LMFDB - Embedded newform 429.2.s.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Character	$\chi$	$=$	429.199
Dual form			429.2.s.b.166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14836 - 1.24036i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.07696 + 3.59741i) q^{4} +0.0418579i q^{5} +(2.14836 - 1.24036i) q^{6} +(-3.59366 + 2.07480i) q^{7} -5.34327i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.14836 - 1.24036i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.07696 + 3.59741i) q^{4} +0.0418579i q^{5} +(2.14836 - 1.24036i) q^{6} +(-3.59366 + 2.07480i) q^{7} -5.34327i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0519187 - 0.0899258i) q^{10} +(0.866025 + 0.500000i) q^{11} -4.15393 q^{12} +(-2.67075 + 2.42220i) q^{13} +10.2939 q^{14} +(-0.0362500 - 0.0209289i) q^{15} +(-2.47363 + 4.28444i) q^{16} +(-2.02096 - 3.50040i) q^{17} +2.48071i q^{18} +(0.934832 - 0.539726i) q^{19} +(-0.150580 + 0.0869373i) q^{20} -4.14960i q^{21} +(-1.24036 - 2.14836i) q^{22} +(4.60578 - 7.97744i) q^{23} +(4.62741 + 2.67163i) q^{24} +4.99825 q^{25} +(8.74213 - 1.89108i) q^{26} +1.00000 q^{27} +(-14.9278 - 8.61856i) q^{28} +(-0.227219 + 0.393556i) q^{29} +(0.0519187 + 0.0899258i) q^{30} -4.20347i q^{31} +(1.37366 - 0.793081i) q^{32} +(-0.866025 + 0.500000i) q^{33} +10.0268i q^{34} +(-0.0868467 - 0.150423i) q^{35} +(2.07696 - 3.59741i) q^{36} +(-9.10494 - 5.25674i) q^{37} -2.67781 q^{38} +(-0.762313 - 3.52404i) q^{39} +0.223658 q^{40} +(-3.50226 - 2.02203i) q^{41} +(-5.14697 + 8.91482i) q^{42} +(3.31806 + 5.74705i) q^{43} +4.15393i q^{44} +(0.0362500 - 0.0209289i) q^{45} +(-19.7897 + 11.4256i) q^{46} -5.44687i q^{47} +(-2.47363 - 4.28444i) q^{48} +(5.10958 - 8.85004i) q^{49} +(-10.7380 - 6.19960i) q^{50} +4.04191 q^{51} +(-14.2607 - 4.57696i) q^{52} -12.4710 q^{53} +(-2.14836 - 1.24036i) q^{54} +(-0.0209289 + 0.0362500i) q^{55} +(11.0862 + 19.2019i) q^{56} +1.07945i q^{57} +(0.976298 - 0.563666i) q^{58} +(-1.53204 + 0.884525i) q^{59} -0.173875i q^{60} +(-4.46559 - 7.73463i) q^{61} +(-5.21380 + 9.03057i) q^{62} +(3.59366 + 2.07480i) q^{63} +5.95969 q^{64} +(-0.101388 - 0.111792i) q^{65} +2.48071 q^{66} +(10.0773 + 5.81812i) q^{67} +(8.39490 - 14.5404i) q^{68} +(4.60578 + 7.97744i) q^{69} +0.430883i q^{70} +(-4.63347 + 2.67513i) q^{71} +(-4.62741 + 2.67163i) q^{72} -9.96335i q^{73} +(13.0404 + 22.5867i) q^{74} +(-2.49912 + 4.32861i) q^{75} +(3.88323 + 2.24198i) q^{76} -4.14960 q^{77} +(-2.73334 + 8.51645i) q^{78} +4.52858 q^{79} +(-0.179338 - 0.103541i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.01608 + 8.68810i) q^{82} -7.60730i q^{83} +(14.9278 - 8.61856i) q^{84} +(0.146519 - 0.0845930i) q^{85} -16.4623i q^{86} +(-0.227219 - 0.393556i) q^{87} +(2.67163 - 4.62741i) q^{88} +(-2.34979 - 1.35665i) q^{89} -0.103837 q^{90} +(4.57219 - 14.2458i) q^{91} +38.2641 q^{92} +(3.64032 + 2.10174i) q^{93} +(-6.75606 + 11.7018i) q^{94} +(0.0225918 + 0.0391301i) q^{95} +1.58616i q^{96} +(-7.33448 + 4.23456i) q^{97} +(-21.9544 + 12.6754i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−2.14836	−	1.24036i	−1.51912	−	0.877064i	−0.999746	−	0.0225157i	$-0.992832\pi$
$2$	−2.14836	−	1.24036i	−1.51912	−	0.877064i	−0.519372	−	0.854548i	$-0.673834\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	2.07696	+	3.59741i	1.03848	+	1.79870i
$5$			0.0418579i			0.0187194i	0.999956	+	0.00935971i	$0.00297933\pi$
$5$			0.0418579i			0.0187194i	−0.999956	+	0.00935971i	$0.997021\pi$
$6$	2.14836	−	1.24036i	0.877064	−	0.506373i
$7$	−3.59366	+	2.07480i	−1.35827	+	0.784200i	−0.989391	−	0.145276i	$-0.953593\pi$
$7$	−3.59366	+	2.07480i	−1.35827	+	0.784200i	−0.368883	+	0.929476i	$0.620260\pi$
$8$		−	5.34327i		−	1.88913i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.0519187	−	0.0899258i	0.0164181	−	0.0284370i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$	−4.15393			−1.19914
$13$	−2.67075	+	2.42220i	−0.740734	+	0.671798i
$13$	−2.67075	+	2.42220i	−0.740734	+	0.671798i
$14$	10.2939			2.75117
$15$	−0.0362500	−	0.0209289i	−0.00935971	−	0.00540383i
$16$	−2.47363	+	4.28444i	−0.618406	+	1.07111i
$17$	−2.02096	−	3.50040i	−0.490154	−	0.848971i	0.509782	−	0.860304i	$-0.329726\pi$
$17$	−2.02096	−	3.50040i	−0.490154	−	0.848971i	−0.999936	+	0.0113323i	$0.996393\pi$
$18$			2.48071i			0.584709i
$19$	0.934832	−	0.539726i	0.214465	−	0.123822i	−0.388920	−	0.921272i	$-0.627152\pi$
$19$	0.934832	−	0.539726i	0.214465	−	0.123822i	0.603385	+	0.797450i	$0.293818\pi$
$20$	−0.150580	+	0.0869373i	−0.0336707	+	0.0194398i
$21$		−	4.14960i		−	0.905516i
$22$	−1.24036	−	2.14836i	−0.264445	−	0.458032i
$23$	4.60578	−	7.97744i	0.960371	−	1.66341i	0.238804	−	0.971068i	$-0.423245\pi$
$23$	4.60578	−	7.97744i	0.960371	−	1.66341i	0.721567	−	0.692344i	$-0.243422\pi$
$24$	4.62741	+	2.67163i	0.944565	+	0.545345i
$25$	4.99825			0.999650
$26$	8.74213	−	1.89108i	1.71447	−	0.370871i
$27$	1.00000			0.192450
$28$	−14.9278	−	8.61856i	−2.82109	−	1.62875i
$29$	−0.227219	+	0.393556i	−0.0421936	+	0.0730815i	−0.886351	−	0.463014i	$-0.846768\pi$
$29$	−0.227219	+	0.393556i	−0.0421936	+	0.0730815i	0.844157	+	0.536095i	$0.180101\pi$
$30$	0.0519187	+	0.0899258i	0.00947901	+	0.0164181i
$31$		−	4.20347i		−	0.754966i	−0.926016	−	0.377483i	$-0.876790\pi$
$31$		−	4.20347i		−	0.754966i	0.926016	−	0.377483i	$-0.123210\pi$
$32$	1.37366	−	0.793081i	0.242830	−	0.140198i
$33$	−0.866025	+	0.500000i	−0.150756	+	0.0870388i
$34$			10.0268i			1.71958i
$35$	−0.0868467	−	0.150423i	−0.0146798	−	0.0254261i
$36$	2.07696	−	3.59741i	0.346161	−	0.599568i
$37$	−9.10494	−	5.25674i	−1.49684	−	0.864202i	−0.496849	−	0.867837i	$-0.665510\pi$
$37$	−9.10494	−	5.25674i	−1.49684	−	0.864202i	−0.999993	+	0.00363470i	$0.998843\pi$
$38$	−2.67781			−0.434398
$39$	−0.762313	−	3.52404i	−0.122068	−	0.564299i
$40$	0.223658			0.0353634
$41$	−3.50226	−	2.02203i	−0.546961	−	0.315788i	0.200934	−	0.979605i	$-0.435602\pi$
$41$	−3.50226	−	2.02203i	−0.546961	−	0.315788i	−0.747896	+	0.663816i	$0.768936\pi$
$42$	−5.14697	+	8.91482i	−0.794195	+	1.37559i
$43$	3.31806	+	5.74705i	0.505999	+	0.876416i	0.999976	+	0.00694109i	$0.00220943\pi$
$43$	3.31806	+	5.74705i	0.505999	+	0.876416i	−0.493977	+	0.869475i	$0.664457\pi$
$44$			4.15393i			0.626228i
$45$	0.0362500	−	0.0209289i	0.00540383	−	0.00311990i
$46$	−19.7897	+	11.4256i	−2.91784	+	1.68461i
$47$		−	5.44687i		−	0.794508i	−0.917709	−	0.397254i	$-0.869963\pi$
$47$		−	5.44687i		−	0.794508i	0.917709	−	0.397254i	$-0.130037\pi$
$48$	−2.47363	−	4.28444i	−0.357037	−	0.618406i
$49$	5.10958	−	8.85004i	0.729939	−	1.26429i
$50$	−10.7380	−	6.19960i	−1.51859	−	0.876756i
$51$	4.04191			0.565981
$52$	−14.2607	−	4.57696i	−1.97760	−	0.634710i
$53$	−12.4710			−1.71303			−0.856515	−	0.516122i	$-0.827375\pi$
$53$	−12.4710			−1.71303			−0.856515	+	0.516122i	$0.827375\pi$
$54$	−2.14836	−	1.24036i	−0.292355	−	0.168791i
$55$	−0.0209289	+	0.0362500i	−0.00282206	+	0.00488795i
$56$	11.0862	+	19.2019i	1.48146	+	2.56596i
$57$			1.07945i			0.142977i
$58$	0.976298	−	0.563666i	0.128194	−	0.0740129i
$59$	−1.53204	+	0.884525i	−0.199455	+	0.115155i	−0.596401	−	0.802687i	$-0.703403\pi$
$59$	−1.53204	+	0.884525i	−0.199455	+	0.115155i	0.396946	+	0.917842i	$0.370070\pi$
$60$		−	0.173875i		−	0.0224471i
$61$	−4.46559	−	7.73463i	−0.571760	−	0.990318i	−0.996385	−	0.0849487i	$-0.972927\pi$
$61$	−4.46559	−	7.73463i	−0.571760	−	0.990318i	0.424625	−	0.905369i	$-0.360406\pi$
$62$	−5.21380	+	9.03057i	−0.662154	+	1.14688i
$63$	3.59366	+	2.07480i	0.452758	+	0.261400i
$64$	5.95969			0.744962
$65$	−0.101388	−	0.111792i	−0.0125757	−	0.0138661i
$66$	2.48071			0.305354
$67$	10.0773	+	5.81812i	1.23114	+	0.710797i	0.967267	−	0.253761i	$-0.0816678\pi$
$67$	10.0773	+	5.81812i	1.23114	+	0.710797i	0.263870	+	0.964558i	$0.415001\pi$
$68$	8.39490	−	14.5404i	1.01803	−	1.76328i
$69$	4.60578	+	7.97744i	0.554471	+	0.960371i
$70$			0.430883i			0.0515004i
$71$	−4.63347	+	2.67513i	−0.549892	+	0.317480i	−0.749078	−	0.662481i	$-0.769503\pi$
$71$	−4.63347	+	2.67513i	−0.549892	+	0.317480i	0.199187	+	0.979962i	$0.436170\pi$
$72$	−4.62741	+	2.67163i	−0.545345	+	0.314855i
$73$		−	9.96335i		−	1.16612i	−0.812428	−	0.583061i	$-0.801855\pi$
$73$		−	9.96335i		−	1.16612i	0.812428	−	0.583061i	$-0.198145\pi$
$74$	13.0404	+	22.5867i	1.51592	+	2.62565i
$75$	−2.49912	+	4.32861i	−0.288574	+	0.499825i
$76$	3.88323	+	2.24198i	0.445436	+	0.257173i
$77$	−4.14960			−0.472890
$78$	−2.73334	+	8.51645i	−0.309490	+	0.964298i
$79$	4.52858			0.509505			0.254752	−	0.967006i	$-0.418006\pi$
$79$	4.52858			0.509505			0.254752	+	0.967006i	$0.418006\pi$
$80$	−0.179338	−	0.103541i	−0.0200506	−	0.0115762i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.01608	+	8.68810i	0.553933	+	0.959440i
$83$		−	7.60730i		−	0.835009i	−0.908675	−	0.417505i	$-0.862905\pi$
$83$		−	7.60730i		−	0.835009i	0.908675	−	0.417505i	$-0.137095\pi$
$84$	14.9278	−	8.61856i	1.62875	−	0.940362i
$85$	0.146519	−	0.0845930i	0.0158922	−	0.00917539i
$86$		−	16.4623i		−	1.77517i
$87$	−0.227219	−	0.393556i	−0.0243605	−	0.0421936i
$88$	2.67163	−	4.62741i	0.284797	−	0.493283i
$89$	−2.34979	−	1.35665i	−0.249078	−	0.143805i	0.370264	−	0.928926i	$-0.379267\pi$
$89$	−2.34979	−	1.35665i	−0.249078	−	0.143805i	−0.619342	+	0.785121i	$0.712600\pi$
$90$	−0.103837			−0.0109454
$91$	4.57219	−	14.2458i	0.479296	−	1.49337i
$92$	38.2641			3.98931
$93$	3.64032	+	2.10174i	0.377483	+	0.217940i
$94$	−6.75606	+	11.7018i	−0.696834	+	1.20695i
$95$	0.0225918	+	0.0391301i	0.00231787	+	0.00401467i
$96$			1.58616i			0.161887i
$97$	−7.33448	+	4.23456i	−0.744703	+	0.429955i	−0.823777	−	0.566914i	$-0.808137\pi$
$97$	−7.33448	+	4.23456i	−0.744703	+	0.429955i	0.0790736	+	0.996869i	$0.474804\pi$
$98$	−21.9544	+	12.6754i	−2.21773	+	1.28041i
$99$		−	1.00000i		−	0.100504i
$100$	10.3812	+	17.9807i	1.03812	+	1.79807i
$101$	4.20718	−	7.28705i	0.418630	−	0.725089i	−0.577172	−	0.816623i	$-0.695844\pi$
$101$	4.20718	−	7.28705i	0.418630	−	0.725089i	0.995802	+	0.0915339i	$0.0291770\pi$
$102$	−8.68348	−	5.01341i	−0.859792	−	0.496401i
$103$	4.39686			0.433235			0.216618	−	0.976257i	$-0.430498\pi$
$103$	4.39686			0.433235			0.216618	+	0.976257i	$0.430498\pi$
$104$	12.9425	+	14.2706i	1.26911	+	1.39934i
$105$	0.173693			0.0169507
$106$	26.7923	+	15.4685i	2.60230	+	1.50244i
$107$	4.85095	−	8.40209i	0.468959	−	0.812261i	−0.530411	−	0.847741i	$-0.677962\pi$
$107$	4.85095	−	8.40209i	0.468959	−	0.812261i	0.999370	+	0.0354793i	$0.0112958\pi$
$108$	2.07696	+	3.59741i	0.199856	+	0.346161i
$109$		−	2.15314i		−	0.206234i	−0.994669	−	0.103117i	$-0.967118\pi$
$109$		−	2.15314i		−	0.206234i	0.994669	−	0.103117i	$-0.0328815\pi$
$110$	0.0899258	−	0.0519187i	0.00857409	−	0.00495025i
$111$	9.10494	−	5.25674i	0.864202	−	0.498947i
$112$		−	20.5291i		−	1.93982i
$113$	6.13932	+	10.6336i	0.577538	+	1.00033i	0.995761	+	0.0919811i	$0.0293199\pi$
$113$	6.13932	+	10.6336i	0.577538	+	1.00033i	−0.418222	+	0.908345i	$0.637347\pi$
$114$	1.33890	−	2.31905i	0.125400	−	0.217199i
$115$	0.333919	+	0.192788i	0.0311381	+	0.0179776i
$116$	−1.88771			−0.175269
$117$	3.43307	+	1.10184i	0.317387	+	0.101865i
$118$	4.38850			0.403994
$119$	14.5252	+	8.38615i	1.33153	+	0.768757i
$120$	−0.111829	+	0.193693i	−0.0102085	+	0.0176817i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$			22.1557i			2.00588i
$123$	3.50226	−	2.02203i	0.315788	−	0.182320i
$124$	15.1216	−	8.73046i	1.35796	−	0.784019i
$125$			0.418506i			0.0374323i
$126$	−5.14697	−	8.91482i	−0.458529	−	0.794195i
$127$	0.742306	−	1.28571i	0.0658690	−	0.114089i	−0.831210	−	0.555958i	$-0.812351\pi$
$127$	0.742306	−	1.28571i	0.0658690	−	0.114089i	0.897079	+	0.441870i	$0.145685\pi$
$128$	−15.5509	−	8.97830i	−1.37452	−	0.793577i
$129$	−6.63612			−0.584277
$130$	0.0791565	+	0.365927i	0.00694249	+	0.0320939i
$131$	−13.1128			−1.14567			−0.572836	−	0.819670i	$-0.694157\pi$
$131$	−13.1128			−1.14567			−0.572836	+	0.819670i	$0.694157\pi$
$132$	−3.59741	−	2.07696i	−0.313114	−	0.180776i
$133$	−2.23964	+	3.87918i	−0.194202	+	0.336367i
$134$	−14.4331	−	24.9988i	−1.24683	−	2.15957i
$135$			0.0418579i			0.00360255i
$136$	−18.7036	+	10.7985i	−1.60382	+	0.925965i
$137$	−17.3151	+	9.99689i	−1.47933	+	0.854092i	−0.999726	−	0.0233935i	$-0.992553\pi$
$137$	−17.3151	+	9.99689i	−1.47933	+	0.854092i	−0.479604	+	0.877485i	$0.659220\pi$
$138$		−	22.8512i		−	1.94522i
$139$	4.65885	+	8.06936i	0.395158	+	0.684434i	0.993121	−	0.117089i	$-0.0373564\pi$
$139$	4.65885	+	8.06936i	0.395158	+	0.684434i	−0.597963	+	0.801524i	$0.704023\pi$
$140$	0.360755	−	0.624845i	0.0304893	−	0.0528091i
$141$	4.71713	+	2.72344i	0.397254	+	0.229355i
$142$	13.2725			1.11380
$143$	−3.52404	+	0.762313i	−0.294695	+	0.0637478i
$144$	4.94725			0.412271
$145$	−0.0164734	−	0.00951093i	−0.00136804	−	0.000789840i
$146$	−12.3581	+	21.4048i	−1.02276	+	1.77148i
$147$	5.10958	+	8.85004i	0.421431	+	0.729939i
$148$		−	43.6722i		−	3.58983i
$149$	8.88779	−	5.13137i	0.728116	−	0.420378i	−0.0896164	−	0.995976i	$-0.528564\pi$
$149$	8.88779	−	5.13137i	0.728116	−	0.420378i	0.817733	+	0.575598i	$0.195231\pi$
$150$	10.7380	−	6.19960i	0.876756	−	0.506196i
$151$		−	3.09272i		−	0.251682i	−0.992050	−	0.125841i	$-0.959837\pi$
$151$		−	3.09272i		−	0.251682i	0.992050	−	0.125841i	$-0.0401630\pi$
$152$	−2.88390	−	4.99506i	−0.233915	−	0.405153i
$153$	−2.02096	+	3.50040i	−0.163385	+	0.282990i
$154$	8.91482	+	5.14697i	0.718377	+	0.414755i
$155$	0.175949			0.0141325
$156$	11.0941	−	10.0617i	0.888240	−	0.805577i
$157$	−5.15673			−0.411552			−0.205776	−	0.978599i	$-0.565972\pi$
$157$	−5.15673			−0.411552			−0.205776	+	0.978599i	$0.565972\pi$
$158$	−9.72901	−	5.61705i	−0.773999	−	0.446868i
$159$	6.23552	−	10.8002i	0.494509	−	0.856515i
$160$	0.0331967	+	0.0574984i	0.00262443	+	0.00454565i
$161$			38.2243i			3.01249i
$162$	2.14836	−	1.24036i	0.168791	−	0.0974515i
$163$	−12.9798	+	7.49387i	−1.01665	+	0.586965i	−0.913133	−	0.407662i	$-0.866344\pi$
$163$	−12.9798	+	7.49387i	−1.01665	+	0.586965i	−0.103520	+	0.994627i	$0.533011\pi$
$164$		−	16.7987i		−	1.31176i
$165$	−0.0209289	−	0.0362500i	−0.00162932	−	0.00282206i
$166$	−9.43575	+	16.3432i	−0.732356	+	1.26848i
$167$	14.5637	+	8.40834i	1.12697	+	0.650657i	0.943171	−	0.332307i	$-0.107827\pi$
$167$	14.5637	+	8.40834i	1.12697	+	0.650657i	0.183800	+	0.982964i	$0.441160\pi$
$168$	−22.1724			−1.71064
$169$	1.26586	−	12.9382i	0.0973737	−	0.995248i
$170$	−0.419701			−0.0321896
$171$	−0.934832	−	0.539726i	−0.0714884	−	0.0412739i
$172$	−13.7830	+	23.8728i	−1.05094	+	1.82028i
$173$	−8.59651	−	14.8896i	−0.653581	−	1.13203i	−0.982248	−	0.187589i	$-0.939933\pi$
$173$	−8.59651	−	14.8896i	−0.653581	−	1.13203i	0.328667	−	0.944446i	$-0.393401\pi$
$174$			1.12733i			0.0854628i
$175$	−17.9620	+	10.3704i	−1.35780	+	0.783925i
$176$	−4.28444	+	2.47363i	−0.322952	+	0.186457i
$177$		−	1.76905i		−	0.132970i
$178$	3.36547	+	5.82916i	0.252252	+	0.436914i
$179$	−6.35778	+	11.0120i	−0.475203	+	0.823075i	−0.999597	−	0.0284005i	$-0.990959\pi$
$179$	−6.35778	+	11.0120i	−0.475203	+	0.823075i	0.524394	+	0.851476i	$0.324292\pi$
$180$	0.150580	+	0.0869373i	0.0112236	+	0.00647992i
$181$	−11.6302			−0.864466			−0.432233	−	0.901762i	$-0.642274\pi$
$181$	−11.6302			−0.864466			−0.432233	+	0.901762i	$0.642274\pi$
$182$	−27.4926	+	24.9340i	−2.03789	+	1.84823i
$183$	8.93118			0.660212
$184$	−42.6256	−	24.6099i	−3.14240	−	1.81427i
$185$	0.220036	−	0.381113i	0.0161774	−	0.0280200i
$186$	−5.21380	−	9.03057i	−0.382295	−	0.662154i
$187$		−	4.04191i		−	0.295574i
$188$	19.5946	−	11.3130i	1.42908	−	0.825082i
$189$	−3.59366	+	2.07480i	−0.261400	+	0.150919i
$190$		−	0.112087i		−	0.00813167i
$191$	1.26557	+	2.19203i	0.0915733	+	0.158610i	0.908173	−	0.418594i	$-0.137477\pi$
$191$	1.26557	+	2.19203i	0.0915733	+	0.158610i	−0.816600	+	0.577204i	$0.804144\pi$
$192$	−2.97985	+	5.16124i	−0.215052	+	0.372481i
$193$	18.9532	+	10.9426i	1.36428	+	0.787669i	0.990191	−	0.139723i	$-0.0446211\pi$
$193$	18.9532	+	10.9426i	1.36428	+	0.787669i	0.374092	+	0.927392i	$0.377954\pi$
$194$	21.0094			1.50839
$195$	0.147509	−	0.0319088i	0.0105633	−	0.00228504i
$196$	42.4496			3.03211
$197$	−1.48037	−	0.854694i	−0.105472	−	0.0608944i	0.446336	−	0.894865i	$-0.352729\pi$
$197$	−1.48037	−	0.854694i	−0.105472	−	0.0608944i	−0.551808	+	0.833971i	$0.686062\pi$
$198$	−1.24036	+	2.14836i	−0.0881482	+	0.152677i
$199$	−8.76050	−	15.1736i	−0.621016	−	1.07563i	−0.989297	−	0.145916i	$-0.953387\pi$
$199$	−8.76050	−	15.1736i	−0.621016	−	1.07563i	0.368281	−	0.929714i	$-0.379946\pi$
$200$		−	26.7070i		−	1.88847i
$201$	−10.0773	+	5.81812i	−0.710797	+	0.410379i
$202$	−18.0771	+	10.4368i	−1.27190	+	0.734331i
$203$		−	1.88574i		−	0.132353i
$204$	8.39490	+	14.5404i	0.587761	+	1.01803i
$205$	0.0846380	−	0.146597i	0.00591137	−	0.0102388i
$206$	−9.44602	−	5.45366i	−0.658136	−	0.379975i
$207$	−9.21156			−0.640248
$208$	−3.77135	−	17.4343i	−0.261496	−	1.20885i
$209$	1.07945			0.0746672
$210$	−0.373156	−	0.215442i	−0.0257502	−	0.0148669i
$211$	−8.13880	+	14.0968i	−0.560298	+	0.970464i	0.437172	+	0.899378i	$0.355980\pi$
$211$	−8.13880	+	14.0968i	−0.560298	+	0.970464i	−0.997470	+	0.0710866i	$0.977353\pi$
$212$	−25.9019	−	44.8634i	−1.77895	−	3.08123i
$213$		−	5.35027i		−	0.366594i
$214$	−20.8432	+	12.0338i	−1.42481	+	0.822614i
$215$	−0.240559	+	0.138887i	−0.0164060	+	0.00947201i
$216$		−	5.34327i		−	0.363563i
$217$	8.72136	+	15.1058i	0.592045	+	1.02545i
$218$	−2.67066	+	4.62572i	−0.180880	+	0.313293i
$219$	8.62851	+	4.98167i	0.583061	+	0.336630i
$220$	−0.173875			−0.0117226
$221$	13.8762	+	4.45354i	0.933411	+	0.299577i
$222$	−26.0809			−1.75043
$223$	1.66726	+	0.962594i	0.111648	+	0.0644601i	0.554784	−	0.831994i	$-0.312801\pi$
$223$	1.66726	+	0.962594i	0.111648	+	0.0644601i	−0.443136	+	0.896454i	$0.646134\pi$
$224$	−3.29097	+	5.70012i	−0.219887	+	0.380855i
$225$	−2.49912	−	4.32861i	−0.166608	−	0.288574i
$226$		−	30.4597i		−	2.02615i
$227$	5.46454	−	3.15495i	0.362694	−	0.209401i	−0.307568	−	0.951526i	$-0.599515\pi$
$227$	5.46454	−	3.15495i	0.362694	−	0.209401i	0.670262	+	0.742125i	$0.266182\pi$
$228$	−3.88323	+	2.24198i	−0.257173	+	0.148479i
$229$		−	8.85114i		−	0.584899i	−0.956281	−	0.292450i	$-0.905530\pi$
$229$		−	8.85114i		−	0.584899i	0.956281	−	0.292450i	$-0.0944704\pi$
$230$	−0.478252	−	0.828356i	−0.0315350	−	0.0546202i
$231$	2.07480	−	3.59366i	0.136512	−	0.236445i
$232$	2.10287	+	1.21409i	0.138060	+	0.0797092i
$233$	−27.1486			−1.77856			−0.889280	−	0.457362i	$-0.848794\pi$
$233$	−27.1486			−1.77856			−0.889280	+	0.457362i	$0.848794\pi$
$234$	−6.00879	−	6.62537i	−0.392807	−	0.433114i
$235$	0.227995			0.0148727
$236$	−6.36399	−	3.67425i	−0.414260	−	0.239173i
$237$	−2.26429	+	3.92186i	−0.147081	+	0.254752i
$238$	−20.8036	−	36.0329i	−1.34850	−	2.33567i
$239$		−	7.90715i		−	0.511471i	−0.966747	−	0.255735i	$-0.917682\pi$
$239$		−	7.90715i		−	0.511471i	0.966747	−	0.255735i	$-0.0823176\pi$
$240$	0.179338	−	0.103541i	0.0115762	−	0.00668353i
$241$	23.3206	−	13.4641i	1.50221	−	0.867301i	0.502212	−	0.864744i	$-0.332520\pi$
$241$	23.3206	−	13.4641i	1.50221	−	0.867301i	0.999997	−	0.00255653i	$-0.000813769\pi$
$242$		−	2.48071i		−	0.159466i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	18.5497	−	32.1291i	1.18753	−	2.05685i
$245$	0.370444	+	0.213876i	0.0236668	+	0.0136640i
$246$	−10.0322			−0.639627
$247$	−1.18938	+	3.70583i	−0.0756786	+	0.235796i
$248$	−22.4603			−1.42623
$249$	6.58811	+	3.80365i	0.417505	+	0.241046i
$250$	0.519096	−	0.899100i	0.0328305	−	0.0568641i
$251$	−3.74222	−	6.48171i	−0.236207	−	0.409122i	0.723416	−	0.690412i	$-0.242571\pi$
$251$	−3.74222	−	6.48171i	−0.236207	−	0.409122i	−0.959623	+	0.281290i	$0.909238\pi$
$252$			17.2371i			1.08584i
$253$	7.97744	−	4.60578i	0.501538	−	0.289563i
$254$	−3.18948	+	1.84145i	−0.200126	+	0.115543i
$255$			0.169186i			0.0105948i
$256$	16.3129	+	28.2547i	1.01955	+	1.76592i
$257$	8.06034	−	13.9609i	0.502790	−	0.870858i	−0.497205	−	0.867633i	$-0.665640\pi$
$257$	8.06034	−	13.9609i	0.502790	−	0.870858i	0.999995	−	0.00322491i	$-0.00102652\pi$
$258$	14.2568	+	8.23114i	0.887587	+	0.512449i
$259$	43.6267			2.71083
$260$	0.191582	−	0.596923i	0.0118814	−	0.0370196i
$261$	0.454439			0.0281291
$262$	28.1710	+	16.2646i	1.74041	+	1.00483i
$263$	5.57544	−	9.65695i	0.343796	−	0.595473i	−0.641338	−	0.767259i	$-0.721620\pi$
$263$	5.57544	−	9.65695i	0.343796	−	0.595473i	0.985134	+	0.171786i	$0.0549537\pi$
$264$	2.67163	+	4.62741i	0.164428	+	0.284797i
$265$		−	0.522012i		−	0.0320669i
$266$	9.62312	−	5.55591i	0.590031	−	0.340655i
$267$	2.34979	−	1.35665i	0.143805	−	0.0830259i
$268$			48.3361i			2.95260i
$269$	8.07788	+	13.9913i	0.492517	+	0.853065i	0.999963	−	0.00861884i	$-0.00274350\pi$
$269$	8.07788	+	13.9913i	0.492517	+	0.853065i	−0.507446	+	0.861684i	$0.669410\pi$
$270$	0.0519187	−	0.0899258i	0.00315967	−	0.00547271i
$271$	−21.3987	−	12.3545i	−1.29988	−	0.750484i	−0.319494	−	0.947588i	$-0.603513\pi$
$271$	−21.3987	−	12.3545i	−1.29988	−	0.750484i	−0.980383	+	0.197104i	$0.936846\pi$
$272$	19.9964			1.21246
$273$	10.0512	+	11.0826i	0.608324	+	0.670747i
$274$	49.5988			2.99637
$275$	4.32861	+	2.49912i	0.261025	+	0.150703i
$276$	−19.1321	+	33.1377i	−1.15162	+	1.99466i
$277$	−3.51265	−	6.08409i	−0.211055	−	0.365558i	0.740990	−	0.671516i	$-0.234357\pi$
$277$	−3.51265	−	6.08409i	−0.211055	−	0.365558i	−0.952045	+	0.305958i	$0.901023\pi$
$278$		−	23.1145i		−	1.38632i
$279$	−3.64032	+	2.10174i	−0.217940	+	0.125828i
$280$	−0.803750	+	0.464045i	−0.0480332	+	0.0277320i
$281$		−	13.5924i		−	0.810855i	−0.914127	−	0.405427i	$-0.867123\pi$
$281$		−	13.5924i		−	0.810855i	0.914127	−	0.405427i	$-0.132877\pi$
$282$	−6.75606	−	11.7018i	−0.402317	−	0.696834i
$283$	−14.7592	+	25.5638i	−0.877346	+	1.51961i	−0.0231032	+	0.999733i	$0.507355\pi$
$283$	−14.7592	+	25.5638i	−0.877346	+	1.51961i	−0.854243	+	0.519875i	$0.825979\pi$
$284$	−19.2471	−	11.1123i	−1.14210	−	0.659394i
$285$	−0.0451836			−0.00267644
$286$	8.51645	+	2.73334i	0.503588	+	0.161626i
$287$	16.7812			0.990565
$288$	−1.37366	−	0.793081i	−0.0809435	−	0.0467327i
$289$	0.331474	−	0.574130i	0.0194985	−	0.0337723i
$290$	0.0235939	+	0.0408658i	0.00138548	+	0.00239972i
$291$		−	8.46912i		−	0.496469i
$292$	35.8422	−	20.6935i	2.09751	−	1.21100i
$293$	−8.87517	+	5.12408i	−0.518493	+	0.299352i	−0.736318	−	0.676636i	$-0.763437\pi$
$293$	−8.87517	+	5.12408i	−0.518493	+	0.299352i	0.217825	+	0.975988i	$0.430104\pi$
$294$		−	25.3508i		−	1.47849i
$295$	−0.0370243	−	0.0641280i	−0.00215564	−	0.00373368i
$296$	−28.0882	+	48.6501i	−1.63259	+	2.82773i
$297$	0.866025	+	0.500000i	0.0502519	+	0.0290129i
$298$	−25.4589			−1.47479
$299$	7.02209	+	32.4619i	0.406098	+	1.87732i
$300$	−20.7624			−1.19872
$301$	−23.8479	−	13.7686i	−1.37457	−	0.793609i
$302$	−3.83608	+	6.64428i	−0.220741	+	0.382335i
$303$	4.20718	+	7.28705i	0.241696	+	0.418630i
$304$			5.34032i			0.306288i
$305$	0.323755	−	0.186920i	0.0185382	−	0.0107030i
$306$	8.68348	−	5.01341i	0.496401	−	0.286597i
$307$		−	24.1418i		−	1.37785i	−0.724834	−	0.688923i	$-0.758084\pi$
$307$		−	24.1418i		−	1.37785i	0.724834	−	0.688923i	$-0.241916\pi$
$308$	−8.61856	−	14.9278i	−0.491088	−	0.850589i
$309$	−2.19843	+	3.80779i	−0.125064	+	0.216618i
$310$	−0.378001	−	0.218239i	−0.0214690	−	0.0123951i
$311$	−24.6909			−1.40009			−0.700045	−	0.714099i	$-0.746837\pi$
$311$	−24.6909			−1.40009			−0.700045	+	0.714099i	$0.746837\pi$
$312$	−18.8299	+	4.07324i	−1.06603	+	0.230602i
$313$	−3.63527			−0.205478			−0.102739	−	0.994708i	$-0.532761\pi$
$313$	−3.63527			−0.205478			−0.102739	+	0.994708i	$0.532761\pi$
$314$	11.0785	+	6.39617i	0.625196	+	0.360957i
$315$	−0.0868467	+	0.150423i	−0.00489326	+	0.00847537i
$316$	9.40569	+	16.2911i	0.529111	+	0.916448i
$317$			21.2211i			1.19190i	0.803023	+	0.595948i	$0.203224\pi$
$317$			21.2211i			1.19190i	−0.803023	+	0.595948i	$0.796776\pi$
$318$	−26.7923	+	15.4685i	−1.50244	+	0.867432i
$319$	−0.393556	+	0.227219i	−0.0220349	+	0.0127218i
$320$			0.249460i			0.0139452i
$321$	4.85095	+	8.40209i	0.270754	+	0.468959i
$322$	47.4117	−	82.1194i	2.64215	−	4.57634i
$323$	−3.77851	−	2.18152i	−0.210242	−	0.121383i
$324$	−4.15393			−0.230774
$325$	−13.3491	+	12.1068i	−0.740474	+	0.671563i
$326$	37.1802			2.05922
$327$	1.86467	+	1.07657i	0.103117	+	0.0595345i
$328$	−10.8043	+	18.7135i	−0.596565	+	1.03328i
$329$	11.3012	+	19.5742i	0.623053	+	1.07916i
$330$			0.103837i			0.00571606i
$331$	−12.4482	+	7.18695i	−0.684213	+	0.395030i	−0.801440	−	0.598075i	$-0.795933\pi$
$331$	−12.4482	+	7.18695i	−0.684213	+	0.395030i	0.117228	+	0.993105i	$0.462599\pi$
$332$	27.3665	−	15.8001i	1.50193	−	0.867142i
$333$			10.5135i			0.576135i
$334$	−20.8587	−	36.1283i	−1.14134	−	1.97685i
$335$	−0.243534	+	0.421814i	−0.0133057	+	0.0230462i
$336$	17.7787	+	10.2645i	0.969909	+	0.559977i
$337$	−22.4289			−1.22178			−0.610890	−	0.791715i	$-0.709188\pi$
$337$	−22.4289			−1.22178			−0.610890	+	0.791715i	$0.709188\pi$
$338$	−18.7675	+	26.2258i	−1.02082	+	1.42650i
$339$	−12.2786			−0.666884
$340$	0.608630	+	0.351393i	0.0330076	+	0.0190570i
$341$	2.10174	−	3.64032i	0.113815	−	0.197134i
$342$	1.33890	+	2.31905i	0.0723996	+	0.125400i
$343$			13.3582i			0.721274i
$344$	30.7080	−	17.7293i	1.65566	−	0.955898i
$345$	−0.333919	+	0.192788i	−0.0179776	+	0.0103794i
$346$			42.6509i			2.29293i
$347$	−11.2628	−	19.5077i	−0.604617	−	1.04723i	−0.992112	−	0.125356i	$-0.959993\pi$
$347$	−11.2628	−	19.5077i	−0.604617	−	1.04723i	0.387494	−	0.921872i	$-0.373341\pi$
$348$	0.943853	−	1.63480i	0.0505958	−	0.0876345i
$349$	−9.43103	−	5.44501i	−0.504831	−	0.291465i	0.225875	−	0.974156i	$-0.427476\pi$
$349$	−9.43103	−	5.44501i	−0.504831	−	0.291465i	−0.730707	+	0.682692i	$0.760809\pi$
$350$	51.4517			2.75021
$351$	−2.67075	+	2.42220i	−0.142554	+	0.129288i
$352$	1.58616			0.0845427
$353$	−1.50545	−	0.869169i	−0.0801268	−	0.0462612i	0.459401	−	0.888229i	$-0.348064\pi$
$353$	−1.50545	−	0.869169i	−0.0801268	−	0.0462612i	−0.539528	+	0.841968i	$0.681397\pi$
$354$	−2.19425	+	3.80055i	−0.116623	+	0.201997i
$355$	−0.111976	−	0.193947i	−0.00594304	−	0.0102937i
$356$		−	11.2709i		−	0.597356i
$357$	−14.5252	+	8.38615i	−0.768757	+	0.443842i
$358$	27.3176	−	15.7718i	1.44378	−	0.833566i
$359$			14.8440i			0.783436i	0.920085	+	0.391718i	$0.128119\pi$
$359$			14.8440i			0.783436i	−0.920085	+	0.391718i	$0.871881\pi$
$360$	−0.111829	−	0.193693i	−0.00589390	−	0.0102085i
$361$	−8.91739	+	15.4454i	−0.469336	+	0.812915i
$362$	24.9858	+	14.4256i	1.31323	+	0.758192i
$363$	−1.00000			−0.0524864
$364$	60.7443	−	13.1401i	3.18387	−	0.688727i
$365$	0.417045			0.0218291
$366$	−19.1874	−	11.0778i	−1.00294	−	0.579048i
$367$	6.12920	−	10.6161i	0.319942	−	0.554155i	−0.660534	−	0.750796i	$-0.729670\pi$
$367$	6.12920	−	10.6161i	0.319942	−	0.554155i	0.980476	+	0.196641i	$0.0630034\pi$
$368$	22.7859	+	39.4664i	1.18780	+	2.05733i
$369$			4.04406i			0.210526i
$370$	−0.945432	+	0.545846i	−0.0491507	+	0.0283772i
$371$	44.8167	−	25.8749i	2.32677	−	1.34336i
$372$			17.4609i			0.905307i
$373$	12.4821	+	21.6196i	0.646298	+	1.11942i	0.984000	+	0.178168i	$0.0570170\pi$
$373$	12.4821	+	21.6196i	0.646298	+	1.11942i	−0.337702	+	0.941253i	$0.609650\pi$
$374$	−5.01341	+	8.68348i	−0.259237	+	0.449012i
$375$	−0.362436	−	0.209253i	−0.0187161	−	0.0108058i
$376$	−29.1041			−1.50093
$377$	−0.346425	−	1.60146i	−0.0178418	−	0.0824795i
$378$	10.2939			0.529464
$379$	10.3776	+	5.99149i	0.533060	+	0.307762i	0.742262	−	0.670110i	$-0.233753\pi$
$379$	10.3776	+	5.99149i	0.533060	+	0.307762i	−0.209202	+	0.977873i	$0.567087\pi$
$380$	−0.0938446	+	0.162544i	−0.00481413	+	0.00833831i
$381$	0.742306	+	1.28571i	0.0380295	+	0.0658690i
$382$		−	6.27902i		−	0.321263i
$383$	24.0804	−	13.9028i	1.23045	−	0.710402i	0.263329	−	0.964706i	$-0.415180\pi$
$383$	24.0804	−	13.9028i	1.23045	−	0.710402i	0.967124	+	0.254304i	$0.0818463\pi$
$384$	15.5509	−	8.97830i	0.793577	−	0.458172i
$385$		−	0.173693i		−	0.00885223i
$386$	−27.1455	−	47.0175i	−1.38167	−	2.39313i
$387$	3.31806	−	5.74705i	0.168666	−	0.292139i
$388$	−30.4669	−	17.5901i	−1.54672	−	0.893000i
$389$	−20.0837			−1.01828			−0.509141	−	0.860683i	$-0.670037\pi$
$389$	−20.0837			−1.01828			−0.509141	+	0.860683i	$0.670037\pi$
$390$	−0.356481	−	0.114412i	−0.0180511	−	0.00579348i
$391$	−37.2323			−1.88292
$392$	−47.2882	−	27.3018i	−2.38841	−	1.37895i
$393$	6.55641	−	11.3560i	0.330727	−	0.572836i
$394$	2.12025	+	3.67238i	0.106817	+	0.185012i
$395$			0.189557i			0.00953764i
$396$	3.59741	−	2.07696i	0.180776	−	0.104371i
$397$	30.5893	−	17.6607i	1.53523	−	0.886368i	0.536126	−	0.844138i	$-0.319887\pi$
$397$	30.5893	−	17.6607i	1.53523	−	0.886368i	0.999108	−	0.0422294i	$-0.0134460\pi$
$398$			43.4645i			2.17868i
$399$	−2.23964	−	3.87918i	−0.112122	−	0.194202i
$400$	−12.3638	+	21.4147i	−0.618190	+	1.07074i
$401$	−4.10053	−	2.36744i	−0.204771	−	0.118224i	0.394108	−	0.919064i	$-0.371054\pi$
$401$	−4.10053	−	2.36744i	−0.204771	−	0.118224i	−0.598879	+	0.800840i	$0.704387\pi$
$402$	28.8662			1.43971
$403$	10.1817	+	11.2264i	0.507185	+	0.559229i
$404$	34.9527			1.73896
$405$	−0.0362500	−	0.0209289i	−0.00180128	−	0.00103997i
$406$	−2.33899	+	4.05124i	−0.116082	+	0.201060i
$407$	−5.25674	−	9.10494i	−0.260567	−	0.451315i
$408$		−	21.5970i		−	1.06921i
$409$	−19.6210	+	11.3282i	−0.970195	+	0.560142i	−0.899296	−	0.437341i	$-0.855920\pi$
$409$	−19.6210	+	11.3282i	−0.970195	+	0.560142i	−0.0708992	+	0.997483i	$0.522587\pi$
$410$	−0.363665	+	0.209962i	−0.0179602	+	0.0103693i
$411$		−	19.9938i		−	0.986220i
$412$	9.13211	+	15.8173i	0.449907	+	0.779261i
$413$	3.67042	−	6.35735i	0.180610	−	0.312825i
$414$	19.7897	+	11.4256i	0.972612	+	0.561538i
$415$	0.318425			0.0156309
$416$	−1.74770	+	5.44540i	−0.0856878	+	0.266983i
$417$	−9.31770			−0.456290
$418$	−2.31905	−	1.33890i	−0.113428	−	0.0654879i
$419$	−6.01791	+	10.4233i	−0.293994	+	0.509213i	−0.974750	−	0.223297i	$-0.928318\pi$
$419$	−6.01791	+	10.4233i	−0.293994	+	0.509213i	0.680756	+	0.732510i	$0.261651\pi$
$420$	0.360755	+	0.624845i	0.0176030	+	0.0304893i
$421$			20.6795i			1.00786i	0.863745	+	0.503929i	$0.168113\pi$
$421$			20.6795i			1.00786i	−0.863745	+	0.503929i	$0.831887\pi$
$422$	34.9701	−	20.1900i	1.70232	−	0.982834i
$423$	−4.71713	+	2.72344i	−0.229355	+	0.132418i
$424$			66.6362i			3.23614i
$425$	−10.1012	−	17.4959i	−0.489982	−	0.848674i
$426$	−6.63624	+	11.4943i	−0.321527	+	0.556901i
$427$	32.0956	+	18.5304i	1.55321	+	0.896749i
$428$	40.3010			1.94802
$429$	1.10184	−	3.43307i	0.0531973	−	0.165750i
$430$	0.689077			0.0332302
$431$	−17.3478	−	10.0157i	−0.835612	−	0.482441i	0.0201584	−	0.999797i	$-0.493583\pi$
$431$	−17.3478	−	10.0157i	−0.835612	−	0.482441i	−0.855770	+	0.517356i	$0.826916\pi$
$432$	−2.47363	+	4.28444i	−0.119012	+	0.206135i
$433$	−13.5877	−	23.5346i	−0.652982	−	1.13100i	−0.982396	−	0.186813i	$-0.940184\pi$
$433$	−13.5877	−	23.5346i	−0.652982	−	1.13100i	0.329413	−	0.944186i	$-0.393149\pi$
$434$		−	43.2703i		−	2.07704i
$435$	0.0164734	−	0.00951093i	0.000789840	−	0.000456014i
$436$	7.74572	−	4.47199i	0.370953	−	0.214170i
$437$		−	9.94343i		−	0.475659i
$438$	−12.3581	−	21.4048i	−0.590493	−	1.02276i
$439$	−1.75994	+	3.04830i	−0.0839973	+	0.145488i	−0.904963	−	0.425489i	$-0.860102\pi$
$439$	−1.75994	+	3.04830i	−0.0839973	+	0.145488i	0.820966	+	0.570977i	$0.193435\pi$
$440$	0.193693	+	0.111829i	0.00923397	+	0.00533124i
$441$	−10.2192			−0.486626
$442$	−24.2870	−	26.7792i	−1.15521	−	1.27375i
$443$	0.667919			0.0317338			0.0158669	−	0.999874i	$-0.494949\pi$
$443$	0.667919			0.0317338			0.0158669	+	0.999874i	$0.494949\pi$
$444$	37.8212	+	21.8361i	1.79492	+	1.03630i
$445$	0.0567867	−	0.0983574i	0.00269195	−	0.00466259i
$446$	−2.38792	−	4.13599i	−0.113071	−	0.195845i
$447$			10.2627i			0.485411i
$448$	−21.4171	+	12.3652i	−1.01186	+	0.584199i
$449$	−28.2635	+	16.3179i	−1.33384	+	0.770091i	−0.985886	−	0.167421i	$-0.946456\pi$
$449$	−28.2635	+	16.3179i	−1.33384	+	0.770091i	−0.347952	+	0.937512i	$0.613123\pi$
$450$			12.3992i			0.584504i
$451$	−2.02203	−	3.50226i	−0.0952137	−	0.164915i
$452$	−25.5023	+	44.1712i	−1.19953	+	2.07764i
$453$	2.67838	+	1.54636i	0.125841	+	0.0726544i
$454$	−15.6530			−0.734634
$455$	0.596301	+	0.191382i	0.0279550	+	0.00897213i
$456$	5.76780			0.270102
$457$	−4.42442	−	2.55444i	−0.206966	−	0.119492i	0.392935	−	0.919566i	$-0.371460\pi$
$457$	−4.42442	−	2.55444i	−0.206966	−	0.119492i	−0.599900	+	0.800075i	$0.704793\pi$
$458$	−10.9786	+	19.0154i	−0.512994	+	0.888532i
$459$	−2.02096	−	3.50040i	−0.0943301	−	0.163385i
$460$			1.60166i			0.0746776i
$461$	−19.4607	+	11.2356i	−0.906373	+	0.523295i	−0.879262	−	0.476338i	$-0.841964\pi$
$461$	−19.4607	+	11.2356i	−0.906373	+	0.523295i	−0.0271105	+	0.999632i	$0.508631\pi$
$462$	−8.91482	+	5.14697i	−0.414755	+	0.239459i
$463$		−	38.2207i		−	1.77627i	−0.459587	−	0.888133i	$-0.652003\pi$
$463$		−	38.2207i		−	1.77627i	0.459587	−	0.888133i	$-0.347997\pi$
$464$	−1.12411	−	1.94702i	−0.0521856	−	0.0903881i
$465$	−0.0879743	+	0.152376i	−0.00407971	+	0.00706626i
$466$	58.3248	+	33.6739i	2.70185	+	1.55991i
$467$	31.5306			1.45906			0.729532	−	0.683947i	$-0.239738\pi$
$467$	31.5306			1.45906			0.729532	+	0.683947i	$0.239738\pi$
$468$	3.16659	+	14.6386i	0.146376	+	0.676670i
$469$	−48.2857			−2.22963
$470$	−0.489814	−	0.282794i	−0.0225934	−	0.0130443i
$471$	2.57836	−	4.46586i	0.118805	−	0.205776i
$472$	4.72625	+	8.18611i	0.217543	+	0.376796i
$473$			6.63612i			0.305129i
$474$	9.72901	−	5.61705i	0.446868	−	0.258000i
$475$	4.67252	−	2.69768i	0.214390	−	0.123778i
$476$			69.6709i			3.19336i
$477$	6.23552	+	10.8002i	0.285505	+	0.494509i
$478$	−9.80767	+	16.9874i	−0.448592	+	0.776985i
$479$	11.5981	+	6.69619i	0.529933	+	0.305957i	0.740989	−	0.671517i	$-0.234357\pi$
$479$	11.5981	+	6.69619i	0.529933	+	0.305957i	−0.211056	+	0.977474i	$0.567690\pi$
$480$	−0.0663934			−0.00303043
$481$	37.0499	−	8.01456i	1.68933	−	0.365432i
$482$	−66.8012			−3.04271
$483$	−33.1032	−	19.1121i	−1.50625	−	0.869632i
$484$	−2.07696	+	3.59741i	−0.0944074	+	0.163518i
$485$	−0.177250	−	0.307006i	−0.00804850	−	0.0139404i
$486$			2.48071i			0.112527i
$487$	−16.0637	+	9.27437i	−0.727915	+	0.420262i	−0.817659	−	0.575703i	$-0.804728\pi$
$487$	−16.0637	+	9.27437i	−0.727915	+	0.420262i	0.0897440	+	0.995965i	$0.471395\pi$
$488$	−41.3282	+	23.8609i	−1.87084	+	1.08013i
$489$		−	14.9877i		−	0.677769i
$490$	−0.530565	−	0.918965i	−0.0239685	−	0.0415146i
$491$	8.78131	−	15.2097i	0.396295	−	0.686403i	−0.596971	−	0.802263i	$-0.703629\pi$
$491$	8.78131	−	15.2097i	0.396295	−	0.686403i	0.993266	+	0.115860i	$0.0369624\pi$
$492$	14.5481	+	8.39937i	0.655881	+	0.378673i
$493$	1.83680			0.0827254
$494$	7.15177	−	6.48619i	0.321773	−	0.291828i
$495$	0.0418579			0.00188137
$496$	18.0096	+	10.3978i	0.808653	+	0.466876i
$497$	11.1007	−	19.2270i	0.497936	−	0.862450i
$498$	−9.43575	−	16.3432i	−0.422826	−	0.732356i
$499$			25.8400i			1.15676i	0.815769	+	0.578379i	$0.196314\pi$
$499$			25.8400i			1.15676i	−0.815769	+	0.578379i	$0.803686\pi$
$500$	−1.50553	+	0.869221i	−0.0673295	+	0.0388727i
$501$	−14.5637	+	8.40834i	−0.650657	+	0.375657i
$502$			18.5667i			0.828674i
$503$	6.25940	+	10.8416i	0.279093	+	0.483403i	0.971160	−	0.238431i	$-0.0766330\pi$
$503$	6.25940	+	10.8416i	0.279093	+	0.483403i	−0.692067	+	0.721833i	$0.743300\pi$
$504$	11.0862	−	19.2019i	0.493819	−	0.855319i
$505$	0.305021	+	0.176104i	0.0135732	+	0.00783652i
$506$	−22.8512			−1.01586
$507$	10.5719	+	7.56538i	0.469515	+	0.335990i
$508$	6.16697			0.273615
$509$	7.51605	+	4.33939i	0.333143	+	0.192340i	0.657236	−	0.753685i	$-0.271726\pi$
$509$	7.51605	+	4.33939i	0.333143	+	0.192340i	−0.324093	+	0.946025i	$0.605059\pi$
$510$	0.209851	−	0.363472i	0.00929234	−	0.0160948i
$511$	20.6719	+	35.8048i	0.914473	+	1.58391i
$512$		−	45.0218i		−	1.98970i
$513$	0.934832	−	0.539726i	0.0412739	−	0.0238295i
$514$	−34.6330	+	19.9954i	−1.52760	+	0.881958i
$515$			0.184043i			0.00810991i
$516$	−13.7830	−	23.8728i	−0.606761	−	1.05094i
$517$	2.72344	−	4.71713i	0.119777	−	0.207459i
$518$	−93.7258	−	54.1126i	−4.11807	−	2.37757i
$519$	17.1930			0.754690
$520$	−0.597335	+	0.541745i	−0.0261949	+	0.0237571i
$521$	35.2802			1.54565			0.772827	−	0.634617i	$-0.218842\pi$
$521$	35.2802			1.54565			0.772827	+	0.634617i	$0.218842\pi$
$522$	−0.976298	−	0.563666i	−0.0427314	−	0.0246710i
$523$	15.7507	−	27.2810i	0.688730	−	1.19291i	−0.283519	−	0.958967i	$-0.591502\pi$
$523$	15.7507	−	27.2810i	0.688730	−	1.19291i	0.972249	−	0.233948i	$-0.0751647\pi$
$524$	−27.2349	−	47.1721i	−1.18976	−	2.06072i
$525$		−	20.7407i		−	0.905199i
$526$	−23.9561	+	13.8311i	−1.04454	+	0.603063i
$527$	−14.7138	+	8.49504i	−0.640945	+	0.370050i
$528$		−	4.94725i		−	0.215301i
$529$	−30.9264	−	53.5661i	−1.34463	−	2.32896i
$530$	−0.647480	+	1.12147i	−0.0281247	+	0.0487135i
$531$	1.53204	+	0.884525i	0.0664849	+	0.0383851i
$532$	−18.6066			−0.806700
$533$	14.2515	−	3.08284i	0.617299	−	0.133533i
$534$	−6.73093			−0.291276
$535$	0.351694	+	0.203051i	0.0152051	+	0.00877864i
$536$	31.0878	−	53.8456i	1.34279	−	2.32578i
$537$	−6.35778	−	11.0120i	−0.274358	−	0.475203i
$538$		−	40.0778i		−	1.72788i
$539$	8.85004	−	5.10958i	0.381198	−	0.220085i
$540$	−0.150580	+	0.0869373i	−0.00647992	+	0.00374119i
$541$		−	22.3842i		−	0.962374i	−0.876618	−	0.481187i	$-0.840206\pi$
$541$		−	22.3842i		−	0.962374i	0.876618	−	0.481187i	$-0.159794\pi$
$542$	30.6480	+	53.0839i	1.31644	+	2.28015i
$543$	5.81510	−	10.0720i	0.249550	−	0.432233i
$544$	−5.55220	−	3.20556i	−0.238049	−	0.137437i
$545$	0.0901259			0.00386057
$546$	−7.84721	−	36.2763i	−0.335830	−	1.55248i
$547$	−21.9823			−0.939894			−0.469947	−	0.882695i	$-0.655727\pi$
$547$	−21.9823			−0.939894			−0.469947	+	0.882695i	$0.655727\pi$
$548$	−71.9257	−	41.5263i	−3.07251	−	1.77392i
$549$	−4.46559	+	7.73463i	−0.190587	+	0.330106i
$550$	−6.19960	−	10.7380i	−0.264352	−	0.457871i
$551$			0.490545i			0.0208979i
$552$	42.6256	−	24.6099i	1.81427	−	1.04747i
$553$	−16.2742	+	9.39589i	−0.692047	+	0.399554i
$554$			17.4277i			0.740434i
$555$	0.220036	+	0.381113i	0.00934001	+	0.0161774i
$556$	−19.3525	+	33.5195i	−0.820729	+	1.42154i
$557$	−1.22802	−	0.708997i	−0.0520329	−	0.0300412i	0.473758	−	0.880655i	$-0.342897\pi$
$557$	−1.22802	−	0.708997i	−0.0520329	−	0.0300412i	−0.525791	+	0.850614i	$0.676231\pi$
$558$	10.4276			0.441436
$559$	−22.7822	−	7.31193i	−0.963586	−	0.309262i
$560$	0.859305			0.0363122
$561$	3.50040	+	2.02096i	0.147787	+	0.0853248i
$562$	−16.8594	+	29.2013i	−0.711171	+	1.23178i
$563$	6.02994	+	10.4442i	0.254132	+	0.440169i	0.964659	−	0.263500i	$-0.0848770\pi$
$563$	6.02994	+	10.4442i	0.254132	+	0.440169i	−0.710528	+	0.703669i	$0.751544\pi$
$564$			22.6259i			0.952722i
$565$	−0.445100	+	0.256979i	−0.0187255	+	0.0108112i
$566$	63.4163	−	36.6134i	2.66559	−	1.53898i
$567$		−	4.14960i		−	0.174267i
$568$	14.2940	+	24.7579i	0.599761	+	1.03882i
$569$	−7.65470	+	13.2583i	−0.320902	+	0.555818i	−0.980674	−	0.195647i	$-0.937319\pi$
$569$	−7.65470	+	13.2583i	−0.320902	+	0.555818i	0.659773	+	0.751465i	$0.270653\pi$
$570$	0.0970705	+	0.0560437i	0.00406584	+	0.00234741i
$571$	11.5095			0.481659			0.240829	−	0.970567i	$-0.422581\pi$
$571$	11.5095			0.481659			0.240829	+	0.970567i	$0.422581\pi$
$572$	−10.0617	−	11.0941i	−0.420699	−	0.463868i
$573$	−2.53114			−0.105740
$574$	−36.0521	−	20.8147i	−1.50479	−	0.868788i
$575$	23.0208	−	39.8732i	0.960035	−	1.66283i
$576$	−2.97985	−	5.16124i	−0.124160	−	0.215052i
$577$		−	30.0609i		−	1.25145i	−0.780043	−	0.625726i	$-0.784803\pi$
$577$		−	30.0609i		−	1.25145i	0.780043	−	0.625726i	$-0.215197\pi$
$578$	−1.42425	+	0.822291i	−0.0592410	+	0.0342028i
$579$	−18.9532	+	10.9426i	−0.787669	+	0.454761i
$580$		−	0.0790154i		−	0.00328094i
$581$	15.7836	+	27.3380i	0.654814	+	1.13417i
$582$	−10.5047	+	18.1947i	−0.435435	+	0.754195i
$583$	−10.8002	−	6.23552i	−0.447300	−	0.258249i
$584$	−53.2368			−2.20296
$585$	−0.0461207	+	0.143701i	−0.00190685	+	0.00594130i
$586$	25.4227			1.05020
$587$	10.1064	+	5.83496i	0.417137	+	0.240834i	0.693852	−	0.720118i	$-0.255912\pi$
$587$	10.1064	+	5.83496i	0.417137	+	0.240834i	−0.276714	+	0.960952i	$0.589246\pi$
$588$	−21.2248	+	36.7624i	−0.875296	+	1.51606i
$589$	−2.26872	−	3.92954i	−0.0934811	−	0.161914i
$590$			0.183693i			0.00756254i
$591$	1.48037	−	0.854694i	0.0608944	−	0.0351574i
$592$	45.0444	−	26.0064i	1.85131	−	1.06886i
$593$			32.5573i			1.33697i	0.743726	+	0.668484i	$0.233057\pi$
$593$			32.5573i			1.33697i	−0.743726	+	0.668484i	$0.766943\pi$
$594$	−1.24036	−	2.14836i	−0.0508924	−	0.0881482i
$595$	−0.351027	+	0.607996i	−0.0143907	+	0.0249254i
$596$	36.9192	+	21.3153i	1.51227	+	0.873110i
$597$	17.5210			0.717087
$598$	25.1784	−	78.4498i	1.02962	−	3.20805i
$599$	2.19670			0.0897547			0.0448774	−	0.998993i	$-0.485710\pi$
$599$	2.19670			0.0897547			0.0448774	+	0.998993i	$0.485710\pi$
$600$	23.1289	+	13.3535i	0.944234	+	0.545154i
$601$	−8.93607	+	15.4777i	−0.364510	+	0.631350i	−0.988697	−	0.149925i	$-0.952097\pi$
$601$	−8.93607	+	15.4777i	−0.364510	+	0.631350i	0.624188	+	0.781275i	$0.285430\pi$
$602$	34.1559	+	59.1598i	1.39209	+	2.41117i
$603$		−	11.6362i		−	0.473865i
$604$	11.1258	−	6.42347i	0.452702	−	0.261367i
$605$	−0.0362500	+	0.0209289i	−0.00147377	+	0.000850883i
$606$		−	20.8736i		−	0.847932i
$607$	6.28592	+	10.8875i	0.255137	+	0.441911i	0.964933	−	0.262497i	$-0.0845459\pi$
$607$	6.28592	+	10.8875i	0.255137	+	0.441911i	−0.709795	+	0.704408i	$0.751213\pi$
$608$	0.856093	−	1.48280i	0.0347191	−	0.0601353i
$609$	1.63310	+	0.942869i	0.0661764	+	0.0382070i
$610$	−0.927390			−0.0375489
$611$	13.1934	+	14.5473i	0.533749	+	0.588519i
$612$	−16.7898			−0.678688
$613$	30.7286	+	17.7412i	1.24112	+	0.716559i	0.969322	−	0.245796i	$-0.0790494\pi$
$613$	30.7286	+	17.7412i	1.24112	+	0.716559i	0.271795	+	0.962355i	$0.412383\pi$
$614$	−29.9444	+	51.8653i	−1.20846	+	2.09311i
$615$	0.0846380	+	0.146597i	0.00341293	+	0.00591137i
$616$			22.1724i			0.893352i
$617$	26.0159	−	15.0203i	1.04736	−	0.604693i	0.125451	−	0.992100i	$-0.459962\pi$
$617$	26.0159	−	15.0203i	1.04736	−	0.604693i	0.921909	+	0.387407i	$0.126629\pi$
$618$	9.44602	−	5.45366i	0.379975	−	0.219379i
$619$			20.0547i			0.806065i	0.915186	+	0.403032i	$0.132044\pi$
$619$			20.0547i			0.806065i	−0.915186	+	0.403032i	$0.867956\pi$
$620$	0.365439	+	0.632958i	0.0146764	+	0.0254202i
$621$	4.60578	−	7.97744i	0.184824	−	0.320124i
$622$	53.0448	+	30.6254i	2.12690	+	1.22797i
$623$	11.2591			0.451088
$624$	16.9842	+	5.45107i	0.679914	+	0.218218i
$625$	24.9737			0.998949
$626$	7.80987	+	4.50903i	0.312145	+	0.180217i
$627$	−0.539726	+	0.934832i	−0.0215546	+	0.0373336i
$628$	−10.7103	−	18.5508i	−0.427389	−	0.740259i
$629$			42.4945i			1.69437i
$630$	0.373156	−	0.215442i	0.0148669	−	0.00858339i
$631$	−3.09377	+	1.78619i	−0.123161	+	0.0711070i	−0.560315	−	0.828280i	$-0.689320\pi$
$631$	−3.09377	+	1.78619i	−0.123161	+	0.0711070i	0.437154	+	0.899387i	$0.355987\pi$
$632$		−	24.1974i		−	0.962521i
$633$	−8.13880	−	14.0968i	−0.323488	−	0.560298i
$634$	26.3217	−	45.5906i	1.04537	−	1.81063i
$635$	0.0538172	+	0.0310714i	0.00213567	+	0.00123303i
$636$	51.8038			2.05416
$637$	7.79019	+	36.0127i	0.308659	+	1.42688i
$638$	1.12733			0.0446315
$639$	4.63347	+	2.67513i	0.183297	+	0.105827i
$640$	0.375813	−	0.650927i	0.0148553	−	0.0257301i
$641$	−16.6535	−	28.8447i	−0.657772	−	1.13930i	−0.981191	−	0.193039i	$-0.938166\pi$
$641$	−16.6535	−	28.8447i	−0.657772	−	1.13930i	0.323419	−	0.946256i	$-0.395168\pi$
$642$		−	24.0676i		−	0.949873i
$643$	38.8154	−	22.4101i	1.53073	−	0.883766i	0.531400	−	0.847121i	$-0.321666\pi$
$643$	38.8154	−	22.4101i	1.53073	−	0.883766i	0.999328	−	0.0366453i	$-0.0116672\pi$
$644$	−137.508	+	79.3904i	−5.41858	+	3.12842i
$645$		−	0.277774i		−	0.0109373i
$646$	5.41173	+	9.37339i	0.212922	+	0.368791i
$647$	−24.3374	+	42.1536i	−0.956802	+	1.65723i	−0.226613	+	0.973985i	$0.572765\pi$
$647$	−24.3374	+	42.1536i	−0.956802	+	1.65723i	−0.730189	+	0.683245i	$0.760568\pi$
$648$	4.62741	+	2.67163i	0.181782	+	0.104952i
$649$	−1.76905			−0.0694413
$650$	43.6953	−	9.45207i	1.71387	−	0.370741i
$651$	−17.4427			−0.683634
$652$	−53.9170	−	31.1290i	−2.11155	−	1.21910i
$653$	−14.4219	+	24.9795i	−0.564374	+	0.977525i	0.432733	+	0.901522i	$0.357549\pi$
$653$	−14.4219	+	24.9795i	−0.564374	+	0.977525i	−0.997108	+	0.0760030i	$0.975784\pi$
$654$	−2.67066	−	4.62572i	−0.104431	−	0.180880i
$655$		−	0.548875i		−	0.0214463i
$656$	17.3266	−	10.0035i	0.676489	−	0.390571i
$657$	−8.62851	+	4.98167i	−0.336630	+	0.194354i
$658$		−	56.0698i		−	2.18583i
$659$	−0.304250	−	0.526977i	−0.0118519	−	0.0205281i	0.860039	−	0.510229i	$-0.170439\pi$
$659$	−0.304250	−	0.526977i	−0.0118519	−	0.0205281i	−0.871891	+	0.489701i	$0.837106\pi$
$660$	0.0869373	−	0.150580i	0.00338403	−	0.00586131i
$661$	−40.1041	−	23.1541i	−1.55987	−	0.900591i	−0.997268	−	0.0738635i	$-0.976467\pi$
$661$	−40.1041	−	23.1541i	−1.55987	−	0.900591i	−0.562602	−	0.826728i	$-0.690200\pi$
$662$	35.6575			1.38587
$663$	−10.7950	+	9.79033i	−0.419241	+	0.380225i
$664$	−40.6478			−1.57744
$665$	−0.162374	−	0.0937468i	−0.00629660	−	0.00363534i
$666$	13.0404	−	22.5867i	0.505307	−	0.875217i
$667$	2.09305	+	3.62526i	0.0810430	+	0.140371i
$668$			69.8553i			2.70278i
$669$	−1.66726	+	0.962594i	−0.0644601	+	0.0372160i
$670$	1.04640	−	0.604138i	0.0404259	−	0.0233399i
$671$		−	8.93118i		−	0.344784i
$672$	−3.29097	−	5.70012i	−0.126952	−	0.219887i
$673$	6.34139	−	10.9836i	0.244442	−	0.423387i	−0.717532	−	0.696525i	$-0.754728\pi$
$673$	6.34139	−	10.9836i	0.244442	−	0.423387i	0.961975	+	0.273138i	$0.0880617\pi$
$674$	48.1853	+	27.8198i	1.85603	+	1.07158i
$675$	4.99825			0.192383
$676$	49.1732	−	22.3184i	1.89128	−	0.858400i
$677$	−9.42554			−0.362253			−0.181126	−	0.983460i	$-0.557974\pi$
$677$	−9.42554			−0.362253			−0.181126	+	0.983460i	$0.557974\pi$
$678$	26.3789	+	15.2299i	1.01308	+	0.584900i
$679$	17.5717	−	30.4351i	0.674341	−	1.16799i
$680$	−0.452003	−	0.782892i	−0.0173335	−	0.0300225i
$681$			6.30990i			0.241796i
$682$	−9.03057	+	5.21380i	−0.345798	+	0.199647i
$683$	−6.98891	+	4.03505i	−0.267423	+	0.154397i	−0.627716	−	0.778442i	$-0.716010\pi$
$683$	−6.98891	+	4.03505i	−0.267423	+	0.154397i	0.360293	+	0.932839i	$0.382677\pi$
$684$		−	4.48396i		−	0.171449i
$685$	−0.418449	−	0.724774i	−0.0159881	−	0.0276922i
$686$	16.5689	−	28.6982i	0.632603	−	1.09570i
$687$	7.66531	+	4.42557i	0.292450	+	0.168846i
$688$	−32.8305			−1.25165
$689$	33.3071	−	30.2074i	1.26890	−	1.15081i
$690$	0.956504			0.0364135
$691$	6.72243	+	3.88120i	0.255733	+	0.147648i	0.622387	−	0.782710i	$-0.286163\pi$
$691$	6.72243	+	3.88120i	0.255733	+	0.147648i	−0.366653	+	0.930358i	$0.619497\pi$
$692$	35.7093	−	61.8503i	1.35746	−	2.35119i
$693$	2.07480	+	3.59366i	0.0788151	+	0.136512i
$694$			55.8794i			2.12115i
$695$	−0.337766	+	0.195010i	−0.0128122	+	0.00739713i
$696$	−2.10287	+	1.21409i	−0.0797092	+	0.0460201i
$697$			16.3457i			0.619139i
$698$	13.5075	+	23.3957i	0.511266	+	0.885539i
$699$	13.5743	−	23.5113i	0.513426	−	0.889280i
$700$	−74.6128	−	43.0777i	−2.82010	−	1.62818i
$701$	10.4965			0.396449			0.198225	−	0.980157i	$-0.436482\pi$
$701$	10.4965			0.396449			0.198225	+	0.980157i	$0.436482\pi$
$702$	8.74213	−	1.89108i	0.329950	−	0.0713741i
$703$	−11.3488			−0.428028
$704$	5.16124	+	2.97985i	0.194522	+	0.112307i
$705$	−0.113997	+	0.197449i	−0.00429339	+	0.00743636i
$706$	2.15616	+	3.73457i	0.0811481	+	0.140553i
$707$			34.9162i			1.31316i
$708$	6.36399	−	3.67425i	0.239173	−	0.138087i
$709$	13.6078	−	7.85647i	0.511052	−	0.295056i	−0.222214	−	0.974998i	$-0.571328\pi$
$709$	13.6078	−	7.85647i	0.511052	−	0.295056i	0.733266	+	0.679942i	$0.237995\pi$
$710$			0.555558i			0.0208497i
$711$	−2.26429	−	3.92186i	−0.0849175	−	0.147081i
$712$	−7.24897	+	12.5556i	−0.271666	+	0.470540i
$713$	−33.5330	−	19.3603i	−1.25582	−	0.725048i
$714$	41.6072			1.55711
$715$	−0.0319088	−	0.147509i	−0.00119332	−	0.00551652i
$716$	−52.8195			−1.97396
$717$	6.84779	+	3.95357i	0.255735	+	0.147649i
$718$	18.4118	−	31.8902i	0.687123	−	1.19013i
$719$	−18.6016	−	32.2189i	−0.693723	−	1.20156i	−0.970609	−	0.240661i	$-0.922636\pi$
$719$	−18.6016	−	32.2189i	−0.693723	−	1.20156i	0.276886	−	0.960903i	$-0.410697\pi$
$720$			0.207081i			0.00771747i
$721$	−15.8008	+	9.12259i	−0.588452	+	0.339743i
$722$	38.3155	−	22.1215i	1.42596	−	0.823276i
$723$			26.9283i			1.00147i
$724$	−24.1555	−	41.8386i	−0.897732	−	1.55492i
$725$	−1.13570	+	1.96709i	−0.0421788	+	0.0730558i
$726$	2.14836	+	1.24036i	0.0797331	+	0.0460339i
$727$	−5.86824			−0.217641			−0.108821	−	0.994061i	$-0.534707\pi$
$727$	−5.86824			−0.217641			−0.108821	+	0.994061i	$0.534707\pi$
$728$	−76.1194	−	24.4304i	−2.82117	−	0.905452i
$729$	1.00000			0.0370370
$730$	−0.895962	−	0.517284i	−0.0331610	−	0.0191455i
$731$	13.4113	−	23.2291i	0.496035	−	0.859157i
$732$	18.5497	+	32.1291i	0.685618	+	1.18753i
$733$			14.4486i			0.533672i	0.963742	+	0.266836i	$0.0859782\pi$
$733$			14.4486i			0.533672i	−0.963742	+	0.266836i	$0.914022\pi$
$734$	−26.3354	+	15.2048i	−0.972059	+	0.561218i
$735$	−0.370444	+	0.213876i	−0.0136640	+	0.00788894i
$736$		−	14.6110i		−	0.538569i
$737$	5.81812	+	10.0773i	0.214313	+	0.371202i
$738$	5.01608	−	8.68810i	0.184644	−	0.319813i
$739$	31.1901	+	18.0076i	1.14735	+	0.662421i	0.948239	−	0.317557i	$-0.102862\pi$
$739$	31.1901	+	18.0076i	1.14735	+	0.662421i	0.199107	+	0.979978i	$0.436196\pi$
$740$	1.82803			0.0671996
$741$	−2.61465	−	2.88295i	−0.0960516	−	0.105908i
$742$	−128.376			−4.71284
$743$	−34.6661	−	20.0145i	−1.27177	−	0.734260i	−0.296453	−	0.955047i	$-0.595804\pi$
$743$	−34.6661	−	20.0145i	−1.27177	−	0.734260i	−0.975322	+	0.220788i	$0.929137\pi$
$744$	11.2301	−	19.4512i	0.411717	−	0.713115i
$745$	0.214788	+	0.372024i	0.00786923	+	0.0136299i
$746$		−	61.9289i		−	2.26738i
$747$	−6.58811	+	3.80365i	−0.241046	+	0.139168i
$748$	14.5404	−	8.39490i	0.531650	−	0.306948i
$749$			40.2590i			1.47103i
$750$	0.519096	+	0.899100i	0.0189547	+	0.0328305i
$751$	15.6490	−	27.1049i	0.571040	−	0.989070i	−0.425419	−	0.904996i	$-0.639873\pi$
$751$	15.6490	−	27.1049i	0.571040	−	0.989070i	0.996460	−	0.0840741i	$-0.0267933\pi$
$752$	23.3368	+	13.4735i	0.851006	+	0.491329i
$753$	7.48444			0.272748
$754$	−1.24214	+	3.87021i	−0.0452360	+	0.140945i
$755$	0.129455			0.00471135
$756$	−14.9278	−	8.61856i	−0.542918	−	0.313454i
$757$	10.8631	−	18.8154i	0.394826	−	0.683859i	−0.598253	−	0.801307i	$-0.704138\pi$
$757$	10.8631	−	18.8154i	0.394826	−	0.683859i	0.993079	+	0.117448i	$0.0374715\pi$
$758$	−14.8632	−	25.7437i	−0.539854	−	0.935055i
$759$			9.21156i			0.334358i
$760$	0.209083	−	0.120714i	0.00758423	−	0.00437876i
$761$	4.20926	−	2.43022i	0.152585	−	0.0880953i	−0.421763	−	0.906706i	$-0.638589\pi$
$761$	4.20926	−	2.43022i	0.152585	−	0.0880953i	0.574349	+	0.818611i	$0.305255\pi$
$762$		−	3.68289i		−	0.133417i
$763$	4.46733	+	7.73765i	0.161728	+	0.280122i
$764$	−5.25708	+	9.10553i	−0.190194	+	0.329426i
$765$	−0.146519	−	0.0845930i	−0.00529742	−	0.00305846i
$766$	−68.9779			−2.49227
$767$	1.94921	−	6.07327i	0.0703818	−	0.219293i
$768$	−32.6257			−1.17728
$769$	−26.2717	−	15.1680i	−0.947382	−	0.546971i	−0.0551151	−	0.998480i	$-0.517553\pi$
$769$	−26.2717	−	15.1680i	−0.947382	−	0.546971i	−0.892267	+	0.451509i	$0.850886\pi$
$770$	−0.215442	+	0.373156i	−0.00776397	+	0.0134476i
$771$	8.06034	+	13.9609i	0.290286	+	0.502790i
$772$			90.9099i			3.27192i
$773$	37.2819	−	21.5247i	1.34094	−	0.774191i	0.353993	−	0.935248i	$-0.384824\pi$
$773$	37.2819	−	21.5247i	1.34094	−	0.774191i	0.986945	+	0.161057i	$0.0514903\pi$
$774$	−14.2568	+	8.23114i	−0.512449	+	0.295862i
$775$		−	21.0100i		−	0.754702i
$776$	22.6264	+	39.1901i	0.812240	+	1.40684i
$777$	−21.8133	+	37.7818i	−0.782549	+	1.35541i
$778$	43.1469	+	24.9109i	1.54689	+	0.893098i
$779$	−4.36537			−0.156406
$780$	0.421160	+	0.464376i	0.0150799	+	0.0166273i
$781$	−5.35027			−0.191448
$782$	79.9884	+	46.1813i	2.86038	+	1.65144i
$783$	−0.227219	+	0.393556i	−0.00812016	+	0.0140645i
$784$	25.2783	+	43.7834i	0.902798	+	1.56369i
$785$		−	0.215850i		−	0.00770401i
$786$	−28.1710	+	16.2646i	−1.00483	+	0.580138i
$787$	−0.191603	+	0.110622i	−0.00682993	+	0.00394326i	−0.503411	−	0.864047i	$-0.667922\pi$
$787$	−0.191603	+	0.110622i	−0.00682993	+	0.00394326i	0.496581	+	0.867990i	$0.334589\pi$
$788$		−	7.10067i		−	0.252951i
$789$	5.57544	+	9.65695i	0.198491	+	0.343796i
$790$	0.235118	−	0.407236i	0.00836511	−	0.0144888i
$791$	−44.1252	−	25.4757i	−1.56891	−	0.905811i
$792$	−5.34327			−0.189865
$793$	30.6613	+	9.84073i	1.08882	+	0.349454i
$794$	−87.6224			−3.10960
$795$	0.452076	+	0.261006i	0.0160335	+	0.00925693i
$796$	36.3905	−	63.0302i	1.28983	−	2.23404i
$797$	6.60040	+	11.4322i	0.233798	+	0.404951i	0.958923	−	0.283667i	$-0.0915511\pi$
$797$	6.60040	+	11.4322i	0.233798	+	0.404951i	−0.725124	+	0.688618i	$0.758218\pi$
$798$			11.1118i			0.393354i
$799$	−19.0662	+	11.0079i	−0.674514	+	0.389431i
$800$	6.86588	−	3.96402i	0.242745	−	0.140149i
$801$			2.71331i			0.0958700i
$802$	5.87293	+	10.1722i	0.207381	+	0.359194i
$803$	4.98167	−	8.62851i	0.175799	−	0.304494i
$804$	−41.8603	−	24.1681i	−1.47630	−	0.852342i
$805$	−1.59999			−0.0563921
$806$	−7.94910	−	36.7473i	−0.279995	−	1.29437i
$807$	−16.1558			−0.568710
$808$	−38.9367	−	22.4801i	−1.36979	−	0.790847i
$809$	6.88274	−	11.9213i	0.241984	−	0.419129i	−0.719295	−	0.694705i	$-0.755535\pi$
$809$	6.88274	−	11.9213i	0.241984	−	0.419129i	0.961279	+	0.275575i	$0.0888684\pi$
$810$	0.0519187	+	0.0899258i	0.00182424	+	0.00315967i
$811$		−	36.6936i		−	1.28849i	−0.764821	−	0.644243i	$-0.777173\pi$
$811$		−	36.6936i		−	1.28849i	0.764821	−	0.644243i	$-0.222827\pi$
$812$	6.78377	−	3.91661i	0.238063	−	0.137446i
$813$	21.3987	−	12.3545i	0.750484	−	0.433292i
$814$			26.0809i			0.914135i
$815$	−0.313677	−	0.543305i	−0.0109876	−	0.0190312i
$816$	−9.99818	+	17.3173i	−0.350006	+	0.606228i
$817$	6.20366	+	3.58168i	0.217038	+	0.125307i
$818$	56.2039			1.96512
$819$	−14.6234	+	3.16329i	−0.510981	+	0.110534i
$820$	0.703160			0.0245554
$821$	−7.70219	−	4.44686i	−0.268808	−	0.155196i	0.359538	−	0.933131i	$-0.382934\pi$
$821$	−7.70219	−	4.44686i	−0.268808	−	0.155196i	−0.628346	+	0.777934i	$0.716268\pi$
$822$	−24.7994	+	42.9538i	−0.864978	+	1.49819i
$823$	−1.17356	−	2.03267i	−0.0409078	−	0.0708544i	0.844847	−	0.535009i	$-0.179692\pi$
$823$	−1.17356	−	2.03267i	−0.0409078	−	0.0708544i	−0.885754	+	0.464154i	$0.846358\pi$
$824$		−	23.4936i		−	0.818438i
$825$	−4.32861	+	2.49912i	−0.150703	+	0.0870083i
$826$	−15.7708	+	9.10525i	−0.548735	+	0.316812i
$827$		−	12.2870i		−	0.427261i	−0.976915	−	0.213630i	$-0.931471\pi$
$827$		−	12.2870i		−	0.427261i	0.976915	−	0.213630i	$-0.0685288\pi$
$828$	−19.1321	−	33.1377i	−0.664885	−	1.15162i
$829$	−20.6177	+	35.7110i	−0.716084	+	1.24029i	0.246456	+	0.969154i	$0.420734\pi$
$829$	−20.6177	+	35.7110i	−0.716084	+	1.24029i	−0.962540	+	0.271139i	$0.912600\pi$
$830$	−0.684092	−	0.394961i	−0.0237452	−	0.0137093i
$831$	7.02530			0.243705
$832$	−15.9169	+	14.4356i	−0.551818	+	0.500464i
$833$	−41.3049			−1.43113
$834$	20.0178	+	11.5573i	0.693158	+	0.400195i
$835$	−0.351955	+	0.609605i	−0.0121799	+	0.0210962i
$836$	2.24198	+	3.88323i	0.0775405	+	0.134304i
$837$		−	4.20347i		−	0.145293i
$838$	25.8573	−	14.9287i	0.893224	−	0.515703i
$839$	−14.9419	+	8.62671i	−0.515852	+	0.297827i	−0.735236	−	0.677811i	$-0.762929\pi$
$839$	−14.9419	+	8.62671i	−0.515852	+	0.297827i	0.219384	+	0.975639i	$0.429595\pi$
$840$		−	0.928090i		−	0.0320222i
$841$	14.3967	+	24.9359i	0.496439	+	0.859858i
$842$	25.6499	−	44.4270i	0.883956	−	1.53106i
$843$	11.7714	+	6.79620i	0.405427	+	0.234074i
$844$	−67.6159			−2.32744
$845$	0.541567	+	0.0529861i	0.0186305	+	0.00182278i
$846$	13.5121			0.464556
$847$	−3.59366	−	2.07480i	−0.123479	−	0.0712909i
$848$	30.8487	−	53.4315i	1.05935	−	1.83485i
$849$	−14.7592	−	25.5638i	−0.506536	−	0.877346i
$850$			50.1165i			1.71898i
$851$	−83.8707	+	48.4227i	−2.87505	+	1.65991i
$852$	19.2471	−	11.1123i	0.659394	−	0.380702i
$853$			18.6542i			0.638706i	0.947636	+	0.319353i	$0.103466\pi$
$853$			18.6542i			0.638706i	−0.947636	+	0.319353i	$0.896534\pi$
$854$	−45.9686	−	79.6199i	−1.57301	−	2.72454i
$855$	0.0225918	−	0.0391301i	0.000772623	−	0.00133822i
$856$	−44.8946	−	25.9199i	−1.53447	−	0.885925i
$857$	37.7858			1.29074			0.645369	−	0.763871i	$-0.276704\pi$
$857$	37.7858			1.29074			0.645369	+	0.763871i	$0.276704\pi$
$858$	−6.62537	+	6.00879i	−0.226186	+	0.205137i
$859$	−0.575485			−0.0196353			−0.00981765	−	0.999952i	$-0.503125\pi$
$859$	−0.575485			−0.0196353			−0.00981765	+	0.999952i	$0.503125\pi$
$860$	−0.999265	−	0.576926i	−0.0340747	−	0.0196730i
$861$	−8.39061	+	14.5330i	−0.285951	+	0.495282i
$862$	24.8461	+	43.0348i	0.846263	+	1.46577i
$863$			32.7063i			1.11334i	0.830735	+	0.556668i	$0.187921\pi$
$863$			32.7063i			1.11334i	−0.830735	+	0.556668i	$0.812079\pi$
$864$	1.37366	−	0.793081i	0.0467327	−	0.0269812i
$865$	0.623247	−	0.359832i	0.0211910	−	0.0122346i
$866$			67.4142i			2.29083i
$867$	0.331474	+	0.574130i	0.0112574	+	0.0194985i
$868$	−36.2279	+	62.7485i	−1.22965	+	2.12982i
$869$	3.92186	+	2.26429i	0.133040	+	0.0768108i
$870$	−0.0471877			−0.00159981
$871$	−41.0066	+	8.87046i	−1.38946	+	0.300564i
$872$	−11.5048			−0.389602
$873$	7.33448	+	4.23456i	0.248234	+	0.143318i
$874$	−12.3334	+	21.3621i	−0.417183	+	0.722582i
$875$	−0.868315	−	1.50397i	−0.0293544	−	0.0508433i
$876$			41.3870i			1.39834i
$877$	12.1995	−	7.04341i	0.411949	−	0.237839i	−0.279678	−	0.960094i	$-0.590228\pi$
$877$	12.1995	−	7.04341i	0.411949	−	0.237839i	0.691627	+	0.722255i	$0.256894\pi$
$878$	7.56196	−	4.36590i	0.255204	−	0.147342i
$879$		−	10.2482i		−	0.345662i
$880$	−0.103541	−	0.179338i	−0.00349036	−	0.00604548i
$881$	21.7335	−	37.6436i	0.732222	−	1.26825i	−0.223710	−	0.974656i	$-0.571817\pi$
$881$	21.7335	−	37.6436i	0.732222	−	1.26825i	0.955932	−	0.293589i	$-0.0948498\pi$
$882$	21.9544	+	12.6754i	0.739243	+	0.426802i
$883$	−10.6478			−0.358326			−0.179163	−	0.983819i	$-0.557339\pi$
$883$	−10.6478			−0.358326			−0.179163	+	0.983819i	$0.557339\pi$
$884$	12.7991	+	59.1680i	0.430480	+	1.99003i
$885$	0.0740487			0.00248912
$886$	−1.43493	−	0.828457i	−0.0482074	−	0.0278325i
$887$	−6.02695	+	10.4390i	−0.202365	+	0.350507i	−0.949290	−	0.314402i	$-0.898196\pi$
$887$	−6.02695	+	10.4390i	−0.202365	+	0.350507i	0.746925	+	0.664909i	$0.231530\pi$
$888$	−28.0882	−	48.6501i	−0.942577	−	1.63259i
$889$			6.16054i			0.206618i
$890$	−0.243996	+	0.140871i	−0.00817877	+	0.00472202i
$891$	−0.866025	+	0.500000i	−0.0290129	+	0.0167506i
$892$			7.99709i			0.267762i
$893$	−2.93982	−	5.09191i	−0.0983772	−	0.170394i
$894$	12.7294	−	22.0480i	0.425736	−	0.737397i
$895$	−0.460939	−	0.266123i	−0.0154075	−	0.00889552i
$896$	74.5126			2.48929
$897$	−31.6239	−	10.1497i	−1.05589	−	0.338887i
$898$	80.9602			2.70168
$899$	1.65430	+	0.955111i	0.0551740	+	0.0318547i
$900$	10.3812	−	17.9807i	0.346039	−	0.599358i
$901$	25.2034	+	43.6536i	0.839648	+	1.45431i
$902$			10.0322i			0.334034i
$903$	23.8479	−	13.7686i	0.793609	−	0.458190i
$904$	56.8182	−	32.8040i	1.88975	−	1.09105i
$905$		−	0.486816i		−	0.0161823i
$906$	−3.83608	−	6.64428i	−0.127445	−	0.220741i
$907$	−19.8302	+	34.3469i	−0.658451	+	1.14047i	0.322566	+	0.946547i	$0.395455\pi$
$907$	−19.8302	+	34.3469i	−0.658451	+	1.14047i	−0.981017	+	0.193923i	$0.937879\pi$
$908$	22.6993	+	13.1054i	0.753302	+	0.434919i
$909$	−8.41437			−0.279087
$910$	−1.04369	−	1.15078i	−0.0345979	−	0.0381481i
$911$	19.0996			0.632799			0.316400	−	0.948626i	$-0.397526\pi$
$911$	19.0996			0.632799			0.316400	+	0.948626i	$0.397526\pi$
$912$	−4.62485	−	2.67016i	−0.153144	−	0.0884178i
$913$	3.80365	−	6.58811i	0.125882	−	0.218035i
$914$	6.33683	+	10.9757i	0.209604	+	0.363044i
$915$			0.373840i			0.0123588i
$916$	31.8411	−	18.3835i	1.05206	−	0.607407i
$917$	47.1230	−	27.2065i	1.55614	−	0.898437i
$918$			10.0268i			0.330934i
$919$	28.0327	+	48.5540i	0.924713	+	1.60165i	0.792022	+	0.610492i	$0.209028\pi$
$919$	28.0327	+	48.5540i	0.924713	+	1.60165i	0.132691	+	0.991158i	$0.457638\pi$
$920$	1.03012	−	1.78422i	0.0339620	−	0.0588239i
$921$	20.9074	+	12.0709i	0.688923	+	0.397750i
$922$	55.7446			1.83585
$923$	5.89514	−	18.3678i	0.194041	−	0.604585i
$924$	17.2371			0.567060
$925$	−45.5087	−	26.2745i	−1.49632	−	0.863900i
$926$	−47.4072	+	82.1117i	−1.55790	+	2.69836i
$927$	−2.19843	−	3.80779i	−0.0722059	−	0.125064i
$928$			0.720814i			0.0236619i
$929$	−24.8200	+	14.3298i	−0.814317	+	0.470146i	−0.848453	−	0.529271i	$-0.822465\pi$
$929$	−24.8200	+	14.3298i	−0.814317	+	0.470146i	0.0341357	+	0.999417i	$0.489132\pi$
$930$	0.378001	−	0.218239i	0.0123951	−	0.00715633i
$931$		−	11.0311i		−	0.361529i
$932$	−56.3865	−	97.6644i	−1.84700	−	3.19910i
$933$	12.3454	−	21.3829i	0.404171	−	0.700045i
$934$	−67.7391	−	39.1092i	−2.21649	−	1.27969i
$935$	0.169186			0.00553297
$936$	5.88742	−	18.3438i	0.192436	−	0.599586i
$937$	52.4989			1.71506			0.857532	−	0.514431i	$-0.171997\pi$
$937$	52.4989			1.71506			0.857532	+	0.514431i	$0.171997\pi$
$938$	103.735	+	59.8915i	3.38707	+	1.95553i
$939$	1.81764	−	3.14824i	0.0593163	−	0.102739i
$940$	0.473536	+	0.820189i	0.0154451	+	0.0267516i
$941$		−	11.8677i		−	0.386875i	−0.981113	−	0.193438i	$-0.938036\pi$
$941$		−	11.8677i		−	0.386875i	0.981113	−	0.193438i	$-0.0619638\pi$
$942$	−11.0785	+	6.39617i	−0.360957	+	0.208399i
$943$	−32.2613	+	18.6261i	−1.05057	+	0.606548i
$944$		−	8.75193i		−	0.284851i
$945$	−0.0868467	−	0.150423i	−0.00282512	−	0.00489326i
$946$	8.23114	−	14.2568i	0.267618	−	0.463527i
$947$	15.7449	+	9.09030i	0.511639	+	0.295395i	0.733507	−	0.679682i	$-0.237882\pi$
$947$	15.7449	+	9.09030i	0.511639	+	0.295395i	−0.221868	+	0.975077i	$0.571215\pi$
$948$	−18.8114			−0.610965
$949$	24.1333	+	26.6097i	0.783399	+	0.863786i
$950$	−13.3843			−0.434245
$951$	−18.3780	−	10.6106i	−0.595948	−	0.344071i
$952$	44.8095	−	77.6123i	1.45228	−	2.51543i
$953$	7.72495	+	13.3800i	0.250236	+	0.433421i	0.963591	−	0.267382i	$-0.0861585\pi$
$953$	7.72495	+	13.3800i	0.250236	+	0.433421i	−0.713355	+	0.700803i	$0.752825\pi$
$954$		−	30.9371i		−	1.00162i
$955$	−0.0917537	+	0.0529740i	−0.00296908	+	0.00171420i
$956$	28.4452	−	16.4229i	0.919984	−	0.531153i
$957$		−	0.454439i		−	0.0146899i
$958$	−16.6113	−	28.7717i	−0.536687	−	0.929570i
$959$	41.4830	−	71.8507i	1.33956	−	2.32018i
$960$	−0.216039	−	0.124730i	−0.00697262	−	0.00402565i
$961$	13.3308			0.430026
$962$	−89.5375	−	28.7370i	−2.88680	−	0.926516i
$963$	−9.70190			−0.312639
$964$	96.8719	+	55.9290i	3.12003	+	1.80135i
$965$	−0.458036	+	0.793342i	−0.0147447	+	0.0255386i
$966$	47.4117	+	82.1194i	1.52545	+	2.64215i
$967$			18.6853i			0.600878i	0.953801	+	0.300439i	$0.0971332\pi$
$967$			18.6853i			0.600878i	−0.953801	+	0.300439i	$0.902867\pi$
$968$	4.62741	−	2.67163i	0.148730	−	0.0858696i
$969$	3.77851	−	2.18152i	0.121383	−	0.0700807i
$970$			0.879411i			0.0282362i
$971$	−9.34629	−	16.1883i	−0.299937	−	0.519506i	0.676184	−	0.736732i	$-0.263632\pi$
$971$	−9.34629	−	16.1883i	−0.299937	−	0.519506i	−0.976121	+	0.217227i	$0.930299\pi$
$972$	2.07696	−	3.59741i	0.0666186	−	0.115387i
$973$	−33.4846	−	19.3323i	−1.07347	−	0.619766i
$974$	46.0141			1.47439
$975$	−3.81023	−	17.6140i	−0.122025	−	0.564101i
$976$	44.1848			1.41432
$977$	48.2216	+	27.8407i	1.54275	+	0.890704i	0.998664	+	0.0516718i	$0.0164550\pi$
$977$	48.2216	+	27.8407i	1.54275	+	0.890704i	0.544081	+	0.839033i	$0.316878\pi$
$978$	−18.5901	+	32.1990i	−0.594446	+	1.02961i
$979$	−1.35665	−	2.34979i	−0.0433589	−	0.0750997i
$980$			1.77685i			0.0567594i
$981$	−1.86467	+	1.07657i	−0.0595345	+	0.0343723i
$982$	−37.7308	+	21.7839i	−1.20404	+	0.695152i
$983$		−	24.7651i		−	0.789885i	−0.918706	−	0.394943i	$-0.870764\pi$
$983$		−	24.7651i		−	0.789885i	0.918706	−	0.394943i	$-0.129236\pi$
$984$	−10.8043	−	18.7135i	−0.344427	−	0.596565i
$985$	0.0357757	−	0.0619653i	0.00113991	−	0.00197438i
$986$	−3.94611	−	2.27829i	−0.125670	−	0.0725555i
$987$	−22.6023			−0.719440
$988$	−15.8017	+	3.41818i	−0.502718	+	0.108747i
$989$	61.1290			1.94379
$990$	−0.0899258	−	0.0519187i	−0.00285803	−	0.00165008i
$991$	20.2732	−	35.1142i	0.643999	−	1.11544i	−0.340533	−	0.940233i	$-0.610608\pi$
$991$	20.2732	−	35.1142i	0.643999	−	1.11544i	0.984532	−	0.175206i	$-0.0560591\pi$
$992$	−3.33370	−	5.77413i	−0.105845	−	0.183329i
$993$		−	14.3739i		−	0.456142i
$994$	−47.6967	+	27.5377i	−1.51285	+	0.873443i
$995$	0.635136	−	0.366696i	0.0201352	−	0.0116250i
$996$			31.6002i			1.00129i
$997$	−2.63178	−	4.55838i	−0.0833494	−	0.144365i	0.821337	−	0.570443i	$-0.193228\pi$
$997$	−2.63178	−	4.55838i	−0.0833494	−	0.144365i	−0.904687	+	0.426078i	$0.859895\pi$
$998$	32.0508	−	55.5136i	1.01455	−	1.75725i
$999$	−9.10494	−	5.25674i	−0.288067	−	0.166316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.b.199.1	yes	28
13.6	odd	12		5577.2.a.bg.1.13		14
13.7	odd	12		5577.2.a.bf.1.2		14
13.10	even	6	inner	429.2.s.b.166.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.1	✓	28	13.10	even	6	inner
429.2.s.b.199.1	yes	28	1.1	even	1	trivial
5577.2.a.bf.1.2		14	13.7	odd	12
5577.2.a.bg.1.13		14	13.6	odd	12

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14836 - 1.24036i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.07696 + 3.59741i) q^{4} +0.0418579i q^{5} +(2.14836 - 1.24036i) q^{6} +(-3.59366 + 2.07480i) q^{7} -5.34327i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.14836 - 1.24036i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.07696 + 3.59741i) q^{4} +0.0418579i q^{5} +(2.14836 - 1.24036i) q^{6} +(-3.59366 + 2.07480i) q^{7} -5.34327i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0519187 - 0.0899258i) q^{10} +(0.866025 + 0.500000i) q^{11} -4.15393 q^{12} +(-2.67075 + 2.42220i) q^{13} +10.2939 q^{14} +(-0.0362500 - 0.0209289i) q^{15} +(-2.47363 + 4.28444i) q^{16} +(-2.02096 - 3.50040i) q^{17} +2.48071i q^{18} +(0.934832 - 0.539726i) q^{19} +(-0.150580 + 0.0869373i) q^{20} -4.14960i q^{21} +(-1.24036 - 2.14836i) q^{22} +(4.60578 - 7.97744i) q^{23} +(4.62741 + 2.67163i) q^{24} +4.99825 q^{25} +(8.74213 - 1.89108i) q^{26} +1.00000 q^{27} +(-14.9278 - 8.61856i) q^{28} +(-0.227219 + 0.393556i) q^{29} +(0.0519187 + 0.0899258i) q^{30} -4.20347i q^{31} +(1.37366 - 0.793081i) q^{32} +(-0.866025 + 0.500000i) q^{33} +10.0268i q^{34} +(-0.0868467 - 0.150423i) q^{35} +(2.07696 - 3.59741i) q^{36} +(-9.10494 - 5.25674i) q^{37} -2.67781 q^{38} +(-0.762313 - 3.52404i) q^{39} +0.223658 q^{40} +(-3.50226 - 2.02203i) q^{41} +(-5.14697 + 8.91482i) q^{42} +(3.31806 + 5.74705i) q^{43} +4.15393i q^{44} +(0.0362500 - 0.0209289i) q^{45} +(-19.7897 + 11.4256i) q^{46} -5.44687i q^{47} +(-2.47363 - 4.28444i) q^{48} +(5.10958 - 8.85004i) q^{49} +(-10.7380 - 6.19960i) q^{50} +4.04191 q^{51} +(-14.2607 - 4.57696i) q^{52} -12.4710 q^{53} +(-2.14836 - 1.24036i) q^{54} +(-0.0209289 + 0.0362500i) q^{55} +(11.0862 + 19.2019i) q^{56} +1.07945i q^{57} +(0.976298 - 0.563666i) q^{58} +(-1.53204 + 0.884525i) q^{59} -0.173875i q^{60} +(-4.46559 - 7.73463i) q^{61} +(-5.21380 + 9.03057i) q^{62} +(3.59366 + 2.07480i) q^{63} +5.95969 q^{64} +(-0.101388 - 0.111792i) q^{65} +2.48071 q^{66} +(10.0773 + 5.81812i) q^{67} +(8.39490 - 14.5404i) q^{68} +(4.60578 + 7.97744i) q^{69} +0.430883i q^{70} +(-4.63347 + 2.67513i) q^{71} +(-4.62741 + 2.67163i) q^{72} -9.96335i q^{73} +(13.0404 + 22.5867i) q^{74} +(-2.49912 + 4.32861i) q^{75} +(3.88323 + 2.24198i) q^{76} -4.14960 q^{77} +(-2.73334 + 8.51645i) q^{78} +4.52858 q^{79} +(-0.179338 - 0.103541i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.01608 + 8.68810i) q^{82} -7.60730i q^{83} +(14.9278 - 8.61856i) q^{84} +(0.146519 - 0.0845930i) q^{85} -16.4623i q^{86} +(-0.227219 - 0.393556i) q^{87} +(2.67163 - 4.62741i) q^{88} +(-2.34979 - 1.35665i) q^{89} -0.103837 q^{90} +(4.57219 - 14.2458i) q^{91} +38.2641 q^{92} +(3.64032 + 2.10174i) q^{93} +(-6.75606 + 11.7018i) q^{94} +(0.0225918 + 0.0391301i) q^{95} +1.58616i q^{96} +(-7.33448 + 4.23456i) q^{97} +(-21.9544 + 12.6754i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Introduction

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