LMFDB - Embedded newform 690.2.j.b.643.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(367,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("690.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			643.6
Character	$\chi$	$=$	690.643
Dual form			690.2.j.b.367.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} +(-0.124800 - 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} +(-0.124800 - 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.666968 + 2.13428i) q^{10} +0.552534i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.68793 + 2.68793i) q^{13} +0.176495 q^{14} +(-2.13428 - 0.666968i) q^{15} -1.00000 q^{16} +(3.61968 + 3.61968i) q^{17} +(-0.707107 - 0.707107i) q^{18} -1.08434 q^{19} +(-1.03755 - 1.98078i) q^{20} +0.176495i q^{21} +(-0.390701 - 0.390701i) q^{22} +(0.0741463 - 4.79526i) q^{23} -1.00000i q^{24} +(2.84699 - 4.11031i) q^{25} -3.80130 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.124800 + 0.124800i) q^{28} -8.68275i q^{29} +(1.98078 - 1.03755i) q^{30} +2.45605 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.390701 - 0.390701i) q^{33} -5.11901 q^{34} +(-0.376689 - 0.117716i) q^{35} +1.00000 q^{36} +(7.79545 + 7.79545i) q^{37} +(0.766741 - 0.766741i) q^{38} -3.80130i q^{39} +(2.13428 + 0.666968i) q^{40} -2.27486 q^{41} +(-0.124800 - 0.124800i) q^{42} +(-1.06804 + 1.06804i) q^{43} +0.552534 q^{44} +(1.03755 + 1.98078i) q^{45} +(3.33833 + 3.44319i) q^{46} +(-0.597335 + 0.597335i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.96885i q^{49} +(0.893297 + 4.91955i) q^{50} -5.11901i q^{51} +(2.68793 - 2.68793i) q^{52} +(5.95295 - 5.95295i) q^{53} +1.00000i q^{54} +(0.573280 + 1.09445i) q^{55} -0.176495i q^{56} +(0.766741 + 0.766741i) q^{57} +(6.13963 + 6.13963i) q^{58} -10.4090i q^{59} +(-0.666968 + 2.13428i) q^{60} +9.12081i q^{61} +(-1.73669 + 1.73669i) q^{62} +(0.124800 - 0.124800i) q^{63} +1.00000i q^{64} +(8.11305 + 2.53535i) q^{65} +0.552534i q^{66} +(5.38491 + 5.38491i) q^{67} +(3.61968 - 3.61968i) q^{68} +(-3.44319 + 3.33833i) q^{69} +(0.349597 - 0.183121i) q^{70} +8.16755 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.12378 + 3.12378i) q^{73} -11.0244 q^{74} +(-4.91955 + 0.893297i) q^{75} +1.08434i q^{76} +(0.0689566 - 0.0689566i) q^{77} +(2.68793 + 2.68793i) q^{78} +6.76975 q^{79} +(-1.98078 + 1.03755i) q^{80} -1.00000 q^{81} +(1.60857 - 1.60857i) q^{82} +(0.190970 - 0.190970i) q^{83} +0.176495 q^{84} +(10.9254 + 3.41421i) q^{85} -1.51043i q^{86} +(-6.13963 + 6.13963i) q^{87} +(-0.390701 + 0.390701i) q^{88} -8.76193 q^{89} +(-2.13428 - 0.666968i) q^{90} -0.670909i q^{91} +(-4.79526 - 0.0741463i) q^{92} +(-1.73669 - 1.73669i) q^{93} -0.844759i q^{94} +(-2.14783 + 1.12505i) q^{95} -1.00000 q^{96} +(1.62982 + 1.62982i) q^{97} +(4.92772 + 4.92772i) q^{98} -0.552534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{6}+O(q^{10}) $ 24 * q + 24 * q^6	$ 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) $ 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.98078	−	1.03755i	0.885833	−	0.464005i
$5$	1.98078	−	1.03755i	0.885833	−	0.464005i
$6$	1.00000			0.408248
$7$	−0.124800	−	0.124800i	−0.0471701	−	0.0471701i	0.683128	−	0.730298i	$-0.260619\pi$
$7$	−0.124800	−	0.124800i	−0.0471701	−	0.0471701i	−0.730298	+	0.683128i	$0.760619\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.666968	+	2.13428i	−0.210914	+	0.674919i
$11$			0.552534i			0.166595i	0.996525	+	0.0832977i	$0.0265452\pi$
$11$			0.552534i			0.166595i	−0.996525	+	0.0832977i	$0.973455\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	2.68793	+	2.68793i	0.745497	+	0.745497i	0.973630	−	0.228133i	$-0.0732621\pi$
$13$	2.68793	+	2.68793i	0.745497	+	0.745497i	−0.228133	+	0.973630i	$0.573262\pi$
$14$	0.176495			0.0471701
$15$	−2.13428	−	0.666968i	−0.551069	−	0.172210i
$16$	−1.00000			−0.250000
$17$	3.61968	+	3.61968i	0.877902	+	0.877902i	0.993317	−	0.115415i	$-0.0368198\pi$
$17$	3.61968	+	3.61968i	0.877902	+	0.877902i	−0.115415	+	0.993317i	$0.536820\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−1.08434			−0.248764			−0.124382	−	0.992234i	$-0.539695\pi$
$19$	−1.08434			−0.248764			−0.124382	+	0.992234i	$0.539695\pi$
$20$	−1.03755	−	1.98078i	−0.232002	−	0.442916i
$21$			0.176495i			0.0385143i
$22$	−0.390701	−	0.390701i	−0.0832977	−	0.0832977i
$23$	0.0741463	−	4.79526i	0.0154606	−	0.999880i
$23$	0.0741463	−	4.79526i	0.0154606	−	0.999880i
$24$		−	1.00000i		−	0.204124i
$25$	2.84699	−	4.11031i	0.569399	−	0.822061i
$26$	−3.80130			−0.745497
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.124800	+	0.124800i	−0.0235851	+	0.0235851i
$29$		−	8.68275i		−	1.61235i	−0.591679	−	0.806173i	$-0.701535\pi$
$29$		−	8.68275i		−	1.61235i	0.591679	−	0.806173i	$-0.298465\pi$
$30$	1.98078	−	1.03755i	0.361640	−	0.189429i
$31$	2.45605			0.441119			0.220559	−	0.975374i	$-0.429212\pi$
$31$	2.45605			0.441119			0.220559	+	0.975374i	$0.429212\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.390701	−	0.390701i	0.0680123	−	0.0680123i
$34$	−5.11901			−0.877902
$35$	−0.376689	−	0.117716i	−0.0636720	−	0.0198977i
$36$	1.00000			0.166667
$37$	7.79545	+	7.79545i	1.28156	+	1.28156i	0.939777	+	0.341787i	$0.111032\pi$
$37$	7.79545	+	7.79545i	1.28156	+	1.28156i	0.341787	+	0.939777i	$0.388968\pi$
$38$	0.766741	−	0.766741i	0.124382	−	0.124382i
$39$		−	3.80130i		−	0.608696i
$40$	2.13428	+	0.666968i	0.337459	+	0.105457i
$41$	−2.27486			−0.355274			−0.177637	−	0.984096i	$-0.556845\pi$
$41$	−2.27486			−0.355274			−0.177637	+	0.984096i	$0.556845\pi$
$42$	−0.124800	−	0.124800i	−0.0192571	−	0.0192571i
$43$	−1.06804	+	1.06804i	−0.162874	+	0.162874i	−0.783839	−	0.620965i	$-0.786741\pi$
$43$	−1.06804	+	1.06804i	−0.162874	+	0.162874i	0.620965	+	0.783839i	$0.286741\pi$
$44$	0.552534			0.0832977
$45$	1.03755	+	1.98078i	0.154668	+	0.295278i
$46$	3.33833	+	3.44319i	0.492210	+	0.507671i
$47$	−0.597335	+	0.597335i	−0.0871302	+	0.0871302i	−0.749329	−	0.662198i	$-0.769624\pi$
$47$	−0.597335	+	0.597335i	−0.0871302	+	0.0871302i	0.662198	+	0.749329i	$0.269624\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	6.96885i		−	0.995550i
$50$	0.893297	+	4.91955i	0.126331	+	0.695730i
$51$		−	5.11901i		−	0.716804i
$52$	2.68793	−	2.68793i	0.372748	−	0.372748i
$53$	5.95295	−	5.95295i	0.817701	−	0.817701i	−0.168073	−	0.985774i	$-0.553755\pi$
$53$	5.95295	−	5.95295i	0.817701	−	0.817701i	0.985774	+	0.168073i	$0.0537546\pi$
$54$			1.00000i			0.136083i
$55$	0.573280	+	1.09445i	0.0773011	+	0.147576i
$56$		−	0.176495i		−	0.0235851i
$57$	0.766741	+	0.766741i	0.101557	+	0.101557i
$58$	6.13963	+	6.13963i	0.806173	+	0.806173i
$59$		−	10.4090i		−	1.35514i	−0.735460	−	0.677569i	$-0.763034\pi$
$59$		−	10.4090i		−	1.35514i	0.735460	−	0.677569i	$-0.236966\pi$
$60$	−0.666968	+	2.13428i	−0.0861052	+	0.275534i
$61$			9.12081i			1.16780i	0.811825	+	0.583900i	$0.198474\pi$
$61$			9.12081i			1.16780i	−0.811825	+	0.583900i	$0.801526\pi$
$62$	−1.73669	+	1.73669i	−0.220559	+	0.220559i
$63$	0.124800	−	0.124800i	0.0157234	−	0.0157234i
$64$			1.00000i			0.125000i
$65$	8.11305	+	2.53535i	1.00630	+	0.314471i
$66$			0.552534i			0.0680123i
$67$	5.38491	+	5.38491i	0.657871	+	0.657871i	0.954876	−	0.297005i	$-0.0959878\pi$
$67$	5.38491	+	5.38491i	0.657871	+	0.657871i	−0.297005	+	0.954876i	$0.595988\pi$
$68$	3.61968	−	3.61968i	0.438951	−	0.438951i
$69$	−3.44319	+	3.33833i	−0.414511	+	0.401888i
$70$	0.349597	−	0.183121i	0.0417849	−	0.0218872i
$71$	8.16755			0.969309			0.484655	−	0.874706i	$-0.338945\pi$
$71$	8.16755			0.969309			0.484655	+	0.874706i	$0.338945\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	3.12378	+	3.12378i	0.365610	+	0.365610i	0.865873	−	0.500263i	$-0.166763\pi$
$73$	3.12378	+	3.12378i	0.365610	+	0.365610i	−0.500263	+	0.865873i	$0.666763\pi$
$74$	−11.0244			−1.28156
$75$	−4.91955	+	0.893297i	−0.568061	+	0.103149i
$76$			1.08434i			0.124382i
$77$	0.0689566	−	0.0689566i	0.00785833	−	0.00785833i
$78$	2.68793	+	2.68793i	0.304348	+	0.304348i
$79$	6.76975			0.761656			0.380828	−	0.924646i	$-0.375639\pi$
$79$	6.76975			0.761656			0.380828	+	0.924646i	$0.375639\pi$
$80$	−1.98078	+	1.03755i	−0.221458	+	0.116001i
$81$	−1.00000			−0.111111
$82$	1.60857	−	1.60857i	0.177637	−	0.177637i
$83$	0.190970	−	0.190970i	0.0209616	−	0.0209616i	−0.696548	−	0.717510i	$-0.745282\pi$
$83$	0.190970	−	0.190970i	0.0209616	−	0.0209616i	0.717510	+	0.696548i	$0.245282\pi$
$84$	0.176495			0.0192571
$85$	10.9254	+	3.41421i	1.18503	+	0.370323i
$86$		−	1.51043i		−	0.162874i
$87$	−6.13963	+	6.13963i	−0.658238	+	0.658238i
$88$	−0.390701	+	0.390701i	−0.0416489	+	0.0416489i
$89$	−8.76193			−0.928762			−0.464381	−	0.885635i	$-0.653723\pi$
$89$	−8.76193			−0.928762			−0.464381	+	0.885635i	$0.653723\pi$
$90$	−2.13428	−	0.666968i	−0.224973	−	0.0703046i
$91$		−	0.670909i		−	0.0703304i
$92$	−4.79526	−	0.0741463i	−0.499940	−	0.00773029i
$93$	−1.73669	−	1.73669i	−0.180086	−	0.180086i
$94$		−	0.844759i		−	0.0871302i
$95$	−2.14783	+	1.12505i	−0.220363	+	0.115428i
$96$	−1.00000			−0.102062
$97$	1.62982	+	1.62982i	0.165484	+	0.165484i	0.784991	−	0.619507i	$-0.212668\pi$
$97$	1.62982	+	1.62982i	0.165484	+	0.165484i	−0.619507	+	0.784991i	$0.712668\pi$
$98$	4.92772	+	4.92772i	0.497775	+	0.497775i
$99$	−0.552534			−0.0555318
$100$	−4.11031	−	2.84699i	−0.411031	−	0.284699i
$101$	−5.93104			−0.590161			−0.295080	−	0.955472i	$-0.595346\pi$
$101$	−5.93104			−0.590161			−0.295080	+	0.955472i	$0.595346\pi$
$102$	3.61968	+	3.61968i	0.358402	+	0.358402i
$103$	3.77864	−	3.77864i	0.372321	−	0.372321i	−0.496001	−	0.868322i	$-0.665199\pi$
$103$	3.77864	−	3.77864i	0.372321	−	0.372321i	0.868322	+	0.496001i	$0.165199\pi$
$104$			3.80130i			0.372748i
$105$	0.183121	+	0.349597i	0.0178708	+	0.0341172i
$106$			8.41875i			0.817701i
$107$	−9.09321	−	9.09321i	−0.879074	−	0.879074i	0.114365	−	0.993439i	$-0.463517\pi$
$107$	−9.09321	−	9.09321i	−0.879074	−	0.879074i	−0.993439	+	0.114365i	$0.963517\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−13.5947			−1.30213			−0.651067	−	0.759021i	$-0.725678\pi$
$109$	−13.5947			−1.30213			−0.651067	+	0.759021i	$0.725678\pi$
$110$	−1.17926	−	0.368523i	−0.112438	−	0.0351373i
$111$		−	11.0244i		−	1.04639i
$112$	0.124800	+	0.124800i	0.0117925	+	0.0117925i
$113$	−9.30335	+	9.30335i	−0.875186	+	0.875186i	−0.993032	−	0.117846i	$-0.962401\pi$
$113$	−9.30335	+	9.30335i	−0.875186	+	0.875186i	0.117846	+	0.993032i	$0.462401\pi$
$114$	−1.08434			−0.101557
$115$	−4.82844	−	9.57529i	−0.450254	−	0.892901i
$116$	−8.68275			−0.806173
$117$	−2.68793	+	2.68793i	−0.248499	+	0.248499i
$118$	7.36028	+	7.36028i	0.677569	+	0.677569i
$119$		−	0.903477i		−	0.0828216i
$120$	−1.03755	−	1.98078i	−0.0947146	−	0.180820i
$121$	10.6947			0.972246
$122$	−6.44939	−	6.44939i	−0.583900	−	0.583900i
$123$	1.60857	+	1.60857i	0.145040	+	0.145040i
$124$		−	2.45605i		−	0.220559i
$125$	1.37464	−	11.0955i	0.122952	−	0.992413i
$126$			0.176495i			0.0157234i
$127$	−14.8431	+	14.8431i	−1.31711	+	1.31711i	−0.401054	+	0.916054i	$0.631356\pi$
$127$	−14.8431	+	14.8431i	−1.31711	+	1.31711i	−0.916054	+	0.401054i	$0.868644\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.51043			0.132986
$130$	−7.52955	+	3.94403i	−0.660386	+	0.345914i
$131$	−8.69869			−0.760008			−0.380004	−	0.924985i	$-0.624077\pi$
$131$	−8.69869			−0.760008			−0.380004	+	0.924985i	$0.624077\pi$
$132$	−0.390701	−	0.390701i	−0.0340061	−	0.0340061i
$133$	0.135326	+	0.135326i	0.0117342	+	0.0117342i
$134$	−7.61541			−0.657871
$135$	0.666968	−	2.13428i	0.0574035	−	0.183690i
$136$			5.11901i			0.438951i
$137$	6.93107	+	6.93107i	0.592161	+	0.592161i	0.938215	−	0.346053i	$-0.112478\pi$
$137$	6.93107	+	6.93107i	0.592161	+	0.592161i	−0.346053	+	0.938215i	$0.612478\pi$
$138$	0.0741463	−	4.79526i	0.00631175	−	0.408199i
$139$		−	2.07505i		−	0.176003i	−0.996120	−	0.0880017i	$-0.971952\pi$
$139$		−	2.07505i		−	0.176003i	0.996120	−	0.0880017i	$-0.0280481\pi$
$140$	−0.117716	+	0.376689i	−0.00994884	+	0.0318360i
$141$	0.844759			0.0711415
$142$	−5.77533	+	5.77533i	−0.484655	+	0.484655i
$143$	−1.48517	+	1.48517i	−0.124196	+	0.124196i
$144$		−	1.00000i		−	0.0833333i
$145$	−9.00876	−	17.1986i	−0.748137	−	1.42827i
$146$	−4.41769			−0.365610
$147$	−4.92772	+	4.92772i	−0.406432	+	0.406432i
$148$	7.79545	−	7.79545i	0.640782	−	0.640782i
$149$	12.3141			1.00881			0.504406	−	0.863466i	$-0.331711\pi$
$149$	12.3141			1.00881			0.504406	+	0.863466i	$0.331711\pi$
$150$	2.84699	−	4.11031i	0.232456	−	0.335605i
$151$	−10.0500			−0.817860			−0.408930	−	0.912566i	$-0.634098\pi$
$151$	−10.0500			−0.817860			−0.408930	+	0.912566i	$0.634098\pi$
$152$	−0.766741	−	0.766741i	−0.0621909	−	0.0621909i
$153$	−3.61968	+	3.61968i	−0.292634	+	0.292634i
$154$			0.0975193i			0.00785833i
$155$	4.86489	−	2.54826i	0.390758	−	0.204681i
$156$	−3.80130			−0.304348
$157$	3.40779	+	3.40779i	0.271972	+	0.271972i	0.829893	−	0.557922i	$-0.188401\pi$
$157$	3.40779	+	3.40779i	0.271972	+	0.271972i	−0.557922	+	0.829893i	$0.688401\pi$
$158$	−4.78694	+	4.78694i	−0.380828	+	0.380828i
$159$	−8.41875			−0.667650
$160$	0.666968	−	2.13428i	0.0527285	−	0.168730i
$161$	−0.607704	+	0.589197i	−0.0478938	+	0.0464352i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−10.9785	−	10.9785i	−0.859900	−	0.859900i	0.131426	−	0.991326i	$-0.458044\pi$
$163$	−10.9785	−	10.9785i	−0.859900	−	0.859900i	−0.991326	+	0.131426i	$0.958044\pi$
$164$			2.27486i			0.177637i
$165$	0.368523	−	1.17926i	0.0286895	−	0.0918055i
$166$			0.270072i			0.0209616i
$167$	0.393053	−	0.393053i	0.0304153	−	0.0304153i	−0.691736	−	0.722151i	$-0.743154\pi$
$167$	0.393053	−	0.393053i	0.0304153	−	0.0304153i	0.722151	+	0.691736i	$0.243154\pi$
$168$	−0.124800	+	0.124800i	−0.00962857	+	0.00962857i
$169$			1.44991i			0.111531i
$170$	−10.1396	+	5.31121i	−0.777674	+	0.407351i
$171$		−	1.08434i		−	0.0829212i
$172$	1.06804	+	1.06804i	0.0814370	+	0.0814370i
$173$	−6.09087	−	6.09087i	−0.463081	−	0.463081i	0.436583	−	0.899664i	$-0.356188\pi$
$173$	−6.09087	−	6.09087i	−0.463081	−	0.463081i	−0.899664	+	0.436583i	$0.856188\pi$
$174$		−	8.68275i		−	0.658238i
$175$	−0.868275	+	0.157662i	−0.0656354	+	0.0119181i
$176$		−	0.552534i		−	0.0416489i
$177$	−7.36028	+	7.36028i	−0.553233	+	0.553233i
$178$	6.19562	−	6.19562i	0.464381	−	0.464381i
$179$			23.2150i			1.73517i	0.497291	+	0.867584i	$0.334328\pi$
$179$			23.2150i			1.73517i	−0.497291	+	0.867584i	$0.665672\pi$
$180$	1.98078	−	1.03755i	0.147639	−	0.0773342i
$181$		−	6.45396i		−	0.479719i	−0.970808	−	0.239860i	$-0.922899\pi$
$181$		−	6.45396i		−	0.479719i	0.970808	−	0.239860i	$-0.0771014\pi$
$182$	0.474405	+	0.474405i	0.0351652	+	0.0351652i
$183$	6.44939	−	6.44939i	0.476753	−	0.476753i
$184$	3.44319	−	3.33833i	0.253835	−	0.246105i
$185$	23.5292	+	7.35295i	1.72990	+	0.540599i
$186$	2.45605			0.180086
$187$	−2.00000	+	2.00000i	−0.146254	+	0.146254i
$188$	0.597335	+	0.597335i	0.0435651	+	0.0435651i
$189$	−0.176495			−0.0128381
$190$	0.723217	−	2.31428i	0.0524677	−	0.167895i
$191$		−	22.6724i		−	1.64052i	−0.571991	−	0.820260i	$-0.693829\pi$
$191$		−	22.6724i		−	1.64052i	0.571991	−	0.820260i	$-0.306171\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	7.13533	+	7.13533i	0.513612	+	0.513612i	0.915631	−	0.402019i	$-0.131692\pi$
$193$	7.13533	+	7.13533i	0.513612	+	0.513612i	−0.402019	+	0.915631i	$0.631692\pi$
$194$	−2.30492			−0.165484
$195$	−3.94403	−	7.52955i	−0.282438	−	0.539203i
$196$	−6.96885			−0.497775
$197$	2.41931	−	2.41931i	0.172369	−	0.172369i	−0.615651	−	0.788019i	$-0.711107\pi$
$197$	2.41931	−	2.41931i	0.172369	−	0.172369i	0.788019	+	0.615651i	$0.211107\pi$
$198$	0.390701	−	0.390701i	0.0277659	−	0.0277659i
$199$	−22.7308			−1.61134			−0.805672	−	0.592362i	$-0.798195\pi$
$199$	−22.7308			−1.61134			−0.805672	+	0.592362i	$0.798195\pi$
$200$	4.91955	−	0.893297i	0.347865	−	0.0631656i
$201$		−	7.61541i		−	0.537149i
$202$	4.19388	−	4.19388i	0.295080	−	0.295080i
$203$	−1.08361	+	1.08361i	−0.0760546	+	0.0760546i
$204$	−5.11901			−0.358402
$205$	−4.50600	+	2.36027i	−0.314713	+	0.164849i
$206$			5.34381i			0.372321i
$207$	4.79526	+	0.0741463i	0.333293	+	0.00515352i
$208$	−2.68793	−	2.68793i	−0.186374	−	0.186374i
$209$		−	0.599133i		−	0.0414429i
$210$	−0.376689	−	0.117716i	−0.0259940	−	0.00812319i
$211$	−22.6042			−1.55613			−0.778067	−	0.628181i	$-0.783800\pi$
$211$	−22.6042			−1.55613			−0.778067	+	0.628181i	$0.783800\pi$
$212$	−5.95295	−	5.95295i	−0.408851	−	0.408851i
$213$	−5.77533	−	5.77533i	−0.395719	−	0.395719i
$214$	12.8597			0.879074
$215$	−1.00741	+	3.22368i	−0.0687047	+	0.219853i
$216$	1.00000			0.0680414
$217$	−0.306516	−	0.306516i	−0.0208076	−	0.0208076i
$218$	9.61288	−	9.61288i	0.651067	−	0.651067i
$219$		−	4.41769i		−	0.298520i
$220$	1.09445	−	0.573280i	0.0737878	−	0.0386505i
$221$			19.4589i			1.30895i
$222$	7.79545	+	7.79545i	0.523197	+	0.523197i
$223$	10.6254	+	10.6254i	0.711531	+	0.711531i	0.966855	−	0.255325i	$-0.0821823\pi$
$223$	10.6254	+	10.6254i	0.711531	+	0.711531i	−0.255325	+	0.966855i	$0.582182\pi$
$224$	−0.176495			−0.0117925
$225$	4.11031	+	2.84699i	0.274020	+	0.189800i
$226$		−	13.1569i		−	0.875186i
$227$	4.66128	+	4.66128i	0.309380	+	0.309380i	0.844669	−	0.535289i	$-0.179797\pi$
$227$	4.66128	+	4.66128i	0.309380	+	0.309380i	−0.535289	+	0.844669i	$0.679797\pi$
$228$	0.766741	−	0.766741i	0.0507787	−	0.0507787i
$229$	6.63852			0.438686			0.219343	−	0.975648i	$-0.429609\pi$
$229$	6.63852			0.438686			0.219343	+	0.975648i	$0.429609\pi$
$230$	10.1850	+	3.35653i	0.671577	+	0.221323i
$231$	−0.0975193			−0.00641630
$232$	6.13963	−	6.13963i	0.403087	−	0.403087i
$233$	−3.52576	−	3.52576i	−0.230980	−	0.230980i	0.582122	−	0.813102i	$-0.302223\pi$
$233$	−3.52576	−	3.52576i	−0.230980	−	0.230980i	−0.813102	+	0.582122i	$0.802223\pi$
$234$		−	3.80130i		−	0.248499i
$235$	−0.563427	+	1.80295i	−0.0367539	+	0.117612i
$236$	−10.4090			−0.677569
$237$	−4.78694	−	4.78694i	−0.310945	−	0.310945i
$238$	0.638854	+	0.638854i	0.0414108	+	0.0414108i
$239$			19.3650i			1.25262i	0.779574	+	0.626310i	$0.215436\pi$
$239$			19.3650i			1.25262i	−0.779574	+	0.626310i	$0.784564\pi$
$240$	2.13428	+	0.666968i	0.137767	+	0.0430526i
$241$			20.0648i			1.29248i	0.763132	+	0.646242i	$0.223661\pi$
$241$			20.0648i			1.29248i	−0.763132	+	0.646242i	$0.776339\pi$
$242$	−7.56230	+	7.56230i	−0.486123	+	0.486123i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	9.12081			0.583900
$245$	−7.23051	−	13.8038i	−0.461940	−	0.881891i
$246$	−2.27486			−0.145040
$247$	−2.91461	−	2.91461i	−0.185452	−	0.185452i
$248$	1.73669	+	1.73669i	0.110280	+	0.110280i
$249$	−0.270072			−0.0171151
$250$	6.87369	+	8.81773i	0.434731	+	0.557682i
$251$			29.2252i			1.84468i	0.386381	+	0.922339i	$0.373725\pi$
$251$			29.2252i			1.84468i	−0.386381	+	0.922339i	$0.626275\pi$
$252$	−0.124800	−	0.124800i	−0.00786169	−	0.00786169i
$253$	2.64955	+	0.0409684i	0.166576	+	0.00257566i
$254$		−	20.9913i		−	1.31711i
$255$	−5.31121	−	10.1396i	−0.332601	−	0.634969i
$256$	1.00000			0.0625000
$257$	2.47796	−	2.47796i	0.154571	−	0.154571i	−0.625585	−	0.780156i	$-0.715140\pi$
$257$	2.47796	−	2.47796i	0.154571	−	0.154571i	0.780156	+	0.625585i	$0.215140\pi$
$258$	−1.06804	+	1.06804i	−0.0664930	+	0.0664930i
$259$		−	1.94575i		−	0.120903i
$260$	2.53535	−	8.11305i	0.157236	−	0.503150i
$261$	8.68275			0.537449
$262$	6.15090	−	6.15090i	0.380004	−	0.380004i
$263$	−6.69369	+	6.69369i	−0.412751	+	0.412751i	−0.882696	−	0.469945i	$-0.844274\pi$
$263$	−6.69369	+	6.69369i	−0.412751	+	0.412751i	0.469945	+	0.882696i	$0.344274\pi$
$264$	0.552534			0.0340061
$265$	5.61504	−	17.9680i	0.344929	−	1.10376i
$266$	−0.191379			−0.0117342
$267$	6.19562	+	6.19562i	0.379166	+	0.379166i
$268$	5.38491	−	5.38491i	0.328935	−	0.328935i
$269$		−	8.21211i		−	0.500701i	−0.968155	−	0.250350i	$-0.919454\pi$
$269$		−	8.21211i		−	0.500701i	0.968155	−	0.250350i	$-0.0805459\pi$
$270$	1.03755	+	1.98078i	0.0631431	+	0.120547i
$271$	8.60224			0.522549			0.261274	−	0.965265i	$-0.415857\pi$
$271$	8.60224			0.522549			0.261274	+	0.965265i	$0.415857\pi$
$272$	−3.61968	−	3.61968i	−0.219476	−	0.219476i
$273$	−0.474405	+	0.474405i	−0.0287123	+	0.0287123i
$274$	−9.80202			−0.592161
$275$	2.27109	+	1.57306i	0.136952	+	0.0948592i
$276$	3.33833	+	3.44319i	0.200944	+	0.207256i
$277$	−9.28544	+	9.28544i	−0.557908	+	0.557908i	−0.928711	−	0.370803i	$-0.879082\pi$
$277$	−9.28544	+	9.28544i	−0.557908	+	0.557908i	0.370803	+	0.928711i	$0.379082\pi$
$278$	1.46728	+	1.46728i	0.0880017	+	0.0880017i
$279$			2.45605i			0.147040i
$280$	−0.183121	−	0.349597i	−0.0109436	−	0.0208924i
$281$			15.2296i			0.908521i	0.890869	+	0.454261i	$0.150097\pi$
$281$			15.2296i			0.908521i	−0.890869	+	0.454261i	$0.849903\pi$
$282$	−0.597335	+	0.597335i	−0.0355708	+	0.0355708i
$283$	11.6676	−	11.6676i	0.693566	−	0.693566i	−0.269449	−	0.963015i	$-0.586842\pi$
$283$	11.6676	−	11.6676i	0.693566	−	0.693566i	0.963015	+	0.269449i	$0.0868415\pi$
$284$		−	8.16755i		−	0.484655i
$285$	2.31428	+	0.723217i	0.137086	+	0.0428397i
$286$		−	2.10035i		−	0.124196i
$287$	0.283904	+	0.283904i	0.0167583	+	0.0167583i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			9.20422i			0.541425i
$290$	18.5314	+	5.79112i	1.08820	+	0.340066i
$291$		−	2.30492i		−	0.135117i
$292$	3.12378	−	3.12378i	0.182805	−	0.182805i
$293$	−21.8568	+	21.8568i	−1.27689	+	1.27689i	−0.334484	+	0.942401i	$0.608562\pi$
$293$	−21.8568	+	21.8568i	−1.27689	+	1.27689i	−0.942401	+	0.334484i	$0.891438\pi$
$294$		−	6.96885i		−	0.406432i
$295$	−10.7998	−	20.6180i	−0.628790	−	1.20042i
$296$			11.0244i			0.640782i
$297$	0.390701	+	0.390701i	0.0226708	+	0.0226708i
$298$	−8.70740	+	8.70740i	−0.504406	+	0.504406i
$299$	13.0886	−	12.6900i	0.756934	−	0.733882i
$300$	0.893297	+	4.91955i	0.0515745	+	0.284031i
$301$	0.266583			0.0153656
$302$	7.10645	−	7.10645i	0.408930	−	0.408930i
$303$	4.19388	+	4.19388i	0.240932	+	0.240932i
$304$	1.08434			0.0621909
$305$	9.46327	+	18.0663i	0.541865	+	1.03448i
$306$		−	5.11901i		−	0.292634i
$307$	−6.33351	+	6.33351i	−0.361473	+	0.361473i	−0.864355	−	0.502882i	$-0.832273\pi$
$307$	−6.33351	+	6.33351i	−0.361473	+	0.361473i	0.502882	+	0.864355i	$0.332273\pi$
$308$	−0.0689566	−	0.0689566i	−0.00392917	−	0.00392917i
$309$	−5.34381			−0.303999
$310$	−1.63810	+	5.24189i	−0.0930381	+	0.297719i
$311$	21.7763			1.23482			0.617410	−	0.786641i	$-0.288182\pi$
$311$	21.7763			1.23482			0.617410	+	0.786641i	$0.288182\pi$
$312$	2.68793	−	2.68793i	0.152174	−	0.152174i
$313$	−21.2955	+	21.2955i	−1.20369	+	1.20369i	−0.230658	+	0.973035i	$0.574088\pi$
$313$	−21.2955	+	21.2955i	−1.20369	+	1.20369i	−0.973035	+	0.230658i	$0.925912\pi$
$314$	−4.81935			−0.271972
$315$	0.117716	−	0.376689i	0.00663256	−	0.0212240i
$316$		−	6.76975i		−	0.380828i
$317$	13.1005	−	13.1005i	0.735797	−	0.735797i	−0.235965	−	0.971762i	$-0.575825\pi$
$317$	13.1005	−	13.1005i	0.735797	−	0.735797i	0.971762	+	0.235965i	$0.0758251\pi$
$318$	5.95295	−	5.95295i	0.333825	−	0.333825i
$319$	4.79752			0.268610
$320$	1.03755	+	1.98078i	0.0580006	+	0.110729i
$321$			12.8597i			0.717761i
$322$	0.0130864	−	0.846337i	0.000729278	−	0.0471645i
$323$	−3.92495	−	3.92495i	−0.218390	−	0.218390i
$324$			1.00000i			0.0555556i
$325$	18.7007	−	3.39569i	1.03733	−	0.188359i
$326$	15.5259			0.859900
$327$	9.61288	+	9.61288i	0.531594	+	0.531594i
$328$	−1.60857	−	1.60857i	−0.0888184	−	0.0888184i
$329$	0.149095			0.00821989
$330$	0.573280	+	1.09445i	0.0315580	+	0.0602475i
$331$	−18.0446			−0.991822			−0.495911	−	0.868373i	$-0.665166\pi$
$331$	−18.0446			−0.991822			−0.495911	+	0.868373i	$0.665166\pi$
$332$	−0.190970	−	0.190970i	−0.0104808	−	0.0104808i
$333$	−7.79545	+	7.79545i	−0.427188	+	0.427188i
$334$			0.555860i			0.0304153i
$335$	16.2534	+	5.07923i	0.888019	+	0.277508i
$336$		−	0.176495i		−	0.00962857i
$337$	−11.3825	−	11.3825i	−0.620045	−	0.620045i	0.325498	−	0.945543i	$-0.394468\pi$
$337$	−11.3825	−	11.3825i	−0.620045	−	0.620045i	−0.945543	+	0.325498i	$0.894468\pi$
$338$	−1.02524	−	1.02524i	−0.0557657	−	0.0557657i
$339$	13.1569			0.714586
$340$	3.41421	−	10.9254i	0.185162	−	0.592513i
$341$			1.35705i			0.0734884i
$342$	0.766741	+	0.766741i	0.0414606	+	0.0414606i
$343$	−1.74332	+	1.74332i	−0.0941304	+	0.0941304i
$344$	−1.51043			−0.0814370
$345$	−3.35653	+	10.1850i	−0.180710	+	0.548341i
$346$	8.61380			0.463081
$347$	0.783931	−	0.783931i	0.0420836	−	0.0420836i	−0.685752	−	0.727835i	$-0.740526\pi$
$347$	0.783931	−	0.783931i	0.0420836	−	0.0420836i	0.727835	+	0.685752i	$0.240526\pi$
$348$	6.13963	+	6.13963i	0.329119	+	0.329119i
$349$		−	2.79894i		−	0.149824i	−0.997190	−	0.0749120i	$-0.976132\pi$
$349$		−	2.79894i		−	0.149824i	0.997190	−	0.0749120i	$-0.0238676\pi$
$350$	0.502479	−	0.725447i	0.0268586	−	0.0387768i
$351$	3.80130			0.202899
$352$	0.390701	+	0.390701i	0.0208244	+	0.0208244i
$353$	−8.28523	−	8.28523i	−0.440978	−	0.440978i	0.451362	−	0.892341i	$-0.350938\pi$
$353$	−8.28523	−	8.28523i	−0.440978	−	0.440978i	−0.892341	+	0.451362i	$0.850938\pi$
$354$		−	10.4090i		−	0.553233i
$355$	16.1781	−	8.47421i	0.858646	−	0.449764i
$356$			8.76193i			0.464381i
$357$	−0.638854	+	0.638854i	−0.0338118	+	0.0338118i
$358$	−16.4155	−	16.4155i	−0.867584	−	0.867584i
$359$	−18.5465			−0.978847			−0.489424	−	0.872046i	$-0.662793\pi$
$359$	−18.5465			−0.978847			−0.489424	+	0.872046i	$0.662793\pi$
$360$	−0.666968	+	2.13428i	−0.0351523	+	0.112486i
$361$	−17.8242			−0.938117
$362$	4.56364	+	4.56364i	0.239860	+	0.239860i
$363$	−7.56230	−	7.56230i	−0.396918	−	0.396918i
$364$	−0.670909			−0.0351652
$365$	9.42859	+	2.94646i	0.493515	+	0.154225i
$366$			9.12081i			0.476753i
$367$	14.6933	+	14.6933i	0.766985	+	0.766985i	0.977574	−	0.210590i	$-0.0675385\pi$
$367$	14.6933	+	14.6933i	0.766985	+	0.766985i	−0.210590	+	0.977574i	$0.567538\pi$
$368$	−0.0741463	+	4.79526i	−0.00386514	+	0.249970i
$369$		−	2.27486i		−	0.118425i
$370$	−21.8370	+	11.4384i	−1.13525	+	0.594652i
$371$	−1.48586			−0.0771422
$372$	−1.73669	+	1.73669i	−0.0900430	+	0.0900430i
$373$	3.14679	−	3.14679i	0.162935	−	0.162935i	−0.620931	−	0.783865i	$-0.713245\pi$
$373$	3.14679	−	3.14679i	0.162935	−	0.162935i	0.783865	+	0.620931i	$0.213245\pi$
$374$		−	2.82843i		−	0.146254i
$375$	−8.81773	+	6.87369i	−0.455346	+	0.354956i
$376$	−0.844759			−0.0435651
$377$	23.3386	−	23.3386i	1.20200	−	1.20200i
$378$	0.124800	−	0.124800i	0.00641904	−	0.00641904i
$379$	16.5615			0.850706			0.425353	−	0.905028i	$-0.360150\pi$
$379$	16.5615			0.850706			0.425353	+	0.905028i	$0.360150\pi$
$380$	1.12505	+	2.14783i	0.0577138	+	0.110181i
$381$	20.9913			1.07541
$382$	16.0318	+	16.0318i	0.820260	+	0.820260i
$383$	−11.2204	+	11.2204i	−0.573338	+	0.573338i	−0.933060	−	0.359722i	$-0.882872\pi$
$383$	−11.2204	+	11.2204i	−0.573338	+	0.573338i	0.359722	+	0.933060i	$0.382872\pi$
$384$			1.00000i			0.0510310i
$385$	0.0650423	−	0.208134i	0.00331486	−	0.0106075i
$386$	−10.0909			−0.513612
$387$	−1.06804	−	1.06804i	−0.0542913	−	0.0542913i
$388$	1.62982	−	1.62982i	0.0827418	−	0.0827418i
$389$	26.6584			1.35164			0.675818	−	0.737068i	$-0.263790\pi$
$389$	26.6584			1.35164			0.675818	+	0.737068i	$0.263790\pi$
$390$	8.11305	+	2.53535i	0.410820	+	0.128382i
$391$	17.6257	−	17.0889i	0.891370	−	0.864224i
$392$	4.92772	−	4.92772i	0.248887	−	0.248887i
$393$	6.15090	+	6.15090i	0.310272	+	0.310272i
$394$			3.42142i			0.172369i
$395$	13.4094	−	7.02393i	0.674700	−	0.353412i
$396$			0.552534i			0.0277659i
$397$	1.03788	−	1.03788i	0.0520899	−	0.0520899i	−0.680582	−	0.732672i	$-0.738273\pi$
$397$	1.03788	−	1.03788i	0.0520899	−	0.0520899i	0.732672	+	0.680582i	$0.238273\pi$
$398$	16.0731	−	16.0731i	0.805672	−	0.805672i
$399$		−	0.191379i		−	0.00958095i
$400$	−2.84699	+	4.11031i	−0.142350	+	0.205515i
$401$		−	24.1332i		−	1.20516i	−0.798060	−	0.602578i	$-0.794140\pi$
$401$		−	24.1332i		−	1.20516i	0.798060	−	0.602578i	$-0.205860\pi$
$402$	5.38491	+	5.38491i	0.268575	+	0.268575i
$403$	6.60168	+	6.60168i	0.328853	+	0.328853i
$404$			5.93104i			0.295080i
$405$	−1.98078	+	1.03755i	−0.0984258	+	0.0515561i
$406$		−	1.53246i		−	0.0760546i
$407$	−4.30726	+	4.30726i	−0.213503	+	0.213503i
$408$	3.61968	−	3.61968i	0.179201	−	0.179201i
$409$			17.2612i			0.853511i	0.904367	+	0.426756i	$0.140344\pi$
$409$			17.2612i			0.853511i	−0.904367	+	0.426756i	$0.859656\pi$
$410$	1.51726	−	4.85519i	0.0749321	−	0.239781i
$411$		−	9.80202i		−	0.483498i
$412$	−3.77864	−	3.77864i	−0.186160	−	0.186160i
$413$	−1.29905	+	1.29905i	−0.0639220	+	0.0639220i
$414$	−3.44319	+	3.33833i	−0.169224	+	0.164070i
$415$	0.180129	−	0.576409i	0.00884220	−	0.0282948i
$416$	3.80130			0.186374
$417$	−1.46728	+	1.46728i	−0.0718531	+	0.0718531i
$418$	0.423651	+	0.423651i	0.0207214	+	0.0207214i
$419$	8.83329			0.431534			0.215767	−	0.976445i	$-0.430775\pi$
$419$	8.83329			0.431534			0.215767	+	0.976445i	$0.430775\pi$
$420$	0.349597	−	0.183121i	0.0170586	−	0.00893540i
$421$		−	22.9157i		−	1.11684i	−0.829558	−	0.558421i	$-0.811408\pi$
$421$		−	22.9157i		−	1.11684i	0.829558	−	0.558421i	$-0.188592\pi$
$422$	15.9836	−	15.9836i	0.778067	−	0.778067i
$423$	−0.597335	−	0.597335i	−0.0290434	−	0.0290434i
$424$	8.41875			0.408851
$425$	25.1832	−	4.57279i	1.22157	−	0.221813i
$426$	8.16755			0.395719
$427$	1.13828	−	1.13828i	0.0550853	−	0.0550853i
$428$	−9.09321	+	9.09321i	−0.439537	+	0.439537i
$429$	2.10035			0.101406
$430$	−1.56714	−	2.99183i	−0.0755743	−	0.144279i
$431$			4.11877i			0.198394i	0.995068	+	0.0991970i	$0.0316274\pi$
$431$			4.11877i			0.198394i	−0.995068	+	0.0991970i	$0.968373\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	13.2007	−	13.2007i	0.634383	−	0.634383i	−0.314781	−	0.949164i	$-0.601931\pi$
$433$	13.2007	−	13.2007i	0.634383	−	0.634383i	0.949164	+	0.314781i	$0.101931\pi$
$434$	0.433479			0.0208076
$435$	−5.79112	+	18.5314i	−0.277663	+	0.888514i
$436$			13.5947i			0.651067i
$437$	−0.0803995	+	5.19967i	−0.00384603	+	0.248734i
$438$	3.12378	+	3.12378i	0.149260	+	0.149260i
$439$			13.3446i			0.636905i	0.947939	+	0.318452i	$0.103163\pi$
$439$			13.3446i			0.636905i	−0.947939	+	0.318452i	$0.896837\pi$
$440$	−0.368523	+	1.17926i	−0.0175686	+	0.0562192i
$441$	6.96885			0.331850
$442$	−13.7595	−	13.7595i	−0.654473	−	0.654473i
$443$	−17.1528	−	17.1528i	−0.814955	−	0.814955i	0.170417	−	0.985372i	$-0.445489\pi$
$443$	−17.1528	−	17.1528i	−0.814955	−	0.814955i	−0.985372	+	0.170417i	$0.945489\pi$
$444$	−11.0244			−0.523197
$445$	−17.3555	+	9.09091i	−0.822728	+	0.430950i
$446$	−15.0266			−0.711531
$447$	−8.70740	−	8.70740i	−0.411846	−	0.411846i
$448$	0.124800	−	0.124800i	0.00589627	−	0.00589627i
$449$			7.35156i			0.346942i	0.984839	+	0.173471i	$0.0554982\pi$
$449$			7.35156i			0.346942i	−0.984839	+	0.173471i	$0.944502\pi$
$450$	−4.91955	+	0.893297i	−0.231910	+	0.0421104i
$451$		−	1.25694i		−	0.0591870i
$452$	9.30335	+	9.30335i	0.437593	+	0.437593i
$453$	7.10645	+	7.10645i	0.333890	+	0.333890i
$454$	−6.59205			−0.309380
$455$	−0.696100	−	1.32893i	−0.0326337	−	0.0623010i
$456$			1.08434i			0.0507787i
$457$	−1.61697	−	1.61697i	−0.0756388	−	0.0756388i	0.668275	−	0.743914i	$-0.267033\pi$
$457$	−1.61697	−	1.61697i	−0.0756388	−	0.0756388i	−0.743914	+	0.668275i	$0.767033\pi$
$458$	−4.69415	+	4.69415i	−0.219343	+	0.219343i
$459$	5.11901			0.238935
$460$	−9.57529	+	4.82844i	−0.446450	+	0.225127i
$461$	−19.4223			−0.904586			−0.452293	−	0.891869i	$-0.649394\pi$
$461$	−19.4223			−0.904586			−0.452293	+	0.891869i	$0.649394\pi$
$462$	0.0689566	−	0.0689566i	0.00320815	−	0.00320815i
$463$	−16.6725	−	16.6725i	−0.774836	−	0.774836i	0.204112	−	0.978948i	$-0.434569\pi$
$463$	−16.6725	−	16.6725i	−0.774836	−	0.774836i	−0.978948	+	0.204112i	$0.934569\pi$
$464$			8.68275i			0.403087i
$465$	−5.24189	−	1.63810i	−0.243087	−	0.0759653i
$466$	4.98618			0.230980
$467$	−18.7427	−	18.7427i	−0.867310	−	0.867310i	0.124864	−	0.992174i	$-0.460150\pi$
$467$	−18.7427	−	18.7427i	−0.867310	−	0.867310i	−0.992174	+	0.124864i	$0.960150\pi$
$468$	2.68793	+	2.68793i	0.124249	+	0.124249i
$469$		−	1.34408i		−	0.0620637i
$470$	−0.876477	−	1.67328i	−0.0404289	−	0.0771828i
$471$		−	4.81935i		−	0.222064i
$472$	7.36028	−	7.36028i	0.338784	−	0.338784i
$473$	−0.590127	−	0.590127i	−0.0271341	−	0.0271341i
$474$	6.76975			0.310945
$475$	−3.08710	+	4.45695i	−0.141646	+	0.204499i
$476$	−0.903477			−0.0414108
$477$	5.95295	+	5.95295i	0.272567	+	0.272567i
$478$	−13.6932	−	13.6932i	−0.626310	−	0.626310i
$479$	−4.02931			−0.184104			−0.0920520	−	0.995754i	$-0.529343\pi$
$479$	−4.02931			−0.184104			−0.0920520	+	0.995754i	$0.529343\pi$
$480$	−1.98078	+	1.03755i	−0.0904099	+	0.0473573i
$481$			41.9072i			1.91081i
$482$	−14.1879	−	14.1879i	−0.646242	−	0.646242i
$483$	0.846337	+	0.0130864i	0.0385097	+	0.000595453i
$484$		−	10.6947i		−	0.486123i
$485$	4.91935	+	1.53731i	0.223376	+	0.0698056i
$486$	−1.00000			−0.0453609
$487$	−15.4120	+	15.4120i	−0.698385	+	0.698385i	−0.964062	−	0.265677i	$-0.914404\pi$
$487$	−15.4120	+	15.4120i	−0.698385	+	0.698385i	0.265677	+	0.964062i	$0.414404\pi$
$488$	−6.44939	+	6.44939i	−0.291950	+	0.291950i
$489$			15.5259i			0.702105i
$490$	14.8735	+	4.64800i	0.671915	+	0.209975i
$491$	2.44078			0.110151			0.0550755	−	0.998482i	$-0.482460\pi$
$491$	2.44078			0.110151			0.0550755	+	0.998482i	$0.482460\pi$
$492$	1.60857	−	1.60857i	0.0725199	−	0.0725199i
$493$	31.4288	−	31.4288i	1.41548	−	1.41548i
$494$	4.12189			0.185452
$495$	−1.09445	+	0.573280i	−0.0491919	+	0.0257670i
$496$	−2.45605			−0.110280
$497$	−1.01931	−	1.01931i	−0.0457225	−	0.0457225i
$498$	0.190970	−	0.190970i	0.00855756	−	0.00855756i
$499$		−	42.3741i		−	1.89693i	−0.316889	−	0.948463i	$-0.602638\pi$
$499$		−	42.3741i		−	1.89693i	0.316889	−	0.948463i	$-0.397362\pi$
$500$	−11.0955	−	1.37464i	−0.496206	−	0.0614758i
$501$	−0.555860			−0.0248340
$502$	−20.6653	−	20.6653i	−0.922339	−	0.922339i
$503$	−28.9820	+	28.9820i	−1.29224	+	1.29224i	−0.358846	+	0.933397i	$0.616830\pi$
$503$	−28.9820	+	28.9820i	−1.29224	+	1.29224i	−0.933397	+	0.358846i	$0.883170\pi$
$504$	0.176495			0.00786169
$505$	−11.7481	+	6.15373i	−0.522784	+	0.273838i
$506$	−1.90248	+	1.84454i	−0.0845756	+	0.0819999i
$507$	1.02524	−	1.02524i	0.0455325	−	0.0455325i
$508$	14.8431	+	14.8431i	0.658554	+	0.658554i
$509$		−	3.86372i		−	0.171257i	−0.996327	−	0.0856283i	$-0.972710\pi$
$509$		−	3.86372i		−	0.171257i	0.996327	−	0.0856283i	$-0.0272897\pi$
$510$	10.9254	+	3.41421i	0.483785	+	0.151184i
$511$		−	0.779698i		−	0.0344918i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.766741	+	0.766741i	−0.0338524	+	0.0338524i
$514$			3.50437i			0.154571i
$515$	3.56415	−	11.4052i	0.157055	−	0.502573i
$516$		−	1.51043i		−	0.0664930i
$517$	−0.330048	−	0.330048i	−0.0145155	−	0.0145155i
$518$	1.37586	+	1.37586i	0.0604516	+	0.0604516i
$519$			8.61380i			0.378104i
$520$	3.94403	+	7.52955i	0.172957	+	0.330193i
$521$		−	19.8403i		−	0.869221i	−0.900619	−	0.434610i	$-0.856886\pi$
$521$		−	19.8403i		−	0.869221i	0.900619	−	0.434610i	$-0.143114\pi$
$522$	−6.13963	+	6.13963i	−0.268724	+	0.268724i
$523$	13.6045	−	13.6045i	0.594883	−	0.594883i	−0.344063	−	0.938946i	$-0.611803\pi$
$523$	13.6045	−	13.6045i	0.594883	−	0.594883i	0.938946	+	0.344063i	$0.111803\pi$
$524$			8.69869i			0.380004i
$525$	0.725447	+	0.502479i	0.0316611	+	0.0219300i
$526$		−	9.46631i		−	0.412751i
$527$	8.89011	+	8.89011i	0.387259	+	0.387259i
$528$	−0.390701	+	0.390701i	−0.0170031	+	0.0170031i
$529$	−22.9890	−	0.711101i	−0.999522	−	0.0309175i
$530$	8.73484	+	16.6757i	0.379417	+	0.724346i
$531$	10.4090			0.451712
$532$	0.135326	−	0.135326i	0.00586711	−	0.00586711i
$533$	−6.11466	−	6.11466i	−0.264855	−	0.264855i
$534$	−8.76193			−0.379166
$535$	−27.4463	−	8.57704i	−1.18661	−	0.370818i
$536$			7.61541i			0.328935i
$537$	16.4155	−	16.4155i	0.708379	−	0.708379i
$538$	5.80684	+	5.80684i	0.250350	+	0.250350i
$539$	3.85053			0.165854
$540$	−2.13428	−	0.666968i	−0.0918448	−	0.0287017i
$541$	−21.3249			−0.916828			−0.458414	−	0.888739i	$-0.651582\pi$
$541$	−21.3249			−0.916828			−0.458414	+	0.888739i	$0.651582\pi$
$542$	−6.08270	+	6.08270i	−0.261274	+	0.261274i
$543$	−4.56364	+	4.56364i	−0.195845	+	0.195845i
$544$	5.11901			0.219476
$545$	−26.9281	+	14.1051i	−1.15347	+	0.604196i
$546$		−	0.670909i		−	0.0287123i
$547$	21.0991	−	21.0991i	0.902131	−	0.902131i	−0.0934889	−	0.995620i	$-0.529802\pi$
$547$	21.0991	−	21.0991i	0.902131	−	0.902131i	0.995620	+	0.0934889i	$0.0298020\pi$
$548$	6.93107	−	6.93107i	0.296081	−	0.296081i
$549$	−9.12081			−0.389267
$550$	−2.71822	+	0.493577i	−0.115905	+	0.0210462i
$551$			9.41502i			0.401093i
$552$	−4.79526	−	0.0741463i	−0.204100	−	0.00315588i
$553$	−0.844868	−	0.844868i	−0.0359274	−	0.0359274i
$554$		−	13.1316i		−	0.557908i
$555$	−11.4384	−	21.8370i	−0.485532	−	0.926929i
$556$	−2.07505			−0.0880017
$557$	−27.8064	−	27.8064i	−1.17820	−	1.17820i	−0.980203	−	0.197993i	$-0.936558\pi$
$557$	−27.8064	−	27.8064i	−1.17820	−	1.17820i	−0.197993	−	0.980203i	$-0.563442\pi$
$558$	−1.73669	−	1.73669i	−0.0735198	−	0.0735198i
$559$	−5.74161			−0.242844
$560$	0.376689	+	0.117716i	0.0159180	+	0.00497442i
$561$	2.82843			0.119416
$562$	−10.7689	−	10.7689i	−0.454261	−	0.454261i
$563$	22.4843	−	22.4843i	0.947602	−	0.947602i	−0.0510924	−	0.998694i	$-0.516270\pi$
$563$	22.4843	−	22.4843i	0.947602	−	0.947602i	0.998694	+	0.0510924i	$0.0162703\pi$
$564$		−	0.844759i		−	0.0355708i
$565$	−8.77525	+	28.0806i	−0.369178	+	1.18136i
$566$			16.5005i			0.693566i
$567$	0.124800	+	0.124800i	0.00524113	+	0.00524113i
$568$	5.77533	+	5.77533i	0.242327	+	0.242327i
$569$	33.7165			1.41347			0.706735	−	0.707479i	$-0.250168\pi$
$569$	33.7165			1.41347			0.706735	+	0.707479i	$0.250168\pi$
$570$	−2.14783	+	1.12505i	−0.0899628	+	0.0471231i
$571$		−	36.2733i		−	1.51799i	−0.651097	−	0.758995i	$-0.725691\pi$
$571$		−	36.2733i		−	1.51799i	0.651097	−	0.758995i	$-0.274309\pi$
$572$	1.48517	+	1.48517i	0.0620982	+	0.0620982i
$573$	−16.0318	+	16.0318i	−0.669740	+	0.669740i
$574$	−0.401501			−0.0167583
$575$	−19.4989	−	13.9568i	−0.813160	−	0.582040i
$576$	−1.00000			−0.0416667
$577$	−21.9088	+	21.9088i	−0.912076	+	0.912076i	−0.996435	−	0.0843592i	$-0.973116\pi$
$577$	−21.9088	+	21.9088i	−0.912076	+	0.912076i	0.0843592	+	0.996435i	$0.473116\pi$
$578$	−6.50837	−	6.50837i	−0.270712	−	0.270712i
$579$		−	10.0909i		−	0.419362i
$580$	−17.1986	+	9.00876i	−0.714135	+	0.374068i
$581$	−0.0476662			−0.00197753
$582$	1.62982	+	1.62982i	0.0675584	+	0.0675584i
$583$	3.28921	+	3.28921i	0.136225	+	0.136225i
$584$			4.41769i			0.182805i
$585$	−2.53535	+	8.11305i	−0.104824	+	0.335433i
$586$		−	30.9101i		−	1.27689i
$587$	28.8834	−	28.8834i	1.19215	−	1.19215i	0.215684	−	0.976463i	$-0.430802\pi$
$587$	28.8834	−	28.8834i	1.19215	−	1.19215i	0.976463	−	0.215684i	$-0.0691980\pi$
$588$	4.92772	+	4.92772i	0.203216	+	0.203216i
$589$	−2.66318			−0.109734
$590$	22.2157	+	6.94248i	0.914608	+	0.285817i
$591$	−3.42142			−0.140738
$592$	−7.79545	−	7.79545i	−0.320391	−	0.320391i
$593$	−21.3435	−	21.3435i	−0.876474	−	0.876474i	0.116694	−	0.993168i	$-0.462770\pi$
$593$	−21.3435	−	21.3435i	−0.876474	−	0.876474i	−0.993168	+	0.116694i	$0.962770\pi$
$594$	−0.552534			−0.0226708
$595$	−0.937399	−	1.78959i	−0.0384296	−	0.0733660i
$596$		−	12.3141i		−	0.504406i
$597$	16.0731	+	16.0731i	0.657828	+	0.657828i
$598$	−0.281853	+	18.2282i	−0.0115258	+	0.745408i
$599$			38.3444i			1.56671i	0.621576	+	0.783354i	$0.286493\pi$
$599$			38.3444i			1.56671i	−0.621576	+	0.783354i	$0.713507\pi$
$600$	−4.11031	−	2.84699i	−0.167803	−	0.116228i
$601$	16.2980			0.664808			0.332404	−	0.943137i	$-0.392140\pi$
$601$	16.2980			0.664808			0.332404	+	0.943137i	$0.392140\pi$
$602$	−0.188502	+	0.188502i	−0.00768279	+	0.00768279i
$603$	−5.38491	+	5.38491i	−0.219290	+	0.219290i
$604$			10.0500i			0.408930i
$605$	21.1839	−	11.0963i	0.861247	−	0.451127i
$606$	−5.93104			−0.240932
$607$	1.17706	−	1.17706i	0.0477754	−	0.0477754i	−0.682815	−	0.730591i	$-0.739245\pi$
$607$	1.17706	−	1.17706i	0.0477754	−	0.0477754i	0.730591	+	0.682815i	$0.239245\pi$
$608$	−0.766741	+	0.766741i	−0.0310954	+	0.0310954i
$609$	1.53246			0.0620984
$610$	−19.4664	−	6.08329i	−0.788171	−	0.246305i
$611$	−3.21119			−0.129911
$612$	3.61968	+	3.61968i	0.146317	+	0.146317i
$613$	−20.0004	+	20.0004i	−0.807808	+	0.807808i	−0.984302	−	0.176494i	$-0.943524\pi$
$613$	−20.0004	+	20.0004i	−0.807808	+	0.807808i	0.176494	+	0.984302i	$0.443524\pi$
$614$		−	8.95694i		−	0.361473i
$615$	4.85519	+	1.51726i	0.195780	+	0.0611818i
$616$	0.0975193			0.00392917
$617$	−18.9554	−	18.9554i	−0.763117	−	0.763117i	0.213767	−	0.976885i	$-0.431427\pi$
$617$	−18.9554	−	18.9554i	−0.763117	−	0.763117i	−0.976885	+	0.213767i	$0.931427\pi$
$618$	3.77864	−	3.77864i	0.151999	−	0.151999i
$619$	3.91634			0.157411			0.0787055	−	0.996898i	$-0.474921\pi$
$619$	3.91634			0.157411			0.0787055	+	0.996898i	$0.474921\pi$
$620$	−2.54826	−	4.86489i	−0.102341	−	0.195379i
$621$	−3.33833	−	3.44319i	−0.133963	−	0.138170i
$622$	−15.3982	+	15.3982i	−0.617410	+	0.617410i
$623$	1.09349	+	1.09349i	0.0438099	+	0.0438099i
$624$			3.80130i			0.152174i
$625$	−8.78925	−	23.4040i	−0.351570	−	0.936162i
$626$		−	30.1164i		−	1.20369i
$627$	−0.423651	+	0.423651i	−0.0169190	+	0.0169190i
$628$	3.40779	−	3.40779i	0.135986	−	0.135986i
$629$			56.4342i			2.25018i
$630$	0.183121	+	0.349597i	0.00729573	+	0.0139283i
$631$		−	34.6601i		−	1.37980i	−0.723906	−	0.689899i	$-0.757655\pi$
$631$		−	34.6601i		−	1.37980i	0.723906	−	0.689899i	$-0.242345\pi$
$632$	4.78694	+	4.78694i	0.190414	+	0.190414i
$633$	15.9836	+	15.9836i	0.635289	+	0.635289i
$634$			18.5269i			0.735797i
$635$	−14.0005	+	44.8012i	−0.555593	+	1.77788i
$636$			8.41875i			0.333825i
$637$	18.7318	−	18.7318i	0.742179	−	0.742179i
$638$	−3.39236	+	3.39236i	−0.134305	+	0.134305i
$639$			8.16755i			0.323103i
$640$	−2.13428	−	0.666968i	−0.0843648	−	0.0263642i
$641$			39.3379i			1.55375i	0.629653	+	0.776876i	$0.283197\pi$
$641$			39.3379i			1.55375i	−0.629653	+	0.776876i	$0.716803\pi$
$642$	−9.09321	−	9.09321i	−0.358880	−	0.358880i
$643$	−16.8975	+	16.8975i	−0.666371	+	0.666371i	−0.956874	−	0.290503i	$-0.906177\pi$
$643$	−16.8975	+	16.8975i	−0.666371	+	0.666371i	0.290503	+	0.956874i	$0.406177\pi$
$644$	0.589197	+	0.607704i	0.0232176	+	0.0239469i
$645$	2.99183	−	1.56714i	0.117803	−	0.0617062i
$646$	5.55072			0.218390
$647$	−29.2297	+	29.2297i	−1.14914	+	1.14914i	−0.162414	+	0.986723i	$0.551928\pi$
$647$	−29.2297	+	29.2297i	−1.14914	+	1.14914i	−0.986723	+	0.162414i	$0.948072\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	5.75134			0.225760
$650$	−10.8223	+	15.6245i	−0.424485	+	0.612844i
$651$			0.433479i			0.0169894i
$652$	−10.9785	+	10.9785i	−0.429950	+	0.429950i
$653$	−17.2954	−	17.2954i	−0.676820	−	0.676820i	0.282459	−	0.959279i	$-0.408850\pi$
$653$	−17.2954	−	17.2954i	−0.676820	−	0.676820i	−0.959279	+	0.282459i	$0.908850\pi$
$654$	−13.5947			−0.531594
$655$	−17.2302	+	9.02529i	−0.673240	+	0.352647i
$656$	2.27486			0.0888184
$657$	−3.12378	+	3.12378i	−0.121870	+	0.121870i
$658$	−0.105426	+	0.105426i	−0.00410995	+	0.00410995i
$659$	12.9859			0.505860			0.252930	−	0.967485i	$-0.418606\pi$
$659$	12.9859			0.505860			0.252930	+	0.967485i	$0.418606\pi$
$660$	−1.17926	−	0.368523i	−0.0459028	−	0.0143447i
$661$			30.6022i			1.19029i	0.803620	+	0.595143i	$0.202905\pi$
$661$			30.6022i			1.19029i	−0.803620	+	0.595143i	$0.797095\pi$
$662$	12.7595	−	12.7595i	0.495911	−	0.495911i
$663$	13.7595	−	13.7595i	0.534375	−	0.534375i
$664$	0.270072			0.0104808
$665$	0.408457	+	0.127644i	0.0158393	+	0.00494982i
$666$		−	11.0244i		−	0.427188i
$667$	−41.6360	−	0.643794i	−1.61215	−	0.0249278i
$668$	−0.393053	−	0.393053i	−0.0152077	−	0.0152077i
$669$		−	15.0266i		−	0.580963i
$670$	−15.0845	+	7.90134i	−0.582764	+	0.305255i
$671$	−5.03956			−0.194550
$672$	0.124800	+	0.124800i	0.00481428	+	0.00481428i
$673$	6.26582	+	6.26582i	0.241530	+	0.241530i	0.817483	−	0.575953i	$-0.195369\pi$
$673$	6.26582	+	6.26582i	0.241530	+	0.241530i	−0.575953	+	0.817483i	$0.695369\pi$
$674$	16.0973			0.620045
$675$	−0.893297	−	4.91955i	−0.0343830	−	0.189354i
$676$	1.44991			0.0557657
$677$	−31.0473	−	31.0473i	−1.19325	−	1.19325i	−0.976150	−	0.217096i	$-0.930342\pi$
$677$	−31.0473	−	31.0473i	−1.19325	−	1.19325i	−0.217096	−	0.976150i	$-0.569658\pi$
$678$	−9.30335	+	9.30335i	−0.357293	+	0.357293i
$679$		−	0.406806i		−	0.0156118i
$680$	5.31121	+	10.1396i	0.203675	+	0.388837i
$681$		−	6.59205i		−	0.252608i
$682$	−0.959580	−	0.959580i	−0.0367442	−	0.0367442i
$683$	36.0336	+	36.0336i	1.37879	+	1.37879i	0.846669	+	0.532120i	$0.178605\pi$
$683$	36.0336	+	36.0336i	1.37879	+	1.37879i	0.532120	+	0.846669i	$0.321395\pi$
$684$	−1.08434			−0.0414606
$685$	20.9203	+	6.53763i	0.799322	+	0.249790i
$686$		−	2.46543i		−	0.0941304i
$687$	−4.69415	−	4.69415i	−0.179093	−	0.179093i
$688$	1.06804	−	1.06804i	0.0407185	−	0.0407185i
$689$	32.0022			1.21919
$690$	−4.82844	−	9.57529i	−0.183815	−	0.364525i
$691$	13.8803			0.528031			0.264016	−	0.964518i	$-0.414953\pi$
$691$	13.8803			0.528031			0.264016	+	0.964518i	$0.414953\pi$
$692$	−6.09087	+	6.09087i	−0.231540	+	0.231540i
$693$	0.0689566	+	0.0689566i	0.00261944	+	0.00261944i
$694$			1.10865i			0.0420836i
$695$	−2.15296	−	4.11022i	−0.0816664	−	0.155910i
$696$	−8.68275			−0.329119
$697$	−8.23428	−	8.23428i	−0.311896	−	0.311896i
$698$	1.97915	+	1.97915i	0.0749120	+	0.0749120i
$699$			4.98618i			0.188595i
$700$	0.157662	+	0.868275i	0.00595907	+	0.0328177i
$701$		−	18.1607i		−	0.685920i	−0.939350	−	0.342960i	$-0.888570\pi$
$701$		−	18.1607i		−	0.685920i	0.939350	−	0.342960i	$-0.111430\pi$
$702$	−2.68793	+	2.68793i	−0.101449	+	0.101449i
$703$	−8.45289	−	8.45289i	−0.318807	−	0.318807i
$704$	−0.552534			−0.0208244
$705$	1.67328	−	0.876477i	0.0630195	−	0.0330100i
$706$	11.7171			0.440978
$707$	0.740197	+	0.740197i	0.0278380	+	0.0278380i
$708$	7.36028	+	7.36028i	0.276616	+	0.276616i
$709$	7.89324			0.296437			0.148218	−	0.988955i	$-0.452646\pi$
$709$	7.89324			0.296437			0.148218	+	0.988955i	$0.452646\pi$
$710$	−5.44749	+	17.4318i	−0.204441	+	0.654205i
$711$			6.76975i			0.253885i
$712$	−6.19562	−	6.19562i	−0.232191	−	0.232191i
$713$	0.182107	−	11.7774i	0.00681995	−	0.441066i
$714$		−	0.903477i		−	0.0338118i
$715$	−1.40087	+	4.48274i	−0.0523895	+	0.167645i
$716$	23.2150			0.867584
$717$	13.6932	−	13.6932i	0.511380	−	0.511380i
$718$	13.1144	−	13.1144i	0.489424	−	0.489424i
$719$			21.8935i			0.816490i	0.912872	+	0.408245i	$0.133859\pi$
$719$			21.8935i			0.816490i	−0.912872	+	0.408245i	$0.866141\pi$
$720$	−1.03755	−	1.98078i	−0.0386671	−	0.0738194i
$721$	−0.943153			−0.0351249
$722$	12.6036	−	12.6036i	0.469058	−	0.469058i
$723$	14.1879	−	14.1879i	0.527655	−	0.527655i
$724$	−6.45396			−0.239860
$725$	−35.6888	−	24.7197i	−1.32545	−	0.918068i
$726$	10.6947			0.396918
$727$	−2.54984	−	2.54984i	−0.0945684	−	0.0945684i	0.658240	−	0.752808i	$-0.271301\pi$
$727$	−2.54984	−	2.54984i	−0.0945684	−	0.0945684i	−0.752808	+	0.658240i	$0.771301\pi$
$728$	0.474405	−	0.474405i	0.0175826	−	0.0175826i
$729$		−	1.00000i		−	0.0370370i
$730$	−8.75048	+	4.58356i	−0.323870	+	0.169645i
$731$	−7.73190			−0.285975
$732$	−6.44939	−	6.44939i	−0.238376	−	0.238376i
$733$	22.3443	−	22.3443i	0.825304	−	0.825304i	−0.161559	−	0.986863i	$-0.551652\pi$
$733$	22.3443	−	22.3443i	0.825304	−	0.825304i	0.986863	+	0.161559i	$0.0516523\pi$
$734$	−20.7795			−0.766985
$735$	−4.64800	+	14.8735i	−0.171444	+	0.548617i
$736$	−3.33833	−	3.44319i	−0.123052	−	0.126918i
$737$	−2.97535	+	2.97535i	−0.109598	+	0.109598i
$738$	1.60857	+	1.60857i	0.0592123	+	0.0592123i
$739$			11.6646i			0.429089i	0.976714	+	0.214545i	$0.0688267\pi$
$739$			11.6646i			0.429089i	−0.976714	+	0.214545i	$0.931173\pi$
$740$	7.35295	−	23.5292i	0.270300	−	0.864952i
$741$			4.12189i			0.151421i
$742$	1.05066	−	1.05066i	0.0385711	−	0.0385711i
$743$	−1.05995	+	1.05995i	−0.0388859	+	0.0388859i	−0.726282	−	0.687396i	$-0.758754\pi$
$743$	−1.05995	+	1.05995i	−0.0388859	+	0.0388859i	0.687396	+	0.726282i	$0.258754\pi$
$744$		−	2.45605i		−	0.0900430i
$745$	24.3916	−	12.7765i	0.893639	−	0.468094i
$746$			4.45023i			0.162935i
$747$	0.190970	+	0.190970i	0.00698722	+	0.00698722i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$			2.26967i			0.0829321i
$750$	1.37464	−	11.0955i	0.0501947	−	0.405151i
$751$		−	20.0466i		−	0.731510i	−0.930711	−	0.365755i	$-0.880811\pi$
$751$		−	20.0466i		−	0.731510i	0.930711	−	0.365755i	$-0.119189\pi$
$752$	0.597335	−	0.597335i	0.0217826	−	0.0217826i
$753$	20.6653	−	20.6653i	0.753087	−	0.753087i
$754$			33.0058i			1.20200i
$755$	−19.9069	+	10.4274i	−0.724487	+	0.379491i
$756$			0.176495i			0.00641904i
$757$	35.9979	+	35.9979i	1.30837	+	1.30837i	0.922595	+	0.385770i	$0.126064\pi$
$757$	35.9979	+	35.9979i	1.30837	+	1.30837i	0.385770	+	0.922595i	$0.373936\pi$
$758$	−11.7107	+	11.7107i	−0.425353	+	0.425353i
$759$	−1.84454	−	1.90248i	−0.0669527	−	0.0690557i
$760$	−2.31428	−	0.723217i	−0.0839476	−	0.0262338i
$761$	−13.7196			−0.497334			−0.248667	−	0.968589i	$-0.579992\pi$
$761$	−13.7196			−0.497334			−0.248667	+	0.968589i	$0.579992\pi$
$762$	−14.8431	+	14.8431i	−0.537707	+	0.537707i
$763$	1.69662	+	1.69662i	0.0614218	+	0.0614218i
$764$	−22.6724			−0.820260
$765$	−3.41421	+	10.9254i	−0.123441	+	0.395008i
$766$		−	15.8681i		−	0.573338i
$767$	27.9787	−	27.9787i	1.01025	−	1.01025i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−2.88500			−0.104036			−0.0520179	−	0.998646i	$-0.516565\pi$
$769$	−2.88500			−0.104036			−0.0520179	+	0.998646i	$0.516565\pi$
$770$	0.101181	+	0.193165i	0.00364630	+	0.00696117i
$771$	−3.50437			−0.126207
$772$	7.13533	−	7.13533i	0.256806	−	0.256806i
$773$	−26.4041	+	26.4041i	−0.949689	+	0.949689i	−0.998794	−	0.0491046i	$-0.984363\pi$
$773$	−26.4041	+	26.4041i	−0.949689	+	0.949689i	0.0491046	+	0.998794i	$0.484363\pi$
$774$	1.51043			0.0542913
$775$	6.99235	−	10.0951i	0.251173	−	0.362627i
$776$			2.30492i			0.0827418i
$777$	−1.37586	+	1.37586i	−0.0493585	+	0.0493585i
$778$	−18.8504	+	18.8504i	−0.675818	+	0.675818i
$779$	2.46671			0.0883791
$780$	−7.52955	+	3.94403i	−0.269601	+	0.141219i
$781$			4.51285i			0.161483i
$782$	−0.379555	+	24.5470i	−0.0135729	+	0.877797i
$783$	−6.13963	−	6.13963i	−0.219413	−	0.219413i
$784$			6.96885i			0.248887i
$785$	10.2858	+	3.21435i	0.367117	+	0.114725i
$786$	−8.69869			−0.310272
$787$	36.1586	+	36.1586i	1.28891	+	1.28891i	0.935447	+	0.353466i	$0.114997\pi$
$787$	36.1586	+	36.1586i	1.28891	+	1.28891i	0.353466	+	0.935447i	$0.385003\pi$
$788$	−2.41931	−	2.41931i	−0.0861844	−	0.0861844i
$789$	9.46631			0.337010
$790$	−4.51521	+	14.4485i	−0.160644	+	0.514056i
$791$	2.32213			0.0825653
$792$	−0.390701	−	0.390701i	−0.0138830	−	0.0138830i
$793$	−24.5161	+	24.5161i	−0.870592	+	0.870592i
$794$			1.46779i			0.0520899i
$795$	−16.6757	+	8.73484i	−0.591426	+	0.309793i
$796$			22.7308i			0.805672i
$797$	−19.2279	−	19.2279i	−0.681088	−	0.681088i	0.279157	−	0.960245i	$-0.409945\pi$
$797$	−19.2279	−	19.2279i	−0.681088	−	0.681088i	−0.960245	+	0.279157i	$0.909945\pi$
$798$	0.135326	+	0.135326i	0.00479047	+	0.00479047i
$799$	−4.32433			−0.152984
$800$	−0.893297	−	4.91955i	−0.0315828	−	0.173933i
$801$		−	8.76193i		−	0.309587i
$802$	17.0648	+	17.0648i	0.602578	+	0.602578i
$803$	−1.72599	+	1.72599i	−0.0609090	+	0.0609090i
$804$	−7.61541			−0.268575
$805$	−0.592410	+	1.79759i	−0.0208797	+	0.0633568i
$806$	−9.33618			−0.328853
$807$	−5.80684	+	5.80684i	−0.204410	+	0.204410i
$808$	−4.19388	−	4.19388i	−0.147540	−	0.147540i
$809$			5.62570i			0.197789i	0.995098	+	0.0988946i	$0.0315307\pi$
$809$			5.62570i			0.197789i	−0.995098	+	0.0988946i	$0.968469\pi$
$810$	0.666968	−	2.13428i	0.0234349	−	0.0749910i
$811$	47.8518			1.68030			0.840151	−	0.542352i	$-0.182466\pi$
$811$	47.8518			1.68030			0.840151	+	0.542352i	$0.182466\pi$
$812$	1.08361	+	1.08361i	0.0380273	+	0.0380273i
$813$	−6.08270	−	6.08270i	−0.213330	−	0.213330i
$814$		−	6.09138i		−	0.213503i
$815$	−33.1366	−	10.3553i	−1.16072	−	0.362729i
$816$			5.11901i			0.179201i
$817$	1.15811	−	1.15811i	0.0405171	−	0.0405171i
$818$	−12.2055	−	12.2055i	−0.426756	−	0.426756i
$819$	0.670909			0.0234435
$820$	2.36027	+	4.50600i	0.0824244	+	0.157356i
$821$	−11.4696			−0.400291			−0.200145	−	0.979766i	$-0.564141\pi$
$821$	−11.4696			−0.400291			−0.200145	+	0.979766i	$0.564141\pi$
$822$	6.93107	+	6.93107i	0.241749	+	0.241749i
$823$	−8.97892	−	8.97892i	−0.312985	−	0.312985i	0.533080	−	0.846065i	$-0.321035\pi$
$823$	−8.97892	−	8.97892i	−0.312985	−	0.312985i	−0.846065	+	0.533080i	$0.821035\pi$
$824$	5.34381			0.186160
$825$	−0.493577	−	2.71822i	−0.0171842	−	0.0946364i
$826$		−	1.83713i		−	0.0639220i
$827$	20.4092	+	20.4092i	0.709697	+	0.709697i	0.966471	−	0.256775i	$-0.0826598\pi$
$827$	20.4092	+	20.4092i	0.709697	+	0.709697i	−0.256775	+	0.966471i	$0.582660\pi$
$828$	0.0741463	−	4.79526i	0.00257676	−	0.166647i
$829$		−	29.9611i		−	1.04059i	−0.853985	−	0.520297i	$-0.825821\pi$
$829$		−	29.9611i		−	1.04059i	0.853985	−	0.520297i	$-0.174179\pi$
$830$	0.280212	+	0.534954i	0.00972631	+	0.0185685i
$831$	13.1316			0.455530
$832$	−2.68793	+	2.68793i	−0.0931871	+	0.0931871i
$833$	25.2250	−	25.2250i	0.873996	−	0.873996i
$834$		−	2.07505i		−	0.0718531i
$835$	0.370741	−	1.18636i	0.0128300	−	0.0410558i
$836$	−0.599133			−0.0207214
$837$	1.73669	−	1.73669i	0.0600287	−	0.0600287i
$838$	−6.24608	+	6.24608i	−0.215767	+	0.215767i
$839$	12.7197			0.439133			0.219566	−	0.975598i	$-0.429536\pi$
$839$	12.7197			0.439133			0.219566	+	0.975598i	$0.429536\pi$
$840$	−0.117716	+	0.376689i	−0.00406160	+	0.0129970i
$841$	−46.3902			−1.59966
$842$	16.2038	+	16.2038i	0.558421	+	0.558421i
$843$	10.7689	−	10.7689i	0.370902	−	0.370902i
$844$			22.6042i			0.778067i
$845$	1.50435	+	2.87195i	0.0517511	+	0.0987982i
$846$	0.844759			0.0290434
$847$	−1.33470	−	1.33470i	−0.0458610	−	0.0458610i
$848$	−5.95295	+	5.95295i	−0.204425	+	0.204425i
$849$	−16.5005			−0.566294
$850$	−14.5738	+	21.0407i	−0.499877	+	0.721690i
$851$	37.9592	−	36.8032i	1.30123	−	1.26160i
$852$	−5.77533	+	5.77533i	−0.197859	+	0.197859i
$853$	4.45279	+	4.45279i	0.152461	+	0.152461i	0.779216	−	0.626755i	$-0.215617\pi$
$853$	4.45279	+	4.45279i	0.152461	+	0.152461i	−0.626755	+	0.779216i	$0.715617\pi$
$854$			1.60977i			0.0550853i
$855$	−1.12505	−	2.14783i	−0.0384758	−	0.0734543i
$856$		−	12.8597i		−	0.439537i
$857$	31.4578	−	31.4578i	1.07458	−	1.07458i	0.0775921	−	0.996985i	$-0.475277\pi$
$857$	31.4578	−	31.4578i	1.07458	−	1.07458i	0.996985	−	0.0775921i	$-0.0247232\pi$
$858$	−1.48517	+	1.48517i	−0.0507030	+	0.0507030i
$859$		−	37.1082i		−	1.26611i	−0.774105	−	0.633057i	$-0.781800\pi$
$859$		−	37.1082i		−	1.26611i	0.774105	−	0.633057i	$-0.218200\pi$
$860$	3.22368	+	1.00741i	0.109927	+	0.0343524i
$861$		−	0.401501i		−	0.0136831i
$862$	−2.91241	−	2.91241i	−0.0991970	−	0.0991970i
$863$	6.80762	+	6.80762i	0.231734	+	0.231734i	0.813416	−	0.581682i	$-0.197605\pi$
$863$	6.80762	+	6.80762i	0.231734	+	0.231734i	−0.581682	+	0.813416i	$0.697605\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	−18.3843	−	5.74513i	−0.625084	−	0.195340i
$866$			18.6686i			0.634383i
$867$	6.50837	−	6.50837i	0.221036	−	0.221036i
$868$	−0.306516	+	0.306516i	−0.0104038	+	0.0104038i
$869$			3.74052i			0.126888i
$870$	−9.00876	−	17.1986i	−0.305426	−	0.583089i
$871$			28.9485i			0.980882i
$872$	−9.61288	−	9.61288i	−0.325533	−	0.325533i
$873$	−1.62982	+	1.62982i	−0.0551612	+	0.0551612i
$874$	−3.61987	−	3.73357i	−0.122444	−	0.126290i
$875$	−1.55628	+	1.21317i	−0.0526119	+	0.0410126i
$876$	−4.41769			−0.149260
$877$	−2.87923	+	2.87923i	−0.0972247	+	0.0972247i	−0.754046	−	0.656821i	$-0.771901\pi$
$877$	−2.87923	+	2.87923i	−0.0972247	+	0.0972247i	0.656821	+	0.754046i	$0.271901\pi$
$878$	−9.43609	−	9.43609i	−0.318452	−	0.318452i
$879$	30.9101			1.04257
$880$	−0.573280	−	1.09445i	−0.0193253	−	0.0368939i
$881$		−	34.1144i		−	1.14934i	−0.818384	−	0.574672i	$-0.805130\pi$
$881$		−	34.1144i		−	1.14934i	0.818384	−	0.574672i	$-0.194870\pi$
$882$	−4.92772	+	4.92772i	−0.165925	+	0.165925i
$883$	9.96963	+	9.96963i	0.335505	+	0.335505i	0.854672	−	0.519168i	$-0.173758\pi$
$883$	9.96963	+	9.96963i	0.335505	+	0.335505i	−0.519168	+	0.854672i	$0.673758\pi$
$884$	19.4589			0.654473
$885$	−6.94248	+	22.2157i	−0.233369	+	0.746774i
$886$	24.2577			0.814955
$887$	−0.170309	+	0.170309i	−0.00571841	+	0.00571841i	−0.709960	−	0.704242i	$-0.751287\pi$
$887$	−0.170309	+	0.170309i	−0.00571841	+	0.00571841i	0.704242	+	0.709960i	$0.251287\pi$
$888$	7.79545	−	7.79545i	0.261598	−	0.261598i
$889$	3.70484			0.124256
$890$	5.84393	−	18.7004i	0.195889	−	0.626839i
$891$		−	0.552534i		−	0.0185106i
$892$	10.6254	−	10.6254i	0.355765	−	0.355765i
$893$	0.647711	−	0.647711i	0.0216748	−	0.0216748i
$894$	12.3141			0.411846
$895$	24.0866	+	45.9838i	0.805126	+	1.53707i
$896$			0.176495i			0.00589627i
$897$	−18.2282	−	0.281853i	−0.608623	−	0.00941079i
$898$	−5.19834	−	5.19834i	−0.173471	−	0.173471i
$899$		−	21.3252i		−	0.711237i
$900$	2.84699	−	4.11031i	0.0948998	−	0.137010i
$901$	43.0956			1.43572
$902$	0.888790	+	0.888790i	0.0295935	+	0.0295935i
$903$	−0.188502	−	0.188502i	−0.00627297	−	0.00627297i
$904$	−13.1569			−0.437593
$905$	−6.69629	−	12.7839i	−0.222592	−	0.424951i
$906$	−10.0500			−0.333890
$907$	11.8107	+	11.8107i	0.392168	+	0.392168i	0.875459	−	0.483292i	$-0.160559\pi$
$907$	11.8107	+	11.8107i	0.392168	+	0.392168i	−0.483292	+	0.875459i	$0.660559\pi$
$908$	4.66128	−	4.66128i	0.154690	−	0.154690i
$909$		−	5.93104i		−	0.196720i
$910$	1.43191	+	0.447475i	0.0474673	+	0.0148337i
$911$			35.6840i			1.18226i	0.806575	+	0.591132i	$0.201319\pi$
$911$			35.6840i			1.18226i	−0.806575	+	0.591132i	$0.798681\pi$
$912$	−0.766741	−	0.766741i	−0.0253893	−	0.0253893i
$913$	0.105517	+	0.105517i	0.00349211	+	0.00349211i
$914$	2.28675			0.0756388
$915$	6.08329	−	19.4664i	0.201107	−	0.643539i
$916$		−	6.63852i		−	0.219343i
$917$	1.08560	+	1.08560i	0.0358497	+	0.0358497i
$918$	−3.61968	+	3.61968i	−0.119467	+	0.119467i
$919$	−33.7384			−1.11293			−0.556463	−	0.830872i	$-0.687842\pi$
$919$	−33.7384			−1.11293			−0.556463	+	0.830872i	$0.687842\pi$
$920$	3.35653	−	10.1850i	0.110662	−	0.335789i
$921$	8.95694			0.295141
$922$	13.7336	−	13.7336i	0.452293	−	0.452293i
$923$	21.9538	+	21.9538i	0.722617	+	0.722617i
$924$			0.0975193i			0.00320815i
$925$	54.2353	−	9.84810i	1.78325	−	0.323803i
$926$	23.5785			0.774836
$927$	3.77864	+	3.77864i	0.124107	+	0.124107i
$928$	−6.13963	−	6.13963i	−0.201543	−	0.201543i
$929$		−	21.5707i		−	0.707711i	−0.935300	−	0.353856i	$-0.884870\pi$
$929$		−	21.5707i		−	0.707711i	0.935300	−	0.353856i	$-0.115130\pi$
$930$	4.86489	−	2.54826i	0.159526	−	0.0835608i
$931$			7.55657i			0.247657i
$932$	−3.52576	+	3.52576i	−0.115490	+	0.115490i
$933$	−15.3982	−	15.3982i	−0.504113	−	0.504113i
$934$	26.5062			0.867310
$935$	−1.88647	+	6.03666i	−0.0616942	+	0.197420i
$936$	−3.80130			−0.124249
$937$	2.45269	+	2.45269i	0.0801260	+	0.0801260i	0.746034	−	0.665908i	$-0.231956\pi$
$937$	2.45269	+	2.45269i	0.0801260	+	0.0801260i	−0.665908	+	0.746034i	$0.731956\pi$
$938$	0.950406	+	0.950406i	0.0310319	+	0.0310319i
$939$	30.1164			0.982811
$940$	1.80295	+	0.563427i	0.0588058	+	0.0183770i
$941$		−	41.3511i		−	1.34801i	−0.738729	−	0.674003i	$-0.764573\pi$
$941$		−	41.3511i		−	1.34801i	0.738729	−	0.674003i	$-0.235427\pi$
$942$	3.40779	+	3.40779i	0.111032	+	0.111032i
$943$	−0.168673	+	10.9085i	−0.00549273	+	0.355231i
$944$			10.4090i			0.338784i
$945$	−0.349597	+	0.183121i	−0.0113724	+	0.00595694i
$946$	0.834565			0.0271341
$947$	−10.8386	+	10.8386i	−0.352208	+	0.352208i	−0.860930	−	0.508723i	$-0.830118\pi$
$947$	−10.8386	+	10.8386i	−0.352208	+	0.352208i	0.508723	+	0.860930i	$0.330118\pi$
$948$	−4.78694	+	4.78694i	−0.155472	+	0.155472i
$949$			16.7930i			0.545123i
$950$	−0.968634	−	5.33445i	−0.0314266	−	0.173072i
$951$	−18.5269			−0.600775
$952$	0.638854	−	0.638854i	0.0207054	−	0.0207054i
$953$	−22.1223	+	22.1223i	−0.716612	+	0.716612i	−0.967910	−	0.251298i	$-0.919143\pi$
$953$	−22.1223	+	22.1223i	−0.716612	+	0.716612i	0.251298	+	0.967910i	$0.419143\pi$
$954$	−8.41875			−0.272567
$955$	−23.5237	−	44.9092i	−0.761210	−	1.45323i
$956$	19.3650			0.626310
$957$	−3.39236	−	3.39236i	−0.109659	−	0.109659i
$958$	2.84915	−	2.84915i	0.0920520	−	0.0920520i
$959$		−	1.73000i		−	0.0558647i
$960$	0.666968	−	2.13428i	0.0215263	−	0.0688836i
$961$	−24.9678			−0.805414
$962$	−29.6329	−	29.6329i	−0.955403	−	0.955403i
$963$	9.09321	−	9.09321i	0.293025	−	0.293025i
$964$	20.0648			0.646242
$965$	21.5368	+	6.73029i	0.693293	+	0.216656i
$966$	−0.607704	+	0.589197i	−0.0195526	+	0.0189571i
$967$	4.75663	−	4.75663i	0.152963	−	0.152963i	−0.626477	−	0.779440i	$-0.715504\pi$
$967$	4.75663	−	4.75663i	0.152963	−	0.152963i	0.779440	+	0.626477i	$0.215504\pi$
$968$	7.56230	+	7.56230i	0.243061	+	0.243061i
$969$			5.55072i			0.178315i
$970$	−4.56554	+	2.39146i	−0.146591	+	0.0767852i
$971$		−	7.39491i		−	0.237314i	−0.992935	−	0.118657i	$-0.962141\pi$
$971$		−	7.39491i		−	0.237314i	0.992935	−	0.118657i	$-0.0378589\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−0.258967	+	0.258967i	−0.00830211	+	0.00830211i
$974$		−	21.7959i		−	0.698385i
$975$	−15.6245	−	10.8223i	−0.500385	−	0.346591i
$976$		−	9.12081i		−	0.291950i
$977$	−1.90875	−	1.90875i	−0.0610662	−	0.0610662i	0.675914	−	0.736980i	$-0.263749\pi$
$977$	−1.90875	−	1.90875i	−0.0610662	−	0.0610662i	−0.736980	+	0.675914i	$0.763749\pi$
$978$	−10.9785	−	10.9785i	−0.351053	−	0.351053i
$979$		−	4.84127i		−	0.154728i
$980$	−13.8038	+	7.23051i	−0.440945	+	0.230970i
$981$		−	13.5947i		−	0.434044i
$982$	−1.72590	+	1.72590i	−0.0550755	+	0.0550755i
$983$	−2.58513	+	2.58513i	−0.0824528	+	0.0824528i	−0.747130	−	0.664678i	$-0.768569\pi$
$983$	−2.58513	+	2.58513i	−0.0824528	+	0.0824528i	0.664678	+	0.747130i	$0.268569\pi$
$984$			2.27486i			0.0725199i
$985$	2.28198	−	7.30227i	0.0727099	−	0.232670i
$986$			44.4471i			1.41548i
$987$	−0.105426	−	0.105426i	−0.00335576	−	0.00335576i
$988$	−2.91461	+	2.91461i	−0.0927262	+	0.0927262i
$989$	5.04232	+	5.20070i	0.160336	+	0.165373i
$990$	0.368523	−	1.17926i	0.0117124	−	0.0374795i
$991$	48.3443			1.53571			0.767853	−	0.640626i	$-0.221325\pi$
$991$	48.3443			1.53571			0.767853	+	0.640626i	$0.221325\pi$
$992$	1.73669	−	1.73669i	0.0551399	−	0.0551399i
$993$	12.7595	+	12.7595i	0.404910	+	0.404910i
$994$	1.44153			0.0457225
$995$	−45.0248	+	23.5843i	−1.42738	+	0.747671i
$996$			0.270072i			0.00855756i
$997$	6.62156	−	6.62156i	0.209707	−	0.209707i	−0.594436	−	0.804143i	$-0.702625\pi$
$997$	6.62156	−	6.62156i	0.209707	−	0.209707i	0.804143	+	0.594436i	$0.202625\pi$
$998$	29.9630	+	29.9630i	0.948463	+	0.948463i
$999$	11.0244			0.348798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.b.643.6	yes	24
5.2	odd	4	inner	690.2.j.b.367.1	✓	24
23.22	odd	2	inner	690.2.j.b.643.1	yes	24
115.22	even	4	inner	690.2.j.b.367.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.b.367.1	✓	24	5.2	odd	4	inner
690.2.j.b.367.6	yes	24	115.22	even	4	inner
690.2.j.b.643.1	yes	24	23.22	odd	2	inner
690.2.j.b.643.6	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} +(-0.124800 - 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} +(-0.124800 - 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.666968 + 2.13428i) q^{10} +0.552534i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.68793 + 2.68793i) q^{13} +0.176495 q^{14} +(-2.13428 - 0.666968i) q^{15} -1.00000 q^{16} +(3.61968 + 3.61968i) q^{17} +(-0.707107 - 0.707107i) q^{18} -1.08434 q^{19} +(-1.03755 - 1.98078i) q^{20} +0.176495i q^{21} +(-0.390701 - 0.390701i) q^{22} +(0.0741463 - 4.79526i) q^{23} -1.00000i q^{24} +(2.84699 - 4.11031i) q^{25} -3.80130 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.124800 + 0.124800i) q^{28} -8.68275i q^{29} +(1.98078 - 1.03755i) q^{30} +2.45605 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.390701 - 0.390701i) q^{33} -5.11901 q^{34} +(-0.376689 - 0.117716i) q^{35} +1.00000 q^{36} +(7.79545 + 7.79545i) q^{37} +(0.766741 - 0.766741i) q^{38} -3.80130i q^{39} +(2.13428 + 0.666968i) q^{40} -2.27486 q^{41} +(-0.124800 - 0.124800i) q^{42} +(-1.06804 + 1.06804i) q^{43} +0.552534 q^{44} +(1.03755 + 1.98078i) q^{45} +(3.33833 + 3.44319i) q^{46} +(-0.597335 + 0.597335i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.96885i q^{49} +(0.893297 + 4.91955i) q^{50} -5.11901i q^{51} +(2.68793 - 2.68793i) q^{52} +(5.95295 - 5.95295i) q^{53} +1.00000i q^{54} +(0.573280 + 1.09445i) q^{55} -0.176495i q^{56} +(0.766741 + 0.766741i) q^{57} +(6.13963 + 6.13963i) q^{58} -10.4090i q^{59} +(-0.666968 + 2.13428i) q^{60} +9.12081i q^{61} +(-1.73669 + 1.73669i) q^{62} +(0.124800 - 0.124800i) q^{63} +1.00000i q^{64} +(8.11305 + 2.53535i) q^{65} +0.552534i q^{66} +(5.38491 + 5.38491i) q^{67} +(3.61968 - 3.61968i) q^{68} +(-3.44319 + 3.33833i) q^{69} +(0.349597 - 0.183121i) q^{70} +8.16755 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.12378 + 3.12378i) q^{73} -11.0244 q^{74} +(-4.91955 + 0.893297i) q^{75} +1.08434i q^{76} +(0.0689566 - 0.0689566i) q^{77} +(2.68793 + 2.68793i) q^{78} +6.76975 q^{79} +(-1.98078 + 1.03755i) q^{80} -1.00000 q^{81} +(1.60857 - 1.60857i) q^{82} +(0.190970 - 0.190970i) q^{83} +0.176495 q^{84} +(10.9254 + 3.41421i) q^{85} -1.51043i q^{86} +(-6.13963 + 6.13963i) q^{87} +(-0.390701 + 0.390701i) q^{88} -8.76193 q^{89} +(-2.13428 - 0.666968i) q^{90} -0.670909i q^{91} +(-4.79526 - 0.0741463i) q^{92} +(-1.73669 - 1.73669i) q^{93} -0.844759i q^{94} +(-2.14783 + 1.12505i) q^{95} -1.00000 q^{96} +(1.62982 + 1.62982i) q^{97} +(4.92772 + 4.92772i) q^{98} -0.552534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{6}+O(q^{10}) \) 24 * q + 24 * q^6	\( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) \) 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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