LMFDB - Embedded newform 276.2.c.a.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.a.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15961 - 0.809507i) q^{2} +(-1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} +3.47795i q^{5} +(2.40584 - 0.460365i) q^{6} +0.968466i q^{7} +(0.720358 - 2.73516i) q^{8} +(-0.0786444 - 2.99897i) q^{9} +O(q^{10})$	\(q+(-1.15961 - 0.809507i) q^{2} +(-1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} +3.47795i q^{5} +(2.40584 - 0.460365i) q^{6} +0.968466i q^{7} +(0.720358 - 2.73516i) q^{8} +(-0.0786444 - 2.99897i) q^{9} +(2.81542 - 4.03307i) q^{10} -2.17307 q^{11} +(-3.16251 - 1.41370i) q^{12} -3.21098 q^{13} +(0.783980 - 1.12304i) q^{14} +(-4.31507 - 4.20339i) q^{15} +(-3.04946 + 2.58858i) q^{16} +1.26490i q^{17} +(-2.33649 + 3.54130i) q^{18} -4.03623i q^{19} +(-6.52959 + 2.39769i) q^{20} +(-1.20157 - 1.17047i) q^{21} +(2.51992 + 1.75912i) q^{22} +1.00000 q^{23} +(2.52288 + 4.19941i) q^{24} -7.09612 q^{25} +(3.72349 + 2.59931i) q^{26} +(3.81585 + 3.52694i) q^{27} +(-1.81822 + 0.667657i) q^{28} +8.56092i q^{29} +(1.60113 + 8.36738i) q^{30} -1.32974i q^{31} +(5.63167 - 0.533190i) q^{32} +(2.62634 - 2.69612i) q^{33} +(1.02395 - 1.46679i) q^{34} -3.36827 q^{35} +(5.57613 - 2.21513i) q^{36} -10.0527 q^{37} +(-3.26735 + 4.68045i) q^{38} +(3.88075 - 3.98385i) q^{39} +(9.51273 + 2.50537i) q^{40} -7.60029i q^{41} +(0.445848 + 2.32997i) q^{42} +1.64095i q^{43} +(-1.49811 - 4.07978i) q^{44} +(10.4303 - 0.273521i) q^{45} +(-1.15961 - 0.809507i) q^{46} -12.6881 q^{47} +(0.473894 - 6.91198i) q^{48} +6.06207 q^{49} +(8.22874 + 5.74436i) q^{50} +(-1.56936 - 1.52874i) q^{51} +(-2.21364 - 6.02839i) q^{52} +8.41184i q^{53} +(-1.56983 - 7.17883i) q^{54} -7.55782i q^{55} +(2.64891 + 0.697642i) q^{56} +(5.00772 + 4.87812i) q^{57} +(6.93013 - 9.92734i) q^{58} -1.24592 q^{59} +(4.91677 - 10.9990i) q^{60} +5.28282 q^{61} +(-1.07643 + 1.54198i) q^{62} +(2.90440 - 0.0761644i) q^{63} +(-6.96217 - 3.94058i) q^{64} -11.1676i q^{65} +(-5.22806 + 1.00041i) q^{66} +14.1014i q^{67} +(-2.37476 + 0.872019i) q^{68} +(-1.20859 + 1.24069i) q^{69} +(3.90589 + 2.72664i) q^{70} +12.0576 q^{71} +(-8.25930 - 1.94523i) q^{72} +4.42105 q^{73} +(11.6572 + 8.13772i) q^{74} +(8.57626 - 8.80411i) q^{75} +(7.57772 - 2.78256i) q^{76} -2.10454i q^{77} +(-7.72511 + 1.47822i) q^{78} +7.01409i q^{79} +(-9.00296 - 10.6059i) q^{80} +(-8.98763 + 0.471704i) q^{81} +(-6.15249 + 8.81338i) q^{82} +8.36193 q^{83} +(1.36912 - 3.06278i) q^{84} -4.39926 q^{85} +(1.32836 - 1.90287i) q^{86} +(-10.6215 - 10.3466i) q^{87} +(-1.56539 + 5.94369i) q^{88} +3.00302i q^{89} +(-12.3165 - 8.12619i) q^{90} -3.10973i q^{91} +(0.689397 + 1.87743i) q^{92} +(1.64980 + 1.60710i) q^{93} +(14.7133 + 10.2711i) q^{94} +14.0378 q^{95} +(-6.14483 + 7.63159i) q^{96} -9.68965 q^{97} +(-7.02965 - 4.90729i) q^{98} +(0.170900 + 6.51697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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 $

$2$	−1.15961	−	0.809507i	−0.819969	−	0.572408i
$2$	−1.15961	−	0.809507i	−0.819969	−	0.572408i
$3$	−1.20859	+	1.24069i	−0.697777	+	0.716315i
$3$	−1.20859	+	1.24069i	−0.697777	+	0.716315i
$4$	0.689397	+	1.87743i	0.344698	+	0.938713i
$5$			3.47795i			1.55539i	0.628645	+	0.777693i	$0.283610\pi$
$5$			3.47795i			1.55539i	−0.628645	+	0.777693i	$0.716390\pi$
$6$	2.40584	−	0.460365i	0.982180	−	0.187943i
$7$			0.968466i			0.366046i	0.983109	+	0.183023i	$0.0585882\pi$
$7$			0.968466i			0.366046i	−0.983109	+	0.183023i	$0.941412\pi$
$8$	0.720358	−	2.73516i	0.254685	−	0.967024i
$9$	−0.0786444	−	2.99897i	−0.0262148	−	0.999656i
$10$	2.81542	−	4.03307i	0.890315	−	1.27537i
$11$	−2.17307			−0.655205			−0.327603	−	0.944816i	$-0.606241\pi$
$11$	−2.17307			−0.655205			−0.327603	+	0.944816i	$0.606241\pi$
$12$	−3.16251	−	1.41370i	−0.912937	−	0.408100i
$13$	−3.21098			−0.890567			−0.445283	−	0.895390i	$-0.646897\pi$
$13$	−3.21098			−0.890567			−0.445283	+	0.895390i	$0.646897\pi$
$14$	0.783980	−	1.12304i	0.209527	−	0.300146i
$15$	−4.31507	−	4.20339i	−1.11415	−	1.08531i
$16$	−3.04946	+	2.58858i	−0.762366	+	0.647146i
$17$			1.26490i			0.306784i	0.988165	+	0.153392i	$0.0490197\pi$
$17$			1.26490i			0.306784i	−0.988165	+	0.153392i	$0.950980\pi$
$18$	−2.33649	+	3.54130i	−0.550716	+	0.834693i
$19$		−	4.03623i		−	0.925974i	−0.886365	−	0.462987i	$-0.846778\pi$
$19$		−	4.03623i		−	0.925974i	0.886365	−	0.462987i	$-0.153222\pi$
$20$	−6.52959	+	2.39769i	−1.46006	+	0.536139i
$21$	−1.20157	−	1.17047i	−0.262204	−	0.255418i
$22$	2.51992	+	1.75912i	0.537248	+	0.375045i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.52288	+	4.19941i	0.514981	+	0.857202i
$25$	−7.09612			−1.41922
$26$	3.72349	+	2.59931i	0.730237	+	0.509767i
$27$	3.81585	+	3.52694i	0.734361	+	0.678759i
$28$	−1.81822	+	0.667657i	−0.343612	+	0.126175i
$29$			8.56092i			1.58972i	0.606791	+	0.794862i	$0.292457\pi$
$29$			8.56092i			1.58972i	−0.606791	+	0.794862i	$0.707543\pi$
$30$	1.60113	+	8.36738i	0.292324	+	1.52767i
$31$		−	1.32974i		−	0.238828i	−0.992845	−	0.119414i	$-0.961898\pi$
$31$		−	1.32974i		−	0.238828i	0.992845	−	0.119414i	$-0.0381015\pi$
$32$	5.63167	−	0.533190i	0.995548	−	0.0942555i
$33$	2.62634	−	2.69612i	0.457187	−	0.469334i
$34$	1.02395	−	1.46679i	0.175605	−	0.251553i
$35$	−3.36827			−0.569342
$36$	5.57613	−	2.21513i	0.929355	−	0.369188i
$37$	−10.0527			−1.65265			−0.826325	−	0.563193i	$-0.809573\pi$
$37$	−10.0527			−1.65265			−0.826325	+	0.563193i	$0.809573\pi$
$38$	−3.26735	+	4.68045i	−0.530035	+	0.759270i
$39$	3.88075	−	3.98385i	0.621417	−	0.637926i
$40$	9.51273	+	2.50537i	1.50409	+	0.396133i
$41$		−	7.60029i		−	1.18697i	−0.804847	−	0.593483i	$-0.797752\pi$
$41$		−	7.60029i		−	1.18697i	0.804847	−	0.593483i	$-0.202248\pi$
$42$	0.445848	+	2.32997i	0.0687958	+	0.359523i
$43$			1.64095i			0.250243i	0.992141	+	0.125122i	$0.0399321\pi$
$43$			1.64095i			0.250243i	−0.992141	+	0.125122i	$0.960068\pi$
$44$	−1.49811	−	4.07978i	−0.225848	−	0.615050i
$45$	10.4303	−	0.273521i	1.55485	−	0.0407741i
$46$	−1.15961	−	0.809507i	−0.170975	−	0.119355i
$47$	−12.6881			−1.85075			−0.925375	−	0.379052i	$-0.876250\pi$
$47$	−12.6881			−1.85075			−0.925375	+	0.379052i	$0.876250\pi$
$48$	0.473894	−	6.91198i	0.0684008	−	0.997658i
$49$	6.06207			0.866011
$50$	8.22874	+	5.74436i	1.16372	+	0.812375i
$51$	−1.56936	−	1.52874i	−0.219754	−	0.214067i
$52$	−2.21364	−	6.02839i	−0.306977	−	0.835987i
$53$			8.41184i			1.15545i	0.816230	+	0.577727i	$0.196060\pi$
$53$			8.41184i			1.15545i	−0.816230	+	0.577727i	$0.803940\pi$
$54$	−1.56983	−	7.17883i	−0.213626	−	0.976915i
$55$		−	7.55782i		−	1.01910i
$56$	2.64891	+	0.697642i	0.353975	+	0.0932263i
$57$	5.00772	+	4.87812i	0.663289	+	0.646123i
$58$	6.93013	−	9.92734i	0.909970	−	1.30352i
$59$	−1.24592			−0.162206			−0.0811028	−	0.996706i	$-0.525844\pi$
$59$	−1.24592			−0.162206			−0.0811028	+	0.996706i	$0.525844\pi$
$60$	4.91677	−	10.9990i	0.634752	−	1.41997i
$61$	5.28282			0.676396			0.338198	−	0.941075i	$-0.390183\pi$
$61$	5.28282			0.676396			0.338198	+	0.941075i	$0.390183\pi$
$62$	−1.07643	+	1.54198i	−0.136707	+	0.195831i
$63$	2.90440	−	0.0761644i	0.365920	−	0.00959581i
$64$	−6.96217	−	3.94058i	−0.870271	−	0.492573i
$65$		−	11.1676i		−	1.38517i
$66$	−5.22806	+	1.00041i	−0.643530	+	0.123141i
$67$			14.1014i			1.72276i	0.507964	+	0.861378i	$0.330398\pi$
$67$			14.1014i			1.72276i	−0.507964	+	0.861378i	$0.669602\pi$
$68$	−2.37476	+	0.872019i	−0.287982	+	0.105748i
$69$	−1.20859	+	1.24069i	−0.145497	+	0.149362i
$70$	3.90589	+	2.72664i	0.466843	+	0.325896i
$71$	12.0576			1.43098			0.715488	−	0.698625i	$-0.246204\pi$
$71$	12.0576			1.43098			0.715488	+	0.698625i	$0.246204\pi$
$72$	−8.25930	−	1.94523i	−0.973368	−	0.229247i
$73$	4.42105			0.517445			0.258722	−	0.965952i	$-0.416699\pi$
$73$	4.42105			0.517445			0.258722	+	0.965952i	$0.416699\pi$
$74$	11.6572	+	8.13772i	1.35512	+	0.945990i
$75$	8.57626	−	8.80411i	0.990301	−	1.01661i
$76$	7.57772	−	2.78256i	0.869224	−	0.319182i
$77$		−	2.10454i		−	0.239835i
$78$	−7.72511	+	1.47822i	−0.874697	+	0.167376i
$79$			7.01409i			0.789147i	0.918864	+	0.394574i	$0.129108\pi$
$79$			7.01409i			0.789147i	−0.918864	+	0.394574i	$0.870892\pi$
$80$	−9.00296	−	10.6059i	−1.00656	−	1.18577i
$81$	−8.98763	+	0.471704i	−0.998626	+	0.0524116i
$82$	−6.15249	+	8.81338i	−0.679429	+	0.973275i
$83$	8.36193			0.917841			0.458920	−	0.888477i	$-0.348236\pi$
$83$	8.36193			0.917841			0.458920	+	0.888477i	$0.348236\pi$
$84$	1.36912	−	3.06278i	0.149383	−	0.334177i
$85$	−4.39926			−0.477167
$86$	1.32836	−	1.90287i	0.143241	−	0.205192i
$87$	−10.6215	−	10.3466i	−1.13874	−	1.10927i
$88$	−1.56539	+	5.94369i	−0.166871	+	0.633599i
$89$			3.00302i			0.318319i	0.987253	+	0.159160i	$0.0508785\pi$
$89$			3.00302i			0.318319i	−0.987253	+	0.159160i	$0.949122\pi$
$90$	−12.3165	−	8.12619i	−1.29827	−	0.856575i
$91$		−	3.10973i		−	0.325988i
$92$	0.689397	+	1.87743i	0.0718746	+	0.195735i
$93$	1.64980	+	1.60710i	0.171076	+	0.166649i
$94$	14.7133	+	10.2711i	1.51756	+	1.05938i
$95$	14.0378			1.44025
$96$	−6.14483	+	7.63159i	−0.627154	+	0.778895i
$97$	−9.68965			−0.983835			−0.491918	−	0.870642i	$-0.663704\pi$
$97$	−9.68965			−0.983835			−0.491918	+	0.870642i	$0.663704\pi$
$98$	−7.02965	−	4.90729i	−0.710102	−	0.495711i
$99$	0.170900	+	6.51697i	0.0171761	+	0.654980i
$100$	−4.89204	−	13.3224i	−0.489204	−	1.33224i
$101$		−	9.71644i		−	0.966822i	−0.875394	−	0.483411i	$-0.839398\pi$
$101$		−	9.71644i		−	0.966822i	0.875394	−	0.483411i	$-0.160602\pi$
$102$	0.582317	+	3.04315i	0.0576579	+	0.301317i
$103$			10.8186i			1.06599i	0.846119	+	0.532994i	$0.178933\pi$
$103$			10.8186i			1.06599i	−0.846119	+	0.532994i	$0.821067\pi$
$104$	−2.31306	+	8.78254i	−0.226814	+	0.861199i
$105$	4.07084	−	4.17900i	0.397274	−	0.407828i
$106$	6.80944	−	9.75446i	0.661391	−	0.947437i
$107$	−0.893799			−0.0864068			−0.0432034	−	0.999066i	$-0.513756\pi$
$107$	−0.893799			−0.0864068			−0.0432034	+	0.999066i	$0.513756\pi$
$108$	−3.99093	+	9.59544i	−0.384027	+	0.923322i
$109$	16.3878			1.56967			0.784834	−	0.619706i	$-0.212748\pi$
$109$	16.3878			1.56967			0.784834	+	0.619706i	$0.212748\pi$
$110$	−6.11811	+	8.76414i	−0.583339	+	0.835628i
$111$	12.1495	−	12.4723i	1.15318	−	1.18382i
$112$	−2.50696	−	2.95330i	−0.236885	−	0.279061i
$113$			11.1150i			1.04561i	0.852451	+	0.522807i	$0.175115\pi$
$113$			11.1150i			1.04561i	−0.852451	+	0.522807i	$0.824885\pi$
$114$	−1.85814	−	9.71051i	−0.174030	−	0.909473i
$115$			3.47795i			0.324320i
$116$	−16.0725	+	5.90187i	−1.49229	+	0.547975i
$117$	0.252526	+	9.62964i	0.0233460	+	0.890260i
$118$	1.44479	+	1.00858i	0.133004	+	0.0928478i
$119$	−1.22501			−0.112297
$120$	−14.6053	+	8.77444i	−1.33328	+	0.800993i
$121$	−6.27777			−0.570706
$122$	−6.12602	−	4.27648i	−0.554624	−	0.387174i
$123$	9.42964	+	9.18560i	0.850242	+	0.828237i
$124$	2.49648	−	0.916717i	0.224191	−	0.0823236i
$125$		−	7.29018i		−	0.652054i
$126$	−3.42963	−	2.26281i	−0.305536	−	0.201587i
$127$			11.8811i			1.05428i	0.849779	+	0.527139i	$0.176735\pi$
$127$			11.8811i			1.05428i	−0.849779	+	0.527139i	$0.823265\pi$
$128$	4.88348	+	10.2055i	0.431643	+	0.902045i
$129$	−2.03592	−	1.98323i	−0.179253	−	0.174614i
$130$	−9.04027	+	12.9501i	−0.792885	+	1.13580i
$131$	−19.7266			−1.72352			−0.861759	−	0.507319i	$-0.830637\pi$
$131$	−19.7266			−1.72352			−0.861759	+	0.507319i	$0.830637\pi$
$132$	6.87235	+	3.07207i	0.598161	+	0.267389i
$133$	3.90895			0.338949
$134$	11.4152	−	16.3521i	0.986119	−	1.41261i
$135$	−12.2665	+	13.2713i	−1.05573	+	1.14221i
$136$	3.45971	+	0.911182i	0.296667	+	0.0781332i
$137$		−	5.08776i		−	0.434677i	−0.976096	−	0.217339i	$-0.930262\pi$
$137$		−	5.08776i		−	0.434677i	0.976096	−	0.217339i	$-0.0697376\pi$
$138$	2.40584	−	0.460365i	0.204799	−	0.0391889i
$139$			1.70015i			0.144205i	0.997397	+	0.0721023i	$0.0229708\pi$
$139$			1.70015i			0.144205i	−0.997397	+	0.0721023i	$0.977029\pi$
$140$	−2.32208	−	6.32368i	−0.196251	−	0.534449i
$141$	15.3347	−	15.7421i	1.29141	−	1.32572i
$142$	−13.9822	−	9.76073i	−1.17336	−	0.819102i
$143$	6.97769			0.583504
$144$	8.00291	+	8.94167i	0.666909	+	0.745139i
$145$	−29.7744			−2.47263
$146$	−5.12670	−	3.57887i	−0.424289	−	0.296189i
$147$	−7.32653	+	7.52118i	−0.604282	+	0.620337i
$148$	−6.93029	−	18.8732i	−0.569666	−	1.55137i
$149$			3.77498i			0.309258i	0.987973	+	0.154629i	$0.0494183\pi$
$149$			3.77498i			0.309258i	−0.987973	+	0.154629i	$0.950582\pi$
$150$	−17.0721	+	3.26680i	−1.39393	+	0.266733i
$151$			19.5955i			1.59466i	0.603545	+	0.797329i	$0.293755\pi$
$151$			19.5955i			1.59466i	−0.603545	+	0.797329i	$0.706245\pi$
$152$	−11.0397	−	2.90753i	−0.895439	−	0.235832i
$153$	3.79340	−	0.0994775i	0.306678	−	0.00804228i
$154$	−1.70364	+	2.44045i	−0.137283	+	0.196657i
$155$	4.62475			0.371469
$156$	10.1548	+	4.53937i	0.813031	+	0.363440i
$157$	10.3968			0.829758			0.414879	−	0.909877i	$-0.363824\pi$
$157$	10.3968			0.829758			0.414879	+	0.909877i	$0.363824\pi$
$158$	5.67796	−	8.13362i	0.451714	−	0.647076i
$159$	−10.4365	−	10.1664i	−0.827670	−	0.806250i
$160$	1.85441	+	19.5867i	0.146604	+	1.54846i
$161$			0.968466i			0.0763258i
$162$	10.8040	+	6.72856i	0.848843	+	0.528645i
$163$		−	5.65715i		−	0.443102i	−0.975149	−	0.221551i	$-0.928888\pi$
$163$		−	5.65715i		−	0.443102i	0.975149	−	0.221551i	$-0.0711119\pi$
$164$	14.2690	−	5.23962i	1.11422	−	0.409145i
$165$	9.37695	+	9.13427i	0.729994	+	0.711102i
$166$	−9.69659	−	6.76904i	−0.752601	−	0.525379i
$167$	14.4620			1.11910			0.559550	−	0.828796i	$-0.310974\pi$
$167$	14.4620			1.11910			0.559550	+	0.828796i	$0.310974\pi$
$168$	−4.06699	+	2.44332i	−0.313775	+	0.188506i
$169$	−2.68959			−0.206891
$170$	5.10143	+	3.56123i	0.391262	+	0.273134i
$171$	−12.1045	+	0.317427i	−0.925655	+	0.0242742i
$172$	−3.08077	+	1.13127i	−0.234907	+	0.0862584i
$173$			5.19603i			0.395047i	0.980298	+	0.197523i	$0.0632898\pi$
$173$			5.19603i			0.395047i	−0.980298	+	0.197523i	$0.936710\pi$
$174$	3.94115	+	20.5962i	0.298778	+	1.56139i
$175$		−	6.87234i		−	0.519500i
$176$	6.62670	−	5.62518i	0.499506	−	0.424014i
$177$	1.50581	−	1.54581i	0.113183	−	0.116190i
$178$	2.43097	−	3.48234i	0.182209	−	0.261012i
$179$	1.56350			0.116861			0.0584307	−	0.998291i	$-0.481390\pi$
$179$	1.56350			0.116861			0.0584307	+	0.998291i	$0.481390\pi$
$180$	7.70410	+	19.3935i	0.574230	+	1.44550i
$181$	7.64219			0.568040			0.284020	−	0.958818i	$-0.408332\pi$
$181$	7.64219			0.568040			0.284020	+	0.958818i	$0.408332\pi$
$182$	−2.51735	+	3.60607i	−0.186598	+	0.267300i
$183$	−6.38474	+	6.55436i	−0.471973	+	0.484513i
$184$	0.720358	−	2.73516i	0.0531055	−	0.201638i
$185$		−	34.9627i		−	2.57051i
$186$	−0.612164	−	3.19913i	−0.0448861	−	0.234572i
$187$		−	2.74872i		−	0.201006i
$188$	−8.74714	−	23.8210i	−0.637951	−	1.73732i
$189$	−3.41572	+	3.69552i	−0.248457	+	0.268810i
$190$	−16.2784	−	11.3637i	−1.18096	−	0.824408i
$191$	−10.7297			−0.776375			−0.388187	−	0.921580i	$-0.626899\pi$
$191$	−10.7297			−0.776375			−0.388187	+	0.921580i	$0.626899\pi$
$192$	13.3034	−	3.87539i	0.960093	−	0.279682i
$193$	−6.69309			−0.481779			−0.240890	−	0.970553i	$-0.577439\pi$
$193$	−6.69309			−0.481779			−0.240890	+	0.970553i	$0.577439\pi$
$194$	11.2362	+	7.84384i	0.806715	+	0.563155i
$195$	13.8556	+	13.4970i	0.992221	+	0.966542i
$196$	4.17918	+	11.3811i	0.298513	+	0.812936i
$197$		−	5.79072i		−	0.412572i	−0.978492	−	0.206286i	$-0.933862\pi$
$197$		−	5.79072i		−	0.412572i	0.978492	−	0.206286i	$-0.0661377\pi$
$198$	5.07736	−	7.69550i	0.360832	−	0.546895i
$199$		−	21.6024i		−	1.53135i	−0.643226	−	0.765676i	$-0.722405\pi$
$199$		−	21.6024i		−	1.53135i	0.643226	−	0.765676i	$-0.277595\pi$
$200$	−5.11174	+	19.4090i	−0.361455	+	1.37242i
$201$	−17.4955	−	17.0427i	−1.23404	−	1.20210i
$202$	−7.86553	+	11.2673i	−0.553416	+	0.792764i
$203$	−8.29096			−0.581911
$204$	1.78819	−	4.00026i	0.125198	−	0.280074i
$205$	26.4334			1.84619
$206$	8.75773	−	12.5454i	0.610180	−	0.874077i
$207$	−0.0786444	−	2.99897i	−0.00546616	−	0.208443i
$208$	9.79178	−	8.31190i	0.678938	−	0.576327i
$209$			8.77100i			0.606703i
$210$	−8.10352	+	1.55063i	−0.559196	+	0.107004i
$211$			4.59546i			0.316365i	0.987410	+	0.158182i	$0.0505634\pi$
$211$			4.59546i			0.316365i	−0.987410	+	0.158182i	$0.949437\pi$
$212$	−15.7926	+	5.79910i	−1.08464	+	0.398283i
$213$	−14.5727	+	14.9598i	−0.998502	+	1.02503i
$214$	1.03646	+	0.723537i	0.0708509	+	0.0494600i
$215$	−5.70715			−0.389224
$216$	12.3955	−	7.89630i	0.843407	−	0.537275i
$217$	1.28780			0.0874219
$218$	−19.0035	−	13.2661i	−1.28708	−	0.898491i
$219$	−5.34321	+	5.48517i	−0.361061	+	0.370653i
$220$	14.1893	−	5.21034i	0.956640	−	0.351281i
$221$		−	4.06158i		−	0.273211i
$222$	−24.1851	+	4.62790i	−1.62320	+	0.310605i
$223$		−	19.0355i		−	1.27471i	−0.770568	−	0.637357i	$-0.780028\pi$
$223$		−	19.0355i		−	1.27471i	0.770568	−	0.637357i	$-0.219972\pi$
$224$	0.516376	+	5.45408i	0.0345018	+	0.364416i
$225$	0.558070	+	21.2810i	0.0372047	+	1.41874i
$226$	8.99770	−	12.8891i	0.598518	−	0.857371i
$227$	−2.91162			−0.193251			−0.0966256	−	0.995321i	$-0.530805\pi$
$227$	−2.91162			−0.193251			−0.0966256	+	0.995321i	$0.530805\pi$
$228$	−5.70601	+	12.7646i	−0.377890	+	0.845356i
$229$	−12.8792			−0.851082			−0.425541	−	0.904939i	$-0.639916\pi$
$229$	−12.8792			−0.851082			−0.425541	+	0.904939i	$0.639916\pi$
$230$	2.81542	−	4.03307i	0.185643	−	0.265933i
$231$	2.61110	+	2.54352i	0.171797	+	0.167351i
$232$	23.4155	+	6.16693i	1.53730	+	0.404879i
$233$		−	7.10818i		−	0.465672i	−0.972516	−	0.232836i	$-0.925199\pi$
$233$		−	7.10818i		−	0.465672i	0.972516	−	0.232836i	$-0.0748006\pi$
$234$	7.50243	−	11.3711i	0.490449	−	0.743349i
$235$		−	44.1286i		−	2.87863i
$236$	−0.858937	−	2.33913i	−0.0559120	−	0.152265i
$237$	−8.70234	−	8.47713i	−0.565278	−	0.550649i
$238$	1.42054	+	0.991657i	0.0920799	+	0.0642796i
$239$	7.54379			0.487967			0.243984	−	0.969779i	$-0.421546\pi$
$239$	7.54379			0.487967			0.243984	+	0.969779i	$0.421546\pi$
$240$	24.0395	+	1.64818i	1.55174	+	0.106390i
$241$	29.2219			1.88235			0.941174	−	0.337923i	$-0.109725\pi$
$241$	29.2219			1.88235			0.941174	+	0.337923i	$0.109725\pi$
$242$	7.27977	+	5.08189i	0.467961	+	0.326677i
$243$	10.2771	−	11.7210i	0.659275	−	0.751902i
$244$	3.64196	+	9.91811i	0.233153	+	0.634942i
$245$			21.0836i			1.34698i
$246$	−3.49891	−	18.2851i	−0.223082	−	1.16581i
$247$			12.9603i			0.824641i
$248$	−3.63704	−	0.957886i	−0.230952	−	0.0608258i
$249$	−10.1061	+	10.3746i	−0.640448	+	0.657463i
$250$	−5.90145	+	8.45378i	−0.373241	+	0.534664i
$251$	8.74423			0.551931			0.275965	−	0.961168i	$-0.411002\pi$
$251$	8.74423			0.551931			0.275965	+	0.961168i	$0.411002\pi$
$252$	2.14528	+	5.40029i	0.135140	+	0.340186i
$253$	−2.17307			−0.136620
$254$	9.61783	−	13.7775i	0.603477	−	0.864475i
$255$	5.31688	−	5.45814i	0.332956	−	0.341802i
$256$	2.59846	−	15.7876i	0.162404	−	0.986724i
$257$		−	4.42023i		−	0.275726i	−0.990451	−	0.137863i	$-0.955977\pi$
$257$		−	4.42023i		−	0.275726i	0.990451	−	0.137863i	$-0.0440234\pi$
$258$	0.755438	+	3.94787i	0.0470315	+	0.245784i
$259$		−	9.73568i		−	0.604946i
$260$	20.9664	−	7.69893i	1.30028	−	0.477467i
$261$	25.6739	−	0.673269i	1.58918	−	0.0416743i
$262$	22.8751	+	15.9688i	1.41323	+	0.986555i
$263$	6.11158			0.376856			0.188428	−	0.982087i	$-0.439661\pi$
$263$	6.11158			0.376856			0.188428	+	0.982087i	$0.439661\pi$
$264$	−5.48240	−	9.12562i	−0.337418	−	0.561643i
$265$	−29.2559			−1.79718
$266$	−4.53286	−	3.16432i	−0.277927	−	0.194017i
$267$	−3.72583	−	3.62941i	−0.228017	−	0.222116i
$268$	−26.4743	+	9.72144i	−1.61717	+	0.593831i
$269$			16.8382i			1.02664i	0.858196	+	0.513322i	$0.171585\pi$
$269$			16.8382i			1.02664i	−0.858196	+	0.513322i	$0.828415\pi$
$270$	24.9676	−	5.45977i	1.51948	−	0.332271i
$271$			19.5135i			1.18536i	0.805437	+	0.592682i	$0.201931\pi$
$271$			19.5135i			1.18536i	−0.805437	+	0.592682i	$0.798069\pi$
$272$	−3.27431	−	3.85727i	−0.198534	−	0.233882i
$273$	3.85822	+	3.75837i	0.233510	+	0.227467i
$274$	−4.11858	+	5.89983i	−0.248813	+	0.356422i
$275$	15.4204			0.929883
$276$	−3.16251	−	1.41370i	−0.190361	−	0.0850947i
$277$	−17.4006			−1.04550			−0.522751	−	0.852485i	$-0.675094\pi$
$277$	−17.4006			−1.04550			−0.522751	+	0.852485i	$0.675094\pi$
$278$	1.37628	−	1.97151i	0.0825438	−	0.118243i
$279$	−3.98784	+	0.104576i	−0.238746	+	0.00626082i
$280$	−2.42636	+	9.21275i	−0.145003	+	0.550567i
$281$			27.2670i			1.62661i	0.581834	+	0.813307i	$0.302335\pi$
$281$			27.2670i			1.62661i	−0.581834	+	0.813307i	$0.697665\pi$
$282$	−30.5255	+	5.84116i	−1.81777	+	0.347836i
$283$		−	18.6980i		−	1.11148i	−0.831356	−	0.555740i	$-0.812435\pi$
$283$		−	18.6980i		−	1.11148i	0.831356	−	0.555740i	$-0.187565\pi$
$284$	8.31249	+	22.6373i	0.493255	+	1.34328i
$285$	−16.9658	+	17.4166i	−1.00497	+	1.03167i
$286$	−8.09141	−	5.64849i	−0.478455	−	0.334002i
$287$	7.36062			0.434484
$288$	−2.04192	−	16.8473i	−0.120321	−	0.992735i
$289$	15.4000			0.905884
$290$	34.5268	+	24.1026i	2.02748	+	1.41535i
$291$	11.7108	−	12.0219i	0.686498	−	0.704736i
$292$	3.04786	+	8.30020i	0.178362	+	0.485732i
$293$		−	23.4417i		−	1.36948i	−0.728788	−	0.684739i	$-0.759916\pi$
$293$		−	23.4417i		−	1.36948i	0.728788	−	0.684739i	$-0.240084\pi$
$294$	14.5844	−	2.79077i	0.850578	−	0.162761i
$295$		−	4.33326i		−	0.252292i
$296$	−7.24153	+	27.4957i	−0.420905	+	1.59815i
$297$	−8.29211	−	7.66428i	−0.481157	−	0.444727i
$298$	3.05587	−	4.37751i	0.177022	−	0.253582i
$299$	−3.21098			−0.185696
$300$	22.4415	+	10.0318i	1.29566	+	0.579185i
$301$	−1.58921			−0.0916004
$302$	15.8627	−	22.7232i	0.912795	−	1.30757i
$303$	12.0551	+	11.7431i	0.692549	+	0.674626i
$304$	10.4481	+	12.3083i	0.599240	+	0.705931i
$305$			18.3734i			1.05206i
$306$	−4.47940	−	2.95543i	−0.256070	−	0.168951i
$307$			6.00519i			0.342734i	0.985207	+	0.171367i	$0.0548184\pi$
$307$			6.00519i			0.342734i	−0.985207	+	0.171367i	$0.945182\pi$
$308$	3.95113	−	1.45087i	0.225136	−	0.0826708i
$309$	−13.4226	−	13.0752i	−0.763583	−	0.743822i
$310$	−5.36292	−	3.74377i	−0.304593	−	0.212632i
$311$	−21.3726			−1.21193			−0.605965	−	0.795491i	$-0.707213\pi$
$311$	−21.3726			−1.21193			−0.605965	+	0.795491i	$0.707213\pi$
$312$	−8.10093	−	13.4842i	−0.458625	−	0.763395i
$313$	16.5423			0.935026			0.467513	−	0.883986i	$-0.345150\pi$
$313$	16.5423			0.935026			0.467513	+	0.883986i	$0.345150\pi$
$314$	−12.0563	−	8.41631i	−0.680376	−	0.474960i
$315$	0.264896	+	10.1013i	0.0149252	+	0.569146i
$316$	−13.1684	+	4.83549i	−0.740783	+	0.272018i
$317$			11.2127i			0.629771i	0.949130	+	0.314885i	$0.101966\pi$
$317$			11.2127i			0.629771i	−0.949130	+	0.314885i	$0.898034\pi$
$318$	3.87252	+	20.2375i	0.217160	+	1.13486i
$319$		−	18.6035i		−	1.04160i
$320$	13.7051	−	24.2141i	0.766141	−	1.35361i
$321$	1.08023	−	1.10893i	0.0602927	−	0.0618945i
$322$	0.783980	−	1.12304i	0.0436895	−	0.0625848i
$323$	5.10543			0.284074
$324$	−7.08163	−	16.5484i	−0.393424	−	0.919357i
$325$	22.7855			1.26391
$326$	−4.57950	+	6.56009i	−0.253635	+	0.363330i
$327$	−19.8061	+	20.3323i	−1.09528	+	1.12438i
$328$	−20.7880	−	5.47493i	−1.14782	−	0.302302i
$329$		−	12.2880i		−	0.677459i
$330$	−3.47936	−	18.1829i	−0.191532	−	1.00094i
$331$		−	10.8174i		−	0.594576i	−0.954788	−	0.297288i	$-0.903918\pi$
$331$		−	10.8174i		−	0.594576i	0.954788	−	0.297288i	$-0.0960822\pi$
$332$	5.76469	+	15.6989i	0.316378	+	0.861589i
$333$	0.790587	+	30.1477i	0.0433239	+	1.65208i
$334$	−16.7703	−	11.7071i	−0.917628	−	0.640582i
$335$	−49.0438			−2.67955
$336$	6.69401	+	0.458950i	0.365188	+	0.0250378i
$337$	−23.7190			−1.29205			−0.646027	−	0.763315i	$-0.723571\pi$
$337$	−23.7190			−1.29205			−0.646027	+	0.763315i	$0.723571\pi$
$338$	3.11887	+	2.17724i	0.169644	+	0.118426i
$339$	−13.7904	−	13.4335i	−0.748989	−	0.729606i
$340$	−3.03284	−	8.25929i	−0.164479	−	0.447923i
$341$			2.88961i			0.156481i
$342$	14.2935	+	9.43060i	0.772904	+	0.509948i
$343$			12.6502i			0.683045i
$344$	4.48827	+	1.18207i	0.241991	+	0.0637331i
$345$	−4.31507	−	4.20339i	−0.232316	−	0.226303i
$346$	4.20622	−	6.02537i	0.226128	−	0.323926i
$347$	−21.0417			−1.12958			−0.564789	−	0.825235i	$-0.691042\pi$
$347$	−21.0417			−1.12958			−0.564789	+	0.825235i	$0.691042\pi$
$348$	12.1026	−	27.0740i	0.648766	−	1.45132i
$349$	5.31487			0.284499			0.142249	−	0.989831i	$-0.454567\pi$
$349$	5.31487			0.284499			0.142249	+	0.989831i	$0.454567\pi$
$350$	−5.56321	+	7.96925i	−0.297366	+	0.425974i
$351$	−12.2526	−	11.3249i	−0.653997	−	0.604480i
$352$	−12.2380	+	1.15866i	−0.652288	+	0.0617567i
$353$			4.77728i			0.254269i	0.991885	+	0.127135i	$0.0405780\pi$
$353$			4.77728i			0.254269i	−0.991885	+	0.127135i	$0.959422\pi$
$354$	−2.99750	+	0.573580i	−0.159315	+	0.0304854i
$355$			41.9358i			2.22572i
$356$	−5.63795	+	2.07027i	−0.298811	+	0.109724i
$357$	1.48053	−	1.51987i	0.0783581	−	0.0804399i
$358$	−1.81305	−	1.26566i	−0.0958228	−	0.0668924i
$359$	2.32014			0.122452			0.0612261	−	0.998124i	$-0.480499\pi$
$359$	2.32014			0.122452			0.0612261	+	0.998124i	$0.480499\pi$
$360$	6.76539	−	28.7254i	0.356567	−	1.51396i
$361$	2.70888			0.142573
$362$	−8.86197	−	6.18641i	−0.465775	−	0.325150i
$363$	7.58721	−	7.78879i	0.398225	−	0.408805i
$364$	5.83829	−	2.14384i	0.306009	−	0.112368i
$365$			15.3762i			0.804826i
$366$	12.7096	−	2.43203i	0.664342	−	0.127124i
$367$		−	5.02862i		−	0.262492i	−0.991350	−	0.131246i	$-0.958102\pi$
$367$		−	5.02862i		−	0.262492i	0.991350	−	0.131246i	$-0.0418977\pi$
$368$	−3.04946	+	2.58858i	−0.158964	+	0.134939i
$369$	−22.7930	+	0.597720i	−1.18656	+	0.0311161i
$370$	−28.3026	+	40.5431i	−1.47138	+	2.10774i
$371$	−8.14658			−0.422949
$372$	−1.87985	+	4.20530i	−0.0974656	+	0.218035i
$373$	−2.47323			−0.128059			−0.0640296	−	0.997948i	$-0.520395\pi$
$373$	−2.47323			−0.128059			−0.0640296	+	0.997948i	$0.520395\pi$
$374$	−2.22511	+	3.18745i	−0.115058	+	0.164819i
$375$	9.04488	+	8.81080i	0.467076	+	0.454988i
$376$	−9.13998	+	34.7040i	−0.471358	+	1.78972i
$377$		−	27.4890i		−	1.41575i
$378$	6.95245	−	1.52032i	0.357596	−	0.0781970i
$379$		−	33.4612i		−	1.71879i	−0.511315	−	0.859393i	$-0.670842\pi$
$379$		−	33.4612i		−	1.71879i	0.511315	−	0.859393i	$-0.329158\pi$
$380$	9.67760	+	26.3549i	0.496450	+	1.35198i
$381$	−14.7408	−	14.3593i	−0.755195	−	0.735650i
$382$	12.4423	+	8.68578i	0.636603	+	0.444403i
$383$	21.8474			1.11635			0.558176	−	0.829722i	$-0.311501\pi$
$383$	21.8474			1.11635			0.558176	+	0.829722i	$0.311501\pi$
$384$	−18.5640	−	6.27527i	−0.947339	−	0.320234i
$385$	7.31949			0.373036
$386$	7.76138	+	5.41810i	0.395044	+	0.275774i
$387$	4.92117	−	0.129052i	0.250157	−	0.00656007i
$388$	−6.68002	−	18.1916i	−0.339127	−	0.923539i
$389$			6.25554i			0.317168i	0.987345	+	0.158584i	$0.0506929\pi$
$389$			6.25554i			0.317168i	−0.987345	+	0.158584i	$0.949307\pi$
$390$	−5.14119	−	26.8675i	−0.260334	−	1.36049i
$391$			1.26490i			0.0639688i
$392$	4.36686	−	16.5807i	0.220560	−	0.837453i
$393$	23.8412	−	24.4746i	1.20263	−	1.23458i
$394$	−4.68763	+	6.71499i	−0.236159	+	0.338296i
$395$	−24.3946			−1.22743
$396$	−12.1173	+	4.81363i	−0.608918	+	0.241894i
$397$	29.8282			1.49704			0.748518	−	0.663114i	$-0.230766\pi$
$397$	29.8282			1.49704			0.748518	+	0.663114i	$0.230766\pi$
$398$	−17.4873	+	25.0504i	−0.876558	+	1.25566i
$399$	−4.72429	+	4.84981i	−0.236510	+	0.242794i
$400$	21.6393	−	18.3689i	1.08197	−	0.918445i
$401$		−	17.6227i		−	0.880033i	−0.897990	−	0.440017i	$-0.854973\pi$
$401$		−	17.6227i		−	0.880033i	0.897990	−	0.440017i	$-0.145027\pi$
$402$	6.49178	+	33.9256i	0.323780	+	1.69206i
$403$			4.26976i			0.212692i
$404$	18.2419	−	6.69848i	0.907569	−	0.333262i
$405$	−1.64056	−	31.2585i	−0.0815202	−	1.55325i
$406$	9.61429	+	6.71159i	0.477149	+	0.333091i
$407$	21.8452			1.08283
$408$	−5.31185	+	3.19120i	−0.262976	+	0.157988i
$409$	−31.3375			−1.54954			−0.774769	−	0.632244i	$-0.782134\pi$
$409$	−31.3375			−1.54954			−0.774769	+	0.632244i	$0.782134\pi$
$410$	−30.6525	−	21.3980i	−1.51382	−	1.05677i
$411$	6.31236	+	6.14900i	0.311366	+	0.303308i
$412$	−20.3111	+	7.45831i	−1.00066	+	0.367444i
$413$		−	1.20664i		−	0.0593746i
$414$	−2.33649	+	3.54130i	−0.114832	+	0.174045i
$415$			29.0823i			1.42760i
$416$	−18.0832	+	1.71206i	−0.886602	+	0.0839408i
$417$	−2.10936	−	2.05477i	−0.103296	−	0.100623i
$418$	7.10019	−	10.1710i	0.347281	−	0.497478i
$419$	−8.72402			−0.426196			−0.213098	−	0.977031i	$-0.568355\pi$
$419$	−8.72402			−0.426196			−0.213098	+	0.977031i	$0.568355\pi$
$420$	10.6522	+	4.76172i	0.519773	+	0.232348i
$421$	7.78947			0.379636			0.189818	−	0.981819i	$-0.439210\pi$
$421$	7.78947			0.379636			0.189818	+	0.981819i	$0.439210\pi$
$422$	3.72006	−	5.32895i	0.181090	−	0.259409i
$423$	0.997849	+	38.0512i	0.0485171	+	1.85011i
$424$	23.0077	+	6.05953i	1.11735	+	0.294277i
$425$		−	8.97589i		−	0.435395i
$426$	29.0087	−	5.55091i	1.40548	−	0.268942i
$427$			5.11623i			0.247592i
$428$	−0.616182	−	1.67804i	−0.0297843	−	0.0811113i
$429$	−8.43313	+	8.65718i	−0.407156	+	0.417973i
$430$	6.61808	+	4.61998i	0.319152	+	0.222795i
$431$	12.1743			0.586416			0.293208	−	0.956049i	$-0.405277\pi$
$431$	12.1743			0.586416			0.293208	+	0.956049i	$0.405277\pi$
$432$	−20.7661	−	0.877606i	−0.999108	−	0.0422238i
$433$	35.1939			1.69131			0.845656	−	0.533729i	$-0.179210\pi$
$433$	35.1939			1.69131			0.845656	+	0.533729i	$0.179210\pi$
$434$	−1.49335	−	1.04249i	−0.0716832	−	0.0500410i
$435$	35.9849	−	36.9410i	1.72535	−	1.77118i
$436$	11.2977	+	30.7669i	0.541062	+	1.47347i
$437$		−	4.03623i		−	0.193079i
$438$	10.6363	−	2.03530i	0.508224	−	0.0972502i
$439$		−	18.3988i		−	0.878127i	−0.898456	−	0.439063i	$-0.855310\pi$
$439$		−	18.3988i		−	0.878127i	0.898456	−	0.439063i	$-0.144690\pi$
$440$	−20.6718	−	5.44434i	−0.985491	−	0.259549i
$441$	−0.476748	−	18.1800i	−0.0227023	−	0.865713i
$442$	−3.28788	+	4.70985i	−0.156388	+	0.224025i
$443$	−10.1139			−0.480528			−0.240264	−	0.970708i	$-0.577234\pi$
$443$	−10.1139			−0.480528			−0.240264	+	0.970708i	$0.577234\pi$
$444$	31.7917	+	14.2115i	1.50877	+	0.674447i
$445$	−10.4443			−0.495109
$446$	−15.4094	+	22.0738i	−0.729657	+	1.04523i
$447$	−4.68359	−	4.56238i	−0.221526	−	0.215793i
$448$	3.81632	−	6.74262i	0.180304	−	0.318559i
$449$		−	7.51879i		−	0.354834i	−0.984136	−	0.177417i	$-0.943226\pi$
$449$		−	7.51879i		−	0.354834i	0.984136	−	0.177417i	$-0.0567741\pi$
$450$	16.5800	−	25.1295i	0.781589	−	1.18462i
$451$			16.5160i			0.777706i
$452$	−20.8677	+	7.66267i	−0.981532	+	0.360422i
$453$	−24.3120	−	23.6828i	−1.14228	−	1.11272i
$454$	3.37635	+	2.35698i	0.158460	+	0.110619i
$455$	10.8155			0.507037
$456$	16.9498	−	10.1829i	0.793746	−	0.476859i
$457$	−2.08553			−0.0975568			−0.0487784	−	0.998810i	$-0.515533\pi$
$457$	−2.08553			−0.0975568			−0.0487784	+	0.998810i	$0.515533\pi$
$458$	14.9349	+	10.4258i	0.697861	+	0.487166i
$459$	−4.46123	+	4.82668i	−0.208232	+	0.225290i
$460$	−6.52959	+	2.39769i	−0.304444	+	0.111793i
$461$			15.7777i			0.734843i	0.930055	+	0.367421i	$0.119759\pi$
$461$			15.7777i			0.734843i	−0.930055	+	0.367421i	$0.880241\pi$
$462$	−0.968859	−	5.06319i	−0.0450754	−	0.235561i
$463$		−	2.55088i		−	0.118550i	−0.998242	−	0.0592748i	$-0.981121\pi$
$463$		−	2.55088i		−	0.118550i	0.998242	−	0.0592748i	$-0.0188788\pi$
$464$	−22.1607	−	26.1062i	−1.02878	−	1.21195i
$465$	−5.58941	+	5.73791i	−0.259203	+	0.266089i
$466$	−5.75412	+	8.24272i	−0.266554	+	0.381837i
$467$	−33.4176			−1.54638			−0.773191	−	0.634173i	$-0.781341\pi$
$467$	−33.4176			−1.54638			−0.773191	+	0.634173i	$0.781341\pi$
$468$	−17.9049	+	7.11274i	−0.827652	+	0.328787i
$469$	−13.6567			−0.630607
$470$	−35.7224	+	51.1720i	−1.64775	+	2.36039i
$471$	−12.5655	+	12.8993i	−0.578986	+	0.594368i
$472$	−0.897512	+	3.40780i	−0.0413113	+	0.156857i
$473$		−	3.56591i		−	0.163961i
$474$	3.22904	+	16.8748i	0.148315	+	0.775084i
$475$			28.6415i			1.31416i
$476$	−0.844521	−	2.29987i	−0.0387085	−	0.105415i
$477$	25.2268	−	0.661544i	1.15506	−	0.0302900i
$478$	−8.74787	−	6.10675i	−0.400118	−	0.279316i
$479$	39.1406			1.78838			0.894191	−	0.447686i	$-0.147752\pi$
$479$	39.1406			1.78838			0.894191	+	0.447686i	$0.147752\pi$
$480$	−26.5423	−	21.3714i	−1.21148	−	0.975466i
$481$	32.2790			1.47180
$482$	−33.8860	−	23.6553i	−1.54347	−	1.07747i
$483$	−1.20157	−	1.17047i	−0.0546733	−	0.0532584i
$484$	−4.32787	−	11.7860i	−0.196721	−	0.535729i
$485$		−	33.7001i		−	1.53024i
$486$	−21.4056	+	5.27244i	−0.970980	+	0.239163i
$487$		−	21.4979i		−	0.974164i	−0.873356	−	0.487082i	$-0.838061\pi$
$487$		−	21.4979i		−	0.974164i	0.873356	−	0.487082i	$-0.161939\pi$
$488$	3.80552	−	14.4493i	0.172268	−	0.654091i
$489$	7.01879	+	6.83714i	0.317401	+	0.309186i
$490$	17.0673	−	24.4488i	0.771022	−	1.10448i
$491$	12.9162			0.582901			0.291450	−	0.956586i	$-0.405862\pi$
$491$	12.9162			0.582901			0.291450	+	0.956586i	$0.405862\pi$
$492$	−10.7445	+	24.0360i	−0.484401	+	1.08363i
$493$	−10.8287			−0.487701
$494$	10.4914	−	15.0289i	0.472031	−	0.676180i
$495$	−22.6657	+	0.594381i	−1.01875	+	0.0267154i
$496$	3.44214	+	4.05498i	0.154557	+	0.182074i
$497$			11.6774i			0.523803i
$498$	20.1175	−	3.84954i	0.901485	−	0.172502i
$499$			0.320130i			0.0143310i	0.999974	+	0.00716550i	$0.00228087\pi$
$499$			0.320130i			0.0143310i	−0.999974	+	0.00716550i	$0.997719\pi$
$500$	13.6868	−	5.02583i	0.612091	−	0.224762i
$501$	−17.4785	+	17.9429i	−0.780882	+	0.801629i
$502$	−10.1399	−	7.07852i	−0.452566	−	0.315930i
$503$	43.6123			1.94457			0.972287	−	0.233788i	$-0.0751123\pi$
$503$	43.6123			1.94457			0.972287	+	0.233788i	$0.0751123\pi$
$504$	1.88388	−	7.99885i	0.0839149	−	0.356297i
$505$	33.7933			1.50378
$506$	2.51992	+	1.75912i	0.112024	+	0.0782022i
$507$	3.25059	−	3.33695i	0.144364	−	0.148199i
$508$	−22.3059	+	8.19079i	−0.989664	+	0.363408i
$509$			29.9888i			1.32923i	0.747185	+	0.664616i	$0.231405\pi$
$509$			29.9888i			1.32923i	−0.747185	+	0.664616i	$0.768595\pi$
$510$	−10.5839	+	2.02527i	−0.468664	+	0.0896803i
$511$			4.28163i			0.189408i
$512$	−15.7934	+	16.2040i	−0.697975	+	0.716122i
$513$	14.2355	−	15.4016i	0.628513	−	0.679999i
$514$	−3.57821	+	5.12575i	−0.157828	+	0.226087i
$515$	−37.6265			−1.65802
$516$	2.31982	−	5.18953i	0.102124	−	0.228456i
$517$	27.5721			1.21262
$518$	−7.88110	+	11.2896i	−0.346276	+	0.496037i
$519$	−6.44668	−	6.27984i	−0.282978	−	0.275654i
$520$	−30.5452	−	8.04469i	−1.33950	−	0.352783i
$521$			23.0966i			1.01188i	0.862569	+	0.505940i	$0.168854\pi$
$521$			23.0966i			1.01188i	−0.862569	+	0.505940i	$0.831146\pi$
$522$	−30.3168	−	20.0025i	−1.32693	−	0.875486i
$523$			0.00853164i			0.000373063i	1.00000		0.000186531i	$5.93747e-5\pi$
$523$			0.00853164i			0.000373063i	−1.00000		0.000186531i	$0.999941\pi$
$524$	−13.5994	−	37.0352i	−0.594094	−	1.61789i
$525$	8.52648	+	8.30581i	0.372126	+	0.362495i
$526$	−7.08706	−	4.94737i	−0.309011	−	0.215716i
$527$	1.68199			0.0732685
$528$	−1.02981	+	15.0202i	−0.0448165	+	0.653671i
$529$	1.00000			0.0434783
$530$	33.9255	+	23.6829i	1.47363	+	1.02872i
$531$	0.0979850	+	3.73649i	0.00425219	+	0.162150i
$532$	2.69481	+	7.33876i	0.116835	+	0.318176i
$533$			24.4044i			1.05707i
$534$	1.38249	+	7.22478i	0.0598260	+	0.312647i
$535$		−	3.10859i		−	0.134396i
$536$	38.5695	+	10.1580i	1.66595	+	0.438760i
$537$	−1.88962	+	1.93983i	−0.0815432	+	0.0837096i
$538$	13.6306	−	19.5258i	0.587659	−	0.841816i
$539$	−13.1733			−0.567415
$540$	−33.3724	−	13.8802i	−1.43612	−	0.597310i
$541$	−13.8833			−0.596889			−0.298444	−	0.954427i	$-0.596468\pi$
$541$	−13.8833			−0.596889			−0.298444	+	0.954427i	$0.596468\pi$
$542$	15.7964	−	22.6281i	0.678511	−	0.971961i
$543$	−9.23624	+	9.48162i	−0.396365	+	0.406895i
$544$	0.674433	+	7.12351i	0.0289161	+	0.305418i
$545$			56.9960i			2.44144i
$546$	−1.43161	−	7.48150i	−0.0612672	−	0.320179i
$547$			30.7960i			1.31674i	0.752694	+	0.658371i	$0.228754\pi$
$547$			30.7960i			1.31674i	−0.752694	+	0.658371i	$0.771246\pi$
$548$	9.55191	−	3.50749i	0.408037	−	0.149832i
$549$	−0.415464	−	15.8430i	−0.0177316	−	0.676163i
$550$	−17.8816	−	12.4829i	−0.762475	−	0.532272i
$551$	34.5538			1.47204
$552$	2.52288	+	4.19941i	0.107381	+	0.178739i
$553$	−6.79291			−0.288864
$554$	20.1780	+	14.0859i	0.857280	+	0.598454i
$555$	43.3780	+	42.2554i	1.84129	+	1.79364i
$556$	−3.19190	+	1.17208i	−0.135367	+	0.0497071i
$557$		−	1.22730i		−	0.0520025i	−0.999662	−	0.0260013i	$-0.991723\pi$
$557$		−	1.22730i		−	0.0520025i	0.999662	−	0.0260013i	$-0.00827739\pi$
$558$	4.70900	+	3.10692i	0.199348	+	0.131526i
$559$		−	5.26907i		−	0.222858i
$560$	10.2714	−	8.71906i	0.434047	−	0.368447i
$561$	3.41032	+	3.32206i	0.143984	+	0.140258i
$562$	22.0729	−	31.6192i	0.931087	−	1.33377i
$563$	38.4789			1.62169			0.810845	−	0.585260i	$-0.199008\pi$
$563$	38.4789			1.62169			0.810845	+	0.585260i	$0.199008\pi$
$564$	40.1262	+	17.9372i	1.68962	+	0.755291i
$565$	−38.6575			−1.62633
$566$	−15.1361	+	21.6824i	−0.636219	+	0.911378i
$567$	−0.456829	−	8.70421i	−0.0191850	−	0.365542i
$568$	8.68580	−	32.9795i	0.364448	−	1.38379i
$569$			20.2841i			0.850352i	0.905111	+	0.425176i	$0.139788\pi$
$569$			20.2841i			0.850352i	−0.905111	+	0.425176i	$0.860212\pi$
$570$	33.7726	−	6.46250i	1.41458	−	0.270684i
$571$			24.8535i			1.04009i	0.854140	+	0.520043i	$0.174084\pi$
$571$			24.8535i			1.04009i	−0.854140	+	0.520043i	$0.825916\pi$
$572$	4.81040	+	13.1001i	0.201133	+	0.547743i
$573$	12.9678	−	13.3123i	0.541736	−	0.556129i
$574$	−8.53546	−	5.95847i	−0.356263	−	0.248702i
$575$	−7.09612			−0.295928
$576$	−11.2702	+	21.1892i	−0.469590	+	0.882885i
$577$	−8.07340			−0.336100			−0.168050	−	0.985778i	$-0.553747\pi$
$577$	−8.07340			−0.336100			−0.168050	+	0.985778i	$0.553747\pi$
$578$	−17.8580	−	12.4664i	−0.742797	−	0.518535i
$579$	8.08917	−	8.30408i	0.336174	−	0.345106i
$580$	−20.5264	−	55.8993i	−0.852313	−	2.32109i
$581$			8.09824i			0.335972i
$582$	−23.3118	+	4.46078i	−0.966303	+	0.184905i
$583$		−	18.2795i		−	0.757060i
$584$	3.18474	−	12.0923i	0.131785	−	0.500381i
$585$	−33.4914	+	0.878272i	−1.38470	+	0.0363121i
$586$	−18.9762	+	27.1833i	−0.783900	+	1.12293i
$587$	29.4596			1.21593			0.607963	−	0.793965i	$-0.291987\pi$
$587$	29.4596			1.21593			0.607963	+	0.793965i	$0.291987\pi$
$588$	−19.1714	−	8.56995i	−0.790613	−	0.353419i
$589$	−5.36712			−0.221148
$590$	−3.50780	+	5.02490i	−0.144414	+	0.206872i
$591$	7.18452	+	6.99858i	0.295531	+	0.287883i
$592$	30.6553	−	26.0222i	1.25992	−	1.06951i
$593$		−	33.5340i		−	1.37708i	−0.725201	−	0.688538i	$-0.758253\pi$
$593$		−	33.5340i		−	1.37708i	0.725201	−	0.688538i	$-0.241747\pi$
$594$	3.41134	+	15.6001i	0.139969	+	0.640080i
$595$		−	4.26053i		−	0.174665i
$596$	−7.08724	+	2.60246i	−0.290305	+	0.106601i
$597$	26.8019	+	26.1083i	1.09693	+	1.06854i
$598$	3.72349	+	2.59931i	0.152265	+	0.106294i
$599$	−7.01737			−0.286722			−0.143361	−	0.989670i	$-0.545791\pi$
$599$	−7.01737			−0.286722			−0.143361	+	0.989670i	$0.545791\pi$
$600$	−17.9026	−	29.7995i	−0.730873	−	1.21656i
$601$	−12.3163			−0.502394			−0.251197	−	0.967936i	$-0.580824\pi$
$601$	−12.3163			−0.502394			−0.251197	+	0.967936i	$0.580824\pi$
$602$	1.84286	+	1.28647i	0.0751095	+	0.0524328i
$603$	42.2896	−	1.10899i	1.72216	−	0.0451617i
$604$	−36.7891	+	13.5091i	−1.49693	+	0.549676i
$605$		−	21.8337i		−	0.887668i
$606$	−4.47311	−	23.3762i	−0.181708	−	0.949593i
$607$			5.90740i			0.239774i	0.992788	+	0.119887i	$0.0382532\pi$
$607$			5.90740i			0.239774i	−0.992788	+	0.119887i	$0.961747\pi$
$608$	−2.15207	−	22.7307i	−0.0872781	−	0.921851i
$609$	10.0203	−	10.2865i	0.406044	−	0.416832i
$610$	14.8734	−	21.3060i	0.602205	−	0.862653i
$611$	40.7413			1.64822
$612$	2.80192	+	7.05325i	0.113261	+	0.285111i
$613$	22.8771			0.923998			0.461999	−	0.886880i	$-0.347132\pi$
$613$	22.8771			0.923998			0.461999	+	0.886880i	$0.347132\pi$
$614$	4.86124	−	6.96369i	0.196184	−	0.281031i
$615$	−31.9470	+	32.7958i	−1.28823	+	1.32245i
$616$	−5.75626	−	1.51602i	−0.231926	−	0.0610824i
$617$		−	21.9932i		−	0.885412i	−0.896667	−	0.442706i	$-0.854019\pi$
$617$		−	21.9932i		−	0.885412i	0.896667	−	0.442706i	$-0.145981\pi$
$618$	4.98050	+	26.0278i	0.200345	+	1.04699i
$619$		−	24.4284i		−	0.981860i	−0.871199	−	0.490930i	$-0.836657\pi$
$619$		−	24.4284i		−	0.981860i	0.871199	−	0.490930i	$-0.163343\pi$
$620$	3.18829	+	8.68264i	0.128045	+	0.348703i
$621$	3.81585	+	3.52694i	0.153125	+	0.141531i
$622$	24.7839	+	17.3013i	0.993745	+	0.693718i
$623$	−2.90832			−0.116519
$624$	−1.52167	+	22.1942i	−0.0609154	+	0.888481i
$625$	−10.1257			−0.405029
$626$	−19.1826	−	13.3911i	−0.766693	−	0.535217i
$627$	−10.8821	−	10.6005i	−0.434590	−	0.423343i
$628$	7.16755	+	19.5193i	0.286016	+	0.778905i
$629$		−	12.7157i		−	0.507007i
$630$	7.86993	−	11.9281i	0.313546	−	0.475226i
$631$		−	35.8355i		−	1.42659i	−0.700864	−	0.713295i	$-0.747202\pi$
$631$		−	35.8355i		−	1.42659i	0.700864	−	0.713295i	$-0.252798\pi$
$632$	19.1846	+	5.05266i	0.763124	+	0.200984i
$633$	−5.70156	−	5.55401i	−0.226617	−	0.220752i
$634$	9.07680	−	13.0024i	0.360486	−	0.516392i
$635$	−41.3218			−1.63981
$636$	11.8918	−	26.6025i	0.471541	−	1.05486i
$637$	−19.4652			−0.771240
$638$	−15.0597	+	21.5728i	−0.596217	+	0.854076i
$639$	−0.948265	−	36.1604i	−0.0375128	−	1.43048i
$640$	−35.4941	+	16.9845i	−1.40303	+	0.671371i
$641$			1.09239i			0.0431470i	0.999767	+	0.0215735i	$0.00686759\pi$
$641$			1.09239i			0.0431470i	−0.999767	+	0.0215735i	$0.993132\pi$
$642$	−2.15034	+	0.411474i	−0.0848671	+	0.0162396i
$643$		−	2.35877i		−	0.0930209i	−0.998918	−	0.0465104i	$-0.985190\pi$
$643$		−	2.35877i		−	0.0930209i	0.998918	−	0.0465104i	$-0.0148101\pi$
$644$	−1.81822	+	0.667657i	−0.0716480	+	0.0263094i
$645$	6.89758	−	7.08083i	0.271592	−	0.278807i
$646$	−5.92031	−	4.13288i	−0.232932	−	0.162606i
$647$	−29.6773			−1.16673			−0.583367	−	0.812209i	$-0.698265\pi$
$647$	−29.6773			−1.16673			−0.583367	+	0.812209i	$0.698265\pi$
$648$	−5.18412	+	24.9224i	−0.203652	+	0.979043i
$649$	2.70748			0.106278
$650$	−26.4223	−	18.4450i	−1.03637	−	0.723474i
$651$	−1.55642	+	1.59777i	−0.0610010	+	0.0626216i
$652$	10.6209	−	3.90002i	0.415946	−	0.152737i
$653$		−	24.5837i		−	0.962036i	−0.876711	−	0.481018i	$-0.840267\pi$
$653$		−	24.5837i		−	0.962036i	0.876711	−	0.481018i	$-0.159733\pi$
$654$	39.4265	−	7.54438i	1.54170	−	0.295009i
$655$		−	68.6079i		−	2.68073i
$656$	19.6740	+	23.1768i	0.768140	+	0.904902i
$657$	−0.347691	−	13.2586i	−0.0135647	−	0.517267i
$658$	−9.94722	+	14.2493i	−0.387783	+	0.555495i
$659$	17.1318			0.667360			0.333680	−	0.942686i	$-0.391710\pi$
$659$	17.1318			0.667360			0.333680	+	0.942686i	$0.391710\pi$
$660$	−10.6845	+	23.9017i	−0.415893	+	0.930371i
$661$	−14.2786			−0.555372			−0.277686	−	0.960672i	$-0.589568\pi$
$661$	−14.2786			−0.555372			−0.277686	+	0.960672i	$0.589568\pi$
$662$	−8.75674	+	12.5439i	−0.340340	+	0.487534i
$663$	5.03918	+	4.90876i	0.195705	+	0.190641i
$664$	6.02358	−	22.8712i	0.233760	−	0.887574i
$665$			13.5951i			0.527196i
$666$	23.4880	−	35.5996i	0.910141	−	1.37946i
$667$			8.56092i			0.331480i
$668$	9.97003	+	27.1513i	0.385752	+	1.05051i
$669$	23.6173	+	23.0061i	0.913097	+	0.889466i
$670$	56.8718	+	39.7013i	2.19715	+	1.53380i
$671$	−11.4799			−0.443178
$672$	−7.39093	−	5.95105i	−0.285111	−	0.229567i
$673$	49.5003			1.90809			0.954047	−	0.299656i	$-0.0968719\pi$
$673$	49.5003			1.90809			0.954047	+	0.299656i	$0.0968719\pi$
$674$	27.5048	+	19.2007i	1.05944	+	0.739582i
$675$	−27.0777	−	25.0275i	−1.04222	−	0.963311i
$676$	−1.85419	−	5.04950i	−0.0713151	−	0.194212i
$677$		−	27.9706i		−	1.07500i	−0.843265	−	0.537499i	$-0.819369\pi$
$677$		−	27.9706i		−	1.07500i	0.843265	−	0.537499i	$-0.180631\pi$
$678$	5.11697	+	26.7410i	0.196516	+	1.02698i
$679$		−	9.38410i		−	0.360129i
$680$	−3.16904	+	12.0327i	−0.121527	+	0.461432i
$681$	3.51894	−	3.61243i	0.134846	−	0.138429i
$682$	2.33916	−	3.35083i	0.0895711	−	0.128310i
$683$	6.90440			0.264190			0.132095	−	0.991237i	$-0.457830\pi$
$683$	6.90440			0.264190			0.132095	+	0.991237i	$0.457830\pi$
$684$	−8.94076	−	22.5065i	−0.341859	−	0.860558i
$685$	17.6950			0.676090
$686$	10.2404	−	14.6693i	0.390980	−	0.560076i
$687$	15.5656	−	15.9792i	0.593865	−	0.609643i
$688$	−4.24775	−	5.00403i	−0.161944	−	0.190777i
$689$		−	27.0103i		−	1.02901i
$690$	1.60113	+	8.36738i	0.0609538	+	0.318541i
$691$		−	22.9606i		−	0.873464i	−0.899592	−	0.436732i	$-0.856136\pi$
$691$		−	22.9606i		−	0.873464i	0.899592	−	0.436732i	$-0.143864\pi$
$692$	−9.75516	+	3.58213i	−0.370836	+	0.136172i
$693$	−6.31146	+	0.165511i	−0.239753	+	0.00628723i
$694$	24.4002	+	17.0334i	0.926219	+	0.646579i
$695$	−5.91302			−0.224294
$696$	−35.9509	+	21.5982i	−1.36271	+	0.818677i
$697$	9.61362			0.364142
$698$	−6.16318	−	4.30242i	−0.233280	−	0.162849i
$699$	8.81908	+	8.59084i	0.333568	+	0.324935i
$700$	12.9023	−	4.73777i	0.487662	−	0.179071i
$701$		−	5.56795i		−	0.210299i	−0.994456	−	0.105149i	$-0.966468\pi$
$701$		−	5.56795i		−	0.210299i	0.994456	−	0.105149i	$-0.0335321\pi$
$702$	5.04069	+	23.0511i	0.190248	+	0.870008i
$703$			40.5749i			1.53031i
$704$	15.1293	+	8.56316i	0.570206	+	0.322736i
$705$	54.7501	+	53.3331i	2.06201	+	2.00864i
$706$	3.86724	−	5.53979i	0.145546	−	0.208493i
$707$	9.41004			0.353901
$708$	3.94025	+	1.76136i	0.148084	+	0.0661961i
$709$	−20.8573			−0.783312			−0.391656	−	0.920112i	$-0.628098\pi$
$709$	−20.8573			−0.783312			−0.391656	+	0.920112i	$0.628098\pi$
$710$	33.9473	−	48.6292i	1.27402	−	1.82502i
$711$	21.0350	−	0.551619i	0.788876	−	0.0206873i
$712$	8.21373	+	2.16325i	0.307823	+	0.0810712i
$713$		−	1.32974i		−	0.0497990i
$714$	−2.94719	+	0.563954i	−0.110296	+	0.0211054i
$715$			24.2680i			0.907573i
$716$	1.07787	+	2.93536i	0.0402820	+	0.109699i
$717$	−9.11731	+	9.35954i	−0.340492	+	0.349538i
$718$	−2.69046	−	1.87817i	−0.100407	−	0.0700927i
$719$	−7.25040			−0.270394			−0.135197	−	0.990819i	$-0.543167\pi$
$719$	−7.25040			−0.270394			−0.135197	+	0.990819i	$0.543167\pi$
$720$	−31.0987	+	27.8337i	−1.15898	+	1.03730i
$721$	−10.4774			−0.390200
$722$	−3.14125	−	2.19286i	−0.116905	−	0.0816098i
$723$	−35.3171	+	36.2554i	−1.31346	+	1.34835i
$724$	5.26850	+	14.3477i	0.195802	+	0.533226i
$725$		−	60.7493i		−	2.25617i
$726$	−15.1033	+	2.89006i	−0.560536	+	0.107260i
$727$			23.1133i			0.857226i	0.903488	+	0.428613i	$0.140998\pi$
$727$			23.1133i			0.857226i	−0.903488	+	0.428613i	$0.859002\pi$
$728$	−8.50559	−	2.24012i	−0.315238	−	0.0830242i
$729$	2.12145	+	26.9165i	0.0785723	+	0.996908i
$730$	12.4471	−	17.8304i	0.460689	−	0.659932i
$731$	−2.07565			−0.0767705
$732$	−16.7070	−	7.46832i	−0.617507	−	0.276037i
$733$	−16.3066			−0.602298			−0.301149	−	0.953577i	$-0.597370\pi$
$733$	−16.3066			−0.602298			−0.301149	+	0.953577i	$0.597370\pi$
$734$	−4.07070	+	5.83124i	−0.150252	+	0.215235i
$735$	−26.1583	−	25.4813i	−0.964862	−	0.939892i
$736$	5.63167	−	0.533190i	0.207586	−	0.0196536i
$737$		−	30.6433i		−	1.12876i
$738$	26.9149	+	17.7580i	0.990752	+	0.653681i
$739$			0.249325i			0.00917157i	0.999989	+	0.00458578i	$0.00145971\pi$
$739$			0.249325i			0.00917157i	−0.999989	+	0.00458578i	$0.998540\pi$
$740$	65.6399	−	24.1032i	2.41297	−	0.886050i
$741$	−16.0797	−	15.6636i	−0.590703	−	0.575416i
$742$	9.44686	+	6.59471i	0.346805	+	0.242099i
$743$	5.26258			0.193065			0.0965327	−	0.995330i	$-0.469225\pi$
$743$	5.26258			0.193065			0.0965327	+	0.995330i	$0.469225\pi$
$744$	5.58412	−	3.35477i	0.204724	−	0.122992i
$745$	−13.1292			−0.481016
$746$	2.86799	+	2.00210i	0.105005	+	0.0733021i
$747$	−0.657619	−	25.0772i	−0.0240610	−	0.917525i
$748$	5.16052	−	1.89496i	0.188687	−	0.0692866i
$749$		−	0.865614i		−	0.0316288i
$750$	−3.35614	−	17.5390i	−0.122549	−	0.640434i
$751$			39.6947i			1.44848i	0.689548	+	0.724240i	$0.257809\pi$
$751$			39.6947i			1.44848i	−0.689548	+	0.724240i	$0.742191\pi$
$752$	38.6919	−	32.8442i	1.41095	−	1.19771i
$753$	−10.5681	+	10.8489i	−0.385125	+	0.395357i
$754$	−22.2525	+	31.8765i	−0.810389	+	1.16087i
$755$	−68.1521			−2.48031
$756$	−9.29286	−	3.86508i	−0.337978	−	0.140571i
$757$	−33.3186			−1.21098			−0.605492	−	0.795851i	$-0.707024\pi$
$757$	−33.3186			−1.21098			−0.605492	+	0.795851i	$0.707024\pi$
$758$	−27.0871	+	38.8020i	−0.983847	+	1.40935i
$759$	2.62634	−	2.69612i	0.0953301	−	0.0978628i
$760$	10.1122	−	38.3955i	0.366809	−	1.39275i
$761$			32.9587i			1.19475i	0.801961	+	0.597376i	$0.203790\pi$
$761$			32.9587i			1.19475i	−0.801961	+	0.597376i	$0.796210\pi$
$762$	5.46964	+	28.5840i	0.198144	+	1.03549i
$763$			15.8710i			0.574570i
$764$	−7.39703	−	20.1443i	−0.267615	−	0.728794i
$765$	0.345977	+	13.1932i	0.0125088	+	0.477003i
$766$	−25.3345	−	17.6857i	−0.915374	−	0.639009i
$767$	4.00064			0.144455
$768$	16.4471	+	22.3045i	0.593484	+	0.804846i
$769$	−4.87232			−0.175700			−0.0878501	−	0.996134i	$-0.528000\pi$
$769$	−4.87232			−0.175700			−0.0878501	+	0.996134i	$0.528000\pi$
$770$	−8.48777	−	5.92518i	−0.305878	−	0.213529i
$771$	5.48416	+	5.34223i	0.197507	+	0.192396i
$772$	−4.61420	−	12.5658i	−0.166069	−	0.452253i
$773$		−	31.4066i		−	1.12962i	−0.825222	−	0.564809i	$-0.808950\pi$
$773$		−	31.4066i		−	1.12962i	0.825222	−	0.564809i	$-0.191050\pi$
$774$	−5.81111	−	3.83407i	−0.208876	−	0.137813i
$775$			9.43597i			0.338950i
$776$	−6.98002	+	26.5027i	−0.250568	+	0.951392i
$777$	12.0790	+	11.7664i	0.433332	+	0.422117i
$778$	5.06390	−	7.25399i	0.181550	−	0.260068i
$779$	−30.6765			−1.09910
$780$	−15.7877	+	35.3177i	−0.565289	+	1.26458i
$781$	−26.2021			−0.937584
$782$	1.02395	−	1.46679i	0.0366163	−	0.0524525i
$783$	−30.1938	+	32.6672i	−1.07904	+	1.16743i
$784$	−18.4861	+	15.6922i	−0.660217	+	0.560435i
$785$			36.1597i			1.29059i
$786$	−47.4589	+	9.08142i	−1.69280	+	0.323923i
$787$		−	2.31176i		−	0.0824055i	−0.999151	−	0.0412027i	$-0.986881\pi$
$787$		−	2.31176i		−	0.0824055i	0.999151	−	0.0412027i	$-0.0131189\pi$
$788$	10.8717	−	3.99211i	0.387287	−	0.142213i
$789$	−7.38637	+	7.58261i	−0.262962	+	0.269948i
$790$	28.2883	+	19.7476i	1.00645	+	0.702589i
$791$	−10.7645			−0.382743
$792$	17.9480	+	4.22711i	0.637756	+	0.150204i
$793$	−16.9630			−0.602375
$794$	−34.5892	−	24.1462i	−1.22752	−	0.856915i
$795$	35.3583	−	36.2977i	1.25403	−	1.28735i
$796$	40.5569	−	14.8926i	1.43750	−	0.527855i
$797$			31.0641i			1.10035i	0.835050	+	0.550174i	$0.185439\pi$
$797$			31.0641i			1.10035i	−0.835050	+	0.550174i	$0.814561\pi$
$798$	9.40430	−	1.79954i	0.332908	−	0.0637031i
$799$		−	16.0492i		−	0.567780i
$800$	−39.9630	+	3.78358i	−1.41290	+	0.133770i
$801$	9.00596	−	0.236171i	0.318210	−	0.00834468i
$802$	−14.2657	+	20.4354i	−0.503738	+	0.721600i
$803$	−9.60725			−0.339032
$804$	19.9351	−	44.5957i	0.703057	−	1.57277i
$805$	−3.36827			−0.118716
$806$	3.45640	−	4.95127i	0.121747	−	0.174401i
$807$	−20.8911	−	20.3504i	−0.735400	−	0.716368i
$808$	−26.5760	−	6.99931i	−0.934940	−	0.246235i
$809$		−	0.108932i		−	0.00382986i	−0.999998	−	0.00191493i	$-0.999390\pi$
$809$		−	0.108932i		−	0.00382986i	0.999998	−	0.00191493i	$-0.000609542\pi$
$810$	−23.4016	+	37.5758i	−0.822247	+	1.32028i
$811$			8.77168i			0.308015i	0.988070	+	0.154008i	$0.0492181\pi$
$811$			8.77168i			0.308015i	−0.988070	+	0.154008i	$0.950782\pi$
$812$	−5.71576	−	15.5657i	−0.200584	−	0.546248i
$813$	−24.2103	−	23.5838i	−0.849094	−	0.827119i
$814$	−25.3319	−	17.6838i	−0.887884	−	0.619818i
$815$	19.6753			0.689194
$816$	8.74297	+	0.599430i	0.306065	+	0.0209842i
$817$	6.62326			0.231718
$818$	36.3393	+	25.3679i	1.27057	+	0.886968i
$819$	−9.32597	+	0.244563i	−0.325876	+	0.00854571i
$820$	18.2231	+	49.6268i	0.636378	+	1.73304i
$821$		−	5.77012i		−	0.201379i	−0.994918	−	0.100689i	$-0.967895\pi$
$821$		−	5.77012i		−	0.201379i	0.994918	−	0.100689i	$-0.0321048\pi$
$822$	−2.34223	−	12.2403i	−0.0816946	−	0.426931i
$823$		−	15.1010i		−	0.526388i	−0.964743	−	0.263194i	$-0.915224\pi$
$823$		−	15.1010i		−	0.526388i	0.964743	−	0.263194i	$-0.0847760\pi$
$824$	29.5906	+	7.79326i	1.03084	+	0.271491i
$825$	−18.6368	+	19.1320i	−0.648851	+	0.666089i
$826$	−0.976780	+	1.39923i	−0.0339865	+	0.0486854i
$827$	−18.2056			−0.633070			−0.316535	−	0.948581i	$-0.602519\pi$
$827$	−18.2056			−0.633070			−0.316535	+	0.948581i	$0.602519\pi$
$828$	5.57613	−	2.21513i	0.193784	−	0.0769811i
$829$	−5.98714			−0.207942			−0.103971	−	0.994580i	$-0.533155\pi$
$829$	−5.98714			−0.207942			−0.103971	+	0.994580i	$0.533155\pi$
$830$	23.5424	−	33.7242i	0.817167	−	1.17058i
$831$	21.0301	−	21.5889i	0.729528	−	0.748909i
$832$	22.3554	+	12.6531i	0.775034	+	0.438669i
$833$			7.66793i			0.265678i
$834$	0.782688	+	4.09028i	0.0271023	+	0.141635i
$835$			50.2979i			1.74063i
$836$	−16.4669	+	6.04670i	−0.569520	+	0.209130i
$837$	4.68990	−	5.07408i	0.162107	−	0.175386i
$838$	10.1165	+	7.06215i	0.349468	+	0.243958i
$839$	−15.7901			−0.545135			−0.272568	−	0.962137i	$-0.587873\pi$
$839$	−15.7901			−0.545135			−0.272568	+	0.962137i	$0.587873\pi$
$840$	−8.49775	−	14.1448i	−0.293200	−	0.488041i
$841$	−44.2894			−1.52722
$842$	−9.03276	−	6.30563i	−0.311289	−	0.217306i
$843$	−33.8300	−	32.9545i	−1.16517	−	1.13501i
$844$	−8.62765	+	3.16810i	−0.296976	+	0.109050i
$845$		−	9.35424i		−	0.321796i
$846$	29.6456	−	44.9324i	1.01924	−	1.54481i
$847$		−	6.07980i		−	0.208904i
$848$	−21.7748	−	25.6516i	−0.747748	−	0.880879i
$849$	23.1985	+	22.5981i	0.796169	+	0.775564i
$850$	−7.26605	+	10.4085i	−0.249223	+	0.357010i
$851$	−10.0527			−0.344602
$852$	−38.1323	−	17.0459i	−1.30639	−	0.583981i
$853$	35.0159			1.19892			0.599460	−	0.800405i	$-0.295382\pi$
$853$	35.0159			1.19892			0.599460	+	0.800405i	$0.295382\pi$
$854$	4.14162	−	5.93284i	0.141723	−	0.203018i
$855$	−1.10399	−	42.0989i	−0.0377558	−	1.43975i
$856$	−0.643855	+	2.44468i	−0.0220065	+	0.0835575i
$857$		−	0.666549i		−	0.0227689i	−0.999935	−	0.0113844i	$-0.996376\pi$
$857$		−	0.666549i		−	0.0227689i	0.999935	−	0.0113844i	$-0.00362386\pi$
$858$	16.7872	−	3.21229i	0.573106	−	0.109666i
$859$			49.7997i			1.69914i	0.527473	+	0.849572i	$0.323139\pi$
$859$			49.7997i			1.69914i	−0.527473	+	0.849572i	$0.676861\pi$
$860$	−3.93449	−	10.7148i	−0.134165	−	0.365370i
$861$	−8.89593	+	9.13228i	−0.303173	+	0.311227i
$862$	−14.1175	−	9.85519i	−0.480843	−	0.335669i
$863$	−26.0464			−0.886630			−0.443315	−	0.896366i	$-0.646198\pi$
$863$	−26.0464			−0.886630			−0.443315	+	0.896366i	$0.646198\pi$
$864$	23.3701	+	17.8280i	0.795069	+	0.606520i
$865$	−18.0715			−0.614450
$866$	−40.8113	−	28.4897i	−1.38682	−	0.968120i
$867$	−18.6122	+	19.1067i	−0.632105	+	0.648898i
$868$	0.887808	+	2.41776i	0.0301342	+	0.0820641i
$869$		−	15.2421i		−	0.517053i
$870$	−71.6325	+	13.7071i	−2.42857	+	0.464715i
$871$		−	45.2793i		−	1.53423i
$872$	11.8051	−	44.8233i	0.399771	−	1.51791i
$873$	0.762037	+	29.0590i	0.0257910	+	0.983497i
$874$	−3.26735	+	4.68045i	−0.110520	+	0.158319i
$875$	7.06029			0.238681
$876$	−13.9816	−	6.25003i	−0.472394	−	0.211169i
$877$	−32.8441			−1.10907			−0.554534	−	0.832161i	$-0.687103\pi$
$877$	−32.8441			−1.10907			−0.554534	+	0.832161i	$0.687103\pi$
$878$	−14.8940	+	21.3354i	−0.502647	+	0.720037i
$879$	29.0840	+	28.3313i	0.980978	+	0.955590i
$880$	19.5641	+	23.0473i	0.659505	+	0.776925i
$881$			32.7570i			1.10361i	0.833973	+	0.551806i	$0.186061\pi$
$881$			32.7570i			1.10361i	−0.833973	+	0.551806i	$0.813939\pi$
$882$	−14.1640	+	21.4676i	−0.476926	+	0.722853i
$883$		−	6.19776i		−	0.208571i	−0.994547	−	0.104286i	$-0.966744\pi$
$883$		−	6.19776i		−	0.208571i	0.994547	−	0.104286i	$-0.0332556\pi$
$884$	7.62532	−	2.80004i	0.256467	−	0.0941755i
$885$	5.37625	+	5.23711i	0.180721	+	0.176044i
$886$	11.7282	+	8.18730i	0.394018	+	0.275058i
$887$	4.08365			0.137116			0.0685578	−	0.997647i	$-0.478160\pi$
$887$	4.08365			0.137116			0.0685578	+	0.997647i	$0.478160\pi$
$888$	−25.3617	−	42.2154i	−0.851083	−	1.41666i
$889$	−11.5064			−0.385913
$890$	12.1114	+	8.45477i	0.405974	+	0.283405i
$891$	19.5308	−	1.02505i	0.654305	−	0.0343404i
$892$	35.7378	−	13.1230i	1.19659	−	0.439392i
$893$			51.2121i			1.71375i
$894$	1.73787	+	9.08199i	0.0581230	+	0.303747i
$895$			5.43777i			0.181765i
$896$	−9.88365	+	4.72948i	−0.330189	+	0.158001i
$897$	3.88075	−	3.98385i	0.129574	−	0.133017i
$898$	−6.08651	+	8.71887i	−0.203109	+	0.290952i
$899$	11.3838			0.379670
$900$	−39.5688	+	15.7188i	−1.31896	+	0.523960i
$901$	−10.6402			−0.354475
$902$	13.3698	−	19.1521i	0.445165	−	0.637695i
$903$	1.92069	−	1.97172i	0.0639166	−	0.0656147i
$904$	30.4014	+	8.00680i	1.01113	+	0.266302i
$905$			26.5791i			0.883520i
$906$	9.02108	+	47.1436i	0.299705	+	1.56624i
$907$			1.12490i			0.0373518i	0.999826	+	0.0186759i	$0.00594507\pi$
$907$			1.12490i			0.0373518i	−0.999826	+	0.0186759i	$0.994055\pi$
$908$	−2.00726	−	5.46636i	−0.0666134	−	0.181407i
$909$	−29.1393	+	0.764144i	−0.966490	+	0.0253450i
$910$	−12.5417	−	8.75520i	−0.415755	−	0.290232i
$911$	34.1959			1.13296			0.566480	−	0.824076i	$-0.308305\pi$
$911$	34.1959			1.13296			0.566480	+	0.824076i	$0.308305\pi$
$912$	−27.8983	−	1.91274i	−0.923805	−	0.0633373i
$913$	−18.1711			−0.601374
$914$	2.41840	+	1.68825i	0.0799936	+	0.0558423i
$915$	−22.7957	−	22.2058i	−0.753604	−	0.734100i
$916$	−8.87888	−	24.1798i	−0.293367	−	0.798922i
$917$		−	19.1045i		−	0.630886i
$918$	9.08052	−	1.98568i	0.299702	−	0.0655371i
$919$			23.3449i			0.770077i	0.922900	+	0.385039i	$0.125812\pi$
$919$			23.3449i			0.770077i	−0.922900	+	0.385039i	$0.874188\pi$
$920$	9.51273	+	2.50537i	0.313625	+	0.0825995i
$921$	−7.45060	−	7.25778i	−0.245506	−	0.239152i
$922$	12.7722	−	18.2961i	0.420630	−	0.602548i
$923$	−38.7168			−1.27438
$924$	−2.97519	+	6.65564i	−0.0978766	+	0.218954i
$925$	71.3350			2.34548
$926$	−2.06496	+	2.95803i	−0.0678587	+	0.0972069i
$927$	32.4446	−	0.850822i	1.06562	−	0.0279447i
$928$	4.56460	+	48.2123i	0.149840	+	1.58265i
$929$		−	37.2985i		−	1.22372i	−0.790964	−	0.611862i	$-0.790421\pi$
$929$		−	37.2985i		−	1.22372i	0.790964	−	0.611862i	$-0.209579\pi$
$930$	11.1264	−	2.12908i	0.364850	−	0.0698151i
$931$		−	24.4679i		−	0.801903i
$932$	13.3451	−	4.90036i	0.437133	−	0.160517i
$933$	25.8306	−	26.5169i	0.845657	−	0.868124i
$934$	38.7514	+	27.0518i	1.26799	+	0.885162i
$935$	9.55991			0.312642
$936$	26.5205	+	6.24609i	0.866849	+	0.204160i
$937$	2.97285			0.0971187			0.0485594	−	0.998820i	$-0.484537\pi$
$937$	2.97285			0.0971187			0.0485594	+	0.998820i	$0.484537\pi$
$938$	15.8365	+	11.0552i	0.517078	+	0.360965i
$939$	−19.9928	+	20.5239i	−0.652440	+	0.669774i
$940$	82.8482	−	30.4221i	2.70221	−	0.992259i
$941$			11.8277i			0.385574i	0.981241	+	0.192787i	$0.0617526\pi$
$941$			11.8277i			0.385574i	−0.981241	+	0.192787i	$0.938247\pi$
$942$	25.0131	−	4.78634i	0.814972	−	0.155947i
$943$		−	7.60029i		−	0.247499i
$944$	3.79940	−	3.22518i	0.123660	−	0.104971i
$945$	−12.8528	−	11.8797i	−0.418103	−	0.386446i
$946$	−2.88663	+	4.13507i	−0.0938523	+	0.134443i
$947$	57.2763			1.86123			0.930614	−	0.366001i	$-0.119273\pi$
$947$	57.2763			1.86123			0.930614	+	0.366001i	$0.119273\pi$
$948$	9.91582	−	22.1821i	0.322051	−	0.720442i
$949$	−14.1959			−0.460819
$950$	23.1855	−	33.2130i	0.752237	−	1.07757i
$951$	−13.9116	−	13.5516i	−0.451114	−	0.439439i
$952$	−0.882448	+	3.35061i	−0.0286003	+	0.108594i
$953$			6.33817i			0.205313i	0.994717	+	0.102657i	$0.0327343\pi$
$953$			6.33817i			0.205313i	−0.994717	+	0.102657i	$0.967266\pi$
$954$	−29.7889	−	19.6542i	−0.964450	−	0.636327i
$955$		−	37.3174i		−	1.20756i
$956$	5.20067	+	14.1629i	0.168202	+	0.458062i
$957$	23.0812	+	22.4839i	0.746111	+	0.726801i
$958$	−45.3879	−	31.6846i	−1.46642	−	1.02368i
$959$	4.92732			0.159112
$960$	13.4784	+	46.2686i	0.435014	+	1.49331i
$961$	29.2318			0.942961
$962$	−37.4311	−	26.1301i	−1.20683	−	0.842467i
$963$	0.0702923	+	2.68048i	0.00226514	+	0.0863771i
$964$	20.1455	+	54.8620i	0.648842	+	1.76698i
$965$		−	23.2782i		−	0.749352i
$966$	0.445848	+	2.32997i	0.0143449	+	0.0749656i
$967$			33.4403i			1.07537i	0.843147	+	0.537683i	$0.180700\pi$
$967$			33.4403i			1.07537i	−0.843147	+	0.537683i	$0.819300\pi$
$968$	−4.52224	+	17.1707i	−0.145350	+	0.551886i
$969$	−6.17035	+	6.33428i	−0.198220	+	0.203486i
$970$	−27.2805	+	39.0790i	−0.875923	+	1.25475i
$971$	−4.33228			−0.139029			−0.0695147	−	0.997581i	$-0.522145\pi$
$971$	−4.33228			−0.139029			−0.0695147	+	0.997581i	$0.522145\pi$
$972$	29.0903	+	11.2140i	0.933072	+	0.359690i
$973$	−1.64653			−0.0527854
$974$	−17.4027	+	24.9292i	−0.557619	+	0.798785i
$975$	−27.5382	+	28.2699i	−0.881929	+	0.905360i
$976$	−16.1098	+	13.6750i	−0.515661	+	0.437727i
$977$			46.2330i			1.47913i	0.673087	+	0.739563i	$0.264968\pi$
$977$			46.2330i			1.47913i	−0.673087	+	0.739563i	$0.735032\pi$
$978$	−2.60435	−	13.6102i	−0.0832780	−	0.435206i
$979$		−	6.52577i		−	0.208565i
$980$	−39.5829	+	14.5350i	−1.26443	+	0.464302i
$981$	−1.28881	−	49.1466i	−0.0411486	−	1.56913i
$982$	−14.9778	−	10.4558i	−0.477961	−	0.333657i
$983$	10.8968			0.347553			0.173777	−	0.984785i	$-0.444403\pi$
$983$	10.8968			0.347553			0.173777	+	0.984785i	$0.444403\pi$
$984$	31.9168	−	19.1746i	1.01747	−	0.611265i
$985$	20.1398			0.641708
$986$	12.5571	+	8.76593i	0.399900	+	0.279164i
$987$	15.2456	+	14.8511i	0.485274	+	0.472715i
$988$	−24.3319	+	8.93476i	−0.774102	+	0.284253i
$989$			1.64095i			0.0521793i
$990$	26.7645	+	17.6588i	0.850633	+	0.561233i
$991$			50.1034i			1.59159i	0.605568	+	0.795794i	$0.292946\pi$
$991$			50.1034i			1.59159i	−0.605568	+	0.795794i	$0.707054\pi$
$992$	−0.709002	−	7.48864i	−0.0225108	−	0.237765i
$993$	13.4210	+	13.0737i	0.425904	+	0.414882i
$994$	9.45293	−	13.5412i	0.299829	−	0.429502i
$995$	75.1319			2.38184
$996$	−26.4447	−	11.8213i	−0.837931	−	0.374571i
$997$	−11.2113			−0.355066			−0.177533	−	0.984115i	$-0.556812\pi$
$997$	−11.2113			−0.355066			−0.177533	+	0.984115i	$0.556812\pi$
$998$	0.259148	−	0.371227i	0.00820318	−	0.0117510i
$999$	−38.3596	−	35.4552i	−1.21364	−	1.12175i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-1.15961 - 0.809507i) q^{2} +(-1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} +3.47795i q^{5} +(2.40584 - 0.460365i) q^{6} +0.968466i q^{7} +(0.720358 - 2.73516i) q^{8} +(-0.0786444 - 2.99897i) q^{9} +O(q^{10})\)	\(q+(-1.15961 - 0.809507i) q^{2} +(-1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} +3.47795i q^{5} +(2.40584 - 0.460365i) q^{6} +0.968466i q^{7} +(0.720358 - 2.73516i) q^{8} +(-0.0786444 - 2.99897i) q^{9} +(2.81542 - 4.03307i) q^{10} -2.17307 q^{11} +(-3.16251 - 1.41370i) q^{12} -3.21098 q^{13} +(0.783980 - 1.12304i) q^{14} +(-4.31507 - 4.20339i) q^{15} +(-3.04946 + 2.58858i) q^{16} +1.26490i q^{17} +(-2.33649 + 3.54130i) q^{18} -4.03623i q^{19} +(-6.52959 + 2.39769i) q^{20} +(-1.20157 - 1.17047i) q^{21} +(2.51992 + 1.75912i) q^{22} +1.00000 q^{23} +(2.52288 + 4.19941i) q^{24} -7.09612 q^{25} +(3.72349 + 2.59931i) q^{26} +(3.81585 + 3.52694i) q^{27} +(-1.81822 + 0.667657i) q^{28} +8.56092i q^{29} +(1.60113 + 8.36738i) q^{30} -1.32974i q^{31} +(5.63167 - 0.533190i) q^{32} +(2.62634 - 2.69612i) q^{33} +(1.02395 - 1.46679i) q^{34} -3.36827 q^{35} +(5.57613 - 2.21513i) q^{36} -10.0527 q^{37} +(-3.26735 + 4.68045i) q^{38} +(3.88075 - 3.98385i) q^{39} +(9.51273 + 2.50537i) q^{40} -7.60029i q^{41} +(0.445848 + 2.32997i) q^{42} +1.64095i q^{43} +(-1.49811 - 4.07978i) q^{44} +(10.4303 - 0.273521i) q^{45} +(-1.15961 - 0.809507i) q^{46} -12.6881 q^{47} +(0.473894 - 6.91198i) q^{48} +6.06207 q^{49} +(8.22874 + 5.74436i) q^{50} +(-1.56936 - 1.52874i) q^{51} +(-2.21364 - 6.02839i) q^{52} +8.41184i q^{53} +(-1.56983 - 7.17883i) q^{54} -7.55782i q^{55} +(2.64891 + 0.697642i) q^{56} +(5.00772 + 4.87812i) q^{57} +(6.93013 - 9.92734i) q^{58} -1.24592 q^{59} +(4.91677 - 10.9990i) q^{60} +5.28282 q^{61} +(-1.07643 + 1.54198i) q^{62} +(2.90440 - 0.0761644i) q^{63} +(-6.96217 - 3.94058i) q^{64} -11.1676i q^{65} +(-5.22806 + 1.00041i) q^{66} +14.1014i q^{67} +(-2.37476 + 0.872019i) q^{68} +(-1.20859 + 1.24069i) q^{69} +(3.90589 + 2.72664i) q^{70} +12.0576 q^{71} +(-8.25930 - 1.94523i) q^{72} +4.42105 q^{73} +(11.6572 + 8.13772i) q^{74} +(8.57626 - 8.80411i) q^{75} +(7.57772 - 2.78256i) q^{76} -2.10454i q^{77} +(-7.72511 + 1.47822i) q^{78} +7.01409i q^{79} +(-9.00296 - 10.6059i) q^{80} +(-8.98763 + 0.471704i) q^{81} +(-6.15249 + 8.81338i) q^{82} +8.36193 q^{83} +(1.36912 - 3.06278i) q^{84} -4.39926 q^{85} +(1.32836 - 1.90287i) q^{86} +(-10.6215 - 10.3466i) q^{87} +(-1.56539 + 5.94369i) q^{88} +3.00302i q^{89} +(-12.3165 - 8.12619i) q^{90} -3.10973i q^{91} +(0.689397 + 1.87743i) q^{92} +(1.64980 + 1.60710i) q^{93} +(14.7133 + 10.2711i) q^{94} +14.0378 q^{95} +(-6.14483 + 7.63159i) q^{96} -9.68965 q^{97} +(-7.02965 - 4.90729i) q^{98} +(0.170900 + 6.51697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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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