−	7.68893i		−	1.17255i	0.810112	−	0.586276i	$-0.199406\pi$
$44$	0.127017	+	1.33756i	0.0191485	+	0.201644i
$45$	0.849889	+	0.185264i	0.126694	+	0.0276175i
$46$	1.04620	+	0.951558i	0.154254	+	0.140300i
$47$	−1.47052			−0.214498			−0.107249	−	0.994232i	$-0.534204\pi$
$47$	−1.47052			−0.214498			−0.107249	+	0.994232i	$0.534204\pi$
$48$	−5.28397	−	4.48103i	−0.762676	−	0.646781i
$49$	4.36434			0.623477
$50$	−5.14305	−	4.67779i	−0.727337	−	0.661540i
$51$	−4.16584	+	3.35557i	−0.583334	+	0.469874i
$52$	0.152616	+	1.60713i	0.0211641	+	0.222869i
$53$		−	3.50905i		−	0.482005i	−0.970524	−	0.241003i	$-0.922524\pi$
$53$		−	3.50905i		−	0.482005i	0.970524	−	0.241003i	$-0.0774763\pi$
$54$	7.07314	+	1.99265i	0.962533	+	0.271165i
$55$		−	0.194784i		−	0.0262647i
$56$	3.67383	+	2.75468i	0.490936	+	0.368110i
$57$	−7.88929	+	6.35480i	−1.04496	+	0.841714i
$58$	−2.97190	+	3.26749i	−0.390230	+	0.429043i
$59$	−12.7702			−1.66254			−0.831269	−	0.555871i	$-0.812385\pi$
$59$	−12.7702			−1.66254			−0.831269	+	0.555871i	$0.812385\pi$
$60$	0.701197	+	0.719145i	0.0905241	+	0.0928412i
$61$	−2.00798			−0.257096			−0.128548	−	0.991703i	$-0.541032\pi$
$61$	−2.00798			−0.257096			−0.128548	+	0.991703i	$0.541032\pi$
$62$	−2.02666	+	2.22823i	−0.257386	+	0.282986i
$63$	−4.75867	−	1.03732i	−0.599536	−	0.130690i
$64$	−2.24184	−	7.67946i	−0.280230	−	0.959933i
$65$		−	0.234041i		−	0.0290292i
$66$	0.0986319	−	1.64258i	0.0121407	−	0.202187i
$67$		−	2.36664i		−	0.289131i	−0.989495	−	0.144566i	$-0.953822\pi$
$67$		−	2.36664i		−	0.289131i	0.989495	−	0.144566i	$-0.0461785\pi$
$68$	−6.14907	+	0.583928i	−0.745684	+	0.0708117i
$69$	−1.08652	−	1.34888i	−0.130802	−	0.162386i
$70$	−0.492472	−	0.447922i	−0.0588617	−	0.0535369i
$71$	−4.11689			−0.488585			−0.244292	−	0.969702i	$-0.578556\pi$
$71$	−4.11689			−0.488585			−0.244292	+	0.969702i	$0.578556\pi$
$72$	5.54891	+	6.41947i	0.653945	+	0.756542i
$73$	−9.56775			−1.11982			−0.559910	−	0.828553i	$-0.689164\pi$
$73$	−9.56775			−1.11982			−0.559910	+	0.828553i	$0.689164\pi$
$74$	−7.72724	−	7.02821i	−0.898273	−	0.817013i
$75$	5.34125	+	6.63100i	0.616755	+	0.765682i
$76$	−11.6452	+	1.10585i	−1.33579	+	0.126849i
$77$			1.09063i			0.124289i
$78$	0.118510	−	1.97362i	0.0134186	−	0.223469i
$79$		−	12.6712i		−	1.42562i	−0.701357	−	0.712810i	$-0.747422\pi$
$79$		−	12.6712i		−	1.42562i	0.701357	−	0.712810i	$-0.252578\pi$
$80$	0.218304	+	1.13907i	0.0244072	+	0.127351i
$81$	−8.18348	−	3.74575i	−0.909276	−	0.416195i
$82$	−4.47349	+	4.91843i	−0.494014	+	0.543149i
$83$	15.6752			1.72057			0.860286	−	0.509811i	$-0.170285\pi$
$83$	15.6752			1.72057			0.860286	+	0.509811i	$0.170285\pi$
$84$	−3.92611	−	4.02661i	−0.428374	−	0.439339i
$85$	0.895469			0.0971273
$86$	−7.31647	+	8.04417i	−0.788955	+	0.867425i
$87$	4.21282	−	3.39341i	0.451661	−	0.363812i
$88$	1.13988	−	1.52022i	0.121511	−	0.162056i
$89$			5.78814i			0.613541i	0.951783	+	0.306771i	$0.0992484\pi$
$89$			5.78814i			0.613541i	−0.951783	+	0.306771i	$0.900752\pi$
$90$	−0.712866	−	1.00254i	−0.0751427	−	0.105677i
$91$			1.31043i			0.137371i
$92$	−0.189073	−	1.99104i	−0.0197123	−	0.207581i
$93$	2.87289	−	2.31411i	0.297905	−	0.239962i
$94$	1.53846	+	1.39929i	0.158680	+	0.144326i
$95$	1.69585			0.173990
$96$	1.26414	+	9.71607i	0.129020	+	0.991642i
$97$	−6.57624			−0.667716			−0.333858	−	0.942623i	$-0.608351\pi$
$97$	−6.57624			−0.667716			−0.333858	+	0.942623i	$0.608351\pi$
$98$	−4.56598	−	4.15292i	−0.461233	−	0.419509i
$99$	−0.429240	+	1.96912i	−0.0431402	+	0.197904i
$100$	0.929471	+	9.78783i	0.0929471	+	0.978783i
$101$		−	17.5497i		−	1.74626i	−0.487484	−	0.873132i	$-0.662085\pi$
$101$		−	17.5497i		−	1.74626i	0.487484	−	0.873132i	$-0.337915\pi$
$102$	7.55132	+	0.453435i	0.747692	+	0.0448967i
$103$		−	9.41661i		−	0.927846i	−0.885876	−	0.463923i	$-0.846441\pi$
$103$		−	9.41661i		−	0.927846i	0.885876	−	0.463923i	$-0.153559\pi$
$104$	1.36961	−	1.82660i	0.134301	−	0.179113i
$105$	0.511451	+	0.634950i	0.0499125	+	0.0619648i
$106$	−3.33907	+	3.67117i	−0.324319	+	0.356576i
$107$	15.7394			1.52159			0.760794	−	0.648993i	$-0.224810\pi$
$107$	15.7394			1.52159			0.760794	+	0.648993i	$0.224810\pi$
$108$	−5.50381	−	8.81522i	−0.529604	−	0.848245i
$109$	17.8833			1.71291			0.856453	−	0.516225i	$-0.172663\pi$
$109$	17.8833			1.71291			0.856453	+	0.516225i	$0.172663\pi$
$110$	−0.185348	+	0.203783i	−0.0176723	+	0.0194300i
$111$	8.02503	+	9.96282i	0.761702	+	0.945629i
$112$	−1.22232	−	6.37781i	−0.115499	−	0.602647i
$113$			14.1284i			1.32909i	0.747247	+	0.664546i	$0.231375\pi$
$113$			14.1284i			1.32909i	−0.747247	+	0.664546i	$0.768625\pi$
$114$	14.3007	+	0.858718i	1.33939	+	0.0804263i
$115$			0.289949i			0.0270379i
$116$	6.21842	−	0.590513i	0.577366	−	0.0548278i
$117$	−0.515750	+	2.36598i	−0.0476811	+	0.218735i
$118$	13.3602	+	12.1516i	1.22990	+	1.11864i
$119$	−5.01388			−0.459621
$120$	−0.0492842	−	1.41960i	−0.00449901	−	0.129591i
$121$	−10.5487			−0.958973
$122$	2.10075	+	1.91071i	0.190193	+	0.172988i
$123$	6.34139	−	5.10797i	0.571784	−	0.460570i
$124$	4.24059	−	0.402695i	0.380816	−	0.0361631i
$125$		−	2.87512i		−	0.257158i
$126$	3.99145	+	5.61340i	0.355587	+	0.500081i
$127$		−	12.6694i		−	1.12423i	−0.827059	−	0.562116i	$-0.809988\pi$
$127$		−	12.6694i		−	1.12423i	0.827059	−	0.562116i	$-0.190012\pi$
$128$	−4.96204	+	10.1675i	−0.438586	+	0.898689i
$129$	10.3714	−	8.35417i	0.913155	−	0.735544i
$130$	−0.222704	+	0.244854i	−0.0195324	+	0.0214751i
$131$	1.79636			0.156949			0.0784743	−	0.996916i	$-0.474995\pi$
$131$	1.79636			0.156949			0.0784743	+	0.996916i	$0.474995\pi$
$132$	−1.66620	+	1.62461i	−0.145024	+	0.141404i
$133$	−9.49532			−0.823349
$134$	−2.25200	+	2.47598i	−0.194543	+	0.213892i
$135$	0.673523	+	1.34769i	0.0579676	+	0.115991i
$136$	6.98881	+	5.24029i	0.599285	+	0.449352i
$137$			11.3603i			0.970576i	0.874354	+	0.485288i	$0.161285\pi$
$137$			11.3603i			0.970576i	−0.874354	+	0.485288i	$0.838715\pi$
$138$	−0.146820	+	2.44509i	−0.0124982	+	0.208140i
$139$		−	7.42496i		−	0.629777i	−0.949129	−	0.314888i	$-0.898033\pi$
$139$		−	7.42496i		−	0.629777i	0.949129	−	0.314888i	$-0.101967\pi$
$140$	0.0890014	+	0.937232i	0.00752199	+	0.0792106i
$141$	−1.59775	−	1.98356i	−0.134555	−	0.167046i
$142$	4.30709	+	3.91746i	0.361443	+	0.328746i
$143$	0.542253			0.0453455
$144$	0.303232	−	11.9962i	0.0252693	−	0.999681i
$145$	−0.905568			−0.0752033
$146$	10.0098	+	9.10427i	0.828416	+	0.753475i
$147$	4.74194	+	5.88697i	0.391108	+	0.485549i
$148$	1.39650	+	14.7058i	0.114791	+	1.20881i
$149$			8.57740i			0.702688i	0.936246	+	0.351344i	$0.114275\pi$
$149$			8.57740i			0.702688i	−0.936246	+	0.351344i	$0.885725\pi$
$150$	0.721757	−	12.0199i	0.0589313	−	0.981418i
$151$			1.64243i			0.133659i	0.997764	+	0.0668296i	$0.0212884\pi$
$151$			1.64243i			0.133659i	−0.997764	+	0.0668296i	$0.978712\pi$
$152$	13.2355	+	9.92411i	1.07354	+	0.804951i
$153$	−9.05252	−	1.97332i	−0.731853	−	0.159533i
$154$	1.03780	−	1.14102i	0.0836280	−	0.0919456i
$155$	−0.617543			−0.0496023
$156$	−2.00200	+	1.95204i	−0.160289	+	0.156288i
$157$	20.5892			1.64320			0.821600	−	0.570065i	$-0.193082\pi$
$157$	20.5892			1.64320			0.821600	+	0.570065i	$0.193082\pi$
$158$	−12.0574	+	13.2566i	−0.959233	+	1.05464i
$159$	4.73329	−	3.81265i	0.375374	−	0.302363i
$160$	0.855497	−	1.39942i	0.0676330	−	0.110634i
$161$		−	1.62347i		−	0.127948i
$162$	4.99726	+	11.7059i	0.392622	+	0.919700i
$163$			18.0647i			1.41494i	0.706745	+	0.707469i	$0.250163\pi$
$163$			18.0647i			1.41494i	−0.706745	+	0.707469i	$0.749837\pi$
$164$	9.36034	−	0.888876i	0.730920	−	0.0694096i
$165$	0.262740	−	0.211637i	0.0204543	−	0.0164759i
$166$	−16.3994	−	14.9158i	−1.27284	−	1.15769i
$167$	10.5760			0.818395			0.409198	−	0.912446i	$-0.365809\pi$
$167$	10.5760			0.818395			0.409198	+	0.912446i	$0.365809\pi$
$168$	0.275950	+	7.94857i	0.0212900	+	0.613245i
$169$	−12.3485			−0.949882
$170$	−0.936841	−	0.852091i	−0.0718524	−	0.0653524i
$171$	−17.1437	−	3.73709i	−1.31101	−	0.285782i
$172$	15.3090	−	1.45377i	1.16730	−	0.110849i
$173$		−	19.0577i		−	1.44893i	−0.689310	−	0.724466i	$-0.742086\pi$
$173$		−	19.0577i		−	1.44893i	0.689310	−	0.724466i	$-0.257914\pi$
$174$	−7.63648	−	0.458548i	−0.578920	−	0.0347624i
$175$			7.98087i			0.603297i
$176$	−2.63912	+	0.505793i	−0.198931	+	0.0381255i
$177$	−13.8751	−	17.2254i	−1.04291	−	1.29474i
$178$	5.50775	−	6.05555i	0.412823	−	0.453883i
$179$	−3.06094			−0.228786			−0.114393	−	0.993436i	$-0.536492\pi$
$179$	−3.06094			−0.228786			−0.114393	+	0.993436i	$0.536492\pi$
$180$	−0.208176	+	1.72719i	−0.0155166	+	0.128737i
$181$	−20.3829			−1.51505			−0.757525	−	0.652806i	$-0.773592\pi$
$181$	−20.3829			−1.51505			−0.757525	+	0.652806i	$0.773592\pi$
$182$	1.24695	−	1.37098i	0.0924304	−	0.101624i
$183$	−2.18171	−	2.70853i	−0.161277	−	0.200220i
$184$	−1.69678	+	2.26295i	−0.125089	+	0.166827i
$185$		−	2.14156i		−	0.157451i
$186$	−5.20763	−	0.312702i	−0.381842	−	0.0229285i
$187$			2.07473i			0.151719i
$188$	−0.278037	−	2.92788i	−0.0202779	−	0.213537i
$189$	−3.77116	−	7.54594i	−0.274312	−	0.548886i
$190$	−1.77420	−	1.61370i	−0.128714	−	0.117070i
$191$	−9.77702			−0.707440			−0.353720	−	0.935351i	$-0.615083\pi$
$191$	−9.77702			−0.707440			−0.353720	+	0.935351i	$0.615083\pi$
$192$	7.92286	−	11.3679i	0.571783	−	0.820405i
$193$	22.3232			1.60686			0.803430	−	0.595399i	$-0.203006\pi$
$193$	22.3232			1.60686			0.803430	+	0.595399i	$0.203006\pi$
$194$	6.88007	+	6.25767i	0.493960	+	0.449275i
$195$	0.315693	−	0.254290i	0.0226073	−	0.0182101i
$196$	0.825180	+	8.68958i	0.0589414	+	0.620685i
$197$			4.54333i			0.323699i	0.986815	+	0.161850i	$0.0517459\pi$
$197$			4.54333i			0.323699i	−0.986815	+	0.161850i	$0.948254\pi$
$198$	2.32280	−	1.65165i	0.165074	−	0.117378i
$199$			20.8950i			1.48121i	0.671943	+	0.740603i	$0.265460\pi$
$199$			20.8950i			1.48121i	−0.671943	+	0.740603i	$0.734540\pi$
$200$	8.34127	−	11.1245i	0.589817	−	0.786620i
$201$	3.19232	−	2.57140i	0.225169	−	0.181373i
$202$	−16.6996	+	18.3605i	−1.17498	+	1.29184i
$203$	5.07042			0.355874
$204$	−7.46873	−	7.65991i	−0.522916	−	0.536301i
$205$	−1.36312			−0.0952041
$206$	−8.96045	+	9.85166i	−0.624304	+	0.686398i
$207$	0.638952	−	2.93117i	0.0444102	−	0.203730i
$208$	−3.17101	+	0.607731i	−0.219870	+	0.0421386i
$209$			3.92913i			0.271784i
$210$	0.0691118	−	1.15096i	0.00476917	−	0.0794239i
$211$		−	11.5049i		−	0.792029i	−0.918244	−	0.396014i	$-0.870393\pi$
$211$		−	11.5049i		−	0.792029i	0.918244	−	0.396014i	$-0.129607\pi$
$212$	6.98667	−	0.663468i	0.479847	−	0.0455672i
$213$	−4.47308	−	5.55319i	−0.306490	−	0.380498i
$214$	−16.4666	−	14.9770i	−1.12563	−	1.02381i
$215$	−2.22940			−0.152044
$216$	−2.63010	+	14.4597i	−0.178956	+	0.983857i
$217$	3.45773			0.234726
$218$	−18.7095	−	17.0170i	−1.26717	−	1.15253i
$219$	−10.3955	−	12.9057i	−0.702466	−	0.872089i
$220$	0.387823	−	0.0368285i	0.0261470	−	0.00248297i
$221$			2.49287i			0.167689i
$222$	1.08441	−	18.0594i	0.0727810	−	1.21207i
$223$			4.04594i			0.270936i	0.990782	+	0.135468i	$0.0432538\pi$
$223$			4.04594i			0.270936i	−0.990782	+	0.135468i	$0.956746\pi$
$224$	−4.79007	+	7.83559i	−0.320050	+	0.523537i
$225$	−3.14104	+	14.4094i	−0.209403	+	0.960627i
$226$	13.4440	−	14.7812i	0.894284	−	0.983230i
$227$	−6.73718			−0.447163			−0.223581	−	0.974685i	$-0.571775\pi$
$227$	−6.73718			−0.447163			−0.223581	+	0.974685i	$0.571775\pi$
$228$	−14.1443	−	14.5064i	−0.936732	−	0.960709i
$229$	7.28866			0.481648			0.240824	−	0.970569i	$-0.422582\pi$
$229$	7.28866			0.481648			0.240824	+	0.970569i	$0.422582\pi$
$230$	0.275904	−	0.303345i	0.0181925	−	0.0200020i
$231$	−1.47112	+	1.18499i	−0.0967929	+	0.0779665i
$232$	−7.06762	−	5.29939i	−0.464012	−	0.347922i
$233$			25.1124i			1.64517i	0.568642	+	0.822585i	$0.307469\pi$
$233$			25.1124i			1.64517i	−0.568642	+	0.822585i	$0.692531\pi$
$234$	2.79095	−	1.98452i	0.182450	−	0.129732i
$235$			0.426377i			0.0278138i
$236$	−2.41450	−	25.4260i	−0.157171	−	1.65509i
$237$	17.0919	−	13.7675i	1.11024	−	0.894294i
$238$	5.24552	+	4.77100i	0.340017	+	0.309258i
$239$	−19.0646			−1.23319			−0.616593	−	0.787282i	$-0.711487\pi$
$239$	−19.0646			−1.23319			−0.616593	+	0.787282i	$0.711487\pi$
$240$	−1.29927	+	1.53208i	−0.0838676	+	0.0988956i
$241$	−15.7503			−1.01457			−0.507283	−	0.861780i	$-0.669350\pi$
$241$	−15.7503			−1.01457			−0.507283	+	0.861780i	$0.669350\pi$
$242$	11.0361	+	10.0377i	0.709425	+	0.645248i
$243$	−3.83894	−	15.1084i	−0.246268	−	0.969202i
$244$	−0.379656	−	3.99798i	−0.0243050	−	0.255944i
$245$		−	1.26544i		−	0.0808457i
$246$	−11.4949	−	0.690234i	−0.732888	−	0.0440077i
$247$			4.72101i			0.300391i
$248$	−4.81970	−	3.61387i	−0.306051	−	0.229481i
$249$	17.0314	+	21.1439i	1.07932	+	1.33994i
$250$	−2.73584	+	3.00795i	−0.173030	+	0.190239i
$251$	0.950908			0.0600208			0.0300104	−	0.999550i	$-0.490446\pi$
$251$	0.950908			0.0600208			0.0300104	+	0.999550i	$0.490446\pi$
$252$	1.16561	−	9.67084i	0.0734267	−	0.609206i
$253$	−0.671787			−0.0422349
$254$	−12.0557	+	13.2548i	−0.756443	+	0.831679i
$255$	0.972945	+	1.20788i	0.0609282	+	0.0756404i
$256$	14.8663	−	5.91559i	0.929142	−	0.369724i
$257$			9.40992i			0.586975i	0.955963	+	0.293487i	$0.0948158\pi$
$257$			9.40992i			0.586975i	−0.955963	+	0.293487i	$0.905184\pi$
$258$	−18.8001	−	1.12889i	−1.17044	−	0.0702816i
$259$			11.9910i			0.745082i
$260$	0.465986	−	0.0442509i	0.0288992	−	0.00274433i
$261$	9.15461	+	1.99557i	0.566656	+	0.123523i
$262$	−1.87935	−	1.70934i	−0.116107	−	0.105603i
$263$	−2.80667			−0.173067			−0.0865335	−	0.996249i	$-0.527579\pi$
$263$	−2.80667			−0.173067			−0.0865335	+	0.996249i	$0.527579\pi$
$264$	3.28909	−	0.114187i	0.202429	−	0.00702774i
$265$	−1.01745			−0.0625013
$266$	9.93401	+	9.03535i	0.609093	+	0.553993i
$267$	−7.80750	+	6.28892i	−0.477811	+	0.384876i
$268$	4.71209	−	0.447469i	0.287836	−	0.0273335i
$269$			4.85563i			0.296053i	0.988983	+	0.148026i	$0.0472921\pi$
$269$			4.85563i			0.296053i	−0.988983	+	0.148026i	$0.952708\pi$
$270$	0.577766	−	2.05085i	0.0351617	−	0.124811i
$271$			12.7177i			0.772547i	0.922384	+	0.386273i	$0.126238\pi$
$271$			12.7177i			0.772547i	−0.922384	+	0.386273i	$0.873762\pi$
$272$	−2.32525	−	12.1327i	−0.140989	−	0.735651i
$273$	−1.76762	+	1.42381i	−0.106981	+	0.0861730i
$274$	10.8100	−	11.8852i	0.653055	−	0.718009i
$275$	3.30246			0.199146
$276$	2.48025	−	2.41834i	0.149293	−	0.145567i
$277$	18.5992			1.11752			0.558760	−	0.829330i	$-0.311277\pi$
$277$	18.5992			1.11752			0.558760	+	0.829330i	$0.311277\pi$
$278$	−7.06528	+	7.76800i	−0.423747	+	0.465894i
$279$	6.24290	+	1.36086i	0.373753	+	0.0814727i
$280$	0.798718	−	1.06522i	0.0477325	−	0.0636593i
$281$		−	8.84726i		−	0.527784i	−0.964552	−	0.263892i	$-0.914994\pi$
$281$		−	8.84726i		−	0.527784i	0.964552	−	0.263892i	$-0.0850062\pi$
$282$	−0.215902	+	3.59556i	−0.0128568	+	0.214112i
$283$		−	16.3859i		−	0.974042i	−0.873390	−	0.487021i	$-0.838084\pi$
$283$		−	16.3859i		−	0.974042i	0.873390	−	0.487021i	$-0.161916\pi$
$284$	−0.778394	−	8.19690i	−0.0461892	−	0.486396i
$285$	1.84257	+	2.28749i	0.109144	+	0.135499i
$286$	−0.567306	−	0.515985i	−0.0335455	−	0.0305109i
$287$	7.63231			0.450521
$288$	−11.7323	+	12.2619i	−0.691332	+	0.722537i
$289$	7.46199			0.438940
$290$	0.947406	+	0.861701i	0.0556336	+	0.0506008i
$291$	−7.14521	−	8.87055i	−0.418860	−	0.520001i
$292$	−1.80901	−	19.0498i	−0.105864	−	1.11480i
$293$			23.6342i			1.38072i	0.723464	+	0.690362i	$0.242549\pi$
$293$			23.6342i			1.38072i	−0.723464	+	0.690362i	$0.757451\pi$
$294$	0.640773	−	10.6712i	0.0373706	−	0.622356i
$295$			3.70271i			0.215580i
$296$	12.5324	−	16.7141i	0.728434	−	0.971488i
$297$	−3.12248	+	1.56049i	−0.181185	+	0.0905490i
$298$	8.16190	−	8.97368i	0.472806	−	0.519832i
$299$	−0.807180			−0.0466804
$300$	−12.1927	+	11.8884i	−0.703946	+	0.686377i
$301$	12.4828			0.719495
$302$	1.56287	−	1.71831i	0.0899331	−	0.0988779i
$303$	23.6725	−	19.0681i	1.35995	−	1.09543i
$304$	−4.40358	−	22.9769i	−0.252562	−	1.31782i
$305$			0.582213i			0.0333374i
$306$	7.59303	+	10.6785i	0.434065	+	0.610449i
$307$			8.71034i			0.497126i	0.968616	+	0.248563i	$0.0799582\pi$
$307$			8.71034i			0.497126i	−0.968616	+	0.248563i	$0.920042\pi$
$308$	−2.17149	+	0.206209i	−0.123732	+	0.0117498i
$309$	12.7019	−	10.2313i	0.722584	−	0.582040i
$310$	0.646075	+	0.587629i	0.0366946	+	0.0333751i
$311$	−18.6036			−1.05491			−0.527455	−	0.849583i	$-0.676854\pi$
$311$	−18.6036			−1.05491			−0.527455	+	0.849583i	$0.676854\pi$
$312$	3.95198	−	0.137201i	0.223737	−	0.00776746i
$313$	−0.127928			−0.00723091			−0.00361545	−	0.999993i	$-0.501151\pi$
$313$	−0.127928			−0.00723091			−0.00361545	+	0.999993i	$0.501151\pi$
$314$	−21.5405	−	19.5919i	−1.21560	−	1.10563i
$315$	−0.300770	+	1.37977i	−0.0169465	+	0.0777413i
$316$	25.2289	−	2.39578i	1.41924	−	0.134773i
$317$		−	26.6844i		−	1.49875i	−0.662148	−	0.749373i	$-0.730355\pi$
$317$		−	26.6844i		−	1.49875i	0.662148	−	0.749373i	$-0.269645\pi$
$318$	−8.57993	−	0.515200i	−0.481139	−	0.0288910i
$319$		−	2.09812i		−	0.117472i
$320$	−2.22665	+	0.650021i	−0.124474	+	0.0363373i
$321$	17.1012	+	21.2306i	0.954495	+	1.18498i
$322$	−1.54483	+	1.69848i	−0.0860899	+	0.0946525i
$323$	−18.0632			−1.00506
$324$	5.91067	−	17.0019i	0.328371	−	0.944549i
$325$	3.96804			0.220107
$326$	17.1896	−	18.8993i	0.952045	−	1.04674i
$327$	19.4305	+	24.1224i	1.07451	+	1.33397i
$328$	−10.6386	−	7.97697i	−0.587419	−	0.440454i
$329$		−	2.38735i		−	0.131619i
$330$	−0.476264	−	0.0285982i	−0.0262175	−	0.00157428i
$331$		−	20.3412i		−	1.11805i	−0.829150	−	0.559027i	$-0.811175\pi$
$331$		−	20.3412i		−	1.11805i	0.829150	−	0.559027i	$-0.188825\pi$
$332$	2.96375	+	31.2099i	0.162657	+	1.71287i
$333$	−4.71930	+	21.6496i	−0.258616	+	1.18639i
$334$	−11.0646	−	10.0637i	−0.605429	−	0.550660i
$335$	−0.686206			−0.0374914
$336$	7.27483	−	8.57838i	0.396874	−	0.467989i
$337$	−20.9576			−1.14163			−0.570817	−	0.821077i	$-0.693373\pi$
$337$	−20.9576			−1.14163			−0.570817	+	0.821077i	$0.693373\pi$
$338$	12.9190	+	11.7503i	0.702699	+	0.639131i
$339$	−19.0576	+	15.3508i	−1.03507	+	0.833742i
$340$	0.169309	+	1.78292i	0.00918209	+	0.0966923i
$341$		−	1.43079i		−	0.0774819i
$342$	14.3797	+	20.2230i	0.777567	+	1.09353i
$343$			18.4497i			0.996189i
$344$	−17.3996	−	13.0465i	−0.938125	−	0.703418i
$345$	−0.391106	+	0.315035i	−0.0210565	+	0.0169609i
$346$	−18.1345	+	19.9382i	−0.974919	+	1.07189i
$347$	25.4807			1.36788			0.683939	−	0.729540i	$-0.260266\pi$
$347$	25.4807			1.36788			0.683939	+	0.729540i	$0.260266\pi$
$348$	7.55296	+	7.74629i	0.404881	+	0.415245i
$349$	−8.17851			−0.437786			−0.218893	−	0.975749i	$-0.570245\pi$
$349$	−8.17851			−0.437786			−0.218893	+	0.975749i	$0.570245\pi$
$350$	7.59427	−	8.34960i	0.405931	−	0.446305i
$351$	−3.75179	+	1.87500i	−0.200256	+	0.100080i
$352$	3.24234	+	1.98211i	0.172817	+	0.105647i
$353$		−	10.2019i		−	0.542994i	−0.962439	−	0.271497i	$-0.912481\pi$
$353$		−	10.2019i		−	0.542994i	0.962439	−	0.271497i	$-0.0875186\pi$
$354$	−1.87492	+	31.2242i	−0.0996509	+	1.65955i
$355$			1.19369i			0.0633544i
$356$	−11.5244	+	1.09438i	−0.610793	+	0.0580021i
$357$	−5.44767	−	6.76312i	−0.288322	−	0.357942i
$358$	3.20236	+	2.91266i	0.169250	+	0.153939i
$359$	−29.8079			−1.57320			−0.786600	−	0.617463i	$-0.788160\pi$
$359$	−29.8079			−1.57320			−0.786600	+	0.617463i	$0.788160\pi$
$360$	1.86132	−	1.60890i	0.0981002	−	0.0847965i
$361$	−15.2081			−0.800428
$362$	21.3246	+	19.3955i	1.12080	+	1.01941i
$363$	−11.4614	−	14.2289i	−0.601566	−	0.746825i
$364$	−2.60913	+	0.247768i	−0.136756	+	0.0129866i
$365$			2.77416i			0.145206i
$366$	−0.294812	+	4.90969i	−0.0154101	+	0.256634i
$367$			24.6613i			1.28731i	0.765316	+	0.643654i	$0.222583\pi$
$367$			24.6613i			1.28731i	−0.765316	+	0.643654i	$0.777417\pi$
$368$	3.92850	−	0.752906i	0.204787	−	0.0392479i
$369$	13.7801	+	3.00386i	0.717362	+	0.156375i
$370$	−2.03782	+	2.24051i	−0.105941	+	0.116478i
$371$	5.69685			0.295766
$372$	5.15067	+	5.28251i	0.267050	+	0.273885i
$373$	−19.3362			−1.00119			−0.500596	−	0.865681i	$-0.666886\pi$
$373$	−19.3362			−1.00119			−0.500596	+	0.865681i	$0.666886\pi$
$374$	1.97422	−	2.17058i	0.102085	−	0.112238i
$375$	3.87818	−	3.12387i	0.200269	−	0.161316i
$376$	−2.49516	+	3.32771i	−0.128678	+	0.171614i
$377$		−	2.52098i		−	0.129837i
$378$	−3.23501	+	11.4831i	−0.166391	+	0.590624i
$379$			7.95372i			0.408555i	0.978913	+	0.204278i	$0.0654845\pi$
$379$			7.95372i			0.408555i	−0.978913	+	0.204278i	$0.934515\pi$
$380$	0.320639	+	3.37650i	0.0164485	+	0.173211i
$381$	17.0896	−	13.7656i	0.875525	−	0.705233i
$382$	10.2287	+	9.30340i	0.523347	+	0.476004i
$383$	7.85245			0.401242			0.200621	−	0.979669i	$-0.435704\pi$
$383$	7.85245			0.401242			0.200621	+	0.979669i	$0.435704\pi$
$384$	−19.1061	+	4.35400i	−0.975004	+	0.222189i
$385$	0.316226			0.0161164
$386$	−23.3546	−	21.2419i	−1.18872	−	1.08118i
$387$	22.5375	+	4.91286i	1.14565	+	0.249735i
$388$	−1.24339	−	13.0936i	−0.0631236	−	0.664725i
$389$			18.4341i			0.934644i	0.884087	+	0.467322i	$0.154781\pi$
$389$			18.4341i			0.934644i	−0.884087	+	0.467322i	$0.845219\pi$
$390$	−0.572251	−	0.0343620i	−0.0289770	−	0.00173999i
$391$		−	3.08837i		−	0.156185i
$392$	7.40534	−	9.87626i	0.374026	−	0.498826i
$393$	1.95178	+	2.42307i	0.0984541	+	0.122228i
$394$	4.32325	−	4.75324i	0.217802	−	0.239465i
$395$	−3.67400			−0.184859
$396$	−4.00176	−	0.482327i	−0.201096	−	0.0242378i
$397$	−35.0649			−1.75986			−0.879928	−	0.475108i	$-0.842409\pi$
$397$	−35.0649			−1.75986			−0.879928	+	0.475108i	$0.842409\pi$
$398$	19.8828	−	21.8603i	0.996634	−	1.09576i
$399$	−10.3168	−	12.8080i	−0.516488	−	0.641204i
$400$	−19.3122	+	3.70123i	−0.965612	+	0.185062i
$401$		−	28.8631i		−	1.44136i	−0.693270	−	0.720678i	$-0.743831\pi$
$401$		−	28.8631i		−	1.44136i	0.693270	−	0.720678i	$-0.256169\pi$
$402$	−5.78664	−	0.347471i	−0.288611	−	0.0173303i
$403$		−	1.71916i		−	0.0856374i
$404$	34.9423	−	3.31819i	1.73844	−	0.165086i
$405$	−1.08608	+	2.37279i	−0.0539676	+	0.117905i
$406$	−5.30468	−	4.82480i	−0.263267	−	0.239451i
$407$	4.96182			0.245948
$408$	0.524946	+	15.1207i	0.0259887	+	0.748588i
$409$	−10.3350			−0.511031			−0.255515	−	0.966805i	$-0.582245\pi$
$409$	−10.3350			−0.511031			−0.255515	+	0.966805i	$0.582245\pi$
$410$	1.42609	+	1.29708i	0.0704297	+	0.0640584i
$411$	−15.3237	+	12.3432i	−0.755861	+	0.608844i
$412$	18.7489	−	1.78043i	0.923690	−	0.0877154i
$413$		−	20.7320i		−	1.02016i
$414$	−3.45765	+	2.45859i	−0.169934	+	0.120833i
$415$		−	4.54500i		−	0.223105i
$416$	3.89580	+	2.38159i	0.191008	+	0.116767i
$417$	10.0154	−	8.06736i	0.490455	−	0.395060i
$418$	3.73880	−	4.11066i	0.182870	−	0.201059i
$419$	15.4394			0.754263			0.377131	−	0.926160i	$-0.376911\pi$
$419$	15.4394			0.754263			0.377131	+	0.926160i	$0.376911\pi$
$420$	−1.16751	+	1.13837i	−0.0569687	+	0.0555469i
$421$	0.172879			0.00842559			0.00421280	−	0.999991i	$-0.498659\pi$
$421$	0.172879			0.00842559			0.00421280	+	0.999991i	$0.498659\pi$
$422$	−10.9476	+	12.0364i	−0.532919	+	0.585924i
$423$	0.939594	−	4.31035i	0.0456846	−	0.209576i
$424$	−7.94079	−	5.95411i	−0.385639	−	0.289157i
$425$			15.1822i			0.736445i
$426$	−0.604442	+	10.0661i	−0.0292853	+	0.487706i
$427$		−	3.25990i		−	0.157758i
$428$	2.97591	+	31.3379i	0.143846	+	1.51477i
$429$	0.589168	+	0.731434i	0.0284453	+	0.0353140i
$430$	2.33240	+	2.12140i	0.112478	+	0.102303i
$431$	25.4462			1.22570			0.612850	−	0.790200i	$-0.290023\pi$
$431$	25.4462			1.22570			0.612850	+	0.790200i	$0.290023\pi$
$432$	16.5109	−	12.6250i	0.794379	−	0.607423i
$433$	−9.00790			−0.432892			−0.216446	−	0.976295i	$-0.569447\pi$
$433$	−9.00790			−0.432892			−0.216446	+	0.976295i	$0.569447\pi$
$434$	−3.61748	−	3.29023i	−0.173644	−	0.157936i
$435$	−0.983917	−	1.22150i	−0.0471752	−	0.0585665i
$436$	3.38125	+	35.6063i	0.161932	+	1.70523i
$437$		−	5.84877i		−	0.279785i
$438$	−1.40474	+	23.3940i	−0.0671210	+	1.11781i
$439$			15.5705i			0.743141i	0.928405	+	0.371571i	$0.121181\pi$
$439$			15.5705i			0.743141i	−0.928405	+	0.371571i	$0.878819\pi$
$440$	−0.440786	−	0.330507i	−0.0210136	−	0.0157563i
$441$	−2.78860	+	12.7926i	−0.132791	+	0.609172i
$442$	2.37211	−	2.60804i	0.112830	−	0.124052i
$443$	35.8791			1.70467			0.852333	−	0.523000i	$-0.175187\pi$
$443$	35.8791			1.70467			0.852333	+	0.523000i	$0.175187\pi$
$444$	−18.3191	+	17.8619i	−0.869385	+	0.847687i
$445$	1.67826			0.0795574
$446$	3.84995	−	4.23287i	0.182300	−	0.200432i
$447$	−11.5699	+	9.31951i	−0.547237	+	0.440798i
$448$	12.4674	−	3.63957i	0.589029	−	0.171954i
$449$		−	23.5222i		−	1.11008i	−0.831823	−	0.555041i	$-0.812702\pi$
$449$		−	23.5222i		−	1.11008i	0.831823	−	0.555041i	$-0.187298\pi$
$450$	16.9976	−	12.0863i	0.801273	−	0.569751i
$451$		−	3.15822i		−	0.148715i
$452$	−28.1303	+	2.67131i	−1.32314	+	0.125648i
$453$	−2.21544	+	1.78453i	−0.104091	+	0.0838447i
$454$	7.04845	+	6.41082i	0.330800	+	0.300875i
$455$	0.379959			0.0178128
$456$	0.994147	+	28.6358i	0.0465552	+	1.34099i
$457$	3.74569			0.175216			0.0876079	−	0.996155i	$-0.472078\pi$
$457$	3.74569			0.175216			0.0876079	+	0.996155i	$0.472078\pi$
$458$	−7.62540	−	6.93559i	−0.356312	−	0.324079i
$459$	−7.17397	−	14.3548i	−0.334852	−	0.670025i
$460$	−0.577301	+	0.0548216i	−0.0269168	+	0.00255607i
$461$		−	42.1686i		−	1.96399i	−0.188916	−	0.981993i	$-0.560497\pi$
$461$		−	42.1686i		−	1.96399i	0.188916	−	0.981993i	$-0.439503\pi$
$462$	2.66668	+	0.160126i	0.124065	+	0.00744974i
$463$		−	25.0700i		−	1.16510i	−0.812795	−	0.582550i	$-0.802055\pi$
$463$		−	25.0700i		−	1.16510i	0.812795	−	0.582550i	$-0.197945\pi$
$464$	2.35147	+	12.2695i	0.109164	+	0.569597i
$465$	−0.670973	−	0.832992i	−0.0311156	−	0.0386291i
$466$	23.8959	−	26.2726i	1.10696	−	1.21706i
$467$	−10.9772			−0.507962			−0.253981	−	0.967209i	$-0.581740\pi$
$467$	−10.9772			−0.507962			−0.253981	+	0.967209i	$0.581740\pi$
$468$	−4.80828	−	0.579536i	−0.222263	−	0.0267890i
$469$	3.84218			0.177415
$470$	0.405723	−	0.446076i	0.0187146	−	0.0205760i
$471$	22.3706	+	27.7724i	1.03078	+	1.27968i
$472$	−21.6683	+	28.8982i	−0.997363	+	1.33015i
$473$		−	5.16532i		−	0.237502i
$474$	−30.9821	−	1.86039i	−1.42306	−	0.0854503i
$475$			28.7522i			1.31924i
$476$	−0.947991	−	9.98285i	−0.0434511	−	0.457563i
$477$	10.2856	+	2.24212i	0.470946	+	0.102659i
$478$	19.9454	+	18.1411i	0.912281	+	0.829753i
$479$	−31.3968			−1.43456			−0.717279	−	0.696786i	$-0.754613\pi$
$479$	−31.3968			−1.43456			−0.717279	+	0.696786i	$0.754613\pi$
$480$	2.81717	−	0.366535i	0.128585	−	0.0167300i
$481$	5.96183			0.271836
$482$	16.4780	+	14.9873i	0.750551	+	0.682654i
$483$	2.18987	−	1.76393i	0.0996425	−	0.0802618i
$484$	−1.99448	−	21.0029i	−0.0906581	−	0.954678i
$485$			1.90677i			0.0865822i
$486$	−10.3602	+	19.4594i	−0.469947	+	0.882694i
$487$			8.72762i			0.395486i	0.980254	+	0.197743i	$0.0633612\pi$
$487$			8.72762i			0.395486i	−0.980254	+	0.197743i	$0.936639\pi$
$488$	−3.40711	+	4.54396i	−0.154233	+	0.205695i
$489$	−24.3671	+	19.6277i	−1.10192	+	0.887593i
$490$	−1.20414	+	1.32390i	−0.0543973	+	0.0598077i
$491$	9.66232			0.436054			0.218027	−	0.975943i	$-0.430038\pi$
$491$	9.66232			0.436054			0.218027	+	0.975943i	$0.430038\pi$
$492$	11.3692	+	11.6602i	0.512562	+	0.525682i
$493$	9.64558			0.434415
$494$	4.49232	−	4.93913i	0.202119	−	0.222222i
$495$	0.570945	+	0.124458i	0.0256620	+	0.00559396i
$496$	1.60356	+	8.36706i	0.0720022	+	0.375692i
$497$		−	6.68365i		−	0.299803i
$498$	2.30143	−	38.3271i	0.103130	−	1.71748i
$499$		−	11.5355i		−	0.516400i	−0.966091	−	0.258200i	$-0.916871\pi$
$499$		−	11.5355i		−	0.516400i	0.966091	−	0.258200i	$-0.0831294\pi$
$500$	5.72448	−	0.543608i	0.256006	−	0.0243109i
$501$	11.4910	+	14.2658i	0.513381	+	0.637347i
$502$	−0.994841	−	0.904845i	−0.0444019	−	0.0403852i
$503$	30.9643			1.38063			0.690316	−	0.723508i	$-0.257472\pi$
$503$	30.9643			1.38063			0.690316	+	0.723508i	$0.257472\pi$
$504$	−10.4218	+	9.00849i	−0.464225	+	0.401270i
$505$	−5.08853			−0.226437
$506$	0.702824	+	0.639245i	0.0312443	+	0.0284179i
$507$	−13.4168	−	16.6566i	−0.595863	−	0.739745i
$508$	25.2254	−	2.39545i	1.11920	−	0.106281i
$509$			35.8267i			1.58799i	0.607925	+	0.793994i	$0.292002\pi$
$509$			35.8267i			1.58799i	−0.607925	+	0.793994i	$0.707998\pi$
$510$	0.131473	−	2.18950i	0.00582172	−	0.0969527i
$511$		−	15.5330i		−	0.687138i
$512$	−21.1821	−	7.95722i	−0.936127	−	0.351663i
$513$	−13.5861	−	27.1852i	−0.599841	−	1.20026i
$514$	8.95409	−	9.84467i	0.394948	−	0.434230i
$515$	−2.73034			−0.120313
$516$	18.5945	+	19.0704i	0.818576	+	0.839529i
$517$	−0.987878			−0.0434468
$518$	11.4101	−	12.5450i	0.501331	−	0.551194i
$519$	25.7066	−	20.7066i	1.12839	−	0.908919i
$520$	−0.529622	−	0.397117i	−0.0232255	−	0.0174148i
$521$			20.8711i			0.914379i	0.889369	+	0.457189i	$0.151144\pi$
$521$			20.8711i			0.914379i	−0.889369	+	0.457189i	$0.848856\pi$
$522$	−7.67866	−	10.7989i	−0.336086	−	0.472656i
$523$		−	26.5965i		−	1.16299i	−0.813552	−	0.581493i	$-0.802469\pi$
$523$		−	26.5965i		−	1.16299i	0.813552	−	0.581493i	$-0.197531\pi$
$524$	0.339643	+	3.57663i	0.0148374	+	0.156246i
$525$	−10.7652	+	8.67137i	−0.469834	+	0.378450i
$526$	2.93634	+	2.67071i	0.128031	+	0.116449i
$527$	6.57771			0.286530
$528$	−3.54970	−	3.01030i	−0.154481	−	0.131006i
$529$	1.00000			0.0434783
$530$	1.06445	+	0.968160i	0.0462369	+	0.0420542i
$531$	8.15954	−	37.4316i	0.354094	−	1.62439i
$532$	−1.79531	−	18.9056i	−0.0778366	−	0.819661i
$533$		−	3.79474i		−	0.164368i
$534$	14.1525	+	0.849815i	0.612438	+	0.0367751i
$535$		−	4.56363i		−	0.197303i
$536$	−5.35558	−	4.01568i	−0.231326	−	0.173451i
$537$	−3.32577	−	4.12884i	−0.143518	−	0.178173i
$538$	4.62041	−	5.07996i	0.199200	−	0.219013i
$539$	2.93191			0.126286
$540$	−2.55596	+	1.59582i	−0.109991	+	0.0686734i
$541$	−7.29891			−0.313805			−0.156902	−	0.987614i	$-0.550151\pi$
$541$	−7.29891			−0.313805			−0.156902	+	0.987614i	$0.550151\pi$
$542$	12.1017	−	13.3053i	0.519811	−	0.571511i
$543$	−22.1464	−	27.4941i	−0.950395	−	1.17989i
$544$	−9.11225	+	14.9058i	−0.390685	+	0.639081i
$545$		−	5.18524i		−	0.222111i
$546$	3.20412	+	0.192398i	0.137124	+	0.00823388i
$547$			4.93012i			0.210797i	0.994430	+	0.105398i	$0.0336118\pi$
$547$			4.93012i			0.210797i	−0.994430	+	0.105398i	$0.966388\pi$
$548$	−22.6188	+	2.14793i	−0.966229	+	0.0917550i
$549$	1.28301	−	5.88573i	0.0547573	−	0.251197i
$550$	−3.45503	−	3.14248i	−0.147323	−	0.133996i
$551$	18.2669			0.778195
$552$	−4.89603	+	0.169975i	−0.208389	+	0.00723463i
$553$	20.5713			0.874781
$554$	−19.4585	−	17.6982i	−0.826714	−	0.751927i
$555$	2.88871	−	2.32685i	0.122619	−	0.0987693i
$556$	14.7834	−	1.40386i	0.626956	−	0.0595370i
$557$			9.99008i			0.423293i	0.977346	+	0.211647i	$0.0678826\pi$
$557$			9.99008i			0.423293i	−0.977346	+	0.211647i	$0.932117\pi$
$558$	−5.23639	−	7.36422i	−0.221674	−	0.311752i
$559$		−	6.20635i		−	0.262501i
$560$	−1.84924	+	0.354411i	−0.0781447	+	0.0149766i
$561$	−2.79855	+	2.25423i	−0.118155	+	0.0951736i
$562$	−8.41869	+	9.25602i	−0.355121	+	0.390442i
$563$	6.34809			0.267540			0.133770	−	0.991012i	$-0.457292\pi$
$563$	6.34809			0.267540			0.133770	+	0.991012i	$0.457292\pi$
$564$	3.64726	−	3.55623i	0.153577	−	0.149744i
$565$	4.09653			0.172342
$566$	−15.5922	+	17.1430i	−0.655387	+	0.720572i
$567$	6.08112	−	13.2857i	0.255383	−	0.557945i
$568$	−6.98547	+	9.31629i	−0.293104	+	0.390903i
$569$		−	23.5397i		−	0.986834i	−0.869793	−	0.493417i	$-0.835748\pi$
$569$		−	23.5397i		−	0.986834i	0.869793	−	0.493417i	$-0.164252\pi$
$570$	0.248984	−	4.14649i	0.0104288	−	0.173677i
$571$		−	9.80902i		−	0.410495i	−0.978710	−	0.205247i	$-0.934200\pi$
$571$		−	9.80902i		−	0.410495i	0.978710	−	0.205247i	$-0.0657999\pi$
$572$	0.102526	+	1.07965i	0.00428681	+	0.0451424i
$573$	−10.6229	−	13.1880i	−0.443779	−	0.550938i
$574$	−7.98493	−	7.26259i	−0.333284	−	0.303134i
$575$	−4.91593			−0.205008
$576$	23.9422	−	1.66441i	0.997592	−	0.0693503i
$577$	−12.7939			−0.532618			−0.266309	−	0.963888i	$-0.585804\pi$
$577$	−12.7939			−0.532618			−0.266309	+	0.963888i	$0.585804\pi$
$578$	−7.80674	−	7.10052i	−0.324717	−	0.295342i
$579$	24.2546	+	30.1113i	1.00799	+	1.25138i
$580$	−0.171219	−	1.80302i	−0.00710947	−	0.0748665i
$581$			25.4482i			1.05577i
$582$	−0.965524	+	16.0795i	−0.0400223	+	0.666515i
$583$		−	2.35734i		−	0.0976309i
$584$	−16.2344	+	21.6513i	−0.671785	+	0.895937i
$585$	0.686014	+	0.149541i	0.0283632	+	0.00618276i
$586$	22.4893	−	24.7261i	0.929025	−	1.02143i
$587$	−21.8610			−0.902301			−0.451151	−	0.892448i	$-0.648986\pi$
$587$	−21.8610			−0.902301			−0.451151	+	0.892448i	$0.648986\pi$
$588$	−10.8246	+	10.5545i	−0.446400	+	0.435259i
$589$	12.4569			0.513278
$590$	3.52334	−	3.87377i	0.145054	−	0.159481i
$591$	−6.12841	+	4.93642i	−0.252089	+	0.203057i
$592$	−29.0159	+	5.56096i	−1.19255	+	0.228554i
$593$		−	10.9606i		−	0.450098i	−0.974347	−	0.225049i	$-0.927746\pi$
$593$		−	10.9606i		−	0.450098i	0.974347	−	0.225049i	$-0.0722542\pi$
$594$	4.75165	+	1.33863i	0.194962	+	0.0549248i
$595$			1.45377i			0.0595987i
$596$	−17.0780	+	1.62176i	−0.699541	+	0.0664298i
$597$	−28.1848	+	22.7028i	−1.15353	+	0.929163i
$598$	0.844473	+	0.768079i	0.0345331	+	0.0314091i
$599$	−30.3016			−1.23809			−0.619046	−	0.785355i	$-0.712480\pi$
$599$	−30.3016			−1.23809			−0.619046	+	0.785355i	$0.712480\pi$
$600$	24.0685	−	0.835587i	0.982594	−	0.0341127i
$601$	−11.6834			−0.476575			−0.238287	−	0.971195i	$-0.576586\pi$
$601$	−11.6834			−0.476575			−0.238287	+	0.971195i	$0.576586\pi$
$602$	−13.0595	−	11.8781i	−0.532265	−	0.484114i
$603$	6.93702	+	1.51217i	0.282497	+	0.0615804i
$604$	−3.27015	+	0.310540i	−0.133061	+	0.0126357i
$605$			3.05859i			0.124349i
$606$	−42.9106	−	2.57665i	−1.74312	−	0.104669i
$607$		−	23.5232i		−	0.954776i	−0.878693	−	0.477388i	$-0.841584\pi$
$607$		−	23.5232i		−	0.954776i	0.878693	−	0.477388i	$-0.158416\pi$
$608$	−17.2569	+	28.2287i	−0.699858	+	1.14483i
$609$	5.50911	+	6.83939i	0.223240	+	0.277146i
$610$	0.554010	−	0.609112i	0.0224312	−	0.0246622i
$611$	−1.18698			−0.0480200
$612$	2.21737	−	18.3971i	0.0896320	−	0.743657i
$613$	−29.6962			−1.19942			−0.599708	−	0.800219i	$-0.704717\pi$
$613$	−29.6962			−1.19942			−0.599708	+	0.800219i	$0.704717\pi$
$614$	8.28840	−	9.11277i	0.334493	−	0.367762i
$615$	−1.48105	−	1.83868i	−0.0597218	−	0.0741427i
$616$	2.46803	+	1.85056i	0.0994398	+	0.0745612i
$617$			29.5860i			1.19109i	0.803322	+	0.595545i	$0.203064\pi$
$617$			29.5860i			1.19109i	−0.803322	+	0.595545i	$0.796936\pi$
$618$	−23.0244	−	1.38255i	−0.926178	−	0.0556142i
$619$			28.7850i			1.15697i	0.815694	+	0.578484i	$0.196356\pi$
$619$			28.7850i			1.15697i	−0.815694	+	0.578484i	$0.803644\pi$
$620$	−0.116761	−	1.22956i	−0.00468923	−	0.0493801i
$621$	4.64803	−	2.32290i	0.186519	−	0.0932147i
$622$	19.4631	+	17.7024i	0.780398	+	0.709800i
$623$	−9.39688			−0.376478
$624$	−4.26512	−	3.61700i	−0.170741	−	0.144796i
$625$	23.7460			0.949840
$626$	0.133838	+	0.121731i	0.00534925	+	0.00486534i
$627$	−5.29992	+	4.26907i	−0.211658	+	0.170490i
$628$	3.89287	+	40.9940i	0.155343	+	1.63584i
$629$			22.8107i			0.909521i
$630$	1.62760	−	1.15732i	0.0648451	−	0.0461087i
$631$		−	39.1690i		−	1.55929i	−0.626220	−	0.779646i	$-0.715399\pi$
$631$		−	39.1690i		−	1.55929i	0.626220	−	0.779646i	$-0.284601\pi$
$632$	−28.6742	−	21.5003i	−1.14060	−	0.855235i
$633$	15.5187	−	12.5003i	0.616813	−	0.496841i
$634$	−25.3918	+	27.9173i	−1.00844	+	1.10874i
$635$	−3.67350			−0.145778
$636$	8.48609	+	8.70331i	0.336495	+	0.345109i
$637$	3.52281			0.139579
$638$	−1.99649	+	2.19506i	−0.0790416	+	0.0869032i
$639$	2.63049	−	12.0673i	0.104061	−	0.477374i
$640$	2.94806	+	1.43874i	0.116532	+	0.0568711i
$641$		−	14.8780i		−	0.587644i	−0.955860	−	0.293822i	$-0.905073\pi$
$641$		−	14.8780i		−	0.587644i	0.955860	−	0.293822i	$-0.0949274\pi$
$642$	2.31087	−	38.4843i	0.0912026	−	1.51885i
$643$			19.7257i			0.777904i	0.921258	+	0.388952i	$0.127163\pi$
$643$			19.7257i			0.777904i	−0.921258	+	0.388952i	$0.872837\pi$
$644$	3.23240	−	0.306955i	0.127374	−	0.0120957i
$645$	−2.42229	−	3.00719i	−0.0953774	−	0.118408i
$646$	18.8977	+	17.1882i	0.743520	+	0.676259i
$647$	−37.6201			−1.47900			−0.739499	−	0.673157i	$-0.764938\pi$
$647$	−37.6201			−1.47900			−0.739499	+	0.673157i	$0.764938\pi$
$648$	−22.3620	+	12.1630i	−0.878464	+	0.477809i
$649$	−8.57885			−0.336749
$650$	−4.15137	−	3.77582i	−0.162830	−	0.148100i
$651$	3.75688	+	4.66406i	0.147244	+	0.182799i
$652$	−35.9676	+	3.41555i	−1.40860	+	0.133763i
$653$		−	50.5654i		−	1.97878i	−0.145288	−	0.989389i	$-0.546411\pi$
$653$		−	50.5654i		−	1.97878i	0.145288	−	0.989389i	$-0.453589\pi$
$654$	2.62562	−	43.7261i	0.102670	−	1.70983i
$655$		−	0.520852i		−	0.0203514i
$656$	3.53958	+	18.4688i	0.138197	+	0.721084i
$657$	6.11333	−	28.0447i	0.238504	−	1.09413i
$658$	−2.27171	+	2.49765i	−0.0885603	+	0.0973686i
$659$	7.37032			0.287107			0.143554	−	0.989643i	$-0.454147\pi$
$659$	7.37032			0.287107			0.143554	+	0.989643i	$0.454147\pi$
$660$	0.471055	+	0.483112i	0.0183358	+	0.0188051i
$661$	21.1821			0.823889			0.411945	−	0.911209i	$-0.364850\pi$
$661$	21.1821			0.823889			0.411945	+	0.911209i	$0.364850\pi$
$662$	−19.3558	+	21.2810i	−0.752286	+	0.827109i
$663$	−3.36258	+	2.70855i	−0.130592	+	0.105191i
$664$	26.5974	−	35.4720i	1.03218	−	1.37658i
$665$			2.75316i			0.106763i
$666$	25.5382	−	18.1591i	0.989585	−	0.703652i
$667$			3.12320i			0.120931i
$668$	1.99964	+	21.0573i	0.0773684	+	0.814730i
$669$	−5.45749	+	4.39599i	−0.210999	+	0.169959i
$670$	0.717909	+	0.652965i	0.0277353	+	0.0252262i
$671$	−1.34894			−0.0520751
$672$	−15.7738	+	2.05229i	−0.608486	+	0.0791688i
$673$	10.6805			0.411702			0.205851	−	0.978583i	$-0.434004\pi$
$673$	10.6805			0.411702			0.205851	+	0.978583i	$0.434004\pi$
$674$	21.9259	+	19.9424i	0.844553	+	0.768152i
$675$	−22.8494	+	11.4192i	−0.879472	+	0.439526i
$676$	−2.33476	−	24.5863i	−0.0897986	−	0.945627i
$677$			13.0841i			0.502862i	0.967875	+	0.251431i	$0.0809012\pi$
$677$			13.0841i			0.502862i	−0.967875	+	0.251431i	$0.919099\pi$
$678$	34.5453	+	2.07434i	1.32670	+	0.0796646i
$679$		−	10.6763i		−	0.409720i
$680$	1.51942	−	2.02640i	0.0582671	−	0.0777088i
$681$	−7.32008	−	9.08765i	−0.280506	−	0.348240i
$682$	−1.36148	+	1.49690i	−0.0521339	+	0.0573192i
$683$	0.343731			0.0131525			0.00657625	−	0.999978i	$-0.497907\pi$
$683$	0.343731			0.0131525			0.00657625	+	0.999978i	$0.497907\pi$
$684$	4.19928	−	34.8405i	0.160563	−	1.33216i
$685$	3.29391			0.125854
$686$	17.5560	−	19.3021i	0.670289	−	0.736957i
$687$	7.91927	+	9.83153i	0.302139	+	0.375096i
$688$	5.78905	+	30.2060i	0.220705	+	1.15159i
$689$		−	2.83244i		−	0.107907i
$690$	0.708950	+	0.0425704i	0.0269893	+	0.00162063i
$691$		−	5.14164i		−	0.195597i	−0.995206	−	0.0977986i	$-0.968820\pi$
$691$		−	5.14164i		−	0.195597i	0.995206	−	0.0977986i	$-0.0311801\pi$
$692$	37.9448	−	3.60331i	1.44244	−	0.136977i
$693$	−3.19681	−	0.696859i	−0.121437	−	0.0264715i
$694$	−26.6580	−	24.2464i	−1.01192	−	0.920381i
$695$	−2.15286			−0.0816627
$696$	−0.530866	−	15.2913i	−0.0201224	−	0.579614i
$697$	14.5191			0.549950
$698$	8.55637	+	7.78233i	0.323863	+	0.294566i
$699$	−33.8736	+	27.2851i	−1.28122	+	1.03202i
$700$	−15.8903	+	1.50897i	−0.600595	+	0.0570337i
$701$		−	29.6251i		−	1.11892i	−0.828856	−	0.559462i	$-0.811008\pi$
$701$		−	29.6251i		−	1.11892i	0.828856	−	0.559462i	$-0.188992\pi$
$702$	5.70930	+	1.60843i	0.215484	+	0.0607061i
$703$			43.1990i			1.62928i
$704$	−1.50604	−	5.15896i	−0.0567611	−	0.194436i
$705$	−0.575131	+	0.463267i	−0.0216607	+	0.0174476i
$706$	−9.70772	+	10.6733i	−0.365355	+	0.401694i
$707$	28.4915			1.07153
$708$	31.6732	−	30.8827i	1.19035	−	1.16064i
$709$	−45.7535			−1.71831			−0.859155	−	0.511715i	$-0.829010\pi$
$709$	−45.7535			−1.71831			−0.859155	+	0.511715i	$0.829010\pi$
$710$	1.13586	−	1.24884i	0.0426282	−	0.0468680i
$711$	37.1414	+	8.09628i	1.39291	+	0.303634i
$712$	13.0982	+	9.82122i	0.490877	+	0.368066i
$713$			2.12983i			0.0797629i
$714$	−0.736138	+	12.2594i	−0.0275493	+	0.458795i
$715$		−	0.157226i		−	0.00587991i
$716$	−0.578742	−	6.09447i	−0.0216286	−	0.227761i
$717$	−20.7140	−	25.7158i	−0.773580	−	0.960375i
$718$	31.1850	+	28.3639i	1.16382	+	1.05853i
$719$	−20.4239			−0.761682			−0.380841	−	0.924641i	$-0.624365\pi$
$719$	−20.4239			−0.761682			−0.380841	+	0.924641i	$0.624365\pi$
$720$	−3.47828	−	0.0879218i	−0.129628	−	0.00327665i
$721$	15.2876			0.569340
$722$	15.9108	+	14.4714i	0.592138	+	0.538571i
$723$	−17.1130	−	21.2452i	−0.636439	−	0.790119i
$724$	−3.85387	−	40.5833i	−0.143228	−	1.50827i
$725$		−	15.3534i		−	0.570211i
$726$	−1.54876	+	25.7925i	−0.0574799	+	0.957249i
$727$		−	22.2862i		−	0.826550i	−0.910606	−	0.413275i	$-0.864385\pi$
$727$		−	22.2862i		−	0.826550i	0.910606	−	0.413275i	$-0.135615\pi$
$728$	2.96544	+	2.22352i	0.109907	+	0.0824093i
$729$	16.2083	−	21.5938i	0.600306	−	0.799770i
$730$	2.63978	−	2.90233i	0.0977025	−	0.107420i
$731$	23.7463			0.878287
$732$	4.98029	−	4.85599i	0.184077	−	0.179483i
$733$	35.5649			1.31362			0.656810	−	0.754056i	$-0.271905\pi$
$733$	35.5649			1.31362			0.656810	+	0.754056i	$0.271905\pi$
$734$	23.4667	−	25.8007i	0.866170	−	0.952320i
$735$	1.70692	−	1.37492i	0.0629607	−	0.0507147i
$736$	−4.82644	−	2.95051i	−0.177905	−	0.108757i
$737$		−	1.58988i		−	0.0585640i
$738$	−11.5584	−	16.2552i	−0.425470	−	0.598362i
$739$			35.2029i			1.29496i	0.762082	+	0.647480i	$0.224177\pi$
$739$			35.2029i			1.29496i	−0.762082	+	0.647480i	$0.775823\pi$
$740$	4.26394	−	0.404913i	0.156746	−	0.0148849i
$741$	−6.36808	+	5.12947i	−0.233937	+	0.188436i
$742$	−5.96005	−	5.42088i	−0.218800	−	0.199007i
$743$	−49.7485			−1.82509			−0.912547	−	0.408971i	$-0.865888\pi$
$743$	−49.7485			−1.82509			−0.912547	+	0.408971i	$0.865888\pi$
$744$	−0.362019	−	10.4277i	−0.0132723	−	0.382299i
$745$	2.48701			0.0911170
$746$	20.2296	+	18.3996i	0.740658	+	0.673656i
$747$	−10.0157	+	45.9465i	−0.366455	+	1.68110i
$748$	−4.13087	+	0.392275i	−0.151039	+	0.0143430i
$749$			25.5525i			0.933669i
$750$	−7.02990	−	0.422125i	−0.256696	−	0.0154138i
$751$			1.81560i			0.0662521i	0.999451	+	0.0331261i	$0.0105463\pi$
$751$			1.81560i			0.0662521i	−0.999451	+	0.0331261i	$0.989454\pi$
$752$	5.77696	−	1.10717i	0.210664	−	0.0403742i
$753$	1.03318	+	1.28266i	0.0376512	+	0.0467428i
$754$	−2.39886	+	2.63745i	−0.0873614	+	0.0960504i
$755$	0.476222			0.0173315
$756$	14.3113	−	8.93528i	0.520496	−	0.324973i
$757$	−2.90069			−0.105427			−0.0527137	−	0.998610i	$-0.516787\pi$
$757$	−2.90069			−0.105427			−0.0527137	+	0.998610i	$0.516787\pi$
$758$	7.56843	−	8.32119i	0.274898	−	0.302239i
$759$	−0.729909	−	0.906160i	−0.0264940	−	0.0328915i
$760$	2.87749	−	3.83761i	0.104377	−	0.139205i
$761$			12.6470i			0.458454i	0.973373	+	0.229227i	$0.0736198\pi$
$761$			12.6470i			0.458454i	−0.973373	+	0.229227i	$0.926380\pi$
$762$	−30.9779	−	1.86013i	−1.12221	−	0.0673854i
$763$			29.0330i			1.05106i
$764$	−1.84857	−	19.4665i	−0.0668790	−	0.704272i
$765$	−0.572162	+	2.62477i	−0.0206866	+	0.0948988i
$766$	−8.21524	−	7.47207i	−0.296829	−	0.269977i
$767$	−10.3078			−0.372195
$768$	24.1319	+	13.6254i	0.870785	+	0.491664i
$769$	48.0699			1.73344			0.866722	−	0.498792i	$-0.166223\pi$
$769$	48.0699			1.73344			0.866722	+	0.498792i	$0.166223\pi$
$770$	−0.330836	−	0.300908i	−0.0119225	−	0.0108440i
$771$	−12.6928	+	10.2241i	−0.457122	+	0.368210i
$772$	4.22073	+	44.4465i	0.151907	+	1.59966i
$773$			41.3556i			1.48746i	0.668482	+	0.743729i	$0.266945\pi$
$773$			41.3556i			1.48746i	−0.668482	+	0.743729i	$0.733055\pi$
$774$	−18.9039	−	26.5856i	−0.679488	−	0.955601i
$775$		−	10.4701i		−	0.376098i
$776$	−11.1585	+	14.8817i	−0.400565	+	0.534221i
$777$	−16.1744	+	13.0284i	−0.580252	+	0.467392i
$778$	17.5411	−	19.2857i	0.628878	−	0.691427i
$779$	27.4964			0.985161
$780$	0.565992	+	0.580479i	0.0202658	+	0.0207845i
$781$	−2.76567			−0.0989635
$782$	−2.93876	+	3.23105i	−0.105090	+	0.115542i
$783$	7.25487	+	14.5167i	0.259268	+	0.518784i
$784$	−17.1453	+	3.28594i	−0.612333	+	0.117355i
$785$		−	5.96983i		−	0.213072i
$786$	0.263742	−	4.39225i	0.00940735	−	0.156666i
$787$		−	40.2401i		−	1.43440i	−0.696865	−	0.717202i	$-0.745422\pi$
$787$		−	40.2401i		−	1.43440i	0.696865	−	0.717202i	$-0.254578\pi$
$788$	−9.04597	+	0.859023i	−0.322249	+	0.0306014i
$789$	−3.04950	−	3.78586i	−0.108565	−	0.134780i
$790$	3.84374	+	3.49603i	0.136754	+	0.124383i
$791$	−22.9371			−0.815551
$792$	3.72768	+	4.31252i	0.132457	+	0.153239i
$793$	−1.62080			−0.0575564
$794$	36.6849	+	33.3663i	1.30190	+	1.18412i
$795$	−1.10548	−	1.37241i	−0.0392072	−	0.0486745i
$796$	−41.6028	+	3.95068i	−1.47457	+	0.140028i
$797$			23.4713i			0.831397i	0.909503	+	0.415698i	$0.136463\pi$
$797$			23.4713i			0.831397i	−0.909503	+	0.415698i	$0.863537\pi$
$798$	−1.39410	+	23.2169i	−0.0493508	+	0.821868i
$799$		−	4.54152i		−	0.160667i
$800$	23.7264	+	14.5045i	0.838856	+	0.512811i
$801$	−16.9660	−	3.69834i	−0.599464	−	0.130675i
$802$	−27.4649	+	30.1966i	−0.969821	+	1.06628i
$803$	−6.42749			−0.226821
$804$	5.72335	+	5.86985i	0.201847	+	0.207014i
$805$	−0.470724			−0.0165909
$806$	−1.63588	+	1.79859i	−0.0576214	+	0.0633525i
$807$	−6.54966	+	5.27573i	−0.230559	+	0.185715i
$808$	−39.7141	−	29.7781i	−1.39714	−	1.04759i
$809$			24.6190i			0.865557i	0.901500	+	0.432778i	$0.142467\pi$
$809$			24.6190i			0.865557i	−0.901500	+	0.432778i	$0.857533\pi$
$810$	3.39411	−	1.44895i	0.119257	−	0.0509110i
$811$		−	11.3551i		−	0.398733i	−0.979925	−	0.199366i	$-0.936112\pi$
$811$		−	11.3551i		−	0.398733i	0.979925	−	0.199366i	$-0.0638884\pi$
$812$	0.958682	+	10.0954i	0.0336431	+	0.354280i
$813$	−17.1547	+	13.8181i	−0.601641	+	0.484620i
$814$	−5.19106	−	4.72146i	−0.181946	−	0.165487i
$815$	5.23785			0.183474
$816$	13.8391	−	16.3189i	0.484464	−	0.571274i
$817$	44.9708			1.57333
$818$	10.8124	+	9.83432i	0.378048	+	0.343849i
$819$	−3.84110	−	0.837305i	−0.134219	−	0.0292578i
$820$	−0.257729	−	2.71402i	−0.00900028	−	0.0947778i
$821$			50.5263i			1.76338i	0.471829	+	0.881690i	$0.343594\pi$
$821$			50.5263i			1.76338i	−0.471829	+	0.881690i	$0.656406\pi$
$822$	27.7769	+	1.66792i	0.968831	+	0.0581754i
$823$			24.7576i			0.862995i	0.902114	+	0.431498i	$0.142015\pi$
$823$			24.7576i			0.862995i	−0.902114	+	0.431498i	$0.857985\pi$
$824$	−21.3093	−	15.9780i	−0.742343	−	0.556618i
$825$	3.58818	+	4.45462i	0.124925	+	0.155090i
$826$	−19.7278	+	21.6899i	−0.686416	+	0.754688i
$827$	35.1040			1.22069			0.610343	−	0.792137i	$-0.291032\pi$
$827$	35.1040			1.22069			0.610343	+	0.792137i	$0.291032\pi$
$828$	5.95689	+	0.717976i	0.207016	+	0.0249514i
$829$	−15.3815			−0.534220			−0.267110	−	0.963666i	$-0.586069\pi$
$829$	−15.3815			−0.534220			−0.267110	+	0.963666i	$0.586069\pi$
$830$	−4.32483	+	4.75498i	−0.150117	+	0.165048i
$831$	20.2084	+	25.0881i	0.701022	+	0.870297i
$832$	−1.80957	−	6.19871i	−0.0627356	−	0.214902i
$833$			13.4787i			0.467009i
$834$	−18.1547	−	1.09013i	−0.628645	−	0.0377482i
$835$		−	3.06650i		−	0.106121i
$836$	−7.82306	+	0.742894i	−0.270566	+	0.0256935i
$837$	4.94739	+	9.89952i	0.171007	+	0.342177i
$838$	−16.1527	−	14.6915i	−0.557985	−	0.507508i
$839$	57.4614			1.98379			0.991893	−	0.127073i	$-0.0405584\pi$
$839$	57.4614			1.98379			0.991893	+	0.127073i	$0.0405584\pi$
$840$	2.30468	−	0.0800115i	0.0795190	−	0.00276066i
$841$	19.2456			0.663643
$842$	−0.180866	−	0.164504i	−0.00623305	−	0.00566919i
$843$	11.9339	−	9.61272i	0.411025	−	0.331080i
$844$	22.9067	−	2.17527i	0.788482	−	0.0748758i
$845$			3.58043i			0.123170i
$846$	−5.08455	+	3.61541i	−0.174811	+	0.124300i
$847$		−	17.1255i		−	0.588440i
$848$	2.64199	+	13.7853i	0.0907262	+	0.473390i
$849$	22.1026	−	17.8036i	0.758560	−	0.611018i
$850$	14.4467	−	15.8836i	0.495519	−	0.544804i
$851$	−7.38600			−0.253189
$852$	10.2109	−	9.95605i	0.349819	−	0.341089i
$853$	−46.0708			−1.57743			−0.788717	−	0.614756i	$-0.789255\pi$
$853$	−46.0708			−1.57743			−0.788717	+	0.614756i	$0.789255\pi$
$854$	−3.10199	+	3.41052i	−0.106148	+	0.116705i
$855$	−1.08356	+	4.97081i	−0.0370571	+	0.169998i
$856$	26.7064	−	35.6175i	0.912807	−	1.21738i
$857$			11.2362i			0.383821i	0.981412	+	0.191910i	$0.0614683\pi$
$857$			11.2362i			0.383821i	−0.981412	+	0.191910i	$0.938532\pi$
$858$	0.0796137	−	1.32586i	0.00271797	−	0.0452640i
$859$			33.9263i			1.15755i	0.815487	+	0.578775i	$0.196469\pi$
$859$			33.9263i			1.15755i	−0.815487	+	0.578775i	$0.803531\pi$
$860$	−0.421520	−	4.43883i	−0.0143737	−	0.151363i
$861$	8.29265	+	10.2951i	0.282613	+	0.350855i
$862$	−26.6218	−	24.2135i	−0.906743	−	0.824716i
$863$	39.7972			1.35471			0.677356	−	0.735655i	$-0.263126\pi$
$863$	39.7972			1.35471			0.677356	+	0.735655i	$0.263126\pi$
$864$	−29.2871	−	2.50271i	−0.996369	−	0.0851438i
$865$	−5.52577			−0.187882
$866$	9.42408	+	8.57155i	0.320243	+	0.291273i
$867$	8.10759	+	10.0653i	0.275348	+	0.341836i
$868$	0.653764	+	6.88448i	0.0221902	+	0.233674i
$869$		−	8.51234i		−	0.288761i
$870$	−0.132956	+	2.21419i	−0.00450762	+	0.0750681i
$871$		−	1.91031i		−	0.0647283i
$872$	30.3441	−	40.4689i	1.02758	−	1.37045i
$873$	4.20190	−	19.2761i	0.142213	−	0.652395i
$874$	−5.56545	+	6.11899i	−0.188254	+	0.206978i
$875$	4.66767			0.157796
$876$	23.7304	−	23.1381i	0.801774	−	0.781764i
$877$	18.7692			0.633792			0.316896	−	0.948460i	$-0.397359\pi$
$877$	18.7692			0.633792			0.316896	+	0.948460i	$0.397359\pi$
$878$	14.8163	−	16.2899i	0.500025	−	0.549758i
$879$	−31.8797	+	25.6790i	−1.07527	+	0.866131i
$880$	0.146654	+	0.765210i	0.00494371	+	0.0257952i
$881$		−	7.15564i		−	0.241080i	−0.992708	−	0.120540i	$-0.961537\pi$
$881$		−	7.15564i		−	0.241080i	0.992708	−	0.120540i	$-0.0384625\pi$
$882$	15.0904	−	10.7301i	0.508119	−	0.361302i
$883$		−	47.5052i		−	1.59868i	−0.600880	−	0.799339i	$-0.705183\pi$
$883$		−	47.5052i		−	1.59868i	0.600880	−	0.799339i	$-0.294817\pi$
$884$	−4.96341	+	0.471335i	−0.166937	+	0.0158527i
$885$	−4.99450	+	4.02306i	−0.167888	+	0.135234i
$886$	−37.5367	−	34.1410i	−1.26107	−	1.14699i
$887$	−41.4374			−1.39133			−0.695666	−	0.718366i	$-0.744890\pi$
$887$	−41.4374			−1.39133			−0.695666	+	0.718366i	$0.744890\pi$
$888$	36.1621	−	1.25544i	1.21352	−	0.0421297i
$889$	20.5685			0.689845
$890$	−1.75580	−	1.59697i	−0.0588546	−	0.0535305i
$891$	−5.49756	−	2.51635i	−0.184175	−	0.0843008i
$892$	−8.05564	+	0.764979i	−0.269723	+	0.0256134i
$893$		−	8.60076i		−	0.287813i
$894$	20.9725	+	1.25934i	0.701425	+	0.0421185i
$895$			0.887517i			0.0296664i
$896$	−16.5067	−	8.05573i	−0.551449	−	0.269123i
$897$	−0.877017	−	1.08879i	−0.0292827	−	0.0363536i
$898$	−22.3828	+	24.6090i	−0.746923	+	0.821212i
$899$	−6.65189			−0.221853
$900$	−29.2836	−	3.52952i	−0.976121	−	0.117651i
$901$	10.8372			0.361041
$902$	−3.00523	+	3.30413i	−0.100063	+	0.110016i
$903$	13.5628	+	16.8378i	0.451341	+	0.560325i
$904$	31.9719	+	23.9729i	1.06337	+	0.797328i
$905$			5.91001i			0.196455i
$906$	4.01589	+	0.241142i	0.133419	+	0.00801141i
$907$			16.0649i			0.533428i	0.963776	+	0.266714i	$0.0859379\pi$
$907$			16.0649i			0.533428i	−0.963776	+	0.266714i	$0.914062\pi$
$908$	−1.27382	−	13.4140i	−0.0422733	−	0.445160i
$909$	51.4412	+	11.2134i	1.70620	+	0.371926i
$910$	−0.397514	−	0.361553i	−0.0131775	−	0.0119854i
$911$	31.9519			1.05861			0.529307	−	0.848430i	$-0.322452\pi$
$911$	31.9519			1.05861			0.529307	+	0.848430i	$0.322452\pi$
$912$	26.2085	−	30.9048i	0.867851	−	1.02336i
$913$	10.5304			0.348504
$914$	−3.91874	−	3.56424i	−0.129620	−	0.117895i
$915$	−0.785335	+	0.632585i	−0.0259624	+	0.0209126i
$916$	1.37809	+	14.5120i	0.0455334	+	0.479491i
$917$			2.91634i			0.0963059i
$918$	−6.15403	+	21.8445i	−0.203113	+	0.720975i
$919$		−	17.9098i		−	0.590790i	−0.955375	−	0.295395i	$-0.904549\pi$
$919$		−	17.9098i		−	0.590790i	0.955375	−	0.295395i	$-0.0954513\pi$
$920$	0.656139	+	0.491981i	0.0216323	+	0.0162201i
$921$	−11.7492	+	9.46396i	−0.387149	+	0.311848i
$922$	−40.1259	+	44.1168i	−1.32147	+	1.45291i
$923$	−3.32307			−0.109380
$924$	−2.63751	−	2.70502i	−0.0867678	−	0.0889887i
$925$	36.3090			1.19383
$926$	−23.8555	+	26.2282i	−0.783942	+	0.861913i
$927$	27.6016	+	6.01676i	0.906557	+	0.197616i
$928$	9.21502	−	15.0739i	0.302498	−	0.494825i
$929$			18.2806i			0.599768i	0.953976	+	0.299884i	$0.0969480\pi$
$929$			18.2806i			0.599768i	−0.953976	+	0.299884i	$0.903052\pi$
$930$	−0.0906678	+	1.50995i	−0.00297311	+	0.0495131i
$931$			25.5260i			0.836582i
$932$	−49.9999	+	4.74809i	−1.63780	+	0.155529i
$933$	−20.2131	−	25.0940i	−0.661748	−	0.821539i
$934$	11.4843	+	10.4454i	0.375778	+	0.341784i
$935$	0.601565			0.0196733
$936$	4.47897	+	5.18167i	0.146400	+	0.169368i
$937$	−32.4827			−1.06116			−0.530581	−	0.847634i	$-0.678026\pi$
$937$	−32.4827			−1.06116			−0.530581	+	0.847634i	$0.678026\pi$
$938$	−4.01969	−	3.65606i	−0.131248	−	0.119374i
$939$	−0.138996	−	0.172559i	−0.00453596	−	0.00563126i
$940$	−0.848935	+	0.0806165i	−0.0276892	+	0.00262942i
$941$			47.9679i			1.56371i	0.623460	+	0.781855i	$0.285726\pi$
$941$			47.9679i			1.56371i	−0.623460	+	0.781855i	$0.714274\pi$
$942$	3.02291	−	50.3424i	0.0984918	−	1.64024i
$943$			4.70122i			0.153093i
$944$	50.1677	−	9.61475i	1.63282	−	0.312934i
$945$	−2.18794	+	1.09345i	−0.0711736	+	0.0355698i
$946$	−4.91511	+	5.40397i	−0.159804	+	0.175698i
$947$	−48.6007			−1.57931			−0.789655	−	0.613551i	$-0.789741\pi$
$947$	−48.6007			−1.57931			−0.789655	+	0.613551i	$0.789741\pi$
$948$	30.6433	+	31.4277i	0.995248	+	1.02072i
$949$	−7.72290			−0.250696
$950$	27.3594	−	30.0805i	0.887655	−	0.975941i
$951$	35.9941	−	28.9931i	1.16719	−	0.940167i
$952$	−8.50747	+	11.3461i	−0.275729	+	0.367730i
$953$		−	54.8880i		−	1.77800i	−0.457911	−	0.888998i	$-0.651402\pi$
$953$		−	54.8880i		−	1.77800i	0.457911	−	0.888998i	$-0.348598\pi$
$954$	−8.62732	−	12.1331i	−0.279320	−	0.392823i
$955$			2.83484i			0.0917332i
$956$	−3.60460	−	37.9584i	−0.116581	−	1.22766i
$957$	2.83011	−	2.27965i	0.0914846	−	0.0736906i
$958$	32.8474	+	29.8759i	1.06125	+	0.965247i
$959$	−18.4431			−0.595560
$960$	−3.29610	−	2.29723i	−0.106381	−	0.0741427i
$961$	26.4638			0.853671
$962$	−6.23727	−	5.67303i	−0.201098	−	0.182906i
$963$	−10.0567	+	46.1349i	−0.324074	+	1.48668i
$964$	−2.97796	−	31.3595i	−0.0959136	−	1.01002i
$965$		−	6.47260i		−	0.208360i
$966$	−3.96953	−	0.238358i	−0.127717	−	0.00766906i
$967$		−	37.4190i		−	1.20332i	−0.798754	−	0.601658i	$-0.794507\pi$
$967$		−	37.4190i		−	1.20332i	0.798754	−	0.601658i	$-0.205493\pi$
$968$	−17.8989	+	23.8711i	−0.575292	+	0.767247i
$969$	−19.6260	−	24.3650i	−0.630477	−	0.782717i
$970$	1.81441	−	1.99487i	0.0582571	−	0.0640514i
$971$	5.43513			0.174422			0.0872108	−	0.996190i	$-0.472205\pi$
$971$	5.43513			0.174422			0.0872108	+	0.996190i	$0.472205\pi$
$972$	29.3555	−	10.5001i	0.941580	−	0.336790i
$973$	12.0542			0.386440
$974$	8.30484	−	9.13084i	0.266104	−	0.292571i
$975$	4.31135	+	5.35241i	0.138074	+	0.171414i
$976$	7.88837	−	1.51182i	0.252500	−	0.0483923i
$977$			11.4481i			0.366258i	0.983089	+	0.183129i	$0.0586227\pi$
$977$			11.4481i			0.366258i	−0.983089	+	0.183129i	$0.941377\pi$
$978$	44.1698	+	2.65226i	1.41239	+	0.0848100i
$979$			3.88839i			0.124274i
$980$	2.51954	−	0.239260i	0.0804837	−	0.00764289i
$981$	−11.4266	+	52.4188i	−0.364822	+	1.67360i
$982$	−10.1087	−	9.19426i	−0.322583	−	0.293401i
$983$	−47.3570			−1.51045			−0.755227	−	0.655463i	$-0.772473\pi$
$983$	−47.3570			−1.51045			−0.755227	+	0.655463i	$0.772473\pi$
$984$	−0.799092	−	23.0173i	−0.0254741	−	0.733766i
$985$	1.31734			0.0419738
$986$	−10.0912	−	9.17833i	−0.321370	−	0.292298i
$987$	3.22025	−	2.59391i	0.102502	−	0.0825649i
$988$	−9.39974	+	0.892618i	−0.299046	+	0.0283980i
$989$			7.68893i			0.244494i
$990$	−0.478894	−	0.673495i	−0.0152203	−	0.0214051i
$991$			9.09986i			0.289067i	0.989500	+	0.144533i	$0.0461681\pi$
$991$			9.09986i			0.289067i	−0.989500	+	0.144533i	$0.953832\pi$
$992$	6.28409	−	10.2795i	0.199520	−	0.326375i
$993$	27.4378	−	22.1011i	0.870713	−	0.701357i
$994$	−6.35988	+	6.99244i	−0.201723	+	0.221787i
$995$	6.05848			0.192067
$996$	−38.8782	+	37.9079i	−1.23190	+	1.20116i
$997$	21.7371			0.688420			0.344210	−	0.938893i	$-0.388147\pi$
$997$	21.7371			0.688420			0.344210	+	0.938893i	$0.388147\pi$
$998$	−10.9767	+	12.0685i	−0.347462	+	0.382020i
$999$	−34.3303	+	17.1569i	−1.08616	+	0.542821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.b.47.5	yes	22
3.2	odd	2		276.2.c.a.47.18	yes	22
4.3	odd	2		276.2.c.a.47.17	✓	22
12.11	even	2	inner	276.2.c.b.47.6	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.17	✓	22	4.3	odd	2
276.2.c.a.47.18	yes	22	3.2	odd	2
276.2.c.b.47.5	yes	22	1.1	even	1	trivial
276.2.c.b.47.6	yes	22	12.11	even	2	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04620 - 0.951558i) q^{2} +(1.08652 + 1.34888i) q^{3} +(0.189073 + 1.99104i) q^{4} -0.289949i q^{5} +(0.146820 - 2.44509i) q^{6} +1.62347i q^{7} +(1.69678 - 2.26295i) q^{8} +(-0.638952 + 2.93117i) q^{9} +O(q^{10})\)	\(q+(-1.04620 - 0.951558i) q^{2} +(1.08652 + 1.34888i) q^{3} +(0.189073 + 1.99104i) q^{4} -0.289949i q^{5} +(0.146820 - 2.44509i) q^{6} +1.62347i q^{7} +(1.69678 - 2.26295i) q^{8} +(-0.638952 + 2.93117i) q^{9} +(-0.275904 + 0.303345i) q^{10} +0.671787 q^{11} +(-2.48025 + 2.41834i) q^{12} +0.807180 q^{13} +(1.54483 - 1.69848i) q^{14} +(0.391106 - 0.315035i) q^{15} +(-3.92850 + 0.752906i) q^{16} +3.08837i q^{17} +(3.45765 - 2.45859i) q^{18} +5.84877i q^{19} +(0.577301 - 0.0548216i) q^{20} +(-2.18987 + 1.76393i) q^{21} +(-0.702824 - 0.639245i) q^{22} -1.00000 q^{23} +(4.89603 - 0.169975i) q^{24} +4.91593 q^{25} +(-0.844473 - 0.768079i) q^{26} +(-4.64803 + 2.32290i) q^{27} +(-3.23240 + 0.306955i) q^{28} -3.12320i q^{29} +(-0.708950 - 0.0425704i) q^{30} -2.12983i q^{31} +(4.82644 + 2.95051i) q^{32} +(0.729909 + 0.906160i) q^{33} +(2.93876 - 3.23105i) q^{34} +0.470724 q^{35} +(-5.95689 - 0.717976i) q^{36} +7.38600 q^{37} +(5.56545 - 6.11899i) q^{38} +(0.877017 + 1.08879i) q^{39} +(-0.656139 - 0.491981i) q^{40} -4.70122i q^{41} +(3.96953 + 0.238358i) q^{42} -7.68893i q^{43} +(0.127017 + 1.33756i) q^{44} +(0.849889 + 0.185264i) q^{45} +(1.04620 + 0.951558i) q^{46} -1.47052 q^{47} +(-5.28397 - 4.48103i) q^{48} +4.36434 q^{49} +(-5.14305 - 4.67779i) q^{50} +(-4.16584 + 3.35557i) q^{51} +(0.152616 + 1.60713i) q^{52} -3.50905i q^{53} +(7.07314 + 1.99265i) q^{54} -0.194784i q^{55} +(3.67383 + 2.75468i) q^{56} +(-7.88929 + 6.35480i) q^{57} +(-2.97190 + 3.26749i) q^{58} -12.7702 q^{59} +(0.701197 + 0.719145i) q^{60} -2.00798 q^{61} +(-2.02666 + 2.22823i) q^{62} +(-4.75867 - 1.03732i) q^{63} +(-2.24184 - 7.67946i) q^{64} -0.234041i q^{65} +(0.0986319 - 1.64258i) q^{66} -2.36664i q^{67} +(-6.14907 + 0.583928i) q^{68} +(-1.08652 - 1.34888i) q^{69} +(-0.492472 - 0.447922i) q^{70} -4.11689 q^{71} +(5.54891 + 6.41947i) q^{72} -9.56775 q^{73} +(-7.72724 - 7.02821i) q^{74} +(5.34125 + 6.63100i) q^{75} +(-11.6452 + 1.10585i) q^{76} +1.09063i q^{77} +(0.118510 - 1.97362i) q^{78} -12.6712i q^{79} +(0.218304 + 1.13907i) q^{80} +(-8.18348 - 3.74575i) q^{81} +(-4.47349 + 4.91843i) q^{82} +15.6752 q^{83} +(-3.92611 - 4.02661i) q^{84} +0.895469 q^{85} +(-7.31647 + 8.04417i) q^{86} +(4.21282 - 3.39341i) q^{87} +(1.13988 - 1.52022i) q^{88} +5.78814i q^{89} +(-0.712866 - 1.00254i) q^{90} +1.31043i q^{91} +(-0.189073 - 1.99104i) q^{92} +(2.87289 - 2.31411i) q^{93} +(1.53846 + 1.39929i) q^{94} +1.69585 q^{95} +(1.26414 + 9.71607i) q^{96} -6.57624 q^{97} +(-4.56598 - 4.15292i) q^{98} +(-0.429240 + 1.96912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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