LMFDB - Embedded newform 429.2.m.a.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Character	$\chi$	$=$	429.307
Dual form			429.2.m.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06339 + 1.06339i) q^{2} -1.00000 q^{3} -0.261597i q^{4} +(0.340859 + 0.340859i) q^{5} +(1.06339 - 1.06339i) q^{6} +(-0.593196 - 0.593196i) q^{7} +(-1.84860 - 1.84860i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.06339 + 1.06339i) q^{2} -1.00000 q^{3} -0.261597i q^{4} +(0.340859 + 0.340859i) q^{5} +(1.06339 - 1.06339i) q^{6} +(-0.593196 - 0.593196i) q^{7} +(-1.84860 - 1.84860i) q^{8} +1.00000 q^{9} -0.724932 q^{10} +(-1.96021 - 2.67537i) q^{11} +0.261597i q^{12} +(2.47736 - 2.61967i) q^{13} +1.26160 q^{14} +(-0.340859 - 0.340859i) q^{15} +4.45476 q^{16} -0.904472 q^{17} +(-1.06339 + 1.06339i) q^{18} +(-2.48574 + 2.48574i) q^{19} +(0.0891677 - 0.0891677i) q^{20} +(0.593196 + 0.593196i) q^{21} +(4.92942 + 0.760497i) q^{22} -4.23536i q^{23} +(1.84860 + 1.84860i) q^{24} -4.76763i q^{25} +(0.151333 + 5.42013i) q^{26} -1.00000 q^{27} +(-0.155178 + 0.155178i) q^{28} -3.83750i q^{29} +0.724932 q^{30} +(5.60966 + 5.60966i) q^{31} +(-1.03995 + 1.03995i) q^{32} +(1.96021 + 2.67537i) q^{33} +(0.961806 - 0.961806i) q^{34} -0.404392i q^{35} -0.261597i q^{36} +(5.73990 - 5.73990i) q^{37} -5.28663i q^{38} +(-2.47736 + 2.61967i) q^{39} -1.26022i q^{40} +(2.91199 - 2.91199i) q^{41} -1.26160 q^{42} +11.0774 q^{43} +(-0.699868 + 0.512784i) q^{44} +(0.340859 + 0.340859i) q^{45} +(4.50384 + 4.50384i) q^{46} +(-5.97825 + 5.97825i) q^{47} -4.45476 q^{48} -6.29624i q^{49} +(5.06985 + 5.06985i) q^{50} +0.904472 q^{51} +(-0.685299 - 0.648070i) q^{52} +3.19429 q^{53} +(1.06339 - 1.06339i) q^{54} +(0.243769 - 1.58008i) q^{55} +2.19316i q^{56} +(2.48574 - 2.48574i) q^{57} +(4.08076 + 4.08076i) q^{58} +(-5.71636 + 5.71636i) q^{59} +(-0.0891677 + 0.0891677i) q^{60} +3.56455i q^{61} -11.9305 q^{62} +(-0.593196 - 0.593196i) q^{63} +6.69778i q^{64} +(1.73737 - 0.0485081i) q^{65} +(-4.92942 - 0.760497i) q^{66} +(-10.0412 - 10.0412i) q^{67} +0.236607i q^{68} +4.23536i q^{69} +(0.430027 + 0.430027i) q^{70} +(-10.7137 - 10.7137i) q^{71} +(-1.84860 - 1.84860i) q^{72} +(-10.3258 - 10.3258i) q^{73} +12.2075i q^{74} +4.76763i q^{75} +(0.650263 + 0.650263i) q^{76} +(-0.424231 + 2.74980i) q^{77} +(-0.151333 - 5.42013i) q^{78} +7.59368i q^{79} +(1.51845 + 1.51845i) q^{80} +1.00000 q^{81} +6.19316i q^{82} +(5.02820 - 5.02820i) q^{83} +(0.155178 - 0.155178i) q^{84} +(-0.308297 - 0.308297i) q^{85} +(-11.7796 + 11.7796i) q^{86} +3.83750i q^{87} +(-1.32205 + 8.56932i) q^{88} +(3.53432 - 3.53432i) q^{89} -0.724932 q^{90} +(-3.02354 + 0.0844186i) q^{91} -1.10796 q^{92} +(-5.60966 - 5.60966i) q^{93} -12.7144i q^{94} -1.69458 q^{95} +(1.03995 - 1.03995i) q^{96} +(0.0569832 + 0.0569832i) q^{97} +(6.69536 + 6.69536i) q^{98} +(-1.96021 - 2.67537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.06339	+	1.06339i	−0.751930	+	0.751930i	−0.974839	−	0.222909i	$-0.928445\pi$
$2$	−1.06339	+	1.06339i	−0.751930	+	0.751930i	0.222909	+	0.974839i	$0.428445\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	0.261597i		−	0.130799i
$5$	0.340859	+	0.340859i	0.152437	+	0.152437i	0.779205	−	0.626769i	$-0.215623\pi$
$5$	0.340859	+	0.340859i	0.152437	+	0.152437i	−0.626769	+	0.779205i	$0.715623\pi$
$6$	1.06339	−	1.06339i	0.434127	−	0.434127i
$7$	−0.593196	−	0.593196i	−0.224207	−	0.224207i	0.586060	−	0.810267i	$-0.300678\pi$
$7$	−0.593196	−	0.593196i	−0.224207	−	0.224207i	−0.810267	+	0.586060i	$0.800678\pi$
$8$	−1.84860	−	1.84860i	−0.653579	−	0.653579i
$9$	1.00000			0.333333
$10$	−0.724932			−0.229244
$11$	−1.96021	−	2.67537i	−0.591024	−	0.806654i
$11$	−1.96021	−	2.67537i	−0.591024	−	0.806654i
$12$			0.261597i			0.0755166i
$13$	2.47736	−	2.61967i	0.687096	−	0.726566i
$13$	2.47736	−	2.61967i	0.687096	−	0.726566i
$14$	1.26160			0.337176
$15$	−0.340859	−	0.340859i	−0.0880094	−	0.0880094i
$16$	4.45476			1.11369
$17$	−0.904472			−0.219367			−0.109683	−	0.993967i	$-0.534984\pi$
$17$	−0.904472			−0.219367			−0.109683	+	0.993967i	$0.534984\pi$
$18$	−1.06339	+	1.06339i	−0.250643	+	0.250643i
$19$	−2.48574	+	2.48574i	−0.570269	+	0.570269i	−0.932203	−	0.361935i	$-0.882116\pi$
$19$	−2.48574	+	2.48574i	−0.570269	+	0.570269i	0.361935	+	0.932203i	$0.382116\pi$
$20$	0.0891677	−	0.0891677i	0.0199385	−	0.0199385i
$21$	0.593196	+	0.593196i	0.129446	+	0.129446i
$22$	4.92942	+	0.760497i	1.05096	+	0.162138i
$23$		−	4.23536i		−	0.883133i	−0.897228	−	0.441567i	$-0.854423\pi$
$23$		−	4.23536i		−	0.883133i	0.897228	−	0.441567i	$-0.145577\pi$
$24$	1.84860	+	1.84860i	0.377344	+	0.377344i
$25$		−	4.76763i		−	0.953526i
$26$	0.151333	+	5.42013i	0.0296788	+	1.06298i
$27$	−1.00000			−0.192450
$28$	−0.155178	+	0.155178i	−0.0293259	+	0.0293259i
$29$		−	3.83750i		−	0.712605i	−0.934371	−	0.356303i	$-0.884037\pi$
$29$		−	3.83750i		−	0.712605i	0.934371	−	0.356303i	$-0.115963\pi$
$30$	0.724932			0.132354
$31$	5.60966	+	5.60966i	1.00752	+	1.00752i	0.999971	+	0.00755339i	$0.00240434\pi$
$31$	5.60966	+	5.60966i	1.00752	+	1.00752i	0.00755339	+	0.999971i	$0.497596\pi$
$32$	−1.03995	+	1.03995i	−0.183839	+	0.183839i
$33$	1.96021	+	2.67537i	0.341228	+	0.465722i
$34$	0.961806	−	0.961806i	0.164948	−	0.164948i
$35$		−	0.404392i		−	0.0683547i
$36$		−	0.261597i		−	0.0435995i
$37$	5.73990	−	5.73990i	0.943633	−	0.943633i	−0.0548608	−	0.998494i	$-0.517471\pi$
$37$	5.73990	−	5.73990i	0.943633	−	0.943633i	0.998494	+	0.0548608i	$0.0174715\pi$
$38$		−	5.28663i		−	0.857605i
$39$	−2.47736	+	2.61967i	−0.396695	+	0.419483i
$40$		−	1.26022i		−	0.199259i
$41$	2.91199	−	2.91199i	0.454777	−	0.454777i	−0.442160	−	0.896936i	$-0.645788\pi$
$41$	2.91199	−	2.91199i	0.454777	−	0.454777i	0.896936	+	0.442160i	$0.145788\pi$
$42$	−1.26160			−0.194669
$43$	11.0774			1.68929			0.844643	−	0.535330i	$-0.179813\pi$
$43$	11.0774			1.68929			0.844643	+	0.535330i	$0.179813\pi$
$44$	−0.699868	+	0.512784i	−0.105509	+	0.0773051i
$45$	0.340859	+	0.340859i	0.0508122	+	0.0508122i
$46$	4.50384	+	4.50384i	0.664055	+	0.664055i
$47$	−5.97825	+	5.97825i	−0.872018	+	0.872018i	−0.992692	−	0.120674i	$-0.961494\pi$
$47$	−5.97825	+	5.97825i	−0.872018	+	0.872018i	0.120674	+	0.992692i	$0.461494\pi$
$48$	−4.45476			−0.642989
$49$		−	6.29624i		−	0.899462i
$50$	5.06985	+	5.06985i	0.716985	+	0.716985i
$51$	0.904472			0.126651
$52$	−0.685299	−	0.648070i	−0.0950338	−	0.0898712i
$53$	3.19429			0.438769			0.219385	−	0.975638i	$-0.429595\pi$
$53$	3.19429			0.438769			0.219385	+	0.975638i	$0.429595\pi$
$54$	1.06339	−	1.06339i	0.144709	−	0.144709i
$55$	0.243769	−	1.58008i	0.0328699	−	0.213057i
$56$			2.19316i			0.293074i
$57$	2.48574	−	2.48574i	0.329245	−	0.329245i
$58$	4.08076	+	4.08076i	0.535829	+	0.535829i
$59$	−5.71636	+	5.71636i	−0.744206	+	0.744206i	−0.973385	−	0.229178i	$-0.926396\pi$
$59$	−5.71636	+	5.71636i	−0.744206	+	0.744206i	0.229178	+	0.973385i	$0.426396\pi$
$60$	−0.0891677	+	0.0891677i	−0.0115115	+	0.0115115i
$61$			3.56455i			0.456393i	0.973615	+	0.228197i	$0.0732829\pi$
$61$			3.56455i			0.456393i	−0.973615	+	0.228197i	$0.926717\pi$
$62$	−11.9305			−1.51518
$63$	−0.593196	−	0.593196i	−0.0747356	−	0.0747356i
$64$			6.69778i			0.837223i
$65$	1.73737	−	0.0485081i	0.215494	−	0.00601669i
$66$	−4.92942	−	0.760497i	−0.606770	−	0.0936107i
$67$	−10.0412	−	10.0412i	−1.22673	−	1.22673i	−0.965195	−	0.261530i	$-0.915773\pi$
$67$	−10.0412	−	10.0412i	−1.22673	−	1.22673i	−0.261530	−	0.965195i	$-0.584227\pi$
$68$			0.236607i			0.0286928i
$69$			4.23536i			0.509877i
$70$	0.430027	+	0.430027i	0.0513980	+	0.0513980i
$71$	−10.7137	−	10.7137i	−1.27148	−	1.27148i	−0.945313	−	0.326164i	$-0.894244\pi$
$71$	−10.7137	−	10.7137i	−1.27148	−	1.27148i	−0.326164	−	0.945313i	$-0.605756\pi$
$72$	−1.84860	−	1.84860i	−0.217860	−	0.217860i
$73$	−10.3258	−	10.3258i	−1.20854	−	1.20854i	−0.971499	−	0.237045i	$-0.923821\pi$
$73$	−10.3258	−	10.3258i	−1.20854	−	1.20854i	−0.237045	−	0.971499i	$-0.576179\pi$
$74$			12.2075i			1.41909i
$75$			4.76763i			0.550519i
$76$	0.650263	+	0.650263i	0.0745903	+	0.0745903i
$77$	−0.424231	+	2.74980i	−0.0483456	+	0.313369i
$78$	−0.151333	−	5.42013i	−0.0171350	−	0.613709i
$79$			7.59368i			0.854356i	0.904168	+	0.427178i	$0.140492\pi$
$79$			7.59368i			0.854356i	−0.904168	+	0.427178i	$0.859508\pi$
$80$	1.51845	+	1.51845i	0.169767	+	0.169767i
$81$	1.00000			0.111111
$82$			6.19316i			0.683921i
$83$	5.02820	−	5.02820i	0.551916	−	0.551916i	−0.375077	−	0.926994i	$-0.622384\pi$
$83$	5.02820	−	5.02820i	0.551916	−	0.551916i	0.926994	+	0.375077i	$0.122384\pi$
$84$	0.155178	−	0.155178i	0.0169313	−	0.0169313i
$85$	−0.308297	−	0.308297i	−0.0334395	−	0.0334395i
$86$	−11.7796	+	11.7796i	−1.27023	+	1.27023i
$87$			3.83750i			0.411423i
$88$	−1.32205	+	8.56932i	−0.140931	+	0.913493i
$89$	3.53432	−	3.53432i	0.374637	−	0.374637i	−0.494526	−	0.869163i	$-0.664658\pi$
$89$	3.53432	−	3.53432i	0.374637	−	0.374637i	0.869163	+	0.494526i	$0.164658\pi$
$90$	−0.724932			−0.0764145
$91$	−3.02354	+	0.0844186i	−0.316953	+	0.00884947i
$92$	−1.10796			−0.115513
$93$	−5.60966	−	5.60966i	−0.581695	−	0.581695i
$94$		−	12.7144i		−	1.31139i
$95$	−1.69458			−0.173860
$96$	1.03995	−	1.03995i	0.106139	−	0.106139i
$97$	0.0569832	+	0.0569832i	0.00578577	+	0.00578577i	0.709994	−	0.704208i	$-0.248698\pi$
$97$	0.0569832	+	0.0569832i	0.00578577	+	0.00578577i	−0.704208	+	0.709994i	$0.748698\pi$
$98$	6.69536	+	6.69536i	0.676333	+	0.676333i
$99$	−1.96021	−	2.67537i	−0.197008	−	0.268885i
$100$	−1.24720			−0.124720
$101$	4.22512			0.420416			0.210208	−	0.977657i	$-0.432586\pi$
$101$	4.22512			0.420416			0.210208	+	0.977657i	$0.432586\pi$
$102$	−0.961806	+	0.961806i	−0.0952330	+	0.0952330i
$103$		−	15.4692i		−	1.52422i	−0.647446	−	0.762111i	$-0.724163\pi$
$103$		−	15.4692i		−	1.52422i	0.647446	−	0.762111i	$-0.275837\pi$
$104$	−9.42238	+	0.263077i	−0.923940	+	0.0257968i
$105$			0.404392i			0.0394646i
$106$	−3.39678	+	3.39678i	−0.329924	+	0.329924i
$107$		−	1.72944i		−	0.167192i	−0.996500	−	0.0835958i	$-0.973360\pi$
$107$		−	1.72944i		−	0.167192i	0.996500	−	0.0835958i	$-0.0266405\pi$
$108$			0.261597i			0.0251722i
$109$	−10.9131	+	10.9131i	−1.04529	+	1.04529i	−0.0463649	+	0.998925i	$0.514764\pi$
$109$	−10.9131	+	10.9131i	−1.04529	+	1.04529i	−0.998925	+	0.0463649i	$0.985236\pi$
$110$	1.42102	+	1.93946i	0.135489	+	0.184920i
$111$	−5.73990	+	5.73990i	−0.544807	+	0.544807i
$112$	−2.64255	−	2.64255i	−0.249697	−	0.249697i
$113$	−2.42476			−0.228102			−0.114051	−	0.993475i	$-0.536383\pi$
$113$	−2.42476			−0.228102			−0.114051	+	0.993475i	$0.536383\pi$
$114$			5.28663i			0.495138i
$115$	1.44366	−	1.44366i	0.134622	−	0.134622i
$116$	−1.00388			−0.0932077
$117$	2.47736	−	2.61967i	0.229032	−	0.242189i
$118$		−	12.1574i		−	1.11918i
$119$	0.536529	+	0.536529i	0.0491835	+	0.0491835i
$120$			1.26022i			0.115042i
$121$	−3.31519	+	10.4885i	−0.301381	+	0.953504i
$122$	−3.79050	−	3.79050i	−0.343176	−	0.343176i
$123$	−2.91199	+	2.91199i	−0.262565	+	0.262565i
$124$	1.46747	−	1.46747i	0.131783	−	0.131783i
$125$	3.32938	−	3.32938i	0.297789	−	0.297789i
$126$	1.26160			0.112392
$127$	−8.96709			−0.795701			−0.397850	−	0.917450i	$-0.630244\pi$
$127$	−8.96709			−0.795701			−0.397850	+	0.917450i	$0.630244\pi$
$128$	−9.20225	−	9.20225i	−0.813372	−	0.813372i
$129$	−11.0774			−0.975310
$130$	−1.79592	+	1.89908i	−0.157512	+	0.166561i
$131$		−	7.91810i		−	0.691808i	−0.938270	−	0.345904i	$-0.887572\pi$
$131$		−	7.91810i		−	0.691808i	0.938270	−	0.345904i	$-0.112428\pi$
$132$	0.699868	−	0.512784i	0.0609157	−	0.0446321i
$133$	2.94906			0.255716
$134$	21.3554			1.84482
$135$	−0.340859	−	0.340859i	−0.0293365	−	0.0293365i
$136$	1.67201	+	1.67201i	0.143373	+	0.143373i
$137$	8.64502	−	8.64502i	0.738594	−	0.738594i	−0.233712	−	0.972306i	$-0.575087\pi$
$137$	8.64502	−	8.64502i	0.738594	−	0.738594i	0.972306	+	0.233712i	$0.0750873\pi$
$138$	−4.50384	−	4.50384i	−0.383392	−	0.383392i
$139$			4.37603i			0.371170i	0.982628	+	0.185585i	$0.0594180\pi$
$139$			4.37603i			0.371170i	−0.982628	+	0.185585i	$0.940582\pi$
$140$	−0.105788			−0.00894070
$141$	5.97825	−	5.97825i	0.503460	−	0.503460i
$142$	22.7856			1.91212
$143$	−11.8647	−	1.49276i	−0.992178	−	0.124830i
$144$	4.45476			0.371230
$145$	1.30804	−	1.30804i	0.108627	−	0.108627i
$146$	21.9607			1.81748
$147$			6.29624i			0.519305i
$148$	−1.50154	−	1.50154i	−0.123426	−	0.123426i
$149$	−12.7872	+	12.7872i	−1.04757	+	1.04757i	−0.0487563	+	0.998811i	$0.515526\pi$
$149$	−12.7872	+	12.7872i	−1.04757	+	1.04757i	−0.998811	+	0.0487563i	$0.984474\pi$
$150$	−5.06985	−	5.06985i	−0.413952	−	0.413952i
$151$	−0.961423	−	0.961423i	−0.0782395	−	0.0782395i	0.666904	−	0.745144i	$-0.267619\pi$
$151$	−0.961423	−	0.961423i	−0.0782395	−	0.0782395i	−0.745144	+	0.666904i	$0.767619\pi$
$152$	9.19029			0.745431
$153$	−0.904472			−0.0731222
$154$	−2.47299	−	3.37524i	−0.199279	−	0.271984i
$155$			3.82421i			0.307168i
$156$	0.685299	+	0.648070i	0.0548678	+	0.0518872i
$157$	−1.39512			−0.111342			−0.0556712	−	0.998449i	$-0.517730\pi$
$157$	−1.39512			−0.111342			−0.0556712	+	0.998449i	$0.517730\pi$
$158$	−8.07504	−	8.07504i	−0.642416	−	0.642416i
$159$	−3.19429			−0.253324
$160$	−0.708951			−0.0560475
$161$	−2.51240	+	2.51240i	−0.198005	+	0.198005i
$162$	−1.06339	+	1.06339i	−0.0835478	+	0.0835478i
$163$	−6.57771	+	6.57771i	−0.515206	+	0.515206i	−0.916117	−	0.400911i	$-0.868694\pi$
$163$	−6.57771	+	6.57771i	−0.515206	+	0.515206i	0.400911	+	0.916117i	$0.368694\pi$
$164$	−0.761768	−	0.761768i	−0.0594841	−	0.0594841i
$165$	−0.243769	+	1.58008i	−0.0189774	+	0.123009i
$166$			10.6939i			0.830005i
$167$	15.9976	+	15.9976i	1.23793	+	1.23793i	0.960845	+	0.277085i	$0.0893683\pi$
$167$	15.9976	+	15.9976i	1.23793	+	1.23793i	0.277085	+	0.960845i	$0.410632\pi$
$168$		−	2.19316i		−	0.169206i
$169$	−0.725366	−	12.9797i	−0.0557974	−	0.998442i
$170$	0.655681			0.0502884
$171$	−2.48574	+	2.48574i	−0.190090	+	0.190090i
$172$		−	2.89781i		−	0.220956i
$173$	20.7838			1.58017			0.790083	−	0.613000i	$-0.210037\pi$
$173$	20.7838			1.58017			0.790083	+	0.613000i	$0.210037\pi$
$174$	−4.08076	−	4.08076i	−0.309361	−	0.309361i
$175$	−2.82814	+	2.82814i	−0.213787	+	0.213787i
$176$	−8.73225	−	11.9181i	−0.658218	−	0.898363i
$177$	5.71636	−	5.71636i	0.429668	−	0.429668i
$178$			7.51672i			0.563402i
$179$			9.07529i			0.678319i	0.940729	+	0.339160i	$0.110143\pi$
$179$			9.07529i			0.678319i	−0.940729	+	0.339160i	$0.889857\pi$
$180$	0.0891677	−	0.0891677i	0.00664617	−	0.00664617i
$181$			5.13239i			0.381488i	0.981640	+	0.190744i	$0.0610900\pi$
$181$			5.13239i			0.381488i	−0.981640	+	0.190744i	$0.938910\pi$
$182$	3.12543	−	3.30497i	0.231672	−	0.244981i
$183$		−	3.56455i		−	0.263499i
$184$	−7.82948	+	7.82948i	−0.577197	+	0.577197i
$185$	3.91299			0.287689
$186$	11.9305			0.874788
$187$	1.77295	+	2.41979i	0.129651	+	0.176953i
$188$	1.56389	+	1.56389i	0.114059	+	0.114059i
$189$	0.593196	+	0.593196i	0.0431486	+	0.0431486i
$190$	1.80199	−	1.80199i	0.130730	−	0.130730i
$191$	15.2998			1.10706			0.553528	−	0.832830i	$-0.313281\pi$
$191$	15.2998			1.10706			0.553528	+	0.832830i	$0.313281\pi$
$192$		−	6.69778i		−	0.483371i
$193$	3.02269	+	3.02269i	0.217578	+	0.217578i	0.807477	−	0.589899i	$-0.200832\pi$
$193$	3.02269	+	3.02269i	0.217578	+	0.217578i	−0.589899	+	0.807477i	$0.700832\pi$
$194$	−0.121191			−0.00870099
$195$	−1.73737	+	0.0485081i	−0.124416	+	0.00347374i
$196$	−1.64708			−0.117648
$197$	2.43306	−	2.43306i	0.173348	−	0.173348i	−0.615100	−	0.788449i	$-0.710885\pi$
$197$	2.43306	−	2.43306i	0.173348	−	0.173348i	0.788449	+	0.615100i	$0.210885\pi$
$198$	4.92942	+	0.760497i	0.350319	+	0.0540461i
$199$		−	12.0900i		−	0.857037i	−0.903533	−	0.428519i	$-0.859036\pi$
$199$		−	12.0900i		−	0.857037i	0.903533	−	0.428519i	$-0.140964\pi$
$200$	−8.81344	+	8.81344i	−0.623205	+	0.623205i
$201$	10.0412	+	10.0412i	0.708250	+	0.708250i
$202$	−4.49295	+	4.49295i	−0.316123	+	0.316123i
$203$	−2.27639	+	2.27639i	−0.159771	+	0.159771i
$204$		−	0.236607i		−	0.0165658i
$205$	1.98516			0.138649
$206$	16.4498	+	16.4498i	1.14611	+	1.14611i
$207$		−	4.23536i		−	0.294378i
$208$	11.0361	−	11.6700i	0.765212	−	0.809170i
$209$	11.5228	+	1.77771i	0.797052	+	0.122967i
$210$	−0.430027	−	0.430027i	−0.0296747	−	0.0296747i
$211$		−	10.8700i		−	0.748322i	−0.927364	−	0.374161i	$-0.877931\pi$
$211$		−	10.8700i		−	0.748322i	0.927364	−	0.374161i	$-0.122069\pi$
$212$		−	0.835617i		−	0.0573904i
$213$	10.7137	+	10.7137i	0.734088	+	0.734088i
$214$	1.83907	+	1.83907i	0.125716	+	0.125716i
$215$	3.77583	+	3.77583i	0.257509	+	0.257509i
$216$	1.84860	+	1.84860i	0.125781	+	0.125781i
$217$		−	6.65525i		−	0.451788i
$218$		−	23.2099i		−	1.57197i
$219$	10.3258	+	10.3258i	0.697753	+	0.697753i
$220$	−0.413343	−	0.0637694i	−0.0278676	−	0.00429933i
$221$	−2.24070	+	2.36942i	−0.150726	+	0.159384i
$222$		−	12.2075i		−	0.819314i
$223$	−11.0822	−	11.0822i	−0.742122	−	0.742122i	0.230864	−	0.972986i	$-0.425845\pi$
$223$	−11.0822	−	11.0822i	−0.742122	−	0.742122i	−0.972986	+	0.230864i	$0.925845\pi$
$224$	1.23379			0.0824358
$225$		−	4.76763i		−	0.317842i
$226$	2.57847	−	2.57847i	0.171517	−	0.171517i
$227$	−2.78480	+	2.78480i	−0.184834	+	0.184834i	−0.793458	−	0.608624i	$-0.791722\pi$
$227$	−2.78480	+	2.78480i	−0.184834	+	0.184834i	0.608624	+	0.793458i	$0.291722\pi$
$228$	−0.650263	−	0.650263i	−0.0430647	−	0.0430647i
$229$	7.16234	−	7.16234i	0.473301	−	0.473301i	−0.429680	−	0.902981i	$-0.641374\pi$
$229$	7.16234	−	7.16234i	0.473301	−	0.473301i	0.902981	+	0.429680i	$0.141374\pi$
$230$			3.07035i			0.202453i
$231$	0.424231	−	2.74980i	0.0279124	−	0.180924i
$232$	−7.09400	+	7.09400i	−0.465744	+	0.465744i
$233$	−6.23108			−0.408211			−0.204106	−	0.978949i	$-0.565429\pi$
$233$	−6.23108			−0.408211			−0.204106	+	0.978949i	$0.565429\pi$
$234$	0.151333	+	5.42013i	0.00989292	+	0.354325i
$235$	−4.07548			−0.265855
$236$	1.49538	+	1.49538i	0.0973411	+	0.0973411i
$237$		−	7.59368i		−	0.493263i
$238$	−1.14108			−0.0739652
$239$	10.9034	−	10.9034i	0.705284	−	0.705284i	−0.260255	−	0.965540i	$-0.583807\pi$
$239$	10.9034	−	10.9034i	0.705284	−	0.705284i	0.965540	+	0.260255i	$0.0838067\pi$
$240$	−1.51845	−	1.51845i	−0.0980152	−	0.0980152i
$241$	20.0666	+	20.0666i	1.29260	+	1.29260i	0.933171	+	0.359433i	$0.117030\pi$
$241$	20.0666	+	20.0666i	1.29260	+	1.29260i	0.359433	+	0.933171i	$0.382970\pi$
$242$	−7.62807	−	14.6788i	−0.490351	−	0.943586i
$243$	−1.00000			−0.0641500
$244$	0.932475			0.0596956
$245$	2.14613	−	2.14613i	0.137111	−	0.137111i
$246$		−	6.19316i		−	0.394862i
$247$	0.353750	+	12.6699i	0.0225086	+	0.806167i
$248$		−	20.7400i		−	1.31699i
$249$	−5.02820	+	5.02820i	−0.318649	+	0.318649i
$250$			7.08087i			0.447833i
$251$			10.5928i			0.668611i	0.942465	+	0.334305i	$0.108502\pi$
$251$			10.5928i			0.668611i	−0.942465	+	0.334305i	$0.891498\pi$
$252$	−0.155178	+	0.155178i	−0.00977531	+	0.00977531i
$253$	−11.3311	+	8.30217i	−0.712383	+	0.521953i
$254$	9.53552	−	9.53552i	0.598312	−	0.598312i
$255$	0.308297	+	0.308297i	0.0193063	+	0.0193063i
$256$	6.17560			0.385975
$257$			3.34272i			0.208513i	0.994550	+	0.104257i	$0.0332463\pi$
$257$			3.34272i			0.208513i	−0.994550	+	0.104257i	$0.966754\pi$
$258$	11.7796	−	11.7796i	0.733365	−	0.733365i
$259$	−6.80977			−0.423138
$260$	−0.0126896	−	0.454491i	−0.000786975	−	0.0281863i
$261$		−	3.83750i		−	0.237535i
$262$	8.42003	+	8.42003i	0.520191	+	0.520191i
$263$			2.69990i			0.166483i	0.996529	+	0.0832416i	$0.0265273\pi$
$263$			2.69990i			0.166483i	−0.996529	+	0.0832416i	$0.973473\pi$
$264$	1.32205	−	8.56932i	0.0813665	−	0.527405i
$265$	1.08880	+	1.08880i	0.0668846	+	0.0668846i
$266$	−3.13601	+	3.13601i	−0.192281	+	0.192281i
$267$	−3.53432	+	3.53432i	−0.216297	+	0.216297i
$268$	−2.62674	+	2.62674i	−0.160454	+	0.160454i
$269$	24.0709			1.46763			0.733816	−	0.679349i	$-0.237738\pi$
$269$	24.0709			1.46763			0.733816	+	0.679349i	$0.237738\pi$
$270$	0.724932			0.0441180
$271$	−14.5615	−	14.5615i	−0.884551	−	0.884551i	0.109443	−	0.993993i	$-0.465093\pi$
$271$	−14.5615	−	14.5615i	−0.884551	−	0.884551i	−0.993993	+	0.109443i	$0.965093\pi$
$272$	−4.02921			−0.244306
$273$	3.02354	−	0.0844186i	0.182993	−	0.00510924i
$274$			18.3861i			1.11074i
$275$	−12.7552	+	9.34554i	−0.769165	+	0.563557i
$276$	1.10796			0.0666912
$277$	14.0099			0.841776			0.420888	−	0.907113i	$-0.361719\pi$
$277$	14.0099			0.841776			0.420888	+	0.907113i	$0.361719\pi$
$278$	−4.65343	−	4.65343i	−0.279094	−	0.279094i
$279$	5.60966	+	5.60966i	0.335842	+	0.335842i
$280$	−0.747560	+	0.747560i	−0.0446752	+	0.0446752i
$281$	−10.0982	−	10.0982i	−0.602408	−	0.602408i	0.338543	−	0.940951i	$-0.390066\pi$
$281$	−10.0982	−	10.0982i	−0.602408	−	0.602408i	−0.940951	+	0.338543i	$0.890066\pi$
$282$			12.7144i			0.757133i
$283$	−1.31783			−0.0783370			−0.0391685	−	0.999233i	$-0.512471\pi$
$283$	−1.31783			−0.0783370			−0.0391685	+	0.999233i	$0.512471\pi$
$284$	−2.80266	+	2.80266i	−0.166307	+	0.166307i
$285$	1.69458			0.100378
$286$	14.2042	−	11.0294i	0.839913	−	0.652185i
$287$	−3.45476			−0.203928
$288$	−1.03995	+	1.03995i	−0.0612795	+	0.0612795i
$289$	−16.1819			−0.951878
$290$			2.78192i			0.163360i
$291$	−0.0569832	−	0.0569832i	−0.00334041	−	0.00334041i
$292$	−2.70120	+	2.70120i	−0.158076	+	0.158076i
$293$	−18.6057	−	18.6057i	−1.08696	−	1.08696i	−0.995840	−	0.0911161i	$-0.970957\pi$
$293$	−18.6057	−	18.6057i	−1.08696	−	1.08696i	−0.0911161	−	0.995840i	$-0.529043\pi$
$294$	−6.69536	−	6.69536i	−0.390481	−	0.390481i
$295$	−3.89694			−0.226889
$296$	−21.2216			−1.23348
$297$	1.96021	+	2.67537i	0.113743	+	0.155241i
$298$		−	27.1955i		−	1.57539i
$299$	−11.0952	−	10.4925i	−0.641655	−	0.606797i
$300$	1.24720			0.0720070
$301$	−6.57106	−	6.57106i	−0.378750	−	0.378750i
$302$	2.04473			0.117661
$303$	−4.22512			−0.242727
$304$	−11.0734	+	11.0734i	−0.635103	+	0.635103i
$305$	−1.21501	+	1.21501i	−0.0695711	+	0.0695711i
$306$	0.961806	−	0.961806i	0.0549828	−	0.0549828i
$307$	4.32402	+	4.32402i	0.246785	+	0.246785i	0.819650	−	0.572865i	$-0.194168\pi$
$307$	4.32402	+	4.32402i	0.246785	+	0.246785i	−0.572865	+	0.819650i	$0.694168\pi$
$308$	0.719340	+	0.110978i	0.0409882	+	0.00632354i
$309$			15.4692i			0.880010i
$310$	−4.06662	−	4.06662i	−0.230969	−	0.230969i
$311$			25.3397i			1.43688i	0.695589	+	0.718440i	$0.255144\pi$
$311$			25.3397i			1.43688i	−0.695589	+	0.718440i	$0.744856\pi$
$312$	9.42238	−	0.263077i	0.533437	−	0.0148938i
$313$	−2.06572			−0.116761			−0.0583807	−	0.998294i	$-0.518594\pi$
$313$	−2.06572			−0.116761			−0.0583807	+	0.998294i	$0.518594\pi$
$314$	1.48355	−	1.48355i	0.0837217	−	0.0837217i
$315$		−	0.404392i		−	0.0227849i
$316$	1.98648			0.111748
$317$	11.9778	+	11.9778i	0.672740	+	0.672740i	0.958347	−	0.285607i	$-0.0921952\pi$
$317$	11.9778	+	11.9778i	0.672740	+	0.672740i	−0.285607	+	0.958347i	$0.592195\pi$
$318$	3.39678	−	3.39678i	0.190482	−	0.190482i
$319$	−10.2667	+	7.52228i	−0.574826	+	0.421167i
$320$	−2.28300	+	2.28300i	−0.127623	+	0.127623i
$321$			1.72944i			0.0965281i
$322$		−	5.34331i		−	0.297771i
$323$	2.24828	−	2.24828i	0.125098	−	0.125098i
$324$		−	0.261597i		−	0.0145332i
$325$	−12.4896	−	11.8111i	−0.692800	−	0.655164i
$326$		−	13.9893i		−	0.774798i
$327$	10.9131	−	10.9131i	0.603498	−	0.603498i
$328$	−10.7662			−0.594465
$329$	7.09255			0.391025
$330$	−1.42102	−	1.93946i	−0.0782243	−	0.106764i
$331$	16.0602	+	16.0602i	0.882747	+	0.882747i	0.993813	−	0.111066i	$-0.0354266\pi$
$331$	16.0602	+	16.0602i	0.882747	+	0.882747i	−0.111066	+	0.993813i	$0.535427\pi$
$332$	−1.31536	−	1.31536i	−0.0721898	−	0.0721898i
$333$	5.73990	−	5.73990i	0.314544	−	0.314544i
$334$	−34.0233			−1.86167
$335$		−	6.84525i		−	0.373996i
$336$	2.64255	+	2.64255i	0.144163	+	0.144163i
$337$	25.2824			1.37722			0.688611	−	0.725131i	$-0.258221\pi$
$337$	25.2824			1.37722			0.688611	+	0.725131i	$0.258221\pi$
$338$	14.5739	+	13.0312i	0.792715	+	0.708803i
$339$	2.42476			0.131695
$340$	−0.0806497	+	0.0806497i	−0.00437384	+	0.00437384i
$341$	4.01182	−	26.0040i	0.217252	−	1.40820i
$342$		−	5.28663i		−	0.285868i
$343$	−7.88727	+	7.88727i	−0.425873	+	0.425873i
$344$	−20.4777	−	20.4777i	−1.10408	−	1.10408i
$345$	−1.44366	+	1.44366i	−0.0777240	+	0.0777240i
$346$	−22.1013	+	22.1013i	−1.18817	+	1.18817i
$347$			25.8728i			1.38893i	0.719528	+	0.694464i	$0.244358\pi$
$347$			25.8728i			1.38893i	−0.719528	+	0.694464i	$0.755642\pi$
$348$	1.00388			0.0538135
$349$	3.71099	+	3.71099i	0.198645	+	0.198645i	0.799419	−	0.600774i	$-0.205141\pi$
$349$	3.71099	+	3.71099i	0.198645	+	0.198645i	−0.600774	+	0.799419i	$0.705141\pi$
$350$		−	6.01483i		−	0.321506i
$351$	−2.47736	+	2.61967i	−0.132232	+	0.139828i
$352$	4.82076	+	0.743732i	0.256947	+	0.0396410i
$353$	12.5514	+	12.5514i	0.668045	+	0.668045i	0.957263	−	0.289218i	$-0.0933952\pi$
$353$	12.5514	+	12.5514i	0.668045	+	0.668045i	−0.289218	+	0.957263i	$0.593395\pi$
$354$			12.1574i			0.646161i
$355$		−	7.30369i		−	0.387640i
$356$	−0.924568	−	0.924568i	−0.0490020	−	0.0490020i
$357$	−0.536529	−	0.536529i	−0.0283961	−	0.0283961i
$358$	−9.65057	−	9.65057i	−0.510049	−	0.510049i
$359$	−9.87601	−	9.87601i	−0.521236	−	0.521236i	0.396709	−	0.917945i	$-0.370152\pi$
$359$	−9.87601	−	9.87601i	−0.521236	−	0.521236i	−0.917945	+	0.396709i	$0.870152\pi$
$360$		−	1.26022i		−	0.0664196i
$361$			6.64216i			0.349587i
$362$	−5.45774	−	5.45774i	−0.286852	−	0.286852i
$363$	3.31519	−	10.4885i	0.174002	−	0.550506i
$364$	0.0220837	+	0.790949i	0.00115750	+	0.0414570i
$365$		−	7.03928i		−	0.368453i
$366$	3.79050	+	3.79050i	0.198133	+	0.198133i
$367$	−11.1557			−0.582320			−0.291160	−	0.956674i	$-0.594041\pi$
$367$	−11.1557			−0.582320			−0.291160	+	0.956674i	$0.594041\pi$
$368$		−	18.8675i		−	0.983537i
$369$	2.91199	−	2.91199i	0.151592	−	0.151592i
$370$	−4.16103	+	4.16103i	−0.216322	+	0.216322i
$371$	−1.89484	−	1.89484i	−0.0983751	−	0.0983751i
$372$	−1.46747	+	1.46747i	−0.0760848	+	0.0760848i
$373$		−	16.1948i		−	0.838533i	−0.907863	−	0.419266i	$-0.862287\pi$
$373$		−	16.1948i		−	0.838533i	0.907863	−	0.419266i	$-0.137713\pi$
$374$	−4.45852	−	0.687848i	−0.230545	−	0.0355678i
$375$	−3.32938	+	3.32938i	−0.171929	+	0.171929i
$376$	22.1028			1.13987
$377$	−10.0530	−	9.50686i	−0.517755	−	0.489628i
$378$	−1.26160			−0.0648896
$379$	15.5419	+	15.5419i	0.798332	+	0.798332i	0.982832	−	0.184501i	$-0.0590667\pi$
$379$	15.5419	+	15.5419i	0.798332	+	0.798332i	−0.184501	+	0.982832i	$0.559067\pi$
$380$			0.443296i			0.0227406i
$381$	8.96709			0.459398
$382$	−16.2697	+	16.2697i	−0.832429	+	0.832429i
$383$	−19.3045	−	19.3045i	−0.986415	−	0.986415i	0.0134936	−	0.999909i	$-0.495705\pi$
$383$	−19.3045	−	19.3045i	−0.986415	−	0.986415i	−0.999909	+	0.0134936i	$0.995705\pi$
$384$	9.20225	+	9.20225i	0.469600	+	0.469600i
$385$	−1.08190	+	0.792692i	−0.0551386	+	0.0403993i
$386$	−6.42860			−0.327207
$387$	11.0774			0.563095
$388$	0.0149066	−	0.0149066i	0.000756770	−	0.000756770i
$389$			31.5524i			1.59977i	0.600152	+	0.799886i	$0.295107\pi$
$389$			31.5524i			1.59977i	−0.600152	+	0.799886i	$0.704893\pi$
$390$	1.79592	−	1.89908i	0.0909399	−	0.0961639i
$391$			3.83076i			0.193730i
$392$	−11.6392	+	11.6392i	−0.587870	+	0.587870i
$393$			7.91810i			0.399415i
$394$			5.17459i			0.260692i
$395$	−2.58837	+	2.58837i	−0.130235	+	0.130235i
$396$	−0.699868	+	0.512784i	−0.0351697	+	0.0257684i
$397$	−13.5145	+	13.5145i	−0.678273	+	0.678273i	−0.959609	−	0.281337i	$-0.909222\pi$
$397$	−13.5145	+	13.5145i	−0.678273	+	0.678273i	0.281337	+	0.959609i	$0.409222\pi$
$398$	12.8564	+	12.8564i	0.644432	+	0.644432i
$399$	−2.94906			−0.147638
$400$		−	21.2387i		−	1.06193i
$401$	−23.2634	+	23.2634i	−1.16172	+	1.16172i	−0.177617	+	0.984100i	$0.556839\pi$
$401$	−23.2634	+	23.2634i	−1.16172	+	1.16172i	−0.984100	+	0.177617i	$0.943161\pi$
$402$	−21.3554			−1.06511
$403$	28.5926	−	0.798319i	1.42430	−	0.0397671i
$404$		−	1.10528i		−	0.0549897i
$405$	0.340859	+	0.340859i	0.0169374	+	0.0169374i
$406$		−	4.84137i		−	0.240273i
$407$	−26.6077	−	4.10496i	−1.31890	−	0.203475i
$408$	−1.67201	−	1.67201i	−0.0827767	−	0.0827767i
$409$	−14.9710	+	14.9710i	−0.740270	+	0.740270i	−0.972630	−	0.232360i	$-0.925355\pi$
$409$	−14.9710	+	14.9710i	−0.740270	+	0.740270i	0.232360	+	0.972630i	$0.425355\pi$
$410$	−2.11100	+	2.11100i	−0.104255	+	0.104255i
$411$	−8.64502	+	8.64502i	−0.426427	+	0.426427i
$412$	−4.04669			−0.199366
$413$	6.78184			0.333712
$414$	4.50384	+	4.50384i	0.221352	+	0.221352i
$415$	3.42781			0.168265
$416$	0.147997	+	5.30065i	0.00725613	+	0.259886i
$417$		−	4.37603i		−	0.214295i
$418$	−14.1437	+	10.3629i	−0.691790	+	0.506865i
$419$	−32.0945			−1.56792			−0.783960	−	0.620811i	$-0.786804\pi$
$419$	−32.0945			−1.56792			−0.783960	+	0.620811i	$0.786804\pi$
$420$	0.105788			0.00516192
$421$	−13.4184	−	13.4184i	−0.653971	−	0.653971i	0.299976	−	0.953947i	$-0.403021\pi$
$421$	−13.4184	−	13.4184i	−0.653971	−	0.653971i	−0.953947	+	0.299976i	$0.903021\pi$
$422$	11.5591	+	11.5591i	0.562686	+	0.562686i
$423$	−5.97825	+	5.97825i	−0.290673	+	0.290673i
$424$	−5.90496	−	5.90496i	−0.286770	−	0.286770i
$425$			4.31219i			0.209172i
$426$	−22.7856			−1.10397
$427$	2.11447	−	2.11447i	0.102327	−	0.102327i
$428$	−0.452418			−0.0218684
$429$	11.8647	+	1.49276i	0.572834	+	0.0720709i
$430$	−8.03035			−0.387258
$431$	10.1064	−	10.1064i	0.486806	−	0.486806i	−0.420491	−	0.907297i	$-0.638142\pi$
$431$	10.1064	−	10.1064i	0.486806	−	0.486806i	0.907297	+	0.420491i	$0.138142\pi$
$432$	−4.45476			−0.214330
$433$		−	5.96793i		−	0.286800i	−0.989665	−	0.143400i	$-0.954196\pi$
$433$		−	5.96793i		−	0.286800i	0.989665	−	0.143400i	$-0.0458036\pi$
$434$	7.07713	+	7.07713i	0.339713	+	0.339713i
$435$	−1.30804	+	1.30804i	−0.0627160	+	0.0627160i
$436$	2.85485	+	2.85485i	0.136722	+	0.136722i
$437$	10.5280	+	10.5280i	0.503623	+	0.503623i
$438$	−21.9607			−1.04932
$439$	22.3499			1.06670			0.533351	−	0.845894i	$-0.320933\pi$
$439$	22.3499			1.06670			0.533351	+	0.845894i	$0.320933\pi$
$440$	−3.37156	+	2.47030i	−0.160733	+	0.117767i
$441$		−	6.29624i		−	0.299821i
$442$	−0.136876	−	4.90236i	−0.00651053	−	0.233181i
$443$	8.50146			0.403916			0.201958	−	0.979394i	$-0.435269\pi$
$443$	8.50146			0.403916			0.201958	+	0.979394i	$0.435269\pi$
$444$	1.50154	+	1.50154i	0.0712600	+	0.0712600i
$445$	2.40941			0.114217
$446$	23.5695			1.11605
$447$	12.7872	−	12.7872i	0.604813	−	0.604813i
$448$	3.97310	−	3.97310i	0.187711	−	0.187711i
$449$	27.2084	−	27.2084i	1.28405	−	1.28405i	0.345701	−	0.938345i	$-0.387641\pi$
$449$	27.2084	−	27.2084i	1.28405	−	1.28405i	0.938345	−	0.345701i	$-0.112359\pi$
$450$	5.06985	+	5.06985i	0.238995	+	0.238995i
$451$	−13.4987	−	2.08255i	−0.635631	−	0.0980633i
$452$			0.634311i			0.0298355i
$453$	0.961423	+	0.961423i	0.0451716	+	0.0451716i
$454$		−	5.92267i		−	0.277964i
$455$	−1.05937	−	1.00183i	−0.0496643	−	0.0469663i
$456$	−9.19029			−0.430375
$457$	−10.0923	+	10.0923i	−0.472100	+	0.472100i	−0.902594	−	0.430494i	$-0.858339\pi$
$457$	−10.0923	+	10.0923i	−0.472100	+	0.472100i	0.430494	+	0.902594i	$0.358339\pi$
$458$			15.2327i			0.711778i
$459$	0.904472			0.0422171
$460$	−0.377657	−	0.377657i	−0.0176084	−	0.0176084i
$461$	−4.18937	+	4.18937i	−0.195118	+	0.195118i	−0.797904	−	0.602785i	$-0.794058\pi$
$461$	−4.18937	+	4.18937i	−0.195118	+	0.195118i	0.602785	+	0.797904i	$0.294058\pi$
$462$	2.47299	+	3.37524i	0.115054	+	0.157030i
$463$	11.1196	−	11.1196i	0.516772	−	0.516772i	−0.399821	−	0.916593i	$-0.630928\pi$
$463$	11.1196	−	11.1196i	0.516772	−	0.516772i	0.916593	+	0.399821i	$0.130928\pi$
$464$		−	17.0951i		−	0.793621i
$465$		−	3.82421i		−	0.177343i
$466$	6.62607	−	6.62607i	0.306947	−	0.306947i
$467$			31.9283i			1.47747i	0.673998	+	0.738733i	$0.264575\pi$
$467$			31.9283i			1.47747i	−0.673998	+	0.738733i	$0.735425\pi$
$468$	−0.685299	−	0.648070i	−0.0316779	−	0.0299571i
$469$			11.9128i			0.550081i
$470$	4.33383	−	4.33383i	0.199905	−	0.199905i
$471$	1.39512			0.0642836
$472$	21.1345			0.972795
$473$	−21.7140	−	29.6361i	−0.998409	−	1.36267i
$474$	8.07504	+	8.07504i	0.370899	+	0.370899i
$475$	11.8511	+	11.8511i	0.543766	+	0.543766i
$476$	0.140354	−	0.140354i	0.00643313	−	0.00643313i
$477$	3.19429			0.146256
$478$			23.1892i			1.06065i
$479$	23.1088	+	23.1088i	1.05587	+	1.05587i	0.998344	+	0.0575245i	$0.0183207\pi$
$479$	23.1088	+	23.1088i	1.05587	+	1.05587i	0.0575245	+	0.998344i	$0.481679\pi$
$480$	0.708951			0.0323590
$481$	−0.816853	−	29.2564i	−0.0372453	−	1.33398i
$482$	−42.6773			−1.94390
$483$	2.51240	−	2.51240i	0.114318	−	0.114318i
$484$	2.74377	+	0.867243i	0.124717	+	0.0394202i
$485$			0.0388465i			0.00176393i
$486$	1.06339	−	1.06339i	0.0482364	−	0.0482364i
$487$	−11.5087	−	11.5087i	−0.521510	−	0.521510i	0.396517	−	0.918027i	$-0.370219\pi$
$487$	−11.5087	−	11.5087i	−0.521510	−	0.521510i	−0.918027	+	0.396517i	$0.870219\pi$
$488$	6.58942	−	6.58942i	0.298289	−	0.298289i
$489$	6.57771	−	6.57771i	0.297454	−	0.297454i
$490$			4.56434i			0.206196i
$491$	14.9382			0.674153			0.337076	−	0.941477i	$-0.390562\pi$
$491$	14.9382			0.674153			0.337076	+	0.941477i	$0.390562\pi$
$492$	0.761768	+	0.761768i	0.0343432	+	0.0343432i
$493$			3.47091i			0.156322i
$494$	−13.8492	−	13.0969i	−0.623107	−	0.589257i
$495$	0.243769	−	1.58008i	0.0109566	−	0.0710192i
$496$	24.9897	+	24.9897i	1.12207	+	1.12207i
$497$			12.7106i			0.570148i
$498$		−	10.6939i		−	0.479204i
$499$	9.54732	+	9.54732i	0.427397	+	0.427397i	0.887741	−	0.460344i	$-0.152274\pi$
$499$	9.54732	+	9.54732i	0.427397	+	0.427397i	−0.460344	+	0.887741i	$0.652274\pi$
$500$	−0.870957	−	0.870957i	−0.0389504	−	0.0389504i
$501$	−15.9976	−	15.9976i	−0.714719	−	0.714719i
$502$	−11.2643	−	11.2643i	−0.502749	−	0.502749i
$503$			9.79846i			0.436892i	0.975849	+	0.218446i	$0.0700987\pi$
$503$			9.79846i			0.436892i	−0.975849	+	0.218446i	$0.929901\pi$
$504$			2.19316i			0.0976913i
$505$	1.44017	+	1.44017i	0.0640868	+	0.0640868i
$506$	3.22098	−	20.8779i	0.143190	−	0.928135i
$507$	0.725366	+	12.9797i	0.0322147	+	0.576451i
$508$			2.34577i			0.104077i
$509$	16.9617	+	16.9617i	0.751816	+	0.751816i	0.974818	−	0.223002i	$-0.0715857\pi$
$509$	16.9617	+	16.9617i	0.751816	+	0.751816i	−0.223002	+	0.974818i	$0.571586\pi$
$510$	−0.655681			−0.0290340
$511$			12.2504i			0.541928i
$512$	11.8374	−	11.8374i	0.523145	−	0.523145i
$513$	2.48574	−	2.48574i	0.109748	−	0.109748i
$514$	−3.55461	−	3.55461i	−0.156787	−	0.156787i
$515$	5.27280	−	5.27280i	0.232348	−	0.232348i
$516$			2.89781i			0.127569i
$517$	27.7126	+	4.27542i	1.21880	+	0.188033i
$518$	7.24144	−	7.24144i	0.318170	−	0.318170i
$519$	−20.7838			−0.912309
$520$	−3.30137	−	3.12203i	−0.144775	−	0.136910i
$521$	15.1733			0.664755			0.332377	−	0.943146i	$-0.392149\pi$
$521$	15.1733			0.664755			0.332377	+	0.943146i	$0.392149\pi$
$522$	4.08076	+	4.08076i	0.178610	+	0.178610i
$523$		−	9.34555i		−	0.408653i	−0.978903	−	0.204326i	$-0.934500\pi$
$523$		−	9.34555i		−	0.408653i	0.978903	−	0.204326i	$-0.0655003\pi$
$524$	−2.07135			−0.0904874
$525$	2.82814	−	2.82814i	0.123430	−	0.123430i
$526$	−2.87105	−	2.87105i	−0.125184	−	0.125184i
$527$	−5.07378	−	5.07378i	−0.221017	−	0.221017i
$528$	8.73225	+	11.9181i	0.380022	+	0.518670i
$529$	5.06175			0.220076
$530$	−2.31564			−0.100585
$531$	−5.71636	+	5.71636i	−0.248069	+	0.248069i
$532$		−	0.771467i		−	0.0334473i
$533$	−0.414410	−	14.8425i	−0.0179501	−	0.642901i
$534$		−	7.51672i		−	0.325280i
$535$	0.589496	−	0.589496i	0.0254862	−	0.0254862i
$536$			37.1243i			1.60352i
$537$		−	9.07529i		−	0.391628i
$538$	−25.5968	+	25.5968i	−1.10356	+	1.10356i
$539$	−16.8448	+	12.3419i	−0.725555	+	0.531604i
$540$	−0.0891677	+	0.0891677i	−0.00383717	+	0.00383717i
$541$	−0.419846	−	0.419846i	−0.0180506	−	0.0180506i	0.698024	−	0.716074i	$-0.254063\pi$
$541$	−0.419846	−	0.419846i	−0.0180506	−	0.0180506i	−0.716074	+	0.698024i	$0.754063\pi$
$542$	30.9692			1.33024
$543$		−	5.13239i		−	0.220252i
$544$	0.940604	−	0.940604i	0.0403280	−	0.0403280i
$545$	−7.43968			−0.318681
$546$	−3.12543	+	3.30497i	−0.133756	+	0.141440i
$547$		−	27.8941i		−	1.19266i	−0.802738	−	0.596332i	$-0.796624\pi$
$547$		−	27.8941i		−	1.19266i	0.802738	−	0.596332i	$-0.203376\pi$
$548$	−2.26151	−	2.26151i	−0.0966070	−	0.0966070i
$549$			3.56455i			0.152131i
$550$	3.62577	−	23.5017i	0.154603	−	1.00211i
$551$	9.53903	+	9.53903i	0.406376	+	0.406376i
$552$	7.82948	−	7.82948i	0.333245	−	0.333245i
$553$	4.50454	−	4.50454i	0.191552	−	0.191552i
$554$	−14.8980	+	14.8980i	−0.632957	+	0.632957i
$555$	−3.91299			−0.166097
$556$	1.14476			0.0485485
$557$	4.62070	+	4.62070i	0.195785	+	0.195785i	0.798190	−	0.602405i	$-0.205791\pi$
$557$	4.62070	+	4.62070i	0.195785	+	0.195785i	−0.602405	+	0.798190i	$0.705791\pi$
$558$	−11.9305			−0.505059
$559$	27.4427	−	29.0191i	1.16070	−	1.22738i
$560$		−	1.80147i		−	0.0761260i
$561$	−1.77295	−	2.41979i	−0.0748540	−	0.102164i
$562$	21.4767			0.905938
$563$	10.6608			0.449298			0.224649	−	0.974440i	$-0.427876\pi$
$563$	10.6608			0.449298			0.224649	+	0.974440i	$0.427876\pi$
$564$	−1.56389	−	1.56389i	−0.0658518	−	0.0658518i
$565$	−0.826502	−	0.826502i	−0.0347712	−	0.0347712i
$566$	1.40137	−	1.40137i	0.0589040	−	0.0589040i
$567$	−0.593196	−	0.593196i	−0.0249119	−	0.0249119i
$568$			39.6105i			1.66202i
$569$	18.7238			0.784942			0.392471	−	0.919764i	$-0.371620\pi$
$569$	18.7238			0.784942			0.392471	+	0.919764i	$0.371620\pi$
$570$	−1.80199	+	1.80199i	−0.0754773	+	0.0754773i
$571$	−30.4275			−1.27335			−0.636676	−	0.771131i	$-0.719691\pi$
$571$	−30.4275			−1.27335			−0.636676	+	0.771131i	$0.719691\pi$
$572$	−0.390500	+	3.10378i	−0.0163276	+	0.129775i
$573$	−15.2998			−0.639159
$574$	3.67376	−	3.67376i	0.153340	−	0.153340i
$575$	−20.1926			−0.842090
$576$			6.69778i			0.279074i
$577$	19.8858	+	19.8858i	0.827856	+	0.827856i	0.987220	−	0.159364i	$-0.0509444\pi$
$577$	19.8858	+	19.8858i	0.827856	+	0.827856i	−0.159364	+	0.987220i	$0.550944\pi$
$578$	17.2077	−	17.2077i	0.715746	−	0.715746i
$579$	−3.02269	−	3.02269i	−0.125619	−	0.125619i
$580$	−0.342181	−	0.342181i	−0.0142083	−	0.0142083i
$581$	−5.96541			−0.247487
$582$	0.121191			0.00502352
$583$	−6.26146	−	8.54590i	−0.259323	−	0.353935i
$584$			38.1766i			1.57976i
$585$	1.73737	−	0.0485081i	0.0718314	−	0.00200556i
$586$	39.5702			1.63463
$587$	8.71948	+	8.71948i	0.359891	+	0.359891i	0.863773	−	0.503881i	$-0.168095\pi$
$587$	8.71948	+	8.71948i	0.359891	+	0.359891i	−0.503881	+	0.863773i	$0.668095\pi$
$588$	1.64708			0.0679243
$589$	−27.8884			−1.14912
$590$	4.14397	−	4.14397i	0.170605	−	0.170605i
$591$	−2.43306	+	2.43306i	−0.100083	+	0.100083i
$592$	25.5699	−	25.5699i	1.05092	−	1.05092i
$593$	−10.4881	−	10.4881i	−0.430693	−	0.430693i	0.458171	−	0.888864i	$-0.348505\pi$
$593$	−10.4881	−	10.4881i	−0.430693	−	0.430693i	−0.888864	+	0.458171i	$0.848505\pi$
$594$	−4.92942	−	0.760497i	−0.202257	−	0.0312036i
$595$			0.365761i			0.0149948i
$596$	3.34509	+	3.34509i	0.137020	+	0.137020i
$597$			12.0900i			0.494811i
$598$	22.9562	−	0.640948i	0.938749	−	0.0262103i
$599$	−1.39995			−0.0572002			−0.0286001	−	0.999591i	$-0.509105\pi$
$599$	−1.39995			−0.0572002			−0.0286001	+	0.999591i	$0.509105\pi$
$600$	8.81344	−	8.81344i	0.359807	−	0.359807i
$601$		−	39.0742i		−	1.59387i	−0.604066	−	0.796934i	$-0.706454\pi$
$601$		−	39.0742i		−	1.59387i	0.604066	−	0.796934i	$-0.293546\pi$
$602$	13.9752			0.569587
$603$	−10.0412	−	10.0412i	−0.408909	−	0.408909i
$604$	−0.251505	+	0.251505i	−0.0102336	+	0.0102336i
$605$	−4.70512	+	2.44510i	−0.191291	+	0.0994075i
$606$	4.49295	−	4.49295i	0.182514	−	0.182514i
$607$		−	34.0152i		−	1.38063i	−0.723507	−	0.690317i	$-0.757471\pi$
$607$		−	34.0152i		−	1.38063i	0.723507	−	0.690317i	$-0.242529\pi$
$608$		−	5.17009i		−	0.209675i
$609$	2.27639	−	2.27639i	0.0922438	−	0.0922438i
$610$		−	2.58405i		−	0.104625i
$611$	0.850774	+	30.4714i	0.0344186	+	1.23274i
$612$			0.236607i			0.00956428i
$613$	−13.4425	+	13.4425i	−0.542939	+	0.542939i	−0.924389	−	0.381450i	$-0.875425\pi$
$613$	−13.4425	+	13.4425i	−0.542939	+	0.542939i	0.381450	+	0.924389i	$0.375425\pi$
$614$	−9.19624			−0.371130
$615$	−1.98516			−0.0800492
$616$	5.86752	−	4.29905i	0.236409	−	0.173214i
$617$	−2.49119	−	2.49119i	−0.100292	−	0.100292i	0.655181	−	0.755472i	$-0.272592\pi$
$617$	−2.49119	−	2.49119i	−0.100292	−	0.100292i	−0.755472	+	0.655181i	$0.772592\pi$
$618$	−16.4498	−	16.4498i	−0.661707	−	0.661707i
$619$	19.9863	−	19.9863i	0.803318	−	0.803318i	−0.180295	−	0.983613i	$-0.557705\pi$
$619$	19.9863	−	19.9863i	0.803318	−	0.803318i	0.983613	+	0.180295i	$0.0577051\pi$
$620$	1.00040			0.0401771
$621$			4.23536i			0.169959i
$622$	−26.9459	−	26.9459i	−1.08043	−	1.08043i
$623$	−4.19309			−0.167993
$624$	−11.0361	+	11.6700i	−0.441796	+	0.467174i
$625$	−21.5685			−0.862738
$626$	2.19667	−	2.19667i	0.0877965	−	0.0877965i
$627$	−11.5228	−	1.77771i	−0.460178	−	0.0709949i
$628$			0.364958i			0.0145634i
$629$	−5.19157	+	5.19157i	−0.207002	+	0.207002i
$630$	0.430027	+	0.430027i	0.0171327	+	0.0171327i
$631$	28.6905	−	28.6905i	1.14215	−	1.14215i	0.154095	−	0.988056i	$-0.450754\pi$
$631$	28.6905	−	28.6905i	1.14215	−	1.14215i	0.988056	−	0.154095i	$-0.0492462\pi$
$632$	14.0377	−	14.0377i	0.558389	−	0.558389i
$633$			10.8700i			0.432044i
$634$	−25.4741			−1.01171
$635$	−3.05651	−	3.05651i	−0.121294	−	0.121294i
$636$			0.835617i			0.0331344i
$637$	−16.4941	−	15.5981i	−0.653519	−	0.618017i
$638$	2.91840	−	18.9166i	0.115541	−	0.748917i
$639$	−10.7137	−	10.7137i	−0.423826	−	0.423826i
$640$		−	6.27334i		−	0.247975i
$641$		−	24.7358i		−	0.977007i	−0.872562	−	0.488503i	$-0.837543\pi$
$641$		−	24.7358i		−	0.977007i	0.872562	−	0.488503i	$-0.162457\pi$
$642$	−1.83907	−	1.83907i	−0.0725824	−	0.0725824i
$643$	19.2632	+	19.2632i	0.759668	+	0.759668i	0.976262	−	0.216594i	$-0.0694947\pi$
$643$	19.2632	+	19.2632i	0.759668	+	0.759668i	−0.216594	+	0.976262i	$0.569495\pi$
$644$	0.657236	+	0.657236i	0.0258987	+	0.0258987i
$645$	−3.77583	−	3.77583i	−0.148673	−	0.148673i
$646$			4.78161i			0.188130i
$647$		−	21.1882i		−	0.832995i	−0.909137	−	0.416497i	$-0.863258\pi$
$647$		−	21.1882i		−	0.832995i	0.909137	−	0.416497i	$-0.136742\pi$
$648$	−1.84860	−	1.84860i	−0.0726199	−	0.0726199i
$649$	26.4986	+	4.08812i	1.04016	+	0.160473i
$650$	25.8412	−	0.721498i	1.01358	−	0.0282995i
$651$			6.65525i			0.260840i
$652$	1.72071	+	1.72071i	0.0673882	+	0.0673882i
$653$	5.78280			0.226298			0.113149	−	0.993578i	$-0.463906\pi$
$653$	5.78280			0.226298			0.113149	+	0.993578i	$0.463906\pi$
$654$			23.2099i			0.907577i
$655$	2.69895	−	2.69895i	0.105457	−	0.105457i
$656$	12.9722	−	12.9722i	0.506480	−	0.506480i
$657$	−10.3258	−	10.3258i	−0.402848	−	0.402848i
$658$	−7.54215	+	7.54215i	−0.294024	+	0.294024i
$659$		−	49.6324i		−	1.93340i	−0.255906	−	0.966702i	$-0.582374\pi$
$659$		−	49.6324i		−	1.93340i	0.255906	−	0.966702i	$-0.417626\pi$
$660$	0.413343	+	0.0637694i	0.0160894	+	0.00248222i
$661$	−7.29834	+	7.29834i	−0.283872	+	0.283872i	−0.834651	−	0.550779i	$-0.814331\pi$
$661$	−7.29834	+	7.29834i	−0.283872	+	0.283872i	0.550779	+	0.834651i	$0.314331\pi$
$662$	−34.1564			−1.32753
$663$	2.24070	−	2.36942i	0.0870217	−	0.0920206i
$664$	−18.5902			−0.721442
$665$	1.00522	+	1.00522i	0.0389806	+	0.0389806i
$666$			12.2075i			0.473031i
$667$	−16.2532			−0.629325
$668$	4.18492	−	4.18492i	0.161919	−	0.161919i
$669$	11.0822	+	11.0822i	0.428465	+	0.428465i
$670$	7.27917	+	7.27917i	0.281219	+	0.281219i
$671$	9.53647	−	6.98724i	0.368151	−	0.269739i
$672$	−1.23379			−0.0475943
$673$	−28.5157			−1.09920			−0.549600	−	0.835428i	$-0.685220\pi$
$673$	−28.5157			−1.09920			−0.549600	+	0.835428i	$0.685220\pi$
$674$	−26.8851	+	26.8851i	−1.03557	+	1.03557i
$675$			4.76763i			0.183506i
$676$	−3.39546	+	0.189754i	−0.130595	+	0.00729822i
$677$			45.4172i			1.74552i	0.488146	+	0.872762i	$0.337673\pi$
$677$			45.4172i			1.74552i	−0.488146	+	0.872762i	$0.662327\pi$
$678$	−2.57847	+	2.57847i	−0.0990255	+	0.0990255i
$679$		−	0.0676044i		−	0.00259442i
$680$			1.13984i			0.0437108i
$681$	2.78480	−	2.78480i	0.106714	−	0.106714i
$682$	23.3863	+	31.9185i	0.895506	+	1.22222i
$683$	−9.28933	+	9.28933i	−0.355446	+	0.355446i	−0.862131	−	0.506685i	$-0.830871\pi$
$683$	−9.28933	+	9.28933i	−0.355446	+	0.355446i	0.506685	+	0.862131i	$0.330871\pi$
$684$	0.650263	+	0.650263i	0.0248634	+	0.0248634i
$685$	5.89346			0.225178
$686$		−	16.7745i		−	0.640453i
$687$	−7.16234	+	7.16234i	−0.273260	+	0.273260i
$688$	49.3471			1.88134
$689$	7.91341	−	8.36799i	0.301477	−	0.318795i
$690$		−	3.07035i		−	0.116886i
$691$	9.23750	+	9.23750i	0.351411	+	0.351411i	0.860634	−	0.509223i	$-0.170067\pi$
$691$	9.23750	+	9.23750i	0.351411	+	0.351411i	−0.509223	+	0.860634i	$0.670067\pi$
$692$		−	5.43699i		−	0.206683i
$693$	−0.424231	+	2.74980i	−0.0161152	+	0.104456i
$694$	−27.5129	−	27.5129i	−1.04438	−	1.04438i
$695$	−1.49161	+	1.49161i	−0.0565800	+	0.0565800i
$696$	7.09400	−	7.09400i	0.268897	−	0.268897i
$697$	−2.63381	+	2.63381i	−0.0997628	+	0.0997628i
$698$	−7.89245			−0.298734
$699$	6.23108			0.235681
$700$	0.739833	+	0.739833i	0.0279630	+	0.0279630i
$701$	14.4108			0.544287			0.272144	−	0.962257i	$-0.412267\pi$
$701$	14.4108			0.544287			0.272144	+	0.962257i	$0.412267\pi$
$702$	−0.151333	−	5.42013i	−0.00571168	−	0.204570i
$703$			28.5358i			1.07625i
$704$	17.9190	−	13.1290i	0.675349	−	0.494819i
$705$	4.07548			0.153492
$706$	−26.6941			−1.00465
$707$	−2.50633	−	2.50633i	−0.0942601	−	0.0942601i
$708$	−1.49538	−	1.49538i	−0.0561999	−	0.0561999i
$709$	10.7215	−	10.7215i	0.402653	−	0.402653i	−0.476514	−	0.879167i	$-0.658100\pi$
$709$	10.7215	−	10.7215i	0.402653	−	0.402653i	0.879167	+	0.476514i	$0.158100\pi$
$710$	7.76667	+	7.76667i	0.291478	+	0.291478i
$711$			7.59368i			0.284785i
$712$	−13.0671			−0.489710
$713$	23.7589	−	23.7589i	0.889779	−	0.889779i
$714$	1.14108			0.0427038
$715$	−3.53538	−	4.55302i	−0.132216	−	0.170273i
$716$	2.37407			0.0887231
$717$	−10.9034	+	10.9034i	−0.407196	+	0.407196i
$718$	21.0041			0.783867
$719$		−	11.7786i		−	0.439269i	−0.975582	−	0.219635i	$-0.929513\pi$
$719$		−	11.7786i		−	0.439269i	0.975582	−	0.219635i	$-0.0704865\pi$
$720$	1.51845	+	1.51845i	0.0565891	+	0.0565891i
$721$	−9.17625	+	9.17625i	−0.341741	+	0.341741i
$722$	−7.06321	−	7.06321i	−0.262865	−	0.262865i
$723$	−20.0666	−	20.0666i	−0.746285	−	0.746285i
$724$	1.34262			0.0498981
$725$	−18.2958			−0.679488
$726$	7.62807	+	14.6788i	0.283104	+	0.544780i
$727$		−	4.53380i		−	0.168149i	−0.996459	−	0.0840746i	$-0.973207\pi$
$727$		−	4.53380i		−	0.168149i	0.996459	−	0.0840746i	$-0.0267934\pi$
$728$	5.74537	+	5.43326i	0.212938	+	0.201370i
$729$	1.00000			0.0370370
$730$	7.48550	+	7.48550i	0.277051	+	0.277051i
$731$	−10.0192			−0.370573
$732$	−0.932475			−0.0344653
$733$	14.5897	−	14.5897i	0.538883	−	0.538883i	−0.384318	−	0.923201i	$-0.625563\pi$
$733$	14.5897	−	14.5897i	0.538883	−	0.538883i	0.923201	+	0.384318i	$0.125563\pi$
$734$	11.8628	−	11.8628i	0.437864	−	0.437864i
$735$	−2.14613	+	2.14613i	−0.0791611	+	0.0791611i
$736$	4.40455	+	4.40455i	0.162354	+	0.162354i
$737$	−7.18108	+	46.5466i	−0.264518	+	1.71457i
$738$			6.19316i			0.227974i
$739$	10.8534	+	10.8534i	0.399248	+	0.399248i	0.877968	−	0.478720i	$-0.158899\pi$
$739$	10.8534	+	10.8534i	0.399248	+	0.399248i	−0.478720	+	0.877968i	$0.658899\pi$
$740$		−	1.02363i		−	0.0376293i
$741$	−0.353750	−	12.6699i	−0.0129953	−	0.465441i
$742$	4.02991			0.147943
$743$	10.8987	−	10.8987i	0.399836	−	0.399836i	−0.478339	−	0.878175i	$-0.658761\pi$
$743$	10.8987	−	10.8987i	0.399836	−	0.399836i	0.878175	+	0.478339i	$0.158761\pi$
$744$			20.7400i			0.760367i
$745$	−8.71725			−0.319375
$746$	17.2213	+	17.2213i	0.630518	+	0.630518i
$747$	5.02820	−	5.02820i	0.183972	−	0.183972i
$748$	0.633011	−	0.463799i	0.0231452	−	0.0169582i
$749$	−1.02590	+	1.02590i	−0.0374855	+	0.0374855i
$750$		−	7.08087i		−	0.258557i
$751$			14.3910i			0.525136i	0.964913	+	0.262568i	$0.0845694\pi$
$751$			14.3910i			0.525136i	−0.964913	+	0.262568i	$0.915431\pi$
$752$	−26.6317	+	26.6317i	−0.971158	+	0.971158i
$753$		−	10.5928i		−	0.386023i
$754$	20.7997	−	0.580738i	0.757482	−	0.0211492i
$755$		−	0.655419i		−	0.0238531i
$756$	0.155178	−	0.155178i	0.00564378	−	0.00564378i
$757$	−31.3586			−1.13975			−0.569874	−	0.821732i	$-0.693008\pi$
$757$	−31.3586			−1.13975			−0.569874	+	0.821732i	$0.693008\pi$
$758$	−33.0541			−1.20058
$759$	11.3311	−	8.30217i	0.411294	−	0.301350i
$760$	3.13259	+	3.13259i	0.113631	+	0.113631i
$761$	15.8784	+	15.8784i	0.575591	+	0.575591i	0.933685	−	0.358095i	$-0.116574\pi$
$761$	15.8784	+	15.8784i	0.575591	+	0.575591i	−0.358095	+	0.933685i	$0.616574\pi$
$762$	−9.53552	+	9.53552i	−0.345435	+	0.345435i
$763$	12.9473			0.468722
$764$		−	4.00239i		−	0.144801i
$765$	−0.308297	−	0.308297i	−0.0111465	−	0.0111465i
$766$	41.0565			1.48343
$767$	0.813503	+	29.1365i	0.0293739	+	1.05206i
$768$	−6.17560			−0.222843
$769$	29.6154	−	29.6154i	1.06796	−	1.06796i	0.0704438	−	0.997516i	$-0.477558\pi$
$769$	29.6154	−	29.6154i	1.06796	−	1.06796i	0.997516	−	0.0704438i	$-0.0224416\pi$
$770$	0.307539	−	1.99342i	0.0110829	−	0.0718379i
$771$		−	3.34272i		−	0.120385i
$772$	0.790728	−	0.790728i	0.0284589	−	0.0284589i
$773$	−6.78348	−	6.78348i	−0.243985	−	0.243985i	0.574512	−	0.818496i	$-0.305192\pi$
$773$	−6.78348	−	6.78348i	−0.243985	−	0.243985i	−0.818496	+	0.574512i	$0.805192\pi$
$774$	−11.7796	+	11.7796i	−0.423408	+	0.423408i
$775$	26.7448	−	26.7448i	0.960701	−	0.960701i
$776$		−	0.210678i		−	0.00756291i
$777$	6.80977			0.244299
$778$	−33.5526	−	33.5526i	−1.20292	−	1.20292i
$779$			14.4769i			0.518690i
$780$	0.0126896	+	0.454491i	0.000454360	+	0.0162734i
$781$	−7.66200	+	49.6639i	−0.274168	+	1.77712i
$782$	−4.07359	−	4.07359i	−0.145671	−	0.145671i
$783$			3.83750i			0.137141i
$784$		−	28.0482i		−	1.00172i
$785$	−0.475538	−	0.475538i	−0.0169727	−	0.0169727i
$786$	−8.42003	−	8.42003i	−0.300332	−	0.300332i
$787$	32.1568	+	32.1568i	1.14627	+	1.14627i	0.987281	+	0.158985i	$0.0508221\pi$
$787$	32.1568	+	32.1568i	1.14627	+	1.14627i	0.158985	+	0.987281i	$0.449178\pi$
$788$	−0.636482	−	0.636482i	−0.0226737	−	0.0226737i
$789$		−	2.69990i		−	0.0961192i
$790$		−	5.50490i		−	0.195856i
$791$	1.43836	+	1.43836i	0.0511421	+	0.0511421i
$792$	−1.32205	+	8.56932i	−0.0469770	+	0.304498i
$793$	9.33794	+	8.83067i	0.331600	+	0.313586i
$794$		−	28.7423i		−	1.02003i
$795$	−1.08880	−	1.08880i	−0.0386158	−	0.0386158i
$796$	−3.16271			−0.112099
$797$			11.2998i			0.400260i	0.979769	+	0.200130i	$0.0641365\pi$
$797$			11.2998i			0.400260i	−0.979769	+	0.200130i	$0.935864\pi$
$798$	3.13601	−	3.13601i	0.111013	−	0.111013i
$799$	5.40716	−	5.40716i	0.191292	−	0.191292i
$800$	4.95809	+	4.95809i	0.175295	+	0.175295i
$801$	3.53432	−	3.53432i	0.124879	−	0.124879i
$802$		−	49.4760i		−	1.74706i
$803$	−7.38463	+	47.8660i	−0.260598	+	1.68916i
$804$	2.62674	−	2.62674i	0.0926381	−	0.0926381i
$805$	−1.71275			−0.0603663
$806$	−29.5562	+	31.2540i	−1.04107	+	1.10088i
$807$	−24.0709			−0.847337
$808$	−7.81057	−	7.81057i	−0.274775	−	0.274775i
$809$		−	11.2868i		−	0.396822i	−0.980119	−	0.198411i	$-0.936422\pi$
$809$		−	11.2868i		−	0.396822i	0.980119	−	0.198411i	$-0.0635781\pi$
$810$	−0.724932			−0.0254715
$811$	−16.0782	+	16.0782i	−0.564583	+	0.564583i	−0.930606	−	0.366023i	$-0.880719\pi$
$811$	−16.0782	+	16.0782i	−0.564583	+	0.564583i	0.366023	+	0.930606i	$0.380719\pi$
$812$	0.595496	+	0.595496i	0.0208978	+	0.0208978i
$813$	14.5615	+	14.5615i	0.510696	+	0.510696i
$814$	32.6596	−	23.9292i	1.14472	−	0.838718i
$815$	−4.48414			−0.157073
$816$	4.02921			0.141050
$817$	−27.5355	+	27.5355i	−0.963347	+	0.963347i
$818$		−	31.8401i		−	1.11326i
$819$	−3.02354	+	0.0844186i	−0.105651	+	0.00294982i
$820$		−	0.519311i		−	0.0181351i
$821$	−13.3586	+	13.3586i	−0.466219	+	0.466219i	−0.900687	−	0.434468i	$-0.856936\pi$
$821$	−13.3586	+	13.3586i	−0.466219	+	0.466219i	0.434468	+	0.900687i	$0.356936\pi$
$822$		−	18.3861i		−	0.641287i
$823$		−	1.49260i		−	0.0520287i	−0.999662	−	0.0260144i	$-0.991718\pi$
$823$		−	1.49260i		−	0.0520287i	0.999662	−	0.0260144i	$-0.00828156\pi$
$824$	−28.5963	+	28.5963i	−0.996200	+	0.996200i
$825$	12.7552	−	9.34554i	0.444078	−	0.325370i
$826$	−7.21174	+	7.21174i	−0.250929	+	0.250929i
$827$	4.46825	+	4.46825i	0.155376	+	0.155376i	0.780514	−	0.625138i	$-0.214957\pi$
$827$	4.46825	+	4.46825i	0.155376	+	0.155376i	−0.625138	+	0.780514i	$0.714957\pi$
$828$	−1.10796			−0.0385042
$829$		−	6.17244i		−	0.214378i	−0.994239	−	0.107189i	$-0.965815\pi$
$829$		−	6.17244i		−	0.214378i	0.994239	−	0.107189i	$-0.0341850\pi$
$830$	−3.64510	+	3.64510i	−0.126523	+	0.126523i
$831$	−14.0099			−0.485999
$832$	17.5460	+	16.5928i	0.608298	+	0.575253i
$833$			5.69477i			0.197312i
$834$	4.65343	+	4.65343i	0.161135	+	0.161135i
$835$			10.9058i			0.377412i
$836$	0.465044	−	3.01434i	0.0160839	−	0.104253i
$837$	−5.60966	−	5.60966i	−0.193898	−	0.193898i
$838$	34.1290	−	34.1290i	1.17897	−	1.17897i
$839$	11.5079	−	11.5079i	0.397297	−	0.397297i	−0.479981	−	0.877279i	$-0.659357\pi$
$839$	11.5079	−	11.5079i	0.397297	−	0.397297i	0.877279	+	0.479981i	$0.159357\pi$
$840$	0.747560	−	0.747560i	0.0257933	−	0.0257933i
$841$	14.2736			0.492194
$842$	28.5379			0.983481
$843$	10.0982	+	10.0982i	0.347800	+	0.347800i
$844$	−2.84356			−0.0978794
$845$	4.17702	−	4.67151i	0.143694	−	0.160705i
$846$		−	12.7144i		−	0.437131i
$847$	8.18831	−	4.25520i	0.281354	−	0.146211i
$848$	14.2298			0.488653
$849$	1.31783			0.0452279
$850$	−4.58554	−	4.58554i	−0.157283	−	0.157283i
$851$	−24.3105	−	24.3105i	−0.833354	−	0.833354i
$852$	2.80266	−	2.80266i	0.0960176	−	0.0960176i
$853$	5.12828	+	5.12828i	0.175589	+	0.175589i	0.789430	−	0.613841i	$-0.210376\pi$
$853$	5.12828	+	5.12828i	0.175589	+	0.175589i	−0.613841	+	0.789430i	$0.710376\pi$
$854$			4.49702i			0.153885i
$855$	−1.69458			−0.0579533
$856$	−3.19705	+	3.19705i	−0.109273	+	0.109273i
$857$	−35.7213			−1.22022			−0.610108	−	0.792318i	$-0.708874\pi$
$857$	−35.7213			−1.22022			−0.610108	+	0.792318i	$0.708874\pi$
$858$	−14.2042	+	11.0294i	−0.484924	+	0.376539i
$859$	30.2899			1.03348			0.516739	−	0.856143i	$-0.327146\pi$
$859$	30.2899			1.03348			0.516739	+	0.856143i	$0.327146\pi$
$860$	0.987745	−	0.987745i	0.0336818	−	0.0336818i
$861$	3.45476			0.117738
$862$			21.4940i			0.732088i
$863$	−35.6355	−	35.6355i	−1.21305	−	1.21305i	−0.970020	−	0.243026i	$-0.921860\pi$
$863$	−35.6355	−	35.6355i	−1.21305	−	1.21305i	−0.243026	−	0.970020i	$-0.578140\pi$
$864$	1.03995	−	1.03995i	0.0353798	−	0.0353798i
$865$	7.08436	+	7.08436i	0.240875	+	0.240875i
$866$	6.34624	+	6.34624i	0.215654	+	0.215654i
$867$	16.1819			0.549567
$868$	−1.74100			−0.0590932
$869$	20.3159	−	14.8852i	0.689169	−	0.504945i
$870$		−	2.78192i		−	0.0943161i
$871$	−51.1802	+	1.42898i	−1.73418	+	0.0484190i
$872$	40.3481			1.36636
$873$	0.0569832	+	0.0569832i	0.00192859	+	0.00192859i
$874$	−22.3908			−0.757379
$875$	−3.94995			−0.133533
$876$	2.70120	−	2.70120i	0.0912651	−	0.0912651i
$877$	11.0527	−	11.0527i	0.373222	−	0.373222i	−0.495427	−	0.868649i	$-0.664989\pi$
$877$	11.0527	−	11.0527i	0.373222	−	0.373222i	0.868649	+	0.495427i	$0.164989\pi$
$878$	−23.7666	+	23.7666i	−0.802085	+	0.802085i
$879$	18.6057	+	18.6057i	0.627555	+	0.627555i
$880$	1.08593	−	7.03886i	0.0366069	−	0.237280i
$881$		−	3.31294i		−	0.111616i	−0.998442	−	0.0558078i	$-0.982227\pi$
$881$		−	3.31294i		−	0.111616i	0.998442	−	0.0558078i	$-0.0177734\pi$
$882$	6.69536	+	6.69536i	0.225444	+	0.225444i
$883$			45.5406i			1.53256i	0.642504	+	0.766282i	$0.277895\pi$
$883$			45.5406i			1.53256i	−0.642504	+	0.766282i	$0.722105\pi$
$884$	0.619833	+	0.586161i	0.0208472	+	0.0197147i
$885$	3.89694			0.130994
$886$	−9.04037	+	9.04037i	−0.303717	+	0.303717i
$887$			4.15521i			0.139518i	0.997564	+	0.0697591i	$0.0222231\pi$
$887$			4.15521i			0.139518i	−0.997564	+	0.0697591i	$0.977777\pi$
$888$	21.2216			0.712149
$889$	5.31924	+	5.31924i	0.178402	+	0.178402i
$890$	−2.56214	+	2.56214i	−0.0858832	+	0.0858832i
$891$	−1.96021	−	2.67537i	−0.0656694	−	0.0896282i
$892$	−2.89908	+	2.89908i	−0.0970685	+	0.0970685i
$893$		−	29.7208i		−	0.994569i
$894$			27.1955i			0.909555i
$895$	−3.09339	+	3.09339i	−0.103401	+	0.103401i
$896$			10.9175i			0.364727i
$897$	11.0952	+	10.4925i	0.370460	+	0.350335i
$898$			57.8664i			1.93103i
$899$	21.5271	−	21.5271i	0.717967	−	0.717967i
$900$	−1.24720			−0.0415733
$901$	−2.88914			−0.0962514
$902$	16.5690	−	12.1399i	0.551687	−	0.404214i
$903$	6.57106	+	6.57106i	0.218671	+	0.218671i
$904$	4.48242	+	4.48242i	0.149083	+	0.149083i
$905$	−1.74942	+	1.74942i	−0.0581528	+	0.0581528i
$906$	−2.04473			−0.0679318
$907$		−	27.8469i		−	0.924642i	−0.886713	−	0.462321i	$-0.847017\pi$
$907$		−	27.8469i		−	0.924642i	0.886713	−	0.462321i	$-0.152983\pi$
$908$	0.728497	+	0.728497i	0.0241760	+	0.0241760i
$909$	4.22512			0.140139
$910$	2.19186	−	0.0611977i	0.0726594	−	0.00202868i
$911$	0.853342			0.0282725			0.0141362	−	0.999900i	$-0.495500\pi$
$911$	0.853342			0.0282725			0.0141362	+	0.999900i	$0.495500\pi$
$912$	11.0734	−	11.0734i	0.366677	−	0.366677i
$913$	−23.3086	−	3.59598i	−0.771401	−	0.119009i
$914$		−	21.4642i		−	0.709972i
$915$	1.21501	−	1.21501i	0.0401669	−	0.0401669i
$916$	−1.87365	−	1.87365i	−0.0619070	−	0.0619070i
$917$	−4.69698	+	4.69698i	−0.155108	+	0.155108i
$918$	−0.961806	+	0.961806i	−0.0317443	+	0.0317443i
$919$			9.14685i			0.301727i	0.988555	+	0.150863i	$0.0482053\pi$
$919$			9.14685i			0.301727i	−0.988555	+	0.150863i	$0.951795\pi$
$920$	−5.33750			−0.175972
$921$	−4.32402	−	4.32402i	−0.142481	−	0.142481i
$922$		−	8.90987i		−	0.293431i
$923$	−54.6079	+	1.52468i	−1.79744	+	0.0501853i
$924$	−0.719340	−	0.110978i	−0.0236646	−	0.00365090i
$925$	−27.3657	−	27.3657i	−0.899779	−	0.899779i
$926$			23.6490i			0.777153i
$927$		−	15.4692i		−	0.508074i
$928$	3.99080	+	3.99080i	0.131004	+	0.131004i
$929$	1.36910	+	1.36910i	0.0449187	+	0.0449187i	0.729209	−	0.684291i	$-0.239888\pi$
$929$	1.36910	+	1.36910i	0.0449187	+	0.0449187i	−0.684291	+	0.729209i	$0.739888\pi$
$930$	4.06662	+	4.06662i	0.133350	+	0.133350i
$931$	15.6508	+	15.6508i	0.512935	+	0.512935i
$932$			1.63003i			0.0533935i
$933$		−	25.3397i		−	0.829583i
$934$	−33.9522	−	33.9522i	−1.11095	−	1.11095i
$935$	−0.220483	+	1.42913i	−0.00721055	+	0.0467377i
$936$	−9.42238	+	0.263077i	−0.307980	+	0.00859894i
$937$			28.2759i			0.923733i	0.886950	+	0.461866i	$0.152820\pi$
$937$			28.2759i			0.923733i	−0.886950	+	0.461866i	$0.847180\pi$
$938$	−12.6679	−	12.6679i	−0.413622	−	0.413622i
$939$	2.06572			0.0674123
$940$			1.06613i			0.0347735i
$941$	14.4692	−	14.4692i	0.471682	−	0.471682i	−0.430777	−	0.902458i	$-0.641760\pi$
$941$	14.4692	−	14.4692i	0.471682	−	0.471682i	0.902458	+	0.430777i	$0.141760\pi$
$942$	−1.48355	+	1.48355i	−0.0483368	+	0.0483368i
$943$	−12.3333	−	12.3333i	−0.401628	−	0.401628i
$944$	−25.4650	+	25.4650i	−0.828815	+	0.828815i
$945$			0.404392i			0.0131549i
$946$	54.6051	+	8.42432i	1.77537	+	0.273898i
$947$	−24.9844	+	24.9844i	−0.811883	+	0.811883i	−0.984916	−	0.173033i	$-0.944643\pi$
$947$	−24.9844	+	24.9844i	−0.811883	+	0.811883i	0.173033	+	0.984916i	$0.444643\pi$
$948$	−1.98648			−0.0645180
$949$	−52.6310	+	1.46948i	−1.70847	+	0.0477013i
$950$	−25.2047			−0.817748
$951$	−11.9778	−	11.9778i	−0.388407	−	0.388407i
$952$		−	1.98365i		−	0.0642906i
$953$	−33.6749			−1.09084			−0.545419	−	0.838164i	$-0.683629\pi$
$953$	−33.6749			−1.09084			−0.545419	+	0.838164i	$0.683629\pi$
$954$	−3.39678	+	3.39678i	−0.109975	+	0.109975i
$955$	5.21508	+	5.21508i	0.168756	+	0.168756i
$956$	−2.85231	−	2.85231i	−0.0922502	−	0.0922502i
$957$	10.2667	−	7.52228i	0.331876	−	0.243161i
$958$	−49.1474			−1.58788
$959$	−10.2564			−0.331196
$960$	2.28300	−	2.28300i	0.0736835	−	0.0736835i
$961$			31.9366i			1.03021i
$962$	31.9796	+	30.2424i	1.03107	+	0.975053i
$963$		−	1.72944i		−	0.0557306i
$964$	5.24937	−	5.24937i	0.169071	−	0.169071i
$965$			2.06062i			0.0663338i
$966$			5.34331i			0.171918i
$967$	−4.46666	+	4.46666i	−0.143638	+	0.143638i	−0.775269	−	0.631631i	$-0.782386\pi$
$967$	−4.46666	+	4.46666i	−0.143638	+	0.143638i	0.631631	+	0.775269i	$0.282386\pi$
$968$	25.5176	−	13.2607i	0.820166	−	0.426214i
$969$	−2.24828	+	2.24828i	−0.0722253	+	0.0722253i
$970$	−0.0413089	−	0.0413089i	−0.00132635	−	0.00132635i
$971$	9.86851			0.316696			0.158348	−	0.987383i	$-0.449383\pi$
$971$	9.86851			0.316696			0.158348	+	0.987383i	$0.449383\pi$
$972$			0.261597i			0.00839073i
$973$	2.59584	−	2.59584i	0.0832189	−	0.0832189i
$974$	24.4765			0.784278
$975$	12.4896	+	11.8111i	0.399988	+	0.378259i
$976$			15.8792i			0.508281i
$977$	−3.67733	−	3.67733i	−0.117648	−	0.117648i	0.645832	−	0.763480i	$-0.276511\pi$
$977$	−3.67733	−	3.67733i	−0.117648	−	0.117648i	−0.763480	+	0.645832i	$0.776511\pi$
$978$			13.9893i			0.447330i
$979$	−16.3836	−	2.52761i	−0.523622	−	0.0807829i
$980$	−0.561421	−	0.561421i	−0.0179339	−	0.0179339i
$981$	−10.9131	+	10.9131i	−0.348430	+	0.348430i
$982$	−15.8852	+	15.8852i	−0.506916	+	0.506916i
$983$	−3.59212	+	3.59212i	−0.114571	+	0.114571i	−0.762068	−	0.647497i	$-0.775816\pi$
$983$	−3.59212	+	3.59212i	−0.114571	+	0.114571i	0.647497	+	0.762068i	$0.275816\pi$
$984$	10.7662			0.343214
$985$	1.65866			0.0528493
$986$	−3.69093	−	3.69093i	−0.117543	−	0.117543i
$987$	−7.09255			−0.225758
$988$	3.31441	−	0.0925399i	0.105446	−	0.00294409i
$989$		−	46.9167i		−	1.49186i
$990$	1.42102	+	1.93946i	0.0451628	+	0.0616401i
$991$	−19.1798			−0.609266			−0.304633	−	0.952470i	$-0.598534\pi$
$991$	−19.1798			−0.609266			−0.304633	+	0.952470i	$0.598534\pi$
$992$	−11.6675			−0.370444
$993$	−16.0602	−	16.0602i	−0.509654	−	0.509654i
$994$	−13.5163	−	13.5163i	−0.428712	−	0.428712i
$995$	4.12098	−	4.12098i	0.130644	−	0.130644i
$996$	1.31536	+	1.31536i	0.0416788	+	0.0416788i
$997$		−	18.5649i		−	0.587957i	−0.955812	−	0.293978i	$-0.905021\pi$
$997$		−	18.5649i		−	0.587957i	0.955812	−	0.293978i	$-0.0949793\pi$
$998$	−20.3050			−0.642745
$999$	−5.73990	+	5.73990i	−0.181602	+	0.181602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.a.307.4	yes	28
11.10	odd	2	inner	429.2.m.a.307.11	yes	28
13.5	odd	4	inner	429.2.m.a.109.11	yes	28
143.109	even	4	inner	429.2.m.a.109.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.a.109.4	✓	28	143.109	even	4	inner
429.2.m.a.109.11	yes	28	13.5	odd	4	inner
429.2.m.a.307.4	yes	28	1.1	even	1	trivial
429.2.m.a.307.11	yes	28	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06339 + 1.06339i) q^{2} -1.00000 q^{3} -0.261597i q^{4} +(0.340859 + 0.340859i) q^{5} +(1.06339 - 1.06339i) q^{6} +(-0.593196 - 0.593196i) q^{7} +(-1.84860 - 1.84860i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.06339 + 1.06339i) q^{2} -1.00000 q^{3} -0.261597i q^{4} +(0.340859 + 0.340859i) q^{5} +(1.06339 - 1.06339i) q^{6} +(-0.593196 - 0.593196i) q^{7} +(-1.84860 - 1.84860i) q^{8} +1.00000 q^{9} -0.724932 q^{10} +(-1.96021 - 2.67537i) q^{11} +0.261597i q^{12} +(2.47736 - 2.61967i) q^{13} +1.26160 q^{14} +(-0.340859 - 0.340859i) q^{15} +4.45476 q^{16} -0.904472 q^{17} +(-1.06339 + 1.06339i) q^{18} +(-2.48574 + 2.48574i) q^{19} +(0.0891677 - 0.0891677i) q^{20} +(0.593196 + 0.593196i) q^{21} +(4.92942 + 0.760497i) q^{22} -4.23536i q^{23} +(1.84860 + 1.84860i) q^{24} -4.76763i q^{25} +(0.151333 + 5.42013i) q^{26} -1.00000 q^{27} +(-0.155178 + 0.155178i) q^{28} -3.83750i q^{29} +0.724932 q^{30} +(5.60966 + 5.60966i) q^{31} +(-1.03995 + 1.03995i) q^{32} +(1.96021 + 2.67537i) q^{33} +(0.961806 - 0.961806i) q^{34} -0.404392i q^{35} -0.261597i q^{36} +(5.73990 - 5.73990i) q^{37} -5.28663i q^{38} +(-2.47736 + 2.61967i) q^{39} -1.26022i q^{40} +(2.91199 - 2.91199i) q^{41} -1.26160 q^{42} +11.0774 q^{43} +(-0.699868 + 0.512784i) q^{44} +(0.340859 + 0.340859i) q^{45} +(4.50384 + 4.50384i) q^{46} +(-5.97825 + 5.97825i) q^{47} -4.45476 q^{48} -6.29624i q^{49} +(5.06985 + 5.06985i) q^{50} +0.904472 q^{51} +(-0.685299 - 0.648070i) q^{52} +3.19429 q^{53} +(1.06339 - 1.06339i) q^{54} +(0.243769 - 1.58008i) q^{55} +2.19316i q^{56} +(2.48574 - 2.48574i) q^{57} +(4.08076 + 4.08076i) q^{58} +(-5.71636 + 5.71636i) q^{59} +(-0.0891677 + 0.0891677i) q^{60} +3.56455i q^{61} -11.9305 q^{62} +(-0.593196 - 0.593196i) q^{63} +6.69778i q^{64} +(1.73737 - 0.0485081i) q^{65} +(-4.92942 - 0.760497i) q^{66} +(-10.0412 - 10.0412i) q^{67} +0.236607i q^{68} +4.23536i q^{69} +(0.430027 + 0.430027i) q^{70} +(-10.7137 - 10.7137i) q^{71} +(-1.84860 - 1.84860i) q^{72} +(-10.3258 - 10.3258i) q^{73} +12.2075i q^{74} +4.76763i q^{75} +(0.650263 + 0.650263i) q^{76} +(-0.424231 + 2.74980i) q^{77} +(-0.151333 - 5.42013i) q^{78} +7.59368i q^{79} +(1.51845 + 1.51845i) q^{80} +1.00000 q^{81} +6.19316i q^{82} +(5.02820 - 5.02820i) q^{83} +(0.155178 - 0.155178i) q^{84} +(-0.308297 - 0.308297i) q^{85} +(-11.7796 + 11.7796i) q^{86} +3.83750i q^{87} +(-1.32205 + 8.56932i) q^{88} +(3.53432 - 3.53432i) q^{89} -0.724932 q^{90} +(-3.02354 + 0.0844186i) q^{91} -1.10796 q^{92} +(-5.60966 - 5.60966i) q^{93} -12.7144i q^{94} -1.69458 q^{95} +(1.03995 - 1.03995i) q^{96} +(0.0569832 + 0.0569832i) q^{97} +(6.69536 + 6.69536i) q^{98} +(-1.96021 - 2.67537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more