LMFDB - Embedded newform 700.2.be.e.543.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(107,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("700.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			543.18
Character	$\chi$	$=$	700.543
Dual form			700.2.be.e.107.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39811 - 0.212826i) q^{2} +(0.216303 + 0.807254i) q^{3} +(1.90941 - 0.595107i) q^{4} +(0.474220 + 1.08259i) q^{6} +(2.62434 - 0.335905i) q^{7} +(2.54291 - 1.23840i) q^{8} +(1.99320 - 1.15078i) q^{9} +O(q^{10})$	\(q+(1.39811 - 0.212826i) q^{2} +(0.216303 + 0.807254i) q^{3} +(1.90941 - 0.595107i) q^{4} +(0.474220 + 1.08259i) q^{6} +(2.62434 - 0.335905i) q^{7} +(2.54291 - 1.23840i) q^{8} +(1.99320 - 1.15078i) q^{9} +(-4.21811 - 2.43533i) q^{11} +(0.893414 + 1.41266i) q^{12} +(-0.247904 - 0.247904i) q^{13} +(3.59762 - 1.02816i) q^{14} +(3.29169 - 2.27261i) q^{16} +(1.56358 + 5.83537i) q^{17} +(2.54180 - 2.03311i) q^{18} +(-1.48858 - 2.57830i) q^{19} +(0.838814 + 2.04585i) q^{21} +(-6.41567 - 2.50713i) q^{22} +(-6.36754 - 1.70618i) q^{23} +(1.54974 + 1.78490i) q^{24} +(-0.399357 - 0.293836i) q^{26} +(3.13296 + 3.13296i) q^{27} +(4.81104 - 2.20315i) q^{28} +4.67111i q^{29} +(5.75848 + 3.32466i) q^{31} +(4.11847 - 3.87791i) q^{32} +(1.05354 - 3.93186i) q^{33} +(3.42797 + 7.82570i) q^{34} +(3.12101 - 3.38347i) q^{36} +(-2.39496 - 0.641729i) q^{37} +(-2.62993 - 3.28794i) q^{38} +(0.146499 - 0.253744i) q^{39} -1.15345 q^{41} +(1.60816 + 2.68180i) q^{42} +(-3.23212 + 3.23212i) q^{43} +(-9.50338 - 2.13981i) q^{44} +(-9.26562 - 1.03024i) q^{46} +(-1.27127 + 4.74443i) q^{47} +(2.54658 + 2.16566i) q^{48} +(6.77434 - 1.76306i) q^{49} +(-4.37242 + 2.52442i) q^{51} +(-0.620880 - 0.325821i) q^{52} +(0.309032 - 0.0828048i) q^{53} +(5.04699 + 3.71344i) q^{54} +(6.25747 - 4.10415i) q^{56} +(1.75936 - 1.75936i) q^{57} +(0.994133 + 6.53071i) q^{58} +(0.423416 - 0.733378i) q^{59} +(-5.04573 - 8.73945i) q^{61} +(8.75855 + 3.42268i) q^{62} +(4.84429 - 3.68956i) q^{63} +(4.93275 - 6.29825i) q^{64} +(0.636158 - 5.72138i) q^{66} +(-2.69434 + 0.721946i) q^{67} +(6.45819 + 10.2116i) q^{68} -5.50928i q^{69} +6.49911i q^{71} +(3.64341 - 5.39469i) q^{72} +(-1.19801 + 0.321006i) q^{73} +(-3.48499 - 0.387495i) q^{74} +(-4.37668 - 4.03717i) q^{76} +(-11.8878 - 4.97424i) q^{77} +(0.150818 - 0.385940i) q^{78} +(-4.44724 - 7.70284i) q^{79} +(1.60090 - 2.77285i) q^{81} +(-1.61264 + 0.245484i) q^{82} +(-10.8443 + 10.8443i) q^{83} +(2.81914 + 3.40719i) q^{84} +(-3.83097 + 5.20673i) q^{86} +(-3.77077 + 1.01038i) q^{87} +(-13.7422 - 0.969119i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-0.733857 - 0.567313i) q^{91} +(-13.1736 + 0.531576i) q^{92} +(-1.43827 + 5.36769i) q^{93} +(-0.767630 + 6.90379i) q^{94} +(4.02130 + 2.48585i) q^{96} +(2.35897 - 2.35897i) q^{97} +(9.09603 - 3.90670i) q^{98} -11.2101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.39811	−	0.212826i	0.988611	−	0.150491i
$2$	1.39811	−	0.212826i	0.988611	−	0.150491i
$3$	0.216303	+	0.807254i	0.124883	+	0.466069i	0.999835	−	0.0181397i	$-0.00577436\pi$
$3$	0.216303	+	0.807254i	0.124883	+	0.466069i	−0.874953	+	0.484208i	$0.839108\pi$
$4$	1.90941	−	0.595107i	0.954705	−	0.297554i
$5$		0			0
$5$		0			0
$6$	0.474220	+	1.08259i	0.193599	+	0.441967i
$7$	2.62434	−	0.335905i	0.991908	−	0.126960i
$7$	2.62434	−	0.335905i	0.991908	−	0.126960i
$8$	2.54291	−	1.23840i	0.899053	−	0.437839i
$9$	1.99320	−	1.15078i	0.664401	−	0.383592i
$10$		0			0
$11$	−4.21811	−	2.43533i	−1.27181	−	0.734279i	−0.296480	−	0.955039i	$-0.595813\pi$
$11$	−4.21811	−	2.43533i	−1.27181	−	0.734279i	−0.975328	+	0.220760i	$0.929146\pi$
$12$	0.893414	+	1.41266i	0.257907	+	0.407799i
$13$	−0.247904	−	0.247904i	−0.0687562	−	0.0687562i	0.671892	−	0.740649i	$-0.265482\pi$
$13$	−0.247904	−	0.247904i	−0.0687562	−	0.0687562i	−0.740649	+	0.671892i	$0.765482\pi$
$14$	3.59762	−	1.02816i	0.961505	−	0.274787i
$15$		0			0
$16$	3.29169	−	2.27261i	0.822924	−	0.568152i
$17$	1.56358	+	5.83537i	0.379224	+	1.41528i	0.847073	+	0.531476i	$0.178362\pi$
$17$	1.56358	+	5.83537i	0.379224	+	1.41528i	−0.467849	+	0.883808i	$0.654971\pi$
$18$	2.54180	−	2.03311i	0.599108	−	0.479210i
$19$	−1.48858	−	2.57830i	−0.341505	−	0.591503i	0.643208	−	0.765692i	$-0.277603\pi$
$19$	−1.48858	−	2.57830i	−0.341505	−	0.591503i	−0.984712	+	0.174188i	$0.944270\pi$
$20$		0			0
$21$	0.838814	+	2.04585i	0.183044	+	0.446442i
$22$	−6.41567	−	2.50713i	−1.36783	−	0.534521i
$23$	−6.36754	−	1.70618i	−1.32772	−	0.355762i	−0.475858	−	0.879522i	$-0.657862\pi$
$23$	−6.36754	−	1.70618i	−1.32772	−	0.355762i	−0.851866	+	0.523760i	$0.824529\pi$
$24$	1.54974	+	1.78490i	0.316339	+	0.364342i
$25$		0			0
$26$	−0.399357	−	0.293836i	−0.0783204	−	0.0576260i
$27$	3.13296	+	3.13296i	0.602938	+	0.602938i
$28$	4.81104	−	2.20315i	0.909202	−	0.416355i
$29$			4.67111i			0.867403i	0.901057	+	0.433701i	$0.142793\pi$
$29$			4.67111i			0.867403i	−0.901057	+	0.433701i	$0.857207\pi$
$30$		0			0
$31$	5.75848	+	3.32466i	1.03425	+	0.597127i	0.918200	−	0.396116i	$-0.129642\pi$
$31$	5.75848	+	3.32466i	1.03425	+	0.597127i	0.116053	+	0.993243i	$0.462976\pi$
$32$	4.11847	−	3.87791i	0.728050	−	0.685524i
$33$	1.05354	−	3.93186i	0.183397	−	0.684448i
$34$	3.42797	+	7.82570i	0.587892	+	1.34210i
$35$		0			0
$36$	3.12101	−	3.38347i	0.520168	−	0.563912i
$37$	−2.39496	−	0.641729i	−0.393730	−	0.105500i	0.0565217	−	0.998401i	$-0.481999\pi$
$37$	−2.39496	−	0.641729i	−0.393730	−	0.105500i	−0.450251	+	0.892902i	$0.648666\pi$
$38$	−2.62993	−	3.28794i	−0.426631	−	0.533374i
$39$	0.146499	−	0.253744i	0.0234587	−	0.0406316i
$40$		0			0
$41$	−1.15345			−0.180138			−0.0900692	−	0.995936i	$-0.528709\pi$
$41$	−1.15345			−0.180138			−0.0900692	+	0.995936i	$0.528709\pi$
$42$	1.60816	+	2.68180i	0.248145	+	0.413811i
$43$	−3.23212	+	3.23212i	−0.492894	+	0.492894i	−0.909217	−	0.416323i	$-0.863318\pi$
$43$	−3.23212	+	3.23212i	−0.492894	+	0.492894i	0.416323	+	0.909217i	$0.363318\pi$
$44$	−9.50338	−	2.13981i	−1.43269	−	0.322589i
$45$		0			0
$46$	−9.26562	−	1.03024i	−1.36614	−	0.151901i
$47$	−1.27127	+	4.74443i	−0.185433	+	0.692047i	0.809104	+	0.587666i	$0.199953\pi$
$47$	−1.27127	+	4.74443i	−0.185433	+	0.692047i	−0.994537	+	0.104381i	$0.966714\pi$
$48$	2.54658	+	2.16566i	0.367567	+	0.312587i
$49$	6.77434	−	1.76306i	0.967762	−	0.251866i
$50$		0			0
$51$	−4.37242	+	2.52442i	−0.612261	+	0.353489i
$52$	−0.620880	−	0.325821i	−0.0861006	−	0.0451833i
$53$	0.309032	−	0.0828048i	0.0424488	−	0.0113741i	−0.237532	−	0.971380i	$-0.576339\pi$
$53$	0.309032	−	0.0828048i	0.0424488	−	0.0113741i	0.279981	+	0.960006i	$0.409672\pi$
$54$	5.04699	+	3.71344i	0.686808	+	0.505335i
$55$		0			0
$56$	6.25747	−	4.10415i	0.836190	−	0.548440i
$57$	1.75936	−	1.75936i	0.233033	−	0.233033i
$58$	0.994133	+	6.53071i	0.130536	+	0.857524i
$59$	0.423416	−	0.733378i	0.0551240	−	0.0954776i	−0.837147	−	0.546979i	$-0.815778\pi$
$59$	0.423416	−	0.733378i	0.0551240	−	0.0954776i	0.892271	+	0.451501i	$0.149111\pi$
$60$		0			0
$61$	−5.04573	−	8.73945i	−0.646039	−	1.11897i	−0.984060	−	0.177834i	$-0.943091\pi$
$61$	−5.04573	−	8.73945i	−0.646039	−	1.11897i	0.338021	−	0.941138i	$-0.390242\pi$
$62$	8.75855	+	3.42268i	1.11234	+	0.434681i
$63$	4.84429	−	3.68956i	0.610324	−	0.464841i
$64$	4.93275	−	6.29825i	0.616594	−	0.787281i
$65$		0			0
$66$	0.636158	−	5.72138i	0.0783057	−	0.704253i
$67$	−2.69434	+	0.721946i	−0.329166	+	0.0881998i	−0.419617	−	0.907701i	$-0.637836\pi$
$67$	−2.69434	+	0.721946i	−0.329166	+	0.0881998i	0.0904513	+	0.995901i	$0.471169\pi$
$68$	6.45819	+	10.2116i	0.783170	+	1.23834i
$69$		−	5.50928i		−	0.663239i
$70$		0			0
$71$			6.49911i			0.771303i	0.922645	+	0.385651i	$0.126023\pi$
$71$			6.49911i			0.771303i	−0.922645	+	0.385651i	$0.873977\pi$
$72$	3.64341	−	5.39469i	0.429380	−	0.635771i
$73$	−1.19801	+	0.321006i	−0.140217	+	0.0375710i	−0.328245	−	0.944593i	$-0.606457\pi$
$73$	−1.19801	+	0.321006i	−0.140217	+	0.0375710i	0.188028	+	0.982164i	$0.439790\pi$
$74$	−3.48499	−	0.387495i	−0.405122	−	0.0450454i
$75$		0			0
$76$	−4.37668	−	4.03717i	−0.502040	−	0.463095i
$77$	−11.8878	−	4.97424i	−1.35474	−	0.566868i
$78$	0.150818	−	0.385940i	0.0170768	−	0.0436991i
$79$	−4.44724	−	7.70284i	−0.500353	−	0.866637i	−1.00000		0.000408067i	$-0.999870\pi$
$79$	−4.44724	−	7.70284i	−0.500353	−	0.866637i	0.499647	−	0.866229i	$-0.333463\pi$
$80$		0			0
$81$	1.60090	−	2.77285i	0.177878	−	0.308094i
$82$	−1.61264	+	0.245484i	−0.178087	+	0.0271091i
$83$	−10.8443	+	10.8443i	−1.19032	+	1.19032i	−0.213343	+	0.976977i	$0.568435\pi$
$83$	−10.8443	+	10.8443i	−1.19032	+	1.19032i	−0.976977	+	0.213343i	$0.931565\pi$
$84$	2.81914	+	3.40719i	0.307594	+	0.371755i
$85$		0			0
$86$	−3.83097	+	5.20673i	−0.413104	+	0.561456i
$87$	−3.77077	+	1.01038i	−0.404269	+	0.108324i
$88$	−13.7422	−	0.969119i	−1.46492	−	0.103308i
$89$	−8.26789	+	4.77347i	−0.876395	+	0.505987i	−0.869468	−	0.493989i	$-0.835538\pi$
$89$	−8.26789	+	4.77347i	−0.876395	+	0.505987i	−0.00692697	+	0.999976i	$0.502205\pi$
$90$		0			0
$91$	−0.733857	−	0.567313i	−0.0769291	−	0.0594705i
$92$	−13.1736	+	0.531576i	−1.37344	+	0.0554207i
$93$	−1.43827	+	5.36769i	−0.149142	+	0.556604i
$94$	−0.767630	+	6.90379i	−0.0791750	+	0.712071i
$95$		0			0
$96$	4.02130	+	2.48585i	0.410422	+	0.253711i
$97$	2.35897	−	2.35897i	0.239518	−	0.239518i	−0.577133	−	0.816650i	$-0.695828\pi$
$97$	2.35897	−	2.35897i	0.239518	−	0.239518i	0.816650	+	0.577133i	$0.195828\pi$
$98$	9.09603	−	3.90670i	0.918837	−	0.394636i
$99$	−11.2101			−1.12665
$100$		0			0
$101$	−0.729492	+	1.26352i	−0.0725872	+	0.125725i	−0.900034	−	0.435819i	$-0.856459\pi$
$101$	−0.729492	+	1.26352i	−0.0725872	+	0.125725i	0.827447	+	0.561543i	$0.189792\pi$
$102$	−5.57585	+	4.45997i	−0.552091	+	0.441603i
$103$	0.533010	+	0.142820i	0.0525190	+	0.0140724i	0.284983	−	0.958533i	$-0.408012\pi$
$103$	0.533010	+	0.142820i	0.0525190	+	0.0140724i	−0.232464	+	0.972605i	$0.574679\pi$
$104$	−0.937400	−	0.323394i	−0.0919197	−	0.0317113i
$105$		0			0
$106$	0.414437	−	0.181540i	0.0402536	−	0.0176327i
$107$	1.28708	−	4.80344i	0.124426	−	0.464366i	−0.875392	−	0.483414i	$-0.839397\pi$
$107$	1.28708	−	4.80344i	0.124426	−	0.464366i	0.999819	+	0.0190477i	$0.00606343\pi$
$108$	7.84655	+	4.11766i	0.755035	+	0.396222i
$109$	−9.70303	−	5.60205i	−0.929382	−	0.536579i	−0.0427659	−	0.999085i	$-0.513617\pi$
$109$	−9.70303	−	5.60205i	−0.929382	−	0.536579i	−0.886616	+	0.462506i	$0.846950\pi$
$110$		0			0
$111$		−	2.07215i		−	0.196680i
$112$	7.87515	−	7.06979i	0.744132	−	0.668033i
$113$	−5.88750	−	5.88750i	−0.553850	−	0.553850i	0.373700	−	0.927550i	$-0.378089\pi$
$113$	−5.88750	−	5.88750i	−0.553850	−	0.553850i	−0.927550	+	0.373700i	$0.878089\pi$
$114$	2.08534	−	2.83421i	0.195310	−	0.265448i
$115$		0			0
$116$	2.77981	+	8.91906i	0.258099	+	0.828114i
$117$	−0.779405	−	0.208841i	−0.0720561	−	0.0193074i
$118$	0.435899	−	1.11545i	0.0401278	−	0.102686i
$119$	6.06350	+	14.7888i	0.555840	+	1.35568i
$120$		0			0
$121$	6.36163	+	11.0187i	0.578330	+	1.00170i
$122$	−8.91445	−	11.1448i	−0.807076	−	1.00901i
$123$	−0.249494	−	0.931126i	−0.0224962	−	0.0839568i
$124$	12.9738	+	2.92123i	1.16508	+	0.262334i
$125$		0			0
$126$	5.98761	−	6.18939i	0.533419	−	0.551395i
$127$	5.47059	+	5.47059i	0.485436	+	0.485436i	0.906863	−	0.421426i	$-0.138470\pi$
$127$	5.47059	+	5.47059i	0.485436	+	0.485436i	−0.421426	+	0.906863i	$0.638470\pi$
$128$	5.55609	−	9.85545i	0.491093	−	0.871107i
$129$	−3.30826	−	1.91002i	−0.291276	−	0.168168i
$130$		0			0
$131$	4.93009	−	2.84639i	0.430744	−	0.248690i	−0.268920	−	0.963163i	$-0.586667\pi$
$131$	4.93009	−	2.84639i	0.430744	−	0.248690i	0.699663	+	0.714473i	$0.253333\pi$
$132$	−0.328240	−	8.13450i	−0.0285696	−	0.708017i
$133$	−4.77262	−	6.26632i	−0.413838	−	0.543359i
$134$	−3.61333	+	1.58278i	−0.312144	+	0.136732i
$135$		0			0
$136$	11.2025	+	12.9025i	0.960610	+	1.10638i
$137$	−0.128483	−	0.479505i	−0.0109770	−	0.0409668i	0.960220	−	0.279244i	$-0.0900839\pi$
$137$	−0.128483	−	0.479505i	−0.0109770	−	0.0409668i	−0.971197	+	0.238277i	$0.923417\pi$
$138$	−1.17252	−	7.70256i	−0.0998112	−	0.655685i
$139$	−6.37368			−0.540608			−0.270304	−	0.962775i	$-0.587124\pi$
$139$	−6.37368			−0.540608			−0.270304	+	0.962775i	$0.587124\pi$
$140$		0			0
$141$	−4.10494			−0.345699
$142$	1.38318	+	9.08646i	0.116074	+	0.762519i
$143$	0.441959	+	1.64941i	0.0369585	+	0.137931i
$144$	3.94575	−	8.31777i	0.328813	−	0.693148i
$145$		0			0
$146$	−1.60663	+	0.703770i	−0.132966	+	0.0582444i
$147$	2.88855	+	5.08726i	0.238243	+	0.419590i
$148$	−4.95487	+	0.199937i	−0.407288	+	0.0164347i
$149$	5.05558	−	2.91884i	0.414169	−	0.239121i	−0.278410	−	0.960462i	$-0.589808\pi$
$149$	5.05558	−	2.91884i	0.414169	−	0.239121i	0.692579	+	0.721342i	$0.256474\pi$
$150$		0			0
$151$	3.20930	+	1.85289i	0.261169	+	0.150786i	0.624868	−	0.780731i	$-0.285153\pi$
$151$	3.20930	+	1.85289i	0.261169	+	0.150786i	−0.363699	+	0.931517i	$0.618486\pi$
$152$	−6.97829	−	4.71293i	−0.566014	−	0.382269i
$153$	9.83174	+	9.83174i	0.794849	+	0.794849i
$154$	−17.6791	−	4.42450i	−1.42462	−	0.356536i
$155$		0			0
$156$	0.128722	−	0.571684i	0.0103060	−	0.0457714i
$157$	2.85757	+	10.6646i	0.228059	+	0.851127i	0.981156	+	0.193218i	$0.0618923\pi$
$157$	2.85757	+	10.6646i	0.228059	+	0.851127i	−0.753097	+	0.657909i	$0.771441\pi$
$158$	−7.85708	−	9.82292i	−0.625076	−	0.781469i
$159$	0.133689	+	0.231556i	0.0106022	+	0.0183636i
$160$		0			0
$161$	−17.2837	−	2.33870i	−1.36215	−	0.184316i
$162$	1.64810	−	4.21745i	0.129487	−	0.331354i
$163$	−0.699506	−	0.187432i	−0.0547896	−	0.0146808i	0.231320	−	0.972878i	$-0.425696\pi$
$163$	−0.699506	−	0.187432i	−0.0547896	−	0.0146808i	−0.286110	+	0.958197i	$0.592362\pi$
$164$	−2.20241	+	0.686425i	−0.171979	+	0.0536008i
$165$		0			0
$166$	−12.8536	+	17.4695i	−0.997632	+	1.35590i
$167$	2.79303	+	2.79303i	0.216131	+	0.216131i	0.806866	−	0.590735i	$-0.201162\pi$
$167$	2.79303	+	2.79303i	0.216131	+	0.216131i	−0.590735	+	0.806866i	$0.701162\pi$
$168$	4.66660	+	4.16363i	0.360036	+	0.321231i
$169$		−	12.8771i		−	0.990545i
$170$		0			0
$171$	−5.93410	−	3.42606i	−0.453792	−	0.261997i
$172$	−4.24798	+	8.09490i	−0.323906	+	0.617230i
$173$	5.84433	−	21.8113i	0.444336	−	1.65828i	−0.273348	−	0.961915i	$-0.588131\pi$
$173$	5.84433	−	21.8113i	0.444336	−	1.65828i	0.717684	−	0.696369i	$-0.245202\pi$
$174$	−5.05691	+	2.21513i	−0.383363	+	0.167929i
$175$		0			0
$176$	−19.4193	+	1.56975i	−1.46378	+	0.118325i
$177$	0.683609	+	0.183172i	0.0513832	+	0.0137681i
$178$	−10.5435	+	8.43345i	−0.790268	+	0.632114i
$179$	4.66406	−	8.07838i	0.348608	−	0.603807i	−0.637394	−	0.770538i	$-0.719988\pi$
$179$	4.66406	−	8.07838i	0.348608	−	0.603807i	0.986002	+	0.166731i	$0.0533211\pi$
$180$		0			0
$181$	13.7888			1.02492			0.512458	−	0.858712i	$-0.328735\pi$
$181$	13.7888			1.02492			0.512458	+	0.858712i	$0.328735\pi$
$182$	−1.14675	−	0.636980i	−0.0850028	−	0.0472161i
$183$	5.96356	−	5.96356i	0.440839	−	0.440839i
$184$	−18.3050	+	3.54688i	−1.34946	+	0.261480i
$185$		0			0
$186$	−0.868471	+	7.81071i	−0.0636794	+	0.572709i
$187$	7.61566	−	28.4220i	0.556913	−	2.07843i
$188$	0.396076	+	9.81561i	0.0288868	+	0.715877i
$189$	9.27433	+	7.16958i	0.674608	+	0.521510i
$190$		0			0
$191$	−0.149824	+	0.0865011i	−0.0108409	+	0.00625900i	−0.505411	−	0.862879i	$-0.668659\pi$
$191$	−0.149824	+	0.0865011i	−0.0108409	+	0.00625900i	0.494570	+	0.869138i	$0.335326\pi$
$192$	6.15126	+	2.61965i	0.443929	+	0.189057i
$193$	−9.09154	+	2.43607i	−0.654423	+	0.175352i	−0.570728	−	0.821139i	$-0.693339\pi$
$193$	−9.09154	+	2.43607i	−0.654423	+	0.175352i	−0.0836952	+	0.996491i	$0.526672\pi$
$194$	2.79605	−	3.80015i	0.200745	−	0.272835i
$195$		0			0
$196$	11.8858	−	7.39786i	0.848984	−	0.528419i
$197$	10.6666	−	10.6666i	0.759966	−	0.759966i	−0.216350	−	0.976316i	$-0.569415\pi$
$197$	10.6666	−	10.6666i	0.759966	−	0.759966i	0.976316	+	0.216350i	$0.0694151\pi$
$198$	−15.6729	+	2.38579i	−1.11382	+	0.169551i
$199$	−8.58014	+	14.8612i	−0.608230	+	1.05349i	0.383302	+	0.923623i	$0.374787\pi$
$199$	−8.58014	+	14.8612i	−0.608230	+	1.05349i	−0.991532	+	0.129862i	$0.958547\pi$
$200$		0			0
$201$	−1.16559	−	2.01886i	−0.0822143	−	0.142399i
$202$	−0.750999	+	1.92179i	−0.0528401	+	0.135217i
$203$	1.56905	+	12.2586i	0.110126	+	0.860384i
$204$	−6.84644	+	7.42220i	−0.479347	+	0.519658i
$205$		0			0
$206$	0.775601	+	0.0862388i	0.0540387	+	0.00600854i
$207$	−14.6552	+	3.92686i	−1.01861	+	0.272935i
$208$	−1.37941	−	0.252636i	−0.0956451	−	0.0175172i
$209$			14.5008i			1.00304i
$210$		0			0
$211$		−	2.47386i		−	0.170307i	−0.996368	−	0.0851536i	$-0.972862\pi$
$211$		−	2.47386i		−	0.170307i	0.996368	−	0.0851536i	$-0.0271381\pi$
$212$	0.540791	−	0.342015i	0.0371416	−	0.0234897i
$213$	−5.24644	+	1.40578i	−0.359480	+	0.0963224i
$214$	0.777176	−	6.98965i	0.0531267	−	0.477802i
$215$		0			0
$216$	11.8467	+	4.08698i	0.806064	+	0.278084i
$217$	16.2290	+	6.79074i	1.10170	+	0.460985i
$218$	−14.7581	−	5.76721i	−0.999548	−	0.390605i
$219$	−0.518268	−	0.897666i	−0.0350213	−	0.0606587i
$220$		0			0
$221$	1.05899	−	1.83423i	0.0712356	−	0.123384i
$222$	−0.441008	−	2.89709i	−0.0295985	−	0.194440i
$223$	7.05641	−	7.05641i	0.472532	−	0.472532i	−0.430201	−	0.902733i	$-0.641557\pi$
$223$	7.05641	−	7.05641i	0.472532	−	0.472532i	0.902733	+	0.430201i	$0.141557\pi$
$224$	9.50567	−	11.5604i	0.635125	−	0.772410i
$225$		0			0
$226$	−9.48437	−	6.97835i	−0.630891	−	0.464193i
$227$	−19.6779	+	5.27268i	−1.30607	+	0.349960i	−0.843742	−	0.536750i	$-0.819652\pi$
$227$	−19.6779	+	5.27268i	−1.30607	+	0.349960i	−0.462327	+	0.886710i	$0.652985\pi$
$228$	2.31233	−	4.40635i	0.153138	−	0.291818i
$229$	8.26790	−	4.77347i	0.546358	−	0.315440i	−0.201294	−	0.979531i	$-0.564515\pi$
$229$	8.26790	−	4.77347i	0.546358	−	0.315440i	0.747652	+	0.664091i	$0.231181\pi$
$230$		0			0
$231$	1.44411	−	10.6724i	0.0950156	−	0.702194i
$232$	5.78468	+	11.8782i	0.379783	+	0.779841i
$233$	−5.29887	+	19.7757i	−0.347141	+	1.29555i	0.542951	+	0.839765i	$0.317307\pi$
$233$	−5.29887	+	19.7757i	−0.347141	+	1.29555i	−0.890091	+	0.455782i	$0.849360\pi$
$234$	−1.13414	−	0.126105i	−0.0741410	−	0.00824372i
$235$		0			0
$236$	0.372036	−	1.65230i	0.0242175	−	0.107555i
$237$	5.25620	−	5.25620i	0.341427	−	0.341427i
$238$	11.6249	+	19.3858i	0.753528	+	1.25660i
$239$	25.5833			1.65484			0.827422	−	0.561581i	$-0.189807\pi$
$239$	25.5833			1.65484			0.827422	+	0.561581i	$0.189807\pi$
$240$		0			0
$241$	−8.01250	+	13.8781i	−0.516131	+	0.893965i	0.483694	+	0.875237i	$0.339295\pi$
$241$	−8.01250	+	13.8781i	−0.516131	+	0.893965i	−0.999825	+	0.0187274i	$0.994039\pi$
$242$	11.2393	+	14.0514i	0.722490	+	0.903256i
$243$	15.4238	+	4.13279i	0.989436	+	0.265119i
$244$	−14.8353	−	13.6845i	−0.949731	−	0.876057i
$245$		0			0
$246$	−0.546988	−	1.24872i	−0.0348747	−	0.0796152i
$247$	−0.270146	+	1.00820i	−0.0171890	+	0.0641501i
$248$	18.7605	+	1.32302i	1.19129	+	0.0840120i
$249$	−11.0998	−	6.40847i	−0.703421	−	0.406120i
$250$		0			0
$251$			28.9444i			1.82696i	0.406889	+	0.913478i	$0.366614\pi$
$251$			28.9444i			1.82696i	−0.406889	+	0.913478i	$0.633386\pi$
$252$	7.05406	−	9.92775i	0.444364	−	0.625390i
$253$	22.7039	+	22.7039i	1.42738	+	1.42738i
$254$	8.81276	+	6.48419i	0.552962	+	0.406854i
$255$		0			0
$256$	5.67051	−	14.9615i	0.354407	−	0.935091i
$257$	−19.9032	−	5.33306i	−1.24153	−	0.332667i	−0.422471	−	0.906376i	$-0.638837\pi$
$257$	−19.9032	−	5.33306i	−1.24153	−	0.332667i	−0.819059	+	0.573709i	$0.805504\pi$
$258$	−5.03181	−	1.96634i	−0.313267	−	0.122419i
$259$	−6.50076	−	0.879634i	−0.403938	−	0.0546578i
$260$		0			0
$261$	5.37540	+	9.31047i	0.332729	+	0.576303i
$262$	6.28701	−	5.02881i	0.388413	−	0.310681i
$263$	−3.26932	−	12.2013i	−0.201595	−	0.752362i	−0.990461	−	0.137796i	$-0.955998\pi$
$263$	−3.26932	−	12.2013i	−0.201595	−	0.752362i	0.788866	−	0.614566i	$-0.210669\pi$
$264$	−2.19015	−	11.3030i	−0.134794	−	0.695654i
$265$		0			0
$266$	−8.00627	−	7.74526i	−0.490896	−	0.474892i
$267$	−5.64178	−	5.64178i	−0.345271	−	0.345271i
$268$	−4.71497	+	2.98191i	−0.288012	+	0.182149i
$269$	9.69903	+	5.59974i	0.591360	+	0.341422i	0.765635	−	0.643275i	$-0.222425\pi$
$269$	9.69903	+	5.59974i	0.591360	+	0.341422i	−0.174275	+	0.984697i	$0.555758\pi$
$270$		0			0
$271$	20.6434	−	11.9184i	1.25399	−	0.723994i	0.282094	−	0.959387i	$-0.408971\pi$
$271$	20.6434	−	11.9184i	1.25399	−	0.723994i	0.971900	+	0.235392i	$0.0756375\pi$
$272$	18.4083	+	15.6548i	1.11617	+	0.949214i
$273$	0.299230	−	0.715121i	0.0181102	−	0.0432811i
$274$	−0.281684	−	0.643054i	−0.0170171	−	0.0388483i
$275$		0			0
$276$	−3.27861	−	10.5195i	−0.197349	−	0.633197i
$277$	1.42243	+	5.30858i	0.0854656	+	0.318962i	0.995402	−	0.0957860i	$-0.0305364\pi$
$277$	1.42243	+	5.30858i	0.0854656	+	0.318962i	−0.909936	+	0.414748i	$0.863870\pi$
$278$	−8.91109	+	1.35648i	−0.534452	+	0.0813565i
$279$	15.3038			0.916212
$280$		0			0
$281$	29.7858			1.77687			0.888436	−	0.459001i	$-0.151793\pi$
$281$	29.7858			1.77687			0.888436	+	0.459001i	$0.151793\pi$
$282$	−5.73916	+	0.873639i	−0.341762	+	0.0520244i
$283$	−5.60990	−	20.9364i	−0.333474	−	1.24454i	−0.905514	−	0.424316i	$-0.860515\pi$
$283$	−5.60990	−	20.9364i	−0.333474	−	1.24454i	0.572041	−	0.820225i	$-0.306152\pi$
$284$	3.86767	+	12.4095i	0.229504	+	0.736367i
$285$		0			0
$286$	0.968945	+	2.21200i	0.0572949	+	0.130798i
$287$	−3.02704	+	0.387449i	−0.178681	+	0.0228704i
$288$	3.74635	−	12.4689i	0.220756	−	0.734737i
$289$	−16.8843	+	9.74814i	−0.993193	+	0.573420i
$290$		0			0
$291$	2.41455	+	1.39404i	0.141543	+	0.0817200i
$292$	−2.09646	+	1.32588i	−0.122686	+	0.0775912i
$293$	2.85175	+	2.85175i	0.166601	+	0.166601i	0.785484	−	0.618883i	$-0.212414\pi$
$293$	2.85175	+	2.85175i	0.166601	+	0.166601i	−0.618883	+	0.785484i	$0.712414\pi$
$294$	5.12120	+	6.49778i	0.298675	+	0.378958i
$295$		0			0
$296$	−6.88488	+	1.33406i	−0.400176	+	0.0775405i
$297$	−5.58539	−	20.8449i	−0.324097	−	1.20955i
$298$	6.44704	−	5.15681i	0.373467	−	0.298726i
$299$	1.15557	+	2.00151i	0.0668284	+	0.115750i
$300$		0			0
$301$	−7.39650	+	9.56787i	−0.426327	+	0.551483i
$302$	4.88129	+	1.90752i	0.280887	+	0.109765i
$303$	−1.17777	−	0.315583i	−0.0676612	−	0.0181298i
$304$	−10.7594	−	5.10402i	−0.617096	−	0.292736i
$305$		0			0
$306$	15.8383	+	11.6534i	0.905414	+	0.666179i
$307$	−3.58241	−	3.58241i	−0.204459	−	0.204459i	0.597448	−	0.801907i	$-0.296181\pi$
$307$	−3.58241	−	3.58241i	−0.204459	−	0.204459i	−0.801907	+	0.597448i	$0.796181\pi$
$308$	−25.6589	−	2.42336i	−1.46205	−	0.138084i
$309$			0.461167i			0.0262349i
$310$		0			0
$311$	−21.3073	−	12.3018i	−1.20822	−	0.697569i	−0.245854	−	0.969307i	$-0.579068\pi$
$311$	−21.3073	−	12.3018i	−1.20822	−	0.697569i	−0.962371	+	0.271738i	$0.912402\pi$
$312$	0.0582982	−	0.826672i	0.00330049	−	0.0468011i
$313$	1.74036	−	6.49513i	0.0983712	−	0.367126i	−0.899138	−	0.437666i	$-0.855805\pi$
$313$	1.74036	−	6.49513i	0.0983712	−	0.367126i	0.997509	+	0.0705393i	$0.0224720\pi$
$314$	6.26489	+	14.3021i	0.353548	+	0.807113i
$315$		0			0
$316$	−13.0756	−	12.0613i	−0.735561	−	0.678501i
$317$	13.3482	+	3.57664i	0.749709	+	0.200884i	0.613389	−	0.789781i	$-0.289806\pi$
$317$	13.3482	+	3.57664i	0.749709	+	0.200884i	0.136320	+	0.990665i	$0.456472\pi$
$318$	0.236193	+	0.295288i	0.0132450	+	0.0165589i
$319$	11.3757	−	19.7032i	0.636915	−	1.10317i
$320$		0			0
$321$	4.15600			0.231965
$322$	−24.6622	+	0.408665i	−1.37437	+	0.0227740i
$323$	12.7178	−	12.7178i	0.707638	−	0.707638i
$324$	1.40664	−	6.24721i	0.0781467	−	0.347067i
$325$		0			0
$326$	−1.01788	−	0.113177i	−0.0563749	−	0.00626831i
$327$	2.42348	−	9.04456i	0.134019	−	0.500165i
$328$	−2.93311	+	1.42843i	−0.161954	+	0.0788716i
$329$	−1.74256	+	12.8780i	−0.0960704	+	0.709989i
$330$		0			0
$331$	−1.62048	+	0.935587i	−0.0890699	+	0.0514245i	−0.543873	−	0.839167i	$-0.683043\pi$
$331$	−1.62048	+	0.935587i	−0.0890699	+	0.0514245i	0.454804	+	0.890592i	$0.349709\pi$
$332$	−14.2527	+	27.1598i	−0.782221	+	1.49059i
$333$	−5.51214	+	1.47697i	−0.302063	+	0.0809376i
$334$	4.49939	+	3.31053i	0.246196	+	0.181144i
$335$		0			0
$336$	7.41054	+	4.82803i	0.404278	+	0.263391i
$337$	−15.5089	+	15.5089i	−0.844825	+	0.844825i	−0.989482	−	0.144657i	$-0.953792\pi$
$337$	−15.5089	+	15.5089i	−0.844825	+	0.844825i	0.144657	+	0.989482i	$0.453792\pi$
$338$	−2.74058	−	18.0036i	−0.149068	−	0.979264i
$339$	3.47923	−	6.02620i	0.188966	−	0.327298i
$340$		0			0
$341$	−16.1933	−	28.0476i	−0.876915	−	1.51886i
$342$	−9.02567	−	3.52706i	−0.488052	−	0.190722i
$343$	17.1859	−	6.90240i	0.927954	−	0.372695i
$344$	−4.21633	+	12.2216i	−0.227330	+	0.658946i
$345$		0			0
$346$	3.52898	−	31.7384i	0.189719	−	1.70627i
$347$	10.1882	−	2.72992i	0.546931	−	0.146550i	0.0252358	−	0.999682i	$-0.491966\pi$
$347$	10.1882	−	2.72992i	0.546931	−	0.146550i	0.521696	+	0.853132i	$0.325300\pi$
$348$	−6.59867	+	4.17323i	−0.353726	+	0.223709i
$349$			7.92462i			0.424195i	0.977249	+	0.212098i	$0.0680295\pi$
$349$			7.92462i			0.424195i	−0.977249	+	0.212098i	$0.931971\pi$
$350$		0			0
$351$		−	1.55335i		−	0.0829115i
$352$	−26.8161	+	6.32761i	−1.42931	+	0.337263i
$353$	−8.66171	+	2.32090i	−0.461016	+	0.123529i	−0.481849	−	0.876254i	$-0.660035\pi$
$353$	−8.66171	+	2.32090i	−0.461016	+	0.123529i	0.0208332	+	0.999783i	$0.493368\pi$
$354$	0.994742	+	0.110605i	0.0528700	+	0.00587859i
$355$		0			0
$356$	−12.9461	+	14.0348i	−0.686141	+	0.743843i
$357$	−10.6268	+	8.09365i	−0.562427	+	0.428361i
$358$	4.80156	−	12.2871i	0.253771	−	0.649392i
$359$	11.6112	+	20.1111i	0.612814	+	1.06143i	0.990764	+	0.135599i	$0.0432960\pi$
$359$	11.6112	+	20.1111i	0.612814	+	1.06143i	−0.377950	+	0.925826i	$0.623371\pi$
$360$		0			0
$361$	5.06824	−	8.77844i	0.266749	−	0.462023i
$362$	19.2783	−	2.93462i	1.01324	−	0.154240i
$363$	−7.51883	+	7.51883i	−0.394636	+	0.394636i
$364$	−1.73885	−	0.646509i	−0.0911403	−	0.0338863i
$365$		0			0
$366$	7.06850	−	9.60689i	0.369476	−	0.502160i
$367$	30.1327	−	8.07404i	1.57292	−	0.421462i	0.636192	−	0.771530i	$-0.280508\pi$
$367$	30.1327	−	8.07404i	1.57292	−	0.421462i	0.936724	+	0.350069i	$0.113842\pi$
$368$	−24.8375	+	8.85470i	−1.29474	+	0.461583i
$369$	−2.29906	+	1.32736i	−0.119684	+	0.0690997i
$370$		0			0
$371$	0.783190	−	0.321113i	0.0406612	−	0.0166714i
$372$	0.448107	+	11.1051i	0.0232333	+	0.575770i
$373$	4.82267	−	17.9985i	0.249709	−	0.931925i	−0.721250	−	0.692675i	$-0.756432\pi$
$373$	4.82267	−	17.9985i	0.249709	−	0.931925i	0.970958	−	0.239250i	$-0.0769014\pi$
$374$	4.59857	−	41.3579i	0.237786	−	2.13857i
$375$		0			0
$376$	2.64277	+	13.6390i	0.136291	+	0.703377i
$377$	1.15799	−	1.15799i	0.0596393	−	0.0596393i
$378$	14.4924	+	8.05002i	0.745408	+	0.414049i
$379$	18.6149			0.956182			0.478091	−	0.878310i	$-0.341329\pi$
$379$	18.6149			0.956182			0.478091	+	0.878310i	$0.341329\pi$
$380$		0			0
$381$	−3.23285	+	5.59946i	−0.165624	+	0.286869i
$382$	−0.191061	+	0.152824i	−0.00977553	+	0.00781918i
$383$	30.1389	+	8.07570i	1.54003	+	0.412649i	0.926275	−	0.376849i	$-0.122992\pi$
$383$	30.1389	+	8.07570i	1.54003	+	0.412649i	0.613753	+	0.789498i	$0.289659\pi$
$384$	9.15766	+	2.35341i	0.467325	+	0.120097i
$385$		0			0
$386$	−12.1925	+	5.34080i	−0.620581	+	0.271840i
$387$	−2.72282	+	10.1617i	−0.138409	+	0.516549i
$388$	3.10041	−	5.90809i	0.157399	−	0.299938i
$389$	3.21806	+	1.85795i	0.163162	+	0.0942017i	0.579358	−	0.815073i	$-0.303303\pi$
$389$	3.21806	+	1.85795i	0.163162	+	0.0942017i	−0.416196	+	0.909275i	$0.636637\pi$
$390$		0			0
$391$		−	39.8247i		−	2.01402i
$392$	15.0431	−	12.8726i	0.759793	−	0.650165i
$393$	3.36415	+	3.36415i	0.169699	+	0.169699i
$394$	12.6430	−	17.1832i	0.636944	−	0.865679i
$395$		0			0
$396$	−21.4046	+	6.67119i	−1.07562	+	0.335240i
$397$	−4.29450	−	1.15071i	−0.215535	−	0.0577524i	0.149436	−	0.988771i	$-0.452254\pi$
$397$	−4.29450	−	1.15071i	−0.215535	−	0.0577524i	−0.364971	+	0.931019i	$0.618921\pi$
$398$	−8.83310	+	22.6037i	−0.442763	+	1.13302i
$399$	4.02619	−	5.20814i	0.201561	−	0.260733i
$400$		0			0
$401$	−17.5463	−	30.3911i	−0.876220	−	1.51766i	−0.855457	−	0.517873i	$-0.826724\pi$
$401$	−17.5463	−	30.3911i	−0.876220	−	1.51766i	−0.0207625	−	0.999784i	$-0.506609\pi$
$402$	−2.05928	−	2.57451i	−0.102708	−	0.128405i
$403$	−0.603354	−	2.25175i	−0.0300552	−	0.112168i
$404$	−0.640971	+	2.84670i	−0.0318895	+	0.141629i
$405$		0			0
$406$	4.80264	+	16.8049i	0.238351	+	0.834012i
$407$	8.53940	+	8.53940i	0.423282	+	0.423282i
$408$	−7.99242	+	11.8341i	−0.395684	+	0.585877i
$409$	31.9026	+	18.4190i	1.57748	+	0.910759i	0.995210	+	0.0977650i	$0.0311693\pi$
$409$	31.9026	+	18.4190i	1.57748	+	0.910759i	0.582272	+	0.812994i	$0.302164\pi$
$410$		0			0
$411$	0.359291	−	0.207437i	0.0177225	−	0.0102321i
$412$	1.10273	−	0.0444969i	0.0543275	−	0.00219220i
$413$	0.864842	−	2.06686i	0.0425561	−	0.101704i
$414$	−19.6538	+	8.60918i	−0.965934	+	0.423118i
$415$		0			0
$416$	−1.98234	−	0.0596373i	−0.0971920	−	0.00292396i
$417$	−1.37865	−	5.14518i	−0.0675126	−	0.251961i
$418$	3.08614	+	20.2736i	0.150948	+	0.991615i
$419$	−31.8030			−1.55368			−0.776840	−	0.629699i	$-0.783178\pi$
$419$	−31.8030			−1.55368			−0.776840	+	0.629699i	$0.783178\pi$
$420$		0			0
$421$	13.1193			0.639396			0.319698	−	0.947519i	$-0.396418\pi$
$421$	13.1193			0.639396			0.319698	+	0.947519i	$0.396418\pi$
$422$	−0.526501	−	3.45872i	−0.0256296	−	0.168368i
$423$	2.92589	+	10.9196i	0.142262	+	0.530928i
$424$	0.683294	−	0.593269i	0.0331837	−	0.0288117i
$425$		0			0
$426$	−7.03590	+	3.08201i	−0.340890	+	0.149324i
$427$	−16.1773	−	21.2404i	−0.782876	−	1.02790i
$428$	−0.401002	−	9.93768i	−0.0193831	−	0.480356i
$429$	−1.23590	+	0.713547i	−0.0596698	+	0.0344504i
$430$		0			0
$431$	−17.0409	−	9.83859i	−0.820833	−	0.473908i	0.0298705	−	0.999554i	$-0.490491\pi$
$431$	−17.0409	−	9.83859i	−0.820833	−	0.473908i	−0.850704	+	0.525646i	$0.823824\pi$
$432$	17.4327	+	3.19276i	0.838733	+	0.153612i
$433$	12.6198	+	12.6198i	0.606466	+	0.606466i	0.942021	−	0.335554i	$-0.108924\pi$
$433$	12.6198	+	12.6198i	0.606466	+	0.606466i	−0.335554	+	0.942021i	$0.608924\pi$
$434$	24.1351	+	6.04024i	1.15852	+	0.289941i
$435$		0			0
$436$	−21.8609	−	4.92226i	−1.04695	−	0.235734i
$437$	5.07957	+	18.9572i	0.242989	+	0.906847i
$438$	−0.915641	−	1.14473i	−0.0437510	−	0.0546975i
$439$	2.34778	+	4.06648i	0.112054	+	0.194082i	0.916598	−	0.399810i	$-0.130924\pi$
$439$	2.34778	+	4.06648i	0.112054	+	0.194082i	−0.804545	+	0.593892i	$0.797591\pi$
$440$		0			0
$441$	11.4737	−	11.3099i	0.546369	−	0.538566i
$442$	1.09021	−	2.78983i	0.0518562	−	0.132699i
$443$	4.01934	+	1.07698i	0.190965	+	0.0511688i	0.353034	−	0.935611i	$-0.385150\pi$
$443$	4.01934	+	1.07698i	0.190965	+	0.0511688i	−0.162069	+	0.986779i	$0.551817\pi$
$444$	−1.23315	−	3.95659i	−0.0585229	−	0.187771i
$445$		0			0
$446$	8.36383	−	11.3674i	0.396039	−	0.538262i
$447$	3.44978	+	3.44978i	0.163169	+	0.163169i
$448$	10.8296	−	18.1857i	0.511651	−	0.859193i
$449$		−	41.3539i		−	1.95161i	−0.218641	−	0.975805i	$-0.570163\pi$
$449$		−	41.3539i		−	1.95161i	0.218641	−	0.975805i	$-0.429837\pi$
$450$		0			0
$451$	4.86537	+	2.80902i	0.229101	+	0.132272i
$452$	−14.7454	−	7.73796i	−0.693563	−	0.363963i
$453$	−0.801572	+	2.99151i	−0.0376612	+	0.140553i
$454$	−26.3897	+	11.5597i	−1.23853	+	0.542526i
$455$		0			0
$456$	2.29511	−	6.65268i	0.107478	−	0.311540i
$457$	22.3901	+	5.99940i	1.04736	+	0.280640i	0.741162	−	0.671326i	$-0.234275\pi$
$457$	22.3901	+	5.99940i	1.04736	+	0.280640i	0.306202	+	0.951967i	$0.400942\pi$
$458$	10.5435	−	8.43345i	0.492665	−	0.394069i
$459$	−13.3833	+	23.1806i	−0.624680	+	1.08198i
$460$		0			0
$461$	16.9131			0.787723			0.393861	−	0.919170i	$-0.371139\pi$
$461$	16.9131			0.787723			0.393861	+	0.919170i	$0.371139\pi$
$462$	−0.252344	−	15.2285i	−0.0117401	−	0.708496i
$463$	−22.3542	+	22.3542i	−1.03889	+	1.03889i	−0.0396749	+	0.999213i	$0.512632\pi$
$463$	−22.3542	+	22.3542i	−1.03889	+	1.03889i	−0.999213	+	0.0396749i	$0.987368\pi$
$464$	10.6156	+	15.3759i	0.492816	+	0.713806i
$465$		0			0
$466$	−3.19962	+	28.7762i	−0.148220	+	1.33303i
$467$	−2.22089	+	8.28849i	−0.102771	+	0.383546i	−0.998083	−	0.0618940i	$-0.980286\pi$
$467$	−2.22089	+	8.28849i	−0.102771	+	0.383546i	0.895312	+	0.445440i	$0.146953\pi$
$468$	−1.61249	+	0.0650665i	−0.0745373	+	0.00300770i
$469$	−6.82836	+	2.79968i	−0.315305	+	0.129277i
$470$		0			0
$471$	−7.99094	+	4.61357i	−0.368203	+	0.212582i
$472$	0.168495	−	2.38927i	0.00775561	−	0.109975i
$473$	21.5047	−	5.76217i	0.988787	−	0.264945i
$474$	6.23008	−	8.46739i	0.286157	−	0.388920i
$475$		0			0
$476$	20.3786	+	24.6294i	0.934052	+	1.12889i
$477$	0.520673	−	0.520673i	0.0238400	−	0.0238400i
$478$	35.7682	−	5.44478i	1.63600	−	0.249039i
$479$	12.0963	−	20.9514i	0.552694	−	0.957294i	−0.445385	−	0.895339i	$-0.646933\pi$
$479$	12.0963	−	20.9514i	0.552694	−	0.957294i	0.998079	−	0.0619545i	$-0.0197334\pi$
$480$		0			0
$481$	0.434634	+	0.752808i	0.0198176	+	0.0343251i
$482$	−8.24873	+	21.1083i	−0.375719	+	0.961457i
$483$	−1.85059	−	14.4582i	−0.0842049	−	0.657872i
$484$	18.7043	+	17.2533i	0.850194	+	0.784241i
$485$		0			0
$486$	22.4437	+	2.49550i	1.01807	+	0.113198i
$487$	17.9030	−	4.79710i	0.811263	−	0.217377i	0.170740	−	0.985316i	$-0.445384\pi$
$487$	17.9030	−	4.79710i	0.811263	−	0.217377i	0.640523	+	0.767939i	$0.278718\pi$
$488$	−23.6537	−	15.9750i	−1.07075	−	0.723155i
$489$		−	0.605222i		−	0.0273691i
$490$		0			0
$491$			26.3306i			1.18828i	0.804360	+	0.594142i	$0.202508\pi$
$491$			26.3306i			1.18828i	−0.804360	+	0.594142i	$0.797492\pi$
$492$	−1.03051	−	1.62943i	−0.0464589	−	0.0734602i
$493$	−27.2576	+	7.30366i	−1.22762	+	0.328940i
$494$	−0.163122	+	1.46706i	−0.00733922	+	0.0660063i
$495$		0			0
$496$	26.5108	−	2.14300i	1.19037	−	0.0962235i
$497$	2.18309	+	17.0559i	0.0979248	+	0.765061i
$498$	−16.8826	−	6.59741i	−0.756528	−	0.295637i
$499$	−5.41316	−	9.37586i	−0.242326	−	0.419721i	0.719050	−	0.694958i	$-0.244577\pi$
$499$	−5.41316	−	9.37586i	−0.242326	−	0.419721i	−0.961376	+	0.275237i	$0.911244\pi$
$500$		0			0
$501$	−1.65055	+	2.85883i	−0.0737409	+	0.127723i
$502$	6.16012	+	40.4674i	0.274940	+	1.80615i
$503$	1.75566	−	1.75566i	0.0782809	−	0.0782809i	−0.666882	−	0.745163i	$-0.732372\pi$
$503$	1.75566	−	1.75566i	0.0782809	−	0.0782809i	0.745163	+	0.666882i	$0.232372\pi$
$504$	7.74946	−	15.3814i	0.345188	−	0.685140i
$505$		0			0
$506$	36.5744	+	26.9105i	1.62593	+	1.19632i
$507$	10.3951	−	2.78535i	0.461662	−	0.123702i
$508$	13.7012	+	7.19001i	0.607892	+	0.319005i
$509$	−27.6605	+	15.9698i	−1.22603	+	0.707849i	−0.966197	−	0.257804i	$-0.917001\pi$
$509$	−27.6605	+	15.9698i	−1.22603	+	0.707849i	−0.259834	+	0.965653i	$0.583668\pi$
$510$		0			0
$511$	−3.03617	+	1.24485i	−0.134312	+	0.0550689i
$512$	4.74380	−	22.1246i	0.209648	−	0.977777i
$513$	3.41405	−	12.7414i	0.150734	−	0.562546i
$514$	−28.9619	−	3.22026i	−1.27745	−	0.142040i
$515$		0			0
$516$	−7.45350	−	1.67825i	−0.328122	−	0.0738809i
$517$	16.9166	−	16.9166i	0.743991	−	0.743991i
$518$	−9.27598	+	0.153707i	−0.407563	+	0.00675351i
$519$	18.8714			0.828364
$520$		0			0
$521$	−16.3491	+	28.3174i	−0.716265	+	1.24061i	0.246204	+	0.969218i	$0.420817\pi$
$521$	−16.3491	+	28.3174i	−0.716265	+	1.24061i	−0.962469	+	0.271390i	$0.912517\pi$
$522$	9.49690	+	11.8730i	0.415668	+	0.519668i
$523$	−34.3742	−	9.21055i	−1.50308	−	0.402749i	−0.588950	−	0.808170i	$-0.700458\pi$
$523$	−34.3742	−	9.21055i	−1.50308	−	0.402749i	−0.914130	+	0.405421i	$0.867125\pi$
$524$	7.71966	−	8.36885i	0.337235	−	0.365595i
$525$		0			0
$526$	−7.16760	−	16.3629i	−0.312522	−	0.713456i
$527$	−10.3968	+	38.8012i	−0.452890	+	1.69021i
$528$	−5.46764	−	15.3368i	−0.237949	−	0.667446i
$529$	17.7159	+	10.2283i	0.770257	+	0.444708i
$530$		0			0
$531$		−	1.94903i		−	0.0845806i
$532$	−12.8420	−	9.12477i	−0.556772	−	0.395609i
$533$	0.285944	+	0.285944i	0.0123856	+	0.0123856i
$534$	−9.08853	−	6.68710i	−0.393299	−	0.289379i
$535$		0			0
$536$	−5.95740	+	5.17250i	−0.257321	+	0.223418i
$537$	7.53016	+	2.01770i	0.324950	+	0.0870702i
$538$	14.7521	+	5.76483i	0.636006	+	0.248540i
$539$	−32.8685	−	9.06094i	−1.41575	−	0.390282i
$540$		0			0
$541$	18.6970	+	32.3842i	0.803848	+	1.39231i	0.917066	+	0.398736i	$0.130551\pi$
$541$	18.6970	+	32.3842i	0.803848	+	1.39231i	−0.113218	+	0.993570i	$0.536116\pi$
$542$	26.3251	−	21.0567i	1.13076	−	0.904463i
$543$	2.98257	+	11.1311i	0.127994	+	0.477681i
$544$	29.0686	+	17.9694i	1.24631	+	0.770431i
$545$		0			0
$546$	0.266160	−	1.06350i	0.0113906	−	0.0455136i
$547$	−27.0715	−	27.0715i	−1.15749	−	1.15749i	−0.985013	−	0.172480i	$-0.944822\pi$
$547$	−27.0715	−	27.0715i	−1.15749	−	1.15749i	−0.172480	−	0.985013i	$-0.555178\pi$
$548$	−0.530683	−	0.839110i	−0.0226697	−	0.0358450i
$549$	−20.1143	−	11.6130i	−0.858458	−	0.495631i
$550$		0			0
$551$	12.0435	−	6.95334i	0.513072	−	0.296222i
$552$	−6.82266	−	14.0096i	−0.290392	−	0.596287i
$553$	−14.2585	−	18.7210i	−0.606333	−	0.796099i
$554$	3.11852	+	7.11924i	0.132493	+	0.302468i
$555$		0			0
$556$	−12.1700	+	3.79302i	−0.516122	+	0.160860i
$557$	−4.23623	−	15.8098i	−0.179495	−	0.669884i	−0.995742	−	0.0921814i	$-0.970616\pi$
$557$	−4.23623	−	15.8098i	−0.179495	−	0.669884i	0.816247	−	0.577703i	$-0.196051\pi$
$558$	21.3963	−	3.25704i	0.905778	−	0.137881i
$559$	1.60251			0.0677790
$560$		0			0
$561$	24.5911			1.03824
$562$	41.6437	−	6.33919i	1.75664	−	0.267403i
$563$	−6.07440	−	22.6700i	−0.256005	−	0.955425i	−0.967528	−	0.252762i	$-0.918661\pi$
$563$	−6.07440	−	22.6700i	−0.256005	−	0.955425i	0.711523	−	0.702663i	$-0.248006\pi$
$564$	−7.83802	+	2.44288i	−0.330040	+	0.102864i
$565$		0			0
$566$	−12.2991	−	28.0774i	−0.516968	−	1.18018i
$567$	3.26990	−	7.81464i	0.137323	−	0.328184i
$568$	8.04848	+	16.5266i	0.337707	+	0.693443i
$569$	16.8334	−	9.71879i	0.705694	−	0.407433i	−0.103770	−	0.994601i	$-0.533091\pi$
$569$	16.8334	−	9.71879i	0.705694	−	0.407433i	0.809465	+	0.587168i	$0.199757\pi$
$570$		0			0
$571$	40.3258	+	23.2821i	1.68758	+	0.974327i	0.956361	+	0.292189i	$0.0943835\pi$
$571$	40.3258	+	23.2821i	1.68758	+	0.974327i	0.731223	+	0.682138i	$0.238950\pi$
$572$	1.82546	+	2.88639i	0.0763263	+	0.120686i
$573$	−0.102236	−	0.102236i	−0.00427097	−	0.00427097i
$574$	−4.14967	+	1.18593i	−0.173204	+	0.0494997i
$575$		0			0
$576$	2.58410	−	18.2302i	0.107671	−	0.759591i
$577$	−6.29961	−	23.5105i	−0.262256	−	0.978754i	−0.963908	−	0.266234i	$-0.914221\pi$
$577$	−6.29961	−	23.5105i	−0.262256	−	0.978754i	0.701652	−	0.712520i	$-0.252446\pi$
$578$	−21.5314	+	17.2224i	−0.895587	+	0.716356i
$579$	−3.93306	−	6.81225i	−0.163452	−	0.283108i
$580$		0			0
$581$	−24.8166	+	32.1019i	−1.02956	+	1.33181i
$582$	3.67248	+	1.43514i	0.152229	+	0.0594884i
$583$	−1.50519	−	0.403313i	−0.0623385	−	0.0167035i
$584$	−2.64890	+	2.29990i	−0.109612	+	0.0951707i
$585$		0			0
$586$	4.59398	+	3.38013i	0.189776	+	0.139632i
$587$	0.195894	+	0.195894i	0.00808542	+	0.00808542i	0.711138	−	0.703053i	$-0.248180\pi$
$587$	0.195894	+	0.195894i	0.00808542	+	0.00808542i	−0.703053	+	0.711138i	$0.748180\pi$
$588$	8.54289	+	7.99467i	0.352303	+	0.329694i
$589$		−	19.7961i		−	0.815686i
$590$		0			0
$591$	10.9179	+	6.30346i	0.449103	+	0.259290i
$592$	−9.34189	+	3.33044i	−0.383949	+	0.136880i
$593$	1.08042	−	4.03218i	0.0443676	−	0.165582i	−0.940187	−	0.340658i	$-0.889350\pi$
$593$	1.08042	−	4.03218i	0.0443676	−	0.165582i	0.984555	+	0.175076i	$0.0560170\pi$
$594$	−12.2453	−	27.9548i	−0.502432	−	1.14700i
$595$		0			0
$596$	7.91615	−	8.58187i	0.324258	−	0.351527i
$597$	−13.8527	−	3.71182i	−0.566954	−	0.151915i
$598$	2.04158	+	2.55239i	0.0834866	+	0.104375i
$599$	−8.35085	+	14.4641i	−0.341206	+	0.590987i	−0.984657	−	0.174501i	$-0.944169\pi$
$599$	−8.35085	+	14.4641i	−0.341206	+	0.590987i	0.643451	+	0.765488i	$0.277502\pi$
$600$		0			0
$601$	−38.4209			−1.56722			−0.783610	−	0.621253i	$-0.786624\pi$
$601$	−38.4209			−1.56722			−0.783610	+	0.621253i	$0.786624\pi$
$602$	−8.30481	+	14.9511i	−0.338479	+	0.609360i
$603$	−4.53957	+	4.53957i	−0.184866	+	0.184866i
$604$	7.23054	+	1.62805i	0.294207	+	0.0662444i
$605$		0			0
$606$	−1.71382	−	0.190559i	−0.0696190	−	0.00774091i
$607$	−8.26835	+	30.8579i	−0.335602	+	1.25248i	0.567613	+	0.823295i	$0.307867\pi$
$607$	−8.26835	+	30.8579i	−0.335602	+	1.25248i	−0.903215	+	0.429188i	$0.858800\pi$
$608$	−16.1291	−	4.84608i	−0.654122	−	0.196535i
$609$	−9.55640	+	3.91819i	−0.387245	+	0.158773i
$610$		0			0
$611$	1.49132	−	0.861012i	0.0603322	−	0.0348328i
$612$	24.6238	+	12.9219i	0.995357	+	0.522336i
$613$	26.7652	−	7.17171i	1.08104	−	0.289663i	0.326016	−	0.945364i	$-0.394294\pi$
$613$	26.7652	−	7.17171i	1.08104	−	0.289663i	0.755020	+	0.655702i	$0.227627\pi$
$614$	−5.77103	−	4.24617i	−0.232900	−	0.171361i
$615$		0			0
$616$	−36.3897	+	2.07276i	−1.46618	+	0.0835139i
$617$	−10.6961	+	10.6961i	−0.430610	+	0.430610i	−0.888836	−	0.458226i	$-0.848485\pi$
$617$	−10.6961	+	10.6961i	−0.430610	+	0.430610i	0.458226	+	0.888836i	$0.348485\pi$
$618$	0.0981483	+	0.644761i	0.00394810	+	0.0259361i
$619$	1.43357	−	2.48301i	0.0576199	−	0.0998006i	−0.835777	−	0.549070i	$-0.814982\pi$
$619$	1.43357	−	2.48301i	0.0576199	−	0.0998006i	0.893397	+	0.449269i	$0.148316\pi$
$620$		0			0
$621$	−14.6039	−	25.2946i	−0.586033	−	1.01504i
$622$	−32.4080	−	12.6644i	−1.29944	−	0.507798i
$623$	−20.0943	+	15.3044i	−0.805063	+	0.613160i
$624$	−0.0944300	−	1.16818i	−0.00378022	−	0.0467648i
$625$		0			0
$626$	1.05089	−	9.45128i	0.0420018	−	0.377749i
$627$	−11.7058	+	3.13656i	−0.467485	+	0.125262i
$628$	11.8028	+	18.6625i	0.470985	+	0.744715i
$629$		−	14.9789i		−	0.597247i
$630$		0			0
$631$		−	0.116828i		−	0.00465086i	−0.999997	−	0.00232543i	$-0.999260\pi$
$631$		−	0.116828i		−	0.00465086i	0.999997	−	0.00232543i	$-0.000740209\pi$
$632$	−20.8481	−	14.0802i	−0.829292	−	0.560079i
$633$	1.99703	−	0.535103i	0.0793748	−	0.0212684i
$634$	19.4234	+	2.15968i	0.771402	+	0.0857719i
$635$		0			0
$636$	0.393068	+	0.362577i	0.0155862	+	0.0143771i
$637$	−2.11645	−	1.24232i	−0.0838570	−	0.0492223i
$638$	11.7111	−	29.9683i	0.463645	−	1.18646i
$639$	7.47903	+	12.9541i	0.295866	+	0.512455i
$640$		0			0
$641$	−3.64503	+	6.31338i	−0.143970	+	0.249364i	−0.928988	−	0.370109i	$-0.879320\pi$
$641$	−3.64503	+	6.31338i	−0.143970	+	0.249364i	0.785018	+	0.619473i	$0.212654\pi$
$642$	5.81053	−	0.884504i	0.229323	−	0.0349086i
$643$	2.55764	−	2.55764i	0.100863	−	0.100863i	−0.654874	−	0.755738i	$-0.727278\pi$
$643$	2.55764	−	2.55764i	0.100863	−	0.100863i	0.755738	+	0.654874i	$0.227278\pi$
$644$	−34.3935	+	5.82012i	−1.35529	+	0.229345i
$645$		0			0
$646$	15.0742	−	20.4876i	0.593086	−	0.806072i
$647$	−13.3873	+	3.58712i	−0.526309	+	0.141024i	−0.512183	−	0.858876i	$-0.671163\pi$
$647$	−13.3873	+	3.58712i	−0.526309	+	0.141024i	−0.0141258	+	0.999900i	$0.504497\pi$
$648$	0.637067	−	9.03364i	0.0250264	−	0.354875i
$649$	−3.57203	+	2.06231i	−0.140214	+	0.0809528i
$650$		0			0
$651$	−1.97147	+	14.5698i	−0.0772681	+	0.571035i
$652$	−1.44719	+	0.0583963i	−0.0566762	+	0.00228698i
$653$	−7.66070	+	28.5901i	−0.299786	+	1.11882i	0.637555	+	0.770405i	$0.279946\pi$
$653$	−7.66070	+	28.5901i	−0.299786	+	1.11882i	−0.937341	+	0.348413i	$0.886721\pi$
$654$	1.46337	−	13.1610i	0.0572224	−	0.514638i
$655$		0			0
$656$	−3.79680	+	2.62133i	−0.148240	+	0.102346i
$657$	−2.01848	+	2.01848i	−0.0787482	+	0.0787482i
$658$	0.304495	+	18.3757i	0.0118704	+	0.716361i
$659$	−41.1139			−1.60157			−0.800784	−	0.598953i	$-0.795584\pi$
$659$	−41.1139			−1.60157			−0.800784	+	0.598953i	$0.795584\pi$
$660$		0			0
$661$	7.77799	−	13.4719i	0.302529	−	0.523995i	−0.674179	−	0.738568i	$-0.735502\pi$
$661$	7.77799	−	13.4719i	0.302529	−	0.523995i	0.976708	+	0.214572i	$0.0688358\pi$
$662$	−2.06649	+	1.65293i	−0.0803166	+	0.0642430i
$663$	1.70975	+	0.458127i	0.0664013	+	0.0177922i
$664$	−14.1466	+	41.0057i	−0.548993	+	1.59133i
$665$		0			0
$666$	−7.39222	+	3.23809i	−0.286443	+	0.125474i
$667$	7.96973	−	29.7435i	0.308589	−	1.15167i
$668$	6.99520	+	3.67089i	0.270652	+	0.142031i
$669$	7.22264	+	4.16999i	0.279243	+	0.161221i
$670$		0			0
$671$			49.1520i			1.89749i
$672$	11.3883	+	5.17295i	0.439312	+	0.199551i
$673$	−2.25638	−	2.25638i	−0.0869771	−	0.0869771i	0.662280	−	0.749257i	$-0.269589\pi$
$673$	−2.25638	−	2.25638i	−0.0869771	−	0.0869771i	−0.749257	+	0.662280i	$0.769589\pi$
$674$	−18.3824	+	24.9838i	−0.708065	+	0.962342i
$675$		0			0
$676$	−7.66325	−	24.5876i	−0.294740	−	0.945679i
$677$	−40.2278	−	10.7790i	−1.54608	−	0.414271i	−0.617855	−	0.786292i	$-0.711998\pi$
$677$	−40.2278	−	10.7790i	−1.54608	−	0.414271i	−0.928224	+	0.372022i	$0.878665\pi$
$678$	3.58180	−	9.16574i	0.137558	−	0.352008i
$679$	5.39836	−	6.98315i	0.207170	−	0.267989i
$680$		0			0
$681$	−8.51279	−	14.7446i	−0.326211	−	0.565014i
$682$	−28.6092	−	35.7672i	−1.09550	−	1.36960i
$683$	11.2093	+	41.8335i	0.428910	+	1.60072i	0.755233	+	0.655457i	$0.227524\pi$
$683$	11.2093	+	41.8335i	0.428910	+	1.60072i	−0.326322	+	0.945259i	$0.605810\pi$
$684$	−13.3695	−	3.01032i	−0.511196	−	0.115102i
$685$		0			0
$686$	22.5588	−	13.3079i	0.861299	−	0.508099i
$687$	5.64178	+	5.64178i	0.215247	+	0.215247i
$688$	−3.29381	+	17.9845i	−0.125575	+	0.685652i
$689$	−0.0971379	−	0.0560826i	−0.00370066	−	0.00213658i
$690$		0			0
$691$	−37.3091	+	21.5404i	−1.41930	+	0.819436i	−0.996238	−	0.0866626i	$-0.972380\pi$
$691$	−37.3091	+	21.5404i	−1.41930	+	0.819436i	−0.423067	+	0.906098i	$0.639046\pi$
$692$	−1.82086	−	45.1248i	−0.0692186	−	1.71539i
$693$	−29.4190	+	3.76552i	−1.11754	+	0.143040i
$694$	13.6632	−	5.98504i	0.518648	−	0.227189i
$695$		0			0
$696$	−8.33748	+	7.23900i	−0.316031	+	0.274394i
$697$	−1.80351	−	6.73079i	−0.0683128	−	0.254947i
$698$	1.68656	+	11.0795i	0.0638374	+	0.419364i
$699$	−17.1102			−0.647166
$700$		0			0
$701$	−13.3256			−0.503300			−0.251650	−	0.967818i	$-0.580973\pi$
$701$	−13.3256			−0.503300			−0.251650	+	0.967818i	$0.580973\pi$
$702$	−0.330593	−	2.17175i	−0.0124774	−	0.0819673i
$703$	1.91053	+	7.13021i	0.0720572	+	0.268921i
$704$	−36.1452	+	14.5539i	−1.36227	+	0.548519i
$705$		0			0
$706$	−11.6161	+	5.08830i	−0.437176	+	0.191501i
$707$	−1.49001	+	3.56094i	−0.0560378	+	0.133923i
$708$	1.41430	−	0.0570692i	0.0531525	−	0.00214479i
$709$	3.81245	−	2.20112i	0.143180	−	0.0826648i	−0.426699	−	0.904394i	$-0.640324\pi$
$709$	3.81245	−	2.20112i	0.143180	−	0.0826648i	0.569879	+	0.821729i	$0.306990\pi$
$710$		0			0
$711$	−17.7285	−	10.2356i	−0.664871	−	0.383863i
$712$	−15.1130	+	22.3774i	−0.566385	+	0.838629i
$713$	−30.9949	−	30.9949i	−1.16077	−	1.16077i
$714$	−13.1348	+	13.5774i	−0.491558	+	0.508123i
$715$		0			0
$716$	4.09809	−	18.2006i	0.153153	−	0.680187i
$717$	5.53374	+	20.6522i	0.206661	+	0.771271i
$718$	20.5138	+	25.6464i	0.765570	+	0.957114i
$719$	0.144472	+	0.250232i	0.00538788	+	0.00933208i	0.868707	−	0.495327i	$-0.164952\pi$
$719$	0.144472	+	0.250232i	0.00538788	+	0.00933208i	−0.863319	+	0.504659i	$0.831618\pi$
$720$		0			0
$721$	1.44677	+	0.195767i	0.0538807	+	0.00729073i
$722$	5.21766	−	13.3519i	0.194181	−	0.496905i
$723$	−12.9363	−	3.46626i	−0.481105	−	0.128912i
$724$	26.3286	−	8.20584i	0.978493	−	0.304968i
$725$		0			0
$726$	−8.91193	+	12.1123i	−0.330753	+	0.449531i
$727$	4.87969	+	4.87969i	0.180978	+	0.180978i	0.791782	−	0.610804i	$-0.209154\pi$
$727$	4.87969	+	4.87969i	0.180978	+	0.180978i	−0.610804	+	0.791782i	$0.709154\pi$
$728$	−2.56869	−	0.533818i	−0.0952019	−	0.0197846i
$729$			3.73943i			0.138497i
$730$		0			0
$731$	−23.9143	−	13.8069i	−0.884502	−	0.510667i
$732$	7.83792	−	14.9358i	0.289698	−	0.552044i
$733$	5.87292	−	21.9180i	0.216921	−	0.809561i	−0.768560	−	0.639777i	$-0.779027\pi$
$733$	5.87292	−	21.9180i	0.216921	−	0.809561i	0.985481	−	0.169783i	$-0.0543068\pi$
$734$	40.4105	−	17.7014i	1.49158	−	0.653371i
$735$		0			0
$736$	−32.8409	+	17.6659i	−1.21053	+	0.651173i
$737$	13.1232	+	3.51635i	0.483399	+	0.129526i
$738$	−2.93183	+	2.34509i	−0.107922	+	0.0863241i
$739$	2.90840	−	5.03750i	0.106987	−	0.185307i	−0.807561	−	0.589784i	$-0.799213\pi$
$739$	2.90840	−	5.03750i	0.106987	−	0.185307i	0.914548	+	0.404477i	$0.132546\pi$
$740$		0			0
$741$	−0.872306			−0.0320449
$742$	1.02664	−	0.615634i	0.0376892	−	0.0226006i
$743$	−5.70591	+	5.70591i	−0.209329	+	0.209329i	−0.803982	−	0.594653i	$-0.797289\pi$
$743$	−5.70591	+	5.70591i	−0.209329	+	0.209329i	0.594653	+	0.803982i	$0.297289\pi$
$744$	2.98995	+	15.4307i	0.109617	+	0.565717i
$745$		0			0
$746$	2.91208	−	26.1902i	0.106619	−	0.958890i
$747$	−9.13556	+	34.0944i	−0.334253	+	1.24745i
$748$	−2.37274	−	58.8015i	−0.0867558	−	2.15000i
$749$	1.76423	−	13.0382i	0.0644636	−	0.476405i
$750$		0			0
$751$	36.3916	−	21.0107i	1.32795	−	0.766690i	0.342965	−	0.939348i	$-0.388569\pi$
$751$	36.3916	−	21.0107i	1.32795	−	0.766690i	0.984982	+	0.172658i	$0.0552355\pi$
$752$	6.59761	+	18.5063i	0.240590	+	0.674856i
$753$	−23.3655	+	6.26077i	−0.851486	+	0.228155i
$754$	1.37254	−	1.86544i	0.0499850	−	0.0679353i
$755$		0			0
$756$	21.9752	+	8.17044i	0.799229	+	0.297156i
$757$	36.1581	−	36.1581i	1.31419	−	1.31419i	0.395891	−	0.918298i	$-0.370436\pi$
$757$	36.1581	−	36.1581i	1.31419	−	1.31419i	0.918298	−	0.395891i	$-0.129564\pi$
$758$	26.0256	−	3.96173i	0.945292	−	0.143896i
$759$	−13.4169	+	23.2387i	−0.487002	+	0.843512i
$760$		0			0
$761$	−0.178655	−	0.309439i	−0.00647623	−	0.0112172i	0.862769	−	0.505598i	$-0.168728\pi$
$761$	−0.178655	−	0.309439i	−0.00647623	−	0.0112172i	−0.869245	+	0.494381i	$0.835395\pi$
$762$	−3.32816	+	8.51669i	−0.120567	+	0.308527i
$763$	−27.3458	−	11.4424i	−0.989985	−	0.414242i
$764$	−0.234599	+	0.254328i	−0.00848748	+	0.00920125i
$765$		0			0
$766$	43.8562	+	4.87636i	1.58459	+	0.176190i
$767$	−0.286774	+	0.0768408i	−0.0103548	+	0.00277456i
$768$	13.3043	+	1.34133i	0.480076	+	0.0484012i
$769$		−	23.4758i		−	0.846559i	−0.905999	−	0.423279i	$-0.860879\pi$
$769$		−	23.4758i		−	0.846559i	0.905999	−	0.423279i	$-0.139121\pi$
$770$		0			0
$771$		−	17.2205i		−	0.620183i
$772$	−15.9097	+	10.0619i	−0.572604	+	0.362135i
$773$	−24.5409	+	6.57570i	−0.882673	+	0.236512i	−0.671560	−	0.740950i	$-0.734376\pi$
$773$	−24.5409	+	6.57570i	−0.882673	+	0.236512i	−0.211113	+	0.977462i	$0.567709\pi$
$774$	−1.64412	+	14.7867i	−0.0590968	+	0.531496i
$775$		0			0
$776$	3.07731	−	8.92000i	0.110469	−	0.320209i
$777$	−0.696047	−	5.43804i	−0.0249705	−	0.195089i
$778$	4.89461	+	1.91272i	0.175480	+	0.0685745i
$779$	1.71700	+	2.97394i	0.0615181	+	0.106552i
$780$		0			0
$781$	15.8275	−	27.4140i	0.566351	−	0.980949i
$782$	−8.47572	−	55.6792i	−0.303091	−	1.99108i
$783$	−14.6344	+	14.6344i	−0.522990	+	0.522990i
$784$	18.2923	−	21.1989i	0.653297	−	0.757102i
$785$		0			0
$786$	5.41943	+	3.98747i	0.193305	+	0.142228i
$787$	−2.45466	+	0.657725i	−0.0874993	+	0.0234454i	−0.302303	−	0.953212i	$-0.597755\pi$
$787$	−2.45466	+	0.657725i	−0.0874993	+	0.0234454i	0.214804	+	0.976657i	$0.431089\pi$
$788$	14.0192	−	26.7148i	0.499413	−	0.951675i
$789$	9.14236	−	5.27834i	0.325477	−	0.187914i
$790$		0			0
$791$	−17.4285	−	13.4732i	−0.619685	−	0.479051i
$792$	−28.5062	+	13.8825i	−1.01292	+	0.493293i
$793$	−0.915690	+	3.41740i	−0.0325171	+	0.121356i
$794$	−6.24908	−	0.694833i	−0.221771	−	0.0246587i
$795$		0			0
$796$	−7.53898	+	33.4823i	−0.267212	+	1.18675i
$797$	−31.6762	+	31.6762i	−1.12203	+	1.12203i	−0.130593	+	0.991436i	$0.541688\pi$
$797$	−31.6762	+	31.6762i	−1.12203	+	1.12203i	−0.991436	+	0.130593i	$0.958312\pi$
$798$	4.52061	−	8.13842i	0.160028	−	0.288097i
$799$	−29.6732			−1.04976
$800$		0			0
$801$	−10.9864	+	19.0290i	−0.388185	+	0.672357i
$802$	−30.9996	−	38.7557i	−1.09463	−	1.36851i
$803$	5.83510	+	1.56351i	0.205916	+	0.0551751i
$804$	−3.42702	−	3.16118i	−0.120862	−	0.111486i
$805$		0			0
$806$	−1.32278	−	3.01978i	−0.0465931	−	0.106367i
$807$	−2.42248	+	9.04083i	−0.0852754	+	0.318252i
$808$	−0.290296	+	4.11641i	−0.0102126	+	0.144815i
$809$	−40.9623	−	23.6496i	−1.44016	−	0.831475i	−0.442298	−	0.896868i	$-0.645837\pi$
$809$	−40.9623	−	23.6496i	−1.44016	−	0.831475i	−0.997860	+	0.0653930i	$0.979170\pi$
$810$		0			0
$811$			5.30651i			0.186337i	0.995650	+	0.0931683i	$0.0296995\pi$
$811$			5.30651i			0.186337i	−0.995650	+	0.0931683i	$0.970301\pi$
$812$	10.2911	+	22.4729i	0.361148	+	0.788644i
$813$	14.0864	+	14.0864i	0.494033	+	0.494033i
$814$	13.7564	+	10.1216i	0.482162	+	0.354762i
$815$		0			0
$816$	−8.65566	+	18.2464i	−0.303009	+	0.638752i
$817$	13.1447	+	3.52210i	0.459874	+	0.123223i
$818$	48.5233	+	18.9620i	1.69658	+	0.662991i
$819$	−2.11558	−	0.286264i	−0.0739242	−	0.0100029i
$820$		0			0
$821$	3.34048	+	5.78588i	0.116584	+	0.201929i	0.918412	−	0.395626i	$-0.129472\pi$
$821$	3.34048	+	5.78588i	0.116584	+	0.201929i	−0.801828	+	0.597555i	$0.796139\pi$
$822$	0.458179	−	0.366485i	0.0159808	−	0.0127826i
$823$	−7.95140	−	29.6750i	−0.277168	−	1.03441i	−0.954374	−	0.298613i	$-0.903476\pi$
$823$	−7.95140	−	29.6750i	−0.277168	−	1.03441i	0.677206	−	0.735794i	$-0.263191\pi$
$824$	1.53226	−	0.296900i	0.0533789	−	0.0103430i
$825$		0			0
$826$	0.769261	−	3.07375i	0.0267660	−	0.106950i
$827$	34.0292	+	34.0292i	1.18331	+	1.18331i	0.978882	+	0.204428i	$0.0655334\pi$
$827$	34.0292	+	34.0292i	1.18331	+	1.18331i	0.204428	+	0.978882i	$0.434467\pi$
$828$	−25.6459	+	16.2194i	−0.891258	+	0.563663i
$829$	−3.90921	−	2.25698i	−0.135773	−	0.0783883i	0.430575	−	0.902555i	$-0.358311\pi$
$829$	−3.90921	−	2.25698i	−0.135773	−	0.0783883i	−0.566348	+	0.824166i	$0.691644\pi$
$830$		0			0
$831$	−3.97770	+	2.29653i	−0.137985	+	0.0796657i
$832$	−2.78421	+	0.338513i	−0.0965252	+	0.0117358i
$833$	20.8803	+	36.7740i	0.723460	+	1.27414i
$834$	−3.02252	−	6.90010i	−0.104661	−	0.238931i
$835$		0			0
$836$	8.62950	+	27.6879i	0.298458	+	0.957606i
$837$	7.62506	+	28.4571i	0.263561	+	0.983622i
$838$	−44.4640	+	6.76851i	−1.53598	+	0.233814i
$839$	28.1768			0.972772			0.486386	−	0.873744i	$-0.338315\pi$
$839$	28.1768			0.972772			0.486386	+	0.873744i	$0.338315\pi$
$840$		0			0
$841$	7.18076			0.247612
$842$	18.3422	−	2.79213i	0.632115	−	0.0962232i
$843$	6.44276	+	24.0447i	0.221900	+	0.828144i
$844$	−1.47221	−	4.72360i	−0.0506755	−	0.162593i
$845$		0			0
$846$	6.41468	+	14.6440i	0.220541	+	0.503472i
$847$	20.3963	+	26.7799i	0.700826	+	0.920167i
$848$	0.829055	−	0.974876i	0.0284699	−	0.0334774i
$849$	15.6876	−	9.05723i	0.538396	−	0.310843i
$850$		0			0
$851$	14.1551	+	8.17246i	0.485231	+	0.280148i
$852$	−9.18102	+	5.80640i	−0.314536	+	0.198924i
$853$	−7.11404	−	7.11404i	−0.243580	−	0.243580i	0.574749	−	0.818329i	$-0.305100\pi$
$853$	−7.11404	−	7.11404i	−0.243580	−	0.243580i	−0.818329	+	0.574749i	$0.805100\pi$
$854$	−27.1382	−	26.2534i	−0.928649	−	0.898374i
$855$		0			0
$856$	−2.67564	−	13.8086i	−0.0914515	−	0.471968i
$857$	−5.74773	−	21.4508i	−0.196339	−	0.732746i	−0.991916	−	0.126894i	$-0.959499\pi$
$857$	−5.74773	−	21.4508i	−0.196339	−	0.732746i	0.795578	−	0.605852i	$-0.207168\pi$
$858$	−1.57606	+	1.26065i	−0.0538058	+	0.0430378i
$859$	−9.63913	−	16.6955i	−0.328883	−	0.569642i	0.653408	−	0.757006i	$-0.273339\pi$
$859$	−9.63913	−	16.6955i	−0.328883	−	0.569642i	−0.982290	+	0.187364i	$0.940005\pi$
$860$		0			0
$861$	−0.967529	−	2.35979i	−0.0329733	−	0.0804213i
$862$	−25.9190	−	10.1287i	−0.882804	−	0.344983i
$863$	16.0091	+	4.28964i	0.544958	+	0.146021i	0.520787	−	0.853687i	$-0.325639\pi$
$863$	16.0091	+	4.28964i	0.544958	+	0.146021i	0.0241711	+	0.999708i	$0.492305\pi$
$864$	25.0523	+	0.753684i	0.852298	+	0.0256409i
$865$		0			0
$866$	20.3296	+	14.9580i	0.690827	+	0.508292i
$867$	−11.5214	−	11.5214i	−0.391286	−	0.391286i
$868$	35.0290	+	3.30832i	1.18896	+	0.112292i
$869$			43.3219i			1.46960i
$870$		0			0
$871$	0.846911	+	0.488964i	0.0286965	+	0.0165679i
$872$	−31.6115	−	2.22929i	−1.07050	−	0.0754933i
$873$	1.98726	−	7.41657i	0.0672587	−	0.251013i
$874$	11.1364	+	25.4232i	0.376694	+	0.859952i
$875$		0			0
$876$	−1.52379	−	1.40559i	−0.0514842	−	0.0474904i
$877$	−37.4032	−	10.0222i	−1.26302	−	0.338424i	−0.435665	−	0.900109i	$-0.643487\pi$
$877$	−37.4032	−	10.0222i	−1.26302	−	0.338424i	−0.827351	+	0.561685i	$0.810153\pi$
$878$	4.14790	+	5.18571i	0.139985	+	0.175009i
$879$	−1.68525	+	2.91893i	−0.0568419	+	0.0984531i
$880$		0			0
$881$	34.3504			1.15729			0.578647	−	0.815578i	$-0.303581\pi$
$881$	34.3504			1.15729			0.578647	+	0.815578i	$0.303581\pi$
$882$	13.6345	−	18.2543i	0.459097	−	0.614656i
$883$	−34.1114	+	34.1114i	−1.14794	+	1.14794i	−0.160984	+	0.986957i	$0.551467\pi$
$883$	−34.1114	+	34.1114i	−1.14794	+	1.14794i	−0.986957	+	0.160984i	$0.948533\pi$
$884$	0.930489	−	4.13251i	0.0312957	−	0.138991i
$885$		0			0
$886$	5.84868	+	0.650313i	0.196490	+	0.0218477i
$887$	10.8317	−	40.4245i	0.363693	−	1.35732i	−0.505490	−	0.862832i	$-0.668688\pi$
$887$	10.8317	−	40.4245i	0.363693	−	1.35732i	0.869184	−	0.494490i	$-0.164645\pi$
$888$	−2.56615	−	5.26929i	−0.0861142	−	0.176826i
$889$	16.1943	+	12.5191i	0.543139	+	0.419877i
$890$		0			0
$891$	−13.5056	+	7.79744i	−0.452454	+	0.261224i
$892$	9.27425	−	17.6729i	0.310525	−	0.591732i
$893$	14.1250	−	3.78478i	0.472674	−	0.126653i
$894$	5.55737	+	4.08897i	0.185866	+	0.136755i
$895$		0			0
$896$	11.2706	−	27.7304i	0.376523	−	0.926407i
$897$	−1.36577	+	1.36577i	−0.0456018	+	0.0456018i
$898$	−8.80118	−	57.8172i	−0.293699	−	1.92938i
$899$	−15.5298	+	26.8985i	−0.517949	+	0.897114i
$900$		0			0
$901$	0.966393	+	1.67384i	0.0321952	+	0.0557637i
$902$	7.40015	+	2.89184i	0.246398	+	0.0962877i
$903$	−9.32359	−	3.90130i	−0.310270	−	0.129827i
$904$	−22.2624	−	7.68031i	−0.740437	−	0.255443i
$905$		0			0
$906$	−0.484014	+	4.35305i	−0.0160803	+	0.144620i
$907$	27.8397	−	7.45963i	0.924403	−	0.247693i	0.234936	−	0.972011i	$-0.424512\pi$
$907$	27.8397	−	7.45963i	0.924403	−	0.247693i	0.689466	+	0.724318i	$0.257845\pi$
$908$	−34.4354	+	21.7782i	−1.14278	+	0.722734i
$909$			3.35793i			0.111375i
$910$		0			0
$911$		−	19.1234i		−	0.633586i	−0.948495	−	0.316793i	$-0.897394\pi$
$911$		−	19.1234i		−	0.633586i	0.948495	−	0.316793i	$-0.102606\pi$
$912$	1.79294	−	9.78962i	0.0593703	−	0.324167i
$913$	72.1521	−	19.3331i	2.38789	−	0.639832i
$914$	32.5806	+	3.62262i	1.07767	+	0.119826i
$915$		0			0
$916$	12.9461	−	14.0348i	0.427751	−	0.463723i
$917$	11.9821	−	9.12594i	0.395684	−	0.301365i
$918$	−13.7779	+	35.2573i	−0.454738	+	1.16366i
$919$	−13.6744	−	23.6848i	−0.451077	−	0.781289i	0.547376	−	0.836887i	$-0.315627\pi$
$919$	−13.6744	−	23.6848i	−0.451077	−	0.781289i	−0.998453	+	0.0555980i	$0.982293\pi$
$920$		0			0
$921$	2.11703	−	3.66680i	0.0697585	−	0.120825i
$922$	23.6464	−	3.59955i	0.778752	−	0.118545i
$923$	1.61116	−	1.61116i	0.0530319	−	0.0530319i
$924$	−3.59383	−	21.2374i	−0.118228	−	0.698660i
$925$		0			0
$926$	−26.4960	+	36.0111i	−0.870713	+	1.18340i
$927$	1.22675	−	0.328707i	0.0402918	−	0.0107962i
$928$	18.1141	+	19.2378i	0.594625	+	0.631513i
$929$	−12.9501	+	7.47676i	−0.424880	+	0.245305i	−0.697163	−	0.716913i	$-0.745555\pi$
$929$	−12.9501	+	7.47676i	−0.424880	+	0.245305i	0.272283	+	0.962217i	$0.412221\pi$
$930$		0			0
$931$	−14.6299	−	14.8418i	−0.479475	−	0.486421i
$932$	1.65092	+	40.9133i	0.0540776	+	1.34016i
$933$	5.32182	−	19.8613i	0.174229	−	0.650230i
$934$	−1.34104	+	12.0609i	−0.0438803	+	0.394644i
$935$		0			0
$936$	−2.24058	+	0.434149i	−0.0732358	+	0.0141906i
$937$	−22.4138	+	22.4138i	−0.732226	+	0.732226i	−0.971060	−	0.238835i	$-0.923235\pi$
$937$	−22.4138	+	22.4138i	−0.732226	+	0.732226i	0.238835	+	0.971060i	$0.423235\pi$
$938$	−8.95094	+	5.36750i	−0.292259	+	0.175255i
$939$	5.61967			0.183391
$940$		0			0
$941$	12.6079	−	21.8376i	0.411007	−	0.711884i	−0.583994	−	0.811758i	$-0.698511\pi$
$941$	12.6079	−	21.8376i	0.411007	−	0.711884i	0.995000	+	0.0998741i	$0.0318440\pi$
$942$	−10.1903	+	8.15094i	−0.332018	+	0.265572i
$943$	7.34462	+	1.96799i	0.239174	+	0.0640864i
$944$	−0.272924	−	3.37631i	−0.00888292	−	0.109890i
$945$		0			0
$946$	28.8395	−	12.6329i	0.937655	−	0.410731i
$947$	5.60688	−	20.9252i	0.182199	−	0.679976i	−0.813014	−	0.582245i	$-0.802175\pi$
$947$	5.60688	−	20.9252i	0.182199	−	0.679976i	0.995213	−	0.0977318i	$-0.0311587\pi$
$948$	6.90824	−	13.1642i	0.224369	−	0.427555i
$949$	0.376571	+	0.217413i	0.0122240	+	0.00705754i
$950$		0			0
$951$			11.5490i			0.374503i
$952$	33.7333	+	30.0975i	1.09330	+	0.975465i
$953$	−22.8157	−	22.8157i	−0.739074	−	0.739074i	0.233325	−	0.972399i	$-0.425040\pi$
$953$	−22.8157	−	22.8157i	−0.739074	−	0.739074i	−0.972399	+	0.233325i	$0.925040\pi$
$954$	0.617145	−	0.838770i	0.0199808	−	0.0271562i
$955$		0			0
$956$	48.8490	−	15.2248i	1.57989	−	0.492405i
$957$	18.3661	+	4.92119i	0.593692	+	0.159079i
$958$	12.4529	−	31.8667i	0.402336	−	1.02957i
$959$	−0.498251	−	1.21523i	−0.0160894	−	0.0392417i
$960$		0			0
$961$	6.60673	+	11.4432i	0.213120	+	0.369135i
$962$	0.767883	+	0.960006i	0.0247575	+	0.0309518i
$963$	−2.96228	−	11.0554i	−0.0954580	−	0.356254i
$964$	−7.04022	+	31.2672i	−0.226750	+	1.00705i
$965$		0			0
$966$	−5.66441	−	19.8203i	−0.182250	−	0.637707i
$967$	11.0053	+	11.0053i	0.353908	+	0.353908i	0.861561	−	0.507654i	$-0.169487\pi$
$967$	11.0053	+	11.0053i	0.353908	+	0.353908i	−0.507654	+	0.861561i	$0.669487\pi$
$968$	29.8225	+	20.1412i	0.958532	+	0.647364i
$969$	13.0174	+	7.51561i	0.418180	+	0.241436i
$970$		0			0
$971$	15.7328	−	9.08331i	0.504888	−	0.291497i	−0.225842	−	0.974164i	$-0.572513\pi$
$971$	15.7328	−	9.08331i	0.504888	−	0.291497i	0.730730	+	0.682667i	$0.239180\pi$
$972$	31.9098	−	1.28761i	1.02351	−	0.0413002i
$973$	−16.7267	+	2.14095i	−0.536234	+	0.0686357i
$974$	24.0094	−	10.5171i	0.769310	−	0.336989i
$975$		0			0
$976$	−36.4703	−	17.3007i	−1.16739	−	0.553781i
$977$	−0.196456	−	0.733186i	−0.00628520	−	0.0234567i	0.962712	−	0.270528i	$-0.0871984\pi$
$977$	−0.196456	−	0.733186i	−0.00628520	−	0.0234567i	−0.968997	+	0.247072i	$0.920532\pi$
$978$	−0.128807	−	0.846165i	−0.00411879	−	0.0270574i
$979$	46.4999			1.48614
$980$		0			0
$981$	−25.7868			−0.823310
$982$	5.60383	+	36.8130i	0.178826	+	1.17475i
$983$	−8.71176	−	32.5127i	−0.277862	−	1.03699i	−0.953899	−	0.300127i	$-0.902971\pi$
$983$	−8.71176	−	32.5127i	−0.277862	−	1.03699i	0.676037	−	0.736867i	$-0.263696\pi$
$984$	−1.78754	−	2.05879i	−0.0569848	−	0.0656320i
$985$		0			0
$986$	−36.5547	+	16.0124i	−1.16414	+	0.509940i
$987$	−10.7728	+	1.37887i	−0.342901	+	0.0438900i
$988$	0.0841666	+	2.08583i	0.00267770	+	0.0663591i
$989$	26.0952	−	15.0661i	0.829779	−	0.479073i
$990$		0			0
$991$	25.1531	+	14.5222i	0.799016	+	0.461312i	0.843127	−	0.537715i	$-0.180712\pi$
$991$	25.1531	+	14.5222i	0.799016	+	0.461312i	−0.0441111	+	0.999027i	$0.514046\pi$
$992$	36.6089	−	8.63833i	1.16233	−	0.274267i
$993$	−1.10577	−	1.10577i	−0.0350906	−	0.0350906i
$994$	6.68213	+	23.3814i	0.211944	+	0.741612i
$995$		0			0
$996$	−25.0078	−	5.63083i	−0.792402	−	0.178420i
$997$	12.3061	+	45.9271i	0.389739	+	1.45453i	0.830559	+	0.556931i	$0.188021\pi$
$997$	12.3061	+	45.9271i	0.389739	+	1.45453i	−0.440820	+	0.897596i	$0.645312\pi$
$998$	−9.56361	−	11.9564i	−0.302731	−	0.378473i
$999$	−5.49282	−	9.51384i	−0.173785	−	0.301004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.543.18		72
4.3	odd	2	inner	700.2.be.e.543.15		72
5.2	odd	4	inner	700.2.be.e.207.10		72
5.3	odd	4		140.2.w.b.67.9	yes	72
5.4	even	2		140.2.w.b.123.1	yes	72
7.2	even	3	inner	700.2.be.e.443.7		72
20.3	even	4		140.2.w.b.67.12	yes	72
20.7	even	4	inner	700.2.be.e.207.7		72
20.19	odd	2		140.2.w.b.123.4	yes	72
28.23	odd	6	inner	700.2.be.e.443.10		72
35.2	odd	12	inner	700.2.be.e.107.15		72
35.3	even	12		980.2.k.j.687.16		36
35.4	even	6		980.2.k.k.883.12		36
35.9	even	6		140.2.w.b.23.12	yes	72
35.13	even	4		980.2.x.m.67.9		72
35.18	odd	12		980.2.k.k.687.16		36
35.19	odd	6		980.2.x.m.863.12		72
35.23	odd	12		140.2.w.b.107.4	yes	72
35.24	odd	6		980.2.k.j.883.12		36
35.33	even	12		980.2.x.m.667.4		72
35.34	odd	2		980.2.x.m.263.1		72
140.3	odd	12		980.2.k.j.687.12		36
140.19	even	6		980.2.x.m.863.9		72
140.23	even	12		140.2.w.b.107.1	yes	72
140.39	odd	6		980.2.k.k.883.16		36
140.59	even	6		980.2.k.j.883.16		36
140.79	odd	6		140.2.w.b.23.9	✓	72
140.83	odd	4		980.2.x.m.67.12		72
140.103	odd	12		980.2.x.m.667.1		72
140.107	even	12	inner	700.2.be.e.107.18		72
140.123	even	12		980.2.k.k.687.12		36
140.139	even	2		980.2.x.m.263.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.9	✓	72	140.79	odd	6
140.2.w.b.23.12	yes	72	35.9	even	6
140.2.w.b.67.9	yes	72	5.3	odd	4
140.2.w.b.67.12	yes	72	20.3	even	4
140.2.w.b.107.1	yes	72	140.23	even	12
140.2.w.b.107.4	yes	72	35.23	odd	12
140.2.w.b.123.1	yes	72	5.4	even	2
140.2.w.b.123.4	yes	72	20.19	odd	2
700.2.be.e.107.15		72	35.2	odd	12	inner
700.2.be.e.107.18		72	140.107	even	12	inner
700.2.be.e.207.7		72	20.7	even	4	inner
700.2.be.e.207.10		72	5.2	odd	4	inner
700.2.be.e.443.7		72	7.2	even	3	inner
700.2.be.e.443.10		72	28.23	odd	6	inner
700.2.be.e.543.15		72	4.3	odd	2	inner
700.2.be.e.543.18		72	1.1	even	1	trivial
980.2.k.j.687.12		36	140.3	odd	12
980.2.k.j.687.16		36	35.3	even	12
980.2.k.j.883.12		36	35.24	odd	6
980.2.k.j.883.16		36	140.59	even	6
980.2.k.k.687.12		36	140.123	even	12
980.2.k.k.687.16		36	35.18	odd	12
980.2.k.k.883.12		36	35.4	even	6
980.2.k.k.883.16		36	140.39	odd	6
980.2.x.m.67.9		72	35.13	even	4
980.2.x.m.67.12		72	140.83	odd	4
980.2.x.m.263.1		72	35.34	odd	2
980.2.x.m.263.4		72	140.139	even	2
980.2.x.m.667.1		72	140.103	odd	12
980.2.x.m.667.4		72	35.33	even	12
980.2.x.m.863.9		72	140.19	even	6
980.2.x.m.863.12		72	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39811 - 0.212826i) q^{2} +(0.216303 + 0.807254i) q^{3} +(1.90941 - 0.595107i) q^{4} +(0.474220 + 1.08259i) q^{6} +(2.62434 - 0.335905i) q^{7} +(2.54291 - 1.23840i) q^{8} +(1.99320 - 1.15078i) q^{9} +O(q^{10})\)	\(q+(1.39811 - 0.212826i) q^{2} +(0.216303 + 0.807254i) q^{3} +(1.90941 - 0.595107i) q^{4} +(0.474220 + 1.08259i) q^{6} +(2.62434 - 0.335905i) q^{7} +(2.54291 - 1.23840i) q^{8} +(1.99320 - 1.15078i) q^{9} +(-4.21811 - 2.43533i) q^{11} +(0.893414 + 1.41266i) q^{12} +(-0.247904 - 0.247904i) q^{13} +(3.59762 - 1.02816i) q^{14} +(3.29169 - 2.27261i) q^{16} +(1.56358 + 5.83537i) q^{17} +(2.54180 - 2.03311i) q^{18} +(-1.48858 - 2.57830i) q^{19} +(0.838814 + 2.04585i) q^{21} +(-6.41567 - 2.50713i) q^{22} +(-6.36754 - 1.70618i) q^{23} +(1.54974 + 1.78490i) q^{24} +(-0.399357 - 0.293836i) q^{26} +(3.13296 + 3.13296i) q^{27} +(4.81104 - 2.20315i) q^{28} +4.67111i q^{29} +(5.75848 + 3.32466i) q^{31} +(4.11847 - 3.87791i) q^{32} +(1.05354 - 3.93186i) q^{33} +(3.42797 + 7.82570i) q^{34} +(3.12101 - 3.38347i) q^{36} +(-2.39496 - 0.641729i) q^{37} +(-2.62993 - 3.28794i) q^{38} +(0.146499 - 0.253744i) q^{39} -1.15345 q^{41} +(1.60816 + 2.68180i) q^{42} +(-3.23212 + 3.23212i) q^{43} +(-9.50338 - 2.13981i) q^{44} +(-9.26562 - 1.03024i) q^{46} +(-1.27127 + 4.74443i) q^{47} +(2.54658 + 2.16566i) q^{48} +(6.77434 - 1.76306i) q^{49} +(-4.37242 + 2.52442i) q^{51} +(-0.620880 - 0.325821i) q^{52} +(0.309032 - 0.0828048i) q^{53} +(5.04699 + 3.71344i) q^{54} +(6.25747 - 4.10415i) q^{56} +(1.75936 - 1.75936i) q^{57} +(0.994133 + 6.53071i) q^{58} +(0.423416 - 0.733378i) q^{59} +(-5.04573 - 8.73945i) q^{61} +(8.75855 + 3.42268i) q^{62} +(4.84429 - 3.68956i) q^{63} +(4.93275 - 6.29825i) q^{64} +(0.636158 - 5.72138i) q^{66} +(-2.69434 + 0.721946i) q^{67} +(6.45819 + 10.2116i) q^{68} -5.50928i q^{69} +6.49911i q^{71} +(3.64341 - 5.39469i) q^{72} +(-1.19801 + 0.321006i) q^{73} +(-3.48499 - 0.387495i) q^{74} +(-4.37668 - 4.03717i) q^{76} +(-11.8878 - 4.97424i) q^{77} +(0.150818 - 0.385940i) q^{78} +(-4.44724 - 7.70284i) q^{79} +(1.60090 - 2.77285i) q^{81} +(-1.61264 + 0.245484i) q^{82} +(-10.8443 + 10.8443i) q^{83} +(2.81914 + 3.40719i) q^{84} +(-3.83097 + 5.20673i) q^{86} +(-3.77077 + 1.01038i) q^{87} +(-13.7422 - 0.969119i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-0.733857 - 0.567313i) q^{91} +(-13.1736 + 0.531576i) q^{92} +(-1.43827 + 5.36769i) q^{93} +(-0.767630 + 6.90379i) q^{94} +(4.02130 + 2.48585i) q^{96} +(2.35897 - 2.35897i) q^{97} +(9.09603 - 3.90670i) q^{98} -11.2101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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